From 89953d5577d15bb42e43b0c7df640abc6daf8c9b Mon Sep 17 00:00:00 2001 From: Stefano Pigozzi Date: Sun, 1 Mar 2020 21:25:46 +0100 Subject: [PATCH] Update website and README --- LICENSE.md | 676 +- README.md | 29 + docs/CNAME | 2 +- docs/bundle.39cb3.esm.js | 2 + docs/bundle.39cb3.esm.js.map | 1 + docs/bundle.446a2.css | 1 + docs/bundle.57708.js | 2 - docs/bundle.57708.js.map | 1 - docs/bundle.f77a1.js | 2 + docs/bundle.f77a1.js.map | 1 + docs/index.html | 2 +- docs/polyfills.04c22.js | 2 - docs/polyfills.04c22.js.map | 1 - docs/polyfills.06b13.esm.js | 2 + docs/polyfills.06b13.esm.js.map | 1 + docs/polyfills.bb23a.js | 2 + docs/polyfills.bb23a.js.map | 1 + docs/preact_prerender_data.json | 1 + ...st.0f27a05868e94597f6d2279c6bbf2f4a.esm.js | 62 + ...nifest.2df4a1db73a8dca4c45380d964d8e39d.js | 74 + docs/push-manifest.json | 2 +- docs/route-fisica.chunk.823c8.js | 2 + docs/route-fisica.chunk.823c8.js.map | 1 + docs/route-fisica.chunk.98137.css | 1 + docs/route-fisica.chunk.c81bf.esm.js | 2 + docs/route-fisica.chunk.c81bf.esm.js.map | 1 + docs/route-home.chunk.0c2c0.css | 1 + docs/route-home.chunk.0d3d3.esm.js | 2 + docs/route-home.chunk.0d3d3.esm.js.map | 1 + docs/route-home.chunk.b306e.js | 2 + docs/route-home.chunk.b306e.js.map | 1 + docs/route-mingwinstall.chunk.1d3c8.css | 1 + docs/route-mingwinstall.chunk.4b543.js | 2 + docs/route-mingwinstall.chunk.4b543.js.map | 1 + docs/route-mingwinstall.chunk.97b52.esm.js | 2 + .../route-mingwinstall.chunk.97b52.esm.js.map | 1 + docs/route-statistica.chunk.0864e.js | 2 + docs/route-statistica.chunk.0864e.js.map | 1 + docs/route-statistica.chunk.1c94d.esm.js | 40 + docs/route-statistica.chunk.1c94d.esm.js.map | 1 + docs/route-statistica.chunk.57ea3.css | 1 + docs/route-vldigeometria.chunk.5dcf1.js | 2 + docs/route-vldigeometria.chunk.5dcf1.js.map | 1 + docs/route-vldigeometria.chunk.5dea5.css | 1 + docs/route-vldigeometria.chunk.dc16e.esm.js | 36 + ...route-vldigeometria.chunk.dc16e.esm.js.map | 1 + docs/ssr-build/ssr-bundle.js | 18302 ---------------- docs/ssr-build/ssr-bundle.js.map | 1 - docs/ssr-build/style.5336e.css | 2 - docs/ssr-build/style.5336e.css.map | 1 - docs/style.5336e.css | 2 - docs/style.5336e.css.map | 1 - docs/sw-debug.js | 19 + docs/sw-esm.js | 4 + docs/sw-esm.js.map | 1 + docs/sw.js | 5 +- docs/sw.js.map | 1 + package-lock.json | 11929 ++++++++++ package.json | 26 +- preact.config.js | 29 +- src/index.js | 23 +- src/{pages/statistica.css => meta/.nojekyll} | 0 src/meta/CNAME | 1 + src/meta/manifest.json | 16 + src/{pages => routes}/fisica.css | 0 src/{pages => routes}/fisica.js | 0 src/{pages => routes}/home.css | 0 src/{pages => routes}/home.js | 1 - src/{pages => routes}/mingwinstall.css | 0 src/{pages => routes}/mingwinstall.js | 0 src/routes/statistica.css | 0 src/{pages => routes}/statistica.js | 0 src/{pages => routes}/vldigeometria.css | 0 src/{pages => routes}/vldigeometria.js | 0 yarn.lock | 8290 ------- 75 files changed, 12978 insertions(+), 26650 deletions(-) create mode 100644 README.md create mode 100644 docs/bundle.39cb3.esm.js create mode 100644 docs/bundle.39cb3.esm.js.map create mode 100644 docs/bundle.446a2.css delete mode 100644 docs/bundle.57708.js delete mode 100644 docs/bundle.57708.js.map create mode 100644 docs/bundle.f77a1.js create mode 100644 docs/bundle.f77a1.js.map delete mode 100644 docs/polyfills.04c22.js delete mode 100644 docs/polyfills.04c22.js.map create mode 100644 docs/polyfills.06b13.esm.js create mode 100644 docs/polyfills.06b13.esm.js.map create mode 100644 docs/polyfills.bb23a.js create mode 100644 docs/polyfills.bb23a.js.map create mode 100644 docs/preact_prerender_data.json create mode 100644 docs/precache-manifest.0f27a05868e94597f6d2279c6bbf2f4a.esm.js create mode 100644 docs/precache-manifest.2df4a1db73a8dca4c45380d964d8e39d.js create mode 100644 docs/route-fisica.chunk.823c8.js create mode 100644 docs/route-fisica.chunk.823c8.js.map create mode 100644 docs/route-fisica.chunk.98137.css create mode 100644 docs/route-fisica.chunk.c81bf.esm.js create mode 100644 docs/route-fisica.chunk.c81bf.esm.js.map create mode 100644 docs/route-home.chunk.0c2c0.css create mode 100644 docs/route-home.chunk.0d3d3.esm.js create mode 100644 docs/route-home.chunk.0d3d3.esm.js.map create mode 100644 docs/route-home.chunk.b306e.js create mode 100644 docs/route-home.chunk.b306e.js.map create mode 100644 docs/route-mingwinstall.chunk.1d3c8.css create mode 100644 docs/route-mingwinstall.chunk.4b543.js create mode 100644 docs/route-mingwinstall.chunk.4b543.js.map create mode 100644 docs/route-mingwinstall.chunk.97b52.esm.js create mode 100644 docs/route-mingwinstall.chunk.97b52.esm.js.map create mode 100644 docs/route-statistica.chunk.0864e.js create mode 100644 docs/route-statistica.chunk.0864e.js.map create mode 100644 docs/route-statistica.chunk.1c94d.esm.js create mode 100644 docs/route-statistica.chunk.1c94d.esm.js.map create mode 100644 docs/route-statistica.chunk.57ea3.css create mode 100644 docs/route-vldigeometria.chunk.5dcf1.js create mode 100644 docs/route-vldigeometria.chunk.5dcf1.js.map create mode 100644 docs/route-vldigeometria.chunk.5dea5.css create mode 100644 docs/route-vldigeometria.chunk.dc16e.esm.js create mode 100644 docs/route-vldigeometria.chunk.dc16e.esm.js.map delete mode 100644 docs/ssr-build/ssr-bundle.js delete mode 100644 docs/ssr-build/ssr-bundle.js.map delete mode 100644 docs/ssr-build/style.5336e.css delete mode 100644 docs/ssr-build/style.5336e.css.map delete mode 100644 docs/style.5336e.css delete mode 100644 docs/style.5336e.css.map create mode 100644 docs/sw-debug.js create mode 100644 docs/sw-esm.js create mode 100644 docs/sw-esm.js.map create mode 100644 docs/sw.js.map create mode 100644 package-lock.json rename src/{pages/statistica.css => meta/.nojekyll} (100%) create mode 100644 src/meta/CNAME create mode 100644 src/meta/manifest.json rename src/{pages => routes}/fisica.css (100%) rename src/{pages => routes}/fisica.js (100%) rename src/{pages => routes}/home.css (100%) rename src/{pages => routes}/home.js (99%) rename src/{pages => routes}/mingwinstall.css (100%) rename src/{pages => routes}/mingwinstall.js (100%) create mode 100644 src/routes/statistica.css rename src/{pages => routes}/statistica.js (100%) rename src/{pages => routes}/vldigeometria.css (100%) rename src/{pages => routes}/vldigeometria.js (100%) delete mode 100644 yarn.lock diff --git a/LICENSE.md b/LICENSE.md index cac0a0e..caf493c 100644 --- a/LICENSE.md +++ b/LICENSE.md @@ -10,26 +10,668 @@ ## Code -**MIT License** +**Affero GNU Public License v3** ``` -Copyright (c) 2020 Stefano Pigozzi + GNU AFFERO GENERAL PUBLIC LICENSE + Version 3, 19 November 2007 -Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, 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"Knowingly relying" means you have +actual knowledge that, but for the patent license, your conveying the +covered work in a country, or your recipient's use of the covered work +in a country, would infringe one or more identifiable patents in that +country that you have reason to believe are valid. + + If, pursuant to or in connection with a single transaction or +arrangement, you convey, or propagate by procuring conveyance of, a +covered work, and grant a patent license to some of the parties +receiving the covered work authorizing them to use, propagate, modify +or convey a specific copy of the covered work, then the patent license +you grant is automatically extended to all recipients of the covered +work and works based on it. + + A patent license is "discriminatory" if it does not include within +the scope of its coverage, prohibits the exercise of, or is +conditioned on the non-exercise of one or more of the rights that are +specifically granted under this License. You may not convey a covered +work if you are a party to an arrangement with a third party that is +in the business of distributing software, under which you make payment +to the third party based on the extent of your activity of conveying +the work, and under which the third party grants, to any of the +parties who would receive the covered work from you, a discriminatory +patent license (a) in connection with copies of the covered work +conveyed by you (or copies made from those copies), or (b) primarily +for and in connection with specific products or compilations that +contain the covered work, unless you entered into that arrangement, +or that patent license was granted, prior to 28 March 2007. + + Nothing in this License shall be construed as excluding or limiting +any implied license or other defenses to infringement that may +otherwise be available to you under applicable patent law. + + 12. 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Remote Network Interaction; Use with the GNU General Public License. + + Notwithstanding any other provision of this License, if you modify the +Program, your modified version must prominently offer all users +interacting with it remotely through a computer network (if your version +supports such interaction) an opportunity to receive the Corresponding +Source of your version by providing access to the Corresponding Source +from a network server at no charge, through some standard or customary +means of facilitating copying of software. This Corresponding Source +shall include the Corresponding Source for any work covered by version 3 +of the GNU General Public License that is incorporated pursuant to the +following paragraph. + + Notwithstanding any other provision of this License, you have +permission to link or combine any covered work with a work licensed +under version 3 of the GNU General Public License into a single +combined work, and to convey the resulting work. 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If the Program does not specify a version number of the +GNU Affero General Public License, you may choose any version ever published +by the Free Software Foundation. + + If the Program specifies that a proxy can decide which future +versions of the GNU Affero General Public License can be used, that proxy's +public statement of acceptance of a version permanently authorizes you +to choose that version for the Program. + + Later license versions may give you additional or different +permissions. However, no additional obligations are imposed on any +author or copyright holder as a result of your choosing to follow a +later version. + + 15. Disclaimer of Warranty. + + THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY +APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT +HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY +OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, +THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM +IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF +ALL NECESSARY SERVICING, REPAIR OR CORRECTION. + + 16. Limitation of Liability. + + IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS +THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY +GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE +USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF +DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD +PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), +EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF +SUCH DAMAGES. + + 17. Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Affero General Public License as published + by the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Affero General Public License for more details. + + You should have received a copy of the GNU Affero General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If your software can interact with users remotely through a computer +network, you should also make sure that it provides a way for users to +get its source. For example, if your program is a web application, its +interface could display a "Source" link that leads users to an archive +of the code. There are many ways you could offer source, and different +solutions will be better for different programs; see section 13 for the +specific requirements. + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU AGPL, see +. ``` diff --git a/README.md b/README.md new file mode 100644 index 0000000..6446a50 --- /dev/null +++ b/README.md @@ -0,0 +1,29 @@ +# `uni.steffo.eu` + +A [Preact](https://preactjs.com/) website with all things I've used to prepare for university exams! + +## Contributing + +All contributions are welcome! :D + +### Running a local copy + +If you want to run a local copy of the website, ensure [the latest `nodejs`](https://nodejs.org/it/) and `npm` are installed on your machine then run: + +```bash +git clone https://github.com/Steffo99/uni.steffo.eu.git +cd "uni.steffo.eu" +npm install +npm run start +``` + +### Updating the website + +To update the published website, run in the previously cloned folder: + +```bash +npm run build +git add docs +git commit -m "Update website" +git push +``` diff --git a/docs/CNAME b/docs/CNAME index 52bb0e8..936d4e6 100644 --- a/docs/CNAME +++ b/docs/CNAME @@ -1 +1 @@ -uni.steffo.eu \ No newline at end of file +uni.steffo.eu diff --git a/docs/bundle.39cb3.esm.js b/docs/bundle.39cb3.esm.js new file mode 100644 index 0000000..90e6953 --- /dev/null +++ b/docs/bundle.39cb3.esm.js @@ -0,0 +1,2 @@ +!function(t){function e(e){for(var n,r,o=e[0],u=e[1],a=0,c=[];a{e=this.base=this.nextBase||this.__b,t(t=>{this.setState({child:t.default||t})})},this.shouldComponentUpdate=(t,o)=>(n=(o=void 0===o.child)&&void 0===n&&e?3===e.nodeType?e.data:Object(r.h)(e.nodeName,{dangerouslySetInnerHTML:{__html:e.innerHTML}}):"",!o),this.render=(t,e)=>e.child?Object(r.h)(e.child,t):n}return(e.prototype=new r.Component).constructor=e,e}},WC2o:function(t,e,n){"use strict";var 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e}}),r.helper.regexes={asteriskDashAndColon:/([*_:~])/g},r.helper.emojis={"+1":"👍","-1":"👎",100:"💯",1234:"🔢","1st_place_medal":"🥇","2nd_place_medal":"🥈","3rd_place_medal":"🥉","8ball":"🎱",a:"🅰️",ab:"🆎",abc:"🔤",abcd:"🔡",accept:"🉑",aerial_tramway:"🚡",airplane:"✈️",alarm_clock:"⏰",alembic:"⚗️",alien:"👽",ambulance:"🚑",amphora:"🏺",anchor:"⚓️",angel:"👼",anger:"💢",angry:"😠",anguished:"😧",ant:"🐜",apple:"🍎",aquarius:"♒️",aries:"♈️",arrow_backward:"◀️",arrow_double_down:"⏬",arrow_double_up:"⏫",arrow_down:"⬇️",arrow_down_small:"🔽",arrow_forward:"▶️",arrow_heading_down:"⤵️",arrow_heading_up:"⤴️",arrow_left:"⬅️",arrow_lower_left:"↙️",arrow_lower_right:"↘️",arrow_right:"➡️",arrow_right_hook:"↪️",arrow_up:"⬆️",arrow_up_down:"↕️",arrow_up_small:"🔼",arrow_upper_left:"↖️",arrow_upper_right:"↗️",arrows_clockwise:"🔃",arrows_counterclockwise:"🔄",art:"🎨",articulated_lorry:"🚛",artificial_satellite:"🛰",astonished:"😲",athletic_shoe:"👟",atm:"🏧",atom_symbol:"⚛️",avocado:"🥑",b:"🅱️",baby:"👶",baby_bottle:"🍼",baby_chick:"🐤",baby_symbol:"🚼",back:"🔙",bacon:"🥓",badminton:"🏸",baggage_claim:"🛄",baguette_bread:"🥖",balance_scale:"⚖️",balloon:"🎈",ballot_box:"🗳",ballot_box_with_check:"☑️",bamboo:"🎍",banana:"🍌",bangbang:"‼️",bank:"🏦",bar_chart:"📊",barber:"💈",baseball:"⚾️",basketball:"🏀",basketball_man:"⛹️",basketball_woman:"⛹️‍♀️",bat:"🦇",bath:"🛀",bathtub:"🛁",battery:"🔋",beach_umbrella:"🏖",bear:"🐻",bed:"🛏",bee:"🐝",beer:"🍺",beers:"🍻",beetle:"🐞",beginner:"🔰",bell:"🔔",bellhop_bell:"🛎",bento:"🍱",biking_man:"🚴",bike:"🚲",biking_woman:"🚴‍♀️",bikini:"👙",biohazard:"☣️",bird:"🐦",birthday:"🎂",black_circle:"⚫️",black_flag:"🏴",black_heart:"🖤",black_joker:"🃏",black_large_square:"⬛️",black_medium_small_square:"◾️",black_medium_square:"◼️",black_nib:"✒️",black_small_square:"▪️",black_square_button:"🔲",blonde_man:"👱",blonde_woman:"👱‍♀️",blossom:"🌼",blowfish:"🐡",blue_book:"📘",blue_car:"🚙",blue_heart:"💙",blush:"😊",boar:"🐗",boat:"⛵️",bomb:"💣",book:"📖",bookmark:"🔖",bookmark_tabs:"📑",books:"📚",boom:"💥",boot:"👢",bouquet:"💐",bowing_man:"🙇",bow_and_arrow:"🏹",bowing_woman:"🙇‍♀️",bowling:"🎳",boxing_glove:"🥊",boy:"👦",bread:"🍞",bride_with_veil:"👰",bridge_at_night:"🌉",briefcase:"💼",broken_heart:"💔",bug:"🐛",building_construction:"🏗",bulb:"💡",bullettrain_front:"🚅",bullettrain_side:"🚄",burrito:"🌯",bus:"🚌",business_suit_levitating:"🕴",busstop:"🚏",bust_in_silhouette:"👤",busts_in_silhouette:"👥",butterfly:"🦋",cactus:"🌵",cake:"🍰",calendar:"📆",call_me_hand:"🤙",calling:"📲",camel:"🐫",camera:"📷",camera_flash:"📸",camping:"🏕",cancer:"♋️",candle:"🕯",candy:"🍬",canoe:"🛶",capital_abcd:"🔠",capricorn:"♑️",car:"🚗",card_file_box:"🗃",card_index:"📇",card_index_dividers:"🗂",carousel_horse:"🎠",carrot:"🥕",cat:"🐱",cat2:"🐈",cd:"💿",chains:"⛓",champagne:"🍾",chart:"💹",chart_with_downwards_trend:"📉",chart_with_upwards_trend:"📈",checkered_flag:"🏁",cheese:"🧀",cherries:"🍒",cherry_blossom:"🌸",chestnut:"🌰",chicken:"🐔",children_crossing:"🚸",chipmunk:"🐿",chocolate_bar:"🍫",christmas_tree:"🎄",church:"⛪️",cinema:"🎦",circus_tent:"🎪",city_sunrise:"🌇",city_sunset:"🌆",cityscape:"🏙",cl:"🆑",clamp:"🗜",clap:"👏",clapper:"🎬",classical_building:"🏛",clinking_glasses:"🥂",clipboard:"📋",clock1:"🕐",clock10:"🕙",clock1030:"🕥",clock11:"🕚",clock1130:"🕦",clock12:"🕛",clock1230:"🕧",clock130:"🕜",clock2:"🕑",clock230:"🕝",clock3:"🕒",clock330:"🕞",clock4:"🕓",clock430:"🕟",clock5:"🕔",clock530:"🕠",clock6:"🕕",clock630:"🕡",clock7:"🕖",clock730:"🕢",clock8:"🕗",clock830:"🕣",clock9:"🕘",clock930:"🕤",closed_book:"📕",closed_lock_with_key:"🔐",closed_umbrella:"🌂",cloud:"☁️",cloud_with_lightning:"🌩",cloud_with_lightning_and_rain:"⛈",cloud_with_rain:"🌧",cloud_with_snow:"🌨",clown_face:"🤡",clubs:"♣️",cocktail:"🍸",coffee:"☕️",coffin:"⚰️",cold_sweat:"😰",comet:"☄️",computer:"💻",computer_mouse:"🖱",confetti_ball:"🎊",confounded:"😖",confused:"😕",congratulations:"㊗️",construction:"🚧",construction_worker_man:"👷",construction_worker_woman:"👷‍♀️",control_knobs:"🎛",convenience_store:"🏪",cookie:"🍪",cool:"🆒",policeman:"👮",copyright:"©️",corn:"🌽",couch_and_lamp:"🛋",couple:"👫",couple_with_heart_woman_man:"💑",couple_with_heart_man_man:"👨‍❤️‍👨",couple_with_heart_woman_woman:"👩‍❤️‍👩",couplekiss_man_man:"👨‍❤️‍💋‍👨",couplekiss_man_woman:"💏",couplekiss_woman_woman:"👩‍❤️‍💋‍👩",cow:"🐮",cow2:"🐄",cowboy_hat_face:"🤠",crab:"🦀",crayon:"🖍",credit_card:"💳",crescent_moon:"🌙",cricket:"🏏",crocodile:"🐊",croissant:"🥐",crossed_fingers:"🤞",crossed_flags:"🎌",crossed_swords:"⚔️",crown:"👑",cry:"😢",crying_cat_face:"😿",crystal_ball:"🔮",cucumber:"🥒",cupid:"💘",curly_loop:"➰",currency_exchange:"💱",curry:"🍛",custard:"🍮",customs:"🛃",cyclone:"🌀",dagger:"🗡",dancer:"💃",dancing_women:"👯",dancing_men:"👯‍♂️",dango:"🍡",dark_sunglasses:"🕶",dart:"🎯",dash:"💨",date:"📅",deciduous_tree:"🌳",deer:"🦌",department_store:"🏬",derelict_house:"🏚",desert:"🏜",desert_island:"🏝",desktop_computer:"🖥",male_detective:"🕵️",diamond_shape_with_a_dot_inside:"💠",diamonds:"♦️",disappointed:"😞",disappointed_relieved:"😥",dizzy:"💫",dizzy_face:"😵",do_not_litter:"🚯",dog:"🐶",dog2:"🐕",dollar:"💵",dolls:"🎎",dolphin:"🐬",door:"🚪",doughnut:"🍩",dove:"🕊",dragon:"🐉",dragon_face:"🐲",dress:"👗",dromedary_camel:"🐪",drooling_face:"🤤",droplet:"💧",drum:"🥁",duck:"🦆",dvd:"📀","e-mail":"📧",eagle:"🦅",ear:"👂",ear_of_rice:"🌾",earth_africa:"🌍",earth_americas:"🌎",earth_asia:"🌏",egg:"🥚",eggplant:"🍆",eight_pointed_black_star:"✴️",eight_spoked_asterisk:"✳️",electric_plug:"🔌",elephant:"🐘",email:"✉️",end:"🔚",envelope_with_arrow:"📩",euro:"💶",european_castle:"🏰",european_post_office:"🏤",evergreen_tree:"🌲",exclamation:"❗️",expressionless:"😑",eye:"👁",eye_speech_bubble:"👁‍🗨",eyeglasses:"👓",eyes:"👀",face_with_head_bandage:"🤕",face_with_thermometer:"🤒",fist_oncoming:"👊",factory:"🏭",fallen_leaf:"🍂",family_man_woman_boy:"👪",family_man_boy:"👨‍👦",family_man_boy_boy:"👨‍👦‍👦",family_man_girl:"👨‍👧",family_man_girl_boy:"👨‍👧‍👦",family_man_girl_girl:"👨‍👧‍👧",family_man_man_boy:"👨‍👨‍👦",family_man_man_boy_boy:"👨‍👨‍👦‍👦",family_man_man_girl:"👨‍👨‍👧",family_man_man_girl_boy:"👨‍👨‍👧‍👦",family_man_man_girl_girl:"👨‍👨‍👧‍👧",family_man_woman_boy_boy:"👨‍👩‍👦‍👦",family_man_woman_girl:"👨‍👩‍👧",family_man_woman_girl_boy:"👨‍👩‍👧‍👦",family_man_woman_girl_girl:"👨‍👩‍👧‍👧",family_woman_boy:"👩‍👦",family_woman_boy_boy:"👩‍👦‍👦",family_woman_girl:"👩‍👧",family_woman_girl_boy:"👩‍👧‍👦",family_woman_girl_girl:"👩‍👧‍👧",family_woman_woman_boy:"👩‍👩‍👦",family_woman_woman_boy_boy:"👩‍👩‍👦‍👦",family_woman_woman_girl:"👩‍👩‍👧",family_woman_woman_girl_boy:"👩‍👩‍👧‍👦",family_woman_woman_girl_girl:"👩‍👩‍👧‍👧",fast_forward:"⏩",fax:"📠",fearful:"😨",feet:"🐾",female_detective:"🕵️‍♀️",ferris_wheel:"🎡",ferry:"⛴",field_hockey:"🏑",file_cabinet:"🗄",file_folder:"📁",film_projector:"📽",film_strip:"🎞",fire:"🔥",fire_engine:"🚒",fireworks:"🎆",first_quarter_moon:"🌓",first_quarter_moon_with_face:"🌛",fish:"🐟",fish_cake:"🍥",fishing_pole_and_fish:"🎣",fist_raised:"✊",fist_left:"🤛",fist_right:"🤜",flags:"🎏",flashlight:"🔦",fleur_de_lis:"⚜️",flight_arrival:"🛬",flight_departure:"🛫",floppy_disk:"💾",flower_playing_cards:"🎴",flushed:"😳",fog:"🌫",foggy:"🌁",football:"🏈",footprints:"👣",fork_and_knife:"🍴",fountain:"⛲️",fountain_pen:"🖋",four_leaf_clover:"🍀",fox_face:"🦊",framed_picture:"🖼",free:"🆓",fried_egg:"🍳",fried_shrimp:"🍤",fries:"🍟",frog:"🐸",frowning:"😦",frowning_face:"☹️",frowning_man:"🙍‍♂️",frowning_woman:"🙍",middle_finger:"🖕",fuelpump:"⛽️",full_moon:"🌕",full_moon_with_face:"🌝",funeral_urn:"⚱️",game_die:"🎲",gear:"⚙️",gem:"💎",gemini:"♊️",ghost:"👻",gift:"🎁",gift_heart:"💝",girl:"👧",globe_with_meridians:"🌐",goal_net:"🥅",goat:"🐐",golf:"⛳️",golfing_man:"🏌️",golfing_woman:"🏌️‍♀️",gorilla:"🦍",grapes:"🍇",green_apple:"🍏",green_book:"📗",green_heart:"💚",green_salad:"🥗",grey_exclamation:"❕",grey_question:"❔",grimacing:"😬",grin:"😁",grinning:"😀",guardsman:"💂",guardswoman:"💂‍♀️",guitar:"🎸",gun:"🔫",haircut_woman:"💇",haircut_man:"💇‍♂️",hamburger:"🍔",hammer:"🔨",hammer_and_pick:"⚒",hammer_and_wrench:"🛠",hamster:"🐹",hand:"✋",handbag:"👜",handshake:"🤝",hankey:"💩",hatched_chick:"🐥",hatching_chick:"🐣",headphones:"🎧",hear_no_evil:"🙉",heart:"❤️",heart_decoration:"💟",heart_eyes:"😍",heart_eyes_cat:"😻",heartbeat:"💓",heartpulse:"💗",hearts:"♥️",heavy_check_mark:"✔️",heavy_division_sign:"➗",heavy_dollar_sign:"💲",heavy_heart_exclamation:"❣️",heavy_minus_sign:"➖",heavy_multiplication_x:"✖️",heavy_plus_sign:"➕",helicopter:"🚁",herb:"🌿",hibiscus:"🌺",high_brightness:"🔆",high_heel:"👠",hocho:"🔪",hole:"🕳",honey_pot:"🍯",horse:"🐴",horse_racing:"🏇",hospital:"🏥",hot_pepper:"🌶",hotdog:"🌭",hotel:"🏨",hotsprings:"♨️",hourglass:"⌛️",hourglass_flowing_sand:"⏳",house:"🏠",house_with_garden:"🏡",houses:"🏘",hugs:"🤗",hushed:"😯",ice_cream:"🍨",ice_hockey:"🏒",ice_skate:"⛸",icecream:"🍦",id:"🆔",ideograph_advantage:"🉐",imp:"👿",inbox_tray:"📥",incoming_envelope:"📨",tipping_hand_woman:"💁",information_source:"ℹ️",innocent:"😇",interrobang:"⁉️",iphone:"📱",izakaya_lantern:"🏮",jack_o_lantern:"🎃",japan:"🗾",japanese_castle:"🏯",japanese_goblin:"👺",japanese_ogre:"👹",jeans:"👖",joy:"😂",joy_cat:"😹",joystick:"🕹",kaaba:"🕋",key:"🔑",keyboard:"⌨️",keycap_ten:"🔟",kick_scooter:"🛴",kimono:"👘",kiss:"💋",kissing:"😗",kissing_cat:"😽",kissing_closed_eyes:"😚",kissing_heart:"😘",kissing_smiling_eyes:"😙",kiwi_fruit:"🥝",koala:"🐨",koko:"🈁",label:"🏷",large_blue_circle:"🔵",large_blue_diamond:"🔷",large_orange_diamond:"🔶",last_quarter_moon:"🌗",last_quarter_moon_with_face:"🌜",latin_cross:"✝️",laughing:"😆",leaves:"🍃",ledger:"📒",left_luggage:"🛅",left_right_arrow:"↔️",leftwards_arrow_with_hook:"↩️",lemon:"🍋",leo:"♌️",leopard:"🐆",level_slider:"🎚",libra:"♎️",light_rail:"🚈",link:"🔗",lion:"🦁",lips:"👄",lipstick:"💄",lizard:"🦎",lock:"🔒",lock_with_ink_pen:"🔏",lollipop:"🍭",loop:"➿",loud_sound:"🔊",loudspeaker:"📢",love_hotel:"🏩",love_letter:"💌",low_brightness:"🔅",lying_face:"🤥",m:"Ⓜ️",mag:"🔍",mag_right:"🔎",mahjong:"🀄️",mailbox:"📫",mailbox_closed:"📪",mailbox_with_mail:"📬",mailbox_with_no_mail:"📭",man:"👨",man_artist:"👨‍🎨",man_astronaut:"👨‍🚀",man_cartwheeling:"🤸‍♂️",man_cook:"👨‍🍳",man_dancing:"🕺",man_facepalming:"🤦‍♂️",man_factory_worker:"👨‍🏭",man_farmer:"👨‍🌾",man_firefighter:"👨‍🚒",man_health_worker:"👨‍⚕️",man_in_tuxedo:"🤵",man_judge:"👨‍⚖️",man_juggling:"🤹‍♂️",man_mechanic:"👨‍🔧",man_office_worker:"👨‍💼",man_pilot:"👨‍✈️",man_playing_handball:"🤾‍♂️",man_playing_water_polo:"🤽‍♂️",man_scientist:"👨‍🔬",man_shrugging:"🤷‍♂️",man_singer:"👨‍🎤",man_student:"👨‍🎓",man_teacher:"👨‍🏫",man_technologist:"👨‍💻",man_with_gua_pi_mao:"👲",man_with_turban:"👳",tangerine:"🍊",mans_shoe:"👞",mantelpiece_clock:"🕰",maple_leaf:"🍁",martial_arts_uniform:"🥋",mask:"😷",massage_woman:"💆",massage_man:"💆‍♂️",meat_on_bone:"🍖",medal_military:"🎖",medal_sports:"🏅",mega:"📣",melon:"🍈",memo:"📝",men_wrestling:"🤼‍♂️",menorah:"🕎",mens:"🚹",metal:"🤘",metro:"🚇",microphone:"🎤",microscope:"🔬",milk_glass:"🥛",milky_way:"🌌",minibus:"🚐",minidisc:"💽",mobile_phone_off:"📴",money_mouth_face:"🤑",money_with_wings:"💸",moneybag:"💰",monkey:"🐒",monkey_face:"🐵",monorail:"🚝",moon:"🌔",mortar_board:"🎓",mosque:"🕌",motor_boat:"🛥",motor_scooter:"🛵",motorcycle:"🏍",motorway:"🛣",mount_fuji:"🗻",mountain:"⛰",mountain_biking_man:"🚵",mountain_biking_woman:"🚵‍♀️",mountain_cableway:"🚠",mountain_railway:"🚞",mountain_snow:"🏔",mouse:"🐭",mouse2:"🐁",movie_camera:"🎥",moyai:"🗿",mrs_claus:"🤶",muscle:"💪",mushroom:"🍄",musical_keyboard:"🎹",musical_note:"🎵",musical_score:"🎼",mute:"🔇",nail_care:"💅",name_badge:"📛",national_park:"🏞",nauseated_face:"🤢",necktie:"👔",negative_squared_cross_mark:"❎",nerd_face:"🤓",neutral_face:"😐",new:"🆕",new_moon:"🌑",new_moon_with_face:"🌚",newspaper:"📰",newspaper_roll:"🗞",next_track_button:"⏭",ng:"🆖",no_good_man:"🙅‍♂️",no_good_woman:"🙅",night_with_stars:"🌃",no_bell:"🔕",no_bicycles:"🚳",no_entry:"⛔️",no_entry_sign:"🚫",no_mobile_phones:"📵",no_mouth:"😶",no_pedestrians:"🚷",no_smoking:"🚭","non-potable_water":"🚱",nose:"👃",notebook:"📓",notebook_with_decorative_cover:"📔",notes:"🎶",nut_and_bolt:"🔩",o:"⭕️",o2:"🅾️",ocean:"🌊",octopus:"🐙",oden:"🍢",office:"🏢",oil_drum:"🛢",ok:"🆗",ok_hand:"👌",ok_man:"🙆‍♂️",ok_woman:"🙆",old_key:"🗝",older_man:"👴",older_woman:"👵",om:"🕉",on:"🔛",oncoming_automobile:"🚘",oncoming_bus:"🚍",oncoming_police_car:"🚔",oncoming_taxi:"🚖",open_file_folder:"📂",open_hands:"👐",open_mouth:"😮",open_umbrella:"☂️",ophiuchus:"⛎",orange_book:"📙",orthodox_cross:"☦️",outbox_tray:"📤",owl:"🦉",ox:"🐂",package:"📦",page_facing_up:"📄",page_with_curl:"📃",pager:"📟",paintbrush:"🖌",palm_tree:"🌴",pancakes:"🥞",panda_face:"🐼",paperclip:"📎",paperclips:"🖇",parasol_on_ground:"⛱",parking:"🅿️",part_alternation_mark:"〽️",partly_sunny:"⛅️",passenger_ship:"🛳",passport_control:"🛂",pause_button:"⏸",peace_symbol:"☮️",peach:"🍑",peanuts:"🥜",pear:"🍐",pen:"🖊",pencil2:"✏️",penguin:"🐧",pensive:"😔",performing_arts:"🎭",persevere:"😣",person_fencing:"🤺",pouting_woman:"🙎",phone:"☎️",pick:"⛏",pig:"🐷",pig2:"🐖",pig_nose:"🐽",pill:"💊",pineapple:"🍍",ping_pong:"🏓",pisces:"♓️",pizza:"🍕",place_of_worship:"🛐",plate_with_cutlery:"🍽",play_or_pause_button:"⏯",point_down:"👇",point_left:"👈",point_right:"👉",point_up:"☝️",point_up_2:"👆",police_car:"🚓",policewoman:"👮‍♀️",poodle:"🐩",popcorn:"🍿",post_office:"🏣",postal_horn:"📯",postbox:"📮",potable_water:"🚰",potato:"🥔",pouch:"👝",poultry_leg:"🍗",pound:"💷",rage:"😡",pouting_cat:"😾",pouting_man:"🙎‍♂️",pray:"🙏",prayer_beads:"📿",pregnant_woman:"🤰",previous_track_button:"⏮",prince:"🤴",princess:"👸",printer:"🖨",purple_heart:"💜",purse:"👛",pushpin:"📌",put_litter_in_its_place:"🚮",question:"❓",rabbit:"🐰",rabbit2:"🐇",racehorse:"🐎",racing_car:"🏎",radio:"📻",radio_button:"🔘",radioactive:"☢️",railway_car:"🚃",railway_track:"🛤",rainbow:"🌈",rainbow_flag:"🏳️‍🌈",raised_back_of_hand:"🤚",raised_hand_with_fingers_splayed:"🖐",raised_hands:"🙌",raising_hand_woman:"🙋",raising_hand_man:"🙋‍♂️",ram:"🐏",ramen:"🍜",rat:"🐀",record_button:"⏺",recycle:"♻️",red_circle:"🔴",registered:"®️",relaxed:"☺️",relieved:"😌",reminder_ribbon:"🎗",repeat:"🔁",repeat_one:"🔂",rescue_worker_helmet:"⛑",restroom:"🚻",revolving_hearts:"💞",rewind:"⏪",rhinoceros:"🦏",ribbon:"🎀",rice:"🍚",rice_ball:"🍙",rice_cracker:"🍘",rice_scene:"🎑",right_anger_bubble:"🗯",ring:"💍",robot:"🤖",rocket:"🚀",rofl:"🤣",roll_eyes:"🙄",roller_coaster:"🎢",rooster:"🐓",rose:"🌹",rosette:"🏵",rotating_light:"🚨",round_pushpin:"📍",rowing_man:"🚣",rowing_woman:"🚣‍♀️",rugby_football:"🏉",running_man:"🏃",running_shirt_with_sash:"🎽",running_woman:"🏃‍♀️",sa:"🈂️",sagittarius:"♐️",sake:"🍶",sandal:"👡",santa:"🎅",satellite:"📡",saxophone:"🎷",school:"🏫",school_satchel:"🎒",scissors:"✂️",scorpion:"🦂",scorpius:"♏️",scream:"😱",scream_cat:"🙀",scroll:"📜",seat:"💺",secret:"㊙️",see_no_evil:"🙈",seedling:"🌱",selfie:"🤳",shallow_pan_of_food:"🥘",shamrock:"☘️",shark:"🦈",shaved_ice:"🍧",sheep:"🐑",shell:"🐚",shield:"🛡",shinto_shrine:"⛩",ship:"🚢",shirt:"👕",shopping:"🛍",shopping_cart:"🛒",shower:"🚿",shrimp:"🦐",signal_strength:"📶",six_pointed_star:"🔯",ski:"🎿",skier:"⛷",skull:"💀",skull_and_crossbones:"☠️",sleeping:"😴",sleeping_bed:"🛌",sleepy:"😪",slightly_frowning_face:"🙁",slightly_smiling_face:"🙂",slot_machine:"🎰",small_airplane:"🛩",small_blue_diamond:"🔹",small_orange_diamond:"🔸",small_red_triangle:"🔺",small_red_triangle_down:"🔻",smile:"😄",smile_cat:"😸",smiley:"😃",smiley_cat:"😺",smiling_imp:"😈",smirk:"😏",smirk_cat:"😼",smoking:"🚬",snail:"🐌",snake:"🐍",sneezing_face:"🤧",snowboarder:"🏂",snowflake:"❄️",snowman:"⛄️",snowman_with_snow:"☃️",sob:"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left | \vec{F}_{normale} \right |"],["\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |"]),xt=V(["F = -k x"],["F = -k x"]),Ct=V(["Delta \vec{s} = \vec{s}(fine) - \vec{s}(inizio)"],["\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)"]),St=V(["\vec{v} = \frac{Delta \vec{s}}{Delta t}"],["\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}"]),Lt=V(["\vec{v} = lim_{Delta t \to 0} \frac{Delta \vec{s}}{Delta t} = \frac{d \vec{s}}{dt}"],["\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}"]),At=V(["\vec{a} = \frac{Delta \vec{v}}{Delta t}"],["\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}"]),Mt=V(["\vec{a} = lim_{Delta v \to 0} \frac{Delta \vec{v}}{Delta t} = \frac{d \vec{v}}{d t} = \frac{d^2 \vec{s}}{d t^2}"],["\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}"]),Ft=V(["\vec{p} = m \vec{v}"],["\\vec{p} = m \\vec{v}"]),Tt=V(["Sigma \vec{F} = 0 Longleftrightarrow Delta \vec{p} = 0"],["\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0"]),It=V(["s(t) = v cdot Delta t + s(0)"],["s(t) = v \\cdot \\Delta t + s(0)"]),Dt=V(["v(t) = k"],["v(t) = k"]),Nt=V(["a(t) = 0"],["a(t) = 0"]),Bt=V(["s(t) = \frac{1}{2} a cdot (Delta t)^2 + v(0) cdot (Delta t) + s(0)"],["s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)"]),Vt=V(["v(t) = a Delta t + v(0)"],["v(t) = a \\Delta t + v(0)"]),Rt=V(["a(t) = k"],["a(t) = k"]),Ut=V(["omega = \frac{2 pi}{T}"],["\\omega = \\frac{2 \\pi}{T}"]),Yt=V(["s(t) = A sin (omega cdot t + phi)"],["s(t) = A \\sin (\\omega \\cdot t + \\phi)"]),Ht=V(["\frac{pi}{2}"],["\\frac{\\pi}{2}"]),Gt=V(["v(t) = A sin (omega cdot t + phi + \frac{pi}{2})"],["v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})"]),Wt=V(["pi"],["\\pi"]),$t=V(["a(t) = A sin (omega cdot t + phi + pi)"],["a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)"]),Kt=V(["phi"],["\\phi"]),Zt=V(["v = \frac{Delta s}{t} = \frac{2 pi cdot r}{T} = omega r"],["v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r"]),Qt=V(["a = \frac{v^2}{r} = r cdot omega^2 = v cdot omega"],["a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega"]),Jt=V(["F = m cdot a"],["F = m \\cdot a"]),en=V(["W = \vec{F} cdot \vec{s} = F cdot Delta s cdot cos(alpha )"],["W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )"]),tn=V(["E_c = \frac{1}{2} m v^2"],["E_c = \\frac{1}{2} m v^2"]),nn=V(["Delta E_c = W"],["\\Delta E_c = W"]),an=V(["E_{p_g} = m cdot g cdot h"],["E_{p_g} = m \\cdot g \\cdot h"]),ln=V(["E_{p_e} = \frac{1}{2} k x^2"],["E_{p_e} = \\frac{1}{2} k x^2"]),on=V(["E = E_k + E_p"],["E = E_k + E_p"]),rn=V(["P = \frac{Delta E}{Delta t}"],["P = \\frac{\\Delta E}{\\Delta t}"]),cn=V(["C_{elettrone} = 1.602 cdot 10^{-19}"],["C_{elettrone} = 1.602 \\cdot 10^{-19}"]),sn=V(["left | \vec{F}_{elettrica} \right | = \frac{-k cdot q_1 cdot q_2}{s^2}"],["\\left | \\vec{F}_{elettrica} \\right | = \\frac{-k \\cdot q_1 \\cdot q_2}{s^2}"]),un=V(["k"],["k"]),hn=V(["k = 8.99 cdot 10^9 \frac{N cdot m^2}{C^2}"],["k = 8.99 \\cdot 10^9 \\frac{N \\cdot m^2}{C^2}"]),pn=V(["epsilon_0"],["\\epsilon_0"]),bn=V(["k = \frac{1}{4 pi cdot epsilon_0}"],["k = \\frac{1}{4 \\pi \\cdot \\epsilon_0}"]),dn=V(["left | \vec{F}_{elettrica} \right | = \frac{q_1 cdot q_2}{4 pi cdot epsilon_0 cdot s^2}"],["\\left | \\vec{F}_{elettrica} \\right | = \\frac{q_1 \\cdot q_2}{4 \\pi \\cdot \\epsilon_0 \\cdot s^2}"]),mn=V(["\vec{E} = \frac{\vec{F}_{elettrica}}{q} = \frac{-k cdot q}{s^2}"],["\\vec{E} = \\frac{\\vec{F}_{elettrica}}{q} = \\frac{-k \\cdot q}{s^2}"]),fn=V(["Phi_E = \vec{E} cdot \vec{A}"],["\\Phi_E = \\vec{E} \\cdot \\vec{A}"]),jn=V(["Phi_E = \vec{E} cdot \vec{A} = E_perp cdot A cdot cos(alpha)"],["\\Phi_E = \\vec{E} \\cdot \\vec{A} = E_\\perp \\cdot A \\cdot \\cos(\\alpha)"]),On=V(["Phi_E = 4 pi cdot k cdot q = \frac{q}{epsilon_0}"],["\\Phi_E = 4 \\pi \\cdot k \\cdot q = \\frac{q}{\\epsilon_0}"]),_n=V(["U_e"],["U_e"]),gn=V(["V = \frac{U_e}{q}"],["V = \\frac{U_e}{q}"]),vn=V(["V"],["V"]),wn=V(["I = \frac{Delta q}{Delta t}"],["I = \\frac{\\Delta q}{\\Delta t}"]),yn=V(["A"],["A"]),zn=V(["P = \frac{Delta U_e}{Delta t} = I cdot Delta V = I^2 cdot R = \frac{(Delta V)^2}{R}"],["P = \\frac{\\Delta U_e}{\\Delta t} = I \\cdot \\Delta V = I^2 \\cdot R = \\frac{(\\Delta V)^2}{R}"]),kn=V(["V = R cdot I"],["V = R \\cdot I"]),Pn=V(["R"],["R"]),En=V(["Omega"],["\\Omega"]),Xn=V(["R = \rho \frac{L_{unghezza}}{A_{rea}}"],["R = \\rho \\frac{L_{unghezza}}{A_{rea}}"]),qn=V(["\rho"],["\\rho"]),xn=V(["\rho = \rho_0 (1 + alpha(T - T_0))"],["\\rho = \\rho_0 (1 + \\alpha(T - T_0))"]),Cn=V(["C = \frac{q_{massima}}{Delta V}"],["C = \\frac{q_{massima}}{\\Delta V}"]),Sn=V(["C_{nuova} = kappa cdot \frac{epsilon_0 cdot A}{s}"],["C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}"]),Ln=V(["kappa"],["\\kappa"]),An=V(["s"],["s"]),Mn=V(["Fa"],["Fa"]),Fn=V(["R_{serie} = sum_{i=1}^{n} R_i"],["R_{serie} = \\sum_{i=1}^{n} R_i"]),Tn=V(["R_{parallelo} = \frac{1}{sum_{i=1}^{n} \frac{1}{R_i}}"],["R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}"]),In=V(["C_{serie} = \frac{1}{sum_{i=1}^{n} \frac{1}{C_i}}"],["C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}"]),Dn=V(["C_{parallelo} = sum_{i=1}^{n} C_n"],["C_{parallelo} = \\sum_{i=1}^{n} C_n"]),Nn=V(["mu_0 = 4 pi cdot 10^{-7} \frac{H}{m}"],["\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}"]),Bn=V(["\frac{N}{A^2}"],["\\frac{N}{A^2}"]),Vn=V(["B"],["B"]),Rn=V(["Phi_{B_{i}} = \vec{B} cdot \vec{L}_n = B cdot L_i cdot sin(alpha) = B_parallel cdot L_i"],["\\Phi_{B_{i}} = \\vec{B} \\cdot \\vec{L}_n = B \\cdot L_i \\cdot \\sin(\\alpha) = B_\\parallel \\cdot L_i"]),Un=V(["Phi_{B} = sum_{i=0}^{n_{lati}} Phi_{Bn}"],["\\Phi_{B} = \\sum_{i=0}^{n_{lati}} \\Phi_{Bn}"]),Yn=V(["Wb = T cdot m^2"],["Wb = T \\cdot m^2"]),Hn=V(["Phi_B = mu_0 cdot I"],["\\Phi_B = \\mu_0 \\cdot I"]),Gn=V(["\vec{F}_{B} = q cdot (\vec{v} \times \vec{B})"],["\\vec{F}_{B} = q \\cdot (\\vec{v} \\times \\vec{B})"]),Wn=V(["\vec{B}"],["\\vec{B}"]),$n=V(["\vec{v}"],["\\vec{v}"]),Kn=V(["\vec{F}_{magnetica} = I cdot (\vec{L} \times \vec{B})"],["\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})"]),Zn=V(["I"],["I"]),Qn=V(["\vec{L}"],["\\vec{L}"]),Jn=V(["left | \vec{B} \right | = mu_0 cdot I cdot \frac{A_{vvolgimenti}}{L_{unghezzafilo}}"],["\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}"]),ea=V(["left | \vec{B} \right | = \frac{mu cdot I}{2 pi r}"],["\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}"]),ta=V(["Delta V_{indotta} = v cdot B cdot L"],["\\Delta V_{indotta} = v \\cdot B \\cdot L"]),na=V(["Phi_B = \vec{B} cdot \vec{A} = B cdot A cdot cos(alpha)"],["\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)"]),aa=V(["Delta V_{indotta} = - \frac{Delta Phi_B}{Delta t}"],["\\Delta V_{indotta} = - \\frac{\\Delta \\Phi_B}{\\Delta t}"]),la=V(["Delta V_{indotta} = - \frac{N cdot Delta Phi_{B_{spira}}}{Delta t} = - \frac{N cdot B cdot A cdot cos(alpha)}{Delta t}"],["\\Delta V_{indotta} = - \\frac{N \\cdot \\Delta \\Phi_{B_{spira}}}{\\Delta t} = - \\frac{N \\cdot B \\cdot A \\cdot cos(\\alpha)}{\\Delta t}"]),ia=V(["N"],["N"]),oa=V(["E"],["E"]),ra=V(["E = c cdot B"],["E = c \\cdot B"]),ca=V(["c"],["c"]),sa=V(["c = \frac{1}{sqrt{epsilon_0 cdot mu_0}} = 3.00 cdot 10^8 \frac{m}{s}"],["c = \\frac{1}{\\sqrt{\\epsilon_0 \\cdot \\mu_0}} = 3.00 \\cdot 10^8 \\frac{m}{s}"]),ua=V(["A(t) = A_{max} cdot sin left ( \frac{2 pi}{lambda} - omega t + phi \right )"],["A(t) = A_{max} \\cdot \\sin \\left ( \\frac{2 \\pi}{\\lambda} - \\omega t + \\phi \\right )"]),ha=V(["A_{max}"],["A_{max}"]),pa=V(["\frac{2 pi}{lambda} = left | \vec{k} \right |"],["\\frac{2 \\pi}{\\lambda} = \\left | \\vec{k} \\right |"]),ba=V(["omega"],["\\omega"]),da=V(["\frac{1}{lambda} = R left ( \frac{1}{4} - \frac{1}{n^2} \right )"],["\\frac{1}{\\lambda} = R \\left ( \\frac{1}{4} - \\frac{1}{n^2} \\right )"]),ma=V(["R = 1.097 cdot 10^7 \frac{1}{m}"],["R = 1.097 \\cdot 10^7 \\frac{1}{m}"]),fa=V(["n"],["n"]),ja=V(["h"],["h"]),Oa=V(["hbar = left ( \frac{h}{2 pi} \right )"],["\\hbar = \\left ( \\frac{h}{2 \\pi} \\right )"]),_a=V(["m cdot v_n cdot 2 pi cdot r = n cdot h"],["m \\cdot v_n \\cdot 2 \\pi \\cdot r = n \\cdot h"]),ga=V(["r_n = n^2 cdot a_0 = n^2 cdot \frac{hbar}{m_{elettrone} cdot k cdot e^2} "],["r_n = n^2 \\cdot a_0 = n^2 \\cdot \\frac{\\hbar}{m_{elettrone} \\cdot k \\cdot e^2} "]),va=V(["a_0 = left ( \frac{h}{2 pi} \right )^2 cdot \frac{1}{m_{elettrone} cdot k cdot e^2} = 5.29 cdot 10^{-11} m"],["a_0 = \\left ( \\frac{h}{2 \\pi} \\right )^2 \\cdot \\frac{1}{m_{elettrone} \\cdot k \\cdot e^2} = 5.29 \\cdot 10^{-11} m"]),wa=V(["E_n = \frac{1}{n^2} cdot E_1 = - \frac{1}{n^2} cdot \frac{a_0^2}{2 cdot m cdot hbar^4} = - \frac{1}{n^2} cdot \frac{m_{elettrone} cdot k^2 cdot e^4}{2 cdot hbar^2}"],["E_n = \\frac{1}{n^2} \\cdot E_1 = - \\frac{1}{n^2} \\cdot \\frac{a_0^2}{2 \\cdot m \\cdot \\hbar^4} = - \\frac{1}{n^2} \\cdot \\frac{m_{elettrone} \\cdot k^2 \\cdot e^4}{2 \\cdot \\hbar^2}"]),ya=V(["10^1 eV"],["10^1 eV"]),za=V(["1 eV"],["1 eV"]),ka=V(["lambda"],["\\lambda"]),Pa=V(["lambda_{max} cdot T"],["\\lambda_{max} \\cdot T"]),Ea=V(["E_{fotone} = h cdot f"],["E_{fotone} = h \\cdot f"]),Xa=String.raw,qa=Object(Pe.h)("h1",null,"Fisica"),xa=Object(Pe.h)("p",null,"Usa le regole base della trigonometria:"),Ca=Object(Pe.h)("p",null,"Scomponi in componenti, poi sommali:"),Sa=Object(Pe.h)("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma."),La=Object(Pe.h)("p",null,"Alla fine è sempre una somma:"),Aa=Object(Pe.h)("p",null,"Produce il vettore che parte da ",Object(Pe.h)(nt,null,"w")," e arriva a ",Object(Pe.h)(nt,null,"v"),"."),Ma=Object(Pe.h)("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),Fa=Object(Pe.h)("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),Ta=Object(Pe.h)("li",null,Object(Pe.h)("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra")),Ia=Object(Pe.h)("p",null,"Non è commutativo!"),Da=Object(Pe.h)("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),Na=Object(Pe.h)("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",Object(Pe.h)("i",null,"massa"),"."),Ba=Object(Pe.h)("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),Va=Object(Pe.h)("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),Ra=Object(Pe.h)("p",null,Object(Pe.h)(nt,null,"G")," è la ",Object(Pe.h)("i",null,"costante di gravitazione universale")," e vale:"),Ua=Object(Pe.h)("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",Object(Pe.h)("i",null,"peso")," uguale a:"),Ya=Object(Pe.h)("p",null,Object(Pe.h)(nt,null,"g")," è la ",Object(Pe.h)("i",null,"costante di gravità")," della Terra, e vale:"),Ha=Object(Pe.h)("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),Ga=Object(Pe.h)("p",null,"L'unica differenza è che cambia la ",Object(Pe.h)("i",null,"costante di gravità"),":"),Wa=Object(Pe.h)(Be,{title:"Normale"},Object(Pe.h)("p",null,"Si oppone alle forze applicate alla superficie di contatto."),Object(Pe.h)("p",null,"Un libro appoggiato su un tavolo ha la ",Object(Pe.h)("b",null,"forza di gravità")," che lo attira verso il terreno e la ",Object(Pe.h)("b",null,"forza normale")," che lo trattiene dal cadere.")),$a=Object(Pe.h)("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),Ka=Object(Pe.h)("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),Za=Object(Pe.h)(Be,{title:"Tensione"},Object(Pe.h)("p",null,"E' forza trasmessa tra due estremi di una fune."),Object(Pe.h)("p",null,"Può essere redirezionata per mezzo di carrucole.")),Qa=Object(Pe.h)("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),Ja=Object(Pe.h)("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"),el=Object(Pe.h)("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),tl=Object(Pe.h)("p",null,"È un vettore che misura la variazione di posizione nel tempo."),nl=Object(Pe.h)("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",Object(Pe.h)("i",null,"velocità istantanea"),":"),al=Object(Pe.h)("p",null,"È un vettore che misura la variazione di velocità nel tempo."),ll=Object(Pe.h)("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",Object(Pe.h)("i",null,"accelerazione istantanea"),":"),il=Object(Pe.h)("span",null,"Quantità di moto ",Object(Pe.h)("small",null,"(momento lineare)")),ol=Object(Pe.h)("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),rl=Object(Pe.h)("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),cl=Object(Pe.h)("p",null,"La ",Object(Pe.h)("i",null,"legge oraria")," è:"),sl=Object(Pe.h)("p",null,"È costante:"),ul=Object(Pe.h)("p",null,"La velocità non varia:"),hl=Object(Pe.h)(Be,{title:"Forze"},Object(Pe.h)("p",null,"Si applica la prima legge di Newton:"),Object(Pe.h)("p",null,Object(Pe.h)(nt,null,"f(t) = 0"))),pl=Object(Pe.h)("p",null,"La ",Object(Pe.h)("i",null,"legge oraria")," è:"),bl=Object(Pe.h)("p",null,"È una retta:"),dl=Object(Pe.h)("p",null,"È costante:"),ml=Object(Pe.h)(Be,{title:"Forze"},Object(Pe.h)("p",null,"Si applica la prima legge di Newton:"),Object(Pe.h)("p",null,Object(Pe.h)(nt,null,"f(t) = m a"))),fl=Object(Pe.h)(Be,{title:"Ampiezza"},Object(Pe.h)("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),Object(Pe.h)("p",null,"(L'ampiezza di una sinusoide.)")),jl=Object(Pe.h)("p",null,"Indica quanto in fretta cambia la posizione del corpo."),Ol=Object(Pe.h)("p",null,"Dipende dal periodo:"),_l=Object(Pe.h)("p",null,"E' una sinusoide:"),gl=Object(Pe.h)(Be,{title:"Forze"},Object(Pe.h)("p",null,"Si applica la prima legge di Newton:"),Object(Pe.h)("p",null,Object(Pe.h)(nt,null,"f(t) = m a"))),vl=Object(Pe.h)(Be,{title:"Moto parabolico"},Object(Pe.h)("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),wl=Object(Pe.h)("h3",null,"Velocità angolare"),yl=Object(Pe.h)("p",null,"Quanto cambia la fase nel tempo."),zl=Object(Pe.h)("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),kl=Object(Pe.h)("p",null,"Si applicano le formule per la circonferenza:"),Pl=Object(Pe.h)("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),El=Object(Pe.h)("p",null,"È verso il centro e si calcola con:"),Xl=Object(Pe.h)("p",null,"E' compiuto da una forza che sposta un corpo."),ql=Object(Pe.h)("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)"),xl=Object(Pe.h)("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),Cl=Object(Pe.h)("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),Sl=Object(Pe.h)("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),Ll=Object(Pe.h)("p",null,"(Con ",Object(Pe.h)(nt,null,"h")," uguale a un altezza scelta come punto di riferimento.)"),Al=Object(Pe.h)("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),Ml=Object(Pe.h)("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),Fl=Object(Pe.h)("p",null,"Ad esempio, è conservativa la ",Object(Pe.h)("i",null,"forza di gravità"),", ma ",Object(Pe.h)("b",null,"non")," è conservativa la forza di attrito."),Tl=Object(Pe.h)("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),Il=Object(Pe.h)("p",null,"È la velocità di trasferimento di energia:"),Dl=Object(Pe.h)("p",null,"È una proprietà dei corpi che può essere ",Object(Pe.h)(it,null,"positiva")," o ",Object(Pe.h)(ct,null,"negativa"),"."),Nl=Object(Pe.h)("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),Bl=Object(Pe.h)("p",null,"Cariche ",Object(Pe.h)(it,null,"opp"),Object(Pe.h)(ct,null,"oste")," si attraggono; cariche ",Object(Pe.h)(it,null,"uguali")," si respingono."),Vl=Object(Pe.h)(Be,{title:"Conduttori e isolanti"},Object(Pe.h)("p",null,"Più ",Object(Pe.h)("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),Object(Pe.h)("p",null,"I corpi in cui la carica si muove bene sono ",Object(Pe.h)("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",Object(Pe.h)("i",null,"isolanti"),"."),Object(Pe.h)("p",null,Object(Pe.h)("i",null,"Il corpo umano è un buon conduttore."))),Rl=Object(Pe.h)(Ue,{title:"Polarizzazione"},Object(Pe.h)(Be,{title:"Polarizzazione"},Object(Pe.h)("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),Ul=Object(Pe.h)(Ue,null,Object(Pe.h)(Be,{title:"Messa a terra"},Object(Pe.h)("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",Object(Pe.h)("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",Object(Pe.h)(it,null,"cariche positive")," e ",Object(Pe.h)(ct,null,"negative")," all'interno)."))),Yl=Object(Pe.h)(Ue,null,Object(Pe.h)(Be,{title:"Polarizzazione per strofinio"},Object(Pe.h)("p",null,"Strofinando tra loro due corpi isolanti, essi si ",Object(Pe.h)("i",null,"polarizzeranno per strofinio"),".")),Object(Pe.h)(Be,{title:"Polarizzazione per contatto"},Object(Pe.h)("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",Object(Pe.h)("i",null,"polarizzarsi per contatto"),".")),Object(Pe.h)(Be,{title:"Polarizzazione per induzione"},Object(Pe.h)("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',Object(Pe.h)(it,null,"certo segno")," vicino, esso avrà tutte le cariche del ",Object(Pe.h)(ct,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",Object(Pe.h)(it,null,"stesso segno")," più lontano possibile da esse."),Object(Pe.h)("p",null,"Mettendo a terra il conduttore, nuove cariche del ",Object(Pe.h)(ct,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),Object(Pe.h)("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",Object(Pe.h)(ct,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),Hl=Object(Pe.h)("p",null,"Due corpi carichi si attraggono tra loro con forza:"),Gl=Object(Pe.h)("i",null,"costante di Coulomb"),Wl=Object(Pe.h)("i",null,"permeabilità del vuoto"),$l=Object(Pe.h)("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),Kl=Object(Pe.h)("p",null,'È la differenza tra "quanto" campo elettrico ',Object(Pe.h)(it,null,"entra")," e quanto campo elettrico ",Object(Pe.h)(ct,null,"esce")," da una certa area."),Zl=Object(Pe.h)("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),Ql=Object(Pe.h)("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),Jl=Object(Pe.h)("p",null,Object(Pe.h)(Ge,null,"Circa. E' una specie di integrale...")),ei=Object(Pe.h)("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),ti=Object(Pe.h)("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."),ni=Object(Pe.h)("i",null,"energia potenziale elettrica"),ai=Object(Pe.h)("span",null,"Potenziale elettrico ",Object(Pe.h)("small",null,"(tensione)")),li=Object(Pe.h)("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),ii=Object(Pe.h)("p",null,"In una batteria è detto ",Object(Pe.h)("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli."),oi=Object(Pe.h)("span",null,"Corrente elettrica ",Object(Pe.h)("small",null,"(intensità)")),ri=Object(Pe.h)("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),ci=Object(Pe.h)("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),si=Object(Pe.h)(Be,{title:Object(Pe.h)("span",null,"Corrente continua ",Object(Pe.h)("small",null,"(",Object(Pe.h)("abbr",{title:"Direct Current"},"DC"),")"))},Object(Pe.h)("p",null,"Quando in un circuito la direzione della corrente è costante.")),ui=Object(Pe.h)(Be,{title:Object(Pe.h)("span",null,"Corrente alternata ",Object(Pe.h)("small",null,"(",Object(Pe.h)("abbr",{title:"Alternate Current"},"AC"),")"))},Object(Pe.h)("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),hi=Object(Pe.h)("p",null,"Possiamo calcolare la potenza di un circuito:"),pi=Object(Pe.h)("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),bi=Object(Pe.h)("p",null,"Il potenziale utilizzato è pari a:"),di=Object(Pe.h)("i",null,"resistenza"),mi=Object(Pe.h)("p",null,"La resistenza di un conduttore vale:"),fi=Object(Pe.h)("i",null,"resistività"),ji=Object(Pe.h)("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),Oi=Object(Pe.h)("p",null,"Per farlo, cattura cariche ",Object(Pe.h)(it,null,"positive")," e ",Object(Pe.h)(ct,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),_i=Object(Pe.h)("p",null,"Ha una ",Object(Pe.h)("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),gi=Object(Pe.h)("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),vi=Object(Pe.h)("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),wi=Object(Pe.h)("i",null,"costante dielettrica relativa"),yi=Object(Pe.h)("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",Object(Pe.h)("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",Object(Pe.h)("i",null,"breakdown"),"."),zi=Object(Pe.h)(Be,{title:"Amperometro"},Object(Pe.h)("p",null,"Misura la corrente elettrica se messo in serie."),Object(Pe.h)("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),ki=Object(Pe.h)(Be,{title:"Voltmetro"},Object(Pe.h)("p",null,"Misura la differenza di potenziale se messo in parallelo."),Object(Pe.h)("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)")),Pi=Object(Pe.h)(Ue,{title:"Principi di Kirchhoff"},Object(Pe.h)(Be,{title:"Legge dei nodi"},Object(Pe.h)("p",null,"Per nodo si intende un qualsiasi punto del circuito."),Object(Pe.h)("p",null,"Da un nodo entra ed esce la stessa corrente.")),Object(Pe.h)(Be,{title:"Legge delle maglie"},Object(Pe.h)("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),Object(Pe.h)("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),Ei=Object(Pe.h)(Ue,{title:"Serie e Parallelo"},Object(Pe.h)(Be,{title:"Circuito in serie"},Object(Pe.h)("p",null,"Più parti di circuito sono ",Object(Pe.h)("i",null,"in serie")," se sono consecutive e senza biforcazioni."),Object(Pe.h)("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),Object(Pe.h)(Be,{title:"Circuito in parallelo"},Object(Pe.h)("p",null,"Più parti di circuito sono ",Object(Pe.h)("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),Object(Pe.h)("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),Xi=Object(Pe.h)("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),qi=Object(Pe.h)("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),xi=Object(Pe.h)("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),Ci=Object(Pe.h)("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),Si=Object(Pe.h)("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),Li=Object(Pe.h)("p",null,"Come un campo elettrico, ma per i magneti."),Ai=Object(Pe.h)(nt,null,"T"),Mi=Object(Pe.h)("p",null,'È "quanto" campo magnetico ',Object(Pe.h)("b",null,"attraversa")," un percorso chiuso."),Fi=Object(Pe.h)("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),Ti=Object(Pe.h)(Be,{title:"Legge di Gauss per i campi magnetici"},Object(Pe.h)("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),Object(Pe.h)("p",null,"Ovvero, non esistono monopoli magnetici.")),Ii=Object(Pe.h)("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),Di=Object(Pe.h)("span",null,"Forza magnetica su carica puntiforme ",Object(Pe.h)("small",null,"(Forza di Lorentz)")),Ni=Object(Pe.h)("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),Bi=Object(Pe.h)("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),Vi=Object(Pe.h)("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme."),Ri=Object(Pe.h)("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),Ui=Object(Pe.h)("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]"),Yi=Object(Pe.h)(Be,{title:"Campo magnetico in una spira"},Object(Pe.h)("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),Hi=Object(Pe.h)("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),Gi=Object(Pe.h)("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),Wi=Object(Pe.h)("p",null,Object(Pe.h)("i",null,"Caso particolare della ",Object(Pe.h)("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),$i=Object(Pe.h)("p",null,"Il modulo del campo magnetico ",Object(Pe.h)(nt,null,"B")," prodotto da un filo in cui passa una corrente continua ",Object(Pe.h)(nt,null,"I")," alla distanza ",Object(Pe.h)(nt,null,"s")," è:"),Ki=Object(Pe.h)("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),Zi=Object(Pe.h)("p",null,"Due fili attraversati dalla ",Object(Pe.h)(it,null,"stessa corrente")," si attraggono, due fili attraversati da ",Object(Pe.h)(it,null,"corr"),Object(Pe.h)(ct,null,"enti")," ",Object(Pe.h)(it,null,"opp"),Object(Pe.h)(ct,null,"oste")," si respingono."),Qi=Object(Pe.h)("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),Ji=Object(Pe.h)("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),eo=Object(Pe.h)("p",null,"Essa vale:"),to=Object(Pe.h)("p",null,"Dove ",Object(Pe.h)(nt,null,"v")," è la velocità del conduttore, ",Object(Pe.h)(nt,null,"B")," è l'intensità del campo magnetico ed ",Object(Pe.h)(nt,null,"L")," è la lunghezza del conduttore."),no=Object(Pe.h)("i",null,"Legge di Faraday-Neumann-Lenz"),ao=Object(Pe.h)("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),lo=Object(Pe.h)("p",null,"Il meno è dovuto alla ",Object(Pe.h)("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta."),io=Object(Pe.h)("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),oo=Object(Pe.h)(Be,{title:"Legge di Ampère-Maxwell"},Object(Pe.h)("p",null,"Correnti o campi elettrici variabili creano un campo magnetico.")),ro=Object(Pe.h)("p",null,"Si dice quindi che sono ",Object(Pe.h)("i",null,"onde elettromagnetiche"),"."),co=Object(Pe.h)("p",null,"Esse sono legate dalla relazione:"),so=Object(Pe.h)("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",Object(Pe.h)("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),uo=Object(Pe.h)("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),ho=Object(Pe.h)("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),po=Object(Pe.h)("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),bo=Object(Pe.h)("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),mo=Object(Pe.h)("p",null,"Energia, momento angolare e raggio sono quantizzati."),fo=Object(Pe.h)("p",null,"L'energia degli elettroni è quantizzata."),jo=Object(Pe.h)("p",null,"Inoltre, per essi è valido che:"),Oo=Object(Pe.h)("p",null,"Ancora, il raggio delle orbite è uguale a:"),_o=Object(Pe.h)("p",null,"Infine, in ogni stato, l'energia è pari a:"),go=Object(Pe.h)("p",null,"Due elettroni non possono occupare lo stesso stato."),vo=Object(Pe.h)("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"),wo=Object(Pe.h)(Ue,null,Object(Pe.h)(Be,{title:"Nei solidi"},Object(Pe.h)("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),Object(Pe.h)("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),yo=Object(Pe.h)("p",null,Object(Pe.h)(Ge,null,"Refactor this")),zo=Object(Pe.h)("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),ko=Object(Pe.h)(Be,{title:"Lacune"},Object(Pe.h)("p",null,"Legami in cui ",Object(Pe.h)(it,null,"mancano elettroni"),"."),Object(Pe.h)("p",null,Object(Pe.h)(ct,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",Object(Pe.h)(it,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),Po=Object(Pe.h)(Be,{title:"Accettori e donori"},Object(Pe.h)("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),Object(Pe.h)("ul",null,Object(Pe.h)("li",null,"Con numero atomico maggiore, un semiconduttore di ",Object(Pe.h)(ct,null,"tipo N")," con ",Object(Pe.h)(ct,null,"elettroni in eccesso")," liberi di scorrere."),Object(Pe.h)("li",null,"Con numero atomico minore, un semiconduttore di ",Object(Pe.h)(it,null,"tipo P")," con ",Object(Pe.h)(it,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),Object(Pe.h)("p",null,"Maggiore impurezza porta a maggiore conduttività.")),Eo=Object(Pe.h)(Be,{title:"Temperatura"},Object(Pe.h)("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",Object(Pe.h)(ct,null,"elettroni")," e ",Object(Pe.h)(it,null,"lacune"),".")),Xo=Object(Pe.h)("span",null,"Ottica ",Object(Pe.h)("small",null,"(non l'abbiamo fatta)")),qo=Object(Pe.h)(Be,{title:"Assorbimento e riflessione"},Object(Pe.h)("p",null,"I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.")),xo=Object(Pe.h)("p",null,"Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna."),Co=Object(Pe.h)(Be,{title:"Teoria di Planck per il corpo nero"},Object(Pe.h)("p",null,"L'energia assorbita e emessa dai corpi neri è quantizzata.")),So=Object(Pe.h)("p",null,"Un onda magnetica con un quanto di energia è detta ",Object(Pe.h)("i",null,"fotone"),":"),Lo=Object(Pe.h)(Be,{title:"Effetto fotoelettrico"},Object(Pe.h)("p",null,"A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale."),Object(Pe.h)("p",null,"Perchè avvenga, la frequenza deve essere maggiore di una certa soglia."),Object(Pe.h)("p",null,"Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza."),Object(Pe.h)("p",null,"Non c'è 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[Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\n11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\n13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\n20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\n\nNell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\n "],["\nTutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).\n\nPer comodità, ho estratto l'url sorgente del video dall'embed presente nella rispettiva pagina.\n\n1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\n11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\n13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\n20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\n\nNell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\n "]),Ro=String.raw,Uo=Object(Pe.h)("h1",null,"Videolezioni di Geometria"),Yo=function(e){function t(){return $(this,t),K(this,e.apply(this,arguments))}return Z(t,e),t.prototype.render=function(){return Object(Pe.h)("div",{style:Fo.a.vldigeometria},Uo,Object(Pe.h)(Be,null,Object(Pe.h)(Bo,null,Ro(Vo))))},t}(Pe.Component),Ho=n("5m9J"),Go=n.n(Ho),Wo=Object(Pe.h)("h1",null,"Come installare MinGW"),$o=Object(Pe.h)(Be,null,Object(Pe.h)("p",null," Scaricate ",Object(Pe.h)("a",{href:"https://osdn.net/projects/mingw/downloads/68260/mingw-get-setup.exe/"},"l'installer ufficiale"),", ed eseguitelo."),Object(Pe.h)("img",{src:"https://i.imgur.com/mDZSqjV.png",alt:""}),Object(Pe.h)("p",null," Dovrebbe comparire questa schermata. Cliccate su ",Object(Pe.h)("code",null,"Install"),", poi scegliete una cartella di installazione (ricordatevela!) e poi ",Object(Pe.h)("code",null,"Continue"),". Lasciate stare le altre opzioni, dovrebbero essere tutte spuntate, tranne ",Object(Pe.h)("code",null,"For all users"),", che dovrebbe essere disattivato."),Object(Pe.h)("img",{src:"https://i.imgur.com/brdw8Xy.png",alt:""}),Object(Pe.h)("p",null," Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto",Object(Pe.h)("code",null,"Continue"),". Premetelo."),Object(Pe.h)("img",{src:"https://i.imgur.com/aPTwrxz.png",alt:""}),Object(Pe.h)("p",null," Dovrebbe apparirvi questa finestra. L'installer di MinGW è una specie di gestore pacchetti (tipo ",Object(Pe.h)("code",null,"apt")," su Ubuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalità."),Object(Pe.h)("img",{src:"https://i.imgur.com/5QLSkFN.png",alt:""}),Object(Pe.h)("p",null," Nel nostro caso, dovrebbero servirci ",Object(Pe.h)("code",null,"mingw32-base-bin")," (per il C e alcune librerie C++) e",Object(Pe.h)("code",null,"mingw32-gcc-g++-bin")," (per il C++). Cliccate, quindi, sui due quadratini corrispondenti, e premete",Object(Pe.h)("code",null,"Mark for Installation"),". Dovrebbe comparire una freccia gialla sul quadratino."),Object(Pe.h)("img",{src:"https://i.imgur.com/zP74nks.png",alt:""}),Object(Pe.h)("p",null," Ora, è il momento di installare i pacchetti. Aprite il menù ",Object(Pe.h)("code",null,"Installation"),", poi premete",Object(Pe.h)("code",null,"Apply Changes"),", e di nuovo ",Object(Pe.h)("code",null,"Apply"),"."),Object(Pe.h)("img",{src:"https://i.imgur.com/jp4uz5B.png",alt:""}),Object(Pe.h)("p",null," Lasciate che scarichi, ci vorrà un po'. Guardatevi un video nel frattempo, fatevi una partitina a qualcosa, tornate dopo circa 10 minuti."),Object(Pe.h)("img",{src:"https://i.imgur.com/Lq9IepY.png",alt:""}),Object(Pe.h)("p",null," Una volta installato, dobbiamo aggiungere ",Object(Pe.h)("code",null,"g++")," ai programmi eseguibili da Prompt dei Comandi: premete il tasto ",Object(Pe.h)("kbd",null,"Windows"),", e scrivete ",Object(Pe.h)("code",null,"PATH"),". Windows dovrebbe trovarvi automaticamente quell'opzione."),Object(Pe.h)("img",{src:"https://i.imgur.com/dy3b5Ub.png",alt:""}),Object(Pe.h)("p",null," Dentro la finestra di ",Object(Pe.h)("i",null,"Proprietà del Sistema"),", premete ",Object(Pe.h)("code",null,"Variabili d'ambiente"),"."),Object(Pe.h)("img",{src:"https://i.imgur.com/FjYpT1n.png",alt:""}),Object(Pe.h)("p",null," Trovate la variabile d'ambiente globale ",Object(Pe.h)("code",null,"Path"),", e fateci doppio click per modificarla."),Object(Pe.h)("img",{src:"https://i.imgur.com/klZQ9So.png",alt:""}),Object(Pe.h)("p",null," Ora dovreste vedere l'elenco di tutte le cartelle contenenti programmi eseguibili da terminale: dobbiamo aggiungere quella di MinGW! Premete ",Object(Pe.h)("code",null,"Sfoglia"),"."),Object(Pe.h)("img",{src:"https://i.imgur.com/F6lBCqS.png",alt:""}),Object(Pe.h)("p",null," Trovate la cartella in cui avete installato MinGW (vi avevo detto di ricordarvela!); entrateci, poi selezionate la sottocartella ",Object(Pe.h)("code",null,"bin")," e premete ",Object(Pe.h)("code",null,"OK")," su tutte le finestre che avete aperto fino ad ora, chiudendole."),Object(Pe.h)("p",null," Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione",Object(Pe.h)("code",null,"gcc")," e ",Object(Pe.h)("code",null,"g++")," sul Prompt dei Comandi, e potete finalmente creare dei file .exe! ")),Ko=function(e){function t(){return Q(this,t),J(this,e.apply(this,arguments))}return ee(t,e),t.prototype.render=function(){return Object(Pe.h)("div",{style:Go.a.mingwinstall},Wo,$o)},t}(Pe.Component),Zo=n("qMTX"),Qo=n.n(Zo),Jo=Object(Pe.h)("a",{href:"https://creativecommons.org/licenses/by-sa/4.0/"},"CC BY-SA 4.0"),er=Object(Pe.h)("a",{href:"https://github.com/Steffo99/appuntiweb"},"Codice sorgente"),tr=function(e){function t(){return te(this,t),ne(this,e.apply(this,arguments))}return ae(t,e),t.prototype.render=function(){return Object(Pe.h)("div",{class:Qo.a.copyright},"© 2019 - Stefano Pigozzi - ",Jo," - ",er)},t}(Pe.Component),nr=n("WViY"),ar=n.n(nr),lr=n("oNmJ"),ir=n.n(lr),or=(function(e){function t(){return le(this,t),ie(this,e.apply(this,arguments))}oe(t,e),t.prototype.getStyle=function(){return e.prototype.getStyle.call(this)+" "+ir.a.theorem}}(Be),n("pRAn")),rr=n.n(or),cr=Object(Pe.h)("h4",null,"Ipotesi"),sr=(function(e){function t(){return re(this,t),ce(this,e.apply(this,arguments))}se(t,e),t.prototype.render=function(){return Object(Pe.h)("div",{class:rr.a.hypothesis},cr,this.props.children)}}(Pe.Component),n("J9SO")),ur=n.n(sr),hr=Object(Pe.h)("h4",null,"Tesi"),pr=(function(e){function t(){return ue(this,t),he(this,e.apply(this,arguments))}pe(t,e),t.prototype.render=function(){return Object(Pe.h)("div",{class:ur.a.thesis},hr,this.props.children)}}(Pe.Component),n("Oqef")),br=n.n(pr),dr=Object(Pe.h)("h4",null,"Dimostrazione"),mr=(function(e){function t(){return be(this,t),de(this,e.apply(this,arguments))}me(t,e),t.prototype.render=function(){return Object(Pe.h)("div",{class:br.a.proof},dr,this.props.children)}}(Pe.Component),n("Xa+Z")),fr=n.n(mr),jr=function(e){function t(){return fe(this,t),je(this,e.apply(this,arguments))}return Oe(t,e),t.prototype.render=function(){return Object(Pe.h)("blockquote",{class:fr.a.example},this.props.children)},t}(Pe.Component),Or=_e(["P(E) = \frac{casi favorevoli}{casi possibili}"],["P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}"]),_r=_e(["P(E) = \frac{successi}{prove totali}"],["P(E) = \\frac{successi}{prove\\ totali}"]),gr=_e(["Omega = left { 1, 2, 3, 4, 5, 6 \right }"],["\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}"]),vr=_e(["omega = 1"],["\\omega = 1"]),wr=_e(["E = left { 1, 2 \right }"],["E = \\left \\{ 1, 2 \\right \\}"]),yr=_e(["\bar{E} = left { 3, 4, 5, 6 \right }"],["\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}"]),zr=_e(["E cap F = left { 1 \right }"],["E \\cap F = \\left \\{ 1 \\right \\}"]),kr=_e(["E cup F = left { 1, 2, 3, 4 \right }"],["E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}"]),Pr=_e(["E setminus F = E cap \bar{F}"],["E \\setminus F = E \\cap \\bar{F}"]),Er=_e(["E subseteq F"],["E \\subseteq F"]),Xr=_e(["E = emptyset"],["E = \\emptyset"]),qr=_e(["E cap F = emptyset"],["E \\cap F = \\emptyset"]),xr=_e(["mathcal{F}"],["\\mathcal{F}"]),Cr=_e(["sigma"],["\\sigma"]),Sr=_e(["Omega in mathcal{F}"],["\\Omega \\in \\mathcal{F}"]),Lr=_e(["E in mathcal{F} implies \bar{E} in mathcal{F}"],["E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}"]),Ar=_e(["(E, F) in mathcal{F} implies (E cup F, E cap F) in mathcal{F}"],["(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}"]),Mr=_e(["E in mathcal{F} implies mathcal{F} = { emptyset, E, \bar{E}, Omega }"],["E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}"]),Fr=_e(["E_i"],["E_i"]),Tr=_e(["E_1"],["E_1"]),Ir=_e(["E_2"],["E_2"]),Dr=_e(["E_3"],["E_3"]),Nr=_e(["E_n"],["E_n"]),Br=_e(["\forall E in mathcal{F}, 0 leq P(E) leq 1"],["\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1"]),Vr=_e(["P(Omega) = 1"],["P(\\Omega) = 1"]),Rr=_e(["P left ( \bigcup_i E_i \right ) = sum_i P ( E_i )"],["P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )"]),Ur=_e(["P(\bar{E}) = 1 - P({E})"],["P(\\bar{E}) = 1 - P({E})"]),Yr=_e(["F subseteq E implies P(F) leq P(E)"],["F \\subseteq E \\implies P(F) \\leq P(E)"]),Hr=_e(["P(E cup F) = P(E) + P(F) - P(E cap F)"],["P(E \\cup F) = P(E) + P(F) - P(E \\cap F)"]),Gr=_e(["P(E) = \frac{len(E)}{len(Omega)}"],["P(E) = \\frac{len(E)}{len(\\Omega)}"]),Wr=_e(["\boldsymbol{D}_{n, k} = \frac{n!}{(n - k)!}"],["\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}"]),$r=_e(["\boldsymbol{D}^{r}_{n, k} = n^k"],["\\boldsymbol{D}^{r}_{n, k} = n^k"]),Kr=_e(["\boldsymbol{C}_{n, k} = \binom{n}{k} = \frac{n!}{(k)! cdot (n - k)!}"],["\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}"]),Zr=_e(["\boldsymbol{C}^{r}_{n, k} = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{(k)! cdot (n - 1)!}"],["\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}"]),Qr=_e(["\boldsymbol{P}_n = n!"],["\\boldsymbol{P}_n = n!"]),Jr=_e(["P(E|F) = \frac{P(E cap F)}{P(F)}"],["P(E|F) = \\frac{P(E \\cap F)}{P(F)}"]),ec=_e(["E cap F = emptyset Longleftrightarrow P(E|F) = P(F|E) = 0"],["E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0"]),tc=_e(["P(E_1 cap \times cap E_n) = P(E_1) \times P(E_2 | E_1) \times dots \times P(E_n | E_1 cap E_2 cap dots cap E_{n-1})"],["P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})"]),nc=_e(["P(F) = sum_{i} P(F|E_i) cdot P(E_i)"],["P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)"]),ac=_e(["P(F|G) = sum_i P(F|E_i cap G) cdot P(E_i | G)"],["P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)"]),lc=_e(["P(E_h | F) = \frac{P(F | E_h) cdot P(E_h)}{P(F)}"],["P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}"]),ic=_e(["P(E cap F) = P(E) cdot P(F) Longleftrightarrow P(E|F) = P(E) Longleftrightarrow P(F|E) = P(F)"],["P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)"]),oc=_e(["P(E cap F cap G) = P(E) cdot P(F) cdot P(G)"],["P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)"]),rc=_e(["X(omega) : Omega \to mathbb{R}"],["X(\\omega) : \\Omega \\to \\mathbb{R}"]),cc=_e(["A_t = { omega | X(omega) leq t }"],["A_t = \\{ \\omega | X(\\omega) \\leq t \\}"]),sc=_e(["\forall t in mathbb{R}, A_t in mathcal{F}"],["\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}"]),uc=_e(["p_X : X \to [0, 1]"],["p_X : X \\to [0, 1]"]),hc=_e(["p_X (x) = \begin{cases}\n P([X = x]) quad se X mapsto x \\\n 0 qquad qquad quad se X \notmapsto x\n end{cases}"],["p_X (x) = \\begin{cases}\n P([X = x]) \\quad se\\ X \\mapsto x \\\\\n 0 \\qquad \\qquad \\quad se\\ X \\not\\mapsto x\n \\end{cases}"]),pc=_e(["f_X : X \to [0, 1]"],["f_X : X \\to [0, 1]"]),bc=_e(["P([a < X leq b]) = int_a^b f_X (x) dx"],["P([a < X \\leq b]) = \\int_a^b f_X (x) dx"]),dc=_e(["F_X : mathbb{R} \to [0, 1]"],["F_X : \\mathbb{R} \\to [0, 1]"]),mc=_e(["A_t"],["A_t"]),fc=_e(["F_X (t) = P(A_t) = \begin{cases}\n sum_{i = 0}^{t} p_X (x_i) quad nel discreto\\\n \\\n int_{-infty}^t f_X (x) dx quad nel continuo\n end{cases}"],["F_X (t) = P(A_t) = \\begin{cases}\n \\sum_{i = 0}^{t} p_X (x_i) \\quad nel\\ discreto\\\\\n \\\\\n \\int_{-\\infty}^t f_X (x) dx \\quad nel\\ continuo\n \\end{cases}"]),jc=_e(["\forall x_0 in mathbb{R}, F_X (x_0) = lim_{t \to x^+_0} F_X (t)"],["\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)"]),Oc=_e(["P([X = x_0]) = lim_{t \to x^+_0} F_X (t) - lim_{t \to x^-_0} F_X (t)"],["P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)"]),_c=_e(["f_Y (y) = int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)"],["f_Y (y) = \\int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)"]),gc=_e(["E(X) = int_0^{+infty} (1 - F_X (t)) dt - int_{-infty}^{0} F_X (t) dt"],["E(X) = \\int_0^{+infty} (1 - F_X (t)) dt - \\int_{-\\infty}^{0} F_X (t) dt"]),vc=_e(["E(X) = sum_i P(X = x_i) cdot x_i"],["E(X) = \\sum_i P(X = x_i) \\cdot x_i"]),wc=_e(["E(X) = int_{-infty}^{+infty} f_X (x) cdot x cdot dx"],["E(X) = \\int_{-\\infty}^{+\\infty} f_X (x) \\cdot x \\cdot dx"]),yc=_e(["x_{alpha}"],["x_{\\alpha}"]),zc=_e(["0 leq alpha leq 1"],["0 \\leq \\alpha \\leq 1"]),kc=_e(["P([X < x_{alpha}]) leq alpha leq P([X leq x_{alpha}])"],["P([X < x_{\\alpha}]) \\leq \\alpha \\leq P([X \\leq x_{\\alpha}])"]),Pc=_e(["x_{0.5}"],["x_{0.5}"]),Ec=_e(["x_{0.25}"],["x_{0.25}"]),Xc=_e(["x_{0.75}"],["x_{0.75}"]),qc=_e(["\frac{n}{100}"],["\\frac{n}{100}"]),xc=_e(["Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2"],["Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2"]),Cc=_e(["\forall k > 0, P([X geq k]) leq \frac{E(X)}{k}"],["\\forall k > 0, P([X \\geq k]) \\leq \\frac{E(X)}{k}"]),Sc=_e(["P(X < k)"],["P(X < k)"]),Lc=_e(["P(X geq k)"],["P(X \\geq k)"]),Ac=_e(["E(X) = overline{k} cdot P(X < k) + k cdot P(X geq k)"],["E(X) = \\overline{k} \\cdot P(X < k) + k \\cdot P(X \\geq k)"]),Mc=_e(["epsilon"],["\\epsilon"]),Fc=_e(["\frac{Var(X)}{epsilon^2}"],["\\frac{Var(X)}{\\epsilon^2}"]),Tc=_e(["\forall epsilon > 0, P([ left| X - E(X) \right| geq epsilon]) leq \frac{Var(X)}{epsilon^2}"],["\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| \\geq \\epsilon]) \\leq \\frac{Var(X)}{\\epsilon^2}"]),Ic=_e(["\forall epsilon > 0, P([ left| X - E(X) \right| < epsilon]) geq 1 - \frac{Var(X)}{epsilon^2}"],["\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| < \\epsilon]) \\geq 1 - \\frac{Var(X)}{\\epsilon^2}"]),Dc=_e(["mu_k = E ( X^k ) = \begin{cases}\n sum_i x_i^k p_X (x_i) qquad nel discreto\\\n \\\n int_{-infty}^{+infty} x^k f_X (x) dx qquad nel continuo\n end{cases}"],["\\mu_k = E ( X^k ) = \\begin{cases}\n \\sum_i x_i^k p_X (x_i) \\qquad nel\\ discreto\\\\\n \\\\\n \\int_{-\\infty}^{+\\infty} x^k f_X (x) dx \\qquad nel\\ continuo\n \\end{cases}"]),Nc=_e(["m_X (t) = E( e^{t cdot X} )"],["m_X (t) = E( e^{t \\cdot X} )"]),Bc=_e(["H_X (t) = E ( e^{i cdot t cdot X} )"],["H_X (t) = E ( e^{i \\cdot t \\cdot X} )"]),Vc=_e(["X sim Distribuzione()"],["X \\sim Distribuzione()"]),Rc=_e(["Ber(p)"],["Ber(p)"]),Uc=_e(["f_X (k) : {0, 1} = \begin{cases}\n p quad se k = 1\\\n q quad se k = 0\\\n 0 quad altrimenti\n end{cases} = p^x cdot q^{1 - k}"],["f_X (k) : \\{0, 1\\} = \\begin{cases}\n p \\quad se\\ k = 1\\\\\n q \\quad se\\ k = 0\\\\\n 0 \\quad altrimenti\n \\end{cases} = p^x \\cdot q^{1 - k}"]),Yc=_e(["Bin(n, p)"],["Bin(n, p)"]),Hc=_e(["f_X (k) : {0..n} = \binom{n}{k} cdot p^k cdot q^{n - k}"],["f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}"]),Gc=_e(["m_X (t) = (q + p cdot e^t) ^ n"],["m_X (t) = (q + p \\cdot e^t) ^ n"]),Wc=_e(["E(X) = n cdot p"],["E(X) = n \\cdot p"]),$c=_e(["Var(X) = n cdot p cdot q"],["Var(X) = n \\cdot p \\cdot q"]),Kc=_e(["f_X (k) : mathbb{N} = q^{k - 1} p"],["f_X (k) : \\mathbb{N} = q^{k - 1} p"]),Zc=_e(["m_X (t) = \frac{p cdot e^t}{1 - q cdot e^t}"],["m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}"]),Qc=_e(["E(X) = \frac{1}{p}"],["E(X) = \\frac{1}{p}"]),Jc=_e(["Var(X) = \frac{q}{p^2}"],["Var(X) = \\frac{q}{p^2}"]),es=_e(["P([X = i + j | X > i ]) = P([X = j])"],["P([X = i + j | X > i ]) = P([X = j])"]),ts=_e(["overline{Bin}(n, p)"],["\\overline{Bin}(n, p)"]),ns=_e(["f_X (k) : { n .. +infty } in mathbb{N} = \binom{k - 1}{n - 1} cdot p^n cdot q^{k - n} "],["f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} "]),as=_e(["m_X (t) : { t < ln(\frac{1}{q}) } = left( \frac{p cdot e^t}{1 - q cdot e^t} \right) ^n"],["m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n"]),ls=_e(["E(X) = \frac{n}{p}"],["E(X) = \\frac{n}{p}"]),is=_e(["Var(X) = \frac{n cdot q}{p^2}"],["Var(X) = \\frac{n \\cdot q}{p^2}"]),os=_e(["Geo(p)"],["Geo(p)"]),rs=_e(["f_X (k) : mathbb{N} = p cdot q^k "],["f_X (k) : \\mathbb{N} = p \\cdot q^k "]),cs=_e(["m_X (t) : left{ t < ln left( \frac{1}{q} \right) \right} = \frac{p}{1 - q cdot e^t}"],["m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}"]),ss=_e(["E(X) = \frac{q}{p}"],["E(X) = \\frac{q}{p}"]),us=_e(["f_X (k) : mathbb{N} = \binom{k + n - 1}{n - 1} cdot p^n cdot q^k "],["f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k "]),hs=_e(["m_X (t) : left{ t < ln left( \frac{1}{q} \right) \right} = left( \frac{p cdot e^t}{1 - q cdot e^t} \right) ^n"],["m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n"]),ps=_e(["E(X) = \frac{n cdot q}{p}"],["E(X) = \\frac{n \\cdot q}{p}"]),bs=_e(["f_X (k) : {0..n} in mathbb{N} = \frac{\binom{K}{k} cdot \binom{N - K}{n - k}}{\binom{N}{n}}"],["f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}"]),ds=_e(["E(X) = n cdot \frac{K}{N}"],["E(X) = n \\cdot \\frac{K}{N}"]),ms=_e(["Var(X) = n cdot \frac{K}{N} cdot \frac{N - K}{N} cdot \frac{N - n}{N - 1}"],["Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}"]),fs=_e(["X sim Bin(n, p)"],["X \\sim Bin(n, p)"]),js=_e(["n \to +infty"],["n \\to +\\infty"]),Os=_e(["p \to 0"],["p \\to 0"]),_s=_e(["E(X) = n cdot p \to mu \neq 0"],["E(X) = n \\cdot p \\to \\mu \\neq 0"]),gs=_e(["Poi(mu)"],["Poi(\\mu)"]),vs=_e(["f_X (k) : mathbb{N} = \frac{e^{-mu} cdot mu^k}{k!}"],["f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}"]),ws=_e(["m_X (t) = e^{mu cdot (e^t - 1)}"],["m_X (t) = e^{\\mu \\cdot (e^t - 1)}"]),ys=_e(["E(X) = mu"],["E(X) = \\mu"]),zs=_e(["Var(X) = mu"],["Var(X) = \\mu"]),ks=_e(["E(X^2) = mu^2 + mu"],["E(X^2) = \\mu^2 + \\mu"]),Ps=_e(["lambda"],["\\lambda"]),Es=_e(["mu = t cdot lambda"],["\\mu = t \\cdot \\lambda"]),Xs=_e(["Poi(t cdot lambda)"],["Poi(t \\cdot \\lambda)"]),qs=_e(["Esp(lambda)"],["Esp(\\lambda)"]),xs=_e(["f_X (x) = \begin{cases}\n 0 qquad qquad x < 0\\\n lambda cdot e^{-lambda cdot x} quad x > 0\n end{cases}"],["f_X (x) = \\begin{cases}\n 0 \\qquad \\qquad x < 0\\\\\n \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n \\end{cases}"]),Cs=_e(["F_X (t) = \begin{cases}\n 0 qquad qquad t < 0\\\n 1 - e^{-lambda cdot t} quad t geq 0\n end{cases}"],["F_X (t) = \\begin{cases}\n 0 \\qquad \\qquad t < 0\\\\\n 1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n \\end{cases}"]),Ss=_e(["m_X (t) : { t | t < lambda } in mathbb{R} = \frac{lambda}{lambda - t}"],["m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}"]),Ls=_e(["E(X) = \frac{1}{lambda}"],["E(X) = \\frac{1}{\\lambda}"]),As=_e(["Var(X) = \frac{1}{lambda^2}"],["Var(X) = \\frac{1}{\\lambda^2}"]),Ms=_e(["P([X > s + t | X > s]) = P([X > t])"],["P([X > s + t | X > s]) = P([X > t])"]),Fs=_e(["Gamma(n, lambda)"],["\\Gamma(n, \\lambda)"]),Ts=_e(["f_X (x) = \begin{cases}\n 0 qquad qquad qquad qquad qquad x < 0\\\n \frac{1}{(n-1)!} cdot lambda^n cdot x^{n-1} cdot e^{-lambda cdot x} quad k > 0\n end{cases}"],["f_X (x) = \\begin{cases}\n 0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n \\end{cases}"]),Is=_e(["m_X (t) : ( t < lambda ) in mathbb{R} = left( \frac{lambda}{lambda - t} \right) ^alpha"],["m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha"]),Ds=_e(["E(X) = \frac{alpha}{lambda}"],["E(X) = \\frac{\\alpha}{\\lambda}"]),Ns=_e(["Var(X) = \frac{alpha}{lambda^2}"],["Var(X) = \\frac{\\alpha}{\\lambda^2}"]),Bs=_e(["[a, b]"],["[a, b]"]),Vs=_e(["Uni(a, b)"],["Uni(a, b)"]),Rs=_e(["P(X in (c, d)) = \frac{d - c}{b - a}"],["P(X \\in (c, d)) = \\frac{d - c}{b - a}"]),Us=_e(["f_X (x) = \begin{cases}\n \frac{1}{b - a} qquad a leq x leq b\\\n 0 qquad quad altrimenti \n end{cases}"],["f_X (x) = \\begin{cases}\n \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n 0 \\qquad \\quad altrimenti \n \\end{cases}"]),Ys=_e(["f_X (x) = \begin{cases}\n 0 qquad quad x < a \n \frac{1}{b - a} qquad a leq x leq b\\\n 1 qquad quad x > b\n end{cases}"],["f_X (x) = \\begin{cases}\n 0 \\qquad \\quad x < a \n \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n 1 \\qquad \\quad x > b\n \\end{cases}"]),Hs=_e(["m_X (t) = \frac{e^{b cdot t} - e^{a cdot t}}{(b - a) cdot t}"],["m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}"]),Gs=_e(["E(X) = \frac{a + b}{2}"],["E(X) = \\frac{a + b}{2}"]),Ws=_e(["Var(X) = \frac{(b - a)^2}{12}"],["Var(X) = \\frac{(b - a)^2}{12}"]),$s=_e(["Nor(mu, sigma^2)"],["Nor(\\mu, \\sigma^2)"]),Ks=_e(["f_X (x) = \frac{e^{-\frac{(x - mu)^2}{2 sigma^2}}}{sqrt{2 pi cdot sigma^2}}"],["f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}"]),Zs=_e(["m_X (t) = e^{mu cdot t + \frac{sigma^2 cdot t^2}{2}}"],["m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}"]),Qs=_e(["Var(X) = sigma^2"],["Var(X) = \\sigma^2"]),Js=_e(["X sim Nor(m, v^2) implies alpha X + \beta sim Nor(alpha m + \beta, (alpha v)^2)"],["X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)"]),eu=_e(["phi(z)"],["\\phi(z)"]),tu=_e(["F_Z(z) = phi(z) = \frac{1}{sqrt{2 pi}} int_{-infty}^{z} e^{-\frac{x^2}{2}} dx"],["F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx"]),nu=_e(["z_alpha"],["z_\\alpha"]),au=_e(["x_alpha = mu + z_alpha cdot sqrt{sigma^2}"],["x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}"]),lu=_e(["Z^2 sim chi^2 (v = 1)"],["Z^2 \\sim \\chi^2 (v = 1)"]),iu=_e(["Gamma left( \frac{1}{2}, \frac{1}{2} \right) = chi^2 (v = 1)"],["\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)"]),ou=_e(["chi^2 (n) + chi^2 (m) = chi^2 (n + m)"],["\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)"]),ru=_e(["T(v) = \frac{Nor(0, 1)}{sqrt{\frac{chi^2(v)}{v}}}"],["T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}"]),cu=_e(["Ipe(N, K, n) approx Bin(n, \frac{K}{N})"],["Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})"]),su=_e(["Bin(n, p) approx Poi(n cdot p)"],["Bin(n, p) \\approx Poi(n \\cdot p)"]),uu=_e(["Bin(n, p) approx Nor(n cdot p, n cdot p cdot q)"],["Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)"]),hu=_e(["(k - \frac{1}{2}, k + \frac{1}{2})"],["(k - \\frac{1}{2}, k + \\frac{1}{2})"]),pu=_e(["P(X < k) simeq P(Y leq k - \frac{1}{2})"],["P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})"]),bu=_e(["P(X leq k) simeq P(Y leq k + \frac{1}{2})"],["P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})"]),du=_e(["P(X geq k) simeq P(Y geq k - \frac{1}{2})"],["P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})"]),mu=_e(["P(X > k) simeq P(Y geq k + \frac{1}{2})"],["P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})"]),fu=_e(["\boldsymbol{X}"],["\\boldsymbol{X}"]),ju=_e(["X, Y"],["X, Y"]),Ou=_e(["F_{X, Y} (x, y) = P(X leq x, Y leq y)"],["F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)"]),_u=_e(["F_X (x) = P(X leq x) = lim_{y \to +infty} F_{X, Y} (x, y)"],["F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)"]),gu=_e(["p_{X, Y} (x, y) = P(X = x, Y = y)"],["p_{X, Y} (x, y) = P(X = x, Y = y)"]),vu=_e(["p_X (x) = sum_j p_{X, Y} (x_i, y_j)"],["p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)"]),wu=_e(["P(X_1 in A_1, dots, X_n in A_n) = P(X_1 in A_1) \times dots \times P(X_n in A_n)"],["P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)"]),yu=_e(["E(g(X, Y)) = sum_{i, j} g(x_i, y_i) cdot p_{X, Y} (x_i, y_i)"],["E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)"]),zu=_e(["E(X + Y) = E(X) + E(Y)"],["E(X + Y) = E(X) + E(Y)"]),ku=_e(["Cov(X, Y) = E((X - E(X) cdot (Y - E(Y)) = E(XY) - E(X) cdot E(Y)"],["Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)"]),Pu=_e(["Cov(X, alpha) = 0"],["Cov(X, \\alpha) = 0"]),Eu=_e(["Cov(X, Y) = Cov(Y, X)"],["Cov(X, Y) = Cov(Y, X)"]),Xu=_e(["Cov(X, X) = Var(X)"],["Cov(X, X) = Var(X)"]),qu=_e(["Cov(alpha X, \beta Y) = alpha cdot \beta cdot Cov(X, Y)"],["Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)"]),xu=_e(["Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)"],["Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)"]),Cu=_e(["Cov(X, Y) = 0"],["Cov(X, Y) = 0"]),Su=_e(["\boldsymbol{C_X}"],["\\boldsymbol{C_X}"]),Lu=_e(["\n \boldsymbol{C_X} = \n \begin{bmatrix}\n Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\n Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\n Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n end{bmatrix}\n "],["\n \\boldsymbol{C_X} = \n \\begin{bmatrix}\n Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n \\end{bmatrix}\n "]),Au=_e(["\rho_{X, Y} = \frac{Cov(X, Y)}{sqrt{Var(X)} cdot sqrt{Var(Y)}}"],["\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}"]),Mu=_e(["-1 leq \rho_{X, Y} leq 1"],["-1 \\leq \\rho_{X, Y} \\leq 1"]),Fu=_e(["Y = a X + b Longleftrightarrow | \rho_{X, Y} | = 1"],["Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1"]),Tu=_e(["Var(X + Y) = Var(X) + Var(Y) + 2 cdot Cov(X, Y)"],["Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)"]),Iu=_e(["Var left( sum_i X_i \right) = sum_i Var(X_i)"],["Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)"]),Du=_e(["M^{(k)}_n = \frac{1}{n} cdot sum_{i = 1}^n X_i^k "],["M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k "]),Nu=_e(["overline{X}_n"],["\\overline{X}_n"]),Bu=_e(["m = E(X)"],["m = E(X)"]),Vu=_e(["S_0^2 = \frac{1}{n} cdot sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 cdot m cdot overline{X}_n + m^2"],["S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2"]),Ru=_e(["S_n^2 = \frac{1}{n - 1} cdot sum_{i = 1}^n (X_i - overline{X}_n)^2 = \frac{1}{n - 1} cdot ( n cdot M_2^{(2)} - n cdot overline{X}_n^2)"],["S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)"]),Uu=_e(["E(overline{X}_n) = E(X)"],["E(\\overline{X}_n) = E(X)"]),Yu=_e(["Var(overline{X}_n) = \frac{Var(X)}{n}"],["Var(\\overline{X}_n) = \\frac{Var(X)}{n}"]),Hu=_e(["E(S_0^2) = E(S_n^2) = Var(X)"],["E(S_0^2) = E(S_n^2) = Var(X)"]),Gu=_e(["X sim Nor(mu, sigma^2)"],["X \\sim Nor(\\mu, \\sigma^2)"]),Wu=_e(["overline{X}_n sim Nor left( mu, \frac{sigma^2}{n} \right)"],["\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)"]),$u=_e(["S_0^2 sim \frac{sigma^2}{n} cdot chi^2 (n)"],["S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)"]),Ku=_e(["S_n^2 sim \frac{sigma^2}{n - 1} cdot chi^2 (n-1)"],["S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)"]),Zu=_e(["E(X)"],["E(X)"]),Qu=_e(["\forall epsilon > 0, lim_{n \to +infty} P( | overline{X}_n - E(X) | < epsilon) = 1"],["\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1"]),Ju=_e(["P( | overline{X}_n - E(X) | < epsilon) \to 1"],["P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1"]),eh=_e(["\forall epsilon > 0, P left( lim_{n \to +infty} | overline{X}_n - E(X) | < epsilon \right) = 1"],["\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1"]),th=_e(["Nor(0, 1) = Phi()"],["Nor(0, 1) = \\Phi()"]),nh=_e(["overline{X}_n approx Nor left(E(X), \frac{Var(X)}{n} \right)"],["\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)"]),ah=_e(["\forall x in mathbb{R}, lim_{n \to +infty} P left( \frac{overline{X}_n - E(X)}{sqrt{\frac{Var(X)}{n}}} leq x \right) = Phi(x)"],["\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)"]),lh=_e(["overline{Bin} (n, p) approx Nor left( \frac{n}{p}, \frac{n cdot (1 - p)}{p^2} \right)"],["\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)"]),ih=_e(["Poi(lambda) approx Nor(lambda, lambda)"],["Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)"]),oh=_e(["Gamma (alpha, lambda) approx Nor left( \frac{alpha}{lambda}, \frac{alpha}{lambda^2} \right)"],["\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)"]),rh=_e(["Y = sum_{i=1}^{n} X_i"],["Y = \\sum_{i=1}^{n} X_i"]),ch=_e(["T(\boldsymbol{X})"],["T(\\boldsymbol{X})"]),sh=_e(["T(\boldsymbol{X}) = \boldsymbol{X}"],["T(\\boldsymbol{X}) = \\boldsymbol{X}"]),uh=_e(["E(T_n) = \theta"],["E(T_n) = \\theta"]),hh=_e(["lim_{n \to +infty} E(T_n) = \theta"],["\\lim_{n \\to +\\infty} E(T_n) = \\theta"]),ph=_e(["lim_{n \to +infty} E((T_n - \theta)^2) = 0"],["\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0"]),bh=_e(["\forall epsilon > 0, lim_{n \to +infty} P( |T_n - \theta| < epsilon) = 1"],["\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1"]),dh=_e(["lim_{n \to +infty} \frac{T_n - E(T_n)}{sqrt{Var(T_n)}} sim Nor(0, 1)"],["\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)"]),mh=_e(["\theta"],["\\theta"]),fh=_e(["widehat{\theta}_M"],["\\widehat{\\theta}_M"]),jh=_e(["\theta = g(E(X))"],["\\theta = g(E(X))"]),Oh=_e(["widehat{E(X)} = overline{X}_n"],["\\widehat{E(X)} = \\overline{X}_n"]),_h=_e(["widehat{\theta}_M = g( overline{X}_n )"],["\\widehat{\\theta}_M = g( \\overline{X}_n )"]),gh=_e(["M_n^2"],["M_n^2"]),vh=_e(["M_n^3"],["M_n^3"]),wh=_e(["widehat{\theta}_L"],["\\widehat{\\theta}_L"]),yh=_e(["L"],["L"]),zh=_e(["L(x_1, ..., x_n; \theta) = prod_{i=1}^n f_X(x_i; \theta)"],["L(x_1, ..., x_n; \\theta) = \\prod_{i=1}^n f_X(x_i; \\theta)"]),kh=_e(["widehat{g(\theta)}_L = g(widehat{\theta}_L)"],["\\widehat{g(\\theta)}_L = g(\\widehat{\\theta}_L)"]),Ph=_e(["widehat{p}_M = widehat{p}_L = overline{X}_n"],["\\widehat{p}_M = \\widehat{p}_L = \\overline{X}_n"]),Eh=_e(["widehat{mu}_M = widehat{mu}_L = overline{X}_n"],["\\widehat{\\mu}_M = \\widehat{\\mu}_L = \\overline{X}_n"]),Xh=_e(["widehat{lambda}_M = widehat{lambda}_L = \frac{1}{overline{X}_n}"],["\\widehat{\\lambda}_M = \\widehat{\\lambda}_L = \\frac{1}{\\overline{X}_n}"]),qh=_e(["widehat{mu}_L = overline{X}_n"],["\\widehat{\\mu}_L = \\overline{X}_n"]),xh=_e(["widehat{sigma^2}_L = \frac{sum (X_i - overline{X}_n)^2 }{n}"],["\\widehat{\\sigma^2}_L = \\frac{\\sum (X_i - \\overline{X}_n)^2 }{n}"]),Ch=_e(["widehat{W}"],["\\widehat{W}"]),Sh=_e(["P( a < W < b ) = N"],["P( a < W < b ) = N"]),Lh=_e(["mu in left[ overline{x}_n - z_{1 - \frac{alpha}{2}} cdot sqrt{\frac{sigma^2}{n}}, overline{x}_n + z_{1 - \frac{alpha}{2}} cdot sqrt{\frac{sigma^2}{n}} \right]"],["\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]"]),Ah=_e(["mu in left( -infty, overline{x}_n + z_{1 - \frac{alpha}{2}} cdot sqrt{\frac{sigma^2}{n}} \right]"],["\\mu \\in \\left( -\\infty, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]"]),Mh=_e(["mu in left[ overline{x}_n - z_{1 - \frac{alpha}{2}} cdot sqrt{\frac{sigma^2}{n}}, +infty \right)"],["\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, +\\infty \\right)"]),Fh=_e(["mu in left[ overline{x}_n - t_{1 - \frac{alpha}{2}; n-1} cdot sqrt{\frac{s_n^2}{n}}, overline{x}_n + t_{1 - \frac{alpha}{2}; n-1} cdot sqrt{\frac{s_n^2}{n}} \right]"],["\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]"]),Th=_e(["mu in left( -infty, overline{x}_n + t_{1 - \frac{alpha}{2}; n-1} cdot sqrt{\frac{s_n^2}{n}} \right]"],["\\mu \\in \\left( -\\infty, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]"]),Ih=_e(["mu in left[ overline{x}_n - t_{1 - \frac{alpha}{2}; n-1} cdot sqrt{\frac{s_n^2}{n}}, +infty \right)"],["\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, +\\infty \\right)"]),Dh=_e(["t_{alpha, v}"],["t_{\\alpha, v}"]),Nh=_e(["p in left[ overline{p} - z_{1 - \frac{alpha}{2}} cdot sqrt{\frac{overline{p} cdot (1 - overline{p})}{n+4}}, overline{p} + z_{1 - \frac{alpha}{2}} cdot sqrt{\frac{overline{p} cdot (1 - overline{p})}{n+4}} \right]"],["p \\in \\left[ \\overline{p} - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}}, \\overline{p} + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}} \\right]"]),Bh=_e(["m in left[ overline{x}_n - z_{1 - \frac{alpha}{2}} cdot sqrt{\frac{s^2_n}{n}}, overline{x}_n + z_{1 - \frac{alpha}{2}} cdot sqrt{\frac{s^2_n}{n}} \right]"],["m \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}} \\right]"]),Vh=String.raw,Rh=Object(Pe.h)("h1",null,"Statistica ed Elementi di Probabilità"),Uh=Object(Pe.h)(Be,{title:"Soggettiva"},Object(Pe.h)("p",null,"Il prezzo che un individuo coerente riterrebbe equo per ricevere ",Object(Pe.h)("b",null,"1")," nel caso l'evento si verificasse e ",Object(Pe.h)("b",null,"0")," nel caso l'evento non si verificasse.")),Yh=Object(Pe.h)("blockquote",null,'"omegone"'),Hh=Object(Pe.h)("p",null,"L'",Object(Pe.h)("b",null,"insieme")," di tutti gli esiti possibili di un esperimento."),Gh=Object(Pe.h)("blockquote",null,'"omeghino"'),Wh=Object(Pe.h)("p",null,"Un ",Object(Pe.h)("b",null,"elemento")," dello spazio campionario."),$h=Object(Pe.h)("blockquote",null,'"e"'),Kh=Object(Pe.h)("p",null,"Un ",Object(Pe.h)("b",null,"sottoinsieme")," dello spazio campionario."),Zh=Object(Pe.h)("p",null,"Lo spazio campionario stesso è un ",Object(Pe.h)("b",null,"evento certo"),"."),Qh=Object(Pe.h)("blockquote",null,'"not e"'),Jh=Object(Pe.h)("p",null,"Il ",Object(Pe.h)("b",null,"complementare")," di un sottoinsieme."),ep=Object(Pe.h)("blockquote",null,'"e intersecato effe"'),tp=Object(Pe.h)("p",null,"L'",Object(Pe.h)("b",null,"intersezione")," di più sottoinsiemi."),np=Object(Pe.h)("blockquote",null,'"e unito a effe"'),ap=Object(Pe.h)("p",null,"L'",Object(Pe.h)("b",null,"unione")," di più sottoinsiemi."),lp=Object(Pe.h)("blockquote",null,'"e meno effe"'),ip=Object(Pe.h)("blockquote",null,'"e contenuto in effe"'),op=Object(Pe.h)("p",null,"L'",Object(Pe.h)("b",null,"inclusione")," del primo insieme in un altro."),rp=Object(Pe.h)("p",null,"Se si verifica ",Object(Pe.h)(nt,null,"E"),", allora si verifica anche ",Object(Pe.h)(nt,null,"F"),"."),cp=Object(Pe.h)("blockquote",null,'"e è impossibile"'),sp=Object(Pe.h)("p",null,"Un sottoinsieme ",Object(Pe.h)("b",null,"vuoto"),"."),up=Object(Pe.h)("blockquote",null,'"e ed effe si escludono mutualmente"'),hp=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"disgiunzione")," di due insiemi."),pp=Object(Pe.h)("blockquote",null,'"famiglia effe"'),bp=Object(Pe.h)("p",null,"I sottoinsiemi dello spazio campionario formano una ",Object(Pe.h)("b",null,"famiglia")," di sottoinsiemi detta ",Object(Pe.h)("i",null,"famiglia degli eventi"),"."),dp=Object(Pe.h)("blockquote",null,'"sigma algebra"'),mp=Object(Pe.h)("blockquote",null,'"la partizione e composta da e uno, e due, e tre..."'),fp=Object(Pe.h)("p",null,"Un insieme di esiti e eventi:"),jp=Object(Pe.h)("ul",null,Object(Pe.h)("li",null,Object(Pe.h)("b",null,"Finito"),"."),Object(Pe.h)("li",null,"In cui tutti gli eventi hanno ",Object(Pe.h)("b",null,"probabilità diversa da 0"),"."),Object(Pe.h)("li",null,"In cui tutti gli eventi sono ",Object(Pe.h)("b",null,"mutualmente esclusivi"),"."),Object(Pe.h)("li",null,"In cui l'unione di tutti i suoi elementi ",Object(Pe.h)("b",null,"copre lo spazio campionario"),".")),Op=Object(Pe.h)(jr,null,"Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare."),_p=Object(Pe.h)("p",null,"La probabilità di un evento è un numero tra 0 e 1."),gp=Object(Pe.h)("p",null,"La probabilità dello spazio campionario è sempre 1."),vp=Object(Pe.h)("p",null,"La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità."),wp=Object(Pe.h)("p",null,"La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato."),yp=Object(Pe.h)("p",null,"La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso."),zp=Object(Pe.h)("p",null,"La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione."),kp=Object(Pe.h)(jr,null,"Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!"),Pp=Object(Pe.h)("p",null,"Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi."),Ep=Object(Pe.h)(Be,{title:"Spazi equiprobabili geometrici"},Object(Pe.h)("p",null,"Gli spazi campionari possono avere un numero infinito di esiti: sono ",Object(Pe.h)("i",null,"equiprobabili geometrici")," se nessun esito è privilegiato rispetto agli altri.")),Xp=Object(Pe.h)("p",null,"Estraggo un numero, da un sacchetto con ",Object(Pe.h)(nt,null,"n")," numeri, mi segno che numero ho estratto e lo ",Object(Pe.h)("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",Object(Pe.h)(nt,null,"k")," volte."),qp=Object(Pe.h)("p",null,Object(Pe.h)("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),xp=Object(Pe.h)("p",null,"Estraggo un numero, da un sacchetto con ",Object(Pe.h)(nt,null,"n")," numeri, mi segno che numero ho estratto e lo ",Object(Pe.h)("b",null,"rimetto nel sacchetto"),". Ripeto per ",Object(Pe.h)(nt,null,"k")," volte."),Cp=Object(Pe.h)("p",null,Object(Pe.h)("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),Sp=Object(Pe.h)("p",null,"Estraggo un numero, da un sacchetto con ",Object(Pe.h)(nt,null,"n")," numeri, mi segno che numero ho estratto e lo ",Object(Pe.h)("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",Object(Pe.h)(nt,null,"k")," volte."),Lp=Object(Pe.h)("p",null,Object(Pe.h)("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),Ap=Object(Pe.h)("p",null,"Estraggo un numero, da un sacchetto con ",Object(Pe.h)(nt,null,"n")," numeri, mi segno che numero ho estratto e lo ",Object(Pe.h)("b",null,"rimetto nel sacchetto"),". Ripeto per ",Object(Pe.h)(nt,null,"k")," volte."),Mp=Object(Pe.h)("p",null,Object(Pe.h)("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),Fp=Object(Pe.h)("p",null,"Estraggo ",Object(Pe.h)(nt,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),Tp=Object(Pe.h)("blockquote",null,'"E dato F"'),Ip=Object(Pe.h)("p",null,"La probabilità che si verifichi ",Object(Pe.h)(nt,null,"E")," sapendo che ",Object(Pe.h)("b",null,"si è già verificato")," ",Object(Pe.h)(nt,null,"F"),"."),Dp=Object(Pe.h)(jr,null,"Ricorda vagamente le pipe di ",Object(Pe.h)("code",null,"bash"),", però al contrario..."),Np=Object(Pe.h)("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),Bp=Object(Pe.h)("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),Vp=Object(Pe.h)("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),Rp=Object(Pe.h)("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",Object(Pe.h)("b",null,"evento"),":"),Up=Object(Pe.h)("p",null,"Tramite la ",Object(Pe.h)("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),Yp=Object(Pe.h)(jr,null,"In pratica, invertiamo gli eventi."),Hp=Object(Pe.h)("blockquote",null,'"eventi indipendenti a due a due"'),Gp=Object(Pe.h)("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),Wp=Object(Pe.h)("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),$p=Object(Pe.h)("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),Kp=Object(Pe.h)("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa."),Zp=Object(Pe.h)(Be,{title:"Famiglia di eventi indipendenti"},Object(Pe.h)("p",null,"Un insieme di ",Object(Pe.h)(nt,null,"n")," eventi è una ",Object(Pe.h)("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),Object(Pe.h)(jr,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!")),Qp=Object(Pe.h)("abbr",{title:"Nome artigianale dato da Steffo."},"Insieme di ripartizione"),Jp=Object(Pe.h)(nt,null,"t"),eb=Object(Pe.h)("p",null,"Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:"),tb=Object(Pe.h)(jr,null,"All'aumentare di t, l'insieme conterrà sempre più elementi."),nb=Object(Pe.h)(Be,{title:"Supporto"},Object(Pe.h)("blockquote",null,'"supporto di X"'),Object(Pe.h)("p",null,"Il ",Object(Pe.h)("b",null,"codominio")," della variabile aleatoria è il suo ",Object(Pe.h)("i",null,"supporto"),"."),Object(Pe.h)("p",null,"Per indicare che un valore ",Object(Pe.h)(nt,null,"x_0")," appartiene al supporto di ",Object(Pe.h)(nt,null,"X"),", si usa la notazione ",Object(Pe.h)(nt,null,"X \\mapsto x_0"),".")),ab=Object(Pe.h)("i",null,"funzione probabilità"),lb=Object(Pe.h)("b",null,"discreta"),ib=Object(Pe.h)(nt,null,"X"),ob=Object(Pe.h)("i",null,"funzione densità"),rb=Object(Pe.h)("b",null,"continua"),cb=Object(Pe.h)(nt,null,"X"),sb=Object(Pe.h)("p",null,"A differenza della funzione probabilità, è possibile che la funzione densità ",Object(Pe.h)("b",null,"non esista")," per una certa variabile aleatoria."),ub=Object(Pe.h)(jr,null,"Rappresenta \"quanta\" probabilità c'è in un'unità di x!"),hb=Object(Pe.h)("i",null,"funzione di ripartizione"),pb=Object(Pe.h)(nt,null,"t"),bb=Object(Pe.h)("li",null,"È sempre ",Object(Pe.h)("b",null,"monotona crescente")," (non strettamente)."),db=Object(Pe.h)("br",null),mb=Object(Pe.h)("li",null,"Vale ",Object(Pe.h)("b",null,"0")," a ",Object(Pe.h)(nt,null,"-\\infty")," e ",Object(Pe.h)("b",null,"1")," a ",Object(Pe.h)(nt,null,"+\\infty"),"."),fb=Object(Pe.h)("br",null),jb=Object(Pe.h)("b",null,"continua da destra"),Ob=Object(Pe.h)("p",null,"Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:"),_b=Object(Pe.h)(Be,{title:"Nel discreto"},Object(Pe.h)("p",null,"Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.")),gb=Object(Pe.h)("p",null,"Nel continuo applichiamo la formula dell'integrazione per sostituzione:"),vb=Object(Pe.h)(Be,{title:"Nel... digitale"},Object(Pe.h)("p",null,"Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione ",Object(Pe.h)("a",{href:"https://docs.python.org/3/library/random.html#random.random"},Object(Pe.h)("code",null,"random()"))," che restituisce numeri da 0 a 1 con una distribuzione lineare.")),wb=Object(Pe.h)("p",null,"Ogni variabile aleatoria che ha una ",Object(Pe.h)("b",null,"funzione di ripartizione")," e un ",Object(Pe.h)("b",null,"supporto finito")," ha anche una ",Object(Pe.h)("i",null,"media")," (o ",Object(Pe.h)("i",null,"valore medio")," o ",Object(Pe.h)("i",null,"atteso"),"):"),yb=Object(Pe.h)("p",null,"Nel discreto, si può calcolare con:"),zb=Object(Pe.h)("p",null,"Nel continuo, si può calcolare con:"),kb=Object(Pe.h)(Be,{title:"Moda"},Object(Pe.h)("p",null,"Valore per cui la ",Object(Pe.h)("b",null,"funzione probabilità")," o ",Object(Pe.h)("b",null,"funzione densità")," è ",Object(Pe.h)("b",null,"massima"),".")),Pb=Object(Pe.h)("i",null,"quantile"),Eb=Object(Pe.h)(nt,null,"X"),Xb=Object(Pe.h)("p",null),qb=Object(Pe.h)("i",null,"mediana"),xb=Object(Pe.h)("i",null,"quartili"),Cb=Object(Pe.h)("i",null,Object(Pe.h)(nt,null,"n"),"-esima percentile"),Sb=Object(Pe.h)("p",null,"È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:"),Lb=Object(Pe.h)("p",null,"Data una variabile aleatoria non-negativa:"),Ab=Object(Pe.h)("blockquote",null,'"disuguaglianza di cebicev"'),Mb=Object(Pe.h)(nt,null,"X"),Fb=Object(Pe.h)("p",null,"E anche:"),Tb=Object(Pe.h)(jr,null,"Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!"),Ib=Object(Pe.h)("p",null,"Il ",Object(Pe.h)("i",null,"momento")," ",Object(Pe.h)(nt,null,"k"),"-esimo di una variabile aleatoria è:"),Db=Object(Pe.h)(jr,null,"La media di una variabile aleatoria è anche il suo primo momento."),Nb=Object(Pe.h)("p",null,"La ",Object(Pe.h)("i",null,"funzione generatrice dei momenti")," è:"),Bb=Object(Pe.h)("p",null,"Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ",Object(Pe.h)("b",null,"stessa distribuzione"),"."),Vb=Object(Pe.h)("p",null,"E' la ",Object(Pe.h)("b",null,"trasformata di Laplace")," della variabile aleatoria di X."),Rb=Object(Pe.h)("p",null,"La ",Object(Pe.h)("i",null,"funzione caratteristica")," è:"),Ub=Object(Pe.h)("p",null,"Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ",Object(Pe.h)("b",null,"stessa distribuzione"),"."),Yb=Object(Pe.h)("p",null,"E' la ",Object(Pe.h)("b",null,"trasformata di Fourier")," della variabile aleatoria di X."),Hb=Object(Pe.h)("p",null,"Per dire che una variabile ha una certa distribuzione, si usa la notazione:"),Gb=Object(Pe.h)(Be,{title:"Prova di Bernoulli"},Object(Pe.h)("p",null,"Una prova con solo due possibili esiti: ",Object(Pe.h)(it,null,"successo")," e ",Object(Pe.h)(ct,null,"insuccesso"),".")),Wb=Object(Pe.h)(Be,{title:"Schema di Bernoulli"},Object(Pe.h)("p",null,"Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate.")),$b=Object(Pe.h)("p",null,"Una variabile aleatoria che rappresenta una prova di Bernoulli:"),Kb=Object(Pe.h)("ul",null,Object(Pe.h)("li",null,"vale ",Object(Pe.h)(it,null,"1")," in caso di ",Object(Pe.h)(it,null,"successo"),"."),Object(Pe.h)("li",null,"vale ",Object(Pe.h)(ct,null,"0")," in caso di ",Object(Pe.h)(ct,null,"insuccesso"),".")),Zb=Object(Pe.h)("p",null,"La distribuzione bernoulliana ha come densità:"),Qb=Object(Pe.h)("p",null,"Una variabile aleatoria che conta il numero di successi di ",Object(Pe.h)(nt,null,"n")," prove di uno schema di Bernoulli."),Jb=Object(Pe.h)("p",null,"La binomiale ha come densità:"),ed=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della binomiale è:"),td=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," di una binomiale è:"),nd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," di una binomiale è:"),ad=Object(Pe.h)(Be,{title:"Distribuzione geometrica"},Object(Pe.h)("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo."),Object(Pe.h)("p",null,"Il suo simbolo è ",Object(Pe.h)(nt,null,"Geo(p)"),".")),ld=Object(Pe.h)("p",null,"La geometrica ha come densità:"),id=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della geometrica è:"),od=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," della geometrica è:"),rd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," della geometrica è:"),cd=Object(Pe.h)("p",null,"La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),sd=Object(Pe.h)(jr,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."),ud=Object(Pe.h)("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'",Object(Pe.h)(nt,null,"n"),"-esimo successo."),hd=Object(Pe.h)("p",null,"La binomiale negativa ha come densità:"),pd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della binomiale negativa è:"),bd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," della binomiale negativa è:"),dd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," della binomiale negativa è:"),md=Object(Pe.h)("p",null,"Una variabile aleatoria che conta il numero ",Object(Pe.h)(nt,null,"k")," di insuccessi consecutivi in uno schema di Bernoulli:"),fd=Object(Pe.h)("p",null,"La geometrica traslata ha come densità:"),jd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della geometrica traslata è:"),Od=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," della geometrica traslata è:"),_d=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," della geometrica è:"),gd=Object(Pe.h)("p",null,"La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),vd=Object(Pe.h)(jr,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."),wd=Object(Pe.h)("p",null,"Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'",Object(Pe.h)(nt,null,"n"),"-esimo successo."),yd=Object(Pe.h)("p",null,"La binomiale negativa traslata ha come densità:"),zd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della binomiale negativa traslata è:"),kd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," della binomiale negativa traslata è:"),Pd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," della binomiale negativa traslata è:"),Ed=Object(Pe.h)(Be,{title:"Distribuzione ipergeometrica"},Object(Pe.h)("p",null,"Una variabile aleatoria che, sapendo il numero di successi ",Object(Pe.h)(nt,null,"K")," e di insuccessi ",Object(Pe.h)(nt,null,"N-K"),", conta quanti successi si otterrebbero se se ne estraessero ",Object(Pe.h)(nt,null,"n")," in blocco."),Object(Pe.h)("p",null,"Il suo simbolo è ",Object(Pe.h)(nt,null,"Ipe(N, K, n)"),".")),Xd=Object(Pe.h)("p",null,"La ipergeometrica ha come densità:"),qd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della ipergeometrica è trascurabile."),xd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," della ipergeometrica è:"),Cd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," della ipergeometrica è:"),Sd=Object(Pe.h)("p",null,"Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:"),Ld=Object(Pe.h)("p",null,"La poissoniana ha come densità:"),Ad=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della poissoniana è:"),Md=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," della poissoniana è:"),Fd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," della poissoniana è:"),Td=Object(Pe.h)("p",null,"Gli altri momenti della poissoniana sono:"),Id=Object(Pe.h)("p",null,"Una successione di ",Object(Pe.h)("b",null,"arrivi")," avvenuti in un certo arco temporale che:"),Dd=Object(Pe.h)("li",null,"non sono sovrapposti."),Nd=Object(Pe.h)("li",null,"avvengono indipendentemente gli uni dagli altri."),Bd=Object(Pe.h)(nt,null,"N_t"),Vd=Object(Pe.h)(nt,null,"t"),Rd=Object(Pe.h)(jr,null,"E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo)."),Ud=Object(Pe.h)("p",null,"L'esponenziale ha come ",Object(Pe.h)("b",null,"densità"),":"),Yd=Object(Pe.h)("p",null,"L'esponenziale ha come ",Object(Pe.h)("b",null,"funzione di ripartizione"),":"),Hd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," dell'esponenziale è:"),Gd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," dell'esponenziale è:"),Wd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," dell'esponenziale è:"),$d=Object(Pe.h)("p",null,"L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),Kd=Object(Pe.h)(jr,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."),Zd=Object(Pe.h)(nt,null,"n"),Qd=Object(Pe.h)("p",null,"La legge gamma ha come densità:"),Jd=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della legge gamma è:"),em=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," della legge gamma è:"),tm=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," della legge gamma è:"),nm=Object(Pe.h)("p",null,"Su di essa vale la seguente proprietà:"),am=Object(Pe.h)("p",null,"La distribuzione uniforme ha come ",Object(Pe.h)("b",null,"densità"),":"),lm=Object(Pe.h)("p",null,"La distribuzione uniforme ha come ",Object(Pe.h)("b",null,"funzione di ripartizione"),":"),im=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della distribuzione uniforme è:"),om=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," della distribuzione uniforme è:"),rm=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," della distribuzione uniforme è:"),cm=Object(Pe.h)("p",null,"Una variabile aleatoria con una specifica distribuzione."),sm=Object(Pe.h)(jr,null,Object(Pe.h)(nt,null,"\\mu")," e ",Object(Pe.h)(nt,null,"\\sigma^2")," sono rispettivamente la media e la varianza della distribuzione!"),um=Object(Pe.h)("p",null,"La distribuzione normale ha come densità:"),hm=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"funzione generatrice dei momenti")," della distribuzione normale è:"),pm=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"media")," della distribuzione normale è:"),bm=Object(Pe.h)("p",null,"La ",Object(Pe.h)("b",null,"varianza")," della distribuzione normale è:"),dm=Object(Pe.h)("p",null,"Qualsiasi normale può essere trasformata in qualsiasi altra normale:"),mm=Object(Pe.h)("p",null,"La distribuzione normale standard ",Object(Pe.h)(nt,null,"Z")," è:"),fm=Object(Pe.h)("p",null,Object(Pe.h)(nt,null,"Z \\sim Nor(0, 1)")),jm=Object(Pe.h)("p",null,"La distribuzione normale ha una particolare relazione con la distribuzione Gamma:"),Om=Object(Pe.h)("blockquote",null,'"chi-quadro a un grado di libertà"'),_m=Object(Pe.h)("p",null,"Esiste una distribuzione Gamma particolare:"),gm=Object(Pe.h)("p",null,"Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:"),vm=Object(Pe.h)("p",null,"Un'altra funzione particolare è la funzione T di Student:"),wm=Object(Pe.h)("p",null,"La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ",Object(Pe.h)(nt,null,"N")," rispetto a ",Object(Pe.h)(nt,null,"n"),", si può dire che:"),ym=Object(Pe.h)("p",null,"La binomiale non è altro che una poissoniana a tempo discreto, quindi, se ",Object(Pe.h)(nt,null,"n")," è grande e ",Object(Pe.h)(nt,null,"n \\cdot p")," è nell'ordine di grandezza delle unità, allora:"),zm=Object(Pe.h)("p",null,"Per il Teorema di De Moivre-Laplace, se una binomiale ha una ",Object(Pe.h)(nt,null,"n")," grande e ",Object(Pe.h)(nt,null,"p")," non vicina a 0 o 1, si può approssimare con:"),km=Object(Pe.h)(nt,null,"X"),Pm=Object(Pe.h)(nt,null,"Y"),Em=Object(Pe.h)(nt,null,"k"),Xm=Object(Pe.h)("p",null,"Un vettore ",Object(Pe.h)("b",null,"composto da variabili aleatorie"),"."),qm=Object(Pe.h)("p",null,"I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri."),xm=Object(Pe.h)("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",Object(Pe.h)("i",null,"funzione di ripartizione congiunta"),":"),Cm=Object(Pe.h)("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",Object(Pe.h)("i",null,"funzione di ripartizione marginale"),":"),Sm=Object(Pe.h)("p",null,"I vettori aleatori ",Object(Pe.h)("b",null,"discreti")," hanno più densità che si differenziano in base al numero di parametri."),Lm=Object(Pe.h)("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",Object(Pe.h)("i",null,"densità congiunta"),":"),Am=Object(Pe.h)("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",Object(Pe.h)("i",null,"densità marginale"),":"),Mm=Object(Pe.h)("p",null,"Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ",Object(Pe.h)(nt,null,"A_i"),":"),Fm=Object(Pe.h)("p",null,"E' possibile calcolare la media di qualsiasi funzione ",Object(Pe.h)(nt,null,"g(X, Y)")," avente elementi del vettore come variabili:"),Tm=Object(Pe.h)(jr,null,"Solitamente si calcola la media di ",Object(Pe.h)(nt,null,"x \\cdot y"),"."),Im=Object(Pe.h)("p",null,"Le medie di più variabili aleatorie si possono sommare:"),Dm=Object(Pe.h)("p",null,"Un ",Object(Pe.h)("b",null,"operatore")," che misura la correlazione di due variabili aleatorie."),Nm=Object(Pe.h)("p",null,"Si calcola con il valore atteso dei prodotti delle distanze dalla media:"),Bm=Object(Pe.h)("p",null,"Ha diverse proprietà:"),Vm=Object(Pe.h)("b",null,"valore nullo"),Rm=Object(Pe.h)("b",null,"commutativa"),Um=Object(Pe.h)("b",null,"semplificabile"),Ym=Object(Pe.h)("b",null,"lineare"),Hm=Object(Pe.h)("b",null,"distributiva"),Gm=Object(Pe.h)("p",null,"Due variabili sono ",Object(Pe.h)("i",null,"variabili incorrelate")," se:"),Wm=Object(Pe.h)("p",null,"Variabili indipendenti sono sempre incorrelate."),$m=Object(Pe.h)("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",Object(Pe.h)(nt,null,"\\geq 0"),"."),Km=Object(Pe.h)("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),Zm=Object(Pe.h)("p",null,"E' sempre compreso tra -1 e 1:"),Qm=Object(Pe.h)("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),Jm=Object(Pe.h)("p",null,"La varianza di due variabili aleatorie sommate è:"),ef=Object(Pe.h)(jr,null,"Si dimostra applicando le proprietà della covarianza!"),tf=Object(Pe.h)(nt,null,"X_i"),nf=Object(Pe.h)("b",null,"indipendenti"),af=Object(Pe.h)(Be,{title:"Campione casuale"},Object(Pe.h)("p",null,"Una ",Object(Pe.h)("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",Object(Pe.h)(nt,null,"X"),' ("popolazione") ma ',Object(Pe.h)("b",null,"indipendenti")," tra loro."),Object(Pe.h)(jr,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",Object(Pe.h)("b",null,"realizzeranno")," nel loro valore.")),lf=Object(Pe.h)("p",null,"Il valore dato dalla media aritmetica degli ",Object(Pe.h)(nt,null,"n")," elementi del campione elevati alla potenza ",Object(Pe.h)(nt,null,"k"),":"),of=Object(Pe.h)("i",null,"media campionaria"),rf=Object(Pe.h)("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),cf=Object(Pe.h)("p",null,"Altrimenti:"),sf=Object(Pe.h)("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),uf=Object(Pe.h)(jr,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!"),hf=Object(Pe.h)("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),pf=Object(Pe.h)(jr,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"),bf=Object(Pe.h)("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),df=Object(Pe.h)(jr,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"),mf=Object(Pe.h)(nt,null,"X"),ff=Object(Pe.h)("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),jf=Object(Pe.h)("p",null,"...e anche della varianza campionaria!"),Of=Object(Pe.h)(Be,{title:"Indipendenza"},Object(Pe.h)("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!")),_f=Object(Pe.h)("p",null,"Se la successione di variabili aleatorie ",Object(Pe.h)(nt,null,"X_n")," all'infinito ha la ",Object(Pe.h)("b",null,"stessa funzione di ripartizione")," della popolazione ",Object(Pe.h)(nt,null,"X"),", allora essa ",Object(Pe.h)("i",null,"converge in distribuzione"),"."),gf=Object(Pe.h)("p",null,"Se la successione di variabili aleatorie ",Object(Pe.h)(nt,null,"X_n")," all'infinito ha la ",Object(Pe.h)("b",null,"stessa probabilità")," della popolazione ",Object(Pe.h)(nt,null,"X"),", allora essa ",Object(Pe.h)("i",null,"converge in probabilità"),"."),vf=Object(Pe.h)("p",null,"Se la successione di variabili aleatorie ",Object(Pe.h)(nt,null,"X_n")," all'infinito ha la ",Object(Pe.h)("b",null,"stessa probabilità a ")," della popolazione ",Object(Pe.h)(nt,null,"X"),", allora essa ",Object(Pe.h)("i",null,"converge quasi certamente"),"."),wf=Object(Pe.h)("p",null,"Se la successione di variabili aleatorie ",Object(Pe.h)(nt,null,"X_n")," all'infinito ha la ",Object(Pe.h)("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",Object(Pe.h)(nt,null,"X")," ",Object(Pe.h)("b",null,"uguale a 0"),", allora essa ",Object(Pe.h)("i",null,"converge in media quadratica"),"."),yf=Object(Pe.h)("p",null,"In più:"),zf=Object(Pe.h)("b",null,"converge in probabilità"),kf=Object(Pe.h)("p",null,"Ovvero:"),Pf=Object(Pe.h)("b",null,"converge quasi certamente"),Ef=Object(Pe.h)("p",null,"Ovvero:"),Xf=Object(Pe.h)(jr,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"),qf=Object(Pe.h)("b",null,"converge in distribuzione"),xf=Object(Pe.h)("p",null,"Ovvero:"),Cf=Object(Pe.h)("p",null,"E' una somma di ",Object(Pe.h)("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),Sf=Object(Pe.h)("p",null,"E' una somma di ",Object(Pe.h)("b",null,"geometriche"),", e quindi si approssima a una normale:"),Lf=Object(Pe.h)("p",null,"E' una somma di altre ",Object(Pe.h)("b",null,"poissoniane"),", e quindi si approssima a una normale:"),Af=Object(Pe.h)("p",null,"E' una somma di ",Object(Pe.h)("b",null,"esponenziali"),", e quindi si approssima a una normale:"),Mf=Object(Pe.h)("p",null,"Se ",Object(Pe.h)(nt,null,"n")," è grande, allora:"),Ff=Object(Pe.h)(Be,{title:"Parametri sconosciuti"},Object(Pe.h)("p",null,"Per indicare parametri sconosciuti di una legge si usa ",Object(Pe.h)(nt,null,"\\theta"),".")),Tf=Object(Pe.h)("p",null,"Una variabile aleatoria funzione di un campione:"),If=Object(Pe.h)(Be,{title:"Stimatore"},Object(Pe.h)("p",null,"Una statistica ",Object(Pe.h)(nt,null,"T_n")," ottenuta da ",Object(Pe.h)(nt,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),Df=Object(Pe.h)("p",null,"Uno stimatore è ",Object(Pe.h)("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),Nf=Object(Pe.h)("p",null,"Uno stimatore è ",Object(Pe.h)("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),Bf=Object(Pe.h)("p",null,"Uno stimatore è ",Object(Pe.h)("i",null,"consistente in media quadratica")," se:"),Vf=Object(Pe.h)("p",null,"Uno stimatore è ",Object(Pe.h)("i",null,"consistente in probabilità")," se:"),Rf=Object(Pe.h)("p",null,"Uno stimatore è ",Object(Pe.h)("i",null,"asintoticamente normale")," se:"),Uf=Object(Pe.h)("p",null,"Si può usare il ",Object(Pe.h)("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",Object(Pe.h)(nt,null,"X"),"."),Yf=Object(Pe.h)(nt,null,"M"),Hf=Object(Pe.h)(nt,null,"\\theta"),Gf=Object(Pe.h)("p",null,"Visto che:"),Wf=Object(Pe.h)("p",null,"Allora:"),$f=Object(Pe.h)("p",null,"Si può usare il ",Object(Pe.h)("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",Object(Pe.h)(nt,null,"X"),"."),Kf=Object(Pe.h)(nt,null,"L"),Zf=Object(Pe.h)(nt,null,"\\theta"),Qf=Object(Pe.h)("p",null,"Gli stimatori di massima verosomiglianza sono ",Object(Pe.h)("b",null,"asintoticamente corretti"),", ",Object(Pe.h)("b",null,"consistenti in probabilità")," e ",Object(Pe.h)("b",null,"asintoticamente normali"),"."),Jf=Object(Pe.h)("p",null,"Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:"),ej=Object(Pe.h)("li",null,"Sono ",Object(Pe.h)("b",null,"asintoticamente corretti"),"."),tj=Object(Pe.h)("li",null,"Sono ",Object(Pe.h)("b",null,"consistenti in probabilità"),"."),nj=Object(Pe.h)("li",null,"Sono ",Object(Pe.h)("b",null,"asintoticamente normali"),"."),aj=Object(Pe.h)("b",null,"invarianti"),lj=Object(Pe.h)("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),ij=Object(Pe.h)("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),oj=Object(Pe.h)("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),rj=Object(Pe.h)("p",null,"Per il metodo della massima verosomiglianza:"),cj=Object(Pe.h)("br",null),sj=Object(Pe.h)("blockquote",null,'"intervallo di confidenza al 95%"'),uj=Object(Pe.h)("p",null,"L'intervallo di valori di ",Object(Pe.h)(nt,null,"\\theta"),' all\'interno del quale siamo "più o meno sicuri" si trovi il valore effettivo:'),hj=Object(Pe.h)(nt,null,"]a, b["),pj=Object(Pe.h)("p",null,"Può anche essere ",Object(Pe.h)("b",null,"unilatero")," nel caso limiti la stima in una sola direzione, positiva o negativa."),bj=Object(Pe.h)("p",null,"Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",Object(Pe.h)(nt,null,"\\alpha"),"% con queste formule:"),dj=Object(Pe.h)("p",null,"Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",Object(Pe.h)(nt,null,"\\alpha"),"% con queste formule:"),mj=Object(Pe.h)(nt,null,"v"),fj=Object(Pe.h)("p",null,"L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:"),jj=Object(Pe.h)("p",null,"L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:"),Oj=function(e){function t(){return ge(this,t),ve(this,e.apply(this,arguments))}return we(t,e),t.prototype.render=function(){return Object(Pe.h)("div",{style:ar.a.statistica},Rh,Object(Pe.h)(Ue,{title:"Tipi di probabilità"},Object(Pe.h)(Be,{title:"Classica"},Object(Pe.h)("p",null,Object(Pe.h)(nt,null,Vh(Or)))),Object(Pe.h)(Be,{title:"Frequentista"},Object(Pe.h)("p",null,Object(Pe.h)(nt,null,Vh(_r)))),Uh),Object(Pe.h)(Ue,{title:"Linguaggio matematico"},Object(Pe.h)(Be,{title:"Spazio 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eventi"},pp,bp,Object(Pe.h)("p",null,Object(Pe.h)(nt,null,Vh(xr))),Object(Pe.h)("p",null,"Qualsiasi sottoinsieme appartenente a ",Object(Pe.h)(nt,null,Vh(xr))," è considerato un evento.")),Object(Pe.h)(Be,{title:Object(Pe.h)("span",null,Object(Pe.h)(nt,null,Vh(Cr)),"-algebra")},dp,Object(Pe.h)("p",null,"Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta ",Object(Pe.h)("i",null,Object(Pe.h)(nt,null,Vh(Cr)),"-algebra"),":"),Object(Pe.h)("ol",null,Object(Pe.h)("li",null,"Lo spazio campionario è un evento: ",Object(Pe.h)(nt,null,Vh(Sr))),Object(Pe.h)("li",null,"Se un sottoinsieme è un evento, allora anche il suo complementare lo è: ",Object(Pe.h)(nt,null,Vh(Lr))),Object(Pe.h)("li",null,"Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: ",Object(Pe.h)(nt,null,Vh(Ar)))),Object(Pe.h)("p",null,"Un esempio: ",Object(Pe.h)(nt,null,Vh(Mr))))),Object(Pe.h)(Ue,null,Object(Pe.h)(Be,{title:"Partizione"},mp,fp,jp,Object(Pe.h)("p",null,"La 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Valid values: \"lang/language\", \"output/html\" or \"listener\"';\n return ret;\n }\n\n if (type === 'listener') {\n if (showdown.helper.isUndefined(ext.listeners)) {\n ret.valid = false;\n ret.error = baseMsg + '. Extensions of type \"listener\" must have a property called \"listeners\"';\n return ret;\n }\n } else {\n if (showdown.helper.isUndefined(ext.filter) && showdown.helper.isUndefined(ext.regex)) {\n ret.valid = false;\n ret.error = baseMsg + type + ' extensions must define either a \"regex\" property or a \"filter\" method';\n return ret;\n }\n }\n\n if (ext.listeners) {\n if (typeof ext.listeners !== 'object') {\n ret.valid = false;\n ret.error = baseMsg + '\"listeners\" property must be an object but ' + typeof ext.listeners + ' given';\n return ret;\n }\n for (var ln in ext.listeners) {\n if (ext.listeners.hasOwnProperty(ln)) {\n if (typeof ext.listeners[ln] !== 'function') {\n ret.valid = false;\n ret.error = baseMsg + '\"listeners\" property must be an hash of [event name]: [callback]. listeners.' + ln + ' must be a function but ' + typeof ext.listeners[ln] + ' given';\n return ret;\n }\n }\n }\n }\n\n if (ext.filter) {\n if (typeof ext.filter !== 'function') {\n ret.valid = false;\n ret.error = baseMsg + '\"filter\" must be a function, but ' + typeof ext.filter + ' given';\n return ret;\n }\n } else if (ext.regex) {\n if (showdown.helper.isString(ext.regex)) {\n ext.regex = new RegExp(ext.regex, 'g');\n }\n if (!(ext.regex instanceof RegExp)) {\n ret.valid = false;\n ret.error = baseMsg + '\"regex\" property must either be a string or a RegExp object, but ' + typeof ext.regex + ' given';\n return ret;\n }\n if (showdown.helper.isUndefined(ext.replace)) {\n ret.valid = false;\n ret.error = baseMsg + '\"regex\" extensions must implement a replace string or function';\n return ret;\n }\n }\n }\n return ret;\n }\n\n /**\n * Validate extension\n * @param {object} ext\n * @returns {boolean}\n */\n showdown.validateExtension = function (ext) {\n 'use strict';\n\n var validateExtension = validate(ext, null);\n if (!validateExtension.valid) {\n console.warn(validateExtension.error);\n return false;\n }\n return true;\n };\n\n /**\n * showdownjs helper functions\n */\n\n if (!showdown.hasOwnProperty('helper')) {\n showdown.helper = {};\n }\n\n /**\n * Check if var is string\n * @static\n * @param {string} a\n * @returns {boolean}\n */\n showdown.helper.isString = function (a) {\n 'use strict';\n\n return typeof a === 'string' || a instanceof String;\n };\n\n /**\n * Check if var is a function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\n showdown.helper.isFunction = function (a) {\n 'use strict';\n\n var getType = {};\n return a && getType.toString.call(a) === '[object Function]';\n };\n\n /**\n * isArray helper function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\n showdown.helper.isArray = function (a) {\n 'use strict';\n\n return Array.isArray(a);\n };\n\n /**\n * Check if value is undefined\n * @static\n * @param {*} value The value to check.\n * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.\n */\n showdown.helper.isUndefined = function (value) {\n 'use strict';\n\n return typeof value === 'undefined';\n };\n\n /**\n * ForEach helper function\n * Iterates over Arrays and Objects (own properties only)\n * @static\n * @param {*} obj\n * @param {function} callback Accepts 3 params: 1. value, 2. key, 3. the original array/object\n */\n showdown.helper.forEach = function (obj, callback) {\n 'use strict';\n // check if obj is defined\n\n if (showdown.helper.isUndefined(obj)) {\n throw new Error('obj param is required');\n }\n\n if (showdown.helper.isUndefined(callback)) {\n throw new Error('callback param is required');\n }\n\n if (!showdown.helper.isFunction(callback)) {\n throw new Error('callback param must be a function/closure');\n }\n\n if (typeof obj.forEach === 'function') {\n obj.forEach(callback);\n } else if (showdown.helper.isArray(obj)) {\n for (var i = 0; i < obj.length; i++) {\n callback(obj[i], i, obj);\n }\n } else if (typeof obj === 'object') {\n for (var prop in obj) {\n if (obj.hasOwnProperty(prop)) {\n callback(obj[prop], prop, obj);\n }\n }\n } else {\n throw new Error('obj does not seem to be an array or an iterable object');\n }\n };\n\n /**\n * Standardidize extension name\n * @static\n * @param {string} s extension name\n * @returns {string}\n */\n showdown.helper.stdExtName = function (s) {\n 'use strict';\n\n return s.replace(/[_?*+\\/\\\\.^-]/g, '').replace(/\\s/g, '').toLowerCase();\n };\n\n function escapeCharactersCallback(wholeMatch, m1) {\n 'use strict';\n\n var charCodeToEscape = m1.charCodeAt(0);\n return '¨E' + charCodeToEscape + 'E';\n }\n\n /**\n * Callback used to escape characters when passing through String.replace\n * @static\n * @param {string} wholeMatch\n * @param {string} m1\n * @returns {string}\n */\n showdown.helper.escapeCharactersCallback = escapeCharactersCallback;\n\n /**\n * Escape characters in a string\n * @static\n * @param {string} text\n * @param {string} charsToEscape\n * @param {boolean} afterBackslash\n * @returns {XML|string|void|*}\n */\n showdown.helper.escapeCharacters = function (text, charsToEscape, afterBackslash) {\n 'use strict';\n // First we have to escape the escape characters so that\n // we can build a character class out of them\n\n var regexString = '([' + charsToEscape.replace(/([\\[\\]\\\\])/g, '\\\\$1') + '])';\n\n if (afterBackslash) {\n regexString = '\\\\\\\\' + regexString;\n }\n\n var regex = new RegExp(regexString, 'g');\n text = text.replace(regex, escapeCharactersCallback);\n\n return text;\n };\n\n /**\n * Unescape HTML entities\n * @param txt\n * @returns {string}\n */\n showdown.helper.unescapeHTMLEntities = function (txt) {\n 'use strict';\n\n return txt.replace(/"/g, '\"').replace(/</g, '<').replace(/>/g, '>').replace(/&/g, '&');\n };\n\n var rgxFindMatchPos = function rgxFindMatchPos(str, left, right, flags) {\n 'use strict';\n\n var f = flags || '',\n g = f.indexOf('g') > -1,\n x = new RegExp(left + '|' + right, 'g' + f.replace(/g/g, '')),\n l = new RegExp(left, f.replace(/g/g, '')),\n pos = [],\n t,\n s,\n m,\n start,\n end;\n\n do {\n t = 0;\n while (m = x.exec(str)) {\n if (l.test(m[0])) {\n if (!t++) {\n s = x.lastIndex;\n start = s - m[0].length;\n }\n } else if (t) {\n if (! --t) {\n end = m.index + m[0].length;\n var obj = {\n left: { start: start, end: s },\n match: { start: s, end: m.index },\n right: { start: m.index, end: end },\n wholeMatch: { start: start, end: end }\n };\n pos.push(obj);\n if (!g) {\n return pos;\n }\n }\n }\n }\n } while (t && (x.lastIndex = s));\n\n return pos;\n };\n\n /**\n * matchRecursiveRegExp\n *\n * (c) 2007 Steven Levithan \n * MIT License\n *\n * Accepts a string to search, a left and right format delimiter\n * as regex patterns, and optional regex flags. Returns an array\n * of matches, allowing nested instances of left/right delimiters.\n * Use the \"g\" flag to return all matches, otherwise only the\n * first is returned. Be careful to ensure that the left and\n * right format delimiters produce mutually exclusive matches.\n * Backreferences are not supported within the right delimiter\n * due to how it is internally combined with the left delimiter.\n * When matching strings whose format delimiters are unbalanced\n * to the left or right, the output is intentionally as a\n * conventional regex library with recursion support would\n * produce, e.g. \"<\" and \">\" both produce [\"x\"] when using\n * \"<\" and \">\" as the delimiters (both strings contain a single,\n * balanced instance of \"\").\n *\n * examples:\n * matchRecursiveRegExp(\"test\", \"\\\\(\", \"\\\\)\")\n * returns: []\n * matchRecursiveRegExp(\">>t<>\", \"<\", \">\", \"g\")\n * returns: [\"t<>\", \"\"]\n * matchRecursiveRegExp(\"
test
\", \"]*>\", \"\", \"gi\")\n * returns: [\"test\"]\n */\n showdown.helper.matchRecursiveRegExp = function (str, left, right, flags) {\n 'use strict';\n\n var matchPos = rgxFindMatchPos(str, left, right, flags),\n results = [];\n\n for (var i = 0; i < matchPos.length; ++i) {\n results.push([str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end), str.slice(matchPos[i].match.start, matchPos[i].match.end), str.slice(matchPos[i].left.start, matchPos[i].left.end), str.slice(matchPos[i].right.start, matchPos[i].right.end)]);\n }\n return results;\n };\n\n /**\n *\n * @param {string} str\n * @param {string|function} replacement\n * @param {string} left\n * @param {string} right\n * @param {string} flags\n * @returns {string}\n */\n showdown.helper.replaceRecursiveRegExp = function (str, replacement, left, right, flags) {\n 'use strict';\n\n if (!showdown.helper.isFunction(replacement)) {\n var repStr = replacement;\n replacement = function replacement() {\n return repStr;\n };\n }\n\n var matchPos = rgxFindMatchPos(str, left, right, flags),\n finalStr = str,\n lng = matchPos.length;\n\n if (lng > 0) {\n var bits = [];\n if (matchPos[0].wholeMatch.start !== 0) {\n bits.push(str.slice(0, matchPos[0].wholeMatch.start));\n }\n for (var i = 0; i < lng; ++i) {\n bits.push(replacement(str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end), str.slice(matchPos[i].match.start, matchPos[i].match.end), str.slice(matchPos[i].left.start, matchPos[i].left.end), str.slice(matchPos[i].right.start, matchPos[i].right.end)));\n if (i < lng - 1) {\n bits.push(str.slice(matchPos[i].wholeMatch.end, matchPos[i + 1].wholeMatch.start));\n }\n }\n if (matchPos[lng - 1].wholeMatch.end < str.length) {\n bits.push(str.slice(matchPos[lng - 1].wholeMatch.end));\n }\n finalStr = bits.join('');\n }\n return finalStr;\n };\n\n /**\n * Returns the index within the passed String object of the first occurrence of the specified regex,\n * starting the search at fromIndex. Returns -1 if the value is not found.\n *\n * @param {string} str string to search\n * @param {RegExp} regex Regular expression to search\n * @param {int} [fromIndex = 0] Index to start the search\n * @returns {Number}\n * @throws InvalidArgumentError\n */\n showdown.helper.regexIndexOf = function (str, regex, fromIndex) {\n 'use strict';\n\n if (!showdown.helper.isString(str)) {\n throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n }\n if (regex instanceof RegExp === false) {\n throw 'InvalidArgumentError: second parameter of showdown.helper.regexIndexOf function must be an instance of RegExp';\n }\n var indexOf = str.substring(fromIndex || 0).search(regex);\n return indexOf >= 0 ? indexOf + (fromIndex || 0) : indexOf;\n };\n\n /**\n * Splits the passed string object at the defined index, and returns an array composed of the two substrings\n * @param {string} str string to split\n * @param {int} index index to split string at\n * @returns {[string,string]}\n * @throws InvalidArgumentError\n */\n showdown.helper.splitAtIndex = function (str, index) {\n 'use strict';\n\n if (!showdown.helper.isString(str)) {\n throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n }\n return [str.substring(0, index), str.substring(index)];\n };\n\n /**\n * Obfuscate an e-mail address through the use of Character Entities,\n * transforming ASCII characters into their equivalent decimal or hex entities.\n *\n * Since it has a random component, subsequent calls to this function produce different results\n *\n * @param {string} mail\n * @returns {string}\n */\n showdown.helper.encodeEmailAddress = function (mail) {\n 'use strict';\n\n var encode = [function (ch) {\n return '&#' + ch.charCodeAt(0) + ';';\n }, function (ch) {\n return '&#x' + ch.charCodeAt(0).toString(16) + ';';\n }, function (ch) {\n return ch;\n }];\n\n mail = mail.replace(/./g, function (ch) {\n if (ch === '@') {\n // this *must* be encoded. I insist.\n ch = encode[Math.floor(Math.random() * 2)](ch);\n } else {\n var r = Math.random();\n // roughly 10% raw, 45% hex, 45% dec\n ch = r > 0.9 ? encode[2](ch) : r > 0.45 ? encode[1](ch) : encode[0](ch);\n }\n return ch;\n });\n\n return mail;\n };\n\n /**\n *\n * @param str\n * @param targetLength\n * @param padString\n * @returns {string}\n */\n showdown.helper.padEnd = function padEnd(str, targetLength, padString) {\n 'use strict';\n /*jshint bitwise: false*/\n // eslint-disable-next-line space-infix-ops\n\n targetLength = targetLength >> 0; //floor if number or convert non-number to 0;\n /*jshint bitwise: true*/\n padString = String(padString || ' ');\n if (str.length > targetLength) {\n return String(str);\n } else {\n targetLength = targetLength - str.length;\n if (targetLength > padString.length) {\n padString += padString.repeat(targetLength / padString.length); //append to original to ensure we are longer than needed\n }\n return String(str) + padString.slice(0, targetLength);\n }\n };\n\n /**\n * POLYFILLS\n */\n // use this instead of builtin is undefined for IE8 compatibility\n if (typeof console === 'undefined') {\n console = {\n warn: function warn(msg) {\n 'use strict';\n\n alert(msg);\n },\n log: function log(msg) {\n 'use strict';\n\n alert(msg);\n },\n error: function error(msg) {\n 'use strict';\n\n throw msg;\n }\n };\n }\n\n /**\n * Common regexes.\n * We declare some common regexes to improve performance\n */\n showdown.helper.regexes = {\n asteriskDashAndColon: /([*_:~])/g\n };\n\n /**\n * EMOJIS LIST\n */\n showdown.helper.emojis = {\n '+1': '\\uD83D\\uDC4D',\n '-1': '\\uD83D\\uDC4E',\n '100': '\\uD83D\\uDCAF',\n '1234': '\\uD83D\\uDD22',\n '1st_place_medal': '\\uD83E\\uDD47',\n '2nd_place_medal': '\\uD83E\\uDD48',\n '3rd_place_medal': '\\uD83E\\uDD49',\n '8ball': '\\uD83C\\uDFB1',\n 'a': '\\uD83C\\uDD70\\uFE0F',\n 'ab': '\\uD83C\\uDD8E',\n 'abc': '\\uD83D\\uDD24',\n 'abcd': '\\uD83D\\uDD21',\n 'accept': '\\uD83C\\uDE51',\n 'aerial_tramway': '\\uD83D\\uDEA1',\n 'airplane': '\\u2708\\uFE0F',\n 'alarm_clock': '\\u23F0',\n 'alembic': '\\u2697\\uFE0F',\n 'alien': '\\uD83D\\uDC7D',\n 'ambulance': '\\uD83D\\uDE91',\n 'amphora': '\\uD83C\\uDFFA',\n 'anchor': '\\u2693\\uFE0F',\n 'angel': '\\uD83D\\uDC7C',\n 'anger': '\\uD83D\\uDCA2',\n 'angry': '\\uD83D\\uDE20',\n 'anguished': '\\uD83D\\uDE27',\n 'ant': '\\uD83D\\uDC1C',\n 'apple': '\\uD83C\\uDF4E',\n 'aquarius': '\\u2652\\uFE0F',\n 'aries': '\\u2648\\uFE0F',\n 'arrow_backward': '\\u25C0\\uFE0F',\n 'arrow_double_down': '\\u23EC',\n 'arrow_double_up': '\\u23EB',\n 'arrow_down': '\\u2B07\\uFE0F',\n 'arrow_down_small': '\\uD83D\\uDD3D',\n 'arrow_forward': '\\u25B6\\uFE0F',\n 'arrow_heading_down': '\\u2935\\uFE0F',\n 'arrow_heading_up': '\\u2934\\uFE0F',\n 'arrow_left': '\\u2B05\\uFE0F',\n 'arrow_lower_left': '\\u2199\\uFE0F',\n 'arrow_lower_right': '\\u2198\\uFE0F',\n 'arrow_right': '\\u27A1\\uFE0F',\n 'arrow_right_hook': '\\u21AA\\uFE0F',\n 'arrow_up': '\\u2B06\\uFE0F',\n 'arrow_up_down': '\\u2195\\uFE0F',\n 'arrow_up_small': '\\uD83D\\uDD3C',\n 'arrow_upper_left': '\\u2196\\uFE0F',\n 'arrow_upper_right': '\\u2197\\uFE0F',\n 'arrows_clockwise': '\\uD83D\\uDD03',\n 'arrows_counterclockwise': '\\uD83D\\uDD04',\n 'art': '\\uD83C\\uDFA8',\n 'articulated_lorry': '\\uD83D\\uDE9B',\n 'artificial_satellite': '\\uD83D\\uDEF0',\n 'astonished': '\\uD83D\\uDE32',\n 'athletic_shoe': '\\uD83D\\uDC5F',\n 'atm': '\\uD83C\\uDFE7',\n 'atom_symbol': '\\u269B\\uFE0F',\n 'avocado': '\\uD83E\\uDD51',\n 'b': '\\uD83C\\uDD71\\uFE0F',\n 'baby': '\\uD83D\\uDC76',\n 'baby_bottle': '\\uD83C\\uDF7C',\n 'baby_chick': '\\uD83D\\uDC24',\n 'baby_symbol': '\\uD83D\\uDEBC',\n 'back': '\\uD83D\\uDD19',\n 'bacon': '\\uD83E\\uDD53',\n 'badminton': '\\uD83C\\uDFF8',\n 'baggage_claim': '\\uD83D\\uDEC4',\n 'baguette_bread': '\\uD83E\\uDD56',\n 'balance_scale': '\\u2696\\uFE0F',\n 'balloon': '\\uD83C\\uDF88',\n 'ballot_box': '\\uD83D\\uDDF3',\n 'ballot_box_with_check': '\\u2611\\uFE0F',\n 'bamboo': '\\uD83C\\uDF8D',\n 'banana': '\\uD83C\\uDF4C',\n 'bangbang': '\\u203C\\uFE0F',\n 'bank': '\\uD83C\\uDFE6',\n 'bar_chart': '\\uD83D\\uDCCA',\n 'barber': '\\uD83D\\uDC88',\n 'baseball': '\\u26BE\\uFE0F',\n 'basketball': '\\uD83C\\uDFC0',\n 'basketball_man': '\\u26F9\\uFE0F',\n 'basketball_woman': '\\u26F9\\uFE0F‍\\u2640\\uFE0F',\n 'bat': '\\uD83E\\uDD87',\n 'bath': '\\uD83D\\uDEC0',\n 'bathtub': '\\uD83D\\uDEC1',\n 'battery': '\\uD83D\\uDD0B',\n 'beach_umbrella': '\\uD83C\\uDFD6',\n 'bear': '\\uD83D\\uDC3B',\n 'bed': '\\uD83D\\uDECF',\n 'bee': '\\uD83D\\uDC1D',\n 'beer': '\\uD83C\\uDF7A',\n 'beers': '\\uD83C\\uDF7B',\n 'beetle': '\\uD83D\\uDC1E',\n 'beginner': '\\uD83D\\uDD30',\n 'bell': '\\uD83D\\uDD14',\n 'bellhop_bell': '\\uD83D\\uDECE',\n 'bento': '\\uD83C\\uDF71',\n 'biking_man': '\\uD83D\\uDEB4',\n 'bike': '\\uD83D\\uDEB2',\n 'biking_woman': '\\uD83D\\uDEB4‍\\u2640\\uFE0F',\n 'bikini': '\\uD83D\\uDC59',\n 'biohazard': '\\u2623\\uFE0F',\n 'bird': '\\uD83D\\uDC26',\n 'birthday': '\\uD83C\\uDF82',\n 'black_circle': '\\u26AB\\uFE0F',\n 'black_flag': '\\uD83C\\uDFF4',\n 'black_heart': '\\uD83D\\uDDA4',\n 'black_joker': '\\uD83C\\uDCCF',\n 'black_large_square': '\\u2B1B\\uFE0F',\n 'black_medium_small_square': '\\u25FE\\uFE0F',\n 'black_medium_square': '\\u25FC\\uFE0F',\n 'black_nib': '\\u2712\\uFE0F',\n 'black_small_square': '\\u25AA\\uFE0F',\n 'black_square_button': '\\uD83D\\uDD32',\n 'blonde_man': '\\uD83D\\uDC71',\n 'blonde_woman': '\\uD83D\\uDC71‍\\u2640\\uFE0F',\n 'blossom': '\\uD83C\\uDF3C',\n 'blowfish': '\\uD83D\\uDC21',\n 'blue_book': '\\uD83D\\uDCD8',\n 'blue_car': '\\uD83D\\uDE99',\n 'blue_heart': '\\uD83D\\uDC99',\n 'blush': '\\uD83D\\uDE0A',\n 'boar': '\\uD83D\\uDC17',\n 'boat': '\\u26F5\\uFE0F',\n 'bomb': '\\uD83D\\uDCA3',\n 'book': '\\uD83D\\uDCD6',\n 'bookmark': '\\uD83D\\uDD16',\n 'bookmark_tabs': '\\uD83D\\uDCD1',\n 'books': '\\uD83D\\uDCDA',\n 'boom': '\\uD83D\\uDCA5',\n 'boot': '\\uD83D\\uDC62',\n 'bouquet': '\\uD83D\\uDC90',\n 'bowing_man': '\\uD83D\\uDE47',\n 'bow_and_arrow': '\\uD83C\\uDFF9',\n 'bowing_woman': '\\uD83D\\uDE47‍\\u2640\\uFE0F',\n 'bowling': '\\uD83C\\uDFB3',\n 'boxing_glove': '\\uD83E\\uDD4A',\n 'boy': '\\uD83D\\uDC66',\n 'bread': '\\uD83C\\uDF5E',\n 'bride_with_veil': '\\uD83D\\uDC70',\n 'bridge_at_night': '\\uD83C\\uDF09',\n 'briefcase': '\\uD83D\\uDCBC',\n 'broken_heart': '\\uD83D\\uDC94',\n 'bug': '\\uD83D\\uDC1B',\n 'building_construction': '\\uD83C\\uDFD7',\n 'bulb': '\\uD83D\\uDCA1',\n 'bullettrain_front': '\\uD83D\\uDE85',\n 'bullettrain_side': '\\uD83D\\uDE84',\n 'burrito': '\\uD83C\\uDF2F',\n 'bus': '\\uD83D\\uDE8C',\n 'business_suit_levitating': '\\uD83D\\uDD74',\n 'busstop': '\\uD83D\\uDE8F',\n 'bust_in_silhouette': '\\uD83D\\uDC64',\n 'busts_in_silhouette': '\\uD83D\\uDC65',\n 'butterfly': '\\uD83E\\uDD8B',\n 'cactus': '\\uD83C\\uDF35',\n 'cake': '\\uD83C\\uDF70',\n 'calendar': '\\uD83D\\uDCC6',\n 'call_me_hand': '\\uD83E\\uDD19',\n 'calling': '\\uD83D\\uDCF2',\n 'camel': '\\uD83D\\uDC2B',\n 'camera': '\\uD83D\\uDCF7',\n 'camera_flash': '\\uD83D\\uDCF8',\n 'camping': '\\uD83C\\uDFD5',\n 'cancer': '\\u264B\\uFE0F',\n 'candle': '\\uD83D\\uDD6F',\n 'candy': '\\uD83C\\uDF6C',\n 'canoe': '\\uD83D\\uDEF6',\n 'capital_abcd': '\\uD83D\\uDD20',\n 'capricorn': '\\u2651\\uFE0F',\n 'car': '\\uD83D\\uDE97',\n 'card_file_box': '\\uD83D\\uDDC3',\n 'card_index': '\\uD83D\\uDCC7',\n 'card_index_dividers': '\\uD83D\\uDDC2',\n 'carousel_horse': '\\uD83C\\uDFA0',\n 'carrot': '\\uD83E\\uDD55',\n 'cat': '\\uD83D\\uDC31',\n 'cat2': '\\uD83D\\uDC08',\n 'cd': '\\uD83D\\uDCBF',\n 'chains': '\\u26D3',\n 'champagne': '\\uD83C\\uDF7E',\n 'chart': '\\uD83D\\uDCB9',\n 'chart_with_downwards_trend': '\\uD83D\\uDCC9',\n 'chart_with_upwards_trend': '\\uD83D\\uDCC8',\n 'checkered_flag': '\\uD83C\\uDFC1',\n 'cheese': '\\uD83E\\uDDC0',\n 'cherries': '\\uD83C\\uDF52',\n 'cherry_blossom': '\\uD83C\\uDF38',\n 'chestnut': '\\uD83C\\uDF30',\n 'chicken': '\\uD83D\\uDC14',\n 'children_crossing': '\\uD83D\\uDEB8',\n 'chipmunk': '\\uD83D\\uDC3F',\n 'chocolate_bar': '\\uD83C\\uDF6B',\n 'christmas_tree': '\\uD83C\\uDF84',\n 'church': '\\u26EA\\uFE0F',\n 'cinema': '\\uD83C\\uDFA6',\n 'circus_tent': '\\uD83C\\uDFAA',\n 'city_sunrise': '\\uD83C\\uDF07',\n 'city_sunset': '\\uD83C\\uDF06',\n 'cityscape': '\\uD83C\\uDFD9',\n 'cl': '\\uD83C\\uDD91',\n 'clamp': '\\uD83D\\uDDDC',\n 'clap': '\\uD83D\\uDC4F',\n 'clapper': '\\uD83C\\uDFAC',\n 'classical_building': '\\uD83C\\uDFDB',\n 'clinking_glasses': '\\uD83E\\uDD42',\n 'clipboard': '\\uD83D\\uDCCB',\n 'clock1': '\\uD83D\\uDD50',\n 'clock10': '\\uD83D\\uDD59',\n 'clock1030': '\\uD83D\\uDD65',\n 'clock11': '\\uD83D\\uDD5A',\n 'clock1130': '\\uD83D\\uDD66',\n 'clock12': '\\uD83D\\uDD5B',\n 'clock1230': '\\uD83D\\uDD67',\n 'clock130': '\\uD83D\\uDD5C',\n 'clock2': '\\uD83D\\uDD51',\n 'clock230': '\\uD83D\\uDD5D',\n 'clock3': '\\uD83D\\uDD52',\n 'clock330': '\\uD83D\\uDD5E',\n 'clock4': '\\uD83D\\uDD53',\n 'clock430': '\\uD83D\\uDD5F',\n 'clock5': '\\uD83D\\uDD54',\n 'clock530': '\\uD83D\\uDD60',\n 'clock6': '\\uD83D\\uDD55',\n 'clock630': '\\uD83D\\uDD61',\n 'clock7': '\\uD83D\\uDD56',\n 'clock730': '\\uD83D\\uDD62',\n 'clock8': '\\uD83D\\uDD57',\n 'clock830': '\\uD83D\\uDD63',\n 'clock9': '\\uD83D\\uDD58',\n 'clock930': '\\uD83D\\uDD64',\n 'closed_book': '\\uD83D\\uDCD5',\n 'closed_lock_with_key': '\\uD83D\\uDD10',\n 'closed_umbrella': '\\uD83C\\uDF02',\n 'cloud': '\\u2601\\uFE0F',\n 'cloud_with_lightning': '\\uD83C\\uDF29',\n 'cloud_with_lightning_and_rain': '\\u26C8',\n 'cloud_with_rain': '\\uD83C\\uDF27',\n 'cloud_with_snow': '\\uD83C\\uDF28',\n 'clown_face': '\\uD83E\\uDD21',\n 'clubs': '\\u2663\\uFE0F',\n 'cocktail': '\\uD83C\\uDF78',\n 'coffee': '\\u2615\\uFE0F',\n 'coffin': '\\u26B0\\uFE0F',\n 'cold_sweat': '\\uD83D\\uDE30',\n 'comet': '\\u2604\\uFE0F',\n 'computer': '\\uD83D\\uDCBB',\n 'computer_mouse': '\\uD83D\\uDDB1',\n 'confetti_ball': '\\uD83C\\uDF8A',\n 'confounded': '\\uD83D\\uDE16',\n 'confused': '\\uD83D\\uDE15',\n 'congratulations': '\\u3297\\uFE0F',\n 'construction': '\\uD83D\\uDEA7',\n 'construction_worker_man': '\\uD83D\\uDC77',\n 'construction_worker_woman': '\\uD83D\\uDC77‍\\u2640\\uFE0F',\n 'control_knobs': '\\uD83C\\uDF9B',\n 'convenience_store': '\\uD83C\\uDFEA',\n 'cookie': '\\uD83C\\uDF6A',\n 'cool': '\\uD83C\\uDD92',\n 'policeman': '\\uD83D\\uDC6E',\n 'copyright': '\\xA9\\uFE0F',\n 'corn': '\\uD83C\\uDF3D',\n 'couch_and_lamp': '\\uD83D\\uDECB',\n 'couple': '\\uD83D\\uDC6B',\n 'couple_with_heart_woman_man': '\\uD83D\\uDC91',\n 'couple_with_heart_man_man': '\\uD83D\\uDC68‍\\u2764\\uFE0F‍\\uD83D\\uDC68',\n 'couple_with_heart_woman_woman': '\\uD83D\\uDC69‍\\u2764\\uFE0F‍\\uD83D\\uDC69',\n 'couplekiss_man_man': '\\uD83D\\uDC68‍\\u2764\\uFE0F‍\\uD83D\\uDC8B‍\\uD83D\\uDC68',\n 'couplekiss_man_woman': '\\uD83D\\uDC8F',\n 'couplekiss_woman_woman': '\\uD83D\\uDC69‍\\u2764\\uFE0F‍\\uD83D\\uDC8B‍\\uD83D\\uDC69',\n 'cow': '\\uD83D\\uDC2E',\n 'cow2': '\\uD83D\\uDC04',\n 'cowboy_hat_face': '\\uD83E\\uDD20',\n 'crab': '\\uD83E\\uDD80',\n 'crayon': '\\uD83D\\uDD8D',\n 'credit_card': '\\uD83D\\uDCB3',\n 'crescent_moon': '\\uD83C\\uDF19',\n 'cricket': '\\uD83C\\uDFCF',\n 'crocodile': '\\uD83D\\uDC0A',\n 'croissant': '\\uD83E\\uDD50',\n 'crossed_fingers': '\\uD83E\\uDD1E',\n 'crossed_flags': '\\uD83C\\uDF8C',\n 'crossed_swords': '\\u2694\\uFE0F',\n 'crown': '\\uD83D\\uDC51',\n 'cry': '\\uD83D\\uDE22',\n 'crying_cat_face': '\\uD83D\\uDE3F',\n 'crystal_ball': '\\uD83D\\uDD2E',\n 'cucumber': '\\uD83E\\uDD52',\n 'cupid': '\\uD83D\\uDC98',\n 'curly_loop': '\\u27B0',\n 'currency_exchange': '\\uD83D\\uDCB1',\n 'curry': '\\uD83C\\uDF5B',\n 'custard': '\\uD83C\\uDF6E',\n 'customs': '\\uD83D\\uDEC3',\n 'cyclone': '\\uD83C\\uDF00',\n 'dagger': '\\uD83D\\uDDE1',\n 'dancer': '\\uD83D\\uDC83',\n 'dancing_women': '\\uD83D\\uDC6F',\n 'dancing_men': '\\uD83D\\uDC6F‍\\u2642\\uFE0F',\n 'dango': '\\uD83C\\uDF61',\n 'dark_sunglasses': '\\uD83D\\uDD76',\n 'dart': '\\uD83C\\uDFAF',\n 'dash': '\\uD83D\\uDCA8',\n 'date': '\\uD83D\\uDCC5',\n 'deciduous_tree': '\\uD83C\\uDF33',\n 'deer': '\\uD83E\\uDD8C',\n 'department_store': '\\uD83C\\uDFEC',\n 'derelict_house': '\\uD83C\\uDFDA',\n 'desert': '\\uD83C\\uDFDC',\n 'desert_island': '\\uD83C\\uDFDD',\n 'desktop_computer': '\\uD83D\\uDDA5',\n 'male_detective': '\\uD83D\\uDD75\\uFE0F',\n 'diamond_shape_with_a_dot_inside': '\\uD83D\\uDCA0',\n 'diamonds': '\\u2666\\uFE0F',\n 'disappointed': '\\uD83D\\uDE1E',\n 'disappointed_relieved': '\\uD83D\\uDE25',\n 'dizzy': '\\uD83D\\uDCAB',\n 'dizzy_face': '\\uD83D\\uDE35',\n 'do_not_litter': '\\uD83D\\uDEAF',\n 'dog': '\\uD83D\\uDC36',\n 'dog2': '\\uD83D\\uDC15',\n 'dollar': '\\uD83D\\uDCB5',\n 'dolls': '\\uD83C\\uDF8E',\n 'dolphin': '\\uD83D\\uDC2C',\n 'door': '\\uD83D\\uDEAA',\n 'doughnut': '\\uD83C\\uDF69',\n 'dove': '\\uD83D\\uDD4A',\n 'dragon': '\\uD83D\\uDC09',\n 'dragon_face': '\\uD83D\\uDC32',\n 'dress': '\\uD83D\\uDC57',\n 'dromedary_camel': '\\uD83D\\uDC2A',\n 'drooling_face': '\\uD83E\\uDD24',\n 'droplet': '\\uD83D\\uDCA7',\n 'drum': '\\uD83E\\uDD41',\n 'duck': '\\uD83E\\uDD86',\n 'dvd': '\\uD83D\\uDCC0',\n 'e-mail': '\\uD83D\\uDCE7',\n 'eagle': '\\uD83E\\uDD85',\n 'ear': '\\uD83D\\uDC42',\n 'ear_of_rice': '\\uD83C\\uDF3E',\n 'earth_africa': '\\uD83C\\uDF0D',\n 'earth_americas': '\\uD83C\\uDF0E',\n 'earth_asia': '\\uD83C\\uDF0F',\n 'egg': '\\uD83E\\uDD5A',\n 'eggplant': '\\uD83C\\uDF46',\n 'eight_pointed_black_star': '\\u2734\\uFE0F',\n 'eight_spoked_asterisk': '\\u2733\\uFE0F',\n 'electric_plug': '\\uD83D\\uDD0C',\n 'elephant': '\\uD83D\\uDC18',\n 'email': '\\u2709\\uFE0F',\n 'end': '\\uD83D\\uDD1A',\n 'envelope_with_arrow': '\\uD83D\\uDCE9',\n 'euro': '\\uD83D\\uDCB6',\n 'european_castle': '\\uD83C\\uDFF0',\n 'european_post_office': '\\uD83C\\uDFE4',\n 'evergreen_tree': '\\uD83C\\uDF32',\n 'exclamation': '\\u2757\\uFE0F',\n 'expressionless': '\\uD83D\\uDE11',\n 'eye': '\\uD83D\\uDC41',\n 'eye_speech_bubble': '\\uD83D\\uDC41‍\\uD83D\\uDDE8',\n 'eyeglasses': '\\uD83D\\uDC53',\n 'eyes': '\\uD83D\\uDC40',\n 'face_with_head_bandage': '\\uD83E\\uDD15',\n 'face_with_thermometer': '\\uD83E\\uDD12',\n 'fist_oncoming': '\\uD83D\\uDC4A',\n 'factory': '\\uD83C\\uDFED',\n 'fallen_leaf': '\\uD83C\\uDF42',\n 'family_man_woman_boy': '\\uD83D\\uDC6A',\n 'family_man_boy': '\\uD83D\\uDC68‍\\uD83D\\uDC66',\n 'family_man_boy_boy': '\\uD83D\\uDC68‍\\uD83D\\uDC66‍\\uD83D\\uDC66',\n 'family_man_girl': '\\uD83D\\uDC68‍\\uD83D\\uDC67',\n 'family_man_girl_boy': '\\uD83D\\uDC68‍\\uD83D\\uDC67‍\\uD83D\\uDC66',\n 'family_man_girl_girl': '\\uD83D\\uDC68‍\\uD83D\\uDC67‍\\uD83D\\uDC67',\n 'family_man_man_boy': '\\uD83D\\uDC68‍\\uD83D\\uDC68‍\\uD83D\\uDC66',\n 'family_man_man_boy_boy': '\\uD83D\\uDC68‍\\uD83D\\uDC68‍\\uD83D\\uDC66‍\\uD83D\\uDC66',\n 'family_man_man_girl': '\\uD83D\\uDC68‍\\uD83D\\uDC68‍\\uD83D\\uDC67',\n 'family_man_man_girl_boy': '\\uD83D\\uDC68‍\\uD83D\\uDC68‍\\uD83D\\uDC67‍\\uD83D\\uDC66',\n 'family_man_man_girl_girl': '\\uD83D\\uDC68‍\\uD83D\\uDC68‍\\uD83D\\uDC67‍\\uD83D\\uDC67',\n 'family_man_woman_boy_boy': '\\uD83D\\uDC68‍\\uD83D\\uDC69‍\\uD83D\\uDC66‍\\uD83D\\uDC66',\n 'family_man_woman_girl': '\\uD83D\\uDC68‍\\uD83D\\uDC69‍\\uD83D\\uDC67',\n 'family_man_woman_girl_boy': '\\uD83D\\uDC68‍\\uD83D\\uDC69‍\\uD83D\\uDC67‍\\uD83D\\uDC66',\n 'family_man_woman_girl_girl': '\\uD83D\\uDC68‍\\uD83D\\uDC69‍\\uD83D\\uDC67‍\\uD83D\\uDC67',\n 'family_woman_boy': '\\uD83D\\uDC69‍\\uD83D\\uDC66',\n 'family_woman_boy_boy': '\\uD83D\\uDC69‍\\uD83D\\uDC66‍\\uD83D\\uDC66',\n 'family_woman_girl': '\\uD83D\\uDC69‍\\uD83D\\uDC67',\n 'family_woman_girl_boy': '\\uD83D\\uDC69‍\\uD83D\\uDC67‍\\uD83D\\uDC66',\n 'family_woman_girl_girl': '\\uD83D\\uDC69‍\\uD83D\\uDC67‍\\uD83D\\uDC67',\n 'family_woman_woman_boy': '\\uD83D\\uDC69‍\\uD83D\\uDC69‍\\uD83D\\uDC66',\n 'family_woman_woman_boy_boy': '\\uD83D\\uDC69‍\\uD83D\\uDC69‍\\uD83D\\uDC66‍\\uD83D\\uDC66',\n 'family_woman_woman_girl': '\\uD83D\\uDC69‍\\uD83D\\uDC69‍\\uD83D\\uDC67',\n 'family_woman_woman_girl_boy': '\\uD83D\\uDC69‍\\uD83D\\uDC69‍\\uD83D\\uDC67‍\\uD83D\\uDC66',\n 'family_woman_woman_girl_girl': '\\uD83D\\uDC69‍\\uD83D\\uDC69‍\\uD83D\\uDC67‍\\uD83D\\uDC67',\n 'fast_forward': '\\u23E9',\n 'fax': '\\uD83D\\uDCE0',\n 'fearful': '\\uD83D\\uDE28',\n 'feet': '\\uD83D\\uDC3E',\n 'female_detective': '\\uD83D\\uDD75\\uFE0F‍\\u2640\\uFE0F',\n 'ferris_wheel': '\\uD83C\\uDFA1',\n 'ferry': '\\u26F4',\n 'field_hockey': '\\uD83C\\uDFD1',\n 'file_cabinet': '\\uD83D\\uDDC4',\n 'file_folder': '\\uD83D\\uDCC1',\n 'film_projector': '\\uD83D\\uDCFD',\n 'film_strip': '\\uD83C\\uDF9E',\n 'fire': '\\uD83D\\uDD25',\n 'fire_engine': '\\uD83D\\uDE92',\n 'fireworks': '\\uD83C\\uDF86',\n 'first_quarter_moon': '\\uD83C\\uDF13',\n 'first_quarter_moon_with_face': '\\uD83C\\uDF1B',\n 'fish': '\\uD83D\\uDC1F',\n 'fish_cake': '\\uD83C\\uDF65',\n 'fishing_pole_and_fish': '\\uD83C\\uDFA3',\n 'fist_raised': '\\u270A',\n 'fist_left': '\\uD83E\\uDD1B',\n 'fist_right': '\\uD83E\\uDD1C',\n 'flags': '\\uD83C\\uDF8F',\n 'flashlight': '\\uD83D\\uDD26',\n 'fleur_de_lis': '\\u269C\\uFE0F',\n 'flight_arrival': '\\uD83D\\uDEEC',\n 'flight_departure': '\\uD83D\\uDEEB',\n 'floppy_disk': '\\uD83D\\uDCBE',\n 'flower_playing_cards': '\\uD83C\\uDFB4',\n 'flushed': '\\uD83D\\uDE33',\n 'fog': '\\uD83C\\uDF2B',\n 'foggy': '\\uD83C\\uDF01',\n 'football': '\\uD83C\\uDFC8',\n 'footprints': '\\uD83D\\uDC63',\n 'fork_and_knife': '\\uD83C\\uDF74',\n 'fountain': '\\u26F2\\uFE0F',\n 'fountain_pen': '\\uD83D\\uDD8B',\n 'four_leaf_clover': '\\uD83C\\uDF40',\n 'fox_face': '\\uD83E\\uDD8A',\n 'framed_picture': '\\uD83D\\uDDBC',\n 'free': '\\uD83C\\uDD93',\n 'fried_egg': '\\uD83C\\uDF73',\n 'fried_shrimp': '\\uD83C\\uDF64',\n 'fries': '\\uD83C\\uDF5F',\n 'frog': '\\uD83D\\uDC38',\n 'frowning': '\\uD83D\\uDE26',\n 'frowning_face': '\\u2639\\uFE0F',\n 'frowning_man': '\\uD83D\\uDE4D‍\\u2642\\uFE0F',\n 'frowning_woman': '\\uD83D\\uDE4D',\n 'middle_finger': '\\uD83D\\uDD95',\n 'fuelpump': '\\u26FD\\uFE0F',\n 'full_moon': '\\uD83C\\uDF15',\n 'full_moon_with_face': '\\uD83C\\uDF1D',\n 'funeral_urn': '\\u26B1\\uFE0F',\n 'game_die': '\\uD83C\\uDFB2',\n 'gear': '\\u2699\\uFE0F',\n 'gem': '\\uD83D\\uDC8E',\n 'gemini': '\\u264A\\uFE0F',\n 'ghost': '\\uD83D\\uDC7B',\n 'gift': '\\uD83C\\uDF81',\n 'gift_heart': '\\uD83D\\uDC9D',\n 'girl': '\\uD83D\\uDC67',\n 'globe_with_meridians': '\\uD83C\\uDF10',\n 'goal_net': '\\uD83E\\uDD45',\n 'goat': '\\uD83D\\uDC10',\n 'golf': '\\u26F3\\uFE0F',\n 'golfing_man': '\\uD83C\\uDFCC\\uFE0F',\n 'golfing_woman': '\\uD83C\\uDFCC\\uFE0F‍\\u2640\\uFE0F',\n 'gorilla': '\\uD83E\\uDD8D',\n 'grapes': '\\uD83C\\uDF47',\n 'green_apple': '\\uD83C\\uDF4F',\n 'green_book': '\\uD83D\\uDCD7',\n 'green_heart': '\\uD83D\\uDC9A',\n 'green_salad': '\\uD83E\\uDD57',\n 'grey_exclamation': '\\u2755',\n 'grey_question': '\\u2754',\n 'grimacing': '\\uD83D\\uDE2C',\n 'grin': '\\uD83D\\uDE01',\n 'grinning': '\\uD83D\\uDE00',\n 'guardsman': '\\uD83D\\uDC82',\n 'guardswoman': '\\uD83D\\uDC82‍\\u2640\\uFE0F',\n 'guitar': '\\uD83C\\uDFB8',\n 'gun': '\\uD83D\\uDD2B',\n 'haircut_woman': '\\uD83D\\uDC87',\n 'haircut_man': '\\uD83D\\uDC87‍\\u2642\\uFE0F',\n 'hamburger': '\\uD83C\\uDF54',\n 'hammer': '\\uD83D\\uDD28',\n 'hammer_and_pick': '\\u2692',\n 'hammer_and_wrench': '\\uD83D\\uDEE0',\n 'hamster': '\\uD83D\\uDC39',\n 'hand': '\\u270B',\n 'handbag': '\\uD83D\\uDC5C',\n 'handshake': '\\uD83E\\uDD1D',\n 'hankey': '\\uD83D\\uDCA9',\n 'hatched_chick': '\\uD83D\\uDC25',\n 'hatching_chick': '\\uD83D\\uDC23',\n 'headphones': '\\uD83C\\uDFA7',\n 'hear_no_evil': '\\uD83D\\uDE49',\n 'heart': '\\u2764\\uFE0F',\n 'heart_decoration': '\\uD83D\\uDC9F',\n 'heart_eyes': '\\uD83D\\uDE0D',\n 'heart_eyes_cat': '\\uD83D\\uDE3B',\n 'heartbeat': '\\uD83D\\uDC93',\n 'heartpulse': '\\uD83D\\uDC97',\n 'hearts': '\\u2665\\uFE0F',\n 'heavy_check_mark': '\\u2714\\uFE0F',\n 'heavy_division_sign': '\\u2797',\n 'heavy_dollar_sign': '\\uD83D\\uDCB2',\n 'heavy_heart_exclamation': '\\u2763\\uFE0F',\n 'heavy_minus_sign': '\\u2796',\n 'heavy_multiplication_x': '\\u2716\\uFE0F',\n 'heavy_plus_sign': '\\u2795',\n 'helicopter': '\\uD83D\\uDE81',\n 'herb': '\\uD83C\\uDF3F',\n 'hibiscus': '\\uD83C\\uDF3A',\n 'high_brightness': '\\uD83D\\uDD06',\n 'high_heel': '\\uD83D\\uDC60',\n 'hocho': '\\uD83D\\uDD2A',\n 'hole': '\\uD83D\\uDD73',\n 'honey_pot': '\\uD83C\\uDF6F',\n 'horse': '\\uD83D\\uDC34',\n 'horse_racing': '\\uD83C\\uDFC7',\n 'hospital': '\\uD83C\\uDFE5',\n 'hot_pepper': '\\uD83C\\uDF36',\n 'hotdog': '\\uD83C\\uDF2D',\n 'hotel': '\\uD83C\\uDFE8',\n 'hotsprings': '\\u2668\\uFE0F',\n 'hourglass': '\\u231B\\uFE0F',\n 'hourglass_flowing_sand': '\\u23F3',\n 'house': '\\uD83C\\uDFE0',\n 'house_with_garden': '\\uD83C\\uDFE1',\n 'houses': '\\uD83C\\uDFD8',\n 'hugs': '\\uD83E\\uDD17',\n 'hushed': '\\uD83D\\uDE2F',\n 'ice_cream': '\\uD83C\\uDF68',\n 'ice_hockey': '\\uD83C\\uDFD2',\n 'ice_skate': '\\u26F8',\n 'icecream': '\\uD83C\\uDF66',\n 'id': '\\uD83C\\uDD94',\n 'ideograph_advantage': '\\uD83C\\uDE50',\n 'imp': '\\uD83D\\uDC7F',\n 'inbox_tray': '\\uD83D\\uDCE5',\n 'incoming_envelope': '\\uD83D\\uDCE8',\n 'tipping_hand_woman': '\\uD83D\\uDC81',\n 'information_source': '\\u2139\\uFE0F',\n 'innocent': '\\uD83D\\uDE07',\n 'interrobang': '\\u2049\\uFE0F',\n 'iphone': '\\uD83D\\uDCF1',\n 'izakaya_lantern': '\\uD83C\\uDFEE',\n 'jack_o_lantern': '\\uD83C\\uDF83',\n 'japan': '\\uD83D\\uDDFE',\n 'japanese_castle': '\\uD83C\\uDFEF',\n 'japanese_goblin': '\\uD83D\\uDC7A',\n 'japanese_ogre': '\\uD83D\\uDC79',\n 'jeans': '\\uD83D\\uDC56',\n 'joy': '\\uD83D\\uDE02',\n 'joy_cat': '\\uD83D\\uDE39',\n 'joystick': '\\uD83D\\uDD79',\n 'kaaba': '\\uD83D\\uDD4B',\n 'key': '\\uD83D\\uDD11',\n 'keyboard': '\\u2328\\uFE0F',\n 'keycap_ten': '\\uD83D\\uDD1F',\n 'kick_scooter': '\\uD83D\\uDEF4',\n 'kimono': '\\uD83D\\uDC58',\n 'kiss': '\\uD83D\\uDC8B',\n 'kissing': '\\uD83D\\uDE17',\n 'kissing_cat': '\\uD83D\\uDE3D',\n 'kissing_closed_eyes': '\\uD83D\\uDE1A',\n 'kissing_heart': '\\uD83D\\uDE18',\n 'kissing_smiling_eyes': '\\uD83D\\uDE19',\n 'kiwi_fruit': '\\uD83E\\uDD5D',\n 'koala': '\\uD83D\\uDC28',\n 'koko': '\\uD83C\\uDE01',\n 'label': '\\uD83C\\uDFF7',\n 'large_blue_circle': '\\uD83D\\uDD35',\n 'large_blue_diamond': '\\uD83D\\uDD37',\n 'large_orange_diamond': '\\uD83D\\uDD36',\n 'last_quarter_moon': '\\uD83C\\uDF17',\n 'last_quarter_moon_with_face': '\\uD83C\\uDF1C',\n 'latin_cross': '\\u271D\\uFE0F',\n 'laughing': '\\uD83D\\uDE06',\n 'leaves': '\\uD83C\\uDF43',\n 'ledger': '\\uD83D\\uDCD2',\n 'left_luggage': '\\uD83D\\uDEC5',\n 'left_right_arrow': '\\u2194\\uFE0F',\n 'leftwards_arrow_with_hook': '\\u21A9\\uFE0F',\n 'lemon': '\\uD83C\\uDF4B',\n 'leo': '\\u264C\\uFE0F',\n 'leopard': '\\uD83D\\uDC06',\n 'level_slider': '\\uD83C\\uDF9A',\n 'libra': '\\u264E\\uFE0F',\n 'light_rail': '\\uD83D\\uDE88',\n 'link': '\\uD83D\\uDD17',\n 'lion': '\\uD83E\\uDD81',\n 'lips': '\\uD83D\\uDC44',\n 'lipstick': '\\uD83D\\uDC84',\n 'lizard': '\\uD83E\\uDD8E',\n 'lock': '\\uD83D\\uDD12',\n 'lock_with_ink_pen': '\\uD83D\\uDD0F',\n 'lollipop': '\\uD83C\\uDF6D',\n 'loop': '\\u27BF',\n 'loud_sound': '\\uD83D\\uDD0A',\n 'loudspeaker': '\\uD83D\\uDCE2',\n 'love_hotel': '\\uD83C\\uDFE9',\n 'love_letter': '\\uD83D\\uDC8C',\n 'low_brightness': '\\uD83D\\uDD05',\n 'lying_face': '\\uD83E\\uDD25',\n 'm': '\\u24C2\\uFE0F',\n 'mag': '\\uD83D\\uDD0D',\n 'mag_right': '\\uD83D\\uDD0E',\n 'mahjong': '\\uD83C\\uDC04\\uFE0F',\n 'mailbox': '\\uD83D\\uDCEB',\n 'mailbox_closed': '\\uD83D\\uDCEA',\n 'mailbox_with_mail': '\\uD83D\\uDCEC',\n 'mailbox_with_no_mail': '\\uD83D\\uDCED',\n 'man': '\\uD83D\\uDC68',\n 'man_artist': '\\uD83D\\uDC68‍\\uD83C\\uDFA8',\n 'man_astronaut': '\\uD83D\\uDC68‍\\uD83D\\uDE80',\n 'man_cartwheeling': '\\uD83E\\uDD38‍\\u2642\\uFE0F',\n 'man_cook': '\\uD83D\\uDC68‍\\uD83C\\uDF73',\n 'man_dancing': '\\uD83D\\uDD7A',\n 'man_facepalming': '\\uD83E\\uDD26‍\\u2642\\uFE0F',\n 'man_factory_worker': '\\uD83D\\uDC68‍\\uD83C\\uDFED',\n 'man_farmer': '\\uD83D\\uDC68‍\\uD83C\\uDF3E',\n 'man_firefighter': '\\uD83D\\uDC68‍\\uD83D\\uDE92',\n 'man_health_worker': '\\uD83D\\uDC68‍\\u2695\\uFE0F',\n 'man_in_tuxedo': '\\uD83E\\uDD35',\n 'man_judge': '\\uD83D\\uDC68‍\\u2696\\uFE0F',\n 'man_juggling': '\\uD83E\\uDD39‍\\u2642\\uFE0F',\n 'man_mechanic': '\\uD83D\\uDC68‍\\uD83D\\uDD27',\n 'man_office_worker': '\\uD83D\\uDC68‍\\uD83D\\uDCBC',\n 'man_pilot': '\\uD83D\\uDC68‍\\u2708\\uFE0F',\n 'man_playing_handball': '\\uD83E\\uDD3E‍\\u2642\\uFE0F',\n 'man_playing_water_polo': '\\uD83E\\uDD3D‍\\u2642\\uFE0F',\n 'man_scientist': '\\uD83D\\uDC68‍\\uD83D\\uDD2C',\n 'man_shrugging': '\\uD83E\\uDD37‍\\u2642\\uFE0F',\n 'man_singer': '\\uD83D\\uDC68‍\\uD83C\\uDFA4',\n 'man_student': '\\uD83D\\uDC68‍\\uD83C\\uDF93',\n 'man_teacher': '\\uD83D\\uDC68‍\\uD83C\\uDFEB',\n 'man_technologist': '\\uD83D\\uDC68‍\\uD83D\\uDCBB',\n 'man_with_gua_pi_mao': '\\uD83D\\uDC72',\n 'man_with_turban': '\\uD83D\\uDC73',\n 'tangerine': '\\uD83C\\uDF4A',\n 'mans_shoe': '\\uD83D\\uDC5E',\n 'mantelpiece_clock': '\\uD83D\\uDD70',\n 'maple_leaf': '\\uD83C\\uDF41',\n 'martial_arts_uniform': '\\uD83E\\uDD4B',\n 'mask': '\\uD83D\\uDE37',\n 'massage_woman': '\\uD83D\\uDC86',\n 'massage_man': '\\uD83D\\uDC86‍\\u2642\\uFE0F',\n 'meat_on_bone': '\\uD83C\\uDF56',\n 'medal_military': '\\uD83C\\uDF96',\n 'medal_sports': '\\uD83C\\uDFC5',\n 'mega': '\\uD83D\\uDCE3',\n 'melon': '\\uD83C\\uDF48',\n 'memo': '\\uD83D\\uDCDD',\n 'men_wrestling': '\\uD83E\\uDD3C‍\\u2642\\uFE0F',\n 'menorah': '\\uD83D\\uDD4E',\n 'mens': '\\uD83D\\uDEB9',\n 'metal': '\\uD83E\\uDD18',\n 'metro': '\\uD83D\\uDE87',\n 'microphone': '\\uD83C\\uDFA4',\n 'microscope': '\\uD83D\\uDD2C',\n 'milk_glass': '\\uD83E\\uDD5B',\n 'milky_way': '\\uD83C\\uDF0C',\n 'minibus': '\\uD83D\\uDE90',\n 'minidisc': '\\uD83D\\uDCBD',\n 'mobile_phone_off': '\\uD83D\\uDCF4',\n 'money_mouth_face': '\\uD83E\\uDD11',\n 'money_with_wings': '\\uD83D\\uDCB8',\n 'moneybag': '\\uD83D\\uDCB0',\n 'monkey': '\\uD83D\\uDC12',\n 'monkey_face': '\\uD83D\\uDC35',\n 'monorail': '\\uD83D\\uDE9D',\n 'moon': '\\uD83C\\uDF14',\n 'mortar_board': '\\uD83C\\uDF93',\n 'mosque': '\\uD83D\\uDD4C',\n 'motor_boat': '\\uD83D\\uDEE5',\n 'motor_scooter': '\\uD83D\\uDEF5',\n 'motorcycle': '\\uD83C\\uDFCD',\n 'motorway': '\\uD83D\\uDEE3',\n 'mount_fuji': '\\uD83D\\uDDFB',\n 'mountain': '\\u26F0',\n 'mountain_biking_man': '\\uD83D\\uDEB5',\n 'mountain_biking_woman': '\\uD83D\\uDEB5‍\\u2640\\uFE0F',\n 'mountain_cableway': '\\uD83D\\uDEA0',\n 'mountain_railway': '\\uD83D\\uDE9E',\n 'mountain_snow': '\\uD83C\\uDFD4',\n 'mouse': '\\uD83D\\uDC2D',\n 'mouse2': '\\uD83D\\uDC01',\n 'movie_camera': '\\uD83C\\uDFA5',\n 'moyai': '\\uD83D\\uDDFF',\n 'mrs_claus': '\\uD83E\\uDD36',\n 'muscle': '\\uD83D\\uDCAA',\n 'mushroom': '\\uD83C\\uDF44',\n 'musical_keyboard': '\\uD83C\\uDFB9',\n 'musical_note': '\\uD83C\\uDFB5',\n 'musical_score': '\\uD83C\\uDFBC',\n 'mute': '\\uD83D\\uDD07',\n 'nail_care': '\\uD83D\\uDC85',\n 'name_badge': '\\uD83D\\uDCDB',\n 'national_park': '\\uD83C\\uDFDE',\n 'nauseated_face': '\\uD83E\\uDD22',\n 'necktie': '\\uD83D\\uDC54',\n 'negative_squared_cross_mark': '\\u274E',\n 'nerd_face': '\\uD83E\\uDD13',\n 'neutral_face': '\\uD83D\\uDE10',\n 'new': '\\uD83C\\uDD95',\n 'new_moon': '\\uD83C\\uDF11',\n 'new_moon_with_face': '\\uD83C\\uDF1A',\n 'newspaper': '\\uD83D\\uDCF0',\n 'newspaper_roll': '\\uD83D\\uDDDE',\n 'next_track_button': '\\u23ED',\n 'ng': '\\uD83C\\uDD96',\n 'no_good_man': '\\uD83D\\uDE45‍\\u2642\\uFE0F',\n 'no_good_woman': '\\uD83D\\uDE45',\n 'night_with_stars': '\\uD83C\\uDF03',\n 'no_bell': '\\uD83D\\uDD15',\n 'no_bicycles': '\\uD83D\\uDEB3',\n 'no_entry': '\\u26D4\\uFE0F',\n 'no_entry_sign': '\\uD83D\\uDEAB',\n 'no_mobile_phones': '\\uD83D\\uDCF5',\n 'no_mouth': '\\uD83D\\uDE36',\n 'no_pedestrians': '\\uD83D\\uDEB7',\n 'no_smoking': '\\uD83D\\uDEAD',\n 'non-potable_water': '\\uD83D\\uDEB1',\n 'nose': '\\uD83D\\uDC43',\n 'notebook': '\\uD83D\\uDCD3',\n 'notebook_with_decorative_cover': '\\uD83D\\uDCD4',\n 'notes': '\\uD83C\\uDFB6',\n 'nut_and_bolt': '\\uD83D\\uDD29',\n 'o': '\\u2B55\\uFE0F',\n 'o2': '\\uD83C\\uDD7E\\uFE0F',\n 'ocean': '\\uD83C\\uDF0A',\n 'octopus': '\\uD83D\\uDC19',\n 'oden': '\\uD83C\\uDF62',\n 'office': '\\uD83C\\uDFE2',\n 'oil_drum': '\\uD83D\\uDEE2',\n 'ok': '\\uD83C\\uDD97',\n 'ok_hand': '\\uD83D\\uDC4C',\n 'ok_man': '\\uD83D\\uDE46‍\\u2642\\uFE0F',\n 'ok_woman': '\\uD83D\\uDE46',\n 'old_key': '\\uD83D\\uDDDD',\n 'older_man': '\\uD83D\\uDC74',\n 'older_woman': '\\uD83D\\uDC75',\n 'om': '\\uD83D\\uDD49',\n 'on': '\\uD83D\\uDD1B',\n 'oncoming_automobile': '\\uD83D\\uDE98',\n 'oncoming_bus': '\\uD83D\\uDE8D',\n 'oncoming_police_car': '\\uD83D\\uDE94',\n 'oncoming_taxi': '\\uD83D\\uDE96',\n 'open_file_folder': '\\uD83D\\uDCC2',\n 'open_hands': '\\uD83D\\uDC50',\n 'open_mouth': '\\uD83D\\uDE2E',\n 'open_umbrella': '\\u2602\\uFE0F',\n 'ophiuchus': '\\u26CE',\n 'orange_book': '\\uD83D\\uDCD9',\n 'orthodox_cross': '\\u2626\\uFE0F',\n 'outbox_tray': '\\uD83D\\uDCE4',\n 'owl': '\\uD83E\\uDD89',\n 'ox': '\\uD83D\\uDC02',\n 'package': '\\uD83D\\uDCE6',\n 'page_facing_up': '\\uD83D\\uDCC4',\n 'page_with_curl': '\\uD83D\\uDCC3',\n 'pager': '\\uD83D\\uDCDF',\n 'paintbrush': '\\uD83D\\uDD8C',\n 'palm_tree': '\\uD83C\\uDF34',\n 'pancakes': '\\uD83E\\uDD5E',\n 'panda_face': '\\uD83D\\uDC3C',\n 'paperclip': '\\uD83D\\uDCCE',\n 'paperclips': '\\uD83D\\uDD87',\n 'parasol_on_ground': '\\u26F1',\n 'parking': '\\uD83C\\uDD7F\\uFE0F',\n 'part_alternation_mark': '\\u303D\\uFE0F',\n 'partly_sunny': '\\u26C5\\uFE0F',\n 'passenger_ship': '\\uD83D\\uDEF3',\n 'passport_control': '\\uD83D\\uDEC2',\n 'pause_button': '\\u23F8',\n 'peace_symbol': '\\u262E\\uFE0F',\n 'peach': '\\uD83C\\uDF51',\n 'peanuts': '\\uD83E\\uDD5C',\n 'pear': '\\uD83C\\uDF50',\n 'pen': '\\uD83D\\uDD8A',\n 'pencil2': '\\u270F\\uFE0F',\n 'penguin': '\\uD83D\\uDC27',\n 'pensive': '\\uD83D\\uDE14',\n 'performing_arts': '\\uD83C\\uDFAD',\n 'persevere': '\\uD83D\\uDE23',\n 'person_fencing': '\\uD83E\\uDD3A',\n 'pouting_woman': '\\uD83D\\uDE4E',\n 'phone': '\\u260E\\uFE0F',\n 'pick': '\\u26CF',\n 'pig': '\\uD83D\\uDC37',\n 'pig2': '\\uD83D\\uDC16',\n 'pig_nose': '\\uD83D\\uDC3D',\n 'pill': '\\uD83D\\uDC8A',\n 'pineapple': '\\uD83C\\uDF4D',\n 'ping_pong': '\\uD83C\\uDFD3',\n 'pisces': '\\u2653\\uFE0F',\n 'pizza': '\\uD83C\\uDF55',\n 'place_of_worship': '\\uD83D\\uDED0',\n 'plate_with_cutlery': '\\uD83C\\uDF7D',\n 'play_or_pause_button': '\\u23EF',\n 'point_down': '\\uD83D\\uDC47',\n 'point_left': '\\uD83D\\uDC48',\n 'point_right': '\\uD83D\\uDC49',\n 'point_up': '\\u261D\\uFE0F',\n 'point_up_2': '\\uD83D\\uDC46',\n 'police_car': '\\uD83D\\uDE93',\n 'policewoman': '\\uD83D\\uDC6E‍\\u2640\\uFE0F',\n 'poodle': '\\uD83D\\uDC29',\n 'popcorn': '\\uD83C\\uDF7F',\n 'post_office': '\\uD83C\\uDFE3',\n 'postal_horn': '\\uD83D\\uDCEF',\n 'postbox': '\\uD83D\\uDCEE',\n 'potable_water': '\\uD83D\\uDEB0',\n 'potato': '\\uD83E\\uDD54',\n 'pouch': '\\uD83D\\uDC5D',\n 'poultry_leg': '\\uD83C\\uDF57',\n 'pound': '\\uD83D\\uDCB7',\n 'rage': '\\uD83D\\uDE21',\n 'pouting_cat': '\\uD83D\\uDE3E',\n 'pouting_man': '\\uD83D\\uDE4E‍\\u2642\\uFE0F',\n 'pray': '\\uD83D\\uDE4F',\n 'prayer_beads': '\\uD83D\\uDCFF',\n 'pregnant_woman': '\\uD83E\\uDD30',\n 'previous_track_button': '\\u23EE',\n 'prince': '\\uD83E\\uDD34',\n 'princess': '\\uD83D\\uDC78',\n 'printer': '\\uD83D\\uDDA8',\n 'purple_heart': '\\uD83D\\uDC9C',\n 'purse': '\\uD83D\\uDC5B',\n 'pushpin': '\\uD83D\\uDCCC',\n 'put_litter_in_its_place': '\\uD83D\\uDEAE',\n 'question': '\\u2753',\n 'rabbit': '\\uD83D\\uDC30',\n 'rabbit2': '\\uD83D\\uDC07',\n 'racehorse': '\\uD83D\\uDC0E',\n 'racing_car': '\\uD83C\\uDFCE',\n 'radio': '\\uD83D\\uDCFB',\n 'radio_button': '\\uD83D\\uDD18',\n 'radioactive': '\\u2622\\uFE0F',\n 'railway_car': '\\uD83D\\uDE83',\n 'railway_track': '\\uD83D\\uDEE4',\n 'rainbow': '\\uD83C\\uDF08',\n 'rainbow_flag': '\\uD83C\\uDFF3\\uFE0F‍\\uD83C\\uDF08',\n 'raised_back_of_hand': '\\uD83E\\uDD1A',\n 'raised_hand_with_fingers_splayed': '\\uD83D\\uDD90',\n 'raised_hands': '\\uD83D\\uDE4C',\n 'raising_hand_woman': '\\uD83D\\uDE4B',\n 'raising_hand_man': '\\uD83D\\uDE4B‍\\u2642\\uFE0F',\n 'ram': '\\uD83D\\uDC0F',\n 'ramen': '\\uD83C\\uDF5C',\n 'rat': '\\uD83D\\uDC00',\n 'record_button': '\\u23FA',\n 'recycle': '\\u267B\\uFE0F',\n 'red_circle': '\\uD83D\\uDD34',\n 'registered': '\\xAE\\uFE0F',\n 'relaxed': '\\u263A\\uFE0F',\n 'relieved': '\\uD83D\\uDE0C',\n 'reminder_ribbon': '\\uD83C\\uDF97',\n 'repeat': '\\uD83D\\uDD01',\n 'repeat_one': '\\uD83D\\uDD02',\n 'rescue_worker_helmet': '\\u26D1',\n 'restroom': '\\uD83D\\uDEBB',\n 'revolving_hearts': '\\uD83D\\uDC9E',\n 'rewind': '\\u23EA',\n 'rhinoceros': '\\uD83E\\uDD8F',\n 'ribbon': '\\uD83C\\uDF80',\n 'rice': '\\uD83C\\uDF5A',\n 'rice_ball': '\\uD83C\\uDF59',\n 'rice_cracker': '\\uD83C\\uDF58',\n 'rice_scene': '\\uD83C\\uDF91',\n 'right_anger_bubble': '\\uD83D\\uDDEF',\n 'ring': '\\uD83D\\uDC8D',\n 'robot': '\\uD83E\\uDD16',\n 'rocket': '\\uD83D\\uDE80',\n 'rofl': '\\uD83E\\uDD23',\n 'roll_eyes': '\\uD83D\\uDE44',\n 'roller_coaster': '\\uD83C\\uDFA2',\n 'rooster': '\\uD83D\\uDC13',\n 'rose': '\\uD83C\\uDF39',\n 'rosette': '\\uD83C\\uDFF5',\n 'rotating_light': '\\uD83D\\uDEA8',\n 'round_pushpin': '\\uD83D\\uDCCD',\n 'rowing_man': '\\uD83D\\uDEA3',\n 'rowing_woman': '\\uD83D\\uDEA3‍\\u2640\\uFE0F',\n 'rugby_football': '\\uD83C\\uDFC9',\n 'running_man': '\\uD83C\\uDFC3',\n 'running_shirt_with_sash': '\\uD83C\\uDFBD',\n 'running_woman': '\\uD83C\\uDFC3‍\\u2640\\uFE0F',\n 'sa': '\\uD83C\\uDE02\\uFE0F',\n 'sagittarius': '\\u2650\\uFE0F',\n 'sake': '\\uD83C\\uDF76',\n 'sandal': '\\uD83D\\uDC61',\n 'santa': '\\uD83C\\uDF85',\n 'satellite': '\\uD83D\\uDCE1',\n 'saxophone': '\\uD83C\\uDFB7',\n 'school': '\\uD83C\\uDFEB',\n 'school_satchel': '\\uD83C\\uDF92',\n 'scissors': '\\u2702\\uFE0F',\n 'scorpion': '\\uD83E\\uDD82',\n 'scorpius': '\\u264F\\uFE0F',\n 'scream': '\\uD83D\\uDE31',\n 'scream_cat': '\\uD83D\\uDE40',\n 'scroll': '\\uD83D\\uDCDC',\n 'seat': '\\uD83D\\uDCBA',\n 'secret': '\\u3299\\uFE0F',\n 'see_no_evil': '\\uD83D\\uDE48',\n 'seedling': '\\uD83C\\uDF31',\n 'selfie': '\\uD83E\\uDD33',\n 'shallow_pan_of_food': '\\uD83E\\uDD58',\n 'shamrock': '\\u2618\\uFE0F',\n 'shark': '\\uD83E\\uDD88',\n 'shaved_ice': '\\uD83C\\uDF67',\n 'sheep': '\\uD83D\\uDC11',\n 'shell': '\\uD83D\\uDC1A',\n 'shield': '\\uD83D\\uDEE1',\n 'shinto_shrine': '\\u26E9',\n 'ship': '\\uD83D\\uDEA2',\n 'shirt': '\\uD83D\\uDC55',\n 'shopping': '\\uD83D\\uDECD',\n 'shopping_cart': '\\uD83D\\uDED2',\n 'shower': '\\uD83D\\uDEBF',\n 'shrimp': '\\uD83E\\uDD90',\n 'signal_strength': '\\uD83D\\uDCF6',\n 'six_pointed_star': '\\uD83D\\uDD2F',\n 'ski': '\\uD83C\\uDFBF',\n 'skier': '\\u26F7',\n 'skull': '\\uD83D\\uDC80',\n 'skull_and_crossbones': '\\u2620\\uFE0F',\n 'sleeping': '\\uD83D\\uDE34',\n 'sleeping_bed': '\\uD83D\\uDECC',\n 'sleepy': '\\uD83D\\uDE2A',\n 'slightly_frowning_face': '\\uD83D\\uDE41',\n 'slightly_smiling_face': '\\uD83D\\uDE42',\n 'slot_machine': '\\uD83C\\uDFB0',\n 'small_airplane': '\\uD83D\\uDEE9',\n 'small_blue_diamond': '\\uD83D\\uDD39',\n 'small_orange_diamond': '\\uD83D\\uDD38',\n 'small_red_triangle': '\\uD83D\\uDD3A',\n 'small_red_triangle_down': '\\uD83D\\uDD3B',\n 'smile': '\\uD83D\\uDE04',\n 'smile_cat': '\\uD83D\\uDE38',\n 'smiley': '\\uD83D\\uDE03',\n 'smiley_cat': '\\uD83D\\uDE3A',\n 'smiling_imp': '\\uD83D\\uDE08',\n 'smirk': '\\uD83D\\uDE0F',\n 'smirk_cat': '\\uD83D\\uDE3C',\n 'smoking': '\\uD83D\\uDEAC',\n 'snail': '\\uD83D\\uDC0C',\n 'snake': '\\uD83D\\uDC0D',\n 'sneezing_face': '\\uD83E\\uDD27',\n 'snowboarder': '\\uD83C\\uDFC2',\n 'snowflake': '\\u2744\\uFE0F',\n 'snowman': '\\u26C4\\uFE0F',\n 'snowman_with_snow': '\\u2603\\uFE0F',\n 'sob': '\\uD83D\\uDE2D',\n 'soccer': '\\u26BD\\uFE0F',\n 'soon': '\\uD83D\\uDD1C',\n 'sos': '\\uD83C\\uDD98',\n 'sound': '\\uD83D\\uDD09',\n 'space_invader': '\\uD83D\\uDC7E',\n 'spades': '\\u2660\\uFE0F',\n 'spaghetti': '\\uD83C\\uDF5D',\n 'sparkle': '\\u2747\\uFE0F',\n 'sparkler': '\\uD83C\\uDF87',\n 'sparkles': '\\u2728',\n 'sparkling_heart': '\\uD83D\\uDC96',\n 'speak_no_evil': '\\uD83D\\uDE4A',\n 'speaker': '\\uD83D\\uDD08',\n 'speaking_head': '\\uD83D\\uDDE3',\n 'speech_balloon': '\\uD83D\\uDCAC',\n 'speedboat': '\\uD83D\\uDEA4',\n 'spider': '\\uD83D\\uDD77',\n 'spider_web': '\\uD83D\\uDD78',\n 'spiral_calendar': '\\uD83D\\uDDD3',\n 'spiral_notepad': '\\uD83D\\uDDD2',\n 'spoon': '\\uD83E\\uDD44',\n 'squid': '\\uD83E\\uDD91',\n 'stadium': '\\uD83C\\uDFDF',\n 'star': '\\u2B50\\uFE0F',\n 'star2': '\\uD83C\\uDF1F',\n 'star_and_crescent': '\\u262A\\uFE0F',\n 'star_of_david': '\\u2721\\uFE0F',\n 'stars': '\\uD83C\\uDF20',\n 'station': '\\uD83D\\uDE89',\n 'statue_of_liberty': '\\uD83D\\uDDFD',\n 'steam_locomotive': '\\uD83D\\uDE82',\n 'stew': '\\uD83C\\uDF72',\n 'stop_button': '\\u23F9',\n 'stop_sign': '\\uD83D\\uDED1',\n 'stopwatch': '\\u23F1',\n 'straight_ruler': '\\uD83D\\uDCCF',\n 'strawberry': '\\uD83C\\uDF53',\n 'stuck_out_tongue': '\\uD83D\\uDE1B',\n 'stuck_out_tongue_closed_eyes': '\\uD83D\\uDE1D',\n 'stuck_out_tongue_winking_eye': '\\uD83D\\uDE1C',\n 'studio_microphone': '\\uD83C\\uDF99',\n 'stuffed_flatbread': '\\uD83E\\uDD59',\n 'sun_behind_large_cloud': '\\uD83C\\uDF25',\n 'sun_behind_rain_cloud': '\\uD83C\\uDF26',\n 'sun_behind_small_cloud': '\\uD83C\\uDF24',\n 'sun_with_face': '\\uD83C\\uDF1E',\n 'sunflower': '\\uD83C\\uDF3B',\n 'sunglasses': '\\uD83D\\uDE0E',\n 'sunny': '\\u2600\\uFE0F',\n 'sunrise': '\\uD83C\\uDF05',\n 'sunrise_over_mountains': '\\uD83C\\uDF04',\n 'surfing_man': '\\uD83C\\uDFC4',\n 'surfing_woman': '\\uD83C\\uDFC4‍\\u2640\\uFE0F',\n 'sushi': '\\uD83C\\uDF63',\n 'suspension_railway': '\\uD83D\\uDE9F',\n 'sweat': '\\uD83D\\uDE13',\n 'sweat_drops': '\\uD83D\\uDCA6',\n 'sweat_smile': '\\uD83D\\uDE05',\n 'sweet_potato': '\\uD83C\\uDF60',\n 'swimming_man': '\\uD83C\\uDFCA',\n 'swimming_woman': '\\uD83C\\uDFCA‍\\u2640\\uFE0F',\n 'symbols': '\\uD83D\\uDD23',\n 'synagogue': '\\uD83D\\uDD4D',\n 'syringe': '\\uD83D\\uDC89',\n 'taco': '\\uD83C\\uDF2E',\n 'tada': '\\uD83C\\uDF89',\n 'tanabata_tree': '\\uD83C\\uDF8B',\n 'taurus': '\\u2649\\uFE0F',\n 'taxi': '\\uD83D\\uDE95',\n 'tea': '\\uD83C\\uDF75',\n 'telephone_receiver': '\\uD83D\\uDCDE',\n 'telescope': '\\uD83D\\uDD2D',\n 'tennis': '\\uD83C\\uDFBE',\n 'tent': '\\u26FA\\uFE0F',\n 'thermometer': '\\uD83C\\uDF21',\n 'thinking': '\\uD83E\\uDD14',\n 'thought_balloon': '\\uD83D\\uDCAD',\n 'ticket': '\\uD83C\\uDFAB',\n 'tickets': '\\uD83C\\uDF9F',\n 'tiger': '\\uD83D\\uDC2F',\n 'tiger2': '\\uD83D\\uDC05',\n 'timer_clock': '\\u23F2',\n 'tipping_hand_man': '\\uD83D\\uDC81‍\\u2642\\uFE0F',\n 'tired_face': '\\uD83D\\uDE2B',\n 'tm': '\\u2122\\uFE0F',\n 'toilet': '\\uD83D\\uDEBD',\n 'tokyo_tower': '\\uD83D\\uDDFC',\n 'tomato': '\\uD83C\\uDF45',\n 'tongue': '\\uD83D\\uDC45',\n 'top': '\\uD83D\\uDD1D',\n 'tophat': '\\uD83C\\uDFA9',\n 'tornado': '\\uD83C\\uDF2A',\n 'trackball': '\\uD83D\\uDDB2',\n 'tractor': '\\uD83D\\uDE9C',\n 'traffic_light': '\\uD83D\\uDEA5',\n 'train': '\\uD83D\\uDE8B',\n 'train2': '\\uD83D\\uDE86',\n 'tram': '\\uD83D\\uDE8A',\n 'triangular_flag_on_post': '\\uD83D\\uDEA9',\n 'triangular_ruler': '\\uD83D\\uDCD0',\n 'trident': '\\uD83D\\uDD31',\n 'triumph': '\\uD83D\\uDE24',\n 'trolleybus': '\\uD83D\\uDE8E',\n 'trophy': '\\uD83C\\uDFC6',\n 'tropical_drink': '\\uD83C\\uDF79',\n 'tropical_fish': '\\uD83D\\uDC20',\n 'truck': '\\uD83D\\uDE9A',\n 'trumpet': '\\uD83C\\uDFBA',\n 'tulip': '\\uD83C\\uDF37',\n 'tumbler_glass': '\\uD83E\\uDD43',\n 'turkey': '\\uD83E\\uDD83',\n 'turtle': '\\uD83D\\uDC22',\n 'tv': '\\uD83D\\uDCFA',\n 'twisted_rightwards_arrows': '\\uD83D\\uDD00',\n 'two_hearts': '\\uD83D\\uDC95',\n 'two_men_holding_hands': '\\uD83D\\uDC6C',\n 'two_women_holding_hands': '\\uD83D\\uDC6D',\n 'u5272': '\\uD83C\\uDE39',\n 'u5408': '\\uD83C\\uDE34',\n 'u55b6': '\\uD83C\\uDE3A',\n 'u6307': '\\uD83C\\uDE2F\\uFE0F',\n 'u6708': '\\uD83C\\uDE37\\uFE0F',\n 'u6709': '\\uD83C\\uDE36',\n 'u6e80': '\\uD83C\\uDE35',\n 'u7121': '\\uD83C\\uDE1A\\uFE0F',\n 'u7533': '\\uD83C\\uDE38',\n 'u7981': '\\uD83C\\uDE32',\n 'u7a7a': '\\uD83C\\uDE33',\n 'umbrella': '\\u2614\\uFE0F',\n 'unamused': '\\uD83D\\uDE12',\n 'underage': '\\uD83D\\uDD1E',\n 'unicorn': '\\uD83E\\uDD84',\n 'unlock': '\\uD83D\\uDD13',\n 'up': '\\uD83C\\uDD99',\n 'upside_down_face': '\\uD83D\\uDE43',\n 'v': '\\u270C\\uFE0F',\n 'vertical_traffic_light': '\\uD83D\\uDEA6',\n 'vhs': '\\uD83D\\uDCFC',\n 'vibration_mode': '\\uD83D\\uDCF3',\n 'video_camera': '\\uD83D\\uDCF9',\n 'video_game': '\\uD83C\\uDFAE',\n 'violin': '\\uD83C\\uDFBB',\n 'virgo': '\\u264D\\uFE0F',\n 'volcano': '\\uD83C\\uDF0B',\n 'volleyball': '\\uD83C\\uDFD0',\n 'vs': '\\uD83C\\uDD9A',\n 'vulcan_salute': '\\uD83D\\uDD96',\n 'walking_man': '\\uD83D\\uDEB6',\n 'walking_woman': '\\uD83D\\uDEB6‍\\u2640\\uFE0F',\n 'waning_crescent_moon': '\\uD83C\\uDF18',\n 'waning_gibbous_moon': '\\uD83C\\uDF16',\n 'warning': '\\u26A0\\uFE0F',\n 'wastebasket': '\\uD83D\\uDDD1',\n 'watch': '\\u231A\\uFE0F',\n 'water_buffalo': '\\uD83D\\uDC03',\n 'watermelon': '\\uD83C\\uDF49',\n 'wave': '\\uD83D\\uDC4B',\n 'wavy_dash': '\\u3030\\uFE0F',\n 'waxing_crescent_moon': '\\uD83C\\uDF12',\n 'wc': '\\uD83D\\uDEBE',\n 'weary': '\\uD83D\\uDE29',\n 'wedding': '\\uD83D\\uDC92',\n 'weight_lifting_man': '\\uD83C\\uDFCB\\uFE0F',\n 'weight_lifting_woman': '\\uD83C\\uDFCB\\uFE0F‍\\u2640\\uFE0F',\n 'whale': '\\uD83D\\uDC33',\n 'whale2': '\\uD83D\\uDC0B',\n 'wheel_of_dharma': '\\u2638\\uFE0F',\n 'wheelchair': '\\u267F\\uFE0F',\n 'white_check_mark': '\\u2705',\n 'white_circle': '\\u26AA\\uFE0F',\n 'white_flag': '\\uD83C\\uDFF3\\uFE0F',\n 'white_flower': '\\uD83D\\uDCAE',\n 'white_large_square': '\\u2B1C\\uFE0F',\n 'white_medium_small_square': '\\u25FD\\uFE0F',\n 'white_medium_square': '\\u25FB\\uFE0F',\n 'white_small_square': '\\u25AB\\uFE0F',\n 'white_square_button': '\\uD83D\\uDD33',\n 'wilted_flower': '\\uD83E\\uDD40',\n 'wind_chime': '\\uD83C\\uDF90',\n 'wind_face': '\\uD83C\\uDF2C',\n 'wine_glass': '\\uD83C\\uDF77',\n 'wink': '\\uD83D\\uDE09',\n 'wolf': '\\uD83D\\uDC3A',\n 'woman': '\\uD83D\\uDC69',\n 'woman_artist': '\\uD83D\\uDC69‍\\uD83C\\uDFA8',\n 'woman_astronaut': '\\uD83D\\uDC69‍\\uD83D\\uDE80',\n 'woman_cartwheeling': '\\uD83E\\uDD38‍\\u2640\\uFE0F',\n 'woman_cook': '\\uD83D\\uDC69‍\\uD83C\\uDF73',\n 'woman_facepalming': '\\uD83E\\uDD26‍\\u2640\\uFE0F',\n 'woman_factory_worker': '\\uD83D\\uDC69‍\\uD83C\\uDFED',\n 'woman_farmer': '\\uD83D\\uDC69‍\\uD83C\\uDF3E',\n 'woman_firefighter': '\\uD83D\\uDC69‍\\uD83D\\uDE92',\n 'woman_health_worker': '\\uD83D\\uDC69‍\\u2695\\uFE0F',\n 'woman_judge': '\\uD83D\\uDC69‍\\u2696\\uFE0F',\n 'woman_juggling': '\\uD83E\\uDD39‍\\u2640\\uFE0F',\n 'woman_mechanic': '\\uD83D\\uDC69‍\\uD83D\\uDD27',\n 'woman_office_worker': '\\uD83D\\uDC69‍\\uD83D\\uDCBC',\n 'woman_pilot': '\\uD83D\\uDC69‍\\u2708\\uFE0F',\n 'woman_playing_handball': '\\uD83E\\uDD3E‍\\u2640\\uFE0F',\n 'woman_playing_water_polo': '\\uD83E\\uDD3D‍\\u2640\\uFE0F',\n 'woman_scientist': '\\uD83D\\uDC69‍\\uD83D\\uDD2C',\n 'woman_shrugging': '\\uD83E\\uDD37‍\\u2640\\uFE0F',\n 'woman_singer': '\\uD83D\\uDC69‍\\uD83C\\uDFA4',\n 'woman_student': '\\uD83D\\uDC69‍\\uD83C\\uDF93',\n 'woman_teacher': '\\uD83D\\uDC69‍\\uD83C\\uDFEB',\n 'woman_technologist': '\\uD83D\\uDC69‍\\uD83D\\uDCBB',\n 'woman_with_turban': '\\uD83D\\uDC73‍\\u2640\\uFE0F',\n 'womans_clothes': '\\uD83D\\uDC5A',\n 'womans_hat': '\\uD83D\\uDC52',\n 'women_wrestling': '\\uD83E\\uDD3C‍\\u2640\\uFE0F',\n 'womens': '\\uD83D\\uDEBA',\n 'world_map': '\\uD83D\\uDDFA',\n 'worried': '\\uD83D\\uDE1F',\n 'wrench': '\\uD83D\\uDD27',\n 'writing_hand': '\\u270D\\uFE0F',\n 'x': '\\u274C',\n 'yellow_heart': '\\uD83D\\uDC9B',\n 'yen': '\\uD83D\\uDCB4',\n 'yin_yang': '\\u262F\\uFE0F',\n 'yum': '\\uD83D\\uDE0B',\n 'zap': '\\u26A1\\uFE0F',\n 'zipper_mouth_face': '\\uD83E\\uDD10',\n 'zzz': '\\uD83D\\uDCA4',\n\n /* special emojis :P */\n 'octocat': '\":octocat:\"',\n 'showdown': 'S'\n };\n\n /**\n * Created by Estevao on 31-05-2015.\n */\n\n /**\n * Showdown Converter class\n * @class\n * @param {object} [converterOptions]\n * @returns {Converter}\n */\n showdown.Converter = function (converterOptions) {\n 'use strict';\n\n var\n /**\n * Options used by this converter\n * @private\n * @type {{}}\n */\n options = {},\n\n\n /**\n * Language extensions used by this converter\n * @private\n * @type {Array}\n */\n langExtensions = [],\n\n\n /**\n * Output modifiers extensions used by this converter\n * @private\n * @type {Array}\n */\n outputModifiers = [],\n\n\n /**\n * Event listeners\n * @private\n * @type {{}}\n */\n listeners = {},\n\n\n /**\n * The flavor set in this converter\n */\n setConvFlavor = setFlavor,\n\n\n /**\n * Metadata of the document\n * @type {{parsed: {}, raw: string, format: string}}\n */\n metadata = {\n parsed: {},\n raw: '',\n format: ''\n };\n\n _constructor();\n\n /**\n * Converter constructor\n * @private\n */\n function _constructor() {\n converterOptions = converterOptions || {};\n\n for (var gOpt in globalOptions) {\n if (globalOptions.hasOwnProperty(gOpt)) {\n options[gOpt] = globalOptions[gOpt];\n }\n }\n\n // Merge options\n if (typeof converterOptions === 'object') {\n for (var opt in converterOptions) {\n if (converterOptions.hasOwnProperty(opt)) {\n options[opt] = converterOptions[opt];\n }\n }\n } else {\n throw Error('Converter expects the passed parameter to be an object, but ' + typeof converterOptions + ' was passed instead.');\n }\n\n if (options.extensions) {\n showdown.helper.forEach(options.extensions, _parseExtension);\n }\n }\n\n /**\n * Parse extension\n * @param {*} ext\n * @param {string} [name='']\n * @private\n */\n function _parseExtension(ext, name) {\n\n name = name || null;\n // If it's a string, the extension was previously loaded\n if (showdown.helper.isString(ext)) {\n ext = showdown.helper.stdExtName(ext);\n name = ext;\n\n // LEGACY_SUPPORT CODE\n if (showdown.extensions[ext]) {\n console.warn('DEPRECATION WARNING: ' + ext + ' is an old extension that uses a deprecated loading method.' + 'Please inform the developer that the extension should be updated!');\n legacyExtensionLoading(showdown.extensions[ext], ext);\n return;\n // END LEGACY SUPPORT CODE\n } else if (!showdown.helper.isUndefined(extensions[ext])) {\n ext = extensions[ext];\n } else {\n throw Error('Extension \"' + ext + '\" could not be loaded. It was either not found or is not a valid extension.');\n }\n }\n\n if (typeof ext === 'function') {\n ext = ext();\n }\n\n if (!showdown.helper.isArray(ext)) {\n ext = [ext];\n }\n\n var validExt = validate(ext, name);\n if (!validExt.valid) {\n throw Error(validExt.error);\n }\n\n for (var i = 0; i < ext.length; ++i) {\n switch (ext[i].type) {\n\n case 'lang':\n langExtensions.push(ext[i]);\n break;\n\n case 'output':\n outputModifiers.push(ext[i]);\n break;\n }\n if (ext[i].hasOwnProperty('listeners')) {\n for (var ln in ext[i].listeners) {\n if (ext[i].listeners.hasOwnProperty(ln)) {\n listen(ln, ext[i].listeners[ln]);\n }\n }\n }\n }\n }\n\n /**\n * LEGACY_SUPPORT\n * @param {*} ext\n * @param {string} name\n */\n function legacyExtensionLoading(ext, name) {\n if (typeof ext === 'function') {\n ext = ext(new showdown.Converter());\n }\n if (!showdown.helper.isArray(ext)) {\n ext = [ext];\n }\n var valid = validate(ext, name);\n\n if (!valid.valid) {\n throw Error(valid.error);\n }\n\n for (var i = 0; i < ext.length; ++i) {\n switch (ext[i].type) {\n case 'lang':\n langExtensions.push(ext[i]);\n break;\n case 'output':\n outputModifiers.push(ext[i]);\n break;\n default:\n // should never reach here\n throw Error('Extension loader error: Type unrecognized!!!');\n }\n }\n }\n\n /**\n * Listen to an event\n * @param {string} name\n * @param {function} callback\n */\n function listen(name, callback) {\n if (!showdown.helper.isString(name)) {\n throw Error('Invalid argument in converter.listen() method: name must be a string, but ' + typeof name + ' given');\n }\n\n if (typeof callback !== 'function') {\n throw Error('Invalid argument in converter.listen() method: callback must be a function, but ' + typeof callback + ' given');\n }\n\n if (!listeners.hasOwnProperty(name)) {\n listeners[name] = [];\n }\n listeners[name].push(callback);\n }\n\n function rTrimInputText(text) {\n var rsp = text.match(/^\\s*/)[0].length,\n rgx = new RegExp('^\\\\s{0,' + rsp + '}', 'gm');\n return text.replace(rgx, '');\n }\n\n /**\n * Dispatch an event\n * @private\n * @param {string} evtName Event name\n * @param {string} text Text\n * @param {{}} options Converter Options\n * @param {{}} globals\n * @returns {string}\n */\n this._dispatch = function dispatch(evtName, text, options, globals) {\n if (listeners.hasOwnProperty(evtName)) {\n for (var ei = 0; ei < listeners[evtName].length; ++ei) {\n var nText = listeners[evtName][ei](evtName, text, this, options, globals);\n if (nText && typeof nText !== 'undefined') {\n text = nText;\n }\n }\n }\n return text;\n };\n\n /**\n * Listen to an event\n * @param {string} name\n * @param {function} callback\n * @returns {showdown.Converter}\n */\n this.listen = function (name, callback) {\n listen(name, callback);\n return this;\n };\n\n /**\n * Converts a markdown string into HTML\n * @param {string} text\n * @returns {*}\n */\n this.makeHtml = function (text) {\n //check if text is not falsy\n if (!text) {\n return text;\n }\n\n var globals = {\n gHtmlBlocks: [],\n gHtmlMdBlocks: [],\n gHtmlSpans: [],\n gUrls: {},\n gTitles: {},\n gDimensions: {},\n gListLevel: 0,\n hashLinkCounts: {},\n langExtensions: langExtensions,\n outputModifiers: outputModifiers,\n converter: this,\n ghCodeBlocks: [],\n metadata: {\n parsed: {},\n raw: '',\n format: ''\n }\n };\n\n // This lets us use ¨ trema as an escape char to avoid md5 hashes\n // The choice of character is arbitrary; anything that isn't\n // magic in Markdown will work.\n text = text.replace(/¨/g, '¨T');\n\n // Replace $ with ¨D\n // RegExp interprets $ as a special character\n // when it's in a replacement string\n text = text.replace(/\\$/g, '¨D');\n\n // Standardize line endings\n text = text.replace(/\\r\\n/g, '\\n'); // DOS to Unix\n text = text.replace(/\\r/g, '\\n'); // Mac to Unix\n\n // Stardardize line spaces\n text = text.replace(/\\u00A0/g, ' ');\n\n if (options.smartIndentationFix) {\n text = rTrimInputText(text);\n }\n\n // Make sure text begins and ends with a couple of newlines:\n text = '\\n\\n' + text + '\\n\\n';\n\n // detab\n text = showdown.subParser('detab')(text, options, globals);\n\n /**\n * Strip any lines consisting only of spaces and tabs.\n * This makes subsequent regexs easier to write, because we can\n * match consecutive blank lines with /\\n+/ instead of something\n * contorted like /[ \\t]*\\n+/\n */\n text = text.replace(/^[ \\t]+$/mg, '');\n\n //run languageExtensions\n showdown.helper.forEach(langExtensions, function (ext) {\n text = showdown.subParser('runExtension')(ext, text, options, globals);\n });\n\n // run the sub parsers\n text = showdown.subParser('metadata')(text, options, globals);\n text = showdown.subParser('hashPreCodeTags')(text, options, globals);\n text = showdown.subParser('githubCodeBlocks')(text, options, globals);\n text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n text = showdown.subParser('hashCodeTags')(text, options, globals);\n text = showdown.subParser('stripLinkDefinitions')(text, options, globals);\n text = showdown.subParser('blockGamut')(text, options, globals);\n text = showdown.subParser('unhashHTMLSpans')(text, options, globals);\n text = showdown.subParser('unescapeSpecialChars')(text, options, globals);\n\n // attacklab: Restore dollar signs\n text = text.replace(/¨D/g, '$$');\n\n // attacklab: Restore tremas\n text = text.replace(/¨T/g, '¨');\n\n // render a complete html document instead of a partial if the option is enabled\n text = showdown.subParser('completeHTMLDocument')(text, options, globals);\n\n // Run output modifiers\n showdown.helper.forEach(outputModifiers, function (ext) {\n text = showdown.subParser('runExtension')(ext, text, options, globals);\n });\n\n // update metadata\n metadata = globals.metadata;\n return text;\n };\n\n /**\n * Converts an HTML string into a markdown string\n * @param src\n * @param [HTMLParser] A WHATWG DOM and HTML parser, such as JSDOM. If none is supplied, window.document will be used.\n * @returns {string}\n */\n this.makeMarkdown = this.makeMd = function (src, HTMLParser) {\n\n // replace \\r\\n with \\n\n src = src.replace(/\\r\\n/g, '\\n');\n src = src.replace(/\\r/g, '\\n'); // old macs\n\n // due to an edge case, we need to find this: > <\n // to prevent removing of non silent white spaces\n // ex: this is sparta\n src = src.replace(/>[ \\t]+¨NBSP;<');\n\n if (!HTMLParser) {\n if (window && window.document) {\n HTMLParser = window.document;\n } else {\n throw new Error('HTMLParser is undefined. If in a webworker or nodejs environment, you need to provide a WHATWG DOM and HTML such as JSDOM');\n }\n }\n\n var doc = HTMLParser.createElement('div');\n doc.innerHTML = src;\n\n var globals = {\n preList: substitutePreCodeTags(doc)\n };\n\n // remove all newlines and collapse spaces\n clean(doc);\n\n // some stuff, like accidental reference links must now be escaped\n // TODO\n // doc.innerHTML = doc.innerHTML.replace(/\\[[\\S\\t ]]/);\n\n var nodes = doc.childNodes,\n mdDoc = '';\n\n for (var i = 0; i < nodes.length; i++) {\n mdDoc += showdown.subParser('makeMarkdown.node')(nodes[i], globals);\n }\n\n function clean(node) {\n for (var n = 0; n < node.childNodes.length; ++n) {\n var child = node.childNodes[n];\n if (child.nodeType === 3) {\n if (!/\\S/.test(child.nodeValue)) {\n node.removeChild(child);\n --n;\n } else {\n child.nodeValue = child.nodeValue.split('\\n').join(' ');\n child.nodeValue = child.nodeValue.replace(/(\\s)+/g, '$1');\n }\n } else if (child.nodeType === 1) {\n clean(child);\n }\n }\n }\n\n // find all pre tags and replace contents with placeholder\n // we need this so that we can remove all indentation from html\n // to ease up parsing\n function substitutePreCodeTags(doc) {\n\n var pres = doc.querySelectorAll('pre'),\n presPH = [];\n\n for (var i = 0; i < pres.length; ++i) {\n\n if (pres[i].childElementCount === 1 && pres[i].firstChild.tagName.toLowerCase() === 'code') {\n var content = pres[i].firstChild.innerHTML.trim(),\n language = pres[i].firstChild.getAttribute('data-language') || '';\n\n // if data-language attribute is not defined, then we look for class language-*\n if (language === '') {\n var classes = pres[i].firstChild.className.split(' ');\n for (var c = 0; c < classes.length; ++c) {\n var matches = classes[c].match(/^language-(.+)$/);\n if (matches !== null) {\n language = matches[1];\n break;\n }\n }\n }\n\n // unescape html entities in content\n content = showdown.helper.unescapeHTMLEntities(content);\n\n presPH.push(content);\n pres[i].outerHTML = '';\n } else {\n presPH.push(pres[i].innerHTML);\n pres[i].innerHTML = '';\n pres[i].setAttribute('prenum', i.toString());\n }\n }\n return presPH;\n }\n\n return mdDoc;\n };\n\n /**\n * Set an option of this Converter instance\n * @param {string} key\n * @param {*} value\n */\n this.setOption = function (key, value) {\n options[key] = value;\n };\n\n /**\n * Get the option of this Converter instance\n * @param {string} key\n * @returns {*}\n */\n this.getOption = function (key) {\n return options[key];\n };\n\n /**\n * Get the options of this Converter instance\n * @returns {{}}\n */\n this.getOptions = function () {\n return options;\n };\n\n /**\n * Add extension to THIS converter\n * @param {{}} extension\n * @param {string} [name=null]\n */\n this.addExtension = function (extension, name) {\n name = name || null;\n _parseExtension(extension, name);\n };\n\n /**\n * Use a global registered extension with THIS converter\n * @param {string} extensionName Name of the previously registered extension\n */\n this.useExtension = function (extensionName) {\n _parseExtension(extensionName);\n };\n\n /**\n * Set the flavor THIS converter should use\n * @param {string} name\n */\n this.setFlavor = function (name) {\n if (!flavor.hasOwnProperty(name)) {\n throw Error(name + ' flavor was not found');\n }\n var preset = flavor[name];\n setConvFlavor = name;\n for (var option in preset) {\n if (preset.hasOwnProperty(option)) {\n options[option] = preset[option];\n }\n }\n };\n\n /**\n * Get the currently set flavor of this converter\n * @returns {string}\n */\n this.getFlavor = function () {\n return setConvFlavor;\n };\n\n /**\n * Remove an extension from THIS converter.\n * Note: This is a costly operation. It's better to initialize a new converter\n * and specify the extensions you wish to use\n * @param {Array} extension\n */\n this.removeExtension = function (extension) {\n if (!showdown.helper.isArray(extension)) {\n extension = [extension];\n }\n for (var a = 0; a < extension.length; ++a) {\n var ext = extension[a];\n for (var i = 0; i < langExtensions.length; ++i) {\n if (langExtensions[i] === ext) {\n langExtensions[i].splice(i, 1);\n }\n }\n for (var ii = 0; ii < outputModifiers.length; ++i) {\n if (outputModifiers[ii] === ext) {\n outputModifiers[ii].splice(i, 1);\n }\n }\n }\n };\n\n /**\n * Get all extension of THIS converter\n * @returns {{language: Array, output: Array}}\n */\n this.getAllExtensions = function () {\n return {\n language: langExtensions,\n output: outputModifiers\n };\n };\n\n /**\n * Get the metadata of the previously parsed document\n * @param raw\n * @returns {string|{}}\n */\n this.getMetadata = function (raw) {\n if (raw) {\n return metadata.raw;\n } else {\n return metadata.parsed;\n }\n };\n\n /**\n * Get the metadata format of the previously parsed document\n * @returns {string}\n */\n this.getMetadataFormat = function () {\n return metadata.format;\n };\n\n /**\n * Private: set a single key, value metadata pair\n * @param {string} key\n * @param {string} value\n */\n this._setMetadataPair = function (key, value) {\n metadata.parsed[key] = value;\n };\n\n /**\n * Private: set metadata format\n * @param {string} format\n */\n this._setMetadataFormat = function (format) {\n metadata.format = format;\n };\n\n /**\n * Private: set metadata raw text\n * @param {string} raw\n */\n this._setMetadataRaw = function (raw) {\n metadata.raw = raw;\n };\n };\n\n /**\n * Turn Markdown link shortcuts into XHTML tags.\n */\n showdown.subParser('anchors', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('anchors.before', text, options, globals);\n\n var writeAnchorTag = function writeAnchorTag(wholeMatch, linkText, linkId, url, m5, m6, title) {\n if (showdown.helper.isUndefined(title)) {\n title = '';\n }\n linkId = linkId.toLowerCase();\n\n // Special case for explicit empty url\n if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n url = '';\n } else if (!url) {\n if (!linkId) {\n // lower-case and turn embedded newlines into spaces\n linkId = linkText.toLowerCase().replace(/ ?\\n/g, ' ');\n }\n url = '#' + linkId;\n\n if (!showdown.helper.isUndefined(globals.gUrls[linkId])) {\n url = globals.gUrls[linkId];\n if (!showdown.helper.isUndefined(globals.gTitles[linkId])) {\n title = globals.gTitles[linkId];\n }\n } else {\n return wholeMatch;\n }\n }\n\n //url = showdown.helper.escapeCharacters(url, '*_', false); // replaced line to improve performance\n url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n\n var result = '';\n\n return result;\n };\n\n // First, handle reference-style links: [link text] [id]\n text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)] ?(?:\\n *)?\\[(.*?)]()()()()/g, writeAnchorTag);\n\n // Next, inline-style links: [link text](url \"optional title\")\n // cases with crazy urls like ./image/cat1).png\n text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]?<([^>]*)>(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g, writeAnchorTag);\n\n // normal cases\n text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]??(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g, writeAnchorTag);\n\n // handle reference-style shortcuts: [link text]\n // These must come last in case you've also got [link test][1]\n // or [link test](/foo)\n text = text.replace(/\\[([^\\[\\]]+)]()()()()()/g, writeAnchorTag);\n\n // Lastly handle GithubMentions if option is enabled\n if (options.ghMentions) {\n text = text.replace(/(^|\\s)(\\\\)?(@([a-z\\d]+(?:[a-z\\d.-]+?[a-z\\d]+)*))/gmi, function (wm, st, escape, mentions, username) {\n if (escape === '\\\\') {\n return st + mentions;\n }\n\n //check if options.ghMentionsLink is a string\n if (!showdown.helper.isString(options.ghMentionsLink)) {\n throw new Error('ghMentionsLink option must be a string');\n }\n var lnk = options.ghMentionsLink.replace(/\\{u}/g, username),\n target = '';\n if (options.openLinksInNewWindow) {\n target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n }\n return st + '' + mentions + '';\n });\n }\n\n text = globals.converter._dispatch('anchors.after', text, options, globals);\n return text;\n });\n\n // url allowed chars [a-z\\d_.~:/?#[]@!$&'()*+,;=-]\n\n var simpleURLRegex = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+?\\.[^'\">\\s]+?)()(\\1)?(?=\\s|$)(?![\"<>])/gi,\n simpleURLRegex2 = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+\\.[^'\">\\s]+?)([.!?,()\\[\\]])?(\\1)?(?=\\s|$)(?![\"<>])/gi,\n delimUrlRegex = /()<(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+)()>()/gi,\n simpleMailRegex = /(^|\\s)(?:mailto:)?([A-Za-z0-9!#$%&'*+-/=?^_`{|}~.]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)(?=$|\\s)/gmi,\n delimMailRegex = /<()(?:mailto:)?([-.\\w]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)>/gi,\n replaceLink = function replaceLink(options) {\n 'use strict';\n\n return function (wm, leadingMagicChars, link, m2, m3, trailingPunctuation, trailingMagicChars) {\n link = link.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n var lnkTxt = link,\n append = '',\n target = '',\n lmc = leadingMagicChars || '',\n tmc = trailingMagicChars || '';\n if (/^www\\./i.test(link)) {\n link = link.replace(/^www\\./i, 'http://www.');\n }\n if (options.excludeTrailingPunctuationFromURLs && trailingPunctuation) {\n append = trailingPunctuation;\n }\n if (options.openLinksInNewWindow) {\n target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n }\n return lmc + '' + lnkTxt + '' + append + tmc;\n };\n },\n replaceMail = function replaceMail(options, globals) {\n 'use strict';\n\n return function (wholeMatch, b, mail) {\n var href = 'mailto:';\n b = b || '';\n mail = showdown.subParser('unescapeSpecialChars')(mail, options, globals);\n if (options.encodeEmails) {\n href = showdown.helper.encodeEmailAddress(href + mail);\n mail = showdown.helper.encodeEmailAddress(mail);\n } else {\n href = href + mail;\n }\n return b + '' + mail + '';\n };\n };\n\n showdown.subParser('autoLinks', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('autoLinks.before', text, options, globals);\n\n text = text.replace(delimUrlRegex, replaceLink(options));\n text = text.replace(delimMailRegex, replaceMail(options, globals));\n\n text = globals.converter._dispatch('autoLinks.after', text, options, globals);\n\n return text;\n });\n\n showdown.subParser('simplifiedAutoLinks', function (text, options, globals) {\n 'use strict';\n\n if (!options.simplifiedAutoLink) {\n return text;\n }\n\n text = globals.converter._dispatch('simplifiedAutoLinks.before', text, options, globals);\n\n if (options.excludeTrailingPunctuationFromURLs) {\n text = text.replace(simpleURLRegex2, replaceLink(options));\n } else {\n text = text.replace(simpleURLRegex, replaceLink(options));\n }\n text = text.replace(simpleMailRegex, replaceMail(options, globals));\n\n text = globals.converter._dispatch('simplifiedAutoLinks.after', text, options, globals);\n\n return text;\n });\n\n /**\n * These are all the transformations that form block-level\n * tags like paragraphs, headers, and list items.\n */\n showdown.subParser('blockGamut', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('blockGamut.before', text, options, globals);\n\n // we parse blockquotes first so that we can have headings and hrs\n // inside blockquotes\n text = showdown.subParser('blockQuotes')(text, options, globals);\n text = showdown.subParser('headers')(text, options, globals);\n\n // Do Horizontal Rules:\n text = showdown.subParser('horizontalRule')(text, options, globals);\n\n text = showdown.subParser('lists')(text, options, globals);\n text = showdown.subParser('codeBlocks')(text, options, globals);\n text = showdown.subParser('tables')(text, options, globals);\n\n // We already ran _HashHTMLBlocks() before, in Markdown(), but that\n // was to escape raw HTML in the original Markdown source. This time,\n // we're escaping the markup we've just created, so that we don't wrap\n //

tags around block-level tags.\n text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n text = showdown.subParser('paragraphs')(text, options, globals);\n\n text = globals.converter._dispatch('blockGamut.after', text, options, globals);\n\n return text;\n });\n\n showdown.subParser('blockQuotes', function (text, options, globals) {\n 'use strict';\n\n text = globals.converter._dispatch('blockQuotes.before', text, options, globals);\n\n // add a couple extra lines after the text and endtext mark\n text = text + '\\n\\n';\n\n var rgx = /(^ {0,3}>[ \\t]?.+\\n(.+\\n)*\\n*)+/gm;\n\n if (options.splitAdjacentBlockquotes) {\n rgx = /^ {0,3}>[\\s\\S]*?(?:\\n\\n)/gm;\n }\n\n text = text.replace(rgx, function (bq) {\n // attacklab: hack around Konqueror 3.5.4 bug:\n // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n bq = bq.replace(/^[ \\t]*>[ \\t]?/gm, ''); // trim one level of quoting\n\n // attacklab: clean up hack\n bq = bq.replace(/¨0/g, '');\n\n bq = bq.replace(/^[ \\t]+$/gm, ''); // trim whitespace-only lines\n bq = showdown.subParser('githubCodeBlocks')(bq, options, globals);\n bq = showdown.subParser('blockGamut')(bq, options, globals); // recurse\n\n bq = bq.replace(/(^|\\n)/g, '$1 ');\n // These leading spaces screw with 

 content, so we need to fix that:\n      bq = bq.replace(/(\\s*
[^\\r]+?<\\/pre>)/gm, function (wholeMatch, m1) {\n        var pre = m1;\n        // attacklab: hack around Konqueror 3.5.4 bug:\n        pre = pre.replace(/^  /mg, '¨0');\n        pre = pre.replace(/¨0/g, '');\n        return pre;\n      });\n\n      return showdown.subParser('hashBlock')('
\\n' + bq + '\\n
', options, globals);\n    });\n\n    text = globals.converter._dispatch('blockQuotes.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Process Markdown `
` blocks.\n   */\n  showdown.subParser('codeBlocks', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('codeBlocks.before', text, options, globals);\n\n    // sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n    text += '¨0';\n\n    var pattern = /(?:\\n\\n|^)((?:(?:[ ]{4}|\\t).*\\n+)+)(\\n*[ ]{0,3}[^ \\t\\n]|(?=¨0))/g;\n    text = text.replace(pattern, function (wholeMatch, m1, m2) {\n      var codeblock = m1,\n          nextChar = m2,\n          end = '\\n';\n\n      codeblock = showdown.subParser('outdent')(codeblock, options, globals);\n      codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n      codeblock = showdown.subParser('detab')(codeblock, options, globals);\n      codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n      codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing newlines\n\n      if (options.omitExtraWLInCodeBlocks) {\n        end = '';\n      }\n\n      codeblock = '
' + codeblock + end + '
';\n\n      return showdown.subParser('hashBlock')(codeblock, options, globals) + nextChar;\n    });\n\n    // strip sentinel\n    text = text.replace(/¨0/, '');\n\n    text = globals.converter._dispatch('codeBlocks.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   *\n   *   *  Backtick quotes are used for  spans.\n   *\n   *   *  You can use multiple backticks as the delimiters if you want to\n   *     include literal backticks in the code span. So, this input:\n   *\n   *         Just type ``foo `bar` baz`` at the prompt.\n   *\n   *       Will translate to:\n   *\n   *         
Just type foo `bar` baz at the prompt.
\n   *\n   *    There's no arbitrary limit to the number of backticks you\n   *    can use as delimters. If you need three consecutive backticks\n   *    in your code, use four for delimiters, etc.\n   *\n   *  *  You can use spaces to get literal backticks at the edges:\n   *\n   *         ... type `` `bar` `` ...\n   *\n   *       Turns to:\n   *\n   *         ... type `bar` ...\n   */\n  showdown.subParser('codeSpans', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('codeSpans.before', text, options, globals);\n\n    if (typeof text === 'undefined') {\n      text = '';\n    }\n    text = text.replace(/(^|[^\\\\])(`+)([^\\r]*?[^`])\\2(?!`)/gm, function (wholeMatch, m1, m2, m3) {\n      var c = m3;\n      c = c.replace(/^([ \\t]*)/g, ''); // leading whitespace\n      c = c.replace(/[ \\t]*$/g, ''); // trailing whitespace\n      c = showdown.subParser('encodeCode')(c, options, globals);\n      c = m1 + '' + c + '';\n      c = showdown.subParser('hashHTMLSpans')(c, options, globals);\n      return c;\n    });\n\n    text = globals.converter._dispatch('codeSpans.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Create a full HTML document from the processed markdown\n   */\n  showdown.subParser('completeHTMLDocument', function (text, options, globals) {\n    'use strict';\n\n    if (!options.completeHTMLDocument) {\n      return text;\n    }\n\n    text = globals.converter._dispatch('completeHTMLDocument.before', text, options, globals);\n\n    var doctype = 'html',\n        doctypeParsed = '\\n',\n        title = '',\n        charset = '\\n',\n        lang = '',\n        metadata = '';\n\n    if (typeof globals.metadata.parsed.doctype !== 'undefined') {\n      doctypeParsed = '\\n';\n      doctype = globals.metadata.parsed.doctype.toString().toLowerCase();\n      if (doctype === 'html' || doctype === 'html5') {\n        charset = '';\n      }\n    }\n\n    for (var meta in globals.metadata.parsed) {\n      if (globals.metadata.parsed.hasOwnProperty(meta)) {\n        switch (meta.toLowerCase()) {\n          case 'doctype':\n            break;\n\n          case 'title':\n            title = '' + globals.metadata.parsed.title + '\\n';\n            break;\n\n          case 'charset':\n            if (doctype === 'html' || doctype === 'html5') {\n              charset = '\\n';\n            } else {\n              charset = '\\n';\n            }\n            break;\n\n          case 'language':\n          case 'lang':\n            lang = ' lang=\"' + globals.metadata.parsed[meta] + '\"';\n            metadata += '\\n';\n            break;\n\n          default:\n            metadata += '\\n';\n        }\n      }\n    }\n\n    text = doctypeParsed + '\\n\\n' + title + charset + metadata + '\\n\\n' + text.trim() + '\\n\\n';\n\n    text = globals.converter._dispatch('completeHTMLDocument.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Convert all tabs to spaces\n   */\n  showdown.subParser('detab', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('detab.before', text, options, globals);\n\n    // expand first n-1 tabs\n    text = text.replace(/\\t(?=\\t)/g, '    '); // g_tab_width\n\n    // replace the nth with two sentinels\n    text = text.replace(/\\t/g, '¨A¨B');\n\n    // use the sentinel to anchor our regex so it doesn't explode\n    text = text.replace(/¨B(.+?)¨A/g, function (wholeMatch, m1) {\n      var leadingText = m1,\n          numSpaces = 4 - leadingText.length % 4; // g_tab_width\n\n      // there *must* be a better way to do this:\n      for (var i = 0; i < numSpaces; i++) {\n        leadingText += ' ';\n      }\n\n      return leadingText;\n    });\n\n    // clean up sentinels\n    text = text.replace(/¨A/g, '    '); // g_tab_width\n    text = text.replace(/¨B/g, '');\n\n    text = globals.converter._dispatch('detab.after', text, options, globals);\n    return text;\n  });\n\n  showdown.subParser('ellipsis', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('ellipsis.before', text, options, globals);\n\n    text = text.replace(/\\.\\.\\./g, '…');\n\n    text = globals.converter._dispatch('ellipsis.after', text, options, globals);\n\n    return text;\n  });\n\n  /**\n   * Turn emoji codes into emojis\n   *\n   * List of supported emojis: https://github.com/showdownjs/showdown/wiki/Emojis\n   */\n  showdown.subParser('emoji', function (text, options, globals) {\n    'use strict';\n\n    if (!options.emoji) {\n      return text;\n    }\n\n    text = globals.converter._dispatch('emoji.before', text, options, globals);\n\n    var emojiRgx = /:([\\S]+?):/g;\n\n    text = text.replace(emojiRgx, function (wm, emojiCode) {\n      if (showdown.helper.emojis.hasOwnProperty(emojiCode)) {\n        return showdown.helper.emojis[emojiCode];\n      }\n      return wm;\n    });\n\n    text = globals.converter._dispatch('emoji.after', text, options, globals);\n\n    return text;\n  });\n\n  /**\n   * Smart processing for ampersands and angle brackets that need to be encoded.\n   */\n  showdown.subParser('encodeAmpsAndAngles', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('encodeAmpsAndAngles.before', text, options, globals);\n\n    // Ampersand-encoding based entirely on Nat Irons's Amputator MT plugin:\n    // http://bumppo.net/projects/amputator/\n    text = text.replace(/&(?!#?[xX]?(?:[0-9a-fA-F]+|\\w+);)/g, '&');\n\n    // Encode naked <'s\n    text = text.replace(/<(?![a-z\\/?$!])/gi, '<');\n\n    // Encode <\n    text = text.replace(/\n    text = text.replace(/>/g, '>');\n\n    text = globals.converter._dispatch('encodeAmpsAndAngles.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Returns the string, with after processing the following backslash escape sequences.\n   *\n   * attacklab: The polite way to do this is with the new escapeCharacters() function:\n   *\n   *    text = escapeCharacters(text,\"\\\\\",true);\n   *    text = escapeCharacters(text,\"`*_{}[]()>#+-.!\",true);\n   *\n   * ...but we're sidestepping its use of the (slow) RegExp constructor\n   * as an optimization for Firefox.  This function gets called a LOT.\n   */\n  showdown.subParser('encodeBackslashEscapes', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('encodeBackslashEscapes.before', text, options, globals);\n\n    text = text.replace(/\\\\(\\\\)/g, showdown.helper.escapeCharactersCallback);\n    text = text.replace(/\\\\([`*_{}\\[\\]()>#+.!~=|-])/g, showdown.helper.escapeCharactersCallback);\n\n    text = globals.converter._dispatch('encodeBackslashEscapes.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Encode/escape certain characters inside Markdown code runs.\n   * The point is that in code, these characters are literals,\n   * and lose their special Markdown meanings.\n   */\n  showdown.subParser('encodeCode', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('encodeCode.before', text, options, globals);\n\n    // Encode all ampersands; HTML entities are not\n    // entities within a Markdown code span.\n    text = text.replace(/&/g, '&')\n    // Do the angle bracket song and dance:\n    .replace(//g, '>')\n    // Now, escape characters that are magic in Markdown:\n    .replace(/([*_{}\\[\\]\\\\=~-])/g, showdown.helper.escapeCharactersCallback);\n\n    text = globals.converter._dispatch('encodeCode.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Within tags -- meaning between < and > -- encode [\\ ` * _ ~ =] so they\n   * don't conflict with their use in Markdown for code, italics and strong.\n   */\n  showdown.subParser('escapeSpecialCharsWithinTagAttributes', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.before', text, options, globals);\n\n    // Build a regex to find HTML tags.\n    var tags = /<\\/?[a-z\\d_:-]+(?:[\\s]+[\\s\\S]+?)?>/gi,\n        comments = /-]|-[^>])(?:[^-]|-[^-])*)--)>/gi;\n\n    text = text.replace(tags, function (wholeMatch) {\n      return wholeMatch.replace(/(.)<\\/?code>(?=.)/g, '$1`').replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n    });\n\n    text = text.replace(comments, function (wholeMatch) {\n      return wholeMatch.replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n    });\n\n    text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Handle github codeblocks prior to running HashHTML so that\n   * HTML contained within the codeblock gets escaped properly\n   * Example:\n   * ```ruby\n   *     def hello_world(x)\n   *       puts \"Hello, #{x}\"\n   *     end\n   * ```\n   */\n  showdown.subParser('githubCodeBlocks', function (text, options, globals) {\n    'use strict';\n\n    // early exit if option is not enabled\n\n    if (!options.ghCodeBlocks) {\n      return text;\n    }\n\n    text = globals.converter._dispatch('githubCodeBlocks.before', text, options, globals);\n\n    text += '¨0';\n\n    text = text.replace(/(?:^|\\n)(?: {0,3})(```+|~~~+)(?: *)([^\\s`~]*)\\n([\\s\\S]*?)\\n(?: {0,3})\\1/g, function (wholeMatch, delim, language, codeblock) {\n      var end = options.omitExtraWLInCodeBlocks ? '' : '\\n';\n\n      // First parse the github code block\n      codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n      codeblock = showdown.subParser('detab')(codeblock, options, globals);\n      codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n      codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing whitespace\n\n      codeblock = '
' + codeblock + end + '
';\n\n      codeblock = showdown.subParser('hashBlock')(codeblock, options, globals);\n\n      // Since GHCodeblocks can be false positives, we need to\n      // store the primitive text and the parsed text in a global var,\n      // and then return a token\n      return '\\n\\n¨G' + (globals.ghCodeBlocks.push({ text: wholeMatch, codeblock: codeblock }) - 1) + 'G\\n\\n';\n    });\n\n    // attacklab: strip sentinel\n    text = text.replace(/¨0/, '');\n\n    return globals.converter._dispatch('githubCodeBlocks.after', text, options, globals);\n  });\n\n  showdown.subParser('hashBlock', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('hashBlock.before', text, options, globals);\n    text = text.replace(/(^\\n+|\\n+$)/g, '');\n    text = '\\n\\n¨K' + (globals.gHtmlBlocks.push(text) - 1) + 'K\\n\\n';\n    text = globals.converter._dispatch('hashBlock.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Hash and escape  elements that should not be parsed as markdown\n   */\n  showdown.subParser('hashCodeTags', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('hashCodeTags.before', text, options, globals);\n\n    var repFunc = function repFunc(wholeMatch, match, left, right) {\n      var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n      return '¨C' + (globals.gHtmlSpans.push(codeblock) - 1) + 'C';\n    };\n\n    // Hash naked \n    text = showdown.helper.replaceRecursiveRegExp(text, repFunc, ']*>', '', 'gim');\n\n    text = globals.converter._dispatch('hashCodeTags.after', text, options, globals);\n    return text;\n  });\n\n  showdown.subParser('hashElement', function (text, options, globals) {\n    'use strict';\n\n    return function (wholeMatch, m1) {\n      var blockText = m1;\n\n      // Undo double lines\n      blockText = blockText.replace(/\\n\\n/g, '\\n');\n      blockText = blockText.replace(/^\\n/, '');\n\n      // strip trailing blank lines\n      blockText = blockText.replace(/\\n+$/g, '');\n\n      // Replace the element text with a marker (\"¨KxK\" where x is its key)\n      blockText = '\\n\\n¨K' + (globals.gHtmlBlocks.push(blockText) - 1) + 'K\\n\\n';\n\n      return blockText;\n    };\n  });\n\n  showdown.subParser('hashHTMLBlocks', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('hashHTMLBlocks.before', text, options, globals);\n\n    var blockTags = ['pre', 'div', 'h1', 'h2', 'h3', 'h4', 'h5', 'h6', 'blockquote', 'table', 'dl', 'ol', 'ul', 'script', 'noscript', 'form', 'fieldset', 'iframe', 'math', 'style', 'section', 'header', 'footer', 'nav', 'article', 'aside', 'address', 'audio', 'canvas', 'figure', 'hgroup', 'output', 'video', 'p'],\n        repFunc = function repFunc(wholeMatch, match, left, right) {\n      var txt = wholeMatch;\n      // check if this html element is marked as markdown\n      // if so, it's contents should be parsed as markdown\n      if (left.search(/\\bmarkdown\\b/) !== -1) {\n        txt = left + globals.converter.makeHtml(match) + right;\n      }\n      return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n    };\n\n    if (options.backslashEscapesHTMLTags) {\n      // encode backslash escaped HTML tags\n      text = text.replace(/\\\\<(\\/?[^>]+?)>/g, function (wm, inside) {\n        return '<' + inside + '>';\n      });\n    }\n\n    // hash HTML Blocks\n    for (var i = 0; i < blockTags.length; ++i) {\n\n      var opTagPos,\n          rgx1 = new RegExp('^ {0,3}(<' + blockTags[i] + '\\\\b[^>]*>)', 'im'),\n          patLeft = '<' + blockTags[i] + '\\\\b[^>]*>',\n          patRight = '';\n      // 1. Look for the first position of the first opening HTML tag in the text\n      while ((opTagPos = showdown.helper.regexIndexOf(text, rgx1)) !== -1) {\n\n        // if the HTML tag is \\ escaped, we need to escape it and break\n\n\n        //2. Split the text in that position\n        var subTexts = showdown.helper.splitAtIndex(text, opTagPos),\n\n        //3. Match recursively\n        newSubText1 = showdown.helper.replaceRecursiveRegExp(subTexts[1], repFunc, patLeft, patRight, 'im');\n\n        // prevent an infinite loop\n        if (newSubText1 === subTexts[1]) {\n          break;\n        }\n        text = subTexts[0].concat(newSubText1);\n      }\n    }\n    // HR SPECIAL CASE\n    text = text.replace(/(\\n {0,3}(<(hr)\\b([^<>])*?\\/?>)[ \\t]*(?=\\n{2,}))/g, showdown.subParser('hashElement')(text, options, globals));\n\n    // Special case for standalone HTML comments\n    text = showdown.helper.replaceRecursiveRegExp(text, function (txt) {\n      return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n    }, '^ {0,3}', 'gm');\n\n    // PHP and ASP-style processor instructions ( and <%...%>)\n    text = text.replace(/(?:\\n\\n)( {0,3}(?:<([?%])[^\\r]*?\\2>)[ \\t]*(?=\\n{2,}))/g, showdown.subParser('hashElement')(text, options, globals));\n\n    text = globals.converter._dispatch('hashHTMLBlocks.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Hash span elements that should not be parsed as markdown\n   */\n  showdown.subParser('hashHTMLSpans', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('hashHTMLSpans.before', text, options, globals);\n\n    function hashHTMLSpan(html) {\n      return '¨C' + (globals.gHtmlSpans.push(html) - 1) + 'C';\n    }\n\n    // Hash Self Closing tags\n    text = text.replace(/<[^>]+?\\/>/gi, function (wm) {\n      return hashHTMLSpan(wm);\n    });\n\n    // Hash tags without properties\n    text = text.replace(/<([^>]+?)>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n      return hashHTMLSpan(wm);\n    });\n\n    // Hash tags with properties\n    text = text.replace(/<([^>]+?)\\s[^>]+?>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n      return hashHTMLSpan(wm);\n    });\n\n    // Hash self closing tags without />\n    text = text.replace(/<[^>]+?>/gi, function (wm) {\n      return hashHTMLSpan(wm);\n    });\n\n    /*showdown.helper.matchRecursiveRegExp(text, ']*>', '', 'gi');*/\n\n    text = globals.converter._dispatch('hashHTMLSpans.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Unhash HTML spans\n   */\n  showdown.subParser('unhashHTMLSpans', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('unhashHTMLSpans.before', text, options, globals);\n\n    for (var i = 0; i < globals.gHtmlSpans.length; ++i) {\n      var repText = globals.gHtmlSpans[i],\n\n      // limiter to prevent infinite loop (assume 10 as limit for recurse)\n      limit = 0;\n\n      while (/¨C(\\d+)C/.test(repText)) {\n        var num = RegExp.$1;\n        repText = repText.replace('¨C' + num + 'C', globals.gHtmlSpans[num]);\n        if (limit === 10) {\n          console.error('maximum nesting of 10 spans reached!!!');\n          break;\n        }\n        ++limit;\n      }\n      text = text.replace('¨C' + i + 'C', repText);\n    }\n\n    text = globals.converter._dispatch('unhashHTMLSpans.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Hash and escape 
 elements that should not be parsed as markdown\n   */\n  showdown.subParser('hashPreCodeTags', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('hashPreCodeTags.before', text, options, globals);\n\n    var repFunc = function repFunc(wholeMatch, match, left, right) {\n      // encode html entities\n      var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n      return '\\n\\n¨G' + (globals.ghCodeBlocks.push({ text: wholeMatch, codeblock: codeblock }) - 1) + 'G\\n\\n';\n    };\n\n    // Hash 
\n    text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}]*>\\\\s*]*>', '^ {0,3}\\\\s*
', 'gim');\n\n    text = globals.converter._dispatch('hashPreCodeTags.after', text, options, globals);\n    return text;\n  });\n\n  showdown.subParser('headers', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('headers.before', text, options, globals);\n\n    var headerLevelStart = isNaN(parseInt(options.headerLevelStart)) ? 1 : parseInt(options.headerLevelStart),\n\n\n    // Set text-style headers:\n    //\tHeader 1\n    //\t========\n    //\n    //\tHeader 2\n    //\t--------\n    //\n    setextRegexH1 = options.smoothLivePreview ? /^(.+)[ \\t]*\\n={2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n=+[ \\t]*\\n+/gm,\n        setextRegexH2 = options.smoothLivePreview ? /^(.+)[ \\t]*\\n-{2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n-+[ \\t]*\\n+/gm;\n\n    text = text.replace(setextRegexH1, function (wholeMatch, m1) {\n\n      var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n          hID = options.noHeaderId ? '' : ' id=\"' + headerId(m1) + '\"',\n          hLevel = headerLevelStart,\n          hashBlock = '' + spanGamut + '';\n      return showdown.subParser('hashBlock')(hashBlock, options, globals);\n    });\n\n    text = text.replace(setextRegexH2, function (matchFound, m1) {\n      var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n          hID = options.noHeaderId ? '' : ' id=\"' + headerId(m1) + '\"',\n          hLevel = headerLevelStart + 1,\n          hashBlock = '' + spanGamut + '';\n      return showdown.subParser('hashBlock')(hashBlock, options, globals);\n    });\n\n    // atx-style headers:\n    //  # Header 1\n    //  ## Header 2\n    //  ## Header 2 with closing hashes ##\n    //  ...\n    //  ###### Header 6\n    //\n    var atxStyle = options.requireSpaceBeforeHeadingText ? /^(#{1,6})[ \\t]+(.+?)[ \\t]*#*\\n+/gm : /^(#{1,6})[ \\t]*(.+?)[ \\t]*#*\\n+/gm;\n\n    text = text.replace(atxStyle, function (wholeMatch, m1, m2) {\n      var hText = m2;\n      if (options.customizedHeaderId) {\n        hText = m2.replace(/\\s?\\{([^{]+?)}\\s*$/, '');\n      }\n\n      var span = showdown.subParser('spanGamut')(hText, options, globals),\n          hID = options.noHeaderId ? '' : ' id=\"' + headerId(m2) + '\"',\n          hLevel = headerLevelStart - 1 + m1.length,\n          header = '' + span + '';\n\n      return showdown.subParser('hashBlock')(header, options, globals);\n    });\n\n    function headerId(m) {\n      var title, prefix;\n\n      // It is separate from other options to allow combining prefix and customized\n      if (options.customizedHeaderId) {\n        var match = m.match(/\\{([^{]+?)}\\s*$/);\n        if (match && match[1]) {\n          m = match[1];\n        }\n      }\n\n      title = m;\n\n      // Prefix id to prevent causing inadvertent pre-existing style matches.\n      if (showdown.helper.isString(options.prefixHeaderId)) {\n        prefix = options.prefixHeaderId;\n      } else if (options.prefixHeaderId === true) {\n        prefix = 'section-';\n      } else {\n        prefix = '';\n      }\n\n      if (!options.rawPrefixHeaderId) {\n        title = prefix + title;\n      }\n\n      if (options.ghCompatibleHeaderId) {\n        title = title.replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '').replace(/¨T/g, '').replace(/¨D/g, '')\n        // replace rest of the chars (&~$ are repeated as they might have been escaped)\n        // borrowed from github's redcarpet (some they should produce similar results)\n        .replace(/[&+$,\\/:;=?@\"#{}|^¨~\\[\\]`\\\\*)(%.!'<>]/g, '').toLowerCase();\n      } else if (options.rawHeaderId) {\n        title = title.replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '&').replace(/¨T/g, '¨').replace(/¨D/g, '$')\n        // replace \" and '\n        .replace(/[\"']/g, '-').toLowerCase();\n      } else {\n        title = title.replace(/[^\\w]/g, '').toLowerCase();\n      }\n\n      if (options.rawPrefixHeaderId) {\n        title = prefix + title;\n      }\n\n      if (globals.hashLinkCounts[title]) {\n        title = title + '-' + globals.hashLinkCounts[title]++;\n      } else {\n        globals.hashLinkCounts[title] = 1;\n      }\n      return title;\n    }\n\n    text = globals.converter._dispatch('headers.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Turn Markdown link shortcuts into XHTML  tags.\n   */\n  showdown.subParser('horizontalRule', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('horizontalRule.before', text, options, globals);\n\n    var key = showdown.subParser('hashBlock')('
', options, globals);\n    text = text.replace(/^ {0,2}( ?-){3,}[ \\t]*$/gm, key);\n    text = text.replace(/^ {0,2}( ?\\*){3,}[ \\t]*$/gm, key);\n    text = text.replace(/^ {0,2}( ?_){3,}[ \\t]*$/gm, key);\n\n    text = globals.converter._dispatch('horizontalRule.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Turn Markdown image shortcuts into  tags.\n   */\n  showdown.subParser('images', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('images.before', text, options, globals);\n\n    var inlineRegExp = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n        crazyRegExp = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]?<([^>]*)>(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:(?:([\"'])([^\"]*?)\\6))?[ \\t]?\\)/g,\n        base64RegExp = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n        referenceRegExp = /!\\[([^\\]]*?)] ?(?:\\n *)?\\[([\\s\\S]*?)]()()()()()/g,\n        refShortcutRegExp = /!\\[([^\\[\\]]+)]()()()()()/g;\n\n    function writeImageTagBase64(wholeMatch, altText, linkId, url, width, height, m5, title) {\n      url = url.replace(/\\s/g, '');\n      return writeImageTag(wholeMatch, altText, linkId, url, width, height, m5, title);\n    }\n\n    function writeImageTag(wholeMatch, altText, linkId, url, width, height, m5, title) {\n\n      var gUrls = globals.gUrls,\n          gTitles = globals.gTitles,\n          gDims = globals.gDimensions;\n\n      linkId = linkId.toLowerCase();\n\n      if (!title) {\n        title = '';\n      }\n      // Special case for explicit empty url\n      if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n        url = '';\n      } else if (url === '' || url === null) {\n        if (linkId === '' || linkId === null) {\n          // lower-case and turn embedded newlines into spaces\n          linkId = altText.toLowerCase().replace(/ ?\\n/g, ' ');\n        }\n        url = '#' + linkId;\n\n        if (!showdown.helper.isUndefined(gUrls[linkId])) {\n          url = gUrls[linkId];\n          if (!showdown.helper.isUndefined(gTitles[linkId])) {\n            title = gTitles[linkId];\n          }\n          if (!showdown.helper.isUndefined(gDims[linkId])) {\n            width = gDims[linkId].width;\n            height = gDims[linkId].height;\n          }\n        } else {\n          return wholeMatch;\n        }\n      }\n\n      altText = altText.replace(/\"/g, '"')\n      //altText = showdown.helper.escapeCharacters(altText, '*_', false);\n      .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n      //url = showdown.helper.escapeCharacters(url, '*_', false);\n      url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n      var result = '\"'x \"optional title\")\n\n    // base64 encoded images\n    text = text.replace(base64RegExp, writeImageTagBase64);\n\n    // cases with crazy urls like ./image/cat1).png\n    text = text.replace(crazyRegExp, writeImageTag);\n\n    // normal cases\n    text = text.replace(inlineRegExp, writeImageTag);\n\n    // handle reference-style shortcuts: ![img text]\n    text = text.replace(refShortcutRegExp, writeImageTag);\n\n    text = globals.converter._dispatch('images.after', text, options, globals);\n    return text;\n  });\n\n  showdown.subParser('italicsAndBold', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('italicsAndBold.before', text, options, globals);\n\n    // it's faster to have 3 separate regexes for each case than have just one\n    // because of backtracing, in some cases, it could lead to an exponential effect\n    // called \"catastrophic backtrace\". Ominous!\n\n    function parseInside(txt, left, right) {\n      /*\n      if (options.simplifiedAutoLink) {\n        txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n      }\n      */\n      return left + txt + right;\n    }\n\n    // Parse underscores\n    if (options.literalMidWordUnderscores) {\n      text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n        return parseInside(txt, '', '');\n      });\n      text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n        return parseInside(txt, '', '');\n      });\n      text = text.replace(/\\b_(\\S[\\s\\S]*?)_\\b/g, function (wm, txt) {\n        return parseInside(txt, '', '');\n      });\n    } else {\n      text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n        return (/\\S$/.test(m) ? parseInside(m, '', '') : wm\n        );\n      });\n      text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n        return (/\\S$/.test(m) ? parseInside(m, '', '') : wm\n        );\n      });\n      text = text.replace(/_([^\\s_][\\s\\S]*?)_/g, function (wm, m) {\n        // !/^_[^_]/.test(m) - test if it doesn't start with __ (since it seems redundant, we removed it)\n        return (/\\S$/.test(m) ? parseInside(m, '', '') : wm\n        );\n      });\n    }\n\n    // Now parse asterisks\n    if (options.literalMidWordAsterisks) {\n      text = text.replace(/([^*]|^)\\B\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n        return parseInside(txt, lead + '', '');\n      });\n      text = text.replace(/([^*]|^)\\B\\*\\*(\\S[\\s\\S]*?)\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n        return parseInside(txt, lead + '', '');\n      });\n      text = text.replace(/([^*]|^)\\B\\*(\\S[\\s\\S]*?)\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n        return parseInside(txt, lead + '', '');\n      });\n    } else {\n      text = text.replace(/\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*/g, function (wm, m) {\n        return (/\\S$/.test(m) ? parseInside(m, '', '') : wm\n        );\n      });\n      text = text.replace(/\\*\\*(\\S[\\s\\S]*?)\\*\\*/g, function (wm, m) {\n        return (/\\S$/.test(m) ? parseInside(m, '', '') : wm\n        );\n      });\n      text = text.replace(/\\*([^\\s*][\\s\\S]*?)\\*/g, function (wm, m) {\n        // !/^\\*[^*]/.test(m) - test if it doesn't start with ** (since it seems redundant, we removed it)\n        return (/\\S$/.test(m) ? parseInside(m, '', '') : wm\n        );\n      });\n    }\n\n    text = globals.converter._dispatch('italicsAndBold.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Form HTML ordered (numbered) and unordered (bulleted) lists.\n   */\n  showdown.subParser('lists', function (text, options, globals) {\n    'use strict';\n\n    /**\n     * Process the contents of a single ordered or unordered list, splitting it\n     * into individual list items.\n     * @param {string} listStr\n     * @param {boolean} trimTrailing\n     * @returns {string}\n     */\n\n    function processListItems(listStr, trimTrailing) {\n      // The $g_list_level global keeps track of when we're inside a list.\n      // Each time we enter a list, we increment it; when we leave a list,\n      // we decrement. If it's zero, we're not in a list anymore.\n      //\n      // We do this because when we're not inside a list, we want to treat\n      // something like this:\n      //\n      //    I recommend upgrading to version\n      //    8. Oops, now this line is treated\n      //    as a sub-list.\n      //\n      // As a single paragraph, despite the fact that the second line starts\n      // with a digit-period-space sequence.\n      //\n      // Whereas when we're inside a list (or sub-list), that line will be\n      // treated as the start of a sub-list. What a kludge, huh? This is\n      // an aspect of Markdown's syntax that's hard to parse perfectly\n      // without resorting to mind-reading. Perhaps the solution is to\n      // change the syntax rules such that sub-lists must start with a\n      // starting cardinal number; e.g. \"1.\" or \"a.\".\n      globals.gListLevel++;\n\n      // trim trailing blank lines:\n      listStr = listStr.replace(/\\n{2,}$/, '\\n');\n\n      // attacklab: add sentinel to emulate \\z\n      listStr += '¨0';\n\n      var rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0| {0,3}([*+-]|\\d+[.])[ \\t]+))/gm,\n          isParagraphed = /\\n[ \\t]*\\n(?!¨0)/.test(listStr);\n\n      // Since version 1.5, nesting sublists requires 4 spaces (or 1 tab) indentation,\n      // which is a syntax breaking change\n      // activating this option reverts to old behavior\n      if (options.disableForced4SpacesIndentedSublists) {\n        rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0|\\2([*+-]|\\d+[.])[ \\t]+))/gm;\n      }\n\n      listStr = listStr.replace(rgx, function (wholeMatch, m1, m2, m3, m4, taskbtn, checked) {\n        checked = checked && checked.trim() !== '';\n\n        var item = showdown.subParser('outdent')(m4, options, globals),\n            bulletStyle = '';\n\n        // Support for github tasklists\n        if (taskbtn && options.tasklists) {\n          bulletStyle = ' class=\"task-list-item\" style=\"list-style-type: none;\"';\n          item = item.replace(/^[ \\t]*\\[(x|X| )?]/m, function () {\n            var otp = '
  • a
    • \n        // instead of:\n        // 
    • - - a
    \n        // So, to prevent it, we will put a marker (¨A)in the beginning of the line\n        // Kind of hackish/monkey patching, but seems more effective than overcomplicating the list parser\n        item = item.replace(/^([-*+]|\\d\\.)[ \\t]+[\\S\\n ]*/g, function (wm2) {\n          return '¨A' + wm2;\n        });\n\n        // m1 - Leading line or\n        // Has a double return (multi paragraph) or\n        // Has sublist\n        if (m1 || item.search(/\\n{2,}/) > -1) {\n          item = showdown.subParser('githubCodeBlocks')(item, options, globals);\n          item = showdown.subParser('blockGamut')(item, options, globals);\n        } else {\n          // Recursion for sub-lists:\n          item = showdown.subParser('lists')(item, options, globals);\n          item = item.replace(/\\n$/, ''); // chomp(item)\n          item = showdown.subParser('hashHTMLBlocks')(item, options, globals);\n\n          // Colapse double linebreaks\n          item = item.replace(/\\n\\n+/g, '\\n\\n');\n          if (isParagraphed) {\n            item = showdown.subParser('paragraphs')(item, options, globals);\n          } else {\n            item = showdown.subParser('spanGamut')(item, options, globals);\n          }\n        }\n\n        // now we need to remove the marker (¨A)\n        item = item.replace('¨A', '');\n        // we can finally wrap the line in list item tags\n        item = '' + item + '\\n';\n\n        return item;\n      });\n\n      // attacklab: strip sentinel\n      listStr = listStr.replace(/¨0/g, '');\n\n      globals.gListLevel--;\n\n      if (trimTrailing) {\n        listStr = listStr.replace(/\\s+$/, '');\n      }\n\n      return listStr;\n    }\n\n    function styleStartNumber(list, listType) {\n      // check if ol and starts by a number different than 1\n      if (listType === 'ol') {\n        var res = list.match(/^ *(\\d+)\\./);\n        if (res && res[1] !== '1') {\n          return ' start=\"' + res[1] + '\"';\n        }\n      }\n      return '';\n    }\n\n    /**\n     * Check and parse consecutive lists (better fix for issue #142)\n     * @param {string} list\n     * @param {string} listType\n     * @param {boolean} trimTrailing\n     * @returns {string}\n     */\n    function parseConsecutiveLists(list, listType, trimTrailing) {\n      // check if we caught 2 or more consecutive lists by mistake\n      // we use the counterRgx, meaning if listType is UL we look for OL and vice versa\n      var olRgx = options.disableForced4SpacesIndentedSublists ? /^ ?\\d+\\.[ \\t]/gm : /^ {0,3}\\d+\\.[ \\t]/gm,\n          ulRgx = options.disableForced4SpacesIndentedSublists ? /^ ?[*+-][ \\t]/gm : /^ {0,3}[*+-][ \\t]/gm,\n          counterRxg = listType === 'ul' ? olRgx : ulRgx,\n          result = '';\n\n      if (list.search(counterRxg) !== -1) {\n        (function parseCL(txt) {\n          var pos = txt.search(counterRxg),\n              style = styleStartNumber(list, listType);\n          if (pos !== -1) {\n            // slice\n            result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt.slice(0, pos), !!trimTrailing) + '\\n';\n\n            // invert counterType and listType\n            listType = listType === 'ul' ? 'ol' : 'ul';\n            counterRxg = listType === 'ul' ? olRgx : ulRgx;\n\n            //recurse\n            parseCL(txt.slice(pos));\n          } else {\n            result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt, !!trimTrailing) + '\\n';\n          }\n        })(list);\n      } else {\n        var style = styleStartNumber(list, listType);\n        result = '\\n\\n<' + listType + style + '>\\n' + processListItems(list, !!trimTrailing) + '\\n';\n      }\n\n      return result;\n    }\n\n    /** Start of list parsing **/\n    text = globals.converter._dispatch('lists.before', text, options, globals);\n    // add sentinel to hack around khtml/safari bug:\n    // http://bugs.webkit.org/show_bug.cgi?id=11231\n    text += '¨0';\n\n    if (globals.gListLevel) {\n      text = text.replace(/^(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm, function (wholeMatch, list, m2) {\n        var listType = m2.search(/[*+-]/g) > -1 ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, true);\n      });\n    } else {\n      text = text.replace(/(\\n\\n|^\\n?)(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm, function (wholeMatch, m1, list, m3) {\n        var listType = m3.search(/[*+-]/g) > -1 ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, false);\n      });\n    }\n\n    // strip sentinel\n    text = text.replace(/¨0/, '');\n    text = globals.converter._dispatch('lists.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Parse metadata at the top of the document\n   */\n  showdown.subParser('metadata', function (text, options, globals) {\n    'use strict';\n\n    if (!options.metadata) {\n      return text;\n    }\n\n    text = globals.converter._dispatch('metadata.before', text, options, globals);\n\n    function parseMetadataContents(content) {\n      // raw is raw so it's not changed in any way\n      globals.metadata.raw = content;\n\n      // escape chars forbidden in html attributes\n      // double quotes\n      content = content\n      // ampersand first\n      .replace(/&/g, '&')\n      // double quotes\n      .replace(/\"/g, '"');\n\n      content = content.replace(/\\n {4}/g, ' ');\n      content.replace(/^([\\S ]+): +([\\s\\S]+?)$/gm, function (wm, key, value) {\n        globals.metadata.parsed[key] = value;\n        return '';\n      });\n    }\n\n    text = text.replace(/^\\s*«««+(\\S*?)\\n([\\s\\S]+?)\\n»»»+\\n/, function (wholematch, format, content) {\n      parseMetadataContents(content);\n      return '¨M';\n    });\n\n    text = text.replace(/^\\s*---+(\\S*?)\\n([\\s\\S]+?)\\n---+\\n/, function (wholematch, format, content) {\n      if (format) {\n        globals.metadata.format = format;\n      }\n      parseMetadataContents(content);\n      return '¨M';\n    });\n\n    text = text.replace(/¨M/g, '');\n\n    text = globals.converter._dispatch('metadata.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   * Remove one level of line-leading tabs or spaces\n   */\n  showdown.subParser('outdent', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('outdent.before', text, options, globals);\n\n    // attacklab: hack around Konqueror 3.5.4 bug:\n    // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n    text = text.replace(/^(\\t|[ ]{1,4})/gm, '¨0'); // attacklab: g_tab_width\n\n    // attacklab: clean up hack\n    text = text.replace(/¨0/g, '');\n\n    text = globals.converter._dispatch('outdent.after', text, options, globals);\n    return text;\n  });\n\n  /**\n   *\n   */\n  showdown.subParser('paragraphs', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('paragraphs.before', text, options, globals);\n    // Strip leading and trailing lines:\n    text = text.replace(/^\\n+/g, '');\n    text = text.replace(/\\n+$/g, '');\n\n    var grafs = text.split(/\\n{2,}/g),\n        grafsOut = [],\n        end = grafs.length; // Wrap 
     tags\n\n    for (var i = 0; i < end; i++) {\n      var str = grafs[i];\n      // if this is an HTML marker, copy it\n      if (str.search(/¨(K|G)(\\d+)\\1/g) >= 0) {\n        grafsOut.push(str);\n\n        // test for presence of characters to prevent empty lines being parsed\n        // as paragraphs (resulting in undesired extra empty paragraphs)\n      } else if (str.search(/\\S/) >= 0) {\n        str = showdown.subParser('spanGamut')(str, options, globals);\n        str = str.replace(/^([ \\t]*)/g, '
    ');\n        str += '
    ';\n        grafsOut.push(str);\n      }\n    }\n\n    /** Unhashify HTML blocks */\n    end = grafsOut.length;\n    for (i = 0; i < end; i++) {\n      var blockText = '',\n          grafsOutIt = grafsOut[i],\n          codeFlag = false;\n      // if this is a marker for an html block...\n      // use RegExp.test instead of string.search because of QML bug\n      while (/¨(K|G)(\\d+)\\1/.test(grafsOutIt)) {\n        var delim = RegExp.$1,\n            num = RegExp.$2;\n\n        if (delim === 'K') {\n          blockText = globals.gHtmlBlocks[num];\n        } else {\n          // we need to check if ghBlock is a false positive\n          if (codeFlag) {\n            // use encoded version of all text\n            blockText = showdown.subParser('encodeCode')(globals.ghCodeBlocks[num].text, options, globals);\n          } else {\n            blockText = globals.ghCodeBlocks[num].codeblock;\n          }\n        }\n        blockText = blockText.replace(/\\$/g, '$$$$'); // Escape any dollar signs\n\n        grafsOutIt = grafsOutIt.replace(/(\\n\\n)?¨(K|G)\\d+\\2(\\n\\n)?/, blockText);\n        // Check if grafsOutIt is a pre->code\n        if (/^]*>\\s*]*>/.test(grafsOutIt)) {\n          codeFlag = true;\n        }\n      }\n      grafsOut[i] = grafsOutIt;\n    }\n    text = grafsOut.join('\\n');\n    // Strip leading and trailing lines:\n    text = text.replace(/^\\n+/g, '');\n    text = text.replace(/\\n+$/g, '');\n    return globals.converter._dispatch('paragraphs.after', text, options, globals);\n  });\n\n  /**\n   * Run extension\n   */\n  showdown.subParser('runExtension', function (ext, text, options, globals) {\n    'use strict';\n\n    if (ext.filter) {\n      text = ext.filter(text, globals.converter, options);\n    } else if (ext.regex) {\n      // TODO remove this when old extension loading mechanism is deprecated\n      var re = ext.regex;\n      if (!(re instanceof RegExp)) {\n        re = new RegExp(re, 'g');\n      }\n      text = text.replace(re, ext.replace);\n    }\n\n    return text;\n  });\n\n  /**\n   * These are all the transformations that occur *within* block-level\n   * tags like paragraphs, headers, and list items.\n   */\n  showdown.subParser('spanGamut', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('spanGamut.before', text, options, globals);\n    text = showdown.subParser('codeSpans')(text, options, globals);\n    text = showdown.subParser('escapeSpecialCharsWithinTagAttributes')(text, options, globals);\n    text = showdown.subParser('encodeBackslashEscapes')(text, options, globals);\n\n    // Process anchor and image tags. Images must come first,\n    // because ![foo][f] looks like an anchor.\n    text = showdown.subParser('images')(text, options, globals);\n    text = showdown.subParser('anchors')(text, options, globals);\n\n    // Make links out of things like ``\n    // Must come after anchors, because you can use < and >\n    // delimiters in inline links like [this]().\n    text = showdown.subParser('autoLinks')(text, options, globals);\n    text = showdown.subParser('simplifiedAutoLinks')(text, options, globals);\n    text = showdown.subParser('emoji')(text, options, globals);\n    text = showdown.subParser('underline')(text, options, globals);\n    text = showdown.subParser('italicsAndBold')(text, options, globals);\n    text = showdown.subParser('strikethrough')(text, options, globals);\n    text = showdown.subParser('ellipsis')(text, options, globals);\n\n    // we need to hash HTML tags inside spans\n    text = showdown.subParser('hashHTMLSpans')(text, options, globals);\n\n    // now we encode amps and angles\n    text = showdown.subParser('encodeAmpsAndAngles')(text, options, globals);\n\n    // Do hard breaks\n    if (options.simpleLineBreaks) {\n      // GFM style hard breaks\n      // only add line breaks if the text does not contain a block (special case for lists)\n      if (!/\\n\\n¨K/.test(text)) {\n        text = text.replace(/\\n+/g, '
    \\n');\n      }\n    } else {\n      // Vanilla hard breaks\n      text = text.replace(/  +\\n/g, '
    \\n');\n    }\n\n    text = globals.converter._dispatch('spanGamut.after', text, options, globals);\n    return text;\n  });\n\n  showdown.subParser('strikethrough', function (text, options, globals) {\n    'use strict';\n\n    function parseInside(txt) {\n      if (options.simplifiedAutoLink) {\n        txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n      }\n      return '' + txt + '';\n    }\n\n    if (options.strikethrough) {\n      text = globals.converter._dispatch('strikethrough.before', text, options, globals);\n      text = text.replace(/(?:~){2}([\\s\\S]+?)(?:~){2}/g, function (wm, txt) {\n        return parseInside(txt);\n      });\n      text = globals.converter._dispatch('strikethrough.after', text, options, globals);\n    }\n\n    return text;\n  });\n\n  /**\n   * Strips link definitions from text, stores the URLs and titles in\n   * hash references.\n   * Link defs are in the form: ^[id]: url \"optional title\"\n   */\n  showdown.subParser('stripLinkDefinitions', function (text, options, globals) {\n    'use strict';\n\n    var regex = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*\\s]+)>?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n+|(?=¨0))/gm,\n        base64Regex = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n\\n|(?=¨0)|(?=\\n\\[))/gm;\n\n    // attacklab: sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n    text += '¨0';\n\n    var replaceFunc = function replaceFunc(wholeMatch, linkId, url, width, height, blankLines, title) {\n      linkId = linkId.toLowerCase();\n      if (url.match(/^data:.+?\\/.+?;base64,/)) {\n        // remove newlines\n        globals.gUrls[linkId] = url.replace(/\\s/g, '');\n      } else {\n        globals.gUrls[linkId] = showdown.subParser('encodeAmpsAndAngles')(url, options, globals); // Link IDs are case-insensitive\n      }\n\n      if (blankLines) {\n        // Oops, found blank lines, so it's not a title.\n        // Put back the parenthetical statement we stole.\n        return blankLines + title;\n      } else {\n        if (title) {\n          globals.gTitles[linkId] = title.replace(/\"|'/g, '"');\n        }\n        if (options.parseImgDimensions && width && height) {\n          globals.gDimensions[linkId] = {\n            width: width,\n            height: height\n          };\n        }\n      }\n      // Completely remove the definition from the text\n      return '';\n    };\n\n    // first we try to find base64 link references\n    text = text.replace(base64Regex, replaceFunc);\n\n    text = text.replace(regex, replaceFunc);\n\n    // attacklab: strip sentinel\n    text = text.replace(/¨0/, '');\n\n    return text;\n  });\n\n  showdown.subParser('tables', function (text, options, globals) {\n    'use strict';\n\n    if (!options.tables) {\n      return text;\n    }\n\n    var tableRgx = /^ {0,3}\\|?.+\\|.+\\n {0,3}\\|?[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[\\s\\S]+?(?:\\n\\n|¨0)/gm,\n\n    //singeColTblRgx = /^ {0,3}\\|.+\\|\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n(?: {0,3}\\|.+\\|\\n)+(?:\\n\\n|¨0)/gm;\n    singeColTblRgx = /^ {0,3}\\|.+\\|[ \\t]*\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n( {0,3}\\|.+\\|[ \\t]*\\n)*(?:\\n|¨0)/gm;\n\n    function parseStyles(sLine) {\n      if (/^:[ \\t]*--*$/.test(sLine)) {\n        return ' style=\"text-align:left;\"';\n      } else if (/^--*[ \\t]*:[ \\t]*$/.test(sLine)) {\n        return ' style=\"text-align:right;\"';\n      } else if (/^:[ \\t]*--*[ \\t]*:$/.test(sLine)) {\n        return ' style=\"text-align:center;\"';\n      } else {\n        return '';\n      }\n    }\n\n    function parseHeaders(header, style) {\n      var id = '';\n      header = header.trim();\n      // support both tablesHeaderId and tableHeaderId due to error in documentation so we don't break backwards compatibility\n      if (options.tablesHeaderId || options.tableHeaderId) {\n        id = ' id=\"' + header.replace(/ /g, '_').toLowerCase() + '\"';\n      }\n      header = showdown.subParser('spanGamut')(header, options, globals);\n\n      return '' + header + '\\n';\n    }\n\n    function parseCells(cell, style) {\n      var subText = showdown.subParser('spanGamut')(cell, options, globals);\n      return '' + subText + '\\n';\n    }\n\n    function buildTable(headers, cells) {\n      var tb = '\\n\\n\\n',\n          tblLgn = headers.length;\n\n      for (var i = 0; i < tblLgn; ++i) {\n        tb += headers[i];\n      }\n      tb += '\\n\\n\\n';\n\n      for (i = 0; i < cells.length; ++i) {\n        tb += '\\n';\n        for (var ii = 0; ii < tblLgn; ++ii) {\n          tb += cells[i][ii];\n        }\n        tb += '\\n';\n      }\n      tb += '\\n
    \\n';\n      return tb;\n    }\n\n    function parseTable(rawTable) {\n      var i,\n          tableLines = rawTable.split('\\n');\n\n      for (i = 0; i < tableLines.length; ++i) {\n        // strip wrong first and last column if wrapped tables are used\n        if (/^ {0,3}\\|/.test(tableLines[i])) {\n          tableLines[i] = tableLines[i].replace(/^ {0,3}\\|/, '');\n        }\n        if (/\\|[ \\t]*$/.test(tableLines[i])) {\n          tableLines[i] = tableLines[i].replace(/\\|[ \\t]*$/, '');\n        }\n        // parse code spans first, but we only support one line code spans\n        tableLines[i] = showdown.subParser('codeSpans')(tableLines[i], options, globals);\n      }\n\n      var rawHeaders = tableLines[0].split('|').map(function (s) {\n        return s.trim();\n      }),\n          rawStyles = tableLines[1].split('|').map(function (s) {\n        return s.trim();\n      }),\n          rawCells = [],\n          headers = [],\n          styles = [],\n          cells = [];\n\n      tableLines.shift();\n      tableLines.shift();\n\n      for (i = 0; i < tableLines.length; ++i) {\n        if (tableLines[i].trim() === '') {\n          continue;\n        }\n        rawCells.push(tableLines[i].split('|').map(function (s) {\n          return s.trim();\n        }));\n      }\n\n      if (rawHeaders.length < rawStyles.length) {\n        return rawTable;\n      }\n\n      for (i = 0; i < rawStyles.length; ++i) {\n        styles.push(parseStyles(rawStyles[i]));\n      }\n\n      for (i = 0; i < rawHeaders.length; ++i) {\n        if (showdown.helper.isUndefined(styles[i])) {\n          styles[i] = '';\n        }\n        headers.push(parseHeaders(rawHeaders[i], styles[i]));\n      }\n\n      for (i = 0; i < rawCells.length; ++i) {\n        var row = [];\n        for (var ii = 0; ii < headers.length; ++ii) {\n          if (showdown.helper.isUndefined(rawCells[i][ii])) {}\n          row.push(parseCells(rawCells[i][ii], styles[ii]));\n        }\n        cells.push(row);\n      }\n\n      return buildTable(headers, cells);\n    }\n\n    text = globals.converter._dispatch('tables.before', text, options, globals);\n\n    // find escaped pipe characters\n    text = text.replace(/\\\\(\\|)/g, showdown.helper.escapeCharactersCallback);\n\n    // parse multi column tables\n    text = text.replace(tableRgx, parseTable);\n\n    // parse one column tables\n    text = text.replace(singeColTblRgx, parseTable);\n\n    text = globals.converter._dispatch('tables.after', text, options, globals);\n\n    return text;\n  });\n\n  showdown.subParser('underline', function (text, options, globals) {\n    'use strict';\n\n    if (!options.underline) {\n      return text;\n    }\n\n    text = globals.converter._dispatch('underline.before', text, options, globals);\n\n    if (options.literalMidWordUnderscores) {\n      text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n        return '' + txt + '';\n      });\n      text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n        return '' + txt + '';\n      });\n    } else {\n      text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n        return (/\\S$/.test(m) ? '' + m + '' : wm\n        );\n      });\n      text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n        return (/\\S$/.test(m) ? '' + m + '' : wm\n        );\n      });\n    }\n\n    // escape remaining underscores to prevent them being parsed by italic and bold\n    text = text.replace(/(_)/g, showdown.helper.escapeCharactersCallback);\n\n    text = globals.converter._dispatch('underline.after', text, options, globals);\n\n    return text;\n  });\n\n  /**\n   * Swap back in all the special characters we've hidden.\n   */\n  showdown.subParser('unescapeSpecialChars', function (text, options, globals) {\n    'use strict';\n\n    text = globals.converter._dispatch('unescapeSpecialChars.before', text, options, globals);\n\n    text = text.replace(/¨E(\\d+)E/g, function (wholeMatch, m1) {\n      var charCodeToReplace = parseInt(m1);\n      return String.fromCharCode(charCodeToReplace);\n    });\n\n    text = globals.converter._dispatch('unescapeSpecialChars.after', text, options, globals);\n    return text;\n  });\n\n  showdown.subParser('makeMarkdown.blockquote', function (node, globals) {\n    'use strict';\n\n    var txt = '';\n    if (node.hasChildNodes()) {\n      var children = node.childNodes,\n          childrenLength = children.length;\n\n      for (var i = 0; i < childrenLength; ++i) {\n        var innerTxt = showdown.subParser('makeMarkdown.node')(children[i], globals);\n\n        if (innerTxt === '') {\n          continue;\n        }\n        txt += innerTxt;\n      }\n    }\n    // cleanup\n    txt = txt.trim();\n    txt = '> ' + txt.split('\\n').join('\\n> ');\n    return txt;\n  });\n\n  showdown.subParser('makeMarkdown.codeBlock', function (node, globals) {\n    'use strict';\n\n    var lang = node.getAttribute('language'),\n        num = node.getAttribute('precodenum');\n    return '```' + lang + '\\n' + globals.preList[num] + '\\n```';\n  });\n\n  showdown.subParser('makeMarkdown.codeSpan', function (node) {\n    'use strict';\n\n    return '`' + node.innerHTML + '`';\n  });\n\n  showdown.subParser('makeMarkdown.emphasis', function (node, globals) {\n    'use strict';\n\n    var txt = '';\n    if (node.hasChildNodes()) {\n      txt += '*';\n      var children = node.childNodes,\n          childrenLength = children.length;\n      for (var i = 0; i < childrenLength; ++i) {\n        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n      }\n      txt += '*';\n    }\n    return txt;\n  });\n\n  showdown.subParser('makeMarkdown.header', function (node, globals, headerLevel) {\n    'use strict';\n\n    var headerMark = new Array(headerLevel + 1).join('#'),\n        txt = '';\n\n    if (node.hasChildNodes()) {\n      txt = headerMark + ' ';\n      var children = node.childNodes,\n          childrenLength = children.length;\n\n      for (var i = 0; i < childrenLength; ++i) {\n        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n      }\n    }\n    return txt;\n  });\n\n  showdown.subParser('makeMarkdown.hr', function () {\n    'use strict';\n\n    return '---';\n  });\n\n  showdown.subParser('makeMarkdown.image', function (node) {\n    'use strict';\n\n    var txt = '';\n    if (node.hasAttribute('src')) {\n      txt += '![' + node.getAttribute('alt') + '](';\n      txt += '<' + node.getAttribute('src') + '>';\n      if (node.hasAttribute('width') && node.hasAttribute('height')) {\n        txt += ' =' + node.getAttribute('width') + 'x' + node.getAttribute('height');\n      }\n\n      if (node.hasAttribute('title')) {\n        txt += ' \"' + node.getAttribute('title') + '\"';\n      }\n      txt += ')';\n    }\n    return txt;\n  });\n\n  showdown.subParser('makeMarkdown.links', function (node, globals) {\n    'use strict';\n\n    var txt = '';\n    if (node.hasChildNodes() && node.hasAttribute('href')) {\n      var children = node.childNodes,\n          childrenLength = children.length;\n      txt = '[';\n      for (var i = 0; i < childrenLength; ++i) {\n        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n      }\n      txt += '](';\n      txt += '<' + node.getAttribute('href') + '>';\n      if (node.hasAttribute('title')) {\n        txt += ' \"' + node.getAttribute('title') + '\"';\n      }\n      txt += ')';\n    }\n    return txt;\n  });\n\n  showdown.subParser('makeMarkdown.list', function (node, globals, type) {\n    'use strict';\n\n    var txt = '';\n    if (!node.hasChildNodes()) {\n      return '';\n    }\n    var listItems = node.childNodes,\n        listItemsLenght = listItems.length,\n        listNum = node.getAttribute('start') || 1;\n\n    for (var i = 0; i < listItemsLenght; ++i) {\n      if (typeof listItems[i].tagName === 'undefined' || listItems[i].tagName.toLowerCase() !== 'li') {\n        continue;\n      }\n\n      // define the bullet to use in list\n      var bullet = '';\n      if (type === 'ol') {\n        bullet = listNum.toString() + '. ';\n      } else {\n        bullet = '- ';\n      }\n\n      // parse list item\n      txt += bullet + showdown.subParser('makeMarkdown.listItem')(listItems[i], globals);\n      ++listNum;\n    }\n\n    // add comment at the end to prevent consecutive lists to be parsed as one\n    txt += '\\n\\n';\n    return txt.trim();\n  });\n\n  showdown.subParser('makeMarkdown.listItem', function (node, globals) {\n    'use strict';\n\n    var listItemTxt = '';\n\n    var children = node.childNodes,\n        childrenLenght = children.length;\n\n    for (var i = 0; i < childrenLenght; ++i) {\n      listItemTxt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    // if it's only one liner, we need to add a newline at the end\n    if (!/\\n$/.test(listItemTxt)) {\n      listItemTxt += '\\n';\n    } else {\n      // it's multiparagraph, so we need to indent\n      listItemTxt = listItemTxt.split('\\n').join('\\n    ').replace(/^ {4}$/gm, '').replace(/\\n\\n+/g, '\\n\\n');\n    }\n\n    return listItemTxt;\n  });\n\n  showdown.subParser('makeMarkdown.node', function (node, globals, spansOnly) {\n    'use strict';\n\n    spansOnly = spansOnly || false;\n\n    var txt = '';\n\n    // edge case of text without wrapper paragraph\n    if (node.nodeType === 3) {\n      return showdown.subParser('makeMarkdown.txt')(node, globals);\n    }\n\n    // HTML comment\n    if (node.nodeType === 8) {\n      return '\\n\\n';\n    }\n\n    // process only node elements\n    if (node.nodeType !== 1) {\n      return '';\n    }\n\n    var tagName = node.tagName.toLowerCase();\n\n    switch (tagName) {\n\n      //\n      // BLOCKS\n      //\n      case 'h1':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.header')(node, globals, 1) + '\\n\\n';\n        }\n        break;\n      case 'h2':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.header')(node, globals, 2) + '\\n\\n';\n        }\n        break;\n      case 'h3':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.header')(node, globals, 3) + '\\n\\n';\n        }\n        break;\n      case 'h4':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.header')(node, globals, 4) + '\\n\\n';\n        }\n        break;\n      case 'h5':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.header')(node, globals, 5) + '\\n\\n';\n        }\n        break;\n      case 'h6':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.header')(node, globals, 6) + '\\n\\n';\n        }\n        break;\n\n      case 'p':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.paragraph')(node, globals) + '\\n\\n';\n        }\n        break;\n\n      case 'blockquote':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.blockquote')(node, globals) + '\\n\\n';\n        }\n        break;\n\n      case 'hr':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.hr')(node, globals) + '\\n\\n';\n        }\n        break;\n\n      case 'ol':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ol') + '\\n\\n';\n        }\n        break;\n\n      case 'ul':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ul') + '\\n\\n';\n        }\n        break;\n\n      case 'precode':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.codeBlock')(node, globals) + '\\n\\n';\n        }\n        break;\n\n      case 'pre':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.pre')(node, globals) + '\\n\\n';\n        }\n        break;\n\n      case 'table':\n        if (!spansOnly) {\n          txt = showdown.subParser('makeMarkdown.table')(node, globals) + '\\n\\n';\n        }\n        break;\n\n      //\n      // SPANS\n      //\n      case 'code':\n        txt = showdown.subParser('makeMarkdown.codeSpan')(node, globals);\n        break;\n\n      case 'em':\n      case 'i':\n        txt = showdown.subParser('makeMarkdown.emphasis')(node, globals);\n        break;\n\n      case 'strong':\n      case 'b':\n        txt = showdown.subParser('makeMarkdown.strong')(node, globals);\n        break;\n\n      case 'del':\n        txt = showdown.subParser('makeMarkdown.strikethrough')(node, globals);\n        break;\n\n      case 'a':\n        txt = showdown.subParser('makeMarkdown.links')(node, globals);\n        break;\n\n      case 'img':\n        txt = showdown.subParser('makeMarkdown.image')(node, globals);\n        break;\n\n      default:\n        txt = node.outerHTML + '\\n\\n';\n    }\n\n    // common normalization\n    // TODO eventually\n\n    return txt;\n  });\n\n  showdown.subParser('makeMarkdown.paragraph', function (node, globals) {\n    'use strict';\n\n    var txt = '';\n    if (node.hasChildNodes()) {\n      var children = node.childNodes,\n          childrenLength = children.length;\n      for (var i = 0; i < childrenLength; ++i) {\n        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n      }\n    }\n\n    // some text normalization\n    txt = txt.trim();\n\n    return txt;\n  });\n\n  showdown.subParser('makeMarkdown.pre', function (node, globals) {\n    'use strict';\n\n    var num = node.getAttribute('prenum');\n    return '
    ' + globals.preList[num] + '
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i < p.length; i++) {\n\t\t\tvar r = p[i].split('=');\n\t\t\tmatches[decodeURIComponent(r[0])] = decodeURIComponent(r.slice(1).join('='));\n\t\t}\n\t}\n\turl = segmentize(url.replace(reg, ''));\n\troute = segmentize(route || '');\n\tvar max = Math.max(url.length, route.length);\n\tfor (var i$1 = 0; i$1 < max; i$1++) {\n\t\tif (route[i$1] && route[i$1].charAt(0) === ':') {\n\t\t\tvar param = route[i$1].replace(/(^\\:|[+*?]+$)/g, ''),\n\t\t\t    flags = (route[i$1].match(/[+*?]+$/) || EMPTY$1)[0] || '',\n\t\t\t    plus = ~flags.indexOf('+'),\n\t\t\t    star = ~flags.indexOf('*'),\n\t\t\t    val = url[i$1] || '';\n\t\t\tif (!val && !star && (flags.indexOf('?') < 0 || plus)) {\n\t\t\t\tret = false;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t\tmatches[param] = decodeURIComponent(val);\n\t\t\tif (plus || star) {\n\t\t\t\tmatches[param] = url.slice(i$1).map(decodeURIComponent).join('/');\n\t\t\t\tbreak;\n\t\t\t}\n\t\t} else if (route[i$1] !== url[i$1]) {\n\t\t\tret = false;\n\t\t\tbreak;\n\t\t}\n\t}\n\tif (opts.default !== true && ret === false) {\n\t\treturn false;\n\t}\n\treturn matches;\n}\n\nfunction pathRankSort(a, b) {\n\treturn a.rank < b.rank ? 1 : a.rank > b.rank ? -1 : a.index - b.index;\n}\n\n// filter out VNodes without attributes (which are unrankeable), and add `index`/`rank` properties to be used in sorting.\nfunction prepareVNodeForRanking(vnode, index) {\n\tvnode.index = index;\n\tvnode.rank = rankChild(vnode);\n\treturn vnode.attributes;\n}\n\nfunction segmentize(url) {\n\treturn url.replace(/(^\\/+|\\/+$)/g, '').split('/');\n}\n\nfunction rankSegment(segment) {\n\treturn segment.charAt(0) == ':' ? 1 + '*+?'.indexOf(segment.charAt(segment.length - 1)) || 4 : 5;\n}\n\nfunction rank(path) {\n\treturn segmentize(path).map(rankSegment).join('');\n}\n\nfunction rankChild(vnode) {\n\treturn vnode.attributes.default ? 0 : rank(vnode.attributes.path);\n}\n\nvar customHistory = null;\n\nvar ROUTERS = [];\n\nvar subscribers = [];\n\nvar EMPTY = {};\n\nfunction isPreactElement(node) {\n\treturn node.__preactattr_ != null || typeof Symbol !== 'undefined' && node[Symbol.for('preactattr')] != null;\n}\n\nfunction setUrl(url, type) {\n\tif (type === void 0) type = 'push';\n\n\tif (customHistory && customHistory[type]) {\n\t\tcustomHistory[type](url);\n\t} else if (typeof history !== 'undefined' && history[type + 'State']) {\n\t\thistory[type + 'State'](null, null, url);\n\t}\n}\n\nfunction getCurrentUrl() {\n\tvar url;\n\tif (customHistory && customHistory.location) {\n\t\turl = customHistory.location;\n\t} else if (customHistory && customHistory.getCurrentLocation) {\n\t\turl = customHistory.getCurrentLocation();\n\t} else {\n\t\turl = typeof location !== 'undefined' ? location : EMPTY;\n\t}\n\treturn \"\" + (url.pathname || '') + (url.search || '');\n}\n\nfunction route(url, replace) {\n\tif (replace === void 0) replace = false;\n\n\tif (typeof url !== 'string' && url.url) {\n\t\treplace = url.replace;\n\t\turl = url.url;\n\t}\n\n\t// only push URL into history if we can handle it\n\tif (canRoute(url)) {\n\t\tsetUrl(url, replace ? 'replace' : 'push');\n\t}\n\n\treturn routeTo(url);\n}\n\n/** Check if the given URL can be handled by any router instances. */\nfunction canRoute(url) {\n\tfor (var i = ROUTERS.length; i--;) {\n\t\tif (ROUTERS[i].canRoute(url)) {\n\t\t\treturn true;\n\t\t}\n\t}\n\treturn false;\n}\n\n/** Tell all router instances to handle the given URL.  */\nfunction routeTo(url) {\n\tvar didRoute = false;\n\tfor (var i = 0; i < ROUTERS.length; i++) {\n\t\tif (ROUTERS[i].routeTo(url) === true) {\n\t\t\tdidRoute = true;\n\t\t}\n\t}\n\tfor (var i$1 = subscribers.length; i$1--;) {\n\t\tsubscribers[i$1](url);\n\t}\n\treturn didRoute;\n}\n\nfunction routeFromLink(node) {\n\t// only valid elements\n\tif (!node || !node.getAttribute) {\n\t\treturn;\n\t}\n\n\tvar href = node.getAttribute('href'),\n\t    target = node.getAttribute('target');\n\n\t// ignore links with targets and non-path URLs\n\tif (!href || !href.match(/^\\//g) || target && !target.match(/^_?self$/i)) {\n\t\treturn;\n\t}\n\n\t// attempt to route, if no match simply cede control to browser\n\treturn route(href);\n}\n\nfunction handleLinkClick(e) {\n\tif (e.button == 0) {\n\t\trouteFromLink(e.currentTarget || e.target || this);\n\t\treturn prevent(e);\n\t}\n}\n\nfunction prevent(e) {\n\tif (e) {\n\t\tif (e.stopImmediatePropagation) {\n\t\t\te.stopImmediatePropagation();\n\t\t}\n\t\tif (e.stopPropagation) {\n\t\t\te.stopPropagation();\n\t\t}\n\t\te.preventDefault();\n\t}\n\treturn false;\n}\n\nfunction delegateLinkHandler(e) {\n\t// ignore events the browser takes care of already:\n\tif (e.ctrlKey || e.metaKey || e.altKey || e.shiftKey || e.button !== 0) {\n\t\treturn;\n\t}\n\n\tvar t = e.target;\n\tdo {\n\t\tif (String(t.nodeName).toUpperCase() === 'A' && t.getAttribute('href') && isPreactElement(t)) {\n\t\t\tif (t.hasAttribute('native')) {\n\t\t\t\treturn;\n\t\t\t}\n\t\t\t// if link is handled by the router, prevent browser defaults\n\t\t\tif (routeFromLink(t)) {\n\t\t\t\treturn prevent(e);\n\t\t\t}\n\t\t}\n\t} while (t = t.parentNode);\n}\n\nvar eventListenersInitialized = false;\n\nfunction initEventListeners() {\n\tif (eventListenersInitialized) {\n\t\treturn;\n\t}\n\n\tif (typeof addEventListener === 'function') {\n\t\tif (!customHistory) {\n\t\t\taddEventListener('popstate', function () {\n\t\t\t\trouteTo(getCurrentUrl());\n\t\t\t});\n\t\t}\n\t\taddEventListener('click', delegateLinkHandler);\n\t}\n\teventListenersInitialized = true;\n}\n\nvar preact_router_es_Router = function (Component$$1) {\n\tfunction Router(props) {\n\t\tComponent$$1.call(this, props);\n\t\tif (props.history) {\n\t\t\tcustomHistory = props.history;\n\t\t}\n\n\t\tthis.state = {\n\t\t\turl: props.url || getCurrentUrl()\n\t\t};\n\n\t\tinitEventListeners();\n\t}\n\n\tif (Component$$1) Router.__proto__ = Component$$1;\n\tRouter.prototype = Object.create(Component$$1 && Component$$1.prototype);\n\tRouter.prototype.constructor = Router;\n\n\tRouter.prototype.shouldComponentUpdate = function shouldComponentUpdate(props) {\n\t\tif (props.static !== true) {\n\t\t\treturn true;\n\t\t}\n\t\treturn props.url !== this.props.url || props.onChange !== this.props.onChange;\n\t};\n\n\t/** Check if the given URL can be matched against any children */\n\tRouter.prototype.canRoute = function canRoute(url) {\n\t\treturn this.getMatchingChildren(this.props.children, url, false).length > 0;\n\t};\n\n\t/** Re-render children with a new URL to match against. */\n\tRouter.prototype.routeTo = function routeTo(url) {\n\t\tthis._didRoute = false;\n\t\tthis.setState({ url: url });\n\n\t\t// if we're in the middle of an update, don't synchronously re-route.\n\t\tif (this.updating) {\n\t\t\treturn this.canRoute(url);\n\t\t}\n\n\t\tthis.forceUpdate();\n\t\treturn this._didRoute;\n\t};\n\n\tRouter.prototype.componentWillMount = function componentWillMount() {\n\t\tROUTERS.push(this);\n\t\tthis.updating = true;\n\t};\n\n\tRouter.prototype.componentDidMount = function componentDidMount() {\n\t\tvar this$1 = this;\n\n\t\tif (customHistory) {\n\t\t\tthis.unlisten = customHistory.listen(function (location) {\n\t\t\t\tthis$1.routeTo(\"\" + (location.pathname || '') + (location.search || ''));\n\t\t\t});\n\t\t}\n\t\tthis.updating = false;\n\t};\n\n\tRouter.prototype.componentWillUnmount = function componentWillUnmount() {\n\t\tif (typeof this.unlisten === 'function') {\n\t\t\tthis.unlisten();\n\t\t}\n\t\tROUTERS.splice(ROUTERS.indexOf(this), 1);\n\t};\n\n\tRouter.prototype.componentWillUpdate = function componentWillUpdate() {\n\t\tthis.updating = true;\n\t};\n\n\tRouter.prototype.componentDidUpdate = function componentDidUpdate() {\n\t\tthis.updating = false;\n\t};\n\n\tRouter.prototype.getMatchingChildren = function getMatchingChildren(children, url, invoke) {\n\t\treturn children.filter(prepareVNodeForRanking).sort(pathRankSort).map(function (vnode) {\n\t\t\tvar matches = exec(url, vnode.attributes.path, vnode.attributes);\n\t\t\tif (matches) {\n\t\t\t\tif (invoke !== false) {\n\t\t\t\t\tvar newProps = { url: url, matches: matches };\n\t\t\t\t\tpreact_router_es_assign(newProps, matches);\n\t\t\t\t\tdelete newProps.ref;\n\t\t\t\t\tdelete newProps.key;\n\t\t\t\t\treturn Object(preact_min[\"cloneElement\"])(vnode, newProps);\n\t\t\t\t}\n\t\t\t\treturn vnode;\n\t\t\t}\n\t\t}).filter(Boolean);\n\t};\n\n\tRouter.prototype.render = function render(ref, ref$1) {\n\t\tvar children = ref.children;\n\t\tvar onChange = ref.onChange;\n\t\tvar url = ref$1.url;\n\n\t\tvar active = this.getMatchingChildren(children, url, true);\n\n\t\tvar current = active[0] || null;\n\t\tthis._didRoute = !!current;\n\n\t\tvar previous = this.previousUrl;\n\t\tif (url !== previous) {\n\t\t\tthis.previousUrl = url;\n\t\t\tif (typeof onChange === 'function') {\n\t\t\t\tonChange({\n\t\t\t\t\trouter: this,\n\t\t\t\t\turl: url,\n\t\t\t\t\tprevious: previous,\n\t\t\t\t\tactive: active,\n\t\t\t\t\tcurrent: current\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\treturn current;\n\t};\n\n\treturn Router;\n}(preact_min[\"Component\"]);\n\nvar preact_router_es_Link = function Link(props) {\n\treturn Object(preact_min[\"h\"])('a', preact_router_es_assign({ onClick: handleLinkClick }, props));\n};\n\nvar preact_router_es_Route = function Route(props) {\n\treturn Object(preact_min[\"h\"])(props.component, props);\n};\n\npreact_router_es_Router.subscribers = subscribers;\npreact_router_es_Router.getCurrentUrl = getCurrentUrl;\npreact_router_es_Router.route = route;\npreact_router_es_Router.Router = preact_router_es_Router;\npreact_router_es_Router.Route = preact_router_es_Route;\npreact_router_es_Router.Link = preact_router_es_Link;\n\n/* harmony default export */ var preact_router_es = (preact_router_es_Router);\n//# sourceMappingURL=preact-router.es.js.map\n// EXTERNAL MODULE: ./pages/home.css\nvar home = __webpack_require__(\"36Ou\");\nvar home_default = /*#__PURE__*/__webpack_require__.n(home);\n\n// EXTERNAL MODULE: ./components/panel.css\nvar panel = __webpack_require__(\"P9k+\");\nvar panel_default = /*#__PURE__*/__webpack_require__.n(panel);\n\n// CONCATENATED MODULE: ./components/panel.js\n\n\nfunction _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction _possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction _inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar panel_Panel = function (_Component) {\n\t_inherits(Panel, _Component);\n\n\tfunction Panel() {\n\t\t_classCallCheck(this, Panel);\n\n\t\treturn _possibleConstructorReturn(this, _Component.apply(this, arguments));\n\t}\n\n\tPanel.prototype.getStyle = function getStyle() {\n\t\treturn panel_default.a.panel;\n\t};\n\n\tPanel.prototype.render = function render() {\n\t\tvar title = null;\n\t\tif (this.props.title !== undefined) {\n\t\t\ttitle = Object(preact_min[\"h\"])(\n\t\t\t\t\"h3\",\n\t\t\t\tnull,\n\t\t\t\tthis.props.title\n\t\t\t);\n\t\t}\n\n\t\treturn Object(preact_min[\"h\"])(\n\t\t\t\"div\",\n\t\t\t{ \"class\": this.getStyle(), id: this.props.id },\n\t\t\ttitle,\n\t\t\tthis.props.children\n\t\t);\n\t};\n\n\treturn Panel;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./components/split.css\nvar split = __webpack_require__(\"1EpE\");\nvar split_default = /*#__PURE__*/__webpack_require__.n(split);\n\n// CONCATENATED MODULE: ./components/split.js\n\n\nfunction split__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction split__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction split__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar split_Split = function (_Component) {\n    split__inherits(Split, _Component);\n\n    function Split() {\n        split__classCallCheck(this, Split);\n\n        return split__possibleConstructorReturn(this, _Component.apply(this, arguments));\n    }\n\n    Split.prototype.render = function render() {\n        var title = null;\n        if (this.props.title !== undefined) {\n            title = Object(preact_min[\"h\"])(\n                \"h2\",\n                null,\n                this.props.title\n            );\n        }\n\n        var children = void 0;\n        if (Array.isArray(this.props.children)) {\n            children = this.props.children.map(function (element) {\n                return Object(preact_min[\"h\"])(\n                    \"div\",\n                    { \"class\": split_default.a.splitchild },\n                    element\n                );\n            });\n        } else {\n            children = Object(preact_min[\"h\"])(\n                \"div\",\n                { \"class\": split_default.a.splitchild },\n                this.props.children\n            );\n        }\n        return Object(preact_min[\"h\"])(\n            \"div\",\n            { \"class\": split_default.a.split },\n            title,\n            Object(preact_min[\"h\"])(\n                \"div\",\n                { \"class\": split_default.a.splitparent },\n                children\n            )\n        );\n    };\n\n    return Split;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./components/todo.css\nvar todo = __webpack_require__(\"tO1d\");\nvar todo_default = /*#__PURE__*/__webpack_require__.n(todo);\n\n// CONCATENATED MODULE: ./components/todo.js\n\n\nfunction todo__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction todo__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction todo__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar todo_Todo = function (_Component) {\n\ttodo__inherits(Todo, _Component);\n\n\tfunction Todo() {\n\t\ttodo__classCallCheck(this, Todo);\n\n\t\treturn todo__possibleConstructorReturn(this, _Component.apply(this, arguments));\n\t}\n\n\tTodo.prototype.render = function render() {\n\t\treturn Object(preact_min[\"h\"])(\n\t\t\t\"span\",\n\t\t\t{ \"class\": todo_default.a.todo },\n\t\t\tthis.props.children\n\t\t);\n\t};\n\n\treturn Todo;\n}(preact_min[\"Component\"]);\n\n\n// CONCATENATED MODULE: ./pages/home.js\n\n\nfunction home__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction home__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction home__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\n\n\n\nvar _ref = Object(preact_min[\"h\"])(\n    'h1',\n    null,\n    'Indice'\n);\n\nvar _ref2 = Object(preact_min[\"h\"])(\n    split_Split,\n    { title: 'Argomenti' },\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: '/statistica' },\n                'Statistica ed elementi di probabilit\\xE0'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Appunti scritti mentre studiavo per l\\'esame di ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: \"http://personale.unimore.it/rubrica/contenutiad/llarocca/2019/58028/N0/N0/9999\" },\n                'Statistica ed elementi di probabilit\\xE0'\n            ),\n            '  del ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/didattica/mlaurea.html?ID=54' },\n                'corso triennale di Informatica'\n            ),\n            ' all\\'',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/' },\n                'Unimore'\n            ),\n            ' del Prof. ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: \"http://personale.unimore.it/rubrica/dettaglio/llarocca\" },\n                'Luca La Rocca'\n            ),\n            '.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://github.com/Steffo99/cleaver' },\n                'Cleaver'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Progetto in Java sviluppato per l\\'esame di ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'http://personale.unimore.it/rubrica/contenutiad/gcabri/2019/58026/N0/N0/9999' },\n                'Programmazione ad Oggetti'\n            ),\n            ' del ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/didattica/mlaurea.html?ID=54' },\n                'corso triennale di Informatica'\n            ),\n            ' all\\'',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/' },\n                'Unimore'\n            ),\n            ', tenuto dai Prof. ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'http://personale.unimore.it/rubrica/dettaglio/gcabri' },\n                'Giacomo Cabri'\n            ),\n            ' e ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'http://personale.unimore.it/Rubrica/Dettaglio/n.capodieci' },\n                'Nicola Capodieci'\n            ),\n            '.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: '/fisica' },\n                'Fisica'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Appunti delle ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'http://personale.unimore.it/rubrica/contenutiad/brunetti/2019/58025/N0/N0/9999' },\n                'lezioni di Fisica'\n            ),\n            ' del ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/didattica/mlaurea.html?ID=54' },\n                'corso triennale di Informatica'\n            ),\n            ' all\\'',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/' },\n                'Unimore'\n            ),\n            ', tenute dalla ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://personale.unimore.it/rubrica/dettaglio/brunetti' },\n                'Prof.ssa Rossella Brunetti'\n            ),\n            ' nel primo semestre dell\\'Anno Accademico 2019/2020.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://github.com/Steffo99/appunti-universitari/tree/master/2019_SistemiOperativi/Arzigogoli' },\n                'Sistemi Operativi'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Soluzioni agli ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://weblab.ing.unimore.it/people/andreolini/didattica/sistemi-operativi/index.html#arzigogoli' },\n                'Arzigogoli'\n            ),\n            ' proposti dal ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://personale.unimore.it/rubrica/dettaglio/andreolini' },\n                'Prof. Mauro Andreolini'\n            ),\n            ' durante le ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://personale.unimore.it/rubrica/contenutiad/andreolini/2019/58027/N0/N0/9999' },\n                'lezioni di Sistemi Operativi'\n            ),\n            ' del ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/didattica/mlaurea.html?ID=54' },\n                'corso triennale di Informatica'\n            ),\n            ' all\\'',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/' },\n                'Unimore'\n            ),\n            ' tenutesi nel primo semestre dell\\'Anno Accademico 2019/2020.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://github.com/Steffo99/appunti-universitari/tree/master/2018_AlgoritmiEStruttureDati' },\n                'Algoritmi e Strutture Dati'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Appunti delle ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://personale.unimore.it/rubrica/contenutiad/mmontangero/2018/58133/N0/N0/9999' },\n                'lezioni di Algoritmi e Strutture Dati'\n            ),\n            ' del ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/didattica/mlaurea.html?ID=54' },\n                'corso triennale di Informatica'\n            ),\n            ' all\\'',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/' },\n                'Unimore'\n            ),\n            ', tenute dalla ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://personale.unimore.it/rubrica/dettaglio/mmontangero' },\n                'Prof.ssa Manuela Montangero'\n            ),\n            ' nel secondo semestre dell\\'Anno Accademico 2018/2019.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: '/vldigeometria' },\n                'Videolezioni di Geometria'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Ottime videolezioni di Geometria con licenza ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://creativecommons.org/licenses/by-nc-sa/4.0/' },\n                'CC BY-NC-SA 4.0'\n            ),\n            ' che ho trovato sul ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0' },\n                'portale Dolly 2018'\n            ),\n            ' dell\\'',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/' },\n                'Unimore'\n            ),\n            '.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: '/mingwinstall' },\n                'Come installare MinGW'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Un breve tutorial con immagini su come installare e configurare ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://it.wikipedia.org/wiki/MinGW' },\n                'MinGW'\n            ),\n            ' per compilare programmi C e C++ su Windows.'\n        )\n    )\n);\n\nvar _ref3 = Object(preact_min[\"h\"])(\n    split_Split,\n    { title: 'Altri collegamenti utili' },\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://t.me/unimoreinfo' },\n                '@unimoreinfo'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Il gruppo ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://telegram.org/' },\n                'Telegram'\n            ),\n            ' del corso di Informatica dell\\'Unimore!'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://calendar.google.com/calendar?cid=MmYza2o2M3VuZWQ1cmZqaGpmOGY0MWFrNmdAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ' },\n                'Calendario Lezioni'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Calendario Google ',\n            Object(preact_min[\"h\"])(\n                'small',\n                null,\n                'quasi'\n            ),\n            ' sempre aggiornato delle lezioni e degli esami del secondo anno dell\\'',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://www.unimore.it/' },\n                'Unimore'\n            ),\n            ' durante l\\'Anno Accademico 2019/2020.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: 'http://erre2.fermitech.info/dashboard' },\n                'Erre2'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Portale contenente appunti e riassunti mantenuto da ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://github.com/LBindustries' },\n                'Lorenzo Balugani'\n            ),\n            '.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://github.com/vezzalinistefano/Appunti-Algoritmi' },\n                'vezzalinistefano/Appunti-Algoritmi'\n            ) },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Appunti di Algoritmi e Strutture Dati mantenuti da ',\n            Object(preact_min[\"h\"])(\n                'a',\n                { href: 'https://github.com/vezzalinistefano/' },\n                'Vezzalini Stefano'\n            ),\n            '.'\n        )\n    )\n);\n\nvar home_Home = function (_Component) {\n    home__inherits(Home, _Component);\n\n    function Home() {\n        home__classCallCheck(this, Home);\n\n        return home__possibleConstructorReturn(this, _Component.apply(this, arguments));\n    }\n\n    Home.prototype.render = function render() {\n        return Object(preact_min[\"h\"])(\n            'div',\n            { style: home_default.a.home },\n            _ref,\n            _ref2,\n            _ref3\n        );\n    };\n\n    return Home;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./pages/fisica.css\nvar fisica = __webpack_require__(\"0lnO\");\nvar fisica_default = /*#__PURE__*/__webpack_require__.n(fisica);\n\n// EXTERNAL MODULE: ./components/latex.css\nvar latex = __webpack_require__(\"+uq9\");\nvar latex_default = /*#__PURE__*/__webpack_require__.n(latex);\n\n// CONCATENATED MODULE: ./components/latex.js\n\n\nfunction latex__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction latex__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction latex__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar latex_Latex = function (_Component) {\n\tlatex__inherits(Latex, _Component);\n\n\tfunction Latex() {\n\t\tlatex__classCallCheck(this, Latex);\n\n\t\treturn latex__possibleConstructorReturn(this, _Component.apply(this, arguments));\n\t}\n\n\tLatex.prototype.render = function render() {\n\t\tvar equation = '{\\\\color{White} ' + this.props.children + ' }';\n\t\treturn Object(preact_min[\"h\"])('img', { src: 'https://latex.codecogs.com/svg.latex?' + equation,\n\t\t\talt: this.props.children,\n\t\t\ttitle: this.props.children,\n\t\t\t'class': latex_default.a.latex\n\t\t});\n\t};\n\n\treturn Latex;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./components/plus.css\nvar plus = __webpack_require__(\"ddTt\");\nvar plus_default = /*#__PURE__*/__webpack_require__.n(plus);\n\n// CONCATENATED MODULE: ./components/plus.js\n\n\nfunction plus__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction plus__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction plus__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar plus_Plus = function (_Component) {\n\tplus__inherits(Plus, _Component);\n\n\tfunction Plus() {\n\t\tplus__classCallCheck(this, Plus);\n\n\t\treturn plus__possibleConstructorReturn(this, _Component.apply(this, arguments));\n\t}\n\n\tPlus.prototype.render = function render() {\n\t\treturn Object(preact_min[\"h\"])(\n\t\t\t\"span\",\n\t\t\t{ \"class\": plus_default.a.plus },\n\t\t\tthis.props.children\n\t\t);\n\t};\n\n\treturn Plus;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./components/minus.css\nvar minus = __webpack_require__(\"MeW5\");\nvar minus_default = /*#__PURE__*/__webpack_require__.n(minus);\n\n// CONCATENATED MODULE: ./components/minus.js\n\n\nfunction minus__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction minus__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction minus__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar minus_Minus = function (_Component) {\n\tminus__inherits(Minus, _Component);\n\n\tfunction Minus() {\n\t\tminus__classCallCheck(this, Minus);\n\n\t\treturn minus__possibleConstructorReturn(this, _Component.apply(this, arguments));\n\t}\n\n\tMinus.prototype.render = function render() {\n\t\treturn Object(preact_min[\"h\"])(\n\t\t\t\"span\",\n\t\t\t{ \"class\": minus_default.a.minus },\n\t\t\tthis.props.children\n\t\t);\n\t};\n\n\treturn Minus;\n}(preact_min[\"Component\"]);\n\n\n// CONCATENATED MODULE: ./pages/fisica.js\nvar _templateObject = _taggedTemplateLiteralLoose(['\\x0Bec{v} = \\x0Bec{v}_x + \\x0Bec{v}_y'], ['\\\\vec{v} = \\\\vec{v}_x + \\\\vec{v}_y']),\n    _templateObject2 = _taggedTemplateLiteralLoose(['left | \\x0Bec{v}_x \\right | = left | \\x0Bec{v} \\right | sin alpha'], ['\\\\left | \\\\vec{v}_x \\\\right | = \\\\left | \\\\vec{v} \\\\right | \\\\sin \\\\alpha']),\n    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\\frac{1}{n^2} cdot \\frac{m_{elettrone} cdot k^2 cdot e^4}{2 cdot hbar^2}'], ['E_n = \\\\frac{1}{n^2} \\\\cdot E_1 = - \\\\frac{1}{n^2} \\\\cdot \\\\frac{a_0^2}{2 \\\\cdot m \\\\cdot \\\\hbar^4} = - \\\\frac{1}{n^2} \\\\cdot \\\\frac{m_{elettrone} \\\\cdot k^2 \\\\cdot e^4}{2 \\\\cdot \\\\hbar^2}']),\n    _templateObject122 = _taggedTemplateLiteralLoose(['10^1 eV'], ['10^1 eV']),\n    _templateObject123 = _taggedTemplateLiteralLoose(['1 eV'], ['1 eV']),\n    _templateObject124 = _taggedTemplateLiteralLoose(['lambda'], ['\\\\lambda']),\n    _templateObject125 = _taggedTemplateLiteralLoose(['lambda_{max} cdot T'], ['\\\\lambda_{max} \\\\cdot T']),\n    _templateObject126 = _taggedTemplateLiteralLoose(['E_{fotone} = h cdot f'], ['E_{fotone} = h \\\\cdot f']);\n\n\n\nfunction _taggedTemplateLiteralLoose(strings, raw) { strings.raw = raw; return strings; }\n\nfunction fisica__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call 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Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\n\n\n\n\n\n\nvar r = String.raw;\n\nvar fisica__ref = Object(preact_min[\"h\"])(\n    'h1',\n    null,\n    'Fisica'\n);\n\nvar fisica__ref2 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Usa le regole base della trigonometria:'\n);\n\nvar fisica__ref3 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Scomponi in componenti, poi sommali:'\n);\n\nvar _ref4 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Produce il vettore risultante dall\\'applicazione della regola del parallelogramma.'\n);\n\nvar _ref5 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Alla fine \\xE8 sempre una somma:'\n);\n\nvar _ref6 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Produce il vettore che parte da ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'w'\n    ),\n    ' e arriva a ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'v'\n    ),\n    '.'\n);\n\nvar _ref7 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Si chiama scalare perch\\xE8 il risultato \\xE8 uno scalare, non un vettore.'\n);\n\nvar _ref8 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Si chiama vettoriale perch\\xE8 il risultato \\xE8 un altro vettore.'\n);\n\nvar _ref9 = Object(preact_min[\"h\"])(\n    'li',\n    null,\n    Object(preact_min[\"h\"])(\n        'a',\n        { href: 'https://it.wikipedia.org/wiki/Regola_della_mano_destra' },\n        'Regola della mano destra'\n    )\n);\n\nvar _ref10 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Non \\xE8 commutativo!'\n);\n\nvar _ref11 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se un corpo puntiforme ha forza risultante nulla, allora la sua velocit\\xE0 non cambia.'\n);\n\nvar _ref12 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La forza risultante di un corpo \\xE8 direttamente proporzionale alla sua accelerazione, e la costante di proporzionalit\\xE0 \\xE8 la ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'massa'\n    ),\n    '.'\n);\n\nvar _ref13 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Due corpi esercitano forze uguali e opposte uno sull\\'altro.'\n);\n\nvar _ref14 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Due corpi puntiformi si attirano uno verso l\\'altro con forza:'\n);\n\nvar _ref15 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'G'\n    ),\n    ' \\xE8 la ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'costante di gravitazione universale'\n    ),\n    ' e vale:'\n);\n\nvar _ref16 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo \\xE8 attratto verso la Terra con forza ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'peso'\n    ),\n    ' 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panel_Panel,\n    { title: 'Forze' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Si applica la prima legge di Newton:'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'f(t) = m a'\n        )\n    )\n);\n\nvar _ref42 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Ampiezza' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'E\\' la distanza dal centro massima che raggiunge il corpo.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        '(L\\'ampiezza di una sinusoide.)'\n    )\n);\n\nvar _ref43 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Indica quanto in fretta cambia la posizione del corpo.'\n);\n\nvar _ref44 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Dipende dal periodo:'\n);\n\nvar _ref45 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' una 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null,\n            'conduttori'\n        ),\n        ', mentre quelli in cui si muove difficilmente sono ',\n        Object(preact_min[\"h\"])(\n            'i',\n            null,\n            'isolanti'\n        ),\n        '.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        Object(preact_min[\"h\"])(\n            'i',\n            null,\n            'Il corpo umano \\xE8 un buon conduttore.'\n        )\n    )\n);\n\nvar _ref69 = Object(preact_min[\"h\"])(\n    split_Split,\n    { title: 'Polarizzazione' },\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Polarizzazione' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'E\\' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona.'\n        )\n    )\n);\n\nvar _ref70 = Object(preact_min[\"h\"])(\n    split_Split,\n    null,\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Messa a terra' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Se un corpo conduttore \\xE8 in contatto con la Terra, le cariche su di esso saranno ',\n            Object(preact_min[\"h\"])(\n                'i',\n                null,\n                'equilibrate'\n            ),\n            ' e il corpo diventer\\xE0 elettricamente neutro (con stesso numero di ',\n            Object(preact_min[\"h\"])(\n                plus_Plus,\n                null,\n                'cariche positive'\n            ),\n            ' e ',\n            Object(preact_min[\"h\"])(\n                minus_Minus,\n                null,\n                'negative'\n            ),\n            ' all\\'interno).'\n        )\n    )\n);\n\nvar _ref71 = Object(preact_min[\"h\"])(\n    split_Split,\n    null,\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Polarizzazione per strofinio' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Strofinando tra loro due corpi isolanti, essi si ',\n            Object(preact_min[\"h\"])(\n                'i',\n                null,\n                'polarizzeranno per strofinio'\n            ),\n            '.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Polarizzazione per contatto' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Toccando un conduttore con un corpo carico, il conduttore potr\\xE0 ',\n            Object(preact_min[\"h\"])(\n                'i',\n                null,\n                'polarizzarsi per contatto'\n            ),\n            '.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Polarizzazione per induzione' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Se un corpo conduttore ha cariche \"esterne\" di un ',\n            Object(preact_min[\"h\"])(\n                plus_Plus,\n                null,\n                'certo segno'\n            ),\n            ' vicino, esso avr\\xE0 tutte le cariche del ',\n            Object(preact_min[\"h\"])(\n                minus_Minus,\n                null,\n                'segno opposto'\n            ),\n            ' in equilibrio vicino alle cariche esterne, e tutte le cariche dello ',\n            Object(preact_min[\"h\"])(\n                plus_Plus,\n                null,\n                'stesso segno'\n            ),\n            ' pi\\xF9 lontano possibile da esse.'\n        ),\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Mettendo a terra il conduttore, nuove cariche del ',\n            Object(preact_min[\"h\"])(\n                minus_Minus,\n                null,\n                'segno opposto'\n            ),\n            ' saranno attratte all\\'interno del corpo per equilibrare le cariche che si sono allontanate.'\n        ),\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritrover\\xE0 ',\n            Object(preact_min[\"h\"])(\n                minus_Minus,\n                null,\n                'caricato del segno opposto'\n            ),\n            ' rispetto alle cariche esterne.'\n        )\n    )\n);\n\nvar _ref72 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Due corpi carichi si attraggono tra loro con forza:'\n);\n\nvar _ref73 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'costante di Coulomb'\n);\n\nvar _ref74 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'permeabilit\\xE0 del vuoto'\n);\n\nvar _ref75 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Misura che forza viene applicata in ogni punto su una carica unitaria:'\n);\n\nvar _ref76 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    '\\xC8 la differenza tra \"quanto\" campo elettrico ',\n    Object(preact_min[\"h\"])(\n        plus_Plus,\n        null,\n        'entra'\n    ),\n    ' e quanto campo elettrico ',\n    Object(preact_min[\"h\"])(\n        minus_Minus,\n        null,\n        'esce'\n    ),\n    ' da una certa area.'\n);\n\nvar _ref77 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'In qualsiasi superficie chiusa, il flusso elettrico \\xE8 uguale alla componente perpendicolare del campo elettrico moltiplicato per l\\'area.'\n);\n\nvar _ref78 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se il campo elettrico \\xE8 uniforme, se ne pu\\xF2 calcolare facilmente il valore:'\n);\n\nvar _ref79 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    Object(preact_min[\"h\"])(\n        todo_Todo,\n        null,\n        'Circa. E\\' una specie di integrale...'\n    )\n);\n\nvar _ref80 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Il flusso elettrico \\xE8 direttamente proporzionale alla carica presente all\\'interno della superficie.'\n);\n\nvar _ref81 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Ovvero, i campi elettrostatici sono generati dalle cariche elettriche.'\n);\n\nvar _ref82 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'energia potenziale elettrica'\n);\n\nvar _ref83 = Object(preact_min[\"h\"])(\n    'span',\n    null,\n    'Potenziale elettrico ',\n    Object(preact_min[\"h\"])(\n        'small',\n        null,\n        '(tensione)'\n    )\n);\n\nvar _ref84 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    '\\xC8 il valore dell\\'energia potenziale elettrica per una carica unitaria.'\n);\n\nvar _ref85 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'In una batteria \\xE8 detto ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'forza elettromotrice'\n    ),\n    ', e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.'\n);\n\nvar _ref86 = Object(preact_min[\"h\"])(\n    'span',\n    null,\n    'Corrente elettrica ',\n    Object(preact_min[\"h\"])(\n        'small',\n        null,\n        '(intensit\\xE0)'\n    )\n);\n\nvar _ref87 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Quanta carica passa attraverso un\\'area (perpendicolare al flusso) nel tempo.'\n);\n\nvar _ref88 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Fintanto che c\\'\\xE8 differenza di potenziale, ci sar\\xE0 anche intensit\\xE0 non nulla.'\n);\n\nvar _ref89 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: Object(preact_min[\"h\"])(\n            'span',\n            null,\n            'Corrente continua ',\n            Object(preact_min[\"h\"])(\n                'small',\n                null,\n                '(',\n                Object(preact_min[\"h\"])(\n                    'abbr',\n                    { title: 'Direct Current' },\n                    'DC'\n                ),\n                ')'\n            )\n        ) },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Quando in un circuito la direzione della corrente \\xE8 costante.'\n    )\n);\n\nvar _ref90 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: Object(preact_min[\"h\"])(\n            'span',\n            null,\n            'Corrente alternata ',\n            Object(preact_min[\"h\"])(\n                'small',\n                null,\n                '(',\n                Object(preact_min[\"h\"])(\n                    'abbr',\n                    { title: 'Alternate Current' },\n                    'AC'\n                ),\n                ')'\n            )\n        ) },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Quando in un circuito la direzione della corrente si alterna periodicamente.'\n    )\n);\n\nvar _ref91 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Possiamo calcolare la potenza di un circuito:'\n);\n\nvar _ref92 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Riduce l\\'intensit\\xE0 di corrente, e converte parte del potenziale in calore.'\n);\n\nvar _ref93 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Il potenziale utilizzato \\xE8 pari a:'\n);\n\nvar _ref94 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'resistenza'\n);\n\nvar _ref95 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La resistenza di un conduttore vale:'\n);\n\nvar _ref96 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'resistivit\\xE0'\n);\n\nvar _ref97 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito.'\n);\n\nvar _ref98 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Per farlo, cattura cariche ',\n    Object(preact_min[\"h\"])(\n        plus_Plus,\n        null,\n        'positive'\n    ),\n    ' e ',\n    Object(preact_min[\"h\"])(\n        minus_Minus,\n        null,\n        'negative'\n    ),\n    ' sulle sue due armature; perch\\xE8 questo avvenga, deve essere compiuto lavoro.'\n);\n\nvar _ref99 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Ha una ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'capacit\\xE0'\n    ),\n    ' caratteristica, che in un condensatore a facce piane parallele \\xE8:'\n);\n\nvar _ref100 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Condensatori di capacit\\xE0 maggiore immagazzinano pi\\xF9 potenziale con meno carica.'\n);\n\nvar _ref101 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La capacit\\xE0 aumenta se viene messo qualcosa tra le armature:'\n);\n\nvar _ref102 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'costante dielettrica relativa'\n);\n\nvar _ref103 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se il campo elettrico creatosi tra le due armature supera la ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'rigidit\\xE0 dielettrica'\n    ),\n    ' del condensatore, la carica immagazzinata viene persa e ha luogo un ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'breakdown'\n    ),\n    '.'\n);\n\nvar _ref104 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Amperometro' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Misura la corrente elettrica se messo in serie.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        '(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)'\n    )\n);\n\nvar _ref105 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Voltmetro' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Misura la differenza di potenziale se messo in parallelo.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        '(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)'\n    )\n);\n\nvar _ref106 = Object(preact_min[\"h\"])(\n    split_Split,\n    { title: 'Principi di Kirchhoff' },\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Legge dei nodi' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Per nodo si intende un qualsiasi punto del circuito.'\n        ),\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Da un nodo entra ed esce la stessa corrente.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Legge delle maglie' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Per maglia si intende un qualsiasi percorso chiuso all\\'interno del circuito.'\n        ),\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'In una maglia chiusa, la somma delle differenze di potenziale \\xE8 0.'\n        )\n    )\n);\n\nvar _ref107 = Object(preact_min[\"h\"])(\n    split_Split,\n    { title: 'Serie e Parallelo' },\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Circuito in serie' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Pi\\xF9 parti di circuito sono ',\n            Object(preact_min[\"h\"])(\n                'i',\n                null,\n                'in serie'\n            ),\n            ' se sono consecutive e senza biforcazioni.'\n        ),\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Parti di circuito in serie sono attraversate dalla stessa corrente.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Circuito in parallelo' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Pi\\xF9 parti di circuito sono ',\n            Object(preact_min[\"h\"])(\n                'i',\n                null,\n                'in parallelo'\n            ),\n            ' tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo.'\n        ),\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Parti di circuito in parallelo hanno la stessa differenza di potenziale.'\n        )\n    )\n);\n\nvar _ref108 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:'\n);\n\nvar _ref109 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:'\n);\n\nvar _ref110 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacit\\xE0 di:'\n);\n\nvar _ref111 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacit\\xE0 della somma di tutti quelli sostituiti:'\n);\n\nvar _ref112 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente.'\n);\n\nvar _ref113 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Come un campo elettrico, ma per i magneti.'\n);\n\nvar _ref114 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'T'\n);\n\nvar _ref115 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    '\\xC8 \"quanto\" campo magnetico ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'attraversa'\n    ),\n    ' un percorso chiuso.'\n);\n\nvar _ref116 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Per qualsiasi percorso chiuso, il flusso magnetico \\xE8 uguale alla somma di tutti i \"sottoflussi\" magnetici calcolati sui suoi lati.'\n);\n\nvar _ref117 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Legge di Gauss per i campi magnetici' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Il flusso magnetico attraverso qualsiasi superficie chiusa \\xE8 sempre nullo.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Ovvero, non esistono monopoli magnetici.'\n    )\n);\n\nvar _ref118 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'intensit\\xE0 di corrente che attraversa un percorso chiuso \\xE8 direttamente proporzionale al flusso magnetico dello stesso percorso.'\n);\n\nvar _ref119 = Object(preact_min[\"h\"])(\n    'span',\n    null,\n    'Forza magnetica su carica puntiforme ',\n    Object(preact_min[\"h\"])(\n        'small',\n        null,\n        '(Forza di Lorentz)'\n    )\n);\n\nvar _ref120 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'I campi magnetici applicano una forza sulle cariche vicine:'\n);\n\nvar _ref121 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Si ha una forza massima se la velocit\\xE0 \\xE8 perpendicolare al campo magnetico.'\n);\n\nvar _ref122 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'In un campo magnetico uniforme, una velocit\\xE0 perpendicolare al campo porta alla creazione di un moto circolare uniforme.'\n);\n\nvar _ref123 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:'\n);\n\nvar _ref124 = Object(preact_min[\"h\"])(\n    'a',\n    { href: 'https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360' },\n    '[1]'\n);\n\nvar _ref125 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Campo magnetico in una spira' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.'\n    )\n);\n\nvar _ref126 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.'\n);\n\nvar _ref127 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'All\\'interno del solenoide si crea un campo (quasi) uniforme:'\n);\n\nvar _ref128 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'Caso particolare della ',\n        Object(preact_min[\"h\"])(\n            'a',\n            { href: 'https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re' },\n            'Legge di Amp\\xE8re'\n        ),\n        '.'\n    )\n);\n\nvar _ref129 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Il modulo del campo magnetico ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'B'\n    ),\n    ' prodotto da un filo in cui passa una corrente continua ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'I'\n    ),\n    ' alla distanza ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        's'\n    ),\n    ' \\xE8:'\n);\n\nvar _ref130 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Il campo magnetico cos\\xEC creato gira attorno al filo in senso antiorario.'\n);\n\nvar _ref131 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Due fili attraversati dalla ',\n    Object(preact_min[\"h\"])(\n        plus_Plus,\n        null,\n        'stessa corrente'\n    ),\n    ' si attraggono, due fili attraversati da ',\n    Object(preact_min[\"h\"])(\n        plus_Plus,\n        null,\n        'corr'\n    ),\n    Object(preact_min[\"h\"])(\n        minus_Minus,\n        null,\n        'enti'\n    ),\n    ' ',\n    Object(preact_min[\"h\"])(\n        plus_Plus,\n        null,\n        'opp'\n    ),\n    Object(preact_min[\"h\"])(\n        minus_Minus,\n        null,\n        'oste'\n    ),\n    ' si respingono.'\n);\n\nvar _ref132 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un conduttore perpendicolare ad un campo magnetico pu\\xF2 ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo.'\n);\n\nvar _ref133 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore.'\n);\n\nvar _ref134 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Essa vale:'\n);\n\nvar _ref135 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Dove ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'v'\n    ),\n    ' \\xE8 la velocit\\xE0 del conduttore, ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'B'\n    ),\n    ' \\xE8 l\\'intensit\\xE0 del campo magnetico ed ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'L'\n    ),\n    ' \\xE8 la lunghezza del conduttore.'\n);\n\nvar _ref136 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'Legge di Faraday-Neumann-Lenz'\n);\n\nvar _ref137 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.'\n);\n\nvar _ref138 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Il meno \\xE8 dovuto alla ',\n    Object(preact_min[\"h\"])(\n        'a',\n        { href: 'https://it.wikipedia.org/wiki/Legge_di_Lenz' },\n        'Legge di Lenz'\n    ),\n    ', che specifica qualitativamente il verso della forza elettromotrice indotta.'\n);\n\nvar _ref139 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'In un solenoide, la forza elettromotrice indotta \\xE8 uguale a:'\n);\n\nvar _ref140 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Legge di Amp\\xE8re-Maxwell' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Correnti o campi elettrici variabili creano un campo magnetico.'\n    )\n);\n\nvar _ref141 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Si dice quindi che sono ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'onde elettromagnetiche'\n    ),\n    '.'\n);\n\nvar _ref142 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Esse sono legate dalla relazione:'\n);\n\nvar _ref143 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'I solidi, se portati ad alta temperatura, emettono luce con uno ',\n    Object(preact_min[\"h\"])(\n        'a',\n        { href: 'https://it.wikipedia.org/wiki/Spettro_continuo' },\n        'spettro continuo'\n    ),\n    '.'\n);\n\nvar _ref144 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d\\'onda.'\n);\n\nvar _ref145 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'In un gas di idrogeno, le lunghezze d\\'onda emesse sono ricavabili con:'\n);\n\nvar _ref146 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una grandezza si dice quantizzata (o discreta) se pu\\xF2 assumere solo determinati valori.'\n);\n\nvar _ref147 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una grandezza si dice continua se pu\\xF2 assumere qualsiasi valore e quindi se non \\xE8 quantizzata.'\n);\n\nvar _ref148 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Energia, momento angolare e raggio sono quantizzati.'\n);\n\nvar _ref149 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'energia degli elettroni \\xE8 quantizzata.'\n);\n\nvar _ref150 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Inoltre, per essi \\xE8 valido che:'\n);\n\nvar _ref151 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Ancora, il raggio delle orbite \\xE8 uguale a:'\n);\n\nvar _ref152 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Infine, in ogni stato, l\\'energia \\xE8 pari a:'\n);\n\nvar _ref153 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Due elettroni non possono occupare lo stesso stato.'\n);\n\nvar _ref154 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di'\n);\n\nvar _ref155 = Object(preact_min[\"h\"])(\n    split_Split,\n    null,\n    Object(preact_min[\"h\"])(\n        panel_Panel,\n        { title: 'Nei solidi' },\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Nei solidi, le lunghezze d\\'onda sono talmente tanto vicine da poter essere considerate una banda.'\n        ),\n        Object(preact_min[\"h\"])(\n            'p',\n            null,\n            'Possono per\\xF2 comunque avere dei gap dovuti agli intervalli di energia non ammessi.'\n        )\n    )\n);\n\nvar _ref156 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    Object(preact_min[\"h\"])(\n        todo_Todo,\n        null,\n        'Refactor this'\n    )\n);\n\nvar _ref157 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se invece la banda di emissione si sovrappone a un altra, allora il corpo \\xE8 un conduttore.'\n);\n\nvar _ref158 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Lacune' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Legami in cui ',\n        Object(preact_min[\"h\"])(\n            plus_Plus,\n            null,\n            'mancano elettroni'\n        ),\n        '.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        Object(preact_min[\"h\"])(\n            minus_Minus,\n            null,\n            'Elettroni'\n        ),\n        ' di altri legami possono spostarsi per colmare le ',\n        Object(preact_min[\"h\"])(\n            plus_Plus,\n            null,\n            'lacune'\n        ),\n        ', creandone altre, e spostandole in direzione opposta a quella della corrente.'\n    )\n);\n\nvar _ref159 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Accettori e donori' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterr\\xE0:'\n    ),\n    Object(preact_min[\"h\"])(\n        'ul',\n        null,\n        Object(preact_min[\"h\"])(\n            'li',\n            null,\n            'Con numero atomico maggiore, un semiconduttore di ',\n            Object(preact_min[\"h\"])(\n                minus_Minus,\n                null,\n                'tipo N'\n            ),\n            ' con ',\n            Object(preact_min[\"h\"])(\n                minus_Minus,\n                null,\n                'elettroni in eccesso'\n            ),\n            ' liberi di scorrere.'\n        ),\n        Object(preact_min[\"h\"])(\n            'li',\n            null,\n            'Con numero atomico minore, un semiconduttore di ',\n            Object(preact_min[\"h\"])(\n                plus_Plus,\n                null,\n                'tipo P'\n            ),\n            ' con ',\n            Object(preact_min[\"h\"])(\n                plus_Plus,\n                null,\n                'lacune in eccesso'\n            ),\n            ' libere di catturare elettroni da altri legami.'\n        )\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Maggiore impurezza porta a maggiore conduttivit\\xE0.'\n    )\n);\n\nvar _ref160 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Temperatura' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Aumentando la temperatura di un semiconduttore si aumenta la conduttivit\\xE0, perch\\xE8 eccita le particelle e favorisce il movimento di ',\n        Object(preact_min[\"h\"])(\n            minus_Minus,\n            null,\n            'elettroni'\n        ),\n        ' e ',\n        Object(preact_min[\"h\"])(\n            plus_Plus,\n            null,\n            'lacune'\n        ),\n        '.'\n    )\n);\n\nvar _ref161 = Object(preact_min[\"h\"])(\n    'span',\n    null,\n    'Ottica ',\n    Object(preact_min[\"h\"])(\n        'small',\n        null,\n        '(non l\\'abbiamo fatta)'\n    )\n);\n\nvar _ref162 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Assorbimento e riflessione' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.'\n    )\n);\n\nvar _ref163 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un corpo nero \\xE8 un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna.'\n);\n\nvar _ref164 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Teoria di Planck per il corpo nero' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'L\\'energia assorbita e emessa dai corpi neri \\xE8 quantizzata.'\n    )\n);\n\nvar _ref165 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un onda magnetica con un quanto di energia \\xE8 detta ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'fotone'\n    ),\n    ':'\n);\n\nvar _ref166 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: 'Effetto fotoelettrico' },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Perch\\xE8 avvenga, la frequenza deve essere maggiore di una certa soglia.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Il numero di elettroni estratti dipende dall\\'intensit\\xE0 dell\\'onda, mentre l\\'energia cinetica degli elettroni dipende dalla frequenza.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Non c\\'\\xE8 nessun ritardo tra l\\'assorbimento del fotone e l\\'estrazione di elettroni.'\n    )\n);\n\nvar fisica_Fisica = function (_Component) {\n    fisica__inherits(Fisica, _Component);\n\n    function Fisica() {\n        fisica__classCallCheck(this, Fisica);\n\n        return fisica__possibleConstructorReturn(this, _Component.apply(this, arguments));\n    }\n\n    Fisica.prototype.render = function render() {\n        return Object(preact_min[\"h\"])(\n            'div',\n            { style: fisica_default.a.fisica },\n            fisica__ref,\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Vettori' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Componenti cartesiane' },\n                    fisica__ref2,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject2)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject3)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Somma' },\n                    fisica__ref3,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject4)\n                        )\n                    ),\n                    _ref4\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Differenza' },\n                    _ref5,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject5)\n                        )\n                    ),\n                    _ref6\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Prodotto scalare' },\n                    _ref7,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject6)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Produce il modulo della proiezione di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject7)\n                        ),\n                        ' su ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject8)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Prodotto vettoriale' },\n                    _ref8,\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                r(_templateObject9)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                r(_templateObject10)\n                            )\n                        ),\n                        _ref9\n                    ),\n                    _ref10\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Leggi di Newton' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: '1\\u1D43: Inerzia' },\n                    _ref11,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject11)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: '2\\u1D43: Proporzionalit\\xE0' },\n                    _ref12,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject12)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: '3\\u1D43: Azione e reazione' },\n                    _ref13,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject13)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Forza di gravit\\xE0' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Tra due corpi' },\n                    _ref14,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject14)\n                        )\n                    ),\n                    _ref15,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject15)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Verso la Terra' },\n                    _ref16,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject16)\n                        )\n                    ),\n                    _ref17,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject17)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Su pianeti diversi' },\n                    _ref18,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject16)\n                        )\n                    ),\n                    _ref19,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject18)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject19)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Forze di contatto' },\n                _ref20,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Attrito statico' },\n                    _ref21,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject20)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Attrito dinamico' },\n                    _ref22,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject21)\n                        )\n                    )\n                ),\n                _ref23,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Elastica' },\n                    _ref24,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject22)\n                        )\n                    ),\n                    _ref25\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Cinematica' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Spostamento' },\n                    _ref26,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject23)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Velocit\\xE0' },\n                    _ref27,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject24)\n                        )\n                    ),\n                    _ref28,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject25)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Accelerazione' },\n                    _ref29,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject26)\n                        )\n                    ),\n                    _ref30,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject27)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: _ref31 },\n                    _ref32,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject28)\n                        )\n                    ),\n                    _ref33,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject29)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Moto rettilineo uniforme' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Spostamento' },\n                    _ref34,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject30)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Velocit\\xE0' },\n                    _ref35,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject31)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Accelerazione' },\n                    _ref36,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject32)\n                        )\n                    )\n                ),\n                _ref37\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Moto rettilineo uniformemente accelerato' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Spostamento' },\n                    _ref38,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject33)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Velocit\\xE0' },\n                    _ref39,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject34)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Accelerazione' },\n                    _ref40,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject35)\n                        )\n                    )\n                ),\n                _ref41\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Moto armonico semplice' },\n                _ref42,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Velocit\\xE0 angolare' },\n                    _ref43,\n                    _ref44,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject36)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Spostamento' },\n                    _ref45,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject37)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Velocit\\xE0' },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'E\\' la sinusoide dello spostamento, sfasata di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject38)\n                        ),\n                        ':'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject39)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Accelerazione' },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'E\\' la sinusoide della velocit\\xE0, sfasata di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject40)\n                        ),\n                        ':'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject41)\n                        )\n                    )\n                ),\n                _ref46\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Moti composti' },\n                _ref47,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Moto circolare uniforme' },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il moto parabolico \\xE8 dato sommando due moti armonici semplici: uno sull\\'asse X, e l\\'altro, sfasato di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject38)\n                        ),\n                        ', sull\\'asse Y.'\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Moto circolare uniforme' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    null,\n                    _ref48,\n                    _ref49,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject36)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Fase' },\n                    _ref50,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Si indica con ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject42)\n                        ),\n                        ', e generalmente si usa in radianti.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Velocit\\xE0' },\n                    _ref51,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject43)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Accelerazione' },\n                    _ref52,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject44)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Forza centripeta' },\n                    _ref53,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject45)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Lavoro ed energia' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Lavoro' },\n                    _ref54,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject46)\n                        )\n                    ),\n                    _ref55\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Energia cinetica' },\n                    _ref56,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject47)\n                        )\n                    ),\n                    _ref57,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject48)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Energia potenziale gravitazionale' },\n                    _ref58,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject49)\n                        )\n                    ),\n                    _ref59\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Energia potenziale elastica' },\n                    _ref60,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject50)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Forze conservative' },\n                    _ref61,\n                    _ref62,\n                    _ref63,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject51)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Potenza' },\n                    _ref64,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject52)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Elettrostatica' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Carica elettrica' },\n                    _ref65,\n                    _ref66,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Esiste un\\'unit\\xE0 elementare: ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject53)\n                        ),\n                        '.'\n                    ),\n                    _ref67\n                ),\n                _ref68\n            ),\n            _ref69,\n            _ref70,\n            _ref71,\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Forza elettrica' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Legge di Coulomb' },\n                    _ref72,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject54)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject55)\n                        ),\n                        ' \\xE8 la ',\n                        _ref73,\n                        ', e vale ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject56)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Permeabilit\\xE0 dello spazio vuoto' },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La costante ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject55)\n                        ),\n                        ' \\xE8 in realt\\xE0 dipendente da un altra costante, ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject57)\n                        ),\n                        ', la ',\n                        _ref74,\n                        '.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject58)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject59)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Campo elettrico' },\n                    _ref75,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject60)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Flusso elettrico' },\n                    _ref76,\n                    _ref77,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject61)\n                        )\n                    ),\n                    _ref78,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject62)\n                        )\n                    ),\n                    _ref79\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Legge di Gauss per i campi elettrostatici' },\n                    _ref80,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject63)\n                        )\n                    ),\n                    _ref81\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Energia elettrica' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Energia potenziale elettrica' },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Un corpo carico vicino ad altre cariche possiede un\\'',\n                        _ref82,\n                        ' ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject64)\n                        ),\n                        '.'\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Circuiti elettrici' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: _ref83 },\n                    _ref84,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject65)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La sua unit\\xE0 di misura \\xE8 il Volt (',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject66)\n                        ),\n                        ').'\n                    ),\n                    _ref85\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: _ref86 },\n                    _ref87,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject67)\n                        )\n                    ),\n                    _ref88,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La sua unit\\xE0 di misura \\xE8 l\\'Ampere (',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject68)\n                        ),\n                        ').'\n                    )\n                ),\n                _ref89,\n                _ref90,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Potenza elettrica' },\n                    _ref91,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject69)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Elementi di un circuito' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Resistore' },\n                    _ref92,\n                    _ref93,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject70)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Dove ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject71)\n                        ),\n                        ' \\xE8 una costante detta ',\n                        _ref94,\n                        ' con unit\\xE0 di misura Ohm (',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject72)\n                        ),\n                        ').'\n                    ),\n                    _ref95,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject73)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject74)\n                        ),\n                        ' \\xE8 la ',\n                        _ref96,\n                        ' del materiale, e varia in base alla temperatura:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject75)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Condensatore' },\n                    _ref97,\n                    _ref98,\n                    _ref99,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject76)\n                        )\n                    ),\n                    _ref100,\n                    _ref101,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject77)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Dove ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject78)\n                        ),\n                        ' \\xE8 la ',\n                        _ref102,\n                        ' del materiale inserito, ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject68)\n                        ),\n                        ' l\\'area di una armatura e ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject79)\n                        ),\n                        ' la distanza tra le due armature.'\n                    ),\n                    _ref103,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La sua unit\\xE0 di misura \\xE8 il Farad (',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject80)\n                        ),\n                        ')'\n                    )\n                ),\n                _ref104,\n                _ref105\n            ),\n            _ref106,\n            _ref107,\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Resistenze equivalenti' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Circuiti in serie' },\n                    _ref108,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject81)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Circuiti in parallelo' },\n                    _ref109,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject82)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Condensatori equivalenti' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Circuiti in serie' },\n                    _ref110,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject83)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Circuiti in parallelo' },\n                    _ref111,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject84)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Magnetismo' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Permeabilit\\xE0 magnetica dello spazio vuoto' },\n                    _ref112,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject85)\n                        ),\n                        ' (',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject86)\n                        ),\n                        ')'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Campo magnetico' },\n                    _ref113,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject87)\n                        ),\n                        ', e la sua unit\\xE0 di misura \\xE8 il Tesla (',\n                        _ref114,\n                        ').'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Flusso magnetico' },\n                    _ref115,\n                    _ref116,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject88)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject89)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La sua unit\\xE0 di misura \\xE8 il Weber (',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject90)\n                        ),\n                        ').'\n                    )\n                ),\n                _ref117,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Legge di Amp\\xE8re' },\n                    _ref118,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject91)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Forze magnetiche' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: _ref119 },\n                    _ref120,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject92)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Dove ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject93)\n                        ),\n                        ' \\xE8 l\\'intensit\\xE0 del campo magnetico e ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject94)\n                        ),\n                        ' la velocit\\xE0 della carica considerata.'\n                    ),\n                    _ref121,\n                    _ref122\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Forza magnetica in un filo' },\n                    _ref123,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject95)\n                        ),\n                        ' ',\n                        _ref124\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Dove ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject96)\n                        ),\n                        ' \\xE8 la corrente elettrica, ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject97)\n                        ),\n                        ' \\xE8 un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore.'\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Campi magnetici' },\n                _ref125,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Campo magnetico di un solenoide' },\n                    _ref126,\n                    _ref127,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject98)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Legge di Oersted' },\n                    _ref128,\n                    _ref129,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject99)\n                        )\n                    ),\n                    _ref130,\n                    _ref131\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Induzione elettromagnetica' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Forza elettromotrice indotta' },\n                    _ref132,\n                    _ref133,\n                    _ref134,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject100)\n                        )\n                    ),\n                    _ref135\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Flusso magnetico in una spira' },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'In un campo magnetico ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject87)\n                        ),\n                        ' uniforme e perpendicolare al piano di una spira di area ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject68)\n                        ),\n                        ', il flusso magnetico si pu\\xF2 determinare con la ',\n                        _ref136,\n                        ':'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject101)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                null,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Legge di Faraday-Neumann-Lenz' },\n                    _ref137,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject102)\n                        )\n                    ),\n                    _ref138\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Faraday in un solenoide' },\n                    _ref139,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject103)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Dove ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject104)\n                        ),\n                        ' \\xE8 il numero delle spire del solenoide.'\n                    )\n                ),\n                _ref140\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Elettromagnetismo' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Onde elettromagnetiche' },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Nel vuoto, il campo elettrico ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject105)\n                        ),\n                        ' e il campo magnetico ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject87)\n                        ),\n                        ' sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo.'\n                    ),\n                    _ref141,\n                    _ref142,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject106)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Dove ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject107)\n                        ),\n                        ' \\xE8 la velocit\\xE0 delle onde (luce) nel vuoto, e a sua volta \\xE8 uguale a:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject108)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Formula delle onde' },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject109)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Dove ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject110)\n                        ),\n                        ' \\xE8 l\\'ampiezza massima che pu\\xF2 avere l\\'onda, ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject111)\n                        ),\n                        ' \\xE8 il vettore d\\'onda, ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject112)\n                        ),\n                        ' la frequenza angolare e ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject42)\n                        ),\n                        ' la fase.'\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Spettroscopia' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Emissione' },\n                    _ref143,\n                    _ref144,\n                    _ref145,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject113)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Con ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject114)\n                        ),\n                        ', detta costante di Rydberg, e ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject115)\n                        ),\n                        ' un numero intero.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Grandezza quantizzata' },\n                    _ref146,\n                    _ref147,\n                    _ref148,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Nota costante quantica \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject116)\n                        ),\n                        ', la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject117)\n                        ),\n                        '.'\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                null,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Modello di Bohr' },\n                    _ref149,\n                    _ref150,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject118)\n                        )\n                    ),\n                    _ref151,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject119)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Con ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject120)\n                        ),\n                        '.'\n                    ),\n                    _ref152,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject121)\n                        )\n                    ),\n                    _ref153,\n                    _ref154\n                )\n            ),\n            _ref155,\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: 'Semiconduttori' },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Semiconduttori' },\n                    _ref156,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Se la banda di emissione con energia pi\\xF9 alta di un corpo \\xE8 assente o \\xE8 separata da un gap dell\\'ordine di grandezza maggiore di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject122)\n                        ),\n                        ', allora il corpo \\xE8 un isolante.'\n                    ),\n                    _ref157,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Se il gap \\xE8 invece dell\\'ordine di grandezza di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject123)\n                        ),\n                        ', allora il corpo \\xE8 un semiconduttore.'\n                    )\n                ),\n                _ref158,\n                _ref159,\n                _ref160\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: _ref161 },\n                _ref162,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Corpo nero' },\n                    _ref163,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Le onde assorbite vengono poi riemesse sotto forma di un onda di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject124)\n                        ),\n                        ' variabile in base alla temperatura.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject125)\n                        ),\n                        ' \\xE8 costante.'\n                    )\n                ),\n                _ref164,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: 'Fotone' },\n                    _ref165,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            r(_templateObject126)\n                        )\n                    )\n                ),\n                _ref166\n            )\n        );\n    };\n\n    return Fisica;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./pages/vldigeometria.css\nvar vldigeometria = __webpack_require__(\"jHTF\");\nvar vldigeometria_default = /*#__PURE__*/__webpack_require__.n(vldigeometria);\n\n// EXTERNAL MODULE: ./components/markdown.css\nvar markdown = __webpack_require__(\"MKE3\");\nvar markdown_default = /*#__PURE__*/__webpack_require__.n(markdown);\n\n// EXTERNAL MODULE: ../node_modules/showdown/dist/showdown.js\nvar showdown = __webpack_require__(\"6adR\");\nvar showdown_default = /*#__PURE__*/__webpack_require__.n(showdown);\n\n// CONCATENATED MODULE: ./components/markdown.js\n\n\nfunction markdown__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction markdown__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" 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[Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\\n11. [Propriet\\xE0 delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\\n12. 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[Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\\n11. [Propriet\\xE0 delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\\n13. [Propriet\\xE0 e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\\n20. [Teorema diagonalizzabilit\\xE0](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\\n23. 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[Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\\n\\nNell\\'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\\n                    ']);\n\n\n\nfunction vldigeometria__taggedTemplateLiteralLoose(strings, raw) { strings.raw = raw; return strings; }\n\nfunction vldigeometria__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction vldigeometria__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction vldigeometria__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? 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Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\n\nvar mingwinstall__ref = Object(preact_min[\"h\"])(\n\t'h1',\n\tnull,\n\t'Come installare MinGW'\n);\n\nvar mingwinstall__ref2 = Object(preact_min[\"h\"])(\n\tpanel_Panel,\n\tnull,\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Scaricate ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'a',\n\t\t\t{ href: 'https://osdn.net/projects/mingw/downloads/68260/mingw-get-setup.exe/' },\n\t\t\t'l\\'installer ufficiale'\n\t\t),\n\t\t', ed eseguitelo.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/mDZSqjV.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Dovrebbe comparire questa schermata. Cliccate su ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Install'\n\t\t),\n\t\t', poi scegliete una cartella di installazione (ricordatevela!) e poi ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Continue'\n\t\t),\n\t\t'. Lasciate stare le altre opzioni, dovrebbero essere tutte spuntate, tranne ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'For all users'\n\t\t),\n\t\t', che dovrebbe essere disattivato.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/brdw8Xy.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Continue'\n\t\t),\n\t\t'. Premetelo.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/aPTwrxz.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Dovrebbe apparirvi questa finestra. L\\'installer di MinGW \\xE8 una specie di gestore pacchetti (tipo ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'apt'\n\t\t),\n\t\t' su Ubuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalit\\xE0.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/5QLSkFN.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Nel nostro caso, dovrebbero servirci ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'mingw32-base-bin'\n\t\t),\n\t\t' (per il C e alcune librerie C++) e',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'mingw32-gcc-g++-bin'\n\t\t),\n\t\t' (per il C++). Cliccate, quindi, sui due quadratini corrispondenti, e premete',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Mark for Installation'\n\t\t),\n\t\t'. Dovrebbe comparire una freccia gialla sul quadratino.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/zP74nks.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Ora, \\xE8 il momento di installare i pacchetti. Aprite il men\\xF9 ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Installation'\n\t\t),\n\t\t', poi premete',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Apply Changes'\n\t\t),\n\t\t', e di nuovo ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Apply'\n\t\t),\n\t\t'.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/jp4uz5B.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Lasciate che scarichi, ci vorr\\xE0 un po\\'. Guardatevi un video nel frattempo, fatevi una partitina a qualcosa, tornate dopo circa 10 minuti.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/Lq9IepY.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Una volta installato, dobbiamo aggiungere ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'g++'\n\t\t),\n\t\t' ai programmi eseguibili da Prompt dei Comandi: premete il tasto ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'kbd',\n\t\t\tnull,\n\t\t\t'Windows'\n\t\t),\n\t\t', e scrivete ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'PATH'\n\t\t),\n\t\t'. Windows dovrebbe trovarvi automaticamente quell\\'opzione.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/dy3b5Ub.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Dentro la finestra di ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'i',\n\t\t\tnull,\n\t\t\t'Propriet\\xE0 del Sistema'\n\t\t),\n\t\t', premete ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Variabili d\\'ambiente'\n\t\t),\n\t\t'.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/FjYpT1n.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Trovate la variabile d\\'ambiente globale ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Path'\n\t\t),\n\t\t', e fateci doppio click per modificarla.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/klZQ9So.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Ora dovreste vedere l\\'elenco di tutte le cartelle contenenti programmi eseguibili da terminale: dobbiamo aggiungere quella di MinGW! Premete ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'Sfoglia'\n\t\t),\n\t\t'.'\n\t),\n\tObject(preact_min[\"h\"])('img', { src: 'https://i.imgur.com/F6lBCqS.png', alt: '' }),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Trovate la cartella in cui avete installato MinGW (vi avevo detto di ricordarvela!); entrateci, poi selezionate la sottocartella ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'bin'\n\t\t),\n\t\t' e premete ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'OK'\n\t\t),\n\t\t' su tutte le finestre che avete aperto fino ad ora, chiudendole.'\n\t),\n\tObject(preact_min[\"h\"])(\n\t\t'p',\n\t\tnull,\n\t\t' Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'gcc'\n\t\t),\n\t\t' e ',\n\t\tObject(preact_min[\"h\"])(\n\t\t\t'code',\n\t\t\tnull,\n\t\t\t'g++'\n\t\t),\n\t\t' sul Prompt dei Comandi, e potete finalmente creare dei file .exe! '\n\t)\n);\n\nvar mingwinstall_MingwInstall = function (_Component) {\n\tmingwinstall__inherits(MingwInstall, _Component);\n\n\tfunction MingwInstall() {\n\t\tmingwinstall__classCallCheck(this, MingwInstall);\n\n\t\treturn mingwinstall__possibleConstructorReturn(this, _Component.apply(this, arguments));\n\t}\n\n\tMingwInstall.prototype.render = function render() {\n\t\t//Imported from unimore-info-wiki\n\t\treturn Object(preact_min[\"h\"])(\n\t\t\t'div',\n\t\t\t{ style: mingwinstall_default.a.mingwinstall },\n\t\t\tmingwinstall__ref,\n\t\t\tmingwinstall__ref2\n\t\t);\n\t};\n\n\treturn MingwInstall;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./components/copyright.css\nvar copyright = __webpack_require__(\"qMTX\");\nvar copyright_default = /*#__PURE__*/__webpack_require__.n(copyright);\n\n// CONCATENATED MODULE: ./components/copyright.js\n\n\nfunction copyright__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction copyright__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction copyright__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar copyright__ref = Object(preact_min[\"h\"])(\n\t'a',\n\t{ href: 'https://creativecommons.org/licenses/by-sa/4.0/' },\n\t'CC BY-SA 4.0'\n);\n\nvar copyright__ref2 = Object(preact_min[\"h\"])(\n\t'a',\n\t{ href: 'https://github.com/Steffo99/appuntiweb' },\n\t'Codice sorgente'\n);\n\nvar copyright_Copyright = function (_Component) {\n\tcopyright__inherits(Copyright, _Component);\n\n\tfunction Copyright() {\n\t\tcopyright__classCallCheck(this, Copyright);\n\n\t\treturn copyright__possibleConstructorReturn(this, _Component.apply(this, arguments));\n\t}\n\n\tCopyright.prototype.render = function render() {\n\t\treturn Object(preact_min[\"h\"])(\n\t\t\t'div',\n\t\t\t{ 'class': copyright_default.a.copyright },\n\t\t\t'\\xA9 2019 - Stefano Pigozzi - ',\n\t\t\tcopyright__ref,\n\t\t\t' - ',\n\t\t\tcopyright__ref2\n\t\t);\n\t};\n\n\treturn Copyright;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./pages/statistica.css\nvar statistica = __webpack_require__(\"WViY\");\nvar statistica_default = /*#__PURE__*/__webpack_require__.n(statistica);\n\n// EXTERNAL MODULE: ./components/theorem.css\nvar theorem = __webpack_require__(\"oNmJ\");\nvar theorem_default = /*#__PURE__*/__webpack_require__.n(theorem);\n\n// CONCATENATED MODULE: ./components/theorem.js\nfunction theorem__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction theorem__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction theorem__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar theorem_Theorem = function (_Panel) {\n    theorem__inherits(Theorem, _Panel);\n\n    function Theorem() {\n        theorem__classCallCheck(this, Theorem);\n\n        return theorem__possibleConstructorReturn(this, _Panel.apply(this, arguments));\n    }\n\n    Theorem.prototype.getStyle = function getStyle() {\n        return _Panel.prototype.getStyle.call(this) + \" \" + theorem_default.a.theorem;\n    };\n\n    return Theorem;\n}(panel_Panel);\n\n\n// EXTERNAL MODULE: ./components/hypothesis.css\nvar hypothesis = __webpack_require__(\"pRAn\");\nvar hypothesis_default = /*#__PURE__*/__webpack_require__.n(hypothesis);\n\n// CONCATENATED MODULE: ./components/hypothesis.js\n\n\nfunction hypothesis__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction hypothesis__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction hypothesis__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar hypothesis__ref = Object(preact_min[\"h\"])(\n    \"h4\",\n    null,\n    \"Ipotesi\"\n);\n\nvar hypothesis_Hypothesis = function (_Component) {\n    hypothesis__inherits(Hypothesis, _Component);\n\n    function Hypothesis() {\n        hypothesis__classCallCheck(this, Hypothesis);\n\n        return hypothesis__possibleConstructorReturn(this, _Component.apply(this, arguments));\n    }\n\n    Hypothesis.prototype.render = function render() {\n        return Object(preact_min[\"h\"])(\n            \"div\",\n            { \"class\": hypothesis_default.a.hypothesis },\n            hypothesis__ref,\n            this.props.children\n        );\n    };\n\n    return Hypothesis;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./components/thesis.css\nvar thesis = __webpack_require__(\"J9SO\");\nvar thesis_default = /*#__PURE__*/__webpack_require__.n(thesis);\n\n// CONCATENATED MODULE: ./components/thesis.js\n\n\nfunction thesis__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction thesis__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction thesis__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar thesis__ref = Object(preact_min[\"h\"])(\n    \"h4\",\n    null,\n    \"Tesi\"\n);\n\nvar thesis_Thesis = function (_Component) {\n    thesis__inherits(Thesis, _Component);\n\n    function Thesis() {\n        thesis__classCallCheck(this, Thesis);\n\n        return thesis__possibleConstructorReturn(this, _Component.apply(this, arguments));\n    }\n\n    Thesis.prototype.render = function render() {\n        return Object(preact_min[\"h\"])(\n            \"div\",\n            { \"class\": thesis_default.a.thesis },\n            thesis__ref,\n            this.props.children\n        );\n    };\n\n    return Thesis;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./components/proof.css\nvar proof = __webpack_require__(\"Oqef\");\nvar proof_default = /*#__PURE__*/__webpack_require__.n(proof);\n\n// CONCATENATED MODULE: ./components/proof.js\n\n\nfunction proof__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction proof__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction proof__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar proof__ref = Object(preact_min[\"h\"])(\n    \"h4\",\n    null,\n    \"Dimostrazione\"\n);\n\nvar proof_Proof = function (_Component) {\n    proof__inherits(Proof, _Component);\n\n    function Proof() {\n        proof__classCallCheck(this, Proof);\n\n        return proof__possibleConstructorReturn(this, _Component.apply(this, arguments));\n    }\n\n    Proof.prototype.render = function render() {\n        return Object(preact_min[\"h\"])(\n            \"div\",\n            { \"class\": proof_default.a.proof },\n            proof__ref,\n            this.props.children\n        );\n    };\n\n    return Proof;\n}(preact_min[\"Component\"]);\n\n\n// EXTERNAL MODULE: ./components/example.css\nvar example = __webpack_require__(\"Xa+Z\");\nvar example_default = /*#__PURE__*/__webpack_require__.n(example);\n\n// CONCATENATED MODULE: ./components/example.js\n\n\nfunction example__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction example__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction example__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\nvar example_Example = function (_Component) {\n    example__inherits(Example, _Component);\n\n    function Example() {\n        example__classCallCheck(this, Example);\n\n        return example__possibleConstructorReturn(this, _Component.apply(this, arguments));\n    }\n\n    Example.prototype.render = function render() {\n        return Object(preact_min[\"h\"])(\n            \"blockquote\",\n            { \"class\": example_default.a.example },\n            this.props.children\n        );\n    };\n\n    return Example;\n}(preact_min[\"Component\"]);\n\n\n// CONCATENATED MODULE: ./pages/statistica.js\nvar statistica__templateObject = statistica__taggedTemplateLiteralLoose(['P(E) = \\frac{casi favorevoli}{casi possibili}'], ['P(E) = \\\\frac{casi\\\\ favorevoli}{casi\\\\ possibili}']),\n    statistica__templateObject2 = statistica__taggedTemplateLiteralLoose(['P(E) = \\frac{successi}{prove totali}'], ['P(E) = \\\\frac{successi}{prove\\\\ totali}']),\n    statistica__templateObject3 = statistica__taggedTemplateLiteralLoose(['Omega = left { 1, 2, 3, 4, 5, 6 \\right }'], ['\\\\Omega = \\\\left \\\\{ 1, 2, 3, 4, 5, 6 \\\\right \\\\}']),\n    statistica__templateObject4 = statistica__taggedTemplateLiteralLoose(['omega = 1'], ['\\\\omega = 1']),\n    statistica__templateObject5 = statistica__taggedTemplateLiteralLoose(['E = left { 1, 2 \\right }'], ['E = \\\\left \\\\{ 1, 2 \\\\right \\\\}']),\n    statistica__templateObject6 = statistica__taggedTemplateLiteralLoose(['\\bar{E} = left { 3, 4, 5, 6 \\right }'], ['\\\\bar{E} = \\\\left \\\\{ 3, 4, 5, 6 \\\\right \\\\}']),\n    statistica__templateObject7 = statistica__taggedTemplateLiteralLoose(['E cap F = left { 1 \\right }'], ['E \\\\cap F = \\\\left \\\\{ 1 \\\\right \\\\}']),\n    statistica__templateObject8 = statistica__taggedTemplateLiteralLoose(['E cup F = left { 1, 2, 3, 4 \\right }'], ['E \\\\cup F = \\\\left \\\\{ 1, 2, 3, 4 \\\\right \\\\}']),\n    statistica__templateObject9 = statistica__taggedTemplateLiteralLoose(['E setminus F = E cap \\bar{F}'], ['E \\\\setminus F = E \\\\cap \\\\bar{F}']),\n    statistica__templateObject10 = statistica__taggedTemplateLiteralLoose(['E subseteq F'], ['E \\\\subseteq F']),\n    statistica__templateObject11 = statistica__taggedTemplateLiteralLoose(['E = emptyset'], ['E = \\\\emptyset']),\n    statistica__templateObject12 = statistica__taggedTemplateLiteralLoose(['E cap F = emptyset'], ['E \\\\cap F = \\\\emptyset']),\n    statistica__templateObject13 = statistica__taggedTemplateLiteralLoose(['mathcal{F}'], ['\\\\mathcal{F}']),\n    statistica__templateObject14 = statistica__taggedTemplateLiteralLoose(['sigma'], ['\\\\sigma']),\n    statistica__templateObject15 = statistica__taggedTemplateLiteralLoose(['Omega in mathcal{F}'], ['\\\\Omega \\\\in \\\\mathcal{F}']),\n    statistica__templateObject16 = statistica__taggedTemplateLiteralLoose(['E in mathcal{F} implies 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statistica__taggedTemplateLiteralLoose(['mu in left( -infty, overline{x}_n + z_{1 - \\frac{alpha}{2}} cdot sqrt{\\frac{sigma^2}{n}} \\right]'], ['\\\\mu \\\\in \\\\left( -\\\\infty, \\\\overline{x}_n + z_{1 - \\\\frac{\\\\alpha}{2}} \\\\cdot \\\\sqrt{\\\\frac{\\\\sigma^2}{n}} \\\\right]']),\n    _templateObject234 = statistica__taggedTemplateLiteralLoose(['mu in left[ overline{x}_n - z_{1 - \\frac{alpha}{2}} cdot sqrt{\\frac{sigma^2}{n}}, +infty \\right)'], ['\\\\mu \\\\in \\\\left[ \\\\overline{x}_n - z_{1 - \\\\frac{\\\\alpha}{2}} \\\\cdot \\\\sqrt{\\\\frac{\\\\sigma^2}{n}}, +\\\\infty \\\\right)']),\n    _templateObject235 = statistica__taggedTemplateLiteralLoose(['mu in left[ overline{x}_n - t_{1 - \\frac{alpha}{2}; n-1} cdot sqrt{\\frac{s_n^2}{n}}, overline{x}_n + t_{1 - \\frac{alpha}{2}; n-1} cdot sqrt{\\frac{s_n^2}{n}} \\right]'], ['\\\\mu \\\\in \\\\left[ \\\\overline{x}_n - t_{1 - \\\\frac{\\\\alpha}{2}; n-1} \\\\cdot \\\\sqrt{\\\\frac{s_n^2}{n}}, \\\\overline{x}_n + t_{1 - \\\\frac{\\\\alpha}{2}; n-1} \\\\cdot \\\\sqrt{\\\\frac{s_n^2}{n}} \\\\right]']),\n    _templateObject236 = statistica__taggedTemplateLiteralLoose(['mu in left( -infty, overline{x}_n + t_{1 - \\frac{alpha}{2}; n-1} cdot sqrt{\\frac{s_n^2}{n}} \\right]'], ['\\\\mu \\\\in \\\\left( -\\\\infty, \\\\overline{x}_n + t_{1 - \\\\frac{\\\\alpha}{2}; n-1} \\\\cdot \\\\sqrt{\\\\frac{s_n^2}{n}} \\\\right]']),\n    _templateObject237 = statistica__taggedTemplateLiteralLoose(['mu in left[ overline{x}_n - t_{1 - \\frac{alpha}{2}; n-1} cdot sqrt{\\frac{s_n^2}{n}}, +infty \\right)'], ['\\\\mu \\\\in \\\\left[ \\\\overline{x}_n - t_{1 - \\\\frac{\\\\alpha}{2}; n-1} \\\\cdot \\\\sqrt{\\\\frac{s_n^2}{n}}, +\\\\infty \\\\right)']),\n    _templateObject238 = statistica__taggedTemplateLiteralLoose(['t_{alpha, v}'], ['t_{\\\\alpha, v}']),\n    _templateObject239 = statistica__taggedTemplateLiteralLoose(['p in left[ overline{p} - z_{1 - \\frac{alpha}{2}} cdot sqrt{\\frac{overline{p} cdot (1 - overline{p})}{n+4}}, overline{p} + z_{1 - \\frac{alpha}{2}} cdot sqrt{\\frac{overline{p} cdot (1 - overline{p})}{n+4}} \\right]'], ['p \\\\in \\\\left[ \\\\overline{p} - z_{1 - \\\\frac{\\\\alpha}{2}} \\\\cdot \\\\sqrt{\\\\frac{\\\\overline{p} \\\\cdot (1 - \\\\overline{p})}{n+4}}, \\\\overline{p} + z_{1 - \\\\frac{\\\\alpha}{2}} \\\\cdot \\\\sqrt{\\\\frac{\\\\overline{p} \\\\cdot (1 - \\\\overline{p})}{n+4}} \\\\right]']),\n    _templateObject240 = statistica__taggedTemplateLiteralLoose(['m in left[ overline{x}_n - z_{1 - \\frac{alpha}{2}} cdot sqrt{\\frac{s^2_n}{n}}, overline{x}_n + z_{1 - \\frac{alpha}{2}} cdot sqrt{\\frac{s^2_n}{n}} \\right]'], ['m \\\\in \\\\left[ \\\\overline{x}_n - z_{1 - \\\\frac{\\\\alpha}{2}} \\\\cdot \\\\sqrt{\\\\frac{s^2_n}{n}}, \\\\overline{x}_n + z_{1 - \\\\frac{\\\\alpha}{2}} \\\\cdot \\\\sqrt{\\\\frac{s^2_n}{n}} \\\\right]']);\n\n\n\nfunction statistica__taggedTemplateLiteralLoose(strings, raw) { strings.raw = raw; return strings; }\n\nfunction statistica__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction statistica__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return call && (typeof call === \"object\" || typeof call === \"function\") ? call : self; }\n\nfunction statistica__inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function, not \" + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\nvar statistica_r = String.raw;\n\nvar statistica__ref = Object(preact_min[\"h\"])(\n    'h1',\n    null,\n    'Statistica ed Elementi di Probabilit\\xE0'\n);\n\nvar statistica__ref2 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Soggettiva\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Il prezzo che un individuo coerente riterrebbe equo per ricevere ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            '1'\n        ),\n        ' nel caso l\\'evento si verificasse e ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            '0'\n        ),\n        ' nel caso l\\'evento non si verificasse.'\n    )\n);\n\nvar statistica__ref3 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"omegone\"'\n);\n\nvar statistica__ref4 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'insieme'\n    ),\n    ' di tutti gli esiti possibili di un esperimento.'\n);\n\nvar statistica__ref5 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"omeghino\"'\n);\n\nvar statistica__ref6 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'elemento'\n    ),\n    ' dello spazio campionario.'\n);\n\nvar statistica__ref7 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"e\"'\n);\n\nvar statistica__ref8 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'sottoinsieme'\n    ),\n    ' dello spazio campionario.'\n);\n\nvar statistica__ref9 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Lo spazio campionario stesso \\xE8 un ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'evento certo'\n    ),\n    '.'\n);\n\nvar statistica__ref10 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"not e\"'\n);\n\nvar statistica__ref11 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Il ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'complementare'\n    ),\n    ' di un sottoinsieme.'\n);\n\nvar statistica__ref12 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"e intersecato effe\"'\n);\n\nvar statistica__ref13 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'intersezione'\n    ),\n    ' di pi\\xF9 sottoinsiemi.'\n);\n\nvar statistica__ref14 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"e unito a effe\"'\n);\n\nvar statistica__ref15 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'unione'\n    ),\n    ' di pi\\xF9 sottoinsiemi.'\n);\n\nvar statistica__ref16 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"e meno effe\"'\n);\n\nvar statistica__ref17 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"e contenuto in effe\"'\n);\n\nvar statistica__ref18 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'inclusione'\n    ),\n    ' del primo insieme in un altro.'\n);\n\nvar statistica__ref19 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se si verifica ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'E'\n    ),\n    ', allora si verifica anche ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'F'\n    ),\n    '.'\n);\n\nvar statistica__ref20 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"e \\xE8 impossibile\"'\n);\n\nvar statistica__ref21 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un sottoinsieme ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'vuoto'\n    ),\n    '.'\n);\n\nvar statistica__ref22 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"e ed effe si escludono mutualmente\"'\n);\n\nvar statistica__ref23 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'disgiunzione'\n    ),\n    ' di due insiemi.'\n);\n\nvar statistica__ref24 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"famiglia effe\"'\n);\n\nvar statistica__ref25 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'I sottoinsiemi dello spazio campionario formano una ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'famiglia'\n    ),\n    ' di sottoinsiemi detta ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'famiglia degli eventi'\n    ),\n    '.'\n);\n\nvar statistica__ref26 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"sigma algebra\"'\n);\n\nvar statistica__ref27 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"la partizione e composta da e uno, e due, e tre...\"'\n);\n\nvar statistica__ref28 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un insieme di esiti e eventi:'\n);\n\nvar statistica__ref29 = Object(preact_min[\"h\"])(\n    'ul',\n    null,\n    Object(preact_min[\"h\"])(\n        'li',\n        null,\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'Finito'\n        ),\n        '.'\n    ),\n    Object(preact_min[\"h\"])(\n        'li',\n        null,\n        'In cui tutti gli eventi hanno ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'probabilit\\xE0 diversa da 0'\n        ),\n        '.'\n    ),\n    Object(preact_min[\"h\"])(\n        'li',\n        null,\n        'In cui tutti gli eventi sono ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'mutualmente esclusivi'\n        ),\n        '.'\n    ),\n    Object(preact_min[\"h\"])(\n        'li',\n        null,\n        'In cui l\\'unione di tutti i suoi elementi ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'copre lo spazio campionario'\n        ),\n        '.'\n    )\n);\n\nvar statistica__ref30 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Se lo spazio campionario fosse una torta, una sua partizione sarebbe l\\'insieme delle fette di uno dei modi in cui si potrebbe tagliare.'\n);\n\nvar statistica__ref31 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La probabilit\\xE0 di un evento \\xE8 un numero tra 0 e 1.'\n);\n\nvar statistica__ref32 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La probabilit\\xE0 dello spazio campionario \\xE8 sempre 1.'\n);\n\nvar statistica__ref33 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La probabilit\\xE0 dell\\'unione di eventi indipendenti \\xE8 uguale alla somma delle loro probabilit\\xE0.'\n);\n\nvar statistica__ref34 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La probabilit\\xE0 di un evento negato \\xE8 uguale a 1 meno la probabilit\\xE0 dell\\'evento non negato.'\n);\n\nvar statistica__ref35 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La probabilit\\xE0 di un evento incluso in un altro \\xE8 sempre minore o uguale alla probabilit\\xE0 dell\\'evento in cui \\xE8 incluso.'\n);\n\nvar statistica__ref36 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La probabilit\\xE0 di un evento unito a un altro \\xE8 uguale alla somma delle probabilit\\xE0 dei due eventi meno la probabilit\\xE0 della loro intersezione.'\n);\n\nvar statistica__ref37 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Sommando le probabilit\\xE0 dei due eventi, l\\'intersezione viene contata due volte, e va quindi rimossa!'\n);\n\nvar statistica__ref38 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilit\\xE0 di verificarsi.'\n);\n\nvar statistica__ref39 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Spazi equiprobabili geometrici\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Gli spazi campionari possono avere un numero infinito di esiti: sono ',\n        Object(preact_min[\"h\"])(\n            'i',\n            null,\n            'equiprobabili geometrici'\n        ),\n        ' se nessun esito \\xE8 privilegiato rispetto agli altri.'\n    )\n);\n\nvar statistica__ref40 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Estraggo un numero, da un sacchetto con ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' numeri, mi segno che numero ho estratto e lo ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'tengo fuori dal sacchetto'\n    ),\n    '. Ripeto per ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'k'\n    ),\n    ' volte.'\n);\n\nvar statistica__ref41 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'Tengo conto'\n    ),\n    ' dell\\'ordine in cui ho estratto i numeri.'\n);\n\nvar statistica__ref42 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Estraggo un numero, da un sacchetto con ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' numeri, mi segno che numero ho estratto e lo ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'rimetto nel sacchetto'\n    ),\n    '. Ripeto per ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'k'\n    ),\n    ' volte.'\n);\n\nvar statistica__ref43 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'Tengo conto'\n    ),\n    ' dell\\'ordine in cui ho estratto i numeri.'\n);\n\nvar statistica__ref44 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Estraggo un numero, da un sacchetto con ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' numeri, mi segno che numero ho estratto e lo ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'tengo fuori dal sacchetto'\n    ),\n    '. Ripeto per ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'k'\n    ),\n    ' volte.'\n);\n\nvar statistica__ref45 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'Non mi interessa'\n    ),\n    ' l\\'ordine in cui ho estratto i numeri.'\n);\n\nvar statistica__ref46 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Estraggo un numero, da un sacchetto con ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' numeri, mi segno che numero ho estratto e lo ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'rimetto nel sacchetto'\n    ),\n    '. Ripeto per ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'k'\n    ),\n    ' volte.'\n);\n\nvar statistica__ref47 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'Non mi interessa'\n    ),\n    ' l\\'ordine in cui ho estratto i numeri.'\n);\n\nvar statistica__ref48 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Estraggo ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' numeri e guardo in quanti ordini diversi li posso mettere.'\n);\n\nvar statistica__ref49 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"E dato F\"'\n);\n\nvar statistica__ref50 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La probabilit\\xE0 che si verifichi ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'E'\n    ),\n    ' sapendo che ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'si \\xE8 gi\\xE0 verificato'\n    ),\n    ' ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'F'\n    ),\n    '.'\n);\n\nvar statistica__ref51 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Ricorda vagamente le pipe di ',\n    Object(preact_min[\"h\"])(\n        'code',\n        null,\n        'bash'\n    ),\n    ', per\\xF2 al contrario...'\n);\n\nvar statistica__ref52 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se due eventi sono mutualmente esclusivi, entrambe le loro probabilit\\xE0 condizionate saranno uguali a 0.'\n);\n\nvar statistica__ref53 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Si pu\\xF2 sfruttare la formula inversa della probabilit\\xE0 condizionata per calcolare catene di intersezioni:'\n);\n\nvar statistica__ref54 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La probabilit\\xE0 che si verifichi un evento \\xE8 pari alla somma delle probabilit\\xE0 dell\\'evento stesso dati tutti gli eventi di una partizione.'\n);\n\nvar statistica__ref55 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La legge delle alternative funziona anche quando ad essere partizionato \\xE8 un ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'evento'\n    ),\n    ':'\n);\n\nvar statistica__ref56 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Tramite la ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'formula di Bayes'\n    ),\n    ' possiamo risalire alla probabilit\\xE0 di un evento condizionato a un altro partendo dalla probabilit\\xE0 di quest\\'ultimo condizionato al primo:'\n);\n\nvar statistica__ref57 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'In pratica, invertiamo gli eventi.'\n);\n\nvar statistica__ref58 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"eventi indipendenti a due a due\"'\n);\n\nvar statistica__ref59 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se due eventi sono indipendenti, sapere che uno dei due si \\xE8 verificato non influisce sulle probabilit\\xE0 che si sia verificato l\\'altro.'\n);\n\nvar statistica__ref60 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque...\"'\n);\n\nvar statistica__ref61 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Si pu\\xF2 verificare l\\'indipendenza di pi\\xF9 eventi alla volta:'\n);\n\nvar statistica__ref62 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.'\n);\n\nvar statistica__ref63 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Famiglia di eventi indipendenti\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Un insieme di ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'n'\n        ),\n        ' eventi \\xE8 una ',\n        Object(preact_min[\"h\"])(\n            'i',\n            null,\n            'famiglia di eventi indipendenti'\n        ),\n        ' se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.'\n    ),\n    Object(preact_min[\"h\"])(\n        example_Example,\n        null,\n        'Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e cos\\xEC via!'\n    )\n);\n\nvar statistica__ref64 = Object(preact_min[\"h\"])(\n    'abbr',\n    { title: \"Nome artigianale dato da Steffo.\" },\n    'Insieme di ripartizione'\n);\n\nvar statistica__ref65 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    't'\n);\n\nvar statistica__ref66 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:'\n);\n\nvar statistica__ref67 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'All\\'aumentare di t, l\\'insieme conterr\\xE0 sempre pi\\xF9 elementi.'\n);\n\nvar statistica__ref68 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Supporto\" },\n    Object(preact_min[\"h\"])(\n        'blockquote',\n        null,\n        '\"supporto di X\"'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Il ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'codominio'\n        ),\n        ' della variabile aleatoria \\xE8 il suo ',\n        Object(preact_min[\"h\"])(\n            'i',\n            null,\n            'supporto'\n        ),\n        '.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Per indicare che un valore ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'x_0'\n        ),\n        ' appartiene al supporto di ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'X'\n        ),\n        ', si usa la notazione ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'X \\\\mapsto x_0'\n        ),\n        '.'\n    )\n);\n\nvar statistica__ref69 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'funzione probabilit\\xE0'\n);\n\nvar statistica__ref70 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'discreta'\n);\n\nvar statistica__ref71 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'X'\n);\n\nvar statistica__ref72 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'funzione densit\\xE0'\n);\n\nvar statistica__ref73 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'continua'\n);\n\nvar statistica__ref74 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'X'\n);\n\nvar statistica__ref75 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'A differenza della funzione probabilit\\xE0, \\xE8 possibile che la funzione densit\\xE0 ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'non esista'\n    ),\n    ' per una certa variabile aleatoria.'\n);\n\nvar statistica__ref76 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Rappresenta \"quanta\" probabilit\\xE0 c\\'\\xE8 in un\\'unit\\xE0 di x!'\n);\n\nvar statistica__ref77 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'funzione di ripartizione'\n);\n\nvar statistica__ref78 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    't'\n);\n\nvar statistica__ref79 = Object(preact_min[\"h\"])(\n    'li',\n    null,\n    '\\xC8 sempre ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'monotona crescente'\n    ),\n    ' (non strettamente).'\n);\n\nvar statistica__ref80 = Object(preact_min[\"h\"])('br', null);\n\nvar statistica__ref81 = Object(preact_min[\"h\"])(\n    'li',\n    null,\n    'Vale ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        '0'\n    ),\n    ' a ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        '-\\\\infty'\n    ),\n    ' e ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        '1'\n    ),\n    ' a ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        '+\\\\infty'\n    ),\n    '.'\n);\n\nvar statistica__ref82 = Object(preact_min[\"h\"])('br', null);\n\nvar statistica__ref83 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'continua da destra'\n);\n\nvar statistica__ref84 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Possiamo usare la funzione di ripartizione per calcolare la probabilit\\xE0 di un certo valore reale:'\n);\n\nvar statistica__ref85 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Nel discreto\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.'\n    )\n);\n\nvar statistica__ref86 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Nel continuo applichiamo la formula dell\\'integrazione per sostituzione:'\n);\n\nvar statistica__ref87 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Nel... digitale\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Trasformare variabili aleatorie \\xE8 molto utile nell\\'informatica per creare distribuzioni partendo da una funzione ',\n        Object(preact_min[\"h\"])(\n            'a',\n            { href: \"https://docs.python.org/3/library/random.html#random.random\" },\n            Object(preact_min[\"h\"])(\n                'code',\n                null,\n                'random()'\n            )\n        ),\n        ' che restituisce numeri da 0 a 1 con una distribuzione lineare.'\n    )\n);\n\nvar statistica__ref88 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Ogni variabile aleatoria che ha una ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione di ripartizione'\n    ),\n    ' e un ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'supporto finito'\n    ),\n    ' ha anche una ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'media'\n    ),\n    ' (o ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'valore medio'\n    ),\n    ' o ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'atteso'\n    ),\n    '):'\n);\n\nvar statistica__ref89 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Nel discreto, si pu\\xF2 calcolare con:'\n);\n\nvar statistica__ref90 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Nel continuo, si pu\\xF2 calcolare con:'\n);\n\nvar statistica__ref91 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Moda\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Valore per cui la ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'funzione probabilit\\xE0'\n        ),\n        ' o ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'funzione densit\\xE0'\n        ),\n        ' \\xE8 ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'massima'\n        ),\n        '.'\n    )\n);\n\nvar statistica__ref92 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'quantile'\n);\n\nvar statistica__ref93 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'X'\n);\n\nvar statistica__ref94 = Object(preact_min[\"h\"])('p', null);\n\nvar statistica__ref95 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'mediana'\n);\n\nvar statistica__ref96 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'quartili'\n);\n\nvar statistica__ref97 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    '-esima percentile'\n);\n\nvar statistica__ref98 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    '\\xC8 un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:'\n);\n\nvar statistica__ref99 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Data una variabile aleatoria non-negativa:'\n);\n\nvar statistica__ref100 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"disuguaglianza di cebicev\"'\n);\n\nvar statistica__ref101 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'X'\n);\n\nvar statistica__ref102 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E anche:'\n);\n\nvar statistica__ref103 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Serve per semplificare i calcoli quando la funzione di ripartizione \\xE8 difficile da calcolare!'\n);\n\nvar statistica__ref104 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Il ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'momento'\n    ),\n    ' ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'k'\n    ),\n    '-esimo di una variabile aleatoria \\xE8:'\n);\n\nvar statistica__ref105 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'La media di una variabile aleatoria \\xE8 anche il suo primo momento.'\n);\n\nvar statistica__ref106 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' \\xE8:'\n);\n\nvar statistica__ref107 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'stessa distribuzione'\n    ),\n    '.'\n);\n\nvar statistica__ref108 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' la ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'trasformata di Laplace'\n    ),\n    ' della variabile aleatoria di X.'\n);\n\nvar statistica__ref109 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'funzione caratteristica'\n    ),\n    ' \\xE8:'\n);\n\nvar statistica__ref110 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'stessa distribuzione'\n    ),\n    '.'\n);\n\nvar statistica__ref111 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' la ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'trasformata di Fourier'\n    ),\n    ' della variabile aleatoria di X.'\n);\n\nvar statistica__ref112 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Per dire che una variabile ha una certa distribuzione, si usa la notazione:'\n);\n\nvar statistica__ref113 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Prova di Bernoulli\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Una prova con solo due possibili esiti: ',\n        Object(preact_min[\"h\"])(\n            plus_Plus,\n            null,\n            'successo'\n        ),\n        ' e ',\n        Object(preact_min[\"h\"])(\n            minus_Minus,\n            null,\n            'insuccesso'\n        ),\n        '.'\n    )\n);\n\nvar statistica__ref114 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Schema di Bernoulli\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Una sequenza di prove di Bernoulli per le quali le probabilit\\xE0 di successo e fallimento rimangono invariate.'\n    )\n);\n\nvar statistica__ref115 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una variabile aleatoria che rappresenta una prova di Bernoulli:'\n);\n\nvar statistica__ref116 = Object(preact_min[\"h\"])(\n    'ul',\n    null,\n    Object(preact_min[\"h\"])(\n        'li',\n        null,\n        'vale ',\n        Object(preact_min[\"h\"])(\n            plus_Plus,\n            null,\n            '1'\n        ),\n        ' in caso di ',\n        Object(preact_min[\"h\"])(\n            plus_Plus,\n            null,\n            'successo'\n        ),\n        '.'\n    ),\n    Object(preact_min[\"h\"])(\n        'li',\n        null,\n        'vale ',\n        Object(preact_min[\"h\"])(\n            minus_Minus,\n            null,\n            '0'\n        ),\n        ' in caso di ',\n        Object(preact_min[\"h\"])(\n            minus_Minus,\n            null,\n            'insuccesso'\n        ),\n        '.'\n    )\n);\n\nvar statistica__ref117 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La distribuzione bernoulliana ha come densit\\xE0:'\n);\n\nvar statistica__ref118 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una variabile aleatoria che conta il numero di successi di ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' prove di uno schema di Bernoulli.'\n);\n\nvar statistica__ref119 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La binomiale ha come densit\\xE0:'\n);\n\nvar statistica__ref120 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della binomiale \\xE8:'\n);\n\nvar statistica__ref121 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' di una binomiale \\xE8:'\n);\n\nvar statistica__ref122 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' di una binomiale \\xE8:'\n);\n\nvar statistica__ref123 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Distribuzione geometrica\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Il suo simbolo \\xE8 ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'Geo(p)'\n        ),\n        '.'\n    )\n);\n\nvar statistica__ref124 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La geometrica ha come densit\\xE0:'\n);\n\nvar statistica__ref125 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della geometrica \\xE8:'\n);\n\nvar statistica__ref126 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' della geometrica \\xE8:'\n);\n\nvar statistica__ref127 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' della geometrica \\xE8:'\n);\n\nvar statistica__ref128 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La geometrica non tiene conto degli eventi avvenuti in passato: ha la propriet\\xE0 dell\\'assenza di memoria:'\n);\n\nvar statistica__ref129 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Ovvero, riscalando opportunamente l\\'asse Y posso prendere come 0 qualsiasi punto dell\\'asse X.'\n);\n\nvar statistica__ref130 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perch\\xE8 si verifichi l\\'',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    '-esimo successo.'\n);\n\nvar statistica__ref131 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La binomiale negativa ha come densit\\xE0:'\n);\n\nvar statistica__ref132 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della binomiale negativa \\xE8:'\n);\n\nvar statistica__ref133 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' della binomiale negativa \\xE8:'\n);\n\nvar statistica__ref134 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' della binomiale negativa \\xE8:'\n);\n\nvar statistica__ref135 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una variabile aleatoria che conta il numero ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'k'\n    ),\n    ' di insuccessi consecutivi in uno schema di Bernoulli:'\n);\n\nvar statistica__ref136 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La geometrica traslata ha come densit\\xE0:'\n);\n\nvar statistica__ref137 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della geometrica traslata \\xE8:'\n);\n\nvar statistica__ref138 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' della geometrica traslata \\xE8:'\n);\n\nvar statistica__ref139 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' della geometrica \\xE8:'\n);\n\nvar statistica__ref140 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la propriet\\xE0 dell\\'assenza di memoria:'\n);\n\nvar statistica__ref141 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Ovvero, riscalando opportunamente l\\'asse Y posso prendere come 0 qualsiasi punto dell\\'asse X.'\n);\n\nvar statistica__ref142 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l\\'',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    '-esimo successo.'\n);\n\nvar statistica__ref143 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La binomiale negativa traslata ha come densit\\xE0:'\n);\n\nvar statistica__ref144 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della binomiale negativa traslata \\xE8:'\n);\n\nvar statistica__ref145 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' della binomiale negativa traslata \\xE8:'\n);\n\nvar statistica__ref146 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' della binomiale negativa traslata \\xE8:'\n);\n\nvar statistica__ref147 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Distribuzione ipergeometrica\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Una variabile aleatoria che, sapendo il numero di successi ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'K'\n        ),\n        ' e di insuccessi ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'N-K'\n        ),\n        ', conta quanti successi si otterrebbero se se ne estraessero ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'n'\n        ),\n        ' in blocco.'\n    ),\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Il suo simbolo \\xE8 ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'Ipe(N, K, n)'\n        ),\n        '.'\n    )\n);\n\nvar statistica__ref148 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ipergeometrica ha come densit\\xE0:'\n);\n\nvar statistica__ref149 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della ipergeometrica \\xE8 trascurabile.'\n);\n\nvar statistica__ref150 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' della ipergeometrica \\xE8:'\n);\n\nvar statistica__ref151 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' della ipergeometrica \\xE8:'\n);\n\nvar statistica__ref152 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:'\n);\n\nvar statistica__ref153 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La poissoniana ha come densit\\xE0:'\n);\n\nvar statistica__ref154 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della poissoniana \\xE8:'\n);\n\nvar statistica__ref155 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' della poissoniana \\xE8:'\n);\n\nvar statistica__ref156 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' della poissoniana \\xE8:'\n);\n\nvar statistica__ref157 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Gli altri momenti della poissoniana sono:'\n);\n\nvar statistica__ref158 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una successione di ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'arrivi'\n    ),\n    ' avvenuti in un certo arco temporale che:'\n);\n\nvar statistica__ref159 = Object(preact_min[\"h\"])(\n    'li',\n    null,\n    'non sono sovrapposti.'\n);\n\nvar statistica__ref160 = Object(preact_min[\"h\"])(\n    'li',\n    null,\n    'avvengono indipendentemente gli uni dagli altri.'\n);\n\nvar statistica__ref161 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'N_t'\n);\n\nvar statistica__ref162 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    't'\n);\n\nvar statistica__ref163 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'E\\' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo \\xE8 il numero di prove effettuate (ma nel continuo).'\n);\n\nvar statistica__ref164 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'esponenziale ha come ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'densit\\xE0'\n    ),\n    ':'\n);\n\nvar statistica__ref165 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'esponenziale ha come ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione di ripartizione'\n    ),\n    ':'\n);\n\nvar statistica__ref166 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' dell\\'esponenziale \\xE8:'\n);\n\nvar _ref167 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' dell\\'esponenziale \\xE8:'\n);\n\nvar _ref168 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' dell\\'esponenziale \\xE8:'\n);\n\nvar _ref169 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'esponenziale non tiene conto degli eventi avvenuti in passato: ha la propriet\\xE0 dell\\'assenza di memoria:'\n);\n\nvar _ref170 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Ovvero, riscalando opportunamente l\\'asse Y posso prendere come 0 qualsiasi punto dell\\'asse X.'\n);\n\nvar _ref171 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'n'\n);\n\nvar _ref172 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La legge gamma ha come densit\\xE0:'\n);\n\nvar _ref173 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della legge gamma \\xE8:'\n);\n\nvar _ref174 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' della legge gamma \\xE8:'\n);\n\nvar _ref175 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' della legge gamma \\xE8:'\n);\n\nvar _ref176 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Su di essa vale la seguente propriet\\xE0:'\n);\n\nvar _ref177 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La distribuzione uniforme ha come ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'densit\\xE0'\n    ),\n    ':'\n);\n\nvar _ref178 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La distribuzione uniforme ha come ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione di ripartizione'\n    ),\n    ':'\n);\n\nvar _ref179 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della distribuzione uniforme \\xE8:'\n);\n\nvar _ref180 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' della distribuzione uniforme \\xE8:'\n);\n\nvar _ref181 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' della distribuzione uniforme \\xE8:'\n);\n\nvar _ref182 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una variabile aleatoria con una specifica distribuzione.'\n);\n\nvar _ref183 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        '\\\\mu'\n    ),\n    ' e ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        '\\\\sigma^2'\n    ),\n    ' sono rispettivamente la media e la varianza della distribuzione!'\n);\n\nvar _ref184 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La distribuzione normale ha come densit\\xE0:'\n);\n\nvar _ref185 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'funzione generatrice dei momenti'\n    ),\n    ' della distribuzione normale \\xE8:'\n);\n\nvar _ref186 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media'\n    ),\n    ' della distribuzione normale \\xE8:'\n);\n\nvar _ref187 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'varianza'\n    ),\n    ' della distribuzione normale \\xE8:'\n);\n\nvar _ref188 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Qualsiasi normale pu\\xF2 essere trasformata in qualsiasi altra normale:'\n);\n\nvar _ref189 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La distribuzione normale standard ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'Z'\n    ),\n    ' \\xE8:'\n);\n\nvar _ref190 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'Z \\\\sim Nor(0, 1)'\n    )\n);\n\nvar _ref191 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La distribuzione normale ha una particolare relazione con la distribuzione Gamma:'\n);\n\nvar _ref192 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"chi-quadro a un grado di libert\\xE0\"'\n);\n\nvar _ref193 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Esiste una distribuzione Gamma particolare:'\n);\n\nvar _ref194 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Pi\\xF9 chi-quadro possono essere sommate per aumentare i loro gradi di libert\\xE0:'\n);\n\nvar _ref195 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un\\'altra funzione particolare \\xE8 la funzione T di Student:'\n);\n\nvar _ref196 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La binomiale \\xE8 come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'N'\n    ),\n    ' rispetto a ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ', si pu\\xF2 dire che:'\n);\n\nvar _ref197 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La binomiale non \\xE8 altro che una poissoniana a tempo discreto, quindi, se ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' \\xE8 grande e ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n \\\\cdot p'\n    ),\n    ' \\xE8 nell\\'ordine di grandezza delle unit\\xE0, allora:'\n);\n\nvar _ref198 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Per il Teorema di De Moivre-Laplace, se una binomiale ha una ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' grande e ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'p'\n    ),\n    ' non vicina a 0 o 1, si pu\\xF2 approssimare con:'\n);\n\nvar _ref199 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'X'\n);\n\nvar _ref200 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'Y'\n);\n\nvar _ref201 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'k'\n);\n\nvar _ref202 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un vettore ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'composto da variabili aleatorie'\n    ),\n    '.'\n);\n\nvar _ref203 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'I vettori aleatori hanno pi\\xF9 funzioni di ripartizione che si differenziano in base al numero di parametri.'\n);\n\nvar _ref204 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sar\\xE0 una ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'funzione di ripartizione congiunta'\n    ),\n    ':'\n);\n\nvar _ref205 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se il numero di parametri \\xE8 minore della dimensione del vettore aleatorio, allora la funzione sar\\xE0 una ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'funzione di ripartizione marginale'\n    ),\n    ':'\n);\n\nvar _ref206 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'I vettori aleatori ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'discreti'\n    ),\n    ' hanno pi\\xF9 densit\\xE0 che si differenziano in base al numero di parametri.'\n);\n\nvar _ref207 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sar\\xE0 una ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'densit\\xE0 congiunta'\n    ),\n    ':'\n);\n\nvar _ref208 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se il numero di parametri \\xE8 minore della dimensione del vettore aleatorio, allora la funzione sar\\xE0 una ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'densit\\xE0 marginale'\n    ),\n    ':'\n);\n\nvar _ref209 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Pi\\xF9 variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'A_i'\n    ),\n    ':'\n);\n\nvar _ref210 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' possibile calcolare la media di qualsiasi funzione ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'g(X, Y)'\n    ),\n    ' avente elementi del vettore come variabili:'\n);\n\nvar _ref211 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Solitamente si calcola la media di ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'x \\\\cdot y'\n    ),\n    '.'\n);\n\nvar _ref212 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Le medie di pi\\xF9 variabili aleatorie si possono sommare:'\n);\n\nvar _ref213 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'operatore'\n    ),\n    ' che misura la correlazione di due variabili aleatorie.'\n);\n\nvar _ref214 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Si calcola con il valore atteso dei prodotti delle distanze dalla media:'\n);\n\nvar _ref215 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Ha diverse propriet\\xE0:'\n);\n\nvar _ref216 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'valore nullo'\n);\n\nvar _ref217 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'commutativa'\n);\n\nvar _ref218 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'semplificabile'\n);\n\nvar _ref219 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'lineare'\n);\n\nvar _ref220 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'distributiva'\n);\n\nvar _ref221 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Due variabili sono ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'variabili incorrelate'\n    ),\n    ' se:'\n);\n\nvar _ref222 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Variabili indipendenti sono sempre incorrelate.'\n);\n\nvar _ref223 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        '\\\\geq 0'\n    ),\n    '.'\n);\n\nvar _ref224 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Un valore che misura come due variabili aleatorie sono correlate:'\n);\n\nvar _ref225 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' sempre compreso tra -1 e 1:'\n);\n\nvar _ref226 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:'\n);\n\nvar _ref227 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La varianza di due variabili aleatorie sommate \\xE8:'\n);\n\nvar _ref228 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Si dimostra applicando le propriet\\xE0 della covarianza!'\n);\n\nvar _ref229 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'X_i'\n);\n\nvar _ref230 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'indipendenti'\n);\n\nvar _ref231 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Campione casuale\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Una ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'n-pla'\n        ),\n        ' di variabili aleatorie con la stessa distribuzione della variabile aleatoria ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'X'\n        ),\n        ' (\"popolazione\") ma ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'indipendenti'\n        ),\n        ' tra loro.'\n    ),\n    Object(preact_min[\"h\"])(\n        example_Example,\n        null,\n        'Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sar\\xE0 bisogno del loro valore numerico, esse si ',\n        Object(preact_min[\"h\"])(\n            'b',\n            null,\n            'realizzeranno'\n        ),\n        ' nel loro valore.'\n    )\n);\n\nvar _ref232 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Il valore dato dalla media aritmetica degli ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' elementi del campione elevati alla potenza ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'k'\n    ),\n    ':'\n);\n\nvar _ref233 = Object(preact_min[\"h\"])(\n    'i',\n    null,\n    'media campionaria'\n);\n\nvar _ref234 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'La media aritmetica dello scarto quadratico medio degli elementi del campione.'\n);\n\nvar _ref235 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Altrimenti:'\n);\n\nvar _ref236 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se calcoliamo la media della media campionaria, risulter\\xE0 vero che:'\n);\n\nvar _ref237 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Quindi, \\xE8 possibile usare i campioni per trovare la media di una variabile aleatoria!'\n);\n\nvar _ref238 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se calcoliamo la varianza della media campionaria, risulter\\xE0 vero che:'\n);\n\nvar _ref239 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Quindi, possiamo stimare l\\'errore della media calcolata tramite campioni!'\n);\n\nvar _ref240 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se calcoliamo la media della varianza campionaria, risulter\\xE0 vero che:'\n);\n\nvar _ref241 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Quindi, possiamo stimare l\\'errore della media calcolata tramite campioni!'\n);\n\nvar _ref242 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'X'\n);\n\nvar _ref243 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    '...allora sappiamo anche la distribuzione della media campionaria!'\n);\n\nvar _ref244 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    '...e anche della varianza campionaria!'\n);\n\nvar _ref245 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Indipendenza\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        '...e che media campionaria e varianza campionaria sono indipendenti tra loro!'\n    )\n);\n\nvar _ref246 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se la successione di variabili aleatorie ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X_n'\n    ),\n    ' all\\'infinito ha la ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'stessa funzione di ripartizione'\n    ),\n    ' della popolazione ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X'\n    ),\n    ', allora essa ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'converge in distribuzione'\n    ),\n    '.'\n);\n\nvar _ref247 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se la successione di variabili aleatorie ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X_n'\n    ),\n    ' all\\'infinito ha la ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'stessa probabilit\\xE0'\n    ),\n    ' della popolazione ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X'\n    ),\n    ', allora essa ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'converge in probabilit\\xE0'\n    ),\n    '.'\n);\n\nvar _ref248 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se la successione di variabili aleatorie ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X_n'\n    ),\n    ' all\\'infinito ha la ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'stessa probabilit\\xE0 a '\n    ),\n    ' della popolazione ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X'\n    ),\n    ', allora essa ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'converge quasi certamente'\n    ),\n    '.'\n);\n\nvar _ref249 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se la successione di variabili aleatorie ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X_n'\n    ),\n    ' all\\'infinito ha la ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'media del quadrato della distanza'\n    ),\n    ' tra la successione e la popolazione ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X'\n    ),\n    ' ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'uguale a 0'\n    ),\n    ', allora essa ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'converge in media quadratica'\n    ),\n    '.'\n);\n\nvar _ref250 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'In pi\\xF9:'\n);\n\nvar _ref251 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'converge in probabilit\\xE0'\n);\n\nvar _ref252 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Ovvero:'\n);\n\nvar _ref253 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'converge quasi certamente'\n);\n\nvar _ref254 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Ovvero:'\n);\n\nvar _ref255 = Object(preact_min[\"h\"])(\n    example_Example,\n    null,\n    'Dimostra che l\\'interpretazione frequentista della probabilit\\xE0 \\xE8 valida!'\n);\n\nvar _ref256 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'converge in distribuzione'\n);\n\nvar _ref257 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Ovvero:'\n);\n\nvar _ref258 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' una somma di ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'bernoulliane'\n    ),\n    ', e quindi si approssima a una normale:'\n);\n\nvar _ref259 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' una somma di ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'geometriche'\n    ),\n    ', e quindi si approssima a una normale:'\n);\n\nvar _ref260 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' una somma di altre ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'poissoniane'\n    ),\n    ', e quindi si approssima a una normale:'\n);\n\nvar _ref261 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'E\\' una somma di ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'esponenziali'\n    ),\n    ', e quindi si approssima a una normale:'\n);\n\nvar _ref262 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'n'\n    ),\n    ' \\xE8 grande, allora:'\n);\n\nvar _ref263 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Parametri sconosciuti\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Per indicare parametri sconosciuti di una legge si usa ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            '\\\\theta'\n        ),\n        '.'\n    )\n);\n\nvar _ref264 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Una variabile aleatoria funzione di un campione:'\n);\n\nvar _ref265 = Object(preact_min[\"h\"])(\n    panel_Panel,\n    { title: \"Stimatore\" },\n    Object(preact_min[\"h\"])(\n        'p',\n        null,\n        'Una statistica ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'T_n'\n        ),\n        ' ottenuta da ',\n        Object(preact_min[\"h\"])(\n            latex_Latex,\n            null,\n            'n'\n        ),\n        ' osservazioni, che stimi i parametri di una legge e sia indipendente da essi.'\n    )\n);\n\nvar _ref266 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Uno stimatore \\xE8 ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'corretto'\n    ),\n    ' se il suo valore atteso coincide con quello dei parametri che stima:'\n);\n\nvar _ref267 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Uno stimatore \\xE8 ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'asintoticamente corretto'\n    ),\n    ' se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:'\n);\n\nvar _ref268 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Uno stimatore \\xE8 ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'consistente in media quadratica'\n    ),\n    ' se:'\n);\n\nvar _ref269 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Uno stimatore \\xE8 ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'consistente in probabilit\\xE0'\n    ),\n    ' se:'\n);\n\nvar _ref270 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Uno stimatore \\xE8 ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'asintoticamente normale'\n    ),\n    ' se:'\n);\n\nvar _ref271 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Si pu\\xF2 usare il ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'metodo dei momenti'\n    ),\n    ' per ottenere uno stimatore di una popolazione ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X'\n    ),\n    '.'\n);\n\nvar _ref272 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'M'\n);\n\nvar _ref273 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    '\\\\theta'\n);\n\nvar _ref274 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Visto che:'\n);\n\nvar _ref275 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Allora:'\n);\n\nvar _ref276 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Si pu\\xF2 usare il ',\n    Object(preact_min[\"h\"])(\n        'i',\n        null,\n        'metodo della massima verosomiglianza'\n    ),\n    ' per ottenere uno stimatore di una popolazione ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        'X'\n    ),\n    '.'\n);\n\nvar _ref277 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'L'\n);\n\nvar _ref278 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    '\\\\theta'\n);\n\nvar _ref279 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Gli stimatori di massima verosomiglianza sono ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'asintoticamente corretti'\n    ),\n    ', ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'consistenti in probabilit\\xE0'\n    ),\n    ' e ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'asintoticamente normali'\n    ),\n    '.'\n);\n\nvar _ref280 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Gli stimatori di massima verosomiglianza godono delle seguenti propriet\\xE0:'\n);\n\nvar _ref281 = Object(preact_min[\"h\"])(\n    'li',\n    null,\n    'Sono ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'asintoticamente corretti'\n    ),\n    '.'\n);\n\nvar _ref282 = Object(preact_min[\"h\"])(\n    'li',\n    null,\n    'Sono ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'consistenti in probabilit\\xE0'\n    ),\n    '.'\n);\n\nvar _ref283 = Object(preact_min[\"h\"])(\n    'li',\n    null,\n    'Sono ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'asintoticamente normali'\n    ),\n    '.'\n);\n\nvar _ref284 = Object(preact_min[\"h\"])(\n    'b',\n    null,\n    'invarianti'\n);\n\nvar _ref285 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:'\n);\n\nvar _ref286 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:'\n);\n\nvar _ref287 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:'\n);\n\nvar _ref288 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Per il metodo della massima verosomiglianza:'\n);\n\nvar _ref289 = Object(preact_min[\"h\"])('br', null);\n\nvar _ref290 = Object(preact_min[\"h\"])(\n    'blockquote',\n    null,\n    '\"intervallo di confidenza al 95%\"'\n);\n\nvar _ref291 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'intervallo di valori di ',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        '\\\\theta'\n    ),\n    ' all\\'interno del quale siamo \"pi\\xF9 o meno sicuri\" si trovi il valore effettivo:'\n);\n\nvar _ref292 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    ']a, b['\n);\n\nvar _ref293 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Pu\\xF2 anche essere ',\n    Object(preact_min[\"h\"])(\n        'b',\n        null,\n        'unilatero'\n    ),\n    ' nel caso limiti la stima in una sola direzione, positiva o negativa.'\n);\n\nvar _ref294 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all\\'',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        '\\\\alpha'\n    ),\n    '% con queste formule:'\n);\n\nvar _ref295 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all\\'',\n    Object(preact_min[\"h\"])(\n        latex_Latex,\n        null,\n        '\\\\alpha'\n    ),\n    '% con queste formule:'\n);\n\nvar _ref296 = Object(preact_min[\"h\"])(\n    latex_Latex,\n    null,\n    'v'\n);\n\nvar _ref297 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:'\n);\n\nvar _ref298 = Object(preact_min[\"h\"])(\n    'p',\n    null,\n    'L\\'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:'\n);\n\nvar statistica_Statistica = function (_Component) {\n    statistica__inherits(Statistica, _Component);\n\n    function Statistica() {\n        statistica__classCallCheck(this, Statistica);\n\n        return statistica__possibleConstructorReturn(this, _Component.apply(this, arguments));\n    }\n\n    Statistica.prototype.render = function render() {\n        /*\n               \n                   \n                       
    \n                           Gruppo intero di oggetti di cui si cercano informazioni.\n                       
    \n                       \n                   \n                       
    \n                           Popolazione finita di oggetti concreti che possono essere campionati ciascuno solo una volta.\n                       
    \n                       \n                   \n                       
    \n                           Popolazione di valori ottenuti da prove sperimentali indipendenti ripetute più volte.\n                       
    \n                       \n                   \n               \n                   \n                       
    \n                           Sottoinsieme della popolazione che contiene gli oggetti che si sono osservati.\n                       
    \n                   \n                   Simple random sample}>\n                       
    \n                           Campione di una data dimensione in cui qualsiasi selezione di n elementi ha la stessa probabilità di costituire il campione.\n                       
    \n                       \n                   Sample of convenience}>\n                       
    \n                           Campione ottenuto in un modo casuale non ben definito.\n                       
    \n                       \n                   Sample with replacement}>\n                       
    \n                           Campione ottenuto sostituendo nella popolazione gli elementi estratti con dei nuovi elementi.\n                       
    \n                       
    \n                           Dire che un campione è ottenuto with replacement è equivalente a dire che la popolazione che si sta campionando è infinita, e quindi che tutti gli elementi sono indipendenti.\n                       
    \n                       \n                   \n                       
    \n                           Campione ottenuto da una popolazione in cui certi elementi hanno più probabilità di essere stati selezionati di altri.\n                       
    \n                       \n                   Stratified random sample}>\n                       
    \n                           Campione ottenuto da un sottoinsieme della popolazione detto strato.\n                       
    \n                       \n                   Cluster sample}>\n                       
    \n                           Campione ottenuto selezionando più cluster di elementi alla volta.\n                       
    \n                       \n               \n               \n                   Sampling variation}>\n                       
    \n                           Differenza di informazioni presente tra due campioni diversi della stessa popolazione.\n                       
    \n                       \n                   \n                       
    \n                           Gli elementi in un campione sono indipendenti se gli elementi estratti in precedenza non influsicono significativamente sulle probabilità di estrazione dell'elemento successivo.\n                       
    \n                       \n                   \n               \n                   \n                       
    \n                           Esperimento in cui c'è una sola popolazione da cui vengono estratti campioni.\n                       
    \n                       
    \n                           Serve per verificare delle condizioni.\n                       
    \n                       \n                   \n                       
    \n                           Esperimento in cui sono presenti più popolazioni (aventi caratteristiche differenti una dall'altra dette fattori) da cui vengono estratti campioni.\n                       
    \n                       
    \n                           Serve per capire quali fattori influenzano il risultato dell'esperimento.\n                       
    \n                       \n                   \n               \n                   Numerico o quantitativo}>\n                       Il dato descrive un valore numerico relativo all'elemento, come ad esempio una quantità fisica.\n                   \n                   Categorico o qualitativo}>\n                       Il dato indica una categoria a cui appartiene l'elemento, come ad esempio il suo colore.\n                   \n               \n         */\n        return Object(preact_min[\"h\"])(\n            'div',\n            { style: statistica_default.a.statistica },\n            statistica__ref,\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Tipi di probabilità\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Classica\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Frequentista\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject2)\n                        )\n                    )\n                ),\n                statistica__ref2\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Linguaggio matematico\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Spazio campionario\" },\n                    statistica__ref3,\n                    statistica__ref4,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject3)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Esito\" },\n                    statistica__ref5,\n                    statistica__ref6,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject4)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Evento\" },\n                    statistica__ref7,\n                    statistica__ref8,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject5)\n                        )\n                    ),\n                    statistica__ref9\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Not\" },\n                    statistica__ref10,\n                    statistica__ref11,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject6)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"And\" },\n                    statistica__ref12,\n                    statistica__ref13,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject7)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Or\" },\n                    statistica__ref14,\n                    statistica__ref15,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject8)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Differenza\" },\n                    statistica__ref16,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject9)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Implicazione\" },\n                    statistica__ref17,\n                    statistica__ref18,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject10)\n                        )\n                    ),\n                    statistica__ref19\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Evento impossibile\" },\n                    statistica__ref20,\n                    statistica__ref21,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject11)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Mutua esclusione\" },\n                    statistica__ref22,\n                    statistica__ref23,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject12)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                null,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Famiglia degli eventi\" },\n                    statistica__ref24,\n                    statistica__ref25,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject13)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Qualsiasi sottoinsieme appartenente a ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject13)\n                        ),\n                        ' \\xE8 considerato un evento.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: Object(preact_min[\"h\"])(\n                            'span',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject14)\n                            ),\n                            '-algebra'\n                        ) },\n                    statistica__ref26,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta ',\n                        Object(preact_min[\"h\"])(\n                            'i',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject14)\n                            ),\n                            '-algebra'\n                        ),\n                        ':'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'ol',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Lo spazio campionario \\xE8 un evento: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject15)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Se un sottoinsieme \\xE8 un evento, allora anche il suo complementare lo \\xE8: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject16)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject17)\n                            )\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Un esempio: ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject18)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                null,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Partizione\" },\n                    statistica__ref27,\n                    statistica__ref28,\n                    statistica__ref29,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La partizione ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject19)\n                        ),\n                        ' \\xE8 composta dagli eventi ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject20)\n                        ),\n                        ', ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject21)\n                        ),\n                        ', ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject22)\n                        ),\n                        ', fino a ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject23)\n                        ),\n                        '.'\n                    ),\n                    statistica__ref30\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Assiomi della probabilità\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Primo assioma della probabilità\" },\n                    statistica__ref31,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject24)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Secondo assioma della probabilità\" },\n                    statistica__ref32,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject25)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Terzo assioma della probabilità\" },\n                    statistica__ref33,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject26)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Conseguenze degli assiomi\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Probabilità di un evento negato\" },\n                    statistica__ref34,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject27)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Probabilità di un evento incluso\" },\n                    statistica__ref35,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject28)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Unione\" },\n                    statistica__ref36,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject29)\n                        )\n                    ),\n                    statistica__ref37\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Spazi equiprobabili\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Cosa sono?\" },\n                    statistica__ref38,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject30)\n                        )\n                    )\n                ),\n                statistica__ref39\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Calcolo combinatorio\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Disposizioni\" },\n                    statistica__ref40,\n                    statistica__ref41,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject31)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Disposizioni con ripetizione\" },\n                    statistica__ref42,\n                    statistica__ref43,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject32)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Combinazioni\" },\n                    statistica__ref44,\n                    statistica__ref45,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject33)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Combinazioni con ripetizione\" },\n                    statistica__ref46,\n                    statistica__ref47,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject34)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Permutazioni\" },\n                    statistica__ref48,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject35)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Probabilità condizionata\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Eventi condizionati\" },\n                    statistica__ref49,\n                    statistica__ref50,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject36)\n                        )\n                    ),\n                    statistica__ref51\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Eventi mutualmente esclusivi\" },\n                    statistica__ref52,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject37)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                null,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Regola della catena\" },\n                    statistica__ref53,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject38)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Le alternative\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Legge delle alternative\" },\n                    statistica__ref54,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject39)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Legge condizionata delle alternative\" },\n                    statistica__ref55,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject40)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Formula di Bayes\" },\n                    statistica__ref56,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject41)\n                        )\n                    ),\n                    statistica__ref57\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Eventi indipendenti\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Due eventi indipendenti\" },\n                    statistica__ref58,\n                    statistica__ref59,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject42)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Più eventi indipendenti\" },\n                    statistica__ref60,\n                    statistica__ref61,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject43)\n                        )\n                    ),\n                    statistica__ref62\n                ),\n                statistica__ref63\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Variabili aleatorie\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Variabile aleatoria\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject44)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: statistica__ref64 },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Ad ogni variabile aleatoria sono associati gli eventi ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject45)\n                        ),\n                        ', che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a ',\n                        statistica__ref65,\n                        '.'\n                    ),\n                    statistica__ref66,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject46)\n                        )\n                    ),\n                    statistica__ref67\n                ),\n                statistica__ref68\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Densità\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Funzione probabilità\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La ',\n                        statistica__ref69,\n                        ' ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject47)\n                        ),\n                        ' di una variabile aleatoria ',\n                        statistica__ref70,\n                        ' ',\n                        statistica__ref71,\n                        ' \\xE8 la funzione che associa ad ogni esito la sua probabilit\\xE0:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject48)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Funzione densità\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La ',\n                        statistica__ref72,\n                        ' ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject49)\n                        ),\n                        ' di una variabile aleatoria ',\n                        statistica__ref73,\n                        ' ',\n                        statistica__ref74,\n                        ' \\xE8 l\\'equivalente continuo della funzione probabilit\\xE0:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject50)\n                        )\n                    ),\n                    statistica__ref75,\n                    statistica__ref76\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Funzione di ripartizione\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Definizione\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Ogni variabile aleatoria ha una ',\n                        statistica__ref77,\n                        ' ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject51)\n                        ),\n                        ' associata, che rappresenta la probabilit\\xE0 che la variabile aleatoria assuma un valore minore o uguale a ',\n                        statistica__ref78,\n                        ':'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Si pu\\xF2 dire che essa rappresenti la probabilit\\xE0 dell\\'evento ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject52)\n                        ),\n                        ':'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject53)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Proprietà della funzione\" },\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        statistica__ref79,\n                        statistica__ref80,\n                        statistica__ref81,\n                        statistica__ref82,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            '\\xC8 ',\n                            statistica__ref83,\n                            ': ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject54)\n                            )\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Probabilità di un valore\" },\n                    statistica__ref84,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject55)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Trasformazioni di variabili aleatorie\" },\n                statistica__ref85,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Nel continuo (invertibile)\" },\n                    statistica__ref86,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject56)\n                        )\n                    )\n                ),\n                statistica__ref87\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Informazioni delle variabili aleatorie\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Media\" },\n                    statistica__ref88,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject57)\n                        )\n                    ),\n                    statistica__ref89,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject58)\n                        )\n                    ),\n                    statistica__ref90,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject59)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                null,\n                statistica__ref91,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Quantili\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il ',\n                        statistica__ref92,\n                        ' ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject60)\n                        ),\n                        ' di ordine ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject61)\n                        ),\n                        ' della variabile aleatoria ',\n                        statistica__ref93,\n                        ' \\xE8 il pi\\xF9 piccolo numero tale che:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject62)\n                        )\n                    ),\n                    statistica__ref94,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il quantile di ordine 0.5 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject63)\n                        ),\n                        ' \\xE8 detto ',\n                        statistica__ref95,\n                        '.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'I quantili di ordine 0.25 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject64)\n                        ),\n                        ' e 0.75 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject65)\n                        ),\n                        ' sono detti ',\n                        statistica__ref96,\n                        '.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'I quantili di ordine ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject66)\n                        ),\n                        ' sono detti ',\n                        statistica__ref97,\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Varianza\" },\n                    statistica__ref98,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject67)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Disuguaglianze notevoli\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Disuguaglianza di Markov\" },\n                    statistica__ref99,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject68)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Divide in due parti (',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject69)\n                        ),\n                        ' e ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject70)\n                        ),\n                        ') la funzione X, la cui media risulter\\xE0 uguale a:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject71)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Disuguaglianza di Čebyšëv\" },\n                    statistica__ref100,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Se la variabile aleatoria ',\n                        statistica__ref101,\n                        ' ha media e varianza, allora la probabilit\\xE0 che essa abbia un valore a pi\\xF9 di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject72)\n                        ),\n                        ' di distanza dal valore medio \\xE8 minore o uguale a ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject73)\n                        ),\n                        '.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject74)\n                        )\n                    ),\n                    statistica__ref102,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject75)\n                        )\n                    ),\n                    statistica__ref103\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Un momento...!\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momento\" },\n                    statistica__ref104,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject76)\n                        )\n                    ),\n                    statistica__ref105\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Funzione generatrice dei momenti\" },\n                    statistica__ref106,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject77)\n                        )\n                    ),\n                    statistica__ref107,\n                    statistica__ref108\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Funzione caratteristica\" },\n                    statistica__ref109,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject78)\n                        )\n                    ),\n                    statistica__ref110,\n                    statistica__ref111\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Prove e schemi\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Variabile con distribuzione\" },\n                    statistica__ref112,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject79)\n                        )\n                    )\n                ),\n                statistica__ref113,\n                statistica__ref114\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Bernoulliana\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione bernoulliana\" },\n                    statistica__ref115,\n                    statistica__ref116,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject80)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della bernoulliana\" },\n                    statistica__ref117,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject81)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Binomiale\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione binomiale\" },\n                    statistica__ref118,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject82)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della binomiale\" },\n                    statistica__ref119,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject83)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della binomiale\" },\n                    statistica__ref120,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject84)\n                        )\n                    ),\n                    statistica__ref121,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject85)\n                        )\n                    ),\n                    statistica__ref122,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject86)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Geometrica\" },\n                statistica__ref123,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della geometrica\" },\n                    statistica__ref124,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject87)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della geometrica\" },\n                    statistica__ref125,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject88)\n                        )\n                    ),\n                    statistica__ref126,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject89)\n                        )\n                    ),\n                    statistica__ref127,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject90)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Assenza di memoria della geometrica\" },\n                    statistica__ref128,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject91)\n                        )\n                    ),\n                    statistica__ref129\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Binomiale negativa\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione binomiale negativa\" },\n                    statistica__ref130,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject92)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della binomiale negativa\" },\n                    statistica__ref131,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject93)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della binomiale negativa\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        statistica__ref132,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject94)\n                            )\n                        ),\n                        statistica__ref133,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject95)\n                            )\n                        ),\n                        statistica__ref134,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject96)\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Geometrica traslata\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione geometrica traslata\" },\n                    statistica__ref135,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo rimane ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject97)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della geometrica tralsata\" },\n                    statistica__ref136,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject98)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della geometrica traslata\" },\n                    statistica__ref137,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject99)\n                        )\n                    ),\n                    statistica__ref138,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject100)\n                        )\n                    ),\n                    statistica__ref139,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject90)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Assenza di memoria della geometrica traslata\" },\n                    statistica__ref140,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject91)\n                        )\n                    ),\n                    statistica__ref141\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Binomiale negativa traslata\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione binomiale negativa traslata\" },\n                    statistica__ref142,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo rimane ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject92)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della binomiale negativa traslata\" },\n                    statistica__ref143,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject101)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della binomiale negativa traslata\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        statistica__ref144,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject102)\n                            )\n                        ),\n                        statistica__ref145,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject103)\n                            )\n                        ),\n                        statistica__ref146,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject96)\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Ipergeometrica\" },\n                statistica__ref147,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della ipergeometrica\" },\n                    statistica__ref148,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject104)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della ipergeometrica\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        statistica__ref149,\n                        statistica__ref150,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject105)\n                            )\n                        ),\n                        statistica__ref151,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject106)\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Poissoniana\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione poissoniana\" },\n                    statistica__ref152,\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Binomiale: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject107)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Il numero di prove tende a infinito: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject108)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'La probabilit\\xE0 di successo tende a 0: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject109)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'La media \\xE8 finita: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject110)\n                            )\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject111)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della poissoniana\" },\n                    statistica__ref153,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject112)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della poissoniana\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        statistica__ref154,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject113)\n                            )\n                        ),\n                        statistica__ref155,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject114)\n                            )\n                        ),\n                        statistica__ref156,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject115)\n                            )\n                        ),\n                        statistica__ref157,\n                        Object(preact_min[\"h\"])(\n                            'ol',\n                            { start: 2 },\n                            Object(preact_min[\"h\"])(\n                                'li',\n                                null,\n                                Object(preact_min[\"h\"])(\n                                    latex_Latex,\n                                    null,\n                                    statistica_r(statistica__templateObject116)\n                                )\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Un altro schema\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Schema di Poisson\" },\n                    statistica__ref158,\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        statistica__ref159,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'hanno intensit\\xE0 ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject117)\n                            ),\n                            ' costante.'\n                        ),\n                        statistica__ref160\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Processo di Poisson\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Una variabile aleatoria ',\n                        statistica__ref161,\n                        ' che conta il numero di arrivi di uno schema di Poisson di intensit\\xE0 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject117)\n                        ),\n                        ' in un intervallo di tempo di durata ',\n                        statistica__ref162,\n                        '.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'E\\' una distribuzione poissoniana con ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject118)\n                        ),\n                        ': ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject119)\n                        )\n                    ),\n                    statistica__ref163\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Esponenziale\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione esponenziale\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensit\\xE0 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject117)\n                        ),\n                        '.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject120)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità dell'esponenziale\" },\n                    statistica__ref164,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject121)\n                        )\n                    ),\n                    statistica__ref165,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject122)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti dell'esponenziale\" },\n                    statistica__ref166,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject123)\n                        )\n                    ),\n                    _ref167,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject124)\n                        )\n                    ),\n                    _ref168,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject125)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Assenza di memoria della esponenziale\" },\n                    _ref169,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject126)\n                        )\n                    ),\n                    _ref170\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Legge gamma\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione gamma\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Una variabile aleatoria che conta il tempo diwidehattesa prima dell\\'',\n                        _ref171,\n                        '-esimo arrivo di un processo di Poisson di intensit\\xE0 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(statistica__templateObject117)\n                        ),\n                        '.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject127)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della legge gamma\" },\n                    _ref172,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject128)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della legge gamma\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        _ref173,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject129)\n                            )\n                        ),\n                        _ref174,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject130)\n                            )\n                        ),\n                        _ref175,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject131)\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Uniforme\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione uniforme\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Una variabile aleatoria che pu\\xF2 assumere qualsiasi valore in un intervallo ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject132)\n                        ),\n                        ' in modo equiprobabile.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject133)\n                        )\n                    ),\n                    _ref176,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject134)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della distribuzione uniforme\" },\n                    _ref177,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject135)\n                        )\n                    ),\n                    _ref178,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject136)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della distribuzione uniforme\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        _ref179,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject137)\n                            )\n                        ),\n                        _ref180,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject138)\n                            )\n                        ),\n                        _ref181,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject139)\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Normale o Gaussiana\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione normale\" },\n                    _ref182,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject140)\n                        ),\n                        '.'\n                    ),\n                    _ref183\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità della distribuzione normale\" },\n                    _ref184,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject141)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momenti della distribuzione normale\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        _ref185,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject142)\n                            )\n                        ),\n                        _ref186,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(statistica__templateObject114)\n                            )\n                        ),\n                        _ref187,\n                        Object(preact_min[\"h\"])(\n                            'p',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject143)\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                null,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Trasformazione della normale\" },\n                    _ref188,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject144)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Normale standard\" },\n                    _ref189,\n                    _ref190,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La sua funzione di ripartizione \\xE8 detta ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject145)\n                        ),\n                        ' e vale:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject146)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Quantili normali\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Da un quantile ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject147)\n                        ),\n                        ' della normale standard \\xE8 possibile risalire allo stesso quantile di qualsiasi altra normale:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject148)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                null,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Gamma e normale\" },\n                    _ref191,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject149)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"La funzione Chi\" },\n                    _ref192,\n                    _ref193,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject150)\n                        )\n                    ),\n                    _ref194,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject151)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"T di Student\" },\n                    _ref195,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject152)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Approssimazioni notevoli\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Ipergeometrica e binomiale\" },\n                    _ref196,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject153)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Binomiale e poissoniana\" },\n                    _ref197,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject154)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Binomiale e normale\" },\n                    _ref198,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject155)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Correzione di Yates\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Passando da una variabile discreta ',\n                        _ref199,\n                        ' a una continua ',\n                        _ref200,\n                        ', per ogni valore discreto ',\n                        _ref201,\n                        ' la probabilit\\xE0 viene \"spalmata\" su tutto l\\'intervallo ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject156)\n                        ),\n                        ':'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject157)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject158)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject159)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject160)\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Vettori aleatori\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Vettore aleatorio\" },\n                    _ref202,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il suo simbolo generalmente \\xE8 ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject161)\n                        ),\n                        ' oppure ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject162)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Funzioni di ripartizione\" },\n                    _ref203,\n                    _ref204,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject163)\n                        )\n                    ),\n                    _ref205,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject164)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Densità discreta\" },\n                    _ref206,\n                    _ref207,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject165)\n                        )\n                    ),\n                    _ref208,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject166)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Più variabili aleatorie\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Indipendenza delle variabili aleatorie\" },\n                    _ref209,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject167)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Media dei vettori aleatori\" },\n                    _ref210,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject168)\n                        )\n                    ),\n                    _ref211,\n                    _ref212,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject169)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                null,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Covarianza\" },\n                    _ref213,\n                    _ref214,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject170)\n                        )\n                    ),\n                    _ref215,\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Il suo ',\n                            _ref216,\n                            ' \\xE8 0: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject171)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'E\\' ',\n                            _ref217,\n                            ': ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject172)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'E\\' ',\n                            _ref218,\n                            ': ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject173)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'E\\' ',\n                            _ref219,\n                            ': ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject174)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'E\\' ',\n                            _ref220,\n                            ': ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject175)\n                            )\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Variabili incorrelate\" },\n                    _ref221,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject176)\n                        )\n                    ),\n                    _ref222\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Matrice di covarianza\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Una matrice ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject177)\n                        ),\n                        ' che contiene la covarianza tra tutte le variabili di un vettore aleatorio ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject161)\n                        ),\n                        ':'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject178)\n                        )\n                    ),\n                    _ref223\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Coefficiente di correlazione\" },\n                    _ref224,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject179)\n                        )\n                    ),\n                    _ref225,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject180)\n                        )\n                    ),\n                    _ref226,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject181)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Varianza di variabili aleatorie sommate\" },\n                    _ref227,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject182)\n                        )\n                    ),\n                    _ref228,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Se pi\\xF9 variabili aleatorie ',\n                        _ref229,\n                        ' sono ',\n                        _ref230,\n                        ' (',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject176)\n                        ),\n                        '), allora:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject183)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Campioni\" },\n                _ref231,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Momento campionario\" },\n                    _ref232,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject184)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Il momento campionario di primo ordine \\xE8 la ',\n                        _ref233,\n                        ' ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject185)\n                        ),\n                        '.'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Varianza campionaria\" },\n                    _ref234,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Se \\xE8 noto il valore medio ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject186)\n                        ),\n                        ' di X:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject187)\n                        )\n                    ),\n                    _ref235,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject188)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Media-ception\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Media campionaria\" },\n                    _ref236,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject189)\n                        )\n                    ),\n                    _ref237\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Varianza campionaria\" },\n                    _ref238,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject190)\n                        )\n                    ),\n                    _ref239\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Correzione campionaria\" },\n                    _ref240,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject191)\n                        )\n                    ),\n                    _ref241\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Campionamento di una distribuzione normale\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Campionamento di una distribuzione normale\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Se la popolazione ',\n                        _ref242,\n                        ' ha una distribuzione normale (',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject192)\n                        ),\n                        ')...'\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione della media campionaria\" },\n                    _ref243,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject193)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Distribuzione della varianza campionaria\" },\n                    _ref244,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject194)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject195)\n                        )\n                    )\n                ),\n                _ref245\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Quando i campioni hanno dimensioni infinite\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Convergenza in distribuzione\" },\n                    _ref246,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            '\\\\lim_{n \\\\to +\\\\infty} F_{X_n} (x) = F_X (x) \\\\implies X_n \\\\xrightarrow{d} X'\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Convergenza in probabilità\" },\n                    _ref247,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            '\\\\forall \\\\epsilon > 0, \\\\lim_{n \\\\to +\\\\infty} P( | X_n - X | < \\\\epsilon) = 1 \\\\implies X_n \\\\xrightarrow{p} X'\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Convergenza quasi certa\" },\n                    _ref248,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            '\\\\forall \\\\epsilon > 0, P left( \\\\lim_{n \\\\to +\\\\infty} | X_n - X | < \\\\epsilon) \\right) = 1 \\\\implies X_n \\\\xrightarrow{qc} X'\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Convergenza in media quadratica\" },\n                    _ref249,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            '\\\\lim_{n \\\\to +\\\\infty} E( | X_n - X |^2 = 0 \\\\implies X_n \\\\xrightarrow{mq} X'\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Gerarchia delle convergenze\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            '\\n                                \\\\begin{matrix}\\n                                X_n \\\\xrightarrow{mq} X\\\\\\\\\\n                                X_n \\\\xrightarrow{qc} X\\n                                \\\\end{matrix} \\\\implies X_n \\\\xrightarrow{p} X \\\\implies X_n \\\\xrightarrow{d} X'\n                        )\n                    ),\n                    _ref250,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            'X_n \\\\xrightarrow{p} x \\\\Longleftrightarrow X_n \\\\xrightarrow{d} x'\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"I grandi numeri\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Legge debole dei grandi numeri\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La successione delle medie campionarie ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject185)\n                        ),\n                        ' ',\n                        _ref251,\n                        ' alla media della popolazione ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject196)\n                        ),\n                        ', se essa esiste.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            '\\\\overline{X}_n \\\\xrightarrow{p} X'\n                        )\n                    ),\n                    _ref252,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject197)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject198)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Legge forte dei grandi numeri\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La successione delle medie campionarie ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject185)\n                        ),\n                        ' ',\n                        _ref253,\n                        ' alla media della popolazione ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject196)\n                        ),\n                        ', se essa esiste.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            '\\\\overline{X}_n \\\\xrightarrow{qc} X'\n                        )\n                    ),\n                    _ref254,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject199)\n                        )\n                    ),\n                    _ref255\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Al limite\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Teorema centrale del limite\" },\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'La successione delle medie campionarie ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject185)\n                        ),\n                        ' ',\n                        _ref256,\n                        ' a ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject200)\n                        ),\n                        '.'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject201)\n                        )\n                    ),\n                    _ref257,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject202)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Altre approsimazioni\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Binomiale e normale\" },\n                    _ref258,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject155)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Binomiale negativa e normale\" },\n                    _ref259,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject203)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Poissoniana e normale\" },\n                    _ref260,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject204)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Gamma e normale\" },\n                    _ref261,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject205)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"In generale\" },\n                    _ref262,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject206)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Actually statistica\" },\n                _ref263,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Statistica\" },\n                    _ref264,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject207)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        example_Example,\n                        null,\n                        'Ad esempio, sono statistiche media e varianza campionaria, cos\\xEC come il campione stesso ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject208)\n                        ),\n                        '.'\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Stimatori\" },\n                _ref265,\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Corretto\" },\n                    _ref266,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject209)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Asintoticamente corretto\" },\n                    _ref267,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject210)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Consistente in media quadratica\" },\n                    _ref268,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject211)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Consistente in probabilità\" },\n                    _ref269,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject212)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Asintoticamente normale\" },\n                    _ref270,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject213)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Metodo dei momenti\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Metodo dei momenti\" },\n                    _ref271,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Lo stimatore di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject214)\n                        ),\n                        ' cos\\xEC ottenuto sar\\xE0 indicato aggiungendo un cappellino e una ',\n                        _ref272,\n                        ' a ',\n                        _ref273,\n                        ': ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject215)\n                        )\n                    ),\n                    _ref274,\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject216)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject217)\n                            )\n                        )\n                    ),\n                    _ref275,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject218)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Se ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject214)\n                        ),\n                        ' non \\xE8 esprimibile in termini di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject196)\n                        ),\n                        ', si possono usare i momenti successivi ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject219)\n                        ),\n                        ', ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject220)\n                        ),\n                        ', ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject220)\n                        ),\n                        '...'\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Metodo della massima verosomiglianza\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Metodo della massima verosomiglianza\" },\n                    _ref276,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Lo stimatore di ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject214)\n                        ),\n                        ' cos\\xEC ottenuto sar\\xE0 indicato aggiungendo un cappellino e una ',\n                        _ref277,\n                        ' a ',\n                        _ref278,\n                        ': ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject221)\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'Consiste nel trovare il massimo assoluto ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject221)\n                        ),\n                        ' della la funzione di verosomiglianza ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject222)\n                        ),\n                        ':'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject223)\n                        )\n                    ),\n                    _ref279\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Proprietà degli stimatori di massima verosomiglianza\" },\n                    _ref280,\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        _ref281,\n                        _ref282,\n                        _ref283,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Sono ',\n                            _ref284,\n                            ': ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject224)\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Nuove stime notevoli\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Stima di una bernoulliana\" },\n                    _ref285,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject225)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Stima di una poissoniana\" },\n                    _ref286,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject226)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Stima di una esponenziale\" },\n                    _ref287,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject227)\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Stima di una normale\" },\n                    _ref288,\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject228)\n                            )\n                        ),\n                        _ref289,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject229)\n                            )\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Intervalli di confidenza\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Confidenza\" },\n                    _ref290,\n                    _ref291,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        'L\\'intervallo di confidenza a N della stima ',\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject230)\n                        ),\n                        ' \\xE8 l\\'intervallo ',\n                        _ref292,\n                        ' tale che:'\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject231)\n                        )\n                    ),\n                    _ref293\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Confidenza nella media di una normale\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Varianza nota\" },\n                    _ref294,\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Intervalli bilateri: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject232)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Intervallo unilatero da sinistra: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject233)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Intervallo unilatero da destra: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject234)\n                            )\n                        )\n                    )\n                ),\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Varianza incognita\" },\n                    _ref295,\n                    Object(preact_min[\"h\"])(\n                        'ul',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Intervalli bilateri: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject235)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Intervallo unilatero da sinistra: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject236)\n                            )\n                        ),\n                        Object(preact_min[\"h\"])(\n                            'li',\n                            null,\n                            'Intervallo unilatero da destra: ',\n                            Object(preact_min[\"h\"])(\n                                latex_Latex,\n                                null,\n                                statistica_r(_templateObject237)\n                            )\n                        )\n                    ),\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject238)\n                        ),\n                        ' \\xE8 un quantile della distribuzione di Student di parametro ',\n                        _ref296,\n                        '.'\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Confidenza per la proporzione di una bernoulliana\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Terzo metodo corretto\" },\n                    _ref297,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject239)\n                        )\n                    )\n                )\n            ),\n            Object(preact_min[\"h\"])(\n                split_Split,\n                { title: \"Confidenza per la media di qualsiasi popolazione\" },\n                Object(preact_min[\"h\"])(\n                    panel_Panel,\n                    { title: \"Approssimando con la normale\" },\n                    _ref298,\n                    Object(preact_min[\"h\"])(\n                        'p',\n                        null,\n                        Object(preact_min[\"h\"])(\n                            latex_Latex,\n                            null,\n                            statistica_r(_templateObject240)\n                        )\n                    )\n                )\n            )\n        );\n    };\n\n    return Statistica;\n}(preact_min[\"Component\"]);\n\n\n// CONCATENATED MODULE: ./index.js\n/* harmony export (binding) */ __webpack_require__.d(__webpack_exports__, \"default\", function() { return App; });\n\n\nfunction index__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction 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'Error in ' + name + ' extension->' : 'Error in unnamed extension',\n      ret = {\n        valid: true,\n        error: ''\n      };\n\n  if (!showdown.helper.isArray(extension)) {\n    extension = [extension];\n  }\n\n  for (var i = 0; i < extension.length; ++i) {\n    var baseMsg = errMsg + ' sub-extension ' + i + ': ',\n        ext = extension[i];\n    if (typeof ext !== 'object') {\n      ret.valid = false;\n      ret.error = baseMsg + 'must be an object, but ' + typeof ext + ' given';\n      return ret;\n    }\n\n    if (!showdown.helper.isString(ext.type)) {\n      ret.valid = false;\n      ret.error = baseMsg + 'property \"type\" must be a string, but ' + typeof ext.type + ' given';\n      return ret;\n    }\n\n    var type = ext.type = ext.type.toLowerCase();\n\n    // normalize extension type\n    if (type === 'language') {\n      type = ext.type = 'lang';\n    }\n\n    if (type === 'html') {\n      type = ext.type = 'output';\n    }\n\n    if (type !== 'lang' && type !== 'output' && type !== 'listener') {\n      ret.valid = false;\n      ret.error = baseMsg + 'type ' + type + ' is not recognized. Valid values: \"lang/language\", \"output/html\" or \"listener\"';\n      return ret;\n    }\n\n    if (type === 'listener') {\n      if (showdown.helper.isUndefined(ext.listeners)) {\n        ret.valid = false;\n        ret.error = baseMsg + '. Extensions of type \"listener\" must have a property called \"listeners\"';\n        return ret;\n      }\n    } else {\n      if (showdown.helper.isUndefined(ext.filter) && showdown.helper.isUndefined(ext.regex)) {\n        ret.valid = false;\n        ret.error = baseMsg + type + ' extensions must define either a \"regex\" property or a \"filter\" method';\n        return ret;\n      }\n    }\n\n    if (ext.listeners) {\n      if (typeof ext.listeners !== 'object') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"listeners\" property must be an object but ' + typeof ext.listeners + ' given';\n        return ret;\n      }\n      for (var ln in ext.listeners) {\n        if (ext.listeners.hasOwnProperty(ln)) {\n          if (typeof ext.listeners[ln] !== 'function') {\n            ret.valid = false;\n            ret.error = baseMsg + '\"listeners\" property must be an hash of [event name]: [callback]. listeners.' + ln +\n              ' must be a function but ' + typeof ext.listeners[ln] + ' given';\n            return ret;\n          }\n        }\n      }\n    }\n\n    if (ext.filter) {\n      if (typeof ext.filter !== 'function') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"filter\" must be a function, but ' + typeof ext.filter + ' given';\n        return ret;\n      }\n    } else if (ext.regex) {\n      if (showdown.helper.isString(ext.regex)) {\n        ext.regex = new RegExp(ext.regex, 'g');\n      }\n      if (!(ext.regex instanceof RegExp)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" property must either be a string or a RegExp object, but ' + typeof ext.regex + ' given';\n        return ret;\n      }\n      if (showdown.helper.isUndefined(ext.replace)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" extensions must implement a replace string or function';\n        return ret;\n      }\n    }\n  }\n  return ret;\n}\n\n/**\n * Validate extension\n * @param {object} ext\n * @returns {boolean}\n */\nshowdown.validateExtension = function (ext) {\n  'use strict';\n\n  var validateExtension = validate(ext, null);\n  if (!validateExtension.valid) {\n    console.warn(validateExtension.error);\n    return false;\n  }\n  return true;\n};\n\r\n/**\n * showdownjs helper functions\n */\n\nif (!showdown.hasOwnProperty('helper')) {\n  showdown.helper = {};\n}\n\n/**\n * Check if var is string\n * @static\n * @param {string} a\n * @returns {boolean}\n */\nshowdown.helper.isString = function (a) {\n  'use strict';\n  return (typeof a === 'string' || a instanceof String);\n};\n\n/**\n * Check if var is a function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isFunction = function (a) {\n  'use strict';\n  var getType = {};\n  return a && getType.toString.call(a) === '[object Function]';\n};\n\n/**\n * isArray helper function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isArray = function (a) {\n  'use strict';\n  return Array.isArray(a);\n};\n\n/**\n * Check if value is undefined\n * @static\n * @param {*} value The value to check.\n * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.\n */\nshowdown.helper.isUndefined = function (value) {\n  'use strict';\n  return typeof value === 'undefined';\n};\n\n/**\n * ForEach helper function\n * Iterates over Arrays and Objects (own properties only)\n * @static\n * @param {*} obj\n * @param {function} callback Accepts 3 params: 1. value, 2. key, 3. the original array/object\n */\nshowdown.helper.forEach = function (obj, callback) {\n  'use strict';\n  // check if obj is defined\n  if (showdown.helper.isUndefined(obj)) {\n    throw new Error('obj param is required');\n  }\n\n  if (showdown.helper.isUndefined(callback)) {\n    throw new Error('callback param is required');\n  }\n\n  if (!showdown.helper.isFunction(callback)) {\n    throw new Error('callback param must be a function/closure');\n  }\n\n  if (typeof obj.forEach === 'function') {\n    obj.forEach(callback);\n  } else if (showdown.helper.isArray(obj)) {\n    for (var i = 0; i < obj.length; i++) {\n      callback(obj[i], i, obj);\n    }\n  } else if (typeof (obj) === 'object') {\n    for (var prop in obj) {\n      if (obj.hasOwnProperty(prop)) {\n        callback(obj[prop], prop, obj);\n      }\n    }\n  } else {\n    throw new Error('obj does not seem to be an array or an iterable object');\n  }\n};\n\n/**\n * Standardidize extension name\n * @static\n * @param {string} s extension name\n * @returns {string}\n */\nshowdown.helper.stdExtName = function (s) {\n  'use strict';\n  return s.replace(/[_?*+\\/\\\\.^-]/g, '').replace(/\\s/g, '').toLowerCase();\n};\n\nfunction escapeCharactersCallback (wholeMatch, m1) {\n  'use strict';\n  var charCodeToEscape = m1.charCodeAt(0);\n  return '¨E' + charCodeToEscape + 'E';\n}\n\n/**\n * Callback used to escape characters when passing through String.replace\n * @static\n * @param {string} wholeMatch\n * @param {string} m1\n * @returns {string}\n */\nshowdown.helper.escapeCharactersCallback = escapeCharactersCallback;\n\n/**\n * Escape characters in a string\n * @static\n * @param {string} text\n * @param {string} charsToEscape\n * @param {boolean} afterBackslash\n * @returns {XML|string|void|*}\n */\nshowdown.helper.escapeCharacters = function (text, charsToEscape, afterBackslash) {\n  'use strict';\n  // First we have to escape the escape characters so that\n  // we can build a character class out of them\n  var regexString = '([' + charsToEscape.replace(/([\\[\\]\\\\])/g, '\\\\$1') + '])';\n\n  if (afterBackslash) {\n    regexString = '\\\\\\\\' + regexString;\n  }\n\n  var regex = new RegExp(regexString, 'g');\n  text = text.replace(regex, escapeCharactersCallback);\n\n  return text;\n};\n\n/**\n * Unescape HTML entities\n * @param txt\n * @returns {string}\n */\nshowdown.helper.unescapeHTMLEntities = function (txt) {\n  'use strict';\n\n  return txt\n    .replace(/"/g, '\"')\n    .replace(/</g, '<')\n    .replace(/>/g, '>')\n    .replace(/&/g, '&');\n};\n\nvar rgxFindMatchPos = function (str, left, right, flags) {\n  'use strict';\n  var f = flags || '',\n      g = f.indexOf('g') > -1,\n      x = new RegExp(left + '|' + right, 'g' + f.replace(/g/g, '')),\n      l = new RegExp(left, f.replace(/g/g, '')),\n      pos = [],\n      t, s, m, start, end;\n\n  do {\n    t = 0;\n    while ((m = x.exec(str))) {\n      if (l.test(m[0])) {\n        if (!(t++)) {\n          s = x.lastIndex;\n          start = s - m[0].length;\n        }\n      } else if (t) {\n        if (!--t) {\n          end = m.index + m[0].length;\n          var obj = {\n            left: {start: start, end: s},\n            match: {start: s, end: m.index},\n            right: {start: m.index, end: end},\n            wholeMatch: {start: start, end: end}\n          };\n          pos.push(obj);\n          if (!g) {\n            return pos;\n          }\n        }\n      }\n    }\n  } while (t && (x.lastIndex = s));\n\n  return pos;\n};\n\n/**\n * matchRecursiveRegExp\n *\n * (c) 2007 Steven Levithan \n * MIT License\n *\n * Accepts a string to search, a left and right format delimiter\n * as regex patterns, and optional regex flags. Returns an array\n * of matches, allowing nested instances of left/right delimiters.\n * Use the \"g\" flag to return all matches, otherwise only the\n * first is returned. Be careful to ensure that the left and\n * right format delimiters produce mutually exclusive matches.\n * Backreferences are not supported within the right delimiter\n * due to how it is internally combined with the left delimiter.\n * When matching strings whose format delimiters are unbalanced\n * to the left or right, the output is intentionally as a\n * conventional regex library with recursion support would\n * produce, e.g. \"<\" and \">\" both produce [\"x\"] when using\n * \"<\" and \">\" as the delimiters (both strings contain a single,\n * balanced instance of \"\").\n *\n * examples:\n * matchRecursiveRegExp(\"test\", \"\\\\(\", \"\\\\)\")\n * returns: []\n * matchRecursiveRegExp(\">>t<>\", \"<\", \">\", \"g\")\n * returns: [\"t<>\", \"\"]\n * matchRecursiveRegExp(\"
    test
    \", \"]*>\", \"\", \"gi\")\n * returns: [\"test\"]\n */\nshowdown.helper.matchRecursiveRegExp = function (str, left, right, flags) {\n  'use strict';\n\n  var matchPos = rgxFindMatchPos (str, left, right, flags),\n      results = [];\n\n  for (var i = 0; i < matchPos.length; ++i) {\n    results.push([\n      str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n      str.slice(matchPos[i].match.start, matchPos[i].match.end),\n      str.slice(matchPos[i].left.start, matchPos[i].left.end),\n      str.slice(matchPos[i].right.start, matchPos[i].right.end)\n    ]);\n  }\n  return results;\n};\n\n/**\n *\n * @param {string} str\n * @param {string|function} replacement\n * @param {string} left\n * @param {string} right\n * @param {string} flags\n * @returns {string}\n */\nshowdown.helper.replaceRecursiveRegExp = function (str, replacement, left, right, flags) {\n  'use strict';\n\n  if (!showdown.helper.isFunction(replacement)) {\n    var repStr = replacement;\n    replacement = function () {\n      return repStr;\n    };\n  }\n\n  var matchPos = rgxFindMatchPos(str, left, right, flags),\n      finalStr = str,\n      lng = matchPos.length;\n\n  if (lng > 0) {\n    var bits = [];\n    if (matchPos[0].wholeMatch.start !== 0) {\n      bits.push(str.slice(0, matchPos[0].wholeMatch.start));\n    }\n    for (var i = 0; i < lng; ++i) {\n      bits.push(\n        replacement(\n          str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n          str.slice(matchPos[i].match.start, matchPos[i].match.end),\n          str.slice(matchPos[i].left.start, matchPos[i].left.end),\n          str.slice(matchPos[i].right.start, matchPos[i].right.end)\n        )\n      );\n      if (i < lng - 1) {\n        bits.push(str.slice(matchPos[i].wholeMatch.end, matchPos[i + 1].wholeMatch.start));\n      }\n    }\n    if (matchPos[lng - 1].wholeMatch.end < str.length) {\n      bits.push(str.slice(matchPos[lng - 1].wholeMatch.end));\n    }\n    finalStr = bits.join('');\n  }\n  return finalStr;\n};\n\n/**\n * Returns the index within the passed String object of the first occurrence of the specified regex,\n * starting the search at fromIndex. Returns -1 if the value is not found.\n *\n * @param {string} str string to search\n * @param {RegExp} regex Regular expression to search\n * @param {int} [fromIndex = 0] Index to start the search\n * @returns {Number}\n * @throws InvalidArgumentError\n */\nshowdown.helper.regexIndexOf = function (str, regex, fromIndex) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  if (regex instanceof RegExp === false) {\n    throw 'InvalidArgumentError: second parameter of showdown.helper.regexIndexOf function must be an instance of RegExp';\n  }\n  var indexOf = str.substring(fromIndex || 0).search(regex);\n  return (indexOf >= 0) ? (indexOf + (fromIndex || 0)) : indexOf;\n};\n\n/**\n * Splits the passed string object at the defined index, and returns an array composed of the two substrings\n * @param {string} str string to split\n * @param {int} index index to split string at\n * @returns {[string,string]}\n * @throws InvalidArgumentError\n */\nshowdown.helper.splitAtIndex = function (str, index) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  return [str.substring(0, index), str.substring(index)];\n};\n\n/**\n * Obfuscate an e-mail address through the use of Character Entities,\n * transforming ASCII characters into their equivalent decimal or hex entities.\n *\n * Since it has a random component, subsequent calls to this function produce different results\n *\n * @param {string} mail\n * @returns {string}\n */\nshowdown.helper.encodeEmailAddress = function (mail) {\n  'use strict';\n  var encode = [\n    function (ch) {\n      return '&#' + ch.charCodeAt(0) + ';';\n    },\n    function (ch) {\n      return '&#x' + ch.charCodeAt(0).toString(16) + ';';\n    },\n    function (ch) {\n      return ch;\n    }\n  ];\n\n  mail = mail.replace(/./g, function (ch) {\n    if (ch === '@') {\n      // this *must* be encoded. I insist.\n      ch = encode[Math.floor(Math.random() * 2)](ch);\n    } else {\n      var r = Math.random();\n      // roughly 10% raw, 45% hex, 45% dec\n      ch = (\n        r > 0.9 ? encode[2](ch) : r > 0.45 ? encode[1](ch) : encode[0](ch)\n      );\n    }\n    return ch;\n  });\n\n  return mail;\n};\n\n/**\n *\n * @param str\n * @param targetLength\n * @param padString\n * @returns {string}\n */\nshowdown.helper.padEnd = function padEnd (str, targetLength, padString) {\n  'use strict';\n  /*jshint bitwise: false*/\n  // eslint-disable-next-line space-infix-ops\n  targetLength = targetLength>>0; //floor if number or convert non-number to 0;\n  /*jshint bitwise: true*/\n  padString = String(padString || ' ');\n  if (str.length > targetLength) {\n    return String(str);\n  } else {\n    targetLength = targetLength - str.length;\n    if (targetLength > padString.length) {\n      padString += padString.repeat(targetLength / padString.length); //append to original to ensure we are longer than needed\n    }\n    return String(str) + padString.slice(0,targetLength);\n  }\n};\n\n/**\n * POLYFILLS\n */\n// use this instead of builtin is undefined for IE8 compatibility\nif (typeof console === 'undefined') {\n  console = {\n    warn: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    log: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    error: function (msg) {\n      'use strict';\n      throw msg;\n    }\n  };\n}\n\n/**\n * Common regexes.\n * We declare some common regexes to improve performance\n */\nshowdown.helper.regexes = {\n  asteriskDashAndColon: /([*_:~])/g\n};\n\n/**\n * EMOJIS LIST\n */\nshowdown.helper.emojis = {\n  '+1':'\\ud83d\\udc4d',\n  '-1':'\\ud83d\\udc4e',\n  '100':'\\ud83d\\udcaf',\n  '1234':'\\ud83d\\udd22',\n  '1st_place_medal':'\\ud83e\\udd47',\n  '2nd_place_medal':'\\ud83e\\udd48',\n  '3rd_place_medal':'\\ud83e\\udd49',\n  '8ball':'\\ud83c\\udfb1',\n  'a':'\\ud83c\\udd70\\ufe0f',\n  'ab':'\\ud83c\\udd8e',\n  'abc':'\\ud83d\\udd24',\n  'abcd':'\\ud83d\\udd21',\n  'accept':'\\ud83c\\ude51',\n  'aerial_tramway':'\\ud83d\\udea1',\n  'airplane':'\\u2708\\ufe0f',\n  'alarm_clock':'\\u23f0',\n  'alembic':'\\u2697\\ufe0f',\n  'alien':'\\ud83d\\udc7d',\n  'ambulance':'\\ud83d\\ude91',\n  'amphora':'\\ud83c\\udffa',\n  'anchor':'\\u2693\\ufe0f',\n  'angel':'\\ud83d\\udc7c',\n  'anger':'\\ud83d\\udca2',\n  'angry':'\\ud83d\\ude20',\n  'anguished':'\\ud83d\\ude27',\n  'ant':'\\ud83d\\udc1c',\n  'apple':'\\ud83c\\udf4e',\n  'aquarius':'\\u2652\\ufe0f',\n  'aries':'\\u2648\\ufe0f',\n  'arrow_backward':'\\u25c0\\ufe0f',\n  'arrow_double_down':'\\u23ec',\n  'arrow_double_up':'\\u23eb',\n  'arrow_down':'\\u2b07\\ufe0f',\n  'arrow_down_small':'\\ud83d\\udd3d',\n  'arrow_forward':'\\u25b6\\ufe0f',\n  'arrow_heading_down':'\\u2935\\ufe0f',\n  'arrow_heading_up':'\\u2934\\ufe0f',\n  'arrow_left':'\\u2b05\\ufe0f',\n  'arrow_lower_left':'\\u2199\\ufe0f',\n  'arrow_lower_right':'\\u2198\\ufe0f',\n  'arrow_right':'\\u27a1\\ufe0f',\n  'arrow_right_hook':'\\u21aa\\ufe0f',\n  'arrow_up':'\\u2b06\\ufe0f',\n  'arrow_up_down':'\\u2195\\ufe0f',\n  'arrow_up_small':'\\ud83d\\udd3c',\n  'arrow_upper_left':'\\u2196\\ufe0f',\n  'arrow_upper_right':'\\u2197\\ufe0f',\n  'arrows_clockwise':'\\ud83d\\udd03',\n  'arrows_counterclockwise':'\\ud83d\\udd04',\n  'art':'\\ud83c\\udfa8',\n  'articulated_lorry':'\\ud83d\\ude9b',\n  'artificial_satellite':'\\ud83d\\udef0',\n  'astonished':'\\ud83d\\ude32',\n  'athletic_shoe':'\\ud83d\\udc5f',\n  'atm':'\\ud83c\\udfe7',\n  'atom_symbol':'\\u269b\\ufe0f',\n  'avocado':'\\ud83e\\udd51',\n  'b':'\\ud83c\\udd71\\ufe0f',\n  'baby':'\\ud83d\\udc76',\n  'baby_bottle':'\\ud83c\\udf7c',\n  'baby_chick':'\\ud83d\\udc24',\n  'baby_symbol':'\\ud83d\\udebc',\n  'back':'\\ud83d\\udd19',\n  'bacon':'\\ud83e\\udd53',\n  'badminton':'\\ud83c\\udff8',\n  'baggage_claim':'\\ud83d\\udec4',\n  'baguette_bread':'\\ud83e\\udd56',\n  'balance_scale':'\\u2696\\ufe0f',\n  'balloon':'\\ud83c\\udf88',\n  'ballot_box':'\\ud83d\\uddf3',\n  'ballot_box_with_check':'\\u2611\\ufe0f',\n  'bamboo':'\\ud83c\\udf8d',\n  'banana':'\\ud83c\\udf4c',\n  'bangbang':'\\u203c\\ufe0f',\n  'bank':'\\ud83c\\udfe6',\n  'bar_chart':'\\ud83d\\udcca',\n  'barber':'\\ud83d\\udc88',\n  'baseball':'\\u26be\\ufe0f',\n  'basketball':'\\ud83c\\udfc0',\n  'basketball_man':'\\u26f9\\ufe0f',\n  'basketball_woman':'\\u26f9\\ufe0f‍\\u2640\\ufe0f',\n  'bat':'\\ud83e\\udd87',\n  'bath':'\\ud83d\\udec0',\n  'bathtub':'\\ud83d\\udec1',\n  'battery':'\\ud83d\\udd0b',\n  'beach_umbrella':'\\ud83c\\udfd6',\n  'bear':'\\ud83d\\udc3b',\n  'bed':'\\ud83d\\udecf',\n  'bee':'\\ud83d\\udc1d',\n  'beer':'\\ud83c\\udf7a',\n  'beers':'\\ud83c\\udf7b',\n  'beetle':'\\ud83d\\udc1e',\n  'beginner':'\\ud83d\\udd30',\n  'bell':'\\ud83d\\udd14',\n  'bellhop_bell':'\\ud83d\\udece',\n  'bento':'\\ud83c\\udf71',\n  'biking_man':'\\ud83d\\udeb4',\n  'bike':'\\ud83d\\udeb2',\n  'biking_woman':'\\ud83d\\udeb4‍\\u2640\\ufe0f',\n  'bikini':'\\ud83d\\udc59',\n  'biohazard':'\\u2623\\ufe0f',\n  'bird':'\\ud83d\\udc26',\n  'birthday':'\\ud83c\\udf82',\n  'black_circle':'\\u26ab\\ufe0f',\n  'black_flag':'\\ud83c\\udff4',\n  'black_heart':'\\ud83d\\udda4',\n  'black_joker':'\\ud83c\\udccf',\n  'black_large_square':'\\u2b1b\\ufe0f',\n  'black_medium_small_square':'\\u25fe\\ufe0f',\n  'black_medium_square':'\\u25fc\\ufe0f',\n  'black_nib':'\\u2712\\ufe0f',\n  'black_small_square':'\\u25aa\\ufe0f',\n  'black_square_button':'\\ud83d\\udd32',\n  'blonde_man':'\\ud83d\\udc71',\n  'blonde_woman':'\\ud83d\\udc71‍\\u2640\\ufe0f',\n  'blossom':'\\ud83c\\udf3c',\n  'blowfish':'\\ud83d\\udc21',\n  'blue_book':'\\ud83d\\udcd8',\n  'blue_car':'\\ud83d\\ude99',\n  'blue_heart':'\\ud83d\\udc99',\n  'blush':'\\ud83d\\ude0a',\n  'boar':'\\ud83d\\udc17',\n  'boat':'\\u26f5\\ufe0f',\n  'bomb':'\\ud83d\\udca3',\n  'book':'\\ud83d\\udcd6',\n  'bookmark':'\\ud83d\\udd16',\n  'bookmark_tabs':'\\ud83d\\udcd1',\n  'books':'\\ud83d\\udcda',\n  'boom':'\\ud83d\\udca5',\n  'boot':'\\ud83d\\udc62',\n  'bouquet':'\\ud83d\\udc90',\n  'bowing_man':'\\ud83d\\ude47',\n  'bow_and_arrow':'\\ud83c\\udff9',\n  'bowing_woman':'\\ud83d\\ude47‍\\u2640\\ufe0f',\n  'bowling':'\\ud83c\\udfb3',\n  'boxing_glove':'\\ud83e\\udd4a',\n  'boy':'\\ud83d\\udc66',\n  'bread':'\\ud83c\\udf5e',\n  'bride_with_veil':'\\ud83d\\udc70',\n  'bridge_at_night':'\\ud83c\\udf09',\n  'briefcase':'\\ud83d\\udcbc',\n  'broken_heart':'\\ud83d\\udc94',\n  'bug':'\\ud83d\\udc1b',\n  'building_construction':'\\ud83c\\udfd7',\n  'bulb':'\\ud83d\\udca1',\n  'bullettrain_front':'\\ud83d\\ude85',\n  'bullettrain_side':'\\ud83d\\ude84',\n  'burrito':'\\ud83c\\udf2f',\n  'bus':'\\ud83d\\ude8c',\n  'business_suit_levitating':'\\ud83d\\udd74',\n  'busstop':'\\ud83d\\ude8f',\n  'bust_in_silhouette':'\\ud83d\\udc64',\n  'busts_in_silhouette':'\\ud83d\\udc65',\n  'butterfly':'\\ud83e\\udd8b',\n  'cactus':'\\ud83c\\udf35',\n  'cake':'\\ud83c\\udf70',\n  'calendar':'\\ud83d\\udcc6',\n  'call_me_hand':'\\ud83e\\udd19',\n  'calling':'\\ud83d\\udcf2',\n  'camel':'\\ud83d\\udc2b',\n  'camera':'\\ud83d\\udcf7',\n  'camera_flash':'\\ud83d\\udcf8',\n  'camping':'\\ud83c\\udfd5',\n  'cancer':'\\u264b\\ufe0f',\n  'candle':'\\ud83d\\udd6f',\n  'candy':'\\ud83c\\udf6c',\n  'canoe':'\\ud83d\\udef6',\n  'capital_abcd':'\\ud83d\\udd20',\n  'capricorn':'\\u2651\\ufe0f',\n  'car':'\\ud83d\\ude97',\n  'card_file_box':'\\ud83d\\uddc3',\n  'card_index':'\\ud83d\\udcc7',\n  'card_index_dividers':'\\ud83d\\uddc2',\n  'carousel_horse':'\\ud83c\\udfa0',\n  'carrot':'\\ud83e\\udd55',\n  'cat':'\\ud83d\\udc31',\n  'cat2':'\\ud83d\\udc08',\n  'cd':'\\ud83d\\udcbf',\n  'chains':'\\u26d3',\n  'champagne':'\\ud83c\\udf7e',\n  'chart':'\\ud83d\\udcb9',\n  'chart_with_downwards_trend':'\\ud83d\\udcc9',\n  'chart_with_upwards_trend':'\\ud83d\\udcc8',\n  'checkered_flag':'\\ud83c\\udfc1',\n  'cheese':'\\ud83e\\uddc0',\n  'cherries':'\\ud83c\\udf52',\n  'cherry_blossom':'\\ud83c\\udf38',\n  'chestnut':'\\ud83c\\udf30',\n  'chicken':'\\ud83d\\udc14',\n  'children_crossing':'\\ud83d\\udeb8',\n  'chipmunk':'\\ud83d\\udc3f',\n  'chocolate_bar':'\\ud83c\\udf6b',\n  'christmas_tree':'\\ud83c\\udf84',\n  'church':'\\u26ea\\ufe0f',\n  'cinema':'\\ud83c\\udfa6',\n  'circus_tent':'\\ud83c\\udfaa',\n  'city_sunrise':'\\ud83c\\udf07',\n  'city_sunset':'\\ud83c\\udf06',\n  'cityscape':'\\ud83c\\udfd9',\n  'cl':'\\ud83c\\udd91',\n  'clamp':'\\ud83d\\udddc',\n  'clap':'\\ud83d\\udc4f',\n  'clapper':'\\ud83c\\udfac',\n  'classical_building':'\\ud83c\\udfdb',\n  'clinking_glasses':'\\ud83e\\udd42',\n  'clipboard':'\\ud83d\\udccb',\n  'clock1':'\\ud83d\\udd50',\n  'clock10':'\\ud83d\\udd59',\n  'clock1030':'\\ud83d\\udd65',\n  'clock11':'\\ud83d\\udd5a',\n  'clock1130':'\\ud83d\\udd66',\n  'clock12':'\\ud83d\\udd5b',\n  'clock1230':'\\ud83d\\udd67',\n  'clock130':'\\ud83d\\udd5c',\n  'clock2':'\\ud83d\\udd51',\n  'clock230':'\\ud83d\\udd5d',\n  'clock3':'\\ud83d\\udd52',\n  'clock330':'\\ud83d\\udd5e',\n  'clock4':'\\ud83d\\udd53',\n  'clock430':'\\ud83d\\udd5f',\n  'clock5':'\\ud83d\\udd54',\n  'clock530':'\\ud83d\\udd60',\n  'clock6':'\\ud83d\\udd55',\n  'clock630':'\\ud83d\\udd61',\n  'clock7':'\\ud83d\\udd56',\n  'clock730':'\\ud83d\\udd62',\n  'clock8':'\\ud83d\\udd57',\n  'clock830':'\\ud83d\\udd63',\n  'clock9':'\\ud83d\\udd58',\n  'clock930':'\\ud83d\\udd64',\n  'closed_book':'\\ud83d\\udcd5',\n  'closed_lock_with_key':'\\ud83d\\udd10',\n  'closed_umbrella':'\\ud83c\\udf02',\n  'cloud':'\\u2601\\ufe0f',\n  'cloud_with_lightning':'\\ud83c\\udf29',\n  'cloud_with_lightning_and_rain':'\\u26c8',\n  'cloud_with_rain':'\\ud83c\\udf27',\n  'cloud_with_snow':'\\ud83c\\udf28',\n  'clown_face':'\\ud83e\\udd21',\n  'clubs':'\\u2663\\ufe0f',\n  'cocktail':'\\ud83c\\udf78',\n  'coffee':'\\u2615\\ufe0f',\n  'coffin':'\\u26b0\\ufe0f',\n  'cold_sweat':'\\ud83d\\ude30',\n  'comet':'\\u2604\\ufe0f',\n  'computer':'\\ud83d\\udcbb',\n  'computer_mouse':'\\ud83d\\uddb1',\n  'confetti_ball':'\\ud83c\\udf8a',\n  'confounded':'\\ud83d\\ude16',\n  'confused':'\\ud83d\\ude15',\n  'congratulations':'\\u3297\\ufe0f',\n  'construction':'\\ud83d\\udea7',\n  'construction_worker_man':'\\ud83d\\udc77',\n  'construction_worker_woman':'\\ud83d\\udc77‍\\u2640\\ufe0f',\n  'control_knobs':'\\ud83c\\udf9b',\n  'convenience_store':'\\ud83c\\udfea',\n  'cookie':'\\ud83c\\udf6a',\n  'cool':'\\ud83c\\udd92',\n  'policeman':'\\ud83d\\udc6e',\n  'copyright':'\\u00a9\\ufe0f',\n  'corn':'\\ud83c\\udf3d',\n  'couch_and_lamp':'\\ud83d\\udecb',\n  'couple':'\\ud83d\\udc6b',\n  'couple_with_heart_woman_man':'\\ud83d\\udc91',\n  'couple_with_heart_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc68',\n  'couple_with_heart_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc69',\n  'couplekiss_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc68',\n  'couplekiss_man_woman':'\\ud83d\\udc8f',\n  'couplekiss_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc69',\n  'cow':'\\ud83d\\udc2e',\n  'cow2':'\\ud83d\\udc04',\n  'cowboy_hat_face':'\\ud83e\\udd20',\n  'crab':'\\ud83e\\udd80',\n  'crayon':'\\ud83d\\udd8d',\n  'credit_card':'\\ud83d\\udcb3',\n  'crescent_moon':'\\ud83c\\udf19',\n  'cricket':'\\ud83c\\udfcf',\n  'crocodile':'\\ud83d\\udc0a',\n  'croissant':'\\ud83e\\udd50',\n  'crossed_fingers':'\\ud83e\\udd1e',\n  'crossed_flags':'\\ud83c\\udf8c',\n  'crossed_swords':'\\u2694\\ufe0f',\n  'crown':'\\ud83d\\udc51',\n  'cry':'\\ud83d\\ude22',\n  'crying_cat_face':'\\ud83d\\ude3f',\n  'crystal_ball':'\\ud83d\\udd2e',\n  'cucumber':'\\ud83e\\udd52',\n  'cupid':'\\ud83d\\udc98',\n  'curly_loop':'\\u27b0',\n  'currency_exchange':'\\ud83d\\udcb1',\n  'curry':'\\ud83c\\udf5b',\n  'custard':'\\ud83c\\udf6e',\n  'customs':'\\ud83d\\udec3',\n  'cyclone':'\\ud83c\\udf00',\n  'dagger':'\\ud83d\\udde1',\n  'dancer':'\\ud83d\\udc83',\n  'dancing_women':'\\ud83d\\udc6f',\n  'dancing_men':'\\ud83d\\udc6f‍\\u2642\\ufe0f',\n  'dango':'\\ud83c\\udf61',\n  'dark_sunglasses':'\\ud83d\\udd76',\n  'dart':'\\ud83c\\udfaf',\n  'dash':'\\ud83d\\udca8',\n  'date':'\\ud83d\\udcc5',\n  'deciduous_tree':'\\ud83c\\udf33',\n  'deer':'\\ud83e\\udd8c',\n  'department_store':'\\ud83c\\udfec',\n  'derelict_house':'\\ud83c\\udfda',\n  'desert':'\\ud83c\\udfdc',\n  'desert_island':'\\ud83c\\udfdd',\n  'desktop_computer':'\\ud83d\\udda5',\n  'male_detective':'\\ud83d\\udd75\\ufe0f',\n  'diamond_shape_with_a_dot_inside':'\\ud83d\\udca0',\n  'diamonds':'\\u2666\\ufe0f',\n  'disappointed':'\\ud83d\\ude1e',\n  'disappointed_relieved':'\\ud83d\\ude25',\n  'dizzy':'\\ud83d\\udcab',\n  'dizzy_face':'\\ud83d\\ude35',\n  'do_not_litter':'\\ud83d\\udeaf',\n  'dog':'\\ud83d\\udc36',\n  'dog2':'\\ud83d\\udc15',\n  'dollar':'\\ud83d\\udcb5',\n  'dolls':'\\ud83c\\udf8e',\n  'dolphin':'\\ud83d\\udc2c',\n  'door':'\\ud83d\\udeaa',\n  'doughnut':'\\ud83c\\udf69',\n  'dove':'\\ud83d\\udd4a',\n  'dragon':'\\ud83d\\udc09',\n  'dragon_face':'\\ud83d\\udc32',\n  'dress':'\\ud83d\\udc57',\n  'dromedary_camel':'\\ud83d\\udc2a',\n  'drooling_face':'\\ud83e\\udd24',\n  'droplet':'\\ud83d\\udca7',\n  'drum':'\\ud83e\\udd41',\n  'duck':'\\ud83e\\udd86',\n  'dvd':'\\ud83d\\udcc0',\n  'e-mail':'\\ud83d\\udce7',\n  'eagle':'\\ud83e\\udd85',\n  'ear':'\\ud83d\\udc42',\n  'ear_of_rice':'\\ud83c\\udf3e',\n  'earth_africa':'\\ud83c\\udf0d',\n  'earth_americas':'\\ud83c\\udf0e',\n  'earth_asia':'\\ud83c\\udf0f',\n  'egg':'\\ud83e\\udd5a',\n  'eggplant':'\\ud83c\\udf46',\n  'eight_pointed_black_star':'\\u2734\\ufe0f',\n  'eight_spoked_asterisk':'\\u2733\\ufe0f',\n  'electric_plug':'\\ud83d\\udd0c',\n  'elephant':'\\ud83d\\udc18',\n  'email':'\\u2709\\ufe0f',\n  'end':'\\ud83d\\udd1a',\n  'envelope_with_arrow':'\\ud83d\\udce9',\n  'euro':'\\ud83d\\udcb6',\n  'european_castle':'\\ud83c\\udff0',\n  'european_post_office':'\\ud83c\\udfe4',\n  'evergreen_tree':'\\ud83c\\udf32',\n  'exclamation':'\\u2757\\ufe0f',\n  'expressionless':'\\ud83d\\ude11',\n  'eye':'\\ud83d\\udc41',\n  'eye_speech_bubble':'\\ud83d\\udc41‍\\ud83d\\udde8',\n  'eyeglasses':'\\ud83d\\udc53',\n  'eyes':'\\ud83d\\udc40',\n  'face_with_head_bandage':'\\ud83e\\udd15',\n  'face_with_thermometer':'\\ud83e\\udd12',\n  'fist_oncoming':'\\ud83d\\udc4a',\n  'factory':'\\ud83c\\udfed',\n  'fallen_leaf':'\\ud83c\\udf42',\n  'family_man_woman_boy':'\\ud83d\\udc6a',\n  'family_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_woman_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_woman_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_man_woman_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_woman_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'fast_forward':'\\u23e9',\n  'fax':'\\ud83d\\udce0',\n  'fearful':'\\ud83d\\ude28',\n  'feet':'\\ud83d\\udc3e',\n  'female_detective':'\\ud83d\\udd75\\ufe0f‍\\u2640\\ufe0f',\n  'ferris_wheel':'\\ud83c\\udfa1',\n  'ferry':'\\u26f4',\n  'field_hockey':'\\ud83c\\udfd1',\n  'file_cabinet':'\\ud83d\\uddc4',\n  'file_folder':'\\ud83d\\udcc1',\n  'film_projector':'\\ud83d\\udcfd',\n  'film_strip':'\\ud83c\\udf9e',\n  'fire':'\\ud83d\\udd25',\n  'fire_engine':'\\ud83d\\ude92',\n  'fireworks':'\\ud83c\\udf86',\n  'first_quarter_moon':'\\ud83c\\udf13',\n  'first_quarter_moon_with_face':'\\ud83c\\udf1b',\n  'fish':'\\ud83d\\udc1f',\n  'fish_cake':'\\ud83c\\udf65',\n  'fishing_pole_and_fish':'\\ud83c\\udfa3',\n  'fist_raised':'\\u270a',\n  'fist_left':'\\ud83e\\udd1b',\n  'fist_right':'\\ud83e\\udd1c',\n  'flags':'\\ud83c\\udf8f',\n  'flashlight':'\\ud83d\\udd26',\n  'fleur_de_lis':'\\u269c\\ufe0f',\n  'flight_arrival':'\\ud83d\\udeec',\n  'flight_departure':'\\ud83d\\udeeb',\n  'floppy_disk':'\\ud83d\\udcbe',\n  'flower_playing_cards':'\\ud83c\\udfb4',\n  'flushed':'\\ud83d\\ude33',\n  'fog':'\\ud83c\\udf2b',\n  'foggy':'\\ud83c\\udf01',\n  'football':'\\ud83c\\udfc8',\n  'footprints':'\\ud83d\\udc63',\n  'fork_and_knife':'\\ud83c\\udf74',\n  'fountain':'\\u26f2\\ufe0f',\n  'fountain_pen':'\\ud83d\\udd8b',\n  'four_leaf_clover':'\\ud83c\\udf40',\n  'fox_face':'\\ud83e\\udd8a',\n  'framed_picture':'\\ud83d\\uddbc',\n  'free':'\\ud83c\\udd93',\n  'fried_egg':'\\ud83c\\udf73',\n  'fried_shrimp':'\\ud83c\\udf64',\n  'fries':'\\ud83c\\udf5f',\n  'frog':'\\ud83d\\udc38',\n  'frowning':'\\ud83d\\ude26',\n  'frowning_face':'\\u2639\\ufe0f',\n  'frowning_man':'\\ud83d\\ude4d‍\\u2642\\ufe0f',\n  'frowning_woman':'\\ud83d\\ude4d',\n  'middle_finger':'\\ud83d\\udd95',\n  'fuelpump':'\\u26fd\\ufe0f',\n  'full_moon':'\\ud83c\\udf15',\n  'full_moon_with_face':'\\ud83c\\udf1d',\n  'funeral_urn':'\\u26b1\\ufe0f',\n  'game_die':'\\ud83c\\udfb2',\n  'gear':'\\u2699\\ufe0f',\n  'gem':'\\ud83d\\udc8e',\n  'gemini':'\\u264a\\ufe0f',\n  'ghost':'\\ud83d\\udc7b',\n  'gift':'\\ud83c\\udf81',\n  'gift_heart':'\\ud83d\\udc9d',\n  'girl':'\\ud83d\\udc67',\n  'globe_with_meridians':'\\ud83c\\udf10',\n  'goal_net':'\\ud83e\\udd45',\n  'goat':'\\ud83d\\udc10',\n  'golf':'\\u26f3\\ufe0f',\n  'golfing_man':'\\ud83c\\udfcc\\ufe0f',\n  'golfing_woman':'\\ud83c\\udfcc\\ufe0f‍\\u2640\\ufe0f',\n  'gorilla':'\\ud83e\\udd8d',\n  'grapes':'\\ud83c\\udf47',\n  'green_apple':'\\ud83c\\udf4f',\n  'green_book':'\\ud83d\\udcd7',\n  'green_heart':'\\ud83d\\udc9a',\n  'green_salad':'\\ud83e\\udd57',\n  'grey_exclamation':'\\u2755',\n  'grey_question':'\\u2754',\n  'grimacing':'\\ud83d\\ude2c',\n  'grin':'\\ud83d\\ude01',\n  'grinning':'\\ud83d\\ude00',\n  'guardsman':'\\ud83d\\udc82',\n  'guardswoman':'\\ud83d\\udc82‍\\u2640\\ufe0f',\n  'guitar':'\\ud83c\\udfb8',\n  'gun':'\\ud83d\\udd2b',\n  'haircut_woman':'\\ud83d\\udc87',\n  'haircut_man':'\\ud83d\\udc87‍\\u2642\\ufe0f',\n  'hamburger':'\\ud83c\\udf54',\n  'hammer':'\\ud83d\\udd28',\n  'hammer_and_pick':'\\u2692',\n  'hammer_and_wrench':'\\ud83d\\udee0',\n  'hamster':'\\ud83d\\udc39',\n  'hand':'\\u270b',\n  'handbag':'\\ud83d\\udc5c',\n  'handshake':'\\ud83e\\udd1d',\n  'hankey':'\\ud83d\\udca9',\n  'hatched_chick':'\\ud83d\\udc25',\n  'hatching_chick':'\\ud83d\\udc23',\n  'headphones':'\\ud83c\\udfa7',\n  'hear_no_evil':'\\ud83d\\ude49',\n  'heart':'\\u2764\\ufe0f',\n  'heart_decoration':'\\ud83d\\udc9f',\n  'heart_eyes':'\\ud83d\\ude0d',\n  'heart_eyes_cat':'\\ud83d\\ude3b',\n  'heartbeat':'\\ud83d\\udc93',\n  'heartpulse':'\\ud83d\\udc97',\n  'hearts':'\\u2665\\ufe0f',\n  'heavy_check_mark':'\\u2714\\ufe0f',\n  'heavy_division_sign':'\\u2797',\n  'heavy_dollar_sign':'\\ud83d\\udcb2',\n  'heavy_heart_exclamation':'\\u2763\\ufe0f',\n  'heavy_minus_sign':'\\u2796',\n  'heavy_multiplication_x':'\\u2716\\ufe0f',\n  'heavy_plus_sign':'\\u2795',\n  'helicopter':'\\ud83d\\ude81',\n  'herb':'\\ud83c\\udf3f',\n  'hibiscus':'\\ud83c\\udf3a',\n  'high_brightness':'\\ud83d\\udd06',\n  'high_heel':'\\ud83d\\udc60',\n  'hocho':'\\ud83d\\udd2a',\n  'hole':'\\ud83d\\udd73',\n  'honey_pot':'\\ud83c\\udf6f',\n  'horse':'\\ud83d\\udc34',\n  'horse_racing':'\\ud83c\\udfc7',\n  'hospital':'\\ud83c\\udfe5',\n  'hot_pepper':'\\ud83c\\udf36',\n  'hotdog':'\\ud83c\\udf2d',\n  'hotel':'\\ud83c\\udfe8',\n  'hotsprings':'\\u2668\\ufe0f',\n  'hourglass':'\\u231b\\ufe0f',\n  'hourglass_flowing_sand':'\\u23f3',\n  'house':'\\ud83c\\udfe0',\n  'house_with_garden':'\\ud83c\\udfe1',\n  'houses':'\\ud83c\\udfd8',\n  'hugs':'\\ud83e\\udd17',\n  'hushed':'\\ud83d\\ude2f',\n  'ice_cream':'\\ud83c\\udf68',\n  'ice_hockey':'\\ud83c\\udfd2',\n  'ice_skate':'\\u26f8',\n  'icecream':'\\ud83c\\udf66',\n  'id':'\\ud83c\\udd94',\n  'ideograph_advantage':'\\ud83c\\ude50',\n  'imp':'\\ud83d\\udc7f',\n  'inbox_tray':'\\ud83d\\udce5',\n  'incoming_envelope':'\\ud83d\\udce8',\n  'tipping_hand_woman':'\\ud83d\\udc81',\n  'information_source':'\\u2139\\ufe0f',\n  'innocent':'\\ud83d\\ude07',\n  'interrobang':'\\u2049\\ufe0f',\n  'iphone':'\\ud83d\\udcf1',\n  'izakaya_lantern':'\\ud83c\\udfee',\n  'jack_o_lantern':'\\ud83c\\udf83',\n  'japan':'\\ud83d\\uddfe',\n  'japanese_castle':'\\ud83c\\udfef',\n  'japanese_goblin':'\\ud83d\\udc7a',\n  'japanese_ogre':'\\ud83d\\udc79',\n  'jeans':'\\ud83d\\udc56',\n  'joy':'\\ud83d\\ude02',\n  'joy_cat':'\\ud83d\\ude39',\n  'joystick':'\\ud83d\\udd79',\n  'kaaba':'\\ud83d\\udd4b',\n  'key':'\\ud83d\\udd11',\n  'keyboard':'\\u2328\\ufe0f',\n  'keycap_ten':'\\ud83d\\udd1f',\n  'kick_scooter':'\\ud83d\\udef4',\n  'kimono':'\\ud83d\\udc58',\n  'kiss':'\\ud83d\\udc8b',\n  'kissing':'\\ud83d\\ude17',\n  'kissing_cat':'\\ud83d\\ude3d',\n  'kissing_closed_eyes':'\\ud83d\\ude1a',\n  'kissing_heart':'\\ud83d\\ude18',\n  'kissing_smiling_eyes':'\\ud83d\\ude19',\n  'kiwi_fruit':'\\ud83e\\udd5d',\n  'koala':'\\ud83d\\udc28',\n  'koko':'\\ud83c\\ude01',\n  'label':'\\ud83c\\udff7',\n  'large_blue_circle':'\\ud83d\\udd35',\n  'large_blue_diamond':'\\ud83d\\udd37',\n  'large_orange_diamond':'\\ud83d\\udd36',\n  'last_quarter_moon':'\\ud83c\\udf17',\n  'last_quarter_moon_with_face':'\\ud83c\\udf1c',\n  'latin_cross':'\\u271d\\ufe0f',\n  'laughing':'\\ud83d\\ude06',\n  'leaves':'\\ud83c\\udf43',\n  'ledger':'\\ud83d\\udcd2',\n  'left_luggage':'\\ud83d\\udec5',\n  'left_right_arrow':'\\u2194\\ufe0f',\n  'leftwards_arrow_with_hook':'\\u21a9\\ufe0f',\n  'lemon':'\\ud83c\\udf4b',\n  'leo':'\\u264c\\ufe0f',\n  'leopard':'\\ud83d\\udc06',\n  'level_slider':'\\ud83c\\udf9a',\n  'libra':'\\u264e\\ufe0f',\n  'light_rail':'\\ud83d\\ude88',\n  'link':'\\ud83d\\udd17',\n  'lion':'\\ud83e\\udd81',\n  'lips':'\\ud83d\\udc44',\n  'lipstick':'\\ud83d\\udc84',\n  'lizard':'\\ud83e\\udd8e',\n  'lock':'\\ud83d\\udd12',\n  'lock_with_ink_pen':'\\ud83d\\udd0f',\n  'lollipop':'\\ud83c\\udf6d',\n  'loop':'\\u27bf',\n  'loud_sound':'\\ud83d\\udd0a',\n  'loudspeaker':'\\ud83d\\udce2',\n  'love_hotel':'\\ud83c\\udfe9',\n  'love_letter':'\\ud83d\\udc8c',\n  'low_brightness':'\\ud83d\\udd05',\n  'lying_face':'\\ud83e\\udd25',\n  'm':'\\u24c2\\ufe0f',\n  'mag':'\\ud83d\\udd0d',\n  'mag_right':'\\ud83d\\udd0e',\n  'mahjong':'\\ud83c\\udc04\\ufe0f',\n  'mailbox':'\\ud83d\\udceb',\n  'mailbox_closed':'\\ud83d\\udcea',\n  'mailbox_with_mail':'\\ud83d\\udcec',\n  'mailbox_with_no_mail':'\\ud83d\\udced',\n  'man':'\\ud83d\\udc68',\n  'man_artist':'\\ud83d\\udc68‍\\ud83c\\udfa8',\n  'man_astronaut':'\\ud83d\\udc68‍\\ud83d\\ude80',\n  'man_cartwheeling':'\\ud83e\\udd38‍\\u2642\\ufe0f',\n  'man_cook':'\\ud83d\\udc68‍\\ud83c\\udf73',\n  'man_dancing':'\\ud83d\\udd7a',\n  'man_facepalming':'\\ud83e\\udd26‍\\u2642\\ufe0f',\n  'man_factory_worker':'\\ud83d\\udc68‍\\ud83c\\udfed',\n  'man_farmer':'\\ud83d\\udc68‍\\ud83c\\udf3e',\n  'man_firefighter':'\\ud83d\\udc68‍\\ud83d\\ude92',\n  'man_health_worker':'\\ud83d\\udc68‍\\u2695\\ufe0f',\n  'man_in_tuxedo':'\\ud83e\\udd35',\n  'man_judge':'\\ud83d\\udc68‍\\u2696\\ufe0f',\n  'man_juggling':'\\ud83e\\udd39‍\\u2642\\ufe0f',\n  'man_mechanic':'\\ud83d\\udc68‍\\ud83d\\udd27',\n  'man_office_worker':'\\ud83d\\udc68‍\\ud83d\\udcbc',\n  'man_pilot':'\\ud83d\\udc68‍\\u2708\\ufe0f',\n  'man_playing_handball':'\\ud83e\\udd3e‍\\u2642\\ufe0f',\n  'man_playing_water_polo':'\\ud83e\\udd3d‍\\u2642\\ufe0f',\n  'man_scientist':'\\ud83d\\udc68‍\\ud83d\\udd2c',\n  'man_shrugging':'\\ud83e\\udd37‍\\u2642\\ufe0f',\n  'man_singer':'\\ud83d\\udc68‍\\ud83c\\udfa4',\n  'man_student':'\\ud83d\\udc68‍\\ud83c\\udf93',\n  'man_teacher':'\\ud83d\\udc68‍\\ud83c\\udfeb',\n  'man_technologist':'\\ud83d\\udc68‍\\ud83d\\udcbb',\n  'man_with_gua_pi_mao':'\\ud83d\\udc72',\n  'man_with_turban':'\\ud83d\\udc73',\n  'tangerine':'\\ud83c\\udf4a',\n  'mans_shoe':'\\ud83d\\udc5e',\n  'mantelpiece_clock':'\\ud83d\\udd70',\n  'maple_leaf':'\\ud83c\\udf41',\n  'martial_arts_uniform':'\\ud83e\\udd4b',\n  'mask':'\\ud83d\\ude37',\n  'massage_woman':'\\ud83d\\udc86',\n  'massage_man':'\\ud83d\\udc86‍\\u2642\\ufe0f',\n  'meat_on_bone':'\\ud83c\\udf56',\n  'medal_military':'\\ud83c\\udf96',\n  'medal_sports':'\\ud83c\\udfc5',\n  'mega':'\\ud83d\\udce3',\n  'melon':'\\ud83c\\udf48',\n  'memo':'\\ud83d\\udcdd',\n  'men_wrestling':'\\ud83e\\udd3c‍\\u2642\\ufe0f',\n  'menorah':'\\ud83d\\udd4e',\n  'mens':'\\ud83d\\udeb9',\n  'metal':'\\ud83e\\udd18',\n  'metro':'\\ud83d\\ude87',\n  'microphone':'\\ud83c\\udfa4',\n  'microscope':'\\ud83d\\udd2c',\n  'milk_glass':'\\ud83e\\udd5b',\n  'milky_way':'\\ud83c\\udf0c',\n  'minibus':'\\ud83d\\ude90',\n  'minidisc':'\\ud83d\\udcbd',\n  'mobile_phone_off':'\\ud83d\\udcf4',\n  'money_mouth_face':'\\ud83e\\udd11',\n  'money_with_wings':'\\ud83d\\udcb8',\n  'moneybag':'\\ud83d\\udcb0',\n  'monkey':'\\ud83d\\udc12',\n  'monkey_face':'\\ud83d\\udc35',\n  'monorail':'\\ud83d\\ude9d',\n  'moon':'\\ud83c\\udf14',\n  'mortar_board':'\\ud83c\\udf93',\n  'mosque':'\\ud83d\\udd4c',\n  'motor_boat':'\\ud83d\\udee5',\n  'motor_scooter':'\\ud83d\\udef5',\n  'motorcycle':'\\ud83c\\udfcd',\n  'motorway':'\\ud83d\\udee3',\n  'mount_fuji':'\\ud83d\\uddfb',\n  'mountain':'\\u26f0',\n  'mountain_biking_man':'\\ud83d\\udeb5',\n  'mountain_biking_woman':'\\ud83d\\udeb5‍\\u2640\\ufe0f',\n  'mountain_cableway':'\\ud83d\\udea0',\n  'mountain_railway':'\\ud83d\\ude9e',\n  'mountain_snow':'\\ud83c\\udfd4',\n  'mouse':'\\ud83d\\udc2d',\n  'mouse2':'\\ud83d\\udc01',\n  'movie_camera':'\\ud83c\\udfa5',\n  'moyai':'\\ud83d\\uddff',\n  'mrs_claus':'\\ud83e\\udd36',\n  'muscle':'\\ud83d\\udcaa',\n  'mushroom':'\\ud83c\\udf44',\n  'musical_keyboard':'\\ud83c\\udfb9',\n  'musical_note':'\\ud83c\\udfb5',\n  'musical_score':'\\ud83c\\udfbc',\n  'mute':'\\ud83d\\udd07',\n  'nail_care':'\\ud83d\\udc85',\n  'name_badge':'\\ud83d\\udcdb',\n  'national_park':'\\ud83c\\udfde',\n  'nauseated_face':'\\ud83e\\udd22',\n  'necktie':'\\ud83d\\udc54',\n  'negative_squared_cross_mark':'\\u274e',\n  'nerd_face':'\\ud83e\\udd13',\n  'neutral_face':'\\ud83d\\ude10',\n  'new':'\\ud83c\\udd95',\n  'new_moon':'\\ud83c\\udf11',\n  'new_moon_with_face':'\\ud83c\\udf1a',\n  'newspaper':'\\ud83d\\udcf0',\n  'newspaper_roll':'\\ud83d\\uddde',\n  'next_track_button':'\\u23ed',\n  'ng':'\\ud83c\\udd96',\n  'no_good_man':'\\ud83d\\ude45‍\\u2642\\ufe0f',\n  'no_good_woman':'\\ud83d\\ude45',\n  'night_with_stars':'\\ud83c\\udf03',\n  'no_bell':'\\ud83d\\udd15',\n  'no_bicycles':'\\ud83d\\udeb3',\n  'no_entry':'\\u26d4\\ufe0f',\n  'no_entry_sign':'\\ud83d\\udeab',\n  'no_mobile_phones':'\\ud83d\\udcf5',\n  'no_mouth':'\\ud83d\\ude36',\n  'no_pedestrians':'\\ud83d\\udeb7',\n  'no_smoking':'\\ud83d\\udead',\n  'non-potable_water':'\\ud83d\\udeb1',\n  'nose':'\\ud83d\\udc43',\n  'notebook':'\\ud83d\\udcd3',\n  'notebook_with_decorative_cover':'\\ud83d\\udcd4',\n  'notes':'\\ud83c\\udfb6',\n  'nut_and_bolt':'\\ud83d\\udd29',\n  'o':'\\u2b55\\ufe0f',\n  'o2':'\\ud83c\\udd7e\\ufe0f',\n  'ocean':'\\ud83c\\udf0a',\n  'octopus':'\\ud83d\\udc19',\n  'oden':'\\ud83c\\udf62',\n  'office':'\\ud83c\\udfe2',\n  'oil_drum':'\\ud83d\\udee2',\n  'ok':'\\ud83c\\udd97',\n  'ok_hand':'\\ud83d\\udc4c',\n  'ok_man':'\\ud83d\\ude46‍\\u2642\\ufe0f',\n  'ok_woman':'\\ud83d\\ude46',\n  'old_key':'\\ud83d\\udddd',\n  'older_man':'\\ud83d\\udc74',\n  'older_woman':'\\ud83d\\udc75',\n  'om':'\\ud83d\\udd49',\n  'on':'\\ud83d\\udd1b',\n  'oncoming_automobile':'\\ud83d\\ude98',\n  'oncoming_bus':'\\ud83d\\ude8d',\n  'oncoming_police_car':'\\ud83d\\ude94',\n  'oncoming_taxi':'\\ud83d\\ude96',\n  'open_file_folder':'\\ud83d\\udcc2',\n  'open_hands':'\\ud83d\\udc50',\n  'open_mouth':'\\ud83d\\ude2e',\n  'open_umbrella':'\\u2602\\ufe0f',\n  'ophiuchus':'\\u26ce',\n  'orange_book':'\\ud83d\\udcd9',\n  'orthodox_cross':'\\u2626\\ufe0f',\n  'outbox_tray':'\\ud83d\\udce4',\n  'owl':'\\ud83e\\udd89',\n  'ox':'\\ud83d\\udc02',\n  'package':'\\ud83d\\udce6',\n  'page_facing_up':'\\ud83d\\udcc4',\n  'page_with_curl':'\\ud83d\\udcc3',\n  'pager':'\\ud83d\\udcdf',\n  'paintbrush':'\\ud83d\\udd8c',\n  'palm_tree':'\\ud83c\\udf34',\n  'pancakes':'\\ud83e\\udd5e',\n  'panda_face':'\\ud83d\\udc3c',\n  'paperclip':'\\ud83d\\udcce',\n  'paperclips':'\\ud83d\\udd87',\n  'parasol_on_ground':'\\u26f1',\n  'parking':'\\ud83c\\udd7f\\ufe0f',\n  'part_alternation_mark':'\\u303d\\ufe0f',\n  'partly_sunny':'\\u26c5\\ufe0f',\n  'passenger_ship':'\\ud83d\\udef3',\n  'passport_control':'\\ud83d\\udec2',\n  'pause_button':'\\u23f8',\n  'peace_symbol':'\\u262e\\ufe0f',\n  'peach':'\\ud83c\\udf51',\n  'peanuts':'\\ud83e\\udd5c',\n  'pear':'\\ud83c\\udf50',\n  'pen':'\\ud83d\\udd8a',\n  'pencil2':'\\u270f\\ufe0f',\n  'penguin':'\\ud83d\\udc27',\n  'pensive':'\\ud83d\\ude14',\n  'performing_arts':'\\ud83c\\udfad',\n  'persevere':'\\ud83d\\ude23',\n  'person_fencing':'\\ud83e\\udd3a',\n  'pouting_woman':'\\ud83d\\ude4e',\n  'phone':'\\u260e\\ufe0f',\n  'pick':'\\u26cf',\n  'pig':'\\ud83d\\udc37',\n  'pig2':'\\ud83d\\udc16',\n  'pig_nose':'\\ud83d\\udc3d',\n  'pill':'\\ud83d\\udc8a',\n  'pineapple':'\\ud83c\\udf4d',\n  'ping_pong':'\\ud83c\\udfd3',\n  'pisces':'\\u2653\\ufe0f',\n  'pizza':'\\ud83c\\udf55',\n  'place_of_worship':'\\ud83d\\uded0',\n  'plate_with_cutlery':'\\ud83c\\udf7d',\n  'play_or_pause_button':'\\u23ef',\n  'point_down':'\\ud83d\\udc47',\n  'point_left':'\\ud83d\\udc48',\n  'point_right':'\\ud83d\\udc49',\n  'point_up':'\\u261d\\ufe0f',\n  'point_up_2':'\\ud83d\\udc46',\n  'police_car':'\\ud83d\\ude93',\n  'policewoman':'\\ud83d\\udc6e‍\\u2640\\ufe0f',\n  'poodle':'\\ud83d\\udc29',\n  'popcorn':'\\ud83c\\udf7f',\n  'post_office':'\\ud83c\\udfe3',\n  'postal_horn':'\\ud83d\\udcef',\n  'postbox':'\\ud83d\\udcee',\n  'potable_water':'\\ud83d\\udeb0',\n  'potato':'\\ud83e\\udd54',\n  'pouch':'\\ud83d\\udc5d',\n  'poultry_leg':'\\ud83c\\udf57',\n  'pound':'\\ud83d\\udcb7',\n  'rage':'\\ud83d\\ude21',\n  'pouting_cat':'\\ud83d\\ude3e',\n  'pouting_man':'\\ud83d\\ude4e‍\\u2642\\ufe0f',\n  'pray':'\\ud83d\\ude4f',\n  'prayer_beads':'\\ud83d\\udcff',\n  'pregnant_woman':'\\ud83e\\udd30',\n  'previous_track_button':'\\u23ee',\n  'prince':'\\ud83e\\udd34',\n  'princess':'\\ud83d\\udc78',\n  'printer':'\\ud83d\\udda8',\n  'purple_heart':'\\ud83d\\udc9c',\n  'purse':'\\ud83d\\udc5b',\n  'pushpin':'\\ud83d\\udccc',\n  'put_litter_in_its_place':'\\ud83d\\udeae',\n  'question':'\\u2753',\n  'rabbit':'\\ud83d\\udc30',\n  'rabbit2':'\\ud83d\\udc07',\n  'racehorse':'\\ud83d\\udc0e',\n  'racing_car':'\\ud83c\\udfce',\n  'radio':'\\ud83d\\udcfb',\n  'radio_button':'\\ud83d\\udd18',\n  'radioactive':'\\u2622\\ufe0f',\n  'railway_car':'\\ud83d\\ude83',\n  'railway_track':'\\ud83d\\udee4',\n  'rainbow':'\\ud83c\\udf08',\n  'rainbow_flag':'\\ud83c\\udff3\\ufe0f‍\\ud83c\\udf08',\n  'raised_back_of_hand':'\\ud83e\\udd1a',\n  'raised_hand_with_fingers_splayed':'\\ud83d\\udd90',\n  'raised_hands':'\\ud83d\\ude4c',\n  'raising_hand_woman':'\\ud83d\\ude4b',\n  'raising_hand_man':'\\ud83d\\ude4b‍\\u2642\\ufe0f',\n  'ram':'\\ud83d\\udc0f',\n  'ramen':'\\ud83c\\udf5c',\n  'rat':'\\ud83d\\udc00',\n  'record_button':'\\u23fa',\n  'recycle':'\\u267b\\ufe0f',\n  'red_circle':'\\ud83d\\udd34',\n  'registered':'\\u00ae\\ufe0f',\n  'relaxed':'\\u263a\\ufe0f',\n  'relieved':'\\ud83d\\ude0c',\n  'reminder_ribbon':'\\ud83c\\udf97',\n  'repeat':'\\ud83d\\udd01',\n  'repeat_one':'\\ud83d\\udd02',\n  'rescue_worker_helmet':'\\u26d1',\n  'restroom':'\\ud83d\\udebb',\n  'revolving_hearts':'\\ud83d\\udc9e',\n  'rewind':'\\u23ea',\n  'rhinoceros':'\\ud83e\\udd8f',\n  'ribbon':'\\ud83c\\udf80',\n  'rice':'\\ud83c\\udf5a',\n  'rice_ball':'\\ud83c\\udf59',\n  'rice_cracker':'\\ud83c\\udf58',\n  'rice_scene':'\\ud83c\\udf91',\n  'right_anger_bubble':'\\ud83d\\uddef',\n  'ring':'\\ud83d\\udc8d',\n  'robot':'\\ud83e\\udd16',\n  'rocket':'\\ud83d\\ude80',\n  'rofl':'\\ud83e\\udd23',\n  'roll_eyes':'\\ud83d\\ude44',\n  'roller_coaster':'\\ud83c\\udfa2',\n  'rooster':'\\ud83d\\udc13',\n  'rose':'\\ud83c\\udf39',\n  'rosette':'\\ud83c\\udff5',\n  'rotating_light':'\\ud83d\\udea8',\n  'round_pushpin':'\\ud83d\\udccd',\n  'rowing_man':'\\ud83d\\udea3',\n  'rowing_woman':'\\ud83d\\udea3‍\\u2640\\ufe0f',\n  'rugby_football':'\\ud83c\\udfc9',\n  'running_man':'\\ud83c\\udfc3',\n  'running_shirt_with_sash':'\\ud83c\\udfbd',\n  'running_woman':'\\ud83c\\udfc3‍\\u2640\\ufe0f',\n  'sa':'\\ud83c\\ude02\\ufe0f',\n  'sagittarius':'\\u2650\\ufe0f',\n  'sake':'\\ud83c\\udf76',\n  'sandal':'\\ud83d\\udc61',\n  'santa':'\\ud83c\\udf85',\n  'satellite':'\\ud83d\\udce1',\n  'saxophone':'\\ud83c\\udfb7',\n  'school':'\\ud83c\\udfeb',\n  'school_satchel':'\\ud83c\\udf92',\n  'scissors':'\\u2702\\ufe0f',\n  'scorpion':'\\ud83e\\udd82',\n  'scorpius':'\\u264f\\ufe0f',\n  'scream':'\\ud83d\\ude31',\n  'scream_cat':'\\ud83d\\ude40',\n  'scroll':'\\ud83d\\udcdc',\n  'seat':'\\ud83d\\udcba',\n  'secret':'\\u3299\\ufe0f',\n  'see_no_evil':'\\ud83d\\ude48',\n  'seedling':'\\ud83c\\udf31',\n  'selfie':'\\ud83e\\udd33',\n  'shallow_pan_of_food':'\\ud83e\\udd58',\n  'shamrock':'\\u2618\\ufe0f',\n  'shark':'\\ud83e\\udd88',\n  'shaved_ice':'\\ud83c\\udf67',\n  'sheep':'\\ud83d\\udc11',\n  'shell':'\\ud83d\\udc1a',\n  'shield':'\\ud83d\\udee1',\n  'shinto_shrine':'\\u26e9',\n  'ship':'\\ud83d\\udea2',\n  'shirt':'\\ud83d\\udc55',\n  'shopping':'\\ud83d\\udecd',\n  'shopping_cart':'\\ud83d\\uded2',\n  'shower':'\\ud83d\\udebf',\n  'shrimp':'\\ud83e\\udd90',\n  'signal_strength':'\\ud83d\\udcf6',\n  'six_pointed_star':'\\ud83d\\udd2f',\n  'ski':'\\ud83c\\udfbf',\n  'skier':'\\u26f7',\n  'skull':'\\ud83d\\udc80',\n  'skull_and_crossbones':'\\u2620\\ufe0f',\n  'sleeping':'\\ud83d\\ude34',\n  'sleeping_bed':'\\ud83d\\udecc',\n  'sleepy':'\\ud83d\\ude2a',\n  'slightly_frowning_face':'\\ud83d\\ude41',\n  'slightly_smiling_face':'\\ud83d\\ude42',\n  'slot_machine':'\\ud83c\\udfb0',\n  'small_airplane':'\\ud83d\\udee9',\n  'small_blue_diamond':'\\ud83d\\udd39',\n  'small_orange_diamond':'\\ud83d\\udd38',\n  'small_red_triangle':'\\ud83d\\udd3a',\n  'small_red_triangle_down':'\\ud83d\\udd3b',\n  'smile':'\\ud83d\\ude04',\n  'smile_cat':'\\ud83d\\ude38',\n  'smiley':'\\ud83d\\ude03',\n  'smiley_cat':'\\ud83d\\ude3a',\n  'smiling_imp':'\\ud83d\\ude08',\n  'smirk':'\\ud83d\\ude0f',\n  'smirk_cat':'\\ud83d\\ude3c',\n  'smoking':'\\ud83d\\udeac',\n  'snail':'\\ud83d\\udc0c',\n  'snake':'\\ud83d\\udc0d',\n  'sneezing_face':'\\ud83e\\udd27',\n  'snowboarder':'\\ud83c\\udfc2',\n  'snowflake':'\\u2744\\ufe0f',\n  'snowman':'\\u26c4\\ufe0f',\n  'snowman_with_snow':'\\u2603\\ufe0f',\n  'sob':'\\ud83d\\ude2d',\n  'soccer':'\\u26bd\\ufe0f',\n  'soon':'\\ud83d\\udd1c',\n  'sos':'\\ud83c\\udd98',\n  'sound':'\\ud83d\\udd09',\n  'space_invader':'\\ud83d\\udc7e',\n  'spades':'\\u2660\\ufe0f',\n  'spaghetti':'\\ud83c\\udf5d',\n  'sparkle':'\\u2747\\ufe0f',\n  'sparkler':'\\ud83c\\udf87',\n  'sparkles':'\\u2728',\n  'sparkling_heart':'\\ud83d\\udc96',\n  'speak_no_evil':'\\ud83d\\ude4a',\n  'speaker':'\\ud83d\\udd08',\n  'speaking_head':'\\ud83d\\udde3',\n  'speech_balloon':'\\ud83d\\udcac',\n  'speedboat':'\\ud83d\\udea4',\n  'spider':'\\ud83d\\udd77',\n  'spider_web':'\\ud83d\\udd78',\n  'spiral_calendar':'\\ud83d\\uddd3',\n  'spiral_notepad':'\\ud83d\\uddd2',\n  'spoon':'\\ud83e\\udd44',\n  'squid':'\\ud83e\\udd91',\n  'stadium':'\\ud83c\\udfdf',\n  'star':'\\u2b50\\ufe0f',\n  'star2':'\\ud83c\\udf1f',\n  'star_and_crescent':'\\u262a\\ufe0f',\n  'star_of_david':'\\u2721\\ufe0f',\n  'stars':'\\ud83c\\udf20',\n  'station':'\\ud83d\\ude89',\n  'statue_of_liberty':'\\ud83d\\uddfd',\n  'steam_locomotive':'\\ud83d\\ude82',\n  'stew':'\\ud83c\\udf72',\n  'stop_button':'\\u23f9',\n  'stop_sign':'\\ud83d\\uded1',\n  'stopwatch':'\\u23f1',\n  'straight_ruler':'\\ud83d\\udccf',\n  'strawberry':'\\ud83c\\udf53',\n  'stuck_out_tongue':'\\ud83d\\ude1b',\n  'stuck_out_tongue_closed_eyes':'\\ud83d\\ude1d',\n  'stuck_out_tongue_winking_eye':'\\ud83d\\ude1c',\n  'studio_microphone':'\\ud83c\\udf99',\n  'stuffed_flatbread':'\\ud83e\\udd59',\n  'sun_behind_large_cloud':'\\ud83c\\udf25',\n  'sun_behind_rain_cloud':'\\ud83c\\udf26',\n  'sun_behind_small_cloud':'\\ud83c\\udf24',\n  'sun_with_face':'\\ud83c\\udf1e',\n  'sunflower':'\\ud83c\\udf3b',\n  'sunglasses':'\\ud83d\\ude0e',\n  'sunny':'\\u2600\\ufe0f',\n  'sunrise':'\\ud83c\\udf05',\n  'sunrise_over_mountains':'\\ud83c\\udf04',\n  'surfing_man':'\\ud83c\\udfc4',\n  'surfing_woman':'\\ud83c\\udfc4‍\\u2640\\ufe0f',\n  'sushi':'\\ud83c\\udf63',\n  'suspension_railway':'\\ud83d\\ude9f',\n  'sweat':'\\ud83d\\ude13',\n  'sweat_drops':'\\ud83d\\udca6',\n  'sweat_smile':'\\ud83d\\ude05',\n  'sweet_potato':'\\ud83c\\udf60',\n  'swimming_man':'\\ud83c\\udfca',\n  'swimming_woman':'\\ud83c\\udfca‍\\u2640\\ufe0f',\n  'symbols':'\\ud83d\\udd23',\n  'synagogue':'\\ud83d\\udd4d',\n  'syringe':'\\ud83d\\udc89',\n  'taco':'\\ud83c\\udf2e',\n  'tada':'\\ud83c\\udf89',\n  'tanabata_tree':'\\ud83c\\udf8b',\n  'taurus':'\\u2649\\ufe0f',\n  'taxi':'\\ud83d\\ude95',\n  'tea':'\\ud83c\\udf75',\n  'telephone_receiver':'\\ud83d\\udcde',\n  'telescope':'\\ud83d\\udd2d',\n  'tennis':'\\ud83c\\udfbe',\n  'tent':'\\u26fa\\ufe0f',\n  'thermometer':'\\ud83c\\udf21',\n  'thinking':'\\ud83e\\udd14',\n  'thought_balloon':'\\ud83d\\udcad',\n  'ticket':'\\ud83c\\udfab',\n  'tickets':'\\ud83c\\udf9f',\n  'tiger':'\\ud83d\\udc2f',\n  'tiger2':'\\ud83d\\udc05',\n  'timer_clock':'\\u23f2',\n  'tipping_hand_man':'\\ud83d\\udc81‍\\u2642\\ufe0f',\n  'tired_face':'\\ud83d\\ude2b',\n  'tm':'\\u2122\\ufe0f',\n  'toilet':'\\ud83d\\udebd',\n  'tokyo_tower':'\\ud83d\\uddfc',\n  'tomato':'\\ud83c\\udf45',\n  'tongue':'\\ud83d\\udc45',\n  'top':'\\ud83d\\udd1d',\n  'tophat':'\\ud83c\\udfa9',\n  'tornado':'\\ud83c\\udf2a',\n  'trackball':'\\ud83d\\uddb2',\n  'tractor':'\\ud83d\\ude9c',\n  'traffic_light':'\\ud83d\\udea5',\n  'train':'\\ud83d\\ude8b',\n  'train2':'\\ud83d\\ude86',\n  'tram':'\\ud83d\\ude8a',\n  'triangular_flag_on_post':'\\ud83d\\udea9',\n  'triangular_ruler':'\\ud83d\\udcd0',\n  'trident':'\\ud83d\\udd31',\n  'triumph':'\\ud83d\\ude24',\n  'trolleybus':'\\ud83d\\ude8e',\n  'trophy':'\\ud83c\\udfc6',\n  'tropical_drink':'\\ud83c\\udf79',\n  'tropical_fish':'\\ud83d\\udc20',\n  'truck':'\\ud83d\\ude9a',\n  'trumpet':'\\ud83c\\udfba',\n  'tulip':'\\ud83c\\udf37',\n  'tumbler_glass':'\\ud83e\\udd43',\n  'turkey':'\\ud83e\\udd83',\n  'turtle':'\\ud83d\\udc22',\n  'tv':'\\ud83d\\udcfa',\n  'twisted_rightwards_arrows':'\\ud83d\\udd00',\n  'two_hearts':'\\ud83d\\udc95',\n  'two_men_holding_hands':'\\ud83d\\udc6c',\n  'two_women_holding_hands':'\\ud83d\\udc6d',\n  'u5272':'\\ud83c\\ude39',\n  'u5408':'\\ud83c\\ude34',\n  'u55b6':'\\ud83c\\ude3a',\n  'u6307':'\\ud83c\\ude2f\\ufe0f',\n  'u6708':'\\ud83c\\ude37\\ufe0f',\n  'u6709':'\\ud83c\\ude36',\n  'u6e80':'\\ud83c\\ude35',\n  'u7121':'\\ud83c\\ude1a\\ufe0f',\n  'u7533':'\\ud83c\\ude38',\n  'u7981':'\\ud83c\\ude32',\n  'u7a7a':'\\ud83c\\ude33',\n  'umbrella':'\\u2614\\ufe0f',\n  'unamused':'\\ud83d\\ude12',\n  'underage':'\\ud83d\\udd1e',\n  'unicorn':'\\ud83e\\udd84',\n  'unlock':'\\ud83d\\udd13',\n  'up':'\\ud83c\\udd99',\n  'upside_down_face':'\\ud83d\\ude43',\n  'v':'\\u270c\\ufe0f',\n  'vertical_traffic_light':'\\ud83d\\udea6',\n  'vhs':'\\ud83d\\udcfc',\n  'vibration_mode':'\\ud83d\\udcf3',\n  'video_camera':'\\ud83d\\udcf9',\n  'video_game':'\\ud83c\\udfae',\n  'violin':'\\ud83c\\udfbb',\n  'virgo':'\\u264d\\ufe0f',\n  'volcano':'\\ud83c\\udf0b',\n  'volleyball':'\\ud83c\\udfd0',\n  'vs':'\\ud83c\\udd9a',\n  'vulcan_salute':'\\ud83d\\udd96',\n  'walking_man':'\\ud83d\\udeb6',\n  'walking_woman':'\\ud83d\\udeb6‍\\u2640\\ufe0f',\n  'waning_crescent_moon':'\\ud83c\\udf18',\n  'waning_gibbous_moon':'\\ud83c\\udf16',\n  'warning':'\\u26a0\\ufe0f',\n  'wastebasket':'\\ud83d\\uddd1',\n  'watch':'\\u231a\\ufe0f',\n  'water_buffalo':'\\ud83d\\udc03',\n  'watermelon':'\\ud83c\\udf49',\n  'wave':'\\ud83d\\udc4b',\n  'wavy_dash':'\\u3030\\ufe0f',\n  'waxing_crescent_moon':'\\ud83c\\udf12',\n  'wc':'\\ud83d\\udebe',\n  'weary':'\\ud83d\\ude29',\n  'wedding':'\\ud83d\\udc92',\n  'weight_lifting_man':'\\ud83c\\udfcb\\ufe0f',\n  'weight_lifting_woman':'\\ud83c\\udfcb\\ufe0f‍\\u2640\\ufe0f',\n  'whale':'\\ud83d\\udc33',\n  'whale2':'\\ud83d\\udc0b',\n  'wheel_of_dharma':'\\u2638\\ufe0f',\n  'wheelchair':'\\u267f\\ufe0f',\n  'white_check_mark':'\\u2705',\n  'white_circle':'\\u26aa\\ufe0f',\n  'white_flag':'\\ud83c\\udff3\\ufe0f',\n  'white_flower':'\\ud83d\\udcae',\n  'white_large_square':'\\u2b1c\\ufe0f',\n  'white_medium_small_square':'\\u25fd\\ufe0f',\n  'white_medium_square':'\\u25fb\\ufe0f',\n  'white_small_square':'\\u25ab\\ufe0f',\n  'white_square_button':'\\ud83d\\udd33',\n  'wilted_flower':'\\ud83e\\udd40',\n  'wind_chime':'\\ud83c\\udf90',\n  'wind_face':'\\ud83c\\udf2c',\n  'wine_glass':'\\ud83c\\udf77',\n  'wink':'\\ud83d\\ude09',\n  'wolf':'\\ud83d\\udc3a',\n  'woman':'\\ud83d\\udc69',\n  'woman_artist':'\\ud83d\\udc69‍\\ud83c\\udfa8',\n  'woman_astronaut':'\\ud83d\\udc69‍\\ud83d\\ude80',\n  'woman_cartwheeling':'\\ud83e\\udd38‍\\u2640\\ufe0f',\n  'woman_cook':'\\ud83d\\udc69‍\\ud83c\\udf73',\n  'woman_facepalming':'\\ud83e\\udd26‍\\u2640\\ufe0f',\n  'woman_factory_worker':'\\ud83d\\udc69‍\\ud83c\\udfed',\n  'woman_farmer':'\\ud83d\\udc69‍\\ud83c\\udf3e',\n  'woman_firefighter':'\\ud83d\\udc69‍\\ud83d\\ude92',\n  'woman_health_worker':'\\ud83d\\udc69‍\\u2695\\ufe0f',\n  'woman_judge':'\\ud83d\\udc69‍\\u2696\\ufe0f',\n  'woman_juggling':'\\ud83e\\udd39‍\\u2640\\ufe0f',\n  'woman_mechanic':'\\ud83d\\udc69‍\\ud83d\\udd27',\n  'woman_office_worker':'\\ud83d\\udc69‍\\ud83d\\udcbc',\n  'woman_pilot':'\\ud83d\\udc69‍\\u2708\\ufe0f',\n  'woman_playing_handball':'\\ud83e\\udd3e‍\\u2640\\ufe0f',\n  'woman_playing_water_polo':'\\ud83e\\udd3d‍\\u2640\\ufe0f',\n  'woman_scientist':'\\ud83d\\udc69‍\\ud83d\\udd2c',\n  'woman_shrugging':'\\ud83e\\udd37‍\\u2640\\ufe0f',\n  'woman_singer':'\\ud83d\\udc69‍\\ud83c\\udfa4',\n  'woman_student':'\\ud83d\\udc69‍\\ud83c\\udf93',\n  'woman_teacher':'\\ud83d\\udc69‍\\ud83c\\udfeb',\n  'woman_technologist':'\\ud83d\\udc69‍\\ud83d\\udcbb',\n  'woman_with_turban':'\\ud83d\\udc73‍\\u2640\\ufe0f',\n  'womans_clothes':'\\ud83d\\udc5a',\n  'womans_hat':'\\ud83d\\udc52',\n  'women_wrestling':'\\ud83e\\udd3c‍\\u2640\\ufe0f',\n  'womens':'\\ud83d\\udeba',\n  'world_map':'\\ud83d\\uddfa',\n  'worried':'\\ud83d\\ude1f',\n  'wrench':'\\ud83d\\udd27',\n  'writing_hand':'\\u270d\\ufe0f',\n  'x':'\\u274c',\n  'yellow_heart':'\\ud83d\\udc9b',\n  'yen':'\\ud83d\\udcb4',\n  'yin_yang':'\\u262f\\ufe0f',\n  'yum':'\\ud83d\\ude0b',\n  'zap':'\\u26a1\\ufe0f',\n  'zipper_mouth_face':'\\ud83e\\udd10',\n  'zzz':'\\ud83d\\udca4',\n\n  /* special emojis :P */\n  'octocat':  '\":octocat:\"',\n  'showdown': 'S'\n};\n\r\n/**\n * Created by Estevao on 31-05-2015.\n */\n\n/**\n * Showdown Converter class\n * @class\n * @param {object} [converterOptions]\n * @returns {Converter}\n */\nshowdown.Converter = function (converterOptions) {\n  'use strict';\n\n  var\n      /**\n       * Options used by this converter\n       * @private\n       * @type {{}}\n       */\n      options = {},\n\n      /**\n       * Language extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      langExtensions = [],\n\n      /**\n       * Output modifiers extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      outputModifiers = [],\n\n      /**\n       * Event listeners\n       * @private\n       * @type {{}}\n       */\n      listeners = {},\n\n      /**\n       * The flavor set in this converter\n       */\n      setConvFlavor = setFlavor,\n\n      /**\n       * Metadata of the document\n       * @type {{parsed: {}, raw: string, format: string}}\n       */\n      metadata = {\n        parsed: {},\n        raw: '',\n        format: ''\n      };\n\n  _constructor();\n\n  /**\n   * Converter constructor\n   * @private\n   */\n  function _constructor () {\n    converterOptions = converterOptions || {};\n\n    for (var gOpt in globalOptions) {\n      if (globalOptions.hasOwnProperty(gOpt)) {\n        options[gOpt] = globalOptions[gOpt];\n      }\n    }\n\n    // Merge options\n    if (typeof converterOptions === 'object') {\n      for (var opt in converterOptions) {\n        if (converterOptions.hasOwnProperty(opt)) {\n          options[opt] = converterOptions[opt];\n        }\n      }\n    } else {\n      throw Error('Converter expects the passed parameter to be an object, but ' + typeof converterOptions +\n      ' was passed instead.');\n    }\n\n    if (options.extensions) {\n      showdown.helper.forEach(options.extensions, _parseExtension);\n    }\n  }\n\n  /**\n   * Parse extension\n   * @param {*} ext\n   * @param {string} [name='']\n   * @private\n   */\n  function _parseExtension (ext, name) {\n\n    name = name || null;\n    // If it's a string, the extension was previously loaded\n    if (showdown.helper.isString(ext)) {\n      ext = showdown.helper.stdExtName(ext);\n      name = ext;\n\n      // LEGACY_SUPPORT CODE\n      if (showdown.extensions[ext]) {\n        console.warn('DEPRECATION WARNING: ' + ext + ' is an old extension that uses a deprecated loading method.' +\n          'Please inform the developer that the extension should be updated!');\n        legacyExtensionLoading(showdown.extensions[ext], ext);\n        return;\n        // END LEGACY SUPPORT CODE\n\n      } else if (!showdown.helper.isUndefined(extensions[ext])) {\n        ext = extensions[ext];\n\n      } else {\n        throw Error('Extension \"' + ext + '\" could not be loaded. It was either not found or is not a valid extension.');\n      }\n    }\n\n    if (typeof ext === 'function') {\n      ext = ext();\n    }\n\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n\n    var validExt = validate(ext, name);\n    if (!validExt.valid) {\n      throw Error(validExt.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n      }\n      if (ext[i].hasOwnProperty('listeners')) {\n        for (var ln in ext[i].listeners) {\n          if (ext[i].listeners.hasOwnProperty(ln)) {\n            listen(ln, ext[i].listeners[ln]);\n          }\n        }\n      }\n    }\n\n  }\n\n  /**\n   * LEGACY_SUPPORT\n   * @param {*} ext\n   * @param {string} name\n   */\n  function legacyExtensionLoading (ext, name) {\n    if (typeof ext === 'function') {\n      ext = ext(new showdown.Converter());\n    }\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n    var valid = validate(ext, name);\n\n    if (!valid.valid) {\n      throw Error(valid.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n        default:// should never reach here\n          throw Error('Extension loader error: Type unrecognized!!!');\n      }\n    }\n  }\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   */\n  function listen (name, callback) {\n    if (!showdown.helper.isString(name)) {\n      throw Error('Invalid argument in converter.listen() method: name must be a string, but ' + typeof name + ' given');\n    }\n\n    if (typeof callback !== 'function') {\n      throw Error('Invalid argument in converter.listen() method: callback must be a function, but ' + typeof callback + ' given');\n    }\n\n    if (!listeners.hasOwnProperty(name)) {\n      listeners[name] = [];\n    }\n    listeners[name].push(callback);\n  }\n\n  function rTrimInputText (text) {\n    var rsp = text.match(/^\\s*/)[0].length,\n        rgx = new RegExp('^\\\\s{0,' + rsp + '}', 'gm');\n    return text.replace(rgx, '');\n  }\n\n  /**\n   * Dispatch an event\n   * @private\n   * @param {string} evtName Event name\n   * @param {string} text Text\n   * @param {{}} options Converter Options\n   * @param {{}} globals\n   * @returns {string}\n   */\n  this._dispatch = function dispatch (evtName, text, options, globals) {\n    if (listeners.hasOwnProperty(evtName)) {\n      for (var ei = 0; ei < listeners[evtName].length; ++ei) {\n        var nText = listeners[evtName][ei](evtName, text, this, options, globals);\n        if (nText && typeof nText !== 'undefined') {\n          text = nText;\n        }\n      }\n    }\n    return text;\n  };\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   * @returns {showdown.Converter}\n   */\n  this.listen = function (name, callback) {\n    listen(name, callback);\n    return this;\n  };\n\n  /**\n   * Converts a markdown string into HTML\n   * @param {string} text\n   * @returns {*}\n   */\n  this.makeHtml = function (text) {\n    //check if text is not falsy\n    if (!text) {\n      return text;\n    }\n\n    var globals = {\n      gHtmlBlocks:     [],\n      gHtmlMdBlocks:   [],\n      gHtmlSpans:      [],\n      gUrls:           {},\n      gTitles:         {},\n      gDimensions:     {},\n      gListLevel:      0,\n      hashLinkCounts:  {},\n      langExtensions:  langExtensions,\n      outputModifiers: outputModifiers,\n      converter:       this,\n      ghCodeBlocks:    [],\n      metadata: {\n        parsed: {},\n        raw: '',\n        format: ''\n      }\n    };\n\n    // This lets us use ¨ trema as an escape char to avoid md5 hashes\n    // The choice of character is arbitrary; anything that isn't\n    // magic in Markdown will work.\n    text = text.replace(/¨/g, '¨T');\n\n    // Replace $ with ¨D\n    // RegExp interprets $ as a special character\n    // when it's in a replacement string\n    text = text.replace(/\\$/g, '¨D');\n\n    // Standardize line endings\n    text = text.replace(/\\r\\n/g, '\\n'); // DOS to Unix\n    text = text.replace(/\\r/g, '\\n'); // Mac to Unix\n\n    // Stardardize line spaces\n    text = text.replace(/\\u00A0/g, ' ');\n\n    if (options.smartIndentationFix) {\n      text = rTrimInputText(text);\n    }\n\n    // Make sure text begins and ends with a couple of newlines:\n    text = '\\n\\n' + text + '\\n\\n';\n\n    // detab\n    text = showdown.subParser('detab')(text, options, globals);\n\n    /**\n     * Strip any lines consisting only of spaces and tabs.\n     * This makes subsequent regexs easier to write, because we can\n     * match consecutive blank lines with /\\n+/ instead of something\n     * contorted like /[ \\t]*\\n+/\n     */\n    text = text.replace(/^[ \\t]+$/mg, '');\n\n    //run languageExtensions\n    showdown.helper.forEach(langExtensions, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // run the sub parsers\n    text = showdown.subParser('metadata')(text, options, globals);\n    text = showdown.subParser('hashPreCodeTags')(text, options, globals);\n    text = showdown.subParser('githubCodeBlocks')(text, options, globals);\n    text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n    text = showdown.subParser('hashCodeTags')(text, options, globals);\n    text = showdown.subParser('stripLinkDefinitions')(text, options, globals);\n    text = showdown.subParser('blockGamut')(text, options, globals);\n    text = showdown.subParser('unhashHTMLSpans')(text, options, globals);\n    text = showdown.subParser('unescapeSpecialChars')(text, options, globals);\n\n    // attacklab: Restore dollar signs\n    text = text.replace(/¨D/g, '$$');\n\n    // attacklab: Restore tremas\n    text = text.replace(/¨T/g, '¨');\n\n    // render a complete html document instead of a partial if the option is enabled\n    text = showdown.subParser('completeHTMLDocument')(text, options, globals);\n\n    // Run output modifiers\n    showdown.helper.forEach(outputModifiers, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // update metadata\n    metadata = globals.metadata;\n    return text;\n  };\n\n  /**\n   * Converts an HTML string into a markdown string\n   * @param src\n   * @param [HTMLParser] A WHATWG DOM and HTML parser, such as JSDOM. If none is supplied, window.document will be used.\n   * @returns {string}\n   */\n  this.makeMarkdown = this.makeMd = function (src, HTMLParser) {\n\n    // replace \\r\\n with \\n\n    src = src.replace(/\\r\\n/g, '\\n');\n    src = src.replace(/\\r/g, '\\n'); // old macs\n\n    // due to an edge case, we need to find this: > <\n    // to prevent removing of non silent white spaces\n    // ex: this is sparta\n    src = src.replace(/>[ \\t]+¨NBSP;<');\n\n    if (!HTMLParser) {\n      if (window && window.document) {\n        HTMLParser = window.document;\n      } else {\n        throw new Error('HTMLParser is undefined. If in a webworker or nodejs environment, you need to provide a WHATWG DOM and HTML such as JSDOM');\n      }\n    }\n\n    var doc = HTMLParser.createElement('div');\n    doc.innerHTML = src;\n\n    var globals = {\n      preList: substitutePreCodeTags(doc)\n    };\n\n    // remove all newlines and collapse spaces\n    clean(doc);\n\n    // some stuff, like accidental reference links must now be escaped\n    // TODO\n    // doc.innerHTML = doc.innerHTML.replace(/\\[[\\S\\t ]]/);\n\n    var nodes = doc.childNodes,\n        mdDoc = '';\n\n    for (var i = 0; i < nodes.length; i++) {\n      mdDoc += showdown.subParser('makeMarkdown.node')(nodes[i], globals);\n    }\n\n    function clean (node) {\n      for (var n = 0; n < node.childNodes.length; ++n) {\n        var child = node.childNodes[n];\n        if (child.nodeType === 3) {\n          if (!/\\S/.test(child.nodeValue)) {\n            node.removeChild(child);\n            --n;\n          } else {\n            child.nodeValue = child.nodeValue.split('\\n').join(' ');\n            child.nodeValue = child.nodeValue.replace(/(\\s)+/g, '$1');\n          }\n        } else if (child.nodeType === 1) {\n          clean(child);\n        }\n      }\n    }\n\n    // find all pre tags and replace contents with placeholder\n    // we need this so that we can remove all indentation from html\n    // to ease up parsing\n    function substitutePreCodeTags (doc) {\n\n      var pres = doc.querySelectorAll('pre'),\n          presPH = [];\n\n      for (var i = 0; i < pres.length; ++i) {\n\n        if (pres[i].childElementCount === 1 && pres[i].firstChild.tagName.toLowerCase() === 'code') {\n          var content = pres[i].firstChild.innerHTML.trim(),\n              language = pres[i].firstChild.getAttribute('data-language') || '';\n\n          // if data-language attribute is not defined, then we look for class language-*\n          if (language === '') {\n            var classes = pres[i].firstChild.className.split(' ');\n            for (var c = 0; c < classes.length; ++c) {\n              var matches = classes[c].match(/^language-(.+)$/);\n              if (matches !== null) {\n                language = matches[1];\n                break;\n              }\n            }\n          }\n\n          // unescape html entities in content\n          content = showdown.helper.unescapeHTMLEntities(content);\n\n          presPH.push(content);\n          pres[i].outerHTML = '';\n        } else {\n          presPH.push(pres[i].innerHTML);\n          pres[i].innerHTML = '';\n          pres[i].setAttribute('prenum', i.toString());\n        }\n      }\n      return presPH;\n    }\n\n    return mdDoc;\n  };\n\n  /**\n   * Set an option of this Converter instance\n   * @param {string} key\n   * @param {*} value\n   */\n  this.setOption = function (key, value) {\n    options[key] = value;\n  };\n\n  /**\n   * Get the option of this Converter instance\n   * @param {string} key\n   * @returns {*}\n   */\n  this.getOption = function (key) {\n    return options[key];\n  };\n\n  /**\n   * Get the options of this Converter instance\n   * @returns {{}}\n   */\n  this.getOptions = function () {\n    return options;\n  };\n\n  /**\n   * Add extension to THIS converter\n   * @param {{}} extension\n   * @param {string} [name=null]\n   */\n  this.addExtension = function (extension, name) {\n    name = name || null;\n    _parseExtension(extension, name);\n  };\n\n  /**\n   * Use a global registered extension with THIS converter\n   * @param {string} extensionName Name of the previously registered extension\n   */\n  this.useExtension = function (extensionName) {\n    _parseExtension(extensionName);\n  };\n\n  /**\n   * Set the flavor THIS converter should use\n   * @param {string} name\n   */\n  this.setFlavor = function (name) {\n    if (!flavor.hasOwnProperty(name)) {\n      throw Error(name + ' flavor was not found');\n    }\n    var preset = flavor[name];\n    setConvFlavor = name;\n    for (var option in preset) {\n      if (preset.hasOwnProperty(option)) {\n        options[option] = preset[option];\n      }\n    }\n  };\n\n  /**\n   * Get the currently set flavor of this converter\n   * @returns {string}\n   */\n  this.getFlavor = function () {\n    return setConvFlavor;\n  };\n\n  /**\n   * Remove an extension from THIS converter.\n   * Note: This is a costly operation. It's better to initialize a new converter\n   * and specify the extensions you wish to use\n   * @param {Array} extension\n   */\n  this.removeExtension = function (extension) {\n    if (!showdown.helper.isArray(extension)) {\n      extension = [extension];\n    }\n    for (var a = 0; a < extension.length; ++a) {\n      var ext = extension[a];\n      for (var i = 0; i < langExtensions.length; ++i) {\n        if (langExtensions[i] === ext) {\n          langExtensions[i].splice(i, 1);\n        }\n      }\n      for (var ii = 0; ii < outputModifiers.length; ++i) {\n        if (outputModifiers[ii] === ext) {\n          outputModifiers[ii].splice(i, 1);\n        }\n      }\n    }\n  };\n\n  /**\n   * Get all extension of THIS converter\n   * @returns {{language: Array, output: Array}}\n   */\n  this.getAllExtensions = function () {\n    return {\n      language: langExtensions,\n      output: outputModifiers\n    };\n  };\n\n  /**\n   * Get the metadata of the previously parsed document\n   * @param raw\n   * @returns {string|{}}\n   */\n  this.getMetadata = function (raw) {\n    if (raw) {\n      return metadata.raw;\n    } else {\n      return metadata.parsed;\n    }\n  };\n\n  /**\n   * Get the metadata format of the previously parsed document\n   * @returns {string}\n   */\n  this.getMetadataFormat = function () {\n    return metadata.format;\n  };\n\n  /**\n   * Private: set a single key, value metadata pair\n   * @param {string} key\n   * @param {string} value\n   */\n  this._setMetadataPair = function (key, value) {\n    metadata.parsed[key] = value;\n  };\n\n  /**\n   * Private: set metadata format\n   * @param {string} format\n   */\n  this._setMetadataFormat = function (format) {\n    metadata.format = format;\n  };\n\n  /**\n   * Private: set metadata raw text\n   * @param {string} raw\n   */\n  this._setMetadataRaw = function (raw) {\n    metadata.raw = raw;\n  };\n};\n\r\n/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('anchors', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('anchors.before', text, options, globals);\n\n  var writeAnchorTag = function (wholeMatch, linkText, linkId, url, m5, m6, title) {\n    if (showdown.helper.isUndefined(title)) {\n      title = '';\n    }\n    linkId = linkId.toLowerCase();\n\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n    } else if (!url) {\n      if (!linkId) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = linkText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(globals.gUrls[linkId])) {\n        url = globals.gUrls[linkId];\n        if (!showdown.helper.isUndefined(globals.gTitles[linkId])) {\n          title = globals.gTitles[linkId];\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    //url = showdown.helper.escapeCharacters(url, '*_', false); // replaced line to improve performance\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n\n    var result = '';\n\n    return result;\n  };\n\n  // First, handle reference-style links: [link text] [id]\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)] ?(?:\\n *)?\\[(.*?)]()()()()/g, writeAnchorTag);\n\n  // Next, inline-style links: [link text](url \"optional title\")\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]?<([^>]*)>(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // normal cases\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]??(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // handle reference-style shortcuts: [link text]\n  // These must come last in case you've also got [link test][1]\n  // or [link test](/foo)\n  text = text.replace(/\\[([^\\[\\]]+)]()()()()()/g, writeAnchorTag);\n\n  // Lastly handle GithubMentions if option is enabled\n  if (options.ghMentions) {\n    text = text.replace(/(^|\\s)(\\\\)?(@([a-z\\d]+(?:[a-z\\d.-]+?[a-z\\d]+)*))/gmi, function (wm, st, escape, mentions, username) {\n      if (escape === '\\\\') {\n        return st + mentions;\n      }\n\n      //check if options.ghMentionsLink is a string\n      if (!showdown.helper.isString(options.ghMentionsLink)) {\n        throw new Error('ghMentionsLink option must be a string');\n      }\n      var lnk = options.ghMentionsLink.replace(/\\{u}/g, username),\n          target = '';\n      if (options.openLinksInNewWindow) {\n        target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n      }\n      return st + '' + mentions + '';\n    });\n  }\n\n  text = globals.converter._dispatch('anchors.after', text, options, globals);\n  return text;\n});\n\r\n// url allowed chars [a-z\\d_.~:/?#[]@!$&'()*+,;=-]\n\nvar simpleURLRegex  = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+?\\.[^'\">\\s]+?)()(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    simpleURLRegex2 = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+\\.[^'\">\\s]+?)([.!?,()\\[\\]])?(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    delimUrlRegex   = /()<(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+)()>()/gi,\n    simpleMailRegex = /(^|\\s)(?:mailto:)?([A-Za-z0-9!#$%&'*+-/=?^_`{|}~.]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)(?=$|\\s)/gmi,\n    delimMailRegex  = /<()(?:mailto:)?([-.\\w]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)>/gi,\n\n    replaceLink = function (options) {\n      'use strict';\n      return function (wm, leadingMagicChars, link, m2, m3, trailingPunctuation, trailingMagicChars) {\n        link = link.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n        var lnkTxt = link,\n            append = '',\n            target = '',\n            lmc    = leadingMagicChars || '',\n            tmc    = trailingMagicChars || '';\n        if (/^www\\./i.test(link)) {\n          link = link.replace(/^www\\./i, 'http://www.');\n        }\n        if (options.excludeTrailingPunctuationFromURLs && trailingPunctuation) {\n          append = trailingPunctuation;\n        }\n        if (options.openLinksInNewWindow) {\n          target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n        }\n        return lmc + '' + lnkTxt + '' + append + tmc;\n      };\n    },\n\n    replaceMail = function (options, globals) {\n      'use strict';\n      return function (wholeMatch, b, mail) {\n        var href = 'mailto:';\n        b = b || '';\n        mail = showdown.subParser('unescapeSpecialChars')(mail, options, globals);\n        if (options.encodeEmails) {\n          href = showdown.helper.encodeEmailAddress(href + mail);\n          mail = showdown.helper.encodeEmailAddress(mail);\n        } else {\n          href = href + mail;\n        }\n        return b + '' + mail + '';\n      };\n    };\n\nshowdown.subParser('autoLinks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('autoLinks.before', text, options, globals);\n\n  text = text.replace(delimUrlRegex, replaceLink(options));\n  text = text.replace(delimMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('autoLinks.after', text, options, globals);\n\n  return text;\n});\n\nshowdown.subParser('simplifiedAutoLinks', function (text, options, globals) {\n  'use strict';\n\n  if (!options.simplifiedAutoLink) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.before', text, options, globals);\n\n  if (options.excludeTrailingPunctuationFromURLs) {\n    text = text.replace(simpleURLRegex2, replaceLink(options));\n  } else {\n    text = text.replace(simpleURLRegex, replaceLink(options));\n  }\n  text = text.replace(simpleMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.after', text, options, globals);\n\n  return text;\n});\n\r\n/**\n * These are all the transformations that form block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('blockGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockGamut.before', text, options, globals);\n\n  // we parse blockquotes first so that we can have headings and hrs\n  // inside blockquotes\n  text = showdown.subParser('blockQuotes')(text, options, globals);\n  text = showdown.subParser('headers')(text, options, globals);\n\n  // Do Horizontal Rules:\n  text = showdown.subParser('horizontalRule')(text, options, globals);\n\n  text = showdown.subParser('lists')(text, options, globals);\n  text = showdown.subParser('codeBlocks')(text, options, globals);\n  text = showdown.subParser('tables')(text, options, globals);\n\n  // We already ran _HashHTMLBlocks() before, in Markdown(), but that\n  // was to escape raw HTML in the original Markdown source. This time,\n  // we're escaping the markup we've just created, so that we don't wrap\n  // 
     tags around block-level tags.\n  text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n  text = showdown.subParser('paragraphs')(text, options, globals);\n\n  text = globals.converter._dispatch('blockGamut.after', text, options, globals);\n\n  return text;\n});\n\r\nshowdown.subParser('blockQuotes', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockQuotes.before', text, options, globals);\n\n  // add a couple extra lines after the text and endtext mark\n  text = text + '\\n\\n';\n\n  var rgx = /(^ {0,3}>[ \\t]?.+\\n(.+\\n)*\\n*)+/gm;\n\n  if (options.splitAdjacentBlockquotes) {\n    rgx = /^ {0,3}>[\\s\\S]*?(?:\\n\\n)/gm;\n  }\n\n  text = text.replace(rgx, function (bq) {\n    // attacklab: hack around Konqueror 3.5.4 bug:\n    // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n    bq = bq.replace(/^[ \\t]*>[ \\t]?/gm, ''); // trim one level of quoting\n\n    // attacklab: clean up hack\n    bq = bq.replace(/¨0/g, '');\n\n    bq = bq.replace(/^[ \\t]+$/gm, ''); // trim whitespace-only lines\n    bq = showdown.subParser('githubCodeBlocks')(bq, options, globals);\n    bq = showdown.subParser('blockGamut')(bq, options, globals); // recurse\n\n    bq = bq.replace(/(^|\\n)/g, '$1  ');\n    // These leading spaces screw with 
     content, so we need to fix that:\n    bq = bq.replace(/(\\s*
    [^\\r]+?<\\/pre>)/gm, function (wholeMatch, m1) {\n      var pre = m1;\n      // attacklab: hack around Konqueror 3.5.4 bug:\n      pre = pre.replace(/^  /mg, '¨0');\n      pre = pre.replace(/¨0/g, '');\n      return pre;\n    });\n\n    return showdown.subParser('hashBlock')('
    \\n' + bq + '\\n
    ', options, globals);\n  });\n\n  text = globals.converter._dispatch('blockQuotes.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Process Markdown `
    ` blocks.\n */\nshowdown.subParser('codeBlocks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeBlocks.before', text, options, globals);\n\n  // sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var pattern = /(?:\\n\\n|^)((?:(?:[ ]{4}|\\t).*\\n+)+)(\\n*[ ]{0,3}[^ \\t\\n]|(?=¨0))/g;\n  text = text.replace(pattern, function (wholeMatch, m1, m2) {\n    var codeblock = m1,\n        nextChar = m2,\n        end = '\\n';\n\n    codeblock = showdown.subParser('outdent')(codeblock, options, globals);\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing newlines\n\n    if (options.omitExtraWLInCodeBlocks) {\n      end = '';\n    }\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    return showdown.subParser('hashBlock')(codeblock, options, globals) + nextChar;\n  });\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n\n  text = globals.converter._dispatch('codeBlocks.after', text, options, globals);\n  return text;\n});\n\r\n/**\n *\n *   *  Backtick quotes are used for  spans.\n *\n *   *  You can use multiple backticks as the delimiters if you want to\n *     include literal backticks in the code span. So, this input:\n *\n *         Just type ``foo `bar` baz`` at the prompt.\n *\n *       Will translate to:\n *\n *         
    Just type foo `bar` baz at the prompt.
    \n *\n *    There's no arbitrary limit to the number of backticks you\n *    can use as delimters. If you need three consecutive backticks\n *    in your code, use four for delimiters, etc.\n *\n *  *  You can use spaces to get literal backticks at the edges:\n *\n *         ... type `` `bar` `` ...\n *\n *       Turns to:\n *\n *         ... type `bar` ...\n */\nshowdown.subParser('codeSpans', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeSpans.before', text, options, globals);\n\n  if (typeof text === 'undefined') {\n    text = '';\n  }\n  text = text.replace(/(^|[^\\\\])(`+)([^\\r]*?[^`])\\2(?!`)/gm,\n    function (wholeMatch, m1, m2, m3) {\n      var c = m3;\n      c = c.replace(/^([ \\t]*)/g, '');\t// leading whitespace\n      c = c.replace(/[ \\t]*$/g, '');\t// trailing whitespace\n      c = showdown.subParser('encodeCode')(c, options, globals);\n      c = m1 + '' + c + '';\n      c = showdown.subParser('hashHTMLSpans')(c, options, globals);\n      return c;\n    }\n  );\n\n  text = globals.converter._dispatch('codeSpans.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Create a full HTML document from the processed markdown\n */\nshowdown.subParser('completeHTMLDocument', function (text, options, globals) {\n  'use strict';\n\n  if (!options.completeHTMLDocument) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('completeHTMLDocument.before', text, options, globals);\n\n  var doctype = 'html',\n      doctypeParsed = '\\n',\n      title = '',\n      charset = '\\n',\n      lang = '',\n      metadata = '';\n\n  if (typeof globals.metadata.parsed.doctype !== 'undefined') {\n    doctypeParsed = '\\n';\n    doctype = globals.metadata.parsed.doctype.toString().toLowerCase();\n    if (doctype === 'html' || doctype === 'html5') {\n      charset = '';\n    }\n  }\n\n  for (var meta in globals.metadata.parsed) {\n    if (globals.metadata.parsed.hasOwnProperty(meta)) {\n      switch (meta.toLowerCase()) {\n        case 'doctype':\n          break;\n\n        case 'title':\n          title = '' +  globals.metadata.parsed.title + '\\n';\n          break;\n\n        case 'charset':\n          if (doctype === 'html' || doctype === 'html5') {\n            charset = '\\n';\n          } else {\n            charset = '\\n';\n          }\n          break;\n\n        case 'language':\n        case 'lang':\n          lang = ' lang=\"' + globals.metadata.parsed[meta] + '\"';\n          metadata += '\\n';\n          break;\n\n        default:\n          metadata += '\\n';\n      }\n    }\n  }\n\n  text = doctypeParsed + '\\n\\n' + title + charset + metadata + '\\n\\n' + text.trim() + '\\n\\n';\n\n  text = globals.converter._dispatch('completeHTMLDocument.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Convert all tabs to spaces\n */\nshowdown.subParser('detab', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('detab.before', text, options, globals);\n\n  // expand first n-1 tabs\n  text = text.replace(/\\t(?=\\t)/g, '    '); // g_tab_width\n\n  // replace the nth with two sentinels\n  text = text.replace(/\\t/g, '¨A¨B');\n\n  // use the sentinel to anchor our regex so it doesn't explode\n  text = text.replace(/¨B(.+?)¨A/g, function (wholeMatch, m1) {\n    var leadingText = m1,\n        numSpaces = 4 - leadingText.length % 4;  // g_tab_width\n\n    // there *must* be a better way to do this:\n    for (var i = 0; i < numSpaces; i++) {\n      leadingText += ' ';\n    }\n\n    return leadingText;\n  });\n\n  // clean up sentinels\n  text = text.replace(/¨A/g, '    ');  // g_tab_width\n  text = text.replace(/¨B/g, '');\n\n  text = globals.converter._dispatch('detab.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('ellipsis', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('ellipsis.before', text, options, globals);\n\n  text = text.replace(/\\.\\.\\./g, '…');\n\n  text = globals.converter._dispatch('ellipsis.after', text, options, globals);\n\n  return text;\n});\n\r\n/**\n * Turn emoji codes into emojis\n *\n * List of supported emojis: https://github.com/showdownjs/showdown/wiki/Emojis\n */\nshowdown.subParser('emoji', function (text, options, globals) {\n  'use strict';\n\n  if (!options.emoji) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('emoji.before', text, options, globals);\n\n  var emojiRgx = /:([\\S]+?):/g;\n\n  text = text.replace(emojiRgx, function (wm, emojiCode) {\n    if (showdown.helper.emojis.hasOwnProperty(emojiCode)) {\n      return showdown.helper.emojis[emojiCode];\n    }\n    return wm;\n  });\n\n  text = globals.converter._dispatch('emoji.after', text, options, globals);\n\n  return text;\n});\n\r\n/**\n * Smart processing for ampersands and angle brackets that need to be encoded.\n */\nshowdown.subParser('encodeAmpsAndAngles', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeAmpsAndAngles.before', text, options, globals);\n\n  // Ampersand-encoding based entirely on Nat Irons's Amputator MT plugin:\n  // http://bumppo.net/projects/amputator/\n  text = text.replace(/&(?!#?[xX]?(?:[0-9a-fA-F]+|\\w+);)/g, '&');\n\n  // Encode naked <'s\n  text = text.replace(/<(?![a-z\\/?$!])/gi, '<');\n\n  // Encode <\n  text = text.replace(/\n  text = text.replace(/>/g, '>');\n\n  text = globals.converter._dispatch('encodeAmpsAndAngles.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Returns the string, with after processing the following backslash escape sequences.\n *\n * attacklab: The polite way to do this is with the new escapeCharacters() function:\n *\n *    text = escapeCharacters(text,\"\\\\\",true);\n *    text = escapeCharacters(text,\"`*_{}[]()>#+-.!\",true);\n *\n * ...but we're sidestepping its use of the (slow) RegExp constructor\n * as an optimization for Firefox.  This function gets called a LOT.\n */\nshowdown.subParser('encodeBackslashEscapes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeBackslashEscapes.before', text, options, globals);\n\n  text = text.replace(/\\\\(\\\\)/g, showdown.helper.escapeCharactersCallback);\n  text = text.replace(/\\\\([`*_{}\\[\\]()>#+.!~=|-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeBackslashEscapes.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Encode/escape certain characters inside Markdown code runs.\n * The point is that in code, these characters are literals,\n * and lose their special Markdown meanings.\n */\nshowdown.subParser('encodeCode', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('encodeCode.before', text, options, globals);\n\n  // Encode all ampersands; HTML entities are not\n  // entities within a Markdown code span.\n  text = text\n    .replace(/&/g, '&')\n  // Do the angle bracket song and dance:\n    .replace(//g, '>')\n  // Now, escape characters that are magic in Markdown:\n    .replace(/([*_{}\\[\\]\\\\=~-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeCode.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Within tags -- meaning between < and > -- encode [\\ ` * _ ~ =] so they\n * don't conflict with their use in Markdown for code, italics and strong.\n */\nshowdown.subParser('escapeSpecialCharsWithinTagAttributes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.before', text, options, globals);\n\n  // Build a regex to find HTML tags.\n  var tags     = /<\\/?[a-z\\d_:-]+(?:[\\s]+[\\s\\S]+?)?>/gi,\n      comments = /-]|-[^>])(?:[^-]|-[^-])*)--)>/gi;\n\n  text = text.replace(tags, function (wholeMatch) {\n    return wholeMatch\n      .replace(/(.)<\\/?code>(?=.)/g, '$1`')\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = text.replace(comments, function (wholeMatch) {\n    return wholeMatch\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Handle github codeblocks prior to running HashHTML so that\n * HTML contained within the codeblock gets escaped properly\n * Example:\n * ```ruby\n *     def hello_world(x)\n *       puts \"Hello, #{x}\"\n *     end\n * ```\n */\nshowdown.subParser('githubCodeBlocks', function (text, options, globals) {\n  'use strict';\n\n  // early exit if option is not enabled\n  if (!options.ghCodeBlocks) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('githubCodeBlocks.before', text, options, globals);\n\n  text += '¨0';\n\n  text = text.replace(/(?:^|\\n)(?: {0,3})(```+|~~~+)(?: *)([^\\s`~]*)\\n([\\s\\S]*?)\\n(?: {0,3})\\1/g, function (wholeMatch, delim, language, codeblock) {\n    var end = (options.omitExtraWLInCodeBlocks) ? '' : '\\n';\n\n    // First parse the github code block\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing whitespace\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    codeblock = showdown.subParser('hashBlock')(codeblock, options, globals);\n\n    // Since GHCodeblocks can be false positives, we need to\n    // store the primitive text and the parsed text in a global var,\n    // and then return a token\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  });\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return globals.converter._dispatch('githubCodeBlocks.after', text, options, globals);\n});\n\r\nshowdown.subParser('hashBlock', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashBlock.before', text, options, globals);\n  text = text.replace(/(^\\n+|\\n+$)/g, '');\n  text = '\\n\\n¨K' + (globals.gHtmlBlocks.push(text) - 1) + 'K\\n\\n';\n  text = globals.converter._dispatch('hashBlock.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Hash and escape  elements that should not be parsed as markdown\n */\nshowdown.subParser('hashCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '¨C' + (globals.gHtmlSpans.push(codeblock) - 1) + 'C';\n  };\n\n  // Hash naked \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, ']*>', '', 'gim');\n\n  text = globals.converter._dispatch('hashCodeTags.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('hashElement', function (text, options, globals) {\n  'use strict';\n\n  return function (wholeMatch, m1) {\n    var blockText = m1;\n\n    // Undo double lines\n    blockText = blockText.replace(/\\n\\n/g, '\\n');\n    blockText = blockText.replace(/^\\n/, '');\n\n    // strip trailing blank lines\n    blockText = blockText.replace(/\\n+$/g, '');\n\n    // Replace the element text with a marker (\"¨KxK\" where x is its key)\n    blockText = '\\n\\n¨K' + (globals.gHtmlBlocks.push(blockText) - 1) + 'K\\n\\n';\n\n    return blockText;\n  };\n});\n\r\nshowdown.subParser('hashHTMLBlocks', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLBlocks.before', text, options, globals);\n\n  var blockTags = [\n        'pre',\n        'div',\n        'h1',\n        'h2',\n        'h3',\n        'h4',\n        'h5',\n        'h6',\n        'blockquote',\n        'table',\n        'dl',\n        'ol',\n        'ul',\n        'script',\n        'noscript',\n        'form',\n        'fieldset',\n        'iframe',\n        'math',\n        'style',\n        'section',\n        'header',\n        'footer',\n        'nav',\n        'article',\n        'aside',\n        'address',\n        'audio',\n        'canvas',\n        'figure',\n        'hgroup',\n        'output',\n        'video',\n        'p'\n      ],\n      repFunc = function (wholeMatch, match, left, right) {\n        var txt = wholeMatch;\n        // check if this html element is marked as markdown\n        // if so, it's contents should be parsed as markdown\n        if (left.search(/\\bmarkdown\\b/) !== -1) {\n          txt = left + globals.converter.makeHtml(match) + right;\n        }\n        return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n      };\n\n  if (options.backslashEscapesHTMLTags) {\n    // encode backslash escaped HTML tags\n    text = text.replace(/\\\\<(\\/?[^>]+?)>/g, function (wm, inside) {\n      return '<' + inside + '>';\n    });\n  }\n\n  // hash HTML Blocks\n  for (var i = 0; i < blockTags.length; ++i) {\n\n    var opTagPos,\n        rgx1     = new RegExp('^ {0,3}(<' + blockTags[i] + '\\\\b[^>]*>)', 'im'),\n        patLeft  = '<' + blockTags[i] + '\\\\b[^>]*>',\n        patRight = '';\n    // 1. Look for the first position of the first opening HTML tag in the text\n    while ((opTagPos = showdown.helper.regexIndexOf(text, rgx1)) !== -1) {\n\n      // if the HTML tag is \\ escaped, we need to escape it and break\n\n\n      //2. Split the text in that position\n      var subTexts = showdown.helper.splitAtIndex(text, opTagPos),\n          //3. Match recursively\n          newSubText1 = showdown.helper.replaceRecursiveRegExp(subTexts[1], repFunc, patLeft, patRight, 'im');\n\n      // prevent an infinite loop\n      if (newSubText1 === subTexts[1]) {\n        break;\n      }\n      text = subTexts[0].concat(newSubText1);\n    }\n  }\n  // HR SPECIAL CASE\n  text = text.replace(/(\\n {0,3}(<(hr)\\b([^<>])*?\\/?>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  // Special case for standalone HTML comments\n  text = showdown.helper.replaceRecursiveRegExp(text, function (txt) {\n    return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n  }, '^ {0,3}', 'gm');\n\n  // PHP and ASP-style processor instructions ( and <%...%>)\n  text = text.replace(/(?:\\n\\n)( {0,3}(?:<([?%])[^\\r]*?\\2>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  text = globals.converter._dispatch('hashHTMLBlocks.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Hash span elements that should not be parsed as markdown\n */\nshowdown.subParser('hashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLSpans.before', text, options, globals);\n\n  function hashHTMLSpan (html) {\n    return '¨C' + (globals.gHtmlSpans.push(html) - 1) + 'C';\n  }\n\n  // Hash Self Closing tags\n  text = text.replace(/<[^>]+?\\/>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags without properties\n  text = text.replace(/<([^>]+?)>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags with properties\n  text = text.replace(/<([^>]+?)\\s[^>]+?>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash self closing tags without />\n  text = text.replace(/<[^>]+?>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  /*showdown.helper.matchRecursiveRegExp(text, ']*>', '', 'gi');*/\n\n  text = globals.converter._dispatch('hashHTMLSpans.after', text, options, globals);\n  return text;\n});\n\n/**\n * Unhash HTML spans\n */\nshowdown.subParser('unhashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unhashHTMLSpans.before', text, options, globals);\n\n  for (var i = 0; i < globals.gHtmlSpans.length; ++i) {\n    var repText = globals.gHtmlSpans[i],\n        // limiter to prevent infinite loop (assume 10 as limit for recurse)\n        limit = 0;\n\n    while (/¨C(\\d+)C/.test(repText)) {\n      var num = RegExp.$1;\n      repText = repText.replace('¨C' + num + 'C', globals.gHtmlSpans[num]);\n      if (limit === 10) {\n        console.error('maximum nesting of 10 spans reached!!!');\n        break;\n      }\n      ++limit;\n    }\n    text = text.replace('¨C' + i + 'C', repText);\n  }\n\n  text = globals.converter._dispatch('unhashHTMLSpans.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Hash and escape 
     elements that should not be parsed as markdown\n */\nshowdown.subParser('hashPreCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashPreCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    // encode html entities\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  };\n\n  // Hash 
    \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}]*>\\\\s*]*>', '^ {0,3}\\\\s*
    ', 'gim');\n\n  text = globals.converter._dispatch('hashPreCodeTags.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('headers', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('headers.before', text, options, globals);\n\n  var headerLevelStart = (isNaN(parseInt(options.headerLevelStart))) ? 1 : parseInt(options.headerLevelStart),\n\n      // Set text-style headers:\n      //\tHeader 1\n      //\t========\n      //\n      //\tHeader 2\n      //\t--------\n      //\n      setextRegexH1 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n={2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n=+[ \\t]*\\n+/gm,\n      setextRegexH2 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n-{2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n-+[ \\t]*\\n+/gm;\n\n  text = text.replace(setextRegexH1, function (wholeMatch, m1) {\n\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  text = text.replace(setextRegexH2, function (matchFound, m1) {\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart + 1,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  // atx-style headers:\n  //  # Header 1\n  //  ## Header 2\n  //  ## Header 2 with closing hashes ##\n  //  ...\n  //  ###### Header 6\n  //\n  var atxStyle = (options.requireSpaceBeforeHeadingText) ? /^(#{1,6})[ \\t]+(.+?)[ \\t]*#*\\n+/gm : /^(#{1,6})[ \\t]*(.+?)[ \\t]*#*\\n+/gm;\n\n  text = text.replace(atxStyle, function (wholeMatch, m1, m2) {\n    var hText = m2;\n    if (options.customizedHeaderId) {\n      hText = m2.replace(/\\s?\\{([^{]+?)}\\s*$/, '');\n    }\n\n    var span = showdown.subParser('spanGamut')(hText, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m2) + '\"',\n        hLevel = headerLevelStart - 1 + m1.length,\n        header = '' + span + '';\n\n    return showdown.subParser('hashBlock')(header, options, globals);\n  });\n\n  function headerId (m) {\n    var title,\n        prefix;\n\n    // It is separate from other options to allow combining prefix and customized\n    if (options.customizedHeaderId) {\n      var match = m.match(/\\{([^{]+?)}\\s*$/);\n      if (match && match[1]) {\n        m = match[1];\n      }\n    }\n\n    title = m;\n\n    // Prefix id to prevent causing inadvertent pre-existing style matches.\n    if (showdown.helper.isString(options.prefixHeaderId)) {\n      prefix = options.prefixHeaderId;\n    } else if (options.prefixHeaderId === true) {\n      prefix = 'section-';\n    } else {\n      prefix = '';\n    }\n\n    if (!options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (options.ghCompatibleHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '')\n        .replace(/¨T/g, '')\n        .replace(/¨D/g, '')\n        // replace rest of the chars (&~$ are repeated as they might have been escaped)\n        // borrowed from github's redcarpet (some they should produce similar results)\n        .replace(/[&+$,\\/:;=?@\"#{}|^¨~\\[\\]`\\\\*)(%.!'<>]/g, '')\n        .toLowerCase();\n    } else if (options.rawHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '&')\n        .replace(/¨T/g, '¨')\n        .replace(/¨D/g, '$')\n        // replace \" and '\n        .replace(/[\"']/g, '-')\n        .toLowerCase();\n    } else {\n      title = title\n        .replace(/[^\\w]/g, '')\n        .toLowerCase();\n    }\n\n    if (options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (globals.hashLinkCounts[title]) {\n      title = title + '-' + (globals.hashLinkCounts[title]++);\n    } else {\n      globals.hashLinkCounts[title] = 1;\n    }\n    return title;\n  }\n\n  text = globals.converter._dispatch('headers.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('horizontalRule', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('horizontalRule.before', text, options, globals);\n\n  var key = showdown.subParser('hashBlock')('
    ', options, globals);\n  text = text.replace(/^ {0,2}( ?-){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?\\*){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?_){3,}[ \\t]*$/gm, key);\n\n  text = globals.converter._dispatch('horizontalRule.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Turn Markdown image shortcuts into  tags.\n */\nshowdown.subParser('images', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('images.before', text, options, globals);\n\n  var inlineRegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      crazyRegExp       = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]?<([^>]*)>(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:(?:([\"'])([^\"]*?)\\6))?[ \\t]?\\)/g,\n      base64RegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      referenceRegExp   = /!\\[([^\\]]*?)] ?(?:\\n *)?\\[([\\s\\S]*?)]()()()()()/g,\n      refShortcutRegExp = /!\\[([^\\[\\]]+)]()()()()()/g;\n\n  function writeImageTagBase64 (wholeMatch, altText, linkId, url, width, height, m5, title) {\n    url = url.replace(/\\s/g, '');\n    return writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title);\n  }\n\n  function writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title) {\n\n    var gUrls   = globals.gUrls,\n        gTitles = globals.gTitles,\n        gDims   = globals.gDimensions;\n\n    linkId = linkId.toLowerCase();\n\n    if (!title) {\n      title = '';\n    }\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n\n    } else if (url === '' || url === null) {\n      if (linkId === '' || linkId === null) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = altText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(gUrls[linkId])) {\n        url = gUrls[linkId];\n        if (!showdown.helper.isUndefined(gTitles[linkId])) {\n          title = gTitles[linkId];\n        }\n        if (!showdown.helper.isUndefined(gDims[linkId])) {\n          width = gDims[linkId].width;\n          height = gDims[linkId].height;\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    altText = altText\n      .replace(/\"/g, '"')\n    //altText = showdown.helper.escapeCharacters(altText, '*_', false);\n      .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    //url = showdown.helper.escapeCharacters(url, '*_', false);\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    var result = '\"'x \"optional title\")\n\n  // base64 encoded images\n  text = text.replace(base64RegExp, writeImageTagBase64);\n\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(crazyRegExp, writeImageTag);\n\n  // normal cases\n  text = text.replace(inlineRegExp, writeImageTag);\n\n  // handle reference-style shortcuts: ![img text]\n  text = text.replace(refShortcutRegExp, writeImageTag);\n\n  text = globals.converter._dispatch('images.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('italicsAndBold', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('italicsAndBold.before', text, options, globals);\n\n  // it's faster to have 3 separate regexes for each case than have just one\n  // because of backtracing, in some cases, it could lead to an exponential effect\n  // called \"catastrophic backtrace\". Ominous!\n\n  function parseInside (txt, left, right) {\n    /*\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    */\n    return left + txt + right;\n  }\n\n  // Parse underscores\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b_(\\S[\\s\\S]*?)_\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/_([^\\s_][\\s\\S]*?)_/g, function (wm, m) {\n      // !/^_[^_]/.test(m) - test if it doesn't start with __ (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n  // Now parse asterisks\n  if (options.literalMidWordAsterisks) {\n    text = text.replace(/([^*]|^)\\B\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*\\*(\\S[\\s\\S]*?)\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*(\\S[\\s\\S]*?)\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n  } else {\n    text = text.replace(/\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*\\*(\\S[\\s\\S]*?)\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*([^\\s*][\\s\\S]*?)\\*/g, function (wm, m) {\n      // !/^\\*[^*]/.test(m) - test if it doesn't start with ** (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n\n  text = globals.converter._dispatch('italicsAndBold.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Form HTML ordered (numbered) and unordered (bulleted) lists.\n */\nshowdown.subParser('lists', function (text, options, globals) {\n  'use strict';\n\n  /**\n   * Process the contents of a single ordered or unordered list, splitting it\n   * into individual list items.\n   * @param {string} listStr\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function processListItems (listStr, trimTrailing) {\n    // The $g_list_level global keeps track of when we're inside a list.\n    // Each time we enter a list, we increment it; when we leave a list,\n    // we decrement. If it's zero, we're not in a list anymore.\n    //\n    // We do this because when we're not inside a list, we want to treat\n    // something like this:\n    //\n    //    I recommend upgrading to version\n    //    8. Oops, now this line is treated\n    //    as a sub-list.\n    //\n    // As a single paragraph, despite the fact that the second line starts\n    // with a digit-period-space sequence.\n    //\n    // Whereas when we're inside a list (or sub-list), that line will be\n    // treated as the start of a sub-list. What a kludge, huh? This is\n    // an aspect of Markdown's syntax that's hard to parse perfectly\n    // without resorting to mind-reading. Perhaps the solution is to\n    // change the syntax rules such that sub-lists must start with a\n    // starting cardinal number; e.g. \"1.\" or \"a.\".\n    globals.gListLevel++;\n\n    // trim trailing blank lines:\n    listStr = listStr.replace(/\\n{2,}$/, '\\n');\n\n    // attacklab: add sentinel to emulate \\z\n    listStr += '¨0';\n\n    var rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0| {0,3}([*+-]|\\d+[.])[ \\t]+))/gm,\n        isParagraphed = (/\\n[ \\t]*\\n(?!¨0)/.test(listStr));\n\n    // Since version 1.5, nesting sublists requires 4 spaces (or 1 tab) indentation,\n    // which is a syntax breaking change\n    // activating this option reverts to old behavior\n    if (options.disableForced4SpacesIndentedSublists) {\n      rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0|\\2([*+-]|\\d+[.])[ \\t]+))/gm;\n    }\n\n    listStr = listStr.replace(rgx, function (wholeMatch, m1, m2, m3, m4, taskbtn, checked) {\n      checked = (checked && checked.trim() !== '');\n\n      var item = showdown.subParser('outdent')(m4, options, globals),\n          bulletStyle = '';\n\n      // Support for github tasklists\n      if (taskbtn && options.tasklists) {\n        bulletStyle = ' class=\"task-list-item\" style=\"list-style-type: none;\"';\n        item = item.replace(/^[ \\t]*\\[(x|X| )?]/m, function () {\n          var otp = '
  • a
    • \n      // instead of:\n      // 
    • - - a
    \n      // So, to prevent it, we will put a marker (¨A)in the beginning of the line\n      // Kind of hackish/monkey patching, but seems more effective than overcomplicating the list parser\n      item = item.replace(/^([-*+]|\\d\\.)[ \\t]+[\\S\\n ]*/g, function (wm2) {\n        return '¨A' + wm2;\n      });\n\n      // m1 - Leading line or\n      // Has a double return (multi paragraph) or\n      // Has sublist\n      if (m1 || (item.search(/\\n{2,}/) > -1)) {\n        item = showdown.subParser('githubCodeBlocks')(item, options, globals);\n        item = showdown.subParser('blockGamut')(item, options, globals);\n      } else {\n        // Recursion for sub-lists:\n        item = showdown.subParser('lists')(item, options, globals);\n        item = item.replace(/\\n$/, ''); // chomp(item)\n        item = showdown.subParser('hashHTMLBlocks')(item, options, globals);\n\n        // Colapse double linebreaks\n        item = item.replace(/\\n\\n+/g, '\\n\\n');\n        if (isParagraphed) {\n          item = showdown.subParser('paragraphs')(item, options, globals);\n        } else {\n          item = showdown.subParser('spanGamut')(item, options, globals);\n        }\n      }\n\n      // now we need to remove the marker (¨A)\n      item = item.replace('¨A', '');\n      // we can finally wrap the line in list item tags\n      item =  '' + item + '\\n';\n\n      return item;\n    });\n\n    // attacklab: strip sentinel\n    listStr = listStr.replace(/¨0/g, '');\n\n    globals.gListLevel--;\n\n    if (trimTrailing) {\n      listStr = listStr.replace(/\\s+$/, '');\n    }\n\n    return listStr;\n  }\n\n  function styleStartNumber (list, listType) {\n    // check if ol and starts by a number different than 1\n    if (listType === 'ol') {\n      var res = list.match(/^ *(\\d+)\\./);\n      if (res && res[1] !== '1') {\n        return ' start=\"' + res[1] + '\"';\n      }\n    }\n    return '';\n  }\n\n  /**\n   * Check and parse consecutive lists (better fix for issue #142)\n   * @param {string} list\n   * @param {string} listType\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function parseConsecutiveLists (list, listType, trimTrailing) {\n    // check if we caught 2 or more consecutive lists by mistake\n    // we use the counterRgx, meaning if listType is UL we look for OL and vice versa\n    var olRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?\\d+\\.[ \\t]/gm : /^ {0,3}\\d+\\.[ \\t]/gm,\n        ulRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?[*+-][ \\t]/gm : /^ {0,3}[*+-][ \\t]/gm,\n        counterRxg = (listType === 'ul') ? olRgx : ulRgx,\n        result = '';\n\n    if (list.search(counterRxg) !== -1) {\n      (function parseCL (txt) {\n        var pos = txt.search(counterRxg),\n            style = styleStartNumber(list, listType);\n        if (pos !== -1) {\n          // slice\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt.slice(0, pos), !!trimTrailing) + '\\n';\n\n          // invert counterType and listType\n          listType = (listType === 'ul') ? 'ol' : 'ul';\n          counterRxg = (listType === 'ul') ? olRgx : ulRgx;\n\n          //recurse\n          parseCL(txt.slice(pos));\n        } else {\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt, !!trimTrailing) + '\\n';\n        }\n      })(list);\n    } else {\n      var style = styleStartNumber(list, listType);\n      result = '\\n\\n<' + listType + style + '>\\n' + processListItems(list, !!trimTrailing) + '\\n';\n    }\n\n    return result;\n  }\n\n  /** Start of list parsing **/\n  text = globals.converter._dispatch('lists.before', text, options, globals);\n  // add sentinel to hack around khtml/safari bug:\n  // http://bugs.webkit.org/show_bug.cgi?id=11231\n  text += '¨0';\n\n  if (globals.gListLevel) {\n    text = text.replace(/^(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, list, m2) {\n        var listType = (m2.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, true);\n      }\n    );\n  } else {\n    text = text.replace(/(\\n\\n|^\\n?)(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, m1, list, m3) {\n        var listType = (m3.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, false);\n      }\n    );\n  }\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n  text = globals.converter._dispatch('lists.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Parse metadata at the top of the document\n */\nshowdown.subParser('metadata', function (text, options, globals) {\n  'use strict';\n\n  if (!options.metadata) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('metadata.before', text, options, globals);\n\n  function parseMetadataContents (content) {\n    // raw is raw so it's not changed in any way\n    globals.metadata.raw = content;\n\n    // escape chars forbidden in html attributes\n    // double quotes\n    content = content\n      // ampersand first\n      .replace(/&/g, '&')\n      // double quotes\n      .replace(/\"/g, '"');\n\n    content = content.replace(/\\n {4}/g, ' ');\n    content.replace(/^([\\S ]+): +([\\s\\S]+?)$/gm, function (wm, key, value) {\n      globals.metadata.parsed[key] = value;\n      return '';\n    });\n  }\n\n  text = text.replace(/^\\s*«««+(\\S*?)\\n([\\s\\S]+?)\\n»»»+\\n/, function (wholematch, format, content) {\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/^\\s*---+(\\S*?)\\n([\\s\\S]+?)\\n---+\\n/, function (wholematch, format, content) {\n    if (format) {\n      globals.metadata.format = format;\n    }\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/¨M/g, '');\n\n  text = globals.converter._dispatch('metadata.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Remove one level of line-leading tabs or spaces\n */\nshowdown.subParser('outdent', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('outdent.before', text, options, globals);\n\n  // attacklab: hack around Konqueror 3.5.4 bug:\n  // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n  text = text.replace(/^(\\t|[ ]{1,4})/gm, '¨0'); // attacklab: g_tab_width\n\n  // attacklab: clean up hack\n  text = text.replace(/¨0/g, '');\n\n  text = globals.converter._dispatch('outdent.after', text, options, globals);\n  return text;\n});\n\r\n/**\n *\n */\nshowdown.subParser('paragraphs', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('paragraphs.before', text, options, globals);\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n\n  var grafs = text.split(/\\n{2,}/g),\n      grafsOut = [],\n      end = grafs.length; // Wrap 
     tags\n\n  for (var i = 0; i < end; i++) {\n    var str = grafs[i];\n    // if this is an HTML marker, copy it\n    if (str.search(/¨(K|G)(\\d+)\\1/g) >= 0) {\n      grafsOut.push(str);\n\n    // test for presence of characters to prevent empty lines being parsed\n    // as paragraphs (resulting in undesired extra empty paragraphs)\n    } else if (str.search(/\\S/) >= 0) {\n      str = showdown.subParser('spanGamut')(str, options, globals);\n      str = str.replace(/^([ \\t]*)/g, '
    ');\n      str += '
    ';\n      grafsOut.push(str);\n    }\n  }\n\n  /** Unhashify HTML blocks */\n  end = grafsOut.length;\n  for (i = 0; i < end; i++) {\n    var blockText = '',\n        grafsOutIt = grafsOut[i],\n        codeFlag = false;\n    // if this is a marker for an html block...\n    // use RegExp.test instead of string.search because of QML bug\n    while (/¨(K|G)(\\d+)\\1/.test(grafsOutIt)) {\n      var delim = RegExp.$1,\n          num   = RegExp.$2;\n\n      if (delim === 'K') {\n        blockText = globals.gHtmlBlocks[num];\n      } else {\n        // we need to check if ghBlock is a false positive\n        if (codeFlag) {\n          // use encoded version of all text\n          blockText = showdown.subParser('encodeCode')(globals.ghCodeBlocks[num].text, options, globals);\n        } else {\n          blockText = globals.ghCodeBlocks[num].codeblock;\n        }\n      }\n      blockText = blockText.replace(/\\$/g, '$$$$'); // Escape any dollar signs\n\n      grafsOutIt = grafsOutIt.replace(/(\\n\\n)?¨(K|G)\\d+\\2(\\n\\n)?/, blockText);\n      // Check if grafsOutIt is a pre->code\n      if (/^]*>\\s*]*>/.test(grafsOutIt)) {\n        codeFlag = true;\n      }\n    }\n    grafsOut[i] = grafsOutIt;\n  }\n  text = grafsOut.join('\\n');\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n  return globals.converter._dispatch('paragraphs.after', text, options, globals);\n});\n\r\n/**\n * Run extension\n */\nshowdown.subParser('runExtension', function (ext, text, options, globals) {\n  'use strict';\n\n  if (ext.filter) {\n    text = ext.filter(text, globals.converter, options);\n\n  } else if (ext.regex) {\n    // TODO remove this when old extension loading mechanism is deprecated\n    var re = ext.regex;\n    if (!(re instanceof RegExp)) {\n      re = new RegExp(re, 'g');\n    }\n    text = text.replace(re, ext.replace);\n  }\n\n  return text;\n});\n\r\n/**\n * These are all the transformations that occur *within* block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('spanGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('spanGamut.before', text, options, globals);\n  text = showdown.subParser('codeSpans')(text, options, globals);\n  text = showdown.subParser('escapeSpecialCharsWithinTagAttributes')(text, options, globals);\n  text = showdown.subParser('encodeBackslashEscapes')(text, options, globals);\n\n  // Process anchor and image tags. Images must come first,\n  // because ![foo][f] looks like an anchor.\n  text = showdown.subParser('images')(text, options, globals);\n  text = showdown.subParser('anchors')(text, options, globals);\n\n  // Make links out of things like ``\n  // Must come after anchors, because you can use < and >\n  // delimiters in inline links like [this]().\n  text = showdown.subParser('autoLinks')(text, options, globals);\n  text = showdown.subParser('simplifiedAutoLinks')(text, options, globals);\n  text = showdown.subParser('emoji')(text, options, globals);\n  text = showdown.subParser('underline')(text, options, globals);\n  text = showdown.subParser('italicsAndBold')(text, options, globals);\n  text = showdown.subParser('strikethrough')(text, options, globals);\n  text = showdown.subParser('ellipsis')(text, options, globals);\n\n  // we need to hash HTML tags inside spans\n  text = showdown.subParser('hashHTMLSpans')(text, options, globals);\n\n  // now we encode amps and angles\n  text = showdown.subParser('encodeAmpsAndAngles')(text, options, globals);\n\n  // Do hard breaks\n  if (options.simpleLineBreaks) {\n    // GFM style hard breaks\n    // only add line breaks if the text does not contain a block (special case for lists)\n    if (!/\\n\\n¨K/.test(text)) {\n      text = text.replace(/\\n+/g, '
    \\n');\n    }\n  } else {\n    // Vanilla hard breaks\n    text = text.replace(/  +\\n/g, '
    \\n');\n  }\n\n  text = globals.converter._dispatch('spanGamut.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('strikethrough', function (text, options, globals) {\n  'use strict';\n\n  function parseInside (txt) {\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    return '' + txt + '';\n  }\n\n  if (options.strikethrough) {\n    text = globals.converter._dispatch('strikethrough.before', text, options, globals);\n    text = text.replace(/(?:~){2}([\\s\\S]+?)(?:~){2}/g, function (wm, txt) { return parseInside(txt); });\n    text = globals.converter._dispatch('strikethrough.after', text, options, globals);\n  }\n\n  return text;\n});\n\r\n/**\n * Strips link definitions from text, stores the URLs and titles in\n * hash references.\n * Link defs are in the form: ^[id]: url \"optional title\"\n */\nshowdown.subParser('stripLinkDefinitions', function (text, options, globals) {\n  'use strict';\n\n  var regex       = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*\\s]+)>?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n+|(?=¨0))/gm,\n      base64Regex = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n\\n|(?=¨0)|(?=\\n\\[))/gm;\n\n  // attacklab: sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var replaceFunc = function (wholeMatch, linkId, url, width, height, blankLines, title) {\n    linkId = linkId.toLowerCase();\n    if (url.match(/^data:.+?\\/.+?;base64,/)) {\n      // remove newlines\n      globals.gUrls[linkId] = url.replace(/\\s/g, '');\n    } else {\n      globals.gUrls[linkId] = showdown.subParser('encodeAmpsAndAngles')(url, options, globals);  // Link IDs are case-insensitive\n    }\n\n    if (blankLines) {\n      // Oops, found blank lines, so it's not a title.\n      // Put back the parenthetical statement we stole.\n      return blankLines + title;\n\n    } else {\n      if (title) {\n        globals.gTitles[linkId] = title.replace(/\"|'/g, '"');\n      }\n      if (options.parseImgDimensions && width && height) {\n        globals.gDimensions[linkId] = {\n          width:  width,\n          height: height\n        };\n      }\n    }\n    // Completely remove the definition from the text\n    return '';\n  };\n\n  // first we try to find base64 link references\n  text = text.replace(base64Regex, replaceFunc);\n\n  text = text.replace(regex, replaceFunc);\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return text;\n});\n\r\nshowdown.subParser('tables', function (text, options, globals) {\n  'use strict';\n\n  if (!options.tables) {\n    return text;\n  }\n\n  var tableRgx       = /^ {0,3}\\|?.+\\|.+\\n {0,3}\\|?[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[\\s\\S]+?(?:\\n\\n|¨0)/gm,\n      //singeColTblRgx = /^ {0,3}\\|.+\\|\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n(?: {0,3}\\|.+\\|\\n)+(?:\\n\\n|¨0)/gm;\n      singeColTblRgx = /^ {0,3}\\|.+\\|[ \\t]*\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n( {0,3}\\|.+\\|[ \\t]*\\n)*(?:\\n|¨0)/gm;\n\n  function parseStyles (sLine) {\n    if (/^:[ \\t]*--*$/.test(sLine)) {\n      return ' style=\"text-align:left;\"';\n    } else if (/^--*[ \\t]*:[ \\t]*$/.test(sLine)) {\n      return ' style=\"text-align:right;\"';\n    } else if (/^:[ \\t]*--*[ \\t]*:$/.test(sLine)) {\n      return ' style=\"text-align:center;\"';\n    } else {\n      return '';\n    }\n  }\n\n  function parseHeaders (header, style) {\n    var id = '';\n    header = header.trim();\n    // support both tablesHeaderId and tableHeaderId due to error in documentation so we don't break backwards compatibility\n    if (options.tablesHeaderId || options.tableHeaderId) {\n      id = ' id=\"' + header.replace(/ /g, '_').toLowerCase() + '\"';\n    }\n    header = showdown.subParser('spanGamut')(header, options, globals);\n\n    return '' + header + '\\n';\n  }\n\n  function parseCells (cell, style) {\n    var subText = showdown.subParser('spanGamut')(cell, options, globals);\n    return '' + subText + '\\n';\n  }\n\n  function buildTable (headers, cells) {\n    var tb = '\\n\\n\\n',\n        tblLgn = headers.length;\n\n    for (var i = 0; i < tblLgn; ++i) {\n      tb += headers[i];\n    }\n    tb += '\\n\\n\\n';\n\n    for (i = 0; i < cells.length; ++i) {\n      tb += '\\n';\n      for (var ii = 0; ii < tblLgn; ++ii) {\n        tb += cells[i][ii];\n      }\n      tb += '\\n';\n    }\n    tb += '\\n
    \\n';\n    return tb;\n  }\n\n  function parseTable (rawTable) {\n    var i, tableLines = rawTable.split('\\n');\n\n    for (i = 0; i < tableLines.length; ++i) {\n      // strip wrong first and last column if wrapped tables are used\n      if (/^ {0,3}\\|/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/^ {0,3}\\|/, '');\n      }\n      if (/\\|[ \\t]*$/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/\\|[ \\t]*$/, '');\n      }\n      // parse code spans first, but we only support one line code spans\n      tableLines[i] = showdown.subParser('codeSpans')(tableLines[i], options, globals);\n    }\n\n    var rawHeaders = tableLines[0].split('|').map(function (s) { return s.trim();}),\n        rawStyles = tableLines[1].split('|').map(function (s) { return s.trim();}),\n        rawCells = [],\n        headers = [],\n        styles = [],\n        cells = [];\n\n    tableLines.shift();\n    tableLines.shift();\n\n    for (i = 0; i < tableLines.length; ++i) {\n      if (tableLines[i].trim() === '') {\n        continue;\n      }\n      rawCells.push(\n        tableLines[i]\n          .split('|')\n          .map(function (s) {\n            return s.trim();\n          })\n      );\n    }\n\n    if (rawHeaders.length < rawStyles.length) {\n      return rawTable;\n    }\n\n    for (i = 0; i < rawStyles.length; ++i) {\n      styles.push(parseStyles(rawStyles[i]));\n    }\n\n    for (i = 0; i < rawHeaders.length; ++i) {\n      if (showdown.helper.isUndefined(styles[i])) {\n        styles[i] = '';\n      }\n      headers.push(parseHeaders(rawHeaders[i], styles[i]));\n    }\n\n    for (i = 0; i < rawCells.length; ++i) {\n      var row = [];\n      for (var ii = 0; ii < headers.length; ++ii) {\n        if (showdown.helper.isUndefined(rawCells[i][ii])) {\n\n        }\n        row.push(parseCells(rawCells[i][ii], styles[ii]));\n      }\n      cells.push(row);\n    }\n\n    return buildTable(headers, cells);\n  }\n\n  text = globals.converter._dispatch('tables.before', text, options, globals);\n\n  // find escaped pipe characters\n  text = text.replace(/\\\\(\\|)/g, showdown.helper.escapeCharactersCallback);\n\n  // parse multi column tables\n  text = text.replace(tableRgx, parseTable);\n\n  // parse one column tables\n  text = text.replace(singeColTblRgx, parseTable);\n\n  text = globals.converter._dispatch('tables.after', text, options, globals);\n\n  return text;\n});\n\r\nshowdown.subParser('underline', function (text, options, globals) {\n  'use strict';\n\n  if (!options.underline) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('underline.before', text, options, globals);\n\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n  }\n\n  // escape remaining underscores to prevent them being parsed by italic and bold\n  text = text.replace(/(_)/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('underline.after', text, options, globals);\n\n  return text;\n});\n\r\n/**\n * Swap back in all the special characters we've hidden.\n */\nshowdown.subParser('unescapeSpecialChars', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unescapeSpecialChars.before', text, options, globals);\n\n  text = text.replace(/¨E(\\d+)E/g, function (wholeMatch, m1) {\n    var charCodeToReplace = parseInt(m1);\n    return String.fromCharCode(charCodeToReplace);\n  });\n\n  text = globals.converter._dispatch('unescapeSpecialChars.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('makeMarkdown.blockquote', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      var innerTxt = showdown.subParser('makeMarkdown.node')(children[i], globals);\n\n      if (innerTxt === '') {\n        continue;\n      }\n      txt += innerTxt;\n    }\n  }\n  // cleanup\n  txt = txt.trim();\n  txt = '> ' + txt.split('\\n').join('\\n> ');\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.codeBlock', function (node, globals) {\n  'use strict';\n\n  var lang = node.getAttribute('language'),\n      num  = node.getAttribute('precodenum');\n  return '```' + lang + '\\n' + globals.preList[num] + '\\n```';\n});\n\r\nshowdown.subParser('makeMarkdown.codeSpan', function (node) {\n  'use strict';\n\n  return '`' + node.innerHTML + '`';\n});\n\r\nshowdown.subParser('makeMarkdown.emphasis', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '*';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '*';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.header', function (node, globals, headerLevel) {\n  'use strict';\n\n  var headerMark = new Array(headerLevel + 1).join('#'),\n      txt = '';\n\n  if (node.hasChildNodes()) {\n    txt = headerMark + ' ';\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.hr', function () {\n  'use strict';\n\n  return '---';\n});\n\r\nshowdown.subParser('makeMarkdown.image', function (node) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasAttribute('src')) {\n    txt += '![' + node.getAttribute('alt') + '](';\n    txt += '<' + node.getAttribute('src') + '>';\n    if (node.hasAttribute('width') && node.hasAttribute('height')) {\n      txt += ' =' + node.getAttribute('width') + 'x' + node.getAttribute('height');\n    }\n\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.links', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes() && node.hasAttribute('href')) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    txt = '[';\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '](';\n    txt += '<' + node.getAttribute('href') + '>';\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.list', function (node, globals, type) {\n  'use strict';\n\n  var txt = '';\n  if (!node.hasChildNodes()) {\n    return '';\n  }\n  var listItems       = node.childNodes,\n      listItemsLenght = listItems.length,\n      listNum = node.getAttribute('start') || 1;\n\n  for (var i = 0; i < listItemsLenght; ++i) {\n    if (typeof listItems[i].tagName === 'undefined' || listItems[i].tagName.toLowerCase() !== 'li') {\n      continue;\n    }\n\n    // define the bullet to use in list\n    var bullet = '';\n    if (type === 'ol') {\n      bullet = listNum.toString() + '. ';\n    } else {\n      bullet = '- ';\n    }\n\n    // parse list item\n    txt += bullet + showdown.subParser('makeMarkdown.listItem')(listItems[i], globals);\n    ++listNum;\n  }\n\n  // add comment at the end to prevent consecutive lists to be parsed as one\n  txt += '\\n\\n';\n  return txt.trim();\n});\n\r\nshowdown.subParser('makeMarkdown.listItem', function (node, globals) {\n  'use strict';\n\n  var listItemTxt = '';\n\n  var children = node.childNodes,\n      childrenLenght = children.length;\n\n  for (var i = 0; i < childrenLenght; ++i) {\n    listItemTxt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n  }\n  // if it's only one liner, we need to add a newline at the end\n  if (!/\\n$/.test(listItemTxt)) {\n    listItemTxt += '\\n';\n  } else {\n    // it's multiparagraph, so we need to indent\n    listItemTxt = listItemTxt\n      .split('\\n')\n      .join('\\n    ')\n      .replace(/^ {4}$/gm, '')\n      .replace(/\\n\\n+/g, '\\n\\n');\n  }\n\n  return listItemTxt;\n});\n\r\n\n\nshowdown.subParser('makeMarkdown.node', function (node, globals, spansOnly) {\n  'use strict';\n\n  spansOnly = spansOnly || false;\n\n  var txt = '';\n\n  // edge case of text without wrapper paragraph\n  if (node.nodeType === 3) {\n    return showdown.subParser('makeMarkdown.txt')(node, globals);\n  }\n\n  // HTML comment\n  if (node.nodeType === 8) {\n    return '\\n\\n';\n  }\n\n  // process only node elements\n  if (node.nodeType !== 1) {\n    return '';\n  }\n\n  var tagName = node.tagName.toLowerCase();\n\n  switch (tagName) {\n\n    //\n    // BLOCKS\n    //\n    case 'h1':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 1) + '\\n\\n'; }\n      break;\n    case 'h2':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 2) + '\\n\\n'; }\n      break;\n    case 'h3':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 3) + '\\n\\n'; }\n      break;\n    case 'h4':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 4) + '\\n\\n'; }\n      break;\n    case 'h5':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 5) + '\\n\\n'; }\n      break;\n    case 'h6':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 6) + '\\n\\n'; }\n      break;\n\n    case 'p':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.paragraph')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'blockquote':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.blockquote')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'hr':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.hr')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'ol':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ol') + '\\n\\n'; }\n      break;\n\n    case 'ul':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ul') + '\\n\\n'; }\n      break;\n\n    case 'precode':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.codeBlock')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'pre':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.pre')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'table':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.table')(node, globals) + '\\n\\n'; }\n      break;\n\n    //\n    // SPANS\n    //\n    case 'code':\n      txt = showdown.subParser('makeMarkdown.codeSpan')(node, globals);\n      break;\n\n    case 'em':\n    case 'i':\n      txt = showdown.subParser('makeMarkdown.emphasis')(node, globals);\n      break;\n\n    case 'strong':\n    case 'b':\n      txt = showdown.subParser('makeMarkdown.strong')(node, globals);\n      break;\n\n    case 'del':\n      txt = showdown.subParser('makeMarkdown.strikethrough')(node, globals);\n      break;\n\n    case 'a':\n      txt = showdown.subParser('makeMarkdown.links')(node, globals);\n      break;\n\n    case 'img':\n      txt = showdown.subParser('makeMarkdown.image')(node, globals);\n      break;\n\n    default:\n      txt = node.outerHTML + '\\n\\n';\n  }\n\n  // common normalization\n  // TODO eventually\n\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.paragraph', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n\n  // some text normalization\n  txt = txt.trim();\n\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.pre', function (node, globals) {\n  'use strict';\n\n  var num  = node.getAttribute('prenum');\n  return '
    ' + globals.preList[num] + '
    ';\n});\n\r\nshowdown.subParser('makeMarkdown.strikethrough', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '~~';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '~~';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.strong', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '**';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '**';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.table', function (node, globals) {\n  'use strict';\n\n  var txt = '',\n      tableArray = [[], []],\n      headings   = node.querySelectorAll('thead>tr>th'),\n      rows       = node.querySelectorAll('tbody>tr'),\n      i, ii;\n  for (i = 0; i < headings.length; ++i) {\n    var headContent = showdown.subParser('makeMarkdown.tableCell')(headings[i], globals),\n        allign = '---';\n\n    if (headings[i].hasAttribute('style')) {\n      var style = headings[i].getAttribute('style').toLowerCase().replace(/\\s/g, '');\n      switch (style) {\n        case 'text-align:left;':\n          allign = ':---';\n          break;\n        case 'text-align:right;':\n          allign = '---:';\n          break;\n        case 'text-align:center;':\n          allign = ':---:';\n          break;\n      }\n    }\n    tableArray[0][i] = headContent.trim();\n    tableArray[1][i] = allign;\n  }\n\n  for (i = 0; i < rows.length; ++i) {\n    var r = tableArray.push([]) - 1,\n        cols = rows[i].getElementsByTagName('td');\n\n    for (ii = 0; ii < headings.length; ++ii) {\n      var cellContent = ' ';\n      if (typeof cols[ii] !== 'undefined') {\n        cellContent = showdown.subParser('makeMarkdown.tableCell')(cols[ii], globals);\n      }\n      tableArray[r].push(cellContent);\n    }\n  }\n\n  var cellSpacesCount = 3;\n  for (i = 0; i < tableArray.length; ++i) {\n    for (ii = 0; ii < tableArray[i].length; ++ii) {\n      var strLen = tableArray[i][ii].length;\n      if (strLen > cellSpacesCount) {\n        cellSpacesCount = strLen;\n      }\n    }\n  }\n\n  for (i = 0; i < tableArray.length; ++i) {\n    for (ii = 0; ii < tableArray[i].length; ++ii) {\n      if (i === 1) {\n        if (tableArray[i][ii].slice(-1) === ':') {\n          tableArray[i][ii] = showdown.helper.padEnd(tableArray[i][ii].slice(-1), cellSpacesCount - 1, '-') + ':';\n        } else {\n          tableArray[i][ii] = showdown.helper.padEnd(tableArray[i][ii], cellSpacesCount, '-');\n        }\n      } else {\n        tableArray[i][ii] = showdown.helper.padEnd(tableArray[i][ii], cellSpacesCount);\n      }\n    }\n    txt += '| ' + tableArray[i].join(' | ') + ' |\\n';\n  }\n\n  return txt.trim();\n});\n\r\nshowdown.subParser('makeMarkdown.tableCell', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (!node.hasChildNodes()) {\n    return '';\n  }\n  var children = node.childNodes,\n      childrenLength = children.length;\n\n  for (var i = 0; i < childrenLength; ++i) {\n    txt += showdown.subParser('makeMarkdown.node')(children[i], globals, true);\n  }\n  return txt.trim();\n});\n\r\nshowdown.subParser('makeMarkdown.txt', function (node) {\n  'use strict';\n\n  var txt = node.nodeValue;\n\n  // multiple spaces are collapsed\n  txt = txt.replace(/ +/g, ' ');\n\n  // replace the custom ¨NBSP; with a space\n  txt = txt.replace(/¨NBSP;/g, ' ');\n\n  // \", <, > and & should replace escaped html entities\n  txt = showdown.helper.unescapeHTMLEntities(txt);\n\n  // escape markdown magic characters\n  // emphasis, strong and strikethrough - can appear everywhere\n  // we also escape pipe (|) because of tables\n  // and escape ` because of code blocks and spans\n  txt = txt.replace(/([*_~|`])/g, '\\\\$1');\n\n  // escape > because of blockquotes\n  txt = txt.replace(/^(\\s*)>/g, '\\\\$1>');\n\n  // hash character, only troublesome at the beginning of a line because of headers\n  txt = txt.replace(/^#/gm, '\\\\#');\n\n  // horizontal rules\n  txt = txt.replace(/^(\\s*)([-=]{3,})(\\s*)$/, '$1\\\\$2$3');\n\n  // dot, because of ordered lists, only troublesome at the beginning of a line when preceded by an integer\n  txt = txt.replace(/^( {0,3}\\d+)\\./gm, '$1\\\\.');\n\n  // +, * and -, at the beginning of a line becomes a list, so we need to escape them also (asterisk was already escaped)\n  txt = txt.replace(/^( {0,3})([+-])/gm, '$1\\\\$2');\n\n  // images and links, ] followed by ( is problematic, so we escape it\n  txt = txt.replace(/]([\\s]*)\\(/g, '\\\\]$1\\\\(');\n\n  // reference URIs must also be escaped\n  txt = txt.replace(/^ {0,3}\\[([\\S \\t]*?)]:/gm, '\\\\[$1]:');\n\n  return txt;\n});\n\r\nvar root = this;\n\n// AMD Loader\nif (typeof define === 'function' && define.amd) {\n  define(function () {\n    'use strict';\n    return showdown;\n  });\n\n// CommonJS/nodeJS Loader\n} else if (typeof module !== 'undefined' && module.exports) {\n  module.exports = showdown;\n\n// Regular Browser loader\n} else {\n  root.showdown = showdown;\n}\n}).call(this);\r\n\n//# sourceMappingURL=showdown.js.map\r\n\n\n\n// WEBPACK FOOTER //\n// ../node_modules/showdown/dist/showdown.js","// removed by extract-text-webpack-plugin\nmodule.exports = {\"thesis\":\"thesis__3uAQ4\"};\n\n\n//////////////////\n// WEBPACK FOOTER\n// ./components/thesis.css\n// module id = J9SO\n// module chunks = 0","import { Component, cloneElement, h } from 'preact';\n\nvar EMPTY$1 = {};\n\nfunction assign(obj, props) {\n\t// eslint-disable-next-line guard-for-in\n\tfor (var i in props) {\n\t\tobj[i] = props[i];\n\t}\n\treturn obj;\n}\n\nfunction exec(url, route, opts) {\n\tvar reg = /(?:\\?([^#]*))?(#.*)?$/,\n\t\tc = url.match(reg),\n\t\tmatches = {},\n\t\tret;\n\tif (c && c[1]) {\n\t\tvar p = c[1].split('&');\n\t\tfor (var i=0; i b.rank) ? -1 :\n\t\t(a.index - b.index)\n\t);\n}\n\n// filter out VNodes without attributes (which are unrankeable), and add `index`/`rank` properties to be used in sorting.\nfunction prepareVNodeForRanking(vnode, index) {\n\tvnode.index = index;\n\tvnode.rank = rankChild(vnode);\n\treturn vnode.attributes;\n}\n\nfunction segmentize(url) {\n\treturn url.replace(/(^\\/+|\\/+$)/g, '').split('/');\n}\n\nfunction rankSegment(segment) {\n\treturn segment.charAt(0)==':' ? (1 + '*+?'.indexOf(segment.charAt(segment.length-1))) || 4 : 5;\n}\n\nfunction rank(path) {\n\treturn segmentize(path).map(rankSegment).join('');\n}\n\nfunction rankChild(vnode) {\n\treturn vnode.attributes.default ? 0 : rank(vnode.attributes.path);\n}\n\nvar customHistory = null;\n\nvar ROUTERS = [];\n\nvar subscribers = [];\n\nvar EMPTY = {};\n\nfunction isPreactElement(node) {\n\treturn node.__preactattr_!=null || typeof Symbol!=='undefined' && node[Symbol.for('preactattr')]!=null;\n}\n\nfunction setUrl(url, type) {\n\tif ( type === void 0 ) type='push';\n\n\tif (customHistory && customHistory[type]) {\n\t\tcustomHistory[type](url);\n\t}\n\telse if (typeof history!=='undefined' && history[type+'State']) {\n\t\thistory[type+'State'](null, null, url);\n\t}\n}\n\n\nfunction getCurrentUrl() {\n\tvar url;\n\tif (customHistory && customHistory.location) {\n\t\turl = customHistory.location;\n\t}\n\telse if (customHistory && customHistory.getCurrentLocation) {\n\t\turl = customHistory.getCurrentLocation();\n\t}\n\telse {\n\t\turl = typeof location!=='undefined' ? location : EMPTY;\n\t}\n\treturn (\"\" + (url.pathname || '') + (url.search || ''));\n}\n\n\n\nfunction route(url, replace) {\n\tif ( replace === void 0 ) replace=false;\n\n\tif (typeof url!=='string' && url.url) {\n\t\treplace = url.replace;\n\t\turl = url.url;\n\t}\n\n\t// only push URL into history if we can handle it\n\tif (canRoute(url)) {\n\t\tsetUrl(url, replace ? 'replace' : 'push');\n\t}\n\n\treturn routeTo(url);\n}\n\n\n/** Check if the given URL can be handled by any router instances. */\nfunction canRoute(url) {\n\tfor (var i=ROUTERS.length; i--; ) {\n\t\tif (ROUTERS[i].canRoute(url)) { return true; }\n\t}\n\treturn false;\n}\n\n\n/** Tell all router instances to handle the given URL.  */\nfunction routeTo(url) {\n\tvar didRoute = false;\n\tfor (var i=0; i 0;\n\t};\n\n\t/** Re-render children with a new URL to match against. */\n\tRouter.prototype.routeTo = function routeTo (url) {\n\t\tthis._didRoute = false;\n\t\tthis.setState({ url: url });\n\n\t\t// if we're in the middle of an update, don't synchronously re-route.\n\t\tif (this.updating) { return this.canRoute(url); }\n\n\t\tthis.forceUpdate();\n\t\treturn this._didRoute;\n\t};\n\n\tRouter.prototype.componentWillMount = function componentWillMount () {\n\t\tROUTERS.push(this);\n\t\tthis.updating = true;\n\t};\n\n\tRouter.prototype.componentDidMount = function componentDidMount () {\n\t\tvar this$1 = this;\n\n\t\tif (customHistory) {\n\t\t\tthis.unlisten = customHistory.listen(function (location) {\n\t\t\t\tthis$1.routeTo((\"\" + (location.pathname || '') + (location.search || '')));\n\t\t\t});\n\t\t}\n\t\tthis.updating = false;\n\t};\n\n\tRouter.prototype.componentWillUnmount = function componentWillUnmount () {\n\t\tif (typeof this.unlisten==='function') { this.unlisten(); }\n\t\tROUTERS.splice(ROUTERS.indexOf(this), 1);\n\t};\n\n\tRouter.prototype.componentWillUpdate = function componentWillUpdate () {\n\t\tthis.updating = true;\n\t};\n\n\tRouter.prototype.componentDidUpdate = function componentDidUpdate () {\n\t\tthis.updating = false;\n\t};\n\n\tRouter.prototype.getMatchingChildren = function getMatchingChildren (children, url, invoke) {\n\t\treturn children\n\t\t\t.filter(prepareVNodeForRanking)\n\t\t\t.sort(pathRankSort)\n\t\t\t.map( function (vnode) {\n\t\t\t\tvar matches = exec(url, vnode.attributes.path, vnode.attributes);\n\t\t\t\tif (matches) {\n\t\t\t\t\tif (invoke !== false) {\n\t\t\t\t\t\tvar newProps = { url: url, matches: matches };\n\t\t\t\t\t\tassign(newProps, matches);\n\t\t\t\t\t\tdelete newProps.ref;\n\t\t\t\t\t\tdelete newProps.key;\n\t\t\t\t\t\treturn cloneElement(vnode, newProps);\n\t\t\t\t\t}\n\t\t\t\t\treturn vnode;\n\t\t\t\t}\n\t\t\t}).filter(Boolean);\n\t};\n\n\tRouter.prototype.render = function render (ref, ref$1) {\n\t\tvar children = ref.children;\n\t\tvar onChange = ref.onChange;\n\t\tvar url = ref$1.url;\n\n\t\tvar active = this.getMatchingChildren(children, url, true);\n\n\t\tvar current = active[0] || null;\n\t\tthis._didRoute = !!current;\n\n\t\tvar previous = this.previousUrl;\n\t\tif (url!==previous) {\n\t\t\tthis.previousUrl = url;\n\t\t\tif (typeof onChange==='function') {\n\t\t\t\tonChange({\n\t\t\t\t\trouter: this,\n\t\t\t\t\turl: url,\n\t\t\t\t\tprevious: previous,\n\t\t\t\t\tactive: active,\n\t\t\t\t\tcurrent: current\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\treturn current;\n\t};\n\n\treturn Router;\n}(Component));\n\nvar Link = function (props) { return (\n\th('a', assign({ onClick: handleLinkClick }, props))\n); };\n\nvar Route = function (props) { return h(props.component, props); };\n\nRouter.subscribers = subscribers;\nRouter.getCurrentUrl = getCurrentUrl;\nRouter.route = route;\nRouter.Router = Router;\nRouter.Route = Route;\nRouter.Link = Link;\n\nexport { subscribers, getCurrentUrl, route, Router, Route, Link };export default Router;\n//# sourceMappingURL=preact-router.es.js.map\n\n\n\n// WEBPACK FOOTER //\n// ../node_modules/preact-router/dist/preact-router.es.js","import style from \"./panel.css\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (
    {this.props.title}
    );\n\t\t}\n\n\t\treturn (\n\t\t\t
    \n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
    \n\t\t);\n\t}\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/panel.js","import style from \"./split.css\";\nimport { Component } from 'preact';\n\nexport default class Split extends Component {\n\trender() {\n\t    let title = null;\n\t    if(this.props.title !== undefined) {\n            title = (
    {this.props.title}
    )\n        }\n\n        let children;\n        if(Array.isArray(this.props.children)) {\n            children = this.props.children.map(element => {\n                return (
    {element}
    );\n            });\n        }\n        else {\n            children = 
    {this.props.children}
    ;\n        }\n\t\treturn (\n\t        
    \n                {title}\n                
    {children}
    \n            
    \n        );\n\t}\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/split.js","import style from \"./todo.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Todo extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/todo.js","import style from './home.css'\r\nimport { Component } from 'preact';\r\nimport Panel from '../components/panel';\r\nimport Split from '../components/split';\r\nimport Todo from '../components/todo';\r\n\r\nexport default class Home extends Component {\r\n    render() {\r\n        return (\r\n            
    \r\n                
    Indice
    \r\n                \r\n                    Statistica ed elementi di probabilità    }>\r\n                        
    \r\n                            Appunti scritti mentre studiavo per l'esame di Statistica ed elementi di probabilità  del corso triennale di Informatica all'Unimore del Prof. Luca La Rocca.\r\n                        
    \r\n                    \r\n                    Cleaver}>\r\n                        
    \r\n                            Progetto in Java sviluppato per l'esame di Programmazione ad Oggetti del corso triennale di Informatica all'Unimore, tenuto dai Prof. Giacomo Cabri e Nicola Capodieci.\r\n                        
    \r\n                        \r\n                    Fisica}>\r\n                        
    \r\n                            Appunti delle lezioni di Fisica del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Rossella Brunetti nel primo semestre dell'Anno Accademico 2019/2020.\r\n                        
    \r\n                        \r\n                    Sistemi Operativi}>\r\n                        
    \r\n                            Soluzioni agli Arzigogoli proposti dal Prof. Mauro Andreolini durante le lezioni di Sistemi Operativi del corso triennale di Informatica all'Unimore tenutesi nel primo semestre dell'Anno Accademico 2019/2020.\r\n                        
    \r\n                        \r\n                    Algoritmi e Strutture Dati}>\r\n                        
    \r\n                            Appunti delle lezioni di Algoritmi e Strutture Dati del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Manuela Montangero nel secondo semestre dell'Anno Accademico 2018/2019.\r\n                        
    \r\n                        \r\n                    Videolezioni di Geometria}>\r\n                        
    \r\n                            Ottime videolezioni di Geometria con licenza CC BY-NC-SA 4.0 che ho trovato sul portale Dolly 2018 dell'Unimore.\r\n                        
    \r\n                        \r\n                    Come installare MinGW}>\r\n                        
    \r\n                            Un breve tutorial con immagini su come installare e configurare MinGW per compilare programmi C e C++ su Windows.\r\n                        
    \r\n                        \r\n                \r\n                \r\n                    @unimoreinfo}>\r\n                        
    \r\n                            Il gruppo Telegram del corso di Informatica dell'Unimore!\r\n                        
    \r\n                        \r\n                    Calendario Lezioni}>\r\n                        
    \r\n                            Calendario Google quasi sempre aggiornato delle lezioni e degli esami del secondo anno dell'Unimore durante l'Anno Accademico 2019/2020.\r\n                        
    \r\n                        \r\n                    Erre2}>\r\n                        
    \r\n                            Portale contenente appunti e riassunti mantenuto da Lorenzo Balugani.\r\n                        
    \r\n                        \r\n                    vezzalinistefano/Appunti-Algoritmi}>\r\n                        
    \r\n                            Appunti di Algoritmi e Strutture Dati mantenuti da Vezzalini Stefano.\r\n                        
    \r\n                        \r\n                    \r\n            
    \r\n        )\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./pages/home.js","import style from './latex.css';\nimport { Component } from 'preact';\n\nexport default class Latex extends Component {\n\trender() {\n\t\tlet equation = `{\\\\color{White} ${this.props.children} }`;\n\t\treturn (\n\t\t\t{this.props.children}\n\t\t\t);\n\t}\n}\n\n\n// WEBPACK FOOTER //\n// ./components/latex.js","import style from \"./plus.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Plus extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/plus.js","import style from \"./minus.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Minus extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/minus.js","import style from './fisica.css';\nimport { Component } from 'preact';\nimport Latex from '../components/latex';\nimport Panel from '../components/panel';\nimport Split from '../components/split';\nimport Plus from '../components/plus';\nimport Minus from '../components/minus';\nimport Todo from '../components/todo';\n\nconst r = String.raw;\n\nexport default class Fisica extends Component {\n\trender() {\n        return (\n            
    \n                
    Fisica
    \n                \n                    \n                        
    \n                            Usa le regole base della trigonometria:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\vec{v}_x + \\vec{v}_y`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha`}\n                        
    \n                        \n                    \n                        
    \n                            Scomponi in componenti, poi sommali:\n                        
    \n                        
    \n                            {r`\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore risultante dall'applicazione della regola del parallelogramma.\n                        
    \n                        \n                    \n                        
    \n                            Alla fine è sempre una somma:\n                        
    \n                        
    \n                            {r`\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore che parte da w e arriva a v.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama scalare perchè il risultato è uno scalare, non un vettore.\n                        
    \n                        
    \n                            {r`\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha`}\n                        
    \n                        
    \n                            Produce il modulo della proiezione di {r`\\vec{a}`} su {r`\\vec{b}`}.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama vettoriale perchè il risultato è un altro vettore.\n                        
    \n                        
      \n                            
    • {r`\\vec{c} = \\vec{a} \\times \\vec{b}`}
      • \n                            
    • {r`\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)`}
      • \n                            
    • Regola della mano destra
      • \n                        
    \n                        
    \n                            Non è commutativo!\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0`}\n                        
    \n                        \n                    \n                        
    \n                            La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la massa.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = m \\vec{a}`}\n                        
    \n                        \n                    \n                        
    \n                            Due corpi esercitano forze uguali e opposte uno sull'altro. \n                        
    \n                        
    \n                            {r`\\vec{F}_{21} = -\\vec{F}_{12}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Due corpi puntiformi si attirano uno verso l'altro con forza:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}`}\n                        
    \n                        
    \n                            G è la costante di gravitazione universale e vale:\n                        
    \n                        
    \n                            {r`G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza peso uguale a:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            g è la costante di gravità della Terra, e vale:\n                        
    \n                        
    \n                            {r`g = 9.81 \\frac{m}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Per pianeti diversi dalla Terra vale la stessa regola:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            L'unica differenza è che cambia la costante di gravità:\n                        
    \n                        
    \n                            {r`g_{luna} = 1.62 \\frac{m}{s^2}`}\n                        
    \n                        
    \n                            {r`g_{marte} = 3.71 \\frac{m}{s^2}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si oppone alle forze applicate alla superficie di contatto.\n                        
    \n                        
    \n                            Un libro appoggiato su un tavolo ha la forza di gravità che lo attira verso il terreno e la forza normale che lo trattiene dal cadere. \n                        
    \n                        \n                    \n                        
    \n                            Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            Rallenta i corpi che si stanno muovendo finchè essi non si fermano:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            E' forza trasmessa tra due estremi di una fune.\n                        
    \n                        
    \n                            Può essere redirezionata per mezzo di carrucole.\n                        
    \n                        \n                    \n                        
    \n                            Una molla cerca sempre di tornare alla sua posizione indeformata con forza:\n                        
    \n                        
    \n                            {r`F = -k x`}\n                        
    \n                        
    \n                            (E' negativa perchè la forza è opposta a quella applicata per deformarla.)\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            È un vettore che indica la posizione di un corpo rispetto a un'origine.\n                        
    \n                        
    \n                            {r`\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di posizione nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice velocità istantanea:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di velocità nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice accelerazione istantanea:\n                        
    \n                        
    \n                            {r`\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}`}\n                        
    \n                        \n                    Quantità di moto (momento lineare)}>\n                        
    \n                            La quantità di moto è una proprietà vettoriale dei corpi:\n                        
    \n                        
    \n                            {r`\\vec{p} = m \\vec{v}`}\n                        
    \n                        
    \n                            Se la forza risultante è nulla, la quantità di moto non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = v \\cdot \\Delta t + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`v(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            La velocità non varia:\n                        
    \n                        
    \n                            {r`a(t) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = 0\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È una retta:\n                        
    \n                        
    \n                            {r`v(t) = a \\Delta t + v(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`a(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' la distanza dal centro massima che raggiunge il corpo.\n                        
    \n                        
    \n                            (L'ampiezza di una sinusoide.)\n                        
    \n                        \n                    \n                        
    \n                            Indica quanto in fretta cambia la posizione del corpo. \n                        
    \n                        
    \n                            Dipende dal periodo:\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' una sinusoide:\n                        
    \n                        
    \n                            {r`s(t) = A \\sin (\\omega \\cdot t + \\phi)`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide dello spostamento, sfasata di {r`\\frac{\\pi}{2}`}:\n                        
    \n                        
    \n                            {r`v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide della velocità, sfasata di {r`\\pi`}:\n                        
    \n                        
    \n                            {r`a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.\n                        
    \n                        \n                    \n                        
    \n                            Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di {r`\\frac{\\pi}{2}`}, sull'asse Y.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Velocità angolare\n                        
    \n                        
    \n                            Quanto cambia la fase nel tempo.\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' l'angolo percorso dal corpo rispetto alla posizione iniziale.\n                        
    \n                        
    \n                            Si indica con {r`\\phi`}, e generalmente si usa in radianti.\n                        
    \n                        \n                    \n                        
    \n                            Si applicano le formule per la circonferenza:\n                        
    \n                        
    \n                            {r`v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r`}\n                        
    \n                        \n                    \n                        
    \n                            Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto: \n                        
    \n                        
    \n                            {r`a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega`}\n                        
    \n                        \n                    \n                        
    \n                            È verso il centro e si calcola con:\n                        
    \n                        
    \n                            {r`F = m \\cdot a`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' compiuto da una forza che sposta un corpo.\n                        
    \n                        
    \n                            {r`W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )`}\n                        
    \n                        
    \n                            (Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia cinetica in ogni momento uguale a:\n                        
    \n                        
    \n                            {r`E_c = \\frac{1}{2} m v^2`}\n                        
    \n                        
    \n                            Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:\n                        
    \n                        
    \n                            {r`\\Delta E_c = W`}\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia potenziale in ogni momento pari a: \n                        
    \n                        
    \n                            {r`E_{p_g} = m \\cdot g \\cdot h`}\n                        
    \n                        
    \n                            (Con h uguale a un altezza scelta come punto di riferimento.)\n                        
    \n                        \n                    \n                        
    \n                            Una molla ha sempre energia potenziale elastica pari a:\n                        
    \n                        
    \n                            {r`E_{p_e} = \\frac{1}{2} k x^2`}\n                        
    \n                        \n                    \n                        
    \n                            Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo.\n                        
    \n                        
    \n                            Ad esempio, è conservativa la forza di gravità, ma non è conservativa la forza di attrito.\n                        
    \n                        
    \n                            Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:\n                        
    \n                        
    \n                            {r`E = E_k + E_p`}\n                        
    \n                        \n                    \n                        
    \n                            È la velocità di trasferimento di energia:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta E}{\\Delta t}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            È una proprietà dei corpi che può essere positiva o negativa.\n                        
    \n                        
    \n                            Si conserva: in un sistema chiuso la carica totale è costante.\n                        
    \n                        
    \n                            Esiste un'unità elementare: {r`C_{elettrone} = 1.602 \\cdot 10^{-19}`}.\n                        
    \n                        
    \n                            Cariche opposte si attraggono; cariche uguali si respingono.\n                        
    \n                        \n                    \n                        
    \n                            Più ioni ha un corpo, meglio la carica si muove attraverso di esso.\n                        
    \n                        
    \n                            I corpi in cui la carica si muove bene sono conduttori, mentre quelli in cui si muove difficilmente sono isolanti.\n                        
    \n                        
    \n                            Il corpo umano è un buon conduttore.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno equilibrate e il corpo diventerà elettricamente neutro (con stesso numero di cariche positive e negative all'interno).\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Strofinando tra loro due corpi isolanti, essi si polarizzeranno per strofinio.\n                        
    \n                        \n                    \n                        
    \n                            Toccando un conduttore con un corpo carico, il conduttore potrà polarizzarsi per contatto.\n                        
    \n                        \n                    \n                        
    \n                            Se un corpo conduttore ha cariche \"esterne\" di un certo segno vicino, esso avrà tutte le cariche del segno opposto in equilibrio vicino alle cariche esterne, e tutte le cariche dello stesso segno più lontano possibile da esse.\n                        
    \n                        
    \n                            Mettendo a terra il conduttore, nuove cariche del segno opposto saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate.\n                        
    \n                        
    \n                            Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà caricato del segno opposto rispetto alle cariche esterne.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Due corpi carichi si attraggono tra loro con forza: \n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{-k \\cdot q_1 \\cdot q_2}{s^2}`}\n                        
    \n                        
    \n                            {r`k`} è la costante di Coulomb, e vale {r`k = 8.99 \\cdot 10^9 \\frac{N \\cdot m^2}{C^2}`}.\n                        
    \n                        \n                    \n                        
    \n                            La costante {r`k`} è in realtà dipendente da un altra costante, {r`\\epsilon_0`}, la permeabilità del vuoto.\n                        
    \n                        
    \n                            {r`k = \\frac{1}{4 \\pi \\cdot \\epsilon_0}`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{q_1 \\cdot q_2}{4 \\pi \\cdot \\epsilon_0 \\cdot s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Misura che forza viene applicata in ogni punto su una carica unitaria:\n                        
    \n                        
    \n                            {r`\\vec{E} = \\frac{\\vec{F}_{elettrica}}{q} = \\frac{-k \\cdot q}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            È la differenza tra \"quanto\" campo elettrico entra e quanto campo elettrico esce da una certa area.\n                        
    \n                        
    \n                            In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area.\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A}`}\n                        
    \n                        
    \n                            Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A} = E_\\perp \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        
    \n                            Circa. E' una specie di integrale...\n                        
    \n                        \n                    \n                        
    \n                            Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie.\n                        
    \n                        
    \n                            {r`\\Phi_E = 4 \\pi \\cdot k \\cdot q = \\frac{q}{\\epsilon_0}`}\n                        
    \n                        
    \n                            Ovvero, i campi elettrostatici sono generati dalle cariche elettriche.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un corpo carico vicino ad altre cariche possiede un'energia potenziale elettrica {r`U_e`}.\n                        
        \n                        \n                    \n                \n                    Potenziale elettrico (tensione)}>\n                        
    \n                            È il valore dell'energia potenziale elettrica per una carica unitaria.\n                        
    \n                        
    \n                            {r`V = \\frac{U_e}{q}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Volt ({r`V`}).\n                        
                            \n                        
    \n                            In una batteria è detto forza elettromotrice, e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.\n                        
    \n                        \n                    Corrente elettrica (intensità)}>\n                        
    \n                            Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo.\n                        
    \n                        
    \n                            {r`I = \\frac{\\Delta q}{\\Delta t}`}\n                        
    \n                        
    \n                            Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla.\n                        
    \n                        
    \n                            La sua unità di misura è l'Ampere ({r`A`}).\n                        
    \n                        \n                    Corrente continua (DC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente è costante.\n                        
    \n                        \n                    Corrente alternata (AC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente si alterna periodicamente.\n                        
    \n                        \n                    \n                        
    \n                            Possiamo calcolare la potenza di un circuito:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta U_e}{\\Delta t} = I \\cdot \\Delta V = I^2 \\cdot R = \\frac{(\\Delta V)^2}{R}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Riduce l'intensità di corrente, e converte parte del potenziale in calore.\n                        
    \n                        
    \n                            Il potenziale utilizzato è pari a:\n                        
    \n                        
    \n                            {r`V = R \\cdot I`}\n                        
    \n                        
    \n                            Dove {r`R`} è una costante detta resistenza con unità di misura Ohm ({r`\\Omega`}).\n                        
    \n                        
    \n                            La resistenza di un conduttore vale:\n                        
    \n                        
    \n                            {r`R = \\rho \\frac{L_{unghezza}}{A_{rea}}`}\n                        
    \n                        
    \n                            {r`\\rho`} è la resistività del materiale, e varia in base alla temperatura:\n                        
    \n                        
    \n                            {r`\\rho = \\rho_0 (1 + \\alpha(T - T_0))`}\n                        
    \n                        \n                    \n                        
    \n                            Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito.\n                        
    \n                        
    \n                            Per farlo, cattura cariche positive e negative sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro.\n                        
    \n                        
    \n                            Ha una capacità caratteristica, che in un condensatore a facce piane parallele è:\n                        
    \n                        
    \n                            {r`C = \\frac{q_{massima}}{\\Delta V}`}\n                        
    \n                        
    \n                            Condensatori di capacità maggiore immagazzinano più potenziale con meno carica.\n                        
    \n                        
    \n                            La capacità aumenta se viene messo qualcosa tra le armature:\n                        
    \n                        
    \n                            {r`C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}`}\n                        
    \n                        
    \n                            Dove {r`\\kappa`} è la costante dielettrica relativa del materiale inserito, {r`A`} l'area di una armatura e {r`s`} la distanza tra le due armature.\n                        
    \n                        
    \n                            Se il campo elettrico creatosi tra le due armature supera la rigidità dielettrica del condensatore, la carica immagazzinata viene persa e ha luogo un breakdown.\n                        
    \n                        
    \n                            La sua unità di misura è il Farad ({r`Fa`})\n                        
    \n                        \n                    \n                        
    \n                            Misura la corrente elettrica se messo in serie.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)\n                        
    \n                        \n                    \n                        
    \n                            Misura la differenza di potenziale se messo in parallelo.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per nodo si intende un qualsiasi punto del circuito.\n                        
    \n                        
    \n                            Da un nodo entra ed esce la stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito.\n                        
    \n                        
    \n                            In una maglia chiusa, la somma delle differenze di potenziale è 0.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Più parti di circuito sono in serie se sono consecutive e senza biforcazioni.\n                        
    \n                        
    \n                            Parti di circuito in serie sono attraversate dalla stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Più parti di circuito sono in parallelo tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo. \n                        
    \n                        
    \n                            Parti di circuito in parallelo hanno la stessa differenza di potenziale.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:\n                        
    \n                        
    \n                            {r`R_{serie} = \\sum_{i=1}^{n} R_i`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:\n                        
    \n                        
    \n                            {r`R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:\n                        
    \n                        
    \n                            {r`C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:\n                        
    \n                        
    \n                            {r`C_{parallelo} = \\sum_{i=1}^{n} C_n`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente.\n                        
    \n                        
    \n                            {r`\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}`} ({r`\\frac{N}{A^2}`})\n                        
    \n                        \n                    \n                        
    \n                            Come un campo elettrico, ma per i magneti.\n                        
    \n                        
    \n                            Il suo simbolo è {r`B`}, e la sua unità di misura è il Tesla (T).\n                        
    \n                        \n                    \n                        
    \n                            È \"quanto\" campo magnetico attraversa un percorso chiuso.\n                        
    \n                        
    \n                            Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i \"sottoflussi\" magnetici calcolati sui suoi lati.\n                        
    \n                        
    \n                            {r`\\Phi_{B_{i}} = \\vec{B} \\cdot \\vec{L}_n = B \\cdot L_i \\cdot \\sin(\\alpha) = B_\\parallel \\cdot L_i`}\n                        
    \n                        
    \n                            {r`\\Phi_{B} = \\sum_{i=0}^{n_{lati}} \\Phi_{Bn}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Weber ({r`Wb = T \\cdot m^2`}).\n                        
    \n                        \n                    \n                        
    \n                            Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo.\n                        
    \n                        
    \n                            Ovvero, non esistono monopoli magnetici.\n                        
    \n                        \n                    \n                        
    \n                            L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Phi_B = \\mu_0 \\cdot I`}\n                        
    \n                        \n                    \n                \n                    Forza magnetica su carica puntiforme (Forza di Lorentz)}>\n                        
    \n                            I campi magnetici applicano una forza sulle cariche vicine:\n                        
    \n                        
    \n                            {r`\\vec{F}_{B} = q \\cdot (\\vec{v} \\times \\vec{B})`}\n                        
    \n                        
    \n                            Dove {r`\\vec{B}`} è l'intensità del campo magnetico e {r`\\vec{v}`} la velocità della carica considerata.\n                        
    \n                        
    \n                            Si ha una forza massima se la velocità è perpendicolare al campo magnetico.\n                        
    \n                        
    \n                            In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.\n                        
    \n                        \n                    \n                        
    \n                            I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:\n                        
    \n                        
    \n                            {r`\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})`} [1]\n                        
    \n                        
    \n                            Dove {r`I`} è la corrente elettrica, {r`\\vec{L}`} è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.\n                        
    \n                        \n                    \n                        
    \n                            Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.\n                        
    \n                        
    \n                            All'interno del solenoide si crea un campo (quasi) uniforme:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}`}\n                        
    \n                        \n                    \n                        
    \n                            Caso particolare della Legge di Ampère.\n                        
    \n                        
    \n                            Il modulo del campo magnetico B prodotto da un filo in cui passa una corrente continua I alla distanza s è:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}`}\n                        
    \n                        
    \n                            Il campo magnetico così creato gira attorno al filo in senso antiorario.\n                        
    \n                        
    \n                            Due fili attraversati dalla stessa corrente si attraggono, due fili attraversati da correnti opposte si respingono.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo. \n                        
    \n                        
    \n                            La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore. \n                        
    \n                        
    \n                            Essa vale:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = v \\cdot B \\cdot L`}\n                        
    \n                        
    \n                            Dove v è la velocità del conduttore, B è l'intensità del campo magnetico ed L è la lunghezza del conduttore.\n                        
    \n                        \n                    \n                        
    \n                            In un campo magnetico {r`B`} uniforme e perpendicolare al piano di una spira di area {r`A`}, il flusso magnetico si può determinare con la Legge di Faraday-Neumann-Lenz:\n                        
    \n                        
    \n                            {r`\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{\\Delta \\Phi_B}{\\Delta t}`}\n                        
    \n                        
    \n                            Il meno è dovuto alla Legge di Lenz, che specifica qualitativamente il verso della forza elettromotrice indotta.\n                        
    \n                        \n                    \n                        
    \n                            In un solenoide, la forza elettromotrice indotta è uguale a:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{N \\cdot \\Delta \\Phi_{B_{spira}}}{\\Delta t} = - \\frac{N \\cdot B \\cdot A \\cdot cos(\\alpha)}{\\Delta t}`}\n                        
    \n                        
    \n                            Dove {r`N`} è il numero delle spire del solenoide.\n                        
    \n                        \n                    \n                        
    \n                            Correnti o campi elettrici variabili creano un campo magnetico.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nel vuoto, il campo elettrico {r`E`} e il campo magnetico {r`B`} sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo.\n                        
    \n                        
    \n                            Si dice quindi che sono onde elettromagnetiche.\n                        
    \n                        
    \n                            Esse sono legate dalla relazione:\n                        
    \n                        
    \n                            {r`E = c \\cdot B`}\n                        
    \n                        
    \n                            Dove {r`c`} è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:\n                        
    \n                        
    \n                            {r`c = \\frac{1}{\\sqrt{\\epsilon_0 \\cdot \\mu_0}} = 3.00 \\cdot 10^8 \\frac{m}{s}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`A(t) = A_{max} \\cdot \\sin \\left ( \\frac{2 \\pi}{\\lambda} - \\omega t + \\phi \\right )`}\n                        
    \n                        
    \n                            Dove {r`A_{max}`} è l'ampiezza massima che può avere l'onda, {r`\\frac{2 \\pi}{\\lambda} = \\left | \\vec{k} \\right |`} è il vettore d'onda, {r`\\omega`} la frequenza angolare e {r`\\phi`} la fase.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            I solidi, se portati ad alta temperatura, emettono luce con uno spettro continuo.\n                        
    \n                        
    \n                            I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda. \n                        
    \n                        
    \n                            In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:\n                        
    \n                        
    \n                            {r`\\frac{1}{\\lambda} = R \\left ( \\frac{1}{4} - \\frac{1}{n^2} \\right )`}\n                        
    \n                        
    \n                            Con {r`R = 1.097 \\cdot 10^7 \\frac{1}{m}`}, detta costante di Rydberg, e {r`n`} un numero intero.\n                        
    \n                        \n                    \n                        
    \n                            Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori. \n                        
    \n                        
    \n                            Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata.\n                        
    \n                        
    \n                            Energia, momento angolare e raggio sono quantizzati.\n                        
    \n                        
    \n                            Nota costante quantica è {r`h`}, la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come {r`\\hbar = \\left ( \\frac{h}{2 \\pi} \\right )`}.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            L'energia degli elettroni è quantizzata.\n                        
    \n                        
    \n                            Inoltre, per essi è valido che:\n                        
    \n                        
    \n                            {r`m \\cdot v_n \\cdot 2 \\pi \\cdot r = n \\cdot h`}\n                        
    \n                        
    \n                            Ancora, il raggio delle orbite è uguale a:\n                        
    \n                        
    \n                            {r`r_n = n^2 \\cdot a_0 = n^2 \\cdot \\frac{\\hbar}{m_{elettrone} \\cdot k \\cdot e^2} `}\n                        
    \n                        
    \n                            Con {r`a_0 = \\left ( \\frac{h}{2 \\pi} \\right )^2 \\cdot \\frac{1}{m_{elettrone} \\cdot k \\cdot e^2} = 5.29 \\cdot 10^{-11} m`}.\n                        
    \n                        
    \n                            Infine, in ogni stato, l'energia è pari a:\n                        
    \n                        
    \n                            {r`E_n = \\frac{1}{n^2} \\cdot E_1 = - \\frac{1}{n^2} \\cdot \\frac{a_0^2}{2 \\cdot m \\cdot \\hbar^4} = - \\frac{1}{n^2} \\cdot \\frac{m_{elettrone} \\cdot k^2 \\cdot e^4}{2 \\cdot \\hbar^2}`}\n                        
    \n                        
    \n                            Due elettroni non possono occupare lo stesso stato.\n                        
    \n                        
    \n                            Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda.\n                        
    \n                        
    \n                            Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Refactor this\n                        
    \n                        
    \n                            Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di {r`10^1 eV`}, allora il corpo è un isolante.\n                        
    \n                        
    \n                            Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore.\n                        
    \n                        
    \n                            Se il gap è invece dell'ordine di grandezza di {r`1 eV`}, allora il corpo è un semiconduttore.\n                        
    \n                        \n                    \n                        
    \n                            Legami in cui mancano elettroni.\n                        
    \n                        
    \n                            Elettroni di altri legami possono spostarsi per colmare le lacune, creandone altre, e spostandole in direzione opposta a quella della corrente.\n                        
    \n                        \n                    \n                        
    \n                            Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:\n                        
    \n                        
      \n                            
    • Con numero atomico maggiore, un semiconduttore di tipo N con elettroni in eccesso liberi di scorrere.
      • \n                            
    • Con numero atomico minore, un semiconduttore di tipo P con lacune in eccesso libere di catturare elettroni da altri legami.
      • \n                        
    \n                        
    \n                            Maggiore impurezza porta a maggiore conduttività.\n                        
    \n                        \n                    \n                        
    \n                            Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di elettroni e lacune.\n                        
    \n                        \n                    \n                Ottica (non l'abbiamo fatta)}>\n                    \n                        
    \n                            I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.\n                        
    \n                        \n                    \n                        
    \n                            Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna.\n                        
    \n                        
    \n                            Le onde assorbite vengono poi riemesse sotto forma di un onda di {r`\\lambda`} variabile in base alla temperatura.\n                        
    \n                        
    \n                            {r`\\lambda_{max} \\cdot T`} è costante.\n                        
    \n                        \n                    \n                        
    \n                            L'energia assorbita e emessa dai corpi neri è quantizzata.\n                        
    \n                        \n                    \n                        
    \n                            Un onda magnetica con un quanto di energia è detta fotone:\n                        
    \n                        
    \n                            {r`E_{fotone} = h \\cdot f`}\n                        
    \n                        \n                    \n                        
    \n                            A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale.\n                        
    \n                        
    \n                            Perchè avvenga, la frequenza deve essere maggiore di una certa soglia.\n                        
    \n                        
    \n                            Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza.\n                        
    \n                        
    \n                            Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.\n                        
    \n                        \n                    \n            
    \n        )\n\t}\n}\n\n\n// WEBPACK FOOTER //\n// ./pages/fisica.js","import style from \"./markdown.css\";\nimport { Component } from 'preact';\nimport showdown from \"showdown\";\n\nexport default class Markdown extends Component {\n\trender() {\n        let converter = new showdown.Converter();\n        converter.setFlavor(\"github\");\n        let html = converter.makeHtml(`${this.props.children}`);\n        // noinspection CheckTagEmptyBody\n        return 
    ;\n\t}\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/markdown.js","import style from './vldigeometria.css';\r\nimport { Component } from 'preact';\r\nimport Markdown from '../components/markdown';\r\nimport Panel from '../components/panel';\r\n\r\nconst r = String.raw;\r\n\r\nexport default class VlDiGeometria extends Component {\r\n\trender() {\r\n\t\t//Imported from unimore-info-wiki\r\n\t\treturn (\r\n\t\t\t
    \r\n                
    Videolezioni di Geometria
    \r\n                \r\n                    {r`\r\nTutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).\r\n\r\nPer comodità, ho estratto l'url sorgente del video dall'embed presente nella rispettiva pagina.\r\n\r\n1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\r\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\r\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\r\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\r\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\r\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\r\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\r\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\r\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\r\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\r\n11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\r\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\r\n13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\r\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\r\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\r\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\r\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\r\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\r\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\r\n20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\r\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\r\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\r\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\r\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\r\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\r\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\r\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\r\n\r\nNell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\r\n                    `}\r\n                \r\n\t\t\t
    \r\n\t\t);\r\n\t}\r\n}\r\n\r\n\n\n\n// WEBPACK FOOTER //\n// ./pages/vldigeometria.js","import style from './mingwinstall.css';\r\nimport { Component } from 'preact';\r\nimport Panel from '../components/panel';\r\n\r\nexport default class MingwInstall extends Component {\r\n\trender() {\r\n\t\t//Imported from unimore-info-wiki\r\n\t\treturn (\r\n\t\t\t
    \r\n                
    Come installare MinGW
    \r\n                \r\n\t\t\t\t\t
     Scaricate l'installer ufficiale,\r\n\t\t\t\t\t\ted eseguitelo.
    \"\"/\r\n\t\t\t\t\t
     Dovrebbe comparire questa schermata. Cliccate su Install, poi scegliete una cartella di installazione\r\n\t\t\t\t\t\t(ricordatevela!) e poi Continue. Lasciate stare le altre opzioni, dovrebbero essere tutte spuntate,\r\n\t\t\t\t\t\ttranne For all users, che dovrebbe essere disattivato.
    \"\"/\r\n\t\t\t\t\t
     Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto\r\n\t\t\t\t\t\tContinue. Premetelo.
    \"\"/\r\n\t\t\t\t\t
     Dovrebbe apparirvi questa finestra. L'installer di MinGW è una specie di gestore pacchetti (tipo apt su\r\n\t\t\t\t\t\tUbuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalità.
    \"\"/\r\n\t\t\t\t\t
     Nel nostro caso, dovrebbero servirci mingw32-base-bin (per il C e alcune librerie C++) e\r\n\t\t\t\t\t\tmingw32-gcc-g++-bin (per il C++). Cliccate, quindi, sui due quadratini corrispondenti, e premete\r\n\t\t\t\t\t\tMark for Installation. Dovrebbe comparire una freccia gialla sul quadratino.
    \"\"/\r\n\t\t\t\t\t
     Ora, è il momento di installare i pacchetti. Aprite il menù Installation, poi premete\r\n\t\t\t\t\t\tApply Changes, e di nuovo Apply.
    \"\"/\r\n\t\t\t\t\t
     Lasciate che scarichi, ci vorrà un po'. Guardatevi un video nel frattempo, fatevi una partitina a qualcosa, tornate\r\n\t\t\t\t\t\tdopo circa 10 minuti.
    \"\"/\r\n\t\t\t\t\t
     Una volta installato, dobbiamo aggiungere g++ ai programmi eseguibili da Prompt dei Comandi: premete il\r\n\t\t\t\t\t\ttasto Windows, e scrivete PATH. Windows dovrebbe trovarvi automaticamente quell'opzione.
    \r\n\t\t\t\t\t\"\"/\r\n\t\t\t\t\t
     Dentro la finestra di Proprietà del Sistema, premete Variabili d'ambiente.
    \"\"/\r\n\t\t\t\t\t
     Trovate la variabile d'ambiente globale Path, e fateci doppio click per modificarla.
    \"\"/\r\n\t\t\t\t\t
     Ora dovreste vedere l'elenco di tutte le cartelle contenenti programmi eseguibili da terminale: dobbiamo aggiungere\r\n\t\t\t\t\t\tquella di MinGW! Premete Sfoglia.
    \"\"/\r\n\t\t\t\t\t
     Trovate la cartella in cui avete installato MinGW (vi avevo detto di ricordarvela!); entrateci, poi selezionate la\r\n\t\t\t\t\t\tsottocartella bin e premete OK su tutte le finestre che avete aperto fino ad ora,\r\n\t\t\t\t\t\tchiudendole.
    \r\n\t\t\t\t\t
     Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione\r\n\t\t\t\t\t\tgcc e g++ sul Prompt dei Comandi, e potete finalmente creare dei file .exe! 
    \r\n\t\t\t\t    \r\n\t\t\t
    \r\n\t\t);\r\n\t}\r\n}\r\n\r\n\n\n\n// WEBPACK FOOTER //\n// ./pages/mingwinstall.js","import style from './copyright.css';\r\nimport { Component } from 'preact';\r\n\r\nexport default class Copyright extends Component {\r\n\trender() {\r\n\t\treturn 
    © 2019 - Stefano Pigozzi - CC BY-SA 4.0 - Codice sorgente
    ;\r\n\t}\r\n}\n\n\n// WEBPACK FOOTER //\n// ./components/copyright.js","import style from \"./theorem.css\";\r\nimport Panel from \"./panel.js\";\r\n\r\nexport default class Theorem extends Panel {\r\n    getStyle() {\r\n        return super.getStyle() + \" \" + style.theorem;\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/theorem.js","import style from \"./hypothesis.css\";\r\nimport {Component} from \"preact\";\r\n\r\nexport default class Hypothesis extends Component {\r\n    render() {\r\n        return (\r\n            
    \r\n                
    \r\n                    Ipotesi\r\n                
    \r\n                {this.props.children}\r\n            
    \r\n        )\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/hypothesis.js","import style from \"./thesis.css\";\r\nimport {Component} from \"preact\";\r\n\r\nexport default class Thesis extends Component {\r\n    render() {\r\n        return (\r\n            
    \r\n                
    \r\n                    Tesi\r\n                
    \r\n                {this.props.children}\r\n            
    \r\n        )\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/thesis.js","import style from \"./proof.css\";\r\nimport {Component} from \"preact\";\r\n\r\nexport default class Proof extends Component {\r\n    render() {\r\n        return (\r\n            
    \r\n                
    \r\n                    Dimostrazione\r\n                
    \r\n                {this.props.children}\r\n            
    \r\n        )\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/proof.js","import style from \"./example.css\";\nimport {Component} from \"preact\";\n\nexport default class Example extends Component {\n    render() {\n        return (\n            
    \n                {this.props.children}\n            
    \n        )\n    }\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/example.js","import style from './statistica.css';\nimport { Component } from 'preact';\nimport Latex from '../components/latex';\nimport Panel from '../components/panel';\nimport Split from '../components/split';\nimport Todo from '../components/todo';\nimport Theorem from \"../components/theorem\";\nimport Hypothesis from \"../components/hypothesis\";\nimport Thesis from \"../components/thesis\";\nimport Proof from \"../components/proof\";\nimport Example from \"../components/example\";\nimport Plus from \"../components/plus\";\nimport Minus from \"../components/minus\";\n\nconst r = String.raw;\n\nexport default class Statistica extends Component {\n\trender() {\n\t    /*\n            \n                \n                    
    \n                        Gruppo intero di oggetti di cui si cercano informazioni.\n                    
    \n                    \n                \n                    
    \n                        Popolazione finita di oggetti concreti che possono essere campionati ciascuno solo una volta.\n                    
    \n                    \n                \n                    
    \n                        Popolazione di valori ottenuti da prove sperimentali indipendenti ripetute più volte.\n                    
    \n                    \n                \n            \n                \n                    
    \n                        Sottoinsieme della popolazione che contiene gli oggetti che si sono osservati.\n                    
    \n                    \n                Simple random sample}>\n                    
    \n                        Campione di una data dimensione in cui qualsiasi selezione di n elementi ha la stessa probabilità di costituire il campione.\n                    
    \n                    \n                Sample of convenience}>\n                    
    \n                        Campione ottenuto in un modo casuale non ben definito.\n                    
    \n                    \n                Sample with replacement}>\n                    
    \n                        Campione ottenuto sostituendo nella popolazione gli elementi estratti con dei nuovi elementi.\n                    
    \n                    
    \n                        Dire che un campione è ottenuto with replacement è equivalente a dire che la popolazione che si sta campionando è infinita, e quindi che tutti gli elementi sono indipendenti.\n                    
    \n                    \n                \n                    
    \n                        Campione ottenuto da una popolazione in cui certi elementi hanno più probabilità di essere stati selezionati di altri.\n                    
    \n                    \n                Stratified random sample}>\n                    
    \n                        Campione ottenuto da un sottoinsieme della popolazione detto strato.\n                    
    \n                    \n                Cluster sample}>\n                    
    \n                        Campione ottenuto selezionando più cluster di elementi alla volta.\n                    
    \n                    \n                \n            \n                Sampling variation}>\n                    
    \n                        Differenza di informazioni presente tra due campioni diversi della stessa popolazione.\n                    
    \n                    \n                \n                    
    \n                        Gli elementi in un campione sono indipendenti se gli elementi estratti in precedenza non influsicono significativamente sulle probabilità di estrazione dell'elemento successivo.\n                    
    \n                    \n                \n            \n                \n                    
    \n                        Esperimento in cui c'è una sola popolazione da cui vengono estratti campioni.\n                    
    \n                    
    \n                        Serve per verificare delle condizioni.\n                    
    \n                    \n                \n                    
    \n                        Esperimento in cui sono presenti più popolazioni (aventi caratteristiche differenti una dall'altra dette fattori) da cui vengono estratti campioni.\n                    
    \n                    
    \n                        Serve per capire quali fattori influenzano il risultato dell'esperimento.\n                    
    \n                    \n                \n            \n                Numerico o quantitativo}>\n                    Il dato descrive un valore numerico relativo all'elemento, come ad esempio una quantità fisica.\n                \n                Categorico o qualitativo}>\n                    Il dato indica una categoria a cui appartiene l'elemento, come ad esempio il suo colore.\n                \n            \n\t     */\n        return (\n            
    \n                
    Statistica ed Elementi di Probabilità
    \n                \n                    \n                        
    \n                            {r`P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`P(E) = \\frac{successi}{prove\\ totali}`}\n                        
    \n                        \n                    \n                        
    \n                            Il prezzo che un individuo coerente riterrebbe equo per ricevere 1 nel caso l'evento si verificasse e 0 nel caso l'evento non si verificasse.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"omegone\"\n                        
    \n                        
    \n                            L'insieme di tutti gli esiti possibili di un esperimento.\n                        
    \n                        
    \n                            {r`\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"omeghino\"\n                        
    \n                        
    \n                            Un elemento dello spazio campionario.\n                        
    \n                        
    \n                            {r`\\omega = 1`}\n                        
    \n                        \n                    \n                        
    \n                            \"e\"\n                        
    \n                        
    \n                            Un sottoinsieme dello spazio campionario.\n                        
    \n                        
    \n                            {r`E = \\left \\{ 1, 2 \\right \\}`}\n                        
    \n                        
    \n                            Lo spazio campionario stesso è un evento certo.\n                        
    \n                        \n                    \n                        
    \n                            \"not e\"\n                        
    \n                        
    \n                            Il complementare di un sottoinsieme.\n                        
    \n                        
    \n                            {r`\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e intersecato effe\"\n                        
    \n                        
    \n                            L'intersezione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\left \\{ 1 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e unito a effe\"\n                        
    \n                        
    \n                            L'unione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e meno effe\"\n                        
    \n                        
    \n                            {r`E \\setminus F = E \\cap \\bar{F}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e contenuto in effe\"\n                        
    \n                        
    \n                            L'inclusione del primo insieme in un altro.\n                        
    \n                        
    \n                            {r`E \\subseteq F`}\n                        
    \n                        
    \n                            Se si verifica E, allora si verifica anche F.\n                        
    \n                        \n                    \n                        
    \n                            \"e è impossibile\"\n                        
    \n                        
    \n                            Un sottoinsieme vuoto.\n                        
    \n                        
    \n                            {r`E = \\emptyset`}\n                        
    \n                        \n                    \n                        
    \n                            \"e ed effe si escludono mutualmente\"\n                        
    \n                        
    \n                            La disgiunzione di due insiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"famiglia effe\"\n                        
    \n                        
    \n                            I sottoinsiemi dello spazio campionario formano una famiglia di sottoinsiemi detta famiglia degli eventi.\n                        
    \n                        
    \n                            {r`\\mathcal{F}`}\n                        
    \n                        
    \n                            Qualsiasi sottoinsieme appartenente a {r`\\mathcal{F}`} è considerato un evento.\n                        
    \n                        \n                    {r`\\sigma`}-algebra}>\n                        
    \n                            \"sigma algebra\"\n                        
    \n                        
    \n                            Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta {r`\\sigma`}-algebra:\n                        
    \n                        
      \n                            
    1. \n                                Lo spazio campionario è un evento: {r`\\Omega \\in \\mathcal{F}`}\n                            
      2. \n                            
    2. \n                                Se un sottoinsieme è un evento, allora anche il suo complementare lo è: {r`E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}`}\n                            
      3. \n                            
    3. \n                                Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: {r`(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}`}\n                            
      4. \n                        
    \n                        
    \n                            Un esempio: {r`E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"la partizione e composta da e uno, e due, e tre...\"\n                        
    \n                        
    \n                            Un insieme di esiti e eventi:\n                        
    \n                        
      \n                            
    • Finito.
      • \n                            
    • In cui tutti gli eventi hanno probabilità diversa da 0.
      • \n                            
    • In cui tutti gli eventi sono mutualmente esclusivi.
      • \n                            
    • In cui l'unione di tutti i suoi elementi copre lo spazio campionario.
      • \n                        
    \n                        
    \n                            La partizione {r`E_i`} è composta dagli eventi {r`E_1`}, {r`E_2`}, {r`E_3`}, fino a {r`E_n`}.\n                        
    \n                        \n                            Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            La probabilità di un evento è un numero tra 0 e 1.\n                        
    \n                        
    \n                            {r`\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dello spazio campionario è sempre 1.\n                        
    \n                        
    \n                            {r`P(\\Omega) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità.\n                        
    \n                        
    \n                            {r`P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato.\n                        
    \n                        
    \n                            {r`P(\\bar{E}) = 1 - P({E})`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso.\n                        
    \n                        
    \n                            {r`F \\subseteq E \\implies P(F) \\leq P(E)`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione.\n                        
    \n                        
    \n                            {r`P(E \\cup F) = P(E) + P(F) - P(E \\cap F)`}\n                        
    \n                        \n                            Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi.\n                        
    \n                        
    \n                            {r`P(E) = \\frac{len(E)}{len(\\Omega)}`}\n                        
    \n                        \n                    \n                        
    \n                            Gli spazi campionari possono avere un numero infinito di esiti: sono equiprobabili geometrici se nessun esito è privilegiato rispetto agli altri.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}^{r}_{n, k} = n^k`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo n numeri e guardo in quanti ordini diversi li posso mettere.\n                        
    \n                        
    \n                            {r`\\boldsymbol{P}_n = n!`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"E dato F\"\n                        
    \n                        
    \n                            La probabilità che si verifichi E sapendo che si è già verificato F.\n                        
    \n                        
    \n                            {r`P(E|F) = \\frac{P(E \\cap F)}{P(F)}`}\n                        
    \n                        \n                            Ricorda vagamente le pipe di bash, però al contrario...\n                        \n                        \n                    \n                        
    \n                            Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:\n                        
    \n                        
    \n                            {r`P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione.\n                        
    \n                        
    \n                            {r`P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)`}\n                        
    \n                        \n                    \n                        
    \n                            La legge delle alternative funziona anche quando ad essere partizionato è un evento:\n                        
    \n                        
    \n                            {r`P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)`}\n                        
    \n                        \n                    \n                        
    \n                            Tramite la formula di Bayes possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:\n                        
    \n                        
    \n                            {r`P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}`}\n                        
    \n                        \n                            In pratica, invertiamo gli eventi.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            \"eventi indipendenti a due a due\"\n                        
    \n                        
    \n                            Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro.\n                        
    \n                        
    \n                            {r`P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)`}\n                        
    \n                        \n                    \n                        
    \n                            \"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque...\"\n                        
    \n                        
    \n                            Si può verificare l'indipendenza di più eventi alla volta:\n                        
    \n                        
    \n                            {r`P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)`}\n                        
    \n                        
    \n                            Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.\n                        
    \n                        \n                    \n                        
    \n                            Un insieme di n eventi è una famiglia di eventi indipendenti se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.\n                        
    \n                        \n                            Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. {r`X(\\omega) : \\Omega \\to \\mathbb{R}`}.\n                        
    \n                        \n                    Insieme di ripartizione}>\n                        
    \n                            Ad ogni variabile aleatoria sono associati gli eventi {r`A_t = \\{ \\omega | X(\\omega) \\leq t \\}`}, che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a t.\n                        
    \n                        
    \n                            Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:\n                        
    \n                        
    \n                            {r`\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}`}\n                        
    \n                        \n                            All'aumentare di t, l'insieme conterrà sempre più elementi.\n                        \n                        \n                    \n                        
    \n                            \"supporto di X\"\n                        
    \n                        
    \n                            Il codominio della variabile aleatoria è il suo supporto.\n                        
    \n                        
    \n                            Per indicare che un valore x_0 appartiene al supporto di X, si usa la notazione X \\mapsto x_0.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La funzione probabilità {r`p_X : X \\to [0, 1]`} di una variabile aleatoria discreta X è la funzione che associa ad ogni esito la sua probabilità:\n                        
    \n                        
    \n                            {r`p_X (x) = \\begin{cases}\n                            P([X = x]) \\quad se\\ X \\mapsto x \\\\\n                            0 \\qquad \\qquad \\quad se\\ X \\not\\mapsto x\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione densità {r`f_X : X \\to [0, 1]`} di una variabile aleatoria continua X è l'equivalente continuo della funzione probabilità:\n                        
    \n                        
    \n                            {r`P([a < X \\leq b]) = \\int_a^b f_X (x) dx`}\n                        
    \n                        
    \n                            A differenza della funzione probabilità, è possibile che la funzione densità non esista per una certa variabile aleatoria.\n                        
    \n                        \n                            Rappresenta \"quanta\" probabilità c'è in un'unità di x!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Ogni variabile aleatoria ha una funzione di ripartizione {r`F_X : \\mathbb{R} \\to [0, 1]`} associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a t:\n                        
    \n                        
    \n                            Si può dire che essa rappresenti la probabilità dell'evento {r`A_t`}:\n                        
    \n                        
    \n                            {r`F_X (t) = P(A_t) = \\begin{cases}\n                            \\sum_{i = 0}^{t} p_X (x_i) \\quad nel\\ discreto\\\\\n                            \\\\\n                            \\int_{-\\infty}^t f_X (x) dx \\quad nel\\ continuo\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
      \n                            
    • È sempre monotona crescente (non strettamente).

      • \n                            
    • Vale 0 a -\\infty e 1 a +\\infty.

      • \n                            
    • È continua da destra: {r`\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:\n                        
    \n                        
    \n                            {r`P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.\n                        
    \n                        \n                    \n                        
    \n                            Nel continuo applichiamo la formula dell'integrazione per sostituzione:\n                        
    \n                        
    \n                            {r`f_Y (y) = \\int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`}\n                        
    \n                        \n                    \n                        
    \n                            Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione random() che restituisce numeri da 0 a 1 con una distribuzione lineare.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Ogni variabile aleatoria che ha una funzione di ripartizione e un supporto finito ha anche una media (o valore medio o atteso):\n                        
    \n                        
    \n                            {r`E(X) = \\int_0^{+infty} (1 - F_X (t)) dt - \\int_{-\\infty}^{0} F_X (t) dt`}\n                        
    \n                        
    \n                            Nel discreto, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\sum_i P(X = x_i) \\cdot x_i`}\n                        
    \n                        
    \n                            Nel continuo, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\int_{-\\infty}^{+\\infty} f_X (x) \\cdot x \\cdot dx`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Valore per cui la funzione probabilità o funzione densità è massima.\n                        
    \n                        \n                    \n                        
    \n                            Il quantile {r`x_{\\alpha}`} di ordine {r`0 \\leq \\alpha \\leq 1`} della variabile aleatoria X è il più piccolo numero tale che:\n                        
    \n                        
    \n                            \n                                {r`P([X < x_{\\alpha}]) \\leq \\alpha \\leq P([X \\leq x_{\\alpha}])`}\n                            \n                        
    \n                        
    \n\n                        
    \n                        
    \n                            Il quantile di ordine 0.5 {r`x_{0.5}`} è detto mediana.\n                        
    \n                        
    \n                            I quantili di ordine 0.25 {r`x_{0.25}`} e 0.75 {r`x_{0.75}`} sono detti quartili.\n                        
    \n                        
    \n                            I quantili di ordine {r`\\frac{n}{100}`} sono detti n-esima percentile.\n                        
    \n                        \n                    \n                        
    \n                            È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:\n                        
    \n                        
    \n                            {r`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Data una variabile aleatoria non-negativa:\n                        
    \n                        
    \n                            {r`\\forall k > 0, P([X \\geq k]) \\leq \\frac{E(X)}{k}`}\n                        
    \n                        
    \n                            Divide in due parti ({r`P(X < k)`} e {r`P(X \\geq k)`}) la funzione X, la cui media risulterà uguale a:\n                        
    \n                        
    \n                            {r`E(X) = \\overline{k} \\cdot P(X < k) + k \\cdot P(X \\geq k)`}\n                        
    \n                        \n                    \n                        
    \n                            \"disuguaglianza di cebicev\"\n                        
    \n                        
    \n                            Se la variabile aleatoria X ha media e varianza, allora la probabilità che essa abbia un valore a più di {r`\\epsilon`} di distanza dal valore medio è minore o uguale a {r`\\frac{Var(X)}{\\epsilon^2}`}.\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| \\geq \\epsilon]) \\leq \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        
    \n                            E anche:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| < \\epsilon]) \\geq 1 - \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        \n                            Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Il momento k-esimo di una variabile aleatoria è:\n                        
    \n                        
    \n                            \n                                {r`\\mu_k = E ( X^k ) = \\begin{cases}\n                                \\sum_i x_i^k p_X (x_i) \\qquad nel\\ discreto\\\\\n                                \\\\\n                                \\int_{-\\infty}^{+\\infty} x^k f_X (x) dx \\qquad nel\\ continuo\n                                \\end{cases}`}\n                            \n                        
    \n                        \n                            La media di una variabile aleatoria è anche il suo primo momento.\n                        \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti è:\n                        
    \n                        
    \n                            {r`m_X (t) = E( e^{t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Laplace della variabile aleatoria di X.\n                        
    \n                        \n                    \n                        
    \n                            La funzione caratteristica è:\n                        
    \n                        
    \n                            {r`H_X (t) = E ( e^{i \\cdot t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Fourier della variabile aleatoria di X.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per dire che una variabile ha una certa distribuzione, si usa la notazione:\n                        
    \n                        
    \n                            {r`X \\sim Distribuzione()`}\n                        
    \n                        \n                    \n                        
    \n                            Una prova con solo due possibili esiti: successo e insuccesso.\n                        
    \n                        \n                    \n                        
    \n                            Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che rappresenta una prova di Bernoulli:\n                        
    \n                        
      \n                            
    • vale 1 in caso di successo.
      • \n                            
    • vale 0 in caso di insuccesso.
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Ber(p)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione bernoulliana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0, 1\\} = \\begin{cases}\n                            p \\quad se\\ k = 1\\\\\n                            q \\quad se\\ k = 0\\\\\n                            0 \\quad altrimenti\n                            \\end{cases} = p^x \\cdot q^{1 - k}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di successi di n prove di uno schema di Bernoulli.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Bin(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della binomiale è:\n                        
    \n                        
    \n                            {r`m_X (t) = (q + p \\cdot e^t) ^ n`}\n                        
    \n                        
    \n                            La media di una binomiale è:\n                        
    \n                        
    \n                            {r`E(X) = n \\cdot p`}\n                        
    \n                        
    \n                            La varianza di una binomiale è:\n                        
    \n                        
    \n                            {r`Var(X) = n \\cdot p \\cdot q`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.\n                        
    \n                        
    \n                            Il suo simbolo è Geo(p).\n                        
    \n                        \n                    \n                        
    \n                            La geometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = q^{k - 1} p`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica è:\n                        
    \n                        
    \n                            {r`m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero k di insuccessi consecutivi in uno schema di Bernoulli:\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`Geo(p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = p \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica traslata è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica traslata è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{q}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n \\cdot q}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che, sapendo il numero di successi K e di insuccessi N-K, conta quanti successi si otterrebbero se se ne estraessero n in blocco.\n                        
    \n                        
    \n                            Il suo simbolo è Ipe(N, K, n).\n                        
    \n                        \n                    \n                        
    \n                            La ipergeometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della ipergeometrica è trascurabile.\n                            
    \n                            
    \n                                La media della ipergeometrica è:\n                            
    \n                            
    \n                                {r`E(X) = n \\cdot \\frac{K}{N}`}\n                            
    \n                            
    \n                                La varianza della ipergeometrica è:\n                            
    \n                            
    \n                                {r`Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:\n                        
    \n                        
      \n                            
    • Binomiale: {r`X \\sim Bin(n, p)`}
      • \n                            
    • Il numero di prove tende a infinito: {r`n \\to +\\infty`}
      • \n                            
    • La probabilità di successo tende a 0: {r`p \\to 0`}
      • \n                            
    • La media è finita: {r`E(X) = n \\cdot p \\to \\mu \\neq 0`}
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Poi(\\mu)`}\n                        
    \n                        \n                    \n                        
    \n                            La poissoniana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della poissoniana è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot (e^t - 1)}`}\n                            
    \n                            
    \n                                La media della poissoniana è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della poissoniana è:\n                            
    \n                            
    \n                                {r`Var(X) = \\mu`}\n                            
    \n                            
    \n                                Gli altri momenti della poissoniana sono:\n                            
    \n                            
      \n                                
    1. {r`E(X^2) = \\mu^2 + \\mu`}
      2. \n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una successione di arrivi avvenuti in un certo arco temporale che:\n                        
    \n                        
      \n                            
    • non sono sovrapposti.
      • \n                            
    • hanno intensità {r`\\lambda`} costante.
      • \n                            
    • avvengono indipendentemente gli uni dagli altri.
      • \n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria N_t che conta il numero di arrivi di uno schema di Poisson di intensità {r`\\lambda`} in un intervallo di tempo di durata t.\n                        
    \n                        
    \n                            E' una distribuzione poissoniana con {r`\\mu = t \\cdot \\lambda`}: {r`Poi(t \\cdot \\lambda)`}\n                        
    \n                        \n                            E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo).\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Esp(\\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad x < 0\\\\\n                            \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n                            \\end{cases}`}\n                        
    \n                        
    \n                            L'esponenziale ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`F_X (t) = \\begin{cases}\n                            0 \\qquad \\qquad t < 0\\\\\n                            1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti dell'esponenziale è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}`}\n                        
    \n                        
    \n                            La media dell'esponenziale è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{\\lambda}`}\n                        
    \n                        
    \n                            La varianza dell'esponenziale è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{1}{\\lambda^2}`}\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X > s + t | X > s]) = P([X > t])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima dell'n-esimo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\Gamma(n, \\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            La legge gamma ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n                            \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della legge gamma è:\n                            
    \n                            
    \n                                {r`m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha`}\n                            
    \n                            
    \n                                La media della legge gamma è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{\\alpha}{\\lambda}`}\n                            
    \n                            
    \n                                La varianza della legge gamma è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{\\alpha}{\\lambda^2}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che può assumere qualsiasi valore in un intervallo {r`[a, b]`} in modo equiprobabile.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Uni(a, b)`}\n                        
    \n                        
    \n                            Su di essa vale la seguente proprietà:\n                        
    \n                        
    \n                            {r`P(X \\in (c, d)) = \\frac{d - c}{b - a}`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione uniforme ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                0 \\qquad \\quad altrimenti    \n                            \\end{cases}`}\n                        
    \n                        
    \n                            La distribuzione uniforme ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                0 \\qquad \\quad x < a  \n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                1 \\qquad \\quad x > b\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}`}\n                            
    \n                            
    \n                                La media della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{a + b}{2}`}\n                            
    \n                            
    \n                                La varianza della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{(b - a)^2}{12}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria con una specifica distribuzione.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Nor(\\mu, \\sigma^2)`}.\n                        
    \n                        \n                            \\mu e \\sigma^2 sono rispettivamente la media e la varianza della distribuzione!\n                        \n                        \n                    \n                        
    \n                            La distribuzione normale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione normale è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}`}\n                            
    \n                            
    \n                                La media della distribuzione normale è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della distribuzione normale è:\n                            
    \n                            
    \n                                {r`Var(X) = \\sigma^2`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Qualsiasi normale può essere trasformata in qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione normale standard Z è:\n                        
    \n                        
    \n                            Z \\sim Nor(0, 1)\n                        
    \n                        
    \n                            La sua funzione di ripartizione è detta {r`\\phi(z)`} e vale:\n                        
    \n                        
    \n                            {r`F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx`}\n                        
    \n                        \n                    \n                        
    \n                            Da un quantile {r`z_\\alpha`} della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La distribuzione normale ha una particolare relazione con la distribuzione Gamma:\n                        
    \n                        
    \n                            {r`Z^2 \\sim \\chi^2 (v = 1)`}\n                        
    \n                        \n                    \n                        
    \n                            \"chi-quadro a un grado di libertà\"\n                        
    \n                        
    \n                            Esiste una distribuzione Gamma particolare:\n                        
    \n                        
    \n                            {r`\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)`}\n                        
    \n                        
    \n                            Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:\n                        
    \n                        
    \n                            {r`\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)`}\n                        
    \n                        \n                    \n                        
    \n                            Un'altra funzione particolare è la funzione T di Student:\n                        
    \n                        
    \n                            {r`T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di N rispetto a n, si può dire che:\n                        
    \n                        
    \n                            {r`Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})`}\n                        
    \n                        \n                    \n                        
    \n                            La binomiale non è altro che una poissoniana a tempo discreto, quindi, se n è grande e n \\cdot p è nell'ordine di grandezza delle unità, allora:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Poi(n \\cdot p)`}\n                        
    \n                        \n                    \n                        
    \n                            Per il Teorema di De Moivre-Laplace, se una binomiale ha una n grande e p non vicina a 0 o 1, si può approssimare con:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            Passando da una variabile discreta X a una continua Y, per ogni valore discreto k la probabilità viene \"spalmata\" su tutto l'intervallo {r`(k - \\frac{1}{2}, k + \\frac{1}{2})`}:\n                        
    \n                        
      \n                            
    • {r`P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})`}
      • \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un vettore composto da variabili aleatorie.\n                        
    \n                        
    \n                            Il suo simbolo generalmente è {r`\\boldsymbol{X}`} oppure {r`X, Y`}.\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione congiunta:\n                        
    \n                        
    \n                            {r`F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione marginale:\n                        
    \n                        
    \n                            {r`F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)`}\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori discreti hanno più densità che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una densità congiunta:\n                        
    \n                        
    \n                            {r`p_{X, Y} (x, y) = P(X = x, Y = y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una densità marginale:\n                        
    \n                        
    \n                            {r`p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli A_i:\n                        
    \n                        
    \n                            {r`P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)`}\n                        
    \n                        \n                    \n                        
    \n                            E' possibile calcolare la media di qualsiasi funzione g(X, Y) avente elementi del vettore come variabili:\n                        
    \n                        
    \n                            {r`E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)`}\n                        
    \n                        \n                            Solitamente si calcola la media di x \\cdot y.\n                        \n                        
    \n                            Le medie di più variabili aleatorie si possono sommare:\n                        
    \n                        
    \n                            {r`E(X + Y) = E(X) + E(Y)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un operatore che misura la correlazione di due variabili aleatorie.\n                        
    \n                        
    \n                            Si calcola con il valore atteso dei prodotti delle distanze dalla media:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)`}\n                        
    \n                        
    \n                            Ha diverse proprietà:\n                        
    \n                        
      \n                            
    • Il suo valore nullo è 0: {r`Cov(X, \\alpha) = 0`}
      • \n                            
    • E' commutativa: {r`Cov(X, Y) = Cov(Y, X)`}
      • \n                            
    • E' semplificabile: {r`Cov(X, X) = Var(X)`}
      • \n                            
    • E' lineare: {r`Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)`}
      • \n                            
    • E' distributiva: {r`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Due variabili sono variabili incorrelate se:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = 0`}\n                        
    \n                        
    \n                            Variabili indipendenti sono sempre incorrelate.\n                        
    \n                        \n                    \n                        
    \n                            Una matrice {r`\\boldsymbol{C_X}`} che contiene la covarianza tra tutte le variabili di un vettore aleatorio {r`\\boldsymbol{X}`}:\n                        
    \n                        
    \n                            {r`\n                                \\boldsymbol{C_X} = \n                                \\begin{bmatrix}\n                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n                                \\end{bmatrix}\n                            `}\n                        
    \n                        
    \n                            E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono \\geq 0.\n                        
    \n                        \n                    \n                        
    \n                            Un valore che misura come due variabili aleatorie sono correlate:\n                        
    \n                        
    \n                            {r`\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}`}\n                        
    \n                        
    \n                            E' sempre compreso tra -1 e 1:\n                        
    \n                        
    \n                            {r`-1 \\leq \\rho_{X, Y} \\leq 1`}\n                        
    \n                        
    \n                            Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:\n                        
    \n                        
    \n                            {r`Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La varianza di due variabili aleatorie sommate è:\n                        
    \n                        
    \n                            {r`Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)`}\n                        
    \n                        \n                            Si dimostra applicando le proprietà della covarianza!\n                        \n                        
    \n                            Se più variabili aleatorie X_i sono indipendenti ({r`Cov(X, Y) = 0`}), allora:\n                        
    \n                        
    \n                            {r`Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una n-pla di variabili aleatorie con la stessa distribuzione della variabile aleatoria X (\"popolazione\") ma indipendenti tra loro.\n                        
    \n                        \n                            Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si realizzeranno nel loro valore.\n                        \n                        \n                    \n                        
    \n                            Il valore dato dalla media aritmetica degli n elementi del campione elevati alla potenza k:\n                        
    \n                        
    \n                            {r`M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k `}\n                        
    \n                        
    \n                            Il momento campionario di primo ordine è la media campionaria {r`\\overline{X}_n`}.\n                        
    \n                        \n                    \n                        
    \n                            La media aritmetica dello scarto quadratico medio degli elementi del campione.\n                        
    \n                        
    \n                            Se è noto il valore medio {r`m = E(X)`} di X:\n                        
    \n                        
    \n                            {r`S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2`}\n                        
    \n                        
    \n                            Altrimenti:\n                        
    \n                        
    \n                            {r`S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se calcoliamo la media della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(\\overline{X}_n) = E(X)`}\n                        
    \n                        \n                            Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la varianza della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`Var(\\overline{X}_n) = \\frac{Var(X)}{n}`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la media della varianza campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(S_0^2) = E(S_n^2) = Var(X)`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Se la popolazione X ha una distribuzione normale ({r`X \\sim Nor(\\mu, \\sigma^2)`})...\n                        
    \n                        \n                    \n                        
    \n                            ...allora sappiamo anche la distribuzione della media campionaria!\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e anche della varianza campionaria!\n                        
    \n                        
    \n                            {r`S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)`}\n                        
    \n                        
    \n                            {r`S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e che media campionaria e varianza campionaria sono indipendenti tra loro!\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa funzione di ripartizione della popolazione X, allora essa converge in distribuzione.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} F_{X_n} (x) = F_X (x) \\\\implies X_n \\\\xrightarrow{d} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità della popolazione X, allora essa converge in probabilità.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, \\\\lim_{n \\\\to +\\\\infty} P( | X_n - X | < \\\\epsilon) = 1 \\\\implies X_n \\\\xrightarrow{p} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità a  della popolazione X, allora essa converge quasi certamente.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, P \\left( \\\\lim_{n \\\\to +\\\\infty} | X_n - X | < \\\\epsilon) \\right) = 1 \\\\implies X_n \\\\xrightarrow{qc} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la media del quadrato della distanza tra la successione e la popolazione X uguale a 0, allora essa converge in media quadratica.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} E( | X_n - X |^2 = 0 \\\\implies X_n \\\\xrightarrow{mq} X`}\n                        
    \n                        \n                    \n                        
    \n                            {`\n                                \\\\begin{matrix}\n                                X_n \\\\xrightarrow{mq} X\\\\\\\\\n                                X_n \\\\xrightarrow{qc} X\n                                \\\\end{matrix} \\\\implies X_n \\\\xrightarrow{p} X \\\\implies X_n \\\\xrightarrow{d} X`\n                            }\n                        
    \n                        
    \n                            In più:\n                        
    \n                        
    \n                            {`X_n \\\\xrightarrow{p} x \\\\Longleftrightarrow X_n \\\\xrightarrow{d} x`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in probabilità alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{p} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1`}\n                        
    \n                        
    \n                            {r`P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1`}\n                        
    \n                        \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge quasi certamente alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{qc} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1`}\n                        
    \n                        \n                            Dimostra che l'interpretazione frequentista della probabilità è valida!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in distribuzione a {r`Nor(0, 1) = \\Phi()`}.\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' una somma di bernoulliane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di geometriche, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di altre poissoniane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di esponenziali, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            Se n è grande, allora:\n                        
    \n                        
    \n                            {r`Y = \\sum_{i=1}^{n} X_i`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per indicare parametri sconosciuti di una legge si usa \\theta.\n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria funzione di un campione:\n                        
    \n                        
    \n                            {r`T(\\boldsymbol{X})`}\n                        
    \n                        \n                            Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso {r`T(\\boldsymbol{X}) = \\boldsymbol{X}`}.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una statistica T_n ottenuta da n osservazioni, che stimi i parametri di una legge e sia indipendente da essi.\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è corretto se il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente corretto se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in media quadratica se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in probabilità se:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente normale se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si può usare il metodo dei momenti per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una M a \\theta: {r`\\widehat{\\theta}_M`}\n                        
    \n                        
    \n                            Visto che:\n                        
    \n                        
      \n                            
    • {r`\\theta = g(E(X))`}
      • \n                            
    • {r`\\widehat{E(X)} = \\overline{X}_n`}
      • \n                        
    \n                        
    \n                            Allora:\n                        
    \n                        
    \n                            {r`\\widehat{\\theta}_M = g( \\overline{X}_n )`}\n                        
    \n                        
    \n                            Se {r`\\theta`} non è esprimibile in termini di {r`E(X)`}, si possono usare i momenti successivi {r`M_n^2`}, {r`M_n^3`}, {r`M_n^3`}...\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si può usare il metodo della massima verosomiglianza per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una L a \\theta: {r`\\widehat{\\theta}_L`}\n                        
    \n                        
    \n                            Consiste nel trovare il massimo assoluto {r`\\widehat{\\theta}_L`} della la funzione di verosomiglianza {r`L`}:\n                        
    \n                        
    \n                            {r`L(x_1, ..., x_n; \\theta) = \\prod_{i=1}^n f_X(x_i; \\theta)`}\n                        
    \n                        
    \n                            Gli stimatori di massima verosomiglianza sono asintoticamente corretti, consistenti in probabilità e asintoticamente normali.\n                        
    \n                        \n                    \n                        
    \n                            Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:\n                        
    \n                        
      \n                            
    • Sono asintoticamente corretti.
      • \n                            
    • Sono consistenti in probabilità.
      • \n                            
    • Sono asintoticamente normali.
      • \n                            
    • Sono invarianti: {r`\\widehat{g(\\theta)}_L = g(\\widehat{\\theta}_L)`}
      • \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{p}_M = \\widehat{p}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\mu}_M = \\widehat{\\mu}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\lambda}_M = \\widehat{\\lambda}_L = \\frac{1}{\\overline{X}_n}`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo della massima verosomiglianza:\n                        
    \n                        
      \n                            
    • {r`\\widehat{\\mu}_L = \\overline{X}_n`}

      • \n                            
    • {r`\\widehat{\\sigma^2}_L = \\frac{\\sum (X_i - \\overline{X}_n)^2 }{n}`}
      • \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"intervallo di confidenza al 95%\"\n                        
    \n                        
    \n                            L'intervallo di valori di \\theta all'interno del quale siamo \"più o meno sicuri\" si trovi il valore effettivo:\n                        
    \n                        
    \n                            L'intervallo di confidenza a N della stima {r`\\widehat{W}`} è l'intervallo ]a, b[ tale che:\n                        
    \n                        
    \n                            {r`P( a < W < b ) = N`}\n                        
    \n                        
    \n                            Può anche essere unilatero nel caso limiti la stima in una sola direzione, positiva o negativa.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        
    \n                            {r`t_{\\alpha, v}`} è un quantile della distribuzione di Student di parametro v.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`p \\in \\left[ \\overline{p} - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}}, \\overline{p} + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}} \\right]`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`m \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}} \\right]`}\n                        
    \n                        \n                    \n            
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\t\t\t\tonScriptComplete = function (event) {\n \t\t\t\t\t// avoid mem leaks in IE.\n \t\t\t\t\tscript.onerror = script.onload = null;\n \t\t\t\t\tclearTimeout(timeout);\n \t\t\t\t\tvar chunk = installedChunks[chunkId];\n \t\t\t\t\tif(chunk !== 0) {\n \t\t\t\t\t\tif(chunk) {\n \t\t\t\t\t\t\tvar errorType = event && (event.type === 'load' ? 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}.bind(null, key));\n \t\treturn ns;\n \t};\n\n \t// getDefaultExport function for compatibility with non-harmony modules\n \t__webpack_require__.n = function(module) {\n \t\tvar getter = module && module.__esModule ?\n \t\t\tfunction getDefault() { return module['default']; } :\n \t\t\tfunction getModuleExports() { return module; };\n \t\t__webpack_require__.d(getter, 'a', getter);\n \t\treturn getter;\n \t};\n\n \t// Object.prototype.hasOwnProperty.call\n \t__webpack_require__.o = function(object, property) { return Object.prototype.hasOwnProperty.call(object, property); };\n\n \t// __webpack_public_path__\n \t__webpack_require__.p = \"/\";\n\n \t// on error function for async loading\n \t__webpack_require__.oe = function(err) { console.error(err); throw err; };\n\n \tvar jsonpArray = window[\"webpackJsonp\"] = window[\"webpackJsonp\"] || [];\n \tvar oldJsonpFunction = jsonpArray.push.bind(jsonpArray);\n \tjsonpArray.push = webpackJsonpCallback;\n \tjsonpArray = jsonpArray.slice();\n \tfor(var i = 0; i < jsonpArray.length; i++) webpackJsonpCallback(jsonpArray[i]);\n \tvar parentJsonpFunction = oldJsonpFunction;\n\n\n \t// Load entry module and return exports\n \treturn __webpack_require__(__webpack_require__.s = \"mdyV\");\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./vldigeometria.js\") );\n\t\t\t}, \"route-vldigeometria\");\n\t\t}\n\n\t\texport default Async(load);\n\t","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./statistica.js\") );\n\t\t\t}, \"route-statistica\");\n\t\t}\n\n\t\texport default Async(load);\n\t","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./mingwinstall.js\") );\n\t\t\t}, \"route-mingwinstall\");\n\t\t}\n\n\t\texport default Async(load);\n\t","import { Component } from 'preact';\nimport Router from 'preact-router';\nimport Home from './routes/home';\nimport Fisica from './routes/fisica';\nimport VlDiGeometria from './routes/vldigeometria';\nimport MingwInstall from './routes/mingwinstall';\nimport Copyright from './components/copyright';\nimport Statistica from './routes/statistica';\nimport _style from './index.css';\nimport _manifest from './meta/manifest.json';\nimport _cname from './meta/CNAME';\nimport _nojekyll from './meta/.nojekyll';\nimport {createHashHistory} from \"history\";\n\n// noinspection JSUnusedGlobalSymbols\nexport default class App extends Component {\n\trender() {\n\t\treturn (\n\t\t\t
    \n\t\t\t\t
    Appuntiweb di Steffo
    \n\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\t\n\t\t\t\t\n\t\t\t\t\n\t\t\t
    \n\t\t);\n\t}\n}\n","import style from './copyright.css';\r\nimport { Component } from 'preact';\r\n\r\nexport default class Copyright extends Component {\r\n\trender() {\r\n\t\treturn 
    © 2019 - Stefano Pigozzi - CC BY-SA 4.0 - Codice sorgente
    ;\r\n\t}\r\n}","import { h, Component } from 'preact';\n\nexport default function(req) {\n\tfunction Async() {\n\t\tComponent.call(this);\n\n\t\tlet b, old;\n\t\tthis.componentWillMount = () => {\n\t\t\tb = this.base = this.nextBase || this.__b; // short circuits 1st render\n\t\t\treq(m => {\n\t\t\t\tthis.setState({ child: m.default || m });\n\t\t\t});\n\t\t};\n\n\t\tthis.shouldComponentUpdate = (_, nxt) => {\n\t\t\tnxt = nxt.child === void 0;\n\t\t\tif (nxt && old === void 0 && b) {\n\t\t\t\t// Node.TEXT_NODE\n\t\t\t\tif (b.nodeType === 3) {\n\t\t\t\t\told = b.data;\n\t\t\t\t} else {\n\t\t\t\t\told = h(b.nodeName, {\n\t\t\t\t\t\tdangerouslySetInnerHTML: { __html: b.innerHTML },\n\t\t\t\t\t});\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\told = ''; // dump it\n\t\t\t}\n\t\t\treturn !nxt;\n\t\t};\n\n\t\tthis.render = (p, s) => (s.child ? h(s.child, p) : old);\n\t}\n\t(Async.prototype = new Component()).constructor = Async;\n\treturn Async;\n}\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./home.js\") );\n\t\t\t}, \"route-home\");\n\t\t}\n\n\t\texport default Async(load);\n\t","/**\n * Assign properties from `props` to `obj`\n * @template O, P The obj and props types\n * @param {O} obj The object to copy properties to\n * @param {P} props The object to copy properties from\n * @returns {O & P}\n */\nexport function assign(obj, props) {\n\tfor (let i in props) obj[i] = props[i];\n\treturn /** @type {O & P} */ (obj);\n}\n\n/**\n * Remove a child node from its parent if attached. This is a workaround for\n * IE11 which doesn't support `Element.prototype.remove()`. Using this function\n * is smaller than including a dedicated polyfill.\n * @param {Node} node The node to remove\n */\nexport function removeNode(node) {\n\tlet parentNode = node.parentNode;\n\tif (parentNode) parentNode.removeChild(node);\n}\n","import { cloneElement, createElement, Component, toChildArray } from 'preact';\nimport { exec, prepareVNodeForRanking, assign, pathRankSort } from './util';\n\nlet customHistory = null;\n\nconst ROUTERS = [];\n\nconst subscribers = [];\n\nconst EMPTY = {};\n\nfunction setUrl(url, type='push') {\n\tif (customHistory && customHistory[type]) {\n\t\tcustomHistory[type](url);\n\t}\n\telse if (typeof history!=='undefined' && history[type+'State']) {\n\t\thistory[type+'State'](null, null, url);\n\t}\n}\n\n\nfunction getCurrentUrl() {\n\tlet url;\n\tif (customHistory && customHistory.location) {\n\t\turl = customHistory.location;\n\t}\n\telse if (customHistory && customHistory.getCurrentLocation) {\n\t\turl = customHistory.getCurrentLocation();\n\t}\n\telse {\n\t\turl = typeof location!=='undefined' ? location : EMPTY;\n\t}\n\treturn `${url.pathname || ''}${url.search || ''}`;\n}\n\n\n\nfunction route(url, replace=false) {\n\tif (typeof url!=='string' && url.url) {\n\t\treplace = url.replace;\n\t\turl = url.url;\n\t}\n\n\t// only push URL into history if we can handle it\n\tif (canRoute(url)) {\n\t\tsetUrl(url, replace ? 'replace' : 'push');\n\t}\n\n\treturn routeTo(url);\n}\n\n\n/** Check if the given URL can be handled by any router instances. */\nfunction canRoute(url) {\n\tfor (let i=ROUTERS.length; i--; ) {\n\t\tif (ROUTERS[i].canRoute(url)) return true;\n\t}\n\treturn false;\n}\n\n\n/** Tell all router instances to handle the given URL.  */\nfunction routeTo(url) {\n\tlet didRoute = false;\n\tfor (let i=0; i {\n\t\t\t\trouteTo(getCurrentUrl());\n\t\t\t});\n\t\t}\n\t\taddEventListener('click', delegateLinkHandler);\n\t}\n\teventListenersInitialized = true;\n}\n\n\nclass Router extends Component {\n\tconstructor(props) {\n\t\tsuper(props);\n\t\tif (props.history) {\n\t\t\tcustomHistory = props.history;\n\t\t}\n\n\t\tthis.state = {\n\t\t\turl: props.url || getCurrentUrl()\n\t\t};\n\n\t\tinitEventListeners();\n\t}\n\n\tshouldComponentUpdate(props) {\n\t\tif (props.static!==true) return true;\n\t\treturn props.url!==this.props.url || props.onChange!==this.props.onChange;\n\t}\n\n\t/** Check if the given URL can be matched against any children */\n\tcanRoute(url) {\n\t\tconst children = toChildArray(this.props.children);\n\t\treturn this.getMatchingChildren(children, url, false).length > 0;\n\t}\n\n\t/** Re-render children with a new URL to match against. */\n\trouteTo(url) {\n\t\tthis.setState({ url });\n\n\t\tconst didRoute = this.canRoute(url);\n\n\t\t// trigger a manual re-route if we're not in the middle of an update:\n\t\tif (!this.updating) this.forceUpdate();\n\n\t\treturn didRoute;\n\t}\n\n\tcomponentWillMount() {\n\t\tROUTERS.push(this);\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidMount() {\n\t\tif (customHistory) {\n\t\t\tthis.unlisten = customHistory.listen((location) => {\n\t\t\t\tthis.routeTo(`${location.pathname || ''}${location.search || ''}`);\n\t\t\t});\n\t\t}\n\t\tthis.updating = false;\n\t}\n\n\tcomponentWillUnmount() {\n\t\tif (typeof this.unlisten==='function') this.unlisten();\n\t\tROUTERS.splice(ROUTERS.indexOf(this), 1);\n\t}\n\n\tcomponentWillUpdate() {\n\t\tthis.updating = true;\n\t}\n\n\tcomponentDidUpdate() {\n\t\tthis.updating = false;\n\t}\n\n\tgetMatchingChildren(children, url, invoke) {\n\t\treturn children\n\t\t\t.filter(prepareVNodeForRanking)\n\t\t\t.sort(pathRankSort)\n\t\t\t.map( vnode => {\n\t\t\t\tlet matches = exec(url, vnode.props.path, vnode.props);\n\t\t\t\tif (matches) {\n\t\t\t\t\tif (invoke !== false) {\n\t\t\t\t\t\tlet newProps = { url, matches };\n\t\t\t\t\t\tassign(newProps, matches);\n\t\t\t\t\t\tdelete newProps.ref;\n\t\t\t\t\t\tdelete newProps.key;\n\t\t\t\t\t\treturn cloneElement(vnode, newProps);\n\t\t\t\t\t}\n\t\t\t\t\treturn vnode;\n\t\t\t\t}\n\t\t\t}).filter(Boolean);\n\t}\n\n\trender({ children, onChange }, { url }) {\n\t\tlet active = this.getMatchingChildren(toChildArray(children), url, true);\n\n\t\tlet current = active[0] || null;\n\n\t\tlet previous = this.previousUrl;\n\t\tif (url!==previous) {\n\t\t\tthis.previousUrl = url;\n\t\t\tif (typeof onChange==='function') {\n\t\t\t\tonChange({\n\t\t\t\t\trouter: this,\n\t\t\t\t\turl,\n\t\t\t\t\tprevious,\n\t\t\t\t\tactive,\n\t\t\t\t\tcurrent\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\treturn current;\n\t}\n}\n\nconst Link = (props) => (\n\tcreateElement('a', assign({ onClick: handleLinkClick }, props))\n);\n\nconst Route = props => createElement(props.component, props);\n\nRouter.subscribers = subscribers;\nRouter.getCurrentUrl = getCurrentUrl;\nRouter.route = route;\nRouter.Router = Router;\nRouter.Route = Route;\nRouter.Link = Link;\nRouter.exec = exec;\n\nexport { subscribers, getCurrentUrl, route, Router, Route, Link, exec };\nexport default Router;\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"copyright\":\"copyright__2FTnU\"};","import options from './options';\n\n/**\n * Create an virtual node (used for JSX)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * constructor for this virtual node\n * @param {object | null | undefined} [props] The properties of the virtual node\n * @param {Array} [children] The children of the virtual node\n * @returns {import('./internal').VNode}\n */\nexport function createElement(type, props, children) {\n\tlet normalizedProps = {},\n\t\ti;\n\tfor (i in props) {\n\t\tif (i !== 'key' && i !== 'ref') normalizedProps[i] = props[i];\n\t}\n\n\tif (arguments.length > 3) {\n\t\tchildren = [children];\n\t\t// https://github.com/preactjs/preact/issues/1916\n\t\tfor (i = 3; i < arguments.length; i++) {\n\t\t\tchildren.push(arguments[i]);\n\t\t}\n\t}\n\tif (children != null) {\n\t\tnormalizedProps.children = children;\n\t}\n\n\t// If a Component VNode, check for and apply defaultProps\n\t// Note: type may be undefined in development, must never error here.\n\tif (typeof type === 'function' && type.defaultProps != null) {\n\t\tfor (i in type.defaultProps) {\n\t\t\tif (normalizedProps[i] === undefined) {\n\t\t\t\tnormalizedProps[i] = type.defaultProps[i];\n\t\t\t}\n\t\t}\n\t}\n\n\treturn createVNode(\n\t\ttype,\n\t\tnormalizedProps,\n\t\tprops && props.key,\n\t\tprops && props.ref\n\t);\n}\n\n/**\n * Create a VNode (used internally by Preact)\n * @param {import('./internal').VNode[\"type\"]} type The node name or Component\n * Constructor for this virtual node\n * @param {object | string | number | null} props The properties of this virtual node.\n * If this virtual node represents a text node, this is the text of the node (string or number).\n * @param {string | number | null} key The key for this virtual node, used when\n * diffing it against its children\n * @param {import('./internal').VNode[\"ref\"]} ref The ref property that will\n * receive a reference to its created child\n * @returns {import('./internal').VNode}\n */\nexport function createVNode(type, props, key, ref) {\n\t// V8 seems to be better at detecting type shapes if the object is allocated from the same call site\n\t// Do not inline into createElement and coerceToVNode!\n\tconst vnode = {\n\t\ttype,\n\t\tprops,\n\t\tkey,\n\t\tref,\n\t\t_children: null,\n\t\t_parent: null,\n\t\t_depth: 0,\n\t\t_dom: null,\n\t\t// _nextDom must be initialized to undefined b/c it will eventually\n\t\t// be set to dom.nextSibling which can return `null` and it is important\n\t\t// to be able to distinguish between an uninitialized _nextDom and\n\t\t// a _nextDom that has been set to `null`\n\t\t_nextDom: undefined,\n\t\t_component: null,\n\t\tconstructor: undefined\n\t};\n\n\tif (options.vnode) options.vnode(vnode);\n\n\treturn vnode;\n}\n\nexport function createRef() {\n\treturn {};\n}\n\nexport function Fragment(props) {\n\treturn props.children;\n}\n\n/**\n * Check if a the argument is a valid Preact VNode.\n * @param {*} vnode\n * @returns {vnode is import('./internal').VNode}\n */\nexport const isValidElement = vnode =>\n\tvnode != null && vnode.constructor === undefined;\n","import { assign } from './util';\nimport { diff, commitRoot } from './diff/index';\nimport options from './options';\nimport { Fragment } from './create-element';\n\n/**\n * Base Component class. Provides `setState()` and `forceUpdate()`, which\n * trigger rendering\n * @param {object} props The initial component props\n * @param {object} context The initial context from parent components'\n * getChildContext\n */\nexport function Component(props, context) {\n\tthis.props = props;\n\tthis.context = context;\n}\n\n/**\n * Update component state and schedule a re-render.\n * @param {object | ((s: object, p: object) => object)} update A hash of state\n * properties to update with new values or a function that given the current\n * state and props returns a new partial state\n * @param {() => void} [callback] A function to be called once component state is\n * updated\n */\nComponent.prototype.setState = function(update, callback) {\n\t// only clone state when copying to nextState the first time.\n\tlet s;\n\tif (this._nextState !== this.state) {\n\t\ts = this._nextState;\n\t} else {\n\t\ts = this._nextState = assign({}, this.state);\n\t}\n\n\tif (typeof update == 'function') {\n\t\tupdate = update(s, this.props);\n\t}\n\n\tif (update) {\n\t\tassign(s, update);\n\t}\n\n\t// Skip update if updater function returned null\n\tif (update == null) return;\n\n\tif (this._vnode) {\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Immediately perform a synchronous re-render of the component\n * @param {() => void} [callback] A function to be called after component is\n * re-rendered\n */\nComponent.prototype.forceUpdate = function(callback) {\n\tif (this._vnode) {\n\t\t// Set render mode so that we can differentiate where the render request\n\t\t// is coming from. We need this because forceUpdate should never call\n\t\t// shouldComponentUpdate\n\t\tthis._force = true;\n\t\tif (callback) this._renderCallbacks.push(callback);\n\t\tenqueueRender(this);\n\t}\n};\n\n/**\n * Accepts `props` and `state`, and returns a new Virtual DOM tree to build.\n * Virtual DOM is generally constructed via [JSX](http://jasonformat.com/wtf-is-jsx).\n * @param {object} props Props (eg: JSX attributes) received from parent\n * element/component\n * @param {object} state The component's current state\n * @param {object} context Context object, as returned by the nearest\n * ancestor's `getChildContext()`\n * @returns {import('./index').ComponentChildren | void}\n */\nComponent.prototype.render = Fragment;\n\n/**\n * @param {import('./internal').VNode} vnode\n * @param {number | null} [childIndex]\n */\nexport function getDomSibling(vnode, childIndex) {\n\tif (childIndex == null) {\n\t\t// Use childIndex==null as a signal to resume the search from the vnode's sibling\n\t\treturn vnode._parent\n\t\t\t? getDomSibling(vnode._parent, vnode._parent._children.indexOf(vnode) + 1)\n\t\t\t: null;\n\t}\n\n\tlet sibling;\n\tfor (; childIndex < vnode._children.length; childIndex++) {\n\t\tsibling = vnode._children[childIndex];\n\n\t\tif (sibling != null && sibling._dom != null) {\n\t\t\t// Since updateParentDomPointers keeps _dom pointer correct,\n\t\t\t// we can rely on _dom to tell us if this subtree contains a\n\t\t\t// rendered DOM node, and what the first rendered DOM node is\n\t\t\treturn sibling._dom;\n\t\t}\n\t}\n\n\t// If we get here, we have not found a DOM node in this vnode's children.\n\t// We must resume from this vnode's sibling (in it's parent _children array)\n\t// Only climb up and search the parent if we aren't searching through a DOM\n\t// VNode (meaning we reached the DOM parent of the original vnode that began\n\t// the search)\n\treturn typeof vnode.type === 'function' ? getDomSibling(vnode) : null;\n}\n\n/**\n * Trigger in-place re-rendering of a component.\n * @param {import('./internal').Component} component The component to rerender\n */\nfunction renderComponent(component) {\n\tlet vnode = component._vnode,\n\t\toldDom = vnode._dom,\n\t\tparentDom = component._parentDom;\n\n\tif (parentDom) {\n\t\tlet commitQueue = [];\n\t\tlet newDom = diff(\n\t\t\tparentDom,\n\t\t\tvnode,\n\t\t\tassign({}, vnode),\n\t\t\tcomponent._context,\n\t\t\tparentDom.ownerSVGElement !== undefined,\n\t\t\tnull,\n\t\t\tcommitQueue,\n\t\t\toldDom == null ? getDomSibling(vnode) : oldDom\n\t\t);\n\t\tcommitRoot(commitQueue, vnode);\n\n\t\tif (newDom != oldDom) {\n\t\t\tupdateParentDomPointers(vnode);\n\t\t}\n\t}\n}\n\n/**\n * @param {import('./internal').VNode} vnode\n */\nfunction updateParentDomPointers(vnode) {\n\tif ((vnode = vnode._parent) != null && vnode._component != null) {\n\t\tvnode._dom = vnode._component.base = null;\n\t\tfor (let i = 0; i < vnode._children.length; i++) {\n\t\t\tlet child = vnode._children[i];\n\t\t\tif (child != null && child._dom != null) {\n\t\t\t\tvnode._dom = vnode._component.base = child._dom;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\n\t\treturn updateParentDomPointers(vnode);\n\t}\n}\n\n/**\n * The render queue\n * @type {Array}\n */\nlet q = [];\n\n/**\n * Asynchronously schedule a callback\n * @type {(cb: () => void) => void}\n */\n/* istanbul ignore next */\n// Note the following line isn't tree-shaken by rollup cuz of rollup/rollup#2566\nconst defer =\n\ttypeof Promise == 'function'\n\t\t? Promise.prototype.then.bind(Promise.resolve())\n\t\t: setTimeout;\n\n/*\n * The value of `Component.debounce` must asynchronously invoke the passed in callback. It is\n * important that contributors to Preact can consistently reason about what calls to `setState`, etc.\n * do, and when their effects will be applied. See the links below for some further reading on designing\n * asynchronous APIs.\n * * [Designing APIs for Asynchrony](https://blog.izs.me/2013/08/designing-apis-for-asynchrony)\n * * [Callbacks synchronous and asynchronous](https://blog.ometer.com/2011/07/24/callbacks-synchronous-and-asynchronous/)\n */\n\nlet prevDebounce;\n\n/**\n * Enqueue a rerender of a component\n * @param {import('./internal').Component} c The component to rerender\n */\nexport function enqueueRender(c) {\n\tif (\n\t\t(!c._dirty && (c._dirty = true) && q.push(c) === 1) ||\n\t\tprevDebounce !== options.debounceRendering\n\t) {\n\t\tprevDebounce = options.debounceRendering;\n\t\t(prevDebounce || defer)(process);\n\t}\n}\n\n/** Flush the render queue by rerendering all queued components */\nfunction process() {\n\tlet p;\n\tq.sort((a, b) => b._vnode._depth - a._vnode._depth);\n\twhile ((p = q.pop())) {\n\t\t// forceUpdate's callback argument is reused here to indicate a non-forced update.\n\t\tif (p._dirty) renderComponent(p);\n\t}\n}\n","import { diff, unmount, applyRef } from './index';\nimport { createVNode } from '../create-element';\nimport { EMPTY_OBJ, EMPTY_ARR } from '../constants';\nimport { removeNode } from '../util';\nimport { getDomSibling } from '../component';\n\n/**\n * Diff the children of a virtual node\n * @param {import('../internal').PreactElement} parentDom The DOM element whose\n * children are being diffed\n * @param {import('../internal').VNode} newParentVNode The new virtual\n * node whose children should be diff'ed against oldParentVNode\n * @param {import('../internal').VNode} oldParentVNode The old virtual\n * node whose children should be diff'ed against newParentVNode\n * @param {object} context The current context object\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {Array} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Node | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} isHydrating Whether or not we are in hydration\n */\nexport function diffChildren(\n\tparentDom,\n\tnewParentVNode,\n\toldParentVNode,\n\tcontext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet i, j, oldVNode, newDom, sibDom, firstChildDom, refs;\n\n\t// This is a compression of oldParentVNode!=null && oldParentVNode != EMPTY_OBJ && oldParentVNode._children || EMPTY_ARR\n\t// as EMPTY_OBJ._children should be `undefined`.\n\tlet oldChildren = (oldParentVNode && oldParentVNode._children) || EMPTY_ARR;\n\n\tlet oldChildrenLength = oldChildren.length;\n\n\t// Only in very specific places should this logic be invoked (top level `render` and `diffElementNodes`).\n\t// I'm using `EMPTY_OBJ` to signal when `diffChildren` is invoked in these situations. I can't use `null`\n\t// for this purpose, because `null` is a valid value for `oldDom` which can mean to skip to this logic\n\t// (e.g. if mounting a new tree in which the old DOM should be ignored (usually for Fragments).\n\tif (oldDom == EMPTY_OBJ) {\n\t\tif (excessDomChildren != null) {\n\t\t\toldDom = excessDomChildren[0];\n\t\t} else if (oldChildrenLength) {\n\t\t\toldDom = getDomSibling(oldParentVNode, 0);\n\t\t} else {\n\t\t\toldDom = null;\n\t\t}\n\t}\n\n\ti = 0;\n\tnewParentVNode._children = toChildArray(\n\t\tnewParentVNode._children,\n\t\tchildVNode => {\n\t\t\tif (childVNode != null) {\n\t\t\t\tchildVNode._parent = newParentVNode;\n\t\t\t\tchildVNode._depth = newParentVNode._depth + 1;\n\n\t\t\t\t// Check if we find a corresponding element in oldChildren.\n\t\t\t\t// If found, delete the array item by setting to `undefined`.\n\t\t\t\t// We use `undefined`, as `null` is reserved for empty placeholders\n\t\t\t\t// (holes).\n\t\t\t\toldVNode = oldChildren[i];\n\n\t\t\t\tif (\n\t\t\t\t\toldVNode === null ||\n\t\t\t\t\t(oldVNode &&\n\t\t\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\t\t\tchildVNode.type === oldVNode.type)\n\t\t\t\t) {\n\t\t\t\t\toldChildren[i] = undefined;\n\t\t\t\t} else {\n\t\t\t\t\t// Either oldVNode === undefined or oldChildrenLength > 0,\n\t\t\t\t\t// so after this loop oldVNode == null or oldVNode is a valid value.\n\t\t\t\t\tfor (j = 0; j < oldChildrenLength; j++) {\n\t\t\t\t\t\toldVNode = oldChildren[j];\n\t\t\t\t\t\t// If childVNode is unkeyed, we only match similarly unkeyed nodes, otherwise we match by key.\n\t\t\t\t\t\t// We always match by type (in either case).\n\t\t\t\t\t\tif (\n\t\t\t\t\t\t\toldVNode &&\n\t\t\t\t\t\t\tchildVNode.key == oldVNode.key &&\n\t\t\t\t\t\t\tchildVNode.type === oldVNode.type\n\t\t\t\t\t\t) {\n\t\t\t\t\t\t\toldChildren[j] = undefined;\n\t\t\t\t\t\t\tbreak;\n\t\t\t\t\t\t}\n\t\t\t\t\t\toldVNode = null;\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t\toldVNode = oldVNode || EMPTY_OBJ;\n\n\t\t\t\t// Morph the old element into the new one, but don't append it to the dom yet\n\t\t\t\tnewDom = diff(\n\t\t\t\t\tparentDom,\n\t\t\t\t\tchildVNode,\n\t\t\t\t\toldVNode,\n\t\t\t\t\tcontext,\n\t\t\t\t\tisSvg,\n\t\t\t\t\texcessDomChildren,\n\t\t\t\t\tcommitQueue,\n\t\t\t\t\toldDom,\n\t\t\t\t\tisHydrating\n\t\t\t\t);\n\n\t\t\t\tif ((j = childVNode.ref) && oldVNode.ref != j) {\n\t\t\t\t\tif (!refs) refs = [];\n\t\t\t\t\tif (oldVNode.ref) refs.push(oldVNode.ref, null, childVNode);\n\t\t\t\t\trefs.push(j, childVNode._component || newDom, childVNode);\n\t\t\t\t}\n\n\t\t\t\t// Only proceed if the vnode has not been unmounted by `diff()` above.\n\t\t\t\tif (newDom != null) {\n\t\t\t\t\tif (firstChildDom == null) {\n\t\t\t\t\t\tfirstChildDom = newDom;\n\t\t\t\t\t}\n\n\t\t\t\t\tlet nextDom;\n\t\t\t\t\tif (childVNode._nextDom !== undefined) {\n\t\t\t\t\t\t// Only Fragments or components that return Fragment like VNodes will\n\t\t\t\t\t\t// have a non-undefined _nextDom. Continue the diff from the sibling\n\t\t\t\t\t\t// of last DOM child of this child VNode\n\t\t\t\t\t\tnextDom = childVNode._nextDom;\n\n\t\t\t\t\t\t// Eagerly cleanup _nextDom. We don't need to persist the value because\n\t\t\t\t\t\t// it is only used by `diffChildren` to determine where to resume the diff after\n\t\t\t\t\t\t// diffing Components and Fragments. Once we store it the nextDOM local var, we\n\t\t\t\t\t\t// can clean up the property\n\t\t\t\t\t\tchildVNode._nextDom = undefined;\n\t\t\t\t\t} else if (\n\t\t\t\t\t\texcessDomChildren == oldVNode ||\n\t\t\t\t\t\tnewDom != oldDom ||\n\t\t\t\t\t\tnewDom.parentNode == null\n\t\t\t\t\t) {\n\t\t\t\t\t\t// NOTE: excessDomChildren==oldVNode above:\n\t\t\t\t\t\t// This is a compression of excessDomChildren==null && oldVNode==null!\n\t\t\t\t\t\t// The values only have the same type when `null`.\n\n\t\t\t\t\t\touter: if (oldDom == null || oldDom.parentNode !== parentDom) {\n\t\t\t\t\t\t\tparentDom.appendChild(newDom);\n\t\t\t\t\t\t\tnextDom = null;\n\t\t\t\t\t\t} else {\n\t\t\t\t\t\t\t// `j import('../internal').VNode} [callback]\n * A function to invoke for each child before it is added to the flattened list.\n * @param {Array} [flattened] An flat array of children to modify\n * @returns {import('../internal').VNode[]}\n */\nexport function toChildArray(children, callback, flattened) {\n\tif (flattened == null) flattened = [];\n\n\tif (children == null || typeof children === 'boolean') {\n\t\tif (callback) flattened.push(callback(null));\n\t} else if (Array.isArray(children)) {\n\t\tfor (let i = 0; i < children.length; i++) {\n\t\t\ttoChildArray(children[i], callback, flattened);\n\t\t}\n\t} else if (!callback) {\n\t\tflattened.push(children);\n\t} else if (typeof children === 'string' || typeof children === 'number') {\n\t\tflattened.push(callback(createVNode(null, children, null, null)));\n\t} else if (children._dom != null || children._component != null) {\n\t\tflattened.push(\n\t\t\tcallback(createVNode(children.type, children.props, children.key, null))\n\t\t);\n\t} else {\n\t\tflattened.push(callback(children));\n\t}\n\n\treturn flattened;\n}\n","import { IS_NON_DIMENSIONAL } from '../constants';\nimport options from '../options';\n\n/**\n * Diff the old and new properties of a VNode and apply changes to the DOM node\n * @param {import('../internal').PreactElement} dom The DOM node to apply\n * changes to\n * @param {object} newProps The new props\n * @param {object} oldProps The old props\n * @param {boolean} isSvg Whether or not this node is an SVG node\n * @param {boolean} hydrate Whether or not we are in hydration mode\n */\nexport function diffProps(dom, newProps, oldProps, isSvg, hydrate) {\n\tlet i;\n\n\tfor (i in oldProps) {\n\t\tif (!(i in newProps)) {\n\t\t\tsetProperty(dom, i, null, oldProps[i], isSvg);\n\t\t}\n\t}\n\n\tfor (i in newProps) {\n\t\tif (\n\t\t\t(!hydrate || typeof newProps[i] == 'function') &&\n\t\t\ti !== 'value' &&\n\t\t\ti !== 'checked' &&\n\t\t\toldProps[i] !== newProps[i]\n\t\t) {\n\t\t\tsetProperty(dom, i, newProps[i], oldProps[i], isSvg);\n\t\t}\n\t}\n}\n\nfunction setStyle(style, key, value) {\n\tif (key[0] === '-') {\n\t\tstyle.setProperty(key, value);\n\t} else if (\n\t\ttypeof value === 'number' &&\n\t\tIS_NON_DIMENSIONAL.test(key) === false\n\t) {\n\t\tstyle[key] = value + 'px';\n\t} else if (value == null) {\n\t\tstyle[key] = '';\n\t} else {\n\t\tstyle[key] = value;\n\t}\n}\n\n/**\n * Set a property value on a DOM node\n * @param {import('../internal').PreactElement} dom The DOM node to modify\n * @param {string} name The name of the property to set\n * @param {*} value The value to set the property to\n * @param {*} oldValue The old value the property had\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node or not\n */\nfunction setProperty(dom, name, value, oldValue, isSvg) {\n\tif (isSvg) {\n\t\tif (name === 'className') {\n\t\t\tname = 'class';\n\t\t}\n\t} else if (name === 'class') {\n\t\tname = 'className';\n\t}\n\n\tif (name === 'key' || name === 'children') {\n\t} else if (name === 'style') {\n\t\tconst s = dom.style;\n\n\t\tif (typeof value === 'string') {\n\t\t\ts.cssText = value;\n\t\t} else {\n\t\t\tif (typeof oldValue === 'string') {\n\t\t\t\ts.cssText = '';\n\t\t\t\toldValue = null;\n\t\t\t}\n\n\t\t\tif (oldValue) {\n\t\t\t\tfor (let i in oldValue) {\n\t\t\t\t\tif (!(value && i in value)) {\n\t\t\t\t\t\tsetStyle(s, i, '');\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (value) {\n\t\t\t\tfor (let i in value) {\n\t\t\t\t\tif (!oldValue || value[i] !== oldValue[i]) {\n\t\t\t\t\t\tsetStyle(s, i, value[i]);\n\t\t\t\t\t}\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t}\n\t// Benchmark for comparison: https://esbench.com/bench/574c954bdb965b9a00965ac6\n\telse if (name[0] === 'o' && name[1] === 'n') {\n\t\tlet useCapture = name !== (name = name.replace(/Capture$/, ''));\n\t\tlet nameLower = name.toLowerCase();\n\t\tname = (nameLower in dom ? nameLower : name).slice(2);\n\n\t\tif (value) {\n\t\t\tif (!oldValue) dom.addEventListener(name, eventProxy, useCapture);\n\t\t\t(dom._listeners || (dom._listeners = {}))[name] = value;\n\t\t} else {\n\t\t\tdom.removeEventListener(name, eventProxy, useCapture);\n\t\t}\n\t} else if (\n\t\tname !== 'list' &&\n\t\tname !== 'tagName' &&\n\t\t// HTMLButtonElement.form and HTMLInputElement.form are read-only but can be set using\n\t\t// setAttribute\n\t\tname !== 'form' &&\n\t\tname !== 'type' &&\n\t\tname !== 'size' &&\n\t\t!isSvg &&\n\t\tname in dom\n\t) {\n\t\tdom[name] = value == null ? '' : value;\n\t} else if (\n\t\ttypeof value !== 'function' &&\n\t\tname !== 'dangerouslySetInnerHTML'\n\t) {\n\t\tif (name !== (name = name.replace(/^xlink:?/, ''))) {\n\t\t\tif (value == null || value === false) {\n\t\t\t\tdom.removeAttributeNS(\n\t\t\t\t\t'http://www.w3.org/1999/xlink',\n\t\t\t\t\tname.toLowerCase()\n\t\t\t\t);\n\t\t\t} else {\n\t\t\t\tdom.setAttributeNS(\n\t\t\t\t\t'http://www.w3.org/1999/xlink',\n\t\t\t\t\tname.toLowerCase(),\n\t\t\t\t\tvalue\n\t\t\t\t);\n\t\t\t}\n\t\t} else if (\n\t\t\tvalue == null ||\n\t\t\t(value === false &&\n\t\t\t\t// ARIA-attributes have a different notion of boolean values.\n\t\t\t\t// The value `false` is different from the attribute not\n\t\t\t\t// existing on the DOM, so we can't remove it. For non-boolean\n\t\t\t\t// ARIA-attributes we could treat false as a removal, but the\n\t\t\t\t// amount of exceptions would cost us too many bytes. On top of\n\t\t\t\t// that other VDOM frameworks also always stringify `false`.\n\t\t\t\t!/^ar/.test(name))\n\t\t) {\n\t\t\tdom.removeAttribute(name);\n\t\t} else {\n\t\t\tdom.setAttribute(name, value);\n\t\t}\n\t}\n}\n\n/**\n * Proxy an event to hooked event handlers\n * @param {Event} e The event object from the browser\n * @private\n */\nfunction eventProxy(e) {\n\tthis._listeners[e.type](options.event ? options.event(e) : e);\n}\n","import { EMPTY_OBJ, EMPTY_ARR } from '../constants';\nimport { Component } from '../component';\nimport { Fragment } from '../create-element';\nimport { diffChildren } from './children';\nimport { diffProps } from './props';\nimport { assign, removeNode } from '../util';\nimport options from '../options';\n\n/**\n * Diff two virtual nodes and apply proper changes to the DOM\n * @param {import('../internal').PreactElement} parentDom The parent of the DOM element\n * @param {import('../internal').VNode} newVNode The new virtual node\n * @param {import('../internal').VNode} oldVNode The old virtual node\n * @param {object} context The current context object\n * @param {boolean} isSvg Whether or not this element is an SVG node\n * @param {Array} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {Element | Text} oldDom The current attached DOM\n * element any new dom elements should be placed around. Likely `null` on first\n * render (except when hydrating). Can be a sibling DOM element when diffing\n * Fragments that have siblings. In most cases, it starts out as `oldChildren[0]._dom`.\n * @param {boolean} [isHydrating] Whether or not we are in hydration\n */\nexport function diff(\n\tparentDom,\n\tnewVNode,\n\toldVNode,\n\tcontext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\toldDom,\n\tisHydrating\n) {\n\tlet tmp,\n\t\tnewType = newVNode.type;\n\n\t// When passing through createElement it assigns the object\n\t// constructor as undefined. This to prevent JSON-injection.\n\tif (newVNode.constructor !== undefined) return null;\n\n\tif ((tmp = options._diff)) tmp(newVNode);\n\n\ttry {\n\t\touter: if (typeof newType === 'function') {\n\t\t\tlet c, isNew, oldProps, oldState, snapshot, clearProcessingException;\n\t\t\tlet newProps = newVNode.props;\n\n\t\t\t// Necessary for createContext api. Setting this property will pass\n\t\t\t// the context value as `this.context` just for this component.\n\t\t\ttmp = newType.contextType;\n\t\t\tlet provider = tmp && context[tmp._id];\n\t\t\tlet cctx = tmp\n\t\t\t\t? provider\n\t\t\t\t\t? provider.props.value\n\t\t\t\t\t: tmp._defaultValue\n\t\t\t\t: context;\n\n\t\t\t// Get component and set it to `c`\n\t\t\tif (oldVNode._component) {\n\t\t\t\tc = newVNode._component = oldVNode._component;\n\t\t\t\tclearProcessingException = c._processingException = c._pendingError;\n\t\t\t} else {\n\t\t\t\t// Instantiate the new component\n\t\t\t\tif ('prototype' in newType && newType.prototype.render) {\n\t\t\t\t\tnewVNode._component = c = new newType(newProps, cctx); // eslint-disable-line new-cap\n\t\t\t\t} else {\n\t\t\t\t\tnewVNode._component = c = new Component(newProps, cctx);\n\t\t\t\t\tc.constructor = newType;\n\t\t\t\t\tc.render = doRender;\n\t\t\t\t}\n\t\t\t\tif (provider) provider.sub(c);\n\n\t\t\t\tc.props = newProps;\n\t\t\t\tif (!c.state) c.state = {};\n\t\t\t\tc.context = cctx;\n\t\t\t\tc._context = context;\n\t\t\t\tisNew = c._dirty = true;\n\t\t\t\tc._renderCallbacks = [];\n\t\t\t}\n\n\t\t\t// Invoke getDerivedStateFromProps\n\t\t\tif (c._nextState == null) {\n\t\t\t\tc._nextState = c.state;\n\t\t\t}\n\t\t\tif (newType.getDerivedStateFromProps != null) {\n\t\t\t\tif (c._nextState == c.state) {\n\t\t\t\t\tc._nextState = assign({}, c._nextState);\n\t\t\t\t}\n\n\t\t\t\tassign(\n\t\t\t\t\tc._nextState,\n\t\t\t\t\tnewType.getDerivedStateFromProps(newProps, c._nextState)\n\t\t\t\t);\n\t\t\t}\n\n\t\t\toldProps = c.props;\n\t\t\toldState = c.state;\n\n\t\t\t// Invoke pre-render lifecycle methods\n\t\t\tif (isNew) {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tc.componentWillMount != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillMount();\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidMount != null) {\n\t\t\t\t\tc._renderCallbacks.push(c.componentDidMount);\n\t\t\t\t}\n\t\t\t} else {\n\t\t\t\tif (\n\t\t\t\t\tnewType.getDerivedStateFromProps == null &&\n\t\t\t\t\tnewProps !== oldProps &&\n\t\t\t\t\tc.componentWillReceiveProps != null\n\t\t\t\t) {\n\t\t\t\t\tc.componentWillReceiveProps(newProps, cctx);\n\t\t\t\t}\n\n\t\t\t\tif (\n\t\t\t\t\t!c._force &&\n\t\t\t\t\tc.shouldComponentUpdate != null &&\n\t\t\t\t\tc.shouldComponentUpdate(newProps, c._nextState, cctx) === false\n\t\t\t\t) {\n\t\t\t\t\tc.props = newProps;\n\t\t\t\t\tc.state = c._nextState;\n\t\t\t\t\tc._dirty = false;\n\t\t\t\t\tc._vnode = newVNode;\n\t\t\t\t\tnewVNode._dom = oldVNode._dom;\n\t\t\t\t\tnewVNode._children = oldVNode._children;\n\t\t\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\t\t\tcommitQueue.push(c);\n\t\t\t\t\t}\n\t\t\t\t\tfor (tmp = 0; tmp < newVNode._children.length; tmp++) {\n\t\t\t\t\t\tif (newVNode._children[tmp]) {\n\t\t\t\t\t\t\tnewVNode._children[tmp]._parent = newVNode;\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\tbreak outer;\n\t\t\t\t}\n\n\t\t\t\tif (c.componentWillUpdate != null) {\n\t\t\t\t\tc.componentWillUpdate(newProps, c._nextState, cctx);\n\t\t\t\t}\n\n\t\t\t\tif (c.componentDidUpdate != null) {\n\t\t\t\t\tc._renderCallbacks.push(() => {\n\t\t\t\t\t\tc.componentDidUpdate(oldProps, oldState, snapshot);\n\t\t\t\t\t});\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tc.context = cctx;\n\t\t\tc.props = newProps;\n\t\t\tc.state = c._nextState;\n\n\t\t\tif ((tmp = options._render)) tmp(newVNode);\n\n\t\t\tc._dirty = false;\n\t\t\tc._vnode = newVNode;\n\t\t\tc._parentDom = parentDom;\n\n\t\t\ttmp = c.render(c.props, c.state, c.context);\n\t\t\tlet isTopLevelFragment =\n\t\t\t\ttmp != null && tmp.type == Fragment && tmp.key == null;\n\t\t\tnewVNode._children = isTopLevelFragment ? tmp.props.children : tmp;\n\n\t\t\tif (c.getChildContext != null) {\n\t\t\t\tcontext = assign(assign({}, context), c.getChildContext());\n\t\t\t}\n\n\t\t\tif (!isNew && c.getSnapshotBeforeUpdate != null) {\n\t\t\t\tsnapshot = c.getSnapshotBeforeUpdate(oldProps, oldState);\n\t\t\t}\n\n\t\t\tdiffChildren(\n\t\t\t\tparentDom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tcontext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\toldDom,\n\t\t\t\tisHydrating\n\t\t\t);\n\n\t\t\tc.base = newVNode._dom;\n\n\t\t\tif (c._renderCallbacks.length) {\n\t\t\t\tcommitQueue.push(c);\n\t\t\t}\n\n\t\t\tif (clearProcessingException) {\n\t\t\t\tc._pendingError = c._processingException = null;\n\t\t\t}\n\n\t\t\tc._force = false;\n\t\t} else {\n\t\t\tnewVNode._dom = diffElementNodes(\n\t\t\t\toldVNode._dom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tcontext,\n\t\t\t\tisSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\tif ((tmp = options.diffed)) tmp(newVNode);\n\t} catch (e) {\n\t\toptions._catchError(e, newVNode, oldVNode);\n\t}\n\n\treturn newVNode._dom;\n}\n\n/**\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {import('../internal').VNode} root\n */\nexport function commitRoot(commitQueue, root) {\n\tif (options._commit) options._commit(root, commitQueue);\n\n\tcommitQueue.some(c => {\n\t\ttry {\n\t\t\tcommitQueue = c._renderCallbacks;\n\t\t\tc._renderCallbacks = [];\n\t\t\tcommitQueue.some(cb => {\n\t\t\t\tcb.call(c);\n\t\t\t});\n\t\t} catch (e) {\n\t\t\toptions._catchError(e, c._vnode);\n\t\t}\n\t});\n}\n\n/**\n * Diff two virtual nodes representing DOM element\n * @param {import('../internal').PreactElement} dom The DOM element representing\n * the virtual nodes being diffed\n * @param {import('../internal').VNode} newVNode The new virtual node\n * @param {import('../internal').VNode} oldVNode The old virtual node\n * @param {object} context The current context object\n * @param {boolean} isSvg Whether or not this DOM node is an SVG node\n * @param {*} excessDomChildren\n * @param {Array} commitQueue List of components\n * which have callbacks to invoke in commitRoot\n * @param {boolean} isHydrating Whether or not we are in hydration\n * @returns {import('../internal').PreactElement}\n */\nfunction diffElementNodes(\n\tdom,\n\tnewVNode,\n\toldVNode,\n\tcontext,\n\tisSvg,\n\texcessDomChildren,\n\tcommitQueue,\n\tisHydrating\n) {\n\tlet i;\n\tlet oldProps = oldVNode.props;\n\tlet newProps = newVNode.props;\n\n\t// Tracks entering and exiting SVG namespace when descending through the tree.\n\tisSvg = newVNode.type === 'svg' || isSvg;\n\n\tif (dom == null && excessDomChildren != null) {\n\t\tfor (i = 0; i < excessDomChildren.length; i++) {\n\t\t\tconst child = excessDomChildren[i];\n\n\t\t\tif (\n\t\t\t\tchild != null &&\n\t\t\t\t(newVNode.type === null\n\t\t\t\t\t? child.nodeType === 3\n\t\t\t\t\t: child.localName === newVNode.type)\n\t\t\t) {\n\t\t\t\tdom = child;\n\t\t\t\texcessDomChildren[i] = null;\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t}\n\n\tif (dom == null) {\n\t\tif (newVNode.type === null) {\n\t\t\treturn document.createTextNode(newProps);\n\t\t}\n\n\t\tdom = isSvg\n\t\t\t? document.createElementNS('http://www.w3.org/2000/svg', newVNode.type)\n\t\t\t: document.createElement(\n\t\t\t\t\tnewVNode.type,\n\t\t\t\t\tnewProps.is && { is: newProps.is }\n\t\t\t  );\n\t\t// we created a new parent, so none of the previously attached children can be reused:\n\t\texcessDomChildren = null;\n\t}\n\n\tif (newVNode.type === null) {\n\t\tif (excessDomChildren != null) {\n\t\t\texcessDomChildren[excessDomChildren.indexOf(dom)] = null;\n\t\t}\n\n\t\tif (oldProps !== newProps && dom.data != newProps) {\n\t\t\tdom.data = newProps;\n\t\t}\n\t} else if (newVNode !== oldVNode) {\n\t\tif (excessDomChildren != null) {\n\t\t\texcessDomChildren[excessDomChildren.indexOf(dom)] = null;\n\t\t\texcessDomChildren = EMPTY_ARR.slice.call(dom.childNodes);\n\t\t}\n\n\t\toldProps = oldVNode.props || EMPTY_OBJ;\n\n\t\tlet oldHtml = oldProps.dangerouslySetInnerHTML;\n\t\tlet newHtml = newProps.dangerouslySetInnerHTML;\n\n\t\t// During hydration, props are not diffed at all (including dangerouslySetInnerHTML)\n\t\t// @TODO we should warn in debug mode when props don't match here.\n\t\tif (!isHydrating) {\n\t\t\tif (oldProps === EMPTY_OBJ) {\n\t\t\t\toldProps = {};\n\t\t\t\tfor (let i = 0; i < dom.attributes.length; i++) {\n\t\t\t\t\toldProps[dom.attributes[i].name] = dom.attributes[i].value;\n\t\t\t\t}\n\t\t\t}\n\n\t\t\tif (newHtml || oldHtml) {\n\t\t\t\t// Avoid re-applying the same '__html' if it did not changed between re-render\n\t\t\t\tif (!newHtml || !oldHtml || newHtml.__html != oldHtml.__html) {\n\t\t\t\t\tdom.innerHTML = (newHtml && newHtml.__html) || '';\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\n\t\tdiffProps(dom, newProps, oldProps, isSvg, isHydrating);\n\n\t\tnewVNode._children = newVNode.props.children;\n\n\t\t// If the new vnode didn't have dangerouslySetInnerHTML, diff its children\n\t\tif (!newHtml) {\n\t\t\tdiffChildren(\n\t\t\t\tdom,\n\t\t\t\tnewVNode,\n\t\t\t\toldVNode,\n\t\t\t\tcontext,\n\t\t\t\tnewVNode.type === 'foreignObject' ? false : isSvg,\n\t\t\t\texcessDomChildren,\n\t\t\t\tcommitQueue,\n\t\t\t\tEMPTY_OBJ,\n\t\t\t\tisHydrating\n\t\t\t);\n\t\t}\n\n\t\t// (as above, don't diff props during hydration)\n\t\tif (!isHydrating) {\n\t\t\tif (\n\t\t\t\t'value' in newProps &&\n\t\t\t\tnewProps.value !== undefined &&\n\t\t\t\tnewProps.value !== dom.value\n\t\t\t) {\n\t\t\t\tdom.value = newProps.value == null ? '' : newProps.value;\n\t\t\t}\n\t\t\tif (\n\t\t\t\t'checked' in newProps &&\n\t\t\t\tnewProps.checked !== undefined &&\n\t\t\t\tnewProps.checked !== dom.checked\n\t\t\t) {\n\t\t\t\tdom.checked = newProps.checked;\n\t\t\t}\n\t\t}\n\t}\n\n\treturn dom;\n}\n\n/**\n * Invoke or update a ref, depending on whether it is a function or object ref.\n * @param {object|function} ref\n * @param {any} value\n * @param {import('../internal').VNode} vnode\n */\nexport function applyRef(ref, value, vnode) {\n\ttry {\n\t\tif (typeof ref == 'function') ref(value);\n\t\telse ref.current = value;\n\t} catch (e) {\n\t\toptions._catchError(e, vnode);\n\t}\n}\n\n/**\n * Unmount a virtual node from the tree and apply DOM changes\n * @param {import('../internal').VNode} vnode The virtual node to unmount\n * @param {import('../internal').VNode} parentVNode The parent of the VNode that\n * initiated the unmount\n * @param {boolean} [skipRemove] Flag that indicates that a parent node of the\n * current element is already detached from the DOM.\n */\nexport function unmount(vnode, parentVNode, skipRemove) {\n\tlet r;\n\tif (options.unmount) options.unmount(vnode);\n\n\tif ((r = vnode.ref)) {\n\t\tif (!r.current || r.current === vnode._dom) applyRef(r, null, parentVNode);\n\t}\n\n\tlet dom;\n\tif (!skipRemove && typeof vnode.type !== 'function') {\n\t\tskipRemove = (dom = vnode._dom) != null;\n\t}\n\n\t// Must be set to `undefined` to properly clean up `_nextDom`\n\t// for which `null` is a valid value. See comment in `create-element.js`\n\tvnode._dom = vnode._nextDom = undefined;\n\n\tif ((r = vnode._component) != null) {\n\t\tif (r.componentWillUnmount) {\n\t\t\ttry {\n\t\t\t\tr.componentWillUnmount();\n\t\t\t} catch (e) {\n\t\t\t\toptions._catchError(e, parentVNode);\n\t\t\t}\n\t\t}\n\n\t\tr.base = r._parentDom = null;\n\t}\n\n\tif ((r = vnode._children)) {\n\t\tfor (let i = 0; i < r.length; i++) {\n\t\t\tif (r[i]) unmount(r[i], parentVNode, skipRemove);\n\t\t}\n\t}\n\n\tif (dom != null) removeNode(dom);\n}\n\n/** The `.render()` method for a PFC backing instance. */\nfunction doRender(props, state, context) {\n\treturn this.constructor(props, context);\n}\n","import { EMPTY_OBJ, EMPTY_ARR } from './constants';\nimport { commitRoot, diff } from './diff/index';\nimport { createElement, Fragment } from './create-element';\nimport options from './options';\n\nconst IS_HYDRATE = EMPTY_OBJ;\n\n/**\n * Render a Preact virtual node into a DOM element\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * render into\n * @param {Element | Text} [replaceNode] Optional: Attempt to re-use an\n * existing DOM tree rooted at `replaceNode`\n */\nexport function render(vnode, parentDom, replaceNode) {\n\tif (options._root) options._root(vnode, parentDom);\n\n\t// We abuse the `replaceNode` parameter in `hydrate()` to signal if we\n\t// are in hydration mode or not by passing `IS_HYDRATE` instead of a\n\t// DOM element.\n\tlet isHydrating = replaceNode === IS_HYDRATE;\n\n\t// To be able to support calling `render()` multiple times on the same\n\t// DOM node, we need to obtain a reference to the previous tree. We do\n\t// this by assigning a new `_children` property to DOM nodes which points\n\t// to the last rendered tree. By default this property is not present, which\n\t// means that we are mounting a new tree for the first time.\n\tlet oldVNode = isHydrating\n\t\t? null\n\t\t: (replaceNode && replaceNode._children) || parentDom._children;\n\tvnode = createElement(Fragment, null, [vnode]);\n\n\t// List of effects that need to be called after diffing.\n\tlet commitQueue = [];\n\tdiff(\n\t\tparentDom,\n\t\t// Determine the new vnode tree and store it on the DOM element on\n\t\t// our custom `_children` property.\n\t\t((isHydrating ? parentDom : replaceNode || parentDom)._children = vnode),\n\t\toldVNode || EMPTY_OBJ,\n\t\tEMPTY_OBJ,\n\t\tparentDom.ownerSVGElement !== undefined,\n\t\treplaceNode && !isHydrating\n\t\t\t? [replaceNode]\n\t\t\t: oldVNode\n\t\t\t? null\n\t\t\t: EMPTY_ARR.slice.call(parentDom.childNodes),\n\t\tcommitQueue,\n\t\treplaceNode || EMPTY_OBJ,\n\t\tisHydrating\n\t);\n\n\t// Flush all queued effects\n\tcommitRoot(commitQueue, vnode);\n}\n\n/**\n * Update an existing DOM element with data from a Preact virtual node\n * @param {import('./index').ComponentChild} vnode The virtual node to render\n * @param {import('./internal').PreactElement} parentDom The DOM element to\n * update\n */\nexport function hydrate(vnode, parentDom) {\n\trender(vnode, parentDom, IS_HYDRATE);\n}\n","import { assign } from './util';\nimport { EMPTY_ARR } from './constants';\nimport { createVNode } from './create-element';\n\n/**\n * Clones the given VNode, optionally adding attributes/props and replacing its children.\n * @param {import('./internal').VNode} vnode The virtual DOM element to clone\n * @param {object} props Attributes/props to add when cloning\n * @param {Array} rest Any additional arguments will be used as replacement children.\n */\nexport function cloneElement(vnode, props) {\n\tprops = assign(assign({}, vnode.props), props);\n\tif (arguments.length > 2) props.children = EMPTY_ARR.slice.call(arguments, 2);\n\treturn createVNode(\n\t\tvnode.type,\n\t\tprops,\n\t\tprops.key || vnode.key,\n\t\tprops.ref || vnode.ref\n\t);\n}\n","import { enqueueRender } from './component';\n\nexport let i = 0;\n\nexport function createContext(defaultValue) {\n\tconst ctx = {};\n\n\tconst context = {\n\t\t_id: '__cC' + i++,\n\t\t_defaultValue: defaultValue,\n\t\tConsumer(props, context) {\n\t\t\treturn props.children(context);\n\t\t},\n\t\tProvider(props) {\n\t\t\tif (!this.getChildContext) {\n\t\t\t\tconst subs = [];\n\t\t\t\tthis.getChildContext = () => {\n\t\t\t\t\tctx[context._id] = this;\n\t\t\t\t\treturn ctx;\n\t\t\t\t};\n\t\t\t\tthis.shouldComponentUpdate = _props => {\n\t\t\t\t\tif (props.value !== _props.value) {\n\t\t\t\t\t\tsubs.some(c => {\n\t\t\t\t\t\t\tc.context = _props.value;\n\t\t\t\t\t\t\tenqueueRender(c);\n\t\t\t\t\t\t});\n\t\t\t\t\t}\n\t\t\t\t};\n\t\t\t\tthis.sub = c => {\n\t\t\t\t\tsubs.push(c);\n\t\t\t\t\tlet old = c.componentWillUnmount;\n\t\t\t\t\tc.componentWillUnmount = () => {\n\t\t\t\t\t\tsubs.splice(subs.indexOf(c), 1);\n\t\t\t\t\t\told && old.call(c);\n\t\t\t\t\t};\n\t\t\t\t};\n\t\t\t}\n\t\t\treturn props.children;\n\t\t}\n\t};\n\n\tcontext.Consumer.contextType = context;\n\n\treturn context;\n}\n","export const EMPTY_OBJ = {};\nexport const EMPTY_ARR = [];\nexport const IS_NON_DIMENSIONAL = /acit|ex(?:s|g|n|p|$)|rph|grid|ows|mnc|ntw|ine[ch]|zoo|^ord/i;\n","import { _catchError } from './diff/catch-error';\n\n/**\n * The `option` object can potentially contain callback functions\n * that are called during various stages of our renderer. This is the\n * foundation on which all our addons like `preact/debug`, `preact/compat`,\n * and `preact/hooks` are based on. See the `Options` type in `internal.d.ts`\n * for a full list of available option hooks (most editors/IDEs allow you to\n * ctrl+click or cmd+click on mac the type definition below).\n * @type {import('./internal').Options}\n */\nconst options = {\n\t_catchError\n};\n\nexport default options;\n","import { enqueueRender } from '../component';\n\n/**\n * Find the closest error boundary to a thrown error and call it\n * @param {object} error The thrown value\n * @param {import('../internal').VNode} vnode The vnode that threw\n * the error that was caught (except for unmounting when this parameter\n * is the highest parent that was being unmounted)\n */\nexport function _catchError(error, vnode) {\n\t/** @type {import('../internal').Component} */\n\tlet component, hasCaught;\n\n\tfor (; (vnode = vnode._parent); ) {\n\t\tif ((component = vnode._component) && !component._processingException) {\n\t\t\ttry {\n\t\t\t\tif (\n\t\t\t\t\tcomponent.constructor &&\n\t\t\t\t\tcomponent.constructor.getDerivedStateFromError != null\n\t\t\t\t) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.setState(\n\t\t\t\t\t\tcomponent.constructor.getDerivedStateFromError(error)\n\t\t\t\t\t);\n\t\t\t\t}\n\n\t\t\t\tif (component.componentDidCatch != null) {\n\t\t\t\t\thasCaught = true;\n\t\t\t\t\tcomponent.componentDidCatch(error);\n\t\t\t\t}\n\n\t\t\t\tif (hasCaught)\n\t\t\t\t\treturn enqueueRender((component._pendingError = component));\n\t\t\t} catch (e) {\n\t\t\t\terror = e;\n\t\t\t}\n\t\t}\n\t}\n\n\tthrow error;\n}\n","/* global __webpack_public_path__ */\n\nimport * as Preact from 'preact';\nconst { h, render, hydrate } = Preact;\n\nconst interopDefault = m => (m && m.default ? m.default : m);\n\nif (process.env.NODE_ENV === 'development') {\n\t// enable preact devtools\n\trequire('preact/debug');\n\tif (process.env.RHL) {\n\t\t// enable hot loader\n\t\tconst hotLoader = interopDefault(require('react-hot-loader'));\n\t\thotLoader.preact(interopDefault(require('preact')));\n\t}\n\t// only add a debug sw if webpack service worker is not requested.\n\tif (process.env.ADD_SW === undefined && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(__webpack_public_path__ + 'sw-debug.js');\n\t} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t\t// eslint-disable-next-line no-undef\n\t\tnavigator.serviceWorker.register(\n\t\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t\t);\n\t}\n} else if (process.env.ADD_SW && 'serviceWorker' in navigator) {\n\t// eslint-disable-next-line no-undef\n\tnavigator.serviceWorker.register(\n\t\t__webpack_public_path__ + (process.env.ES_BUILD ? 'sw-esm.js' : 'sw.js')\n\t);\n}\n\nlet app = interopDefault(require('preact-cli-entrypoint'));\n\nif (typeof app === 'function') {\n\tlet root =\n\t\tdocument.getElementById('preact_root') || document.body.firstElementChild;\n\n\tlet init = () => {\n\t\tlet app = interopDefault(require('preact-cli-entrypoint'));\n\t\tlet preRenderData = {};\n\t\tconst inlineDataElement = document.querySelector(\n\t\t\t'[type=\"__PREACT_CLI_DATA__\"]'\n\t\t);\n\t\tif (inlineDataElement) {\n\t\t\tpreRenderData = JSON.parse(inlineDataElement.innerHTML).preRenderData;\n\t\t}\n\t\t/* An object named CLI_DATA is passed as a prop,\n\t\t * this keeps us future proof if in case we decide,\n\t\t * to send other data like at some point in time.\n\t\t */\n\t\tconst CLI_DATA = { preRenderData };\n\t\tconst doRender =\n\t\t\tprocess.env.NODE_ENV !== 'production' ||\n\t\t\troot.tagName === 'script' ||\n\t\t\t!hydrate\n\t\t\t\t? render\n\t\t\t\t: hydrate;\n\t\troot = doRender(h(app, { CLI_DATA }), document.body, root);\n\t};\n\n\tif (module.hot) module.hot.accept('preact-cli-entrypoint', init);\n\n\tinit();\n}\n","export default function _extends() {\n  _extends = Object.assign || function (target) {\n    for (var i = 1; i < arguments.length; i++) {\n      var source = arguments[i];\n\n      for (var key in source) {\n        if (Object.prototype.hasOwnProperty.call(source, key)) {\n          target[key] = source[key];\n        }\n      }\n    }\n\n    return target;\n  };\n\n  return _extends.apply(this, arguments);\n}","function isAbsolute(pathname) {\n  return pathname.charAt(0) === '/';\n}\n\n// About 1.5x faster than the two-arg version of Array#splice()\nfunction spliceOne(list, index) {\n  for (var i = index, k = i + 1, n = list.length; k < n; i += 1, k += 1) {\n    list[i] = list[k];\n  }\n\n  list.pop();\n}\n\n// This implementation is based heavily on node's url.parse\nfunction resolvePathname(to, from) {\n  if (from === undefined) from = '';\n\n  var toParts = (to && to.split('/')) || [];\n  var fromParts = (from && from.split('/')) || [];\n\n  var isToAbs = to && isAbsolute(to);\n  var isFromAbs = from && isAbsolute(from);\n  var mustEndAbs = isToAbs || isFromAbs;\n\n  if (to && isAbsolute(to)) {\n    // to is absolute\n    fromParts = toParts;\n  } else if (toParts.length) {\n    // to is relative, drop the filename\n    fromParts.pop();\n    fromParts = fromParts.concat(toParts);\n  }\n\n  if (!fromParts.length) return '/';\n\n  var hasTrailingSlash;\n  if (fromParts.length) {\n    var last = fromParts[fromParts.length - 1];\n    hasTrailingSlash = last === '.' || last === '..' || last === '';\n  } else {\n    hasTrailingSlash = false;\n  }\n\n  var up = 0;\n  for (var i = fromParts.length; i >= 0; i--) {\n    var part = fromParts[i];\n\n    if (part === '.') {\n      spliceOne(fromParts, i);\n    } else if (part === '..') {\n      spliceOne(fromParts, i);\n      up++;\n    } else if (up) {\n      spliceOne(fromParts, i);\n      up--;\n    }\n  }\n\n  if (!mustEndAbs) for (; up--; up) fromParts.unshift('..');\n\n  if (\n    mustEndAbs &&\n    fromParts[0] !== '' &&\n    (!fromParts[0] || !isAbsolute(fromParts[0]))\n  )\n    fromParts.unshift('');\n\n  var result = fromParts.join('/');\n\n  if (hasTrailingSlash && result.substr(-1) !== '/') result += '/';\n\n  return result;\n}\n\nexport default resolvePathname;\n","import _extends from '@babel/runtime/helpers/esm/extends';\nimport resolvePathname from 'resolve-pathname';\nimport valueEqual from 'value-equal';\nimport warning from 'tiny-warning';\nimport invariant from 'tiny-invariant';\n\nfunction addLeadingSlash(path) {\n  return path.charAt(0) === '/' ? path : '/' + path;\n}\nfunction stripLeadingSlash(path) {\n  return path.charAt(0) === '/' ? path.substr(1) : path;\n}\nfunction hasBasename(path, prefix) {\n  return path.toLowerCase().indexOf(prefix.toLowerCase()) === 0 && '/?#'.indexOf(path.charAt(prefix.length)) !== -1;\n}\nfunction stripBasename(path, prefix) {\n  return hasBasename(path, prefix) ? path.substr(prefix.length) : path;\n}\nfunction stripTrailingSlash(path) {\n  return path.charAt(path.length - 1) === '/' ? path.slice(0, -1) : path;\n}\nfunction parsePath(path) {\n  var pathname = path || '/';\n  var search = '';\n  var hash = '';\n  var hashIndex = pathname.indexOf('#');\n\n  if (hashIndex !== -1) {\n    hash = pathname.substr(hashIndex);\n    pathname = pathname.substr(0, hashIndex);\n  }\n\n  var searchIndex = pathname.indexOf('?');\n\n  if (searchIndex !== -1) {\n    search = pathname.substr(searchIndex);\n    pathname = pathname.substr(0, searchIndex);\n  }\n\n  return {\n    pathname: pathname,\n    search: search === '?' ? '' : search,\n    hash: hash === '#' ? '' : hash\n  };\n}\nfunction createPath(location) {\n  var pathname = location.pathname,\n      search = location.search,\n      hash = location.hash;\n  var path = pathname || '/';\n  if (search && search !== '?') path += search.charAt(0) === '?' ? search : \"?\" + search;\n  if (hash && hash !== '#') path += hash.charAt(0) === '#' ? hash : \"#\" + hash;\n  return path;\n}\n\nfunction createLocation(path, state, key, currentLocation) {\n  var location;\n\n  if (typeof path === 'string') {\n    // Two-arg form: push(path, state)\n    location = parsePath(path);\n    location.state = state;\n  } else {\n    // One-arg form: push(location)\n    location = _extends({}, path);\n    if (location.pathname === undefined) location.pathname = '';\n\n    if (location.search) {\n      if (location.search.charAt(0) !== '?') location.search = '?' + location.search;\n    } else {\n      location.search = '';\n    }\n\n    if (location.hash) {\n      if (location.hash.charAt(0) !== '#') location.hash = '#' + location.hash;\n    } else {\n      location.hash = '';\n    }\n\n    if (state !== undefined && location.state === undefined) location.state = state;\n  }\n\n  try {\n    location.pathname = decodeURI(location.pathname);\n  } catch (e) {\n    if (e instanceof URIError) {\n      throw new URIError('Pathname \"' + location.pathname + '\" could not be decoded. ' + 'This is likely caused by an invalid percent-encoding.');\n    } else {\n      throw e;\n    }\n  }\n\n  if (key) location.key = key;\n\n  if (currentLocation) {\n    // Resolve incomplete/relative pathname relative to current location.\n    if (!location.pathname) {\n      location.pathname = currentLocation.pathname;\n    } else if (location.pathname.charAt(0) !== '/') {\n      location.pathname = resolvePathname(location.pathname, currentLocation.pathname);\n    }\n  } else {\n    // When there is no prior location and pathname is empty, set it to /\n    if (!location.pathname) {\n      location.pathname = '/';\n    }\n  }\n\n  return location;\n}\nfunction locationsAreEqual(a, b) {\n  return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash && a.key === b.key && valueEqual(a.state, b.state);\n}\n\nfunction createTransitionManager() {\n  var prompt = null;\n\n  function setPrompt(nextPrompt) {\n    process.env.NODE_ENV !== \"production\" ? warning(prompt == null, 'A history supports only one prompt at a time') : void 0;\n    prompt = nextPrompt;\n    return function () {\n      if (prompt === nextPrompt) prompt = null;\n    };\n  }\n\n  function confirmTransitionTo(location, action, getUserConfirmation, callback) {\n    // TODO: If another transition starts while we're still confirming\n    // the previous one, we may end up in a weird state. Figure out the\n    // best way to handle this.\n    if (prompt != null) {\n      var result = typeof prompt === 'function' ? prompt(location, action) : prompt;\n\n      if (typeof result === 'string') {\n        if (typeof getUserConfirmation === 'function') {\n          getUserConfirmation(result, callback);\n        } else {\n          process.env.NODE_ENV !== \"production\" ? warning(false, 'A history needs a getUserConfirmation function in order to use a prompt message') : void 0;\n          callback(true);\n        }\n      } else {\n        // Return false from a transition hook to cancel the transition.\n        callback(result !== false);\n      }\n    } else {\n      callback(true);\n    }\n  }\n\n  var listeners = [];\n\n  function appendListener(fn) {\n    var isActive = true;\n\n    function listener() {\n      if (isActive) fn.apply(void 0, arguments);\n    }\n\n    listeners.push(listener);\n    return function () {\n      isActive = false;\n      listeners = listeners.filter(function (item) {\n        return item !== listener;\n      });\n    };\n  }\n\n  function notifyListeners() {\n    for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n      args[_key] = arguments[_key];\n    }\n\n    listeners.forEach(function (listener) {\n      return listener.apply(void 0, args);\n    });\n  }\n\n  return {\n    setPrompt: setPrompt,\n    confirmTransitionTo: confirmTransitionTo,\n    appendListener: appendListener,\n    notifyListeners: notifyListeners\n  };\n}\n\nvar canUseDOM = !!(typeof window !== 'undefined' && window.document && window.document.createElement);\nfunction getConfirmation(message, callback) {\n  callback(window.confirm(message)); // eslint-disable-line no-alert\n}\n/**\n * Returns true if the HTML5 history API is supported. Taken from Modernizr.\n *\n * https://github.com/Modernizr/Modernizr/blob/master/LICENSE\n * https://github.com/Modernizr/Modernizr/blob/master/feature-detects/history.js\n * changed to avoid false negatives for Windows Phones: https://github.com/reactjs/react-router/issues/586\n */\n\nfunction supportsHistory() {\n  var ua = window.navigator.userAgent;\n  if ((ua.indexOf('Android 2.') !== -1 || ua.indexOf('Android 4.0') !== -1) && ua.indexOf('Mobile Safari') !== -1 && ua.indexOf('Chrome') === -1 && ua.indexOf('Windows Phone') === -1) return false;\n  return window.history && 'pushState' in window.history;\n}\n/**\n * Returns true if browser fires popstate on hash change.\n * IE10 and IE11 do not.\n */\n\nfunction supportsPopStateOnHashChange() {\n  return window.navigator.userAgent.indexOf('Trident') === -1;\n}\n/**\n * Returns false if using go(n) with hash history causes a full page reload.\n */\n\nfunction supportsGoWithoutReloadUsingHash() {\n  return window.navigator.userAgent.indexOf('Firefox') === -1;\n}\n/**\n * Returns true if a given popstate event is an extraneous WebKit event.\n * Accounts for the fact that Chrome on iOS fires real popstate events\n * containing undefined state when pressing the back button.\n */\n\nfunction isExtraneousPopstateEvent(event) {\n  return event.state === undefined && navigator.userAgent.indexOf('CriOS') === -1;\n}\n\nvar PopStateEvent = 'popstate';\nvar HashChangeEvent = 'hashchange';\n\nfunction getHistoryState() {\n  try {\n    return window.history.state || {};\n  } catch (e) {\n    // IE 11 sometimes throws when accessing window.history.state\n    // See https://github.com/ReactTraining/history/pull/289\n    return {};\n  }\n}\n/**\n * Creates a history object that uses the HTML5 history API including\n * pushState, replaceState, and the popstate event.\n */\n\n\nfunction createBrowserHistory(props) {\n  if (props === void 0) {\n    props = {};\n  }\n\n  !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Browser history needs a DOM') : invariant(false) : void 0;\n  var globalHistory = window.history;\n  var canUseHistory = supportsHistory();\n  var needsHashChangeListener = !supportsPopStateOnHashChange();\n  var _props = props,\n      _props$forceRefresh = _props.forceRefresh,\n      forceRefresh = _props$forceRefresh === void 0 ? false : _props$forceRefresh,\n      _props$getUserConfirm = _props.getUserConfirmation,\n      getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n      _props$keyLength = _props.keyLength,\n      keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n  var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n\n  function getDOMLocation(historyState) {\n    var _ref = historyState || {},\n        key = _ref.key,\n        state = _ref.state;\n\n    var _window$location = window.location,\n        pathname = _window$location.pathname,\n        search = _window$location.search,\n        hash = _window$location.hash;\n    var path = pathname + search + hash;\n    process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n    if (basename) path = stripBasename(path, basename);\n    return createLocation(path, state, key);\n  }\n\n  function createKey() {\n    return Math.random().toString(36).substr(2, keyLength);\n  }\n\n  var transitionManager = createTransitionManager();\n\n  function setState(nextState) {\n    _extends(history, nextState);\n\n    history.length = globalHistory.length;\n    transitionManager.notifyListeners(history.location, history.action);\n  }\n\n  function handlePopState(event) {\n    // Ignore extraneous popstate events in WebKit.\n    if (isExtraneousPopstateEvent(event)) return;\n    handlePop(getDOMLocation(event.state));\n  }\n\n  function handleHashChange() {\n    handlePop(getDOMLocation(getHistoryState()));\n  }\n\n  var forceNextPop = false;\n\n  function handlePop(location) {\n    if (forceNextPop) {\n      forceNextPop = false;\n      setState();\n    } else {\n      var action = 'POP';\n      transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n        if (ok) {\n          setState({\n            action: action,\n            location: location\n          });\n        } else {\n          revertPop(location);\n        }\n      });\n    }\n  }\n\n  function revertPop(fromLocation) {\n    var toLocation = history.location; // TODO: We could probably make this more reliable by\n    // keeping a list of keys we've seen in sessionStorage.\n    // Instead, we just default to 0 for keys we don't know.\n\n    var toIndex = allKeys.indexOf(toLocation.key);\n    if (toIndex === -1) toIndex = 0;\n    var fromIndex = allKeys.indexOf(fromLocation.key);\n    if (fromIndex === -1) fromIndex = 0;\n    var delta = toIndex - fromIndex;\n\n    if (delta) {\n      forceNextPop = true;\n      go(delta);\n    }\n  }\n\n  var initialLocation = getDOMLocation(getHistoryState());\n  var allKeys = [initialLocation.key]; // Public interface\n\n  function createHref(location) {\n    return basename + createPath(location);\n  }\n\n  function push(path, state) {\n    process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n    var action = 'PUSH';\n    var location = createLocation(path, state, createKey(), history.location);\n    transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n      if (!ok) return;\n      var href = createHref(location);\n      var key = location.key,\n          state = location.state;\n\n      if (canUseHistory) {\n        globalHistory.pushState({\n          key: key,\n          state: state\n        }, null, href);\n\n        if (forceRefresh) {\n          window.location.href = href;\n        } else {\n          var prevIndex = allKeys.indexOf(history.location.key);\n          var nextKeys = allKeys.slice(0, prevIndex + 1);\n          nextKeys.push(location.key);\n          allKeys = nextKeys;\n          setState({\n            action: action,\n            location: location\n          });\n        }\n      } else {\n        process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot push state in browsers that do not support HTML5 history') : void 0;\n        window.location.href = href;\n      }\n    });\n  }\n\n  function replace(path, state) {\n    process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n    var action = 'REPLACE';\n    var location = createLocation(path, state, createKey(), history.location);\n    transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n      if (!ok) return;\n      var href = createHref(location);\n      var key = location.key,\n          state = location.state;\n\n      if (canUseHistory) {\n        globalHistory.replaceState({\n          key: key,\n          state: state\n        }, null, href);\n\n        if (forceRefresh) {\n          window.location.replace(href);\n        } else {\n          var prevIndex = allKeys.indexOf(history.location.key);\n          if (prevIndex !== -1) allKeys[prevIndex] = location.key;\n          setState({\n            action: action,\n            location: location\n          });\n        }\n      } else {\n        process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Browser history cannot replace state in browsers that do not support HTML5 history') : void 0;\n        window.location.replace(href);\n      }\n    });\n  }\n\n  function go(n) {\n    globalHistory.go(n);\n  }\n\n  function goBack() {\n    go(-1);\n  }\n\n  function goForward() {\n    go(1);\n  }\n\n  var listenerCount = 0;\n\n  function checkDOMListeners(delta) {\n    listenerCount += delta;\n\n    if (listenerCount === 1 && delta === 1) {\n      window.addEventListener(PopStateEvent, handlePopState);\n      if (needsHashChangeListener) window.addEventListener(HashChangeEvent, handleHashChange);\n    } else if (listenerCount === 0) {\n      window.removeEventListener(PopStateEvent, handlePopState);\n      if (needsHashChangeListener) window.removeEventListener(HashChangeEvent, handleHashChange);\n    }\n  }\n\n  var isBlocked = false;\n\n  function block(prompt) {\n    if (prompt === void 0) {\n      prompt = false;\n    }\n\n    var unblock = transitionManager.setPrompt(prompt);\n\n    if (!isBlocked) {\n      checkDOMListeners(1);\n      isBlocked = true;\n    }\n\n    return function () {\n      if (isBlocked) {\n        isBlocked = false;\n        checkDOMListeners(-1);\n      }\n\n      return unblock();\n    };\n  }\n\n  function listen(listener) {\n    var unlisten = transitionManager.appendListener(listener);\n    checkDOMListeners(1);\n    return function () {\n      checkDOMListeners(-1);\n      unlisten();\n    };\n  }\n\n  var history = {\n    length: globalHistory.length,\n    action: 'POP',\n    location: initialLocation,\n    createHref: createHref,\n    push: push,\n    replace: replace,\n    go: go,\n    goBack: goBack,\n    goForward: goForward,\n    block: block,\n    listen: listen\n  };\n  return history;\n}\n\nvar HashChangeEvent$1 = 'hashchange';\nvar HashPathCoders = {\n  hashbang: {\n    encodePath: function encodePath(path) {\n      return path.charAt(0) === '!' ? path : '!/' + stripLeadingSlash(path);\n    },\n    decodePath: function decodePath(path) {\n      return path.charAt(0) === '!' ? path.substr(1) : path;\n    }\n  },\n  noslash: {\n    encodePath: stripLeadingSlash,\n    decodePath: addLeadingSlash\n  },\n  slash: {\n    encodePath: addLeadingSlash,\n    decodePath: addLeadingSlash\n  }\n};\n\nfunction stripHash(url) {\n  var hashIndex = url.indexOf('#');\n  return hashIndex === -1 ? url : url.slice(0, hashIndex);\n}\n\nfunction getHashPath() {\n  // We can't use window.location.hash here because it's not\n  // consistent across browsers - Firefox will pre-decode it!\n  var href = window.location.href;\n  var hashIndex = href.indexOf('#');\n  return hashIndex === -1 ? '' : href.substring(hashIndex + 1);\n}\n\nfunction pushHashPath(path) {\n  window.location.hash = path;\n}\n\nfunction replaceHashPath(path) {\n  window.location.replace(stripHash(window.location.href) + '#' + path);\n}\n\nfunction createHashHistory(props) {\n  if (props === void 0) {\n    props = {};\n  }\n\n  !canUseDOM ? process.env.NODE_ENV !== \"production\" ? invariant(false, 'Hash history needs a DOM') : invariant(false) : void 0;\n  var globalHistory = window.history;\n  var canGoWithoutReload = supportsGoWithoutReloadUsingHash();\n  var _props = props,\n      _props$getUserConfirm = _props.getUserConfirmation,\n      getUserConfirmation = _props$getUserConfirm === void 0 ? getConfirmation : _props$getUserConfirm,\n      _props$hashType = _props.hashType,\n      hashType = _props$hashType === void 0 ? 'slash' : _props$hashType;\n  var basename = props.basename ? stripTrailingSlash(addLeadingSlash(props.basename)) : '';\n  var _HashPathCoders$hashT = HashPathCoders[hashType],\n      encodePath = _HashPathCoders$hashT.encodePath,\n      decodePath = _HashPathCoders$hashT.decodePath;\n\n  function getDOMLocation() {\n    var path = decodePath(getHashPath());\n    process.env.NODE_ENV !== \"production\" ? warning(!basename || hasBasename(path, basename), 'You are attempting to use a basename on a page whose URL path does not begin ' + 'with the basename. Expected path \"' + path + '\" to begin with \"' + basename + '\".') : void 0;\n    if (basename) path = stripBasename(path, basename);\n    return createLocation(path);\n  }\n\n  var transitionManager = createTransitionManager();\n\n  function setState(nextState) {\n    _extends(history, nextState);\n\n    history.length = globalHistory.length;\n    transitionManager.notifyListeners(history.location, history.action);\n  }\n\n  var forceNextPop = false;\n  var ignorePath = null;\n\n  function locationsAreEqual$$1(a, b) {\n    return a.pathname === b.pathname && a.search === b.search && a.hash === b.hash;\n  }\n\n  function handleHashChange() {\n    var path = getHashPath();\n    var encodedPath = encodePath(path);\n\n    if (path !== encodedPath) {\n      // Ensure we always have a properly-encoded hash.\n      replaceHashPath(encodedPath);\n    } else {\n      var location = getDOMLocation();\n      var prevLocation = history.location;\n      if (!forceNextPop && locationsAreEqual$$1(prevLocation, location)) return; // A hashchange doesn't always == location change.\n\n      if (ignorePath === createPath(location)) return; // Ignore this change; we already setState in push/replace.\n\n      ignorePath = null;\n      handlePop(location);\n    }\n  }\n\n  function handlePop(location) {\n    if (forceNextPop) {\n      forceNextPop = false;\n      setState();\n    } else {\n      var action = 'POP';\n      transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n        if (ok) {\n          setState({\n            action: action,\n            location: location\n          });\n        } else {\n          revertPop(location);\n        }\n      });\n    }\n  }\n\n  function revertPop(fromLocation) {\n    var toLocation = history.location; // TODO: We could probably make this more reliable by\n    // keeping a list of paths we've seen in sessionStorage.\n    // Instead, we just default to 0 for paths we don't know.\n\n    var toIndex = allPaths.lastIndexOf(createPath(toLocation));\n    if (toIndex === -1) toIndex = 0;\n    var fromIndex = allPaths.lastIndexOf(createPath(fromLocation));\n    if (fromIndex === -1) fromIndex = 0;\n    var delta = toIndex - fromIndex;\n\n    if (delta) {\n      forceNextPop = true;\n      go(delta);\n    }\n  } // Ensure the hash is encoded properly before doing anything else.\n\n\n  var path = getHashPath();\n  var encodedPath = encodePath(path);\n  if (path !== encodedPath) replaceHashPath(encodedPath);\n  var initialLocation = getDOMLocation();\n  var allPaths = [createPath(initialLocation)]; // Public interface\n\n  function createHref(location) {\n    var baseTag = document.querySelector('base');\n    var href = '';\n\n    if (baseTag && baseTag.getAttribute('href')) {\n      href = stripHash(window.location.href);\n    }\n\n    return href + '#' + encodePath(basename + createPath(location));\n  }\n\n  function push(path, state) {\n    process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot push state; it is ignored') : void 0;\n    var action = 'PUSH';\n    var location = createLocation(path, undefined, undefined, history.location);\n    transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n      if (!ok) return;\n      var path = createPath(location);\n      var encodedPath = encodePath(basename + path);\n      var hashChanged = getHashPath() !== encodedPath;\n\n      if (hashChanged) {\n        // We cannot tell if a hashchange was caused by a PUSH, so we'd\n        // rather setState here and ignore the hashchange. The caveat here\n        // is that other hash histories in the page will consider it a POP.\n        ignorePath = path;\n        pushHashPath(encodedPath);\n        var prevIndex = allPaths.lastIndexOf(createPath(history.location));\n        var nextPaths = allPaths.slice(0, prevIndex + 1);\n        nextPaths.push(path);\n        allPaths = nextPaths;\n        setState({\n          action: action,\n          location: location\n        });\n      } else {\n        process.env.NODE_ENV !== \"production\" ? warning(false, 'Hash history cannot PUSH the same path; a new entry will not be added to the history stack') : void 0;\n        setState();\n      }\n    });\n  }\n\n  function replace(path, state) {\n    process.env.NODE_ENV !== \"production\" ? warning(state === undefined, 'Hash history cannot replace state; it is ignored') : void 0;\n    var action = 'REPLACE';\n    var location = createLocation(path, undefined, undefined, history.location);\n    transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n      if (!ok) return;\n      var path = createPath(location);\n      var encodedPath = encodePath(basename + path);\n      var hashChanged = getHashPath() !== encodedPath;\n\n      if (hashChanged) {\n        // We cannot tell if a hashchange was caused by a REPLACE, so we'd\n        // rather setState here and ignore the hashchange. The caveat here\n        // is that other hash histories in the page will consider it a POP.\n        ignorePath = path;\n        replaceHashPath(encodedPath);\n      }\n\n      var prevIndex = allPaths.indexOf(createPath(history.location));\n      if (prevIndex !== -1) allPaths[prevIndex] = path;\n      setState({\n        action: action,\n        location: location\n      });\n    });\n  }\n\n  function go(n) {\n    process.env.NODE_ENV !== \"production\" ? warning(canGoWithoutReload, 'Hash history go(n) causes a full page reload in this browser') : void 0;\n    globalHistory.go(n);\n  }\n\n  function goBack() {\n    go(-1);\n  }\n\n  function goForward() {\n    go(1);\n  }\n\n  var listenerCount = 0;\n\n  function checkDOMListeners(delta) {\n    listenerCount += delta;\n\n    if (listenerCount === 1 && delta === 1) {\n      window.addEventListener(HashChangeEvent$1, handleHashChange);\n    } else if (listenerCount === 0) {\n      window.removeEventListener(HashChangeEvent$1, handleHashChange);\n    }\n  }\n\n  var isBlocked = false;\n\n  function block(prompt) {\n    if (prompt === void 0) {\n      prompt = false;\n    }\n\n    var unblock = transitionManager.setPrompt(prompt);\n\n    if (!isBlocked) {\n      checkDOMListeners(1);\n      isBlocked = true;\n    }\n\n    return function () {\n      if (isBlocked) {\n        isBlocked = false;\n        checkDOMListeners(-1);\n      }\n\n      return unblock();\n    };\n  }\n\n  function listen(listener) {\n    var unlisten = transitionManager.appendListener(listener);\n    checkDOMListeners(1);\n    return function () {\n      checkDOMListeners(-1);\n      unlisten();\n    };\n  }\n\n  var history = {\n    length: globalHistory.length,\n    action: 'POP',\n    location: initialLocation,\n    createHref: createHref,\n    push: push,\n    replace: replace,\n    go: go,\n    goBack: goBack,\n    goForward: goForward,\n    block: block,\n    listen: listen\n  };\n  return history;\n}\n\nfunction clamp(n, lowerBound, upperBound) {\n  return Math.min(Math.max(n, lowerBound), upperBound);\n}\n/**\n * Creates a history object that stores locations in memory.\n */\n\n\nfunction createMemoryHistory(props) {\n  if (props === void 0) {\n    props = {};\n  }\n\n  var _props = props,\n      getUserConfirmation = _props.getUserConfirmation,\n      _props$initialEntries = _props.initialEntries,\n      initialEntries = _props$initialEntries === void 0 ? ['/'] : _props$initialEntries,\n      _props$initialIndex = _props.initialIndex,\n      initialIndex = _props$initialIndex === void 0 ? 0 : _props$initialIndex,\n      _props$keyLength = _props.keyLength,\n      keyLength = _props$keyLength === void 0 ? 6 : _props$keyLength;\n  var transitionManager = createTransitionManager();\n\n  function setState(nextState) {\n    _extends(history, nextState);\n\n    history.length = history.entries.length;\n    transitionManager.notifyListeners(history.location, history.action);\n  }\n\n  function createKey() {\n    return Math.random().toString(36).substr(2, keyLength);\n  }\n\n  var index = clamp(initialIndex, 0, initialEntries.length - 1);\n  var entries = initialEntries.map(function (entry) {\n    return typeof entry === 'string' ? createLocation(entry, undefined, createKey()) : createLocation(entry, undefined, entry.key || createKey());\n  }); // Public interface\n\n  var createHref = createPath;\n\n  function push(path, state) {\n    process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to push when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n    var action = 'PUSH';\n    var location = createLocation(path, state, createKey(), history.location);\n    transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n      if (!ok) return;\n      var prevIndex = history.index;\n      var nextIndex = prevIndex + 1;\n      var nextEntries = history.entries.slice(0);\n\n      if (nextEntries.length > nextIndex) {\n        nextEntries.splice(nextIndex, nextEntries.length - nextIndex, location);\n      } else {\n        nextEntries.push(location);\n      }\n\n      setState({\n        action: action,\n        location: location,\n        index: nextIndex,\n        entries: nextEntries\n      });\n    });\n  }\n\n  function replace(path, state) {\n    process.env.NODE_ENV !== \"production\" ? warning(!(typeof path === 'object' && path.state !== undefined && state !== undefined), 'You should avoid providing a 2nd state argument to replace when the 1st ' + 'argument is a location-like object that already has state; it is ignored') : void 0;\n    var action = 'REPLACE';\n    var location = createLocation(path, state, createKey(), history.location);\n    transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n      if (!ok) return;\n      history.entries[history.index] = location;\n      setState({\n        action: action,\n        location: location\n      });\n    });\n  }\n\n  function go(n) {\n    var nextIndex = clamp(history.index + n, 0, history.entries.length - 1);\n    var action = 'POP';\n    var location = history.entries[nextIndex];\n    transitionManager.confirmTransitionTo(location, action, getUserConfirmation, function (ok) {\n      if (ok) {\n        setState({\n          action: action,\n          location: location,\n          index: nextIndex\n        });\n      } else {\n        // Mimic the behavior of DOM histories by\n        // causing a render after a cancelled POP.\n        setState();\n      }\n    });\n  }\n\n  function goBack() {\n    go(-1);\n  }\n\n  function goForward() {\n    go(1);\n  }\n\n  function canGo(n) {\n    var nextIndex = history.index + n;\n    return nextIndex >= 0 && nextIndex < history.entries.length;\n  }\n\n  function block(prompt) {\n    if (prompt === void 0) {\n      prompt = false;\n    }\n\n    return transitionManager.setPrompt(prompt);\n  }\n\n  function listen(listener) {\n    return transitionManager.appendListener(listener);\n  }\n\n  var history = {\n    length: entries.length,\n    action: 'POP',\n    location: entries[index],\n    index: index,\n    entries: entries,\n    createHref: createHref,\n    push: push,\n    replace: replace,\n    go: go,\n    goBack: goBack,\n    goForward: goForward,\n    canGo: canGo,\n    block: block,\n    listen: listen\n  };\n  return history;\n}\n\nexport { createBrowserHistory, createHashHistory, createMemoryHistory, createLocation, locationsAreEqual, parsePath, createPath };\n","var isProduction = process.env.NODE_ENV === 'production';\nvar prefix = 'Invariant failed';\nfunction invariant(condition, message) {\n    if (condition) {\n        return;\n    }\n    if (isProduction) {\n        throw new Error(prefix);\n    }\n    throw new Error(prefix + \": \" + (message || ''));\n}\n\nexport default invariant;\n","\n\t\timport Async from \"../../node_modules/@preact/async-loader/async-legacy.js\";\n\n\t\tfunction load(cb) {\n\t\t\trequire.ensure([], function (require) {\n\t\t\t\tcb( require(\"!!../../node_modules/babel-loader/lib/index.js??ref--4!./fisica.js\") );\n\t\t\t}, \"route-fisica\");\n\t\t}\n\n\t\texport default Async(load);\n\t"],"sourceRoot":""}
\ No newline at end of file
diff --git a/docs/index.html b/docs/index.html
index 282ca30..cd6d2d0 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -1 +1 @@
-Appunti Web
    Appuntiweb di Steffo
    Indice
    Argomenti
    Statistica ed elementi di probabilità
    Appunti scritti mentre studiavo per l'esame di Statistica ed elementi di probabilità del corso triennale di Informatica all'Unimore del Prof. Luca La Rocca.
    Cleaver
    Progetto in Java sviluppato per l'esame di Programmazione ad Oggetti del corso triennale di Informatica all'Unimore, tenuto dai Prof. Giacomo Cabri e Nicola Capodieci.
    Fisica
    Appunti delle lezioni di Fisica del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Rossella Brunetti nel primo semestre dell'Anno Accademico 2019/2020.
    Sistemi Operativi
    Soluzioni agli Arzigogoli proposti dal Prof. Mauro Andreolini durante le lezioni di Sistemi Operativi del corso triennale di Informatica all'Unimore tenutesi nel primo semestre dell'Anno Accademico 2019/2020.
    Algoritmi e Strutture Dati
    Appunti delle lezioni di Algoritmi e Strutture Dati del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Manuela Montangero nel secondo semestre dell'Anno Accademico 2018/2019.
    Videolezioni di Geometria
    Ottime videolezioni di Geometria con licenza CC BY-NC-SA 4.0 che ho trovato sul portale Dolly 2018 dell'Unimore.
    Come installare MinGW
    Un breve tutorial con immagini su come installare e configurare MinGW per compilare programmi C e C++ su Windows.
    Altri collegamenti utili
    @unimoreinfo
    Il gruppo Telegram del corso di Informatica dell'Unimore!
    Calendario Lezioni
    Calendario Google quasi sempre aggiornato delle lezioni e degli esami del secondo anno dell'Unimore durante l'Anno Accademico 2019/2020.
    Erre2
    Portale contenente appunti e riassunti mantenuto da Lorenzo Balugani.
    vezzalinistefano/Appunti-Algoritmi
    Appunti di Algoritmi e Strutture Dati mantenuti da Vezzalini Stefano.
    © 2019 - Stefano Pigozzi - CC BY-SA 4.0 - Codice sorgente
    
\ No newline at end of file
+Appunti Web
\ No newline at end of file
diff --git a/docs/polyfills.04c22.js b/docs/polyfills.04c22.js
deleted file mode 100644
index 36ff627..0000000
--- a/docs/polyfills.04c22.js
+++ /dev/null
@@ -1,2 +0,0 @@
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new file mode 100644
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new file mode 100644
index 0000000..ba2377c
--- /dev/null
+++ b/docs/precache-manifest.0f27a05868e94597f6d2279c6bbf2f4a.esm.js
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+    "revision": "2b714cf154cd80b3949545dfe0c5939a",
+    "url": "/assets/icon.png"
+  },
+  {
+    "revision": "f77a130a2b960711ff18",
+    "url": "/bundle.39cb3.esm.js"
+  },
+  {
+    "revision": "f77a130a2b960711ff18",
+    "url": "/bundle.446a2.css"
+  },
+  {
+    "revision": "83a7cbb32e037c5786b37fd38eb1b89e",
+    "url": "/index.html"
+  },
+  {
+    "revision": "bb23adb3c9bfbb7f047f",
+    "url": "/polyfills.06b13.esm.js"
+  },
+  {
+    "revision": "823c83e54f60049b4aeb",
+    "url": "/route-fisica.chunk.98137.css"
+  },
+  {
+    "revision": "823c83e54f60049b4aeb",
+    "url": "/route-fisica.chunk.c81bf.esm.js"
+  },
+  {
+    "revision": "b306e2ff6ac0904393f3",
+    "url": "/route-home.chunk.0c2c0.css"
+  },
+  {
+    "revision": "b306e2ff6ac0904393f3",
+    "url": "/route-home.chunk.0d3d3.esm.js"
+  },
+  {
+    "revision": "4b543345fcfc4e79c35b",
+    "url": "/route-mingwinstall.chunk.1d3c8.css"
+  },
+  {
+    "revision": "4b543345fcfc4e79c35b",
+    "url": "/route-mingwinstall.chunk.97b52.esm.js"
+  },
+  {
+    "revision": "0864e8194d0d81987c29",
+    "url": "/route-statistica.chunk.1c94d.esm.js"
+  },
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+    "revision": "0864e8194d0d81987c29",
+    "url": "/route-statistica.chunk.57ea3.css"
+  },
+  {
+    "revision": "5dcf173bdcbe145af9f5",
+    "url": "/route-vldigeometria.chunk.5dea5.css"
+  },
+  {
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+    "url": "/route-vldigeometria.chunk.dc16e.esm.js"
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+]);
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new file mode 100644
index 0000000..93ff57d
--- /dev/null
+++ b/docs/precache-manifest.2df4a1db73a8dca4c45380d964d8e39d.js
@@ -0,0 +1,74 @@
+self.__precacheManifest = (self.__precacheManifest || []).concat([
+  {
+    "revision": "2b714cf154cd80b3949545dfe0c5939a",
+    "url": "/assets/icon.png"
+  },
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+    "revision": "f77a130a2b960711ff18",
+    "url": "/bundle.446a2.css"
+  },
+  {
+    "revision": "f77a130a2b960711ff18",
+    "url": "/bundle.f77a1.js"
+  },
+  {
+    "revision": "83a7cbb32e037c5786b37fd38eb1b89e",
+    "url": "/index.html"
+  },
+  {
+    "revision": "bb23adb3c9bfbb7f047f",
+    "url": "/polyfills.bb23a.js"
+  },
+  {
+    "revision": "823c83e54f60049b4aeb",
+    "url": "/route-fisica.chunk.823c8.js"
+  },
+  {
+    "revision": "823c83e54f60049b4aeb",
+    "url": "/route-fisica.chunk.98137.css"
+  },
+  {
+    "revision": "b306e2ff6ac0904393f3",
+    "url": "/route-home.chunk.0c2c0.css"
+  },
+  {
+    "revision": "b306e2ff6ac0904393f3",
+    "url": "/route-home.chunk.b306e.js"
+  },
+  {
+    "revision": "4b543345fcfc4e79c35b",
+    "url": "/route-mingwinstall.chunk.1d3c8.css"
+  },
+  {
+    "revision": "4b543345fcfc4e79c35b",
+    "url": "/route-mingwinstall.chunk.4b543.js"
+  },
+  {
+    "revision": "0864e8194d0d81987c29",
+    "url": "/route-statistica.chunk.0864e.js"
+  },
+  {
+    "revision": "0864e8194d0d81987c29",
+    "url": "/route-statistica.chunk.57ea3.css"
+  },
+  {
+    "revision": "5dcf173bdcbe145af9f5",
+    "url": "/route-vldigeometria.chunk.5dcf1.js"
+  },
+  {
+    "revision": "5dcf173bdcbe145af9f5",
+    "url": "/route-vldigeometria.chunk.5dea5.css"
+  },
+  {
+    "revision": "13b82ed03d648451c57be206f75f0216",
+    "url": "/sw-debug.js"
+  },
+  {
+    "revision": "1fbc72d0ac41c0424585ba10f743f58e",
+    "url": "/sw-esm.js"
+  },
+  {
+    "revision": "bfc5bd18885255982238f3628770f48d",
+    "url": "/sw.js"
+  }
+]);
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diff --git a/docs/push-manifest.json b/docs/push-manifest.json
index e3fd4cb..548afa2 100644
--- a/docs/push-manifest.json
+++ b/docs/push-manifest.json
@@ -1 +1 @@
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diff --git a/docs/route-fisica.chunk.823c8.js b/docs/route-fisica.chunk.823c8.js
new file mode 100644
index 0000000..c75577a
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left | \vec{v} \right | left | \vec{w} \right | cos alpha"],["\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha"]);return Cn=function(){return e},e}function An(){var e=Sn(["\vec{v} - \vec{w} = (\vec{v}_x - \vec{w}_x) + (\vec{v}_y - \vec{w}_y)"],["\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)"]);return An=function(){return e},e}function En(){var e=Sn(["\vec{v} + \vec{w} = (\vec{v}_x + \vec{w}_x) + (\vec{v}_y + \vec{w}_y)"],["\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)"]);return En=function(){return e},e}function Pn(){var e=Sn(["left | \vec{v}_y \right | = left | \vec{v} \right | cos alpha"],["\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha"]);return Pn=function(){return e},e}function yn(){var e=Sn(["left | \vec{v}_x \right | = left | \vec{v} \right | sin alpha"],["\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha"]);return yn=function(){return e},e}function In(){var e=Sn(["\vec{v} = \vec{v}_x + \vec{v}_y"],["\\vec{v} = \\vec{v}_x + \\vec{v}_y"]);return In=function(){return e},e}function Sn(e,n){return n||(n=e.slice(0)),e.raw=n,e}t.d(n,"default",(function(){return Gn}));var Bn=t("dyG3"),kn=t.n(Bn),wn=t("hosL"),xn=t("ZsnK"),Vn=t("9yVG"),Nn=t("ddBW"),Tn=t("bQQT"),Rn=t("GC6P"),Mn=t("7bXG"),Un=String.raw,Gn=function(n){function t(){return n.apply(this,arguments)||this}var Sn,Bn;return Bn=n,(Sn=t).prototype=Object.create(Bn.prototype),Sn.prototype.constructor=Sn,Sn.__proto__=Bn,t.prototype.render=function(){return e("div",{style:kn.a.fisica},e("h1",null,"Fisica"),e(Nn.a,{title:"Vettori"},e(Vn.a,{title:"Componenti cartesiane"},e("p",null,"Usa le regole base della trigonometria:"),e("p",null,e(xn.a,null,Un(In()))),e("p",null,e(xn.a,null,Un(yn()))),e("p",null,e(xn.a,null,Un(Pn())))),e(Vn.a,{title:"Somma"},e("p",null,"Scomponi in componenti, poi sommali:"),e("p",null,e(xn.a,null,Un(En()))),e("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma.")),e(Vn.a,{title:"Differenza"},e("p",null,"Alla fine è sempre una somma:"),e("p",null,e(xn.a,null,Un(An()))),e("p",null,"Produce il vettore che parte da ",e(xn.a,null,"w")," e arriva a ",e(xn.a,null,"v"),".")),e(Vn.a,{title:"Prodotto scalare"},e("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),e("p",null,e(xn.a,null,Un(Cn()))),e("p",null,"Produce il modulo della proiezione di ",e(xn.a,null,Un(Fn()))," su ",e(xn.a,null,Un(qn())),".")),e(Vn.a,{title:"Prodotto vettoriale"},e("p",null,"Si chiama vettoriale perchè il risultato è un altro vettore."),e("ul",null,e("li",null,e(xn.a,null,Un(Ln()))),e("li",null,e(xn.a,null,Un(Dn()))),e("li",null,e("a",{href:"https://it.wikipedia.org/wiki/Regola_della_mano_destra"},"Regola della mano destra"))),e("p",null,"Non è commutativo!"))),e(Nn.a,{title:"Leggi di Newton"},e(Vn.a,{title:"1ᵃ: Inerzia"},e("p",null,"Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia."),e("p",null,e(xn.a,null,Un(bn())))),e(Vn.a,{title:"2ᵃ: Proporzionalità"},e("p",null,"La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la ",e("i",null,"massa"),"."),e("p",null,e(xn.a,null,Un(zn())))),e(Vn.a,{title:"3ᵃ: Azione e reazione"},e("p",null,"Due corpi esercitano forze uguali e opposte uno sull'altro."),e("p",null,e(xn.a,null,Un(_n()))))),e(Nn.a,{title:"Forza di gravità"},e(Vn.a,{title:"Tra due corpi"},e("p",null,"Due corpi puntiformi si attirano uno verso l'altro con forza:"),e("p",null,e(xn.a,null,Un(hn()))),e("p",null,e(xn.a,null,"G")," è la ",e("i",null,"costante di gravitazione universale")," e vale:"),e("p",null,e(xn.a,null,Un(gn())))),e(Vn.a,{title:"Verso la Terra"},e("p",null,"Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza ",e("i",null,"peso")," uguale a:"),e("p",null,e(xn.a,null,Un(mn()))),e("p",null,e(xn.a,null,"g")," è la ",e("i",null,"costante di gravità")," della Terra, e vale:"),e("p",null,e(xn.a,null,Un(vn())))),e(Vn.a,{title:"Su pianeti diversi"},e("p",null,"Per pianeti diversi dalla Terra vale la stessa regola:"),e("p",null,e(xn.a,null,Un(fn()))),e("p",null,"L'unica differenza è che cambia la ",e("i",null,"costante di gravità"),":"),e("p",null,e(xn.a,null,Un(dn()))),e("p",null,e(xn.a,null,Un(sn()))))),e(Nn.a,{title:"Forze di contatto"},e(Vn.a,{title:"Normale"},e("p",null,"Si oppone alle forze applicate alla superficie di contatto."),e("p",null,"Un libro appoggiato su un tavolo ha la ",e("b",null,"forza di gravità")," che lo attira verso il terreno e la ",e("b",null,"forza normale")," che lo trattiene dal cadere.")),e(Vn.a,{title:"Attrito statico"},e("p",null,"Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:"),e("p",null,e(xn.a,null,Un(pn())))),e(Vn.a,{title:"Attrito dinamico"},e("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),e("p",null,e(xn.a,null,Un(cn())))),e(Vn.a,{title:"Tensione"},e("p",null,"E' forza trasmessa tra due estremi di una fune."),e("p",null,"Può essere redirezionata per mezzo di carrucole.")),e(Vn.a,{title:"Elastica"},e("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),e("p",null,e(xn.a,null,Un(un()))),e("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"))),e(Nn.a,{title:"Cinematica"},e(Vn.a,{title:"Spostamento"},e("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),e("p",null,e(xn.a,null,Un(on())))),e(Vn.a,{title:"Velocità"},e("p",null,"È un vettore che misura la variazione di posizione nel tempo."),e("p",null,e(xn.a,null,Un(rn()))),e("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",e("i",null,"velocità istantanea"),":"),e("p",null,e(xn.a,null,Un(ln())))),e(Vn.a,{title:"Accelerazione"},e("p",null,"È un vettore che misura la variazione di velocità nel tempo."),e("p",null,e(xn.a,null,Un(an()))),e("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",e("i",null,"accelerazione istantanea"),":"),e("p",null,e(xn.a,null,Un(tn())))),e(Vn.a,{title:e("span",null,"Quantità di moto ",e("small",null,"(momento lineare)"))},e("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),e("p",null,e(xn.a,null,Un(nn()))),e("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),e("p",null,e(xn.a,null,Un(en()))))),e(Nn.a,{title:"Moto rettilineo uniforme"},e(Vn.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(xn.a,null,Un($e())))),e(Vn.a,{title:"Velocità"},e("p",null,"È costante:"),e("p",null,e(xn.a,null,Un(Ze())))),e(Vn.a,{title:"Accelerazione"},e("p",null,"La velocità non varia:"),e("p",null,e(xn.a,null,Un(Ye())))),e(Vn.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(xn.a,null,"f(t) = 0")))),e(Nn.a,{title:"Moto rettilineo uniformemente accelerato"},e(Vn.a,{title:"Spostamento"},e("p",null,"La ",e("i",null,"legge oraria")," è:"),e("p",null,e(xn.a,null,Un(Xe())))),e(Vn.a,{title:"Velocità"},e("p",null,"È una retta:"),e("p",null,e(xn.a,null,Un(Ke())))),e(Vn.a,{title:"Accelerazione"},e("p",null,"È costante:"),e("p",null,e(xn.a,null,Un(He())))),e(Vn.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(xn.a,null,"f(t) = m a")))),e(Nn.a,{title:"Moto armonico semplice"},e(Vn.a,{title:"Ampiezza"},e("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),e("p",null,"(L'ampiezza di una sinusoide.)")),e(Vn.a,{title:"Velocità angolare"},e("p",null,"Indica quanto in fretta cambia la posizione del corpo."),e("p",null,"Dipende dal periodo:"),e("p",null,e(xn.a,null,Un(Je())))),e(Vn.a,{title:"Spostamento"},e("p",null,"E' una sinusoide:"),e("p",null,e(xn.a,null,Un(je())))),e(Vn.a,{title:"Velocità"},e("p",null,"E' la sinusoide dello spostamento, sfasata di ",e(xn.a,null,Un(We())),":"),e("p",null,e(xn.a,null,Un(Qe())))),e(Vn.a,{title:"Accelerazione"},e("p",null,"E' la sinusoide della velocità, sfasata di ",e(xn.a,null,Un(Oe())),":"),e("p",null,e(xn.a,null,Un(Ge())))),e(Vn.a,{title:"Forze"},e("p",null,"Si applica la prima legge di Newton:"),e("p",null,e(xn.a,null,"f(t) = m a")))),e(Nn.a,{title:"Moti composti"},e(Vn.a,{title:"Moto parabolico"},e("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),e(Vn.a,{title:"Moto circolare uniforme"},e("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",e(xn.a,null,Un(Ue())),", sull'asse Y."))),e(Nn.a,{title:"Moto circolare uniforme"},e(Vn.a,null,e("h3",null,"Velocità angolare"),e("p",null,"Quanto cambia la fase nel tempo."),e("p",null,e(xn.a,null,Un(Me())))),e(Vn.a,{title:"Fase"},e("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),e("p",null,"Si indica con ",e(xn.a,null,Un(Re())),", e generalmente si usa in radianti.")),e(Vn.a,{title:"Velocità"},e("p",null,"Si applicano le formule per la circonferenza:"),e("p",null,e(xn.a,null,Un(Te())))),e(Vn.a,{title:"Accelerazione"},e("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),e("p",null,e(xn.a,null,Un(Ne())))),e(Vn.a,{title:"Forza centripeta"},e("p",null,"È verso il centro e si calcola con:"),e("p",null,e(xn.a,null,Un(Ve()))))),e(Nn.a,{title:"Lavoro ed energia"},e(Vn.a,{title:"Lavoro"},e("p",null,"E' compiuto da una forza che sposta un corpo."),e("p",null,e(xn.a,null,Un(xe()))),e("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),e(Vn.a,{title:"Energia cinetica"},e("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),e("p",null,e(xn.a,null,Un(we()))),e("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),e("p",null,e(xn.a,null,Un(ke())))),e(Vn.a,{title:"Energia potenziale gravitazionale"},e("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),e("p",null,e(xn.a,null,Un(Be()))),e("p",null,"(Con ",e(xn.a,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),e(Vn.a,{title:"Energia potenziale elastica"},e("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),e("p",null,e(xn.a,null,Un(Se())))),e(Vn.a,{title:"Forze conservative"},e("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),e("p",null,"Ad esempio, è conservativa la ",e("i",null,"forza di gravità"),", ma ",e("b",null,"non")," è conservativa la forza di attrito."),e("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),e("p",null,e(xn.a,null,Un(Ie())))),e(Vn.a,{title:"Potenza"},e("p",null,"È la velocità di trasferimento di energia:"),e("p",null,e(xn.a,null,Un(ye()))))),e(Nn.a,{title:"Elettrostatica"},e(Vn.a,{title:"Carica elettrica"},e("p",null,"È una proprietà dei corpi che può essere ",e(Tn.a,null,"positiva")," o ",e(Rn.a,null,"negativa"),"."),e("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),e("p",null,"Esiste un'unità elementare: ",e(xn.a,null,Un(Pe())),"."),e("p",null,"Cariche ",e(Tn.a,null,"opp"),e(Rn.a,null,"oste")," si attraggono; cariche ",e(Tn.a,null,"uguali")," si respingono.")),e(Vn.a,{title:"Conduttori e isolanti"},e("p",null,"Più ",e("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),e("p",null,"I corpi in cui la carica si muove bene sono ",e("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",e("i",null,"isolanti"),"."),e("p",null,e("i",null,"Il corpo umano è un buon conduttore.")))),e(Nn.a,{title:"Polarizzazione"},e(Vn.a,{title:"Polarizzazione"},e("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),e(Nn.a,null,e(Vn.a,{title:"Messa a terra"},e("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",e("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",e(Tn.a,null,"cariche positive")," e ",e(Rn.a,null,"negative")," all'interno)."))),e(Nn.a,null,e(Vn.a,{title:"Polarizzazione per strofinio"},e("p",null,"Strofinando tra loro due corpi isolanti, essi si ",e("i",null,"polarizzeranno per strofinio"),".")),e(Vn.a,{title:"Polarizzazione per contatto"},e("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",e("i",null,"polarizzarsi per contatto"),".")),e(Vn.a,{title:"Polarizzazione per induzione"},e("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',e(Tn.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",e(Rn.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",e(Tn.a,null,"stesso segno")," più lontano possibile da esse."),e("p",null,"Mettendo a terra il conduttore, nuove cariche del ",e(Rn.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),e("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",e(Rn.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),e(Nn.a,{title:"Forza elettrica"},e(Vn.a,{title:"Legge di Coulomb"},e("p",null,"Due corpi carichi si attraggono tra loro con forza:"),e("p",null,e(xn.a,null,Un(Ee()))),e("p",null,e(xn.a,null,Un(Ae()))," è la ",e("i",null,"costante di Coulomb"),", e vale ",e(xn.a,null,Un(Ce())),".")),e(Vn.a,{title:"Permeabilità dello spazio vuoto"},e("p",null,"La costante ",e(xn.a,null,Un(Fe()))," è in realtà dipendente da un altra costante, ",e(xn.a,null,Un(qe())),", la ",e("i",null,"permeabilità del vuoto"),"."),e("p",null,e(xn.a,null,Un(Le()))),e("p",null,e(xn.a,null,Un(De())))),e(Vn.a,{title:"Campo elettrico"},e("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),e("p",null,e(xn.a,null,Un(be())))),e(Vn.a,{title:"Flusso elettrico"},e("p",null,'È la differenza tra "quanto" campo elettrico ',e(Tn.a,null,"entra")," e quanto campo elettrico ",e(Rn.a,null,"esce")," da una certa area."),e("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),e("p",null,e(xn.a,null,Un(ze()))),e("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),e("p",null,e(xn.a,null,Un(_e()))),e("p",null,e(Mn.a,null,"Circa. E' una specie di integrale..."))),e(Vn.a,{title:"Legge di Gauss per i campi elettrostatici"},e("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),e("p",null,e(xn.a,null,Un(he()))),e("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),e(Nn.a,{title:"Energia elettrica"},e(Vn.a,{title:"Energia potenziale elettrica"},e("p",null,"Un corpo carico vicino ad altre cariche possiede un'",e("i",null,"energia potenziale elettrica")," ",e(xn.a,null,Un(ge())),"."))),e(Nn.a,{title:"Circuiti elettrici"},e(Vn.a,{title:e("span",null,"Potenziale elettrico ",e("small",null,"(tensione)"))},e("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),e("p",null,e(xn.a,null,Un(me()))),e("p",null,"La sua unità di misura è il Volt (",e(xn.a,null,Un(ve())),")."),e("p",null,"In una batteria è detto ",e("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),e(Vn.a,{title:e("span",null,"Corrente elettrica ",e("small",null,"(intensità)"))},e("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),e("p",null,e(xn.a,null,Un(fe()))),e("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),e("p",null,"La sua unità di misura è l'Ampere (",e(xn.a,null,Un(de())),").")),e(Vn.a,{title:e("span",null,"Corrente continua ",e("small",null,"(",e("abbr",{title:"Direct Current"},"DC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente è costante.")),e(Vn.a,{title:e("span",null,"Corrente alternata ",e("small",null,"(",e("abbr",{title:"Alternate Current"},"AC"),")"))},e("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),e(Vn.a,{title:"Potenza elettrica"},e("p",null,"Possiamo calcolare la potenza di un circuito:"),e("p",null,e(xn.a,null,Un(se()))))),e(Nn.a,{title:"Elementi di un circuito"},e(Vn.a,{title:"Resistore"},e("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),e("p",null,"Il potenziale utilizzato è pari a:"),e("p",null,e(xn.a,null,Un(pe()))),e("p",null,"Dove ",e(xn.a,null,Un(ce()))," è una costante detta ",e("i",null,"resistenza")," con unità di misura Ohm (",e(xn.a,null,Un(ue())),")."),e("p",null,"La resistenza di un conduttore vale:"),e("p",null,e(xn.a,null,Un(oe()))),e("p",null,e(xn.a,null,Un(re()))," è la ",e("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),e("p",null,e(xn.a,null,Un(ie())))),e(Vn.a,{title:"Condensatore"},e("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),e("p",null,"Per farlo, cattura cariche ",e(Tn.a,null,"positive")," e ",e(Rn.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),e("p",null,"Ha una ",e("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),e("p",null,e(xn.a,null,Un(le()))),e("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),e("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),e("p",null,e(xn.a,null,Un(ae()))),e("p",null,"Dove ",e(xn.a,null,Un(te()))," è la ",e("i",null,"costante dielettrica relativa")," del materiale inserito, ",e(xn.a,null,Un(ne()))," l'area di una armatura e ",e(xn.a,null,Un(ee()))," la distanza tra le due armature."),e("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",e("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",e("i",null,"breakdown"),"."),e("p",null,"La sua unità di misura è il Farad (",e(xn.a,null,Un($())),")")),e(Vn.a,{title:"Amperometro"},e("p",null,"Misura la corrente elettrica se messo in serie."),e("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),e(Vn.a,{title:"Voltmetro"},e("p",null,"Misura la differenza di potenziale se messo in parallelo."),e("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),e(Nn.a,{title:"Principi di Kirchhoff"},e(Vn.a,{title:"Legge dei nodi"},e("p",null,"Per nodo si intende un qualsiasi punto del circuito."),e("p",null,"Da un nodo entra ed esce la stessa corrente.")),e(Vn.a,{title:"Legge delle maglie"},e("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),e("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),e(Nn.a,{title:"Serie e Parallelo"},e(Vn.a,{title:"Circuito in serie"},e("p",null,"Più parti di circuito sono ",e("i",null,"in serie")," se sono consecutive e senza biforcazioni."),e("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),e(Vn.a,{title:"Circuito in parallelo"},e("p",null,"Più parti di circuito sono ",e("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),e("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),e(Nn.a,{title:"Resistenze equivalenti"},e(Vn.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),e("p",null,e(xn.a,null,Un(Z())))),e(Vn.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),e("p",null,e(xn.a,null,Un(Y()))))),e(Nn.a,{title:"Condensatori equivalenti"},e(Vn.a,{title:"Circuiti in serie"},e("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),e("p",null,e(xn.a,null,Un(X())))),e(Vn.a,{title:"Circuiti in parallelo"},e("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),e("p",null,e(xn.a,null,Un(K()))))),e(Nn.a,{title:"Magnetismo"},e(Vn.a,{title:"Permeabilità magnetica dello spazio vuoto"},e("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),e("p",null,e(xn.a,null,Un(H()))," (",e(xn.a,null,Un(J())),")")),e(Vn.a,{title:"Campo magnetico"},e("p",null,"Come un campo elettrico, ma per i magneti."),e("p",null,"Il suo simbolo è ",e(xn.a,null,Un(j())),", e la sua unità di misura è il Tesla (",e(xn.a,null,"T"),").")),e(Vn.a,{title:"Flusso magnetico"},e("p",null,'È "quanto" campo magnetico ',e("b",null,"attraversa")," un percorso chiuso."),e("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),e("p",null,e(xn.a,null,Un(W()))),e("p",null,e(xn.a,null,Un(Q()))),e("p",null,"La sua unità di misura è il Weber (",e(xn.a,null,Un(O())),").")),e(Vn.a,{title:"Legge di Gauss per i campi magnetici"},e("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),e("p",null,"Ovvero, non esistono monopoli magnetici.")),e(Vn.a,{title:"Legge di Ampère"},e("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),e("p",null,e(xn.a,null,Un(G()))))),e(Nn.a,{title:"Forze magnetiche"},e(Vn.a,{title:e("span",null,"Forza magnetica su carica puntiforme ",e("small",null,"(Forza di Lorentz)"))},e("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),e("p",null,e(xn.a,null,Un(U()))),e("p",null,"Dove ",e(xn.a,null,Un(M()))," è l'intensità del campo magnetico e ",e(xn.a,null,Un(R()))," la velocità della carica considerata."),e("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),e("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),e(Vn.a,{title:"Forza magnetica in un filo"},e("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),e("p",null,e(xn.a,null,Un(T()))," ",e("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),e("p",null,"Dove ",e(xn.a,null,Un(N()))," è la corrente elettrica, ",e(xn.a,null,Un(V()))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),e(Nn.a,{title:"Campi magnetici"},e(Vn.a,{title:"Campo magnetico in una spira"},e("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),e(Vn.a,{title:"Campo magnetico di un solenoide"},e("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),e("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),e("p",null,e(xn.a,null,Un(x())))),e(Vn.a,{title:"Legge di Oersted"},e("p",null,e("i",null,"Caso particolare della ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),e("p",null,"Il modulo del campo magnetico ",e(xn.a,null,"B")," prodotto da un filo in cui passa una corrente continua ",e(xn.a,null,"I")," alla distanza ",e(xn.a,null,"s")," è:"),e("p",null,e(xn.a,null,Un(w()))),e("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),e("p",null,"Due fili attraversati dalla ",e(Tn.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",e(Tn.a,null,"corr"),e(Rn.a,null,"enti")," ",e(Tn.a,null,"opp"),e(Rn.a,null,"oste")," si respingono."))),e(Nn.a,{title:"Induzione elettromagnetica"},e(Vn.a,{title:"Forza elettromotrice indotta"},e("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),e("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),e("p",null,"Essa vale:"),e("p",null,e(xn.a,null,Un(k()))),e("p",null,"Dove ",e(xn.a,null,"v")," è la velocità del conduttore, ",e(xn.a,null,"B")," è l'intensità del campo magnetico ed ",e(xn.a,null,"L")," è la lunghezza del conduttore.")),e(Vn.a,{title:"Flusso magnetico in una spira"},e("p",null,"In un campo magnetico ",e(xn.a,null,Un(B()))," uniforme e perpendicolare al piano di una spira di area ",e(xn.a,null,Un(S())),", il flusso magnetico si può determinare con la ",e("i",null,"Legge di Faraday-Neumann-Lenz"),":"),e("p",null,e(xn.a,null,Un(I()))))),e(Nn.a,null,e(Vn.a,{title:"Legge di Faraday-Neumann-Lenz"},e("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),e("p",null,e(xn.a,null,Un(y()))),e("p",null,"Il meno è dovuto alla ",e("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),e(Vn.a,{title:"Faraday in un solenoide"},e("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),e("p",null,e(xn.a,null,Un(P()))),e("p",null,"Dove ",e(xn.a,null,Un(E()))," è il numero delle spire del solenoide.")),e(Vn.a,{title:"Legge di Ampère-Maxwell"},e("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),e(Nn.a,{title:"Elettromagnetismo"},e(Vn.a,{title:"Onde elettromagnetiche"},e("p",null,"Nel vuoto, il campo elettrico ",e(xn.a,null,Un(A()))," e il campo magnetico ",e(xn.a,null,Un(C()))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),e("p",null,"Si dice quindi che sono ",e("i",null,"onde elettromagnetiche"),"."),e("p",null,"Esse sono legate dalla relazione:"),e("p",null,e(xn.a,null,Un(F()))),e("p",null,"Dove ",e(xn.a,null,Un(q()))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),e("p",null,e(xn.a,null,Un(L())))),e(Vn.a,{title:"Formula delle onde"},e("p",null,e(xn.a,null,Un(D()))),e("p",null,"Dove ",e(xn.a,null,Un(b()))," è l'ampiezza massima che può avere l'onda, ",e(xn.a,null,Un(z()))," è il vettore d'onda, ",e(xn.a,null,Un(_()))," la frequenza angolare e ",e(xn.a,null,Un(h()))," la fase."))),e(Nn.a,{title:"Spettroscopia"},e(Vn.a,{title:"Emissione"},e("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",e("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),e("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),e("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),e("p",null,e(xn.a,null,Un(g()))),e("p",null,"Con ",e(xn.a,null,Un(m())),", detta costante di Rydberg, e ",e(xn.a,null,Un(v()))," un numero intero.")),e(Vn.a,{title:"Grandezza quantizzata"},e("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),e("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),e("p",null,"Energia, momento angolare e raggio sono quantizzati."),e("p",null,"Nota costante quantica è ",e(xn.a,null,Un(f())),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",e(xn.a,null,Un(d())),"."))),e(Nn.a,null,e(Vn.a,{title:"Modello di Bohr"},e("p",null,"L'energia degli elettroni è quantizzata."),e("p",null,"Inoltre, per essi è valido che:"),e("p",null,e(xn.a,null,Un(s()))),e("p",null,"Ancora, il raggio delle orbite è uguale a:"),e("p",null,e(xn.a,null,Un(p()))),e("p",null,"Con ",e(xn.a,null,Un(c())),"."),e("p",null,"Infine, in ogni stato, l'energia è pari a:"),e("p",null,e(xn.a,null,Un(u()))),e("p",null,"Due elettroni non possono occupare lo stesso stato."),e("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),e(Nn.a,null,e(Vn.a,{title:"Nei solidi"},e("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),e("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),e(Nn.a,{title:"Semiconduttori"},e(Vn.a,{title:"Semiconduttori"},e("p",null,e(Mn.a,null,"Refactor this")),e("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",e(xn.a,null,Un(o())),", allora il corpo è un isolante."),e("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),e("p",null,"Se il gap è invece dell'ordine di grandezza di ",e(xn.a,null,Un(r())),", allora il corpo è un semiconduttore.")),e(Vn.a,{title:"Lacune"},e("p",null,"Legami in cui ",e(Tn.a,null,"mancano elettroni"),"."),e("p",null,e(Rn.a,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",e(Tn.a,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),e(Vn.a,{title:"Accettori e donori"},e("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),e("ul",null,e("li",null,"Con numero atomico maggiore, un semiconduttore di ",e(Rn.a,null,"tipo N")," con ",e(Rn.a,null,"elettroni in eccesso")," liberi di scorrere."),e("li",null,"Con numero atomico minore, un semiconduttore di ",e(Tn.a,null,"tipo P")," con ",e(Tn.a,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),e("p",null,"Maggiore impurezza porta a maggiore conduttività.")),e(Vn.a,{title:"Temperatura"},e("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",e(Rn.a,null,"elettroni")," e ",e(Tn.a,null,"lacune"),"."))),e(Nn.a,{title:e("span",null,"Ottica ",e("small",null,"(non l'abbiamo fatta)"))},e(Vn.a,{title:"Assorbimento e riflessione"},e("p",null,"I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.")),e(Vn.a,{title:"Corpo nero"},e("p",null,"Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna."),e("p",null,"Le onde assorbite vengono poi riemesse sotto forma di un onda di ",e(xn.a,null,Un(i()))," variabile in base alla temperatura."),e("p",null,e(xn.a,null,Un(l()))," è costante.")),e(Vn.a,{title:"Teoria di Planck per il corpo nero"},e("p",null,"L'energia assorbita e emessa dai corpi neri è quantizzata.")),e(Vn.a,{title:"Fotone"},e("p",null,"Un onda magnetica con un quanto di energia è detta ",e("i",null,"fotone"),":"),e("p",null,e(xn.a,null,Un(a())))),e(Vn.a,{title:"Effetto fotoelettrico"},e("p",null,"A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale."),e("p",null,"Perchè avvenga, la frequenza deve essere maggiore di una certa soglia."),e("p",null,"Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza."),e("p",null,"Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni."))))},t}(wn.Component)}.call(this,t("hosL").h)},ZsnK:function(e,n,t){"use strict";(function(e){t.d(n,"a",(function(){return i}));var a=t("+AyP"),l=t.n(a),i=function(n){function t(){return n.apply(this,arguments)||this}var a,i;return i=n,(a=t).prototype=Object.create(i.prototype),a.prototype.constructor=a,a.__proto__=i,t.prototype.render=function(){return e("img",{src:"https://latex.codecogs.com/svg.latex?"+("{\\color{White} "+this.props.children+" }"),alt:this.props.children,title:this.props.children,class:l.a.latex})},t}(t("hosL").Component)}).call(this,t("hosL").h)},bQQT:function(e,n,t){"use strict";(function(e){t.d(n,"a",(function(){return i}));var a=t("Qnof"),l=t.n(a),i=function(n){function 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extracted by mini-css-extract-plugin\nmodule.exports = {\"latex\":\"latex__3Esv7\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"panel\":\"panel__1ubJw\"};","import style from \"./todo.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Todo extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n","import style from \"./panel.css\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (
    {this.props.title}
    );\n\t\t}\n\n\t\treturn (\n\t\t\t
    \n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
    \n\t\t);\n\t}\n}\n","import style from \"./minus.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Minus extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__29_QM\"};","import style from './fisica.css';\nimport { Component } from 'preact';\nimport Latex from '../components/latex';\nimport Panel from '../components/panel';\nimport Split from '../components/split';\nimport Plus from '../components/plus';\nimport Minus from '../components/minus';\nimport Todo from '../components/todo';\n\nconst r = String.raw;\n\nexport default class Fisica extends Component {\n\trender() {\n        return (\n            
    \n                
    Fisica
    \n                \n                    \n                        
    \n                            Usa le regole base della trigonometria:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\vec{v}_x + \\vec{v}_y`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha`}\n                        
    \n                        \n                    \n                        
    \n                            Scomponi in componenti, poi sommali:\n                        
    \n                        
    \n                            {r`\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore risultante dall'applicazione della regola del parallelogramma.\n                        
    \n                        \n                    \n                        
    \n                            Alla fine è sempre una somma:\n                        
    \n                        
    \n                            {r`\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore che parte da w e arriva a v.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama scalare perchè il risultato è uno scalare, non un vettore.\n                        
    \n                        
    \n                            {r`\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha`}\n                        
    \n                        
    \n                            Produce il modulo della proiezione di {r`\\vec{a}`} su {r`\\vec{b}`}.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama vettoriale perchè il risultato è un altro vettore.\n                        
    \n                        
      \n                            
    • {r`\\vec{c} = \\vec{a} \\times \\vec{b}`}
      • \n                            
    • {r`\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)`}
      • \n                            
    • Regola della mano destra
      • \n                        
    \n                        
    \n                            Non è commutativo!\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0`}\n                        
    \n                        \n                    \n                        
    \n                            La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la massa.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = m \\vec{a}`}\n                        
    \n                        \n                    \n                        
    \n                            Due corpi esercitano forze uguali e opposte uno sull'altro. \n                        
    \n                        
    \n                            {r`\\vec{F}_{21} = -\\vec{F}_{12}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Due corpi puntiformi si attirano uno verso l'altro con forza:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}`}\n                        
    \n                        
    \n                            G è la costante di gravitazione universale e vale:\n                        
    \n                        
    \n                            {r`G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza peso uguale a:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            g è la costante di gravità della Terra, e vale:\n                        
    \n                        
    \n                            {r`g = 9.81 \\frac{m}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Per pianeti diversi dalla Terra vale la stessa regola:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            L'unica differenza è che cambia la costante di gravità:\n                        
    \n                        
    \n                            {r`g_{luna} = 1.62 \\frac{m}{s^2}`}\n                        
    \n                        
    \n                            {r`g_{marte} = 3.71 \\frac{m}{s^2}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si oppone alle forze applicate alla superficie di contatto.\n                        
    \n                        
    \n                            Un libro appoggiato su un tavolo ha la forza di gravità che lo attira verso il terreno e la forza normale che lo trattiene dal cadere. \n                        
    \n                        \n                    \n                        
    \n                            Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            Rallenta i corpi che si stanno muovendo finchè essi non si fermano:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            E' forza trasmessa tra due estremi di una fune.\n                        
    \n                        
    \n                            Può essere redirezionata per mezzo di carrucole.\n                        
    \n                        \n                    \n                        
    \n                            Una molla cerca sempre di tornare alla sua posizione indeformata con forza:\n                        
    \n                        
    \n                            {r`F = -k x`}\n                        
    \n                        
    \n                            (E' negativa perchè la forza è opposta a quella applicata per deformarla.)\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            È un vettore che indica la posizione di un corpo rispetto a un'origine.\n                        
    \n                        
    \n                            {r`\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di posizione nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice velocità istantanea:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di velocità nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice accelerazione istantanea:\n                        
    \n                        
    \n                            {r`\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}`}\n                        
    \n                        \n                    Quantità di moto (momento lineare)}>\n                        
    \n                            La quantità di moto è una proprietà vettoriale dei corpi:\n                        
    \n                        
    \n                            {r`\\vec{p} = m \\vec{v}`}\n                        
    \n                        
    \n                            Se la forza risultante è nulla, la quantità di moto non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = v \\cdot \\Delta t + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`v(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            La velocità non varia:\n                        
    \n                        
    \n                            {r`a(t) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = 0\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È una retta:\n                        
    \n                        
    \n                            {r`v(t) = a \\Delta t + v(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`a(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' la distanza dal centro massima che raggiunge il corpo.\n                        
    \n                        
    \n                            (L'ampiezza di una sinusoide.)\n                        
    \n                        \n                    \n                        
    \n                            Indica quanto in fretta cambia la posizione del corpo. \n                        
    \n                        
    \n                            Dipende dal periodo:\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' una sinusoide:\n                        
    \n                        
    \n                            {r`s(t) = A \\sin (\\omega \\cdot t + \\phi)`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide dello spostamento, sfasata di {r`\\frac{\\pi}{2}`}:\n                        
    \n                        
    \n                            {r`v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide della velocità, sfasata di {r`\\pi`}:\n                        
    \n                        
    \n                            {r`a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.\n                        
    \n                        \n                    \n                        
    \n                            Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di {r`\\frac{\\pi}{2}`}, sull'asse Y.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Velocità angolare\n                        
    \n                        
    \n                            Quanto cambia la fase nel tempo.\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' l'angolo percorso dal corpo rispetto alla posizione iniziale.\n                        
    \n                        
    \n                            Si indica con {r`\\phi`}, e generalmente si usa in radianti.\n                        
    \n                        \n                    \n                        
    \n                            Si applicano le formule per la circonferenza:\n                        
    \n                        
    \n                            {r`v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r`}\n                        
    \n                        \n                    \n                        
    \n                            Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto: \n                        
    \n                        
    \n                            {r`a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega`}\n                        
    \n                        \n                    \n                        
    \n                            È verso il centro e si calcola con:\n                        
    \n                        
    \n                            {r`F = m \\cdot a`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' compiuto da una forza che sposta un corpo.\n                        
    \n                        
    \n                            {r`W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )`}\n                        
    \n                        
    \n                            (Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia cinetica in ogni momento uguale a:\n                        
    \n                        
    \n                            {r`E_c = \\frac{1}{2} m v^2`}\n                        
    \n                        
    \n                            Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:\n                        
    \n                        
    \n                            {r`\\Delta E_c = W`}\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia potenziale in ogni momento pari a: \n                        
    \n                        
    \n                            {r`E_{p_g} = m \\cdot g \\cdot h`}\n                        
    \n                        
    \n                            (Con h uguale a un altezza scelta come punto di riferimento.)\n                        
    \n                        \n                    \n                        
    \n                            Una molla ha sempre energia potenziale elastica pari a:\n                        
    \n                        
    \n                            {r`E_{p_e} = \\frac{1}{2} k x^2`}\n                        
    \n                        \n                    \n                        
    \n                            Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo.\n                        
    \n                        
    \n                            Ad esempio, è conservativa la forza di gravità, ma non è conservativa la forza di attrito.\n                        
    \n                        
    \n                            Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:\n                        
    \n                        
    \n                            {r`E = E_k + E_p`}\n                        
    \n                        \n                    \n                        
    \n                            È la velocità di trasferimento di energia:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta E}{\\Delta t}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            È una proprietà dei corpi che può essere positiva o negativa.\n                        
    \n                        
    \n                            Si conserva: in un sistema chiuso la carica totale è costante.\n                        
    \n                        
    \n                            Esiste un'unità elementare: {r`C_{elettrone} = 1.602 \\cdot 10^{-19}`}.\n                        
    \n                        
    \n                            Cariche opposte si attraggono; cariche uguali si respingono.\n                        
    \n                        \n                    \n                        
    \n                            Più ioni ha un corpo, meglio la carica si muove attraverso di esso.\n                        
    \n                        
    \n                            I corpi in cui la carica si muove bene sono conduttori, mentre quelli in cui si muove difficilmente sono isolanti.\n                        
    \n                        
    \n                            Il corpo umano è un buon conduttore.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno equilibrate e il corpo diventerà elettricamente neutro (con stesso numero di cariche positive e negative all'interno).\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Strofinando tra loro due corpi isolanti, essi si polarizzeranno per strofinio.\n                        
    \n                        \n                    \n                        
    \n                            Toccando un conduttore con un corpo carico, il conduttore potrà polarizzarsi per contatto.\n                        
    \n                        \n                    \n                        
    \n                            Se un corpo conduttore ha cariche \"esterne\" di un certo segno vicino, esso avrà tutte le cariche del segno opposto in equilibrio vicino alle cariche esterne, e tutte le cariche dello stesso segno più lontano possibile da esse.\n                        
    \n                        
    \n                            Mettendo a terra il conduttore, nuove cariche del segno opposto saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate.\n                        
    \n                        
    \n                            Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà caricato del segno opposto rispetto alle cariche esterne.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Due corpi carichi si attraggono tra loro con forza: \n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{-k \\cdot q_1 \\cdot q_2}{s^2}`}\n                        
    \n                        
    \n                            {r`k`} è la costante di Coulomb, e vale {r`k = 8.99 \\cdot 10^9 \\frac{N \\cdot m^2}{C^2}`}.\n                        
    \n                        \n                    \n                        
    \n                            La costante {r`k`} è in realtà dipendente da un altra costante, {r`\\epsilon_0`}, la permeabilità del vuoto.\n                        
    \n                        
    \n                            {r`k = \\frac{1}{4 \\pi \\cdot \\epsilon_0}`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{q_1 \\cdot q_2}{4 \\pi \\cdot \\epsilon_0 \\cdot s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Misura che forza viene applicata in ogni punto su una carica unitaria:\n                        
    \n                        
    \n                            {r`\\vec{E} = \\frac{\\vec{F}_{elettrica}}{q} = \\frac{-k \\cdot q}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            È la differenza tra \"quanto\" campo elettrico entra e quanto campo elettrico esce da una certa area.\n                        
    \n                        
    \n                            In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area.\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A}`}\n                        
    \n                        
    \n                            Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A} = E_\\perp \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        
    \n                            Circa. E' una specie di integrale...\n                        
    \n                        \n                    \n                        
    \n                            Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie.\n                        
    \n                        
    \n                            {r`\\Phi_E = 4 \\pi \\cdot k \\cdot q = \\frac{q}{\\epsilon_0}`}\n                        
    \n                        
    \n                            Ovvero, i campi elettrostatici sono generati dalle cariche elettriche.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un corpo carico vicino ad altre cariche possiede un'energia potenziale elettrica {r`U_e`}.\n                        
        \n                        \n                    \n                \n                    Potenziale elettrico (tensione)}>\n                        
    \n                            È il valore dell'energia potenziale elettrica per una carica unitaria.\n                        
    \n                        
    \n                            {r`V = \\frac{U_e}{q}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Volt ({r`V`}).\n                        
                            \n                        
    \n                            In una batteria è detto forza elettromotrice, e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.\n                        
    \n                        \n                    Corrente elettrica (intensità)}>\n                        
    \n                            Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo.\n                        
    \n                        
    \n                            {r`I = \\frac{\\Delta q}{\\Delta t}`}\n                        
    \n                        
    \n                            Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla.\n                        
    \n                        
    \n                            La sua unità di misura è l'Ampere ({r`A`}).\n                        
    \n                        \n                    Corrente continua (DC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente è costante.\n                        
    \n                        \n                    Corrente alternata (AC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente si alterna periodicamente.\n                        
    \n                        \n                    \n                        
    \n                            Possiamo calcolare la potenza di un circuito:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta U_e}{\\Delta t} = I \\cdot \\Delta V = I^2 \\cdot R = \\frac{(\\Delta V)^2}{R}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Riduce l'intensità di corrente, e converte parte del potenziale in calore.\n                        
    \n                        
    \n                            Il potenziale utilizzato è pari a:\n                        
    \n                        
    \n                            {r`V = R \\cdot I`}\n                        
    \n                        
    \n                            Dove {r`R`} è una costante detta resistenza con unità di misura Ohm ({r`\\Omega`}).\n                        
    \n                        
    \n                            La resistenza di un conduttore vale:\n                        
    \n                        
    \n                            {r`R = \\rho \\frac{L_{unghezza}}{A_{rea}}`}\n                        
    \n                        
    \n                            {r`\\rho`} è la resistività del materiale, e varia in base alla temperatura:\n                        
    \n                        
    \n                            {r`\\rho = \\rho_0 (1 + \\alpha(T - T_0))`}\n                        
    \n                        \n                    \n                        
    \n                            Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito.\n                        
    \n                        
    \n                            Per farlo, cattura cariche positive e negative sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro.\n                        
    \n                        
    \n                            Ha una capacità caratteristica, che in un condensatore a facce piane parallele è:\n                        
    \n                        
    \n                            {r`C = \\frac{q_{massima}}{\\Delta V}`}\n                        
    \n                        
    \n                            Condensatori di capacità maggiore immagazzinano più potenziale con meno carica.\n                        
    \n                        
    \n                            La capacità aumenta se viene messo qualcosa tra le armature:\n                        
    \n                        
    \n                            {r`C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}`}\n                        
    \n                        
    \n                            Dove {r`\\kappa`} è la costante dielettrica relativa del materiale inserito, {r`A`} l'area di una armatura e {r`s`} la distanza tra le due armature.\n                        
    \n                        
    \n                            Se il campo elettrico creatosi tra le due armature supera la rigidità dielettrica del condensatore, la carica immagazzinata viene persa e ha luogo un breakdown.\n                        
    \n                        
    \n                            La sua unità di misura è il Farad ({r`Fa`})\n                        
    \n                        \n                    \n                        
    \n                            Misura la corrente elettrica se messo in serie.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)\n                        
    \n                        \n                    \n                        
    \n                            Misura la differenza di potenziale se messo in parallelo.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per nodo si intende un qualsiasi punto del circuito.\n                        
    \n                        
    \n                            Da un nodo entra ed esce la stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito.\n                        
    \n                        
    \n                            In una maglia chiusa, la somma delle differenze di potenziale è 0.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Più parti di circuito sono in serie se sono consecutive e senza biforcazioni.\n                        
    \n                        
    \n                            Parti di circuito in serie sono attraversate dalla stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Più parti di circuito sono in parallelo tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo. \n                        
    \n                        
    \n                            Parti di circuito in parallelo hanno la stessa differenza di potenziale.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:\n                        
    \n                        
    \n                            {r`R_{serie} = \\sum_{i=1}^{n} R_i`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:\n                        
    \n                        
    \n                            {r`R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:\n                        
    \n                        
    \n                            {r`C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:\n                        
    \n                        
    \n                            {r`C_{parallelo} = \\sum_{i=1}^{n} C_n`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente.\n                        
    \n                        
    \n                            {r`\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}`} ({r`\\frac{N}{A^2}`})\n                        
    \n                        \n                    \n                        
    \n                            Come un campo elettrico, ma per i magneti.\n                        
    \n                        
    \n                            Il suo simbolo è {r`B`}, e la sua unità di misura è il Tesla (T).\n                        
    \n                        \n                    \n                        
    \n                            È \"quanto\" campo magnetico attraversa un percorso chiuso.\n                        
    \n                        
    \n                            Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i \"sottoflussi\" magnetici calcolati sui suoi lati.\n                        
    \n                        
    \n                            {r`\\Phi_{B_{i}} = \\vec{B} \\cdot \\vec{L}_n = B \\cdot L_i \\cdot \\sin(\\alpha) = B_\\parallel \\cdot L_i`}\n                        
    \n                        
    \n                            {r`\\Phi_{B} = \\sum_{i=0}^{n_{lati}} \\Phi_{Bn}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Weber ({r`Wb = T \\cdot m^2`}).\n                        
    \n                        \n                    \n                        
    \n                            Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo.\n                        
    \n                        
    \n                            Ovvero, non esistono monopoli magnetici.\n                        
    \n                        \n                    \n                        
    \n                            L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Phi_B = \\mu_0 \\cdot I`}\n                        
    \n                        \n                    \n                \n                    Forza magnetica su carica puntiforme (Forza di Lorentz)}>\n                        
    \n                            I campi magnetici applicano una forza sulle cariche vicine:\n                        
    \n                        
    \n                            {r`\\vec{F}_{B} = q \\cdot (\\vec{v} \\times \\vec{B})`}\n                        
    \n                        
    \n                            Dove {r`\\vec{B}`} è l'intensità del campo magnetico e {r`\\vec{v}`} la velocità della carica considerata.\n                        
    \n                        
    \n                            Si ha una forza massima se la velocità è perpendicolare al campo magnetico.\n                        
    \n                        
    \n                            In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.\n                        
    \n                        \n                    \n                        
    \n                            I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:\n                        
    \n                        
    \n                            {r`\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})`} [1]\n                        
    \n                        
    \n                            Dove {r`I`} è la corrente elettrica, {r`\\vec{L}`} è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.\n                        
    \n                        \n                    \n                        
    \n                            Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.\n                        
    \n                        
    \n                            All'interno del solenoide si crea un campo (quasi) uniforme:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}`}\n                        
    \n                        \n                    \n                        
    \n                            Caso particolare della Legge di Ampère.\n                        
    \n                        
    \n                            Il modulo del campo magnetico B prodotto da un filo in cui passa una corrente continua I alla distanza s è:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}`}\n                        
    \n                        
    \n                            Il campo magnetico così creato gira attorno al filo in senso antiorario.\n                        
    \n                        
    \n                            Due fili attraversati dalla stessa corrente si attraggono, due fili attraversati da correnti opposte si respingono.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo. \n                        
    \n                        
    \n                            La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore. \n                        
    \n                        
    \n                            Essa vale:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = v \\cdot B \\cdot L`}\n                        
    \n                        
    \n                            Dove v è la velocità del conduttore, B è l'intensità del campo magnetico ed L è la lunghezza del conduttore.\n                        
    \n                        \n                    \n                        
    \n                            In un campo magnetico {r`B`} uniforme e perpendicolare al piano di una spira di area {r`A`}, il flusso magnetico si può determinare con la Legge di Faraday-Neumann-Lenz:\n                        
    \n                        
    \n                            {r`\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{\\Delta \\Phi_B}{\\Delta t}`}\n                        
    \n                        
    \n                            Il meno è dovuto alla Legge di Lenz, che specifica qualitativamente il verso della forza elettromotrice indotta.\n                        
    \n                        \n                    \n                        
    \n                            In un solenoide, la forza elettromotrice indotta è uguale a:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{N \\cdot \\Delta \\Phi_{B_{spira}}}{\\Delta t} = - \\frac{N \\cdot B \\cdot A \\cdot cos(\\alpha)}{\\Delta t}`}\n                        
    \n                        
    \n                            Dove {r`N`} è il numero delle spire del solenoide.\n                        
    \n                        \n                    \n                        
    \n                            Correnti o campi elettrici variabili creano un campo magnetico.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nel vuoto, il campo elettrico {r`E`} e il campo magnetico {r`B`} sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo.\n                        
    \n                        
    \n                            Si dice quindi che sono onde elettromagnetiche.\n                        
    \n                        
    \n                            Esse sono legate dalla relazione:\n                        
    \n                        
    \n                            {r`E = c \\cdot B`}\n                        
    \n                        
    \n                            Dove {r`c`} è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:\n                        
    \n                        
    \n                            {r`c = \\frac{1}{\\sqrt{\\epsilon_0 \\cdot \\mu_0}} = 3.00 \\cdot 10^8 \\frac{m}{s}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`A(t) = A_{max} \\cdot \\sin \\left ( \\frac{2 \\pi}{\\lambda} - \\omega t + \\phi \\right )`}\n                        
    \n                        
    \n                            Dove {r`A_{max}`} è l'ampiezza massima che può avere l'onda, {r`\\frac{2 \\pi}{\\lambda} = \\left | \\vec{k} \\right |`} è il vettore d'onda, {r`\\omega`} la frequenza angolare e {r`\\phi`} la fase.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            I solidi, se portati ad alta temperatura, emettono luce con uno spettro continuo.\n                        
    \n                        
    \n                            I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda. \n                        
    \n                        
    \n                            In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:\n                        
    \n                        
    \n                            {r`\\frac{1}{\\lambda} = R \\left ( \\frac{1}{4} - \\frac{1}{n^2} \\right )`}\n                        
    \n                        
    \n                            Con {r`R = 1.097 \\cdot 10^7 \\frac{1}{m}`}, detta costante di Rydberg, e {r`n`} un numero intero.\n                        
    \n                        \n                    \n                        
    \n                            Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori. \n                        
    \n                        
    \n                            Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata.\n                        
    \n                        
    \n                            Energia, momento angolare e raggio sono quantizzati.\n                        
    \n                        
    \n                            Nota costante quantica è {r`h`}, la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come {r`\\hbar = \\left ( \\frac{h}{2 \\pi} \\right )`}.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            L'energia degli elettroni è quantizzata.\n                        
    \n                        
    \n                            Inoltre, per essi è valido che:\n                        
    \n                        
    \n                            {r`m \\cdot v_n \\cdot 2 \\pi \\cdot r = n \\cdot h`}\n                        
    \n                        
    \n                            Ancora, il raggio delle orbite è uguale a:\n                        
    \n                        
    \n                            {r`r_n = n^2 \\cdot a_0 = n^2 \\cdot \\frac{\\hbar}{m_{elettrone} \\cdot k \\cdot e^2} `}\n                        
    \n                        
    \n                            Con {r`a_0 = \\left ( \\frac{h}{2 \\pi} \\right )^2 \\cdot \\frac{1}{m_{elettrone} \\cdot k \\cdot e^2} = 5.29 \\cdot 10^{-11} m`}.\n                        
    \n                        
    \n                            Infine, in ogni stato, l'energia è pari a:\n                        
    \n                        
    \n                            {r`E_n = \\frac{1}{n^2} \\cdot E_1 = - \\frac{1}{n^2} \\cdot \\frac{a_0^2}{2 \\cdot m \\cdot \\hbar^4} = - \\frac{1}{n^2} \\cdot \\frac{m_{elettrone} \\cdot k^2 \\cdot e^4}{2 \\cdot \\hbar^2}`}\n                        
    \n                        
    \n                            Due elettroni non possono occupare lo stesso stato.\n                        
    \n                        
    \n                            Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda.\n                        
    \n                        
    \n                            Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Refactor this\n                        
    \n                        
    \n                            Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di {r`10^1 eV`}, allora il corpo è un isolante.\n                        
    \n                        
    \n                            Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore.\n                        
    \n                        
    \n                            Se il gap è invece dell'ordine di grandezza di {r`1 eV`}, allora il corpo è un semiconduttore.\n                        
    \n                        \n                    \n                        
    \n                            Legami in cui mancano elettroni.\n                        
    \n                        
    \n                            Elettroni di altri legami possono spostarsi per colmare le lacune, creandone altre, e spostandole in direzione opposta a quella della corrente.\n                        
    \n                        \n                    \n                        
    \n                            Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:\n                        
    \n                        
      \n                            
    • Con numero atomico maggiore, un semiconduttore di tipo N con elettroni in eccesso liberi di scorrere.
      • \n                            
    • Con numero atomico minore, un semiconduttore di tipo P con lacune in eccesso libere di catturare elettroni da altri legami.
      • \n                        
    \n                        
    \n                            Maggiore impurezza porta a maggiore conduttività.\n                        
    \n                        \n                    \n                        
    \n                            Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di elettroni e lacune.\n                        
    \n                        \n                    \n                Ottica (non l'abbiamo fatta)}>\n                    \n                        
    \n                            I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.\n                        
    \n                        \n                    \n                        
    \n                            Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna.\n                        
    \n                        
    \n                            Le onde assorbite vengono poi riemesse sotto forma di un onda di {r`\\lambda`} variabile in base alla temperatura.\n                        
    \n                        
    \n                            {r`\\lambda_{max} \\cdot T`} è costante.\n                        
    \n                        \n                    \n                        
    \n                            L'energia assorbita e emessa dai corpi neri è quantizzata.\n                        
    \n                        \n                    \n                        
    \n                            Un onda magnetica con un quanto di energia è detta fotone:\n                        
    \n                        
    \n                            {r`E_{fotone} = h \\cdot f`}\n                        
    \n                        \n                    \n                        
    \n                            A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale.\n                        
    \n                        
    \n                            Perchè avvenga, la frequenza deve essere maggiore di una certa soglia.\n                        
    \n                        
    \n                            Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza.\n                        
    \n                        
    \n                            Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.\n                        
    \n                        \n                    \n            
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\vec{v}_y`)))),l("p",null,l(o.a,null,Re(m||(m=Me`\left | \vec{v}_x \right | = \left | \vec{v} \right | \sin \alpha`)))),l("p",null,l(o.a,null,Re(v||(v=Me`\left | \vec{v}_y \right | = \left | \vec{v} \right | \cos \alpha`))))),l(r.a,{title:"Somma"},l("p",null,"Scomponi in componenti, poi sommali:"),l("p",null,l(o.a,null,Re(g||(g=Me`\vec{v} + \vec{w} = (\vec{v}_x + \vec{w}_x) + (\vec{v}_y + \vec{w}_y)`)))),l("p",null,"Produce il vettore risultante dall'applicazione della regola del parallelogramma.")),l(r.a,{title:"Differenza"},l("p",null,"Alla fine è sempre una somma:"),l("p",null,l(o.a,null,Re(f||(f=Me`\vec{v} - \vec{w} = (\vec{v}_x - \vec{w}_x) + (\vec{v}_y - \vec{w}_y)`)))),l("p",null,"Produce il vettore che parte da ",l(o.a,null,"w")," e arriva a ",l(o.a,null,"v"),".")),l(r.a,{title:"Prodotto scalare"},l("p",null,"Si chiama scalare perchè il risultato è uno scalare, non un vettore."),l("p",null,l(o.a,null,Re(h||(h=Me`\vec{v} \cdot \vec{w} = \left | \vec{v} \right | \left | \vec{w} 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una forza che supera una certa soglia:"),l("p",null,l(o.a,null,Re(w||(w=Me`\left | \vec{F} \right | \leq \mu_{s} \left | \vec{F}_{normale} \right |`))))),l(r.a,{title:"Attrito dinamico"},l("p",null,"Rallenta i corpi che si stanno muovendo finchè essi non si fermano:"),l("p",null,l(o.a,null,Re(x||(x=Me`\left | \vec{F} \right | \leq \mu_{d} \left | \vec{F}_{normale} \right |`))))),l(r.a,{title:"Tensione"},l("p",null,"E' forza trasmessa tra due estremi di una fune."),l("p",null,"Può essere redirezionata per mezzo di carrucole.")),l(r.a,{title:"Elastica"},l("p",null,"Una molla cerca sempre di tornare alla sua posizione indeformata con forza:"),l("p",null,l(o.a,null,Re(B||(B=Me`F = -k x`)))),l("p",null,"(E' negativa perchè la forza è opposta a quella applicata per deformarla.)"))),l(u.a,{title:"Cinematica"},l(r.a,{title:"Spostamento"},l("p",null,"È un vettore che indica la posizione di un corpo rispetto a un'origine."),l("p",null,l(o.a,null,Re(N||(N=Me`\Delta \vec{s} = \vec{s}(fine) - \vec{s}(inizio)`))))),l(r.a,{title:"Velocità"},l("p",null,"È un vettore che misura la variazione di posizione nel tempo."),l("p",null,l(o.a,null,Re(T||(T=Me`\vec{v} = \frac{\Delta \vec{s}}{\Delta t}`)))),l("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",l("i",null,"velocità istantanea"),":"),l("p",null,l(o.a,null,Re(V||(V=Me`\vec{v} = \lim_{\Delta t \to 0} \frac{\Delta \vec{s}}{\Delta t} = \frac{d \vec{s}}{dt}`))))),l(r.a,{title:"Accelerazione"},l("p",null,"È un vettore che misura la variazione di velocità nel tempo."),l("p",null,l(o.a,null,Re(y||(y=Me`\vec{a} = \frac{\Delta \vec{v}}{\Delta t}`)))),l("p",null,"Se si considera un intervallo di tempo infinitesimale si dice ",l("i",null,"accelerazione istantanea"),":"),l("p",null,l(o.a,null,Re(M||(M=Me`\vec{a} = \lim_{\Delta v \to 0} \frac{\Delta \vec{v}}{\Delta t} = \frac{d \vec{v}}{d t} = \frac{d^2 \vec{s}}{d t^2}`))))),l(r.a,{title:l("span",null,"Quantità di moto ",l("small",null,"(momento lineare)"))},l("p",null,"La quantità di moto è una proprietà vettoriale dei corpi:"),l("p",null,l(o.a,null,Re(R||(R=Me`\vec{p} = m \vec{v}`)))),l("p",null,"Se la forza risultante è nulla, la quantità di moto non cambia."),l("p",null,l(o.a,null,Re(U||(U=Me`\Sigma \vec{F} = 0 \Longleftrightarrow \Delta \vec{p} = 0`)))))),l(u.a,{title:"Moto rettilineo uniforme"},l(r.a,{title:"Spostamento"},l("p",null,"La ",l("i",null,"legge oraria")," è:"),l("p",null,l(o.a,null,Re(Q||(Q=Me`s(t) = v \cdot \Delta t + s(0)`))))),l(r.a,{title:"Velocità"},l("p",null,"È costante:"),l("p",null,l(o.a,null,Re(G||(G=Me`v(t) = k`))))),l(r.a,{title:"Accelerazione"},l("p",null,"La velocità non varia:"),l("p",null,l(o.a,null,Re(O||(O=Me`a(t) = 0`))))),l(r.a,{title:"Forze"},l("p",null,"Si applica la prima legge di Newton:"),l("p",null,l(o.a,null,"f(t) = 0")))),l(u.a,{title:"Moto rettilineo uniformemente accelerato"},l(r.a,{title:"Spostamento"},l("p",null,"La ",l("i",null,"legge oraria")," è:"),l("p",null,l(o.a,null,Re(W||(W=Me`s(t) = \frac{1}{2} a \cdot (\Delta t)^2 + v(0) \cdot (\Delta t) + s(0)`))))),l(r.a,{title:"Velocità"},l("p",null,"È una retta:"),l("p",null,l(o.a,null,Re(J||(J=Me`v(t) = a \Delta t + v(0)`))))),l(r.a,{title:"Accelerazione"},l("p",null,"È costante:"),l("p",null,l(o.a,null,Re(K||(K=Me`a(t) = k`))))),l(r.a,{title:"Forze"},l("p",null,"Si applica la prima legge di Newton:"),l("p",null,l(o.a,null,"f(t) = m a")))),l(u.a,{title:"Moto armonico semplice"},l(r.a,{title:"Ampiezza"},l("p",null,"E' la distanza dal centro massima che raggiunge il corpo."),l("p",null,"(L'ampiezza di una sinusoide.)")),l(r.a,{title:"Velocità angolare"},l("p",null,"Indica quanto in fretta cambia la posizione del corpo."),l("p",null,"Dipende dal periodo:"),l("p",null,l(o.a,null,Re(X||(X=Me`\omega = \frac{2 \pi}{T}`))))),l(r.a,{title:"Spostamento"},l("p",null,"E' una sinusoide:"),l("p",null,l(o.a,null,Re(j||(j=Me`s(t) = A \sin (\omega \cdot t + \phi)`))))),l(r.a,{title:"Velocità"},l("p",null,"E' la sinusoide dello spostamento, sfasata di ",l(o.a,null,Re(H||(H=Me`\frac{\pi}{2}`))),":"),l("p",null,l(o.a,null,Re(Y||(Y=Me`v(t) = A \sin (\omega \cdot t + \phi + \frac{\pi}{2})`))))),l(r.a,{title:"Accelerazione"},l("p",null,"E' la sinusoide della velocità, sfasata di ",l(o.a,null,Re(Z||(Z=Me`\pi`))),":"),l("p",null,l(o.a,null,Re($||($=Me`a(t) = A \sin (\omega \cdot t + \phi + \pi)`))))),l(r.a,{title:"Forze"},l("p",null,"Si applica la prima legge di Newton:"),l("p",null,l(o.a,null,"f(t) = m a")))),l(u.a,{title:"Moti composti"},l(r.a,{title:"Moto parabolico"},l("p",null,"Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.")),l(r.a,{title:"Moto circolare uniforme"},l("p",null,"Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di ",l(o.a,null,Re(ll||(ll=Me`\frac{\pi}{2}`))),", sull'asse Y."))),l(u.a,{title:"Moto circolare uniforme"},l(r.a,null,l("h3",null,"Velocità angolare"),l("p",null,"Quanto cambia la fase nel tempo."),l("p",null,l(o.a,null,Re(el||(el=Me`\omega = \frac{2 \pi}{T}`))))),l(r.a,{title:"Fase"},l("p",null,"E' l'angolo percorso dal corpo rispetto alla posizione iniziale."),l("p",null,"Si indica con ",l(o.a,null,Re(al||(al=Me`\phi`))),", e generalmente si usa in radianti.")),l(r.a,{title:"Velocità"},l("p",null,"Si applicano le formule per la circonferenza:"),l("p",null,l(o.a,null,Re(il||(il=Me`v = \frac{\Delta s}{t} = \frac{2 \pi \cdot r}{T} = \omega r`))))),l(r.a,{title:"Accelerazione"},l("p",null,"Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto:"),l("p",null,l(o.a,null,Re(nl||(nl=Me`a = \frac{v^2}{r} = r \cdot \omega^2 = v \cdot \omega`))))),l(r.a,{title:"Forza centripeta"},l("p",null,"È verso il centro e si calcola con:"),l("p",null,l(o.a,null,Re(tl||(tl=Me`F = m \cdot a`)))))),l(u.a,{title:"Lavoro ed energia"},l(r.a,{title:"Lavoro"},l("p",null,"E' compiuto da una forza che sposta un corpo."),l("p",null,l(o.a,null,Re(ol||(ol=Me`W = \vec{F} \cdot \vec{s} = F \cdot \Delta s \cdot cos(\alpha )`)))),l("p",null,"(Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)")),l(r.a,{title:"Energia cinetica"},l("p",null,"Un corpo ha energia cinetica in ogni momento uguale a:"),l("p",null,l(o.a,null,Re(rl||(rl=Me`E_c = \frac{1}{2} m v^2`)))),l("p",null,"Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:"),l("p",null,l(o.a,null,Re(ul||(ul=Me`\Delta E_c = W`))))),l(r.a,{title:"Energia potenziale gravitazionale"},l("p",null,"Un corpo ha energia potenziale in ogni momento pari a:"),l("p",null,l(o.a,null,Re(cl||(cl=Me`E_{p_g} = m \cdot g \cdot h`)))),l("p",null,"(Con ",l(o.a,null,"h")," uguale a un altezza scelta come punto di riferimento.)")),l(r.a,{title:"Energia potenziale elastica"},l("p",null,"Una molla ha sempre energia potenziale elastica pari a:"),l("p",null,l(o.a,null,Re(sl||(sl=Me`E_{p_e} = \frac{1}{2} k x^2`))))),l(r.a,{title:"Forze conservative"},l("p",null,"Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo."),l("p",null,"Ad esempio, è conservativa la ",l("i",null,"forza di gravità"),", ma ",l("b",null,"non")," è conservativa la forza di attrito."),l("p",null,"Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:"),l("p",null,l(o.a,null,Re(pl||(pl=Me`E = E_k + E_p`))))),l(r.a,{title:"Potenza"},l("p",null,"È la velocità di trasferimento di energia:"),l("p",null,l(o.a,null,Re(dl||(dl=Me`P = \frac{\Delta E}{\Delta t}`)))))),l(u.a,{title:"Elettrostatica"},l(r.a,{title:"Carica elettrica"},l("p",null,"È una proprietà dei corpi che può essere ",l(c.a,null,"positiva")," o ",l(s.a,null,"negativa"),"."),l("p",null,"Si conserva: in un sistema chiuso la carica totale è costante."),l("p",null,"Esiste un'unità elementare: ",l(o.a,null,Re(ml||(ml=Me`C_{elettrone} = 1.602 \cdot 10^{-19}`))),"."),l("p",null,"Cariche ",l(c.a,null,"opp"),l(s.a,null,"oste")," si attraggono; cariche ",l(c.a,null,"uguali")," si respingono.")),l(r.a,{title:"Conduttori e isolanti"},l("p",null,"Più ",l("a",{href:"https://it.wikipedia.org/wiki/Ione"},"ioni")," ha un corpo, meglio la carica si muove attraverso di esso."),l("p",null,"I corpi in cui la carica si muove bene sono ",l("i",null,"conduttori"),", mentre quelli in cui si muove difficilmente sono ",l("i",null,"isolanti"),"."),l("p",null,l("i",null,"Il corpo umano è un buon conduttore.")))),l(u.a,{title:"Polarizzazione"},l(r.a,{title:"Polarizzazione"},l("p",null,"E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona."))),l(u.a,null,l(r.a,{title:"Messa a terra"},l("p",null,"Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno ",l("i",null,"equilibrate")," e il corpo diventerà elettricamente neutro (con stesso numero di ",l(c.a,null,"cariche positive")," e ",l(s.a,null,"negative")," all'interno)."))),l(u.a,null,l(r.a,{title:"Polarizzazione per strofinio"},l("p",null,"Strofinando tra loro due corpi isolanti, essi si ",l("i",null,"polarizzeranno per strofinio"),".")),l(r.a,{title:"Polarizzazione per contatto"},l("p",null,"Toccando un conduttore con un corpo carico, il conduttore potrà ",l("i",null,"polarizzarsi per contatto"),".")),l(r.a,{title:"Polarizzazione per induzione"},l("p",null,'Se un corpo conduttore ha cariche "esterne" di un ',l(c.a,null,"certo segno")," vicino, esso avrà tutte le cariche del ",l(s.a,null,"segno opposto")," in equilibrio vicino alle cariche esterne, e tutte le cariche dello ",l(c.a,null,"stesso segno")," più lontano possibile da esse."),l("p",null,"Mettendo a terra il conduttore, nuove cariche del ",l(s.a,null,"segno opposto")," saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate."),l("p",null,"Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà ",l(s.a,null,"caricato del segno opposto")," rispetto alle cariche esterne."))),l(u.a,{title:"Forza elettrica"},l(r.a,{title:"Legge di Coulomb"},l("p",null,"Due corpi carichi si attraggono tra loro con forza:"),l("p",null,l(o.a,null,Re(vl||(vl=Me`\left | \vec{F}_{elettrica} \right | = \frac{-k \cdot q_1 \cdot q_2}{s^2}`)))),l("p",null,l(o.a,null,Re(gl||(gl=Me`k`)))," è la ",l("i",null,"costante di Coulomb"),", e vale ",l(o.a,null,Re(fl||(fl=Me`k = 8.99 \cdot 10^9 \frac{N \cdot m^2}{C^2}`))),".")),l(r.a,{title:"Permeabilità dello spazio vuoto"},l("p",null,"La costante ",l(o.a,null,Re(hl||(hl=Me`k`)))," è in realtà dipendente da un altra costante, ",l(o.a,null,Re(zl||(zl=Me`\epsilon_0`))),", la ",l("i",null,"permeabilità del vuoto"),"."),l("p",null,l(o.a,null,Re(_l||(_l=Me`k = \frac{1}{4 \pi \cdot \epsilon_0}`)))),l("p",null,l(o.a,null,Re(bl||(bl=Me`\left | \vec{F}_{elettrica} \right | = \frac{q_1 \cdot q_2}{4 \pi \cdot \epsilon_0 \cdot s^2}`))))),l(r.a,{title:"Campo elettrico"},l("p",null,"Misura che forza viene applicata in ogni punto su una carica unitaria:"),l("p",null,l(o.a,null,Re(Ll||(Ll=Me`\vec{E} = \frac{\vec{F}_{elettrica}}{q} = \frac{-k \cdot q}{s^2}`))))),l(r.a,{title:"Flusso elettrico"},l("p",null,'È la differenza tra "quanto" campo elettrico ',l(c.a,null,"entra")," e quanto campo elettrico ",l(s.a,null,"esce")," da una certa area."),l("p",null,"In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area."),l("p",null,l(o.a,null,Re(ql||(ql=Me`\Phi_E = \vec{E} \cdot \vec{A}`)))),l("p",null,"Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:"),l("p",null,l(o.a,null,Re(Cl||(Cl=Me`\Phi_E = \vec{E} \cdot \vec{A} = E_\perp \cdot A \cdot \cos(\alpha)`)))),l("p",null,l(p.a,null,"Circa. E' una specie di integrale..."))),l(r.a,{title:"Legge di Gauss per i campi elettrostatici"},l("p",null,"Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie."),l("p",null,l(o.a,null,Re(Dl||(Dl=Me`\Phi_E = 4 \pi \cdot k \cdot q = \frac{q}{\epsilon_0}`)))),l("p",null,"Ovvero, i campi elettrostatici sono generati dalle cariche elettriche."))),l(u.a,{title:"Energia elettrica"},l(r.a,{title:"Energia potenziale elettrica"},l("p",null,"Un corpo carico vicino ad altre cariche possiede un'",l("i",null,"energia potenziale elettrica")," ",l(o.a,null,Re(Pl||(Pl=Me`U_e`))),"."))),l(u.a,{title:"Circuiti elettrici"},l(r.a,{title:l("span",null,"Potenziale elettrico ",l("small",null,"(tensione)"))},l("p",null,"È il valore dell'energia potenziale elettrica per una carica unitaria."),l("p",null,l(o.a,null,Re(Al||(Al=Me`V = \frac{U_e}{q}`)))),l("p",null,"La sua unità di misura è il Volt (",l(o.a,null,Re(Fl||(Fl=Me`V`))),")."),l("p",null,"In una batteria è detto ",l("i",null,"forza elettromotrice"),", e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.")),l(r.a,{title:l("span",null,"Corrente elettrica ",l("small",null,"(intensità)"))},l("p",null,"Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo."),l("p",null,l(o.a,null,Re(El||(El=Me`I = \frac{\Delta q}{\Delta t}`)))),l("p",null,"Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla."),l("p",null,"La sua unità di misura è l'Ampere (",l(o.a,null,Re(Sl||(Sl=Me`A`))),").")),l(r.a,{title:l("span",null,"Corrente continua ",l("small",null,"(",l("abbr",{title:"Direct Current"},"DC"),")"))},l("p",null,"Quando in un circuito la direzione della corrente è costante.")),l(r.a,{title:l("span",null,"Corrente alternata ",l("small",null,"(",l("abbr",{title:"Alternate Current"},"AC"),")"))},l("p",null,"Quando in un circuito la direzione della corrente si alterna periodicamente.")),l(r.a,{title:"Potenza elettrica"},l("p",null,"Possiamo calcolare la potenza di un circuito:"),l("p",null,l(o.a,null,Re(Il||(Il=Me`P = \frac{\Delta U_e}{\Delta t} = I \cdot \Delta V = I^2 \cdot R = \frac{(\Delta V)^2}{R}`)))))),l(u.a,{title:"Elementi di un circuito"},l(r.a,{title:"Resistore"},l("p",null,"Riduce l'intensità di corrente, e converte parte del potenziale in calore."),l("p",null,"Il potenziale utilizzato è pari a:"),l("p",null,l(o.a,null,Re(kl||(kl=Me`V = R \cdot I`)))),l("p",null,"Dove ",l(o.a,null,Re(wl||(wl=Me`R`)))," è una costante detta ",l("i",null,"resistenza")," con unità di misura Ohm (",l(o.a,null,Re(xl||(xl=Me`\Omega`))),")."),l("p",null,"La resistenza di un conduttore vale:"),l("p",null,l(o.a,null,Re(Bl||(Bl=Me`R = \rho \frac{L_{unghezza}}{A_{rea}}`)))),l("p",null,l(o.a,null,Re(Nl||(Nl=Me`\rho`)))," è la ",l("i",null,"resistività")," del materiale, e varia in base alla temperatura:"),l("p",null,l(o.a,null,Re(Tl||(Tl=Me`\rho = \rho_0 (1 + \alpha(T - T_0))`))))),l(r.a,{title:"Condensatore"},l("p",null,"Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito."),l("p",null,"Per farlo, cattura cariche ",l(c.a,null,"positive")," e ",l(s.a,null,"negative")," sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro."),l("p",null,"Ha una ",l("b",null,"capacità")," caratteristica, che in un condensatore a facce piane parallele è:"),l("p",null,l(o.a,null,Re(Vl||(Vl=Me`C = \frac{q_{massima}}{\Delta V}`)))),l("p",null,"Condensatori di capacità maggiore immagazzinano più potenziale con meno carica."),l("p",null,"La capacità aumenta se viene messo qualcosa tra le armature:"),l("p",null,l(o.a,null,Re(yl||(yl=Me`C_{nuova} = \kappa \cdot \frac{\epsilon_0 \cdot A}{s}`)))),l("p",null,"Dove ",l(o.a,null,Re(Ml||(Ml=Me`\kappa`)))," è la ",l("i",null,"costante dielettrica relativa")," del materiale inserito, ",l(o.a,null,Re(Rl||(Rl=Me`A`)))," l'area di una armatura e ",l(o.a,null,Re(Ul||(Ul=Me`s`)))," la distanza tra le due armature."),l("p",null,"Se il campo elettrico creatosi tra le due armature supera la ",l("i",null,"rigidità dielettrica")," del condensatore, la carica immagazzinata viene persa e ha luogo un ",l("i",null,"breakdown"),"."),l("p",null,"La sua unità di misura è il Farad (",l(o.a,null,Re(Ql||(Ql=Me`Fa`))),")")),l(r.a,{title:"Amperometro"},l("p",null,"Misura la corrente elettrica se messo in serie."),l("p",null,"(Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)")),l(r.a,{title:"Voltmetro"},l("p",null,"Misura la differenza di potenziale se messo in parallelo."),l("p",null,"(Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)"))),l(u.a,{title:"Principi di Kirchhoff"},l(r.a,{title:"Legge dei nodi"},l("p",null,"Per nodo si intende un qualsiasi punto del circuito."),l("p",null,"Da un nodo entra ed esce la stessa corrente.")),l(r.a,{title:"Legge delle maglie"},l("p",null,"Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito."),l("p",null,"In una maglia chiusa, la somma delle differenze di potenziale è 0."))),l(u.a,{title:"Serie e Parallelo"},l(r.a,{title:"Circuito in serie"},l("p",null,"Più parti di circuito sono ",l("i",null,"in serie")," se sono consecutive e senza biforcazioni."),l("p",null,"Parti di circuito in serie sono attraversate dalla stessa corrente.")),l(r.a,{title:"Circuito in parallelo"},l("p",null,"Più parti di circuito sono ",l("i",null,"in parallelo")," tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo."),l("p",null,"Parti di circuito in parallelo hanno la stessa differenza di potenziale."))),l(u.a,{title:"Resistenze equivalenti"},l(r.a,{title:"Circuiti in serie"},l("p",null,"Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:"),l("p",null,l(o.a,null,Re(Gl||(Gl=Me`R_{serie} = \sum_{i=1}^{n} R_i`))))),l(r.a,{title:"Circuiti in parallelo"},l("p",null,"Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:"),l("p",null,l(o.a,null,Re(Ol||(Ol=Me`R_{parallelo} = \frac{1}{\sum_{i=1}^{n} \frac{1}{R_i}}`)))))),l(u.a,{title:"Condensatori equivalenti"},l(r.a,{title:"Circuiti in serie"},l("p",null,"Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:"),l("p",null,l(o.a,null,Re(Wl||(Wl=Me`C_{serie} = \frac{1}{\sum_{i=1}^{n} \frac{1}{C_i}}`))))),l(r.a,{title:"Circuiti in parallelo"},l("p",null,"Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:"),l("p",null,l(o.a,null,Re(Jl||(Jl=Me`C_{parallelo} = \sum_{i=1}^{n} C_n`)))))),l(u.a,{title:"Magnetismo"},l(r.a,{title:"Permeabilità magnetica dello spazio vuoto"},l("p",null,"E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente."),l("p",null,l(o.a,null,Re(Kl||(Kl=Me`\mu_0 = 4 \pi \cdot 10^{-7} \frac{H}{m}`)))," (",l(o.a,null,Re(Xl||(Xl=Me`\frac{N}{A^2}`))),")")),l(r.a,{title:"Campo magnetico"},l("p",null,"Come un campo elettrico, ma per i magneti."),l("p",null,"Il suo simbolo è ",l(o.a,null,Re(jl||(jl=Me`B`))),", e la sua unità di misura è il Tesla (",l(o.a,null,"T"),").")),l(r.a,{title:"Flusso magnetico"},l("p",null,'È "quanto" campo magnetico ',l("b",null,"attraversa")," un percorso chiuso."),l("p",null,'Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'),l("p",null,l(o.a,null,Re(Hl||(Hl=Me`\Phi_{B_{i}} = \vec{B} \cdot \vec{L}_n = B \cdot L_i \cdot \sin(\alpha) = B_\parallel \cdot L_i`)))),l("p",null,l(o.a,null,Re(Yl||(Yl=Me`\Phi_{B} = \sum_{i=0}^{n_{lati}} \Phi_{Bn}`)))),l("p",null,"La sua unità di misura è il Weber (",l(o.a,null,Re(Zl||(Zl=Me`Wb = T \cdot m^2`))),").")),l(r.a,{title:"Legge di Gauss per i campi magnetici"},l("p",null,"Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo."),l("p",null,"Ovvero, non esistono monopoli magnetici.")),l(r.a,{title:"Legge di Ampère"},l("p",null,"L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso."),l("p",null,l(o.a,null,Re($l||($l=Me`\Phi_B = \mu_0 \cdot I`)))))),l(u.a,{title:"Forze magnetiche"},l(r.a,{title:l("span",null,"Forza magnetica su carica puntiforme ",l("small",null,"(Forza di Lorentz)"))},l("p",null,"I campi magnetici applicano una forza sulle cariche vicine:"),l("p",null,l(o.a,null,Re(le||(le=Me`\vec{F}_{B} = q \cdot (\vec{v} \times \vec{B})`)))),l("p",null,"Dove ",l(o.a,null,Re(ee||(ee=Me`\vec{B}`)))," è l'intensità del campo magnetico e ",l(o.a,null,Re(ae||(ae=Me`\vec{v}`)))," la velocità della carica considerata."),l("p",null,"Si ha una forza massima se la velocità è perpendicolare al campo magnetico."),l("p",null,"In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.")),l(r.a,{title:"Forza magnetica in un filo"},l("p",null,"I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:"),l("p",null,l(o.a,null,Re(ie||(ie=Me`\vec{F}_{magnetica} = I \cdot (\vec{L} \times \vec{B})`)))," ",l("a",{href:"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360"},"[1]")),l("p",null,"Dove ",l(o.a,null,Re(ne||(ne=Me`I`)))," è la corrente elettrica, ",l(o.a,null,Re(te||(te=Me`\vec{L}`)))," è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore."))),l(u.a,{title:"Campi magnetici"},l(r.a,{title:"Campo magnetico in una spira"},l("p",null,"Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.")),l(r.a,{title:"Campo magnetico di un solenoide"},l("p",null,"Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro."),l("p",null,"All'interno del solenoide si crea un campo (quasi) uniforme:"),l("p",null,l(o.a,null,Re(oe||(oe=Me`\left | \vec{B} \right | = \mu_0 \cdot I \cdot \frac{A_{vvolgimenti}}{L_{unghezzafilo}}`))))),l(r.a,{title:"Legge di Oersted"},l("p",null,l("i",null,"Caso particolare della ",l("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re"},"Legge di Ampère"),".")),l("p",null,"Il modulo del campo magnetico ",l(o.a,null,"B")," prodotto da un filo in cui passa una corrente continua ",l(o.a,null,"I")," alla distanza ",l(o.a,null,"s")," è:"),l("p",null,l(o.a,null,Re(re||(re=Me`\left | \vec{B} \right | = \frac{\mu \cdot I}{2 \pi r}`)))),l("p",null,"Il campo magnetico così creato gira attorno al filo in senso antiorario."),l("p",null,"Due fili attraversati dalla ",l(c.a,null,"stessa corrente")," si attraggono, due fili attraversati da ",l(c.a,null,"corr"),l(s.a,null,"enti")," ",l(c.a,null,"opp"),l(s.a,null,"oste")," si respingono."))),l(u.a,{title:"Induzione elettromagnetica"},l(r.a,{title:"Forza elettromotrice indotta"},l("p",null,"Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo."),l("p",null,"La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore."),l("p",null,"Essa vale:"),l("p",null,l(o.a,null,Re(ue||(ue=Me`\Delta V_{indotta} = v \cdot B \cdot L`)))),l("p",null,"Dove ",l(o.a,null,"v")," è la velocità del conduttore, ",l(o.a,null,"B")," è l'intensità del campo magnetico ed ",l(o.a,null,"L")," è la lunghezza del conduttore.")),l(r.a,{title:"Flusso magnetico in una spira"},l("p",null,"In un campo magnetico ",l(o.a,null,Re(ce||(ce=Me`B`)))," uniforme e perpendicolare al piano di una spira di area ",l(o.a,null,Re(se||(se=Me`A`))),", il flusso magnetico si può determinare con la ",l("i",null,"Legge di Faraday-Neumann-Lenz"),":"),l("p",null,l(o.a,null,Re(pe||(pe=Me`\Phi_B = \vec{B} \cdot \vec{A} = B \cdot A \cdot \cos(\alpha)`)))))),l(u.a,null,l(r.a,{title:"Legge di Faraday-Neumann-Lenz"},l("p",null,"Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso."),l("p",null,l(o.a,null,Re(de||(de=Me`\Delta V_{indotta} = - \frac{\Delta \Phi_B}{\Delta t}`)))),l("p",null,"Il meno è dovuto alla ",l("a",{href:"https://it.wikipedia.org/wiki/Legge_di_Lenz"},"Legge di Lenz"),", che specifica qualitativamente il verso della forza elettromotrice indotta.")),l(r.a,{title:"Faraday in un solenoide"},l("p",null,"In un solenoide, la forza elettromotrice indotta è uguale a:"),l("p",null,l(o.a,null,Re(me||(me=Me`\Delta V_{indotta} = - \frac{N \cdot \Delta \Phi_{B_{spira}}}{\Delta t} = - \frac{N \cdot B \cdot A \cdot cos(\alpha)}{\Delta t}`)))),l("p",null,"Dove ",l(o.a,null,Re(ve||(ve=Me`N`)))," è il numero delle spire del solenoide.")),l(r.a,{title:"Legge di Ampère-Maxwell"},l("p",null,"Correnti o campi elettrici variabili creano un campo magnetico."))),l(u.a,{title:"Elettromagnetismo"},l(r.a,{title:"Onde elettromagnetiche"},l("p",null,"Nel vuoto, il campo elettrico ",l(o.a,null,Re(ge||(ge=Me`E`)))," e il campo magnetico ",l(o.a,null,Re(fe||(fe=Me`B`)))," sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo."),l("p",null,"Si dice quindi che sono ",l("i",null,"onde elettromagnetiche"),"."),l("p",null,"Esse sono legate dalla relazione:"),l("p",null,l(o.a,null,Re(he||(he=Me`E = c \cdot B`)))),l("p",null,"Dove ",l(o.a,null,Re(ze||(ze=Me`c`)))," è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:"),l("p",null,l(o.a,null,Re(_e||(_e=Me`c = \frac{1}{\sqrt{\epsilon_0 \cdot \mu_0}} = 3.00 \cdot 10^8 \frac{m}{s}`))))),l(r.a,{title:"Formula delle onde"},l("p",null,l(o.a,null,Re(be||(be=Me`A(t) = A_{max} \cdot \sin \left ( \frac{2 \pi}{\lambda} - \omega t + \phi \right )`)))),l("p",null,"Dove ",l(o.a,null,Re(Le||(Le=Me`A_{max}`)))," è l'ampiezza massima che può avere l'onda, ",l(o.a,null,Re(qe||(qe=Me`\frac{2 \pi}{\lambda} = \left | \vec{k} \right |`)))," è il vettore d'onda, ",l(o.a,null,Re(Ce||(Ce=Me`\omega`)))," la frequenza angolare e ",l(o.a,null,Re(De||(De=Me`\phi`)))," la fase."))),l(u.a,{title:"Spettroscopia"},l(r.a,{title:"Emissione"},l("p",null,"I solidi, se portati ad alta temperatura, emettono luce con uno ",l("a",{href:"https://it.wikipedia.org/wiki/Spettro_continuo"},"spettro continuo"),"."),l("p",null,"I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda."),l("p",null,"In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:"),l("p",null,l(o.a,null,Re(Pe||(Pe=Me`\frac{1}{\lambda} = R \left ( \frac{1}{4} - \frac{1}{n^2} \right )`)))),l("p",null,"Con ",l(o.a,null,Re(Ae||(Ae=Me`R = 1.097 \cdot 10^7 \frac{1}{m}`))),", detta costante di Rydberg, e ",l(o.a,null,Re(Fe||(Fe=Me`n`)))," un numero intero.")),l(r.a,{title:"Grandezza quantizzata"},l("p",null,"Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori."),l("p",null,"Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata."),l("p",null,"Energia, momento angolare e raggio sono quantizzati."),l("p",null,"Nota costante quantica è ",l(o.a,null,Re(Ee||(Ee=Me`h`))),", la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come ",l(o.a,null,Re(Se||(Se=Me`\hbar = \left ( \frac{h}{2 \pi} \right )`))),"."))),l(u.a,null,l(r.a,{title:"Modello di Bohr"},l("p",null,"L'energia degli elettroni è quantizzata."),l("p",null,"Inoltre, per essi è valido che:"),l("p",null,l(o.a,null,Re(Ie||(Ie=Me`m \cdot v_n \cdot 2 \pi \cdot r = n \cdot h`)))),l("p",null,"Ancora, il raggio delle orbite è uguale a:"),l("p",null,l(o.a,null,Re(ke||(ke=Me`r_n = n^2 \cdot a_0 = n^2 \cdot \frac{\hbar}{m_{elettrone} \cdot k \cdot e^2} `)))),l("p",null,"Con ",l(o.a,null,Re(we||(we=Me`a_0 = \left ( \frac{h}{2 \pi} \right )^2 \cdot \frac{1}{m_{elettrone} \cdot k \cdot e^2} = 5.29 \cdot 10^{-11} m`))),"."),l("p",null,"Infine, in ogni stato, l'energia è pari a:"),l("p",null,l(o.a,null,Re(xe||(xe=Me`E_n = \frac{1}{n^2} \cdot E_1 = - \frac{1}{n^2} \cdot \frac{a_0^2}{2 \cdot m \cdot \hbar^4} = - \frac{1}{n^2} \cdot \frac{m_{elettrone} \cdot k^2 \cdot e^4}{2 \cdot \hbar^2}`)))),l("p",null,"Due elettroni non possono occupare lo stesso stato."),l("p",null,"Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di"))),l(u.a,null,l(r.a,{title:"Nei solidi"},l("p",null,"Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda."),l("p",null,"Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi."))),l(u.a,{title:"Semiconduttori"},l(r.a,{title:"Semiconduttori"},l("p",null,l(p.a,null,"Refactor this")),l("p",null,"Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di ",l(o.a,null,Re(Be||(Be=Me`10^1 eV`))),", allora il corpo è un isolante."),l("p",null,"Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore."),l("p",null,"Se il gap è invece dell'ordine di grandezza di ",l(o.a,null,Re(Ne||(Ne=Me`1 eV`))),", allora il corpo è un semiconduttore.")),l(r.a,{title:"Lacune"},l("p",null,"Legami in cui ",l(c.a,null,"mancano elettroni"),"."),l("p",null,l(s.a,null,"Elettroni")," di altri legami possono spostarsi per colmare le ",l(c.a,null,"lacune"),", creandone altre, e spostandole in direzione opposta a quella della corrente.")),l(r.a,{title:"Accettori e donori"},l("p",null,"Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:"),l("ul",null,l("li",null,"Con numero atomico maggiore, un semiconduttore di ",l(s.a,null,"tipo N")," con ",l(s.a,null,"elettroni in eccesso")," liberi di scorrere."),l("li",null,"Con numero atomico minore, un semiconduttore di ",l(c.a,null,"tipo P")," con ",l(c.a,null,"lacune in eccesso")," libere di catturare elettroni da altri legami.")),l("p",null,"Maggiore impurezza porta a maggiore conduttività.")),l(r.a,{title:"Temperatura"},l("p",null,"Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di ",l(s.a,null,"elettroni")," e ",l(c.a,null,"lacune"),"."))),l(u.a,{title:l("span",null,"Ottica ",l("small",null,"(non l'abbiamo fatta)"))},l(r.a,{title:"Assorbimento e riflessione"},l("p",null,"I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.")),l(r.a,{title:"Corpo nero"},l("p",null,"Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna."),l("p",null,"Le onde assorbite vengono poi riemesse sotto forma di un onda di ",l(o.a,null,Re(Te||(Te=Me`\lambda`)))," variabile in base alla temperatura."),l("p",null,l(o.a,null,Re(Ve||(Ve=Me`\lambda_{max} \cdot T`)))," è costante.")),l(r.a,{title:"Teoria di Planck per il corpo nero"},l("p",null,"L'energia assorbita e emessa dai corpi neri è quantizzata.")),l(r.a,{title:"Fotone"},l("p",null,"Un onda magnetica con un quanto di energia è detta ",l("i",null,"fotone"),":"),l("p",null,l(o.a,null,Re(ye||(ye=Me`E_{fotone} = h \cdot f`))))),l(r.a,{title:"Effetto fotoelettrico"},l("p",null,"A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale."),l("p",null,"Perchè avvenga, la frequenza deve essere maggiore di una certa soglia."),l("p",null,"Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza."),l("p",null,"Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni."))))}}}.call(this,a("hosL").h)},ZsnK:function(l,e,a){"use strict";(function(l){a.d(e,"a",(function(){return o}));var i=a("+AyP"),n=a.n(i),t=a("hosL");class o extends t.Component{render(){return l("img",{src:`https://latex.codecogs.com/svg.latex?${`{\\color{White} ${this.props.children} }`}`,alt:this.props.children,title:this.props.children,class:n.a.latex})}}}).call(this,a("hosL").h)},bQQT:function(l,e,a){"use strict";(function(l){a.d(e,"a",(function(){return o}));var i=a("Qnof"),n=a.n(i),t=a("hosL");class o extends t.Component{render(){return l("span",{class:n.a.plus},this.props.children)}}}).call(this,a("hosL").h)},ddBW:function(l,e,a){"use strict";(function(l){a.d(e,"a",(function(){return o}));var i=a("rMrT"),n=a.n(i),t=a("hosL");class o extends t.Component{render(){let e,a=null;return void 0!==this.props.title&&(a=l("h2",null,this.props.title)),e=Array.isArray(this.props.children)?this.props.children.map(e=>l("div",{class:n.a.splitchild},e)):l("div",{class:n.a.splitchild},this.props.children),l("div",{class:n.a.split},a,l("div",{class:n.a.splitparent},e))}}}).call(this,a("hosL").h)},dyG3:function(l){l.exports={fisica:"fisica__iNxb9"}},giqd:function(l){l.exports={minus:"minus__2Ld4F"}},kpQM:function(l){l.exports={todo:"todo__1pOoN"}},rMrT:function(l){l.exports={split:"split__3qCWp",splitparent:"splitparent__2xagg",splitchild:"splitchild__3cEoc"}}}]);
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    \r\n                
    Indice
    \r\n                \r\n                    Statistica ed elementi di probabilità}>\r\n                        
    \r\n                            Appunti scritti mentre studiavo per l'esame di Statistica ed elementi di probabilità  del corso triennale di Informatica all'Unimore del Prof. Luca La Rocca.\r\n                        
    \r\n                        \r\n                    Cleaver}>\r\n                        
    \r\n                            Progetto in Java sviluppato per l'esame di Programmazione ad Oggetti del corso triennale di Informatica all'Unimore, tenuto dai Prof. Giacomo Cabri e Nicola Capodieci.\r\n                        
    \r\n                        \r\n                    Fisica}>\r\n                        
    \r\n                            Appunti delle lezioni di Fisica del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Rossella Brunetti nel primo semestre dell'Anno Accademico 2019/2020.\r\n                        
    \r\n                        \r\n                    Sistemi Operativi}>\r\n                        
    \r\n                            Soluzioni agli Arzigogoli proposti dal Prof. Mauro Andreolini durante le lezioni di Sistemi Operativi del corso triennale di Informatica all'Unimore tenutesi nel primo semestre dell'Anno Accademico 2019/2020.\r\n                        
    \r\n                        \r\n                    Algoritmi e Strutture Dati}>\r\n                        
    \r\n                            Appunti delle lezioni di Algoritmi e Strutture Dati del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Manuela Montangero nel secondo semestre dell'Anno Accademico 2018/2019.\r\n                        
    \r\n                        \r\n                    Videolezioni di Geometria}>\r\n                        
    \r\n                            Ottime videolezioni di Geometria con licenza CC BY-NC-SA 4.0 che ho trovato sul portale Dolly 2018 dell'Unimore.\r\n                        
    \r\n                        \r\n                    Come installare MinGW}>\r\n                        
    \r\n                            Un breve tutorial con immagini su come installare e configurare MinGW per compilare programmi C e C++ su Windows.\r\n                        
    \r\n                        \r\n                    \r\n                \r\n                    @unimoreinfo}>\r\n                        
    \r\n                            Il gruppo Telegram del corso di Informatica dell'Unimore!\r\n                        
    \r\n                        \r\n                    Calendario Lezioni}>\r\n                        
    \r\n                            Calendario Google quasi sempre aggiornato delle lezioni e degli esami del secondo anno dell'Unimore durante l'Anno Accademico 2019/2020.\r\n                        
    \r\n                        \r\n                    Erre2}>\r\n                        
    \r\n                            Portale contenente appunti e riassunti mantenuto da Lorenzo Balugani.\r\n                        
    \r\n                        \r\n                    vezzalinistefano/Appunti-Algoritmi}>\r\n                        
    \r\n                            Appunti di Algoritmi e Strutture Dati mantenuti da Vezzalini Stefano.\r\n                        
    \r\n                        \r\n                    \r\n            
    \r\n        )\r\n    }\r\n}\r\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"home\":\"home__3aaQ1\"};","import style from \"./split.css\";\nimport { Component } from 'preact';\n\nexport default class Split extends Component {\n\trender() {\n\t    let title = null;\n\t    if(this.props.title !== undefined) {\n            title = (
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diff --git a/docs/route-mingwinstall.chunk.1d3c8.css b/docs/route-mingwinstall.chunk.1d3c8.css
new file mode 100644
index 0000000..a96cbe6
--- /dev/null
+++ b/docs/route-mingwinstall.chunk.1d3c8.css
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diff --git a/docs/route-mingwinstall.chunk.4b543.js b/docs/route-mingwinstall.chunk.4b543.js
new file mode 100644
index 0000000..bc442e9
--- /dev/null
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n=Zi(["overline{X}_n"],["\\overline{X}_n"]);return en=function(){return n},n}function tn(){var n=Zi(["S_n^2 sim \frac{sigma^2}{n - 1} cdot chi^2 (n-1)"],["S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)"]);return tn=function(){return n},n}function rn(){var n=Zi(["S_0^2 sim \frac{sigma^2}{n} cdot chi^2 (n)"],["S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)"]);return rn=function(){return n},n}function on(){var n=Zi(["overline{X}_n sim Nor left( mu, \frac{sigma^2}{n} \right)"],["\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)"]);return on=function(){return n},n}function un(){var n=Zi(["X sim Nor(mu, sigma^2)"],["X \\sim Nor(\\mu, \\sigma^2)"]);return un=function(){return n},n}function cn(){var n=Zi(["E(S_0^2) = E(S_n^2) = Var(X)"]);return cn=function(){return n},n}function sn(){var n=Zi(["Var(overline{X}_n) = \frac{Var(X)}{n}"],["Var(\\overline{X}_n) = \\frac{Var(X)}{n}"]);return sn=function(){return n},n}function pn(){var n=Zi(["E(overline{X}_n) = E(X)"],["E(\\overline{X}_n) = E(X)"]);return pn=function(){return n},n}function dn(){var n=Zi(["S_n^2 = \frac{1}{n - 1} cdot sum_{i = 1}^n (X_i - overline{X}_n)^2 = \frac{1}{n - 1} cdot ( n cdot M_2^{(2)} - n cdot overline{X}_n^2)"],["S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)"]);return dn=function(){return n},n}function mn(){var n=Zi(["S_0^2 = \frac{1}{n} cdot sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 cdot m cdot overline{X}_n + m^2"],["S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2"]);return mn=function(){return n},n}function fn(){var n=Zi(["m = E(X)"]);return fn=function(){return n},n}function vn(){var n=Zi(["overline{X}_n"],["\\overline{X}_n"]);return vn=function(){return n},n}function bn(){var n=Zi(["M^{(k)}_n = \frac{1}{n} cdot sum_{i = 1}^n X_i^k "],["M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k "]);return bn=function(){return n},n}function _n(){var n=Zi(["Var left( sum_i X_i \right) = sum_i Var(X_i)"],["Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)"]);return _n=function(){return n},n}function hn(){var n=Zi(["Cov(X, Y) = 0"]);return hn=function(){return n},n}function Xn(){var n=Zi(["Var(X + Y) = Var(X) + Var(Y) + 2 cdot Cov(X, Y)"],["Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)"]);return Xn=function(){return n},n}function gn(){var n=Zi(["Y = a X + b Longleftrightarrow | \rho_{X, Y} | = 1"],["Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1"]);return gn=function(){return n},n}function qn(){var n=Zi(["-1 leq \rho_{X, Y} leq 1"],["-1 \\leq \\rho_{X, Y} \\leq 1"]);return qn=function(){return n},n}function zn(){var n=Zi(["\rho_{X, Y} = \frac{Cov(X, Y)}{sqrt{Var(X)} cdot sqrt{Var(Y)}}"],["\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}"]);return zn=function(){return n},n}function En(){var n=Zi(["\n                                \boldsymbol{C_X} = \n                                \begin{bmatrix}\n                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\n                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\n                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n                                end{bmatrix}\n                            "],["\n                                \\boldsymbol{C_X} = \n                                \\begin{bmatrix}\n                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n                                \\end{bmatrix}\n                            "]);return En=function(){return n},n}function Pn(){var n=Zi(["\boldsymbol{X}"],["\\boldsymbol{X}"]);return Pn=function(){return n},n}function xn(){var n=Zi(["\boldsymbol{C_X}"],["\\boldsymbol{C_X}"]);return xn=function(){return n},n}function kn(){var n=Zi(["Cov(X, Y) = 0"]);return kn=function(){return n},n}function yn(){var n=Zi(["Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)"]);return yn=function(){return n},n}function Ln(){var n=Zi(["Cov(alpha X, \beta Y) = alpha cdot \beta cdot Cov(X, Y)"],["Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)"]);return Ln=function(){return n},n}function Fn(){var n=Zi(["Cov(X, X) = Var(X)"]);return Fn=function(){return n},n}function Nn(){var n=Zi(["Cov(X, Y) = Cov(Y, X)"]);return Nn=function(){return n},n}function Vn(){var n=Zi(["Cov(X, alpha) = 0"],["Cov(X, \\alpha) = 0"]);return Vn=function(){return n},n}function Cn(){var n=Zi(["Cov(X, Y) = E((X - E(X) cdot (Y - E(Y)) = E(XY) - E(X) cdot E(Y)"],["Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)"]);return Cn=function(){return n},n}function Sn(){var n=Zi(["E(X + Y) = E(X) + E(Y)"]);return Sn=function(){return n},n}function Yn(){var n=Zi(["E(g(X, Y)) = sum_{i, j} g(x_i, y_i) cdot p_{X, Y} (x_i, y_i)"],["E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)"]);return Yn=function(){return n},n}function wn(){var n=Zi(["P(X_1 in A_1, dots, X_n in A_n) = P(X_1 in A_1) \times dots \times P(X_n in A_n)"],["P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)"]);return wn=function(){return n},n}function In(){var n=Zi(["p_X (x) = sum_j p_{X, Y} (x_i, y_j)"],["p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)"]);return In=function(){return n},n}function Mn(){var n=Zi(["p_{X, Y} (x, y) = P(X = x, Y = y)"]);return Mn=function(){return n},n}function Dn(){var n=Zi(["F_X (x) = P(X leq x) = lim_{y \to +infty} F_{X, Y} (x, y)"],["F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)"]);return Dn=function(){return n},n}function Un(){var n=Zi(["F_{X, Y} (x, y) = P(X leq x, Y leq y)"],["F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)"]);return Un=function(){return n},n}function Bn(){var n=Zi(["X, Y"]);return Bn=function(){return n},n}function An(){var n=Zi(["\boldsymbol{X}"],["\\boldsymbol{X}"]);return An=function(){return n},n}function Tn(){var n=Zi(["P(X > k) simeq P(Y geq k + \frac{1}{2})"],["P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})"]);return Tn=function(){return n},n}function Gn(){var n=Zi(["P(X geq k) simeq P(Y geq k - \frac{1}{2})"],["P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})"]);return Gn=function(){return n},n}function On(){var n=Zi(["P(X leq k) simeq P(Y leq k + \frac{1}{2})"],["P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})"]);return On=function(){return n},n}function jn(){var n=Zi(["P(X < k) simeq P(Y leq k - \frac{1}{2})"],["P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})"]);return jn=function(){return n},n}function Rn(){var n=Zi(["(k - \frac{1}{2}, k + \frac{1}{2})"],["(k - \\frac{1}{2}, k + \\frac{1}{2})"]);return Rn=function(){return n},n}function Kn(){var n=Zi(["Bin(n, p) approx Nor(n cdot p, n cdot p cdot q)"],["Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)"]);return Kn=function(){return n},n}function Qn(){var n=Zi(["Bin(n, p) approx Poi(n cdot p)"],["Bin(n, p) \\approx Poi(n \\cdot p)"]);return Qn=function(){return n},n}function Wn(){var n=Zi(["Ipe(N, K, n) approx Bin(n, \frac{K}{N})"],["Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})"]);return Wn=function(){return n},n}function Zn(){var n=Zi(["T(v) = \frac{Nor(0, 1)}{sqrt{\frac{chi^2(v)}{v}}}"],["T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}"]);return Zn=function(){return n},n}function Hn(){var n=Zi(["chi^2 (n) + chi^2 (m) = chi^2 (n + m)"],["\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)"]);return Hn=function(){return n},n}function Jn(){var n=Zi(["Gamma left( \frac{1}{2}, \frac{1}{2} \right) = chi^2 (v = 1)"],["\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)"]);return Jn=function(){return n},n}function $n(){var n=Zi(["Z^2 sim chi^2 (v = 1)"],["Z^2 \\sim \\chi^2 (v = 1)"]);return $n=function(){return n},n}function na(){var n=Zi(["x_alpha = mu + z_alpha cdot sqrt{sigma^2}"],["x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}"]);return na=function(){return n},n}function aa(){var n=Zi(["z_alpha"],["z_\\alpha"]);return aa=function(){return n},n}function la(){var n=Zi(["F_Z(z) = phi(z) = \frac{1}{sqrt{2 pi}} int_{-infty}^{z} e^{-\frac{x^2}{2}} dx"],["F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx"]);return la=function(){return n},n}function ia(){var n=Zi(["phi(z)"],["\\phi(z)"]);return ia=function(){return n},n}function ea(){var n=Zi(["X sim Nor(m, v^2) implies alpha X + \beta sim Nor(alpha m + \beta, (alpha v)^2)"],["X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)"]);return ea=function(){return n},n}function ta(){var n=Zi(["Var(X) = sigma^2"],["Var(X) = \\sigma^2"]);return ta=function(){return n},n}function ra(){var n=Zi(["E(X) = mu"],["E(X) = \\mu"]);return ra=function(){return n},n}function oa(){var n=Zi(["m_X (t) = e^{mu cdot t + \frac{sigma^2 cdot t^2}{2}}"],["m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}"]);return oa=function(){return n},n}function ua(){var n=Zi(["f_X (x) = \frac{e^{-\frac{(x - mu)^2}{2 sigma^2}}}{sqrt{2 pi cdot sigma^2}}"],["f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}"]);return ua=function(){return n},n}function ca(){var n=Zi(["Nor(mu, sigma^2)"],["Nor(\\mu, \\sigma^2)"]);return ca=function(){return n},n}function sa(){var n=Zi(["Var(X) = \frac{(b - a)^2}{12}"],["Var(X) = \\frac{(b - a)^2}{12}"]);return sa=function(){return n},n}function pa(){var n=Zi(["E(X) = \frac{a + b}{2}"],["E(X) = \\frac{a + b}{2}"]);return pa=function(){return n},n}function da(){var n=Zi(["m_X (t) = \frac{e^{b cdot t} - e^{a cdot t}}{(b - a) cdot t}"],["m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}"]);return da=function(){return n},n}function ma(){var n=Zi(["f_X (x) = \begin{cases}\n                                0 qquad quad x < a  \n                                \frac{1}{b - a} qquad a leq x leq b\\\n                                1 qquad quad x > b\n                            end{cases}"],["f_X (x) = \\begin{cases}\n                                0 \\qquad \\quad x < a  \n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                1 \\qquad \\quad x > b\n                            \\end{cases}"]);return ma=function(){return n},n}function fa(){var n=Zi(["f_X (x) = \begin{cases}\n                                \frac{1}{b - a} qquad a leq x leq b\\\n                                0 qquad quad altrimenti    \n                            end{cases}"],["f_X (x) = \\begin{cases}\n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                0 \\qquad \\quad altrimenti    \n                            \\end{cases}"]);return fa=function(){return n},n}function va(){var n=Zi(["P(X in (c, d)) = \frac{d - c}{b - a}"],["P(X \\in (c, d)) = \\frac{d - c}{b - a}"]);return va=function(){return n},n}function ba(){var n=Zi(["Uni(a, b)"]);return ba=function(){return n},n}function _a(){var n=Zi(["[a, b]"]);return _a=function(){return n},n}function ha(){var n=Zi(["Var(X) = \frac{alpha}{lambda^2}"],["Var(X) = \\frac{\\alpha}{\\lambda^2}"]);return ha=function(){return n},n}function Xa(){var n=Zi(["E(X) = \frac{alpha}{lambda}"],["E(X) = \\frac{\\alpha}{\\lambda}"]);return Xa=function(){return n},n}function ga(){var n=Zi(["m_X (t) : ( t < lambda ) in mathbb{R} = left( \frac{lambda}{lambda - t} \right) ^alpha"],["m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha"]);return ga=function(){return n},n}function qa(){var n=Zi(["f_X (x) = \begin{cases}\n                            0 qquad qquad qquad qquad qquad x < 0\\\n                            \frac{1}{(n-1)!} cdot lambda^n cdot x^{n-1} cdot e^{-lambda cdot x} quad k > 0\n                            end{cases}"],["f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n                            \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n                            \\end{cases}"]);return qa=function(){return n},n}function za(){var n=Zi(["Gamma(n, lambda)"],["\\Gamma(n, \\lambda)"]);return za=function(){return n},n}function Ea(){var n=Zi(["lambda"],["\\lambda"]);return Ea=function(){return n},n}function Pa(){var n=Zi(["P([X > s + t | X > s]) = P([X > t])"]);return Pa=function(){return n},n}function xa(){var n=Zi(["Var(X) = \frac{1}{lambda^2}"],["Var(X) = \\frac{1}{\\lambda^2}"]);return xa=function(){return n},n}function ka(){var n=Zi(["E(X) = \frac{1}{lambda}"],["E(X) = \\frac{1}{\\lambda}"]);return ka=function(){return n},n}function ya(){var n=Zi(["m_X (t) : { t | t < lambda } in mathbb{R} = \frac{lambda}{lambda - t}"],["m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}"]);return ya=function(){return n},n}function La(){var n=Zi(["F_X (t) = \begin{cases}\n                            0 qquad qquad t < 0\\\n                            1 - e^{-lambda cdot t} quad t geq 0\n                            end{cases}"],["F_X (t) = \\begin{cases}\n                            0 \\qquad \\qquad t < 0\\\\\n                            1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n                            \\end{cases}"]);return La=function(){return n},n}function Fa(){var n=Zi(["f_X (x) = \begin{cases}\n                            0 qquad qquad x < 0\\\n                            lambda cdot e^{-lambda cdot x} quad x > 0\n                            end{cases}"],["f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad x < 0\\\\\n                            \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n                            \\end{cases}"]);return Fa=function(){return n},n}function Na(){var n=Zi(["Esp(lambda)"],["Esp(\\lambda)"]);return Na=function(){return n},n}function Va(){var n=Zi(["lambda"],["\\lambda"]);return Va=function(){return n},n}function Ca(){var n=Zi(["Poi(t cdot lambda)"],["Poi(t \\cdot \\lambda)"]);return Ca=function(){return n},n}function Sa(){var n=Zi(["mu = t cdot lambda"],["\\mu = t \\cdot \\lambda"]);return Sa=function(){return n},n}function Ya(){var n=Zi(["lambda"],["\\lambda"]);return Ya=function(){return n},n}function wa(){var n=Zi(["lambda"],["\\lambda"]);return wa=function(){return n},n}function Ia(){var n=Zi(["E(X^2) = mu^2 + mu"],["E(X^2) = \\mu^2 + \\mu"]);return Ia=function(){return n},n}function Ma(){var n=Zi(["Var(X) = mu"],["Var(X) = \\mu"]);return Ma=function(){return n},n}function Da(){var n=Zi(["E(X) = mu"],["E(X) = \\mu"]);return Da=function(){return n},n}function Ua(){var n=Zi(["m_X (t) = e^{mu cdot (e^t - 1)}"],["m_X (t) = e^{\\mu \\cdot (e^t - 1)}"]);return Ua=function(){return n},n}function Ba(){var n=Zi(["f_X (k) : mathbb{N} = \frac{e^{-mu} cdot mu^k}{k!}"],["f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}"]);return Ba=function(){return n},n}function Aa(){var n=Zi(["Poi(mu)"],["Poi(\\mu)"]);return Aa=function(){return n},n}function Ta(){var n=Zi(["E(X) = n cdot p \to mu \neq 0"],["E(X) = n \\cdot p \\to \\mu \\neq 0"]);return Ta=function(){return n},n}function Ga(){var n=Zi(["p \to 0"],["p \\to 0"]);return Ga=function(){return n},n}function Oa(){var n=Zi(["n \to +infty"],["n \\to +\\infty"]);return Oa=function(){return n},n}function ja(){var n=Zi(["X sim Bin(n, p)"],["X \\sim Bin(n, p)"]);return ja=function(){return n},n}function Ra(){var n=Zi(["Var(X) = n cdot \frac{K}{N} cdot \frac{N - K}{N} cdot \frac{N - n}{N - 1}"],["Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}"]);return Ra=function(){return n},n}function Ka(){var n=Zi(["E(X) = n cdot \frac{K}{N}"],["E(X) = n \\cdot \\frac{K}{N}"]);return Ka=function(){return n},n}function Qa(){var n=Zi(["f_X (k) : {0..n} in mathbb{N} = \frac{\binom{K}{k} cdot \binom{N - K}{n - k}}{\binom{N}{n}}"],["f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}"]);return Qa=function(){return n},n}function Wa(){var n=Zi(["Var(X) = \frac{n cdot q}{p^2}"],["Var(X) = \\frac{n \\cdot q}{p^2}"]);return Wa=function(){return n},n}function Za(){var n=Zi(["E(X) = \frac{n cdot q}{p}"],["E(X) = \\frac{n \\cdot q}{p}"]);return Za=function(){return n},n}function Ha(){var n=Zi(["m_X (t) : left{ t < ln left( \frac{1}{q} \right) \right} = left( \frac{p cdot e^t}{1 - q cdot e^t} \right) ^n"],["m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n"]);return Ha=function(){return n},n}function Ja(){var n=Zi(["f_X (k) : mathbb{N} = \binom{k + n - 1}{n - 1} cdot p^n cdot q^k "],["f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k "]);return Ja=function(){return n},n}function 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\\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}"]);return Ti=function(){return n},n}function Gi(){var n=Zi(["E cap F = left { 1 \right }"],["E \\cap F = \\left \\{ 1 \\right \\}"]);return Gi=function(){return n},n}function Oi(){var n=Zi(["\bar{E} = left { 3, 4, 5, 6 \right }"],["\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}"]);return Oi=function(){return n},n}function ji(){var n=Zi(["E = left { 1, 2 \right }"],["E = \\left \\{ 1, 2 \\right \\}"]);return ji=function(){return n},n}function Ri(){var n=Zi(["omega = 1"],["\\omega = 1"]);return Ri=function(){return n},n}function Ki(){var n=Zi(["Omega = left { 1, 2, 3, 4, 5, 6 \right }"],["\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}"]);return Ki=function(){return n},n}function Qi(){var n=Zi(["P(E) = \frac{successi}{prove totali}"],["P(E) = \\frac{successi}{prove\\ totali}"]);return Qi=function(){return n},n}function Wi(){var n=Zi(["P(E) = \frac{casi favorevoli}{casi possibili}"],["P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}"]);return 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verificasse."))),n(le.a,{title:"Linguaggio matematico"},n(ae.a,{title:"Spazio campionario"},n("blockquote",null,'"omegone"'),n("p",null,"L'",n("b",null,"insieme")," di tutti gli esiti possibili di un esperimento."),n("p",null,n(ne.a,null,re(Ki())))),n(ae.a,{title:"Esito"},n("blockquote",null,'"omeghino"'),n("p",null,"Un ",n("b",null,"elemento")," dello spazio campionario."),n("p",null,n(ne.a,null,re(Ri())))),n(ae.a,{title:"Evento"},n("blockquote",null,'"e"'),n("p",null,"Un ",n("b",null,"sottoinsieme")," dello spazio campionario."),n("p",null,n(ne.a,null,re(ji()))),n("p",null,"Lo spazio campionario stesso è un ",n("b",null,"evento certo"),".")),n(ae.a,{title:"Not"},n("blockquote",null,'"not e"'),n("p",null,"Il ",n("b",null,"complementare")," di un sottoinsieme."),n("p",null,n(ne.a,null,re(Oi())))),n(ae.a,{title:"And"},n("blockquote",null,'"e intersecato effe"'),n("p",null,"L'",n("b",null,"intersezione")," di più sottoinsiemi."),n("p",null,n(ne.a,null,re(Gi())))),n(ae.a,{title:"Or"},n("blockquote",null,'"e unito a effe"'),n("p",null,"L'",n("b",null,"unione")," di più sottoinsiemi."),n("p",null,n(ne.a,null,re(Ti())))),n(ae.a,{title:"Differenza"},n("blockquote",null,'"e meno effe"'),n("p",null,n(ne.a,null,re(Ai())))),n(ae.a,{title:"Implicazione"},n("blockquote",null,'"e contenuto in effe"'),n("p",null,"L'",n("b",null,"inclusione")," del primo insieme in un altro."),n("p",null,n(ne.a,null,re(Bi()))),n("p",null,"Se si verifica ",n(ne.a,null,"E"),", allora si verifica anche ",n(ne.a,null,"F"),".")),n(ae.a,{title:"Evento impossibile"},n("blockquote",null,'"e è impossibile"'),n("p",null,"Un sottoinsieme ",n("b",null,"vuoto"),"."),n("p",null,n(ne.a,null,re(Ui())))),n(ae.a,{title:"Mutua esclusione"},n("blockquote",null,'"e ed effe si escludono mutualmente"'),n("p",null,"La ",n("b",null,"disgiunzione")," di due insiemi."),n("p",null,n(ne.a,null,re(Di()))))),n(le.a,null,n(ae.a,{title:"Famiglia degli eventi"},n("blockquote",null,'"famiglia effe"'),n("p",null,"I sottoinsiemi dello spazio campionario formano una ",n("b",null,"famiglia")," di sottoinsiemi detta ",n("i",null,"famiglia degli eventi"),"."),n("p",null,n(ne.a,null,re(Mi()))),n("p",null,"Qualsiasi sottoinsieme appartenente a ",n(ne.a,null,re(Ii()))," è considerato un evento.")),n(ae.a,{title:n("span",null,n(ne.a,null,re(wi())),"-algebra")},n("blockquote",null,'"sigma algebra"'),n("p",null,"Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta ",n("i",null,n(ne.a,null,re(Yi())),"-algebra"),":"),n("ol",null,n("li",null,"Lo spazio campionario è un evento: ",n(ne.a,null,re(Si()))),n("li",null,"Se un sottoinsieme è un evento, allora anche il suo complementare lo è: ",n(ne.a,null,re(Ci()))),n("li",null,"Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: ",n(ne.a,null,re(Vi())))),n("p",null,"Un esempio: ",n(ne.a,null,re(Ni()))))),n(le.a,null,n(ae.a,{title:"Partizione"},n("blockquote",null,'"la partizione e composta da e uno, e due, e tre..."'),n("p",null,"Un insieme di esiti e eventi:"),n("ul",null,n("li",null,n("b",null,"Finito"),"."),n("li",null,"In cui tutti gli eventi hanno ",n("b",null,"probabilità diversa da 0"),"."),n("li",null,"In cui tutti gli eventi sono ",n("b",null,"mutualmente esclusivi"),"."),n("li",null,"In cui l'unione di tutti i suoi elementi ",n("b",null,"copre lo spazio campionario"),".")),n("p",null,"La partizione ",n(ne.a,null,re(Fi()))," è composta dagli eventi ",n(ne.a,null,re(Li())),", ",n(ne.a,null,re(yi())),", ",n(ne.a,null,re(ki())),", fino a ",n(ne.a,null,re(xi())),"."),n(ie.a,null,"Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare."))),n(le.a,{title:"Assiomi della probabilità"},n(ae.a,{title:"Primo assioma della probabilità"},n("p",null,"La probabilità di un evento è un numero tra 0 e 1."),n("p",null,n(ne.a,null,re(Pi())))),n(ae.a,{title:"Secondo assioma della probabilità"},n("p",null,"La probabilità dello spazio campionario è sempre 1."),n("p",null,n(ne.a,null,re(Ei())))),n(ae.a,{title:"Terzo assioma della probabilità"},n("p",null,"La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità."),n("p",null,n(ne.a,null,re(zi()))))),n(le.a,{title:"Conseguenze degli assiomi"},n(ae.a,{title:"Probabilità di un evento negato"},n("p",null,"La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato."),n("p",null,n(ne.a,null,re(qi())))),n(ae.a,{title:"Probabilità di un evento incluso"},n("p",null,"La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso."),n("p",null,n(ne.a,null,re(gi())))),n(ae.a,{title:"Unione"},n("p",null,"La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione."),n("p",null,n(ne.a,null,re(Xi()))),n(ie.a,null,"Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!"))),n(le.a,{title:"Spazi equiprobabili"},n(ae.a,{title:"Cosa sono?"},n("p",null,"Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi."),n("p",null,n(ne.a,null,re(hi())))),n(ae.a,{title:"Spazi equiprobabili geometrici"},n("p",null,"Gli spazi campionari possono avere un numero infinito di esiti: sono ",n("i",null,"equiprobabili geometrici")," se nessun esito è privilegiato rispetto agli altri."))),n(le.a,{title:"Calcolo combinatorio"},n(ae.a,{title:"Disposizioni"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(ne.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",n(ne.a,null,"k")," volte."),n("p",null,n("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),n("p",null,n(ne.a,null,re(_i())))),n(ae.a,{title:"Disposizioni con ripetizione"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(ne.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"rimetto nel sacchetto"),". Ripeto per ",n(ne.a,null,"k")," volte."),n("p",null,n("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),n("p",null,n(ne.a,null,re(bi())))),n(ae.a,{title:"Combinazioni"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(ne.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",n(ne.a,null,"k")," volte."),n("p",null,n("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),n("p",null,n(ne.a,null,re(vi())))),n(ae.a,{title:"Combinazioni con ripetizione"},n("p",null,"Estraggo un numero, da un sacchetto con ",n(ne.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",n("b",null,"rimetto nel sacchetto"),". Ripeto per ",n(ne.a,null,"k")," volte."),n("p",null,n("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),n("p",null,n(ne.a,null,re(fi())))),n(ae.a,{title:"Permutazioni"},n("p",null,"Estraggo ",n(ne.a,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),n("p",null,n(ne.a,null,re(mi()))))),n(le.a,{title:"Probabilità condizionata"},n(ae.a,{title:"Eventi condizionati"},n("blockquote",null,'"E dato F"'),n("p",null,"La probabilità che si verifichi ",n(ne.a,null,"E")," sapendo che ",n("b",null,"si è già verificato")," ",n(ne.a,null,"F"),"."),n("p",null,n(ne.a,null,re(di()))),n(ie.a,null,"Ricorda vagamente le pipe di ",n("code",null,"bash"),", però al contrario...")),n(ae.a,{title:"Eventi mutualmente esclusivi"},n("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),n("p",null,n(ne.a,null,re(pi()))))),n(le.a,null,n(ae.a,{title:"Regola della catena"},n("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),n("p",null,n(ne.a,null,re(si()))))),n(le.a,{title:"Le alternative"},n(ae.a,{title:"Legge delle alternative"},n("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),n("p",null,n(ne.a,null,re(ci())))),n(ae.a,{title:"Legge condizionata delle alternative"},n("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",n("b",null,"evento"),":"),n("p",null,n(ne.a,null,re(ui())))),n(ae.a,{title:"Formula di Bayes"},n("p",null,"Tramite la ",n("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),n("p",null,n(ne.a,null,re(oi()))),n(ie.a,null,"In pratica, invertiamo gli eventi."))),n(le.a,{title:"Eventi indipendenti"},n(ae.a,{title:"Due eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a due a due"'),n("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),n("p",null,n(ne.a,null,re(ri())))),n(ae.a,{title:"Più eventi indipendenti"},n("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),n("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),n("p",null,n(ne.a,null,re(ti()))),n("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),n(ae.a,{title:"Famiglia di eventi indipendenti"},n("p",null,"Un insieme di ",n(ne.a,null,"n")," eventi è una ",n("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),n(ie.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),n(le.a,{title:"Variabili aleatorie"},n(ae.a,{title:"Variabile aleatoria"},n("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. ",n(ne.a,null,re(ei())),".")),n(ae.a,{title:n("abbr",{title:"Nome artigianale dato da Steffo."},"Insieme di ripartizione")},n("p",null,"Ad ogni variabile aleatoria sono associati gli eventi ",n(ne.a,null,re(ii())),", che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a ",n(ne.a,null,"t"),"."),n("p",null,"Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:"),n("p",null,n(ne.a,null,re(li()))),n(ie.a,null,"All'aumentare di t, l'insieme conterrà sempre più elementi.")),n(ae.a,{title:"Supporto"},n("blockquote",null,'"supporto di X"'),n("p",null,"Il ",n("b",null,"codominio")," della variabile aleatoria è il suo ",n("i",null,"supporto"),"."),n("p",null,"Per indicare che un valore ",n(ne.a,null,"x_0")," appartiene al supporto di ",n(ne.a,null,"X"),", si usa la notazione ",n(ne.a,null,"X \\mapsto x_0"),"."))),n(le.a,{title:"Densità"},n(ae.a,{title:"Funzione probabilità"},n("p",null,"La ",n("i",null,"funzione probabilità")," ",n(ne.a,null,re(ai()))," di una variabile aleatoria ",n("b",null,"discreta")," ",n(ne.a,null,"X")," è la funzione che associa ad ogni esito la sua probabilità:"),n("p",null,n(ne.a,null,re(ni())))),n(ae.a,{title:"Funzione densità"},n("p",null,"La ",n("i",null,"funzione densità")," ",n(ne.a,null,re($l()))," di una variabile aleatoria ",n("b",null,"continua")," ",n(ne.a,null,"X")," è l'equivalente continuo della funzione probabilità:"),n("p",null,n(ne.a,null,re(Jl()))),n("p",null,"A differenza della funzione probabilità, è possibile che la funzione densità ",n("b",null,"non esista")," per una certa variabile aleatoria."),n(ie.a,null,"Rappresenta \"quanta\" probabilità c'è in un'unità di x!"))),n(le.a,{title:"Funzione di ripartizione"},n(ae.a,{title:"Definizione"},n("p",null,"Ogni variabile aleatoria ha una ",n("i",null,"funzione di ripartizione")," ",n(ne.a,null,re(Hl()))," associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a ",n(ne.a,null,"t"),":"),n("p",null,"Si può dire che essa rappresenti la probabilità dell'evento ",n(ne.a,null,re(Zl())),":"),n("p",null,n(ne.a,null,re(Wl())))),n(ae.a,{title:"Proprietà della funzione"},n("ul",null,n("li",null,"È sempre ",n("b",null,"monotona crescente")," (non strettamente)."),n("br",null),n("li",null,"Vale ",n("b",null,"0")," a ",n(ne.a,null,"-\\infty")," e ",n("b",null,"1")," a ",n(ne.a,null,"+\\infty"),"."),n("br",null),n("li",null,"È ",n("b",null,"continua da destra"),": ",n(ne.a,null,re(Ql()))))),n(ae.a,{title:"Probabilità di un valore"},n("p",null,"Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:"),n("p",null,n(ne.a,null,re(Kl()))))),n(le.a,{title:"Trasformazioni di variabili aleatorie"},n(ae.a,{title:"Nel discreto"},n("p",null,"Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.")),n(ae.a,{title:"Nel continuo (invertibile)"},n("p",null,"Nel continuo applichiamo la formula dell'integrazione per sostituzione:"),n("p",null,n(ne.a,null,re(Rl())))),n(ae.a,{title:"Nel... digitale"},n("p",null,"Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione ",n("a",{href:"https://docs.python.org/3/library/random.html#random.random"},n("code",null,"random()"))," che restituisce numeri da 0 a 1 con una distribuzione lineare."))),n(le.a,{title:"Informazioni delle variabili aleatorie"},n(ae.a,{title:"Media"},n("p",null,"Ogni variabile aleatoria che ha una ",n("b",null,"funzione di ripartizione")," e un ",n("b",null,"supporto finito")," ha anche una ",n("i",null,"media")," (o ",n("i",null,"valore medio")," o ",n("i",null,"atteso"),"):"),n("p",null,n(ne.a,null,re(jl()))),n("p",null,"Nel discreto, si può calcolare con:"),n("p",null,n(ne.a,null,re(Ol()))),n("p",null,"Nel continuo, si può calcolare con:"),n("p",null,n(ne.a,null,re(Gl()))))),n(le.a,null,n(ae.a,{title:"Moda"},n("p",null,"Valore per cui la ",n("b",null,"funzione probabilità")," o ",n("b",null,"funzione densità")," è ",n("b",null,"massima"),".")),n(ae.a,{title:"Quantili"},n("p",null,"Il ",n("i",null,"quantile")," ",n(ne.a,null,re(Tl()))," di ordine ",n(ne.a,null,re(Al()))," della variabile aleatoria ",n(ne.a,null,"X")," è il più piccolo numero tale che:"),n("p",null,n(ne.a,null,re(Bl()))),n("p",null),n("p",null,"Il quantile di ordine 0.5 ",n(ne.a,null,re(Ul()))," è detto ",n("i",null,"mediana"),"."),n("p",null,"I quantili di ordine 0.25 ",n(ne.a,null,re(Dl()))," e 0.75 ",n(ne.a,null,re(Ml()))," sono detti ",n("i",null,"quartili"),"."),n("p",null,"I quantili di ordine ",n(ne.a,null,re(Il()))," sono detti ",n("i",null,n(ne.a,null,"n"),"-esima percentile"),".")),n(ae.a,{title:"Varianza"},n("p",null,"È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:"),n("p",null,n(ne.a,null,re(wl()))))),n(le.a,{title:"Disuguaglianze notevoli"},n(ae.a,{title:"Disuguaglianza di Markov"},n("p",null,"Data una variabile aleatoria non-negativa:"),n("p",null,n(ne.a,null,re(Yl()))),n("p",null,"Divide in due parti (",n(ne.a,null,re(Sl()))," e ",n(ne.a,null,re(Cl())),") la funzione X, la cui media risulterà uguale a:"),n("p",null,n(ne.a,null,re(Vl())))),n(ae.a,{title:"Disuguaglianza di Čebyšëv"},n("blockquote",null,'"disuguaglianza di cebicev"'),n("p",null,"Se la variabile aleatoria ",n(ne.a,null,"X")," ha media e varianza, allora la probabilità che essa abbia un valore a più di ",n(ne.a,null,re(Nl()))," di distanza dal valore medio è minore o uguale a ",n(ne.a,null,re(Fl())),"."),n("p",null,n(ne.a,null,re(Ll()))),n("p",null,"E anche:"),n("p",null,n(ne.a,null,re(yl()))),n(ie.a,null,"Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!"))),n(le.a,{title:"Un momento...!"},n(ae.a,{title:"Momento"},n("p",null,"Il ",n("i",null,"momento")," ",n(ne.a,null,"k"),"-esimo di una variabile aleatoria è:"),n("p",null,n(ne.a,null,re(kl()))),n(ie.a,null,"La media di una variabile aleatoria è anche il suo primo momento.")),n(ae.a,{title:"Funzione generatrice dei momenti"},n("p",null,"La ",n("i",null,"funzione generatrice dei momenti")," è:"),n("p",null,n(ne.a,null,re(xl()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Laplace")," della variabile aleatoria di X.")),n(ae.a,{title:"Funzione caratteristica"},n("p",null,"La ",n("i",null,"funzione caratteristica")," è:"),n("p",null,n(ne.a,null,re(Pl()))),n("p",null,"Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ",n("b",null,"stessa distribuzione"),"."),n("p",null,"E' la ",n("b",null,"trasformata di Fourier")," della variabile aleatoria di X."))),n(le.a,{title:"Prove e schemi"},n(ae.a,{title:"Variabile con distribuzione"},n("p",null,"Per dire che una variabile ha una certa distribuzione, si usa la notazione:"),n("p",null,n(ne.a,null,re(El())))),n(ae.a,{title:"Prova di Bernoulli"},n("p",null,"Una prova con solo due possibili esiti: ",n(ee.a,null,"successo")," e ",n(te.a,null,"insuccesso"),".")),n(ae.a,{title:"Schema di Bernoulli"},n("p",null,"Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate."))),n(le.a,{title:"Bernoulliana"},n(ae.a,{title:"Distribuzione bernoulliana"},n("p",null,"Una variabile aleatoria che rappresenta una prova di Bernoulli:"),n("ul",null,n("li",null,"vale ",n(ee.a,null,"1")," in caso di ",n(ee.a,null,"successo"),"."),n("li",null,"vale ",n(te.a,null,"0")," in caso di ",n(te.a,null,"insuccesso"),".")),n("p",null,"Il suo simbolo è ",n(ne.a,null,re(zl())))),n(ae.a,{title:"Densità della bernoulliana"},n("p",null,"La distribuzione bernoulliana ha come densità:"),n("p",null,n(ne.a,null,re(ql()))))),n(le.a,{title:"Binomiale"},n(ae.a,{title:"Distribuzione binomiale"},n("p",null,"Una variabile aleatoria che conta il numero di successi di ",n(ne.a,null,"n")," prove di uno schema di Bernoulli."),n("p",null,"Il suo simbolo è ",n(ne.a,null,re(gl())),".")),n(ae.a,{title:"Densità della binomiale"},n("p",null,"La binomiale ha come densità:"),n("p",null,n(ne.a,null,re(Xl())))),n(ae.a,{title:"Momenti della binomiale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale è:"),n("p",null,n(ne.a,null,re(hl()))),n("p",null,"La ",n("b",null,"media")," di una binomiale è:"),n("p",null,n(ne.a,null,re(_l()))),n("p",null,"La ",n("b",null,"varianza")," di una binomiale è:"),n("p",null,n(ne.a,null,re(bl()))))),n(le.a,{title:"Geometrica"},n(ae.a,{title:"Distribuzione geometrica"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo."),n("p",null,"Il suo simbolo è ",n(ne.a,null,"Geo(p)"),".")),n(ae.a,{title:"Densità della geometrica"},n("p",null,"La geometrica ha come densità:"),n("p",null,n(ne.a,null,re(vl())))),n(ae.a,{title:"Momenti della geometrica"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica è:"),n("p",null,n(ne.a,null,re(fl()))),n("p",null,"La ",n("b",null,"media")," della geometrica è:"),n("p",null,n(ne.a,null,re(ml()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(ne.a,null,re(dl())))),n(ae.a,{title:"Assenza di memoria della geometrica"},n("p",null,"La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(ne.a,null,re(pl()))),n(ie.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n(le.a,{title:"Binomiale negativa"},n(ae.a,{title:"Distribuzione binomiale negativa"},n("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'",n(ne.a,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo è ",n(ne.a,null,re(sl())),".")),n(ae.a,{title:"Densità della binomiale negativa"},n("p",null,"La binomiale negativa ha come densità:"),n("p",null,n(ne.a,null,re(cl())))),n(ae.a,{title:"Momenti della binomiale negativa"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa è:"),n("p",null,n(ne.a,null,re(ul()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa è:"),n("p",null,n(ne.a,null,re(ol()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa è:"),n("p",null,n(ne.a,null,re(rl())))))),n(le.a,{title:"Geometrica traslata"},n(ae.a,{title:"Distribuzione geometrica traslata"},n("p",null,"Una variabile aleatoria che conta il numero ",n(ne.a,null,"k")," di insuccessi consecutivi in uno schema di Bernoulli:"),n("p",null,"Il suo simbolo rimane ",n(ne.a,null,re(tl())),".")),n(ae.a,{title:"Densità della geometrica tralsata"},n("p",null,"La geometrica traslata ha come densità:"),n("p",null,n(ne.a,null,re(el())))),n(ae.a,{title:"Momenti della geometrica traslata"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della geometrica traslata è:"),n("p",null,n(ne.a,null,re(il()))),n("p",null,"La ",n("b",null,"media")," della geometrica traslata è:"),n("p",null,n(ne.a,null,re(ll()))),n("p",null,"La ",n("b",null,"varianza")," della geometrica è:"),n("p",null,n(ne.a,null,re(al())))),n(ae.a,{title:"Assenza di memoria della geometrica traslata"},n("p",null,"La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(ne.a,null,re(nl()))),n(ie.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n(le.a,{title:"Binomiale negativa traslata"},n(ae.a,{title:"Distribuzione binomiale negativa traslata"},n("p",null,"Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'",n(ne.a,null,"n"),"-esimo successo."),n("p",null,"Il suo simbolo rimane ",n(ne.a,null,re($a())),".")),n(ae.a,{title:"Densità della binomiale negativa traslata"},n("p",null,"La binomiale negativa traslata ha come densità:"),n("p",null,n(ne.a,null,re(Ja())))),n(ae.a,{title:"Momenti della binomiale negativa traslata"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della binomiale negativa traslata è:"),n("p",null,n(ne.a,null,re(Ha()))),n("p",null,"La ",n("b",null,"media")," della binomiale negativa traslata è:"),n("p",null,n(ne.a,null,re(Za()))),n("p",null,"La ",n("b",null,"varianza")," della binomiale negativa traslata è:"),n("p",null,n(ne.a,null,re(Wa())))))),n(le.a,{title:"Ipergeometrica"},n(ae.a,{title:"Distribuzione ipergeometrica"},n("p",null,"Una variabile aleatoria che, sapendo il numero di successi ",n(ne.a,null,"K")," e di insuccessi ",n(ne.a,null,"N-K"),", conta quanti successi si otterrebbero se se ne estraessero ",n(ne.a,null,"n")," in blocco."),n("p",null,"Il suo simbolo è ",n(ne.a,null,"Ipe(N, K, n)"),".")),n(ae.a,{title:"Densità della ipergeometrica"},n("p",null,"La ipergeometrica ha come densità:"),n("p",null,n(ne.a,null,re(Qa())))),n(ae.a,{title:"Momenti della ipergeometrica"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della ipergeometrica è trascurabile."),n("p",null,"La ",n("b",null,"media")," della ipergeometrica è:"),n("p",null,n(ne.a,null,re(Ka()))),n("p",null,"La ",n("b",null,"varianza")," della ipergeometrica è:"),n("p",null,n(ne.a,null,re(Ra())))))),n(le.a,{title:"Poissoniana"},n(ae.a,{title:"Distribuzione poissoniana"},n("p",null,"Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:"),n("ul",null,n("li",null,"Binomiale: ",n(ne.a,null,re(ja()))),n("li",null,"Il numero di prove tende a infinito: ",n(ne.a,null,re(Oa()))),n("li",null,"La probabilità di successo tende a 0: ",n(ne.a,null,re(Ga()))),n("li",null,"La media è finita: ",n(ne.a,null,re(Ta())))),n("p",null,"Il suo simbolo è ",n(ne.a,null,re(Aa())))),n(ae.a,{title:"Densità della poissoniana"},n("p",null,"La poissoniana ha come densità:"),n("p",null,n(ne.a,null,re(Ba())))),n(ae.a,{title:"Momenti della poissoniana"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della poissoniana è:"),n("p",null,n(ne.a,null,re(Ua()))),n("p",null,"La ",n("b",null,"media")," della poissoniana è:"),n("p",null,n(ne.a,null,re(Da()))),n("p",null,"La ",n("b",null,"varianza")," della poissoniana è:"),n("p",null,n(ne.a,null,re(Ma()))),n("p",null,"Gli altri momenti della poissoniana sono:"),n("ol",{start:2},n("li",null,n(ne.a,null,re(Ia()))))))),n(le.a,{title:"Un altro schema"},n(ae.a,{title:"Schema di Poisson"},n("p",null,"Una successione di ",n("b",null,"arrivi")," avvenuti in un certo arco temporale che:"),n("ul",null,n("li",null,"non sono sovrapposti."),n("li",null,"hanno intensità ",n(ne.a,null,re(wa()))," costante."),n("li",null,"avvengono indipendentemente gli uni dagli altri."))),n(ae.a,{title:"Processo di Poisson"},n("p",null,"Una variabile aleatoria ",n(ne.a,null,"N_t")," che conta il numero di arrivi di uno schema di Poisson di intensità ",n(ne.a,null,re(Ya()))," in un intervallo di tempo di durata ",n(ne.a,null,"t"),"."),n("p",null,"E' una distribuzione poissoniana con ",n(ne.a,null,re(Sa())),": ",n(ne.a,null,re(Ca()))),n(ie.a,null,"E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo)."))),n(le.a,{title:"Esponenziale"},n(ae.a,{title:"Distribuzione esponenziale"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità ",n(ne.a,null,re(Va())),"."),n("p",null,"Il suo simbolo è ",n(ne.a,null,re(Na())),".")),n(ae.a,{title:"Densità dell'esponenziale"},n("p",null,"L'esponenziale ha come ",n("b",null,"densità"),":"),n("p",null,n(ne.a,null,re(Fa()))),n("p",null,"L'esponenziale ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(ne.a,null,re(La())))),n(ae.a,{title:"Momenti dell'esponenziale"},n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," dell'esponenziale è:"),n("p",null,n(ne.a,null,re(ya()))),n("p",null,"La ",n("b",null,"media")," dell'esponenziale è:"),n("p",null,n(ne.a,null,re(ka()))),n("p",null,"La ",n("b",null,"varianza")," dell'esponenziale è:"),n("p",null,n(ne.a,null,re(xa())))),n(ae.a,{title:"Assenza di memoria della esponenziale"},n("p",null,"L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),n("p",null,n(ne.a,null,re(Pa()))),n(ie.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),n(le.a,{title:"Legge gamma"},n(ae.a,{title:"Distribuzione gamma"},n("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima dell'",n(ne.a,null,"n"),"-esimo arrivo di un processo di Poisson di intensità ",n(ne.a,null,re(Ea())),"."),n("p",null,"Il suo simbolo è ",n(ne.a,null,re(za())),".")),n(ae.a,{title:"Densità della legge gamma"},n("p",null,"La legge gamma ha come densità:"),n("p",null,n(ne.a,null,re(qa())))),n(ae.a,{title:"Momenti della legge gamma"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della legge gamma è:"),n("p",null,n(ne.a,null,re(ga()))),n("p",null,"La ",n("b",null,"media")," della legge gamma è:"),n("p",null,n(ne.a,null,re(Xa()))),n("p",null,"La ",n("b",null,"varianza")," della legge gamma è:"),n("p",null,n(ne.a,null,re(ha())))))),n(le.a,{title:"Uniforme"},n(ae.a,{title:"Distribuzione uniforme"},n("p",null,"Una variabile aleatoria che può assumere qualsiasi valore in un intervallo ",n(ne.a,null,re(_a()))," in modo equiprobabile."),n("p",null,"Il suo simbolo è ",n(ne.a,null,re(ba()))),n("p",null,"Su di essa vale la seguente proprietà:"),n("p",null,n(ne.a,null,re(va())))),n(ae.a,{title:"Densità della distribuzione uniforme"},n("p",null,"La distribuzione uniforme ha come ",n("b",null,"densità"),":"),n("p",null,n(ne.a,null,re(fa()))),n("p",null,"La distribuzione uniforme ha come ",n("b",null,"funzione di ripartizione"),":"),n("p",null,n(ne.a,null,re(ma())))),n(ae.a,{title:"Momenti della distribuzione uniforme"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione uniforme è:"),n("p",null,n(ne.a,null,re(da()))),n("p",null,"La ",n("b",null,"media")," della distribuzione uniforme è:"),n("p",null,n(ne.a,null,re(pa()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione uniforme è:"),n("p",null,n(ne.a,null,re(sa())))))),n(le.a,{title:"Normale o Gaussiana"},n(ae.a,{title:"Distribuzione normale"},n("p",null,"Una variabile aleatoria con una specifica distribuzione."),n("p",null,"Il suo simbolo è ",n(ne.a,null,re(ca())),"."),n(ie.a,null,n(ne.a,null,"\\mu")," e ",n(ne.a,null,"\\sigma^2")," sono rispettivamente la media e la varianza della distribuzione!")),n(ae.a,{title:"Densità della distribuzione normale"},n("p",null,"La distribuzione normale ha come densità:"),n("p",null,n(ne.a,null,re(ua())))),n(ae.a,{title:"Momenti della distribuzione normale"},n("p",null,n("p",null,"La ",n("b",null,"funzione generatrice dei momenti")," della distribuzione normale è:"),n("p",null,n(ne.a,null,re(oa()))),n("p",null,"La ",n("b",null,"media")," della distribuzione normale è:"),n("p",null,n(ne.a,null,re(ra()))),n("p",null,"La ",n("b",null,"varianza")," della distribuzione normale è:"),n("p",null,n(ne.a,null,re(ta())))))),n(le.a,null,n(ae.a,{title:"Trasformazione della normale"},n("p",null,"Qualsiasi normale può essere trasformata in qualsiasi altra normale:"),n("p",null,n(ne.a,null,re(ea())))),n(ae.a,{title:"Normale standard"},n("p",null,"La distribuzione normale standard ",n(ne.a,null,"Z")," è:"),n("p",null,n(ne.a,null,"Z \\sim Nor(0, 1)")),n("p",null,"La sua funzione di ripartizione è detta ",n(ne.a,null,re(ia()))," e vale:"),n("p",null,n(ne.a,null,re(la())))),n(ae.a,{title:"Quantili normali"},n("p",null,"Da un quantile ",n(ne.a,null,re(aa()))," della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:"),n("p",null,n(ne.a,null,re(na()))))),n(le.a,null,n(ae.a,{title:"Gamma e normale"},n("p",null,"La distribuzione normale ha una particolare relazione con la distribuzione Gamma:"),n("p",null,n(ne.a,null,re($n())))),n(ae.a,{title:"La funzione Chi"},n("blockquote",null,'"chi-quadro a un grado di libertà"'),n("p",null,"Esiste una distribuzione Gamma particolare:"),n("p",null,n(ne.a,null,re(Jn()))),n("p",null,"Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:"),n("p",null,n(ne.a,null,re(Hn())))),n(ae.a,{title:"T di Student"},n("p",null,"Un'altra funzione particolare è la funzione T di Student:"),n("p",null,n(ne.a,null,re(Zn()))))),n(le.a,{title:"Approssimazioni notevoli"},n(ae.a,{title:"Ipergeometrica e binomiale"},n("p",null,"La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ",n(ne.a,null,"N")," rispetto a ",n(ne.a,null,"n"),", si può dire che:"),n("p",null,n(ne.a,null,re(Wn())))),n(ae.a,{title:"Binomiale e poissoniana"},n("p",null,"La binomiale non è altro che una poissoniana a tempo discreto, quindi, se ",n(ne.a,null,"n")," è grande e ",n(ne.a,null,"n \\cdot p")," è nell'ordine di grandezza delle unità, allora:"),n("p",null,n(ne.a,null,re(Qn())))),n(ae.a,{title:"Binomiale e normale"},n("p",null,"Per il Teorema di De Moivre-Laplace, se una binomiale ha una ",n(ne.a,null,"n")," grande e ",n(ne.a,null,"p")," non vicina a 0 o 1, si può approssimare con:"),n("p",null,n(ne.a,null,re(Kn())))),n(ae.a,{title:"Correzione di Yates"},n("p",null,"Passando da una variabile discreta ",n(ne.a,null,"X")," a una continua ",n(ne.a,null,"Y"),", per ogni valore discreto ",n(ne.a,null,"k"),' la probabilità viene "spalmata" su tutto l\'intervallo ',n(ne.a,null,re(Rn())),":"),n("ul",null,n("li",null,n(ne.a,null,re(jn()))),n("li",null,n(ne.a,null,re(On()))),n("li",null,n(ne.a,null,re(Gn()))),n("li",null,n(ne.a,null,re(Tn())))))),n(le.a,{title:"Vettori aleatori"},n(ae.a,{title:"Vettore aleatorio"},n("p",null,"Un vettore ",n("b",null,"composto da variabili aleatorie"),"."),n("p",null,"Il suo simbolo generalmente è ",n(ne.a,null,re(An()))," oppure ",n(ne.a,null,re(Bn())),".")),n(ae.a,{title:"Funzioni di ripartizione"},n("p",null,"I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione congiunta"),":"),n("p",null,n(ne.a,null,re(Un()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"funzione di ripartizione marginale"),":"),n("p",null,n(ne.a,null,re(Dn())))),n(ae.a,{title:"Densità discreta"},n("p",null,"I vettori aleatori ",n("b",null,"discreti")," hanno più densità che si differenziano in base al numero di parametri."),n("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità congiunta"),":"),n("p",null,n(ne.a,null,re(Mn()))),n("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",n("i",null,"densità marginale"),":"),n("p",null,n(ne.a,null,re(In()))))),n(le.a,{title:"Più variabili aleatorie"},n(ae.a,{title:"Indipendenza delle variabili aleatorie"},n("p",null,"Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ",n(ne.a,null,"A_i"),":"),n("p",null,n(ne.a,null,re(wn())))),n(ae.a,{title:"Media dei vettori aleatori"},n("p",null,"E' possibile calcolare la media di qualsiasi funzione ",n(ne.a,null,"g(X, Y)")," avente elementi del vettore come variabili:"),n("p",null,n(ne.a,null,re(Yn()))),n(ie.a,null,"Solitamente si calcola la media di ",n(ne.a,null,"x \\cdot y"),"."),n("p",null,"Le medie di più variabili aleatorie si possono sommare:"),n("p",null,n(ne.a,null,re(Sn()))))),n(le.a,null,n(ae.a,{title:"Covarianza"},n("p",null,"Un ",n("b",null,"operatore")," che misura la correlazione di due variabili aleatorie."),n("p",null,"Si calcola con il valore atteso dei prodotti delle distanze dalla media:"),n("p",null,n(ne.a,null,re(Cn()))),n("p",null,"Ha diverse proprietà:"),n("ul",null,n("li",null,"Il suo ",n("b",null,"valore nullo")," è 0: ",n(ne.a,null,re(Vn()))),n("li",null,"E' ",n("b",null,"commutativa"),": ",n(ne.a,null,re(Nn()))),n("li",null,"E' ",n("b",null,"semplificabile"),": ",n(ne.a,null,re(Fn()))),n("li",null,"E' ",n("b",null,"lineare"),": ",n(ne.a,null,re(Ln()))),n("li",null,"E' ",n("b",null,"distributiva"),": ",n(ne.a,null,re(yn()))))),n(ae.a,{title:"Variabili incorrelate"},n("p",null,"Due variabili sono ",n("i",null,"variabili incorrelate")," se:"),n("p",null,n(ne.a,null,re(kn()))),n("p",null,"Variabili indipendenti sono sempre incorrelate.")),n(ae.a,{title:"Matrice di covarianza"},n("p",null,"Una matrice ",n(ne.a,null,re(xn()))," che contiene la covarianza tra tutte le variabili di un vettore aleatorio ",n(ne.a,null,re(Pn())),":"),n("p",null,n(ne.a,null,re(En()))),n("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",n(ne.a,null,"\\geq 0"),".")),n(ae.a,{title:"Coefficiente di correlazione"},n("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),n("p",null,n(ne.a,null,re(zn()))),n("p",null,"E' sempre compreso tra -1 e 1:"),n("p",null,n(ne.a,null,re(qn()))),n("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),n("p",null,n(ne.a,null,re(gn())))),n(ae.a,{title:"Varianza di variabili aleatorie sommate"},n("p",null,"La varianza di due variabili aleatorie sommate è:"),n("p",null,n(ne.a,null,re(Xn()))),n(ie.a,null,"Si dimostra applicando le proprietà della covarianza!"),n("p",null,"Se più variabili aleatorie ",n(ne.a,null,"X_i")," sono ",n("b",null,"indipendenti")," (",n(ne.a,null,re(hn())),"), allora:"),n("p",null,n(ne.a,null,re(_n()))))),n(le.a,{title:"Campioni"},n(ae.a,{title:"Campione casuale"},n("p",null,"Una ",n("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",n(ne.a,null,"X"),' ("popolazione") ma ',n("b",null,"indipendenti")," tra loro."),n(ie.a,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",n("b",null,"realizzeranno")," nel loro valore.")),n(ae.a,{title:"Momento campionario"},n("p",null,"Il valore dato dalla media aritmetica degli ",n(ne.a,null,"n")," elementi del campione elevati alla potenza ",n(ne.a,null,"k"),":"),n("p",null,n(ne.a,null,re(bn()))),n("p",null,"Il momento campionario di primo ordine è la ",n("i",null,"media campionaria")," ",n(ne.a,null,re(vn())),".")),n(ae.a,{title:"Varianza campionaria"},n("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),n("p",null,"Se è noto il valore medio ",n(ne.a,null,re(fn()))," di X:"),n("p",null,n(ne.a,null,re(mn()))),n("p",null,"Altrimenti:"),n("p",null,n(ne.a,null,re(dn()))))),n(le.a,{title:"Media-ception"},n(ae.a,{title:"Media campionaria"},n("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),n("p",null,n(ne.a,null,re(pn()))),n(ie.a,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!")),n(ae.a,{title:"Varianza campionaria"},n("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),n("p",null,n(ne.a,null,re(sn()))),n(ie.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!")),n(ae.a,{title:"Correzione campionaria"},n("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),n("p",null,n(ne.a,null,re(cn()))),n(ie.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"))),n(le.a,{title:"Campionamento di una distribuzione normale"},n(ae.a,{title:"Campionamento di una distribuzione normale"},n("p",null,"Se la popolazione ",n(ne.a,null,"X")," ha una distribuzione normale (",n(ne.a,null,re(un())),")...")),n(ae.a,{title:"Distribuzione della media campionaria"},n("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),n("p",null,n(ne.a,null,re(on())))),n(ae.a,{title:"Distribuzione della varianza campionaria"},n("p",null,"...e anche della varianza campionaria!"),n("p",null,n(ne.a,null,re(rn()))),n("p",null,n(ne.a,null,re(tn())))),n(ae.a,{title:"Indipendenza"},n("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!"))),n(le.a,{title:"Quando i campioni hanno dimensioni infinite"},n(ae.a,{title:"Convergenza in distribuzione"},n("p",null,"Se la successione di variabili aleatorie ",n(ne.a,null,"X_n")," all'infinito ha la ",n("b",null,"stessa funzione di ripartizione")," della popolazione ",n(ne.a,null,"X"),", allora essa ",n("i",null,"converge in distribuzione"),"."),n("p",null,n(ne.a,null,"\\lim_{n \\to +\\infty} F_{X_n} (x) = F_X (x) \\implies X_n \\xrightarrow{d} X"))),n(ae.a,{title:"Convergenza in probabilità"},n("p",null,"Se la successione di variabili aleatorie ",n(ne.a,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità")," della popolazione ",n(ne.a,null,"X"),", allora essa ",n("i",null,"converge in probabilità"),"."),n("p",null,n(ne.a,null,"\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | X_n - X | < \\epsilon) = 1 \\implies X_n \\xrightarrow{p} X"))),n(ae.a,{title:"Convergenza quasi certa"},n("p",null,"Se la successione di variabili aleatorie ",n(ne.a,null,"X_n")," all'infinito ha la ",n("b",null,"stessa probabilità a ")," della popolazione ",n(ne.a,null,"X"),", allora essa ",n("i",null,"converge quasi certamente"),"."),n("p",null,n(ne.a,null,"\\forall \\epsilon > 0, P left( \\lim_{n \\to +\\infty} | X_n - X | < \\epsilon) \right) = 1 \\implies X_n \\xrightarrow{qc} X"))),n(ae.a,{title:"Convergenza in media quadratica"},n("p",null,"Se la successione di variabili aleatorie ",n(ne.a,null,"X_n")," all'infinito ha la ",n("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",n(ne.a,null,"X")," ",n("b",null,"uguale a 0"),", allora essa ",n("i",null,"converge in media quadratica"),"."),n("p",null,n(ne.a,null,"\\lim_{n \\to +\\infty} E( | X_n - X |^2 = 0 \\implies X_n \\xrightarrow{mq} X"))),n(ae.a,{title:"Gerarchia delle convergenze"},n("p",null,n(ne.a,null,"\n                                \\begin{matrix}\n                                X_n \\xrightarrow{mq} X\\\\\n                                X_n \\xrightarrow{qc} X\n                                \\end{matrix} \\implies X_n \\xrightarrow{p} X \\implies X_n \\xrightarrow{d} X")),n("p",null,"In più:"),n("p",null,n(ne.a,null,"X_n \\xrightarrow{p} x \\Longleftrightarrow X_n \\xrightarrow{d} x")))),n(le.a,{title:"I grandi numeri"},n(ae.a,{title:"Legge debole dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(ne.a,null,re(en()))," ",n("b",null,"converge in probabilità")," alla media della popolazione ",n(ne.a,null,re(ln())),", se essa esiste."),n("p",null,n(ne.a,null,"\\overline{X}_n \\xrightarrow{p} X")),n("p",null,"Ovvero:"),n("p",null,n(ne.a,null,re(an()))),n("p",null,n(ne.a,null,re(nn())))),n(ae.a,{title:"Legge forte dei grandi numeri"},n("p",null,"La successione delle medie campionarie ",n(ne.a,null,re($()))," ",n("b",null,"converge quasi certamente")," alla media della popolazione ",n(ne.a,null,re(J())),", se essa esiste."),n("p",null,n(ne.a,null,"\\overline{X}_n \\xrightarrow{qc} X")),n("p",null,"Ovvero:"),n("p",null,n(ne.a,null,re(H()))),n(ie.a,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"))),n(le.a,{title:"Al limite"},n(ae.a,{title:"Teorema centrale del limite"},n("p",null,"La successione delle medie campionarie ",n(ne.a,null,re(Z()))," ",n("b",null,"converge in distribuzione")," a ",n(ne.a,null,re(W())),"."),n("p",null,n(ne.a,null,re(Q()))),n("p",null,"Ovvero:"),n("p",null,n(ne.a,null,re(K()))))),n(le.a,{title:"Altre approsimazioni"},n(ae.a,{title:"Binomiale e normale"},n("p",null,"E' una somma di ",n("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),n("p",null,n(ne.a,null,re(R())))),n(ae.a,{title:"Binomiale negativa e normale"},n("p",null,"E' una somma di ",n("b",null,"geometriche"),", e quindi si approssima a una normale:"),n("p",null,n(ne.a,null,re(j())))),n(ae.a,{title:"Poissoniana e normale"},n("p",null,"E' una somma di altre ",n("b",null,"poissoniane"),", e quindi si approssima a una normale:"),n("p",null,n(ne.a,null,re(O())))),n(ae.a,{title:"Gamma e normale"},n("p",null,"E' una somma di ",n("b",null,"esponenziali"),", e quindi si approssima a una normale:"),n("p",null,n(ne.a,null,re(G())))),n(ae.a,{title:"In generale"},n("p",null,"Se ",n(ne.a,null,"n")," è grande, allora:"),n("p",null,n(ne.a,null,re(T()))))),n(le.a,{title:"Actually statistica"},n(ae.a,{title:"Parametri sconosciuti"},n("p",null,"Per indicare parametri sconosciuti di una legge si usa ",n(ne.a,null,"\\theta"),".")),n(ae.a,{title:"Statistica"},n("p",null,"Una variabile aleatoria funzione di un campione:"),n("p",null,n(ne.a,null,re(A()))),n(ie.a,null,"Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso ",n(ne.a,null,re(B())),"."))),n(le.a,{title:"Stimatori"},n(ae.a,{title:"Stimatore"},n("p",null,"Una statistica ",n(ne.a,null,"T_n")," ottenuta da ",n(ne.a,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),n(ae.a,{title:"Corretto"},n("p",null,"Uno stimatore è ",n("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(ne.a,null,re(U())))),n(ae.a,{title:"Asintoticamente corretto"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),n("p",null,n(ne.a,null,re(D())))),n(ae.a,{title:"Consistente in media quadratica"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in media quadratica")," se:"),n("p",null,n(ne.a,null,re(M())))),n(ae.a,{title:"Consistente in probabilità"},n("p",null,"Uno stimatore è ",n("i",null,"consistente in probabilità")," se:"),n("p",null,n(ne.a,null,re(I())))),n(ae.a,{title:"Asintoticamente normale"},n("p",null,"Uno stimatore è ",n("i",null,"asintoticamente normale")," se:"),n("p",null,n(ne.a,null,re(w()))))),n(le.a,{title:"Metodo dei momenti"},n(ae.a,{title:"Metodo dei momenti"},n("p",null,"Si può usare il ",n("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",n(ne.a,null,"X"),"."),n("p",null,"Lo stimatore di ",n(ne.a,null,re(Y()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(ne.a,null,"M")," a ",n(ne.a,null,"\\theta"),": ",n(ne.a,null,re(S()))),n("p",null,"Visto che:"),n("ul",null,n("li",null,n(ne.a,null,re(C()))),n("li",null,n(ne.a,null,re(V())))),n("p",null,"Allora:"),n("p",null,n(ne.a,null,re(N()))),n("p",null,"Se ",n(ne.a,null,re(F()))," non è esprimibile in termini di ",n(ne.a,null,re(L())),", si possono usare i momenti successivi ",n(ne.a,null,re(y())),", ",n(ne.a,null,re(k())),", ",n(ne.a,null,re(x())),"..."))),n(le.a,{title:"Metodo della massima verosomiglianza"},n(ae.a,{title:"Metodo della massima verosomiglianza"},n("p",null,"Si può usare il ",n("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",n(ne.a,null,"X"),"."),n("p",null,"Lo stimatore di ",n(ne.a,null,re(P()))," così ottenuto sarà indicato aggiungendo un cappellino e una ",n(ne.a,null,"L")," a ",n(ne.a,null,"\\theta"),": ",n(ne.a,null,re(E()))),n("p",null,"Consiste nel trovare il massimo assoluto ",n(ne.a,null,re(z()))," della la funzione di verosomiglianza ",n(ne.a,null,re(q())),":"),n("p",null,n(ne.a,null,re(g()))),n("p",null,"Gli stimatori di massima verosomiglianza sono ",n("b",null,"asintoticamente corretti"),", ",n("b",null,"consistenti in probabilità")," e ",n("b",null,"asintoticamente normali"),".")),n(ae.a,{title:"Proprietà degli stimatori di massima verosomiglianza"},n("p",null,"Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:"),n("ul",null,n("li",null,"Sono ",n("b",null,"asintoticamente corretti"),"."),n("li",null,"Sono ",n("b",null,"consistenti in probabilità"),"."),n("li",null,"Sono ",n("b",null,"asintoticamente normali"),"."),n("li",null,"Sono ",n("b",null,"invarianti"),": ",n(ne.a,null,re(X())))))),n(le.a,{title:"Nuove stime notevoli"},n(ae.a,{title:"Stima di una bernoulliana"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(ne.a,null,re(h())))),n(ae.a,{title:"Stima di una poissoniana"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(ne.a,null,re(_())))),n(ae.a,{title:"Stima di una esponenziale"},n("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),n("p",null,n(ne.a,null,re(b())))),n(ae.a,{title:"Stima di una normale"},n("p",null,"Per il metodo della massima verosomiglianza:"),n("ul",null,n("li",null,n(ne.a,null,re(v()))),n("br",null),n("li",null,n(ne.a,null,re(f())))))),n(le.a,{title:"Intervalli di confidenza"},n(ae.a,{title:"Confidenza"},n("blockquote",null,'"intervallo di confidenza al 95%"'),n("p",null,"L'intervallo di valori di ",n(ne.a,null,"\\theta"),' all\'interno del quale siamo "più o meno sicuri" si trovi il valore effettivo:'),n("p",null,"L'intervallo di confidenza a N della stima ",n(ne.a,null,re(m()))," è l'intervallo ",n(ne.a,null,"]a, b[")," tale che:"),n("p",null,n(ne.a,null,re(d()))),n("p",null,"Può anche essere ",n("b",null,"unilatero")," nel caso limiti la stima in una sola direzione, positiva o negativa."))),n(le.a,{title:"Confidenza nella media di una normale"},n(ae.a,{title:"Varianza nota"},n("p",null,"Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(ne.a,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(ne.a,null,re(p()))),n("li",null,"Intervallo unilatero da sinistra: ",n(ne.a,null,re(s()))),n("li",null,"Intervallo unilatero da destra: ",n(ne.a,null,re(c()))))),n(ae.a,{title:"Varianza incognita"},n("p",null,"Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",n(ne.a,null,"\\alpha"),"% con queste formule:"),n("ul",null,n("li",null,"Intervalli bilateri: ",n(ne.a,null,re(u()))),n("li",null,"Intervallo unilatero da sinistra: ",n(ne.a,null,re(o()))),n("li",null,"Intervallo unilatero da destra: ",n(ne.a,null,re(r())))),n("p",null,n(ne.a,null,re(t()))," è un quantile della distribuzione di Student di parametro ",n(ne.a,null,"v"),"."))),n(le.a,{title:"Confidenza per la proporzione di una bernoulliana"},n(ae.a,{title:"Terzo metodo corretto"},n("p",null,"L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:"),n("p",null,n(ne.a,null,re(e()))))),n(le.a,{title:"Confidenza per la media di qualsiasi popolazione"},n(ae.a,{title:"Approssimando con la normale"},n("p",null,"L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:"),n("p",null,n(ne.a,null,re(i()))))))},l}($i.Component)}.call(this,l("hosL").h)}}]);
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extracted by mini-css-extract-plugin\nmodule.exports = {\"latex\":\"latex__3Esv7\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"panel\":\"panel__1ubJw\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"example\":\"example__P0_NL\"};","import style from \"./todo.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Todo extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n","import style from \"./panel.css\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (
    {this.props.title}
    );\n\t\t}\n\n\t\treturn (\n\t\t\t
    \n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
    \n\t\t);\n\t}\n}\n","import style from \"./minus.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Minus extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n","import style from \"./example.css\";\nimport {Component} from \"preact\";\n\nexport default class Example extends Component {\n    render() {\n        return (\n            
    \n                {this.props.children}\n            
    \n        )\n    }\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"plus\":\"plus__29_QM\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"hypothesis\":\"hypothesis__3E-73\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"thesis\":\"thesis__13Kp6\"};","import style from './latex.css';\nimport { Component } from 'preact';\n\nexport default class Latex extends Component {\n\trender() {\n\t\tlet equation = `{\\\\color{White} ${this.props.children} }`;\n\t\treturn (\n\t\t\t{this.props.children}\n\t\t\t);\n\t}\n}","import style from \"./plus.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Plus extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n","import style from \"./split.css\";\nimport { Component } from 'preact';\n\nexport default class Split extends Component {\n\trender() {\n\t    let title = null;\n\t    if(this.props.title !== undefined) {\n            title = (
    {this.props.title}
    )\n        }\n\n        let children;\n        if(Array.isArray(this.props.children)) {\n            children = this.props.children.map(element => {\n                return (
    {element}
    );\n            });\n        }\n        else {\n            children = 
    {this.props.children}
    ;\n        }\n\t\treturn (\n\t        
    \n                {title}\n                
    {children}
    \n            
    \n        );\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"minus\":\"minus__2Ld4F\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"theorem\":\"theorem__3Qv59\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"todo\":\"todo__1pOoN\"};","// extracted by mini-css-extract-plugin\nmodule.exports = {\"split\":\"split__3qCWp\",\"splitparent\":\"splitparent__2xagg\",\"splitchild\":\"splitchild__3cEoc\"};","import style from './statistica.css';\nimport { Component } from 'preact';\nimport Latex from '../components/latex';\nimport Panel from '../components/panel';\nimport Split from '../components/split';\nimport Todo from '../components/todo';\nimport Theorem from \"../components/theorem\";\nimport Hypothesis from \"../components/hypothesis\";\nimport Thesis from \"../components/thesis\";\nimport Proof from \"../components/proof\";\nimport Example from \"../components/example\";\nimport Plus from \"../components/plus\";\nimport Minus from \"../components/minus\";\n\nconst r = String.raw;\n\nexport default class Statistica extends Component {\n\trender() {\n\t    /*\n            \n                \n                    
    \n                        Gruppo intero di oggetti di cui si cercano informazioni.\n                    
    \n                    \n                \n                    
    \n                        Popolazione finita di oggetti concreti che possono essere campionati ciascuno solo una volta.\n                    
    \n                    \n                \n                    
    \n                        Popolazione di valori ottenuti da prove sperimentali indipendenti ripetute più volte.\n                    
    \n                    \n                \n            \n                \n                    
    \n                        Sottoinsieme della popolazione che contiene gli oggetti che si sono osservati.\n                    
    \n                    \n                Simple random sample}>\n                    
    \n                        Campione di una data dimensione in cui qualsiasi selezione di n elementi ha la stessa probabilità di costituire il campione.\n                    
    \n                    \n                Sample of convenience}>\n                    
    \n                        Campione ottenuto in un modo casuale non ben definito.\n                    
    \n                    \n                Sample with replacement}>\n                    
    \n                        Campione ottenuto sostituendo nella popolazione gli elementi estratti con dei nuovi elementi.\n                    
    \n                    
    \n                        Dire che un campione è ottenuto with replacement è equivalente a dire che la popolazione che si sta campionando è infinita, e quindi che tutti gli elementi sono indipendenti.\n                    
    \n                    \n                \n                    
    \n                        Campione ottenuto da una popolazione in cui certi elementi hanno più probabilità di essere stati selezionati di altri.\n                    
    \n                    \n                Stratified random sample}>\n                    
    \n                        Campione ottenuto da un sottoinsieme della popolazione detto strato.\n                    
    \n                    \n                Cluster sample}>\n                    
    \n                        Campione ottenuto selezionando più cluster di elementi alla volta.\n                    
    \n                    \n                \n            \n                Sampling variation}>\n                    
    \n                        Differenza di informazioni presente tra due campioni diversi della stessa popolazione.\n                    
    \n                    \n                \n                    
    \n                        Gli elementi in un campione sono indipendenti se gli elementi estratti in precedenza non influsicono significativamente sulle probabilità di estrazione dell'elemento successivo.\n                    
    \n                    \n                \n            \n                \n                    
    \n                        Esperimento in cui c'è una sola popolazione da cui vengono estratti campioni.\n                    
    \n                    
    \n                        Serve per verificare delle condizioni.\n                    
    \n                    \n                \n                    
    \n                        Esperimento in cui sono presenti più popolazioni (aventi caratteristiche differenti una dall'altra dette fattori) da cui vengono estratti campioni.\n                    
    \n                    
    \n                        Serve per capire quali fattori influenzano il risultato dell'esperimento.\n                    
    \n                    \n                \n            \n                Numerico o quantitativo}>\n                    Il dato descrive un valore numerico relativo all'elemento, come ad esempio una quantità fisica.\n                \n                Categorico o qualitativo}>\n                    Il dato indica una categoria a cui appartiene l'elemento, come ad esempio il suo colore.\n                \n            \n\t     */\n        return (\n            
    \n                
    Statistica ed Elementi di Probabilità
    \n                \n                    \n                        
    \n                            {r`P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`P(E) = \\frac{successi}{prove\\ totali}`}\n                        
    \n                        \n                    \n                        
    \n                            Il prezzo che un individuo coerente riterrebbe equo per ricevere 1 nel caso l'evento si verificasse e 0 nel caso l'evento non si verificasse.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"omegone\"\n                        
    \n                        
    \n                            L'insieme di tutti gli esiti possibili di un esperimento.\n                        
    \n                        
    \n                            {r`\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"omeghino\"\n                        
    \n                        
    \n                            Un elemento dello spazio campionario.\n                        
    \n                        
    \n                            {r`\\omega = 1`}\n                        
    \n                        \n                    \n                        
    \n                            \"e\"\n                        
    \n                        
    \n                            Un sottoinsieme dello spazio campionario.\n                        
    \n                        
    \n                            {r`E = \\left \\{ 1, 2 \\right \\}`}\n                        
    \n                        
    \n                            Lo spazio campionario stesso è un evento certo.\n                        
    \n                        \n                    \n                        
    \n                            \"not e\"\n                        
    \n                        
    \n                            Il complementare di un sottoinsieme.\n                        
    \n                        
    \n                            {r`\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e intersecato effe\"\n                        
    \n                        
    \n                            L'intersezione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\left \\{ 1 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e unito a effe\"\n                        
    \n                        
    \n                            L'unione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e meno effe\"\n                        
    \n                        
    \n                            {r`E \\setminus F = E \\cap \\bar{F}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e contenuto in effe\"\n                        
    \n                        
    \n                            L'inclusione del primo insieme in un altro.\n                        
    \n                        
    \n                            {r`E \\subseteq F`}\n                        
    \n                        
    \n                            Se si verifica E, allora si verifica anche F.\n                        
    \n                        \n                    \n                        
    \n                            \"e è impossibile\"\n                        
    \n                        
    \n                            Un sottoinsieme vuoto.\n                        
    \n                        
    \n                            {r`E = \\emptyset`}\n                        
    \n                        \n                    \n                        
    \n                            \"e ed effe si escludono mutualmente\"\n                        
    \n                        
    \n                            La disgiunzione di due insiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"famiglia effe\"\n                        
    \n                        
    \n                            I sottoinsiemi dello spazio campionario formano una famiglia di sottoinsiemi detta famiglia degli eventi.\n                        
    \n                        
    \n                            {r`\\mathcal{F}`}\n                        
    \n                        
    \n                            Qualsiasi sottoinsieme appartenente a {r`\\mathcal{F}`} è considerato un evento.\n                        
    \n                        \n                    {r`\\sigma`}-algebra}>\n                        
    \n                            \"sigma algebra\"\n                        
    \n                        
    \n                            Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta {r`\\sigma`}-algebra:\n                        
    \n                        
      \n                            
    1. \n                                Lo spazio campionario è un evento: {r`\\Omega \\in \\mathcal{F}`}\n                            
      2. \n                            
    2. \n                                Se un sottoinsieme è un evento, allora anche il suo complementare lo è: {r`E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}`}\n                            
      3. \n                            
    3. \n                                Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: {r`(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}`}\n                            
      4. \n                        
    \n                        
    \n                            Un esempio: {r`E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"la partizione e composta da e uno, e due, e tre...\"\n                        
    \n                        
    \n                            Un insieme di esiti e eventi:\n                        
    \n                        
      \n                            
    • Finito.
      • \n                            
    • In cui tutti gli eventi hanno probabilità diversa da 0.
      • \n                            
    • In cui tutti gli eventi sono mutualmente esclusivi.
      • \n                            
    • In cui l'unione di tutti i suoi elementi copre lo spazio campionario.
      • \n                        
    \n                        
    \n                            La partizione {r`E_i`} è composta dagli eventi {r`E_1`}, {r`E_2`}, {r`E_3`}, fino a {r`E_n`}.\n                        
    \n                        \n                            Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            La probabilità di un evento è un numero tra 0 e 1.\n                        
    \n                        
    \n                            {r`\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dello spazio campionario è sempre 1.\n                        
    \n                        
    \n                            {r`P(\\Omega) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità.\n                        
    \n                        
    \n                            {r`P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato.\n                        
    \n                        
    \n                            {r`P(\\bar{E}) = 1 - P({E})`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso.\n                        
    \n                        
    \n                            {r`F \\subseteq E \\implies P(F) \\leq P(E)`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione.\n                        
    \n                        
    \n                            {r`P(E \\cup F) = P(E) + P(F) - P(E \\cap F)`}\n                        
    \n                        \n                            Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi.\n                        
    \n                        
    \n                            {r`P(E) = \\frac{len(E)}{len(\\Omega)}`}\n                        
    \n                        \n                    \n                        
    \n                            Gli spazi campionari possono avere un numero infinito di esiti: sono equiprobabili geometrici se nessun esito è privilegiato rispetto agli altri.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}^{r}_{n, k} = n^k`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo n numeri e guardo in quanti ordini diversi li posso mettere.\n                        
    \n                        
    \n                            {r`\\boldsymbol{P}_n = n!`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"E dato F\"\n                        
    \n                        
    \n                            La probabilità che si verifichi E sapendo che si è già verificato F.\n                        
    \n                        
    \n                            {r`P(E|F) = \\frac{P(E \\cap F)}{P(F)}`}\n                        
    \n                        \n                            Ricorda vagamente le pipe di bash, però al contrario...\n                        \n                        \n                    \n                        
    \n                            Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:\n                        
    \n                        
    \n                            {r`P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione.\n                        
    \n                        
    \n                            {r`P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)`}\n                        
    \n                        \n                    \n                        
    \n                            La legge delle alternative funziona anche quando ad essere partizionato è un evento:\n                        
    \n                        
    \n                            {r`P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)`}\n                        
    \n                        \n                    \n                        
    \n                            Tramite la formula di Bayes possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:\n                        
    \n                        
    \n                            {r`P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}`}\n                        
    \n                        \n                            In pratica, invertiamo gli eventi.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            \"eventi indipendenti a due a due\"\n                        
    \n                        
    \n                            Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro.\n                        
    \n                        
    \n                            {r`P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)`}\n                        
    \n                        \n                    \n                        
    \n                            \"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque...\"\n                        
    \n                        
    \n                            Si può verificare l'indipendenza di più eventi alla volta:\n                        
    \n                        
    \n                            {r`P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)`}\n                        
    \n                        
    \n                            Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.\n                        
    \n                        \n                    \n                        
    \n                            Un insieme di n eventi è una famiglia di eventi indipendenti se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.\n                        
    \n                        \n                            Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. {r`X(\\omega) : \\Omega \\to \\mathbb{R}`}.\n                        
    \n                        \n                    Insieme di ripartizione}>\n                        
    \n                            Ad ogni variabile aleatoria sono associati gli eventi {r`A_t = \\{ \\omega | X(\\omega) \\leq t \\}`}, che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a t.\n                        
    \n                        
    \n                            Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:\n                        
    \n                        
    \n                            {r`\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}`}\n                        
    \n                        \n                            All'aumentare di t, l'insieme conterrà sempre più elementi.\n                        \n                        \n                    \n                        
    \n                            \"supporto di X\"\n                        
    \n                        
    \n                            Il codominio della variabile aleatoria è il suo supporto.\n                        
    \n                        
    \n                            Per indicare che un valore x_0 appartiene al supporto di X, si usa la notazione X \\mapsto x_0.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La funzione probabilità {r`p_X : X \\to [0, 1]`} di una variabile aleatoria discreta X è la funzione che associa ad ogni esito la sua probabilità:\n                        
    \n                        
    \n                            {r`p_X (x) = \\begin{cases}\n                            P([X = x]) \\quad se\\ X \\mapsto x \\\\\n                            0 \\qquad \\qquad \\quad se\\ X \\not\\mapsto x\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione densità {r`f_X : X \\to [0, 1]`} di una variabile aleatoria continua X è l'equivalente continuo della funzione probabilità:\n                        
    \n                        
    \n                            {r`P([a < X \\leq b]) = \\int_a^b f_X (x) dx`}\n                        
    \n                        
    \n                            A differenza della funzione probabilità, è possibile che la funzione densità non esista per una certa variabile aleatoria.\n                        
    \n                        \n                            Rappresenta \"quanta\" probabilità c'è in un'unità di x!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Ogni variabile aleatoria ha una funzione di ripartizione {r`F_X : \\mathbb{R} \\to [0, 1]`} associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a t:\n                        
    \n                        
    \n                            Si può dire che essa rappresenti la probabilità dell'evento {r`A_t`}:\n                        
    \n                        
    \n                            {r`F_X (t) = P(A_t) = \\begin{cases}\n                            \\sum_{i = 0}^{t} p_X (x_i) \\quad nel\\ discreto\\\\\n                            \\\\\n                            \\int_{-\\infty}^t f_X (x) dx \\quad nel\\ continuo\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
      \n                            
    • È sempre monotona crescente (non strettamente).

      • \n                            
    • Vale 0 a -\\infty e 1 a +\\infty.

      • \n                            
    • È continua da destra: {r`\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:\n                        
    \n                        
    \n                            {r`P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.\n                        
    \n                        \n                    \n                        
    \n                            Nel continuo applichiamo la formula dell'integrazione per sostituzione:\n                        
    \n                        
    \n                            {r`f_Y (y) = \\int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`}\n                        
    \n                        \n                    \n                        
    \n                            Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione random() che restituisce numeri da 0 a 1 con una distribuzione lineare.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Ogni variabile aleatoria che ha una funzione di ripartizione e un supporto finito ha anche una media (o valore medio o atteso):\n                        
    \n                        
    \n                            {r`E(X) = \\int_0^{+infty} (1 - F_X (t)) dt - \\int_{-\\infty}^{0} F_X (t) dt`}\n                        
    \n                        
    \n                            Nel discreto, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\sum_i P(X = x_i) \\cdot x_i`}\n                        
    \n                        
    \n                            Nel continuo, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\int_{-\\infty}^{+\\infty} f_X (x) \\cdot x \\cdot dx`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Valore per cui la funzione probabilità o funzione densità è massima.\n                        
    \n                        \n                    \n                        
    \n                            Il quantile {r`x_{\\alpha}`} di ordine {r`0 \\leq \\alpha \\leq 1`} della variabile aleatoria X è il più piccolo numero tale che:\n                        
    \n                        
    \n                            \n                                {r`P([X < x_{\\alpha}]) \\leq \\alpha \\leq P([X \\leq x_{\\alpha}])`}\n                            \n                        
    \n                        
    \n\n                        
    \n                        
    \n                            Il quantile di ordine 0.5 {r`x_{0.5}`} è detto mediana.\n                        
    \n                        
    \n                            I quantili di ordine 0.25 {r`x_{0.25}`} e 0.75 {r`x_{0.75}`} sono detti quartili.\n                        
    \n                        
    \n                            I quantili di ordine {r`\\frac{n}{100}`} sono detti n-esima percentile.\n                        
    \n                        \n                    \n                        
    \n                            È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:\n                        
    \n                        
    \n                            {r`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Data una variabile aleatoria non-negativa:\n                        
    \n                        
    \n                            {r`\\forall k > 0, P([X \\geq k]) \\leq \\frac{E(X)}{k}`}\n                        
    \n                        
    \n                            Divide in due parti ({r`P(X < k)`} e {r`P(X \\geq k)`}) la funzione X, la cui media risulterà uguale a:\n                        
    \n                        
    \n                            {r`E(X) = \\overline{k} \\cdot P(X < k) + k \\cdot P(X \\geq k)`}\n                        
    \n                        \n                    \n                        
    \n                            \"disuguaglianza di cebicev\"\n                        
    \n                        
    \n                            Se la variabile aleatoria X ha media e varianza, allora la probabilità che essa abbia un valore a più di {r`\\epsilon`} di distanza dal valore medio è minore o uguale a {r`\\frac{Var(X)}{\\epsilon^2}`}.\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| \\geq \\epsilon]) \\leq \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        
    \n                            E anche:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| < \\epsilon]) \\geq 1 - \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        \n                            Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Il momento k-esimo di una variabile aleatoria è:\n                        
    \n                        
    \n                            \n                                {r`\\mu_k = E ( X^k ) = \\begin{cases}\n                                \\sum_i x_i^k p_X (x_i) \\qquad nel\\ discreto\\\\\n                                \\\\\n                                \\int_{-\\infty}^{+\\infty} x^k f_X (x) dx \\qquad nel\\ continuo\n                                \\end{cases}`}\n                            \n                        
    \n                        \n                            La media di una variabile aleatoria è anche il suo primo momento.\n                        \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti è:\n                        
    \n                        
    \n                            {r`m_X (t) = E( e^{t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Laplace della variabile aleatoria di X.\n                        
    \n                        \n                    \n                        
    \n                            La funzione caratteristica è:\n                        
    \n                        
    \n                            {r`H_X (t) = E ( e^{i \\cdot t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Fourier della variabile aleatoria di X.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per dire che una variabile ha una certa distribuzione, si usa la notazione:\n                        
    \n                        
    \n                            {r`X \\sim Distribuzione()`}\n                        
    \n                        \n                    \n                        
    \n                            Una prova con solo due possibili esiti: successo e insuccesso.\n                        
    \n                        \n                    \n                        
    \n                            Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che rappresenta una prova di Bernoulli:\n                        
    \n                        
      \n                            
    • vale 1 in caso di successo.
      • \n                            
    • vale 0 in caso di insuccesso.
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Ber(p)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione bernoulliana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0, 1\\} = \\begin{cases}\n                            p \\quad se\\ k = 1\\\\\n                            q \\quad se\\ k = 0\\\\\n                            0 \\quad altrimenti\n                            \\end{cases} = p^x \\cdot q^{1 - k}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di successi di n prove di uno schema di Bernoulli.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Bin(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della binomiale è:\n                        
    \n                        
    \n                            {r`m_X (t) = (q + p \\cdot e^t) ^ n`}\n                        
    \n                        
    \n                            La media di una binomiale è:\n                        
    \n                        
    \n                            {r`E(X) = n \\cdot p`}\n                        
    \n                        
    \n                            La varianza di una binomiale è:\n                        
    \n                        
    \n                            {r`Var(X) = n \\cdot p \\cdot q`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.\n                        
    \n                        
    \n                            Il suo simbolo è Geo(p).\n                        
    \n                        \n                    \n                        
    \n                            La geometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = q^{k - 1} p`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica è:\n                        
    \n                        
    \n                            {r`m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero k di insuccessi consecutivi in uno schema di Bernoulli:\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`Geo(p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = p \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica traslata è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica traslata è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{q}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n \\cdot q}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che, sapendo il numero di successi K e di insuccessi N-K, conta quanti successi si otterrebbero se se ne estraessero n in blocco.\n                        
    \n                        
    \n                            Il suo simbolo è Ipe(N, K, n).\n                        
    \n                        \n                    \n                        
    \n                            La ipergeometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della ipergeometrica è trascurabile.\n                            
    \n                            
    \n                                La media della ipergeometrica è:\n                            
    \n                            
    \n                                {r`E(X) = n \\cdot \\frac{K}{N}`}\n                            
    \n                            
    \n                                La varianza della ipergeometrica è:\n                            
    \n                            
    \n                                {r`Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:\n                        
    \n                        
      \n                            
    • Binomiale: {r`X \\sim Bin(n, p)`}
      • \n                            
    • Il numero di prove tende a infinito: {r`n \\to +\\infty`}
      • \n                            
    • La probabilità di successo tende a 0: {r`p \\to 0`}
      • \n                            
    • La media è finita: {r`E(X) = n \\cdot p \\to \\mu \\neq 0`}
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Poi(\\mu)`}\n                        
    \n                        \n                    \n                        
    \n                            La poissoniana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della poissoniana è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot (e^t - 1)}`}\n                            
    \n                            
    \n                                La media della poissoniana è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della poissoniana è:\n                            
    \n                            
    \n                                {r`Var(X) = \\mu`}\n                            
    \n                            
    \n                                Gli altri momenti della poissoniana sono:\n                            
    \n                            
      \n                                
    1. {r`E(X^2) = \\mu^2 + \\mu`}
      2. \n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una successione di arrivi avvenuti in un certo arco temporale che:\n                        
    \n                        
      \n                            
    • non sono sovrapposti.
      • \n                            
    • hanno intensità {r`\\lambda`} costante.
      • \n                            
    • avvengono indipendentemente gli uni dagli altri.
      • \n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria N_t che conta il numero di arrivi di uno schema di Poisson di intensità {r`\\lambda`} in un intervallo di tempo di durata t.\n                        
    \n                        
    \n                            E' una distribuzione poissoniana con {r`\\mu = t \\cdot \\lambda`}: {r`Poi(t \\cdot \\lambda)`}\n                        
    \n                        \n                            E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo).\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Esp(\\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad x < 0\\\\\n                            \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n                            \\end{cases}`}\n                        
    \n                        
    \n                            L'esponenziale ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`F_X (t) = \\begin{cases}\n                            0 \\qquad \\qquad t < 0\\\\\n                            1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti dell'esponenziale è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}`}\n                        
    \n                        
    \n                            La media dell'esponenziale è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{\\lambda}`}\n                        
    \n                        
    \n                            La varianza dell'esponenziale è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{1}{\\lambda^2}`}\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X > s + t | X > s]) = P([X > t])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima dell'n-esimo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\Gamma(n, \\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            La legge gamma ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n                            \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della legge gamma è:\n                            
    \n                            
    \n                                {r`m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha`}\n                            
    \n                            
    \n                                La media della legge gamma è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{\\alpha}{\\lambda}`}\n                            
    \n                            
    \n                                La varianza della legge gamma è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{\\alpha}{\\lambda^2}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che può assumere qualsiasi valore in un intervallo {r`[a, b]`} in modo equiprobabile.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Uni(a, b)`}\n                        
    \n                        
    \n                            Su di essa vale la seguente proprietà:\n                        
    \n                        
    \n                            {r`P(X \\in (c, d)) = \\frac{d - c}{b - a}`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione uniforme ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                0 \\qquad \\quad altrimenti    \n                            \\end{cases}`}\n                        
    \n                        
    \n                            La distribuzione uniforme ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                0 \\qquad \\quad x < a  \n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                1 \\qquad \\quad x > b\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}`}\n                            
    \n                            
    \n                                La media della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{a + b}{2}`}\n                            
    \n                            
    \n                                La varianza della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{(b - a)^2}{12}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria con una specifica distribuzione.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Nor(\\mu, \\sigma^2)`}.\n                        
    \n                        \n                            \\mu e \\sigma^2 sono rispettivamente la media e la varianza della distribuzione!\n                        \n                        \n                    \n                        
    \n                            La distribuzione normale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione normale è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}`}\n                            
    \n                            
    \n                                La media della distribuzione normale è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della distribuzione normale è:\n                            
    \n                            
    \n                                {r`Var(X) = \\sigma^2`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Qualsiasi normale può essere trasformata in qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione normale standard Z è:\n                        
    \n                        
    \n                            Z \\sim Nor(0, 1)\n                        
    \n                        
    \n                            La sua funzione di ripartizione è detta {r`\\phi(z)`} e vale:\n                        
    \n                        
    \n                            {r`F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx`}\n                        
    \n                        \n                    \n                        
    \n                            Da un quantile {r`z_\\alpha`} della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La distribuzione normale ha una particolare relazione con la distribuzione Gamma:\n                        
    \n                        
    \n                            {r`Z^2 \\sim \\chi^2 (v = 1)`}\n                        
    \n                        \n                    \n                        
    \n                            \"chi-quadro a un grado di libertà\"\n                        
    \n                        
    \n                            Esiste una distribuzione Gamma particolare:\n                        
    \n                        
    \n                            {r`\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)`}\n                        
    \n                        
    \n                            Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:\n                        
    \n                        
    \n                            {r`\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)`}\n                        
    \n                        \n                    \n                        
    \n                            Un'altra funzione particolare è la funzione T di Student:\n                        
    \n                        
    \n                            {r`T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di N rispetto a n, si può dire che:\n                        
    \n                        
    \n                            {r`Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})`}\n                        
    \n                        \n                    \n                        
    \n                            La binomiale non è altro che una poissoniana a tempo discreto, quindi, se n è grande e n \\cdot p è nell'ordine di grandezza delle unità, allora:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Poi(n \\cdot p)`}\n                        
    \n                        \n                    \n                        
    \n                            Per il Teorema di De Moivre-Laplace, se una binomiale ha una n grande e p non vicina a 0 o 1, si può approssimare con:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            Passando da una variabile discreta X a una continua Y, per ogni valore discreto k la probabilità viene \"spalmata\" su tutto l'intervallo {r`(k - \\frac{1}{2}, k + \\frac{1}{2})`}:\n                        
    \n                        
      \n                            
    • {r`P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})`}
      • \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un vettore composto da variabili aleatorie.\n                        
    \n                        
    \n                            Il suo simbolo generalmente è {r`\\boldsymbol{X}`} oppure {r`X, Y`}.\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione congiunta:\n                        
    \n                        
    \n                            {r`F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione marginale:\n                        
    \n                        
    \n                            {r`F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)`}\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori discreti hanno più densità che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una densità congiunta:\n                        
    \n                        
    \n                            {r`p_{X, Y} (x, y) = P(X = x, Y = y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una densità marginale:\n                        
    \n                        
    \n                            {r`p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli A_i:\n                        
    \n                        
    \n                            {r`P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)`}\n                        
    \n                        \n                    \n                        
    \n                            E' possibile calcolare la media di qualsiasi funzione g(X, Y) avente elementi del vettore come variabili:\n                        
    \n                        
    \n                            {r`E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)`}\n                        
    \n                        \n                            Solitamente si calcola la media di x \\cdot y.\n                        \n                        
    \n                            Le medie di più variabili aleatorie si possono sommare:\n                        
    \n                        
    \n                            {r`E(X + Y) = E(X) + E(Y)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un operatore che misura la correlazione di due variabili aleatorie.\n                        
    \n                        
    \n                            Si calcola con il valore atteso dei prodotti delle distanze dalla media:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)`}\n                        
    \n                        
    \n                            Ha diverse proprietà:\n                        
    \n                        
      \n                            
    • Il suo valore nullo è 0: {r`Cov(X, \\alpha) = 0`}
      • \n                            
    • E' commutativa: {r`Cov(X, Y) = Cov(Y, X)`}
      • \n                            
    • E' semplificabile: {r`Cov(X, X) = Var(X)`}
      • \n                            
    • E' lineare: {r`Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)`}
      • \n                            
    • E' distributiva: {r`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Due variabili sono variabili incorrelate se:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = 0`}\n                        
    \n                        
    \n                            Variabili indipendenti sono sempre incorrelate.\n                        
    \n                        \n                    \n                        
    \n                            Una matrice {r`\\boldsymbol{C_X}`} che contiene la covarianza tra tutte le variabili di un vettore aleatorio {r`\\boldsymbol{X}`}:\n                        
    \n                        
    \n                            {r`\n                                \\boldsymbol{C_X} = \n                                \\begin{bmatrix}\n                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n                                \\end{bmatrix}\n                            `}\n                        
    \n                        
    \n                            E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono \\geq 0.\n                        
    \n                        \n                    \n                        
    \n                            Un valore che misura come due variabili aleatorie sono correlate:\n                        
    \n                        
    \n                            {r`\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}`}\n                        
    \n                        
    \n                            E' sempre compreso tra -1 e 1:\n                        
    \n                        
    \n                            {r`-1 \\leq \\rho_{X, Y} \\leq 1`}\n                        
    \n                        
    \n                            Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:\n                        
    \n                        
    \n                            {r`Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La varianza di due variabili aleatorie sommate è:\n                        
    \n                        
    \n                            {r`Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)`}\n                        
    \n                        \n                            Si dimostra applicando le proprietà della covarianza!\n                        \n                        
    \n                            Se più variabili aleatorie X_i sono indipendenti ({r`Cov(X, Y) = 0`}), allora:\n                        
    \n                        
    \n                            {r`Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una n-pla di variabili aleatorie con la stessa distribuzione della variabile aleatoria X (\"popolazione\") ma indipendenti tra loro.\n                        
    \n                        \n                            Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si realizzeranno nel loro valore.\n                        \n                        \n                    \n                        
    \n                            Il valore dato dalla media aritmetica degli n elementi del campione elevati alla potenza k:\n                        
    \n                        
    \n                            {r`M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k `}\n                        
    \n                        
    \n                            Il momento campionario di primo ordine è la media campionaria {r`\\overline{X}_n`}.\n                        
    \n                        \n                    \n                        
    \n                            La media aritmetica dello scarto quadratico medio degli elementi del campione.\n                        
    \n                        
    \n                            Se è noto il valore medio {r`m = E(X)`} di X:\n                        
    \n                        
    \n                            {r`S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2`}\n                        
    \n                        
    \n                            Altrimenti:\n                        
    \n                        
    \n                            {r`S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se calcoliamo la media della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(\\overline{X}_n) = E(X)`}\n                        
    \n                        \n                            Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la varianza della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`Var(\\overline{X}_n) = \\frac{Var(X)}{n}`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la media della varianza campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(S_0^2) = E(S_n^2) = Var(X)`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Se la popolazione X ha una distribuzione normale ({r`X \\sim Nor(\\mu, \\sigma^2)`})...\n                        
    \n                        \n                    \n                        
    \n                            ...allora sappiamo anche la distribuzione della media campionaria!\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e anche della varianza campionaria!\n                        
    \n                        
    \n                            {r`S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)`}\n                        
    \n                        
    \n                            {r`S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e che media campionaria e varianza campionaria sono indipendenti tra loro!\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa funzione di ripartizione della popolazione X, allora essa converge in distribuzione.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} F_{X_n} (x) = F_X (x) \\\\implies X_n \\\\xrightarrow{d} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità della popolazione X, allora essa converge in probabilità.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, \\\\lim_{n \\\\to +\\\\infty} P( | X_n - X | < \\\\epsilon) = 1 \\\\implies X_n \\\\xrightarrow{p} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità a  della popolazione X, allora essa converge quasi certamente.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, P \\left( \\\\lim_{n \\\\to +\\\\infty} | X_n - X | < \\\\epsilon) \\right) = 1 \\\\implies X_n \\\\xrightarrow{qc} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la media del quadrato della distanza tra la successione e la popolazione X uguale a 0, allora essa converge in media quadratica.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} E( | X_n - X |^2 = 0 \\\\implies X_n \\\\xrightarrow{mq} X`}\n                        
    \n                        \n                    \n                        
    \n                            {`\n                                \\\\begin{matrix}\n                                X_n \\\\xrightarrow{mq} X\\\\\\\\\n                                X_n \\\\xrightarrow{qc} X\n                                \\\\end{matrix} \\\\implies X_n \\\\xrightarrow{p} X \\\\implies X_n \\\\xrightarrow{d} X`\n                            }\n                        
    \n                        
    \n                            In più:\n                        
    \n                        
    \n                            {`X_n \\\\xrightarrow{p} x \\\\Longleftrightarrow X_n \\\\xrightarrow{d} x`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in probabilità alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{p} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1`}\n                        
    \n                        
    \n                            {r`P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1`}\n                        
    \n                        \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge quasi certamente alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{qc} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1`}\n                        
    \n                        \n                            Dimostra che l'interpretazione frequentista della probabilità è valida!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in distribuzione a {r`Nor(0, 1) = \\Phi()`}.\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' una somma di bernoulliane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di geometriche, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di altre poissoniane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di esponenziali, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            Se n è grande, allora:\n                        
    \n                        
    \n                            {r`Y = \\sum_{i=1}^{n} X_i`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per indicare parametri sconosciuti di una legge si usa \\theta.\n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria funzione di un campione:\n                        
    \n                        
    \n                            {r`T(\\boldsymbol{X})`}\n                        
    \n                        \n                            Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso {r`T(\\boldsymbol{X}) = \\boldsymbol{X}`}.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una statistica T_n ottenuta da n osservazioni, che stimi i parametri di una legge e sia indipendente da essi.\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è corretto se il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente corretto se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in media quadratica se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in probabilità se:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente normale se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si può usare il metodo dei momenti per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una M a \\theta: {r`\\widehat{\\theta}_M`}\n                        
    \n                        
    \n                            Visto che:\n                        
    \n                        
      \n                            
    • {r`\\theta = g(E(X))`}
      • \n                            
    • {r`\\widehat{E(X)} = \\overline{X}_n`}
      • \n                        
    \n                        
    \n                            Allora:\n                        
    \n                        
    \n                            {r`\\widehat{\\theta}_M = g( \\overline{X}_n )`}\n                        
    \n                        
    \n                            Se {r`\\theta`} non è esprimibile in termini di {r`E(X)`}, si possono usare i momenti successivi {r`M_n^2`}, {r`M_n^3`}, {r`M_n^3`}...\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si può usare il metodo della massima verosomiglianza per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una L a \\theta: {r`\\widehat{\\theta}_L`}\n                        
    \n                        
    \n                            Consiste nel trovare il massimo assoluto {r`\\widehat{\\theta}_L`} della la funzione di verosomiglianza {r`L`}:\n                        
    \n                        
    \n                            {r`L(x_1, ..., x_n; \\theta) = \\prod_{i=1}^n f_X(x_i; \\theta)`}\n                        
    \n                        
    \n                            Gli stimatori di massima verosomiglianza sono asintoticamente corretti, consistenti in probabilità e asintoticamente normali.\n                        
    \n                        \n                    \n                        
    \n                            Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:\n                        
    \n                        
      \n                            
    • Sono asintoticamente corretti.
      • \n                            
    • Sono consistenti in probabilità.
      • \n                            
    • Sono asintoticamente normali.
      • \n                            
    • Sono invarianti: {r`\\widehat{g(\\theta)}_L = g(\\widehat{\\theta}_L)`}
      • \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{p}_M = \\widehat{p}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\mu}_M = \\widehat{\\mu}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\lambda}_M = \\widehat{\\lambda}_L = \\frac{1}{\\overline{X}_n}`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo della massima verosomiglianza:\n                        
    \n                        
      \n                            
    • {r`\\widehat{\\mu}_L = \\overline{X}_n`}

      • \n                            
    • {r`\\widehat{\\sigma^2}_L = \\frac{\\sum (X_i - \\overline{X}_n)^2 }{n}`}
      • \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"intervallo di confidenza al 95%\"\n                        
    \n                        
    \n                            L'intervallo di valori di \\theta all'interno del quale siamo \"più o meno sicuri\" si trovi il valore effettivo:\n                        
    \n                        
    \n                            L'intervallo di confidenza a N della stima {r`\\widehat{W}`} è l'intervallo ]a, b[ tale che:\n                        
    \n                        
    \n                            {r`P( a < W < b ) = N`}\n                        
    \n                        
    \n                            Può anche essere unilatero nel caso limiti la stima in una sola direzione, positiva o negativa.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        
    \n                            {r`t_{\\alpha, v}`} è un quantile della distribuzione di Student di parametro v.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`p \\in \\left[ \\overline{p} - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}}, \\overline{p} + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}} \\right]`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`m \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}} \\right]`}\n                        
    \n                        \n                    \n            
    \n        )\n\t}\n}"],"sourceRoot":""}
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= \frac{casi\ favorevoli}{casi\ possibili}`))))),l(u.a,{title:"Frequentista"},l("p",null,l(o.a,null,oe(c||(c=te`P(E) = \frac{successi}{prove\ totali}`))))),l(u.a,{title:"Soggettiva"},l("p",null,"Il prezzo che un individuo coerente riterrebbe equo per ricevere ",l("b",null,"1")," nel caso l'evento si verificasse e ",l("b",null,"0")," nel caso l'evento non si verificasse."))),l(r.a,{title:"Linguaggio matematico"},l(u.a,{title:"Spazio campionario"},l("blockquote",null,'"omegone"'),l("p",null,"L'",l("b",null,"insieme")," di tutti gli esiti possibili di un esperimento."),l("p",null,l(o.a,null,oe(b||(b=te`\Omega = \left \{ 1, 2, 3, 4, 5, 6 \right \}`))))),l(u.a,{title:"Esito"},l("blockquote",null,'"omeghino"'),l("p",null,"Un ",l("b",null,"elemento")," dello spazio campionario."),l("p",null,l(o.a,null,oe(v||(v=te`\omega = 1`))))),l(u.a,{title:"Evento"},l("blockquote",null,'"e"'),l("p",null,"Un ",l("b",null,"sottoinsieme")," dello spazio campionario."),l("p",null,l(o.a,null,oe(f||(f=te`E = 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altro."),l("p",null,l(o.a,null,oe(X||(X=te`E \subseteq F`)))),l("p",null,"Se si verifica ",l(o.a,null,"E"),", allora si verifica anche ",l(o.a,null,"F"),".")),l(u.a,{title:"Evento impossibile"},l("blockquote",null,'"e è impossibile"'),l("p",null,"Un sottoinsieme ",l("b",null,"vuoto"),"."),l("p",null,l(o.a,null,oe(q||(q=te`E = \emptyset`))))),l(u.a,{title:"Mutua esclusione"},l("blockquote",null,'"e ed effe si escludono mutualmente"'),l("p",null,"La ",l("b",null,"disgiunzione")," di due insiemi."),l("p",null,l(o.a,null,oe(E||(E=te`E \cap F = \emptyset`)))))),l(r.a,null,l(u.a,{title:"Famiglia degli eventi"},l("blockquote",null,'"famiglia effe"'),l("p",null,"I sottoinsiemi dello spazio campionario formano una ",l("b",null,"famiglia")," di sottoinsiemi detta ",l("i",null,"famiglia degli eventi"),"."),l("p",null,l(o.a,null,oe(L||(L=te`\mathcal{F}`)))),l("p",null,"Qualsiasi sottoinsieme appartenente a ",l(o.a,null,oe(x||(x=te`\mathcal{F}`)))," è considerato un 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tre..."'),l("p",null,"Un insieme di esiti e eventi:"),l("ul",null,l("li",null,l("b",null,"Finito"),"."),l("li",null,"In cui tutti gli eventi hanno ",l("b",null,"probabilità diversa da 0"),"."),l("li",null,"In cui tutti gli eventi sono ",l("b",null,"mutualmente esclusivi"),"."),l("li",null,"In cui l'unione di tutti i suoi elementi ",l("b",null,"copre lo spazio campionario"),".")),l("p",null,"La partizione ",l(o.a,null,oe(I||(I=te`E_i`)))," è composta dagli eventi ",l(o.a,null,oe(N||(N=te`E_1`))),", ",l(o.a,null,oe(V||(V=te`E_2`))),", ",l(o.a,null,oe(Y||(Y=te`E_3`))),", fino a ",l(o.a,null,oe(w||(w=te`E_n`))),"."),l(s.a,null,"Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare."))),l(r.a,{title:"Assiomi della probabilità"},l(u.a,{title:"Primo assioma della probabilità"},l("p",null,"La probabilità di un evento è un numero tra 0 e 1."),l("p",null,l(o.a,null,oe(D||(D=te`\forall E \in \mathcal{F}, 0 \leq P(E) 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probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione."),l("p",null,l(o.a,null,oe(G||(G=te`P(E \cup F) = P(E) + P(F) - P(E \cap F)`)))),l(s.a,null,"Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!"))),l(r.a,{title:"Spazi equiprobabili"},l(u.a,{title:"Cosa sono?"},l("p",null,"Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi."),l("p",null,l(o.a,null,oe(T||(T=te`P(E) = \frac{len(E)}{len(\Omega)}`))))),l(u.a,{title:"Spazi equiprobabili geometrici"},l("p",null,"Gli spazi campionari possono avere un numero infinito di esiti: sono ",l("i",null,"equiprobabili geometrici")," se nessun esito è privilegiato rispetto agli altri."))),l(r.a,{title:"Calcolo combinatorio"},l(u.a,{title:"Disposizioni"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(o.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",l(o.a,null,"k")," volte."),l("p",null,l("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),l("p",null,l(o.a,null,oe(Q||(Q=te`\boldsymbol{D}_{n, k} = \frac{n!}{(n - k)!}`))))),l(u.a,{title:"Disposizioni con ripetizione"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(o.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"rimetto nel sacchetto"),". Ripeto per ",l(o.a,null,"k")," volte."),l("p",null,l("b",null,"Tengo conto")," dell'ordine in cui ho estratto i numeri."),l("p",null,l(o.a,null,oe(O||(O=te`\boldsymbol{D}^{r}_{n, k} = n^k`))))),l(u.a,{title:"Combinazioni"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(o.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"tengo fuori dal sacchetto"),". Ripeto per ",l(o.a,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(o.a,null,oe(R||(R=te`\boldsymbol{C}_{n, k} = \binom{n}{k} = \frac{n!}{(k)! \cdot (n - k)!}`))))),l(u.a,{title:"Combinazioni con ripetizione"},l("p",null,"Estraggo un numero, da un sacchetto con ",l(o.a,null,"n")," numeri, mi segno che numero ho estratto e lo ",l("b",null,"rimetto nel sacchetto"),". Ripeto per ",l(o.a,null,"k")," volte."),l("p",null,l("b",null,"Non mi interessa")," l'ordine in cui ho estratto i numeri."),l("p",null,l(o.a,null,oe(j||(j=te`\boldsymbol{C}^{r}_{n, k} = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{(k)! \cdot (n - 1)!}`))))),l(u.a,{title:"Permutazioni"},l("p",null,"Estraggo ",l(o.a,null,"n")," numeri e guardo in quanti ordini diversi li posso mettere."),l("p",null,l(o.a,null,oe(K||(K=te`\boldsymbol{P}_n = n!`)))))),l(r.a,{title:"Probabilità condizionata"},l(u.a,{title:"Eventi condizionati"},l("blockquote",null,'"E dato F"'),l("p",null,"La probabilità che si verifichi ",l(o.a,null,"E")," sapendo che ",l("b",null,"si è già verificato")," ",l(o.a,null,"F"),"."),l("p",null,l(o.a,null,oe(W||(W=te`P(E|F) = \frac{P(E \cap F)}{P(F)}`)))),l(s.a,null,"Ricorda vagamente le pipe di ",l("code",null,"bash"),", però al contrario...")),l(u.a,{title:"Eventi mutualmente esclusivi"},l("p",null,"Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0."),l("p",null,l(o.a,null,oe(Z||(Z=te`E \cap F = \emptyset \Longleftrightarrow P(E|F) = P(F|E) = 0`)))))),l(r.a,null,l(u.a,{title:"Regola della catena"},l("p",null,"Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:"),l("p",null,l(o.a,null,oe(J||(J=te`P(E_1 \cap \times \cap E_n) = P(E_1) \times P(E_2 | E_1) \times \dots \times P(E_n | E_1 \cap E_2 \cap \dots \cap E_{n-1})`)))))),l(r.a,{title:"Le alternative"},l(u.a,{title:"Legge delle alternative"},l("p",null,"La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione."),l("p",null,l(o.a,null,oe(H||(H=te`P(F) = \sum_{i} P(F|E_i) \cdot P(E_i)`))))),l(u.a,{title:"Legge condizionata delle alternative"},l("p",null,"La legge delle alternative funziona anche quando ad essere partizionato è un ",l("b",null,"evento"),":"),l("p",null,l(o.a,null,oe($||($=te`P(F|G) = \sum_i P(F|E_i \cap G) \cdot P(E_i | G)`))))),l(u.a,{title:"Formula di Bayes"},l("p",null,"Tramite la ",l("i",null,"formula di Bayes")," possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:"),l("p",null,l(o.a,null,oe(ll||(ll=te`P(E_h | F) = \frac{P(F | E_h) \cdot P(E_h)}{P(F)}`)))),l(s.a,null,"In pratica, invertiamo gli eventi."))),l(r.a,{title:"Eventi indipendenti"},l(u.a,{title:"Due eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a due a due"'),l("p",null,"Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro."),l("p",null,l(o.a,null,oe(al||(al=te`P(E \cap F) = P(E) \cdot P(F) \Longleftrightarrow P(E|F) = P(E) \Longleftrightarrow P(F|E) = P(F)`))))),l(u.a,{title:"Più eventi indipendenti"},l("blockquote",null,'"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'),l("p",null,"Si può verificare l'indipendenza di più eventi alla volta:"),l("p",null,l(o.a,null,oe(il||(il=te`P(E \cap F \cap G) = P(E) \cdot P(F) \cdot P(G)`)))),l("p",null,"Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.")),l(u.a,{title:"Famiglia di eventi indipendenti"},l("p",null,"Un insieme di ",l(o.a,null,"n")," eventi è una ",l("i",null,"famiglia di eventi indipendenti")," se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti."),l(s.a,null,"Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!"))),l(r.a,{title:"Variabili aleatorie"},l(u.a,{title:"Variabile aleatoria"},l("p",null,"Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. 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+                            P([X = x]) \quad se\ X \mapsto x \\
+                            0 \qquad \qquad \quad se\ X \not\mapsto x
+                            \end{cases}`))))),l(u.a,{title:"Funzione densità"},l("p",null,"La ",l("i",null,"funzione densità")," ",l(o.a,null,oe(rl||(rl=te`f_X : X \to [0, 1]`)))," di una variabile aleatoria ",l("b",null,"continua")," ",l(o.a,null,"X")," è l'equivalente continuo della funzione probabilità:"),l("p",null,l(o.a,null,oe(sl||(sl=te`P([a < X \leq b]) = \int_a^b f_X (x) dx`)))),l("p",null,"A differenza della funzione probabilità, è possibile che la funzione densità ",l("b",null,"non esista")," per una certa variabile aleatoria."),l(s.a,null,"Rappresenta \"quanta\" probabilità c'è in un'unità di x!"))),l(r.a,{title:"Funzione di ripartizione"},l(u.a,{title:"Definizione"},l("p",null,"Ogni variabile aleatoria ha una ",l("i",null,"funzione di ripartizione")," ",l(o.a,null,oe(pl||(pl=te`F_X : \mathbb{R} \to [0, 1]`)))," associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a ",l(o.a,null,"t"),":"),l("p",null,"Si può dire che essa rappresenti la probabilità dell'evento ",l(o.a,null,oe(dl||(dl=te`A_t`))),":"),l("p",null,l(o.a,null,oe(ml||(ml=te`F_X (t) = P(A_t) = \begin{cases}
+                            \sum_{i = 0}^{t} p_X (x_i) \quad nel\ discreto\\
+                            \\
+                            \int_{-\infty}^t f_X (x) dx \quad nel\ continuo
+                            \end{cases}`))))),l(u.a,{title:"Proprietà della funzione"},l("ul",null,l("li",null,"È sempre ",l("b",null,"monotona crescente")," (non strettamente)."),l("br",null),l("li",null,"Vale ",l("b",null,"0")," a ",l(o.a,null,"-\\infty")," e ",l("b",null,"1")," a ",l(o.a,null,"+\\infty"),"."),l("br",null),l("li",null,"È ",l("b",null,"continua da destra"),": ",l(o.a,null,oe(cl||(cl=te`\forall x_0 \in \mathbb{R}, F_X (x_0) = \lim_{t \to x^+_0} F_X (t)`)))))),l(u.a,{title:"Probabilità di un valore"},l("p",null,"Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:"),l("p",null,l(o.a,null,oe(bl||(bl=te`P([X = x_0]) = \lim_{t \to x^+_0} F_X (t) - \lim_{t \to x^-_0} F_X (t)`)))))),l(r.a,{title:"Trasformazioni di variabili aleatorie"},l(u.a,{title:"Nel discreto"},l("p",null,"Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.")),l(u.a,{title:"Nel continuo (invertibile)"},l("p",null,"Nel continuo applichiamo la formula dell'integrazione per sostituzione:"),l("p",null,l(o.a,null,oe(vl||(vl=te`f_Y (y) = \int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`))))),l(u.a,{title:"Nel... digitale"},l("p",null,"Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione ",l("a",{href:"https://docs.python.org/3/library/random.html#random.random"},l("code",null,"random()"))," che restituisce numeri da 0 a 1 con una distribuzione lineare."))),l(r.a,{title:"Informazioni delle variabili aleatorie"},l(u.a,{title:"Media"},l("p",null,"Ogni variabile aleatoria che ha una ",l("b",null,"funzione di ripartizione")," e un ",l("b",null,"supporto finito")," ha anche una ",l("i",null,"media")," (o ",l("i",null,"valore medio")," o ",l("i",null,"atteso"),"):"),l("p",null,l(o.a,null,oe(fl||(fl=te`E(X) = \int_0^{+infty} (1 - F_X (t)) dt - \int_{-\infty}^{0} F_X (t) dt`)))),l("p",null,"Nel discreto, si può calcolare con:"),l("p",null,l(o.a,null,oe(hl||(hl=te`E(X) = \sum_i P(X = x_i) \cdot x_i`)))),l("p",null,"Nel continuo, si può calcolare con:"),l("p",null,l(o.a,null,oe(gl||(gl=te`E(X) = \int_{-\infty}^{+\infty} f_X (x) \cdot x \cdot dx`)))))),l(r.a,null,l(u.a,{title:"Moda"},l("p",null,"Valore per cui la ",l("b",null,"funzione probabilità")," o ",l("b",null,"funzione densità")," è ",l("b",null,"massima"),".")),l(u.a,{title:"Quantili"},l("p",null,"Il ",l("i",null,"quantile")," ",l(o.a,null,oe(_l||(_l=te`x_{\alpha}`)))," di ordine ",l(o.a,null,oe(zl||(zl=te`0 \leq \alpha \leq 1`)))," della variabile aleatoria ",l(o.a,null,"X")," è il più piccolo numero tale che:"),l("p",null,l(o.a,null,oe(Xl||(Xl=te`P([X < x_{\alpha}]) \leq \alpha \leq P([X \leq x_{\alpha}])`)))),l("p",null),l("p",null,"Il quantile di ordine 0.5 ",l(o.a,null,oe(ql||(ql=te`x_{0.5}`)))," è detto ",l("i",null,"mediana"),"."),l("p",null,"I quantili di ordine 0.25 ",l(o.a,null,oe(El||(El=te`x_{0.25}`)))," e 0.75 ",l(o.a,null,oe(Ll||(Ll=te`x_{0.75}`)))," sono detti ",l("i",null,"quartili"),"."),l("p",null,"I quantili di ordine ",l(o.a,null,oe(xl||(xl=te`\frac{n}{100}`)))," sono detti ",l("i",null,l(o.a,null,"n"),"-esima percentile"),".")),l(u.a,{title:"Varianza"},l("p",null,"È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:"),l("p",null,l(o.a,null,oe(Pl||(Pl=te`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`)))))),l(r.a,{title:"Disuguaglianze notevoli"},l(u.a,{title:"Disuguaglianza di Markov"},l("p",null,"Data una variabile aleatoria non-negativa:"),l("p",null,l(o.a,null,oe(kl||(kl=te`\forall k > 0, P([X \geq k]) \leq \frac{E(X)}{k}`)))),l("p",null,"Divide in due parti (",l(o.a,null,oe(Fl||(Fl=te`P(X < k)`)))," e ",l(o.a,null,oe(yl||(yl=te`P(X \geq k)`))),") la funzione X, la cui media risulterà uguale a:"),l("p",null,l(o.a,null,oe(Sl||(Sl=te`E(X) = \overline{k} \cdot P(X < k) + k \cdot P(X \geq k)`))))),l(u.a,{title:"Disuguaglianza di Čebyšëv"},l("blockquote",null,'"disuguaglianza di cebicev"'),l("p",null,"Se la variabile aleatoria ",l(o.a,null,"X")," ha media e varianza, allora la probabilità che essa abbia un valore a più di ",l(o.a,null,oe(Cl||(Cl=te`\epsilon`)))," di distanza dal valore medio è minore o uguale a ",l(o.a,null,oe(Il||(Il=te`\frac{Var(X)}{\epsilon^2}`))),"."),l("p",null,l(o.a,null,oe(Nl||(Nl=te`\forall \epsilon > 0, P([ \left| X - E(X) \right| \geq \epsilon]) \leq \frac{Var(X)}{\epsilon^2}`)))),l("p",null,"E anche:"),l("p",null,l(o.a,null,oe(Vl||(Vl=te`\forall \epsilon > 0, P([ \left| X - E(X) \right| < \epsilon]) \geq 1 - \frac{Var(X)}{\epsilon^2}`)))),l(s.a,null,"Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!"))),l(r.a,{title:"Un momento...!"},l(u.a,{title:"Momento"},l("p",null,"Il ",l("i",null,"momento")," ",l(o.a,null,"k"),"-esimo di una variabile aleatoria è:"),l("p",null,l(o.a,null,oe(Yl||(Yl=te`\mu_k = E ( X^k ) = \begin{cases}
+                                \sum_i x_i^k p_X (x_i) \qquad nel\ discreto\\
+                                \\
+                                \int_{-\infty}^{+\infty} x^k f_X (x) dx \qquad nel\ continuo
+                                \end{cases}`)))),l(s.a,null,"La media di una variabile aleatoria è anche il suo primo momento.")),l(u.a,{title:"Funzione generatrice dei momenti"},l("p",null,"La ",l("i",null,"funzione generatrice dei momenti")," è:"),l("p",null,l(o.a,null,oe(wl||(wl=te`m_X (t) = E( e^{t \cdot X} )`)))),l("p",null,"Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ",l("b",null,"stessa distribuzione"),"."),l("p",null,"E' la ",l("b",null,"trasformata di Laplace")," della variabile aleatoria di X.")),l(u.a,{title:"Funzione caratteristica"},l("p",null,"La ",l("i",null,"funzione caratteristica")," è:"),l("p",null,l(o.a,null,oe(Dl||(Dl=te`H_X (t) = E ( e^{i \cdot t \cdot X} )`)))),l("p",null,"Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ",l("b",null,"stessa distribuzione"),"."),l("p",null,"E' la ",l("b",null,"trasformata di Fourier")," della variabile aleatoria di X."))),l(r.a,{title:"Prove e schemi"},l(u.a,{title:"Variabile con distribuzione"},l("p",null,"Per dire che una variabile ha una certa distribuzione, si usa la notazione:"),l("p",null,l(o.a,null,oe(Ul||(Ul=te`X \sim Distribuzione()`))))),l(u.a,{title:"Prova di Bernoulli"},l("p",null,"Una prova con solo due possibili esiti: ",l(p.a,null,"successo")," e ",l(d.a,null,"insuccesso"),".")),l(u.a,{title:"Schema di Bernoulli"},l("p",null,"Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate."))),l(r.a,{title:"Bernoulliana"},l(u.a,{title:"Distribuzione bernoulliana"},l("p",null,"Una variabile aleatoria che rappresenta una prova di Bernoulli:"),l("ul",null,l("li",null,"vale ",l(p.a,null,"1")," in caso di ",l(p.a,null,"successo"),"."),l("li",null,"vale ",l(d.a,null,"0")," in caso di ",l(d.a,null,"insuccesso"),".")),l("p",null,"Il suo simbolo è ",l(o.a,null,oe(Ml||(Ml=te`Ber(p)`))))),l(u.a,{title:"Densità della bernoulliana"},l("p",null,"La distribuzione bernoulliana ha come densità:"),l("p",null,l(o.a,null,oe(Bl||(Bl=te`f_X (k) : \{0, 1\} = \begin{cases}
+                            p \quad se\ k = 1\\
+                            q \quad se\ k = 0\\
+                            0 \quad altrimenti
+                            \end{cases} = p^x \cdot q^{1 - k}`)))))),l(r.a,{title:"Binomiale"},l(u.a,{title:"Distribuzione binomiale"},l("p",null,"Una variabile aleatoria che conta il numero di successi di ",l(o.a,null,"n")," prove di uno schema di Bernoulli."),l("p",null,"Il suo simbolo è ",l(o.a,null,oe(Al||(Al=te`Bin(n, p)`))),".")),l(u.a,{title:"Densità della binomiale"},l("p",null,"La binomiale ha come densità:"),l("p",null,l(o.a,null,oe(Gl||(Gl=te`f_X (k) : \{0..n\} = \binom{n}{k} \cdot p^k \cdot q^{n - k}`))))),l(u.a,{title:"Momenti della binomiale"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della binomiale è:"),l("p",null,l(o.a,null,oe(Tl||(Tl=te`m_X (t) = (q + p \cdot e^t) ^ n`)))),l("p",null,"La ",l("b",null,"media")," di una binomiale è:"),l("p",null,l(o.a,null,oe(Ql||(Ql=te`E(X) = n \cdot p`)))),l("p",null,"La ",l("b",null,"varianza")," di una binomiale è:"),l("p",null,l(o.a,null,oe(Ol||(Ol=te`Var(X) = n \cdot p \cdot q`)))))),l(r.a,{title:"Geometrica"},l(u.a,{title:"Distribuzione geometrica"},l("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo."),l("p",null,"Il suo simbolo è ",l(o.a,null,"Geo(p)"),".")),l(u.a,{title:"Densità della geometrica"},l("p",null,"La geometrica ha come densità:"),l("p",null,l(o.a,null,oe(Rl||(Rl=te`f_X (k) : \mathbb{N} = q^{k - 1} p`))))),l(u.a,{title:"Momenti della geometrica"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della geometrica è:"),l("p",null,l(o.a,null,oe(jl||(jl=te`m_X (t) = \frac{p \cdot e^t}{1 - q \cdot e^t}`)))),l("p",null,"La ",l("b",null,"media")," della geometrica è:"),l("p",null,l(o.a,null,oe(Kl||(Kl=te`E(X) = \frac{1}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della geometrica è:"),l("p",null,l(o.a,null,oe(Wl||(Wl=te`Var(X) = \frac{q}{p^2}`))))),l(u.a,{title:"Assenza di memoria della geometrica"},l("p",null,"La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),l("p",null,l(o.a,null,oe(Zl||(Zl=te`P([X = i + j | X > i ]) = P([X = j])`)))),l(s.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),l(r.a,{title:"Binomiale negativa"},l(u.a,{title:"Distribuzione binomiale negativa"},l("p",null,"Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'",l(o.a,null,"n"),"-esimo successo."),l("p",null,"Il suo simbolo è ",l(o.a,null,oe(Jl||(Jl=te`\overline{Bin}(n, p)`))),".")),l(u.a,{title:"Densità della binomiale negativa"},l("p",null,"La binomiale negativa ha come densità:"),l("p",null,l(o.a,null,oe(Hl||(Hl=te`f_X (k) : \{ n .. +\infty \} \in \mathbb{N} = \binom{k - 1}{n - 1} \cdot p^n \cdot q^{k - n} `))))),l(u.a,{title:"Momenti della binomiale negativa"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della binomiale negativa è:"),l("p",null,l(o.a,null,oe($l||($l=te`m_X (t) : \{ t < ln(\frac{1}{q}) \} = \left( \frac{p \cdot e^t}{1 - q \cdot e^t} \right) ^n`)))),l("p",null,"La ",l("b",null,"media")," della binomiale negativa è:"),l("p",null,l(o.a,null,oe(la||(la=te`E(X) = \frac{n}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della binomiale negativa è:"),l("p",null,l(o.a,null,oe(aa||(aa=te`Var(X) = \frac{n \cdot q}{p^2}`))))))),l(r.a,{title:"Geometrica traslata"},l(u.a,{title:"Distribuzione geometrica traslata"},l("p",null,"Una variabile aleatoria che conta il numero ",l(o.a,null,"k")," di insuccessi consecutivi in uno schema di Bernoulli:"),l("p",null,"Il suo simbolo rimane ",l(o.a,null,oe(ia||(ia=te`Geo(p)`))),".")),l(u.a,{title:"Densità della geometrica tralsata"},l("p",null,"La geometrica traslata ha come densità:"),l("p",null,l(o.a,null,oe(na||(na=te`f_X (k) : \mathbb{N} = p \cdot q^k `))))),l(u.a,{title:"Momenti della geometrica traslata"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della geometrica traslata è:"),l("p",null,l(o.a,null,oe(ea||(ea=te`m_X (t) : \left\{ t < ln \left( \frac{1}{q} \right) \right\} = \frac{p}{1 - q \cdot e^t}`)))),l("p",null,"La ",l("b",null,"media")," della geometrica traslata è:"),l("p",null,l(o.a,null,oe(ta||(ta=te`E(X) = \frac{q}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della geometrica è:"),l("p",null,l(o.a,null,oe(oa||(oa=te`Var(X) = \frac{q}{p^2}`))))),l(u.a,{title:"Assenza di memoria della geometrica traslata"},l("p",null,"La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),l("p",null,l(o.a,null,oe(ua||(ua=te`P([X = i + j | X > i ]) = P([X = j])`)))),l(s.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),l(r.a,{title:"Binomiale negativa traslata"},l(u.a,{title:"Distribuzione binomiale negativa traslata"},l("p",null,"Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'",l(o.a,null,"n"),"-esimo successo."),l("p",null,"Il suo simbolo rimane ",l(o.a,null,oe(ra||(ra=te`\overline{Bin}(n, p)`))),".")),l(u.a,{title:"Densità della binomiale negativa traslata"},l("p",null,"La binomiale negativa traslata ha come densità:"),l("p",null,l(o.a,null,oe(sa||(sa=te`f_X (k) : \mathbb{N} = \binom{k + n - 1}{n - 1} \cdot p^n \cdot q^k `))))),l(u.a,{title:"Momenti della binomiale negativa traslata"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della binomiale negativa traslata è:"),l("p",null,l(o.a,null,oe(pa||(pa=te`m_X (t) : \left\{ t < ln \left( \frac{1}{q} \right) \right\} = \left( \frac{p \cdot e^t}{1 - q \cdot e^t} \right) ^n`)))),l("p",null,"La ",l("b",null,"media")," della binomiale negativa traslata è:"),l("p",null,l(o.a,null,oe(da||(da=te`E(X) = \frac{n \cdot q}{p}`)))),l("p",null,"La ",l("b",null,"varianza")," della binomiale negativa traslata è:"),l("p",null,l(o.a,null,oe(ma||(ma=te`Var(X) = \frac{n \cdot q}{p^2}`))))))),l(r.a,{title:"Ipergeometrica"},l(u.a,{title:"Distribuzione ipergeometrica"},l("p",null,"Una variabile aleatoria che, sapendo il numero di successi ",l(o.a,null,"K")," e di insuccessi ",l(o.a,null,"N-K"),", conta quanti successi si otterrebbero se se ne estraessero ",l(o.a,null,"n")," in blocco."),l("p",null,"Il suo simbolo è ",l(o.a,null,"Ipe(N, K, n)"),".")),l(u.a,{title:"Densità della ipergeometrica"},l("p",null,"La ipergeometrica ha come densità:"),l("p",null,l(o.a,null,oe(ca||(ca=te`f_X (k) : \{0..n\} \in \mathbb{N} = \frac{\binom{K}{k} \cdot \binom{N - K}{n - k}}{\binom{N}{n}}`))))),l(u.a,{title:"Momenti della ipergeometrica"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della ipergeometrica è trascurabile."),l("p",null,"La ",l("b",null,"media")," della ipergeometrica è:"),l("p",null,l(o.a,null,oe(ba||(ba=te`E(X) = n \cdot \frac{K}{N}`)))),l("p",null,"La ",l("b",null,"varianza")," della ipergeometrica è:"),l("p",null,l(o.a,null,oe(va||(va=te`Var(X) = n \cdot \frac{K}{N} \cdot \frac{N - K}{N} \cdot \frac{N - n}{N - 1}`))))))),l(r.a,{title:"Poissoniana"},l(u.a,{title:"Distribuzione poissoniana"},l("p",null,"Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:"),l("ul",null,l("li",null,"Binomiale: ",l(o.a,null,oe(fa||(fa=te`X \sim Bin(n, p)`)))),l("li",null,"Il numero di prove tende a infinito: ",l(o.a,null,oe(ha||(ha=te`n \to +\infty`)))),l("li",null,"La probabilità di successo tende a 0: ",l(o.a,null,oe(ga||(ga=te`p \to 0`)))),l("li",null,"La media è finita: ",l(o.a,null,oe(_a||(_a=te`E(X) = n \cdot p \to \mu \neq 0`))))),l("p",null,"Il suo simbolo è ",l(o.a,null,oe(za||(za=te`Poi(\mu)`))))),l(u.a,{title:"Densità della poissoniana"},l("p",null,"La poissoniana ha come densità:"),l("p",null,l(o.a,null,oe(Xa||(Xa=te`f_X (k) : \mathbb{N} = \frac{e^{-\mu} \cdot \mu^k}{k!}`))))),l(u.a,{title:"Momenti della poissoniana"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della poissoniana è:"),l("p",null,l(o.a,null,oe(qa||(qa=te`m_X (t) = e^{\mu \cdot (e^t - 1)}`)))),l("p",null,"La ",l("b",null,"media")," della poissoniana è:"),l("p",null,l(o.a,null,oe(Ea||(Ea=te`E(X) = \mu`)))),l("p",null,"La ",l("b",null,"varianza")," della poissoniana è:"),l("p",null,l(o.a,null,oe(La||(La=te`Var(X) = \mu`)))),l("p",null,"Gli altri momenti della poissoniana sono:"),l("ol",{start:2},l("li",null,l(o.a,null,oe(xa||(xa=te`E(X^2) = \mu^2 + \mu`)))))))),l(r.a,{title:"Un altro schema"},l(u.a,{title:"Schema di Poisson"},l("p",null,"Una successione di ",l("b",null,"arrivi")," avvenuti in un certo arco temporale che:"),l("ul",null,l("li",null,"non sono sovrapposti."),l("li",null,"hanno intensità ",l(o.a,null,oe(Pa||(Pa=te`\lambda`)))," costante."),l("li",null,"avvengono indipendentemente gli uni dagli altri."))),l(u.a,{title:"Processo di Poisson"},l("p",null,"Una variabile aleatoria ",l(o.a,null,"N_t")," che conta il numero di arrivi di uno schema di Poisson di intensità ",l(o.a,null,oe(ka||(ka=te`\lambda`)))," in un intervallo di tempo di durata ",l(o.a,null,"t"),"."),l("p",null,"E' una distribuzione poissoniana con ",l(o.a,null,oe(Fa||(Fa=te`\mu = t \cdot \lambda`))),": ",l(o.a,null,oe(ya||(ya=te`Poi(t \cdot \lambda)`)))),l(s.a,null,"E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo)."))),l(r.a,{title:"Esponenziale"},l(u.a,{title:"Distribuzione esponenziale"},l("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità ",l(o.a,null,oe(Sa||(Sa=te`\lambda`))),"."),l("p",null,"Il suo simbolo è ",l(o.a,null,oe(Ca||(Ca=te`Esp(\lambda)`))),".")),l(u.a,{title:"Densità dell'esponenziale"},l("p",null,"L'esponenziale ha come ",l("b",null,"densità"),":"),l("p",null,l(o.a,null,oe(Ia||(Ia=te`f_X (x) = \begin{cases}
+                            0 \qquad \qquad x < 0\\
+                            \lambda \cdot e^{-\lambda \cdot x} \quad x > 0
+                            \end{cases}`)))),l("p",null,"L'esponenziale ha come ",l("b",null,"funzione di ripartizione"),":"),l("p",null,l(o.a,null,oe(Na||(Na=te`F_X (t) = \begin{cases}
+                            0 \qquad \qquad t < 0\\
+                            1 - e^{-\lambda \cdot t} \quad t \geq 0
+                            \end{cases}`))))),l(u.a,{title:"Momenti dell'esponenziale"},l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," dell'esponenziale è:"),l("p",null,l(o.a,null,oe(Va||(Va=te`m_X (t) : \{ t | t < \lambda \} \in \mathbb{R} = \frac{\lambda}{\lambda - t}`)))),l("p",null,"La ",l("b",null,"media")," dell'esponenziale è:"),l("p",null,l(o.a,null,oe(Ya||(Ya=te`E(X) = \frac{1}{\lambda}`)))),l("p",null,"La ",l("b",null,"varianza")," dell'esponenziale è:"),l("p",null,l(o.a,null,oe(wa||(wa=te`Var(X) = \frac{1}{\lambda^2}`))))),l(u.a,{title:"Assenza di memoria della esponenziale"},l("p",null,"L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:"),l("p",null,l(o.a,null,oe(Da||(Da=te`P([X > s + t | X > s]) = P([X > t])`)))),l(s.a,null,"Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X."))),l(r.a,{title:"Legge gamma"},l(u.a,{title:"Distribuzione gamma"},l("p",null,"Una variabile aleatoria che conta il tempo diwidehattesa prima dell'",l(o.a,null,"n"),"-esimo arrivo di un processo di Poisson di intensità ",l(o.a,null,oe(Ua||(Ua=te`\lambda`))),"."),l("p",null,"Il suo simbolo è ",l(o.a,null,oe(Ma||(Ma=te`\Gamma(n, \lambda)`))),".")),l(u.a,{title:"Densità della legge gamma"},l("p",null,"La legge gamma ha come densità:"),l("p",null,l(o.a,null,oe(Ba||(Ba=te`f_X (x) = \begin{cases}
+                            0 \qquad \qquad \qquad \qquad \qquad x < 0\\
+                            \frac{1}{(n-1)!} \cdot \lambda^n \cdot x^{n-1} \cdot e^{-\lambda \cdot x} \quad k > 0
+                            \end{cases}`))))),l(u.a,{title:"Momenti della legge gamma"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della legge gamma è:"),l("p",null,l(o.a,null,oe(Aa||(Aa=te`m_X (t) : ( t < \lambda ) \in \mathbb{R} = \left( \frac{\lambda}{\lambda - t} \right) ^\alpha`)))),l("p",null,"La ",l("b",null,"media")," della legge gamma è:"),l("p",null,l(o.a,null,oe(Ga||(Ga=te`E(X) = \frac{\alpha}{\lambda}`)))),l("p",null,"La ",l("b",null,"varianza")," della legge gamma è:"),l("p",null,l(o.a,null,oe(Ta||(Ta=te`Var(X) = \frac{\alpha}{\lambda^2}`))))))),l(r.a,{title:"Uniforme"},l(u.a,{title:"Distribuzione uniforme"},l("p",null,"Una variabile aleatoria che può assumere qualsiasi valore in un intervallo ",l(o.a,null,oe(Qa||(Qa=te`[a, b]`)))," in modo equiprobabile."),l("p",null,"Il suo simbolo è ",l(o.a,null,oe(Oa||(Oa=te`Uni(a, b)`)))),l("p",null,"Su di essa vale la seguente proprietà:"),l("p",null,l(o.a,null,oe(Ra||(Ra=te`P(X \in (c, d)) = \frac{d - c}{b - a}`))))),l(u.a,{title:"Densità della distribuzione uniforme"},l("p",null,"La distribuzione uniforme ha come ",l("b",null,"densità"),":"),l("p",null,l(o.a,null,oe(ja||(ja=te`f_X (x) = \begin{cases}
+                                \frac{1}{b - a} \qquad a \leq x \leq b\\
+                                0 \qquad \quad altrimenti    
+                            \end{cases}`)))),l("p",null,"La distribuzione uniforme ha come ",l("b",null,"funzione di ripartizione"),":"),l("p",null,l(o.a,null,oe(Ka||(Ka=te`f_X (x) = \begin{cases}
+                                0 \qquad \quad x < a  
+                                \frac{1}{b - a} \qquad a \leq x \leq b\\
+                                1 \qquad \quad x > b
+                            \end{cases}`))))),l(u.a,{title:"Momenti della distribuzione uniforme"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della distribuzione uniforme è:"),l("p",null,l(o.a,null,oe(Wa||(Wa=te`m_X (t) = \frac{e^{b \cdot t} - e^{a \cdot t}}{(b - a) \cdot t}`)))),l("p",null,"La ",l("b",null,"media")," della distribuzione uniforme è:"),l("p",null,l(o.a,null,oe(Za||(Za=te`E(X) = \frac{a + b}{2}`)))),l("p",null,"La ",l("b",null,"varianza")," della distribuzione uniforme è:"),l("p",null,l(o.a,null,oe(Ja||(Ja=te`Var(X) = \frac{(b - a)^2}{12}`))))))),l(r.a,{title:"Normale o Gaussiana"},l(u.a,{title:"Distribuzione normale"},l("p",null,"Una variabile aleatoria con una specifica distribuzione."),l("p",null,"Il suo simbolo è ",l(o.a,null,oe(Ha||(Ha=te`Nor(\mu, \sigma^2)`))),"."),l(s.a,null,l(o.a,null,"\\mu")," e ",l(o.a,null,"\\sigma^2")," sono rispettivamente la media e la varianza della distribuzione!")),l(u.a,{title:"Densità della distribuzione normale"},l("p",null,"La distribuzione normale ha come densità:"),l("p",null,l(o.a,null,oe($a||($a=te`f_X (x) = \frac{e^{-\frac{(x - \mu)^2}{2 \sigma^2}}}{\sqrt{2 \pi \cdot \sigma^2}}`))))),l(u.a,{title:"Momenti della distribuzione normale"},l("p",null,l("p",null,"La ",l("b",null,"funzione generatrice dei momenti")," della distribuzione normale è:"),l("p",null,l(o.a,null,oe(li||(li=te`m_X (t) = e^{\mu \cdot t + \frac{\sigma^2 \cdot t^2}{2}}`)))),l("p",null,"La ",l("b",null,"media")," della distribuzione normale è:"),l("p",null,l(o.a,null,oe(ai||(ai=te`E(X) = \mu`)))),l("p",null,"La ",l("b",null,"varianza")," della distribuzione normale è:"),l("p",null,l(o.a,null,oe(ii||(ii=te`Var(X) = \sigma^2`))))))),l(r.a,null,l(u.a,{title:"Trasformazione della normale"},l("p",null,"Qualsiasi normale può essere trasformata in qualsiasi altra normale:"),l("p",null,l(o.a,null,oe(ni||(ni=te`X \sim Nor(m, v^2) \implies \alpha X + \beta \sim Nor(\alpha m + \beta, (\alpha v)^2)`))))),l(u.a,{title:"Normale standard"},l("p",null,"La distribuzione normale standard ",l(o.a,null,"Z")," è:"),l("p",null,l(o.a,null,"Z \\sim Nor(0, 1)")),l("p",null,"La sua funzione di ripartizione è detta ",l(o.a,null,oe(ei||(ei=te`\phi(z)`)))," e vale:"),l("p",null,l(o.a,null,oe(ti||(ti=te`F_Z(z) = \phi(z) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{z} e^{-\frac{x^2}{2}} dx`))))),l(u.a,{title:"Quantili normali"},l("p",null,"Da un quantile ",l(o.a,null,oe(oi||(oi=te`z_\alpha`)))," della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:"),l("p",null,l(o.a,null,oe(ui||(ui=te`x_\alpha = \mu + z_\alpha \cdot \sqrt{\sigma^2}`)))))),l(r.a,null,l(u.a,{title:"Gamma e normale"},l("p",null,"La distribuzione normale ha una particolare relazione con la distribuzione Gamma:"),l("p",null,l(o.a,null,oe(ri||(ri=te`Z^2 \sim \chi^2 (v = 1)`))))),l(u.a,{title:"La funzione Chi"},l("blockquote",null,'"chi-quadro a un grado di libertà"'),l("p",null,"Esiste una distribuzione Gamma particolare:"),l("p",null,l(o.a,null,oe(si||(si=te`\Gamma \left( \frac{1}{2}, \frac{1}{2} \right) = \chi^2 (v = 1)`)))),l("p",null,"Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:"),l("p",null,l(o.a,null,oe(pi||(pi=te`\chi^2 (n) + \chi^2 (m) = \chi^2 (n + m)`))))),l(u.a,{title:"T di Student"},l("p",null,"Un'altra funzione particolare è la funzione T di Student:"),l("p",null,l(o.a,null,oe(di||(di=te`T(v) = \frac{Nor(0, 1)}{\sqrt{\frac{\chi^2(v)}{v}}}`)))))),l(r.a,{title:"Approssimazioni notevoli"},l(u.a,{title:"Ipergeometrica e binomiale"},l("p",null,"La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di ",l(o.a,null,"N")," rispetto a ",l(o.a,null,"n"),", si può dire che:"),l("p",null,l(o.a,null,oe(mi||(mi=te`Ipe(N, K, n) \approx Bin(n, \frac{K}{N})`))))),l(u.a,{title:"Binomiale e poissoniana"},l("p",null,"La binomiale non è altro che una poissoniana a tempo discreto, quindi, se ",l(o.a,null,"n")," è grande e ",l(o.a,null,"n \\cdot p")," è nell'ordine di grandezza delle unità, allora:"),l("p",null,l(o.a,null,oe(ci||(ci=te`Bin(n, p) \approx Poi(n \cdot p)`))))),l(u.a,{title:"Binomiale e normale"},l("p",null,"Per il Teorema di De Moivre-Laplace, se una binomiale ha una ",l(o.a,null,"n")," grande e ",l(o.a,null,"p")," non vicina a 0 o 1, si può approssimare con:"),l("p",null,l(o.a,null,oe(bi||(bi=te`Bin(n, p) \approx Nor(n \cdot p, n \cdot p \cdot q)`))))),l(u.a,{title:"Correzione di Yates"},l("p",null,"Passando da una variabile discreta ",l(o.a,null,"X")," a una continua ",l(o.a,null,"Y"),", per ogni valore discreto ",l(o.a,null,"k"),' la probabilità viene "spalmata" su tutto l\'intervallo ',l(o.a,null,oe(vi||(vi=te`(k - \frac{1}{2}, k + \frac{1}{2})`))),":"),l("ul",null,l("li",null,l(o.a,null,oe(fi||(fi=te`P(X < k) \simeq P(Y \leq k - \frac{1}{2})`)))),l("li",null,l(o.a,null,oe(hi||(hi=te`P(X \leq k) \simeq P(Y \leq k + \frac{1}{2})`)))),l("li",null,l(o.a,null,oe(gi||(gi=te`P(X \geq k) \simeq P(Y \geq k - \frac{1}{2})`)))),l("li",null,l(o.a,null,oe(_i||(_i=te`P(X > k) \simeq P(Y \geq k + \frac{1}{2})`))))))),l(r.a,{title:"Vettori aleatori"},l(u.a,{title:"Vettore aleatorio"},l("p",null,"Un vettore ",l("b",null,"composto da variabili aleatorie"),"."),l("p",null,"Il suo simbolo generalmente è ",l(o.a,null,oe(zi||(zi=te`\boldsymbol{X}`)))," oppure ",l(o.a,null,oe(Xi||(Xi=te`X, Y`))),".")),l(u.a,{title:"Funzioni di ripartizione"},l("p",null,"I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri."),l("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"funzione di ripartizione congiunta"),":"),l("p",null,l(o.a,null,oe(qi||(qi=te`F_{X, Y} (x, y) = P(X \leq x, Y \leq y)`)))),l("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"funzione di ripartizione marginale"),":"),l("p",null,l(o.a,null,oe(Ei||(Ei=te`F_X (x) = P(X \leq x) = \lim_{y \to +\infty} F_{X, Y} (x, y)`))))),l(u.a,{title:"Densità discreta"},l("p",null,"I vettori aleatori ",l("b",null,"discreti")," hanno più densità che si differenziano in base al numero di parametri."),l("p",null,"Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"densità congiunta"),":"),l("p",null,l(o.a,null,oe(Li||(Li=te`p_{X, Y} (x, y) = P(X = x, Y = y)`)))),l("p",null,"Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una ",l("i",null,"densità marginale"),":"),l("p",null,l(o.a,null,oe(xi||(xi=te`p_X (x) = \sum_j p_{X, Y} (x_i, y_j)`)))))),l(r.a,{title:"Più variabili aleatorie"},l(u.a,{title:"Indipendenza delle variabili aleatorie"},l("p",null,"Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli ",l(o.a,null,"A_i"),":"),l("p",null,l(o.a,null,oe(Pi||(Pi=te`P(X_1 \in A_1, \dots, X_n \in A_n) = P(X_1 \in A_1) \times \dots \times P(X_n \in A_n)`))))),l(u.a,{title:"Media dei vettori aleatori"},l("p",null,"E' possibile calcolare la media di qualsiasi funzione ",l(o.a,null,"g(X, Y)")," avente elementi del vettore come variabili:"),l("p",null,l(o.a,null,oe(ki||(ki=te`E(g(X, Y)) = \sum_{i, j} g(x_i, y_i) \cdot p_{X, Y} (x_i, y_i)`)))),l(s.a,null,"Solitamente si calcola la media di ",l(o.a,null,"x \\cdot y"),"."),l("p",null,"Le medie di più variabili aleatorie si possono sommare:"),l("p",null,l(o.a,null,oe(Fi||(Fi=te`E(X + Y) = E(X) + E(Y)`)))))),l(r.a,null,l(u.a,{title:"Covarianza"},l("p",null,"Un ",l("b",null,"operatore")," che misura la correlazione di due variabili aleatorie."),l("p",null,"Si calcola con il valore atteso dei prodotti delle distanze dalla media:"),l("p",null,l(o.a,null,oe(yi||(yi=te`Cov(X, Y) = E((X - E(X) \cdot (Y - E(Y)) = E(XY) - E(X) \cdot E(Y)`)))),l("p",null,"Ha diverse proprietà:"),l("ul",null,l("li",null,"Il suo ",l("b",null,"valore nullo")," è 0: ",l(o.a,null,oe(Si||(Si=te`Cov(X, \alpha) = 0`)))),l("li",null,"E' ",l("b",null,"commutativa"),": ",l(o.a,null,oe(Ci||(Ci=te`Cov(X, Y) = Cov(Y, X)`)))),l("li",null,"E' ",l("b",null,"semplificabile"),": ",l(o.a,null,oe(Ii||(Ii=te`Cov(X, X) = Var(X)`)))),l("li",null,"E' ",l("b",null,"lineare"),": ",l(o.a,null,oe(Ni||(Ni=te`Cov(\alpha X, \beta Y) = \alpha \cdot \beta \cdot Cov(X, Y)`)))),l("li",null,"E' ",l("b",null,"distributiva"),": ",l(o.a,null,oe(Vi||(Vi=te`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`)))))),l(u.a,{title:"Variabili incorrelate"},l("p",null,"Due variabili sono ",l("i",null,"variabili incorrelate")," se:"),l("p",null,l(o.a,null,oe(Yi||(Yi=te`Cov(X, Y) = 0`)))),l("p",null,"Variabili indipendenti sono sempre incorrelate.")),l(u.a,{title:"Matrice di covarianza"},l("p",null,"Una matrice ",l(o.a,null,oe(wi||(wi=te`\boldsymbol{C_X}`)))," che contiene la covarianza tra tutte le variabili di un vettore aleatorio ",l(o.a,null,oe(Di||(Di=te`\boldsymbol{X}`))),":"),l("p",null,l(o.a,null,oe(Ui||(Ui=te`
+                                \boldsymbol{C_X} = 
+                                \begin{bmatrix}
+                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\
+                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\
+                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)
+                                \end{bmatrix}
+                            `)))),l("p",null,"E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono ",l(o.a,null,"\\geq 0"),".")),l(u.a,{title:"Coefficiente di correlazione"},l("p",null,"Un valore che misura come due variabili aleatorie sono correlate:"),l("p",null,l(o.a,null,oe(Mi||(Mi=te`\rho_{X, Y} = \frac{Cov(X, Y)}{\sqrt{Var(X)} \cdot \sqrt{Var(Y)}}`)))),l("p",null,"E' sempre compreso tra -1 e 1:"),l("p",null,l(o.a,null,oe(Bi||(Bi=te`-1 \leq \rho_{X, Y} \leq 1`)))),l("p",null,"Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:"),l("p",null,l(o.a,null,oe(Ai||(Ai=te`Y = a X + b \Longleftrightarrow | \rho_{X, Y} | = 1`))))),l(u.a,{title:"Varianza di variabili aleatorie sommate"},l("p",null,"La varianza di due variabili aleatorie sommate è:"),l("p",null,l(o.a,null,oe(Gi||(Gi=te`Var(X + Y) = Var(X) + Var(Y) + 2 \cdot Cov(X, Y)`)))),l(s.a,null,"Si dimostra applicando le proprietà della covarianza!"),l("p",null,"Se più variabili aleatorie ",l(o.a,null,"X_i")," sono ",l("b",null,"indipendenti")," (",l(o.a,null,oe(Ti||(Ti=te`Cov(X, Y) = 0`))),"), allora:"),l("p",null,l(o.a,null,oe(Qi||(Qi=te`Var \left( \sum_i X_i \right) = \sum_i Var(X_i)`)))))),l(r.a,{title:"Campioni"},l(u.a,{title:"Campione casuale"},l("p",null,"Una ",l("b",null,"n-pla")," di variabili aleatorie con la stessa distribuzione della variabile aleatoria ",l(o.a,null,"X"),' ("popolazione") ma ',l("b",null,"indipendenti")," tra loro."),l(s.a,null,"Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si ",l("b",null,"realizzeranno")," nel loro valore.")),l(u.a,{title:"Momento campionario"},l("p",null,"Il valore dato dalla media aritmetica degli ",l(o.a,null,"n")," elementi del campione elevati alla potenza ",l(o.a,null,"k"),":"),l("p",null,l(o.a,null,oe(Oi||(Oi=te`M^{(k)}_n = \frac{1}{n} \cdot \sum_{i = 1}^n X_i^k `)))),l("p",null,"Il momento campionario di primo ordine è la ",l("i",null,"media campionaria")," ",l(o.a,null,oe(Ri||(Ri=te`\overline{X}_n`))),".")),l(u.a,{title:"Varianza campionaria"},l("p",null,"La media aritmetica dello scarto quadratico medio degli elementi del campione."),l("p",null,"Se è noto il valore medio ",l(o.a,null,oe(ji||(ji=te`m = E(X)`)))," di X:"),l("p",null,l(o.a,null,oe(Ki||(Ki=te`S_0^2 = \frac{1}{n} \cdot \sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \cdot m \cdot \overline{X}_n + m^2`)))),l("p",null,"Altrimenti:"),l("p",null,l(o.a,null,oe(Wi||(Wi=te`S_n^2 = \frac{1}{n - 1} \cdot \sum_{i = 1}^n (X_i - \overline{X}_n)^2 = \frac{1}{n - 1} \cdot ( n \cdot M_2^{(2)} - n \cdot \overline{X}_n^2)`)))))),l(r.a,{title:"Media-ception"},l(u.a,{title:"Media campionaria"},l("p",null,"Se calcoliamo la media della media campionaria, risulterà vero che:"),l("p",null,l(o.a,null,oe(Zi||(Zi=te`E(\overline{X}_n) = E(X)`)))),l(s.a,null,"Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!")),l(u.a,{title:"Varianza campionaria"},l("p",null,"Se calcoliamo la varianza della media campionaria, risulterà vero che:"),l("p",null,l(o.a,null,oe(Ji||(Ji=te`Var(\overline{X}_n) = \frac{Var(X)}{n}`)))),l(s.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!")),l(u.a,{title:"Correzione campionaria"},l("p",null,"Se calcoliamo la media della varianza campionaria, risulterà vero che:"),l("p",null,l(o.a,null,oe(Hi||(Hi=te`E(S_0^2) = E(S_n^2) = Var(X)`)))),l(s.a,null,"Quindi, possiamo stimare l'errore della media calcolata tramite campioni!"))),l(r.a,{title:"Campionamento di una distribuzione normale"},l(u.a,{title:"Campionamento di una distribuzione normale"},l("p",null,"Se la popolazione ",l(o.a,null,"X")," ha una distribuzione normale (",l(o.a,null,oe($i||($i=te`X \sim Nor(\mu, \sigma^2)`))),")...")),l(u.a,{title:"Distribuzione della media campionaria"},l("p",null,"...allora sappiamo anche la distribuzione della media campionaria!"),l("p",null,l(o.a,null,oe(ln||(ln=te`\overline{X}_n \sim Nor \left( \mu, \frac{\sigma^2}{n} \right)`))))),l(u.a,{title:"Distribuzione della varianza campionaria"},l("p",null,"...e anche della varianza campionaria!"),l("p",null,l(o.a,null,oe(an||(an=te`S_0^2 \sim \frac{\sigma^2}{n} \cdot \chi^2 (n)`)))),l("p",null,l(o.a,null,oe(nn||(nn=te`S_n^2 \sim \frac{\sigma^2}{n - 1} \cdot \chi^2 (n-1)`))))),l(u.a,{title:"Indipendenza"},l("p",null,"...e che media campionaria e varianza campionaria sono indipendenti tra loro!"))),l(r.a,{title:"Quando i campioni hanno dimensioni infinite"},l(u.a,{title:"Convergenza in distribuzione"},l("p",null,"Se la successione di variabili aleatorie ",l(o.a,null,"X_n")," all'infinito ha la ",l("b",null,"stessa funzione di ripartizione")," della popolazione ",l(o.a,null,"X"),", allora essa ",l("i",null,"converge in distribuzione"),"."),l("p",null,l(o.a,null,"\\lim_{n \\to +\\infty} F_{X_n} (x) = F_X (x) \\implies X_n \\xrightarrow{d} X"))),l(u.a,{title:"Convergenza in probabilità"},l("p",null,"Se la successione di variabili aleatorie ",l(o.a,null,"X_n")," all'infinito ha la ",l("b",null,"stessa probabilità")," della popolazione ",l(o.a,null,"X"),", allora essa ",l("i",null,"converge in probabilità"),"."),l("p",null,l(o.a,null,"\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | X_n - X | < \\epsilon) = 1 \\implies X_n \\xrightarrow{p} X"))),l(u.a,{title:"Convergenza quasi certa"},l("p",null,"Se la successione di variabili aleatorie ",l(o.a,null,"X_n")," all'infinito ha la ",l("b",null,"stessa probabilità a ")," della popolazione ",l(o.a,null,"X"),", allora essa ",l("i",null,"converge quasi certamente"),"."),l("p",null,l(o.a,null,"\\forall \\epsilon > 0, P left( \\lim_{n \\to +\\infty} | X_n - X | < \\epsilon) \right) = 1 \\implies X_n \\xrightarrow{qc} X"))),l(u.a,{title:"Convergenza in media quadratica"},l("p",null,"Se la successione di variabili aleatorie ",l(o.a,null,"X_n")," all'infinito ha la ",l("b",null,"media del quadrato della distanza")," tra la successione e la popolazione ",l(o.a,null,"X")," ",l("b",null,"uguale a 0"),", allora essa ",l("i",null,"converge in media quadratica"),"."),l("p",null,l(o.a,null,"\\lim_{n \\to +\\infty} E( | X_n - X |^2 = 0 \\implies X_n \\xrightarrow{mq} X"))),l(u.a,{title:"Gerarchia delle convergenze"},l("p",null,l(o.a,null,"\n                                \\begin{matrix}\n                                X_n \\xrightarrow{mq} X\\\\\n                                X_n \\xrightarrow{qc} X\n                                \\end{matrix} \\implies X_n \\xrightarrow{p} X \\implies X_n \\xrightarrow{d} X")),l("p",null,"In più:"),l("p",null,l(o.a,null,"X_n \\xrightarrow{p} x \\Longleftrightarrow X_n \\xrightarrow{d} x")))),l(r.a,{title:"I grandi numeri"},l(u.a,{title:"Legge debole dei grandi numeri"},l("p",null,"La successione delle medie campionarie ",l(o.a,null,oe(en||(en=te`\overline{X}_n`)))," ",l("b",null,"converge in probabilità")," alla media della popolazione ",l(o.a,null,oe(tn||(tn=te`E(X)`))),", se essa esiste."),l("p",null,l(o.a,null,"\\overline{X}_n \\xrightarrow{p} X")),l("p",null,"Ovvero:"),l("p",null,l(o.a,null,oe(on||(on=te`\forall \epsilon > 0, \lim_{n \to +\infty} P( | \overline{X}_n - E(X) | < \epsilon) = 1`)))),l("p",null,l(o.a,null,oe(un||(un=te`P( | \overline{X}_n - E(X) | < \epsilon) \to 1`))))),l(u.a,{title:"Legge forte dei grandi numeri"},l("p",null,"La successione delle medie campionarie ",l(o.a,null,oe(rn||(rn=te`\overline{X}_n`)))," ",l("b",null,"converge quasi certamente")," alla media della popolazione ",l(o.a,null,oe(sn||(sn=te`E(X)`))),", se essa esiste."),l("p",null,l(o.a,null,"\\overline{X}_n \\xrightarrow{qc} X")),l("p",null,"Ovvero:"),l("p",null,l(o.a,null,oe(pn||(pn=te`\forall \epsilon > 0, P \left( \lim_{n \to +\infty} | \overline{X}_n - E(X) | < \epsilon \right) = 1`)))),l(s.a,null,"Dimostra che l'interpretazione frequentista della probabilità è valida!"))),l(r.a,{title:"Al limite"},l(u.a,{title:"Teorema centrale del limite"},l("p",null,"La successione delle medie campionarie ",l(o.a,null,oe(dn||(dn=te`\overline{X}_n`)))," ",l("b",null,"converge in distribuzione")," a ",l(o.a,null,oe(mn||(mn=te`Nor(0, 1) = \Phi()`))),"."),l("p",null,l(o.a,null,oe(cn||(cn=te`\overline{X}_n \approx Nor \left(E(X), \frac{Var(X)}{n} \right)`)))),l("p",null,"Ovvero:"),l("p",null,l(o.a,null,oe(bn||(bn=te`\forall x \in \mathbb{R}, \lim_{n \to +\infty} P \left( \frac{\overline{X}_n - E(X)}{\sqrt{\frac{Var(X)}{n}}} \leq x \right) = \Phi(x)`)))))),l(r.a,{title:"Altre approsimazioni"},l(u.a,{title:"Binomiale e normale"},l("p",null,"E' una somma di ",l("b",null,"bernoulliane"),", e quindi si approssima a una normale:"),l("p",null,l(o.a,null,oe(vn||(vn=te`Bin(n, p) \approx Nor(n \cdot p, n \cdot p \cdot q)`))))),l(u.a,{title:"Binomiale negativa e normale"},l("p",null,"E' una somma di ",l("b",null,"geometriche"),", e quindi si approssima a una normale:"),l("p",null,l(o.a,null,oe(fn||(fn=te`\overline{Bin} (n, p) \approx Nor \left( \frac{n}{p}, \frac{n \cdot (1 - p)}{p^2} \right)`))))),l(u.a,{title:"Poissoniana e normale"},l("p",null,"E' una somma di altre ",l("b",null,"poissoniane"),", e quindi si approssima a una normale:"),l("p",null,l(o.a,null,oe(hn||(hn=te`Poi(\lambda) \approx Nor(\lambda, \lambda)`))))),l(u.a,{title:"Gamma e normale"},l("p",null,"E' una somma di ",l("b",null,"esponenziali"),", e quindi si approssima a una normale:"),l("p",null,l(o.a,null,oe(gn||(gn=te`\Gamma (\alpha, \lambda) \approx Nor \left( \frac{\alpha}{\lambda}, \frac{\alpha}{\lambda^2} \right)`))))),l(u.a,{title:"In generale"},l("p",null,"Se ",l(o.a,null,"n")," è grande, allora:"),l("p",null,l(o.a,null,oe(_n||(_n=te`Y = \sum_{i=1}^{n} X_i`)))))),l(r.a,{title:"Actually statistica"},l(u.a,{title:"Parametri sconosciuti"},l("p",null,"Per indicare parametri sconosciuti di una legge si usa ",l(o.a,null,"\\theta"),".")),l(u.a,{title:"Statistica"},l("p",null,"Una variabile aleatoria funzione di un campione:"),l("p",null,l(o.a,null,oe(zn||(zn=te`T(\boldsymbol{X})`)))),l(s.a,null,"Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso ",l(o.a,null,oe(Xn||(Xn=te`T(\boldsymbol{X}) = \boldsymbol{X}`))),"."))),l(r.a,{title:"Stimatori"},l(u.a,{title:"Stimatore"},l("p",null,"Una statistica ",l(o.a,null,"T_n")," ottenuta da ",l(o.a,null,"n")," osservazioni, che stimi i parametri di una legge e sia indipendente da essi.")),l(u.a,{title:"Corretto"},l("p",null,"Uno stimatore è ",l("i",null,"corretto")," se il suo valore atteso coincide con quello dei parametri che stima:"),l("p",null,l(o.a,null,oe(qn||(qn=te`E(T_n) = \theta`))))),l(u.a,{title:"Asintoticamente corretto"},l("p",null,"Uno stimatore è ",l("i",null,"asintoticamente corretto")," se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:"),l("p",null,l(o.a,null,oe(En||(En=te`\lim_{n \to +\infty} E(T_n) = \theta`))))),l(u.a,{title:"Consistente in media quadratica"},l("p",null,"Uno stimatore è ",l("i",null,"consistente in media quadratica")," se:"),l("p",null,l(o.a,null,oe(Ln||(Ln=te`\lim_{n \to +\infty} E((T_n - \theta)^2) = 0`))))),l(u.a,{title:"Consistente in probabilità"},l("p",null,"Uno stimatore è ",l("i",null,"consistente in probabilità")," se:"),l("p",null,l(o.a,null,oe(xn||(xn=te`\forall \epsilon > 0, \lim_{n \to +\infty} P( |T_n - \theta| < \epsilon) = 1`))))),l(u.a,{title:"Asintoticamente normale"},l("p",null,"Uno stimatore è ",l("i",null,"asintoticamente normale")," se:"),l("p",null,l(o.a,null,oe(Pn||(Pn=te`\lim_{n \to +\infty} \frac{T_n - E(T_n)}{\sqrt{Var(T_n)}} \sim Nor(0, 1)`)))))),l(r.a,{title:"Metodo dei momenti"},l(u.a,{title:"Metodo dei momenti"},l("p",null,"Si può usare il ",l("i",null,"metodo dei momenti")," per ottenere uno stimatore di una popolazione ",l(o.a,null,"X"),"."),l("p",null,"Lo stimatore di ",l(o.a,null,oe(kn||(kn=te`\theta`)))," così ottenuto sarà indicato aggiungendo un cappellino e una ",l(o.a,null,"M")," a ",l(o.a,null,"\\theta"),": ",l(o.a,null,oe(Fn||(Fn=te`\widehat{\theta}_M`)))),l("p",null,"Visto che:"),l("ul",null,l("li",null,l(o.a,null,oe(yn||(yn=te`\theta = g(E(X))`)))),l("li",null,l(o.a,null,oe(Sn||(Sn=te`\widehat{E(X)} = \overline{X}_n`))))),l("p",null,"Allora:"),l("p",null,l(o.a,null,oe(Cn||(Cn=te`\widehat{\theta}_M = g( \overline{X}_n )`)))),l("p",null,"Se ",l(o.a,null,oe(In||(In=te`\theta`)))," non è esprimibile in termini di ",l(o.a,null,oe(Nn||(Nn=te`E(X)`))),", si possono usare i momenti successivi ",l(o.a,null,oe(Vn||(Vn=te`M_n^2`))),", ",l(o.a,null,oe(Yn||(Yn=te`M_n^3`))),", ",l(o.a,null,oe(wn||(wn=te`M_n^3`))),"..."))),l(r.a,{title:"Metodo della massima verosomiglianza"},l(u.a,{title:"Metodo della massima verosomiglianza"},l("p",null,"Si può usare il ",l("i",null,"metodo della massima verosomiglianza")," per ottenere uno stimatore di una popolazione ",l(o.a,null,"X"),"."),l("p",null,"Lo stimatore di ",l(o.a,null,oe(Dn||(Dn=te`\theta`)))," così ottenuto sarà indicato aggiungendo un cappellino e una ",l(o.a,null,"L")," a ",l(o.a,null,"\\theta"),": ",l(o.a,null,oe(Un||(Un=te`\widehat{\theta}_L`)))),l("p",null,"Consiste nel trovare il massimo assoluto ",l(o.a,null,oe(Mn||(Mn=te`\widehat{\theta}_L`)))," della la funzione di verosomiglianza ",l(o.a,null,oe(Bn||(Bn=te`L`))),":"),l("p",null,l(o.a,null,oe(An||(An=te`L(x_1, ..., x_n; \theta) = \prod_{i=1}^n f_X(x_i; \theta)`)))),l("p",null,"Gli stimatori di massima verosomiglianza sono ",l("b",null,"asintoticamente corretti"),", ",l("b",null,"consistenti in probabilità")," e ",l("b",null,"asintoticamente normali"),".")),l(u.a,{title:"Proprietà degli stimatori di massima verosomiglianza"},l("p",null,"Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:"),l("ul",null,l("li",null,"Sono ",l("b",null,"asintoticamente corretti"),"."),l("li",null,"Sono ",l("b",null,"consistenti in probabilità"),"."),l("li",null,"Sono ",l("b",null,"asintoticamente normali"),"."),l("li",null,"Sono ",l("b",null,"invarianti"),": ",l(o.a,null,oe(Gn||(Gn=te`\widehat{g(\theta)}_L = g(\widehat{\theta}_L)`))))))),l(r.a,{title:"Nuove stime notevoli"},l(u.a,{title:"Stima di una bernoulliana"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(o.a,null,oe(Tn||(Tn=te`\widehat{p}_M = \widehat{p}_L = \overline{X}_n`))))),l(u.a,{title:"Stima di una poissoniana"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(o.a,null,oe(Qn||(Qn=te`\widehat{\mu}_M = \widehat{\mu}_L = \overline{X}_n`))))),l(u.a,{title:"Stima di una esponenziale"},l("p",null,"Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:"),l("p",null,l(o.a,null,oe(On||(On=te`\widehat{\lambda}_M = \widehat{\lambda}_L = \frac{1}{\overline{X}_n}`))))),l(u.a,{title:"Stima di una normale"},l("p",null,"Per il metodo della massima verosomiglianza:"),l("ul",null,l("li",null,l(o.a,null,oe(Rn||(Rn=te`\widehat{\mu}_L = \overline{X}_n`)))),l("br",null),l("li",null,l(o.a,null,oe(jn||(jn=te`\widehat{\sigma^2}_L = \frac{\sum (X_i - \overline{X}_n)^2 }{n}`))))))),l(r.a,{title:"Intervalli di confidenza"},l(u.a,{title:"Confidenza"},l("blockquote",null,'"intervallo di confidenza al 95%"'),l("p",null,"L'intervallo di valori di ",l(o.a,null,"\\theta"),' all\'interno del quale siamo "più o meno sicuri" si trovi il valore effettivo:'),l("p",null,"L'intervallo di confidenza a N della stima ",l(o.a,null,oe(Kn||(Kn=te`\widehat{W}`)))," è l'intervallo ",l(o.a,null,"]a, b[")," tale che:"),l("p",null,l(o.a,null,oe(Wn||(Wn=te`P( a < W < b ) = N`)))),l("p",null,"Può anche essere ",l("b",null,"unilatero")," nel caso limiti la stima in una sola direzione, positiva o negativa."))),l(r.a,{title:"Confidenza nella media di una normale"},l(u.a,{title:"Varianza nota"},l("p",null,"Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",l(o.a,null,"\\alpha"),"% con queste formule:"),l("ul",null,l("li",null,"Intervalli bilateri: ",l(o.a,null,oe(Zn||(Zn=te`\mu \in \left[ \overline{x}_n - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}}, \overline{x}_n + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da sinistra: ",l(o.a,null,oe(Jn||(Jn=te`\mu \in \left( -\infty, \overline{x}_n + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da destra: ",l(o.a,null,oe(Hn||(Hn=te`\mu \in \left[ \overline{x}_n - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\sigma^2}{n}}, +\infty \right)`)))))),l(u.a,{title:"Varianza incognita"},l("p",null,"Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'",l(o.a,null,"\\alpha"),"% con queste formule:"),l("ul",null,l("li",null,"Intervalli bilateri: ",l(o.a,null,oe($n||($n=te`\mu \in \left[ \overline{x}_n - t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}}, \overline{x}_n + t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da sinistra: ",l(o.a,null,oe(le||(le=te`\mu \in \left( -\infty, \overline{x}_n + t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}} \right]`)))),l("li",null,"Intervallo unilatero da destra: ",l(o.a,null,oe(ae||(ae=te`\mu \in \left[ \overline{x}_n - t_{1 - \frac{\alpha}{2}; n-1} \cdot \sqrt{\frac{s_n^2}{n}}, +\infty \right)`))))),l("p",null,l(o.a,null,oe(ie||(ie=te`t_{\alpha, v}`)))," è un quantile della distribuzione di Student di parametro ",l(o.a,null,"v"),"."))),l(r.a,{title:"Confidenza per la proporzione di una bernoulliana"},l(u.a,{title:"Terzo metodo corretto"},l("p",null,"L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:"),l("p",null,l(o.a,null,oe(ne||(ne=te`p \in \left[ \overline{p} - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\overline{p} \cdot (1 - \overline{p})}{n+4}}, \overline{p} + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{\overline{p} \cdot (1 - \overline{p})}{n+4}} \right]`)))))),l(r.a,{title:"Confidenza per la media di qualsiasi popolazione"},l(u.a,{title:"Approssimando con la normale"},l("p",null,"L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:"),l("p",null,l(o.a,null,oe(ee||(ee=te`m \in \left[ \overline{x}_n - z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{s^2_n}{n}}, \overline{x}_n + z_{1 - \frac{\alpha}{2}} \cdot \sqrt{\frac{s^2_n}{n}} \right]`)))))))}}}.call(this,i("hosL").h)}}]);
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",dragon_face:"🐲",dress:"👗",dromedary_camel:"🐪",drooling_face:"🤤",droplet:"💧",drum:"🥁",duck:"🦆",dvd:"📀","e-mail":"📧",eagle:"🦅",ear:"👂",ear_of_rice:"🌾",earth_africa:"🌍",earth_americas:"🌎",earth_asia:"🌏",egg:"🥚",eggplant:"🍆",eight_pointed_black_star:"✴️",eight_spoked_asterisk:"✳️",electric_plug:"🔌",elephant:"🐘",email:"✉️",end:"🔚",envelope_with_arrow:"📩",euro:"💶",european_castle:"🏰",european_post_office:"🏤",evergreen_tree:"🌲",exclamation:"❗️",expressionless:"😑",eye:"👁",eye_speech_bubble:"👁‍🗨",eyeglasses:"👓",eyes:"👀",face_with_head_bandage:"🤕",face_with_thermometer:"🤒",fist_oncoming:"👊",factory:"🏭",fallen_leaf:"🍂",family_man_woman_boy:"👪",family_man_boy:"👨‍👦",family_man_boy_boy:"👨‍👦‍👦",family_man_girl:"👨‍👧",family_man_girl_boy:"👨‍👧‍👦",family_man_girl_girl:"👨‍👧‍👧",family_man_man_boy:"👨‍👨‍👦",family_man_man_boy_boy:"👨‍👨‍👦‍👦",family_man_man_girl:"👨‍👨‍👧",family_man_man_girl_boy:"👨‍👨‍👧‍👦",family_man_man_girl_girl:"👨‍👨‍👧‍👧",family_man_woman_boy_boy:"👨‍👩‍👦‍👦",family_man_woman_girl:"👨‍👩‍👧",family_man_woman_girl_boy:"👨‍👩‍👧‍👦",family_man_woman_girl_girl:"👨‍👩‍👧‍👧",family_woman_boy:"👩‍👦",family_woman_boy_boy:"👩‍👦‍👦",family_woman_girl:"👩‍👧",family_woman_girl_boy:"👩‍👧‍👦",family_woman_girl_girl:"👩‍👧‍👧",family_woman_woman_boy:"👩‍👩‍👦",family_woman_woman_boy_boy:"👩‍👩‍👦‍👦",family_woman_woman_girl:"👩‍👩‍👧",family_woman_woman_girl_boy:"👩‍👩‍👧‍👦",family_woman_woman_girl_girl:"👩‍👩‍👧‍👧",fast_forward:"⏩",fax:"📠",fearful:"😨",feet:"🐾",female_detective:"🕵️‍♀️",ferris_wheel:"🎡",ferry:"⛴",field_hockey:"🏑",file_cabinet:"🗄",file_folder:"📁",film_projector:"📽",film_strip:"🎞",fire:"🔥",fire_engine:"🚒",fireworks:"🎆",first_quarter_moon:"🌓",first_quarter_moon_with_face:"🌛",fish:"🐟",fish_cake:"🍥",fishing_pole_and_fish:"🎣",fist_raised:"✊",fist_left:"🤛",fist_right:"🤜",flags:"🎏",flashlight:"🔦",fleur_de_lis:"⚜️",flight_arrival:"🛬",flight_departure:"🛫",floppy_disk:"💾",flower_playing_cards:"🎴",flushed:"😳",fog:"🌫",foggy:"🌁",football:"🏈",footprints:"👣",fork_and_knife:"🍴",fountain:"⛲️",fountain_pen:"🖋",four_leaf_clover:"🍀",fox_face:"🦊",framed_picture:"🖼",free:"🆓",fried_egg:"🍳",fried_shrimp:"🍤",fries:"🍟",frog:"🐸",frowning:"😦",frowning_face:"☹️",frowning_man:"🙍‍♂️",frowning_woman:"🙍",middle_finger:"🖕",fuelpump:"⛽️",full_moon:"🌕",full_moon_with_face:"🌝",funeral_urn:"⚱️",game_die:"🎲",gear:"⚙️",gem:"💎",gemini:"♊️",ghost:"👻",gift:"🎁",gift_heart:"💝",girl:"👧",globe_with_meridians:"🌐",goal_net:"🥅",goat:"🐐",golf:"⛳️",golfing_man:"🏌️",golfing_woman:"🏌️‍♀️",gorilla:"🦍",grapes:"🍇",green_apple:"🍏",green_book:"📗",green_heart:"💚",green_salad:"🥗",grey_exclamation:"❕",grey_question:"❔",grimacing:"😬",grin:"😁",grinning:"😀",guardsman:"💂",guardswoman:"💂‍♀️",guitar:"🎸",gun:"🔫",haircut_woman:"💇",haircut_man:"💇‍♂️",hamburger:"🍔",hammer:"🔨",hammer_and_pick:"⚒",hammer_and_wrench:"🛠",hamster:"🐹",hand:"✋",handbag:"👜",handshake:"🤝",hankey:"💩",hatched_chick:"🐥",hatching_chick:"🐣",headphones:"🎧",hear_no_evil:"🙉",heart:"❤️",heart_decoration:"💟",heart_eyes:"😍",heart_eyes_cat:"😻",heartbeat:"💓",heartpulse:"💗",hearts:"♥️",heavy_check_mark:"✔️",heavy_division_sign:"➗",heavy_dollar_sign:"💲",heavy_heart_exclamation:"❣️",heavy_minus_sign:"➖",heavy_multiplication_x:"✖️",heavy_plus_sign:"➕",helicopter:"🚁",herb:"🌿",hibiscus:"🌺",high_brightness:"🔆",high_heel:"👠",hocho:"🔪",hole:"🕳",honey_pot:"🍯",horse:"🐴",horse_racing:"🏇",hospital:"🏥",hot_pepper:"🌶",hotdog:"🌭",hotel:"🏨",hotsprings:"♨️",hourglass:"⌛️",hourglass_flowing_sand:"⏳",house:"🏠",house_with_garden:"🏡",houses:"🏘",hugs:"🤗",hushed:"😯",ice_cream:"🍨",ice_hockey:"🏒",ice_skate:"⛸",icecream:"🍦",id:"🆔",ideograph_advantage:"🉐",imp:"👿",inbox_tray:"📥",incoming_envelope:"📨",tipping_hand_woman:"💁",information_source:"ℹ️",innocent:"😇",interrobang:"⁉️",iphone:"📱",izakaya_lantern:"🏮",jack_o_lantern:"🎃",japan:"🗾",japanese_castle:"🏯",japanese_goblin:"👺",japanese_ogre:"👹",jeans:"👖",joy:"😂",joy_cat:"😹",joystick:"🕹",kaaba:"🕋",key:"🔑",keyboard:"⌨️",keycap_ten:"🔟",kick_scooter:"🛴",kimono:"👘",kiss:"💋",kissing:"😗",kissing_cat:"😽",kissing_closed_eyes:"😚",kissing_heart:"😘",kissing_smiling_eyes:"😙",kiwi_fruit:"🥝",koala:"🐨",koko:"🈁",label:"🏷",large_blue_circle:"🔵",large_blue_diamond:"🔷",large_orange_diamond:"🔶",last_quarter_moon:"🌗",last_quarter_moon_with_face:"🌜",latin_cross:"✝️",laughing:"😆",leaves:"🍃",ledger:"📒",left_luggage:"🛅",left_right_arrow:"↔️",leftwards_arrow_with_hook:"↩️",lemon:"🍋",leo:"♌️",leopard:"🐆",level_slider:"🎚",libra:"♎️",light_rail:"🚈",link:"🔗",lion:"🦁",lips:"👄",lipstick:"💄",lizard:"🦎",lock:"🔒",lock_with_ink_pen:"🔏",lollipop:"🍭",loop:"➿",loud_sound:"🔊",loudspeaker:"📢",love_hotel:"🏩",love_letter:"💌",low_brightness:"🔅",lying_face:"🤥",m:"Ⓜ️",mag:"🔍",mag_right:"🔎",mahjong:"🀄️",mailbox:"📫",mailbox_closed:"📪",mailbox_with_mail:"📬",mailbox_with_no_mail:"📭",man:"👨",man_artist:"👨‍🎨",man_astronaut:"👨‍🚀",man_cartwheeling:"🤸‍♂️",man_cook:"👨‍🍳",man_dancing:"🕺",man_facepalming:"🤦‍♂️",man_factory_worker:"👨‍🏭",man_farmer:"👨‍🌾",man_firefighter:"👨‍🚒",man_health_worker:"👨‍⚕️",man_in_tuxedo:"🤵",man_judge:"👨‍⚖️",man_juggling:"🤹‍♂️",man_mechanic:"👨‍🔧",man_office_worker:"👨‍💼",man_pilot:"👨‍✈️",man_playing_handball:"🤾‍♂️",man_playing_water_polo:"🤽‍♂️",man_scientist:"👨‍🔬",man_shrugging:"🤷‍♂️",man_singer:"👨‍🎤",man_student:"👨‍🎓",man_teacher:"👨‍🏫",man_technologist:"👨‍💻",man_with_gua_pi_mao:"👲",man_with_turban:"👳",tangerine:"🍊",mans_shoe:"👞",mantelpiece_clock:"🕰",maple_leaf:"🍁",martial_arts_uniform:"🥋",mask:"😷",massage_woman:"💆",massage_man:"💆‍♂️",meat_on_bone:"🍖",medal_military:"🎖",medal_sports:"🏅",mega:"📣",melon:"🍈",memo:"📝",men_wrestling:"🤼‍♂️",menorah:"🕎",mens:"🚹",metal:"🤘",metro:"🚇",microphone:"🎤",microscope:"🔬",milk_glass:"🥛",milky_way:"🌌",minibus:"🚐",minidisc:"💽",mobile_phone_off:"📴",money_mouth_face:"🤑",money_with_wings:"💸",moneybag:"💰",monkey:"🐒",monkey_face:"🐵",monorail:"🚝",moon:"🌔",mortar_board:"🎓",mosque:"🕌",motor_boat:"🛥",motor_scooter:"🛵",motorcycle:"🏍",motorway:"🛣",mount_fuji:"🗻",mountain:"⛰",mountain_biking_man:"🚵",mountain_biking_woman:"🚵‍♀️",mountain_cableway:"🚠",mountain_railway:"🚞",mountain_snow:"🏔",mouse:"🐭",mouse2:"🐁",movie_camera:"🎥",moyai:"🗿",mrs_claus:"🤶",muscle:"💪",mushroom:"🍄",musical_keyboard:"🎹",musical_note:"🎵",musical_score:"🎼",mute:"🔇",nail_care:"💅",name_badge:"📛",national_park:"🏞",nauseated_face:"🤢",necktie:"👔",negative_squared_cross_mark:"❎",nerd_face:"🤓",neutral_face:"😐",new:"🆕",new_moon:"🌑",new_moon_with_face:"🌚",newspaper:"📰",newspaper_roll:"🗞",next_track_button:"⏭",ng:"🆖",no_good_man:"🙅‍♂️",no_good_woman:"🙅",night_with_stars:"🌃",no_bell:"🔕",no_bicycles:"🚳",no_entry:"⛔️",no_entry_sign:"🚫",no_mobile_phones:"📵",no_mouth:"😶",no_pedestrians:"🚷",no_smoking:"🚭","non-potable_water":"🚱",nose:"👃",notebook:"📓",notebook_with_decorative_cover:"📔",notes:"🎶",nut_and_bolt:"🔩",o:"⭕️",o2:"🅾️",ocean:"🌊",octopus:"🐙",oden:"🍢",office:"🏢",oil_drum:"🛢",ok:"🆗",ok_hand:"👌",ok_man:"🙆‍♂️",ok_woman:"🙆",old_key:"🗝",older_man:"👴",older_woman:"👵",om:"🕉",on:"🔛",oncoming_automobile:"🚘",oncoming_bus:"🚍",oncoming_police_car:"🚔",oncoming_taxi:"🚖",open_file_folder:"📂",open_hands:"👐",open_mouth:"😮",open_umbrella:"☂️",ophiuchus:"⛎",orange_book:"📙",orthodox_cross:"☦️",outbox_tray:"📤",owl:"🦉",ox:"🐂",package:"📦",page_facing_up:"📄",page_with_curl:"📃",pager:"📟",paintbrush:"🖌",palm_tree:"🌴",pancakes:"🥞",panda_face:"🐼",paperclip:"📎",paperclips:"🖇",parasol_on_ground:"⛱",parking:"🅿️",part_alternation_mark:"〽️",partly_sunny:"⛅️",passenger_ship:"🛳",passport_control:"🛂",pause_button:"⏸",peace_symbol:"☮️",peach:"🍑",peanuts:"🥜",pear:"🍐",pen:"🖊",pencil2:"✏️",penguin:"🐧",pensive:"😔",performing_arts:"🎭",persevere:"😣",person_fencing:"🤺",pouting_woman:"🙎",phone:"☎️",pick:"⛏",pig:"🐷",pig2:"🐖",pig_nose:"🐽",pill:"💊",pineapple:"🍍",ping_pong:"🏓",pisces:"♓️",pizza:"🍕",place_of_worship:"🛐",plate_with_cutlery:"🍽",play_or_pause_button:"⏯",point_down:"👇",point_left:"👈",point_right:"👉",point_up:"☝️",point_up_2:"👆",police_car:"🚓",policewoman:"👮‍♀️",poodle:"🐩",popcorn:"🍿",post_office:"🏣",postal_horn:"📯",postbox:"📮",potable_water:"🚰",potato:"🥔",pouch:"👝",poultry_leg:"🍗",pound:"💷",rage:"😡",pouting_cat:"😾",pouting_man:"🙎‍♂️",pray:"🙏",prayer_beads:"📿",pregnant_woman:"🤰",previous_track_button:"⏮",prince:"🤴",princess:"👸",printer:"🖨",purple_heart:"💜",purse:"👛",pushpin:"📌",put_litter_in_its_place:"🚮",question:"❓",rabbit:"🐰",rabbit2:"🐇",racehorse:"🐎",racing_car:"🏎",radio:"📻",radio_button:"🔘",radioactive:"☢️",railway_car:"🚃",railway_track:"🛤",rainbow:"🌈",rainbow_flag:"🏳️‍🌈",raised_back_of_hand:"🤚",raised_hand_with_fingers_splayed:"🖐",raised_hands:"🙌",raising_hand_woman:"🙋",raising_hand_man:"🙋‍♂️",ram:"🐏",ramen:"🍜",rat:"🐀",record_button:"⏺",recycle:"♻️",red_circle:"🔴",registered:"®️",relaxed:"☺️",relieved:"😌",reminder_ribbon:"🎗",repeat:"🔁",repeat_one:"🔂",rescue_worker_helmet:"⛑",restroom:"🚻",revolving_hearts:"💞",rewind:"⏪",rhinoceros:"🦏",ribbon:"🎀",rice:"🍚",rice_ball:"🍙",rice_cracker:"🍘",rice_scene:"🎑",right_anger_bubble:"🗯",ring:"💍",robot:"🤖",rocket:"🚀",rofl:"🤣",roll_eyes:"🙄",roller_coaster:"🎢",rooster:"🐓",rose:"🌹",rosette:"🏵",rotating_light:"🚨",round_pushpin:"📍",rowing_man:"🚣",rowing_woman:"🚣‍♀️",rugby_football:"🏉",running_man:"🏃",running_shirt_with_sash:"🎽",running_woman:"🏃‍♀️",sa:"🈂️",sagittarius:"♐️",sake:"🍶",sandal:"👡",santa:"🎅",satellite:"📡",saxophone:"🎷",school:"🏫",school_satchel:"🎒",scissors:"✂️",scorpion:"🦂",scorpius:"♏️",scream:"😱",scream_cat:"🙀",scroll:"📜",seat:"💺",secret:"㊙️",see_no_evil:"🙈",seedling:"🌱",selfie:"🤳",shallow_pan_of_food:"🥘",shamrock:"☘️",shark:"🦈",shaved_ice:"🍧",sheep:"🐑",shell:"🐚",shield:"🛡",shinto_shrine:"⛩",ship:"🚢",shirt:"👕",shopping:"🛍",shopping_cart:"🛒",shower:"🚿",shrimp:"🦐",signal_strength:"📶",six_pointed_star:"🔯",ski:"🎿",skier:"⛷",skull:"💀",skull_and_crossbones:"☠️",sleeping:"😴",sleeping_bed:"🛌",sleepy:"😪",slightly_frowning_face:"🙁",slightly_smiling_face:"🙂",slot_machine:"🎰",small_airplane:"🛩",small_blue_diamond:"🔹",small_orange_diamond:"🔸",small_red_triangle:"🔺",small_red_triangle_down:"🔻",smile:"😄",smile_cat:"😸",smiley:"😃",smiley_cat:"😺",smiling_imp:"😈",smirk:"😏",smirk_cat:"😼",smoking:"🚬",snail:"🐌",snake:"🐍",sneezing_face:"🤧",snowboarder:"🏂",snowflake:"❄️",snowman:"⛄️",snowman_with_snow:"☃️",sob:"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extracted by mini-css-extract-plugin\nmodule.exports = {\"panel\":\"panel__1ubJw\"};","import style from \"./panel.css\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (
    {this.props.title}
    );\n\t\t}\n\n\t\treturn (\n\t\t\t
    \n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
    \n\t\t);\n\t}\n}\n","import style from \"./markdown.css\";\nimport { Component } from 'preact';\nimport showdown from \"showdown\";\n\nexport default class Markdown extends Component {\n\trender() {\n        let converter = new showdown.Converter();\n        converter.setFlavor(\"github\");\n        let html = converter.makeHtml(`${this.props.children}`);\n        // noinspection CheckTagEmptyBody\n        return 
    ;\n\t}\n}\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"markdown\":\"markdown__bh-kq\"};","import style from './vldigeometria.css';\r\nimport { Component } from 'preact';\r\nimport Markdown from '../components/markdown';\r\nimport Panel from '../components/panel';\r\n\r\nconst r = String.raw;\r\n\r\nexport default class VlDiGeometria extends Component {\r\n\trender() {\r\n\t\t//Imported from unimore-info-wiki\r\n\t\treturn (\r\n\t\t\t
    \r\n                
    Videolezioni di Geometria
    \r\n                \r\n                    {r`\r\nTutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).\r\n\r\nPer comodità, ho estratto l'url sorgente del video dall'embed presente nella rispettiva pagina.\r\n\r\n1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\r\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\r\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\r\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\r\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\r\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\r\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\r\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\r\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\r\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\r\n11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\r\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\r\n13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\r\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\r\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\r\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\r\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\r\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\r\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\r\n20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\r\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\r\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\r\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\r\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\r\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\r\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\r\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\r\n\r\nNell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\r\n                    `}\r\n                \r\n\t\t\t
    \r\n\t\t);\r\n\t}\r\n}\r\n\r\n","// extracted by mini-css-extract-plugin\nmodule.exports = {\"vldigeometria\":\"vldigeometria__1ouv9\"};","/**\n * Created by Tivie on 13-07-2015.\n */\n\nfunction getDefaultOpts (simple) {\n  'use strict';\n\n  var defaultOptions = {\n    omitExtraWLInCodeBlocks: {\n      defaultValue: false,\n      describe: 'Omit the default extra whiteline added to code blocks',\n      type: 'boolean'\n    },\n    noHeaderId: {\n      defaultValue: false,\n      describe: 'Turn on/off generated header id',\n      type: 'boolean'\n    },\n    prefixHeaderId: {\n      defaultValue: false,\n      describe: 'Add a prefix to the generated header ids. Passing a string will prefix that string to the header id. Setting to true will add a generic \\'section-\\' prefix',\n      type: 'string'\n    },\n    rawPrefixHeaderId: {\n      defaultValue: false,\n      describe: 'Setting this option to true will prevent showdown from modifying the prefix. This might result in malformed IDs (if, for instance, the \" char is used in the prefix)',\n      type: 'boolean'\n    },\n    ghCompatibleHeaderId: {\n      defaultValue: false,\n      describe: 'Generate header ids compatible with github style (spaces are replaced with dashes, a bunch of non alphanumeric chars are removed)',\n      type: 'boolean'\n    },\n    rawHeaderId: {\n      defaultValue: false,\n      describe: 'Remove only spaces, \\' and \" from generated header ids (including prefixes), replacing them with dashes (-). WARNING: This might result in malformed ids',\n      type: 'boolean'\n    },\n    headerLevelStart: {\n      defaultValue: false,\n      describe: 'The header blocks level start',\n      type: 'integer'\n    },\n    parseImgDimensions: {\n      defaultValue: false,\n      describe: 'Turn on/off image dimension parsing',\n      type: 'boolean'\n    },\n    simplifiedAutoLink: {\n      defaultValue: false,\n      describe: 'Turn on/off GFM autolink style',\n      type: 'boolean'\n    },\n    excludeTrailingPunctuationFromURLs: {\n      defaultValue: false,\n      describe: 'Excludes trailing punctuation from links generated with autoLinking',\n      type: 'boolean'\n    },\n    literalMidWordUnderscores: {\n      defaultValue: false,\n      describe: 'Parse midword underscores as literal underscores',\n      type: 'boolean'\n    },\n    literalMidWordAsterisks: {\n      defaultValue: false,\n      describe: 'Parse midword asterisks as literal asterisks',\n      type: 'boolean'\n    },\n    strikethrough: {\n      defaultValue: false,\n      describe: 'Turn on/off strikethrough support',\n      type: 'boolean'\n    },\n    tables: {\n      defaultValue: false,\n      describe: 'Turn on/off tables support',\n      type: 'boolean'\n    },\n    tablesHeaderId: {\n      defaultValue: false,\n      describe: 'Add an id to table headers',\n      type: 'boolean'\n    },\n    ghCodeBlocks: {\n      defaultValue: true,\n      describe: 'Turn on/off GFM fenced code blocks support',\n      type: 'boolean'\n    },\n    tasklists: {\n      defaultValue: false,\n      describe: 'Turn on/off GFM tasklist support',\n      type: 'boolean'\n    },\n    smoothLivePreview: {\n      defaultValue: false,\n      describe: 'Prevents weird effects in live previews due to incomplete input',\n      type: 'boolean'\n    },\n    smartIndentationFix: {\n      defaultValue: false,\n      description: 'Tries to smartly fix indentation in es6 strings',\n      type: 'boolean'\n    },\n    disableForced4SpacesIndentedSublists: {\n      defaultValue: false,\n      description: 'Disables the requirement of indenting nested sublists by 4 spaces',\n      type: 'boolean'\n    },\n    simpleLineBreaks: {\n      defaultValue: false,\n      description: 'Parses simple line breaks as 
     (GFM Style)',\n      type: 'boolean'\n    },\n    requireSpaceBeforeHeadingText: {\n      defaultValue: false,\n      description: 'Makes adding a space between `#` and the header text mandatory (GFM Style)',\n      type: 'boolean'\n    },\n    ghMentions: {\n      defaultValue: false,\n      description: 'Enables github @mentions',\n      type: 'boolean'\n    },\n    ghMentionsLink: {\n      defaultValue: 'https://github.com/{u}',\n      description: 'Changes the link generated by @mentions. Only applies if ghMentions option is enabled.',\n      type: 'string'\n    },\n    encodeEmails: {\n      defaultValue: true,\n      description: 'Encode e-mail addresses through the use of Character Entities, transforming ASCII e-mail addresses into its equivalent decimal entities',\n      type: 'boolean'\n    },\n    openLinksInNewWindow: {\n      defaultValue: false,\n      description: 'Open all links in new windows',\n      type: 'boolean'\n    },\n    backslashEscapesHTMLTags: {\n      defaultValue: false,\n      description: 'Support for HTML Tag escaping. ex: \\
    foo\\
    ',\n      type: 'boolean'\n    },\n    emoji: {\n      defaultValue: false,\n      description: 'Enable emoji support. Ex: `this is a :smile: emoji`',\n      type: 'boolean'\n    },\n    underline: {\n      defaultValue: false,\n      description: 'Enable support for underline. Syntax is double or triple underscores: `__underline word__`. With this option enabled, underscores no longer parses into `` and ``',\n      type: 'boolean'\n    },\n    completeHTMLDocument: {\n      defaultValue: false,\n      description: 'Outputs a complete html document, including ``, `` and `` tags',\n      type: 'boolean'\n    },\n    metadata: {\n      defaultValue: false,\n      description: 'Enable support for document metadata (defined at the top of the document between `«««` and `»»»` or between `---` and `---`).',\n      type: 'boolean'\n    },\n    splitAdjacentBlockquotes: {\n      defaultValue: false,\n      description: 'Split adjacent blockquote blocks',\n      type: 'boolean'\n    }\n  };\n  if (simple === false) {\n    return JSON.parse(JSON.stringify(defaultOptions));\n  }\n  var ret = {};\n  for (var opt in defaultOptions) {\n    if (defaultOptions.hasOwnProperty(opt)) {\n      ret[opt] = defaultOptions[opt].defaultValue;\n    }\n  }\n  return ret;\n}\n\nfunction allOptionsOn () {\n  'use strict';\n  var options = getDefaultOpts(true),\n      ret = {};\n  for (var opt in options) {\n    if (options.hasOwnProperty(opt)) {\n      ret[opt] = true;\n    }\n  }\n  return ret;\n}\n","/**\n * Created by Tivie on 06-01-2015.\n */\n\n// Private properties\nvar showdown = {},\n    parsers = {},\n    extensions = {},\n    globalOptions = getDefaultOpts(true),\n    setFlavor = 'vanilla',\n    flavor = {\n      github: {\n        omitExtraWLInCodeBlocks:              true,\n        simplifiedAutoLink:                   true,\n        excludeTrailingPunctuationFromURLs:   true,\n        literalMidWordUnderscores:            true,\n        strikethrough:                        true,\n        tables:                               true,\n        tablesHeaderId:                       true,\n        ghCodeBlocks:                         true,\n        tasklists:                            true,\n        disableForced4SpacesIndentedSublists: true,\n        simpleLineBreaks:                     true,\n        requireSpaceBeforeHeadingText:        true,\n        ghCompatibleHeaderId:                 true,\n        ghMentions:                           true,\n        backslashEscapesHTMLTags:             true,\n        emoji:                                true,\n        splitAdjacentBlockquotes:             true\n      },\n      original: {\n        noHeaderId:                           true,\n        ghCodeBlocks:                         false\n      },\n      ghost: {\n        omitExtraWLInCodeBlocks:              true,\n        parseImgDimensions:                   true,\n        simplifiedAutoLink:                   true,\n        excludeTrailingPunctuationFromURLs:   true,\n        literalMidWordUnderscores:            true,\n        strikethrough:                        true,\n        tables:                               true,\n        tablesHeaderId:                       true,\n        ghCodeBlocks:                         true,\n        tasklists:                            true,\n        smoothLivePreview:                    true,\n        simpleLineBreaks:                     true,\n        requireSpaceBeforeHeadingText:        true,\n        ghMentions:                           false,\n        encodeEmails:                         true\n      },\n      vanilla: getDefaultOpts(true),\n      allOn: allOptionsOn()\n    };\n\n/**\n * helper namespace\n * @type {{}}\n */\nshowdown.helper = {};\n\n/**\n * TODO LEGACY SUPPORT CODE\n * @type {{}}\n */\nshowdown.extensions = {};\n\n/**\n * Set a global option\n * @static\n * @param {string} key\n * @param {*} value\n * @returns {showdown}\n */\nshowdown.setOption = function (key, value) {\n  'use strict';\n  globalOptions[key] = value;\n  return this;\n};\n\n/**\n * Get a global option\n * @static\n * @param {string} key\n * @returns {*}\n */\nshowdown.getOption = function (key) {\n  'use strict';\n  return globalOptions[key];\n};\n\n/**\n * Get the global options\n * @static\n * @returns {{}}\n */\nshowdown.getOptions = function () {\n  'use strict';\n  return globalOptions;\n};\n\n/**\n * Reset global options to the default values\n * @static\n */\nshowdown.resetOptions = function () {\n  'use strict';\n  globalOptions = getDefaultOpts(true);\n};\n\n/**\n * Set the flavor showdown should use as default\n * @param {string} name\n */\nshowdown.setFlavor = function (name) {\n  'use strict';\n  if (!flavor.hasOwnProperty(name)) {\n    throw Error(name + ' flavor was not found');\n  }\n  showdown.resetOptions();\n  var preset = flavor[name];\n  setFlavor = name;\n  for (var option in preset) {\n    if (preset.hasOwnProperty(option)) {\n      globalOptions[option] = preset[option];\n    }\n  }\n};\n\n/**\n * Get the currently set flavor\n * @returns {string}\n */\nshowdown.getFlavor = function () {\n  'use strict';\n  return setFlavor;\n};\n\n/**\n * Get the options of a specified flavor. Returns undefined if the flavor was not found\n * @param {string} name Name of the flavor\n * @returns {{}|undefined}\n */\nshowdown.getFlavorOptions = function (name) {\n  'use strict';\n  if (flavor.hasOwnProperty(name)) {\n    return flavor[name];\n  }\n};\n\n/**\n * Get the default options\n * @static\n * @param {boolean} [simple=true]\n * @returns {{}}\n */\nshowdown.getDefaultOptions = function (simple) {\n  'use strict';\n  return getDefaultOpts(simple);\n};\n\n/**\n * Get or set a subParser\n *\n * subParser(name)       - Get a registered subParser\n * subParser(name, func) - Register a subParser\n * @static\n * @param {string} name\n * @param {function} [func]\n * @returns {*}\n */\nshowdown.subParser = function (name, func) {\n  'use strict';\n  if (showdown.helper.isString(name)) {\n    if (typeof func !== 'undefined') {\n      parsers[name] = func;\n    } else {\n      if (parsers.hasOwnProperty(name)) {\n        return parsers[name];\n      } else {\n        throw Error('SubParser named ' + name + ' not registered!');\n      }\n    }\n  }\n};\n\n/**\n * Gets or registers an extension\n * @static\n * @param {string} name\n * @param {object|function=} ext\n * @returns {*}\n */\nshowdown.extension = function (name, ext) {\n  'use strict';\n\n  if (!showdown.helper.isString(name)) {\n    throw Error('Extension \\'name\\' must be a string');\n  }\n\n  name = showdown.helper.stdExtName(name);\n\n  // Getter\n  if (showdown.helper.isUndefined(ext)) {\n    if (!extensions.hasOwnProperty(name)) {\n      throw Error('Extension named ' + name + ' is not registered!');\n    }\n    return extensions[name];\n\n    // Setter\n  } else {\n    // Expand extension if it's wrapped in a function\n    if (typeof ext === 'function') {\n      ext = ext();\n    }\n\n    // Ensure extension is an array\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n\n    var validExtension = validate(ext, name);\n\n    if (validExtension.valid) {\n      extensions[name] = ext;\n    } else {\n      throw Error(validExtension.error);\n    }\n  }\n};\n\n/**\n * Gets all extensions registered\n * @returns {{}}\n */\nshowdown.getAllExtensions = function () {\n  'use strict';\n  return extensions;\n};\n\n/**\n * Remove an extension\n * @param {string} name\n */\nshowdown.removeExtension = function (name) {\n  'use strict';\n  delete extensions[name];\n};\n\n/**\n * Removes all extensions\n */\nshowdown.resetExtensions = function () {\n  'use strict';\n  extensions = {};\n};\n\n/**\n * Validate extension\n * @param {array} extension\n * @param {string} name\n * @returns {{valid: boolean, error: string}}\n */\nfunction validate (extension, name) {\n  'use strict';\n\n  var errMsg = (name) ? 'Error in ' + name + ' extension->' : 'Error in unnamed extension',\n      ret = {\n        valid: true,\n        error: ''\n      };\n\n  if (!showdown.helper.isArray(extension)) {\n    extension = [extension];\n  }\n\n  for (var i = 0; i < extension.length; ++i) {\n    var baseMsg = errMsg + ' sub-extension ' + i + ': ',\n        ext = extension[i];\n    if (typeof ext !== 'object') {\n      ret.valid = false;\n      ret.error = baseMsg + 'must be an object, but ' + typeof ext + ' given';\n      return ret;\n    }\n\n    if (!showdown.helper.isString(ext.type)) {\n      ret.valid = false;\n      ret.error = baseMsg + 'property \"type\" must be a string, but ' + typeof ext.type + ' given';\n      return ret;\n    }\n\n    var type = ext.type = ext.type.toLowerCase();\n\n    // normalize extension type\n    if (type === 'language') {\n      type = ext.type = 'lang';\n    }\n\n    if (type === 'html') {\n      type = ext.type = 'output';\n    }\n\n    if (type !== 'lang' && type !== 'output' && type !== 'listener') {\n      ret.valid = false;\n      ret.error = baseMsg + 'type ' + type + ' is not recognized. Valid values: \"lang/language\", \"output/html\" or \"listener\"';\n      return ret;\n    }\n\n    if (type === 'listener') {\n      if (showdown.helper.isUndefined(ext.listeners)) {\n        ret.valid = false;\n        ret.error = baseMsg + '. Extensions of type \"listener\" must have a property called \"listeners\"';\n        return ret;\n      }\n    } else {\n      if (showdown.helper.isUndefined(ext.filter) && showdown.helper.isUndefined(ext.regex)) {\n        ret.valid = false;\n        ret.error = baseMsg + type + ' extensions must define either a \"regex\" property or a \"filter\" method';\n        return ret;\n      }\n    }\n\n    if (ext.listeners) {\n      if (typeof ext.listeners !== 'object') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"listeners\" property must be an object but ' + typeof ext.listeners + ' given';\n        return ret;\n      }\n      for (var ln in ext.listeners) {\n        if (ext.listeners.hasOwnProperty(ln)) {\n          if (typeof ext.listeners[ln] !== 'function') {\n            ret.valid = false;\n            ret.error = baseMsg + '\"listeners\" property must be an hash of [event name]: [callback]. listeners.' + ln +\n              ' must be a function but ' + typeof ext.listeners[ln] + ' given';\n            return ret;\n          }\n        }\n      }\n    }\n\n    if (ext.filter) {\n      if (typeof ext.filter !== 'function') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"filter\" must be a function, but ' + typeof ext.filter + ' given';\n        return ret;\n      }\n    } else if (ext.regex) {\n      if (showdown.helper.isString(ext.regex)) {\n        ext.regex = new RegExp(ext.regex, 'g');\n      }\n      if (!(ext.regex instanceof RegExp)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" property must either be a string or a RegExp object, but ' + typeof ext.regex + ' given';\n        return ret;\n      }\n      if (showdown.helper.isUndefined(ext.replace)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" extensions must implement a replace string or function';\n        return ret;\n      }\n    }\n  }\n  return ret;\n}\n\n/**\n * Validate extension\n * @param {object} ext\n * @returns {boolean}\n */\nshowdown.validateExtension = function (ext) {\n  'use strict';\n\n  var validateExtension = validate(ext, null);\n  if (!validateExtension.valid) {\n    console.warn(validateExtension.error);\n    return false;\n  }\n  return true;\n};\n","/**\n * showdownjs helper functions\n */\n\nif (!showdown.hasOwnProperty('helper')) {\n  showdown.helper = {};\n}\n\n/**\n * Check if var is string\n * @static\n * @param {string} a\n * @returns {boolean}\n */\nshowdown.helper.isString = function (a) {\n  'use strict';\n  return (typeof a === 'string' || a instanceof String);\n};\n\n/**\n * Check if var is a function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isFunction = function (a) {\n  'use strict';\n  var getType = {};\n  return a && getType.toString.call(a) === '[object Function]';\n};\n\n/**\n * isArray helper function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isArray = function (a) {\n  'use strict';\n  return Array.isArray(a);\n};\n\n/**\n * Check if value is undefined\n * @static\n * @param {*} value The value to check.\n * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.\n */\nshowdown.helper.isUndefined = function (value) {\n  'use strict';\n  return typeof value === 'undefined';\n};\n\n/**\n * ForEach helper function\n * Iterates over Arrays and Objects (own properties only)\n * @static\n * @param {*} obj\n * @param {function} callback Accepts 3 params: 1. value, 2. key, 3. the original array/object\n */\nshowdown.helper.forEach = function (obj, callback) {\n  'use strict';\n  // check if obj is defined\n  if (showdown.helper.isUndefined(obj)) {\n    throw new Error('obj param is required');\n  }\n\n  if (showdown.helper.isUndefined(callback)) {\n    throw new Error('callback param is required');\n  }\n\n  if (!showdown.helper.isFunction(callback)) {\n    throw new Error('callback param must be a function/closure');\n  }\n\n  if (typeof obj.forEach === 'function') {\n    obj.forEach(callback);\n  } else if (showdown.helper.isArray(obj)) {\n    for (var i = 0; i < obj.length; i++) {\n      callback(obj[i], i, obj);\n    }\n  } else if (typeof (obj) === 'object') {\n    for (var prop in obj) {\n      if (obj.hasOwnProperty(prop)) {\n        callback(obj[prop], prop, obj);\n      }\n    }\n  } else {\n    throw new Error('obj does not seem to be an array or an iterable object');\n  }\n};\n\n/**\n * Standardidize extension name\n * @static\n * @param {string} s extension name\n * @returns {string}\n */\nshowdown.helper.stdExtName = function (s) {\n  'use strict';\n  return s.replace(/[_?*+\\/\\\\.^-]/g, '').replace(/\\s/g, '').toLowerCase();\n};\n\nfunction escapeCharactersCallback (wholeMatch, m1) {\n  'use strict';\n  var charCodeToEscape = m1.charCodeAt(0);\n  return '¨E' + charCodeToEscape + 'E';\n}\n\n/**\n * Callback used to escape characters when passing through String.replace\n * @static\n * @param {string} wholeMatch\n * @param {string} m1\n * @returns {string}\n */\nshowdown.helper.escapeCharactersCallback = escapeCharactersCallback;\n\n/**\n * Escape characters in a string\n * @static\n * @param {string} text\n * @param {string} charsToEscape\n * @param {boolean} afterBackslash\n * @returns {XML|string|void|*}\n */\nshowdown.helper.escapeCharacters = function (text, charsToEscape, afterBackslash) {\n  'use strict';\n  // First we have to escape the escape characters so that\n  // we can build a character class out of them\n  var regexString = '([' + charsToEscape.replace(/([\\[\\]\\\\])/g, '\\\\$1') + '])';\n\n  if (afterBackslash) {\n    regexString = '\\\\\\\\' + regexString;\n  }\n\n  var regex = new RegExp(regexString, 'g');\n  text = text.replace(regex, escapeCharactersCallback);\n\n  return text;\n};\n\n/**\n * Unescape HTML entities\n * @param txt\n * @returns {string}\n */\nshowdown.helper.unescapeHTMLEntities = function (txt) {\n  'use strict';\n\n  return txt\n    .replace(/"/g, '\"')\n    .replace(/</g, '<')\n    .replace(/>/g, '>')\n    .replace(/&/g, '&');\n};\n\nvar rgxFindMatchPos = function (str, left, right, flags) {\n  'use strict';\n  var f = flags || '',\n      g = f.indexOf('g') > -1,\n      x = new RegExp(left + '|' + right, 'g' + f.replace(/g/g, '')),\n      l = new RegExp(left, f.replace(/g/g, '')),\n      pos = [],\n      t, s, m, start, end;\n\n  do {\n    t = 0;\n    while ((m = x.exec(str))) {\n      if (l.test(m[0])) {\n        if (!(t++)) {\n          s = x.lastIndex;\n          start = s - m[0].length;\n        }\n      } else if (t) {\n        if (!--t) {\n          end = m.index + m[0].length;\n          var obj = {\n            left: {start: start, end: s},\n            match: {start: s, end: m.index},\n            right: {start: m.index, end: end},\n            wholeMatch: {start: start, end: end}\n          };\n          pos.push(obj);\n          if (!g) {\n            return pos;\n          }\n        }\n      }\n    }\n  } while (t && (x.lastIndex = s));\n\n  return pos;\n};\n\n/**\n * matchRecursiveRegExp\n *\n * (c) 2007 Steven Levithan \n * MIT License\n *\n * Accepts a string to search, a left and right format delimiter\n * as regex patterns, and optional regex flags. Returns an array\n * of matches, allowing nested instances of left/right delimiters.\n * Use the \"g\" flag to return all matches, otherwise only the\n * first is returned. Be careful to ensure that the left and\n * right format delimiters produce mutually exclusive matches.\n * Backreferences are not supported within the right delimiter\n * due to how it is internally combined with the left delimiter.\n * When matching strings whose format delimiters are unbalanced\n * to the left or right, the output is intentionally as a\n * conventional regex library with recursion support would\n * produce, e.g. \"<\" and \">\" both produce [\"x\"] when using\n * \"<\" and \">\" as the delimiters (both strings contain a single,\n * balanced instance of \"\").\n *\n * examples:\n * matchRecursiveRegExp(\"test\", \"\\\\(\", \"\\\\)\")\n * returns: []\n * matchRecursiveRegExp(\">>t<>\", \"<\", \">\", \"g\")\n * returns: [\"t<>\", \"\"]\n * matchRecursiveRegExp(\"
    test
    \", \"]*>\", \"\", \"gi\")\n * returns: [\"test\"]\n */\nshowdown.helper.matchRecursiveRegExp = function (str, left, right, flags) {\n  'use strict';\n\n  var matchPos = rgxFindMatchPos (str, left, right, flags),\n      results = [];\n\n  for (var i = 0; i < matchPos.length; ++i) {\n    results.push([\n      str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n      str.slice(matchPos[i].match.start, matchPos[i].match.end),\n      str.slice(matchPos[i].left.start, matchPos[i].left.end),\n      str.slice(matchPos[i].right.start, matchPos[i].right.end)\n    ]);\n  }\n  return results;\n};\n\n/**\n *\n * @param {string} str\n * @param {string|function} replacement\n * @param {string} left\n * @param {string} right\n * @param {string} flags\n * @returns {string}\n */\nshowdown.helper.replaceRecursiveRegExp = function (str, replacement, left, right, flags) {\n  'use strict';\n\n  if (!showdown.helper.isFunction(replacement)) {\n    var repStr = replacement;\n    replacement = function () {\n      return repStr;\n    };\n  }\n\n  var matchPos = rgxFindMatchPos(str, left, right, flags),\n      finalStr = str,\n      lng = matchPos.length;\n\n  if (lng > 0) {\n    var bits = [];\n    if (matchPos[0].wholeMatch.start !== 0) {\n      bits.push(str.slice(0, matchPos[0].wholeMatch.start));\n    }\n    for (var i = 0; i < lng; ++i) {\n      bits.push(\n        replacement(\n          str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n          str.slice(matchPos[i].match.start, matchPos[i].match.end),\n          str.slice(matchPos[i].left.start, matchPos[i].left.end),\n          str.slice(matchPos[i].right.start, matchPos[i].right.end)\n        )\n      );\n      if (i < lng - 1) {\n        bits.push(str.slice(matchPos[i].wholeMatch.end, matchPos[i + 1].wholeMatch.start));\n      }\n    }\n    if (matchPos[lng - 1].wholeMatch.end < str.length) {\n      bits.push(str.slice(matchPos[lng - 1].wholeMatch.end));\n    }\n    finalStr = bits.join('');\n  }\n  return finalStr;\n};\n\n/**\n * Returns the index within the passed String object of the first occurrence of the specified regex,\n * starting the search at fromIndex. Returns -1 if the value is not found.\n *\n * @param {string} str string to search\n * @param {RegExp} regex Regular expression to search\n * @param {int} [fromIndex = 0] Index to start the search\n * @returns {Number}\n * @throws InvalidArgumentError\n */\nshowdown.helper.regexIndexOf = function (str, regex, fromIndex) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  if (regex instanceof RegExp === false) {\n    throw 'InvalidArgumentError: second parameter of showdown.helper.regexIndexOf function must be an instance of RegExp';\n  }\n  var indexOf = str.substring(fromIndex || 0).search(regex);\n  return (indexOf >= 0) ? (indexOf + (fromIndex || 0)) : indexOf;\n};\n\n/**\n * Splits the passed string object at the defined index, and returns an array composed of the two substrings\n * @param {string} str string to split\n * @param {int} index index to split string at\n * @returns {[string,string]}\n * @throws InvalidArgumentError\n */\nshowdown.helper.splitAtIndex = function (str, index) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  return [str.substring(0, index), str.substring(index)];\n};\n\n/**\n * Obfuscate an e-mail address through the use of Character Entities,\n * transforming ASCII characters into their equivalent decimal or hex entities.\n *\n * Since it has a random component, subsequent calls to this function produce different results\n *\n * @param {string} mail\n * @returns {string}\n */\nshowdown.helper.encodeEmailAddress = function (mail) {\n  'use strict';\n  var encode = [\n    function (ch) {\n      return '&#' + ch.charCodeAt(0) + ';';\n    },\n    function (ch) {\n      return '&#x' + ch.charCodeAt(0).toString(16) + ';';\n    },\n    function (ch) {\n      return ch;\n    }\n  ];\n\n  mail = mail.replace(/./g, function (ch) {\n    if (ch === '@') {\n      // this *must* be encoded. I insist.\n      ch = encode[Math.floor(Math.random() * 2)](ch);\n    } else {\n      var r = Math.random();\n      // roughly 10% raw, 45% hex, 45% dec\n      ch = (\n        r > 0.9 ? encode[2](ch) : r > 0.45 ? encode[1](ch) : encode[0](ch)\n      );\n    }\n    return ch;\n  });\n\n  return mail;\n};\n\n/**\n *\n * @param str\n * @param targetLength\n * @param padString\n * @returns {string}\n */\nshowdown.helper.padEnd = function padEnd (str, targetLength, padString) {\n  'use strict';\n  /*jshint bitwise: false*/\n  // eslint-disable-next-line space-infix-ops\n  targetLength = targetLength>>0; //floor if number or convert non-number to 0;\n  /*jshint bitwise: true*/\n  padString = String(padString || ' ');\n  if (str.length > targetLength) {\n    return String(str);\n  } else {\n    targetLength = targetLength - str.length;\n    if (targetLength > padString.length) {\n      padString += padString.repeat(targetLength / padString.length); //append to original to ensure we are longer than needed\n    }\n    return String(str) + padString.slice(0,targetLength);\n  }\n};\n\n/**\n * POLYFILLS\n */\n// use this instead of builtin is undefined for IE8 compatibility\nif (typeof console === 'undefined') {\n  console = {\n    warn: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    log: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    error: function (msg) {\n      'use strict';\n      throw msg;\n    }\n  };\n}\n\n/**\n * Common regexes.\n * We declare some common regexes to improve performance\n */\nshowdown.helper.regexes = {\n  asteriskDashAndColon: /([*_:~])/g\n};\n\n/**\n * EMOJIS LIST\n */\nshowdown.helper.emojis = {\n  '+1':'\\ud83d\\udc4d',\n  '-1':'\\ud83d\\udc4e',\n  '100':'\\ud83d\\udcaf',\n  '1234':'\\ud83d\\udd22',\n  '1st_place_medal':'\\ud83e\\udd47',\n  '2nd_place_medal':'\\ud83e\\udd48',\n  '3rd_place_medal':'\\ud83e\\udd49',\n  '8ball':'\\ud83c\\udfb1',\n  'a':'\\ud83c\\udd70\\ufe0f',\n  'ab':'\\ud83c\\udd8e',\n  'abc':'\\ud83d\\udd24',\n  'abcd':'\\ud83d\\udd21',\n  'accept':'\\ud83c\\ude51',\n  'aerial_tramway':'\\ud83d\\udea1',\n  'airplane':'\\u2708\\ufe0f',\n  'alarm_clock':'\\u23f0',\n  'alembic':'\\u2697\\ufe0f',\n  'alien':'\\ud83d\\udc7d',\n  'ambulance':'\\ud83d\\ude91',\n  'amphora':'\\ud83c\\udffa',\n  'anchor':'\\u2693\\ufe0f',\n  'angel':'\\ud83d\\udc7c',\n  'anger':'\\ud83d\\udca2',\n  'angry':'\\ud83d\\ude20',\n  'anguished':'\\ud83d\\ude27',\n  'ant':'\\ud83d\\udc1c',\n  'apple':'\\ud83c\\udf4e',\n  'aquarius':'\\u2652\\ufe0f',\n  'aries':'\\u2648\\ufe0f',\n  'arrow_backward':'\\u25c0\\ufe0f',\n  'arrow_double_down':'\\u23ec',\n  'arrow_double_up':'\\u23eb',\n  'arrow_down':'\\u2b07\\ufe0f',\n  'arrow_down_small':'\\ud83d\\udd3d',\n  'arrow_forward':'\\u25b6\\ufe0f',\n  'arrow_heading_down':'\\u2935\\ufe0f',\n  'arrow_heading_up':'\\u2934\\ufe0f',\n  'arrow_left':'\\u2b05\\ufe0f',\n  'arrow_lower_left':'\\u2199\\ufe0f',\n  'arrow_lower_right':'\\u2198\\ufe0f',\n  'arrow_right':'\\u27a1\\ufe0f',\n  'arrow_right_hook':'\\u21aa\\ufe0f',\n  'arrow_up':'\\u2b06\\ufe0f',\n  'arrow_up_down':'\\u2195\\ufe0f',\n  'arrow_up_small':'\\ud83d\\udd3c',\n  'arrow_upper_left':'\\u2196\\ufe0f',\n  'arrow_upper_right':'\\u2197\\ufe0f',\n  'arrows_clockwise':'\\ud83d\\udd03',\n  'arrows_counterclockwise':'\\ud83d\\udd04',\n  'art':'\\ud83c\\udfa8',\n  'articulated_lorry':'\\ud83d\\ude9b',\n  'artificial_satellite':'\\ud83d\\udef0',\n  'astonished':'\\ud83d\\ude32',\n  'athletic_shoe':'\\ud83d\\udc5f',\n  'atm':'\\ud83c\\udfe7',\n  'atom_symbol':'\\u269b\\ufe0f',\n  'avocado':'\\ud83e\\udd51',\n  'b':'\\ud83c\\udd71\\ufe0f',\n  'baby':'\\ud83d\\udc76',\n  'baby_bottle':'\\ud83c\\udf7c',\n  'baby_chick':'\\ud83d\\udc24',\n  'baby_symbol':'\\ud83d\\udebc',\n  'back':'\\ud83d\\udd19',\n  'bacon':'\\ud83e\\udd53',\n  'badminton':'\\ud83c\\udff8',\n  'baggage_claim':'\\ud83d\\udec4',\n  'baguette_bread':'\\ud83e\\udd56',\n  'balance_scale':'\\u2696\\ufe0f',\n  'balloon':'\\ud83c\\udf88',\n  'ballot_box':'\\ud83d\\uddf3',\n  'ballot_box_with_check':'\\u2611\\ufe0f',\n  'bamboo':'\\ud83c\\udf8d',\n  'banana':'\\ud83c\\udf4c',\n  'bangbang':'\\u203c\\ufe0f',\n  'bank':'\\ud83c\\udfe6',\n  'bar_chart':'\\ud83d\\udcca',\n  'barber':'\\ud83d\\udc88',\n  'baseball':'\\u26be\\ufe0f',\n  'basketball':'\\ud83c\\udfc0',\n  'basketball_man':'\\u26f9\\ufe0f',\n  'basketball_woman':'\\u26f9\\ufe0f‍\\u2640\\ufe0f',\n  'bat':'\\ud83e\\udd87',\n  'bath':'\\ud83d\\udec0',\n  'bathtub':'\\ud83d\\udec1',\n  'battery':'\\ud83d\\udd0b',\n  'beach_umbrella':'\\ud83c\\udfd6',\n  'bear':'\\ud83d\\udc3b',\n  'bed':'\\ud83d\\udecf',\n  'bee':'\\ud83d\\udc1d',\n  'beer':'\\ud83c\\udf7a',\n  'beers':'\\ud83c\\udf7b',\n  'beetle':'\\ud83d\\udc1e',\n  'beginner':'\\ud83d\\udd30',\n  'bell':'\\ud83d\\udd14',\n  'bellhop_bell':'\\ud83d\\udece',\n  'bento':'\\ud83c\\udf71',\n  'biking_man':'\\ud83d\\udeb4',\n  'bike':'\\ud83d\\udeb2',\n  'biking_woman':'\\ud83d\\udeb4‍\\u2640\\ufe0f',\n  'bikini':'\\ud83d\\udc59',\n  'biohazard':'\\u2623\\ufe0f',\n  'bird':'\\ud83d\\udc26',\n  'birthday':'\\ud83c\\udf82',\n  'black_circle':'\\u26ab\\ufe0f',\n  'black_flag':'\\ud83c\\udff4',\n  'black_heart':'\\ud83d\\udda4',\n  'black_joker':'\\ud83c\\udccf',\n  'black_large_square':'\\u2b1b\\ufe0f',\n  'black_medium_small_square':'\\u25fe\\ufe0f',\n  'black_medium_square':'\\u25fc\\ufe0f',\n  'black_nib':'\\u2712\\ufe0f',\n  'black_small_square':'\\u25aa\\ufe0f',\n  'black_square_button':'\\ud83d\\udd32',\n  'blonde_man':'\\ud83d\\udc71',\n  'blonde_woman':'\\ud83d\\udc71‍\\u2640\\ufe0f',\n  'blossom':'\\ud83c\\udf3c',\n  'blowfish':'\\ud83d\\udc21',\n  'blue_book':'\\ud83d\\udcd8',\n  'blue_car':'\\ud83d\\ude99',\n  'blue_heart':'\\ud83d\\udc99',\n  'blush':'\\ud83d\\ude0a',\n  'boar':'\\ud83d\\udc17',\n  'boat':'\\u26f5\\ufe0f',\n  'bomb':'\\ud83d\\udca3',\n  'book':'\\ud83d\\udcd6',\n  'bookmark':'\\ud83d\\udd16',\n  'bookmark_tabs':'\\ud83d\\udcd1',\n  'books':'\\ud83d\\udcda',\n  'boom':'\\ud83d\\udca5',\n  'boot':'\\ud83d\\udc62',\n  'bouquet':'\\ud83d\\udc90',\n  'bowing_man':'\\ud83d\\ude47',\n  'bow_and_arrow':'\\ud83c\\udff9',\n  'bowing_woman':'\\ud83d\\ude47‍\\u2640\\ufe0f',\n  'bowling':'\\ud83c\\udfb3',\n  'boxing_glove':'\\ud83e\\udd4a',\n  'boy':'\\ud83d\\udc66',\n  'bread':'\\ud83c\\udf5e',\n  'bride_with_veil':'\\ud83d\\udc70',\n  'bridge_at_night':'\\ud83c\\udf09',\n  'briefcase':'\\ud83d\\udcbc',\n  'broken_heart':'\\ud83d\\udc94',\n  'bug':'\\ud83d\\udc1b',\n  'building_construction':'\\ud83c\\udfd7',\n  'bulb':'\\ud83d\\udca1',\n  'bullettrain_front':'\\ud83d\\ude85',\n  'bullettrain_side':'\\ud83d\\ude84',\n  'burrito':'\\ud83c\\udf2f',\n  'bus':'\\ud83d\\ude8c',\n  'business_suit_levitating':'\\ud83d\\udd74',\n  'busstop':'\\ud83d\\ude8f',\n  'bust_in_silhouette':'\\ud83d\\udc64',\n  'busts_in_silhouette':'\\ud83d\\udc65',\n  'butterfly':'\\ud83e\\udd8b',\n  'cactus':'\\ud83c\\udf35',\n  'cake':'\\ud83c\\udf70',\n  'calendar':'\\ud83d\\udcc6',\n  'call_me_hand':'\\ud83e\\udd19',\n  'calling':'\\ud83d\\udcf2',\n  'camel':'\\ud83d\\udc2b',\n  'camera':'\\ud83d\\udcf7',\n  'camera_flash':'\\ud83d\\udcf8',\n  'camping':'\\ud83c\\udfd5',\n  'cancer':'\\u264b\\ufe0f',\n  'candle':'\\ud83d\\udd6f',\n  'candy':'\\ud83c\\udf6c',\n  'canoe':'\\ud83d\\udef6',\n  'capital_abcd':'\\ud83d\\udd20',\n  'capricorn':'\\u2651\\ufe0f',\n  'car':'\\ud83d\\ude97',\n  'card_file_box':'\\ud83d\\uddc3',\n  'card_index':'\\ud83d\\udcc7',\n  'card_index_dividers':'\\ud83d\\uddc2',\n  'carousel_horse':'\\ud83c\\udfa0',\n  'carrot':'\\ud83e\\udd55',\n  'cat':'\\ud83d\\udc31',\n  'cat2':'\\ud83d\\udc08',\n  'cd':'\\ud83d\\udcbf',\n  'chains':'\\u26d3',\n  'champagne':'\\ud83c\\udf7e',\n  'chart':'\\ud83d\\udcb9',\n  'chart_with_downwards_trend':'\\ud83d\\udcc9',\n  'chart_with_upwards_trend':'\\ud83d\\udcc8',\n  'checkered_flag':'\\ud83c\\udfc1',\n  'cheese':'\\ud83e\\uddc0',\n  'cherries':'\\ud83c\\udf52',\n  'cherry_blossom':'\\ud83c\\udf38',\n  'chestnut':'\\ud83c\\udf30',\n  'chicken':'\\ud83d\\udc14',\n  'children_crossing':'\\ud83d\\udeb8',\n  'chipmunk':'\\ud83d\\udc3f',\n  'chocolate_bar':'\\ud83c\\udf6b',\n  'christmas_tree':'\\ud83c\\udf84',\n  'church':'\\u26ea\\ufe0f',\n  'cinema':'\\ud83c\\udfa6',\n  'circus_tent':'\\ud83c\\udfaa',\n  'city_sunrise':'\\ud83c\\udf07',\n  'city_sunset':'\\ud83c\\udf06',\n  'cityscape':'\\ud83c\\udfd9',\n  'cl':'\\ud83c\\udd91',\n  'clamp':'\\ud83d\\udddc',\n  'clap':'\\ud83d\\udc4f',\n  'clapper':'\\ud83c\\udfac',\n  'classical_building':'\\ud83c\\udfdb',\n  'clinking_glasses':'\\ud83e\\udd42',\n  'clipboard':'\\ud83d\\udccb',\n  'clock1':'\\ud83d\\udd50',\n  'clock10':'\\ud83d\\udd59',\n  'clock1030':'\\ud83d\\udd65',\n  'clock11':'\\ud83d\\udd5a',\n  'clock1130':'\\ud83d\\udd66',\n  'clock12':'\\ud83d\\udd5b',\n  'clock1230':'\\ud83d\\udd67',\n  'clock130':'\\ud83d\\udd5c',\n  'clock2':'\\ud83d\\udd51',\n  'clock230':'\\ud83d\\udd5d',\n  'clock3':'\\ud83d\\udd52',\n  'clock330':'\\ud83d\\udd5e',\n  'clock4':'\\ud83d\\udd53',\n  'clock430':'\\ud83d\\udd5f',\n  'clock5':'\\ud83d\\udd54',\n  'clock530':'\\ud83d\\udd60',\n  'clock6':'\\ud83d\\udd55',\n  'clock630':'\\ud83d\\udd61',\n  'clock7':'\\ud83d\\udd56',\n  'clock730':'\\ud83d\\udd62',\n  'clock8':'\\ud83d\\udd57',\n  'clock830':'\\ud83d\\udd63',\n  'clock9':'\\ud83d\\udd58',\n  'clock930':'\\ud83d\\udd64',\n  'closed_book':'\\ud83d\\udcd5',\n  'closed_lock_with_key':'\\ud83d\\udd10',\n  'closed_umbrella':'\\ud83c\\udf02',\n  'cloud':'\\u2601\\ufe0f',\n  'cloud_with_lightning':'\\ud83c\\udf29',\n  'cloud_with_lightning_and_rain':'\\u26c8',\n  'cloud_with_rain':'\\ud83c\\udf27',\n  'cloud_with_snow':'\\ud83c\\udf28',\n  'clown_face':'\\ud83e\\udd21',\n  'clubs':'\\u2663\\ufe0f',\n  'cocktail':'\\ud83c\\udf78',\n  'coffee':'\\u2615\\ufe0f',\n  'coffin':'\\u26b0\\ufe0f',\n  'cold_sweat':'\\ud83d\\ude30',\n  'comet':'\\u2604\\ufe0f',\n  'computer':'\\ud83d\\udcbb',\n  'computer_mouse':'\\ud83d\\uddb1',\n  'confetti_ball':'\\ud83c\\udf8a',\n  'confounded':'\\ud83d\\ude16',\n  'confused':'\\ud83d\\ude15',\n  'congratulations':'\\u3297\\ufe0f',\n  'construction':'\\ud83d\\udea7',\n  'construction_worker_man':'\\ud83d\\udc77',\n  'construction_worker_woman':'\\ud83d\\udc77‍\\u2640\\ufe0f',\n  'control_knobs':'\\ud83c\\udf9b',\n  'convenience_store':'\\ud83c\\udfea',\n  'cookie':'\\ud83c\\udf6a',\n  'cool':'\\ud83c\\udd92',\n  'policeman':'\\ud83d\\udc6e',\n  'copyright':'\\u00a9\\ufe0f',\n  'corn':'\\ud83c\\udf3d',\n  'couch_and_lamp':'\\ud83d\\udecb',\n  'couple':'\\ud83d\\udc6b',\n  'couple_with_heart_woman_man':'\\ud83d\\udc91',\n  'couple_with_heart_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc68',\n  'couple_with_heart_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc69',\n  'couplekiss_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc68',\n  'couplekiss_man_woman':'\\ud83d\\udc8f',\n  'couplekiss_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc69',\n  'cow':'\\ud83d\\udc2e',\n  'cow2':'\\ud83d\\udc04',\n  'cowboy_hat_face':'\\ud83e\\udd20',\n  'crab':'\\ud83e\\udd80',\n  'crayon':'\\ud83d\\udd8d',\n  'credit_card':'\\ud83d\\udcb3',\n  'crescent_moon':'\\ud83c\\udf19',\n  'cricket':'\\ud83c\\udfcf',\n  'crocodile':'\\ud83d\\udc0a',\n  'croissant':'\\ud83e\\udd50',\n  'crossed_fingers':'\\ud83e\\udd1e',\n  'crossed_flags':'\\ud83c\\udf8c',\n  'crossed_swords':'\\u2694\\ufe0f',\n  'crown':'\\ud83d\\udc51',\n  'cry':'\\ud83d\\ude22',\n  'crying_cat_face':'\\ud83d\\ude3f',\n  'crystal_ball':'\\ud83d\\udd2e',\n  'cucumber':'\\ud83e\\udd52',\n  'cupid':'\\ud83d\\udc98',\n  'curly_loop':'\\u27b0',\n  'currency_exchange':'\\ud83d\\udcb1',\n  'curry':'\\ud83c\\udf5b',\n  'custard':'\\ud83c\\udf6e',\n  'customs':'\\ud83d\\udec3',\n  'cyclone':'\\ud83c\\udf00',\n  'dagger':'\\ud83d\\udde1',\n  'dancer':'\\ud83d\\udc83',\n  'dancing_women':'\\ud83d\\udc6f',\n  'dancing_men':'\\ud83d\\udc6f‍\\u2642\\ufe0f',\n  'dango':'\\ud83c\\udf61',\n  'dark_sunglasses':'\\ud83d\\udd76',\n  'dart':'\\ud83c\\udfaf',\n  'dash':'\\ud83d\\udca8',\n  'date':'\\ud83d\\udcc5',\n  'deciduous_tree':'\\ud83c\\udf33',\n  'deer':'\\ud83e\\udd8c',\n  'department_store':'\\ud83c\\udfec',\n  'derelict_house':'\\ud83c\\udfda',\n  'desert':'\\ud83c\\udfdc',\n  'desert_island':'\\ud83c\\udfdd',\n  'desktop_computer':'\\ud83d\\udda5',\n  'male_detective':'\\ud83d\\udd75\\ufe0f',\n  'diamond_shape_with_a_dot_inside':'\\ud83d\\udca0',\n  'diamonds':'\\u2666\\ufe0f',\n  'disappointed':'\\ud83d\\ude1e',\n  'disappointed_relieved':'\\ud83d\\ude25',\n  'dizzy':'\\ud83d\\udcab',\n  'dizzy_face':'\\ud83d\\ude35',\n  'do_not_litter':'\\ud83d\\udeaf',\n  'dog':'\\ud83d\\udc36',\n  'dog2':'\\ud83d\\udc15',\n  'dollar':'\\ud83d\\udcb5',\n  'dolls':'\\ud83c\\udf8e',\n  'dolphin':'\\ud83d\\udc2c',\n  'door':'\\ud83d\\udeaa',\n  'doughnut':'\\ud83c\\udf69',\n  'dove':'\\ud83d\\udd4a',\n  'dragon':'\\ud83d\\udc09',\n  'dragon_face':'\\ud83d\\udc32',\n  'dress':'\\ud83d\\udc57',\n  'dromedary_camel':'\\ud83d\\udc2a',\n  'drooling_face':'\\ud83e\\udd24',\n  'droplet':'\\ud83d\\udca7',\n  'drum':'\\ud83e\\udd41',\n  'duck':'\\ud83e\\udd86',\n  'dvd':'\\ud83d\\udcc0',\n  'e-mail':'\\ud83d\\udce7',\n  'eagle':'\\ud83e\\udd85',\n  'ear':'\\ud83d\\udc42',\n  'ear_of_rice':'\\ud83c\\udf3e',\n  'earth_africa':'\\ud83c\\udf0d',\n  'earth_americas':'\\ud83c\\udf0e',\n  'earth_asia':'\\ud83c\\udf0f',\n  'egg':'\\ud83e\\udd5a',\n  'eggplant':'\\ud83c\\udf46',\n  'eight_pointed_black_star':'\\u2734\\ufe0f',\n  'eight_spoked_asterisk':'\\u2733\\ufe0f',\n  'electric_plug':'\\ud83d\\udd0c',\n  'elephant':'\\ud83d\\udc18',\n  'email':'\\u2709\\ufe0f',\n  'end':'\\ud83d\\udd1a',\n  'envelope_with_arrow':'\\ud83d\\udce9',\n  'euro':'\\ud83d\\udcb6',\n  'european_castle':'\\ud83c\\udff0',\n  'european_post_office':'\\ud83c\\udfe4',\n  'evergreen_tree':'\\ud83c\\udf32',\n  'exclamation':'\\u2757\\ufe0f',\n  'expressionless':'\\ud83d\\ude11',\n  'eye':'\\ud83d\\udc41',\n  'eye_speech_bubble':'\\ud83d\\udc41‍\\ud83d\\udde8',\n  'eyeglasses':'\\ud83d\\udc53',\n  'eyes':'\\ud83d\\udc40',\n  'face_with_head_bandage':'\\ud83e\\udd15',\n  'face_with_thermometer':'\\ud83e\\udd12',\n  'fist_oncoming':'\\ud83d\\udc4a',\n  'factory':'\\ud83c\\udfed',\n  'fallen_leaf':'\\ud83c\\udf42',\n  'family_man_woman_boy':'\\ud83d\\udc6a',\n  'family_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_woman_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_woman_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_man_woman_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_woman_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'fast_forward':'\\u23e9',\n  'fax':'\\ud83d\\udce0',\n  'fearful':'\\ud83d\\ude28',\n  'feet':'\\ud83d\\udc3e',\n  'female_detective':'\\ud83d\\udd75\\ufe0f‍\\u2640\\ufe0f',\n  'ferris_wheel':'\\ud83c\\udfa1',\n  'ferry':'\\u26f4',\n  'field_hockey':'\\ud83c\\udfd1',\n  'file_cabinet':'\\ud83d\\uddc4',\n  'file_folder':'\\ud83d\\udcc1',\n  'film_projector':'\\ud83d\\udcfd',\n  'film_strip':'\\ud83c\\udf9e',\n  'fire':'\\ud83d\\udd25',\n  'fire_engine':'\\ud83d\\ude92',\n  'fireworks':'\\ud83c\\udf86',\n  'first_quarter_moon':'\\ud83c\\udf13',\n  'first_quarter_moon_with_face':'\\ud83c\\udf1b',\n  'fish':'\\ud83d\\udc1f',\n  'fish_cake':'\\ud83c\\udf65',\n  'fishing_pole_and_fish':'\\ud83c\\udfa3',\n  'fist_raised':'\\u270a',\n  'fist_left':'\\ud83e\\udd1b',\n  'fist_right':'\\ud83e\\udd1c',\n  'flags':'\\ud83c\\udf8f',\n  'flashlight':'\\ud83d\\udd26',\n  'fleur_de_lis':'\\u269c\\ufe0f',\n  'flight_arrival':'\\ud83d\\udeec',\n  'flight_departure':'\\ud83d\\udeeb',\n  'floppy_disk':'\\ud83d\\udcbe',\n  'flower_playing_cards':'\\ud83c\\udfb4',\n  'flushed':'\\ud83d\\ude33',\n  'fog':'\\ud83c\\udf2b',\n  'foggy':'\\ud83c\\udf01',\n  'football':'\\ud83c\\udfc8',\n  'footprints':'\\ud83d\\udc63',\n  'fork_and_knife':'\\ud83c\\udf74',\n  'fountain':'\\u26f2\\ufe0f',\n  'fountain_pen':'\\ud83d\\udd8b',\n  'four_leaf_clover':'\\ud83c\\udf40',\n  'fox_face':'\\ud83e\\udd8a',\n  'framed_picture':'\\ud83d\\uddbc',\n  'free':'\\ud83c\\udd93',\n  'fried_egg':'\\ud83c\\udf73',\n  'fried_shrimp':'\\ud83c\\udf64',\n  'fries':'\\ud83c\\udf5f',\n  'frog':'\\ud83d\\udc38',\n  'frowning':'\\ud83d\\ude26',\n  'frowning_face':'\\u2639\\ufe0f',\n  'frowning_man':'\\ud83d\\ude4d‍\\u2642\\ufe0f',\n  'frowning_woman':'\\ud83d\\ude4d',\n  'middle_finger':'\\ud83d\\udd95',\n  'fuelpump':'\\u26fd\\ufe0f',\n  'full_moon':'\\ud83c\\udf15',\n  'full_moon_with_face':'\\ud83c\\udf1d',\n  'funeral_urn':'\\u26b1\\ufe0f',\n  'game_die':'\\ud83c\\udfb2',\n  'gear':'\\u2699\\ufe0f',\n  'gem':'\\ud83d\\udc8e',\n  'gemini':'\\u264a\\ufe0f',\n  'ghost':'\\ud83d\\udc7b',\n  'gift':'\\ud83c\\udf81',\n  'gift_heart':'\\ud83d\\udc9d',\n  'girl':'\\ud83d\\udc67',\n  'globe_with_meridians':'\\ud83c\\udf10',\n  'goal_net':'\\ud83e\\udd45',\n  'goat':'\\ud83d\\udc10',\n  'golf':'\\u26f3\\ufe0f',\n  'golfing_man':'\\ud83c\\udfcc\\ufe0f',\n  'golfing_woman':'\\ud83c\\udfcc\\ufe0f‍\\u2640\\ufe0f',\n  'gorilla':'\\ud83e\\udd8d',\n  'grapes':'\\ud83c\\udf47',\n  'green_apple':'\\ud83c\\udf4f',\n  'green_book':'\\ud83d\\udcd7',\n  'green_heart':'\\ud83d\\udc9a',\n  'green_salad':'\\ud83e\\udd57',\n  'grey_exclamation':'\\u2755',\n  'grey_question':'\\u2754',\n  'grimacing':'\\ud83d\\ude2c',\n  'grin':'\\ud83d\\ude01',\n  'grinning':'\\ud83d\\ude00',\n  'guardsman':'\\ud83d\\udc82',\n  'guardswoman':'\\ud83d\\udc82‍\\u2640\\ufe0f',\n  'guitar':'\\ud83c\\udfb8',\n  'gun':'\\ud83d\\udd2b',\n  'haircut_woman':'\\ud83d\\udc87',\n  'haircut_man':'\\ud83d\\udc87‍\\u2642\\ufe0f',\n  'hamburger':'\\ud83c\\udf54',\n  'hammer':'\\ud83d\\udd28',\n  'hammer_and_pick':'\\u2692',\n  'hammer_and_wrench':'\\ud83d\\udee0',\n  'hamster':'\\ud83d\\udc39',\n  'hand':'\\u270b',\n  'handbag':'\\ud83d\\udc5c',\n  'handshake':'\\ud83e\\udd1d',\n  'hankey':'\\ud83d\\udca9',\n  'hatched_chick':'\\ud83d\\udc25',\n  'hatching_chick':'\\ud83d\\udc23',\n  'headphones':'\\ud83c\\udfa7',\n  'hear_no_evil':'\\ud83d\\ude49',\n  'heart':'\\u2764\\ufe0f',\n  'heart_decoration':'\\ud83d\\udc9f',\n  'heart_eyes':'\\ud83d\\ude0d',\n  'heart_eyes_cat':'\\ud83d\\ude3b',\n  'heartbeat':'\\ud83d\\udc93',\n  'heartpulse':'\\ud83d\\udc97',\n  'hearts':'\\u2665\\ufe0f',\n  'heavy_check_mark':'\\u2714\\ufe0f',\n  'heavy_division_sign':'\\u2797',\n  'heavy_dollar_sign':'\\ud83d\\udcb2',\n  'heavy_heart_exclamation':'\\u2763\\ufe0f',\n  'heavy_minus_sign':'\\u2796',\n  'heavy_multiplication_x':'\\u2716\\ufe0f',\n  'heavy_plus_sign':'\\u2795',\n  'helicopter':'\\ud83d\\ude81',\n  'herb':'\\ud83c\\udf3f',\n  'hibiscus':'\\ud83c\\udf3a',\n  'high_brightness':'\\ud83d\\udd06',\n  'high_heel':'\\ud83d\\udc60',\n  'hocho':'\\ud83d\\udd2a',\n  'hole':'\\ud83d\\udd73',\n  'honey_pot':'\\ud83c\\udf6f',\n  'horse':'\\ud83d\\udc34',\n  'horse_racing':'\\ud83c\\udfc7',\n  'hospital':'\\ud83c\\udfe5',\n  'hot_pepper':'\\ud83c\\udf36',\n  'hotdog':'\\ud83c\\udf2d',\n  'hotel':'\\ud83c\\udfe8',\n  'hotsprings':'\\u2668\\ufe0f',\n  'hourglass':'\\u231b\\ufe0f',\n  'hourglass_flowing_sand':'\\u23f3',\n  'house':'\\ud83c\\udfe0',\n  'house_with_garden':'\\ud83c\\udfe1',\n  'houses':'\\ud83c\\udfd8',\n  'hugs':'\\ud83e\\udd17',\n  'hushed':'\\ud83d\\ude2f',\n  'ice_cream':'\\ud83c\\udf68',\n  'ice_hockey':'\\ud83c\\udfd2',\n  'ice_skate':'\\u26f8',\n  'icecream':'\\ud83c\\udf66',\n  'id':'\\ud83c\\udd94',\n  'ideograph_advantage':'\\ud83c\\ude50',\n  'imp':'\\ud83d\\udc7f',\n  'inbox_tray':'\\ud83d\\udce5',\n  'incoming_envelope':'\\ud83d\\udce8',\n  'tipping_hand_woman':'\\ud83d\\udc81',\n  'information_source':'\\u2139\\ufe0f',\n  'innocent':'\\ud83d\\ude07',\n  'interrobang':'\\u2049\\ufe0f',\n  'iphone':'\\ud83d\\udcf1',\n  'izakaya_lantern':'\\ud83c\\udfee',\n  'jack_o_lantern':'\\ud83c\\udf83',\n  'japan':'\\ud83d\\uddfe',\n  'japanese_castle':'\\ud83c\\udfef',\n  'japanese_goblin':'\\ud83d\\udc7a',\n  'japanese_ogre':'\\ud83d\\udc79',\n  'jeans':'\\ud83d\\udc56',\n  'joy':'\\ud83d\\ude02',\n  'joy_cat':'\\ud83d\\ude39',\n  'joystick':'\\ud83d\\udd79',\n  'kaaba':'\\ud83d\\udd4b',\n  'key':'\\ud83d\\udd11',\n  'keyboard':'\\u2328\\ufe0f',\n  'keycap_ten':'\\ud83d\\udd1f',\n  'kick_scooter':'\\ud83d\\udef4',\n  'kimono':'\\ud83d\\udc58',\n  'kiss':'\\ud83d\\udc8b',\n  'kissing':'\\ud83d\\ude17',\n  'kissing_cat':'\\ud83d\\ude3d',\n  'kissing_closed_eyes':'\\ud83d\\ude1a',\n  'kissing_heart':'\\ud83d\\ude18',\n  'kissing_smiling_eyes':'\\ud83d\\ude19',\n  'kiwi_fruit':'\\ud83e\\udd5d',\n  'koala':'\\ud83d\\udc28',\n  'koko':'\\ud83c\\ude01',\n  'label':'\\ud83c\\udff7',\n  'large_blue_circle':'\\ud83d\\udd35',\n  'large_blue_diamond':'\\ud83d\\udd37',\n  'large_orange_diamond':'\\ud83d\\udd36',\n  'last_quarter_moon':'\\ud83c\\udf17',\n  'last_quarter_moon_with_face':'\\ud83c\\udf1c',\n  'latin_cross':'\\u271d\\ufe0f',\n  'laughing':'\\ud83d\\ude06',\n  'leaves':'\\ud83c\\udf43',\n  'ledger':'\\ud83d\\udcd2',\n  'left_luggage':'\\ud83d\\udec5',\n  'left_right_arrow':'\\u2194\\ufe0f',\n  'leftwards_arrow_with_hook':'\\u21a9\\ufe0f',\n  'lemon':'\\ud83c\\udf4b',\n  'leo':'\\u264c\\ufe0f',\n  'leopard':'\\ud83d\\udc06',\n  'level_slider':'\\ud83c\\udf9a',\n  'libra':'\\u264e\\ufe0f',\n  'light_rail':'\\ud83d\\ude88',\n  'link':'\\ud83d\\udd17',\n  'lion':'\\ud83e\\udd81',\n  'lips':'\\ud83d\\udc44',\n  'lipstick':'\\ud83d\\udc84',\n  'lizard':'\\ud83e\\udd8e',\n  'lock':'\\ud83d\\udd12',\n  'lock_with_ink_pen':'\\ud83d\\udd0f',\n  'lollipop':'\\ud83c\\udf6d',\n  'loop':'\\u27bf',\n  'loud_sound':'\\ud83d\\udd0a',\n  'loudspeaker':'\\ud83d\\udce2',\n  'love_hotel':'\\ud83c\\udfe9',\n  'love_letter':'\\ud83d\\udc8c',\n  'low_brightness':'\\ud83d\\udd05',\n  'lying_face':'\\ud83e\\udd25',\n  'm':'\\u24c2\\ufe0f',\n  'mag':'\\ud83d\\udd0d',\n  'mag_right':'\\ud83d\\udd0e',\n  'mahjong':'\\ud83c\\udc04\\ufe0f',\n  'mailbox':'\\ud83d\\udceb',\n  'mailbox_closed':'\\ud83d\\udcea',\n  'mailbox_with_mail':'\\ud83d\\udcec',\n  'mailbox_with_no_mail':'\\ud83d\\udced',\n  'man':'\\ud83d\\udc68',\n  'man_artist':'\\ud83d\\udc68‍\\ud83c\\udfa8',\n  'man_astronaut':'\\ud83d\\udc68‍\\ud83d\\ude80',\n  'man_cartwheeling':'\\ud83e\\udd38‍\\u2642\\ufe0f',\n  'man_cook':'\\ud83d\\udc68‍\\ud83c\\udf73',\n  'man_dancing':'\\ud83d\\udd7a',\n  'man_facepalming':'\\ud83e\\udd26‍\\u2642\\ufe0f',\n  'man_factory_worker':'\\ud83d\\udc68‍\\ud83c\\udfed',\n  'man_farmer':'\\ud83d\\udc68‍\\ud83c\\udf3e',\n  'man_firefighter':'\\ud83d\\udc68‍\\ud83d\\ude92',\n  'man_health_worker':'\\ud83d\\udc68‍\\u2695\\ufe0f',\n  'man_in_tuxedo':'\\ud83e\\udd35',\n  'man_judge':'\\ud83d\\udc68‍\\u2696\\ufe0f',\n  'man_juggling':'\\ud83e\\udd39‍\\u2642\\ufe0f',\n  'man_mechanic':'\\ud83d\\udc68‍\\ud83d\\udd27',\n  'man_office_worker':'\\ud83d\\udc68‍\\ud83d\\udcbc',\n  'man_pilot':'\\ud83d\\udc68‍\\u2708\\ufe0f',\n  'man_playing_handball':'\\ud83e\\udd3e‍\\u2642\\ufe0f',\n  'man_playing_water_polo':'\\ud83e\\udd3d‍\\u2642\\ufe0f',\n  'man_scientist':'\\ud83d\\udc68‍\\ud83d\\udd2c',\n  'man_shrugging':'\\ud83e\\udd37‍\\u2642\\ufe0f',\n  'man_singer':'\\ud83d\\udc68‍\\ud83c\\udfa4',\n  'man_student':'\\ud83d\\udc68‍\\ud83c\\udf93',\n  'man_teacher':'\\ud83d\\udc68‍\\ud83c\\udfeb',\n  'man_technologist':'\\ud83d\\udc68‍\\ud83d\\udcbb',\n  'man_with_gua_pi_mao':'\\ud83d\\udc72',\n  'man_with_turban':'\\ud83d\\udc73',\n  'tangerine':'\\ud83c\\udf4a',\n  'mans_shoe':'\\ud83d\\udc5e',\n  'mantelpiece_clock':'\\ud83d\\udd70',\n  'maple_leaf':'\\ud83c\\udf41',\n  'martial_arts_uniform':'\\ud83e\\udd4b',\n  'mask':'\\ud83d\\ude37',\n  'massage_woman':'\\ud83d\\udc86',\n  'massage_man':'\\ud83d\\udc86‍\\u2642\\ufe0f',\n  'meat_on_bone':'\\ud83c\\udf56',\n  'medal_military':'\\ud83c\\udf96',\n  'medal_sports':'\\ud83c\\udfc5',\n  'mega':'\\ud83d\\udce3',\n  'melon':'\\ud83c\\udf48',\n  'memo':'\\ud83d\\udcdd',\n  'men_wrestling':'\\ud83e\\udd3c‍\\u2642\\ufe0f',\n  'menorah':'\\ud83d\\udd4e',\n  'mens':'\\ud83d\\udeb9',\n  'metal':'\\ud83e\\udd18',\n  'metro':'\\ud83d\\ude87',\n  'microphone':'\\ud83c\\udfa4',\n  'microscope':'\\ud83d\\udd2c',\n  'milk_glass':'\\ud83e\\udd5b',\n  'milky_way':'\\ud83c\\udf0c',\n  'minibus':'\\ud83d\\ude90',\n  'minidisc':'\\ud83d\\udcbd',\n  'mobile_phone_off':'\\ud83d\\udcf4',\n  'money_mouth_face':'\\ud83e\\udd11',\n  'money_with_wings':'\\ud83d\\udcb8',\n  'moneybag':'\\ud83d\\udcb0',\n  'monkey':'\\ud83d\\udc12',\n  'monkey_face':'\\ud83d\\udc35',\n  'monorail':'\\ud83d\\ude9d',\n  'moon':'\\ud83c\\udf14',\n  'mortar_board':'\\ud83c\\udf93',\n  'mosque':'\\ud83d\\udd4c',\n  'motor_boat':'\\ud83d\\udee5',\n  'motor_scooter':'\\ud83d\\udef5',\n  'motorcycle':'\\ud83c\\udfcd',\n  'motorway':'\\ud83d\\udee3',\n  'mount_fuji':'\\ud83d\\uddfb',\n  'mountain':'\\u26f0',\n  'mountain_biking_man':'\\ud83d\\udeb5',\n  'mountain_biking_woman':'\\ud83d\\udeb5‍\\u2640\\ufe0f',\n  'mountain_cableway':'\\ud83d\\udea0',\n  'mountain_railway':'\\ud83d\\ude9e',\n  'mountain_snow':'\\ud83c\\udfd4',\n  'mouse':'\\ud83d\\udc2d',\n  'mouse2':'\\ud83d\\udc01',\n  'movie_camera':'\\ud83c\\udfa5',\n  'moyai':'\\ud83d\\uddff',\n  'mrs_claus':'\\ud83e\\udd36',\n  'muscle':'\\ud83d\\udcaa',\n  'mushroom':'\\ud83c\\udf44',\n  'musical_keyboard':'\\ud83c\\udfb9',\n  'musical_note':'\\ud83c\\udfb5',\n  'musical_score':'\\ud83c\\udfbc',\n  'mute':'\\ud83d\\udd07',\n  'nail_care':'\\ud83d\\udc85',\n  'name_badge':'\\ud83d\\udcdb',\n  'national_park':'\\ud83c\\udfde',\n  'nauseated_face':'\\ud83e\\udd22',\n  'necktie':'\\ud83d\\udc54',\n  'negative_squared_cross_mark':'\\u274e',\n  'nerd_face':'\\ud83e\\udd13',\n  'neutral_face':'\\ud83d\\ude10',\n  'new':'\\ud83c\\udd95',\n  'new_moon':'\\ud83c\\udf11',\n  'new_moon_with_face':'\\ud83c\\udf1a',\n  'newspaper':'\\ud83d\\udcf0',\n  'newspaper_roll':'\\ud83d\\uddde',\n  'next_track_button':'\\u23ed',\n  'ng':'\\ud83c\\udd96',\n  'no_good_man':'\\ud83d\\ude45‍\\u2642\\ufe0f',\n  'no_good_woman':'\\ud83d\\ude45',\n  'night_with_stars':'\\ud83c\\udf03',\n  'no_bell':'\\ud83d\\udd15',\n  'no_bicycles':'\\ud83d\\udeb3',\n  'no_entry':'\\u26d4\\ufe0f',\n  'no_entry_sign':'\\ud83d\\udeab',\n  'no_mobile_phones':'\\ud83d\\udcf5',\n  'no_mouth':'\\ud83d\\ude36',\n  'no_pedestrians':'\\ud83d\\udeb7',\n  'no_smoking':'\\ud83d\\udead',\n  'non-potable_water':'\\ud83d\\udeb1',\n  'nose':'\\ud83d\\udc43',\n  'notebook':'\\ud83d\\udcd3',\n  'notebook_with_decorative_cover':'\\ud83d\\udcd4',\n  'notes':'\\ud83c\\udfb6',\n  'nut_and_bolt':'\\ud83d\\udd29',\n  'o':'\\u2b55\\ufe0f',\n  'o2':'\\ud83c\\udd7e\\ufe0f',\n  'ocean':'\\ud83c\\udf0a',\n  'octopus':'\\ud83d\\udc19',\n  'oden':'\\ud83c\\udf62',\n  'office':'\\ud83c\\udfe2',\n  'oil_drum':'\\ud83d\\udee2',\n  'ok':'\\ud83c\\udd97',\n  'ok_hand':'\\ud83d\\udc4c',\n  'ok_man':'\\ud83d\\ude46‍\\u2642\\ufe0f',\n  'ok_woman':'\\ud83d\\ude46',\n  'old_key':'\\ud83d\\udddd',\n  'older_man':'\\ud83d\\udc74',\n  'older_woman':'\\ud83d\\udc75',\n  'om':'\\ud83d\\udd49',\n  'on':'\\ud83d\\udd1b',\n  'oncoming_automobile':'\\ud83d\\ude98',\n  'oncoming_bus':'\\ud83d\\ude8d',\n  'oncoming_police_car':'\\ud83d\\ude94',\n  'oncoming_taxi':'\\ud83d\\ude96',\n  'open_file_folder':'\\ud83d\\udcc2',\n  'open_hands':'\\ud83d\\udc50',\n  'open_mouth':'\\ud83d\\ude2e',\n  'open_umbrella':'\\u2602\\ufe0f',\n  'ophiuchus':'\\u26ce',\n  'orange_book':'\\ud83d\\udcd9',\n  'orthodox_cross':'\\u2626\\ufe0f',\n  'outbox_tray':'\\ud83d\\udce4',\n  'owl':'\\ud83e\\udd89',\n  'ox':'\\ud83d\\udc02',\n  'package':'\\ud83d\\udce6',\n  'page_facing_up':'\\ud83d\\udcc4',\n  'page_with_curl':'\\ud83d\\udcc3',\n  'pager':'\\ud83d\\udcdf',\n  'paintbrush':'\\ud83d\\udd8c',\n  'palm_tree':'\\ud83c\\udf34',\n  'pancakes':'\\ud83e\\udd5e',\n  'panda_face':'\\ud83d\\udc3c',\n  'paperclip':'\\ud83d\\udcce',\n  'paperclips':'\\ud83d\\udd87',\n  'parasol_on_ground':'\\u26f1',\n  'parking':'\\ud83c\\udd7f\\ufe0f',\n  'part_alternation_mark':'\\u303d\\ufe0f',\n  'partly_sunny':'\\u26c5\\ufe0f',\n  'passenger_ship':'\\ud83d\\udef3',\n  'passport_control':'\\ud83d\\udec2',\n  'pause_button':'\\u23f8',\n  'peace_symbol':'\\u262e\\ufe0f',\n  'peach':'\\ud83c\\udf51',\n  'peanuts':'\\ud83e\\udd5c',\n  'pear':'\\ud83c\\udf50',\n  'pen':'\\ud83d\\udd8a',\n  'pencil2':'\\u270f\\ufe0f',\n  'penguin':'\\ud83d\\udc27',\n  'pensive':'\\ud83d\\ude14',\n  'performing_arts':'\\ud83c\\udfad',\n  'persevere':'\\ud83d\\ude23',\n  'person_fencing':'\\ud83e\\udd3a',\n  'pouting_woman':'\\ud83d\\ude4e',\n  'phone':'\\u260e\\ufe0f',\n  'pick':'\\u26cf',\n  'pig':'\\ud83d\\udc37',\n  'pig2':'\\ud83d\\udc16',\n  'pig_nose':'\\ud83d\\udc3d',\n  'pill':'\\ud83d\\udc8a',\n  'pineapple':'\\ud83c\\udf4d',\n  'ping_pong':'\\ud83c\\udfd3',\n  'pisces':'\\u2653\\ufe0f',\n  'pizza':'\\ud83c\\udf55',\n  'place_of_worship':'\\ud83d\\uded0',\n  'plate_with_cutlery':'\\ud83c\\udf7d',\n  'play_or_pause_button':'\\u23ef',\n  'point_down':'\\ud83d\\udc47',\n  'point_left':'\\ud83d\\udc48',\n  'point_right':'\\ud83d\\udc49',\n  'point_up':'\\u261d\\ufe0f',\n  'point_up_2':'\\ud83d\\udc46',\n  'police_car':'\\ud83d\\ude93',\n  'policewoman':'\\ud83d\\udc6e‍\\u2640\\ufe0f',\n  'poodle':'\\ud83d\\udc29',\n  'popcorn':'\\ud83c\\udf7f',\n  'post_office':'\\ud83c\\udfe3',\n  'postal_horn':'\\ud83d\\udcef',\n  'postbox':'\\ud83d\\udcee',\n  'potable_water':'\\ud83d\\udeb0',\n  'potato':'\\ud83e\\udd54',\n  'pouch':'\\ud83d\\udc5d',\n  'poultry_leg':'\\ud83c\\udf57',\n  'pound':'\\ud83d\\udcb7',\n  'rage':'\\ud83d\\ude21',\n  'pouting_cat':'\\ud83d\\ude3e',\n  'pouting_man':'\\ud83d\\ude4e‍\\u2642\\ufe0f',\n  'pray':'\\ud83d\\ude4f',\n  'prayer_beads':'\\ud83d\\udcff',\n  'pregnant_woman':'\\ud83e\\udd30',\n  'previous_track_button':'\\u23ee',\n  'prince':'\\ud83e\\udd34',\n  'princess':'\\ud83d\\udc78',\n  'printer':'\\ud83d\\udda8',\n  'purple_heart':'\\ud83d\\udc9c',\n  'purse':'\\ud83d\\udc5b',\n  'pushpin':'\\ud83d\\udccc',\n  'put_litter_in_its_place':'\\ud83d\\udeae',\n  'question':'\\u2753',\n  'rabbit':'\\ud83d\\udc30',\n  'rabbit2':'\\ud83d\\udc07',\n  'racehorse':'\\ud83d\\udc0e',\n  'racing_car':'\\ud83c\\udfce',\n  'radio':'\\ud83d\\udcfb',\n  'radio_button':'\\ud83d\\udd18',\n  'radioactive':'\\u2622\\ufe0f',\n  'railway_car':'\\ud83d\\ude83',\n  'railway_track':'\\ud83d\\udee4',\n  'rainbow':'\\ud83c\\udf08',\n  'rainbow_flag':'\\ud83c\\udff3\\ufe0f‍\\ud83c\\udf08',\n  'raised_back_of_hand':'\\ud83e\\udd1a',\n  'raised_hand_with_fingers_splayed':'\\ud83d\\udd90',\n  'raised_hands':'\\ud83d\\ude4c',\n  'raising_hand_woman':'\\ud83d\\ude4b',\n  'raising_hand_man':'\\ud83d\\ude4b‍\\u2642\\ufe0f',\n  'ram':'\\ud83d\\udc0f',\n  'ramen':'\\ud83c\\udf5c',\n  'rat':'\\ud83d\\udc00',\n  'record_button':'\\u23fa',\n  'recycle':'\\u267b\\ufe0f',\n  'red_circle':'\\ud83d\\udd34',\n  'registered':'\\u00ae\\ufe0f',\n  'relaxed':'\\u263a\\ufe0f',\n  'relieved':'\\ud83d\\ude0c',\n  'reminder_ribbon':'\\ud83c\\udf97',\n  'repeat':'\\ud83d\\udd01',\n  'repeat_one':'\\ud83d\\udd02',\n  'rescue_worker_helmet':'\\u26d1',\n  'restroom':'\\ud83d\\udebb',\n  'revolving_hearts':'\\ud83d\\udc9e',\n  'rewind':'\\u23ea',\n  'rhinoceros':'\\ud83e\\udd8f',\n  'ribbon':'\\ud83c\\udf80',\n  'rice':'\\ud83c\\udf5a',\n  'rice_ball':'\\ud83c\\udf59',\n  'rice_cracker':'\\ud83c\\udf58',\n  'rice_scene':'\\ud83c\\udf91',\n  'right_anger_bubble':'\\ud83d\\uddef',\n  'ring':'\\ud83d\\udc8d',\n  'robot':'\\ud83e\\udd16',\n  'rocket':'\\ud83d\\ude80',\n  'rofl':'\\ud83e\\udd23',\n  'roll_eyes':'\\ud83d\\ude44',\n  'roller_coaster':'\\ud83c\\udfa2',\n  'rooster':'\\ud83d\\udc13',\n  'rose':'\\ud83c\\udf39',\n  'rosette':'\\ud83c\\udff5',\n  'rotating_light':'\\ud83d\\udea8',\n  'round_pushpin':'\\ud83d\\udccd',\n  'rowing_man':'\\ud83d\\udea3',\n  'rowing_woman':'\\ud83d\\udea3‍\\u2640\\ufe0f',\n  'rugby_football':'\\ud83c\\udfc9',\n  'running_man':'\\ud83c\\udfc3',\n  'running_shirt_with_sash':'\\ud83c\\udfbd',\n  'running_woman':'\\ud83c\\udfc3‍\\u2640\\ufe0f',\n  'sa':'\\ud83c\\ude02\\ufe0f',\n  'sagittarius':'\\u2650\\ufe0f',\n  'sake':'\\ud83c\\udf76',\n  'sandal':'\\ud83d\\udc61',\n  'santa':'\\ud83c\\udf85',\n  'satellite':'\\ud83d\\udce1',\n  'saxophone':'\\ud83c\\udfb7',\n  'school':'\\ud83c\\udfeb',\n  'school_satchel':'\\ud83c\\udf92',\n  'scissors':'\\u2702\\ufe0f',\n  'scorpion':'\\ud83e\\udd82',\n  'scorpius':'\\u264f\\ufe0f',\n  'scream':'\\ud83d\\ude31',\n  'scream_cat':'\\ud83d\\ude40',\n  'scroll':'\\ud83d\\udcdc',\n  'seat':'\\ud83d\\udcba',\n  'secret':'\\u3299\\ufe0f',\n  'see_no_evil':'\\ud83d\\ude48',\n  'seedling':'\\ud83c\\udf31',\n  'selfie':'\\ud83e\\udd33',\n  'shallow_pan_of_food':'\\ud83e\\udd58',\n  'shamrock':'\\u2618\\ufe0f',\n  'shark':'\\ud83e\\udd88',\n  'shaved_ice':'\\ud83c\\udf67',\n  'sheep':'\\ud83d\\udc11',\n  'shell':'\\ud83d\\udc1a',\n  'shield':'\\ud83d\\udee1',\n  'shinto_shrine':'\\u26e9',\n  'ship':'\\ud83d\\udea2',\n  'shirt':'\\ud83d\\udc55',\n  'shopping':'\\ud83d\\udecd',\n  'shopping_cart':'\\ud83d\\uded2',\n  'shower':'\\ud83d\\udebf',\n  'shrimp':'\\ud83e\\udd90',\n  'signal_strength':'\\ud83d\\udcf6',\n  'six_pointed_star':'\\ud83d\\udd2f',\n  'ski':'\\ud83c\\udfbf',\n  'skier':'\\u26f7',\n  'skull':'\\ud83d\\udc80',\n  'skull_and_crossbones':'\\u2620\\ufe0f',\n  'sleeping':'\\ud83d\\ude34',\n  'sleeping_bed':'\\ud83d\\udecc',\n  'sleepy':'\\ud83d\\ude2a',\n  'slightly_frowning_face':'\\ud83d\\ude41',\n  'slightly_smiling_face':'\\ud83d\\ude42',\n  'slot_machine':'\\ud83c\\udfb0',\n  'small_airplane':'\\ud83d\\udee9',\n  'small_blue_diamond':'\\ud83d\\udd39',\n  'small_orange_diamond':'\\ud83d\\udd38',\n  'small_red_triangle':'\\ud83d\\udd3a',\n  'small_red_triangle_down':'\\ud83d\\udd3b',\n  'smile':'\\ud83d\\ude04',\n  'smile_cat':'\\ud83d\\ude38',\n  'smiley':'\\ud83d\\ude03',\n  'smiley_cat':'\\ud83d\\ude3a',\n  'smiling_imp':'\\ud83d\\ude08',\n  'smirk':'\\ud83d\\ude0f',\n  'smirk_cat':'\\ud83d\\ude3c',\n  'smoking':'\\ud83d\\udeac',\n  'snail':'\\ud83d\\udc0c',\n  'snake':'\\ud83d\\udc0d',\n  'sneezing_face':'\\ud83e\\udd27',\n  'snowboarder':'\\ud83c\\udfc2',\n  'snowflake':'\\u2744\\ufe0f',\n  'snowman':'\\u26c4\\ufe0f',\n  'snowman_with_snow':'\\u2603\\ufe0f',\n  'sob':'\\ud83d\\ude2d',\n  'soccer':'\\u26bd\\ufe0f',\n  'soon':'\\ud83d\\udd1c',\n  'sos':'\\ud83c\\udd98',\n  'sound':'\\ud83d\\udd09',\n  'space_invader':'\\ud83d\\udc7e',\n  'spades':'\\u2660\\ufe0f',\n  'spaghetti':'\\ud83c\\udf5d',\n  'sparkle':'\\u2747\\ufe0f',\n  'sparkler':'\\ud83c\\udf87',\n  'sparkles':'\\u2728',\n  'sparkling_heart':'\\ud83d\\udc96',\n  'speak_no_evil':'\\ud83d\\ude4a',\n  'speaker':'\\ud83d\\udd08',\n  'speaking_head':'\\ud83d\\udde3',\n  'speech_balloon':'\\ud83d\\udcac',\n  'speedboat':'\\ud83d\\udea4',\n  'spider':'\\ud83d\\udd77',\n  'spider_web':'\\ud83d\\udd78',\n  'spiral_calendar':'\\ud83d\\uddd3',\n  'spiral_notepad':'\\ud83d\\uddd2',\n  'spoon':'\\ud83e\\udd44',\n  'squid':'\\ud83e\\udd91',\n  'stadium':'\\ud83c\\udfdf',\n  'star':'\\u2b50\\ufe0f',\n  'star2':'\\ud83c\\udf1f',\n  'star_and_crescent':'\\u262a\\ufe0f',\n  'star_of_david':'\\u2721\\ufe0f',\n  'stars':'\\ud83c\\udf20',\n  'station':'\\ud83d\\ude89',\n  'statue_of_liberty':'\\ud83d\\uddfd',\n  'steam_locomotive':'\\ud83d\\ude82',\n  'stew':'\\ud83c\\udf72',\n  'stop_button':'\\u23f9',\n  'stop_sign':'\\ud83d\\uded1',\n  'stopwatch':'\\u23f1',\n  'straight_ruler':'\\ud83d\\udccf',\n  'strawberry':'\\ud83c\\udf53',\n  'stuck_out_tongue':'\\ud83d\\ude1b',\n  'stuck_out_tongue_closed_eyes':'\\ud83d\\ude1d',\n  'stuck_out_tongue_winking_eye':'\\ud83d\\ude1c',\n  'studio_microphone':'\\ud83c\\udf99',\n  'stuffed_flatbread':'\\ud83e\\udd59',\n  'sun_behind_large_cloud':'\\ud83c\\udf25',\n  'sun_behind_rain_cloud':'\\ud83c\\udf26',\n  'sun_behind_small_cloud':'\\ud83c\\udf24',\n  'sun_with_face':'\\ud83c\\udf1e',\n  'sunflower':'\\ud83c\\udf3b',\n  'sunglasses':'\\ud83d\\ude0e',\n  'sunny':'\\u2600\\ufe0f',\n  'sunrise':'\\ud83c\\udf05',\n  'sunrise_over_mountains':'\\ud83c\\udf04',\n  'surfing_man':'\\ud83c\\udfc4',\n  'surfing_woman':'\\ud83c\\udfc4‍\\u2640\\ufe0f',\n  'sushi':'\\ud83c\\udf63',\n  'suspension_railway':'\\ud83d\\ude9f',\n  'sweat':'\\ud83d\\ude13',\n  'sweat_drops':'\\ud83d\\udca6',\n  'sweat_smile':'\\ud83d\\ude05',\n  'sweet_potato':'\\ud83c\\udf60',\n  'swimming_man':'\\ud83c\\udfca',\n  'swimming_woman':'\\ud83c\\udfca‍\\u2640\\ufe0f',\n  'symbols':'\\ud83d\\udd23',\n  'synagogue':'\\ud83d\\udd4d',\n  'syringe':'\\ud83d\\udc89',\n  'taco':'\\ud83c\\udf2e',\n  'tada':'\\ud83c\\udf89',\n  'tanabata_tree':'\\ud83c\\udf8b',\n  'taurus':'\\u2649\\ufe0f',\n  'taxi':'\\ud83d\\ude95',\n  'tea':'\\ud83c\\udf75',\n  'telephone_receiver':'\\ud83d\\udcde',\n  'telescope':'\\ud83d\\udd2d',\n  'tennis':'\\ud83c\\udfbe',\n  'tent':'\\u26fa\\ufe0f',\n  'thermometer':'\\ud83c\\udf21',\n  'thinking':'\\ud83e\\udd14',\n  'thought_balloon':'\\ud83d\\udcad',\n  'ticket':'\\ud83c\\udfab',\n  'tickets':'\\ud83c\\udf9f',\n  'tiger':'\\ud83d\\udc2f',\n  'tiger2':'\\ud83d\\udc05',\n  'timer_clock':'\\u23f2',\n  'tipping_hand_man':'\\ud83d\\udc81‍\\u2642\\ufe0f',\n  'tired_face':'\\ud83d\\ude2b',\n  'tm':'\\u2122\\ufe0f',\n  'toilet':'\\ud83d\\udebd',\n  'tokyo_tower':'\\ud83d\\uddfc',\n  'tomato':'\\ud83c\\udf45',\n  'tongue':'\\ud83d\\udc45',\n  'top':'\\ud83d\\udd1d',\n  'tophat':'\\ud83c\\udfa9',\n  'tornado':'\\ud83c\\udf2a',\n  'trackball':'\\ud83d\\uddb2',\n  'tractor':'\\ud83d\\ude9c',\n  'traffic_light':'\\ud83d\\udea5',\n  'train':'\\ud83d\\ude8b',\n  'train2':'\\ud83d\\ude86',\n  'tram':'\\ud83d\\ude8a',\n  'triangular_flag_on_post':'\\ud83d\\udea9',\n  'triangular_ruler':'\\ud83d\\udcd0',\n  'trident':'\\ud83d\\udd31',\n  'triumph':'\\ud83d\\ude24',\n  'trolleybus':'\\ud83d\\ude8e',\n  'trophy':'\\ud83c\\udfc6',\n  'tropical_drink':'\\ud83c\\udf79',\n  'tropical_fish':'\\ud83d\\udc20',\n  'truck':'\\ud83d\\ude9a',\n  'trumpet':'\\ud83c\\udfba',\n  'tulip':'\\ud83c\\udf37',\n  'tumbler_glass':'\\ud83e\\udd43',\n  'turkey':'\\ud83e\\udd83',\n  'turtle':'\\ud83d\\udc22',\n  'tv':'\\ud83d\\udcfa',\n  'twisted_rightwards_arrows':'\\ud83d\\udd00',\n  'two_hearts':'\\ud83d\\udc95',\n  'two_men_holding_hands':'\\ud83d\\udc6c',\n  'two_women_holding_hands':'\\ud83d\\udc6d',\n  'u5272':'\\ud83c\\ude39',\n  'u5408':'\\ud83c\\ude34',\n  'u55b6':'\\ud83c\\ude3a',\n  'u6307':'\\ud83c\\ude2f\\ufe0f',\n  'u6708':'\\ud83c\\ude37\\ufe0f',\n  'u6709':'\\ud83c\\ude36',\n  'u6e80':'\\ud83c\\ude35',\n  'u7121':'\\ud83c\\ude1a\\ufe0f',\n  'u7533':'\\ud83c\\ude38',\n  'u7981':'\\ud83c\\ude32',\n  'u7a7a':'\\ud83c\\ude33',\n  'umbrella':'\\u2614\\ufe0f',\n  'unamused':'\\ud83d\\ude12',\n  'underage':'\\ud83d\\udd1e',\n  'unicorn':'\\ud83e\\udd84',\n  'unlock':'\\ud83d\\udd13',\n  'up':'\\ud83c\\udd99',\n  'upside_down_face':'\\ud83d\\ude43',\n  'v':'\\u270c\\ufe0f',\n  'vertical_traffic_light':'\\ud83d\\udea6',\n  'vhs':'\\ud83d\\udcfc',\n  'vibration_mode':'\\ud83d\\udcf3',\n  'video_camera':'\\ud83d\\udcf9',\n  'video_game':'\\ud83c\\udfae',\n  'violin':'\\ud83c\\udfbb',\n  'virgo':'\\u264d\\ufe0f',\n  'volcano':'\\ud83c\\udf0b',\n  'volleyball':'\\ud83c\\udfd0',\n  'vs':'\\ud83c\\udd9a',\n  'vulcan_salute':'\\ud83d\\udd96',\n  'walking_man':'\\ud83d\\udeb6',\n  'walking_woman':'\\ud83d\\udeb6‍\\u2640\\ufe0f',\n  'waning_crescent_moon':'\\ud83c\\udf18',\n  'waning_gibbous_moon':'\\ud83c\\udf16',\n  'warning':'\\u26a0\\ufe0f',\n  'wastebasket':'\\ud83d\\uddd1',\n  'watch':'\\u231a\\ufe0f',\n  'water_buffalo':'\\ud83d\\udc03',\n  'watermelon':'\\ud83c\\udf49',\n  'wave':'\\ud83d\\udc4b',\n  'wavy_dash':'\\u3030\\ufe0f',\n  'waxing_crescent_moon':'\\ud83c\\udf12',\n  'wc':'\\ud83d\\udebe',\n  'weary':'\\ud83d\\ude29',\n  'wedding':'\\ud83d\\udc92',\n  'weight_lifting_man':'\\ud83c\\udfcb\\ufe0f',\n  'weight_lifting_woman':'\\ud83c\\udfcb\\ufe0f‍\\u2640\\ufe0f',\n  'whale':'\\ud83d\\udc33',\n  'whale2':'\\ud83d\\udc0b',\n  'wheel_of_dharma':'\\u2638\\ufe0f',\n  'wheelchair':'\\u267f\\ufe0f',\n  'white_check_mark':'\\u2705',\n  'white_circle':'\\u26aa\\ufe0f',\n  'white_flag':'\\ud83c\\udff3\\ufe0f',\n  'white_flower':'\\ud83d\\udcae',\n  'white_large_square':'\\u2b1c\\ufe0f',\n  'white_medium_small_square':'\\u25fd\\ufe0f',\n  'white_medium_square':'\\u25fb\\ufe0f',\n  'white_small_square':'\\u25ab\\ufe0f',\n  'white_square_button':'\\ud83d\\udd33',\n  'wilted_flower':'\\ud83e\\udd40',\n  'wind_chime':'\\ud83c\\udf90',\n  'wind_face':'\\ud83c\\udf2c',\n  'wine_glass':'\\ud83c\\udf77',\n  'wink':'\\ud83d\\ude09',\n  'wolf':'\\ud83d\\udc3a',\n  'woman':'\\ud83d\\udc69',\n  'woman_artist':'\\ud83d\\udc69‍\\ud83c\\udfa8',\n  'woman_astronaut':'\\ud83d\\udc69‍\\ud83d\\ude80',\n  'woman_cartwheeling':'\\ud83e\\udd38‍\\u2640\\ufe0f',\n  'woman_cook':'\\ud83d\\udc69‍\\ud83c\\udf73',\n  'woman_facepalming':'\\ud83e\\udd26‍\\u2640\\ufe0f',\n  'woman_factory_worker':'\\ud83d\\udc69‍\\ud83c\\udfed',\n  'woman_farmer':'\\ud83d\\udc69‍\\ud83c\\udf3e',\n  'woman_firefighter':'\\ud83d\\udc69‍\\ud83d\\ude92',\n  'woman_health_worker':'\\ud83d\\udc69‍\\u2695\\ufe0f',\n  'woman_judge':'\\ud83d\\udc69‍\\u2696\\ufe0f',\n  'woman_juggling':'\\ud83e\\udd39‍\\u2640\\ufe0f',\n  'woman_mechanic':'\\ud83d\\udc69‍\\ud83d\\udd27',\n  'woman_office_worker':'\\ud83d\\udc69‍\\ud83d\\udcbc',\n  'woman_pilot':'\\ud83d\\udc69‍\\u2708\\ufe0f',\n  'woman_playing_handball':'\\ud83e\\udd3e‍\\u2640\\ufe0f',\n  'woman_playing_water_polo':'\\ud83e\\udd3d‍\\u2640\\ufe0f',\n  'woman_scientist':'\\ud83d\\udc69‍\\ud83d\\udd2c',\n  'woman_shrugging':'\\ud83e\\udd37‍\\u2640\\ufe0f',\n  'woman_singer':'\\ud83d\\udc69‍\\ud83c\\udfa4',\n  'woman_student':'\\ud83d\\udc69‍\\ud83c\\udf93',\n  'woman_teacher':'\\ud83d\\udc69‍\\ud83c\\udfeb',\n  'woman_technologist':'\\ud83d\\udc69‍\\ud83d\\udcbb',\n  'woman_with_turban':'\\ud83d\\udc73‍\\u2640\\ufe0f',\n  'womans_clothes':'\\ud83d\\udc5a',\n  'womans_hat':'\\ud83d\\udc52',\n  'women_wrestling':'\\ud83e\\udd3c‍\\u2640\\ufe0f',\n  'womens':'\\ud83d\\udeba',\n  'world_map':'\\ud83d\\uddfa',\n  'worried':'\\ud83d\\ude1f',\n  'wrench':'\\ud83d\\udd27',\n  'writing_hand':'\\u270d\\ufe0f',\n  'x':'\\u274c',\n  'yellow_heart':'\\ud83d\\udc9b',\n  'yen':'\\ud83d\\udcb4',\n  'yin_yang':'\\u262f\\ufe0f',\n  'yum':'\\ud83d\\ude0b',\n  'zap':'\\u26a1\\ufe0f',\n  'zipper_mouth_face':'\\ud83e\\udd10',\n  'zzz':'\\ud83d\\udca4',\n\n  /* special emojis :P */\n  'octocat':  '\":octocat:\"',\n  'showdown': 'S'\n};\n","/**\n * Created by Estevao on 31-05-2015.\n */\n\n/**\n * Showdown Converter class\n * @class\n * @param {object} [converterOptions]\n * @returns {Converter}\n */\nshowdown.Converter = function (converterOptions) {\n  'use strict';\n\n  var\n      /**\n       * Options used by this converter\n       * @private\n       * @type {{}}\n       */\n      options = {},\n\n      /**\n       * Language extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      langExtensions = [],\n\n      /**\n       * Output modifiers extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      outputModifiers = [],\n\n      /**\n       * Event listeners\n       * @private\n       * @type {{}}\n       */\n      listeners = {},\n\n      /**\n       * The flavor set in this converter\n       */\n      setConvFlavor = setFlavor,\n\n      /**\n       * Metadata of the document\n       * @type {{parsed: {}, raw: string, format: string}}\n       */\n      metadata = {\n        parsed: {},\n        raw: '',\n        format: ''\n      };\n\n  _constructor();\n\n  /**\n   * Converter constructor\n   * @private\n   */\n  function _constructor () {\n    converterOptions = converterOptions || {};\n\n    for (var gOpt in globalOptions) {\n      if (globalOptions.hasOwnProperty(gOpt)) {\n        options[gOpt] = globalOptions[gOpt];\n      }\n    }\n\n    // Merge options\n    if (typeof converterOptions === 'object') {\n      for (var opt in converterOptions) {\n        if (converterOptions.hasOwnProperty(opt)) {\n          options[opt] = converterOptions[opt];\n        }\n      }\n    } else {\n      throw Error('Converter expects the passed parameter to be an object, but ' + typeof converterOptions +\n      ' was passed instead.');\n    }\n\n    if (options.extensions) {\n      showdown.helper.forEach(options.extensions, _parseExtension);\n    }\n  }\n\n  /**\n   * Parse extension\n   * @param {*} ext\n   * @param {string} [name='']\n   * @private\n   */\n  function _parseExtension (ext, name) {\n\n    name = name || null;\n    // If it's a string, the extension was previously loaded\n    if (showdown.helper.isString(ext)) {\n      ext = showdown.helper.stdExtName(ext);\n      name = ext;\n\n      // LEGACY_SUPPORT CODE\n      if (showdown.extensions[ext]) {\n        console.warn('DEPRECATION WARNING: ' + ext + ' is an old extension that uses a deprecated loading method.' +\n          'Please inform the developer that the extension should be updated!');\n        legacyExtensionLoading(showdown.extensions[ext], ext);\n        return;\n        // END LEGACY SUPPORT CODE\n\n      } else if (!showdown.helper.isUndefined(extensions[ext])) {\n        ext = extensions[ext];\n\n      } else {\n        throw Error('Extension \"' + ext + '\" could not be loaded. It was either not found or is not a valid extension.');\n      }\n    }\n\n    if (typeof ext === 'function') {\n      ext = ext();\n    }\n\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n\n    var validExt = validate(ext, name);\n    if (!validExt.valid) {\n      throw Error(validExt.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n      }\n      if (ext[i].hasOwnProperty('listeners')) {\n        for (var ln in ext[i].listeners) {\n          if (ext[i].listeners.hasOwnProperty(ln)) {\n            listen(ln, ext[i].listeners[ln]);\n          }\n        }\n      }\n    }\n\n  }\n\n  /**\n   * LEGACY_SUPPORT\n   * @param {*} ext\n   * @param {string} name\n   */\n  function legacyExtensionLoading (ext, name) {\n    if (typeof ext === 'function') {\n      ext = ext(new showdown.Converter());\n    }\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n    var valid = validate(ext, name);\n\n    if (!valid.valid) {\n      throw Error(valid.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n        default:// should never reach here\n          throw Error('Extension loader error: Type unrecognized!!!');\n      }\n    }\n  }\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   */\n  function listen (name, callback) {\n    if (!showdown.helper.isString(name)) {\n      throw Error('Invalid argument in converter.listen() method: name must be a string, but ' + typeof name + ' given');\n    }\n\n    if (typeof callback !== 'function') {\n      throw Error('Invalid argument in converter.listen() method: callback must be a function, but ' + typeof callback + ' given');\n    }\n\n    if (!listeners.hasOwnProperty(name)) {\n      listeners[name] = [];\n    }\n    listeners[name].push(callback);\n  }\n\n  function rTrimInputText (text) {\n    var rsp = text.match(/^\\s*/)[0].length,\n        rgx = new RegExp('^\\\\s{0,' + rsp + '}', 'gm');\n    return text.replace(rgx, '');\n  }\n\n  /**\n   * Dispatch an event\n   * @private\n   * @param {string} evtName Event name\n   * @param {string} text Text\n   * @param {{}} options Converter Options\n   * @param {{}} globals\n   * @returns {string}\n   */\n  this._dispatch = function dispatch (evtName, text, options, globals) {\n    if (listeners.hasOwnProperty(evtName)) {\n      for (var ei = 0; ei < listeners[evtName].length; ++ei) {\n        var nText = listeners[evtName][ei](evtName, text, this, options, globals);\n        if (nText && typeof nText !== 'undefined') {\n          text = nText;\n        }\n      }\n    }\n    return text;\n  };\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   * @returns {showdown.Converter}\n   */\n  this.listen = function (name, callback) {\n    listen(name, callback);\n    return this;\n  };\n\n  /**\n   * Converts a markdown string into HTML\n   * @param {string} text\n   * @returns {*}\n   */\n  this.makeHtml = function (text) {\n    //check if text is not falsy\n    if (!text) {\n      return text;\n    }\n\n    var globals = {\n      gHtmlBlocks:     [],\n      gHtmlMdBlocks:   [],\n      gHtmlSpans:      [],\n      gUrls:           {},\n      gTitles:         {},\n      gDimensions:     {},\n      gListLevel:      0,\n      hashLinkCounts:  {},\n      langExtensions:  langExtensions,\n      outputModifiers: outputModifiers,\n      converter:       this,\n      ghCodeBlocks:    [],\n      metadata: {\n        parsed: {},\n        raw: '',\n        format: ''\n      }\n    };\n\n    // This lets us use ¨ trema as an escape char to avoid md5 hashes\n    // The choice of character is arbitrary; anything that isn't\n    // magic in Markdown will work.\n    text = text.replace(/¨/g, '¨T');\n\n    // Replace $ with ¨D\n    // RegExp interprets $ as a special character\n    // when it's in a replacement string\n    text = text.replace(/\\$/g, '¨D');\n\n    // Standardize line endings\n    text = text.replace(/\\r\\n/g, '\\n'); // DOS to Unix\n    text = text.replace(/\\r/g, '\\n'); // Mac to Unix\n\n    // Stardardize line spaces\n    text = text.replace(/\\u00A0/g, ' ');\n\n    if (options.smartIndentationFix) {\n      text = rTrimInputText(text);\n    }\n\n    // Make sure text begins and ends with a couple of newlines:\n    text = '\\n\\n' + text + '\\n\\n';\n\n    // detab\n    text = showdown.subParser('detab')(text, options, globals);\n\n    /**\n     * Strip any lines consisting only of spaces and tabs.\n     * This makes subsequent regexs easier to write, because we can\n     * match consecutive blank lines with /\\n+/ instead of something\n     * contorted like /[ \\t]*\\n+/\n     */\n    text = text.replace(/^[ \\t]+$/mg, '');\n\n    //run languageExtensions\n    showdown.helper.forEach(langExtensions, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // run the sub parsers\n    text = showdown.subParser('metadata')(text, options, globals);\n    text = showdown.subParser('hashPreCodeTags')(text, options, globals);\n    text = showdown.subParser('githubCodeBlocks')(text, options, globals);\n    text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n    text = showdown.subParser('hashCodeTags')(text, options, globals);\n    text = showdown.subParser('stripLinkDefinitions')(text, options, globals);\n    text = showdown.subParser('blockGamut')(text, options, globals);\n    text = showdown.subParser('unhashHTMLSpans')(text, options, globals);\n    text = showdown.subParser('unescapeSpecialChars')(text, options, globals);\n\n    // attacklab: Restore dollar signs\n    text = text.replace(/¨D/g, '$$');\n\n    // attacklab: Restore tremas\n    text = text.replace(/¨T/g, '¨');\n\n    // render a complete html document instead of a partial if the option is enabled\n    text = showdown.subParser('completeHTMLDocument')(text, options, globals);\n\n    // Run output modifiers\n    showdown.helper.forEach(outputModifiers, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // update metadata\n    metadata = globals.metadata;\n    return text;\n  };\n\n  /**\n   * Converts an HTML string into a markdown string\n   * @param src\n   * @param [HTMLParser] A WHATWG DOM and HTML parser, such as JSDOM. If none is supplied, window.document will be used.\n   * @returns {string}\n   */\n  this.makeMarkdown = this.makeMd = function (src, HTMLParser) {\n\n    // replace \\r\\n with \\n\n    src = src.replace(/\\r\\n/g, '\\n');\n    src = src.replace(/\\r/g, '\\n'); // old macs\n\n    // due to an edge case, we need to find this: > <\n    // to prevent removing of non silent white spaces\n    // ex: this is sparta\n    src = src.replace(/>[ \\t]+¨NBSP;<');\n\n    if (!HTMLParser) {\n      if (window && window.document) {\n        HTMLParser = window.document;\n      } else {\n        throw new Error('HTMLParser is undefined. If in a webworker or nodejs environment, you need to provide a WHATWG DOM and HTML such as JSDOM');\n      }\n    }\n\n    var doc = HTMLParser.createElement('div');\n    doc.innerHTML = src;\n\n    var globals = {\n      preList: substitutePreCodeTags(doc)\n    };\n\n    // remove all newlines and collapse spaces\n    clean(doc);\n\n    // some stuff, like accidental reference links must now be escaped\n    // TODO\n    // doc.innerHTML = doc.innerHTML.replace(/\\[[\\S\\t ]]/);\n\n    var nodes = doc.childNodes,\n        mdDoc = '';\n\n    for (var i = 0; i < nodes.length; i++) {\n      mdDoc += showdown.subParser('makeMarkdown.node')(nodes[i], globals);\n    }\n\n    function clean (node) {\n      for (var n = 0; n < node.childNodes.length; ++n) {\n        var child = node.childNodes[n];\n        if (child.nodeType === 3) {\n          if (!/\\S/.test(child.nodeValue)) {\n            node.removeChild(child);\n            --n;\n          } else {\n            child.nodeValue = child.nodeValue.split('\\n').join(' ');\n            child.nodeValue = child.nodeValue.replace(/(\\s)+/g, '$1');\n          }\n        } else if (child.nodeType === 1) {\n          clean(child);\n        }\n      }\n    }\n\n    // find all pre tags and replace contents with placeholder\n    // we need this so that we can remove all indentation from html\n    // to ease up parsing\n    function substitutePreCodeTags (doc) {\n\n      var pres = doc.querySelectorAll('pre'),\n          presPH = [];\n\n      for (var i = 0; i < pres.length; ++i) {\n\n        if (pres[i].childElementCount === 1 && pres[i].firstChild.tagName.toLowerCase() === 'code') {\n          var content = pres[i].firstChild.innerHTML.trim(),\n              language = pres[i].firstChild.getAttribute('data-language') || '';\n\n          // if data-language attribute is not defined, then we look for class language-*\n          if (language === '') {\n            var classes = pres[i].firstChild.className.split(' ');\n            for (var c = 0; c < classes.length; ++c) {\n              var matches = classes[c].match(/^language-(.+)$/);\n              if (matches !== null) {\n                language = matches[1];\n                break;\n              }\n            }\n          }\n\n          // unescape html entities in content\n          content = showdown.helper.unescapeHTMLEntities(content);\n\n          presPH.push(content);\n          pres[i].outerHTML = '';\n        } else {\n          presPH.push(pres[i].innerHTML);\n          pres[i].innerHTML = '';\n          pres[i].setAttribute('prenum', i.toString());\n        }\n      }\n      return presPH;\n    }\n\n    return mdDoc;\n  };\n\n  /**\n   * Set an option of this Converter instance\n   * @param {string} key\n   * @param {*} value\n   */\n  this.setOption = function (key, value) {\n    options[key] = value;\n  };\n\n  /**\n   * Get the option of this Converter instance\n   * @param {string} key\n   * @returns {*}\n   */\n  this.getOption = function (key) {\n    return options[key];\n  };\n\n  /**\n   * Get the options of this Converter instance\n   * @returns {{}}\n   */\n  this.getOptions = function () {\n    return options;\n  };\n\n  /**\n   * Add extension to THIS converter\n   * @param {{}} extension\n   * @param {string} [name=null]\n   */\n  this.addExtension = function (extension, name) {\n    name = name || null;\n    _parseExtension(extension, name);\n  };\n\n  /**\n   * Use a global registered extension with THIS converter\n   * @param {string} extensionName Name of the previously registered extension\n   */\n  this.useExtension = function (extensionName) {\n    _parseExtension(extensionName);\n  };\n\n  /**\n   * Set the flavor THIS converter should use\n   * @param {string} name\n   */\n  this.setFlavor = function (name) {\n    if (!flavor.hasOwnProperty(name)) {\n      throw Error(name + ' flavor was not found');\n    }\n    var preset = flavor[name];\n    setConvFlavor = name;\n    for (var option in preset) {\n      if (preset.hasOwnProperty(option)) {\n        options[option] = preset[option];\n      }\n    }\n  };\n\n  /**\n   * Get the currently set flavor of this converter\n   * @returns {string}\n   */\n  this.getFlavor = function () {\n    return setConvFlavor;\n  };\n\n  /**\n   * Remove an extension from THIS converter.\n   * Note: This is a costly operation. It's better to initialize a new converter\n   * and specify the extensions you wish to use\n   * @param {Array} extension\n   */\n  this.removeExtension = function (extension) {\n    if (!showdown.helper.isArray(extension)) {\n      extension = [extension];\n    }\n    for (var a = 0; a < extension.length; ++a) {\n      var ext = extension[a];\n      for (var i = 0; i < langExtensions.length; ++i) {\n        if (langExtensions[i] === ext) {\n          langExtensions[i].splice(i, 1);\n        }\n      }\n      for (var ii = 0; ii < outputModifiers.length; ++i) {\n        if (outputModifiers[ii] === ext) {\n          outputModifiers[ii].splice(i, 1);\n        }\n      }\n    }\n  };\n\n  /**\n   * Get all extension of THIS converter\n   * @returns {{language: Array, output: Array}}\n   */\n  this.getAllExtensions = function () {\n    return {\n      language: langExtensions,\n      output: outputModifiers\n    };\n  };\n\n  /**\n   * Get the metadata of the previously parsed document\n   * @param raw\n   * @returns {string|{}}\n   */\n  this.getMetadata = function (raw) {\n    if (raw) {\n      return metadata.raw;\n    } else {\n      return metadata.parsed;\n    }\n  };\n\n  /**\n   * Get the metadata format of the previously parsed document\n   * @returns {string}\n   */\n  this.getMetadataFormat = function () {\n    return metadata.format;\n  };\n\n  /**\n   * Private: set a single key, value metadata pair\n   * @param {string} key\n   * @param {string} value\n   */\n  this._setMetadataPair = function (key, value) {\n    metadata.parsed[key] = value;\n  };\n\n  /**\n   * Private: set metadata format\n   * @param {string} format\n   */\n  this._setMetadataFormat = function (format) {\n    metadata.format = format;\n  };\n\n  /**\n   * Private: set metadata raw text\n   * @param {string} raw\n   */\n  this._setMetadataRaw = function (raw) {\n    metadata.raw = raw;\n  };\n};\n","/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('anchors', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('anchors.before', text, options, globals);\n\n  var writeAnchorTag = function (wholeMatch, linkText, linkId, url, m5, m6, title) {\n    if (showdown.helper.isUndefined(title)) {\n      title = '';\n    }\n    linkId = linkId.toLowerCase();\n\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n    } else if (!url) {\n      if (!linkId) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = linkText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(globals.gUrls[linkId])) {\n        url = globals.gUrls[linkId];\n        if (!showdown.helper.isUndefined(globals.gTitles[linkId])) {\n          title = globals.gTitles[linkId];\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    //url = showdown.helper.escapeCharacters(url, '*_', false); // replaced line to improve performance\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n\n    var result = '';\n\n    return result;\n  };\n\n  // First, handle reference-style links: [link text] [id]\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)] ?(?:\\n *)?\\[(.*?)]()()()()/g, writeAnchorTag);\n\n  // Next, inline-style links: [link text](url \"optional title\")\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]?<([^>]*)>(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // normal cases\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]??(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // handle reference-style shortcuts: [link text]\n  // These must come last in case you've also got [link test][1]\n  // or [link test](/foo)\n  text = text.replace(/\\[([^\\[\\]]+)]()()()()()/g, writeAnchorTag);\n\n  // Lastly handle GithubMentions if option is enabled\n  if (options.ghMentions) {\n    text = text.replace(/(^|\\s)(\\\\)?(@([a-z\\d]+(?:[a-z\\d.-]+?[a-z\\d]+)*))/gmi, function (wm, st, escape, mentions, username) {\n      if (escape === '\\\\') {\n        return st + mentions;\n      }\n\n      //check if options.ghMentionsLink is a string\n      if (!showdown.helper.isString(options.ghMentionsLink)) {\n        throw new Error('ghMentionsLink option must be a string');\n      }\n      var lnk = options.ghMentionsLink.replace(/\\{u}/g, username),\n          target = '';\n      if (options.openLinksInNewWindow) {\n        target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n      }\n      return st + '' + mentions + '';\n    });\n  }\n\n  text = globals.converter._dispatch('anchors.after', text, options, globals);\n  return text;\n});\n","// url allowed chars [a-z\\d_.~:/?#[]@!$&'()*+,;=-]\n\nvar simpleURLRegex  = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+?\\.[^'\">\\s]+?)()(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    simpleURLRegex2 = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+\\.[^'\">\\s]+?)([.!?,()\\[\\]])?(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    delimUrlRegex   = /()<(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+)()>()/gi,\n    simpleMailRegex = /(^|\\s)(?:mailto:)?([A-Za-z0-9!#$%&'*+-/=?^_`{|}~.]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)(?=$|\\s)/gmi,\n    delimMailRegex  = /<()(?:mailto:)?([-.\\w]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)>/gi,\n\n    replaceLink = function (options) {\n      'use strict';\n      return function (wm, leadingMagicChars, link, m2, m3, trailingPunctuation, trailingMagicChars) {\n        link = link.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n        var lnkTxt = link,\n            append = '',\n            target = '',\n            lmc    = leadingMagicChars || '',\n            tmc    = trailingMagicChars || '';\n        if (/^www\\./i.test(link)) {\n          link = link.replace(/^www\\./i, 'http://www.');\n        }\n        if (options.excludeTrailingPunctuationFromURLs && trailingPunctuation) {\n          append = trailingPunctuation;\n        }\n        if (options.openLinksInNewWindow) {\n          target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n        }\n        return lmc + '' + lnkTxt + '' + append + tmc;\n      };\n    },\n\n    replaceMail = function (options, globals) {\n      'use strict';\n      return function (wholeMatch, b, mail) {\n        var href = 'mailto:';\n        b = b || '';\n        mail = showdown.subParser('unescapeSpecialChars')(mail, options, globals);\n        if (options.encodeEmails) {\n          href = showdown.helper.encodeEmailAddress(href + mail);\n          mail = showdown.helper.encodeEmailAddress(mail);\n        } else {\n          href = href + mail;\n        }\n        return b + '' + mail + '';\n      };\n    };\n\nshowdown.subParser('autoLinks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('autoLinks.before', text, options, globals);\n\n  text = text.replace(delimUrlRegex, replaceLink(options));\n  text = text.replace(delimMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('autoLinks.after', text, options, globals);\n\n  return text;\n});\n\nshowdown.subParser('simplifiedAutoLinks', function (text, options, globals) {\n  'use strict';\n\n  if (!options.simplifiedAutoLink) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.before', text, options, globals);\n\n  if (options.excludeTrailingPunctuationFromURLs) {\n    text = text.replace(simpleURLRegex2, replaceLink(options));\n  } else {\n    text = text.replace(simpleURLRegex, replaceLink(options));\n  }\n  text = text.replace(simpleMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.after', text, options, globals);\n\n  return text;\n});\n","/**\n * These are all the transformations that form block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('blockGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockGamut.before', text, options, globals);\n\n  // we parse blockquotes first so that we can have headings and hrs\n  // inside blockquotes\n  text = showdown.subParser('blockQuotes')(text, options, globals);\n  text = showdown.subParser('headers')(text, options, globals);\n\n  // Do Horizontal Rules:\n  text = showdown.subParser('horizontalRule')(text, options, globals);\n\n  text = showdown.subParser('lists')(text, options, globals);\n  text = showdown.subParser('codeBlocks')(text, options, globals);\n  text = showdown.subParser('tables')(text, options, globals);\n\n  // We already ran _HashHTMLBlocks() before, in Markdown(), but that\n  // was to escape raw HTML in the original Markdown source. This time,\n  // we're escaping the markup we've just created, so that we don't wrap\n  // 
     tags around block-level tags.\n  text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n  text = showdown.subParser('paragraphs')(text, options, globals);\n\n  text = globals.converter._dispatch('blockGamut.after', text, options, globals);\n\n  return text;\n});\n","showdown.subParser('blockQuotes', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockQuotes.before', text, options, globals);\n\n  // add a couple extra lines after the text and endtext mark\n  text = text + '\\n\\n';\n\n  var rgx = /(^ {0,3}>[ \\t]?.+\\n(.+\\n)*\\n*)+/gm;\n\n  if (options.splitAdjacentBlockquotes) {\n    rgx = /^ {0,3}>[\\s\\S]*?(?:\\n\\n)/gm;\n  }\n\n  text = text.replace(rgx, function (bq) {\n    // attacklab: hack around Konqueror 3.5.4 bug:\n    // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n    bq = bq.replace(/^[ \\t]*>[ \\t]?/gm, ''); // trim one level of quoting\n\n    // attacklab: clean up hack\n    bq = bq.replace(/¨0/g, '');\n\n    bq = bq.replace(/^[ \\t]+$/gm, ''); // trim whitespace-only lines\n    bq = showdown.subParser('githubCodeBlocks')(bq, options, globals);\n    bq = showdown.subParser('blockGamut')(bq, options, globals); // recurse\n\n    bq = bq.replace(/(^|\\n)/g, '$1  ');\n    // These leading spaces screw with 
     content, so we need to fix that:\n    bq = bq.replace(/(\\s*
    [^\\r]+?<\\/pre>)/gm, function (wholeMatch, m1) {\n      var pre = m1;\n      // attacklab: hack around Konqueror 3.5.4 bug:\n      pre = pre.replace(/^  /mg, '¨0');\n      pre = pre.replace(/¨0/g, '');\n      return pre;\n    });\n\n    return showdown.subParser('hashBlock')('
    \\n' + bq + '\\n
    ', options, globals);\n  });\n\n  text = globals.converter._dispatch('blockQuotes.after', text, options, globals);\n  return text;\n});\n","/**\n * Process Markdown `
    ` blocks.\n */\nshowdown.subParser('codeBlocks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeBlocks.before', text, options, globals);\n\n  // sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var pattern = /(?:\\n\\n|^)((?:(?:[ ]{4}|\\t).*\\n+)+)(\\n*[ ]{0,3}[^ \\t\\n]|(?=¨0))/g;\n  text = text.replace(pattern, function (wholeMatch, m1, m2) {\n    var codeblock = m1,\n        nextChar = m2,\n        end = '\\n';\n\n    codeblock = showdown.subParser('outdent')(codeblock, options, globals);\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing newlines\n\n    if (options.omitExtraWLInCodeBlocks) {\n      end = '';\n    }\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    return showdown.subParser('hashBlock')(codeblock, options, globals) + nextChar;\n  });\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n\n  text = globals.converter._dispatch('codeBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n *\n *   *  Backtick quotes are used for  spans.\n *\n *   *  You can use multiple backticks as the delimiters if you want to\n *     include literal backticks in the code span. So, this input:\n *\n *         Just type ``foo `bar` baz`` at the prompt.\n *\n *       Will translate to:\n *\n *         
    Just type foo `bar` baz at the prompt.
    \n *\n *    There's no arbitrary limit to the number of backticks you\n *    can use as delimters. If you need three consecutive backticks\n *    in your code, use four for delimiters, etc.\n *\n *  *  You can use spaces to get literal backticks at the edges:\n *\n *         ... type `` `bar` `` ...\n *\n *       Turns to:\n *\n *         ... type `bar` ...\n */\nshowdown.subParser('codeSpans', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeSpans.before', text, options, globals);\n\n  if (typeof text === 'undefined') {\n    text = '';\n  }\n  text = text.replace(/(^|[^\\\\])(`+)([^\\r]*?[^`])\\2(?!`)/gm,\n    function (wholeMatch, m1, m2, m3) {\n      var c = m3;\n      c = c.replace(/^([ \\t]*)/g, '');\t// leading whitespace\n      c = c.replace(/[ \\t]*$/g, '');\t// trailing whitespace\n      c = showdown.subParser('encodeCode')(c, options, globals);\n      c = m1 + '' + c + '';\n      c = showdown.subParser('hashHTMLSpans')(c, options, globals);\n      return c;\n    }\n  );\n\n  text = globals.converter._dispatch('codeSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Create a full HTML document from the processed markdown\n */\nshowdown.subParser('completeHTMLDocument', function (text, options, globals) {\n  'use strict';\n\n  if (!options.completeHTMLDocument) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('completeHTMLDocument.before', text, options, globals);\n\n  var doctype = 'html',\n      doctypeParsed = '\\n',\n      title = '',\n      charset = '\\n',\n      lang = '',\n      metadata = '';\n\n  if (typeof globals.metadata.parsed.doctype !== 'undefined') {\n    doctypeParsed = '\\n';\n    doctype = globals.metadata.parsed.doctype.toString().toLowerCase();\n    if (doctype === 'html' || doctype === 'html5') {\n      charset = '';\n    }\n  }\n\n  for (var meta in globals.metadata.parsed) {\n    if (globals.metadata.parsed.hasOwnProperty(meta)) {\n      switch (meta.toLowerCase()) {\n        case 'doctype':\n          break;\n\n        case 'title':\n          title = '' +  globals.metadata.parsed.title + '\\n';\n          break;\n\n        case 'charset':\n          if (doctype === 'html' || doctype === 'html5') {\n            charset = '\\n';\n          } else {\n            charset = '\\n';\n          }\n          break;\n\n        case 'language':\n        case 'lang':\n          lang = ' lang=\"' + globals.metadata.parsed[meta] + '\"';\n          metadata += '\\n';\n          break;\n\n        default:\n          metadata += '\\n';\n      }\n    }\n  }\n\n  text = doctypeParsed + '\\n\\n' + title + charset + metadata + '\\n\\n' + text.trim() + '\\n\\n';\n\n  text = globals.converter._dispatch('completeHTMLDocument.after', text, options, globals);\n  return text;\n});\n","/**\n * Convert all tabs to spaces\n */\nshowdown.subParser('detab', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('detab.before', text, options, globals);\n\n  // expand first n-1 tabs\n  text = text.replace(/\\t(?=\\t)/g, '    '); // g_tab_width\n\n  // replace the nth with two sentinels\n  text = text.replace(/\\t/g, '¨A¨B');\n\n  // use the sentinel to anchor our regex so it doesn't explode\n  text = text.replace(/¨B(.+?)¨A/g, function (wholeMatch, m1) {\n    var leadingText = m1,\n        numSpaces = 4 - leadingText.length % 4;  // g_tab_width\n\n    // there *must* be a better way to do this:\n    for (var i = 0; i < numSpaces; i++) {\n      leadingText += ' ';\n    }\n\n    return leadingText;\n  });\n\n  // clean up sentinels\n  text = text.replace(/¨A/g, '    ');  // g_tab_width\n  text = text.replace(/¨B/g, '');\n\n  text = globals.converter._dispatch('detab.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('ellipsis', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('ellipsis.before', text, options, globals);\n\n  text = text.replace(/\\.\\.\\./g, '…');\n\n  text = globals.converter._dispatch('ellipsis.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Turn emoji codes into emojis\n *\n * List of supported emojis: https://github.com/showdownjs/showdown/wiki/Emojis\n */\nshowdown.subParser('emoji', function (text, options, globals) {\n  'use strict';\n\n  if (!options.emoji) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('emoji.before', text, options, globals);\n\n  var emojiRgx = /:([\\S]+?):/g;\n\n  text = text.replace(emojiRgx, function (wm, emojiCode) {\n    if (showdown.helper.emojis.hasOwnProperty(emojiCode)) {\n      return showdown.helper.emojis[emojiCode];\n    }\n    return wm;\n  });\n\n  text = globals.converter._dispatch('emoji.after', text, options, globals);\n\n  return text;\n});\n","/**\n * Smart processing for ampersands and angle brackets that need to be encoded.\n */\nshowdown.subParser('encodeAmpsAndAngles', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeAmpsAndAngles.before', text, options, globals);\n\n  // Ampersand-encoding based entirely on Nat Irons's Amputator MT plugin:\n  // http://bumppo.net/projects/amputator/\n  text = text.replace(/&(?!#?[xX]?(?:[0-9a-fA-F]+|\\w+);)/g, '&');\n\n  // Encode naked <'s\n  text = text.replace(/<(?![a-z\\/?$!])/gi, '<');\n\n  // Encode <\n  text = text.replace(/\n  text = text.replace(/>/g, '>');\n\n  text = globals.converter._dispatch('encodeAmpsAndAngles.after', text, options, globals);\n  return text;\n});\n","/**\n * Returns the string, with after processing the following backslash escape sequences.\n *\n * attacklab: The polite way to do this is with the new escapeCharacters() function:\n *\n *    text = escapeCharacters(text,\"\\\\\",true);\n *    text = escapeCharacters(text,\"`*_{}[]()>#+-.!\",true);\n *\n * ...but we're sidestepping its use of the (slow) RegExp constructor\n * as an optimization for Firefox.  This function gets called a LOT.\n */\nshowdown.subParser('encodeBackslashEscapes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeBackslashEscapes.before', text, options, globals);\n\n  text = text.replace(/\\\\(\\\\)/g, showdown.helper.escapeCharactersCallback);\n  text = text.replace(/\\\\([`*_{}\\[\\]()>#+.!~=|-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeBackslashEscapes.after', text, options, globals);\n  return text;\n});\n","/**\n * Encode/escape certain characters inside Markdown code runs.\n * The point is that in code, these characters are literals,\n * and lose their special Markdown meanings.\n */\nshowdown.subParser('encodeCode', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('encodeCode.before', text, options, globals);\n\n  // Encode all ampersands; HTML entities are not\n  // entities within a Markdown code span.\n  text = text\n    .replace(/&/g, '&')\n  // Do the angle bracket song and dance:\n    .replace(//g, '>')\n  // Now, escape characters that are magic in Markdown:\n    .replace(/([*_{}\\[\\]\\\\=~-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeCode.after', text, options, globals);\n  return text;\n});\n","/**\n * Within tags -- meaning between < and > -- encode [\\ ` * _ ~ =] so they\n * don't conflict with their use in Markdown for code, italics and strong.\n */\nshowdown.subParser('escapeSpecialCharsWithinTagAttributes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.before', text, options, globals);\n\n  // Build a regex to find HTML tags.\n  var tags     = /<\\/?[a-z\\d_:-]+(?:[\\s]+[\\s\\S]+?)?>/gi,\n      comments = /-]|-[^>])(?:[^-]|-[^-])*)--)>/gi;\n\n  text = text.replace(tags, function (wholeMatch) {\n    return wholeMatch\n      .replace(/(.)<\\/?code>(?=.)/g, '$1`')\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = text.replace(comments, function (wholeMatch) {\n    return wholeMatch\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.after', text, options, globals);\n  return text;\n});\n","/**\n * Handle github codeblocks prior to running HashHTML so that\n * HTML contained within the codeblock gets escaped properly\n * Example:\n * ```ruby\n *     def hello_world(x)\n *       puts \"Hello, #{x}\"\n *     end\n * ```\n */\nshowdown.subParser('githubCodeBlocks', function (text, options, globals) {\n  'use strict';\n\n  // early exit if option is not enabled\n  if (!options.ghCodeBlocks) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('githubCodeBlocks.before', text, options, globals);\n\n  text += '¨0';\n\n  text = text.replace(/(?:^|\\n)(?: {0,3})(```+|~~~+)(?: *)([^\\s`~]*)\\n([\\s\\S]*?)\\n(?: {0,3})\\1/g, function (wholeMatch, delim, language, codeblock) {\n    var end = (options.omitExtraWLInCodeBlocks) ? '' : '\\n';\n\n    // First parse the github code block\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing whitespace\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    codeblock = showdown.subParser('hashBlock')(codeblock, options, globals);\n\n    // Since GHCodeblocks can be false positives, we need to\n    // store the primitive text and the parsed text in a global var,\n    // and then return a token\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  });\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return globals.converter._dispatch('githubCodeBlocks.after', text, options, globals);\n});\n","showdown.subParser('hashBlock', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashBlock.before', text, options, globals);\n  text = text.replace(/(^\\n+|\\n+$)/g, '');\n  text = '\\n\\n¨K' + (globals.gHtmlBlocks.push(text) - 1) + 'K\\n\\n';\n  text = globals.converter._dispatch('hashBlock.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape  elements that should not be parsed as markdown\n */\nshowdown.subParser('hashCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '¨C' + (globals.gHtmlSpans.push(codeblock) - 1) + 'C';\n  };\n\n  // Hash naked \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, ']*>', '', 'gim');\n\n  text = globals.converter._dispatch('hashCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('hashElement', function (text, options, globals) {\n  'use strict';\n\n  return function (wholeMatch, m1) {\n    var blockText = m1;\n\n    // Undo double lines\n    blockText = blockText.replace(/\\n\\n/g, '\\n');\n    blockText = blockText.replace(/^\\n/, '');\n\n    // strip trailing blank lines\n    blockText = blockText.replace(/\\n+$/g, '');\n\n    // Replace the element text with a marker (\"¨KxK\" where x is its key)\n    blockText = '\\n\\n¨K' + (globals.gHtmlBlocks.push(blockText) - 1) + 'K\\n\\n';\n\n    return blockText;\n  };\n});\n","showdown.subParser('hashHTMLBlocks', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLBlocks.before', text, options, globals);\n\n  var blockTags = [\n        'pre',\n        'div',\n        'h1',\n        'h2',\n        'h3',\n        'h4',\n        'h5',\n        'h6',\n        'blockquote',\n        'table',\n        'dl',\n        'ol',\n        'ul',\n        'script',\n        'noscript',\n        'form',\n        'fieldset',\n        'iframe',\n        'math',\n        'style',\n        'section',\n        'header',\n        'footer',\n        'nav',\n        'article',\n        'aside',\n        'address',\n        'audio',\n        'canvas',\n        'figure',\n        'hgroup',\n        'output',\n        'video',\n        'p'\n      ],\n      repFunc = function (wholeMatch, match, left, right) {\n        var txt = wholeMatch;\n        // check if this html element is marked as markdown\n        // if so, it's contents should be parsed as markdown\n        if (left.search(/\\bmarkdown\\b/) !== -1) {\n          txt = left + globals.converter.makeHtml(match) + right;\n        }\n        return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n      };\n\n  if (options.backslashEscapesHTMLTags) {\n    // encode backslash escaped HTML tags\n    text = text.replace(/\\\\<(\\/?[^>]+?)>/g, function (wm, inside) {\n      return '<' + inside + '>';\n    });\n  }\n\n  // hash HTML Blocks\n  for (var i = 0; i < blockTags.length; ++i) {\n\n    var opTagPos,\n        rgx1     = new RegExp('^ {0,3}(<' + blockTags[i] + '\\\\b[^>]*>)', 'im'),\n        patLeft  = '<' + blockTags[i] + '\\\\b[^>]*>',\n        patRight = '';\n    // 1. Look for the first position of the first opening HTML tag in the text\n    while ((opTagPos = showdown.helper.regexIndexOf(text, rgx1)) !== -1) {\n\n      // if the HTML tag is \\ escaped, we need to escape it and break\n\n\n      //2. Split the text in that position\n      var subTexts = showdown.helper.splitAtIndex(text, opTagPos),\n          //3. Match recursively\n          newSubText1 = showdown.helper.replaceRecursiveRegExp(subTexts[1], repFunc, patLeft, patRight, 'im');\n\n      // prevent an infinite loop\n      if (newSubText1 === subTexts[1]) {\n        break;\n      }\n      text = subTexts[0].concat(newSubText1);\n    }\n  }\n  // HR SPECIAL CASE\n  text = text.replace(/(\\n {0,3}(<(hr)\\b([^<>])*?\\/?>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  // Special case for standalone HTML comments\n  text = showdown.helper.replaceRecursiveRegExp(text, function (txt) {\n    return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n  }, '^ {0,3}', 'gm');\n\n  // PHP and ASP-style processor instructions ( and <%...%>)\n  text = text.replace(/(?:\\n\\n)( {0,3}(?:<([?%])[^\\r]*?\\2>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  text = globals.converter._dispatch('hashHTMLBlocks.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash span elements that should not be parsed as markdown\n */\nshowdown.subParser('hashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLSpans.before', text, options, globals);\n\n  function hashHTMLSpan (html) {\n    return '¨C' + (globals.gHtmlSpans.push(html) - 1) + 'C';\n  }\n\n  // Hash Self Closing tags\n  text = text.replace(/<[^>]+?\\/>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags without properties\n  text = text.replace(/<([^>]+?)>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags with properties\n  text = text.replace(/<([^>]+?)\\s[^>]+?>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash self closing tags without />\n  text = text.replace(/<[^>]+?>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  /*showdown.helper.matchRecursiveRegExp(text, ']*>', '', 'gi');*/\n\n  text = globals.converter._dispatch('hashHTMLSpans.after', text, options, globals);\n  return text;\n});\n\n/**\n * Unhash HTML spans\n */\nshowdown.subParser('unhashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unhashHTMLSpans.before', text, options, globals);\n\n  for (var i = 0; i < globals.gHtmlSpans.length; ++i) {\n    var repText = globals.gHtmlSpans[i],\n        // limiter to prevent infinite loop (assume 10 as limit for recurse)\n        limit = 0;\n\n    while (/¨C(\\d+)C/.test(repText)) {\n      var num = RegExp.$1;\n      repText = repText.replace('¨C' + num + 'C', globals.gHtmlSpans[num]);\n      if (limit === 10) {\n        console.error('maximum nesting of 10 spans reached!!!');\n        break;\n      }\n      ++limit;\n    }\n    text = text.replace('¨C' + i + 'C', repText);\n  }\n\n  text = globals.converter._dispatch('unhashHTMLSpans.after', text, options, globals);\n  return text;\n});\n","/**\n * Hash and escape 
     elements that should not be parsed as markdown\n */\nshowdown.subParser('hashPreCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashPreCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    // encode html entities\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  };\n\n  // Hash 
    \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}]*>\\\\s*]*>', '^ {0,3}\\\\s*
    ', 'gim');\n\n  text = globals.converter._dispatch('hashPreCodeTags.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('headers', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('headers.before', text, options, globals);\n\n  var headerLevelStart = (isNaN(parseInt(options.headerLevelStart))) ? 1 : parseInt(options.headerLevelStart),\n\n      // Set text-style headers:\n      //\tHeader 1\n      //\t========\n      //\n      //\tHeader 2\n      //\t--------\n      //\n      setextRegexH1 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n={2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n=+[ \\t]*\\n+/gm,\n      setextRegexH2 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n-{2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n-+[ \\t]*\\n+/gm;\n\n  text = text.replace(setextRegexH1, function (wholeMatch, m1) {\n\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  text = text.replace(setextRegexH2, function (matchFound, m1) {\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart + 1,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  // atx-style headers:\n  //  # Header 1\n  //  ## Header 2\n  //  ## Header 2 with closing hashes ##\n  //  ...\n  //  ###### Header 6\n  //\n  var atxStyle = (options.requireSpaceBeforeHeadingText) ? /^(#{1,6})[ \\t]+(.+?)[ \\t]*#*\\n+/gm : /^(#{1,6})[ \\t]*(.+?)[ \\t]*#*\\n+/gm;\n\n  text = text.replace(atxStyle, function (wholeMatch, m1, m2) {\n    var hText = m2;\n    if (options.customizedHeaderId) {\n      hText = m2.replace(/\\s?\\{([^{]+?)}\\s*$/, '');\n    }\n\n    var span = showdown.subParser('spanGamut')(hText, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m2) + '\"',\n        hLevel = headerLevelStart - 1 + m1.length,\n        header = '' + span + '';\n\n    return showdown.subParser('hashBlock')(header, options, globals);\n  });\n\n  function headerId (m) {\n    var title,\n        prefix;\n\n    // It is separate from other options to allow combining prefix and customized\n    if (options.customizedHeaderId) {\n      var match = m.match(/\\{([^{]+?)}\\s*$/);\n      if (match && match[1]) {\n        m = match[1];\n      }\n    }\n\n    title = m;\n\n    // Prefix id to prevent causing inadvertent pre-existing style matches.\n    if (showdown.helper.isString(options.prefixHeaderId)) {\n      prefix = options.prefixHeaderId;\n    } else if (options.prefixHeaderId === true) {\n      prefix = 'section-';\n    } else {\n      prefix = '';\n    }\n\n    if (!options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (options.ghCompatibleHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '')\n        .replace(/¨T/g, '')\n        .replace(/¨D/g, '')\n        // replace rest of the chars (&~$ are repeated as they might have been escaped)\n        // borrowed from github's redcarpet (some they should produce similar results)\n        .replace(/[&+$,\\/:;=?@\"#{}|^¨~\\[\\]`\\\\*)(%.!'<>]/g, '')\n        .toLowerCase();\n    } else if (options.rawHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '&')\n        .replace(/¨T/g, '¨')\n        .replace(/¨D/g, '$')\n        // replace \" and '\n        .replace(/[\"']/g, '-')\n        .toLowerCase();\n    } else {\n      title = title\n        .replace(/[^\\w]/g, '')\n        .toLowerCase();\n    }\n\n    if (options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (globals.hashLinkCounts[title]) {\n      title = title + '-' + (globals.hashLinkCounts[title]++);\n    } else {\n      globals.hashLinkCounts[title] = 1;\n    }\n    return title;\n  }\n\n  text = globals.converter._dispatch('headers.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('horizontalRule', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('horizontalRule.before', text, options, globals);\n\n  var key = showdown.subParser('hashBlock')('
    ', options, globals);\n  text = text.replace(/^ {0,2}( ?-){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?\\*){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?_){3,}[ \\t]*$/gm, key);\n\n  text = globals.converter._dispatch('horizontalRule.after', text, options, globals);\n  return text;\n});\n","/**\n * Turn Markdown image shortcuts into  tags.\n */\nshowdown.subParser('images', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('images.before', text, options, globals);\n\n  var inlineRegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      crazyRegExp       = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]?<([^>]*)>(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:(?:([\"'])([^\"]*?)\\6))?[ \\t]?\\)/g,\n      base64RegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      referenceRegExp   = /!\\[([^\\]]*?)] ?(?:\\n *)?\\[([\\s\\S]*?)]()()()()()/g,\n      refShortcutRegExp = /!\\[([^\\[\\]]+)]()()()()()/g;\n\n  function writeImageTagBase64 (wholeMatch, altText, linkId, url, width, height, m5, title) {\n    url = url.replace(/\\s/g, '');\n    return writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title);\n  }\n\n  function writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title) {\n\n    var gUrls   = globals.gUrls,\n        gTitles = globals.gTitles,\n        gDims   = globals.gDimensions;\n\n    linkId = linkId.toLowerCase();\n\n    if (!title) {\n      title = '';\n    }\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n\n    } else if (url === '' || url === null) {\n      if (linkId === '' || linkId === null) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = altText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(gUrls[linkId])) {\n        url = gUrls[linkId];\n        if (!showdown.helper.isUndefined(gTitles[linkId])) {\n          title = gTitles[linkId];\n        }\n        if (!showdown.helper.isUndefined(gDims[linkId])) {\n          width = gDims[linkId].width;\n          height = gDims[linkId].height;\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    altText = altText\n      .replace(/\"/g, '"')\n    //altText = showdown.helper.escapeCharacters(altText, '*_', false);\n      .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    //url = showdown.helper.escapeCharacters(url, '*_', false);\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    var result = '\"'x \"optional title\")\n\n  // base64 encoded images\n  text = text.replace(base64RegExp, writeImageTagBase64);\n\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(crazyRegExp, writeImageTag);\n\n  // normal cases\n  text = text.replace(inlineRegExp, writeImageTag);\n\n  // handle reference-style shortcuts: ![img text]\n  text = text.replace(refShortcutRegExp, writeImageTag);\n\n  text = globals.converter._dispatch('images.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('italicsAndBold', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('italicsAndBold.before', text, options, globals);\n\n  // it's faster to have 3 separate regexes for each case than have just one\n  // because of backtracing, in some cases, it could lead to an exponential effect\n  // called \"catastrophic backtrace\". Ominous!\n\n  function parseInside (txt, left, right) {\n    /*\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    */\n    return left + txt + right;\n  }\n\n  // Parse underscores\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b_(\\S[\\s\\S]*?)_\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/_([^\\s_][\\s\\S]*?)_/g, function (wm, m) {\n      // !/^_[^_]/.test(m) - test if it doesn't start with __ (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n  // Now parse asterisks\n  if (options.literalMidWordAsterisks) {\n    text = text.replace(/([^*]|^)\\B\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*\\*(\\S[\\s\\S]*?)\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*(\\S[\\s\\S]*?)\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n  } else {\n    text = text.replace(/\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*\\*(\\S[\\s\\S]*?)\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*([^\\s*][\\s\\S]*?)\\*/g, function (wm, m) {\n      // !/^\\*[^*]/.test(m) - test if it doesn't start with ** (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n\n  text = globals.converter._dispatch('italicsAndBold.after', text, options, globals);\n  return text;\n});\n","/**\n * Form HTML ordered (numbered) and unordered (bulleted) lists.\n */\nshowdown.subParser('lists', function (text, options, globals) {\n  'use strict';\n\n  /**\n   * Process the contents of a single ordered or unordered list, splitting it\n   * into individual list items.\n   * @param {string} listStr\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function processListItems (listStr, trimTrailing) {\n    // The $g_list_level global keeps track of when we're inside a list.\n    // Each time we enter a list, we increment it; when we leave a list,\n    // we decrement. If it's zero, we're not in a list anymore.\n    //\n    // We do this because when we're not inside a list, we want to treat\n    // something like this:\n    //\n    //    I recommend upgrading to version\n    //    8. Oops, now this line is treated\n    //    as a sub-list.\n    //\n    // As a single paragraph, despite the fact that the second line starts\n    // with a digit-period-space sequence.\n    //\n    // Whereas when we're inside a list (or sub-list), that line will be\n    // treated as the start of a sub-list. What a kludge, huh? This is\n    // an aspect of Markdown's syntax that's hard to parse perfectly\n    // without resorting to mind-reading. Perhaps the solution is to\n    // change the syntax rules such that sub-lists must start with a\n    // starting cardinal number; e.g. \"1.\" or \"a.\".\n    globals.gListLevel++;\n\n    // trim trailing blank lines:\n    listStr = listStr.replace(/\\n{2,}$/, '\\n');\n\n    // attacklab: add sentinel to emulate \\z\n    listStr += '¨0';\n\n    var rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0| {0,3}([*+-]|\\d+[.])[ \\t]+))/gm,\n        isParagraphed = (/\\n[ \\t]*\\n(?!¨0)/.test(listStr));\n\n    // Since version 1.5, nesting sublists requires 4 spaces (or 1 tab) indentation,\n    // which is a syntax breaking change\n    // activating this option reverts to old behavior\n    if (options.disableForced4SpacesIndentedSublists) {\n      rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0|\\2([*+-]|\\d+[.])[ \\t]+))/gm;\n    }\n\n    listStr = listStr.replace(rgx, function (wholeMatch, m1, m2, m3, m4, taskbtn, checked) {\n      checked = (checked && checked.trim() !== '');\n\n      var item = showdown.subParser('outdent')(m4, options, globals),\n          bulletStyle = '';\n\n      // Support for github tasklists\n      if (taskbtn && options.tasklists) {\n        bulletStyle = ' class=\"task-list-item\" style=\"list-style-type: none;\"';\n        item = item.replace(/^[ \\t]*\\[(x|X| )?]/m, function () {\n          var otp = '
  • a
    • \n      // instead of:\n      // 
    • - - a
    \n      // So, to prevent it, we will put a marker (¨A)in the beginning of the line\n      // Kind of hackish/monkey patching, but seems more effective than overcomplicating the list parser\n      item = item.replace(/^([-*+]|\\d\\.)[ \\t]+[\\S\\n ]*/g, function (wm2) {\n        return '¨A' + wm2;\n      });\n\n      // m1 - Leading line or\n      // Has a double return (multi paragraph) or\n      // Has sublist\n      if (m1 || (item.search(/\\n{2,}/) > -1)) {\n        item = showdown.subParser('githubCodeBlocks')(item, options, globals);\n        item = showdown.subParser('blockGamut')(item, options, globals);\n      } else {\n        // Recursion for sub-lists:\n        item = showdown.subParser('lists')(item, options, globals);\n        item = item.replace(/\\n$/, ''); // chomp(item)\n        item = showdown.subParser('hashHTMLBlocks')(item, options, globals);\n\n        // Colapse double linebreaks\n        item = item.replace(/\\n\\n+/g, '\\n\\n');\n        if (isParagraphed) {\n          item = showdown.subParser('paragraphs')(item, options, globals);\n        } else {\n          item = showdown.subParser('spanGamut')(item, options, globals);\n        }\n      }\n\n      // now we need to remove the marker (¨A)\n      item = item.replace('¨A', '');\n      // we can finally wrap the line in list item tags\n      item =  '' + item + '\\n';\n\n      return item;\n    });\n\n    // attacklab: strip sentinel\n    listStr = listStr.replace(/¨0/g, '');\n\n    globals.gListLevel--;\n\n    if (trimTrailing) {\n      listStr = listStr.replace(/\\s+$/, '');\n    }\n\n    return listStr;\n  }\n\n  function styleStartNumber (list, listType) {\n    // check if ol and starts by a number different than 1\n    if (listType === 'ol') {\n      var res = list.match(/^ *(\\d+)\\./);\n      if (res && res[1] !== '1') {\n        return ' start=\"' + res[1] + '\"';\n      }\n    }\n    return '';\n  }\n\n  /**\n   * Check and parse consecutive lists (better fix for issue #142)\n   * @param {string} list\n   * @param {string} listType\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function parseConsecutiveLists (list, listType, trimTrailing) {\n    // check if we caught 2 or more consecutive lists by mistake\n    // we use the counterRgx, meaning if listType is UL we look for OL and vice versa\n    var olRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?\\d+\\.[ \\t]/gm : /^ {0,3}\\d+\\.[ \\t]/gm,\n        ulRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?[*+-][ \\t]/gm : /^ {0,3}[*+-][ \\t]/gm,\n        counterRxg = (listType === 'ul') ? olRgx : ulRgx,\n        result = '';\n\n    if (list.search(counterRxg) !== -1) {\n      (function parseCL (txt) {\n        var pos = txt.search(counterRxg),\n            style = styleStartNumber(list, listType);\n        if (pos !== -1) {\n          // slice\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt.slice(0, pos), !!trimTrailing) + '\\n';\n\n          // invert counterType and listType\n          listType = (listType === 'ul') ? 'ol' : 'ul';\n          counterRxg = (listType === 'ul') ? olRgx : ulRgx;\n\n          //recurse\n          parseCL(txt.slice(pos));\n        } else {\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt, !!trimTrailing) + '\\n';\n        }\n      })(list);\n    } else {\n      var style = styleStartNumber(list, listType);\n      result = '\\n\\n<' + listType + style + '>\\n' + processListItems(list, !!trimTrailing) + '\\n';\n    }\n\n    return result;\n  }\n\n  /** Start of list parsing **/\n  text = globals.converter._dispatch('lists.before', text, options, globals);\n  // add sentinel to hack around khtml/safari bug:\n  // http://bugs.webkit.org/show_bug.cgi?id=11231\n  text += '¨0';\n\n  if (globals.gListLevel) {\n    text = text.replace(/^(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, list, m2) {\n        var listType = (m2.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, true);\n      }\n    );\n  } else {\n    text = text.replace(/(\\n\\n|^\\n?)(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, m1, list, m3) {\n        var listType = (m3.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, false);\n      }\n    );\n  }\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n  text = globals.converter._dispatch('lists.after', text, options, globals);\n  return text;\n});\n","/**\n * Parse metadata at the top of the document\n */\nshowdown.subParser('metadata', function (text, options, globals) {\n  'use strict';\n\n  if (!options.metadata) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('metadata.before', text, options, globals);\n\n  function parseMetadataContents (content) {\n    // raw is raw so it's not changed in any way\n    globals.metadata.raw = content;\n\n    // escape chars forbidden in html attributes\n    // double quotes\n    content = content\n      // ampersand first\n      .replace(/&/g, '&')\n      // double quotes\n      .replace(/\"/g, '"');\n\n    content = content.replace(/\\n {4}/g, ' ');\n    content.replace(/^([\\S ]+): +([\\s\\S]+?)$/gm, function (wm, key, value) {\n      globals.metadata.parsed[key] = value;\n      return '';\n    });\n  }\n\n  text = text.replace(/^\\s*«««+(\\S*?)\\n([\\s\\S]+?)\\n»»»+\\n/, function (wholematch, format, content) {\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/^\\s*---+(\\S*?)\\n([\\s\\S]+?)\\n---+\\n/, function (wholematch, format, content) {\n    if (format) {\n      globals.metadata.format = format;\n    }\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/¨M/g, '');\n\n  text = globals.converter._dispatch('metadata.after', text, options, globals);\n  return text;\n});\n","/**\n * Remove one level of line-leading tabs or spaces\n */\nshowdown.subParser('outdent', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('outdent.before', text, options, globals);\n\n  // attacklab: hack around Konqueror 3.5.4 bug:\n  // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n  text = text.replace(/^(\\t|[ ]{1,4})/gm, '¨0'); // attacklab: g_tab_width\n\n  // attacklab: clean up hack\n  text = text.replace(/¨0/g, '');\n\n  text = globals.converter._dispatch('outdent.after', text, options, globals);\n  return text;\n});\n","/**\n *\n */\nshowdown.subParser('paragraphs', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('paragraphs.before', text, options, globals);\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n\n  var grafs = text.split(/\\n{2,}/g),\n      grafsOut = [],\n      end = grafs.length; // Wrap 
     tags\n\n  for (var i = 0; i < end; i++) {\n    var str = grafs[i];\n    // if this is an HTML marker, copy it\n    if (str.search(/¨(K|G)(\\d+)\\1/g) >= 0) {\n      grafsOut.push(str);\n\n    // test for presence of characters to prevent empty lines being parsed\n    // as paragraphs (resulting in undesired extra empty paragraphs)\n    } else if (str.search(/\\S/) >= 0) {\n      str = showdown.subParser('spanGamut')(str, options, globals);\n      str = str.replace(/^([ \\t]*)/g, '
    ');\n      str += '
    ';\n      grafsOut.push(str);\n    }\n  }\n\n  /** Unhashify HTML blocks */\n  end = grafsOut.length;\n  for (i = 0; i < end; i++) {\n    var blockText = '',\n        grafsOutIt = grafsOut[i],\n        codeFlag = false;\n    // if this is a marker for an html block...\n    // use RegExp.test instead of string.search because of QML bug\n    while (/¨(K|G)(\\d+)\\1/.test(grafsOutIt)) {\n      var delim = RegExp.$1,\n          num   = RegExp.$2;\n\n      if (delim === 'K') {\n        blockText = globals.gHtmlBlocks[num];\n      } else {\n        // we need to check if ghBlock is a false positive\n        if (codeFlag) {\n          // use encoded version of all text\n          blockText = showdown.subParser('encodeCode')(globals.ghCodeBlocks[num].text, options, globals);\n        } else {\n          blockText = globals.ghCodeBlocks[num].codeblock;\n        }\n      }\n      blockText = blockText.replace(/\\$/g, '$$$$'); // Escape any dollar signs\n\n      grafsOutIt = grafsOutIt.replace(/(\\n\\n)?¨(K|G)\\d+\\2(\\n\\n)?/, blockText);\n      // Check if grafsOutIt is a pre->code\n      if (/^]*>\\s*]*>/.test(grafsOutIt)) {\n        codeFlag = true;\n      }\n    }\n    grafsOut[i] = grafsOutIt;\n  }\n  text = grafsOut.join('\\n');\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n  return globals.converter._dispatch('paragraphs.after', text, options, globals);\n});\n","/**\n * Run extension\n */\nshowdown.subParser('runExtension', function (ext, text, options, globals) {\n  'use strict';\n\n  if (ext.filter) {\n    text = ext.filter(text, globals.converter, options);\n\n  } else if (ext.regex) {\n    // TODO remove this when old extension loading mechanism is deprecated\n    var re = ext.regex;\n    if (!(re instanceof RegExp)) {\n      re = new RegExp(re, 'g');\n    }\n    text = text.replace(re, ext.replace);\n  }\n\n  return text;\n});\n","/**\n * These are all the transformations that occur *within* block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('spanGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('spanGamut.before', text, options, globals);\n  text = showdown.subParser('codeSpans')(text, options, globals);\n  text = showdown.subParser('escapeSpecialCharsWithinTagAttributes')(text, options, globals);\n  text = showdown.subParser('encodeBackslashEscapes')(text, options, globals);\n\n  // Process anchor and image tags. Images must come first,\n  // because ![foo][f] looks like an anchor.\n  text = showdown.subParser('images')(text, options, globals);\n  text = showdown.subParser('anchors')(text, options, globals);\n\n  // Make links out of things like ``\n  // Must come after anchors, because you can use < and >\n  // delimiters in inline links like [this]().\n  text = showdown.subParser('autoLinks')(text, options, globals);\n  text = showdown.subParser('simplifiedAutoLinks')(text, options, globals);\n  text = showdown.subParser('emoji')(text, options, globals);\n  text = showdown.subParser('underline')(text, options, globals);\n  text = showdown.subParser('italicsAndBold')(text, options, globals);\n  text = showdown.subParser('strikethrough')(text, options, globals);\n  text = showdown.subParser('ellipsis')(text, options, globals);\n\n  // we need to hash HTML tags inside spans\n  text = showdown.subParser('hashHTMLSpans')(text, options, globals);\n\n  // now we encode amps and angles\n  text = showdown.subParser('encodeAmpsAndAngles')(text, options, globals);\n\n  // Do hard breaks\n  if (options.simpleLineBreaks) {\n    // GFM style hard breaks\n    // only add line breaks if the text does not contain a block (special case for lists)\n    if (!/\\n\\n¨K/.test(text)) {\n      text = text.replace(/\\n+/g, '
    \\n');\n    }\n  } else {\n    // Vanilla hard breaks\n    text = text.replace(/  +\\n/g, '
    \\n');\n  }\n\n  text = globals.converter._dispatch('spanGamut.after', text, options, globals);\n  return text;\n});\n","showdown.subParser('strikethrough', function (text, options, globals) {\n  'use strict';\n\n  function parseInside (txt) {\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    return '' + txt + '';\n  }\n\n  if (options.strikethrough) {\n    text = globals.converter._dispatch('strikethrough.before', text, options, globals);\n    text = text.replace(/(?:~){2}([\\s\\S]+?)(?:~){2}/g, function (wm, txt) { return parseInside(txt); });\n    text = globals.converter._dispatch('strikethrough.after', text, options, globals);\n  }\n\n  return text;\n});\n","/**\n * Strips link definitions from text, stores the URLs and titles in\n * hash references.\n * Link defs are in the form: ^[id]: url \"optional title\"\n */\nshowdown.subParser('stripLinkDefinitions', function (text, options, globals) {\n  'use strict';\n\n  var regex       = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*\\s]+)>?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n+|(?=¨0))/gm,\n      base64Regex = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n\\n|(?=¨0)|(?=\\n\\[))/gm;\n\n  // attacklab: sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var replaceFunc = function (wholeMatch, linkId, url, width, height, blankLines, title) {\n    linkId = linkId.toLowerCase();\n    if (url.match(/^data:.+?\\/.+?;base64,/)) {\n      // remove newlines\n      globals.gUrls[linkId] = url.replace(/\\s/g, '');\n    } else {\n      globals.gUrls[linkId] = showdown.subParser('encodeAmpsAndAngles')(url, options, globals);  // Link IDs are case-insensitive\n    }\n\n    if (blankLines) {\n      // Oops, found blank lines, so it's not a title.\n      // Put back the parenthetical statement we stole.\n      return blankLines + title;\n\n    } else {\n      if (title) {\n        globals.gTitles[linkId] = title.replace(/\"|'/g, '"');\n      }\n      if (options.parseImgDimensions && width && height) {\n        globals.gDimensions[linkId] = {\n          width:  width,\n          height: height\n        };\n      }\n    }\n    // Completely remove the definition from the text\n    return '';\n  };\n\n  // first we try to find base64 link references\n  text = text.replace(base64Regex, replaceFunc);\n\n  text = text.replace(regex, replaceFunc);\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return text;\n});\n","showdown.subParser('tables', function (text, options, globals) {\n  'use strict';\n\n  if (!options.tables) {\n    return text;\n  }\n\n  var tableRgx       = /^ {0,3}\\|?.+\\|.+\\n {0,3}\\|?[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[\\s\\S]+?(?:\\n\\n|¨0)/gm,\n      //singeColTblRgx = /^ {0,3}\\|.+\\|\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n(?: {0,3}\\|.+\\|\\n)+(?:\\n\\n|¨0)/gm;\n      singeColTblRgx = /^ {0,3}\\|.+\\|[ \\t]*\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n( {0,3}\\|.+\\|[ \\t]*\\n)*(?:\\n|¨0)/gm;\n\n  function parseStyles (sLine) {\n    if (/^:[ \\t]*--*$/.test(sLine)) {\n      return ' style=\"text-align:left;\"';\n    } else if (/^--*[ \\t]*:[ \\t]*$/.test(sLine)) {\n      return ' style=\"text-align:right;\"';\n    } else if (/^:[ \\t]*--*[ \\t]*:$/.test(sLine)) {\n      return ' style=\"text-align:center;\"';\n    } else {\n      return '';\n    }\n  }\n\n  function parseHeaders (header, style) {\n    var id = '';\n    header = header.trim();\n    // support both tablesHeaderId and tableHeaderId due to error in documentation so we don't break backwards compatibility\n    if (options.tablesHeaderId || options.tableHeaderId) {\n      id = ' id=\"' + header.replace(/ /g, '_').toLowerCase() + '\"';\n    }\n    header = showdown.subParser('spanGamut')(header, options, globals);\n\n    return '' + header + '\\n';\n  }\n\n  function parseCells (cell, style) {\n    var subText = showdown.subParser('spanGamut')(cell, options, globals);\n    return '' + subText + '\\n';\n  }\n\n  function buildTable (headers, cells) {\n    var tb = '\\n\\n\\n',\n        tblLgn = headers.length;\n\n    for (var i = 0; i < tblLgn; ++i) {\n      tb += headers[i];\n    }\n    tb += '\\n\\n\\n';\n\n    for (i = 0; i < cells.length; ++i) {\n      tb += '\\n';\n      for (var ii = 0; ii < tblLgn; ++ii) {\n        tb += cells[i][ii];\n      }\n      tb += '\\n';\n    }\n    tb += '\\n
    \\n';\n    return tb;\n  }\n\n  function parseTable (rawTable) {\n    var i, tableLines = rawTable.split('\\n');\n\n    for (i = 0; i < tableLines.length; ++i) {\n      // strip wrong first and last column if wrapped tables are used\n      if (/^ {0,3}\\|/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/^ {0,3}\\|/, '');\n      }\n      if (/\\|[ \\t]*$/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/\\|[ \\t]*$/, '');\n      }\n      // parse code spans first, but we only support one line code spans\n      tableLines[i] = showdown.subParser('codeSpans')(tableLines[i], options, globals);\n    }\n\n    var rawHeaders = tableLines[0].split('|').map(function (s) { return s.trim();}),\n        rawStyles = tableLines[1].split('|').map(function (s) { return s.trim();}),\n        rawCells = [],\n        headers = [],\n        styles = [],\n        cells = [];\n\n    tableLines.shift();\n    tableLines.shift();\n\n    for (i = 0; i < tableLines.length; ++i) {\n      if (tableLines[i].trim() === '') {\n        continue;\n      }\n      rawCells.push(\n        tableLines[i]\n          .split('|')\n          .map(function (s) {\n            return s.trim();\n          })\n      );\n    }\n\n    if (rawHeaders.length < rawStyles.length) {\n      return rawTable;\n    }\n\n    for (i = 0; i < rawStyles.length; ++i) {\n      styles.push(parseStyles(rawStyles[i]));\n    }\n\n    for (i = 0; i < rawHeaders.length; ++i) {\n      if (showdown.helper.isUndefined(styles[i])) {\n        styles[i] = '';\n      }\n      headers.push(parseHeaders(rawHeaders[i], styles[i]));\n    }\n\n    for (i = 0; i < rawCells.length; ++i) {\n      var row = [];\n      for (var ii = 0; ii < headers.length; ++ii) {\n        if (showdown.helper.isUndefined(rawCells[i][ii])) {\n\n        }\n        row.push(parseCells(rawCells[i][ii], styles[ii]));\n      }\n      cells.push(row);\n    }\n\n    return buildTable(headers, cells);\n  }\n\n  text = globals.converter._dispatch('tables.before', text, options, globals);\n\n  // find escaped pipe characters\n  text = text.replace(/\\\\(\\|)/g, showdown.helper.escapeCharactersCallback);\n\n  // parse multi column tables\n  text = text.replace(tableRgx, parseTable);\n\n  // parse one column tables\n  text = text.replace(singeColTblRgx, parseTable);\n\n  text = globals.converter._dispatch('tables.after', text, options, globals);\n\n  return text;\n});\n","showdown.subParser('underline', function (text, options, globals) {\n  'use strict';\n\n  if (!options.underline) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('underline.before', text, options, globals);\n\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? 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diff --git a/docs/route-vldigeometria.chunk.5dea5.css b/docs/route-vldigeometria.chunk.5dea5.css
new file mode 100644
index 0000000..a96cbe6
--- /dev/null
+++ b/docs/route-vldigeometria.chunk.5dea5.css
@@ -0,0 +1 @@
+.panel__1ubJw{background-color:rgba(160,204,255,.1);padding:4px;border-radius:4px;margin:4px;height:calc(100% - 8px);min-width:256px}
\ No newline at end of file
diff --git a/docs/route-vldigeometria.chunk.dc16e.esm.js b/docs/route-vldigeometria.chunk.dc16e.esm.js
new file mode 100644
index 0000000..f31da91
--- /dev/null
+++ b/docs/route-vldigeometria.chunk.dc16e.esm.js
@@ -0,0 +1,36 @@
+(window.webpackJsonp=window.webpackJsonp||[]).push([[6],{"1nLj":function(e){e.exports={panel:"panel__1ubJw"}},"9yVG":function(e,r,t){"use strict";(function(e){t.d(r,"a",(function(){return o}));var a=t("1nLj"),n=t.n(a),s=t("hosL");class o extends s.Component{getStyle(){return n.a.panel}render(){let r=null;return void 0!==this.props.title&&(r=e("h3",null,this.props.title)),e("div",{class:this.getStyle(),id:this.props.id},r,this.props.children)}}}).call(this,t("hosL").h)},CoLn:function(e,r,t){"use strict";(function(e){t.d(r,"a",(function(){return l}));var a=t("DUL8"),n=t.n(a),s=t("hosL"),o=t("W7OS"),i=t.n(o);class l extends s.Component{render(){let r=new i.a.Converter;r.setFlavor("github");let t=r.makeHtml(`${this.props.children}`);return e("div",{style:n.a.markdown,dangerouslySetInnerHTML:{__html:t}})}}}).call(this,t("hosL").h)},DUL8:function(e){e.exports={markdown:"markdown__bh-kq"}},QBAg:function(e,r,t){"use strict";t.r(r),function(e){t.d(r,"default",(function(){return d}));var a=t("Surb"),n=t.n(a),s=t("hosL"),o=t("CoLn"),i=t("9yVG");let l,c=e=>e;const u=String.raw;class d extends s.Component{render(){return e("div",{style:n.a.vldigeometria},e("h1",null,"Videolezioni di Geometria"),e(i.a,null,e(o.a,null,u(l||(l=c`
+Tutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).
+
+Per comodità, ho estratto l'url sorgente del video dall'embed presente nella rispettiva pagina.
+
+1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)
+2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)
+3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)
+4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)
+5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)
+6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)
+7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)
+8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)
+9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)
+10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)
+11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)
+12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)
+13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)
+14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)
+15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)
+16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)
+17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)
+18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)
+19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)
+20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)
+21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)
+22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)
+23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)
+24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)
+25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)
+26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)
+27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)
+
+Nell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.
+                    `)))))}}}.call(this,t("hosL").h)},Surb:function(e){e.exports={vldigeometria:"vldigeometria__1ouv9"}},W7OS:function(e,r,t){var a;(function(){function n(e){"use strict";var r={omitExtraWLInCodeBlocks:{defaultValue:!1,describe:"Omit the default extra whiteline added to code blocks",type:"boolean"},noHeaderId:{defaultValue:!1,describe:"Turn on/off generated header id",type:"boolean"},prefixHeaderId:{defaultValue:!1,describe:"Add a prefix to the generated header ids. Passing a string will prefix that string to the header id. Setting to true will add a generic 'section-' prefix",type:"string"},rawPrefixHeaderId:{defaultValue:!1,describe:'Setting this option to true will prevent showdown from modifying the prefix. This might result in malformed IDs (if, for instance, the " char is used in the prefix)',type:"boolean"},ghCompatibleHeaderId:{defaultValue:!1,describe:"Generate header ids compatible with github style (spaces are replaced with dashes, a bunch of non alphanumeric chars are removed)",type:"boolean"},rawHeaderId:{defaultValue:!1,describe:"Remove only spaces, ' and \" from generated header ids (including prefixes), replacing them with dashes (-). WARNING: This might result in malformed ids",type:"boolean"},headerLevelStart:{defaultValue:!1,describe:"The header blocks level start",type:"integer"},parseImgDimensions:{defaultValue:!1,describe:"Turn on/off image dimension parsing",type:"boolean"},simplifiedAutoLink:{defaultValue:!1,describe:"Turn on/off GFM autolink style",type:"boolean"},excludeTrailingPunctuationFromURLs:{defaultValue:!1,describe:"Excludes trailing punctuation from links generated with autoLinking",type:"boolean"},literalMidWordUnderscores:{defaultValue:!1,describe:"Parse midword underscores as literal underscores",type:"boolean"},literalMidWordAsterisks:{defaultValue:!1,describe:"Parse midword asterisks as literal asterisks",type:"boolean"},strikethrough:{defaultValue:!1,describe:"Turn on/off strikethrough support",type:"boolean"},tables:{defaultValue:!1,describe:"Turn on/off tables support",type:"boolean"},tablesHeaderId:{defaultValue:!1,describe:"Add an id to table headers",type:"boolean"},ghCodeBlocks:{defaultValue:!0,describe:"Turn on/off GFM fenced code blocks support",type:"boolean"},tasklists:{defaultValue:!1,describe:"Turn on/off GFM tasklist support",type:"boolean"},smoothLivePreview:{defaultValue:!1,describe:"Prevents weird effects in live previews due to incomplete input",type:"boolean"},smartIndentationFix:{defaultValue:!1,description:"Tries to smartly fix indentation in es6 strings",type:"boolean"},disableForced4SpacesIndentedSublists:{defaultValue:!1,description:"Disables the requirement of indenting nested sublists by 4 spaces",type:"boolean"},simpleLineBreaks:{defaultValue:!1,description:"Parses simple line breaks as 
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e}}),i.helper.regexes={asteriskDashAndColon:/([*_:~])/g},i.helper.emojis={"+1":"👍","-1":"👎",100:"💯",1234:"🔢","1st_place_medal":"🥇","2nd_place_medal":"🥈","3rd_place_medal":"🥉","8ball":"🎱",a:"🅰️",ab:"🆎",abc:"🔤",abcd:"🔡",accept:"🉑",aerial_tramway:"🚡",airplane:"✈️",alarm_clock:"⏰",alembic:"⚗️",alien:"👽",ambulance:"🚑",amphora:"🏺",anchor:"⚓️",angel:"👼",anger:"💢",angry:"😠",anguished:"😧",ant:"🐜",apple:"🍎",aquarius:"♒️",aries:"♈️",arrow_backward:"◀️",arrow_double_down:"⏬",arrow_double_up:"⏫",arrow_down:"⬇️",arrow_down_small:"🔽",arrow_forward:"▶️",arrow_heading_down:"⤵️",arrow_heading_up:"⤴️",arrow_left:"⬅️",arrow_lower_left:"↙️",arrow_lower_right:"↘️",arrow_right:"➡️",arrow_right_hook:"↪️",arrow_up:"⬆️",arrow_up_down:"↕️",arrow_up_small:"🔼",arrow_upper_left:"↖️",arrow_upper_right:"↗️",arrows_clockwise:"🔃",arrows_counterclockwise:"🔄",art:"🎨",articulated_lorry:"🚛",artificial_satellite:"🛰",astonished:"😲",athletic_shoe:"👟",atm:"🏧",atom_symbol:"⚛️",avocado:"🥑",b:"🅱️",baby:"👶",baby_bottle:"🍼",baby_chick:"🐤",baby_symbol:"🚼",back:"🔙",bacon:"🥓",badminton:"🏸",baggage_claim:"🛄",baguette_bread:"🥖",balance_scale:"⚖️",balloon:"🎈",ballot_box:"🗳",ballot_box_with_check:"☑️",bamboo:"🎍",banana:"🍌",bangbang:"‼️",bank:"🏦",bar_chart:"📊",barber:"💈",baseball:"⚾️",basketball:"🏀",basketball_man:"⛹️",basketball_woman:"⛹️‍♀️",bat:"🦇",bath:"🛀",bathtub:"🛁",battery:"🔋",beach_umbrella:"🏖",bear:"🐻",bed:"🛏",bee:"🐝",beer:"🍺",beers:"🍻",beetle:"🐞",beginner:"🔰",bell:"🔔",bellhop_bell:"🛎",bento:"🍱",biking_man:"🚴",bike:"🚲",biking_woman:"🚴‍♀️",bikini:"👙",biohazard:"☣️",bird:"🐦",birthday:"🎂",black_circle:"⚫️",black_flag:"🏴",black_heart:"🖤",black_joker:"🃏",black_large_square:"⬛️",black_medium_small_square:"◾️",black_medium_square:"◼️",black_nib:"✒️",black_small_square:"▪️",black_square_button:"🔲",blonde_man:"👱",blonde_woman:"👱‍♀️",blossom:"🌼",blowfish:"🐡",blue_book:"📘",blue_car:"🚙",blue_heart:"💙",blush:"😊",boar:"🐗",boat:"⛵️",bomb:"💣",book:"📖",bookmark:"🔖",bookmark_tabs:"📑",books:"📚",boom:"💥",boot:"👢",bouquet:"💐",bowing_man:"🙇",bow_and_arrow:"🏹",bowing_woman:"🙇‍♀️",bowling:"🎳",boxing_glove:"🥊",boy:"👦",bread:"🍞",bride_with_veil:"👰",bridge_at_night:"🌉",briefcase:"💼",broken_heart:"💔",bug:"🐛",building_construction:"🏗",bulb:"💡",bullettrain_front:"🚅",bullettrain_side:"🚄",burrito:"🌯",bus:"🚌",business_suit_levitating:"🕴",busstop:"🚏",bust_in_silhouette:"👤",busts_in_silhouette:"👥",butterfly:"🦋",cactus:"🌵",cake:"🍰",calendar:"📆",call_me_hand:"🤙",calling:"📲",camel:"🐫",camera:"📷",camera_flash:"📸",camping:"🏕",cancer:"♋️",candle:"🕯",candy:"🍬",canoe:"🛶",capital_abcd:"🔠",capricorn:"♑️",car:"🚗",card_file_box:"🗃",card_index:"📇",card_index_dividers:"🗂",carousel_horse:"🎠",carrot:"🥕",cat:"🐱",cat2:"🐈",cd:"💿",chains:"⛓",champagne:"🍾",chart:"💹",chart_with_downwards_trend:"📉",chart_with_upwards_trend:"📈",checkered_flag:"🏁",cheese:"🧀",cherries:"🍒",cherry_blossom:"🌸",chestnut:"🌰",chicken:"🐔",children_crossing:"🚸",chipmunk:"🐿",chocolate_bar:"🍫",christmas_tree:"🎄",church:"⛪️",cinema:"🎦",circus_tent:"🎪",city_sunrise:"🌇",city_sunset:"🌆",cityscape:"🏙",cl:"🆑",clamp:"🗜",clap:"👏",clapper:"🎬",classical_building:"🏛",clinking_glasses:"🥂",clipboard:"📋",clock1:"🕐",clock10:"🕙",clock1030:"🕥",clock11:"🕚",clock1130:"🕦",clock12:"🕛",clock1230:"🕧",clock130:"🕜",clock2:"🕑",clock230:"🕝",clock3:"🕒",clock330:"🕞",clock4:"🕓",clock430:"🕟",clock5:"🕔",clock530:"🕠",clock6:"🕕",clock630:"🕡",clock7:"🕖",clock730:"🕢",clock8:"🕗",clock830:"🕣",clock9:"🕘",clock930:"🕤",closed_book:"📕",closed_lock_with_key:"🔐",closed_umbrella:"🌂",cloud:"☁️",cloud_with_lightning:"🌩",cloud_with_lightning_and_rain:"⛈",cloud_with_rain:"🌧",cloud_with_snow:"🌨",clown_face:"🤡",clubs:"♣️",cocktail:"🍸",coffee:"☕️",coffin:"⚰️",cold_sweat:"😰",comet:"☄️",computer:"💻",computer_mouse:"🖱",confetti_ball:"🎊",confounded:"😖",confused:"😕",congratulations:"㊗️",construction:"🚧",construction_worker_man:"👷",construction_worker_woman:"👷‍♀️",control_knobs:"🎛",convenience_store:"🏪",cookie:"🍪",cool:"🆒",policeman:"👮",copyright:"©️",corn:"🌽",couch_and_lamp:"🛋",couple:"👫",couple_with_heart_woman_man:"💑",couple_with_heart_man_man:"👨‍❤️‍👨",couple_with_heart_woman_woman:"👩‍❤️‍👩",couplekiss_man_man:"👨‍❤️‍💋‍👨",couplekiss_man_woman:"💏",couplekiss_woman_woman:"👩‍❤️‍💋‍👩",cow:"🐮",cow2:"🐄",cowboy_hat_face:"🤠",crab:"🦀",crayon:"🖍",credit_card:"💳",crescent_moon:"🌙",cricket:"🏏",crocodile:"🐊",croissant:"🥐",crossed_fingers:"🤞",crossed_flags:"🎌",crossed_swords:"⚔️",crown:"👑",cry:"😢",crying_cat_face:"😿",crystal_ball:"🔮",cucumber:"🥒",cupid:"💘",curly_loop:"➰",currency_exchange:"💱",curry:"🍛",custard:"🍮",customs:"🛃",cyclone:"🌀",dagger:"🗡",dancer:"💃",dancing_women:"👯",dancing_men:"👯‍♂️",dango:"🍡",dark_sunglasses:"🕶",dart:"🎯",dash:"💨",date:"📅",deciduous_tree:"🌳",deer:"🦌",department_store:"🏬",derelict_house:"🏚",desert:"🏜",desert_island:"🏝",desktop_computer:"🖥",male_detective:"🕵️",diamond_shape_with_a_dot_inside:"💠",diamonds:"♦️",disappointed:"😞",disappointed_relieved:"😥",dizzy:"💫",dizzy_face:"😵",do_not_litter:"🚯",dog:"🐶",dog2:"🐕",dollar:"💵",dolls:"🎎",dolphin:"🐬",door:"🚪",doughnut:"🍩",dove:"🕊",dragon:"🐉",dragon_face:"🐲",dress:"👗",dromedary_camel:"🐪",drooling_face:"🤤",droplet:"💧",drum:"🥁",duck:"🦆",dvd:"📀","e-mail":"📧",eagle:"🦅",ear:"👂",ear_of_rice:"🌾",earth_africa:"🌍",earth_americas:"🌎",earth_asia:"🌏",egg:"🥚",eggplant:"🍆",eight_pointed_black_star:"✴️",eight_spoked_asterisk:"✳️",electric_plug:"🔌",elephant:"🐘",email:"✉️",end:"🔚",envelope_with_arrow:"📩",euro:"💶",european_castle:"🏰",european_post_office:"🏤",evergreen_tree:"🌲",exclamation:"❗️",expressionless:"😑",eye:"👁",eye_speech_bubble:"👁‍🗨",eyeglasses:"👓",eyes:"👀",face_with_head_bandage:"🤕",face_with_thermometer:"🤒",fist_oncoming:"👊",factory:"🏭",fallen_leaf:"🍂",family_man_woman_boy:"👪",family_man_boy:"👨‍👦",family_man_boy_boy:"👨‍👦‍👦",family_man_girl:"👨‍👧",family_man_girl_boy:"👨‍👧‍👦",family_man_girl_girl:"👨‍👧‍👧",family_man_man_boy:"👨‍👨‍👦",family_man_man_boy_boy:"👨‍👨‍👦‍👦",family_man_man_girl:"👨‍👨‍👧",family_man_man_girl_boy:"👨‍👨‍👧‍👦",family_man_man_girl_girl:"👨‍👨‍👧‍👧",family_man_woman_boy_boy:"👨‍👩‍👦‍👦",family_man_woman_girl:"👨‍👩‍👧",family_man_woman_girl_boy:"👨‍👩‍👧‍👦",family_man_woman_girl_girl:"👨‍👩‍👧‍👧",family_woman_boy:"👩‍👦",family_woman_boy_boy:"👩‍👦‍👦",family_woman_girl:"👩‍👧",family_woman_girl_boy:"👩‍👧‍👦",family_woman_girl_girl:"👩‍👧‍👧",family_woman_woman_boy:"👩‍👩‍👦",family_woman_woman_boy_boy:"👩‍👩‍👦‍👦",family_woman_woman_girl:"👩‍👩‍👧",family_woman_woman_girl_boy:"👩‍👩‍👧‍👦",family_woman_woman_girl_girl:"👩‍👩‍👧‍👧",fast_forward:"⏩",fax:"📠",fearful:"😨",feet:"🐾",female_detective:"🕵️‍♀️",ferris_wheel:"🎡",ferry:"⛴",field_hockey:"🏑",file_cabinet:"🗄",file_folder:"📁",film_projector:"📽",film_strip:"🎞",fire:"🔥",fire_engine:"🚒",fireworks:"🎆",first_quarter_moon:"🌓",first_quarter_moon_with_face:"🌛",fish:"🐟",fish_cake:"🍥",fishing_pole_and_fish:"🎣",fist_raised:"✊",fist_left:"🤛",fist_right:"🤜",flags:"🎏",flashlight:"🔦",fleur_de_lis:"⚜️",flight_arrival:"🛬",flight_departure:"🛫",floppy_disk:"💾",flower_playing_cards:"🎴",flushed:"😳",fog:"🌫",foggy:"🌁",football:"🏈",footprints:"👣",fork_and_knife:"🍴",fountain:"⛲️",fountain_pen:"🖋",four_leaf_clover:"🍀",fox_face:"🦊",framed_picture:"🖼",free:"🆓",fried_egg:"🍳",fried_shrimp:"🍤",fries:"🍟",frog:"🐸",frowning:"😦",frowning_face:"☹️",frowning_man:"🙍‍♂️",frowning_woman:"🙍",middle_finger:"🖕",fuelpump:"⛽️",full_moon:"🌕",full_moon_with_face:"🌝",funeral_urn:"⚱️",game_die:"🎲",gear:"⚙️",gem:"💎",gemini:"♊️",ghost:"👻",gift:"🎁",gift_heart:"💝",girl:"👧",globe_with_meridians:"🌐",goal_net:"🥅",goat:"🐐",golf:"⛳️",golfing_man:"🏌️",golfing_woman:"🏌️‍♀️",gorilla:"🦍",grapes:"🍇",green_apple:"🍏",green_book:"📗",green_heart:"💚",green_salad:"🥗",grey_exclamation:"❕",grey_question:"❔",grimacing:"😬",grin:"😁",grinning:"😀",guardsman:"💂",guardswoman:"💂‍♀️",guitar:"🎸",gun:"🔫",haircut_woman:"💇",haircut_man:"💇‍♂️",hamburger:"🍔",hammer:"🔨",hammer_and_pick:"⚒",hammer_and_wrench:"🛠",hamster:"🐹",hand:"✋",handbag:"👜",handshake:"🤝",hankey:"💩",hatched_chick:"🐥",hatching_chick:"🐣",headphones:"🎧",hear_no_evil:"🙉",heart:"❤️",heart_decoration:"💟",heart_eyes:"😍",heart_eyes_cat:"😻",heartbeat:"💓",heartpulse:"💗",hearts:"♥️",heavy_check_mark:"✔️",heavy_division_sign:"➗",heavy_dollar_sign:"💲",heavy_heart_exclamation:"❣️",heavy_minus_sign:"➖",heavy_multiplication_x:"✖️",heavy_plus_sign:"➕",helicopter:"🚁",herb:"🌿",hibiscus:"🌺",high_brightness:"🔆",high_heel:"👠",hocho:"🔪",hole:"🕳",honey_pot:"🍯",horse:"🐴",horse_racing:"🏇",hospital:"🏥",hot_pepper:"🌶",hotdog:"🌭",hotel:"🏨",hotsprings:"♨️",hourglass:"⌛️",hourglass_flowing_sand:"⏳",house:"🏠",house_with_garden:"🏡",houses:"🏘",hugs:"🤗",hushed:"😯",ice_cream:"🍨",ice_hockey:"🏒",ice_skate:"⛸",icecream:"🍦",id:"🆔",ideograph_advantage:"🉐",imp:"👿",inbox_tray:"📥",incoming_envelope:"📨",tipping_hand_woman:"💁",information_source:"ℹ️",innocent:"😇",interrobang:"⁉️",iphone:"📱",izakaya_lantern:"🏮",jack_o_lantern:"🎃",japan:"🗾",japanese_castle:"🏯",japanese_goblin:"👺",japanese_ogre:"👹",jeans:"👖",joy:"😂",joy_cat:"😹",joystick:"🕹",kaaba:"🕋",key:"🔑",keyboard:"⌨️",keycap_ten:"🔟",kick_scooter:"🛴",kimono:"👘",kiss:"💋",kissing:"😗",kissing_cat:"😽",kissing_closed_eyes:"😚",kissing_heart:"😘",kissing_smiling_eyes:"😙",kiwi_fruit:"🥝",koala:"🐨",koko:"🈁",label:"🏷",large_blue_circle:"🔵",large_blue_diamond:"🔷",large_orange_diamond:"🔶",last_quarter_moon:"🌗",last_quarter_moon_with_face:"🌜",latin_cross:"✝️",laughing:"😆",leaves:"🍃",ledger:"📒",left_luggage:"🛅",left_right_arrow:"↔️",leftwards_arrow_with_hook:"↩️",lemon:"🍋",leo:"♌️",leopard:"🐆",level_slider:"🎚",libra:"♎️",light_rail:"🚈",link:"🔗",lion:"🦁",lips:"👄",lipstick:"💄",lizard:"🦎",lock:"🔒",lock_with_ink_pen:"🔏",lollipop:"🍭",loop:"➿",loud_sound:"🔊",loudspeaker:"📢",love_hotel:"🏩",love_letter:"💌",low_brightness:"🔅",lying_face:"🤥",m:"Ⓜ️",mag:"🔍",mag_right:"🔎",mahjong:"🀄️",mailbox:"📫",mailbox_closed:"📪",mailbox_with_mail:"📬",mailbox_with_no_mail:"📭",man:"👨",man_artist:"👨‍🎨",man_astronaut:"👨‍🚀",man_cartwheeling:"🤸‍♂️",man_cook:"👨‍🍳",man_dancing:"🕺",man_facepalming:"🤦‍♂️",man_factory_worker:"👨‍🏭",man_farmer:"👨‍🌾",man_firefighter:"👨‍🚒",man_health_worker:"👨‍⚕️",man_in_tuxedo:"🤵",man_judge:"👨‍⚖️",man_juggling:"🤹‍♂️",man_mechanic:"👨‍🔧",man_office_worker:"👨‍💼",man_pilot:"👨‍✈️",man_playing_handball:"🤾‍♂️",man_playing_water_polo:"🤽‍♂️",man_scientist:"👨‍🔬",man_shrugging:"🤷‍♂️",man_singer:"👨‍🎤",man_student:"👨‍🎓",man_teacher:"👨‍🏫",man_technologist:"👨‍💻",man_with_gua_pi_mao:"👲",man_with_turban:"👳",tangerine:"🍊",mans_shoe:"👞",mantelpiece_clock:"🕰",maple_leaf:"🍁",martial_arts_uniform:"🥋",mask:"😷",massage_woman:"💆",massage_man:"💆‍♂️",meat_on_bone:"🍖",medal_military:"🎖",medal_sports:"🏅",mega:"📣",melon:"🍈",memo:"📝",men_wrestling:"🤼‍♂️",menorah:"🕎",mens:"🚹",metal:"🤘",metro:"🚇",microphone:"🎤",microscope:"🔬",milk_glass:"🥛",milky_way:"🌌",minibus:"🚐",minidisc:"💽",mobile_phone_off:"📴",money_mouth_face:"🤑",money_with_wings:"💸",moneybag:"💰",monkey:"🐒",monkey_face:"🐵",monorail:"🚝",moon:"🌔",mortar_board:"🎓",mosque:"🕌",motor_boat:"🛥",motor_scooter:"🛵",motorcycle:"🏍",motorway:"🛣",mount_fuji:"🗻",mountain:"⛰",mountain_biking_man:"🚵",mountain_biking_woman:"🚵‍♀️",mountain_cableway:"🚠",mountain_railway:"🚞",mountain_snow:"🏔",mouse:"🐭",mouse2:"🐁",movie_camera:"🎥",moyai:"🗿",mrs_claus:"🤶",muscle:"💪",mushroom:"🍄",musical_keyboard:"🎹",musical_note:"🎵",musical_score:"🎼",mute:"🔇",nail_care:"💅",name_badge:"📛",national_park:"🏞",nauseated_face:"🤢",necktie:"👔",negative_squared_cross_mark:"❎",nerd_face:"🤓",neutral_face:"😐",new:"🆕",new_moon:"🌑",new_moon_with_face:"🌚",newspaper:"📰",newspaper_roll:"🗞",next_track_button:"⏭",ng:"🆖",no_good_man:"🙅‍♂️",no_good_woman:"🙅",night_with_stars:"🌃",no_bell:"🔕",no_bicycles:"🚳",no_entry:"⛔️",no_entry_sign:"🚫",no_mobile_phones:"📵",no_mouth:"😶",no_pedestrians:"🚷",no_smoking:"🚭","non-potable_water":"🚱",nose:"👃",notebook:"📓",notebook_with_decorative_cover:"📔",notes:"🎶",nut_and_bolt:"🔩",o:"⭕️",o2:"🅾️",ocean:"🌊",octopus:"🐙",oden:"🍢",office:"🏢",oil_drum:"🛢",ok:"🆗",ok_hand:"👌",ok_man:"🙆‍♂️",ok_woman:"🙆",old_key:"🗝",older_man:"👴",older_woman:"👵",om:"🕉",on:"🔛",oncoming_automobile:"🚘",oncoming_bus:"🚍",oncoming_police_car:"🚔",oncoming_taxi:"🚖",open_file_folder:"📂",open_hands:"👐",open_mouth:"😮",open_umbrella:"☂️",ophiuchus:"⛎",orange_book:"📙",orthodox_cross:"☦️",outbox_tray:"📤",owl:"🦉",ox:"🐂",package:"📦",page_facing_up:"📄",page_with_curl:"📃",pager:"📟",paintbrush:"🖌",palm_tree:"🌴",pancakes:"🥞",panda_face:"🐼",paperclip:"📎",paperclips:"🖇",parasol_on_ground:"⛱",parking:"🅿️",part_alternation_mark:"〽️",partly_sunny:"⛅️",passenger_ship:"🛳",passport_control:"🛂",pause_button:"⏸",peace_symbol:"☮️",peach:"🍑",peanuts:"🥜",pear:"🍐",pen:"🖊",pencil2:"✏️",penguin:"🐧",pensive:"😔",performing_arts:"🎭",persevere:"😣",person_fencing:"🤺",pouting_woman:"🙎",phone:"☎️",pick:"⛏",pig:"🐷",pig2:"🐖",pig_nose:"🐽",pill:"💊",pineapple:"🍍",ping_pong:"🏓",pisces:"♓️",pizza:"🍕",place_of_worship:"🛐",plate_with_cutlery:"🍽",play_or_pause_button:"⏯",point_down:"👇",point_left:"👈",point_right:"👉",point_up:"☝️",point_up_2:"👆",police_car:"🚓",policewoman:"👮‍♀️",poodle:"🐩",popcorn:"🍿",post_office:"🏣",postal_horn:"📯",postbox:"📮",potable_water:"🚰",potato:"🥔",pouch:"👝",poultry_leg:"🍗",pound:"💷",rage:"😡",pouting_cat:"😾",pouting_man:"🙎‍♂️",pray:"🙏",prayer_beads:"📿",pregnant_woman:"🤰",previous_track_button:"⏮",prince:"🤴",princess:"👸",printer:"🖨",purple_heart:"💜",purse:"👛",pushpin:"📌",put_litter_in_its_place:"🚮",question:"❓",rabbit:"🐰",rabbit2:"🐇",racehorse:"🐎",racing_car:"🏎",radio:"📻",radio_button:"🔘",radioactive:"☢️",railway_car:"🚃",railway_track:"🛤",rainbow:"🌈",rainbow_flag:"🏳️‍🌈",raised_back_of_hand:"🤚",raised_hand_with_fingers_splayed:"🖐",raised_hands:"🙌",raising_hand_woman:"🙋",raising_hand_man:"🙋‍♂️",ram:"🐏",ramen:"🍜",rat:"🐀",record_button:"⏺",recycle:"♻️",red_circle:"🔴",registered:"®️",relaxed:"☺️",relieved:"😌",reminder_ribbon:"🎗",repeat:"🔁",repeat_one:"🔂",rescue_worker_helmet:"⛑",restroom:"🚻",revolving_hearts:"💞",rewind:"⏪",rhinoceros:"🦏",ribbon:"🎀",rice:"🍚",rice_ball:"🍙",rice_cracker:"🍘",rice_scene:"🎑",right_anger_bubble:"🗯",ring:"💍",robot:"🤖",rocket:"🚀",rofl:"🤣",roll_eyes:"🙄",roller_coaster:"🎢",rooster:"🐓",rose:"🌹",rosette:"🏵",rotating_light:"🚨",round_pushpin:"📍",rowing_man:"🚣",rowing_woman:"🚣‍♀️",rugby_football:"🏉",running_man:"🏃",running_shirt_with_sash:"🎽",running_woman:"🏃‍♀️",sa:"🈂️",sagittarius:"♐️",sake:"🍶",sandal:"👡",santa:"🎅",satellite:"📡",saxophone:"🎷",school:"🏫",school_satchel:"🎒",scissors:"✂️",scorpion:"🦂",scorpius:"♏️",scream:"😱",scream_cat:"🙀",scroll:"📜",seat:"💺",secret:"㊙️",see_no_evil:"🙈",seedling:"🌱",selfie:"🤳",shallow_pan_of_food:"🥘",shamrock:"☘️",shark:"🦈",shaved_ice:"🍧",sheep:"🐑",shell:"🐚",shield:"🛡",shinto_shrine:"⛩",ship:"🚢",shirt:"👕",shopping:"🛍",shopping_cart:"🛒",shower:"🚿",shrimp:"🦐",signal_strength:"📶",six_pointed_star:"🔯",ski:"🎿",skier:"⛷",skull:"💀",skull_and_crossbones:"☠️",sleeping:"😴",sleeping_bed:"🛌",sleepy:"😪",slightly_frowning_face:"🙁",slightly_smiling_face:"🙂",slot_machine:"🎰",small_airplane:"🛩",small_blue_diamond:"🔹",small_orange_diamond:"🔸",small_red_triangle:"🔺",small_red_triangle_down:"🔻",smile:"😄",smile_cat:"😸",smiley:"😃",smiley_cat:"😺",smiling_imp:"😈",smirk:"😏",smirk_cat:"😼",smoking:"🚬",snail:"🐌",snake:"🐍",sneezing_face:"🤧",snowboarder:"🏂",snowflake:"❄️",snowman:"⛄️",snowman_with_snow:"☃️",sob:"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-        type: 'boolean'
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-      rawHeaderId: {
-        defaultValue: false,
-        describe: 'Remove only spaces, \' and " from generated header ids (including prefixes), replacing them with dashes (-). WARNING: This might result in malformed ids',
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-    if (!showdown.helper.isString(name)) {
-      throw Error('Extension \'name\' must be a string');
-    }
-
-    name = showdown.helper.stdExtName(name);
-
-    // Getter
-    if (showdown.helper.isUndefined(ext)) {
-      if (!extensions.hasOwnProperty(name)) {
-        throw Error('Extension named ' + name + ' is not registered!');
-      }
-      return extensions[name];
-
-      // Setter
-    } else {
-      // Expand extension if it's wrapped in a function
-      if (typeof ext === 'function') {
-        ext = ext();
-      }
-
-      // Ensure extension is an array
-      if (!showdown.helper.isArray(ext)) {
-        ext = [ext];
-      }
-
-      var validExtension = validate(ext, name);
-
-      if (validExtension.valid) {
-        extensions[name] = ext;
-      } else {
-        throw Error(validExtension.error);
-      }
-    }
-  };
-
-  /**
-   * Gets all extensions registered
-   * @returns {{}}
-   */
-  showdown.getAllExtensions = function () {
-    'use strict';
-
-    return extensions;
-  };
-
-  /**
-   * Remove an extension
-   * @param {string} name
-   */
-  showdown.removeExtension = function (name) {
-    'use strict';
-
-    delete extensions[name];
-  };
-
-  /**
-   * Removes all extensions
-   */
-  showdown.resetExtensions = function () {
-    'use strict';
-
-    extensions = {};
-  };
-
-  /**
-   * Validate extension
-   * @param {array} extension
-   * @param {string} name
-   * @returns {{valid: boolean, error: string}}
-   */
-  function validate(extension, name) {
-    'use strict';
-
-    var errMsg = name ? 'Error in ' + name + ' extension->' : 'Error in unnamed extension',
-        ret = {
-      valid: true,
-      error: ''
-    };
-
-    if (!showdown.helper.isArray(extension)) {
-      extension = [extension];
-    }
-
-    for (var i = 0; i < extension.length; ++i) {
-      var baseMsg = errMsg + ' sub-extension ' + i + ': ',
-          ext = extension[i];
-      if (typeof ext !== 'object') {
-        ret.valid = false;
-        ret.error = baseMsg + 'must be an object, but ' + typeof ext + ' given';
-        return ret;
-      }
-
-      if (!showdown.helper.isString(ext.type)) {
-        ret.valid = false;
-        ret.error = baseMsg + 'property "type" must be a string, but ' + typeof ext.type + ' given';
-        return ret;
-      }
-
-      var type = ext.type = ext.type.toLowerCase();
-
-      // normalize extension type
-      if (type === 'language') {
-        type = ext.type = 'lang';
-      }
-
-      if (type === 'html') {
-        type = ext.type = 'output';
-      }
-
-      if (type !== 'lang' && type !== 'output' && type !== 'listener') {
-        ret.valid = false;
-        ret.error = baseMsg + 'type ' + type + ' is not recognized. Valid values: "lang/language", "output/html" or "listener"';
-        return ret;
-      }
-
-      if (type === 'listener') {
-        if (showdown.helper.isUndefined(ext.listeners)) {
-          ret.valid = false;
-          ret.error = baseMsg + '. Extensions of type "listener" must have a property called "listeners"';
-          return ret;
-        }
-      } else {
-        if (showdown.helper.isUndefined(ext.filter) && showdown.helper.isUndefined(ext.regex)) {
-          ret.valid = false;
-          ret.error = baseMsg + type + ' extensions must define either a "regex" property or a "filter" method';
-          return ret;
-        }
-      }
-
-      if (ext.listeners) {
-        if (typeof ext.listeners !== 'object') {
-          ret.valid = false;
-          ret.error = baseMsg + '"listeners" property must be an object but ' + typeof ext.listeners + ' given';
-          return ret;
-        }
-        for (var ln in ext.listeners) {
-          if (ext.listeners.hasOwnProperty(ln)) {
-            if (typeof ext.listeners[ln] !== 'function') {
-              ret.valid = false;
-              ret.error = baseMsg + '"listeners" property must be an hash of [event name]: [callback]. listeners.' + ln + ' must be a function but ' + typeof ext.listeners[ln] + ' given';
-              return ret;
-            }
-          }
-        }
-      }
-
-      if (ext.filter) {
-        if (typeof ext.filter !== 'function') {
-          ret.valid = false;
-          ret.error = baseMsg + '"filter" must be a function, but ' + typeof ext.filter + ' given';
-          return ret;
-        }
-      } else if (ext.regex) {
-        if (showdown.helper.isString(ext.regex)) {
-          ext.regex = new RegExp(ext.regex, 'g');
-        }
-        if (!(ext.regex instanceof RegExp)) {
-          ret.valid = false;
-          ret.error = baseMsg + '"regex" property must either be a string or a RegExp object, but ' + typeof ext.regex + ' given';
-          return ret;
-        }
-        if (showdown.helper.isUndefined(ext.replace)) {
-          ret.valid = false;
-          ret.error = baseMsg + '"regex" extensions must implement a replace string or function';
-          return ret;
-        }
-      }
-    }
-    return ret;
-  }
-
-  /**
-   * Validate extension
-   * @param {object} ext
-   * @returns {boolean}
-   */
-  showdown.validateExtension = function (ext) {
-    'use strict';
-
-    var validateExtension = validate(ext, null);
-    if (!validateExtension.valid) {
-      console.warn(validateExtension.error);
-      return false;
-    }
-    return true;
-  };
-
-  /**
-   * showdownjs helper functions
-   */
-
-  if (!showdown.hasOwnProperty('helper')) {
-    showdown.helper = {};
-  }
-
-  /**
-   * Check if var is string
-   * @static
-   * @param {string} a
-   * @returns {boolean}
-   */
-  showdown.helper.isString = function (a) {
-    'use strict';
-
-    return typeof a === 'string' || a instanceof String;
-  };
-
-  /**
-   * Check if var is a function
-   * @static
-   * @param {*} a
-   * @returns {boolean}
-   */
-  showdown.helper.isFunction = function (a) {
-    'use strict';
-
-    var getType = {};
-    return a && getType.toString.call(a) === '[object Function]';
-  };
-
-  /**
-   * isArray helper function
-   * @static
-   * @param {*} a
-   * @returns {boolean}
-   */
-  showdown.helper.isArray = function (a) {
-    'use strict';
-
-    return Array.isArray(a);
-  };
-
-  /**
-   * Check if value is undefined
-   * @static
-   * @param {*} value The value to check.
-   * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.
-   */
-  showdown.helper.isUndefined = function (value) {
-    'use strict';
-
-    return typeof value === 'undefined';
-  };
-
-  /**
-   * ForEach helper function
-   * Iterates over Arrays and Objects (own properties only)
-   * @static
-   * @param {*} obj
-   * @param {function} callback Accepts 3 params: 1. value, 2. key, 3. the original array/object
-   */
-  showdown.helper.forEach = function (obj, callback) {
-    'use strict';
-    // check if obj is defined
-
-    if (showdown.helper.isUndefined(obj)) {
-      throw new Error('obj param is required');
-    }
-
-    if (showdown.helper.isUndefined(callback)) {
-      throw new Error('callback param is required');
-    }
-
-    if (!showdown.helper.isFunction(callback)) {
-      throw new Error('callback param must be a function/closure');
-    }
-
-    if (typeof obj.forEach === 'function') {
-      obj.forEach(callback);
-    } else if (showdown.helper.isArray(obj)) {
-      for (var i = 0; i < obj.length; i++) {
-        callback(obj[i], i, obj);
-      }
-    } else if (typeof obj === 'object') {
-      for (var prop in obj) {
-        if (obj.hasOwnProperty(prop)) {
-          callback(obj[prop], prop, obj);
-        }
-      }
-    } else {
-      throw new Error('obj does not seem to be an array or an iterable object');
-    }
-  };
-
-  /**
-   * Standardidize extension name
-   * @static
-   * @param {string} s extension name
-   * @returns {string}
-   */
-  showdown.helper.stdExtName = function (s) {
-    'use strict';
-
-    return s.replace(/[_?*+\/\\.^-]/g, '').replace(/\s/g, '').toLowerCase();
-  };
-
-  function escapeCharactersCallback(wholeMatch, m1) {
-    'use strict';
-
-    var charCodeToEscape = m1.charCodeAt(0);
-    return '¨E' + charCodeToEscape + 'E';
-  }
-
-  /**
-   * Callback used to escape characters when passing through String.replace
-   * @static
-   * @param {string} wholeMatch
-   * @param {string} m1
-   * @returns {string}
-   */
-  showdown.helper.escapeCharactersCallback = escapeCharactersCallback;
-
-  /**
-   * Escape characters in a string
-   * @static
-   * @param {string} text
-   * @param {string} charsToEscape
-   * @param {boolean} afterBackslash
-   * @returns {XML|string|void|*}
-   */
-  showdown.helper.escapeCharacters = function (text, charsToEscape, afterBackslash) {
-    'use strict';
-    // First we have to escape the escape characters so that
-    // we can build a character class out of them
-
-    var regexString = '([' + charsToEscape.replace(/([\[\]\\])/g, '\\$1') + '])';
-
-    if (afterBackslash) {
-      regexString = '\\\\' + regexString;
-    }
-
-    var regex = new RegExp(regexString, 'g');
-    text = text.replace(regex, escapeCharactersCallback);
-
-    return text;
-  };
-
-  /**
-   * Unescape HTML entities
-   * @param txt
-   * @returns {string}
-   */
-  showdown.helper.unescapeHTMLEntities = function (txt) {
-    'use strict';
-
-    return txt.replace(/"/g, '"').replace(/</g, '<').replace(/>/g, '>').replace(/&/g, '&');
-  };
-
-  var rgxFindMatchPos = function rgxFindMatchPos(str, left, right, flags) {
-    'use strict';
-
-    var f = flags || '',
-        g = f.indexOf('g') > -1,
-        x = new RegExp(left + '|' + right, 'g' + f.replace(/g/g, '')),
-        l = new RegExp(left, f.replace(/g/g, '')),
-        pos = [],
-        t,
-        s,
-        m,
-        start,
-        end;
-
-    do {
-      t = 0;
-      while (m = x.exec(str)) {
-        if (l.test(m[0])) {
-          if (!t++) {
-            s = x.lastIndex;
-            start = s - m[0].length;
-          }
-        } else if (t) {
-          if (! --t) {
-            end = m.index + m[0].length;
-            var obj = {
-              left: { start: start, end: s },
-              match: { start: s, end: m.index },
-              right: { start: m.index, end: end },
-              wholeMatch: { start: start, end: end }
-            };
-            pos.push(obj);
-            if (!g) {
-              return pos;
-            }
-          }
-        }
-      }
-    } while (t && (x.lastIndex = s));
-
-    return pos;
-  };
-
-  /**
-   * matchRecursiveRegExp
-   *
-   * (c) 2007 Steven Levithan 
-   * MIT License
-   *
-   * Accepts a string to search, a left and right format delimiter
-   * as regex patterns, and optional regex flags. Returns an array
-   * of matches, allowing nested instances of left/right delimiters.
-   * Use the "g" flag to return all matches, otherwise only the
-   * first is returned. Be careful to ensure that the left and
-   * right format delimiters produce mutually exclusive matches.
-   * Backreferences are not supported within the right delimiter
-   * due to how it is internally combined with the left delimiter.
-   * When matching strings whose format delimiters are unbalanced
-   * to the left or right, the output is intentionally as a
-   * conventional regex library with recursion support would
-   * produce, e.g. "<" and ">" both produce ["x"] when using
-   * "<" and ">" as the delimiters (both strings contain a single,
-   * balanced instance of "").
-   *
-   * examples:
-   * matchRecursiveRegExp("test", "\\(", "\\)")
-   * returns: []
-   * matchRecursiveRegExp(">>t<>", "<", ">", "g")
-   * returns: ["t<>", ""]
-   * matchRecursiveRegExp("
    test
    ", "]*>", "", "gi")
-   * returns: ["test"]
-   */
-  showdown.helper.matchRecursiveRegExp = function (str, left, right, flags) {
-    'use strict';
-
-    var matchPos = rgxFindMatchPos(str, left, right, flags),
-        results = [];
-
-    for (var i = 0; i < matchPos.length; ++i) {
-      results.push([str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end), str.slice(matchPos[i].match.start, matchPos[i].match.end), str.slice(matchPos[i].left.start, matchPos[i].left.end), str.slice(matchPos[i].right.start, matchPos[i].right.end)]);
-    }
-    return results;
-  };
-
-  /**
-   *
-   * @param {string} str
-   * @param {string|function} replacement
-   * @param {string} left
-   * @param {string} right
-   * @param {string} flags
-   * @returns {string}
-   */
-  showdown.helper.replaceRecursiveRegExp = function (str, replacement, left, right, flags) {
-    'use strict';
-
-    if (!showdown.helper.isFunction(replacement)) {
-      var repStr = replacement;
-      replacement = function replacement() {
-        return repStr;
-      };
-    }
-
-    var matchPos = rgxFindMatchPos(str, left, right, flags),
-        finalStr = str,
-        lng = matchPos.length;
-
-    if (lng > 0) {
-      var bits = [];
-      if (matchPos[0].wholeMatch.start !== 0) {
-        bits.push(str.slice(0, matchPos[0].wholeMatch.start));
-      }
-      for (var i = 0; i < lng; ++i) {
-        bits.push(replacement(str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end), str.slice(matchPos[i].match.start, matchPos[i].match.end), str.slice(matchPos[i].left.start, matchPos[i].left.end), str.slice(matchPos[i].right.start, matchPos[i].right.end)));
-        if (i < lng - 1) {
-          bits.push(str.slice(matchPos[i].wholeMatch.end, matchPos[i + 1].wholeMatch.start));
-        }
-      }
-      if (matchPos[lng - 1].wholeMatch.end < str.length) {
-        bits.push(str.slice(matchPos[lng - 1].wholeMatch.end));
-      }
-      finalStr = bits.join('');
-    }
-    return finalStr;
-  };
-
-  /**
-   * Returns the index within the passed String object of the first occurrence of the specified regex,
-   * starting the search at fromIndex. Returns -1 if the value is not found.
-   *
-   * @param {string} str string to search
-   * @param {RegExp} regex Regular expression to search
-   * @param {int} [fromIndex = 0] Index to start the search
-   * @returns {Number}
-   * @throws InvalidArgumentError
-   */
-  showdown.helper.regexIndexOf = function (str, regex, fromIndex) {
-    'use strict';
-
-    if (!showdown.helper.isString(str)) {
-      throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';
-    }
-    if (regex instanceof RegExp === false) {
-      throw 'InvalidArgumentError: second parameter of showdown.helper.regexIndexOf function must be an instance of RegExp';
-    }
-    var indexOf = str.substring(fromIndex || 0).search(regex);
-    return indexOf >= 0 ? indexOf + (fromIndex || 0) : indexOf;
-  };
-
-  /**
-   * Splits the passed string object at the defined index, and returns an array composed of the two substrings
-   * @param {string} str string to split
-   * @param {int} index index to split string at
-   * @returns {[string,string]}
-   * @throws InvalidArgumentError
-   */
-  showdown.helper.splitAtIndex = function (str, index) {
-    'use strict';
-
-    if (!showdown.helper.isString(str)) {
-      throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';
-    }
-    return [str.substring(0, index), str.substring(index)];
-  };
-
-  /**
-   * Obfuscate an e-mail address through the use of Character Entities,
-   * transforming ASCII characters into their equivalent decimal or hex entities.
-   *
-   * Since it has a random component, subsequent calls to this function produce different results
-   *
-   * @param {string} mail
-   * @returns {string}
-   */
-  showdown.helper.encodeEmailAddress = function (mail) {
-    'use strict';
-
-    var encode = [function (ch) {
-      return '&#' + ch.charCodeAt(0) + ';';
-    }, function (ch) {
-      return '&#x' + ch.charCodeAt(0).toString(16) + ';';
-    }, function (ch) {
-      return ch;
-    }];
-
-    mail = mail.replace(/./g, function (ch) {
-      if (ch === '@') {
-        // this *must* be encoded. I insist.
-        ch = encode[Math.floor(Math.random() * 2)](ch);
-      } else {
-        var r = Math.random();
-        // roughly 10% raw, 45% hex, 45% dec
-        ch = r > 0.9 ? encode[2](ch) : r > 0.45 ? encode[1](ch) : encode[0](ch);
-      }
-      return ch;
-    });
-
-    return mail;
-  };
-
-  /**
-   *
-   * @param str
-   * @param targetLength
-   * @param padString
-   * @returns {string}
-   */
-  showdown.helper.padEnd = function padEnd(str, targetLength, padString) {
-    'use strict';
-    /*jshint bitwise: false*/
-    // eslint-disable-next-line space-infix-ops
-
-    targetLength = targetLength >> 0; //floor if number or convert non-number to 0;
-    /*jshint bitwise: true*/
-    padString = String(padString || ' ');
-    if (str.length > targetLength) {
-      return String(str);
-    } else {
-      targetLength = targetLength - str.length;
-      if (targetLength > padString.length) {
-        padString += padString.repeat(targetLength / padString.length); //append to original to ensure we are longer than needed
-      }
-      return String(str) + padString.slice(0, targetLength);
-    }
-  };
-
-  /**
-   * POLYFILLS
-   */
-  // use this instead of builtin is undefined for IE8 compatibility
-  if (typeof console === 'undefined') {
-    console = {
-      warn: function warn(msg) {
-        'use strict';
-
-        alert(msg);
-      },
-      log: function log(msg) {
-        'use strict';
-
-        alert(msg);
-      },
-      error: function error(msg) {
-        'use strict';
-
-        throw msg;
-      }
-    };
-  }
-
-  /**
-   * Common regexes.
-   * We declare some common regexes to improve performance
-   */
-  showdown.helper.regexes = {
-    asteriskDashAndColon: /([*_:~])/g
-  };
-
-  /**
-   * EMOJIS LIST
-   */
-  showdown.helper.emojis = {
-    '+1': '\uD83D\uDC4D',
-    '-1': '\uD83D\uDC4E',
-    '100': '\uD83D\uDCAF',
-    '1234': '\uD83D\uDD22',
-    '1st_place_medal': '\uD83E\uDD47',
-    '2nd_place_medal': '\uD83E\uDD48',
-    '3rd_place_medal': '\uD83E\uDD49',
-    '8ball': '\uD83C\uDFB1',
-    'a': '\uD83C\uDD70\uFE0F',
-    'ab': '\uD83C\uDD8E',
-    'abc': '\uD83D\uDD24',
-    'abcd': '\uD83D\uDD21',
-    'accept': '\uD83C\uDE51',
-    'aerial_tramway': '\uD83D\uDEA1',
-    'airplane': '\u2708\uFE0F',
-    'alarm_clock': '\u23F0',
-    'alembic': '\u2697\uFE0F',
-    'alien': '\uD83D\uDC7D',
-    'ambulance': '\uD83D\uDE91',
-    'amphora': '\uD83C\uDFFA',
-    'anchor': '\u2693\uFE0F',
-    'angel': '\uD83D\uDC7C',
-    'anger': '\uD83D\uDCA2',
-    'angry': '\uD83D\uDE20',
-    'anguished': '\uD83D\uDE27',
-    'ant': '\uD83D\uDC1C',
-    'apple': '\uD83C\uDF4E',
-    'aquarius': '\u2652\uFE0F',
-    'aries': '\u2648\uFE0F',
-    'arrow_backward': '\u25C0\uFE0F',
-    'arrow_double_down': '\u23EC',
-    'arrow_double_up': '\u23EB',
-    'arrow_down': '\u2B07\uFE0F',
-    'arrow_down_small': '\uD83D\uDD3D',
-    'arrow_forward': '\u25B6\uFE0F',
-    'arrow_heading_down': '\u2935\uFE0F',
-    'arrow_heading_up': '\u2934\uFE0F',
-    'arrow_left': '\u2B05\uFE0F',
-    'arrow_lower_left': '\u2199\uFE0F',
-    'arrow_lower_right': '\u2198\uFE0F',
-    'arrow_right': '\u27A1\uFE0F',
-    'arrow_right_hook': '\u21AA\uFE0F',
-    'arrow_up': '\u2B06\uFE0F',
-    'arrow_up_down': '\u2195\uFE0F',
-    'arrow_up_small': '\uD83D\uDD3C',
-    'arrow_upper_left': '\u2196\uFE0F',
-    'arrow_upper_right': '\u2197\uFE0F',
-    'arrows_clockwise': '\uD83D\uDD03',
-    'arrows_counterclockwise': '\uD83D\uDD04',
-    'art': '\uD83C\uDFA8',
-    'articulated_lorry': '\uD83D\uDE9B',
-    'artificial_satellite': '\uD83D\uDEF0',
-    'astonished': '\uD83D\uDE32',
-    'athletic_shoe': '\uD83D\uDC5F',
-    'atm': '\uD83C\uDFE7',
-    'atom_symbol': '\u269B\uFE0F',
-    'avocado': '\uD83E\uDD51',
-    'b': '\uD83C\uDD71\uFE0F',
-    'baby': '\uD83D\uDC76',
-    'baby_bottle': '\uD83C\uDF7C',
-    'baby_chick': '\uD83D\uDC24',
-    'baby_symbol': '\uD83D\uDEBC',
-    'back': '\uD83D\uDD19',
-    'bacon': '\uD83E\uDD53',
-    'badminton': '\uD83C\uDFF8',
-    'baggage_claim': '\uD83D\uDEC4',
-    'baguette_bread': '\uD83E\uDD56',
-    'balance_scale': '\u2696\uFE0F',
-    'balloon': '\uD83C\uDF88',
-    'ballot_box': '\uD83D\uDDF3',
-    'ballot_box_with_check': '\u2611\uFE0F',
-    'bamboo': '\uD83C\uDF8D',
-    'banana': '\uD83C\uDF4C',
-    'bangbang': '\u203C\uFE0F',
-    'bank': '\uD83C\uDFE6',
-    'bar_chart': '\uD83D\uDCCA',
-    'barber': '\uD83D\uDC88',
-    'baseball': '\u26BE\uFE0F',
-    'basketball': '\uD83C\uDFC0',
-    'basketball_man': '\u26F9\uFE0F',
-    'basketball_woman': '\u26F9\uFE0F‍\u2640\uFE0F',
-    'bat': '\uD83E\uDD87',
-    'bath': '\uD83D\uDEC0',
-    'bathtub': '\uD83D\uDEC1',
-    'battery': '\uD83D\uDD0B',
-    'beach_umbrella': '\uD83C\uDFD6',
-    'bear': '\uD83D\uDC3B',
-    'bed': '\uD83D\uDECF',
-    'bee': '\uD83D\uDC1D',
-    'beer': '\uD83C\uDF7A',
-    'beers': '\uD83C\uDF7B',
-    'beetle': '\uD83D\uDC1E',
-    'beginner': '\uD83D\uDD30',
-    'bell': '\uD83D\uDD14',
-    'bellhop_bell': '\uD83D\uDECE',
-    'bento': '\uD83C\uDF71',
-    'biking_man': '\uD83D\uDEB4',
-    'bike': '\uD83D\uDEB2',
-    'biking_woman': '\uD83D\uDEB4‍\u2640\uFE0F',
-    'bikini': '\uD83D\uDC59',
-    'biohazard': '\u2623\uFE0F',
-    'bird': '\uD83D\uDC26',
-    'birthday': '\uD83C\uDF82',
-    'black_circle': '\u26AB\uFE0F',
-    'black_flag': '\uD83C\uDFF4',
-    'black_heart': '\uD83D\uDDA4',
-    'black_joker': '\uD83C\uDCCF',
-    'black_large_square': '\u2B1B\uFE0F',
-    'black_medium_small_square': '\u25FE\uFE0F',
-    'black_medium_square': '\u25FC\uFE0F',
-    'black_nib': '\u2712\uFE0F',
-    'black_small_square': '\u25AA\uFE0F',
-    'black_square_button': '\uD83D\uDD32',
-    'blonde_man': '\uD83D\uDC71',
-    'blonde_woman': '\uD83D\uDC71‍\u2640\uFE0F',
-    'blossom': '\uD83C\uDF3C',
-    'blowfish': '\uD83D\uDC21',
-    'blue_book': '\uD83D\uDCD8',
-    'blue_car': '\uD83D\uDE99',
-    'blue_heart': '\uD83D\uDC99',
-    'blush': '\uD83D\uDE0A',
-    'boar': '\uD83D\uDC17',
-    'boat': '\u26F5\uFE0F',
-    'bomb': '\uD83D\uDCA3',
-    'book': '\uD83D\uDCD6',
-    'bookmark': '\uD83D\uDD16',
-    'bookmark_tabs': '\uD83D\uDCD1',
-    'books': '\uD83D\uDCDA',
-    'boom': '\uD83D\uDCA5',
-    'boot': '\uD83D\uDC62',
-    'bouquet': '\uD83D\uDC90',
-    'bowing_man': '\uD83D\uDE47',
-    'bow_and_arrow': '\uD83C\uDFF9',
-    'bowing_woman': '\uD83D\uDE47‍\u2640\uFE0F',
-    'bowling': '\uD83C\uDFB3',
-    'boxing_glove': '\uD83E\uDD4A',
-    'boy': '\uD83D\uDC66',
-    'bread': '\uD83C\uDF5E',
-    'bride_with_veil': '\uD83D\uDC70',
-    'bridge_at_night': '\uD83C\uDF09',
-    'briefcase': '\uD83D\uDCBC',
-    'broken_heart': '\uD83D\uDC94',
-    'bug': '\uD83D\uDC1B',
-    'building_construction': '\uD83C\uDFD7',
-    'bulb': '\uD83D\uDCA1',
-    'bullettrain_front': '\uD83D\uDE85',
-    'bullettrain_side': '\uD83D\uDE84',
-    'burrito': '\uD83C\uDF2F',
-    'bus': '\uD83D\uDE8C',
-    'business_suit_levitating': '\uD83D\uDD74',
-    'busstop': '\uD83D\uDE8F',
-    'bust_in_silhouette': '\uD83D\uDC64',
-    'busts_in_silhouette': '\uD83D\uDC65',
-    'butterfly': '\uD83E\uDD8B',
-    'cactus': '\uD83C\uDF35',
-    'cake': '\uD83C\uDF70',
-    'calendar': '\uD83D\uDCC6',
-    'call_me_hand': '\uD83E\uDD19',
-    'calling': '\uD83D\uDCF2',
-    'camel': '\uD83D\uDC2B',
-    'camera': '\uD83D\uDCF7',
-    'camera_flash': '\uD83D\uDCF8',
-    'camping': '\uD83C\uDFD5',
-    'cancer': '\u264B\uFE0F',
-    'candle': '\uD83D\uDD6F',
-    'candy': '\uD83C\uDF6C',
-    'canoe': '\uD83D\uDEF6',
-    'capital_abcd': '\uD83D\uDD20',
-    'capricorn': '\u2651\uFE0F',
-    'car': '\uD83D\uDE97',
-    'card_file_box': '\uD83D\uDDC3',
-    'card_index': '\uD83D\uDCC7',
-    'card_index_dividers': '\uD83D\uDDC2',
-    'carousel_horse': '\uD83C\uDFA0',
-    'carrot': '\uD83E\uDD55',
-    'cat': '\uD83D\uDC31',
-    'cat2': '\uD83D\uDC08',
-    'cd': '\uD83D\uDCBF',
-    'chains': '\u26D3',
-    'champagne': '\uD83C\uDF7E',
-    'chart': '\uD83D\uDCB9',
-    'chart_with_downwards_trend': '\uD83D\uDCC9',
-    'chart_with_upwards_trend': '\uD83D\uDCC8',
-    'checkered_flag': '\uD83C\uDFC1',
-    'cheese': '\uD83E\uDDC0',
-    'cherries': '\uD83C\uDF52',
-    'cherry_blossom': '\uD83C\uDF38',
-    'chestnut': '\uD83C\uDF30',
-    'chicken': '\uD83D\uDC14',
-    'children_crossing': '\uD83D\uDEB8',
-    'chipmunk': '\uD83D\uDC3F',
-    'chocolate_bar': '\uD83C\uDF6B',
-    'christmas_tree': '\uD83C\uDF84',
-    'church': '\u26EA\uFE0F',
-    'cinema': '\uD83C\uDFA6',
-    'circus_tent': '\uD83C\uDFAA',
-    'city_sunrise': '\uD83C\uDF07',
-    'city_sunset': '\uD83C\uDF06',
-    'cityscape': '\uD83C\uDFD9',
-    'cl': '\uD83C\uDD91',
-    'clamp': '\uD83D\uDDDC',
-    'clap': '\uD83D\uDC4F',
-    'clapper': '\uD83C\uDFAC',
-    'classical_building': '\uD83C\uDFDB',
-    'clinking_glasses': '\uD83E\uDD42',
-    'clipboard': '\uD83D\uDCCB',
-    'clock1': '\uD83D\uDD50',
-    'clock10': '\uD83D\uDD59',
-    'clock1030': '\uD83D\uDD65',
-    'clock11': '\uD83D\uDD5A',
-    'clock1130': '\uD83D\uDD66',
-    'clock12': '\uD83D\uDD5B',
-    'clock1230': '\uD83D\uDD67',
-    'clock130': '\uD83D\uDD5C',
-    'clock2': '\uD83D\uDD51',
-    'clock230': '\uD83D\uDD5D',
-    'clock3': '\uD83D\uDD52',
-    'clock330': '\uD83D\uDD5E',
-    'clock4': '\uD83D\uDD53',
-    'clock430': '\uD83D\uDD5F',
-    'clock5': '\uD83D\uDD54',
-    'clock530': '\uD83D\uDD60',
-    'clock6': '\uD83D\uDD55',
-    'clock630': '\uD83D\uDD61',
-    'clock7': '\uD83D\uDD56',
-    'clock730': '\uD83D\uDD62',
-    'clock8': '\uD83D\uDD57',
-    'clock830': '\uD83D\uDD63',
-    'clock9': '\uD83D\uDD58',
-    'clock930': '\uD83D\uDD64',
-    'closed_book': '\uD83D\uDCD5',
-    'closed_lock_with_key': '\uD83D\uDD10',
-    'closed_umbrella': '\uD83C\uDF02',
-    'cloud': '\u2601\uFE0F',
-    'cloud_with_lightning': '\uD83C\uDF29',
-    'cloud_with_lightning_and_rain': '\u26C8',
-    'cloud_with_rain': '\uD83C\uDF27',
-    'cloud_with_snow': '\uD83C\uDF28',
-    'clown_face': '\uD83E\uDD21',
-    'clubs': '\u2663\uFE0F',
-    'cocktail': '\uD83C\uDF78',
-    'coffee': '\u2615\uFE0F',
-    'coffin': '\u26B0\uFE0F',
-    'cold_sweat': '\uD83D\uDE30',
-    'comet': '\u2604\uFE0F',
-    'computer': '\uD83D\uDCBB',
-    'computer_mouse': '\uD83D\uDDB1',
-    'confetti_ball': '\uD83C\uDF8A',
-    'confounded': '\uD83D\uDE16',
-    'confused': '\uD83D\uDE15',
-    'congratulations': '\u3297\uFE0F',
-    'construction': '\uD83D\uDEA7',
-    'construction_worker_man': '\uD83D\uDC77',
-    'construction_worker_woman': '\uD83D\uDC77‍\u2640\uFE0F',
-    'control_knobs': '\uD83C\uDF9B',
-    'convenience_store': '\uD83C\uDFEA',
-    'cookie': '\uD83C\uDF6A',
-    'cool': '\uD83C\uDD92',
-    'policeman': '\uD83D\uDC6E',
-    'copyright': '\xA9\uFE0F',
-    'corn': '\uD83C\uDF3D',
-    'couch_and_lamp': '\uD83D\uDECB',
-    'couple': '\uD83D\uDC6B',
-    'couple_with_heart_woman_man': '\uD83D\uDC91',
-    'couple_with_heart_man_man': '\uD83D\uDC68‍\u2764\uFE0F‍\uD83D\uDC68',
-    'couple_with_heart_woman_woman': '\uD83D\uDC69‍\u2764\uFE0F‍\uD83D\uDC69',
-    'couplekiss_man_man': '\uD83D\uDC68‍\u2764\uFE0F‍\uD83D\uDC8B‍\uD83D\uDC68',
-    'couplekiss_man_woman': '\uD83D\uDC8F',
-    'couplekiss_woman_woman': '\uD83D\uDC69‍\u2764\uFE0F‍\uD83D\uDC8B‍\uD83D\uDC69',
-    'cow': '\uD83D\uDC2E',
-    'cow2': '\uD83D\uDC04',
-    'cowboy_hat_face': '\uD83E\uDD20',
-    'crab': '\uD83E\uDD80',
-    'crayon': '\uD83D\uDD8D',
-    'credit_card': '\uD83D\uDCB3',
-    'crescent_moon': '\uD83C\uDF19',
-    'cricket': '\uD83C\uDFCF',
-    'crocodile': '\uD83D\uDC0A',
-    'croissant': '\uD83E\uDD50',
-    'crossed_fingers': '\uD83E\uDD1E',
-    'crossed_flags': '\uD83C\uDF8C',
-    'crossed_swords': '\u2694\uFE0F',
-    'crown': '\uD83D\uDC51',
-    'cry': '\uD83D\uDE22',
-    'crying_cat_face': '\uD83D\uDE3F',
-    'crystal_ball': '\uD83D\uDD2E',
-    'cucumber': '\uD83E\uDD52',
-    'cupid': '\uD83D\uDC98',
-    'curly_loop': '\u27B0',
-    'currency_exchange': '\uD83D\uDCB1',
-    'curry': '\uD83C\uDF5B',
-    'custard': '\uD83C\uDF6E',
-    'customs': '\uD83D\uDEC3',
-    'cyclone': '\uD83C\uDF00',
-    'dagger': '\uD83D\uDDE1',
-    'dancer': '\uD83D\uDC83',
-    'dancing_women': '\uD83D\uDC6F',
-    'dancing_men': '\uD83D\uDC6F‍\u2642\uFE0F',
-    'dango': '\uD83C\uDF61',
-    'dark_sunglasses': '\uD83D\uDD76',
-    'dart': '\uD83C\uDFAF',
-    'dash': '\uD83D\uDCA8',
-    'date': '\uD83D\uDCC5',
-    'deciduous_tree': '\uD83C\uDF33',
-    'deer': '\uD83E\uDD8C',
-    'department_store': '\uD83C\uDFEC',
-    'derelict_house': '\uD83C\uDFDA',
-    'desert': '\uD83C\uDFDC',
-    'desert_island': '\uD83C\uDFDD',
-    'desktop_computer': '\uD83D\uDDA5',
-    'male_detective': '\uD83D\uDD75\uFE0F',
-    'diamond_shape_with_a_dot_inside': '\uD83D\uDCA0',
-    'diamonds': '\u2666\uFE0F',
-    'disappointed': '\uD83D\uDE1E',
-    'disappointed_relieved': '\uD83D\uDE25',
-    'dizzy': '\uD83D\uDCAB',
-    'dizzy_face': '\uD83D\uDE35',
-    'do_not_litter': '\uD83D\uDEAF',
-    'dog': '\uD83D\uDC36',
-    'dog2': '\uD83D\uDC15',
-    'dollar': '\uD83D\uDCB5',
-    'dolls': '\uD83C\uDF8E',
-    'dolphin': '\uD83D\uDC2C',
-    'door': '\uD83D\uDEAA',
-    'doughnut': '\uD83C\uDF69',
-    'dove': '\uD83D\uDD4A',
-    'dragon': '\uD83D\uDC09',
-    'dragon_face': '\uD83D\uDC32',
-    'dress': '\uD83D\uDC57',
-    'dromedary_camel': '\uD83D\uDC2A',
-    'drooling_face': '\uD83E\uDD24',
-    'droplet': '\uD83D\uDCA7',
-    'drum': '\uD83E\uDD41',
-    'duck': '\uD83E\uDD86',
-    'dvd': '\uD83D\uDCC0',
-    'e-mail': '\uD83D\uDCE7',
-    'eagle': '\uD83E\uDD85',
-    'ear': '\uD83D\uDC42',
-    'ear_of_rice': '\uD83C\uDF3E',
-    'earth_africa': '\uD83C\uDF0D',
-    'earth_americas': '\uD83C\uDF0E',
-    'earth_asia': '\uD83C\uDF0F',
-    'egg': '\uD83E\uDD5A',
-    'eggplant': '\uD83C\uDF46',
-    'eight_pointed_black_star': '\u2734\uFE0F',
-    'eight_spoked_asterisk': '\u2733\uFE0F',
-    'electric_plug': '\uD83D\uDD0C',
-    'elephant': '\uD83D\uDC18',
-    'email': '\u2709\uFE0F',
-    'end': '\uD83D\uDD1A',
-    'envelope_with_arrow': '\uD83D\uDCE9',
-    'euro': '\uD83D\uDCB6',
-    'european_castle': '\uD83C\uDFF0',
-    'european_post_office': '\uD83C\uDFE4',
-    'evergreen_tree': '\uD83C\uDF32',
-    'exclamation': '\u2757\uFE0F',
-    'expressionless': '\uD83D\uDE11',
-    'eye': '\uD83D\uDC41',
-    'eye_speech_bubble': '\uD83D\uDC41‍\uD83D\uDDE8',
-    'eyeglasses': '\uD83D\uDC53',
-    'eyes': '\uD83D\uDC40',
-    'face_with_head_bandage': '\uD83E\uDD15',
-    'face_with_thermometer': '\uD83E\uDD12',
-    'fist_oncoming': '\uD83D\uDC4A',
-    'factory': '\uD83C\uDFED',
-    'fallen_leaf': '\uD83C\uDF42',
-    'family_man_woman_boy': '\uD83D\uDC6A',
-    'family_man_boy': '\uD83D\uDC68‍\uD83D\uDC66',
-    'family_man_boy_boy': '\uD83D\uDC68‍\uD83D\uDC66‍\uD83D\uDC66',
-    'family_man_girl': '\uD83D\uDC68‍\uD83D\uDC67',
-    'family_man_girl_boy': '\uD83D\uDC68‍\uD83D\uDC67‍\uD83D\uDC66',
-    'family_man_girl_girl': '\uD83D\uDC68‍\uD83D\uDC67‍\uD83D\uDC67',
-    'family_man_man_boy': '\uD83D\uDC68‍\uD83D\uDC68‍\uD83D\uDC66',
-    'family_man_man_boy_boy': '\uD83D\uDC68‍\uD83D\uDC68‍\uD83D\uDC66‍\uD83D\uDC66',
-    'family_man_man_girl': '\uD83D\uDC68‍\uD83D\uDC68‍\uD83D\uDC67',
-    'family_man_man_girl_boy': '\uD83D\uDC68‍\uD83D\uDC68‍\uD83D\uDC67‍\uD83D\uDC66',
-    'family_man_man_girl_girl': '\uD83D\uDC68‍\uD83D\uDC68‍\uD83D\uDC67‍\uD83D\uDC67',
-    'family_man_woman_boy_boy': '\uD83D\uDC68‍\uD83D\uDC69‍\uD83D\uDC66‍\uD83D\uDC66',
-    'family_man_woman_girl': '\uD83D\uDC68‍\uD83D\uDC69‍\uD83D\uDC67',
-    'family_man_woman_girl_boy': '\uD83D\uDC68‍\uD83D\uDC69‍\uD83D\uDC67‍\uD83D\uDC66',
-    'family_man_woman_girl_girl': '\uD83D\uDC68‍\uD83D\uDC69‍\uD83D\uDC67‍\uD83D\uDC67',
-    'family_woman_boy': '\uD83D\uDC69‍\uD83D\uDC66',
-    'family_woman_boy_boy': '\uD83D\uDC69‍\uD83D\uDC66‍\uD83D\uDC66',
-    'family_woman_girl': '\uD83D\uDC69‍\uD83D\uDC67',
-    'family_woman_girl_boy': '\uD83D\uDC69‍\uD83D\uDC67‍\uD83D\uDC66',
-    'family_woman_girl_girl': '\uD83D\uDC69‍\uD83D\uDC67‍\uD83D\uDC67',
-    'family_woman_woman_boy': '\uD83D\uDC69‍\uD83D\uDC69‍\uD83D\uDC66',
-    'family_woman_woman_boy_boy': '\uD83D\uDC69‍\uD83D\uDC69‍\uD83D\uDC66‍\uD83D\uDC66',
-    'family_woman_woman_girl': '\uD83D\uDC69‍\uD83D\uDC69‍\uD83D\uDC67',
-    'family_woman_woman_girl_boy': '\uD83D\uDC69‍\uD83D\uDC69‍\uD83D\uDC67‍\uD83D\uDC66',
-    'family_woman_woman_girl_girl': '\uD83D\uDC69‍\uD83D\uDC69‍\uD83D\uDC67‍\uD83D\uDC67',
-    'fast_forward': '\u23E9',
-    'fax': '\uD83D\uDCE0',
-    'fearful': '\uD83D\uDE28',
-    'feet': '\uD83D\uDC3E',
-    'female_detective': '\uD83D\uDD75\uFE0F‍\u2640\uFE0F',
-    'ferris_wheel': '\uD83C\uDFA1',
-    'ferry': '\u26F4',
-    'field_hockey': '\uD83C\uDFD1',
-    'file_cabinet': '\uD83D\uDDC4',
-    'file_folder': '\uD83D\uDCC1',
-    'film_projector': '\uD83D\uDCFD',
-    'film_strip': '\uD83C\uDF9E',
-    'fire': '\uD83D\uDD25',
-    'fire_engine': '\uD83D\uDE92',
-    'fireworks': '\uD83C\uDF86',
-    'first_quarter_moon': '\uD83C\uDF13',
-    'first_quarter_moon_with_face': '\uD83C\uDF1B',
-    'fish': '\uD83D\uDC1F',
-    'fish_cake': '\uD83C\uDF65',
-    'fishing_pole_and_fish': '\uD83C\uDFA3',
-    'fist_raised': '\u270A',
-    'fist_left': '\uD83E\uDD1B',
-    'fist_right': '\uD83E\uDD1C',
-    'flags': '\uD83C\uDF8F',
-    'flashlight': '\uD83D\uDD26',
-    'fleur_de_lis': '\u269C\uFE0F',
-    'flight_arrival': '\uD83D\uDEEC',
-    'flight_departure': '\uD83D\uDEEB',
-    'floppy_disk': '\uD83D\uDCBE',
-    'flower_playing_cards': '\uD83C\uDFB4',
-    'flushed': '\uD83D\uDE33',
-    'fog': '\uD83C\uDF2B',
-    'foggy': '\uD83C\uDF01',
-    'football': '\uD83C\uDFC8',
-    'footprints': '\uD83D\uDC63',
-    'fork_and_knife': '\uD83C\uDF74',
-    'fountain': '\u26F2\uFE0F',
-    'fountain_pen': '\uD83D\uDD8B',
-    'four_leaf_clover': '\uD83C\uDF40',
-    'fox_face': '\uD83E\uDD8A',
-    'framed_picture': '\uD83D\uDDBC',
-    'free': '\uD83C\uDD93',
-    'fried_egg': '\uD83C\uDF73',
-    'fried_shrimp': '\uD83C\uDF64',
-    'fries': '\uD83C\uDF5F',
-    'frog': '\uD83D\uDC38',
-    'frowning': '\uD83D\uDE26',
-    'frowning_face': '\u2639\uFE0F',
-    'frowning_man': '\uD83D\uDE4D‍\u2642\uFE0F',
-    'frowning_woman': '\uD83D\uDE4D',
-    'middle_finger': '\uD83D\uDD95',
-    'fuelpump': '\u26FD\uFE0F',
-    'full_moon': '\uD83C\uDF15',
-    'full_moon_with_face': '\uD83C\uDF1D',
-    'funeral_urn': '\u26B1\uFE0F',
-    'game_die': '\uD83C\uDFB2',
-    'gear': '\u2699\uFE0F',
-    'gem': '\uD83D\uDC8E',
-    'gemini': '\u264A\uFE0F',
-    'ghost': '\uD83D\uDC7B',
-    'gift': '\uD83C\uDF81',
-    'gift_heart': '\uD83D\uDC9D',
-    'girl': '\uD83D\uDC67',
-    'globe_with_meridians': '\uD83C\uDF10',
-    'goal_net': '\uD83E\uDD45',
-    'goat': '\uD83D\uDC10',
-    'golf': '\u26F3\uFE0F',
-    'golfing_man': '\uD83C\uDFCC\uFE0F',
-    'golfing_woman': '\uD83C\uDFCC\uFE0F‍\u2640\uFE0F',
-    'gorilla': '\uD83E\uDD8D',
-    'grapes': '\uD83C\uDF47',
-    'green_apple': '\uD83C\uDF4F',
-    'green_book': '\uD83D\uDCD7',
-    'green_heart': '\uD83D\uDC9A',
-    'green_salad': '\uD83E\uDD57',
-    'grey_exclamation': '\u2755',
-    'grey_question': '\u2754',
-    'grimacing': '\uD83D\uDE2C',
-    'grin': '\uD83D\uDE01',
-    'grinning': '\uD83D\uDE00',
-    'guardsman': '\uD83D\uDC82',
-    'guardswoman': '\uD83D\uDC82‍\u2640\uFE0F',
-    'guitar': '\uD83C\uDFB8',
-    'gun': '\uD83D\uDD2B',
-    'haircut_woman': '\uD83D\uDC87',
-    'haircut_man': '\uD83D\uDC87‍\u2642\uFE0F',
-    'hamburger': '\uD83C\uDF54',
-    'hammer': '\uD83D\uDD28',
-    'hammer_and_pick': '\u2692',
-    'hammer_and_wrench': '\uD83D\uDEE0',
-    'hamster': '\uD83D\uDC39',
-    'hand': '\u270B',
-    'handbag': '\uD83D\uDC5C',
-    'handshake': '\uD83E\uDD1D',
-    'hankey': '\uD83D\uDCA9',
-    'hatched_chick': '\uD83D\uDC25',
-    'hatching_chick': '\uD83D\uDC23',
-    'headphones': '\uD83C\uDFA7',
-    'hear_no_evil': '\uD83D\uDE49',
-    'heart': '\u2764\uFE0F',
-    'heart_decoration': '\uD83D\uDC9F',
-    'heart_eyes': '\uD83D\uDE0D',
-    'heart_eyes_cat': '\uD83D\uDE3B',
-    'heartbeat': '\uD83D\uDC93',
-    'heartpulse': '\uD83D\uDC97',
-    'hearts': '\u2665\uFE0F',
-    'heavy_check_mark': '\u2714\uFE0F',
-    'heavy_division_sign': '\u2797',
-    'heavy_dollar_sign': '\uD83D\uDCB2',
-    'heavy_heart_exclamation': '\u2763\uFE0F',
-    'heavy_minus_sign': '\u2796',
-    'heavy_multiplication_x': '\u2716\uFE0F',
-    'heavy_plus_sign': '\u2795',
-    'helicopter': '\uD83D\uDE81',
-    'herb': '\uD83C\uDF3F',
-    'hibiscus': '\uD83C\uDF3A',
-    'high_brightness': '\uD83D\uDD06',
-    'high_heel': '\uD83D\uDC60',
-    'hocho': '\uD83D\uDD2A',
-    'hole': '\uD83D\uDD73',
-    'honey_pot': '\uD83C\uDF6F',
-    'horse': '\uD83D\uDC34',
-    'horse_racing': '\uD83C\uDFC7',
-    'hospital': '\uD83C\uDFE5',
-    'hot_pepper': '\uD83C\uDF36',
-    'hotdog': '\uD83C\uDF2D',
-    'hotel': '\uD83C\uDFE8',
-    'hotsprings': '\u2668\uFE0F',
-    'hourglass': '\u231B\uFE0F',
-    'hourglass_flowing_sand': '\u23F3',
-    'house': '\uD83C\uDFE0',
-    'house_with_garden': '\uD83C\uDFE1',
-    'houses': '\uD83C\uDFD8',
-    'hugs': '\uD83E\uDD17',
-    'hushed': '\uD83D\uDE2F',
-    'ice_cream': '\uD83C\uDF68',
-    'ice_hockey': '\uD83C\uDFD2',
-    'ice_skate': '\u26F8',
-    'icecream': '\uD83C\uDF66',
-    'id': '\uD83C\uDD94',
-    'ideograph_advantage': '\uD83C\uDE50',
-    'imp': '\uD83D\uDC7F',
-    'inbox_tray': '\uD83D\uDCE5',
-    'incoming_envelope': '\uD83D\uDCE8',
-    'tipping_hand_woman': '\uD83D\uDC81',
-    'information_source': '\u2139\uFE0F',
-    'innocent': '\uD83D\uDE07',
-    'interrobang': '\u2049\uFE0F',
-    'iphone': '\uD83D\uDCF1',
-    'izakaya_lantern': '\uD83C\uDFEE',
-    'jack_o_lantern': '\uD83C\uDF83',
-    'japan': '\uD83D\uDDFE',
-    'japanese_castle': '\uD83C\uDFEF',
-    'japanese_goblin': '\uD83D\uDC7A',
-    'japanese_ogre': '\uD83D\uDC79',
-    'jeans': '\uD83D\uDC56',
-    'joy': '\uD83D\uDE02',
-    'joy_cat': '\uD83D\uDE39',
-    'joystick': '\uD83D\uDD79',
-    'kaaba': '\uD83D\uDD4B',
-    'key': '\uD83D\uDD11',
-    'keyboard': '\u2328\uFE0F',
-    'keycap_ten': '\uD83D\uDD1F',
-    'kick_scooter': '\uD83D\uDEF4',
-    'kimono': '\uD83D\uDC58',
-    'kiss': '\uD83D\uDC8B',
-    'kissing': '\uD83D\uDE17',
-    'kissing_cat': '\uD83D\uDE3D',
-    'kissing_closed_eyes': '\uD83D\uDE1A',
-    'kissing_heart': '\uD83D\uDE18',
-    'kissing_smiling_eyes': '\uD83D\uDE19',
-    'kiwi_fruit': '\uD83E\uDD5D',
-    'koala': '\uD83D\uDC28',
-    'koko': '\uD83C\uDE01',
-    'label': '\uD83C\uDFF7',
-    'large_blue_circle': '\uD83D\uDD35',
-    'large_blue_diamond': '\uD83D\uDD37',
-    'large_orange_diamond': '\uD83D\uDD36',
-    'last_quarter_moon': '\uD83C\uDF17',
-    'last_quarter_moon_with_face': '\uD83C\uDF1C',
-    'latin_cross': '\u271D\uFE0F',
-    'laughing': '\uD83D\uDE06',
-    'leaves': '\uD83C\uDF43',
-    'ledger': '\uD83D\uDCD2',
-    'left_luggage': '\uD83D\uDEC5',
-    'left_right_arrow': '\u2194\uFE0F',
-    'leftwards_arrow_with_hook': '\u21A9\uFE0F',
-    'lemon': '\uD83C\uDF4B',
-    'leo': '\u264C\uFE0F',
-    'leopard': '\uD83D\uDC06',
-    'level_slider': '\uD83C\uDF9A',
-    'libra': '\u264E\uFE0F',
-    'light_rail': '\uD83D\uDE88',
-    'link': '\uD83D\uDD17',
-    'lion': '\uD83E\uDD81',
-    'lips': '\uD83D\uDC44',
-    'lipstick': '\uD83D\uDC84',
-    'lizard': '\uD83E\uDD8E',
-    'lock': '\uD83D\uDD12',
-    'lock_with_ink_pen': '\uD83D\uDD0F',
-    'lollipop': '\uD83C\uDF6D',
-    'loop': '\u27BF',
-    'loud_sound': '\uD83D\uDD0A',
-    'loudspeaker': '\uD83D\uDCE2',
-    'love_hotel': '\uD83C\uDFE9',
-    'love_letter': '\uD83D\uDC8C',
-    'low_brightness': '\uD83D\uDD05',
-    'lying_face': '\uD83E\uDD25',
-    'm': '\u24C2\uFE0F',
-    'mag': '\uD83D\uDD0D',
-    'mag_right': '\uD83D\uDD0E',
-    'mahjong': '\uD83C\uDC04\uFE0F',
-    'mailbox': '\uD83D\uDCEB',
-    'mailbox_closed': '\uD83D\uDCEA',
-    'mailbox_with_mail': '\uD83D\uDCEC',
-    'mailbox_with_no_mail': '\uD83D\uDCED',
-    'man': '\uD83D\uDC68',
-    'man_artist': '\uD83D\uDC68‍\uD83C\uDFA8',
-    'man_astronaut': '\uD83D\uDC68‍\uD83D\uDE80',
-    'man_cartwheeling': '\uD83E\uDD38‍\u2642\uFE0F',
-    'man_cook': '\uD83D\uDC68‍\uD83C\uDF73',
-    'man_dancing': '\uD83D\uDD7A',
-    'man_facepalming': '\uD83E\uDD26‍\u2642\uFE0F',
-    'man_factory_worker': '\uD83D\uDC68‍\uD83C\uDFED',
-    'man_farmer': '\uD83D\uDC68‍\uD83C\uDF3E',
-    'man_firefighter': '\uD83D\uDC68‍\uD83D\uDE92',
-    'man_health_worker': '\uD83D\uDC68‍\u2695\uFE0F',
-    'man_in_tuxedo': '\uD83E\uDD35',
-    'man_judge': '\uD83D\uDC68‍\u2696\uFE0F',
-    'man_juggling': '\uD83E\uDD39‍\u2642\uFE0F',
-    'man_mechanic': '\uD83D\uDC68‍\uD83D\uDD27',
-    'man_office_worker': '\uD83D\uDC68‍\uD83D\uDCBC',
-    'man_pilot': '\uD83D\uDC68‍\u2708\uFE0F',
-    'man_playing_handball': '\uD83E\uDD3E‍\u2642\uFE0F',
-    'man_playing_water_polo': '\uD83E\uDD3D‍\u2642\uFE0F',
-    'man_scientist': '\uD83D\uDC68‍\uD83D\uDD2C',
-    'man_shrugging': '\uD83E\uDD37‍\u2642\uFE0F',
-    'man_singer': '\uD83D\uDC68‍\uD83C\uDFA4',
-    'man_student': '\uD83D\uDC68‍\uD83C\uDF93',
-    'man_teacher': '\uD83D\uDC68‍\uD83C\uDFEB',
-    'man_technologist': '\uD83D\uDC68‍\uD83D\uDCBB',
-    'man_with_gua_pi_mao': '\uD83D\uDC72',
-    'man_with_turban': '\uD83D\uDC73',
-    'tangerine': '\uD83C\uDF4A',
-    'mans_shoe': '\uD83D\uDC5E',
-    'mantelpiece_clock': '\uD83D\uDD70',
-    'maple_leaf': '\uD83C\uDF41',
-    'martial_arts_uniform': '\uD83E\uDD4B',
-    'mask': '\uD83D\uDE37',
-    'massage_woman': '\uD83D\uDC86',
-    'massage_man': '\uD83D\uDC86‍\u2642\uFE0F',
-    'meat_on_bone': '\uD83C\uDF56',
-    'medal_military': '\uD83C\uDF96',
-    'medal_sports': '\uD83C\uDFC5',
-    'mega': '\uD83D\uDCE3',
-    'melon': '\uD83C\uDF48',
-    'memo': '\uD83D\uDCDD',
-    'men_wrestling': '\uD83E\uDD3C‍\u2642\uFE0F',
-    'menorah': '\uD83D\uDD4E',
-    'mens': '\uD83D\uDEB9',
-    'metal': '\uD83E\uDD18',
-    'metro': '\uD83D\uDE87',
-    'microphone': '\uD83C\uDFA4',
-    'microscope': '\uD83D\uDD2C',
-    'milk_glass': '\uD83E\uDD5B',
-    'milky_way': '\uD83C\uDF0C',
-    'minibus': '\uD83D\uDE90',
-    'minidisc': '\uD83D\uDCBD',
-    'mobile_phone_off': '\uD83D\uDCF4',
-    'money_mouth_face': '\uD83E\uDD11',
-    'money_with_wings': '\uD83D\uDCB8',
-    'moneybag': '\uD83D\uDCB0',
-    'monkey': '\uD83D\uDC12',
-    'monkey_face': '\uD83D\uDC35',
-    'monorail': '\uD83D\uDE9D',
-    'moon': '\uD83C\uDF14',
-    'mortar_board': '\uD83C\uDF93',
-    'mosque': '\uD83D\uDD4C',
-    'motor_boat': '\uD83D\uDEE5',
-    'motor_scooter': '\uD83D\uDEF5',
-    'motorcycle': '\uD83C\uDFCD',
-    'motorway': '\uD83D\uDEE3',
-    'mount_fuji': '\uD83D\uDDFB',
-    'mountain': '\u26F0',
-    'mountain_biking_man': '\uD83D\uDEB5',
-    'mountain_biking_woman': '\uD83D\uDEB5‍\u2640\uFE0F',
-    'mountain_cableway': '\uD83D\uDEA0',
-    'mountain_railway': '\uD83D\uDE9E',
-    'mountain_snow': '\uD83C\uDFD4',
-    'mouse': '\uD83D\uDC2D',
-    'mouse2': '\uD83D\uDC01',
-    'movie_camera': '\uD83C\uDFA5',
-    'moyai': '\uD83D\uDDFF',
-    'mrs_claus': '\uD83E\uDD36',
-    'muscle': '\uD83D\uDCAA',
-    'mushroom': '\uD83C\uDF44',
-    'musical_keyboard': '\uD83C\uDFB9',
-    'musical_note': '\uD83C\uDFB5',
-    'musical_score': '\uD83C\uDFBC',
-    'mute': '\uD83D\uDD07',
-    'nail_care': '\uD83D\uDC85',
-    'name_badge': '\uD83D\uDCDB',
-    'national_park': '\uD83C\uDFDE',
-    'nauseated_face': '\uD83E\uDD22',
-    'necktie': '\uD83D\uDC54',
-    'negative_squared_cross_mark': '\u274E',
-    'nerd_face': '\uD83E\uDD13',
-    'neutral_face': '\uD83D\uDE10',
-    'new': '\uD83C\uDD95',
-    'new_moon': '\uD83C\uDF11',
-    'new_moon_with_face': '\uD83C\uDF1A',
-    'newspaper': '\uD83D\uDCF0',
-    'newspaper_roll': '\uD83D\uDDDE',
-    'next_track_button': '\u23ED',
-    'ng': '\uD83C\uDD96',
-    'no_good_man': '\uD83D\uDE45‍\u2642\uFE0F',
-    'no_good_woman': '\uD83D\uDE45',
-    'night_with_stars': '\uD83C\uDF03',
-    'no_bell': '\uD83D\uDD15',
-    'no_bicycles': '\uD83D\uDEB3',
-    'no_entry': '\u26D4\uFE0F',
-    'no_entry_sign': '\uD83D\uDEAB',
-    'no_mobile_phones': '\uD83D\uDCF5',
-    'no_mouth': '\uD83D\uDE36',
-    'no_pedestrians': '\uD83D\uDEB7',
-    'no_smoking': '\uD83D\uDEAD',
-    'non-potable_water': '\uD83D\uDEB1',
-    'nose': '\uD83D\uDC43',
-    'notebook': '\uD83D\uDCD3',
-    'notebook_with_decorative_cover': '\uD83D\uDCD4',
-    'notes': '\uD83C\uDFB6',
-    'nut_and_bolt': '\uD83D\uDD29',
-    'o': '\u2B55\uFE0F',
-    'o2': '\uD83C\uDD7E\uFE0F',
-    'ocean': '\uD83C\uDF0A',
-    'octopus': '\uD83D\uDC19',
-    'oden': '\uD83C\uDF62',
-    'office': '\uD83C\uDFE2',
-    'oil_drum': '\uD83D\uDEE2',
-    'ok': '\uD83C\uDD97',
-    'ok_hand': '\uD83D\uDC4C',
-    'ok_man': '\uD83D\uDE46‍\u2642\uFE0F',
-    'ok_woman': '\uD83D\uDE46',
-    'old_key': '\uD83D\uDDDD',
-    'older_man': '\uD83D\uDC74',
-    'older_woman': '\uD83D\uDC75',
-    'om': '\uD83D\uDD49',
-    'on': '\uD83D\uDD1B',
-    'oncoming_automobile': '\uD83D\uDE98',
-    'oncoming_bus': '\uD83D\uDE8D',
-    'oncoming_police_car': '\uD83D\uDE94',
-    'oncoming_taxi': '\uD83D\uDE96',
-    'open_file_folder': '\uD83D\uDCC2',
-    'open_hands': '\uD83D\uDC50',
-    'open_mouth': '\uD83D\uDE2E',
-    'open_umbrella': '\u2602\uFE0F',
-    'ophiuchus': '\u26CE',
-    'orange_book': '\uD83D\uDCD9',
-    'orthodox_cross': '\u2626\uFE0F',
-    'outbox_tray': '\uD83D\uDCE4',
-    'owl': '\uD83E\uDD89',
-    'ox': '\uD83D\uDC02',
-    'package': '\uD83D\uDCE6',
-    'page_facing_up': '\uD83D\uDCC4',
-    'page_with_curl': '\uD83D\uDCC3',
-    'pager': '\uD83D\uDCDF',
-    'paintbrush': '\uD83D\uDD8C',
-    'palm_tree': '\uD83C\uDF34',
-    'pancakes': '\uD83E\uDD5E',
-    'panda_face': '\uD83D\uDC3C',
-    'paperclip': '\uD83D\uDCCE',
-    'paperclips': '\uD83D\uDD87',
-    'parasol_on_ground': '\u26F1',
-    'parking': '\uD83C\uDD7F\uFE0F',
-    'part_alternation_mark': '\u303D\uFE0F',
-    'partly_sunny': '\u26C5\uFE0F',
-    'passenger_ship': '\uD83D\uDEF3',
-    'passport_control': '\uD83D\uDEC2',
-    'pause_button': '\u23F8',
-    'peace_symbol': '\u262E\uFE0F',
-    'peach': '\uD83C\uDF51',
-    'peanuts': '\uD83E\uDD5C',
-    'pear': '\uD83C\uDF50',
-    'pen': '\uD83D\uDD8A',
-    'pencil2': '\u270F\uFE0F',
-    'penguin': '\uD83D\uDC27',
-    'pensive': '\uD83D\uDE14',
-    'performing_arts': '\uD83C\uDFAD',
-    'persevere': '\uD83D\uDE23',
-    'person_fencing': '\uD83E\uDD3A',
-    'pouting_woman': '\uD83D\uDE4E',
-    'phone': '\u260E\uFE0F',
-    'pick': '\u26CF',
-    'pig': '\uD83D\uDC37',
-    'pig2': '\uD83D\uDC16',
-    'pig_nose': '\uD83D\uDC3D',
-    'pill': '\uD83D\uDC8A',
-    'pineapple': '\uD83C\uDF4D',
-    'ping_pong': '\uD83C\uDFD3',
-    'pisces': '\u2653\uFE0F',
-    'pizza': '\uD83C\uDF55',
-    'place_of_worship': '\uD83D\uDED0',
-    'plate_with_cutlery': '\uD83C\uDF7D',
-    'play_or_pause_button': '\u23EF',
-    'point_down': '\uD83D\uDC47',
-    'point_left': '\uD83D\uDC48',
-    'point_right': '\uD83D\uDC49',
-    'point_up': '\u261D\uFE0F',
-    'point_up_2': '\uD83D\uDC46',
-    'police_car': '\uD83D\uDE93',
-    'policewoman': '\uD83D\uDC6E‍\u2640\uFE0F',
-    'poodle': '\uD83D\uDC29',
-    'popcorn': '\uD83C\uDF7F',
-    'post_office': '\uD83C\uDFE3',
-    'postal_horn': '\uD83D\uDCEF',
-    'postbox': '\uD83D\uDCEE',
-    'potable_water': '\uD83D\uDEB0',
-    'potato': '\uD83E\uDD54',
-    'pouch': '\uD83D\uDC5D',
-    'poultry_leg': '\uD83C\uDF57',
-    'pound': '\uD83D\uDCB7',
-    'rage': '\uD83D\uDE21',
-    'pouting_cat': '\uD83D\uDE3E',
-    'pouting_man': '\uD83D\uDE4E‍\u2642\uFE0F',
-    'pray': '\uD83D\uDE4F',
-    'prayer_beads': '\uD83D\uDCFF',
-    'pregnant_woman': '\uD83E\uDD30',
-    'previous_track_button': '\u23EE',
-    'prince': '\uD83E\uDD34',
-    'princess': '\uD83D\uDC78',
-    'printer': '\uD83D\uDDA8',
-    'purple_heart': '\uD83D\uDC9C',
-    'purse': '\uD83D\uDC5B',
-    'pushpin': '\uD83D\uDCCC',
-    'put_litter_in_its_place': '\uD83D\uDEAE',
-    'question': '\u2753',
-    'rabbit': '\uD83D\uDC30',
-    'rabbit2': '\uD83D\uDC07',
-    'racehorse': '\uD83D\uDC0E',
-    'racing_car': '\uD83C\uDFCE',
-    'radio': '\uD83D\uDCFB',
-    'radio_button': '\uD83D\uDD18',
-    'radioactive': '\u2622\uFE0F',
-    'railway_car': '\uD83D\uDE83',
-    'railway_track': '\uD83D\uDEE4',
-    'rainbow': '\uD83C\uDF08',
-    'rainbow_flag': '\uD83C\uDFF3\uFE0F‍\uD83C\uDF08',
-    'raised_back_of_hand': '\uD83E\uDD1A',
-    'raised_hand_with_fingers_splayed': '\uD83D\uDD90',
-    'raised_hands': '\uD83D\uDE4C',
-    'raising_hand_woman': '\uD83D\uDE4B',
-    'raising_hand_man': '\uD83D\uDE4B‍\u2642\uFE0F',
-    'ram': '\uD83D\uDC0F',
-    'ramen': '\uD83C\uDF5C',
-    'rat': '\uD83D\uDC00',
-    'record_button': '\u23FA',
-    'recycle': '\u267B\uFE0F',
-    'red_circle': '\uD83D\uDD34',
-    'registered': '\xAE\uFE0F',
-    'relaxed': '\u263A\uFE0F',
-    'relieved': '\uD83D\uDE0C',
-    'reminder_ribbon': '\uD83C\uDF97',
-    'repeat': '\uD83D\uDD01',
-    'repeat_one': '\uD83D\uDD02',
-    'rescue_worker_helmet': '\u26D1',
-    'restroom': '\uD83D\uDEBB',
-    'revolving_hearts': '\uD83D\uDC9E',
-    'rewind': '\u23EA',
-    'rhinoceros': '\uD83E\uDD8F',
-    'ribbon': '\uD83C\uDF80',
-    'rice': '\uD83C\uDF5A',
-    'rice_ball': '\uD83C\uDF59',
-    'rice_cracker': '\uD83C\uDF58',
-    'rice_scene': '\uD83C\uDF91',
-    'right_anger_bubble': '\uD83D\uDDEF',
-    'ring': '\uD83D\uDC8D',
-    'robot': '\uD83E\uDD16',
-    'rocket': '\uD83D\uDE80',
-    'rofl': '\uD83E\uDD23',
-    'roll_eyes': '\uD83D\uDE44',
-    'roller_coaster': '\uD83C\uDFA2',
-    'rooster': '\uD83D\uDC13',
-    'rose': '\uD83C\uDF39',
-    'rosette': '\uD83C\uDFF5',
-    'rotating_light': '\uD83D\uDEA8',
-    'round_pushpin': '\uD83D\uDCCD',
-    'rowing_man': '\uD83D\uDEA3',
-    'rowing_woman': '\uD83D\uDEA3‍\u2640\uFE0F',
-    'rugby_football': '\uD83C\uDFC9',
-    'running_man': '\uD83C\uDFC3',
-    'running_shirt_with_sash': '\uD83C\uDFBD',
-    'running_woman': '\uD83C\uDFC3‍\u2640\uFE0F',
-    'sa': '\uD83C\uDE02\uFE0F',
-    'sagittarius': '\u2650\uFE0F',
-    'sake': '\uD83C\uDF76',
-    'sandal': '\uD83D\uDC61',
-    'santa': '\uD83C\uDF85',
-    'satellite': '\uD83D\uDCE1',
-    'saxophone': '\uD83C\uDFB7',
-    'school': '\uD83C\uDFEB',
-    'school_satchel': '\uD83C\uDF92',
-    'scissors': '\u2702\uFE0F',
-    'scorpion': '\uD83E\uDD82',
-    'scorpius': '\u264F\uFE0F',
-    'scream': '\uD83D\uDE31',
-    'scream_cat': '\uD83D\uDE40',
-    'scroll': '\uD83D\uDCDC',
-    'seat': '\uD83D\uDCBA',
-    'secret': '\u3299\uFE0F',
-    'see_no_evil': '\uD83D\uDE48',
-    'seedling': '\uD83C\uDF31',
-    'selfie': '\uD83E\uDD33',
-    'shallow_pan_of_food': '\uD83E\uDD58',
-    'shamrock': '\u2618\uFE0F',
-    'shark': '\uD83E\uDD88',
-    'shaved_ice': '\uD83C\uDF67',
-    'sheep': '\uD83D\uDC11',
-    'shell': '\uD83D\uDC1A',
-    'shield': '\uD83D\uDEE1',
-    'shinto_shrine': '\u26E9',
-    'ship': '\uD83D\uDEA2',
-    'shirt': '\uD83D\uDC55',
-    'shopping': '\uD83D\uDECD',
-    'shopping_cart': '\uD83D\uDED2',
-    'shower': '\uD83D\uDEBF',
-    'shrimp': '\uD83E\uDD90',
-    'signal_strength': '\uD83D\uDCF6',
-    'six_pointed_star': '\uD83D\uDD2F',
-    'ski': '\uD83C\uDFBF',
-    'skier': '\u26F7',
-    'skull': '\uD83D\uDC80',
-    'skull_and_crossbones': '\u2620\uFE0F',
-    'sleeping': '\uD83D\uDE34',
-    'sleeping_bed': '\uD83D\uDECC',
-    'sleepy': '\uD83D\uDE2A',
-    'slightly_frowning_face': '\uD83D\uDE41',
-    'slightly_smiling_face': '\uD83D\uDE42',
-    'slot_machine': '\uD83C\uDFB0',
-    'small_airplane': '\uD83D\uDEE9',
-    'small_blue_diamond': '\uD83D\uDD39',
-    'small_orange_diamond': '\uD83D\uDD38',
-    'small_red_triangle': '\uD83D\uDD3A',
-    'small_red_triangle_down': '\uD83D\uDD3B',
-    'smile': '\uD83D\uDE04',
-    'smile_cat': '\uD83D\uDE38',
-    'smiley': '\uD83D\uDE03',
-    'smiley_cat': '\uD83D\uDE3A',
-    'smiling_imp': '\uD83D\uDE08',
-    'smirk': '\uD83D\uDE0F',
-    'smirk_cat': '\uD83D\uDE3C',
-    'smoking': '\uD83D\uDEAC',
-    'snail': '\uD83D\uDC0C',
-    'snake': '\uD83D\uDC0D',
-    'sneezing_face': '\uD83E\uDD27',
-    'snowboarder': '\uD83C\uDFC2',
-    'snowflake': '\u2744\uFE0F',
-    'snowman': '\u26C4\uFE0F',
-    'snowman_with_snow': '\u2603\uFE0F',
-    'sob': '\uD83D\uDE2D',
-    'soccer': '\u26BD\uFE0F',
-    'soon': '\uD83D\uDD1C',
-    'sos': '\uD83C\uDD98',
-    'sound': '\uD83D\uDD09',
-    'space_invader': '\uD83D\uDC7E',
-    'spades': '\u2660\uFE0F',
-    'spaghetti': '\uD83C\uDF5D',
-    'sparkle': '\u2747\uFE0F',
-    'sparkler': '\uD83C\uDF87',
-    'sparkles': '\u2728',
-    'sparkling_heart': '\uD83D\uDC96',
-    'speak_no_evil': '\uD83D\uDE4A',
-    'speaker': '\uD83D\uDD08',
-    'speaking_head': '\uD83D\uDDE3',
-    'speech_balloon': '\uD83D\uDCAC',
-    'speedboat': '\uD83D\uDEA4',
-    'spider': '\uD83D\uDD77',
-    'spider_web': '\uD83D\uDD78',
-    'spiral_calendar': '\uD83D\uDDD3',
-    'spiral_notepad': '\uD83D\uDDD2',
-    'spoon': '\uD83E\uDD44',
-    'squid': '\uD83E\uDD91',
-    'stadium': '\uD83C\uDFDF',
-    'star': '\u2B50\uFE0F',
-    'star2': '\uD83C\uDF1F',
-    'star_and_crescent': '\u262A\uFE0F',
-    'star_of_david': '\u2721\uFE0F',
-    'stars': '\uD83C\uDF20',
-    'station': '\uD83D\uDE89',
-    'statue_of_liberty': '\uD83D\uDDFD',
-    'steam_locomotive': '\uD83D\uDE82',
-    'stew': '\uD83C\uDF72',
-    'stop_button': '\u23F9',
-    'stop_sign': '\uD83D\uDED1',
-    'stopwatch': '\u23F1',
-    'straight_ruler': '\uD83D\uDCCF',
-    'strawberry': '\uD83C\uDF53',
-    'stuck_out_tongue': '\uD83D\uDE1B',
-    'stuck_out_tongue_closed_eyes': '\uD83D\uDE1D',
-    'stuck_out_tongue_winking_eye': '\uD83D\uDE1C',
-    'studio_microphone': '\uD83C\uDF99',
-    'stuffed_flatbread': '\uD83E\uDD59',
-    'sun_behind_large_cloud': '\uD83C\uDF25',
-    'sun_behind_rain_cloud': '\uD83C\uDF26',
-    'sun_behind_small_cloud': '\uD83C\uDF24',
-    'sun_with_face': '\uD83C\uDF1E',
-    'sunflower': '\uD83C\uDF3B',
-    'sunglasses': '\uD83D\uDE0E',
-    'sunny': '\u2600\uFE0F',
-    'sunrise': '\uD83C\uDF05',
-    'sunrise_over_mountains': '\uD83C\uDF04',
-    'surfing_man': '\uD83C\uDFC4',
-    'surfing_woman': '\uD83C\uDFC4‍\u2640\uFE0F',
-    'sushi': '\uD83C\uDF63',
-    'suspension_railway': '\uD83D\uDE9F',
-    'sweat': '\uD83D\uDE13',
-    'sweat_drops': '\uD83D\uDCA6',
-    'sweat_smile': '\uD83D\uDE05',
-    'sweet_potato': '\uD83C\uDF60',
-    'swimming_man': '\uD83C\uDFCA',
-    'swimming_woman': '\uD83C\uDFCA‍\u2640\uFE0F',
-    'symbols': '\uD83D\uDD23',
-    'synagogue': '\uD83D\uDD4D',
-    'syringe': '\uD83D\uDC89',
-    'taco': '\uD83C\uDF2E',
-    'tada': '\uD83C\uDF89',
-    'tanabata_tree': '\uD83C\uDF8B',
-    'taurus': '\u2649\uFE0F',
-    'taxi': '\uD83D\uDE95',
-    'tea': '\uD83C\uDF75',
-    'telephone_receiver': '\uD83D\uDCDE',
-    'telescope': '\uD83D\uDD2D',
-    'tennis': '\uD83C\uDFBE',
-    'tent': '\u26FA\uFE0F',
-    'thermometer': '\uD83C\uDF21',
-    'thinking': '\uD83E\uDD14',
-    'thought_balloon': '\uD83D\uDCAD',
-    'ticket': '\uD83C\uDFAB',
-    'tickets': '\uD83C\uDF9F',
-    'tiger': '\uD83D\uDC2F',
-    'tiger2': '\uD83D\uDC05',
-    'timer_clock': '\u23F2',
-    'tipping_hand_man': '\uD83D\uDC81‍\u2642\uFE0F',
-    'tired_face': '\uD83D\uDE2B',
-    'tm': '\u2122\uFE0F',
-    'toilet': '\uD83D\uDEBD',
-    'tokyo_tower': '\uD83D\uDDFC',
-    'tomato': '\uD83C\uDF45',
-    'tongue': '\uD83D\uDC45',
-    'top': '\uD83D\uDD1D',
-    'tophat': '\uD83C\uDFA9',
-    'tornado': '\uD83C\uDF2A',
-    'trackball': '\uD83D\uDDB2',
-    'tractor': '\uD83D\uDE9C',
-    'traffic_light': '\uD83D\uDEA5',
-    'train': '\uD83D\uDE8B',
-    'train2': '\uD83D\uDE86',
-    'tram': '\uD83D\uDE8A',
-    'triangular_flag_on_post': '\uD83D\uDEA9',
-    'triangular_ruler': '\uD83D\uDCD0',
-    'trident': '\uD83D\uDD31',
-    'triumph': '\uD83D\uDE24',
-    'trolleybus': '\uD83D\uDE8E',
-    'trophy': '\uD83C\uDFC6',
-    'tropical_drink': '\uD83C\uDF79',
-    'tropical_fish': '\uD83D\uDC20',
-    'truck': '\uD83D\uDE9A',
-    'trumpet': '\uD83C\uDFBA',
-    'tulip': '\uD83C\uDF37',
-    'tumbler_glass': '\uD83E\uDD43',
-    'turkey': '\uD83E\uDD83',
-    'turtle': '\uD83D\uDC22',
-    'tv': '\uD83D\uDCFA',
-    'twisted_rightwards_arrows': '\uD83D\uDD00',
-    'two_hearts': '\uD83D\uDC95',
-    'two_men_holding_hands': '\uD83D\uDC6C',
-    'two_women_holding_hands': '\uD83D\uDC6D',
-    'u5272': '\uD83C\uDE39',
-    'u5408': '\uD83C\uDE34',
-    'u55b6': '\uD83C\uDE3A',
-    'u6307': '\uD83C\uDE2F\uFE0F',
-    'u6708': '\uD83C\uDE37\uFE0F',
-    'u6709': '\uD83C\uDE36',
-    'u6e80': '\uD83C\uDE35',
-    'u7121': '\uD83C\uDE1A\uFE0F',
-    'u7533': '\uD83C\uDE38',
-    'u7981': '\uD83C\uDE32',
-    'u7a7a': '\uD83C\uDE33',
-    'umbrella': '\u2614\uFE0F',
-    'unamused': '\uD83D\uDE12',
-    'underage': '\uD83D\uDD1E',
-    'unicorn': '\uD83E\uDD84',
-    'unlock': '\uD83D\uDD13',
-    'up': '\uD83C\uDD99',
-    'upside_down_face': '\uD83D\uDE43',
-    'v': '\u270C\uFE0F',
-    'vertical_traffic_light': '\uD83D\uDEA6',
-    'vhs': '\uD83D\uDCFC',
-    'vibration_mode': '\uD83D\uDCF3',
-    'video_camera': '\uD83D\uDCF9',
-    'video_game': '\uD83C\uDFAE',
-    'violin': '\uD83C\uDFBB',
-    'virgo': '\u264D\uFE0F',
-    'volcano': '\uD83C\uDF0B',
-    'volleyball': '\uD83C\uDFD0',
-    'vs': '\uD83C\uDD9A',
-    'vulcan_salute': '\uD83D\uDD96',
-    'walking_man': '\uD83D\uDEB6',
-    'walking_woman': '\uD83D\uDEB6‍\u2640\uFE0F',
-    'waning_crescent_moon': '\uD83C\uDF18',
-    'waning_gibbous_moon': '\uD83C\uDF16',
-    'warning': '\u26A0\uFE0F',
-    'wastebasket': '\uD83D\uDDD1',
-    'watch': '\u231A\uFE0F',
-    'water_buffalo': '\uD83D\uDC03',
-    'watermelon': '\uD83C\uDF49',
-    'wave': '\uD83D\uDC4B',
-    'wavy_dash': '\u3030\uFE0F',
-    'waxing_crescent_moon': '\uD83C\uDF12',
-    'wc': '\uD83D\uDEBE',
-    'weary': '\uD83D\uDE29',
-    'wedding': '\uD83D\uDC92',
-    'weight_lifting_man': '\uD83C\uDFCB\uFE0F',
-    'weight_lifting_woman': '\uD83C\uDFCB\uFE0F‍\u2640\uFE0F',
-    'whale': '\uD83D\uDC33',
-    'whale2': '\uD83D\uDC0B',
-    'wheel_of_dharma': '\u2638\uFE0F',
-    'wheelchair': '\u267F\uFE0F',
-    'white_check_mark': '\u2705',
-    'white_circle': '\u26AA\uFE0F',
-    'white_flag': '\uD83C\uDFF3\uFE0F',
-    'white_flower': '\uD83D\uDCAE',
-    'white_large_square': '\u2B1C\uFE0F',
-    'white_medium_small_square': '\u25FD\uFE0F',
-    'white_medium_square': '\u25FB\uFE0F',
-    'white_small_square': '\u25AB\uFE0F',
-    'white_square_button': '\uD83D\uDD33',
-    'wilted_flower': '\uD83E\uDD40',
-    'wind_chime': '\uD83C\uDF90',
-    'wind_face': '\uD83C\uDF2C',
-    'wine_glass': '\uD83C\uDF77',
-    'wink': '\uD83D\uDE09',
-    'wolf': '\uD83D\uDC3A',
-    'woman': '\uD83D\uDC69',
-    'woman_artist': '\uD83D\uDC69‍\uD83C\uDFA8',
-    'woman_astronaut': '\uD83D\uDC69‍\uD83D\uDE80',
-    'woman_cartwheeling': '\uD83E\uDD38‍\u2640\uFE0F',
-    'woman_cook': '\uD83D\uDC69‍\uD83C\uDF73',
-    'woman_facepalming': '\uD83E\uDD26‍\u2640\uFE0F',
-    'woman_factory_worker': '\uD83D\uDC69‍\uD83C\uDFED',
-    'woman_farmer': '\uD83D\uDC69‍\uD83C\uDF3E',
-    'woman_firefighter': '\uD83D\uDC69‍\uD83D\uDE92',
-    'woman_health_worker': '\uD83D\uDC69‍\u2695\uFE0F',
-    'woman_judge': '\uD83D\uDC69‍\u2696\uFE0F',
-    'woman_juggling': '\uD83E\uDD39‍\u2640\uFE0F',
-    'woman_mechanic': '\uD83D\uDC69‍\uD83D\uDD27',
-    'woman_office_worker': '\uD83D\uDC69‍\uD83D\uDCBC',
-    'woman_pilot': '\uD83D\uDC69‍\u2708\uFE0F',
-    'woman_playing_handball': '\uD83E\uDD3E‍\u2640\uFE0F',
-    'woman_playing_water_polo': '\uD83E\uDD3D‍\u2640\uFE0F',
-    'woman_scientist': '\uD83D\uDC69‍\uD83D\uDD2C',
-    'woman_shrugging': '\uD83E\uDD37‍\u2640\uFE0F',
-    'woman_singer': '\uD83D\uDC69‍\uD83C\uDFA4',
-    'woman_student': '\uD83D\uDC69‍\uD83C\uDF93',
-    'woman_teacher': '\uD83D\uDC69‍\uD83C\uDFEB',
-    'woman_technologist': '\uD83D\uDC69‍\uD83D\uDCBB',
-    'woman_with_turban': '\uD83D\uDC73‍\u2640\uFE0F',
-    'womans_clothes': '\uD83D\uDC5A',
-    'womans_hat': '\uD83D\uDC52',
-    'women_wrestling': '\uD83E\uDD3C‍\u2640\uFE0F',
-    'womens': '\uD83D\uDEBA',
-    'world_map': '\uD83D\uDDFA',
-    'worried': '\uD83D\uDE1F',
-    'wrench': '\uD83D\uDD27',
-    'writing_hand': '\u270D\uFE0F',
-    'x': '\u274C',
-    'yellow_heart': '\uD83D\uDC9B',
-    'yen': '\uD83D\uDCB4',
-    'yin_yang': '\u262F\uFE0F',
-    'yum': '\uD83D\uDE0B',
-    'zap': '\u26A1\uFE0F',
-    'zipper_mouth_face': '\uD83E\uDD10',
-    'zzz': '\uD83D\uDCA4',
-
-    /* special emojis :P */
-    'octocat': ':octocat:',
-    'showdown': 'S'
-  };
-
-  /**
-   * Created by Estevao on 31-05-2015.
-   */
-
-  /**
-   * Showdown Converter class
-   * @class
-   * @param {object} [converterOptions]
-   * @returns {Converter}
-   */
-  showdown.Converter = function (converterOptions) {
-    'use strict';
-
-    var
-    /**
-     * Options used by this converter
-     * @private
-     * @type {{}}
-     */
-    options = {},
-
-
-    /**
-     * Language extensions used by this converter
-     * @private
-     * @type {Array}
-     */
-    langExtensions = [],
-
-
-    /**
-     * Output modifiers extensions used by this converter
-     * @private
-     * @type {Array}
-     */
-    outputModifiers = [],
-
-
-    /**
-     * Event listeners
-     * @private
-     * @type {{}}
-     */
-    listeners = {},
-
-
-    /**
-     * The flavor set in this converter
-     */
-    setConvFlavor = setFlavor,
-
-
-    /**
-     * Metadata of the document
-     * @type {{parsed: {}, raw: string, format: string}}
-     */
-    metadata = {
-      parsed: {},
-      raw: '',
-      format: ''
-    };
-
-    _constructor();
-
-    /**
-     * Converter constructor
-     * @private
-     */
-    function _constructor() {
-      converterOptions = converterOptions || {};
-
-      for (var gOpt in globalOptions) {
-        if (globalOptions.hasOwnProperty(gOpt)) {
-          options[gOpt] = globalOptions[gOpt];
-        }
-      }
-
-      // Merge options
-      if (typeof converterOptions === 'object') {
-        for (var opt in converterOptions) {
-          if (converterOptions.hasOwnProperty(opt)) {
-            options[opt] = converterOptions[opt];
-          }
-        }
-      } else {
-        throw Error('Converter expects the passed parameter to be an object, but ' + typeof converterOptions + ' was passed instead.');
-      }
-
-      if (options.extensions) {
-        showdown.helper.forEach(options.extensions, _parseExtension);
-      }
-    }
-
-    /**
-     * Parse extension
-     * @param {*} ext
-     * @param {string} [name='']
-     * @private
-     */
-    function _parseExtension(ext, name) {
-
-      name = name || null;
-      // If it's a string, the extension was previously loaded
-      if (showdown.helper.isString(ext)) {
-        ext = showdown.helper.stdExtName(ext);
-        name = ext;
-
-        // LEGACY_SUPPORT CODE
-        if (showdown.extensions[ext]) {
-          console.warn('DEPRECATION WARNING: ' + ext + ' is an old extension that uses a deprecated loading method.' + 'Please inform the developer that the extension should be updated!');
-          legacyExtensionLoading(showdown.extensions[ext], ext);
-          return;
-          // END LEGACY SUPPORT CODE
-        } else if (!showdown.helper.isUndefined(extensions[ext])) {
-          ext = extensions[ext];
-        } else {
-          throw Error('Extension "' + ext + '" could not be loaded. It was either not found or is not a valid extension.');
-        }
-      }
-
-      if (typeof ext === 'function') {
-        ext = ext();
-      }
-
-      if (!showdown.helper.isArray(ext)) {
-        ext = [ext];
-      }
-
-      var validExt = validate(ext, name);
-      if (!validExt.valid) {
-        throw Error(validExt.error);
-      }
-
-      for (var i = 0; i < ext.length; ++i) {
-        switch (ext[i].type) {
-
-          case 'lang':
-            langExtensions.push(ext[i]);
-            break;
-
-          case 'output':
-            outputModifiers.push(ext[i]);
-            break;
-        }
-        if (ext[i].hasOwnProperty('listeners')) {
-          for (var ln in ext[i].listeners) {
-            if (ext[i].listeners.hasOwnProperty(ln)) {
-              listen(ln, ext[i].listeners[ln]);
-            }
-          }
-        }
-      }
-    }
-
-    /**
-     * LEGACY_SUPPORT
-     * @param {*} ext
-     * @param {string} name
-     */
-    function legacyExtensionLoading(ext, name) {
-      if (typeof ext === 'function') {
-        ext = ext(new showdown.Converter());
-      }
-      if (!showdown.helper.isArray(ext)) {
-        ext = [ext];
-      }
-      var valid = validate(ext, name);
-
-      if (!valid.valid) {
-        throw Error(valid.error);
-      }
-
-      for (var i = 0; i < ext.length; ++i) {
-        switch (ext[i].type) {
-          case 'lang':
-            langExtensions.push(ext[i]);
-            break;
-          case 'output':
-            outputModifiers.push(ext[i]);
-            break;
-          default:
-            // should never reach here
-            throw Error('Extension loader error: Type unrecognized!!!');
-        }
-      }
-    }
-
-    /**
-     * Listen to an event
-     * @param {string} name
-     * @param {function} callback
-     */
-    function listen(name, callback) {
-      if (!showdown.helper.isString(name)) {
-        throw Error('Invalid argument in converter.listen() method: name must be a string, but ' + typeof name + ' given');
-      }
-
-      if (typeof callback !== 'function') {
-        throw Error('Invalid argument in converter.listen() method: callback must be a function, but ' + typeof callback + ' given');
-      }
-
-      if (!listeners.hasOwnProperty(name)) {
-        listeners[name] = [];
-      }
-      listeners[name].push(callback);
-    }
-
-    function rTrimInputText(text) {
-      var rsp = text.match(/^\s*/)[0].length,
-          rgx = new RegExp('^\\s{0,' + rsp + '}', 'gm');
-      return text.replace(rgx, '');
-    }
-
-    /**
-     * Dispatch an event
-     * @private
-     * @param {string} evtName Event name
-     * @param {string} text Text
-     * @param {{}} options Converter Options
-     * @param {{}} globals
-     * @returns {string}
-     */
-    this._dispatch = function dispatch(evtName, text, options, globals) {
-      if (listeners.hasOwnProperty(evtName)) {
-        for (var ei = 0; ei < listeners[evtName].length; ++ei) {
-          var nText = listeners[evtName][ei](evtName, text, this, options, globals);
-          if (nText && typeof nText !== 'undefined') {
-            text = nText;
-          }
-        }
-      }
-      return text;
-    };
-
-    /**
-     * Listen to an event
-     * @param {string} name
-     * @param {function} callback
-     * @returns {showdown.Converter}
-     */
-    this.listen = function (name, callback) {
-      listen(name, callback);
-      return this;
-    };
-
-    /**
-     * Converts a markdown string into HTML
-     * @param {string} text
-     * @returns {*}
-     */
-    this.makeHtml = function (text) {
-      //check if text is not falsy
-      if (!text) {
-        return text;
-      }
-
-      var globals = {
-        gHtmlBlocks: [],
-        gHtmlMdBlocks: [],
-        gHtmlSpans: [],
-        gUrls: {},
-        gTitles: {},
-        gDimensions: {},
-        gListLevel: 0,
-        hashLinkCounts: {},
-        langExtensions: langExtensions,
-        outputModifiers: outputModifiers,
-        converter: this,
-        ghCodeBlocks: [],
-        metadata: {
-          parsed: {},
-          raw: '',
-          format: ''
-        }
-      };
-
-      // This lets us use ¨ trema as an escape char to avoid md5 hashes
-      // The choice of character is arbitrary; anything that isn't
-      // magic in Markdown will work.
-      text = text.replace(/¨/g, '¨T');
-
-      // Replace $ with ¨D
-      // RegExp interprets $ as a special character
-      // when it's in a replacement string
-      text = text.replace(/\$/g, '¨D');
-
-      // Standardize line endings
-      text = text.replace(/\r\n/g, '\n'); // DOS to Unix
-      text = text.replace(/\r/g, '\n'); // Mac to Unix
-
-      // Stardardize line spaces
-      text = text.replace(/\u00A0/g, ' ');
-
-      if (options.smartIndentationFix) {
-        text = rTrimInputText(text);
-      }
-
-      // Make sure text begins and ends with a couple of newlines:
-      text = '\n\n' + text + '\n\n';
-
-      // detab
-      text = showdown.subParser('detab')(text, options, globals);
-
-      /**
-       * Strip any lines consisting only of spaces and tabs.
-       * This makes subsequent regexs easier to write, because we can
-       * match consecutive blank lines with /\n+/ instead of something
-       * contorted like /[ \t]*\n+/
-       */
-      text = text.replace(/^[ \t]+$/mg, '');
-
-      //run languageExtensions
-      showdown.helper.forEach(langExtensions, function (ext) {
-        text = showdown.subParser('runExtension')(ext, text, options, globals);
-      });
-
-      // run the sub parsers
-      text = showdown.subParser('metadata')(text, options, globals);
-      text = showdown.subParser('hashPreCodeTags')(text, options, globals);
-      text = showdown.subParser('githubCodeBlocks')(text, options, globals);
-      text = showdown.subParser('hashHTMLBlocks')(text, options, globals);
-      text = showdown.subParser('hashCodeTags')(text, options, globals);
-      text = showdown.subParser('stripLinkDefinitions')(text, options, globals);
-      text = showdown.subParser('blockGamut')(text, options, globals);
-      text = showdown.subParser('unhashHTMLSpans')(text, options, globals);
-      text = showdown.subParser('unescapeSpecialChars')(text, options, globals);
-
-      // attacklab: Restore dollar signs
-      text = text.replace(/¨D/g, '$$');
-
-      // attacklab: Restore tremas
-      text = text.replace(/¨T/g, '¨');
-
-      // render a complete html document instead of a partial if the option is enabled
-      text = showdown.subParser('completeHTMLDocument')(text, options, globals);
-
-      // Run output modifiers
-      showdown.helper.forEach(outputModifiers, function (ext) {
-        text = showdown.subParser('runExtension')(ext, text, options, globals);
-      });
-
-      // update metadata
-      metadata = globals.metadata;
-      return text;
-    };
-
-    /**
-     * Converts an HTML string into a markdown string
-     * @param src
-     * @param [HTMLParser] A WHATWG DOM and HTML parser, such as JSDOM. If none is supplied, window.document will be used.
-     * @returns {string}
-     */
-    this.makeMarkdown = this.makeMd = function (src, HTMLParser) {
-
-      // replace \r\n with \n
-      src = src.replace(/\r\n/g, '\n');
-      src = src.replace(/\r/g, '\n'); // old macs
-
-      // due to an edge case, we need to find this: > <
-      // to prevent removing of non silent white spaces
-      // ex: this is sparta
-      src = src.replace(/>[ \t]+¨NBSP;<');
-
-      if (!HTMLParser) {
-        if (window && window.document) {
-          HTMLParser = window.document;
-        } else {
-          throw new Error('HTMLParser is undefined. If in a webworker or nodejs environment, you need to provide a WHATWG DOM and HTML such as JSDOM');
-        }
-      }
-
-      var doc = HTMLParser.createElement('div');
-      doc.innerHTML = src;
-
-      var globals = {
-        preList: substitutePreCodeTags(doc)
-      };
-
-      // remove all newlines and collapse spaces
-      clean(doc);
-
-      // some stuff, like accidental reference links must now be escaped
-      // TODO
-      // doc.innerHTML = doc.innerHTML.replace(/\[[\S\t ]]/);
-
-      var nodes = doc.childNodes,
-          mdDoc = '';
-
-      for (var i = 0; i < nodes.length; i++) {
-        mdDoc += showdown.subParser('makeMarkdown.node')(nodes[i], globals);
-      }
-
-      function clean(node) {
-        for (var n = 0; n < node.childNodes.length; ++n) {
-          var child = node.childNodes[n];
-          if (child.nodeType === 3) {
-            if (!/\S/.test(child.nodeValue)) {
-              node.removeChild(child);
-              --n;
-            } else {
-              child.nodeValue = child.nodeValue.split('\n').join(' ');
-              child.nodeValue = child.nodeValue.replace(/(\s)+/g, '$1');
-            }
-          } else if (child.nodeType === 1) {
-            clean(child);
-          }
-        }
-      }
-
-      // find all pre tags and replace contents with placeholder
-      // we need this so that we can remove all indentation from html
-      // to ease up parsing
-      function substitutePreCodeTags(doc) {
-
-        var pres = doc.querySelectorAll('pre'),
-            presPH = [];
-
-        for (var i = 0; i < pres.length; ++i) {
-
-          if (pres[i].childElementCount === 1 && pres[i].firstChild.tagName.toLowerCase() === 'code') {
-            var content = pres[i].firstChild.innerHTML.trim(),
-                language = pres[i].firstChild.getAttribute('data-language') || '';
-
-            // if data-language attribute is not defined, then we look for class language-*
-            if (language === '') {
-              var classes = pres[i].firstChild.className.split(' ');
-              for (var c = 0; c < classes.length; ++c) {
-                var matches = classes[c].match(/^language-(.+)$/);
-                if (matches !== null) {
-                  language = matches[1];
-                  break;
-                }
-              }
-            }
-
-            // unescape html entities in content
-            content = showdown.helper.unescapeHTMLEntities(content);
-
-            presPH.push(content);
-            pres[i].outerHTML = '';
-          } else {
-            presPH.push(pres[i].innerHTML);
-            pres[i].innerHTML = '';
-            pres[i].setAttribute('prenum', i.toString());
-          }
-        }
-        return presPH;
-      }
-
-      return mdDoc;
-    };
-
-    /**
-     * Set an option of this Converter instance
-     * @param {string} key
-     * @param {*} value
-     */
-    this.setOption = function (key, value) {
-      options[key] = value;
-    };
-
-    /**
-     * Get the option of this Converter instance
-     * @param {string} key
-     * @returns {*}
-     */
-    this.getOption = function (key) {
-      return options[key];
-    };
-
-    /**
-     * Get the options of this Converter instance
-     * @returns {{}}
-     */
-    this.getOptions = function () {
-      return options;
-    };
-
-    /**
-     * Add extension to THIS converter
-     * @param {{}} extension
-     * @param {string} [name=null]
-     */
-    this.addExtension = function (extension, name) {
-      name = name || null;
-      _parseExtension(extension, name);
-    };
-
-    /**
-     * Use a global registered extension with THIS converter
-     * @param {string} extensionName Name of the previously registered extension
-     */
-    this.useExtension = function (extensionName) {
-      _parseExtension(extensionName);
-    };
-
-    /**
-     * Set the flavor THIS converter should use
-     * @param {string} name
-     */
-    this.setFlavor = function (name) {
-      if (!flavor.hasOwnProperty(name)) {
-        throw Error(name + ' flavor was not found');
-      }
-      var preset = flavor[name];
-      setConvFlavor = name;
-      for (var option in preset) {
-        if (preset.hasOwnProperty(option)) {
-          options[option] = preset[option];
-        }
-      }
-    };
-
-    /**
-     * Get the currently set flavor of this converter
-     * @returns {string}
-     */
-    this.getFlavor = function () {
-      return setConvFlavor;
-    };
-
-    /**
-     * Remove an extension from THIS converter.
-     * Note: This is a costly operation. It's better to initialize a new converter
-     * and specify the extensions you wish to use
-     * @param {Array} extension
-     */
-    this.removeExtension = function (extension) {
-      if (!showdown.helper.isArray(extension)) {
-        extension = [extension];
-      }
-      for (var a = 0; a < extension.length; ++a) {
-        var ext = extension[a];
-        for (var i = 0; i < langExtensions.length; ++i) {
-          if (langExtensions[i] === ext) {
-            langExtensions[i].splice(i, 1);
-          }
-        }
-        for (var ii = 0; ii < outputModifiers.length; ++i) {
-          if (outputModifiers[ii] === ext) {
-            outputModifiers[ii].splice(i, 1);
-          }
-        }
-      }
-    };
-
-    /**
-     * Get all extension of THIS converter
-     * @returns {{language: Array, output: Array}}
-     */
-    this.getAllExtensions = function () {
-      return {
-        language: langExtensions,
-        output: outputModifiers
-      };
-    };
-
-    /**
-     * Get the metadata of the previously parsed document
-     * @param raw
-     * @returns {string|{}}
-     */
-    this.getMetadata = function (raw) {
-      if (raw) {
-        return metadata.raw;
-      } else {
-        return metadata.parsed;
-      }
-    };
-
-    /**
-     * Get the metadata format of the previously parsed document
-     * @returns {string}
-     */
-    this.getMetadataFormat = function () {
-      return metadata.format;
-    };
-
-    /**
-     * Private: set a single key, value metadata pair
-     * @param {string} key
-     * @param {string} value
-     */
-    this._setMetadataPair = function (key, value) {
-      metadata.parsed[key] = value;
-    };
-
-    /**
-     * Private: set metadata format
-     * @param {string} format
-     */
-    this._setMetadataFormat = function (format) {
-      metadata.format = format;
-    };
-
-    /**
-     * Private: set metadata raw text
-     * @param {string} raw
-     */
-    this._setMetadataRaw = function (raw) {
-      metadata.raw = raw;
-    };
-  };
-
-  /**
-   * Turn Markdown link shortcuts into XHTML  tags.
-   */
-  showdown.subParser('anchors', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('anchors.before', text, options, globals);
-
-    var writeAnchorTag = function writeAnchorTag(wholeMatch, linkText, linkId, url, m5, m6, title) {
-      if (showdown.helper.isUndefined(title)) {
-        title = '';
-      }
-      linkId = linkId.toLowerCase();
-
-      // Special case for explicit empty url
-      if (wholeMatch.search(/\(? ?(['"].*['"])?\)$/m) > -1) {
-        url = '';
-      } else if (!url) {
-        if (!linkId) {
-          // lower-case and turn embedded newlines into spaces
-          linkId = linkText.toLowerCase().replace(/ ?\n/g, ' ');
-        }
-        url = '#' + linkId;
-
-        if (!showdown.helper.isUndefined(globals.gUrls[linkId])) {
-          url = globals.gUrls[linkId];
-          if (!showdown.helper.isUndefined(globals.gTitles[linkId])) {
-            title = globals.gTitles[linkId];
-          }
-        } else {
-          return wholeMatch;
-        }
-      }
-
-      //url = showdown.helper.escapeCharacters(url, '*_', false); // replaced line to improve performance
-      url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);
-
-      var result = '';
-
-      return result;
-    };
-
-    // First, handle reference-style links: [link text] [id]
-    text = text.replace(/\[((?:\[[^\]]*]|[^\[\]])*)] ?(?:\n *)?\[(.*?)]()()()()/g, writeAnchorTag);
-
-    // Next, inline-style links: [link text](url "optional title")
-    // cases with crazy urls like ./image/cat1).png
-    text = text.replace(/\[((?:\[[^\]]*]|[^\[\]])*)]()[ \t]*\([ \t]?<([^>]*)>(?:[ \t]*((["'])([^"]*?)\5))?[ \t]?\)/g, writeAnchorTag);
-
-    // normal cases
-    text = text.replace(/\[((?:\[[^\]]*]|[^\[\]])*)]()[ \t]*\([ \t]??(?:[ \t]*((["'])([^"]*?)\5))?[ \t]?\)/g, writeAnchorTag);
-
-    // handle reference-style shortcuts: [link text]
-    // These must come last in case you've also got [link test][1]
-    // or [link test](/foo)
-    text = text.replace(/\[([^\[\]]+)]()()()()()/g, writeAnchorTag);
-
-    // Lastly handle GithubMentions if option is enabled
-    if (options.ghMentions) {
-      text = text.replace(/(^|\s)(\\)?(@([a-z\d]+(?:[a-z\d.-]+?[a-z\d]+)*))/gmi, function (wm, st, escape, mentions, username) {
-        if (escape === '\\') {
-          return st + mentions;
-        }
-
-        //check if options.ghMentionsLink is a string
-        if (!showdown.helper.isString(options.ghMentionsLink)) {
-          throw new Error('ghMentionsLink option must be a string');
-        }
-        var lnk = options.ghMentionsLink.replace(/\{u}/g, username),
-            target = '';
-        if (options.openLinksInNewWindow) {
-          target = ' rel="noopener noreferrer" target="¨E95Eblank"';
-        }
-        return st + '' + mentions + '';
-      });
-    }
-
-    text = globals.converter._dispatch('anchors.after', text, options, globals);
-    return text;
-  });
-
-  // url allowed chars [a-z\d_.~:/?#[]@!$&'()*+,;=-]
-
-  var simpleURLRegex = /([*~_]+|\b)(((https?|ftp|dict):\/\/|www\.)[^'">\s]+?\.[^'">\s]+?)()(\1)?(?=\s|$)(?!["<>])/gi,
-      simpleURLRegex2 = /([*~_]+|\b)(((https?|ftp|dict):\/\/|www\.)[^'">\s]+\.[^'">\s]+?)([.!?,()\[\]])?(\1)?(?=\s|$)(?!["<>])/gi,
-      delimUrlRegex = /()<(((https?|ftp|dict):\/\/|www\.)[^'">\s]+)()>()/gi,
-      simpleMailRegex = /(^|\s)(?:mailto:)?([A-Za-z0-9!#$%&'*+-/=?^_`{|}~.]+@[-a-z0-9]+(\.[-a-z0-9]+)*\.[a-z]+)(?=$|\s)/gmi,
-      delimMailRegex = /<()(?:mailto:)?([-.\w]+@[-a-z0-9]+(\.[-a-z0-9]+)*\.[a-z]+)>/gi,
-      replaceLink = function replaceLink(options) {
-    'use strict';
-
-    return function (wm, leadingMagicChars, link, m2, m3, trailingPunctuation, trailingMagicChars) {
-      link = link.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);
-      var lnkTxt = link,
-          append = '',
-          target = '',
-          lmc = leadingMagicChars || '',
-          tmc = trailingMagicChars || '';
-      if (/^www\./i.test(link)) {
-        link = link.replace(/^www\./i, 'http://www.');
-      }
-      if (options.excludeTrailingPunctuationFromURLs && trailingPunctuation) {
-        append = trailingPunctuation;
-      }
-      if (options.openLinksInNewWindow) {
-        target = ' rel="noopener noreferrer" target="¨E95Eblank"';
-      }
-      return lmc + '' + lnkTxt + '' + append + tmc;
-    };
-  },
-      replaceMail = function replaceMail(options, globals) {
-    'use strict';
-
-    return function (wholeMatch, b, mail) {
-      var href = 'mailto:';
-      b = b || '';
-      mail = showdown.subParser('unescapeSpecialChars')(mail, options, globals);
-      if (options.encodeEmails) {
-        href = showdown.helper.encodeEmailAddress(href + mail);
-        mail = showdown.helper.encodeEmailAddress(mail);
-      } else {
-        href = href + mail;
-      }
-      return b + '' + mail + '';
-    };
-  };
-
-  showdown.subParser('autoLinks', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('autoLinks.before', text, options, globals);
-
-    text = text.replace(delimUrlRegex, replaceLink(options));
-    text = text.replace(delimMailRegex, replaceMail(options, globals));
-
-    text = globals.converter._dispatch('autoLinks.after', text, options, globals);
-
-    return text;
-  });
-
-  showdown.subParser('simplifiedAutoLinks', function (text, options, globals) {
-    'use strict';
-
-    if (!options.simplifiedAutoLink) {
-      return text;
-    }
-
-    text = globals.converter._dispatch('simplifiedAutoLinks.before', text, options, globals);
-
-    if (options.excludeTrailingPunctuationFromURLs) {
-      text = text.replace(simpleURLRegex2, replaceLink(options));
-    } else {
-      text = text.replace(simpleURLRegex, replaceLink(options));
-    }
-    text = text.replace(simpleMailRegex, replaceMail(options, globals));
-
-    text = globals.converter._dispatch('simplifiedAutoLinks.after', text, options, globals);
-
-    return text;
-  });
-
-  /**
-   * These are all the transformations that form block-level
-   * tags like paragraphs, headers, and list items.
-   */
-  showdown.subParser('blockGamut', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('blockGamut.before', text, options, globals);
-
-    // we parse blockquotes first so that we can have headings and hrs
-    // inside blockquotes
-    text = showdown.subParser('blockQuotes')(text, options, globals);
-    text = showdown.subParser('headers')(text, options, globals);
-
-    // Do Horizontal Rules:
-    text = showdown.subParser('horizontalRule')(text, options, globals);
-
-    text = showdown.subParser('lists')(text, options, globals);
-    text = showdown.subParser('codeBlocks')(text, options, globals);
-    text = showdown.subParser('tables')(text, options, globals);
-
-    // We already ran _HashHTMLBlocks() before, in Markdown(), but that
-    // was to escape raw HTML in the original Markdown source. This time,
-    // we're escaping the markup we've just created, so that we don't wrap
-    // 
     tags around block-level tags.
-    text = showdown.subParser('hashHTMLBlocks')(text, options, globals);
-    text = showdown.subParser('paragraphs')(text, options, globals);
-
-    text = globals.converter._dispatch('blockGamut.after', text, options, globals);
-
-    return text;
-  });
-
-  showdown.subParser('blockQuotes', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('blockQuotes.before', text, options, globals);
-
-    // add a couple extra lines after the text and endtext mark
-    text = text + '\n\n';
-
-    var rgx = /(^ {0,3}>[ \t]?.+\n(.+\n)*\n*)+/gm;
-
-    if (options.splitAdjacentBlockquotes) {
-      rgx = /^ {0,3}>[\s\S]*?(?:\n\n)/gm;
-    }
-
-    text = text.replace(rgx, function (bq) {
-      // attacklab: hack around Konqueror 3.5.4 bug:
-      // "----------bug".replace(/^-/g,"") == "bug"
-      bq = bq.replace(/^[ \t]*>[ \t]?/gm, ''); // trim one level of quoting
-
-      // attacklab: clean up hack
-      bq = bq.replace(/¨0/g, '');
-
-      bq = bq.replace(/^[ \t]+$/gm, ''); // trim whitespace-only lines
-      bq = showdown.subParser('githubCodeBlocks')(bq, options, globals);
-      bq = showdown.subParser('blockGamut')(bq, options, globals); // recurse
-
-      bq = bq.replace(/(^|\n)/g, '$1  ');
-      // These leading spaces screw with 
     content, so we need to fix that:
-      bq = bq.replace(/(\s*
    [^\r]+?<\/pre>)/gm, function (wholeMatch, m1) {
-        var pre = m1;
-        // attacklab: hack around Konqueror 3.5.4 bug:
-        pre = pre.replace(/^  /mg, '¨0');
-        pre = pre.replace(/¨0/g, '');
-        return pre;
-      });
-
-      return showdown.subParser('hashBlock')('
    \n' + bq + '\n
    ', options, globals);
-    });
-
-    text = globals.converter._dispatch('blockQuotes.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Process Markdown `
    ` blocks.
-   */
-  showdown.subParser('codeBlocks', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('codeBlocks.before', text, options, globals);
-
-    // sentinel workarounds for lack of \A and \Z, safari\khtml bug
-    text += '¨0';
-
-    var pattern = /(?:\n\n|^)((?:(?:[ ]{4}|\t).*\n+)+)(\n*[ ]{0,3}[^ \t\n]|(?=¨0))/g;
-    text = text.replace(pattern, function (wholeMatch, m1, m2) {
-      var codeblock = m1,
-          nextChar = m2,
-          end = '\n';
-
-      codeblock = showdown.subParser('outdent')(codeblock, options, globals);
-      codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);
-      codeblock = showdown.subParser('detab')(codeblock, options, globals);
-      codeblock = codeblock.replace(/^\n+/g, ''); // trim leading newlines
-      codeblock = codeblock.replace(/\n+$/g, ''); // trim trailing newlines
-
-      if (options.omitExtraWLInCodeBlocks) {
-        end = '';
-      }
-
-      codeblock = '
    ' + codeblock + end + '
    ';
-
-      return showdown.subParser('hashBlock')(codeblock, options, globals) + nextChar;
-    });
-
-    // strip sentinel
-    text = text.replace(/¨0/, '');
-
-    text = globals.converter._dispatch('codeBlocks.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   *
-   *   *  Backtick quotes are used for  spans.
-   *
-   *   *  You can use multiple backticks as the delimiters if you want to
-   *     include literal backticks in the code span. So, this input:
-   *
-   *         Just type ``foo `bar` baz`` at the prompt.
-   *
-   *       Will translate to:
-   *
-   *         
    Just type foo `bar` baz at the prompt.
    
-   *
-   *    There's no arbitrary limit to the number of backticks you
-   *    can use as delimters. If you need three consecutive backticks
-   *    in your code, use four for delimiters, etc.
-   *
-   *  *  You can use spaces to get literal backticks at the edges:
-   *
-   *         ... type `` `bar` `` ...
-   *
-   *       Turns to:
-   *
-   *         ... type `bar` ...
-   */
-  showdown.subParser('codeSpans', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('codeSpans.before', text, options, globals);
-
-    if (typeof text === 'undefined') {
-      text = '';
-    }
-    text = text.replace(/(^|[^\\])(`+)([^\r]*?[^`])\2(?!`)/gm, function (wholeMatch, m1, m2, m3) {
-      var c = m3;
-      c = c.replace(/^([ \t]*)/g, ''); // leading whitespace
-      c = c.replace(/[ \t]*$/g, ''); // trailing whitespace
-      c = showdown.subParser('encodeCode')(c, options, globals);
-      c = m1 + '' + c + '';
-      c = showdown.subParser('hashHTMLSpans')(c, options, globals);
-      return c;
-    });
-
-    text = globals.converter._dispatch('codeSpans.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Create a full HTML document from the processed markdown
-   */
-  showdown.subParser('completeHTMLDocument', function (text, options, globals) {
-    'use strict';
-
-    if (!options.completeHTMLDocument) {
-      return text;
-    }
-
-    text = globals.converter._dispatch('completeHTMLDocument.before', text, options, globals);
-
-    var doctype = 'html',
-        doctypeParsed = '\n',
-        title = '',
-        charset = '\n',
-        lang = '',
-        metadata = '';
-
-    if (typeof globals.metadata.parsed.doctype !== 'undefined') {
-      doctypeParsed = '\n';
-      doctype = globals.metadata.parsed.doctype.toString().toLowerCase();
-      if (doctype === 'html' || doctype === 'html5') {
-        charset = '';
-      }
-    }
-
-    for (var meta in globals.metadata.parsed) {
-      if (globals.metadata.parsed.hasOwnProperty(meta)) {
-        switch (meta.toLowerCase()) {
-          case 'doctype':
-            break;
-
-          case 'title':
-            title = '' + globals.metadata.parsed.title + '\n';
-            break;
-
-          case 'charset':
-            if (doctype === 'html' || doctype === 'html5') {
-              charset = '\n';
-            } else {
-              charset = '\n';
-            }
-            break;
-
-          case 'language':
-          case 'lang':
-            lang = ' lang="' + globals.metadata.parsed[meta] + '"';
-            metadata += '\n';
-            break;
-
-          default:
-            metadata += '\n';
-        }
-      }
-    }
-
-    text = doctypeParsed + '\n\n' + title + charset + metadata + '\n\n' + text.trim() + '\n\n';
-
-    text = globals.converter._dispatch('completeHTMLDocument.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Convert all tabs to spaces
-   */
-  showdown.subParser('detab', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('detab.before', text, options, globals);
-
-    // expand first n-1 tabs
-    text = text.replace(/\t(?=\t)/g, '    '); // g_tab_width
-
-    // replace the nth with two sentinels
-    text = text.replace(/\t/g, '¨A¨B');
-
-    // use the sentinel to anchor our regex so it doesn't explode
-    text = text.replace(/¨B(.+?)¨A/g, function (wholeMatch, m1) {
-      var leadingText = m1,
-          numSpaces = 4 - leadingText.length % 4; // g_tab_width
-
-      // there *must* be a better way to do this:
-      for (var i = 0; i < numSpaces; i++) {
-        leadingText += ' ';
-      }
-
-      return leadingText;
-    });
-
-    // clean up sentinels
-    text = text.replace(/¨A/g, '    '); // g_tab_width
-    text = text.replace(/¨B/g, '');
-
-    text = globals.converter._dispatch('detab.after', text, options, globals);
-    return text;
-  });
-
-  showdown.subParser('ellipsis', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('ellipsis.before', text, options, globals);
-
-    text = text.replace(/\.\.\./g, '…');
-
-    text = globals.converter._dispatch('ellipsis.after', text, options, globals);
-
-    return text;
-  });
-
-  /**
-   * Turn emoji codes into emojis
-   *
-   * List of supported emojis: https://github.com/showdownjs/showdown/wiki/Emojis
-   */
-  showdown.subParser('emoji', function (text, options, globals) {
-    'use strict';
-
-    if (!options.emoji) {
-      return text;
-    }
-
-    text = globals.converter._dispatch('emoji.before', text, options, globals);
-
-    var emojiRgx = /:([\S]+?):/g;
-
-    text = text.replace(emojiRgx, function (wm, emojiCode) {
-      if (showdown.helper.emojis.hasOwnProperty(emojiCode)) {
-        return showdown.helper.emojis[emojiCode];
-      }
-      return wm;
-    });
-
-    text = globals.converter._dispatch('emoji.after', text, options, globals);
-
-    return text;
-  });
-
-  /**
-   * Smart processing for ampersands and angle brackets that need to be encoded.
-   */
-  showdown.subParser('encodeAmpsAndAngles', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('encodeAmpsAndAngles.before', text, options, globals);
-
-    // Ampersand-encoding based entirely on Nat Irons's Amputator MT plugin:
-    // http://bumppo.net/projects/amputator/
-    text = text.replace(/&(?!#?[xX]?(?:[0-9a-fA-F]+|\w+);)/g, '&');
-
-    // Encode naked <'s
-    text = text.replace(/<(?![a-z\/?$!])/gi, '<');
-
-    // Encode <
-    text = text.replace(/
-    text = text.replace(/>/g, '>');
-
-    text = globals.converter._dispatch('encodeAmpsAndAngles.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Returns the string, with after processing the following backslash escape sequences.
-   *
-   * attacklab: The polite way to do this is with the new escapeCharacters() function:
-   *
-   *    text = escapeCharacters(text,"\\",true);
-   *    text = escapeCharacters(text,"`*_{}[]()>#+-.!",true);
-   *
-   * ...but we're sidestepping its use of the (slow) RegExp constructor
-   * as an optimization for Firefox.  This function gets called a LOT.
-   */
-  showdown.subParser('encodeBackslashEscapes', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('encodeBackslashEscapes.before', text, options, globals);
-
-    text = text.replace(/\\(\\)/g, showdown.helper.escapeCharactersCallback);
-    text = text.replace(/\\([`*_{}\[\]()>#+.!~=|-])/g, showdown.helper.escapeCharactersCallback);
-
-    text = globals.converter._dispatch('encodeBackslashEscapes.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Encode/escape certain characters inside Markdown code runs.
-   * The point is that in code, these characters are literals,
-   * and lose their special Markdown meanings.
-   */
-  showdown.subParser('encodeCode', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('encodeCode.before', text, options, globals);
-
-    // Encode all ampersands; HTML entities are not
-    // entities within a Markdown code span.
-    text = text.replace(/&/g, '&')
-    // Do the angle bracket song and dance:
-    .replace(//g, '>')
-    // Now, escape characters that are magic in Markdown:
-    .replace(/([*_{}\[\]\\=~-])/g, showdown.helper.escapeCharactersCallback);
-
-    text = globals.converter._dispatch('encodeCode.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Within tags -- meaning between < and > -- encode [\ ` * _ ~ =] so they
-   * don't conflict with their use in Markdown for code, italics and strong.
-   */
-  showdown.subParser('escapeSpecialCharsWithinTagAttributes', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.before', text, options, globals);
-
-    // Build a regex to find HTML tags.
-    var tags = /<\/?[a-z\d_:-]+(?:[\s]+[\s\S]+?)?>/gi,
-        comments = /-]|-[^>])(?:[^-]|-[^-])*)--)>/gi;
-
-    text = text.replace(tags, function (wholeMatch) {
-      return wholeMatch.replace(/(.)<\/?code>(?=.)/g, '$1`').replace(/([\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);
-    });
-
-    text = text.replace(comments, function (wholeMatch) {
-      return wholeMatch.replace(/([\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);
-    });
-
-    text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Handle github codeblocks prior to running HashHTML so that
-   * HTML contained within the codeblock gets escaped properly
-   * Example:
-   * ```ruby
-   *     def hello_world(x)
-   *       puts "Hello, #{x}"
-   *     end
-   * ```
-   */
-  showdown.subParser('githubCodeBlocks', function (text, options, globals) {
-    'use strict';
-
-    // early exit if option is not enabled
-
-    if (!options.ghCodeBlocks) {
-      return text;
-    }
-
-    text = globals.converter._dispatch('githubCodeBlocks.before', text, options, globals);
-
-    text += '¨0';
-
-    text = text.replace(/(?:^|\n)(?: {0,3})(```+|~~~+)(?: *)([^\s`~]*)\n([\s\S]*?)\n(?: {0,3})\1/g, function (wholeMatch, delim, language, codeblock) {
-      var end = options.omitExtraWLInCodeBlocks ? '' : '\n';
-
-      // First parse the github code block
-      codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);
-      codeblock = showdown.subParser('detab')(codeblock, options, globals);
-      codeblock = codeblock.replace(/^\n+/g, ''); // trim leading newlines
-      codeblock = codeblock.replace(/\n+$/g, ''); // trim trailing whitespace
-
-      codeblock = '
    ' + codeblock + end + '
    ';
-
-      codeblock = showdown.subParser('hashBlock')(codeblock, options, globals);
-
-      // Since GHCodeblocks can be false positives, we need to
-      // store the primitive text and the parsed text in a global var,
-      // and then return a token
-      return '\n\n¨G' + (globals.ghCodeBlocks.push({ text: wholeMatch, codeblock: codeblock }) - 1) + 'G\n\n';
-    });
-
-    // attacklab: strip sentinel
-    text = text.replace(/¨0/, '');
-
-    return globals.converter._dispatch('githubCodeBlocks.after', text, options, globals);
-  });
-
-  showdown.subParser('hashBlock', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('hashBlock.before', text, options, globals);
-    text = text.replace(/(^\n+|\n+$)/g, '');
-    text = '\n\n¨K' + (globals.gHtmlBlocks.push(text) - 1) + 'K\n\n';
-    text = globals.converter._dispatch('hashBlock.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Hash and escape  elements that should not be parsed as markdown
-   */
-  showdown.subParser('hashCodeTags', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('hashCodeTags.before', text, options, globals);
-
-    var repFunc = function repFunc(wholeMatch, match, left, right) {
-      var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;
-      return '¨C' + (globals.gHtmlSpans.push(codeblock) - 1) + 'C';
-    };
-
-    // Hash naked 
-    text = showdown.helper.replaceRecursiveRegExp(text, repFunc, ']*>', '', 'gim');
-
-    text = globals.converter._dispatch('hashCodeTags.after', text, options, globals);
-    return text;
-  });
-
-  showdown.subParser('hashElement', function (text, options, globals) {
-    'use strict';
-
-    return function (wholeMatch, m1) {
-      var blockText = m1;
-
-      // Undo double lines
-      blockText = blockText.replace(/\n\n/g, '\n');
-      blockText = blockText.replace(/^\n/, '');
-
-      // strip trailing blank lines
-      blockText = blockText.replace(/\n+$/g, '');
-
-      // Replace the element text with a marker ("¨KxK" where x is its key)
-      blockText = '\n\n¨K' + (globals.gHtmlBlocks.push(blockText) - 1) + 'K\n\n';
-
-      return blockText;
-    };
-  });
-
-  showdown.subParser('hashHTMLBlocks', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('hashHTMLBlocks.before', text, options, globals);
-
-    var blockTags = ['pre', 'div', 'h1', 'h2', 'h3', 'h4', 'h5', 'h6', 'blockquote', 'table', 'dl', 'ol', 'ul', 'script', 'noscript', 'form', 'fieldset', 'iframe', 'math', 'style', 'section', 'header', 'footer', 'nav', 'article', 'aside', 'address', 'audio', 'canvas', 'figure', 'hgroup', 'output', 'video', 'p'],
-        repFunc = function repFunc(wholeMatch, match, left, right) {
-      var txt = wholeMatch;
-      // check if this html element is marked as markdown
-      // if so, it's contents should be parsed as markdown
-      if (left.search(/\bmarkdown\b/) !== -1) {
-        txt = left + globals.converter.makeHtml(match) + right;
-      }
-      return '\n\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\n\n';
-    };
-
-    if (options.backslashEscapesHTMLTags) {
-      // encode backslash escaped HTML tags
-      text = text.replace(/\\<(\/?[^>]+?)>/g, function (wm, inside) {
-        return '<' + inside + '>';
-      });
-    }
-
-    // hash HTML Blocks
-    for (var i = 0; i < blockTags.length; ++i) {
-
-      var opTagPos,
-          rgx1 = new RegExp('^ {0,3}(<' + blockTags[i] + '\\b[^>]*>)', 'im'),
-          patLeft = '<' + blockTags[i] + '\\b[^>]*>',
-          patRight = '';
-      // 1. Look for the first position of the first opening HTML tag in the text
-      while ((opTagPos = showdown.helper.regexIndexOf(text, rgx1)) !== -1) {
-
-        // if the HTML tag is \ escaped, we need to escape it and break
-
-
-        //2. Split the text in that position
-        var subTexts = showdown.helper.splitAtIndex(text, opTagPos),
-
-        //3. Match recursively
-        newSubText1 = showdown.helper.replaceRecursiveRegExp(subTexts[1], repFunc, patLeft, patRight, 'im');
-
-        // prevent an infinite loop
-        if (newSubText1 === subTexts[1]) {
-          break;
-        }
-        text = subTexts[0].concat(newSubText1);
-      }
-    }
-    // HR SPECIAL CASE
-    text = text.replace(/(\n {0,3}(<(hr)\b([^<>])*?\/?>)[ \t]*(?=\n{2,}))/g, showdown.subParser('hashElement')(text, options, globals));
-
-    // Special case for standalone HTML comments
-    text = showdown.helper.replaceRecursiveRegExp(text, function (txt) {
-      return '\n\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\n\n';
-    }, '^ {0,3}', 'gm');
-
-    // PHP and ASP-style processor instructions ( and <%...%>)
-    text = text.replace(/(?:\n\n)( {0,3}(?:<([?%])[^\r]*?\2>)[ \t]*(?=\n{2,}))/g, showdown.subParser('hashElement')(text, options, globals));
-
-    text = globals.converter._dispatch('hashHTMLBlocks.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Hash span elements that should not be parsed as markdown
-   */
-  showdown.subParser('hashHTMLSpans', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('hashHTMLSpans.before', text, options, globals);
-
-    function hashHTMLSpan(html) {
-      return '¨C' + (globals.gHtmlSpans.push(html) - 1) + 'C';
-    }
-
-    // Hash Self Closing tags
-    text = text.replace(/<[^>]+?\/>/gi, function (wm) {
-      return hashHTMLSpan(wm);
-    });
-
-    // Hash tags without properties
-    text = text.replace(/<([^>]+?)>[\s\S]*?<\/\1>/g, function (wm) {
-      return hashHTMLSpan(wm);
-    });
-
-    // Hash tags with properties
-    text = text.replace(/<([^>]+?)\s[^>]+?>[\s\S]*?<\/\1>/g, function (wm) {
-      return hashHTMLSpan(wm);
-    });
-
-    // Hash self closing tags without />
-    text = text.replace(/<[^>]+?>/gi, function (wm) {
-      return hashHTMLSpan(wm);
-    });
-
-    /*showdown.helper.matchRecursiveRegExp(text, ']*>', '', 'gi');*/
-
-    text = globals.converter._dispatch('hashHTMLSpans.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Unhash HTML spans
-   */
-  showdown.subParser('unhashHTMLSpans', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('unhashHTMLSpans.before', text, options, globals);
-
-    for (var i = 0; i < globals.gHtmlSpans.length; ++i) {
-      var repText = globals.gHtmlSpans[i],
-
-      // limiter to prevent infinite loop (assume 10 as limit for recurse)
-      limit = 0;
-
-      while (/¨C(\d+)C/.test(repText)) {
-        var num = RegExp.$1;
-        repText = repText.replace('¨C' + num + 'C', globals.gHtmlSpans[num]);
-        if (limit === 10) {
-          console.error('maximum nesting of 10 spans reached!!!');
-          break;
-        }
-        ++limit;
-      }
-      text = text.replace('¨C' + i + 'C', repText);
-    }
-
-    text = globals.converter._dispatch('unhashHTMLSpans.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Hash and escape 
     elements that should not be parsed as markdown
-   */
-  showdown.subParser('hashPreCodeTags', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('hashPreCodeTags.before', text, options, globals);
-
-    var repFunc = function repFunc(wholeMatch, match, left, right) {
-      // encode html entities
-      var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;
-      return '\n\n¨G' + (globals.ghCodeBlocks.push({ text: wholeMatch, codeblock: codeblock }) - 1) + 'G\n\n';
-    };
-
-    // Hash 
    
-    text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}]*>\\s*]*>', '^ {0,3}\\s*
    ', 'gim');
-
-    text = globals.converter._dispatch('hashPreCodeTags.after', text, options, globals);
-    return text;
-  });
-
-  showdown.subParser('headers', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('headers.before', text, options, globals);
-
-    var headerLevelStart = isNaN(parseInt(options.headerLevelStart)) ? 1 : parseInt(options.headerLevelStart),
-
-
-    // Set text-style headers:
-    //	Header 1
-    //	========
-    //
-    //	Header 2
-    //	--------
-    //
-    setextRegexH1 = options.smoothLivePreview ? /^(.+)[ \t]*\n={2,}[ \t]*\n+/gm : /^(.+)[ \t]*\n=+[ \t]*\n+/gm,
-        setextRegexH2 = options.smoothLivePreview ? /^(.+)[ \t]*\n-{2,}[ \t]*\n+/gm : /^(.+)[ \t]*\n-+[ \t]*\n+/gm;
-
-    text = text.replace(setextRegexH1, function (wholeMatch, m1) {
-
-      var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),
-          hID = options.noHeaderId ? '' : ' id="' + headerId(m1) + '"',
-          hLevel = headerLevelStart,
-          hashBlock = '' + spanGamut + '';
-      return showdown.subParser('hashBlock')(hashBlock, options, globals);
-    });
-
-    text = text.replace(setextRegexH2, function (matchFound, m1) {
-      var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),
-          hID = options.noHeaderId ? '' : ' id="' + headerId(m1) + '"',
-          hLevel = headerLevelStart + 1,
-          hashBlock = '' + spanGamut + '';
-      return showdown.subParser('hashBlock')(hashBlock, options, globals);
-    });
-
-    // atx-style headers:
-    //  # Header 1
-    //  ## Header 2
-    //  ## Header 2 with closing hashes ##
-    //  ...
-    //  ###### Header 6
-    //
-    var atxStyle = options.requireSpaceBeforeHeadingText ? /^(#{1,6})[ \t]+(.+?)[ \t]*#*\n+/gm : /^(#{1,6})[ \t]*(.+?)[ \t]*#*\n+/gm;
-
-    text = text.replace(atxStyle, function (wholeMatch, m1, m2) {
-      var hText = m2;
-      if (options.customizedHeaderId) {
-        hText = m2.replace(/\s?\{([^{]+?)}\s*$/, '');
-      }
-
-      var span = showdown.subParser('spanGamut')(hText, options, globals),
-          hID = options.noHeaderId ? '' : ' id="' + headerId(m2) + '"',
-          hLevel = headerLevelStart - 1 + m1.length,
-          header = '' + span + '';
-
-      return showdown.subParser('hashBlock')(header, options, globals);
-    });
-
-    function headerId(m) {
-      var title, prefix;
-
-      // It is separate from other options to allow combining prefix and customized
-      if (options.customizedHeaderId) {
-        var match = m.match(/\{([^{]+?)}\s*$/);
-        if (match && match[1]) {
-          m = match[1];
-        }
-      }
-
-      title = m;
-
-      // Prefix id to prevent causing inadvertent pre-existing style matches.
-      if (showdown.helper.isString(options.prefixHeaderId)) {
-        prefix = options.prefixHeaderId;
-      } else if (options.prefixHeaderId === true) {
-        prefix = 'section-';
-      } else {
-        prefix = '';
-      }
-
-      if (!options.rawPrefixHeaderId) {
-        title = prefix + title;
-      }
-
-      if (options.ghCompatibleHeaderId) {
-        title = title.replace(/ /g, '-')
-        // replace previously escaped chars (&, ¨ and $)
-        .replace(/&/g, '').replace(/¨T/g, '').replace(/¨D/g, '')
-        // replace rest of the chars (&~$ are repeated as they might have been escaped)
-        // borrowed from github's redcarpet (some they should produce similar results)
-        .replace(/[&+$,\/:;=?@"#{}|^¨~\[\]`\\*)(%.!'<>]/g, '').toLowerCase();
-      } else if (options.rawHeaderId) {
-        title = title.replace(/ /g, '-')
-        // replace previously escaped chars (&, ¨ and $)
-        .replace(/&/g, '&').replace(/¨T/g, '¨').replace(/¨D/g, '$')
-        // replace " and '
-        .replace(/["']/g, '-').toLowerCase();
-      } else {
-        title = title.replace(/[^\w]/g, '').toLowerCase();
-      }
-
-      if (options.rawPrefixHeaderId) {
-        title = prefix + title;
-      }
-
-      if (globals.hashLinkCounts[title]) {
-        title = title + '-' + globals.hashLinkCounts[title]++;
-      } else {
-        globals.hashLinkCounts[title] = 1;
-      }
-      return title;
-    }
-
-    text = globals.converter._dispatch('headers.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Turn Markdown link shortcuts into XHTML  tags.
-   */
-  showdown.subParser('horizontalRule', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('horizontalRule.before', text, options, globals);
-
-    var key = showdown.subParser('hashBlock')('
    ', options, globals);
-    text = text.replace(/^ {0,2}( ?-){3,}[ \t]*$/gm, key);
-    text = text.replace(/^ {0,2}( ?\*){3,}[ \t]*$/gm, key);
-    text = text.replace(/^ {0,2}( ?_){3,}[ \t]*$/gm, key);
-
-    text = globals.converter._dispatch('horizontalRule.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Turn Markdown image shortcuts into  tags.
-   */
-  showdown.subParser('images', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('images.before', text, options, globals);
-
-    var inlineRegExp = /!\[([^\]]*?)][ \t]*()\([ \t]??(?: =([*\d]+[A-Za-z%]{0,4})x([*\d]+[A-Za-z%]{0,4}))?[ \t]*(?:(["'])([^"]*?)\6)?[ \t]?\)/g,
-        crazyRegExp = /!\[([^\]]*?)][ \t]*()\([ \t]?<([^>]*)>(?: =([*\d]+[A-Za-z%]{0,4})x([*\d]+[A-Za-z%]{0,4}))?[ \t]*(?:(?:(["'])([^"]*?)\6))?[ \t]?\)/g,
-        base64RegExp = /!\[([^\]]*?)][ \t]*()\([ \t]??(?: =([*\d]+[A-Za-z%]{0,4})x([*\d]+[A-Za-z%]{0,4}))?[ \t]*(?:(["'])([^"]*?)\6)?[ \t]?\)/g,
-        referenceRegExp = /!\[([^\]]*?)] ?(?:\n *)?\[([\s\S]*?)]()()()()()/g,
-        refShortcutRegExp = /!\[([^\[\]]+)]()()()()()/g;
-
-    function writeImageTagBase64(wholeMatch, altText, linkId, url, width, height, m5, title) {
-      url = url.replace(/\s/g, '');
-      return writeImageTag(wholeMatch, altText, linkId, url, width, height, m5, title);
-    }
-
-    function writeImageTag(wholeMatch, altText, linkId, url, width, height, m5, title) {
-
-      var gUrls = globals.gUrls,
-          gTitles = globals.gTitles,
-          gDims = globals.gDimensions;
-
-      linkId = linkId.toLowerCase();
-
-      if (!title) {
-        title = '';
-      }
-      // Special case for explicit empty url
-      if (wholeMatch.search(/\(? ?(['"].*['"])?\)$/m) > -1) {
-        url = '';
-      } else if (url === '' || url === null) {
-        if (linkId === '' || linkId === null) {
-          // lower-case and turn embedded newlines into spaces
-          linkId = altText.toLowerCase().replace(/ ?\n/g, ' ');
-        }
-        url = '#' + linkId;
-
-        if (!showdown.helper.isUndefined(gUrls[linkId])) {
-          url = gUrls[linkId];
-          if (!showdown.helper.isUndefined(gTitles[linkId])) {
-            title = gTitles[linkId];
-          }
-          if (!showdown.helper.isUndefined(gDims[linkId])) {
-            width = gDims[linkId].width;
-            height = gDims[linkId].height;
-          }
-        } else {
-          return wholeMatch;
-        }
-      }
-
-      altText = altText.replace(/"/g, '"')
-      //altText = showdown.helper.escapeCharacters(altText, '*_', false);
-      .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);
-      //url = showdown.helper.escapeCharacters(url, '*_', false);
-      url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);
-      var result = '' + altText + 'x "optional title")
-
-    // base64 encoded images
-    text = text.replace(base64RegExp, writeImageTagBase64);
-
-    // cases with crazy urls like ./image/cat1).png
-    text = text.replace(crazyRegExp, writeImageTag);
-
-    // normal cases
-    text = text.replace(inlineRegExp, writeImageTag);
-
-    // handle reference-style shortcuts: ![img text]
-    text = text.replace(refShortcutRegExp, writeImageTag);
-
-    text = globals.converter._dispatch('images.after', text, options, globals);
-    return text;
-  });
-
-  showdown.subParser('italicsAndBold', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('italicsAndBold.before', text, options, globals);
-
-    // it's faster to have 3 separate regexes for each case than have just one
-    // because of backtracing, in some cases, it could lead to an exponential effect
-    // called "catastrophic backtrace". Ominous!
-
-    function parseInside(txt, left, right) {
-      /*
-      if (options.simplifiedAutoLink) {
-        txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);
-      }
-      */
-      return left + txt + right;
-    }
-
-    // Parse underscores
-    if (options.literalMidWordUnderscores) {
-      text = text.replace(/\b___(\S[\s\S]*?)___\b/g, function (wm, txt) {
-        return parseInside(txt, '', '');
-      });
-      text = text.replace(/\b__(\S[\s\S]*?)__\b/g, function (wm, txt) {
-        return parseInside(txt, '', '');
-      });
-      text = text.replace(/\b_(\S[\s\S]*?)_\b/g, function (wm, txt) {
-        return parseInside(txt, '', '');
-      });
-    } else {
-      text = text.replace(/___(\S[\s\S]*?)___/g, function (wm, m) {
-        return (/\S$/.test(m) ? parseInside(m, '', '') : wm
-        );
-      });
-      text = text.replace(/__(\S[\s\S]*?)__/g, function (wm, m) {
-        return (/\S$/.test(m) ? parseInside(m, '', '') : wm
-        );
-      });
-      text = text.replace(/_([^\s_][\s\S]*?)_/g, function (wm, m) {
-        // !/^_[^_]/.test(m) - test if it doesn't start with __ (since it seems redundant, we removed it)
-        return (/\S$/.test(m) ? parseInside(m, '', '') : wm
-        );
-      });
-    }
-
-    // Now parse asterisks
-    if (options.literalMidWordAsterisks) {
-      text = text.replace(/([^*]|^)\B\*\*\*(\S[\s\S]*?)\*\*\*\B(?!\*)/g, function (wm, lead, txt) {
-        return parseInside(txt, lead + '', '');
-      });
-      text = text.replace(/([^*]|^)\B\*\*(\S[\s\S]*?)\*\*\B(?!\*)/g, function (wm, lead, txt) {
-        return parseInside(txt, lead + '', '');
-      });
-      text = text.replace(/([^*]|^)\B\*(\S[\s\S]*?)\*\B(?!\*)/g, function (wm, lead, txt) {
-        return parseInside(txt, lead + '', '');
-      });
-    } else {
-      text = text.replace(/\*\*\*(\S[\s\S]*?)\*\*\*/g, function (wm, m) {
-        return (/\S$/.test(m) ? parseInside(m, '', '') : wm
-        );
-      });
-      text = text.replace(/\*\*(\S[\s\S]*?)\*\*/g, function (wm, m) {
-        return (/\S$/.test(m) ? parseInside(m, '', '') : wm
-        );
-      });
-      text = text.replace(/\*([^\s*][\s\S]*?)\*/g, function (wm, m) {
-        // !/^\*[^*]/.test(m) - test if it doesn't start with ** (since it seems redundant, we removed it)
-        return (/\S$/.test(m) ? parseInside(m, '', '') : wm
-        );
-      });
-    }
-
-    text = globals.converter._dispatch('italicsAndBold.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Form HTML ordered (numbered) and unordered (bulleted) lists.
-   */
-  showdown.subParser('lists', function (text, options, globals) {
-    'use strict';
-
-    /**
-     * Process the contents of a single ordered or unordered list, splitting it
-     * into individual list items.
-     * @param {string} listStr
-     * @param {boolean} trimTrailing
-     * @returns {string}
-     */
-
-    function processListItems(listStr, trimTrailing) {
-      // The $g_list_level global keeps track of when we're inside a list.
-      // Each time we enter a list, we increment it; when we leave a list,
-      // we decrement. If it's zero, we're not in a list anymore.
-      //
-      // We do this because when we're not inside a list, we want to treat
-      // something like this:
-      //
-      //    I recommend upgrading to version
-      //    8. Oops, now this line is treated
-      //    as a sub-list.
-      //
-      // As a single paragraph, despite the fact that the second line starts
-      // with a digit-period-space sequence.
-      //
-      // Whereas when we're inside a list (or sub-list), that line will be
-      // treated as the start of a sub-list. What a kludge, huh? This is
-      // an aspect of Markdown's syntax that's hard to parse perfectly
-      // without resorting to mind-reading. Perhaps the solution is to
-      // change the syntax rules such that sub-lists must start with a
-      // starting cardinal number; e.g. "1." or "a.".
-      globals.gListLevel++;
-
-      // trim trailing blank lines:
-      listStr = listStr.replace(/\n{2,}$/, '\n');
-
-      // attacklab: add sentinel to emulate \z
-      listStr += '¨0';
-
-      var rgx = /(\n)?(^ {0,3})([*+-]|\d+[.])[ \t]+((\[(x|X| )?])?[ \t]*[^\r]+?(\n{1,2}))(?=\n*(¨0| {0,3}([*+-]|\d+[.])[ \t]+))/gm,
-          isParagraphed = /\n[ \t]*\n(?!¨0)/.test(listStr);
-
-      // Since version 1.5, nesting sublists requires 4 spaces (or 1 tab) indentation,
-      // which is a syntax breaking change
-      // activating this option reverts to old behavior
-      if (options.disableForced4SpacesIndentedSublists) {
-        rgx = /(\n)?(^ {0,3})([*+-]|\d+[.])[ \t]+((\[(x|X| )?])?[ \t]*[^\r]+?(\n{1,2}))(?=\n*(¨0|\2([*+-]|\d+[.])[ \t]+))/gm;
-      }
-
-      listStr = listStr.replace(rgx, function (wholeMatch, m1, m2, m3, m4, taskbtn, checked) {
-        checked = checked && checked.trim() !== '';
-
-        var item = showdown.subParser('outdent')(m4, options, globals),
-            bulletStyle = '';
-
-        // Support for github tasklists
-        if (taskbtn && options.tasklists) {
-          bulletStyle = ' class="task-list-item" style="list-style-type: none;"';
-          item = item.replace(/^[ \t]*\[(x|X| )?]/m, function () {
-            var otp = '
  • a
    • 
-        // instead of:
-        // 
    • - - a
    
-        // So, to prevent it, we will put a marker (¨A)in the beginning of the line
-        // Kind of hackish/monkey patching, but seems more effective than overcomplicating the list parser
-        item = item.replace(/^([-*+]|\d\.)[ \t]+[\S\n ]*/g, function (wm2) {
-          return '¨A' + wm2;
-        });
-
-        // m1 - Leading line or
-        // Has a double return (multi paragraph) or
-        // Has sublist
-        if (m1 || item.search(/\n{2,}/) > -1) {
-          item = showdown.subParser('githubCodeBlocks')(item, options, globals);
-          item = showdown.subParser('blockGamut')(item, options, globals);
-        } else {
-          // Recursion for sub-lists:
-          item = showdown.subParser('lists')(item, options, globals);
-          item = item.replace(/\n$/, ''); // chomp(item)
-          item = showdown.subParser('hashHTMLBlocks')(item, options, globals);
-
-          // Colapse double linebreaks
-          item = item.replace(/\n\n+/g, '\n\n');
-          if (isParagraphed) {
-            item = showdown.subParser('paragraphs')(item, options, globals);
-          } else {
-            item = showdown.subParser('spanGamut')(item, options, globals);
-          }
-        }
-
-        // now we need to remove the marker (¨A)
-        item = item.replace('¨A', '');
-        // we can finally wrap the line in list item tags
-        item = '' + item + '\n';
-
-        return item;
-      });
-
-      // attacklab: strip sentinel
-      listStr = listStr.replace(/¨0/g, '');
-
-      globals.gListLevel--;
-
-      if (trimTrailing) {
-        listStr = listStr.replace(/\s+$/, '');
-      }
-
-      return listStr;
-    }
-
-    function styleStartNumber(list, listType) {
-      // check if ol and starts by a number different than 1
-      if (listType === 'ol') {
-        var res = list.match(/^ *(\d+)\./);
-        if (res && res[1] !== '1') {
-          return ' start="' + res[1] + '"';
-        }
-      }
-      return '';
-    }
-
-    /**
-     * Check and parse consecutive lists (better fix for issue #142)
-     * @param {string} list
-     * @param {string} listType
-     * @param {boolean} trimTrailing
-     * @returns {string}
-     */
-    function parseConsecutiveLists(list, listType, trimTrailing) {
-      // check if we caught 2 or more consecutive lists by mistake
-      // we use the counterRgx, meaning if listType is UL we look for OL and vice versa
-      var olRgx = options.disableForced4SpacesIndentedSublists ? /^ ?\d+\.[ \t]/gm : /^ {0,3}\d+\.[ \t]/gm,
-          ulRgx = options.disableForced4SpacesIndentedSublists ? /^ ?[*+-][ \t]/gm : /^ {0,3}[*+-][ \t]/gm,
-          counterRxg = listType === 'ul' ? olRgx : ulRgx,
-          result = '';
-
-      if (list.search(counterRxg) !== -1) {
-        (function parseCL(txt) {
-          var pos = txt.search(counterRxg),
-              style = styleStartNumber(list, listType);
-          if (pos !== -1) {
-            // slice
-            result += '\n\n<' + listType + style + '>\n' + processListItems(txt.slice(0, pos), !!trimTrailing) + '\n';
-
-            // invert counterType and listType
-            listType = listType === 'ul' ? 'ol' : 'ul';
-            counterRxg = listType === 'ul' ? olRgx : ulRgx;
-
-            //recurse
-            parseCL(txt.slice(pos));
-          } else {
-            result += '\n\n<' + listType + style + '>\n' + processListItems(txt, !!trimTrailing) + '\n';
-          }
-        })(list);
-      } else {
-        var style = styleStartNumber(list, listType);
-        result = '\n\n<' + listType + style + '>\n' + processListItems(list, !!trimTrailing) + '\n';
-      }
-
-      return result;
-    }
-
-    /** Start of list parsing **/
-    text = globals.converter._dispatch('lists.before', text, options, globals);
-    // add sentinel to hack around khtml/safari bug:
-    // http://bugs.webkit.org/show_bug.cgi?id=11231
-    text += '¨0';
-
-    if (globals.gListLevel) {
-      text = text.replace(/^(( {0,3}([*+-]|\d+[.])[ \t]+)[^\r]+?(¨0|\n{2,}(?=\S)(?![ \t]*(?:[*+-]|\d+[.])[ \t]+)))/gm, function (wholeMatch, list, m2) {
-        var listType = m2.search(/[*+-]/g) > -1 ? 'ul' : 'ol';
-        return parseConsecutiveLists(list, listType, true);
-      });
-    } else {
-      text = text.replace(/(\n\n|^\n?)(( {0,3}([*+-]|\d+[.])[ \t]+)[^\r]+?(¨0|\n{2,}(?=\S)(?![ \t]*(?:[*+-]|\d+[.])[ \t]+)))/gm, function (wholeMatch, m1, list, m3) {
-        var listType = m3.search(/[*+-]/g) > -1 ? 'ul' : 'ol';
-        return parseConsecutiveLists(list, listType, false);
-      });
-    }
-
-    // strip sentinel
-    text = text.replace(/¨0/, '');
-    text = globals.converter._dispatch('lists.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Parse metadata at the top of the document
-   */
-  showdown.subParser('metadata', function (text, options, globals) {
-    'use strict';
-
-    if (!options.metadata) {
-      return text;
-    }
-
-    text = globals.converter._dispatch('metadata.before', text, options, globals);
-
-    function parseMetadataContents(content) {
-      // raw is raw so it's not changed in any way
-      globals.metadata.raw = content;
-
-      // escape chars forbidden in html attributes
-      // double quotes
-      content = content
-      // ampersand first
-      .replace(/&/g, '&')
-      // double quotes
-      .replace(/"/g, '"');
-
-      content = content.replace(/\n {4}/g, ' ');
-      content.replace(/^([\S ]+): +([\s\S]+?)$/gm, function (wm, key, value) {
-        globals.metadata.parsed[key] = value;
-        return '';
-      });
-    }
-
-    text = text.replace(/^\s*«««+(\S*?)\n([\s\S]+?)\n»»»+\n/, function (wholematch, format, content) {
-      parseMetadataContents(content);
-      return '¨M';
-    });
-
-    text = text.replace(/^\s*---+(\S*?)\n([\s\S]+?)\n---+\n/, function (wholematch, format, content) {
-      if (format) {
-        globals.metadata.format = format;
-      }
-      parseMetadataContents(content);
-      return '¨M';
-    });
-
-    text = text.replace(/¨M/g, '');
-
-    text = globals.converter._dispatch('metadata.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   * Remove one level of line-leading tabs or spaces
-   */
-  showdown.subParser('outdent', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('outdent.before', text, options, globals);
-
-    // attacklab: hack around Konqueror 3.5.4 bug:
-    // "----------bug".replace(/^-/g,"") == "bug"
-    text = text.replace(/^(\t|[ ]{1,4})/gm, '¨0'); // attacklab: g_tab_width
-
-    // attacklab: clean up hack
-    text = text.replace(/¨0/g, '');
-
-    text = globals.converter._dispatch('outdent.after', text, options, globals);
-    return text;
-  });
-
-  /**
-   *
-   */
-  showdown.subParser('paragraphs', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('paragraphs.before', text, options, globals);
-    // Strip leading and trailing lines:
-    text = text.replace(/^\n+/g, '');
-    text = text.replace(/\n+$/g, '');
-
-    var grafs = text.split(/\n{2,}/g),
-        grafsOut = [],
-        end = grafs.length; // Wrap 
     tags
-
-    for (var i = 0; i < end; i++) {
-      var str = grafs[i];
-      // if this is an HTML marker, copy it
-      if (str.search(/¨(K|G)(\d+)\1/g) >= 0) {
-        grafsOut.push(str);
-
-        // test for presence of characters to prevent empty lines being parsed
-        // as paragraphs (resulting in undesired extra empty paragraphs)
-      } else if (str.search(/\S/) >= 0) {
-        str = showdown.subParser('spanGamut')(str, options, globals);
-        str = str.replace(/^([ \t]*)/g, '
    ');
-        str += '
    ';
-        grafsOut.push(str);
-      }
-    }
-
-    /** Unhashify HTML blocks */
-    end = grafsOut.length;
-    for (i = 0; i < end; i++) {
-      var blockText = '',
-          grafsOutIt = grafsOut[i],
-          codeFlag = false;
-      // if this is a marker for an html block...
-      // use RegExp.test instead of string.search because of QML bug
-      while (/¨(K|G)(\d+)\1/.test(grafsOutIt)) {
-        var delim = RegExp.$1,
-            num = RegExp.$2;
-
-        if (delim === 'K') {
-          blockText = globals.gHtmlBlocks[num];
-        } else {
-          // we need to check if ghBlock is a false positive
-          if (codeFlag) {
-            // use encoded version of all text
-            blockText = showdown.subParser('encodeCode')(globals.ghCodeBlocks[num].text, options, globals);
-          } else {
-            blockText = globals.ghCodeBlocks[num].codeblock;
-          }
-        }
-        blockText = blockText.replace(/\$/g, '$$$$'); // Escape any dollar signs
-
-        grafsOutIt = grafsOutIt.replace(/(\n\n)?¨(K|G)\d+\2(\n\n)?/, blockText);
-        // Check if grafsOutIt is a pre->code
-        if (/^]*>\s*]*>/.test(grafsOutIt)) {
-          codeFlag = true;
-        }
-      }
-      grafsOut[i] = grafsOutIt;
-    }
-    text = grafsOut.join('\n');
-    // Strip leading and trailing lines:
-    text = text.replace(/^\n+/g, '');
-    text = text.replace(/\n+$/g, '');
-    return globals.converter._dispatch('paragraphs.after', text, options, globals);
-  });
-
-  /**
-   * Run extension
-   */
-  showdown.subParser('runExtension', function (ext, text, options, globals) {
-    'use strict';
-
-    if (ext.filter) {
-      text = ext.filter(text, globals.converter, options);
-    } else if (ext.regex) {
-      // TODO remove this when old extension loading mechanism is deprecated
-      var re = ext.regex;
-      if (!(re instanceof RegExp)) {
-        re = new RegExp(re, 'g');
-      }
-      text = text.replace(re, ext.replace);
-    }
-
-    return text;
-  });
-
-  /**
-   * These are all the transformations that occur *within* block-level
-   * tags like paragraphs, headers, and list items.
-   */
-  showdown.subParser('spanGamut', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('spanGamut.before', text, options, globals);
-    text = showdown.subParser('codeSpans')(text, options, globals);
-    text = showdown.subParser('escapeSpecialCharsWithinTagAttributes')(text, options, globals);
-    text = showdown.subParser('encodeBackslashEscapes')(text, options, globals);
-
-    // Process anchor and image tags. Images must come first,
-    // because ![foo][f] looks like an anchor.
-    text = showdown.subParser('images')(text, options, globals);
-    text = showdown.subParser('anchors')(text, options, globals);
-
-    // Make links out of things like ``
-    // Must come after anchors, because you can use < and >
-    // delimiters in inline links like [this]().
-    text = showdown.subParser('autoLinks')(text, options, globals);
-    text = showdown.subParser('simplifiedAutoLinks')(text, options, globals);
-    text = showdown.subParser('emoji')(text, options, globals);
-    text = showdown.subParser('underline')(text, options, globals);
-    text = showdown.subParser('italicsAndBold')(text, options, globals);
-    text = showdown.subParser('strikethrough')(text, options, globals);
-    text = showdown.subParser('ellipsis')(text, options, globals);
-
-    // we need to hash HTML tags inside spans
-    text = showdown.subParser('hashHTMLSpans')(text, options, globals);
-
-    // now we encode amps and angles
-    text = showdown.subParser('encodeAmpsAndAngles')(text, options, globals);
-
-    // Do hard breaks
-    if (options.simpleLineBreaks) {
-      // GFM style hard breaks
-      // only add line breaks if the text does not contain a block (special case for lists)
-      if (!/\n\n¨K/.test(text)) {
-        text = text.replace(/\n+/g, '
    \n');
-      }
-    } else {
-      // Vanilla hard breaks
-      text = text.replace(/  +\n/g, '
    \n');
-    }
-
-    text = globals.converter._dispatch('spanGamut.after', text, options, globals);
-    return text;
-  });
-
-  showdown.subParser('strikethrough', function (text, options, globals) {
-    'use strict';
-
-    function parseInside(txt) {
-      if (options.simplifiedAutoLink) {
-        txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);
-      }
-      return '' + txt + '';
-    }
-
-    if (options.strikethrough) {
-      text = globals.converter._dispatch('strikethrough.before', text, options, globals);
-      text = text.replace(/(?:~){2}([\s\S]+?)(?:~){2}/g, function (wm, txt) {
-        return parseInside(txt);
-      });
-      text = globals.converter._dispatch('strikethrough.after', text, options, globals);
-    }
-
-    return text;
-  });
-
-  /**
-   * Strips link definitions from text, stores the URLs and titles in
-   * hash references.
-   * Link defs are in the form: ^[id]: url "optional title"
-   */
-  showdown.subParser('stripLinkDefinitions', function (text, options, globals) {
-    'use strict';
-
-    var regex = /^ {0,3}\[(.+)]:[ \t]*\n?[ \t]*\s]+)>?(?: =([*\d]+[A-Za-z%]{0,4})x([*\d]+[A-Za-z%]{0,4}))?[ \t]*\n?[ \t]*(?:(\n*)["|'(](.+?)["|')][ \t]*)?(?:\n+|(?=¨0))/gm,
-        base64Regex = /^ {0,3}\[(.+)]:[ \t]*\n?[ \t]*?(?: =([*\d]+[A-Za-z%]{0,4})x([*\d]+[A-Za-z%]{0,4}))?[ \t]*\n?[ \t]*(?:(\n*)["|'(](.+?)["|')][ \t]*)?(?:\n\n|(?=¨0)|(?=\n\[))/gm;
-
-    // attacklab: sentinel workarounds for lack of \A and \Z, safari\khtml bug
-    text += '¨0';
-
-    var replaceFunc = function replaceFunc(wholeMatch, linkId, url, width, height, blankLines, title) {
-      linkId = linkId.toLowerCase();
-      if (url.match(/^data:.+?\/.+?;base64,/)) {
-        // remove newlines
-        globals.gUrls[linkId] = url.replace(/\s/g, '');
-      } else {
-        globals.gUrls[linkId] = showdown.subParser('encodeAmpsAndAngles')(url, options, globals); // Link IDs are case-insensitive
-      }
-
-      if (blankLines) {
-        // Oops, found blank lines, so it's not a title.
-        // Put back the parenthetical statement we stole.
-        return blankLines + title;
-      } else {
-        if (title) {
-          globals.gTitles[linkId] = title.replace(/"|'/g, '"');
-        }
-        if (options.parseImgDimensions && width && height) {
-          globals.gDimensions[linkId] = {
-            width: width,
-            height: height
-          };
-        }
-      }
-      // Completely remove the definition from the text
-      return '';
-    };
-
-    // first we try to find base64 link references
-    text = text.replace(base64Regex, replaceFunc);
-
-    text = text.replace(regex, replaceFunc);
-
-    // attacklab: strip sentinel
-    text = text.replace(/¨0/, '');
-
-    return text;
-  });
-
-  showdown.subParser('tables', function (text, options, globals) {
-    'use strict';
-
-    if (!options.tables) {
-      return text;
-    }
-
-    var tableRgx = /^ {0,3}\|?.+\|.+\n {0,3}\|?[ \t]*:?[ \t]*(?:[-=]){2,}[ \t]*:?[ \t]*\|[ \t]*:?[ \t]*(?:[-=]){2,}[\s\S]+?(?:\n\n|¨0)/gm,
-
-    //singeColTblRgx = /^ {0,3}\|.+\|\n {0,3}\|[ \t]*:?[ \t]*(?:[-=]){2,}[ \t]*:?[ \t]*\|[ \t]*\n(?: {0,3}\|.+\|\n)+(?:\n\n|¨0)/gm;
-    singeColTblRgx = /^ {0,3}\|.+\|[ \t]*\n {0,3}\|[ \t]*:?[ \t]*(?:[-=]){2,}[ \t]*:?[ \t]*\|[ \t]*\n( {0,3}\|.+\|[ \t]*\n)*(?:\n|¨0)/gm;
-
-    function parseStyles(sLine) {
-      if (/^:[ \t]*--*$/.test(sLine)) {
-        return ' style="text-align:left;"';
-      } else if (/^--*[ \t]*:[ \t]*$/.test(sLine)) {
-        return ' style="text-align:right;"';
-      } else if (/^:[ \t]*--*[ \t]*:$/.test(sLine)) {
-        return ' style="text-align:center;"';
-      } else {
-        return '';
-      }
-    }
-
-    function parseHeaders(header, style) {
-      var id = '';
-      header = header.trim();
-      // support both tablesHeaderId and tableHeaderId due to error in documentation so we don't break backwards compatibility
-      if (options.tablesHeaderId || options.tableHeaderId) {
-        id = ' id="' + header.replace(/ /g, '_').toLowerCase() + '"';
-      }
-      header = showdown.subParser('spanGamut')(header, options, globals);
-
-      return '' + header + '\n';
-    }
-
-    function parseCells(cell, style) {
-      var subText = showdown.subParser('spanGamut')(cell, options, globals);
-      return '' + subText + '\n';
-    }
-
-    function buildTable(headers, cells) {
-      var tb = '\n\n\n',
-          tblLgn = headers.length;
-
-      for (var i = 0; i < tblLgn; ++i) {
-        tb += headers[i];
-      }
-      tb += '\n\n\n';
-
-      for (i = 0; i < cells.length; ++i) {
-        tb += '\n';
-        for (var ii = 0; ii < tblLgn; ++ii) {
-          tb += cells[i][ii];
-        }
-        tb += '\n';
-      }
-      tb += '\n
    \n';
-      return tb;
-    }
-
-    function parseTable(rawTable) {
-      var i,
-          tableLines = rawTable.split('\n');
-
-      for (i = 0; i < tableLines.length; ++i) {
-        // strip wrong first and last column if wrapped tables are used
-        if (/^ {0,3}\|/.test(tableLines[i])) {
-          tableLines[i] = tableLines[i].replace(/^ {0,3}\|/, '');
-        }
-        if (/\|[ \t]*$/.test(tableLines[i])) {
-          tableLines[i] = tableLines[i].replace(/\|[ \t]*$/, '');
-        }
-        // parse code spans first, but we only support one line code spans
-        tableLines[i] = showdown.subParser('codeSpans')(tableLines[i], options, globals);
-      }
-
-      var rawHeaders = tableLines[0].split('|').map(function (s) {
-        return s.trim();
-      }),
-          rawStyles = tableLines[1].split('|').map(function (s) {
-        return s.trim();
-      }),
-          rawCells = [],
-          headers = [],
-          styles = [],
-          cells = [];
-
-      tableLines.shift();
-      tableLines.shift();
-
-      for (i = 0; i < tableLines.length; ++i) {
-        if (tableLines[i].trim() === '') {
-          continue;
-        }
-        rawCells.push(tableLines[i].split('|').map(function (s) {
-          return s.trim();
-        }));
-      }
-
-      if (rawHeaders.length < rawStyles.length) {
-        return rawTable;
-      }
-
-      for (i = 0; i < rawStyles.length; ++i) {
-        styles.push(parseStyles(rawStyles[i]));
-      }
-
-      for (i = 0; i < rawHeaders.length; ++i) {
-        if (showdown.helper.isUndefined(styles[i])) {
-          styles[i] = '';
-        }
-        headers.push(parseHeaders(rawHeaders[i], styles[i]));
-      }
-
-      for (i = 0; i < rawCells.length; ++i) {
-        var row = [];
-        for (var ii = 0; ii < headers.length; ++ii) {
-          if (showdown.helper.isUndefined(rawCells[i][ii])) {}
-          row.push(parseCells(rawCells[i][ii], styles[ii]));
-        }
-        cells.push(row);
-      }
-
-      return buildTable(headers, cells);
-    }
-
-    text = globals.converter._dispatch('tables.before', text, options, globals);
-
-    // find escaped pipe characters
-    text = text.replace(/\\(\|)/g, showdown.helper.escapeCharactersCallback);
-
-    // parse multi column tables
-    text = text.replace(tableRgx, parseTable);
-
-    // parse one column tables
-    text = text.replace(singeColTblRgx, parseTable);
-
-    text = globals.converter._dispatch('tables.after', text, options, globals);
-
-    return text;
-  });
-
-  showdown.subParser('underline', function (text, options, globals) {
-    'use strict';
-
-    if (!options.underline) {
-      return text;
-    }
-
-    text = globals.converter._dispatch('underline.before', text, options, globals);
-
-    if (options.literalMidWordUnderscores) {
-      text = text.replace(/\b___(\S[\s\S]*?)___\b/g, function (wm, txt) {
-        return '' + txt + '';
-      });
-      text = text.replace(/\b__(\S[\s\S]*?)__\b/g, function (wm, txt) {
-        return '' + txt + '';
-      });
-    } else {
-      text = text.replace(/___(\S[\s\S]*?)___/g, function (wm, m) {
-        return (/\S$/.test(m) ? '' + m + '' : wm
-        );
-      });
-      text = text.replace(/__(\S[\s\S]*?)__/g, function (wm, m) {
-        return (/\S$/.test(m) ? '' + m + '' : wm
-        );
-      });
-    }
-
-    // escape remaining underscores to prevent them being parsed by italic and bold
-    text = text.replace(/(_)/g, showdown.helper.escapeCharactersCallback);
-
-    text = globals.converter._dispatch('underline.after', text, options, globals);
-
-    return text;
-  });
-
-  /**
-   * Swap back in all the special characters we've hidden.
-   */
-  showdown.subParser('unescapeSpecialChars', function (text, options, globals) {
-    'use strict';
-
-    text = globals.converter._dispatch('unescapeSpecialChars.before', text, options, globals);
-
-    text = text.replace(/¨E(\d+)E/g, function (wholeMatch, m1) {
-      var charCodeToReplace = parseInt(m1);
-      return String.fromCharCode(charCodeToReplace);
-    });
-
-    text = globals.converter._dispatch('unescapeSpecialChars.after', text, options, globals);
-    return text;
-  });
-
-  showdown.subParser('makeMarkdown.blockquote', function (node, globals) {
-    'use strict';
-
-    var txt = '';
-    if (node.hasChildNodes()) {
-      var children = node.childNodes,
-          childrenLength = children.length;
-
-      for (var i = 0; i < childrenLength; ++i) {
-        var innerTxt = showdown.subParser('makeMarkdown.node')(children[i], globals);
-
-        if (innerTxt === '') {
-          continue;
-        }
-        txt += innerTxt;
-      }
-    }
-    // cleanup
-    txt = txt.trim();
-    txt = '> ' + txt.split('\n').join('\n> ');
-    return txt;
-  });
-
-  showdown.subParser('makeMarkdown.codeBlock', function (node, globals) {
-    'use strict';
-
-    var lang = node.getAttribute('language'),
-        num = node.getAttribute('precodenum');
-    return '```' + lang + '\n' + globals.preList[num] + '\n```';
-  });
-
-  showdown.subParser('makeMarkdown.codeSpan', function (node) {
-    'use strict';
-
-    return '`' + node.innerHTML + '`';
-  });
-
-  showdown.subParser('makeMarkdown.emphasis', function (node, globals) {
-    'use strict';
-
-    var txt = '';
-    if (node.hasChildNodes()) {
-      txt += '*';
-      var children = node.childNodes,
-          childrenLength = children.length;
-      for (var i = 0; i < childrenLength; ++i) {
-        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);
-      }
-      txt += '*';
-    }
-    return txt;
-  });
-
-  showdown.subParser('makeMarkdown.header', function (node, globals, headerLevel) {
-    'use strict';
-
-    var headerMark = new Array(headerLevel + 1).join('#'),
-        txt = '';
-
-    if (node.hasChildNodes()) {
-      txt = headerMark + ' ';
-      var children = node.childNodes,
-          childrenLength = children.length;
-
-      for (var i = 0; i < childrenLength; ++i) {
-        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);
-      }
-    }
-    return txt;
-  });
-
-  showdown.subParser('makeMarkdown.hr', function () {
-    'use strict';
-
-    return '---';
-  });
-
-  showdown.subParser('makeMarkdown.image', function (node) {
-    'use strict';
-
-    var txt = '';
-    if (node.hasAttribute('src')) {
-      txt += '![' + node.getAttribute('alt') + '](';
-      txt += '<' + node.getAttribute('src') + '>';
-      if (node.hasAttribute('width') && node.hasAttribute('height')) {
-        txt += ' =' + node.getAttribute('width') + 'x' + node.getAttribute('height');
-      }
-
-      if (node.hasAttribute('title')) {
-        txt += ' "' + node.getAttribute('title') + '"';
-      }
-      txt += ')';
-    }
-    return txt;
-  });
-
-  showdown.subParser('makeMarkdown.links', function (node, globals) {
-    'use strict';
-
-    var txt = '';
-    if (node.hasChildNodes() && node.hasAttribute('href')) {
-      var children = node.childNodes,
-          childrenLength = children.length;
-      txt = '[';
-      for (var i = 0; i < childrenLength; ++i) {
-        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);
-      }
-      txt += '](';
-      txt += '<' + node.getAttribute('href') + '>';
-      if (node.hasAttribute('title')) {
-        txt += ' "' + node.getAttribute('title') + '"';
-      }
-      txt += ')';
-    }
-    return txt;
-  });
-
-  showdown.subParser('makeMarkdown.list', function (node, globals, type) {
-    'use strict';
-
-    var txt = '';
-    if (!node.hasChildNodes()) {
-      return '';
-    }
-    var listItems = node.childNodes,
-        listItemsLenght = listItems.length,
-        listNum = node.getAttribute('start') || 1;
-
-    for (var i = 0; i < listItemsLenght; ++i) {
-      if (typeof listItems[i].tagName === 'undefined' || listItems[i].tagName.toLowerCase() !== 'li') {
-        continue;
-      }
-
-      // define the bullet to use in list
-      var bullet = '';
-      if (type === 'ol') {
-        bullet = listNum.toString() + '. ';
-      } else {
-        bullet = '- ';
-      }
-
-      // parse list item
-      txt += bullet + showdown.subParser('makeMarkdown.listItem')(listItems[i], globals);
-      ++listNum;
-    }
-
-    // add comment at the end to prevent consecutive lists to be parsed as one
-    txt += '\n\n';
-    return txt.trim();
-  });
-
-  showdown.subParser('makeMarkdown.listItem', function (node, globals) {
-    'use strict';
-
-    var listItemTxt = '';
-
-    var children = node.childNodes,
-        childrenLenght = children.length;
-
-    for (var i = 0; i < childrenLenght; ++i) {
-      listItemTxt += showdown.subParser('makeMarkdown.node')(children[i], globals);
-    }
-    // if it's only one liner, we need to add a newline at the end
-    if (!/\n$/.test(listItemTxt)) {
-      listItemTxt += '\n';
-    } else {
-      // it's multiparagraph, so we need to indent
-      listItemTxt = listItemTxt.split('\n').join('\n    ').replace(/^ {4}$/gm, '').replace(/\n\n+/g, '\n\n');
-    }
-
-    return listItemTxt;
-  });
-
-  showdown.subParser('makeMarkdown.node', function (node, globals, spansOnly) {
-    'use strict';
-
-    spansOnly = spansOnly || false;
-
-    var txt = '';
-
-    // edge case of text without wrapper paragraph
-    if (node.nodeType === 3) {
-      return showdown.subParser('makeMarkdown.txt')(node, globals);
-    }
-
-    // HTML comment
-    if (node.nodeType === 8) {
-      return '\n\n';
-    }
-
-    // process only node elements
-    if (node.nodeType !== 1) {
-      return '';
-    }
-
-    var tagName = node.tagName.toLowerCase();
-
-    switch (tagName) {
-
-      //
-      // BLOCKS
-      //
-      case 'h1':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.header')(node, globals, 1) + '\n\n';
-        }
-        break;
-      case 'h2':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.header')(node, globals, 2) + '\n\n';
-        }
-        break;
-      case 'h3':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.header')(node, globals, 3) + '\n\n';
-        }
-        break;
-      case 'h4':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.header')(node, globals, 4) + '\n\n';
-        }
-        break;
-      case 'h5':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.header')(node, globals, 5) + '\n\n';
-        }
-        break;
-      case 'h6':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.header')(node, globals, 6) + '\n\n';
-        }
-        break;
-
-      case 'p':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.paragraph')(node, globals) + '\n\n';
-        }
-        break;
-
-      case 'blockquote':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.blockquote')(node, globals) + '\n\n';
-        }
-        break;
-
-      case 'hr':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.hr')(node, globals) + '\n\n';
-        }
-        break;
-
-      case 'ol':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ol') + '\n\n';
-        }
-        break;
-
-      case 'ul':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ul') + '\n\n';
-        }
-        break;
-
-      case 'precode':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.codeBlock')(node, globals) + '\n\n';
-        }
-        break;
-
-      case 'pre':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.pre')(node, globals) + '\n\n';
-        }
-        break;
-
-      case 'table':
-        if (!spansOnly) {
-          txt = showdown.subParser('makeMarkdown.table')(node, globals) + '\n\n';
-        }
-        break;
-
-      //
-      // SPANS
-      //
-      case 'code':
-        txt = showdown.subParser('makeMarkdown.codeSpan')(node, globals);
-        break;
-
-      case 'em':
-      case 'i':
-        txt = showdown.subParser('makeMarkdown.emphasis')(node, globals);
-        break;
-
-      case 'strong':
-      case 'b':
-        txt = showdown.subParser('makeMarkdown.strong')(node, globals);
-        break;
-
-      case 'del':
-        txt = showdown.subParser('makeMarkdown.strikethrough')(node, globals);
-        break;
-
-      case 'a':
-        txt = showdown.subParser('makeMarkdown.links')(node, globals);
-        break;
-
-      case 'img':
-        txt = showdown.subParser('makeMarkdown.image')(node, globals);
-        break;
-
-      default:
-        txt = node.outerHTML + '\n\n';
-    }
-
-    // common normalization
-    // TODO eventually
-
-    return txt;
-  });
-
-  showdown.subParser('makeMarkdown.paragraph', function (node, globals) {
-    'use strict';
-
-    var txt = '';
-    if (node.hasChildNodes()) {
-      var children = node.childNodes,
-          childrenLength = children.length;
-      for (var i = 0; i < childrenLength; ++i) {
-        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);
-      }
-    }
-
-    // some text normalization
-    txt = txt.trim();
-
-    return txt;
-  });
-
-  showdown.subParser('makeMarkdown.pre', function (node, globals) {
-    'use strict';
-
-    var num = node.getAttribute('prenum');
-    return '
    ' + globals.preList[num] + '
    ';
-  });
-
-  showdown.subParser('makeMarkdown.strikethrough', function (node, globals) {
-    'use strict';
-
-    var txt = '';
-    if (node.hasChildNodes()) {
-      txt += '~~';
-      var children = node.childNodes,
-          childrenLength = children.length;
-      for (var i = 0; i < childrenLength; ++i) {
-        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);
-      }
-      txt += '~~';
-    }
-    return txt;
-  });
-
-  showdown.subParser('makeMarkdown.strong', function (node, globals) {
-    'use strict';
-
-    var txt = '';
-    if (node.hasChildNodes()) {
-      txt += '**';
-      var children = node.childNodes,
-          childrenLength = children.length;
-      for (var i = 0; i < childrenLength; ++i) {
-        txt += showdown.subParser('makeMarkdown.node')(children[i], globals);
-      }
-      txt += '**';
-    }
-    return txt;
-  });
-
-  showdown.subParser('makeMarkdown.table', function (node, globals) {
-    'use strict';
-
-    var txt = '',
-        tableArray = [[], []],
-        headings = node.querySelectorAll('thead>tr>th'),
-        rows = node.querySelectorAll('tbody>tr'),
-        i,
-        ii;
-    for (i = 0; i < headings.length; ++i) {
-      var headContent = showdown.subParser('makeMarkdown.tableCell')(headings[i], globals),
-          allign = '---';
-
-      if (headings[i].hasAttribute('style')) {
-        var style = headings[i].getAttribute('style').toLowerCase().replace(/\s/g, '');
-        switch (style) {
-          case 'text-align:left;':
-            allign = ':---';
-            break;
-          case 'text-align:right;':
-            allign = '---:';
-            break;
-          case 'text-align:center;':
-            allign = ':---:';
-            break;
-        }
-      }
-      tableArray[0][i] = headContent.trim();
-      tableArray[1][i] = allign;
-    }
-
-    for (i = 0; i < rows.length; ++i) {
-      var r = tableArray.push([]) - 1,
-          cols = rows[i].getElementsByTagName('td');
-
-      for (ii = 0; ii < headings.length; ++ii) {
-        var cellContent = ' ';
-        if (typeof cols[ii] !== 'undefined') {
-          cellContent = showdown.subParser('makeMarkdown.tableCell')(cols[ii], globals);
-        }
-        tableArray[r].push(cellContent);
-      }
-    }
-
-    var cellSpacesCount = 3;
-    for (i = 0; i < tableArray.length; ++i) {
-      for (ii = 0; ii < tableArray[i].length; ++ii) {
-        var strLen = tableArray[i][ii].length;
-        if (strLen > cellSpacesCount) {
-          cellSpacesCount = strLen;
-        }
-      }
-    }
-
-    for (i = 0; i < tableArray.length; ++i) {
-      for (ii = 0; ii < tableArray[i].length; ++ii) {
-        if (i === 1) {
-          if (tableArray[i][ii].slice(-1) === ':') {
-            tableArray[i][ii] = showdown.helper.padEnd(tableArray[i][ii].slice(-1), cellSpacesCount - 1, '-') + ':';
-          } else {
-            tableArray[i][ii] = showdown.helper.padEnd(tableArray[i][ii], cellSpacesCount, '-');
-          }
-        } else {
-          tableArray[i][ii] = showdown.helper.padEnd(tableArray[i][ii], cellSpacesCount);
-        }
-      }
-      txt += '| ' + tableArray[i].join(' | ') + ' |\n';
-    }
-
-    return txt.trim();
-  });
-
-  showdown.subParser('makeMarkdown.tableCell', function (node, globals) {
-    'use strict';
-
-    var txt = '';
-    if (!node.hasChildNodes()) {
-      return '';
-    }
-    var children = node.childNodes,
-        childrenLength = children.length;
-
-    for (var i = 0; i < childrenLength; ++i) {
-      txt += showdown.subParser('makeMarkdown.node')(children[i], globals, true);
-    }
-    return txt.trim();
-  });
-
-  showdown.subParser('makeMarkdown.txt', function (node) {
-    'use strict';
-
-    var txt = node.nodeValue;
-
-    // multiple spaces are collapsed
-    txt = txt.replace(/ +/g, ' ');
-
-    // replace the custom ¨NBSP; with a space
-    txt = txt.replace(/¨NBSP;/g, ' ');
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-    // ", <, > and & should replace escaped html entities
-    txt = showdown.helper.unescapeHTMLEntities(txt);
-
-    // escape markdown magic characters
-    // emphasis, strong and strikethrough - can appear everywhere
-    // we also escape pipe (|) because of tables
-    // and escape ` because of code blocks and spans
-    txt = txt.replace(/([*_~|`])/g, '\\$1');
-
-    // escape > because of blockquotes
-    txt = txt.replace(/^(\s*)>/g, '\\$1>');
-
-    // hash character, only troublesome at the beginning of a line because of headers
-    txt = txt.replace(/^#/gm, '\\#');
-
-    // horizontal rules
-    txt = txt.replace(/^(\s*)([-=]{3,})(\s*)$/, '$1\\$2$3');
-
-    // dot, because of ordered lists, only troublesome at the beginning of a line when preceded by an integer
-    txt = txt.replace(/^( {0,3}\d+)\./gm, '$1\\.');
-
-    // +, * and -, at the beginning of a line becomes a list, so we need to escape them also (asterisk was already escaped)
-    txt = txt.replace(/^( {0,3})([+-])/gm, '$1\\$2');
-
-    // images and links, ] followed by ( is problematic, so we escape it
-    txt = txt.replace(/]([\s]*)\(/g, '\\]$1\\(');
-
-    // reference URIs must also be escaped
-    txt = txt.replace(/^ {0,3}\[([\S \t]*?)]:/gm, '\\[$1]:');
-
-    return txt;
-  });
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-  var root = this;
-
-  // AMD Loader
-  if (true) {
-    !(__WEBPACK_AMD_DEFINE_RESULT__ = (function () {
-      'use strict';
-
-      return showdown;
-    }).call(exports, __webpack_require__, exports, module),
-				__WEBPACK_AMD_DEFINE_RESULT__ !== undefined && (module.exports = __WEBPACK_AMD_DEFINE_RESULT__));
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-    // CommonJS/nodeJS Loader
-  } else if (typeof module !== 'undefined' && module.exports) {
-    module.exports = showdown;
-
-    // Regular Browser loader
-  } else {
-    root.showdown = showdown;
-  }
-}).call(this);
-
-//# sourceMappingURL=showdown.js.map
-
-/***/ }),
-
-/***/ "J9SO":
-/***/ (function(module, exports) {
-
-// removed by extract-text-webpack-plugin
-module.exports = {"thesis":"thesis__3uAQ4"};
-
-/***/ }),
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-/***/ "JkW7":
-/***/ (function(module, __webpack_exports__, __webpack_require__) {
-
-"use strict";
-Object.defineProperty(__webpack_exports__, "__esModule", { value: true });
-
-// EXTERNAL MODULE: ../node_modules/preact/dist/preact.min.js
-var preact_min = __webpack_require__("KM04");
-var preact_min_default = /*#__PURE__*/__webpack_require__.n(preact_min);
-
-// EXTERNAL MODULE: ./index.css
-var index = __webpack_require__("xHuH");
-var index_default = /*#__PURE__*/__webpack_require__.n(index);
-
-// EXTERNAL MODULE: ./manifest.json
-var manifest = __webpack_require__("ZcXo");
-var manifest_default = /*#__PURE__*/__webpack_require__.n(manifest);
-
-// CONCATENATED MODULE: ../node_modules/preact-router/dist/preact-router.es.js
-
-
-var EMPTY$1 = {};
-
-function preact_router_es_assign(obj, props) {
-	// eslint-disable-next-line guard-for-in
-	for (var i in props) {
-		obj[i] = props[i];
-	}
-	return obj;
-}
-
-function exec(url, route, opts) {
-	var reg = /(?:\?([^#]*))?(#.*)?$/,
-	    c = url.match(reg),
-	    matches = {},
-	    ret;
-	if (c && c[1]) {
-		var p = c[1].split('&');
-		for (var i = 0; i < p.length; i++) {
-			var r = p[i].split('=');
-			matches[decodeURIComponent(r[0])] = decodeURIComponent(r.slice(1).join('='));
-		}
-	}
-	url = segmentize(url.replace(reg, ''));
-	route = segmentize(route || '');
-	var max = Math.max(url.length, route.length);
-	for (var i$1 = 0; i$1 < max; i$1++) {
-		if (route[i$1] && route[i$1].charAt(0) === ':') {
-			var param = route[i$1].replace(/(^\:|[+*?]+$)/g, ''),
-			    flags = (route[i$1].match(/[+*?]+$/) || EMPTY$1)[0] || '',
-			    plus = ~flags.indexOf('+'),
-			    star = ~flags.indexOf('*'),
-			    val = url[i$1] || '';
-			if (!val && !star && (flags.indexOf('?') < 0 || plus)) {
-				ret = false;
-				break;
-			}
-			matches[param] = decodeURIComponent(val);
-			if (plus || star) {
-				matches[param] = url.slice(i$1).map(decodeURIComponent).join('/');
-				break;
-			}
-		} else if (route[i$1] !== url[i$1]) {
-			ret = false;
-			break;
-		}
-	}
-	if (opts.default !== true && ret === false) {
-		return false;
-	}
-	return matches;
-}
-
-function pathRankSort(a, b) {
-	return a.rank < b.rank ? 1 : a.rank > b.rank ? -1 : a.index - b.index;
-}
-
-// filter out VNodes without attributes (which are unrankeable), and add `index`/`rank` properties to be used in sorting.
-function prepareVNodeForRanking(vnode, index) {
-	vnode.index = index;
-	vnode.rank = rankChild(vnode);
-	return vnode.attributes;
-}
-
-function segmentize(url) {
-	return url.replace(/(^\/+|\/+$)/g, '').split('/');
-}
-
-function rankSegment(segment) {
-	return segment.charAt(0) == ':' ? 1 + '*+?'.indexOf(segment.charAt(segment.length - 1)) || 4 : 5;
-}
-
-function rank(path) {
-	return segmentize(path).map(rankSegment).join('');
-}
-
-function rankChild(vnode) {
-	return vnode.attributes.default ? 0 : rank(vnode.attributes.path);
-}
-
-var customHistory = null;
-
-var ROUTERS = [];
-
-var subscribers = [];
-
-var EMPTY = {};
-
-function isPreactElement(node) {
-	return node.__preactattr_ != null || typeof Symbol !== 'undefined' && node[Symbol.for('preactattr')] != null;
-}
-
-function setUrl(url, type) {
-	if (type === void 0) type = 'push';
-
-	if (customHistory && customHistory[type]) {
-		customHistory[type](url);
-	} else if (typeof history !== 'undefined' && history[type + 'State']) {
-		history[type + 'State'](null, null, url);
-	}
-}
-
-function getCurrentUrl() {
-	var url;
-	if (customHistory && customHistory.location) {
-		url = customHistory.location;
-	} else if (customHistory && customHistory.getCurrentLocation) {
-		url = customHistory.getCurrentLocation();
-	} else {
-		url = typeof location !== 'undefined' ? location : EMPTY;
-	}
-	return "" + (url.pathname || '') + (url.search || '');
-}
-
-function route(url, replace) {
-	if (replace === void 0) replace = false;
-
-	if (typeof url !== 'string' && url.url) {
-		replace = url.replace;
-		url = url.url;
-	}
-
-	// only push URL into history if we can handle it
-	if (canRoute(url)) {
-		setUrl(url, replace ? 'replace' : 'push');
-	}
-
-	return routeTo(url);
-}
-
-/** Check if the given URL can be handled by any router instances. */
-function canRoute(url) {
-	for (var i = ROUTERS.length; i--;) {
-		if (ROUTERS[i].canRoute(url)) {
-			return true;
-		}
-	}
-	return false;
-}
-
-/** Tell all router instances to handle the given URL.  */
-function routeTo(url) {
-	var didRoute = false;
-	for (var i = 0; i < ROUTERS.length; i++) {
-		if (ROUTERS[i].routeTo(url) === true) {
-			didRoute = true;
-		}
-	}
-	for (var i$1 = subscribers.length; i$1--;) {
-		subscribers[i$1](url);
-	}
-	return didRoute;
-}
-
-function routeFromLink(node) {
-	// only valid elements
-	if (!node || !node.getAttribute) {
-		return;
-	}
-
-	var href = node.getAttribute('href'),
-	    target = node.getAttribute('target');
-
-	// ignore links with targets and non-path URLs
-	if (!href || !href.match(/^\//g) || target && !target.match(/^_?self$/i)) {
-		return;
-	}
-
-	// attempt to route, if no match simply cede control to browser
-	return route(href);
-}
-
-function handleLinkClick(e) {
-	if (e.button == 0) {
-		routeFromLink(e.currentTarget || e.target || this);
-		return prevent(e);
-	}
-}
-
-function prevent(e) {
-	if (e) {
-		if (e.stopImmediatePropagation) {
-			e.stopImmediatePropagation();
-		}
-		if (e.stopPropagation) {
-			e.stopPropagation();
-		}
-		e.preventDefault();
-	}
-	return false;
-}
-
-function delegateLinkHandler(e) {
-	// ignore events the browser takes care of already:
-	if (e.ctrlKey || e.metaKey || e.altKey || e.shiftKey || e.button !== 0) {
-		return;
-	}
-
-	var t = e.target;
-	do {
-		if (String(t.nodeName).toUpperCase() === 'A' && t.getAttribute('href') && isPreactElement(t)) {
-			if (t.hasAttribute('native')) {
-				return;
-			}
-			// if link is handled by the router, prevent browser defaults
-			if (routeFromLink(t)) {
-				return prevent(e);
-			}
-		}
-	} while (t = t.parentNode);
-}
-
-var eventListenersInitialized = false;
-
-function initEventListeners() {
-	if (eventListenersInitialized) {
-		return;
-	}
-
-	if (typeof addEventListener === 'function') {
-		if (!customHistory) {
-			addEventListener('popstate', function () {
-				routeTo(getCurrentUrl());
-			});
-		}
-		addEventListener('click', delegateLinkHandler);
-	}
-	eventListenersInitialized = true;
-}
-
-var preact_router_es_Router = function (Component$$1) {
-	function Router(props) {
-		Component$$1.call(this, props);
-		if (props.history) {
-			customHistory = props.history;
-		}
-
-		this.state = {
-			url: props.url || getCurrentUrl()
-		};
-
-		initEventListeners();
-	}
-
-	if (Component$$1) Router.__proto__ = Component$$1;
-	Router.prototype = Object.create(Component$$1 && Component$$1.prototype);
-	Router.prototype.constructor = Router;
-
-	Router.prototype.shouldComponentUpdate = function shouldComponentUpdate(props) {
-		if (props.static !== true) {
-			return true;
-		}
-		return props.url !== this.props.url || props.onChange !== this.props.onChange;
-	};
-
-	/** Check if the given URL can be matched against any children */
-	Router.prototype.canRoute = function canRoute(url) {
-		return this.getMatchingChildren(this.props.children, url, false).length > 0;
-	};
-
-	/** Re-render children with a new URL to match against. */
-	Router.prototype.routeTo = function routeTo(url) {
-		this._didRoute = false;
-		this.setState({ url: url });
-
-		// if we're in the middle of an update, don't synchronously re-route.
-		if (this.updating) {
-			return this.canRoute(url);
-		}
-
-		this.forceUpdate();
-		return this._didRoute;
-	};
-
-	Router.prototype.componentWillMount = function componentWillMount() {
-		ROUTERS.push(this);
-		this.updating = true;
-	};
-
-	Router.prototype.componentDidMount = function componentDidMount() {
-		var this$1 = this;
-
-		if (customHistory) {
-			this.unlisten = customHistory.listen(function (location) {
-				this$1.routeTo("" + (location.pathname || '') + (location.search || ''));
-			});
-		}
-		this.updating = false;
-	};
-
-	Router.prototype.componentWillUnmount = function componentWillUnmount() {
-		if (typeof this.unlisten === 'function') {
-			this.unlisten();
-		}
-		ROUTERS.splice(ROUTERS.indexOf(this), 1);
-	};
-
-	Router.prototype.componentWillUpdate = function componentWillUpdate() {
-		this.updating = true;
-	};
-
-	Router.prototype.componentDidUpdate = function componentDidUpdate() {
-		this.updating = false;
-	};
-
-	Router.prototype.getMatchingChildren = function getMatchingChildren(children, url, invoke) {
-		return children.filter(prepareVNodeForRanking).sort(pathRankSort).map(function (vnode) {
-			var matches = exec(url, vnode.attributes.path, vnode.attributes);
-			if (matches) {
-				if (invoke !== false) {
-					var newProps = { url: url, matches: matches };
-					preact_router_es_assign(newProps, matches);
-					delete newProps.ref;
-					delete newProps.key;
-					return Object(preact_min["cloneElement"])(vnode, newProps);
-				}
-				return vnode;
-			}
-		}).filter(Boolean);
-	};
-
-	Router.prototype.render = function render(ref, ref$1) {
-		var children = ref.children;
-		var onChange = ref.onChange;
-		var url = ref$1.url;
-
-		var active = this.getMatchingChildren(children, url, true);
-
-		var current = active[0] || null;
-		this._didRoute = !!current;
-
-		var previous = this.previousUrl;
-		if (url !== previous) {
-			this.previousUrl = url;
-			if (typeof onChange === 'function') {
-				onChange({
-					router: this,
-					url: url,
-					previous: previous,
-					active: active,
-					current: current
-				});
-			}
-		}
-
-		return current;
-	};
-
-	return Router;
-}(preact_min["Component"]);
-
-var preact_router_es_Link = function Link(props) {
-	return Object(preact_min["h"])('a', preact_router_es_assign({ onClick: handleLinkClick }, props));
-};
-
-var preact_router_es_Route = function Route(props) {
-	return Object(preact_min["h"])(props.component, props);
-};
-
-preact_router_es_Router.subscribers = subscribers;
-preact_router_es_Router.getCurrentUrl = getCurrentUrl;
-preact_router_es_Router.route = route;
-preact_router_es_Router.Router = preact_router_es_Router;
-preact_router_es_Router.Route = preact_router_es_Route;
-preact_router_es_Router.Link = preact_router_es_Link;
-
-/* harmony default export */ var preact_router_es = (preact_router_es_Router);
-//# sourceMappingURL=preact-router.es.js.map
-// EXTERNAL MODULE: ./pages/home.css
-var home = __webpack_require__("36Ou");
-var home_default = /*#__PURE__*/__webpack_require__.n(home);
-
-// EXTERNAL MODULE: ./components/panel.css
-var panel = __webpack_require__("P9k+");
-var panel_default = /*#__PURE__*/__webpack_require__.n(panel);
-
-// CONCATENATED MODULE: ./components/panel.js
-
-
-function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
-
-function _possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
-
-function _inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
-
-
-
-
-var panel_Panel = function (_Component) {
-	_inherits(Panel, _Component);
-
-	function Panel() {
-		_classCallCheck(this, Panel);
-
-		return _possibleConstructorReturn(this, _Component.apply(this, arguments));
-	}
-
-	Panel.prototype.getStyle = function getStyle() {
-		return panel_default.a.panel;
-	};
-
-	Panel.prototype.render = function render() {
-		var title = null;
-		if (this.props.title !== undefined) {
-			title = Object(preact_min["h"])(
-				"h3",
-				null,
-				this.props.title
-			);
-		}
-
-		return Object(preact_min["h"])(
-			"div",
-			{ "class": this.getStyle(), id: this.props.id },
-			title,
-			this.props.children
-		);
-	};
-
-	return Panel;
-}(preact_min["Component"]);
-
-
-// EXTERNAL MODULE: ./components/split.css
-var split = __webpack_require__("1EpE");
-var split_default = /*#__PURE__*/__webpack_require__.n(split);
-
-// CONCATENATED MODULE: ./components/split.js
-
-
-function split__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
-
-function split__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
-
-function split__inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
-
-
-
-
-var split_Split = function (_Component) {
-    split__inherits(Split, _Component);
-
-    function Split() {
-        split__classCallCheck(this, Split);
-
-        return split__possibleConstructorReturn(this, _Component.apply(this, arguments));
-    }
-
-    Split.prototype.render = function render() {
-        var title = null;
-        if (this.props.title !== undefined) {
-            title = Object(preact_min["h"])(
-                "h2",
-                null,
-                this.props.title
-            );
-        }
-
-        var children = void 0;
-        if (Array.isArray(this.props.children)) {
-            children = this.props.children.map(function (element) {
-                return Object(preact_min["h"])(
-                    "div",
-                    { "class": split_default.a.splitchild },
-                    element
-                );
-            });
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-                { href: 'http://personale.unimore.it/rubrica/contenutiad/gcabri/2019/58026/N0/N0/9999' },
-                'Programmazione ad Oggetti'
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-            Object(preact_min["h"])(
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-            Object(preact_min["h"])(
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-                'Unimore'
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-                { href: 'https://www.unimore.it/didattica/mlaurea.html?ID=54' },
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-                { href: 'https://personale.unimore.it/rubrica/dettaglio/mmontangero' },
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-        null,
-        '(L\'ampiezza di una sinusoide.)'
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-    'Indica quanto in fretta cambia la posizione del corpo.'
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-var _ref48 = Object(preact_min["h"])(
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-    'Quanto cambia la fase nel tempo.'
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-    'Si applicano le formule per la circonferenza:'
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-    'Un corpo ha energia cinetica in ogni momento uguale a:'
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-    'p',
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-    'Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all\'arrivo.'
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-        'non'
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-    null,
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-var _ref64 = Object(preact_min["h"])(
-    'p',
-    null,
-    '\xC8 la velocit\xE0 di trasferimento di energia:'
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-var _ref65 = Object(preact_min["h"])(
-    'p',
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-        'positiva'
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-        'negativa'
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-var _ref66 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Si conserva: in un sistema chiuso la carica totale \xE8 costante.'
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-var _ref67 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Cariche ',
-    Object(preact_min["h"])(
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-        null,
-        'opp'
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-    Object(preact_min["h"])(
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-        null,
-        'oste'
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-    ' si attraggono; cariche ',
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-        null,
-        'uguali'
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-    ' si respingono.'
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-            null,
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-                'i',
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-            'p',
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-            'Mettendo a terra il conduttore, nuove cariche del ',
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-            'p',
-            null,
-            'Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritrover\xE0 ',
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-    'p',
-    null,
-    'Due corpi carichi si attraggono tra loro con forza:'
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-    'i',
-    null,
-    'costante di Coulomb'
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-    'i',
-    null,
-    'permeabilit\xE0 del vuoto'
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-var _ref75 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Misura che forza viene applicata in ogni punto su una carica unitaria:'
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-var _ref76 = Object(preact_min["h"])(
-    'p',
-    null,
-    '\xC8 la differenza tra "quanto" campo elettrico ',
-    Object(preact_min["h"])(
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-        'entra'
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-        'esce'
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-    null,
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-var _ref85 = Object(preact_min["h"])(
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-    null,
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-        null,
-        '(intensit\xE0)'
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-    null,
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-    'p',
-    null,
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-    'Possiamo calcolare la potenza di un circuito:'
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-
-var _ref95 = Object(preact_min["h"])(
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-
-var _ref99 = Object(preact_min["h"])(
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-var _ref101 = Object(preact_min["h"])(
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-
-var _ref102 = Object(preact_min["h"])(
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-var _ref103 = Object(preact_min["h"])(
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-var _ref105 = Object(preact_min["h"])(
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-            'In una maglia chiusa, la somma delle differenze di potenziale \xE8 0.'
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-            'Parti di circuito in parallelo hanno la stessa differenza di potenziale.'
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-var _ref109 = Object(preact_min["h"])(
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-    null,
-    'Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:'
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-
-var _ref110 = Object(preact_min["h"])(
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-
-var _ref111 = Object(preact_min["h"])(
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-
-var _ref112 = Object(preact_min["h"])(
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-    null,
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-var _ref113 = Object(preact_min["h"])(
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-    null,
-    'Come un campo elettrico, ma per i magneti.'
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-var _ref114 = Object(preact_min["h"])(
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-var _ref115 = Object(preact_min["h"])(
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-
-var _ref116 = Object(preact_min["h"])(
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-    'Per qualsiasi percorso chiuso, il flusso magnetico \xE8 uguale alla somma di tutti i "sottoflussi" magnetici calcolati sui suoi lati.'
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-var _ref117 = Object(preact_min["h"])(
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-        null,
-        'Ovvero, non esistono monopoli magnetici.'
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-
-var _ref118 = Object(preact_min["h"])(
-    'p',
-    null,
-    'L\'intensit\xE0 di corrente che attraversa un percorso chiuso \xE8 direttamente proporzionale al flusso magnetico dello stesso percorso.'
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-var _ref119 = Object(preact_min["h"])(
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-
-var _ref120 = Object(preact_min["h"])(
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-    'I campi magnetici applicano una forza sulle cariche vicine:'
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-var _ref121 = Object(preact_min["h"])(
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-    'Si ha una forza massima se la velocit\xE0 \xE8 perpendicolare al campo magnetico.'
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-    null,
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-
-var _ref123 = Object(preact_min["h"])(
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-    'I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:'
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-
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-    'a',
-    { href: 'https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360' },
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-
-var _ref125 = Object(preact_min["h"])(
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-var _ref126 = Object(preact_min["h"])(
-    'p',
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-    'Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.'
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-var _ref127 = Object(preact_min["h"])(
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-    null,
-    'All\'interno del solenoide si crea un campo (quasi) uniforme:'
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-
-var _ref128 = Object(preact_min["h"])(
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-var _ref129 = Object(preact_min["h"])(
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-
-var _ref130 = Object(preact_min["h"])(
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-    'Il campo magnetico cos\xEC creato gira attorno al filo in senso antiorario.'
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-var _ref131 = Object(preact_min["h"])(
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-        'opp'
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-        'oste'
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-var _ref132 = Object(preact_min["h"])(
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-    null,
-    'Un conduttore perpendicolare ad un campo magnetico pu\xF2 ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo.'
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-    null,
-    'La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore.'
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-var _ref134 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Essa vale:'
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-
-var _ref135 = Object(preact_min["h"])(
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-    'Dove ',
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-        'B'
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-    ' \xE8 l\'intensit\xE0 del campo magnetico ed ',
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-        'L'
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-
-var _ref136 = Object(preact_min["h"])(
-    'i',
-    null,
-    'Legge di Faraday-Neumann-Lenz'
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-
-var _ref137 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.'
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-var _ref138 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Il meno \xE8 dovuto alla ',
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-    'p',
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-        'Correnti o campi elettrici variabili creano un campo magnetico.'
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-
-var _ref141 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Si dice quindi che sono ',
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-        'i',
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-
-var _ref142 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Esse sono legate dalla relazione:'
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-    'p',
-    null,
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-        'a',
-        { href: 'https://it.wikipedia.org/wiki/Spettro_continuo' },
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-
-var _ref144 = Object(preact_min["h"])(
-    'p',
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-
-var _ref145 = Object(preact_min["h"])(
-    'p',
-    null,
-    'In un gas di idrogeno, le lunghezze d\'onda emesse sono ricavabili con:'
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-
-var _ref146 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Una grandezza si dice quantizzata (o discreta) se pu\xF2 assumere solo determinati valori.'
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-
-var _ref147 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Una grandezza si dice continua se pu\xF2 assumere qualsiasi valore e quindi se non \xE8 quantizzata.'
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-var _ref148 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Energia, momento angolare e raggio sono quantizzati.'
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-
-var _ref149 = Object(preact_min["h"])(
-    'p',
-    null,
-    'L\'energia degli elettroni \xE8 quantizzata.'
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-
-var _ref150 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Inoltre, per essi \xE8 valido che:'
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-
-var _ref151 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Ancora, il raggio delle orbite \xE8 uguale a:'
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-
-var _ref152 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Infine, in ogni stato, l\'energia \xE8 pari a:'
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-
-var _ref153 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Due elettroni non possono occupare lo stesso stato.'
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-
-var _ref154 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di'
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-            'p',
-            null,
-            'Possono per\xF2 comunque avere dei gap dovuti agli intervalli di energia non ammessi.'
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-var _ref156 = Object(preact_min["h"])(
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-var _ref157 = Object(preact_min["h"])(
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-    'Se invece la banda di emissione si sovrappone a un altra, allora il corpo \xE8 un conduttore.'
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-        'Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterr\xE0:'
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-            null,
-            'Con numero atomico minore, un semiconduttore di ',
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-            Object(preact_min["h"])(
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-        'Aumentando la temperatura di un semiconduttore si aumenta la conduttivit\xE0, perch\xE8 eccita le particelle e favorisce il movimento di ',
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-
-var _ref161 = Object(preact_min["h"])(
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-    'Ottica ',
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-var _ref162 = Object(preact_min["h"])(
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-var vldigeometria__templateObject = vldigeometria__taggedTemplateLiteralLoose(['\nTutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell\'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).\n\nPer comodit\xE0, ho estratto l\'url sorgente del video dall\'embed presente nella rispettiva pagina.\n\n1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\n11. [Propriet\xE0 delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\n13. [Propriet\xE0 e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\n20. [Teorema diagonalizzabilit\xE0](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\n\nNell\'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\n                    '], ['\nTutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell\'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).\n\nPer comodit\xE0, ho estratto l\'url sorgente del video dall\'embed presente nella rispettiva pagina.\n\n1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\n11. [Propriet\xE0 delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\n13. [Propriet\xE0 e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\n20. [Teorema diagonalizzabilit\xE0](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\n\nNell\'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\n                    ']);
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-
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-function vldigeometria__taggedTemplateLiteralLoose(strings, raw) { strings.raw = raw; return strings; }
-
-function vldigeometria__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
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-function vldigeometria__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
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-function vldigeometria__inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
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-var vldigeometria_r = String.raw;
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-	function VlDiGeometria() {
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-		return vldigeometria__possibleConstructorReturn(this, _Component.apply(this, arguments));
-	}
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-	VlDiGeometria.prototype.render = function render() {
-		//Imported from unimore-info-wiki
-		return Object(preact_min["h"])(
-			'div',
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-			vldigeometria__ref,
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-				)
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-			'l\'installer ufficiale'
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-	Object(preact_min["h"])('img', { src: 'https://i.imgur.com/mDZSqjV.png', alt: '' }),
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-	Object(preact_min["h"])(
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-		Object(preact_min["h"])(
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-		'. Premetelo.'
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-	Object(preact_min["h"])(
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-	Object(preact_min["h"])(
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-	Object(preact_min["h"])(
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-		' Lasciate che scarichi, ci vorr\xE0 un po\'. Guardatevi un video nel frattempo, fatevi una partitina a qualcosa, tornate dopo circa 10 minuti.'
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-	Object(preact_min["h"])(
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-		' Una volta installato, dobbiamo aggiungere ',
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-		Object(preact_min["h"])(
-			'i',
-			null,
-			'Propriet\xE0 del Sistema'
-		),
-		', premete ',
-		Object(preact_min["h"])(
-			'code',
-			null,
-			'Variabili d\'ambiente'
-		),
-		'.'
-	),
-	Object(preact_min["h"])('img', { src: 'https://i.imgur.com/FjYpT1n.png', alt: '' }),
-	Object(preact_min["h"])(
-		'p',
-		null,
-		' Trovate la variabile d\'ambiente globale ',
-		Object(preact_min["h"])(
-			'code',
-			null,
-			'Path'
-		),
-		', e fateci doppio click per modificarla.'
-	),
-	Object(preact_min["h"])('img', { src: 'https://i.imgur.com/klZQ9So.png', alt: '' }),
-	Object(preact_min["h"])(
-		'p',
-		null,
-		' Ora dovreste vedere l\'elenco di tutte le cartelle contenenti programmi eseguibili da terminale: dobbiamo aggiungere quella di MinGW! Premete ',
-		Object(preact_min["h"])(
-			'code',
-			null,
-			'Sfoglia'
-		),
-		'.'
-	),
-	Object(preact_min["h"])('img', { src: 'https://i.imgur.com/F6lBCqS.png', alt: '' }),
-	Object(preact_min["h"])(
-		'p',
-		null,
-		' Trovate la cartella in cui avete installato MinGW (vi avevo detto di ricordarvela!); entrateci, poi selezionate la sottocartella ',
-		Object(preact_min["h"])(
-			'code',
-			null,
-			'bin'
-		),
-		' e premete ',
-		Object(preact_min["h"])(
-			'code',
-			null,
-			'OK'
-		),
-		' su tutte le finestre che avete aperto fino ad ora, chiudendole.'
-	),
-	Object(preact_min["h"])(
-		'p',
-		null,
-		' Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione',
-		Object(preact_min["h"])(
-			'code',
-			null,
-			'gcc'
-		),
-		' e ',
-		Object(preact_min["h"])(
-			'code',
-			null,
-			'g++'
-		),
-		' sul Prompt dei Comandi, e potete finalmente creare dei file .exe! '
-	)
-);
-
-var mingwinstall_MingwInstall = function (_Component) {
-	mingwinstall__inherits(MingwInstall, _Component);
-
-	function MingwInstall() {
-		mingwinstall__classCallCheck(this, MingwInstall);
-
-		return mingwinstall__possibleConstructorReturn(this, _Component.apply(this, arguments));
-	}
-
-	MingwInstall.prototype.render = function render() {
-		//Imported from unimore-info-wiki
-		return Object(preact_min["h"])(
-			'div',
-			{ style: mingwinstall_default.a.mingwinstall },
-			mingwinstall__ref,
-			mingwinstall__ref2
-		);
-	};
-
-	return MingwInstall;
-}(preact_min["Component"]);
-
-
-// EXTERNAL MODULE: ./components/copyright.css
-var copyright = __webpack_require__("qMTX");
-var copyright_default = /*#__PURE__*/__webpack_require__.n(copyright);
-
-// CONCATENATED MODULE: ./components/copyright.js
-
-
-function copyright__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
-
-function copyright__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
-
-function copyright__inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
-
-
-
-
-var copyright__ref = Object(preact_min["h"])(
-	'a',
-	{ href: 'https://creativecommons.org/licenses/by-sa/4.0/' },
-	'CC BY-SA 4.0'
-);
-
-var copyright__ref2 = Object(preact_min["h"])(
-	'a',
-	{ href: 'https://github.com/Steffo99/appuntiweb' },
-	'Codice sorgente'
-);
-
-var copyright_Copyright = function (_Component) {
-	copyright__inherits(Copyright, _Component);
-
-	function Copyright() {
-		copyright__classCallCheck(this, Copyright);
-
-		return copyright__possibleConstructorReturn(this, _Component.apply(this, arguments));
-	}
-
-	Copyright.prototype.render = function render() {
-		return Object(preact_min["h"])(
-			'div',
-			{ 'class': copyright_default.a.copyright },
-			'\xA9 2019 - Stefano Pigozzi - ',
-			copyright__ref,
-			' - ',
-			copyright__ref2
-		);
-	};
-
-	return Copyright;
-}(preact_min["Component"]);
-
-
-// EXTERNAL MODULE: ./pages/statistica.css
-var statistica = __webpack_require__("WViY");
-var statistica_default = /*#__PURE__*/__webpack_require__.n(statistica);
-
-// EXTERNAL MODULE: ./components/theorem.css
-var theorem = __webpack_require__("oNmJ");
-var theorem_default = /*#__PURE__*/__webpack_require__.n(theorem);
-
-// CONCATENATED MODULE: ./components/theorem.js
-function theorem__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
-
-function theorem__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
-
-function theorem__inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
-
-
-
-
-var theorem_Theorem = function (_Panel) {
-    theorem__inherits(Theorem, _Panel);
-
-    function Theorem() {
-        theorem__classCallCheck(this, Theorem);
-
-        return theorem__possibleConstructorReturn(this, _Panel.apply(this, arguments));
-    }
-
-    Theorem.prototype.getStyle = function getStyle() {
-        return _Panel.prototype.getStyle.call(this) + " " + theorem_default.a.theorem;
-    };
-
-    return Theorem;
-}(panel_Panel);
-
-
-// EXTERNAL MODULE: ./components/hypothesis.css
-var hypothesis = __webpack_require__("pRAn");
-var hypothesis_default = /*#__PURE__*/__webpack_require__.n(hypothesis);
-
-// CONCATENATED MODULE: ./components/hypothesis.js
-
-
-function hypothesis__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
-
-function hypothesis__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
-
-function hypothesis__inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
-
-
-
-
-var hypothesis__ref = Object(preact_min["h"])(
-    "h4",
-    null,
-    "Ipotesi"
-);
-
-var hypothesis_Hypothesis = function (_Component) {
-    hypothesis__inherits(Hypothesis, _Component);
-
-    function Hypothesis() {
-        hypothesis__classCallCheck(this, Hypothesis);
-
-        return hypothesis__possibleConstructorReturn(this, _Component.apply(this, arguments));
-    }
-
-    Hypothesis.prototype.render = function render() {
-        return Object(preact_min["h"])(
-            "div",
-            { "class": hypothesis_default.a.hypothesis },
-            hypothesis__ref,
-            this.props.children
-        );
-    };
-
-    return Hypothesis;
-}(preact_min["Component"]);
-
-
-// EXTERNAL MODULE: ./components/thesis.css
-var thesis = __webpack_require__("J9SO");
-var thesis_default = /*#__PURE__*/__webpack_require__.n(thesis);
-
-// CONCATENATED MODULE: ./components/thesis.js
-
-
-function thesis__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
-
-function thesis__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
-
-function thesis__inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
-
-
-
-
-var thesis__ref = Object(preact_min["h"])(
-    "h4",
-    null,
-    "Tesi"
-);
-
-var thesis_Thesis = function (_Component) {
-    thesis__inherits(Thesis, _Component);
-
-    function Thesis() {
-        thesis__classCallCheck(this, Thesis);
-
-        return thesis__possibleConstructorReturn(this, _Component.apply(this, arguments));
-    }
-
-    Thesis.prototype.render = function render() {
-        return Object(preact_min["h"])(
-            "div",
-            { "class": thesis_default.a.thesis },
-            thesis__ref,
-            this.props.children
-        );
-    };
-
-    return Thesis;
-}(preact_min["Component"]);
-
-
-// EXTERNAL MODULE: ./components/proof.css
-var proof = __webpack_require__("Oqef");
-var proof_default = /*#__PURE__*/__webpack_require__.n(proof);
-
-// CONCATENATED MODULE: ./components/proof.js
-
-
-function proof__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
-
-function proof__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
-
-function proof__inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
-
-
-
-
-var proof__ref = Object(preact_min["h"])(
-    "h4",
-    null,
-    "Dimostrazione"
-);
-
-var proof_Proof = function (_Component) {
-    proof__inherits(Proof, _Component);
-
-    function Proof() {
-        proof__classCallCheck(this, Proof);
-
-        return proof__possibleConstructorReturn(this, _Component.apply(this, arguments));
-    }
-
-    Proof.prototype.render = function render() {
-        return Object(preact_min["h"])(
-            "div",
-            { "class": proof_default.a.proof },
-            proof__ref,
-            this.props.children
-        );
-    };
-
-    return Proof;
-}(preact_min["Component"]);
-
-
-// EXTERNAL MODULE: ./components/example.css
-var example = __webpack_require__("Xa+Z");
-var example_default = /*#__PURE__*/__webpack_require__.n(example);
-
-// CONCATENATED MODULE: ./components/example.js
-
-
-function example__classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }
-
-function example__possibleConstructorReturn(self, call) { if (!self) { throw new ReferenceError("this hasn't been initialised - super() hasn't been called"); } return call && (typeof call === "object" || typeof call === "function") ? call : self; }
-
-function example__inherits(subClass, superClass) { if (typeof superClass !== "function" && superClass !== null) { throw new TypeError("Super expression must either be null or a function, not " + typeof superClass); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, enumerable: false, writable: true, configurable: true } }); if (superClass) Object.setPrototypeOf ? Object.setPrototypeOf(subClass, superClass) : subClass.__proto__ = superClass; }
-
-
-
-
-var example_Example = function (_Component) {
-    example__inherits(Example, _Component);
-
-    function Example() {
-        example__classCallCheck(this, Example);
-
-        return example__possibleConstructorReturn(this, _Component.apply(this, arguments));
-    }
-
-    Example.prototype.render = function render() {
-        return Object(preact_min["h"])(
-            "blockquote",
-            { "class": example_default.a.example },
-            this.props.children
-        );
-    };
-
-    return Example;
-}(preact_min["Component"]);
-
-
-// CONCATENATED MODULE: ./pages/statistica.js
-var statistica__templateObject = statistica__taggedTemplateLiteralLoose(['P(E) = \frac{casi favorevoli}{casi possibili}'], ['P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}']),
-    statistica__templateObject2 = statistica__taggedTemplateLiteralLoose(['P(E) = \frac{successi}{prove totali}'], ['P(E) = \\frac{successi}{prove\\ totali}']),
-    statistica__templateObject3 = statistica__taggedTemplateLiteralLoose(['Omega = left { 1, 2, 3, 4, 5, 6 \right }'], ['\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}']),
-    statistica__templateObject4 = statistica__taggedTemplateLiteralLoose(['omega = 1'], ['\\omega = 1']),
-    statistica__templateObject5 = statistica__taggedTemplateLiteralLoose(['E = left { 1, 2 \right }'], ['E = \\left \\{ 1, 2 \\right \\}']),
-    statistica__templateObject6 = statistica__taggedTemplateLiteralLoose(['\bar{E} = left { 3, 4, 5, 6 \right }'], ['\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}']),
-    statistica__templateObject7 = statistica__taggedTemplateLiteralLoose(['E cap F = left { 1 \right }'], ['E \\cap F = \\left \\{ 1 \\right \\}']),
-    statistica__templateObject8 = statistica__taggedTemplateLiteralLoose(['E cup F = left { 1, 2, 3, 4 \right }'], ['E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}']),
-    statistica__templateObject9 = statistica__taggedTemplateLiteralLoose(['E setminus F = E cap \bar{F}'], ['E \\setminus F = E \\cap \\bar{F}']),
-    statistica__templateObject10 = statistica__taggedTemplateLiteralLoose(['E subseteq F'], ['E \\subseteq F']),
-    statistica__templateObject11 = statistica__taggedTemplateLiteralLoose(['E = emptyset'], ['E = \\emptyset']),
-    statistica__templateObject12 = statistica__taggedTemplateLiteralLoose(['E cap F = emptyset'], ['E \\cap F = \\emptyset']),
-    statistica__templateObject13 = statistica__taggedTemplateLiteralLoose(['mathcal{F}'], ['\\mathcal{F}']),
-    statistica__templateObject14 = statistica__taggedTemplateLiteralLoose(['sigma'], ['\\sigma']),
-    statistica__templateObject15 = statistica__taggedTemplateLiteralLoose(['Omega in mathcal{F}'], ['\\Omega \\in \\mathcal{F}']),
-    statistica__templateObject16 = statistica__taggedTemplateLiteralLoose(['E in mathcal{F} implies \bar{E} in mathcal{F}'], ['E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}']),
-    statistica__templateObject17 = statistica__taggedTemplateLiteralLoose(['(E, F) in mathcal{F} implies (E cup F, E cap F) in mathcal{F}'], ['(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}']),
-    statistica__templateObject18 = statistica__taggedTemplateLiteralLoose(['E in mathcal{F} implies mathcal{F} = { emptyset, E, \bar{E}, Omega }'], ['E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}']),
-    statistica__templateObject19 = statistica__taggedTemplateLiteralLoose(['E_i'], ['E_i']),
-    statistica__templateObject20 = statistica__taggedTemplateLiteralLoose(['E_1'], ['E_1']),
-    statistica__templateObject21 = statistica__taggedTemplateLiteralLoose(['E_2'], ['E_2']),
-    statistica__templateObject22 = statistica__taggedTemplateLiteralLoose(['E_3'], ['E_3']),
-    statistica__templateObject23 = statistica__taggedTemplateLiteralLoose(['E_n'], ['E_n']),
-    statistica__templateObject24 = statistica__taggedTemplateLiteralLoose(['\forall E in mathcal{F}, 0 leq P(E) leq 1'], ['\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1']),
-    statistica__templateObject25 = statistica__taggedTemplateLiteralLoose(['P(Omega) = 1'], ['P(\\Omega) = 1']),
-    statistica__templateObject26 = statistica__taggedTemplateLiteralLoose(['P left ( \bigcup_i E_i \right ) = sum_i P ( E_i )'], ['P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )']),
-    statistica__templateObject27 = statistica__taggedTemplateLiteralLoose(['P(\bar{E}) = 1 - P({E})'], ['P(\\bar{E}) = 1 - P({E})']),
-    statistica__templateObject28 = statistica__taggedTemplateLiteralLoose(['F subseteq E implies P(F) leq P(E)'], ['F \\subseteq E \\implies P(F) \\leq P(E)']),
-    statistica__templateObject29 = statistica__taggedTemplateLiteralLoose(['P(E cup F) = P(E) + P(F) - P(E cap F)'], ['P(E \\cup F) = P(E) + P(F) - P(E \\cap F)']),
-    statistica__templateObject30 = statistica__taggedTemplateLiteralLoose(['P(E) = \frac{len(E)}{len(Omega)}'], ['P(E) = \\frac{len(E)}{len(\\Omega)}']),
-    statistica__templateObject31 = statistica__taggedTemplateLiteralLoose(['\boldsymbol{D}_{n, k} = \frac{n!}{(n - k)!}'], ['\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}']),
-    statistica__templateObject32 = statistica__taggedTemplateLiteralLoose(['\boldsymbol{D}^{r}_{n, k} = n^k'], ['\\boldsymbol{D}^{r}_{n, k} = n^k']),
-    statistica__templateObject33 = statistica__taggedTemplateLiteralLoose(['\boldsymbol{C}_{n, k} = \binom{n}{k} = \frac{n!}{(k)! cdot (n - k)!}'], ['\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}']),
-    statistica__templateObject34 = statistica__taggedTemplateLiteralLoose(['\boldsymbol{C}^{r}_{n, k} = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{(k)! cdot (n - 1)!}'], ['\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}']),
-    statistica__templateObject35 = statistica__taggedTemplateLiteralLoose(['\boldsymbol{P}_n = n!'], ['\\boldsymbol{P}_n = n!']),
-    statistica__templateObject36 = statistica__taggedTemplateLiteralLoose(['P(E|F) = \frac{P(E cap F)}{P(F)}'], ['P(E|F) = \\frac{P(E \\cap F)}{P(F)}']),
-    statistica__templateObject37 = statistica__taggedTemplateLiteralLoose(['E cap F = emptyset Longleftrightarrow P(E|F) = P(F|E) = 0'], ['E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0']),
-    statistica__templateObject38 = statistica__taggedTemplateLiteralLoose(['P(E_1 cap \times cap E_n) = P(E_1) \times P(E_2 | E_1) \times dots \times P(E_n | E_1 cap E_2 cap dots cap E_{n-1})'], ['P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})']),
-    statistica__templateObject39 = statistica__taggedTemplateLiteralLoose(['P(F) = sum_{i} P(F|E_i) cdot P(E_i)'], ['P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)']),
-    statistica__templateObject40 = statistica__taggedTemplateLiteralLoose(['P(F|G) = sum_i P(F|E_i cap G) cdot P(E_i | G)'], ['P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)']),
-    statistica__templateObject41 = statistica__taggedTemplateLiteralLoose(['P(E_h | F) = \frac{P(F | E_h) cdot P(E_h)}{P(F)}'], ['P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}']),
-    statistica__templateObject42 = statistica__taggedTemplateLiteralLoose(['P(E cap F) = P(E) cdot P(F) Longleftrightarrow P(E|F) = P(E) Longleftrightarrow P(F|E) = P(F)'], ['P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)']),
-    statistica__templateObject43 = statistica__taggedTemplateLiteralLoose(['P(E cap F cap G) = P(E) cdot P(F) cdot P(G)'], ['P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)']),
-    statistica__templateObject44 = statistica__taggedTemplateLiteralLoose(['X(omega) : Omega \to mathbb{R}'], ['X(\\omega) : \\Omega \\to \\mathbb{R}']),
-    statistica__templateObject45 = statistica__taggedTemplateLiteralLoose(['A_t = { omega | X(omega) leq t }'], ['A_t = \\{ \\omega | X(\\omega) \\leq t \\}']),
-    statistica__templateObject46 = statistica__taggedTemplateLiteralLoose(['\forall t in mathbb{R}, A_t in mathcal{F}'], ['\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}']),
-    statistica__templateObject47 = statistica__taggedTemplateLiteralLoose(['p_X : X \to [0, 1]'], ['p_X : X \\to [0, 1]']),
-    statistica__templateObject48 = statistica__taggedTemplateLiteralLoose(['p_X (x) = \begin{cases}\n                            P([X = x]) quad se X mapsto x \\\n                            0 qquad qquad quad se X \notmapsto x\n                            end{cases}'], ['p_X (x) = \\begin{cases}\n                            P([X = x]) \\quad se\\ X \\mapsto x \\\\\n                            0 \\qquad \\qquad \\quad se\\ X \\not\\mapsto x\n                            \\end{cases}']),
-    statistica__templateObject49 = statistica__taggedTemplateLiteralLoose(['f_X : X \to [0, 1]'], ['f_X : X \\to [0, 1]']),
-    statistica__templateObject50 = statistica__taggedTemplateLiteralLoose(['P([a < X leq b]) = int_a^b f_X (x) dx'], ['P([a < X \\leq b]) = \\int_a^b f_X (x) dx']),
-    statistica__templateObject51 = statistica__taggedTemplateLiteralLoose(['F_X : mathbb{R} \to [0, 1]'], ['F_X : \\mathbb{R} \\to [0, 1]']),
-    statistica__templateObject52 = statistica__taggedTemplateLiteralLoose(['A_t'], ['A_t']),
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-    statistica__templateObject54 = statistica__taggedTemplateLiteralLoose(['\forall x_0 in mathbb{R}, F_X (x_0) = lim_{t \to x^+_0} F_X (t)'], ['\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)']),
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-
-var statistica__ref28 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Un insieme di esiti e eventi:'
-);
-
-var statistica__ref29 = Object(preact_min["h"])(
-    'ul',
-    null,
-    Object(preact_min["h"])(
-        'li',
-        null,
-        Object(preact_min["h"])(
-            'b',
-            null,
-            'Finito'
-        ),
-        '.'
-    ),
-    Object(preact_min["h"])(
-        'li',
-        null,
-        'In cui tutti gli eventi hanno ',
-        Object(preact_min["h"])(
-            'b',
-            null,
-            'probabilit\xE0 diversa da 0'
-        ),
-        '.'
-    ),
-    Object(preact_min["h"])(
-        'li',
-        null,
-        'In cui tutti gli eventi sono ',
-        Object(preact_min["h"])(
-            'b',
-            null,
-            'mutualmente esclusivi'
-        ),
-        '.'
-    ),
-    Object(preact_min["h"])(
-        'li',
-        null,
-        'In cui l\'unione di tutti i suoi elementi ',
-        Object(preact_min["h"])(
-            'b',
-            null,
-            'copre lo spazio campionario'
-        ),
-        '.'
-    )
-);
-
-var statistica__ref30 = Object(preact_min["h"])(
-    example_Example,
-    null,
-    'Se lo spazio campionario fosse una torta, una sua partizione sarebbe l\'insieme delle fette di uno dei modi in cui si potrebbe tagliare.'
-);
-
-var statistica__ref31 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La probabilit\xE0 di un evento \xE8 un numero tra 0 e 1.'
-);
-
-var statistica__ref32 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La probabilit\xE0 dello spazio campionario \xE8 sempre 1.'
-);
-
-var statistica__ref33 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La probabilit\xE0 dell\'unione di eventi indipendenti \xE8 uguale alla somma delle loro probabilit\xE0.'
-);
-
-var statistica__ref34 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La probabilit\xE0 di un evento negato \xE8 uguale a 1 meno la probabilit\xE0 dell\'evento non negato.'
-);
-
-var statistica__ref35 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La probabilit\xE0 di un evento incluso in un altro \xE8 sempre minore o uguale alla probabilit\xE0 dell\'evento in cui \xE8 incluso.'
-);
-
-var statistica__ref36 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La probabilit\xE0 di un evento unito a un altro \xE8 uguale alla somma delle probabilit\xE0 dei due eventi meno la probabilit\xE0 della loro intersezione.'
-);
-
-var statistica__ref37 = Object(preact_min["h"])(
-    example_Example,
-    null,
-    'Sommando le probabilit\xE0 dei due eventi, l\'intersezione viene contata due volte, e va quindi rimossa!'
-);
-
-var statistica__ref38 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilit\xE0 di verificarsi.'
-);
-
-var statistica__ref39 = Object(preact_min["h"])(
-    panel_Panel,
-    { title: "Spazi equiprobabili geometrici" },
-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Gli spazi campionari possono avere un numero infinito di esiti: sono ',
-        Object(preact_min["h"])(
-            'i',
-            null,
-            'equiprobabili geometrici'
-        ),
-        ' se nessun esito \xE8 privilegiato rispetto agli altri.'
-    )
-);
-
-var statistica__ref40 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Estraggo un numero, da un sacchetto con ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'n'
-    ),
-    ' numeri, mi segno che numero ho estratto e lo ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'tengo fuori dal sacchetto'
-    ),
-    '. Ripeto per ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'k'
-    ),
-    ' volte.'
-);
-
-var statistica__ref41 = Object(preact_min["h"])(
-    'p',
-    null,
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'Tengo conto'
-    ),
-    ' dell\'ordine in cui ho estratto i numeri.'
-);
-
-var statistica__ref42 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Estraggo un numero, da un sacchetto con ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'n'
-    ),
-    ' numeri, mi segno che numero ho estratto e lo ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'rimetto nel sacchetto'
-    ),
-    '. Ripeto per ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'k'
-    ),
-    ' volte.'
-);
-
-var statistica__ref43 = Object(preact_min["h"])(
-    'p',
-    null,
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'Tengo conto'
-    ),
-    ' dell\'ordine in cui ho estratto i numeri.'
-);
-
-var statistica__ref44 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Estraggo un numero, da un sacchetto con ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'n'
-    ),
-    ' numeri, mi segno che numero ho estratto e lo ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'tengo fuori dal sacchetto'
-    ),
-    '. Ripeto per ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'k'
-    ),
-    ' volte.'
-);
-
-var statistica__ref45 = Object(preact_min["h"])(
-    'p',
-    null,
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'Non mi interessa'
-    ),
-    ' l\'ordine in cui ho estratto i numeri.'
-);
-
-var statistica__ref46 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Estraggo un numero, da un sacchetto con ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'n'
-    ),
-    ' numeri, mi segno che numero ho estratto e lo ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'rimetto nel sacchetto'
-    ),
-    '. Ripeto per ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'k'
-    ),
-    ' volte.'
-);
-
-var statistica__ref47 = Object(preact_min["h"])(
-    'p',
-    null,
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'Non mi interessa'
-    ),
-    ' l\'ordine in cui ho estratto i numeri.'
-);
-
-var statistica__ref48 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Estraggo ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'n'
-    ),
-    ' numeri e guardo in quanti ordini diversi li posso mettere.'
-);
-
-var statistica__ref49 = Object(preact_min["h"])(
-    'blockquote',
-    null,
-    '"E dato F"'
-);
-
-var statistica__ref50 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La probabilit\xE0 che si verifichi ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'E'
-    ),
-    ' sapendo che ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'si \xE8 gi\xE0 verificato'
-    ),
-    ' ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'F'
-    ),
-    '.'
-);
-
-var statistica__ref51 = Object(preact_min["h"])(
-    example_Example,
-    null,
-    'Ricorda vagamente le pipe di ',
-    Object(preact_min["h"])(
-        'code',
-        null,
-        'bash'
-    ),
-    ', per\xF2 al contrario...'
-);
-
-var statistica__ref52 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Se due eventi sono mutualmente esclusivi, entrambe le loro probabilit\xE0 condizionate saranno uguali a 0.'
-);
-
-var statistica__ref53 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Si pu\xF2 sfruttare la formula inversa della probabilit\xE0 condizionata per calcolare catene di intersezioni:'
-);
-
-var statistica__ref54 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La probabilit\xE0 che si verifichi un evento \xE8 pari alla somma delle probabilit\xE0 dell\'evento stesso dati tutti gli eventi di una partizione.'
-);
-
-var statistica__ref55 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La legge delle alternative funziona anche quando ad essere partizionato \xE8 un ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'evento'
-    ),
-    ':'
-);
-
-var statistica__ref56 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Tramite la ',
-    Object(preact_min["h"])(
-        'i',
-        null,
-        'formula di Bayes'
-    ),
-    ' possiamo risalire alla probabilit\xE0 di un evento condizionato a un altro partendo dalla probabilit\xE0 di quest\'ultimo condizionato al primo:'
-);
-
-var statistica__ref57 = Object(preact_min["h"])(
-    example_Example,
-    null,
-    'In pratica, invertiamo gli eventi.'
-);
-
-var statistica__ref58 = Object(preact_min["h"])(
-    'blockquote',
-    null,
-    '"eventi indipendenti a due a due"'
-);
-
-var statistica__ref59 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Se due eventi sono indipendenti, sapere che uno dei due si \xE8 verificato non influisce sulle probabilit\xE0 che si sia verificato l\'altro.'
-);
-
-var statistica__ref60 = Object(preact_min["h"])(
-    'blockquote',
-    null,
-    '"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque..."'
-);
-
-var statistica__ref61 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Si pu\xF2 verificare l\'indipendenza di pi\xF9 eventi alla volta:'
-);
-
-var statistica__ref62 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.'
-);
-
-var statistica__ref63 = Object(preact_min["h"])(
-    panel_Panel,
-    { title: "Famiglia di eventi indipendenti" },
-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Un insieme di ',
-        Object(preact_min["h"])(
-            latex_Latex,
-            null,
-            'n'
-        ),
-        ' eventi \xE8 una ',
-        Object(preact_min["h"])(
-            'i',
-            null,
-            'famiglia di eventi indipendenti'
-        ),
-        ' se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.'
-    ),
-    Object(preact_min["h"])(
-        example_Example,
-        null,
-        'Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e cos\xEC via!'
-    )
-);
-
-var statistica__ref64 = Object(preact_min["h"])(
-    'abbr',
-    { title: "Nome artigianale dato da Steffo." },
-    'Insieme di ripartizione'
-);
-
-var statistica__ref65 = Object(preact_min["h"])(
-    latex_Latex,
-    null,
-    't'
-);
-
-var statistica__ref66 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:'
-);
-
-var statistica__ref67 = Object(preact_min["h"])(
-    example_Example,
-    null,
-    'All\'aumentare di t, l\'insieme conterr\xE0 sempre pi\xF9 elementi.'
-);
-
-var statistica__ref68 = Object(preact_min["h"])(
-    panel_Panel,
-    { title: "Supporto" },
-    Object(preact_min["h"])(
-        'blockquote',
-        null,
-        '"supporto di X"'
-    ),
-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Il ',
-        Object(preact_min["h"])(
-            'b',
-            null,
-            'codominio'
-        ),
-        ' della variabile aleatoria \xE8 il suo ',
-        Object(preact_min["h"])(
-            'i',
-            null,
-            'supporto'
-        ),
-        '.'
-    ),
-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Per indicare che un valore ',
-        Object(preact_min["h"])(
-            latex_Latex,
-            null,
-            'x_0'
-        ),
-        ' appartiene al supporto di ',
-        Object(preact_min["h"])(
-            latex_Latex,
-            null,
-            'X'
-        ),
-        ', si usa la notazione ',
-        Object(preact_min["h"])(
-            latex_Latex,
-            null,
-            'X \\mapsto x_0'
-        ),
-        '.'
-    )
-);
-
-var statistica__ref69 = Object(preact_min["h"])(
-    'i',
-    null,
-    'funzione probabilit\xE0'
-);
-
-var statistica__ref70 = Object(preact_min["h"])(
-    'b',
-    null,
-    'discreta'
-);
-
-var statistica__ref71 = Object(preact_min["h"])(
-    latex_Latex,
-    null,
-    'X'
-);
-
-var statistica__ref72 = Object(preact_min["h"])(
-    'i',
-    null,
-    'funzione densit\xE0'
-);
-
-var statistica__ref73 = Object(preact_min["h"])(
-    'b',
-    null,
-    'continua'
-);
-
-var statistica__ref74 = Object(preact_min["h"])(
-    latex_Latex,
-    null,
-    'X'
-);
-
-var statistica__ref75 = Object(preact_min["h"])(
-    'p',
-    null,
-    'A differenza della funzione probabilit\xE0, \xE8 possibile che la funzione densit\xE0 ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'non esista'
-    ),
-    ' per una certa variabile aleatoria.'
-);
-
-var statistica__ref76 = Object(preact_min["h"])(
-    example_Example,
-    null,
-    'Rappresenta "quanta" probabilit\xE0 c\'\xE8 in un\'unit\xE0 di x!'
-);
-
-var statistica__ref77 = Object(preact_min["h"])(
-    'i',
-    null,
-    'funzione di ripartizione'
-);
-
-var statistica__ref78 = Object(preact_min["h"])(
-    latex_Latex,
-    null,
-    't'
-);
-
-var statistica__ref79 = Object(preact_min["h"])(
-    'li',
-    null,
-    '\xC8 sempre ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'monotona crescente'
-    ),
-    ' (non strettamente).'
-);
-
-var statistica__ref80 = Object(preact_min["h"])('br', null);
-
-var statistica__ref81 = Object(preact_min["h"])(
-    'li',
-    null,
-    'Vale ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        '0'
-    ),
-    ' a ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        '-\\infty'
-    ),
-    ' e ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        '1'
-    ),
-    ' a ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        '+\\infty'
-    ),
-    '.'
-);
-
-var statistica__ref82 = Object(preact_min["h"])('br', null);
-
-var statistica__ref83 = Object(preact_min["h"])(
-    'b',
-    null,
-    'continua da destra'
-);
-
-var statistica__ref84 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Possiamo usare la funzione di ripartizione per calcolare la probabilit\xE0 di un certo valore reale:'
-);
-
-var statistica__ref85 = Object(preact_min["h"])(
-    panel_Panel,
-    { title: "Nel discreto" },
-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.'
-    )
-);
-
-var statistica__ref86 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Nel continuo applichiamo la formula dell\'integrazione per sostituzione:'
-);
-
-var statistica__ref87 = Object(preact_min["h"])(
-    panel_Panel,
-    { title: "Nel... digitale" },
-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Trasformare variabili aleatorie \xE8 molto utile nell\'informatica per creare distribuzioni partendo da una funzione ',
-        Object(preact_min["h"])(
-            'a',
-            { href: "https://docs.python.org/3/library/random.html#random.random" },
-            Object(preact_min["h"])(
-                'code',
-                null,
-                'random()'
-            )
-        ),
-        ' che restituisce numeri da 0 a 1 con una distribuzione lineare.'
-    )
-);
-
-var statistica__ref88 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Ogni variabile aleatoria che ha una ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione di ripartizione'
-    ),
-    ' e un ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'supporto finito'
-    ),
-    ' ha anche una ',
-    Object(preact_min["h"])(
-        'i',
-        null,
-        'media'
-    ),
-    ' (o ',
-    Object(preact_min["h"])(
-        'i',
-        null,
-        'valore medio'
-    ),
-    ' o ',
-    Object(preact_min["h"])(
-        'i',
-        null,
-        'atteso'
-    ),
-    '):'
-);
-
-var statistica__ref89 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Nel discreto, si pu\xF2 calcolare con:'
-);
-
-var statistica__ref90 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Nel continuo, si pu\xF2 calcolare con:'
-);
-
-var statistica__ref91 = Object(preact_min["h"])(
-    panel_Panel,
-    { title: "Moda" },
-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Valore per cui la ',
-        Object(preact_min["h"])(
-            'b',
-            null,
-            'funzione probabilit\xE0'
-        ),
-        ' o ',
-        Object(preact_min["h"])(
-            'b',
-            null,
-            'funzione densit\xE0'
-        ),
-        ' \xE8 ',
-        Object(preact_min["h"])(
-            'b',
-            null,
-            'massima'
-        ),
-        '.'
-    )
-);
-
-var statistica__ref92 = Object(preact_min["h"])(
-    'i',
-    null,
-    'quantile'
-);
-
-var statistica__ref93 = Object(preact_min["h"])(
-    latex_Latex,
-    null,
-    'X'
-);
-
-var statistica__ref94 = Object(preact_min["h"])('p', null);
-
-var statistica__ref95 = Object(preact_min["h"])(
-    'i',
-    null,
-    'mediana'
-);
-
-var statistica__ref96 = Object(preact_min["h"])(
-    'i',
-    null,
-    'quartili'
-);
-
-var statistica__ref97 = Object(preact_min["h"])(
-    'i',
-    null,
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'n'
-    ),
-    '-esima percentile'
-);
-
-var statistica__ref98 = Object(preact_min["h"])(
-    'p',
-    null,
-    '\xC8 un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:'
-);
-
-var statistica__ref99 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Data una variabile aleatoria non-negativa:'
-);
-
-var statistica__ref100 = Object(preact_min["h"])(
-    'blockquote',
-    null,
-    '"disuguaglianza di cebicev"'
-);
-
-var statistica__ref101 = Object(preact_min["h"])(
-    latex_Latex,
-    null,
-    'X'
-);
-
-var statistica__ref102 = Object(preact_min["h"])(
-    'p',
-    null,
-    'E anche:'
-);
-
-var statistica__ref103 = Object(preact_min["h"])(
-    example_Example,
-    null,
-    'Serve per semplificare i calcoli quando la funzione di ripartizione \xE8 difficile da calcolare!'
-);
-
-var statistica__ref104 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Il ',
-    Object(preact_min["h"])(
-        'i',
-        null,
-        'momento'
-    ),
-    ' ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'k'
-    ),
-    '-esimo di una variabile aleatoria \xE8:'
-);
-
-var statistica__ref105 = Object(preact_min["h"])(
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-    'La media di una variabile aleatoria \xE8 anche il suo primo momento.'
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-var statistica__ref106 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'i',
-        null,
-        'funzione generatrice dei momenti'
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-    ' \xE8:'
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-
-var statistica__ref107 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'stessa distribuzione'
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-    '.'
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-
-var statistica__ref108 = Object(preact_min["h"])(
-    'p',
-    null,
-    'E\' la ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'trasformata di Laplace'
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-    ' della variabile aleatoria di X.'
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-
-var statistica__ref109 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'i',
-        null,
-        'funzione caratteristica'
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-    ' \xE8:'
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-
-var statistica__ref110 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'stessa distribuzione'
-    ),
-    '.'
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-
-var statistica__ref111 = Object(preact_min["h"])(
-    'p',
-    null,
-    'E\' la ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'trasformata di Fourier'
-    ),
-    ' della variabile aleatoria di X.'
-);
-
-var statistica__ref112 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Per dire che una variabile ha una certa distribuzione, si usa la notazione:'
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-
-var statistica__ref113 = Object(preact_min["h"])(
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-    { title: "Prova di Bernoulli" },
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-        'p',
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-        'Una prova con solo due possibili esiti: ',
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-        Object(preact_min["h"])(
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-var statistica__ref114 = Object(preact_min["h"])(
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-    Object(preact_min["h"])(
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-        'Una sequenza di prove di Bernoulli per le quali le probabilit\xE0 di successo e fallimento rimangono invariate.'
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-
-var statistica__ref115 = Object(preact_min["h"])(
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-    null,
-    'Una variabile aleatoria che rappresenta una prova di Bernoulli:'
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-var statistica__ref116 = Object(preact_min["h"])(
-    'ul',
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-            '1'
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-
-var statistica__ref117 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La distribuzione bernoulliana ha come densit\xE0:'
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-
-var statistica__ref118 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Una variabile aleatoria che conta il numero di successi di ',
-    Object(preact_min["h"])(
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-        null,
-        'n'
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-    ' prove di uno schema di Bernoulli.'
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-
-var statistica__ref119 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La binomiale ha come densit\xE0:'
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-
-var statistica__ref120 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
-    ),
-    ' della binomiale \xE8:'
-);
-
-var statistica__ref121 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
-    ),
-    ' di una binomiale \xE8:'
-);
-
-var statistica__ref122 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' di una binomiale \xE8:'
-);
-
-var statistica__ref123 = Object(preact_min["h"])(
-    panel_Panel,
-    { title: "Distribuzione geometrica" },
-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.'
-    ),
-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Il suo simbolo \xE8 ',
-        Object(preact_min["h"])(
-            latex_Latex,
-            null,
-            'Geo(p)'
-        ),
-        '.'
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-);
-
-var statistica__ref124 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La geometrica ha come densit\xE0:'
-);
-
-var statistica__ref125 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
-    ),
-    ' della geometrica \xE8:'
-);
-
-var statistica__ref126 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
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-    ' della geometrica \xE8:'
-);
-
-var statistica__ref127 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' della geometrica \xE8:'
-);
-
-var statistica__ref128 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La geometrica non tiene conto degli eventi avvenuti in passato: ha la propriet\xE0 dell\'assenza di memoria:'
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-
-var statistica__ref129 = Object(preact_min["h"])(
-    example_Example,
-    null,
-    'Ovvero, riscalando opportunamente l\'asse Y posso prendere come 0 qualsiasi punto dell\'asse X.'
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-
-var statistica__ref130 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perch\xE8 si verifichi l\'',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'n'
-    ),
-    '-esimo successo.'
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-
-var statistica__ref131 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La binomiale negativa ha come densit\xE0:'
-);
-
-var statistica__ref132 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
-    ),
-    ' della binomiale negativa \xE8:'
-);
-
-var statistica__ref133 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
-    ),
-    ' della binomiale negativa \xE8:'
-);
-
-var statistica__ref134 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' della binomiale negativa \xE8:'
-);
-
-var statistica__ref135 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Una variabile aleatoria che conta il numero ',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'k'
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-    ' di insuccessi consecutivi in uno schema di Bernoulli:'
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-
-var statistica__ref136 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La geometrica traslata ha come densit\xE0:'
-);
-
-var statistica__ref137 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
-    ),
-    ' della geometrica traslata \xE8:'
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-
-var statistica__ref138 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
-    ),
-    ' della geometrica traslata \xE8:'
-);
-
-var statistica__ref139 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' della geometrica \xE8:'
-);
-
-var statistica__ref140 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la propriet\xE0 dell\'assenza di memoria:'
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-
-var statistica__ref141 = Object(preact_min["h"])(
-    example_Example,
-    null,
-    'Ovvero, riscalando opportunamente l\'asse Y posso prendere come 0 qualsiasi punto dell\'asse X.'
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-
-var statistica__ref142 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l\'',
-    Object(preact_min["h"])(
-        latex_Latex,
-        null,
-        'n'
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-    '-esimo successo.'
-);
-
-var statistica__ref143 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La binomiale negativa traslata ha come densit\xE0:'
-);
-
-var statistica__ref144 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
-    ),
-    ' della binomiale negativa traslata \xE8:'
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-
-var statistica__ref145 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
-    ),
-    ' della binomiale negativa traslata \xE8:'
-);
-
-var statistica__ref146 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' della binomiale negativa traslata \xE8:'
-);
-
-var statistica__ref147 = Object(preact_min["h"])(
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-    { title: "Distribuzione ipergeometrica" },
-    Object(preact_min["h"])(
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-        null,
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-        Object(preact_min["h"])(
-            latex_Latex,
-            null,
-            'K'
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-        ' e di insuccessi ',
-        Object(preact_min["h"])(
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-            null,
-            'N-K'
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-        ', conta quanti successi si otterrebbero se se ne estraessero ',
-        Object(preact_min["h"])(
-            latex_Latex,
-            null,
-            'n'
-        ),
-        ' in blocco.'
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-    Object(preact_min["h"])(
-        'p',
-        null,
-        'Il suo simbolo \xE8 ',
-        Object(preact_min["h"])(
-            latex_Latex,
-            null,
-            'Ipe(N, K, n)'
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-        '.'
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-
-var statistica__ref148 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ipergeometrica ha come densit\xE0:'
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-var statistica__ref149 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
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-    ' della ipergeometrica \xE8 trascurabile.'
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-
-var statistica__ref150 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
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-    ' della ipergeometrica \xE8:'
-);
-
-var statistica__ref151 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' della ipergeometrica \xE8:'
-);
-
-var statistica__ref152 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:'
-);
-
-var statistica__ref153 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La poissoniana ha come densit\xE0:'
-);
-
-var statistica__ref154 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
-    ),
-    ' della poissoniana \xE8:'
-);
-
-var statistica__ref155 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
-    ),
-    ' della poissoniana \xE8:'
-);
-
-var statistica__ref156 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' della poissoniana \xE8:'
-);
-
-var statistica__ref157 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Gli altri momenti della poissoniana sono:'
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-
-var statistica__ref158 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Una successione di ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'arrivi'
-    ),
-    ' avvenuti in un certo arco temporale che:'
-);
-
-var statistica__ref159 = Object(preact_min["h"])(
-    'li',
-    null,
-    'non sono sovrapposti.'
-);
-
-var statistica__ref160 = Object(preact_min["h"])(
-    'li',
-    null,
-    'avvengono indipendentemente gli uni dagli altri.'
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-
-var statistica__ref161 = Object(preact_min["h"])(
-    latex_Latex,
-    null,
-    'N_t'
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-
-var statistica__ref162 = Object(preact_min["h"])(
-    latex_Latex,
-    null,
-    't'
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-
-var statistica__ref163 = Object(preact_min["h"])(
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-
-var statistica__ref164 = Object(preact_min["h"])(
-    'p',
-    null,
-    'L\'esponenziale ha come ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'densit\xE0'
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-    ':'
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-
-var statistica__ref165 = Object(preact_min["h"])(
-    'p',
-    null,
-    'L\'esponenziale ha come ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione di ripartizione'
-    ),
-    ':'
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-
-var statistica__ref166 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
-    ),
-    ' dell\'esponenziale \xE8:'
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-
-var _ref167 = Object(preact_min["h"])(
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-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
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-    ' dell\'esponenziale \xE8:'
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-
-var _ref168 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' dell\'esponenziale \xE8:'
-);
-
-var _ref169 = Object(preact_min["h"])(
-    'p',
-    null,
-    'L\'esponenziale non tiene conto degli eventi avvenuti in passato: ha la propriet\xE0 dell\'assenza di memoria:'
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-
-var _ref170 = Object(preact_min["h"])(
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-
-var _ref171 = Object(preact_min["h"])(
-    latex_Latex,
-    null,
-    'n'
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-
-var _ref172 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La legge gamma ha come densit\xE0:'
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-
-var _ref173 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
-    ),
-    ' della legge gamma \xE8:'
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-
-var _ref174 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
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-    ' della legge gamma \xE8:'
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-
-var _ref175 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' della legge gamma \xE8:'
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-
-var _ref176 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Su di essa vale la seguente propriet\xE0:'
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-
-var _ref177 = Object(preact_min["h"])(
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-    null,
-    'La distribuzione uniforme ha come ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'densit\xE0'
-    ),
-    ':'
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-
-var _ref178 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La distribuzione uniforme ha come ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione di ripartizione'
-    ),
-    ':'
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-
-var _ref179 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
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-    ' della distribuzione uniforme \xE8:'
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-var _ref180 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'media'
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-    ' della distribuzione uniforme \xE8:'
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-
-var _ref181 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'varianza'
-    ),
-    ' della distribuzione uniforme \xE8:'
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-
-var _ref182 = Object(preact_min["h"])(
-    'p',
-    null,
-    'Una variabile aleatoria con una specifica distribuzione.'
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-var _ref183 = Object(preact_min["h"])(
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-        '\\mu'
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-    ' e ',
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-        null,
-        '\\sigma^2'
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-    ' sono rispettivamente la media e la varianza della distribuzione!'
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-
-var _ref184 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La distribuzione normale ha come densit\xE0:'
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-
-var _ref185 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
-        'funzione generatrice dei momenti'
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-    ' della distribuzione normale \xE8:'
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-
-var _ref186 = Object(preact_min["h"])(
-    'p',
-    null,
-    'La ',
-    Object(preact_min["h"])(
-        'b',
-        null,
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-var _ref217 = Object(preact_min["h"])(
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-var _ref218 = Object(preact_min["h"])(
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-        '\\geq 0'
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-var _ref224 = Object(preact_min["h"])(
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-var _ref236 = Object(preact_min["h"])(
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-var statistica_Statistica = function (_Component) {
-    statistica__inherits(Statistica, _Component);
-
-    function Statistica() {
-        statistica__classCallCheck(this, Statistica);
-
-        return statistica__possibleConstructorReturn(this, _Component.apply(this, arguments));
-    }
-
-    Statistica.prototype.render = function render() {
-        /*
-               
-                   
-                       
    
-                           Gruppo intero di oggetti di cui si cercano informazioni.
-                       
    
-                       
-                   
-                       
    
-                           Popolazione finita di oggetti concreti che possono essere campionati ciascuno solo una volta.
-                       
    
-                       
-                   
-                       
    
-                           Popolazione di valori ottenuti da prove sperimentali indipendenti ripetute più volte.
-                       
    
-                       
-                   
-               
-                   
-                       
    
-                           Sottoinsieme della popolazione che contiene gli oggetti che si sono osservati.
-                       
    
-                   
-                   Simple random sample}>
-                       
    
-                           Campione di una data dimensione in cui qualsiasi selezione di n elementi ha la stessa probabilità di costituire il campione.
-                       
    
-                       
-                   Sample of convenience}>
-                       
    
-                           Campione ottenuto in un modo casuale non ben definito.
-                       
    
-                       
-                   Sample with replacement}>
-                       
    
-                           Campione ottenuto sostituendo nella popolazione gli elementi estratti con dei nuovi elementi.
-                       
    
-                       
    
-                           Dire che un campione è ottenuto with replacement è equivalente a dire che la popolazione che si sta campionando è infinita, e quindi che tutti gli elementi sono indipendenti.
-                       
    
-                       
-                   
-                       
    
-                           Campione ottenuto da una popolazione in cui certi elementi hanno più probabilità di essere stati selezionati di altri.
-                       
    
-                       
-                   Stratified random sample}>
-                       
    
-                           Campione ottenuto da un sottoinsieme della popolazione detto strato.
-                       
    
-                       
-                   Cluster sample}>
-                       
    
-                           Campione ottenuto selezionando più cluster di elementi alla volta.
-                       
    
-                       
-               
-               
-                   Sampling variation}>
-                       
    
-                           Differenza di informazioni presente tra due campioni diversi della stessa popolazione.
-                       
    
-                       
-                   
-                       
    
-                           Gli elementi in un campione sono indipendenti se gli elementi estratti in precedenza non influsicono significativamente sulle probabilità di estrazione dell'elemento successivo.
-                       
    
-                       
-                   
-               
-                   
-                       
    
-                           Esperimento in cui c'è una sola popolazione da cui vengono estratti campioni.
-                       
    
-                       
    
-                           Serve per verificare delle condizioni.
-                       
    
-                       
-                   
-                       
    
-                           Esperimento in cui sono presenti più popolazioni (aventi caratteristiche differenti una dall'altra dette fattori) da cui vengono estratti campioni.
-                       
    
-                       
    
-                           Serve per capire quali fattori influenzano il risultato dell'esperimento.
-                       
    
-                       
-                   
-               
-                   Numerico o quantitativo}>
-                       Il dato descrive un valore numerico relativo all'elemento, come ad esempio una quantità fisica.
-                   
-                   Categorico o qualitativo}>
-                       Il dato indica una categoria a cui appartiene l'elemento, come ad esempio il suo colore.
-                   
-               
-         */
-        return Object(preact_min["h"])(
-            'div',
-            { style: statistica_default.a.statistica },
-            statistica__ref,
-            Object(preact_min["h"])(
-                split_Split,
-                { title: "Tipi di probabilità" },
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Classica" },
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject)
-                        )
-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Frequentista" },
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject2)
-                        )
-                    )
-                ),
-                statistica__ref2
-            ),
-            Object(preact_min["h"])(
-                split_Split,
-                { title: "Linguaggio matematico" },
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Spazio campionario" },
-                    statistica__ref3,
-                    statistica__ref4,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject3)
-                        )
-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Esito" },
-                    statistica__ref5,
-                    statistica__ref6,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject4)
-                        )
-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Evento" },
-                    statistica__ref7,
-                    statistica__ref8,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject5)
-                        )
-                    ),
-                    statistica__ref9
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Not" },
-                    statistica__ref10,
-                    statistica__ref11,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject6)
-                        )
-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "And" },
-                    statistica__ref12,
-                    statistica__ref13,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject7)
-                        )
-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Or" },
-                    statistica__ref14,
-                    statistica__ref15,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject8)
-                        )
-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Differenza" },
-                    statistica__ref16,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject9)
-                        )
-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Implicazione" },
-                    statistica__ref17,
-                    statistica__ref18,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject10)
-                        )
-                    ),
-                    statistica__ref19
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Evento impossibile" },
-                    statistica__ref20,
-                    statistica__ref21,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject11)
-                        )
-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Mutua esclusione" },
-                    statistica__ref22,
-                    statistica__ref23,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject12)
-                        )
-                    )
-                )
-            ),
-            Object(preact_min["h"])(
-                split_Split,
-                null,
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Famiglia degli eventi" },
-                    statistica__ref24,
-                    statistica__ref25,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject13)
-                        )
-                    ),
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        'Qualsiasi sottoinsieme appartenente a ',
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject13)
-                        ),
-                        ' \xE8 considerato un evento.'
-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: Object(preact_min["h"])(
-                            'span',
-                            null,
-                            Object(preact_min["h"])(
-                                latex_Latex,
-                                null,
-                                statistica_r(statistica__templateObject14)
-                            ),
-                            '-algebra'
-                        ) },
-                    statistica__ref26,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        'Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta ',
-                        Object(preact_min["h"])(
-                            'i',
-                            null,
-                            Object(preact_min["h"])(
-                                latex_Latex,
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-                            '-algebra'
-                        ),
-                        ':'
-                    ),
-                    Object(preact_min["h"])(
-                        'ol',
-                        null,
-                        Object(preact_min["h"])(
-                            'li',
-                            null,
-                            'Lo spazio campionario \xE8 un evento: ',
-                            Object(preact_min["h"])(
-                                latex_Latex,
-                                null,
-                                statistica_r(statistica__templateObject15)
-                            )
-                        ),
-                        Object(preact_min["h"])(
-                            'li',
-                            null,
-                            'Se un sottoinsieme \xE8 un evento, allora anche il suo complementare lo \xE8: ',
-                            Object(preact_min["h"])(
-                                latex_Latex,
-                                null,
-                                statistica_r(statistica__templateObject16)
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-                        ),
-                        Object(preact_min["h"])(
-                            'li',
-                            null,
-                            'Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: ',
-                            Object(preact_min["h"])(
-                                latex_Latex,
-                                null,
-                                statistica_r(statistica__templateObject17)
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-                        )
-                    ),
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        'Un esempio: ',
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject18)
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-                    )
-                )
-            ),
-            Object(preact_min["h"])(
-                split_Split,
-                null,
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Partizione" },
-                    statistica__ref27,
-                    statistica__ref28,
-                    statistica__ref29,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        'La partizione ',
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject19)
-                        ),
-                        ' \xE8 composta dagli eventi ',
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject20)
-                        ),
-                        ', ',
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject21)
-                        ),
-                        ', ',
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject22)
-                        ),
-                        ', fino a ',
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject23)
-                        ),
-                        '.'
-                    ),
-                    statistica__ref30
-                )
-            ),
-            Object(preact_min["h"])(
-                split_Split,
-                { title: "Assiomi della probabilità" },
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Primo assioma della probabilità" },
-                    statistica__ref31,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject24)
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-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Secondo assioma della probabilità" },
-                    statistica__ref32,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject25)
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-                ),
-                Object(preact_min["h"])(
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-                    statistica__ref33,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject26)
-                        )
-                    )
-                )
-            ),
-            Object(preact_min["h"])(
-                split_Split,
-                { title: "Conseguenze degli assiomi" },
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Probabilità di un evento negato" },
-                    statistica__ref34,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject27)
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-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Probabilità di un evento incluso" },
-                    statistica__ref35,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject28)
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-                    )
-                ),
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Unione" },
-                    statistica__ref36,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject29)
-                        )
-                    ),
-                    statistica__ref37
-                )
-            ),
-            Object(preact_min["h"])(
-                split_Split,
-                { title: "Spazi equiprobabili" },
-                Object(preact_min["h"])(
-                    panel_Panel,
-                    { title: "Cosa sono?" },
-                    statistica__ref38,
-                    Object(preact_min["h"])(
-                        'p',
-                        null,
-                        Object(preact_min["h"])(
-                            latex_Latex,
-                            null,
-                            statistica_r(statistica__templateObject30)
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-                    )
-                ),
-                statistica__ref39
-            ),
-            Object(preact_min["h"])(
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\t\tif(!__webpack_require__.o(exports, name)) {\n \t\t\tObject.defineProperty(exports, name, {\n \t\t\t\tconfigurable: false,\n \t\t\t\tenumerable: true,\n \t\t\t\tget: getter\n \t\t\t});\n \t\t}\n \t};\n\n \t// getDefaultExport function for compatibility with non-harmony modules\n \t__webpack_require__.n = function(module) {\n \t\tvar getter = module && module.__esModule ?\n \t\t\tfunction getDefault() { return module['default']; } :\n \t\t\tfunction getModuleExports() { return module; };\n \t\t__webpack_require__.d(getter, 'a', getter);\n \t\treturn getter;\n \t};\n\n \t// Object.prototype.hasOwnProperty.call\n \t__webpack_require__.o = function(object, property) { return Object.prototype.hasOwnProperty.call(object, property); };\n\n \t// __webpack_public_path__\n \t__webpack_require__.p = \"/\";\n\n \t// Load entry module and return exports\n \treturn __webpack_require__(__webpack_require__.s = \"JkW7\");\n\n\n\n// WEBPACK FOOTER //\n// webpack/bootstrap a5c34269c357436dbef7","// 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*/\r\n(function(){\r\n/**\n * Created by Tivie on 13-07-2015.\n */\n\nfunction getDefaultOpts (simple) {\n  'use strict';\n\n  var defaultOptions = {\n    omitExtraWLInCodeBlocks: {\n      defaultValue: false,\n      describe: 'Omit the default extra whiteline added to code blocks',\n      type: 'boolean'\n    },\n    noHeaderId: {\n      defaultValue: false,\n      describe: 'Turn on/off generated header id',\n      type: 'boolean'\n    },\n    prefixHeaderId: {\n      defaultValue: false,\n      describe: 'Add a prefix to the generated header ids. Passing a string will prefix that string to the header id. Setting to true will add a generic \\'section-\\' prefix',\n      type: 'string'\n    },\n    rawPrefixHeaderId: {\n      defaultValue: false,\n      describe: 'Setting this option to true will prevent showdown from modifying the prefix. This might result in malformed IDs (if, for instance, the \" char is used in the prefix)',\n      type: 'boolean'\n    },\n    ghCompatibleHeaderId: {\n      defaultValue: false,\n      describe: 'Generate header ids compatible with github style (spaces are replaced with dashes, a bunch of non alphanumeric chars are removed)',\n      type: 'boolean'\n    },\n    rawHeaderId: {\n      defaultValue: false,\n      describe: 'Remove only spaces, \\' and \" from generated header ids (including prefixes), replacing them with dashes (-). WARNING: This might result in malformed ids',\n      type: 'boolean'\n    },\n    headerLevelStart: {\n      defaultValue: false,\n      describe: 'The header blocks level start',\n      type: 'integer'\n    },\n    parseImgDimensions: {\n      defaultValue: false,\n      describe: 'Turn on/off image dimension parsing',\n      type: 'boolean'\n    },\n    simplifiedAutoLink: {\n      defaultValue: false,\n      describe: 'Turn on/off GFM autolink style',\n      type: 'boolean'\n    },\n    excludeTrailingPunctuationFromURLs: {\n      defaultValue: false,\n      describe: 'Excludes trailing punctuation from links generated with autoLinking',\n      type: 'boolean'\n    },\n    literalMidWordUnderscores: {\n      defaultValue: false,\n      describe: 'Parse midword underscores as literal underscores',\n      type: 'boolean'\n    },\n    literalMidWordAsterisks: {\n      defaultValue: false,\n      describe: 'Parse midword asterisks as literal asterisks',\n      type: 'boolean'\n    },\n    strikethrough: {\n      defaultValue: false,\n      describe: 'Turn on/off strikethrough support',\n      type: 'boolean'\n    },\n    tables: {\n      defaultValue: false,\n      describe: 'Turn on/off tables support',\n      type: 'boolean'\n    },\n    tablesHeaderId: {\n      defaultValue: false,\n      describe: 'Add an id to table headers',\n      type: 'boolean'\n    },\n    ghCodeBlocks: {\n      defaultValue: true,\n      describe: 'Turn on/off GFM fenced code blocks support',\n      type: 'boolean'\n    },\n    tasklists: {\n      defaultValue: false,\n      describe: 'Turn on/off GFM tasklist support',\n      type: 'boolean'\n    },\n    smoothLivePreview: {\n      defaultValue: false,\n      describe: 'Prevents weird effects in live previews due to incomplete input',\n      type: 'boolean'\n    },\n    smartIndentationFix: {\n      defaultValue: false,\n      description: 'Tries to smartly fix indentation in es6 strings',\n      type: 'boolean'\n    },\n    disableForced4SpacesIndentedSublists: {\n      defaultValue: false,\n      description: 'Disables the requirement of indenting nested sublists by 4 spaces',\n      type: 'boolean'\n    },\n    simpleLineBreaks: {\n      defaultValue: false,\n      description: 'Parses simple line breaks as 
     (GFM Style)',\n      type: 'boolean'\n    },\n    requireSpaceBeforeHeadingText: {\n      defaultValue: false,\n      description: 'Makes adding a space between `#` and the header text mandatory (GFM Style)',\n      type: 'boolean'\n    },\n    ghMentions: {\n      defaultValue: false,\n      description: 'Enables github @mentions',\n      type: 'boolean'\n    },\n    ghMentionsLink: {\n      defaultValue: 'https://github.com/{u}',\n      description: 'Changes the link generated by @mentions. Only applies if ghMentions option is enabled.',\n      type: 'string'\n    },\n    encodeEmails: {\n      defaultValue: true,\n      description: 'Encode e-mail addresses through the use of Character Entities, transforming ASCII e-mail addresses into its equivalent decimal entities',\n      type: 'boolean'\n    },\n    openLinksInNewWindow: {\n      defaultValue: false,\n      description: 'Open all links in new windows',\n      type: 'boolean'\n    },\n    backslashEscapesHTMLTags: {\n      defaultValue: false,\n      description: 'Support for HTML Tag escaping. ex: \\
    foo\\
    ',\n      type: 'boolean'\n    },\n    emoji: {\n      defaultValue: false,\n      description: 'Enable emoji support. Ex: `this is a :smile: emoji`',\n      type: 'boolean'\n    },\n    underline: {\n      defaultValue: false,\n      description: 'Enable support for underline. Syntax is double or triple underscores: `__underline word__`. With this option enabled, underscores no longer parses into `` and ``',\n      type: 'boolean'\n    },\n    completeHTMLDocument: {\n      defaultValue: false,\n      description: 'Outputs a complete html document, including ``, `` and `` tags',\n      type: 'boolean'\n    },\n    metadata: {\n      defaultValue: false,\n      description: 'Enable support for document metadata (defined at the top of the document between `«««` and `»»»` or between `---` and `---`).',\n      type: 'boolean'\n    },\n    splitAdjacentBlockquotes: {\n      defaultValue: false,\n      description: 'Split adjacent blockquote blocks',\n      type: 'boolean'\n    }\n  };\n  if (simple === false) {\n    return JSON.parse(JSON.stringify(defaultOptions));\n  }\n  var ret = {};\n  for (var opt in defaultOptions) {\n    if (defaultOptions.hasOwnProperty(opt)) {\n      ret[opt] = defaultOptions[opt].defaultValue;\n    }\n  }\n  return ret;\n}\n\nfunction allOptionsOn () {\n  'use strict';\n  var options = getDefaultOpts(true),\n      ret = {};\n  for (var opt in options) {\n    if (options.hasOwnProperty(opt)) {\n      ret[opt] = true;\n    }\n  }\n  return ret;\n}\n\r\n/**\n * Created by Tivie on 06-01-2015.\n */\n\n// Private properties\nvar showdown = {},\n    parsers = {},\n    extensions = {},\n    globalOptions = getDefaultOpts(true),\n    setFlavor = 'vanilla',\n    flavor = {\n      github: {\n        omitExtraWLInCodeBlocks:              true,\n        simplifiedAutoLink:                   true,\n        excludeTrailingPunctuationFromURLs:   true,\n        literalMidWordUnderscores:            true,\n        strikethrough:                        true,\n        tables:                               true,\n        tablesHeaderId:                       true,\n        ghCodeBlocks:                         true,\n        tasklists:                            true,\n        disableForced4SpacesIndentedSublists: true,\n        simpleLineBreaks:                     true,\n        requireSpaceBeforeHeadingText:        true,\n        ghCompatibleHeaderId:                 true,\n        ghMentions:                           true,\n        backslashEscapesHTMLTags:             true,\n        emoji:                                true,\n        splitAdjacentBlockquotes:             true\n      },\n      original: {\n        noHeaderId:                           true,\n        ghCodeBlocks:                         false\n      },\n      ghost: {\n        omitExtraWLInCodeBlocks:              true,\n        parseImgDimensions:                   true,\n        simplifiedAutoLink:                   true,\n        excludeTrailingPunctuationFromURLs:   true,\n        literalMidWordUnderscores:            true,\n        strikethrough:                        true,\n        tables:                               true,\n        tablesHeaderId:                       true,\n        ghCodeBlocks:                         true,\n        tasklists:                            true,\n        smoothLivePreview:                    true,\n        simpleLineBreaks:                     true,\n        requireSpaceBeforeHeadingText:        true,\n        ghMentions:                           false,\n        encodeEmails:                         true\n      },\n      vanilla: getDefaultOpts(true),\n      allOn: allOptionsOn()\n    };\n\n/**\n * helper namespace\n * @type {{}}\n */\nshowdown.helper = {};\n\n/**\n * TODO LEGACY SUPPORT CODE\n * @type {{}}\n */\nshowdown.extensions = {};\n\n/**\n * Set a global option\n * @static\n * @param {string} key\n * @param {*} value\n * @returns {showdown}\n */\nshowdown.setOption = function (key, value) {\n  'use strict';\n  globalOptions[key] = value;\n  return this;\n};\n\n/**\n * Get a global option\n * @static\n * @param {string} key\n * @returns {*}\n */\nshowdown.getOption = function (key) {\n  'use strict';\n  return globalOptions[key];\n};\n\n/**\n * Get the global options\n * @static\n * @returns {{}}\n */\nshowdown.getOptions = function () {\n  'use strict';\n  return globalOptions;\n};\n\n/**\n * Reset global options to the default values\n * @static\n */\nshowdown.resetOptions = function () {\n  'use strict';\n  globalOptions = getDefaultOpts(true);\n};\n\n/**\n * Set the flavor showdown should use as default\n * @param {string} name\n */\nshowdown.setFlavor = function (name) {\n  'use strict';\n  if (!flavor.hasOwnProperty(name)) {\n    throw Error(name + ' flavor was not found');\n  }\n  showdown.resetOptions();\n  var preset = flavor[name];\n  setFlavor = name;\n  for (var option in preset) {\n    if (preset.hasOwnProperty(option)) {\n      globalOptions[option] = preset[option];\n    }\n  }\n};\n\n/**\n * Get the currently set flavor\n * @returns {string}\n */\nshowdown.getFlavor = function () {\n  'use strict';\n  return setFlavor;\n};\n\n/**\n * Get the options of a specified flavor. Returns undefined if the flavor was not found\n * @param {string} name Name of the flavor\n * @returns {{}|undefined}\n */\nshowdown.getFlavorOptions = function (name) {\n  'use strict';\n  if (flavor.hasOwnProperty(name)) {\n    return flavor[name];\n  }\n};\n\n/**\n * Get the default options\n * @static\n * @param {boolean} [simple=true]\n * @returns {{}}\n */\nshowdown.getDefaultOptions = function (simple) {\n  'use strict';\n  return getDefaultOpts(simple);\n};\n\n/**\n * Get or set a subParser\n *\n * subParser(name)       - Get a registered subParser\n * subParser(name, func) - Register a subParser\n * @static\n * @param {string} name\n * @param {function} [func]\n * @returns {*}\n */\nshowdown.subParser = function (name, func) {\n  'use strict';\n  if (showdown.helper.isString(name)) {\n    if (typeof func !== 'undefined') {\n      parsers[name] = func;\n    } else {\n      if (parsers.hasOwnProperty(name)) {\n        return parsers[name];\n      } else {\n        throw Error('SubParser named ' + name + ' not registered!');\n      }\n    }\n  }\n};\n\n/**\n * Gets or registers an extension\n * @static\n * @param {string} name\n * @param {object|function=} ext\n * @returns {*}\n */\nshowdown.extension = function (name, ext) {\n  'use strict';\n\n  if (!showdown.helper.isString(name)) {\n    throw Error('Extension \\'name\\' must be a string');\n  }\n\n  name = showdown.helper.stdExtName(name);\n\n  // Getter\n  if (showdown.helper.isUndefined(ext)) {\n    if (!extensions.hasOwnProperty(name)) {\n      throw Error('Extension named ' + name + ' is not registered!');\n    }\n    return extensions[name];\n\n    // Setter\n  } else {\n    // Expand extension if it's wrapped in a function\n    if (typeof ext === 'function') {\n      ext = ext();\n    }\n\n    // Ensure extension is an array\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n\n    var validExtension = validate(ext, name);\n\n    if (validExtension.valid) {\n      extensions[name] = ext;\n    } else {\n      throw Error(validExtension.error);\n    }\n  }\n};\n\n/**\n * Gets all extensions registered\n * @returns {{}}\n */\nshowdown.getAllExtensions = function () {\n  'use strict';\n  return extensions;\n};\n\n/**\n * Remove an extension\n * @param {string} name\n */\nshowdown.removeExtension = function (name) {\n  'use strict';\n  delete extensions[name];\n};\n\n/**\n * Removes all extensions\n */\nshowdown.resetExtensions = function () {\n  'use strict';\n  extensions = {};\n};\n\n/**\n * Validate extension\n * @param {array} extension\n * @param {string} name\n * @returns {{valid: boolean, error: string}}\n */\nfunction validate (extension, name) {\n  'use strict';\n\n  var errMsg = (name) ? 'Error in ' + name + ' extension->' : 'Error in unnamed extension',\n      ret = {\n        valid: true,\n        error: ''\n      };\n\n  if (!showdown.helper.isArray(extension)) {\n    extension = [extension];\n  }\n\n  for (var i = 0; i < extension.length; ++i) {\n    var baseMsg = errMsg + ' sub-extension ' + i + ': ',\n        ext = extension[i];\n    if (typeof ext !== 'object') {\n      ret.valid = false;\n      ret.error = baseMsg + 'must be an object, but ' + typeof ext + ' given';\n      return ret;\n    }\n\n    if (!showdown.helper.isString(ext.type)) {\n      ret.valid = false;\n      ret.error = baseMsg + 'property \"type\" must be a string, but ' + typeof ext.type + ' given';\n      return ret;\n    }\n\n    var type = ext.type = ext.type.toLowerCase();\n\n    // normalize extension type\n    if (type === 'language') {\n      type = ext.type = 'lang';\n    }\n\n    if (type === 'html') {\n      type = ext.type = 'output';\n    }\n\n    if (type !== 'lang' && type !== 'output' && type !== 'listener') {\n      ret.valid = false;\n      ret.error = baseMsg + 'type ' + type + ' is not recognized. Valid values: \"lang/language\", \"output/html\" or \"listener\"';\n      return ret;\n    }\n\n    if (type === 'listener') {\n      if (showdown.helper.isUndefined(ext.listeners)) {\n        ret.valid = false;\n        ret.error = baseMsg + '. Extensions of type \"listener\" must have a property called \"listeners\"';\n        return ret;\n      }\n    } else {\n      if (showdown.helper.isUndefined(ext.filter) && showdown.helper.isUndefined(ext.regex)) {\n        ret.valid = false;\n        ret.error = baseMsg + type + ' extensions must define either a \"regex\" property or a \"filter\" method';\n        return ret;\n      }\n    }\n\n    if (ext.listeners) {\n      if (typeof ext.listeners !== 'object') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"listeners\" property must be an object but ' + typeof ext.listeners + ' given';\n        return ret;\n      }\n      for (var ln in ext.listeners) {\n        if (ext.listeners.hasOwnProperty(ln)) {\n          if (typeof ext.listeners[ln] !== 'function') {\n            ret.valid = false;\n            ret.error = baseMsg + '\"listeners\" property must be an hash of [event name]: [callback]. listeners.' + ln +\n              ' must be a function but ' + typeof ext.listeners[ln] + ' given';\n            return ret;\n          }\n        }\n      }\n    }\n\n    if (ext.filter) {\n      if (typeof ext.filter !== 'function') {\n        ret.valid = false;\n        ret.error = baseMsg + '\"filter\" must be a function, but ' + typeof ext.filter + ' given';\n        return ret;\n      }\n    } else if (ext.regex) {\n      if (showdown.helper.isString(ext.regex)) {\n        ext.regex = new RegExp(ext.regex, 'g');\n      }\n      if (!(ext.regex instanceof RegExp)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" property must either be a string or a RegExp object, but ' + typeof ext.regex + ' given';\n        return ret;\n      }\n      if (showdown.helper.isUndefined(ext.replace)) {\n        ret.valid = false;\n        ret.error = baseMsg + '\"regex\" extensions must implement a replace string or function';\n        return ret;\n      }\n    }\n  }\n  return ret;\n}\n\n/**\n * Validate extension\n * @param {object} ext\n * @returns {boolean}\n */\nshowdown.validateExtension = function (ext) {\n  'use strict';\n\n  var validateExtension = validate(ext, null);\n  if (!validateExtension.valid) {\n    console.warn(validateExtension.error);\n    return false;\n  }\n  return true;\n};\n\r\n/**\n * showdownjs helper functions\n */\n\nif (!showdown.hasOwnProperty('helper')) {\n  showdown.helper = {};\n}\n\n/**\n * Check if var is string\n * @static\n * @param {string} a\n * @returns {boolean}\n */\nshowdown.helper.isString = function (a) {\n  'use strict';\n  return (typeof a === 'string' || a instanceof String);\n};\n\n/**\n * Check if var is a function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isFunction = function (a) {\n  'use strict';\n  var getType = {};\n  return a && getType.toString.call(a) === '[object Function]';\n};\n\n/**\n * isArray helper function\n * @static\n * @param {*} a\n * @returns {boolean}\n */\nshowdown.helper.isArray = function (a) {\n  'use strict';\n  return Array.isArray(a);\n};\n\n/**\n * Check if value is undefined\n * @static\n * @param {*} value The value to check.\n * @returns {boolean} Returns `true` if `value` is `undefined`, else `false`.\n */\nshowdown.helper.isUndefined = function (value) {\n  'use strict';\n  return typeof value === 'undefined';\n};\n\n/**\n * ForEach helper function\n * Iterates over Arrays and Objects (own properties only)\n * @static\n * @param {*} obj\n * @param {function} callback Accepts 3 params: 1. value, 2. key, 3. the original array/object\n */\nshowdown.helper.forEach = function (obj, callback) {\n  'use strict';\n  // check if obj is defined\n  if (showdown.helper.isUndefined(obj)) {\n    throw new Error('obj param is required');\n  }\n\n  if (showdown.helper.isUndefined(callback)) {\n    throw new Error('callback param is required');\n  }\n\n  if (!showdown.helper.isFunction(callback)) {\n    throw new Error('callback param must be a function/closure');\n  }\n\n  if (typeof obj.forEach === 'function') {\n    obj.forEach(callback);\n  } else if (showdown.helper.isArray(obj)) {\n    for (var i = 0; i < obj.length; i++) {\n      callback(obj[i], i, obj);\n    }\n  } else if (typeof (obj) === 'object') {\n    for (var prop in obj) {\n      if (obj.hasOwnProperty(prop)) {\n        callback(obj[prop], prop, obj);\n      }\n    }\n  } else {\n    throw new Error('obj does not seem to be an array or an iterable object');\n  }\n};\n\n/**\n * Standardidize extension name\n * @static\n * @param {string} s extension name\n * @returns {string}\n */\nshowdown.helper.stdExtName = function (s) {\n  'use strict';\n  return s.replace(/[_?*+\\/\\\\.^-]/g, '').replace(/\\s/g, '').toLowerCase();\n};\n\nfunction escapeCharactersCallback (wholeMatch, m1) {\n  'use strict';\n  var charCodeToEscape = m1.charCodeAt(0);\n  return '¨E' + charCodeToEscape + 'E';\n}\n\n/**\n * Callback used to escape characters when passing through String.replace\n * @static\n * @param {string} wholeMatch\n * @param {string} m1\n * @returns {string}\n */\nshowdown.helper.escapeCharactersCallback = escapeCharactersCallback;\n\n/**\n * Escape characters in a string\n * @static\n * @param {string} text\n * @param {string} charsToEscape\n * @param {boolean} afterBackslash\n * @returns {XML|string|void|*}\n */\nshowdown.helper.escapeCharacters = function (text, charsToEscape, afterBackslash) {\n  'use strict';\n  // First we have to escape the escape characters so that\n  // we can build a character class out of them\n  var regexString = '([' + charsToEscape.replace(/([\\[\\]\\\\])/g, '\\\\$1') + '])';\n\n  if (afterBackslash) {\n    regexString = '\\\\\\\\' + regexString;\n  }\n\n  var regex = new RegExp(regexString, 'g');\n  text = text.replace(regex, escapeCharactersCallback);\n\n  return text;\n};\n\n/**\n * Unescape HTML entities\n * @param txt\n * @returns {string}\n */\nshowdown.helper.unescapeHTMLEntities = function (txt) {\n  'use strict';\n\n  return txt\n    .replace(/"/g, '\"')\n    .replace(/</g, '<')\n    .replace(/>/g, '>')\n    .replace(/&/g, '&');\n};\n\nvar rgxFindMatchPos = function (str, left, right, flags) {\n  'use strict';\n  var f = flags || '',\n      g = f.indexOf('g') > -1,\n      x = new RegExp(left + '|' + right, 'g' + f.replace(/g/g, '')),\n      l = new RegExp(left, f.replace(/g/g, '')),\n      pos = [],\n      t, s, m, start, end;\n\n  do {\n    t = 0;\n    while ((m = x.exec(str))) {\n      if (l.test(m[0])) {\n        if (!(t++)) {\n          s = x.lastIndex;\n          start = s - m[0].length;\n        }\n      } else if (t) {\n        if (!--t) {\n          end = m.index + m[0].length;\n          var obj = {\n            left: {start: start, end: s},\n            match: {start: s, end: m.index},\n            right: {start: m.index, end: end},\n            wholeMatch: {start: start, end: end}\n          };\n          pos.push(obj);\n          if (!g) {\n            return pos;\n          }\n        }\n      }\n    }\n  } while (t && (x.lastIndex = s));\n\n  return pos;\n};\n\n/**\n * matchRecursiveRegExp\n *\n * (c) 2007 Steven Levithan \n * MIT License\n *\n * Accepts a string to search, a left and right format delimiter\n * as regex patterns, and optional regex flags. Returns an array\n * of matches, allowing nested instances of left/right delimiters.\n * Use the \"g\" flag to return all matches, otherwise only the\n * first is returned. Be careful to ensure that the left and\n * right format delimiters produce mutually exclusive matches.\n * Backreferences are not supported within the right delimiter\n * due to how it is internally combined with the left delimiter.\n * When matching strings whose format delimiters are unbalanced\n * to the left or right, the output is intentionally as a\n * conventional regex library with recursion support would\n * produce, e.g. \"<\" and \">\" both produce [\"x\"] when using\n * \"<\" and \">\" as the delimiters (both strings contain a single,\n * balanced instance of \"\").\n *\n * examples:\n * matchRecursiveRegExp(\"test\", \"\\\\(\", \"\\\\)\")\n * returns: []\n * matchRecursiveRegExp(\">>t<>\", \"<\", \">\", \"g\")\n * returns: [\"t<>\", \"\"]\n * matchRecursiveRegExp(\"
    test
    \", \"]*>\", \"\", \"gi\")\n * returns: [\"test\"]\n */\nshowdown.helper.matchRecursiveRegExp = function (str, left, right, flags) {\n  'use strict';\n\n  var matchPos = rgxFindMatchPos (str, left, right, flags),\n      results = [];\n\n  for (var i = 0; i < matchPos.length; ++i) {\n    results.push([\n      str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n      str.slice(matchPos[i].match.start, matchPos[i].match.end),\n      str.slice(matchPos[i].left.start, matchPos[i].left.end),\n      str.slice(matchPos[i].right.start, matchPos[i].right.end)\n    ]);\n  }\n  return results;\n};\n\n/**\n *\n * @param {string} str\n * @param {string|function} replacement\n * @param {string} left\n * @param {string} right\n * @param {string} flags\n * @returns {string}\n */\nshowdown.helper.replaceRecursiveRegExp = function (str, replacement, left, right, flags) {\n  'use strict';\n\n  if (!showdown.helper.isFunction(replacement)) {\n    var repStr = replacement;\n    replacement = function () {\n      return repStr;\n    };\n  }\n\n  var matchPos = rgxFindMatchPos(str, left, right, flags),\n      finalStr = str,\n      lng = matchPos.length;\n\n  if (lng > 0) {\n    var bits = [];\n    if (matchPos[0].wholeMatch.start !== 0) {\n      bits.push(str.slice(0, matchPos[0].wholeMatch.start));\n    }\n    for (var i = 0; i < lng; ++i) {\n      bits.push(\n        replacement(\n          str.slice(matchPos[i].wholeMatch.start, matchPos[i].wholeMatch.end),\n          str.slice(matchPos[i].match.start, matchPos[i].match.end),\n          str.slice(matchPos[i].left.start, matchPos[i].left.end),\n          str.slice(matchPos[i].right.start, matchPos[i].right.end)\n        )\n      );\n      if (i < lng - 1) {\n        bits.push(str.slice(matchPos[i].wholeMatch.end, matchPos[i + 1].wholeMatch.start));\n      }\n    }\n    if (matchPos[lng - 1].wholeMatch.end < str.length) {\n      bits.push(str.slice(matchPos[lng - 1].wholeMatch.end));\n    }\n    finalStr = bits.join('');\n  }\n  return finalStr;\n};\n\n/**\n * Returns the index within the passed String object of the first occurrence of the specified regex,\n * starting the search at fromIndex. Returns -1 if the value is not found.\n *\n * @param {string} str string to search\n * @param {RegExp} regex Regular expression to search\n * @param {int} [fromIndex = 0] Index to start the search\n * @returns {Number}\n * @throws InvalidArgumentError\n */\nshowdown.helper.regexIndexOf = function (str, regex, fromIndex) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  if (regex instanceof RegExp === false) {\n    throw 'InvalidArgumentError: second parameter of showdown.helper.regexIndexOf function must be an instance of RegExp';\n  }\n  var indexOf = str.substring(fromIndex || 0).search(regex);\n  return (indexOf >= 0) ? (indexOf + (fromIndex || 0)) : indexOf;\n};\n\n/**\n * Splits the passed string object at the defined index, and returns an array composed of the two substrings\n * @param {string} str string to split\n * @param {int} index index to split string at\n * @returns {[string,string]}\n * @throws InvalidArgumentError\n */\nshowdown.helper.splitAtIndex = function (str, index) {\n  'use strict';\n  if (!showdown.helper.isString(str)) {\n    throw 'InvalidArgumentError: first parameter of showdown.helper.regexIndexOf function must be a string';\n  }\n  return [str.substring(0, index), str.substring(index)];\n};\n\n/**\n * Obfuscate an e-mail address through the use of Character Entities,\n * transforming ASCII characters into their equivalent decimal or hex entities.\n *\n * Since it has a random component, subsequent calls to this function produce different results\n *\n * @param {string} mail\n * @returns {string}\n */\nshowdown.helper.encodeEmailAddress = function (mail) {\n  'use strict';\n  var encode = [\n    function (ch) {\n      return '&#' + ch.charCodeAt(0) + ';';\n    },\n    function (ch) {\n      return '&#x' + ch.charCodeAt(0).toString(16) + ';';\n    },\n    function (ch) {\n      return ch;\n    }\n  ];\n\n  mail = mail.replace(/./g, function (ch) {\n    if (ch === '@') {\n      // this *must* be encoded. I insist.\n      ch = encode[Math.floor(Math.random() * 2)](ch);\n    } else {\n      var r = Math.random();\n      // roughly 10% raw, 45% hex, 45% dec\n      ch = (\n        r > 0.9 ? encode[2](ch) : r > 0.45 ? encode[1](ch) : encode[0](ch)\n      );\n    }\n    return ch;\n  });\n\n  return mail;\n};\n\n/**\n *\n * @param str\n * @param targetLength\n * @param padString\n * @returns {string}\n */\nshowdown.helper.padEnd = function padEnd (str, targetLength, padString) {\n  'use strict';\n  /*jshint bitwise: false*/\n  // eslint-disable-next-line space-infix-ops\n  targetLength = targetLength>>0; //floor if number or convert non-number to 0;\n  /*jshint bitwise: true*/\n  padString = String(padString || ' ');\n  if (str.length > targetLength) {\n    return String(str);\n  } else {\n    targetLength = targetLength - str.length;\n    if (targetLength > padString.length) {\n      padString += padString.repeat(targetLength / padString.length); //append to original to ensure we are longer than needed\n    }\n    return String(str) + padString.slice(0,targetLength);\n  }\n};\n\n/**\n * POLYFILLS\n */\n// use this instead of builtin is undefined for IE8 compatibility\nif (typeof console === 'undefined') {\n  console = {\n    warn: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    log: function (msg) {\n      'use strict';\n      alert(msg);\n    },\n    error: function (msg) {\n      'use strict';\n      throw msg;\n    }\n  };\n}\n\n/**\n * Common regexes.\n * We declare some common regexes to improve performance\n */\nshowdown.helper.regexes = {\n  asteriskDashAndColon: /([*_:~])/g\n};\n\n/**\n * EMOJIS LIST\n */\nshowdown.helper.emojis = {\n  '+1':'\\ud83d\\udc4d',\n  '-1':'\\ud83d\\udc4e',\n  '100':'\\ud83d\\udcaf',\n  '1234':'\\ud83d\\udd22',\n  '1st_place_medal':'\\ud83e\\udd47',\n  '2nd_place_medal':'\\ud83e\\udd48',\n  '3rd_place_medal':'\\ud83e\\udd49',\n  '8ball':'\\ud83c\\udfb1',\n  'a':'\\ud83c\\udd70\\ufe0f',\n  'ab':'\\ud83c\\udd8e',\n  'abc':'\\ud83d\\udd24',\n  'abcd':'\\ud83d\\udd21',\n  'accept':'\\ud83c\\ude51',\n  'aerial_tramway':'\\ud83d\\udea1',\n  'airplane':'\\u2708\\ufe0f',\n  'alarm_clock':'\\u23f0',\n  'alembic':'\\u2697\\ufe0f',\n  'alien':'\\ud83d\\udc7d',\n  'ambulance':'\\ud83d\\ude91',\n  'amphora':'\\ud83c\\udffa',\n  'anchor':'\\u2693\\ufe0f',\n  'angel':'\\ud83d\\udc7c',\n  'anger':'\\ud83d\\udca2',\n  'angry':'\\ud83d\\ude20',\n  'anguished':'\\ud83d\\ude27',\n  'ant':'\\ud83d\\udc1c',\n  'apple':'\\ud83c\\udf4e',\n  'aquarius':'\\u2652\\ufe0f',\n  'aries':'\\u2648\\ufe0f',\n  'arrow_backward':'\\u25c0\\ufe0f',\n  'arrow_double_down':'\\u23ec',\n  'arrow_double_up':'\\u23eb',\n  'arrow_down':'\\u2b07\\ufe0f',\n  'arrow_down_small':'\\ud83d\\udd3d',\n  'arrow_forward':'\\u25b6\\ufe0f',\n  'arrow_heading_down':'\\u2935\\ufe0f',\n  'arrow_heading_up':'\\u2934\\ufe0f',\n  'arrow_left':'\\u2b05\\ufe0f',\n  'arrow_lower_left':'\\u2199\\ufe0f',\n  'arrow_lower_right':'\\u2198\\ufe0f',\n  'arrow_right':'\\u27a1\\ufe0f',\n  'arrow_right_hook':'\\u21aa\\ufe0f',\n  'arrow_up':'\\u2b06\\ufe0f',\n  'arrow_up_down':'\\u2195\\ufe0f',\n  'arrow_up_small':'\\ud83d\\udd3c',\n  'arrow_upper_left':'\\u2196\\ufe0f',\n  'arrow_upper_right':'\\u2197\\ufe0f',\n  'arrows_clockwise':'\\ud83d\\udd03',\n  'arrows_counterclockwise':'\\ud83d\\udd04',\n  'art':'\\ud83c\\udfa8',\n  'articulated_lorry':'\\ud83d\\ude9b',\n  'artificial_satellite':'\\ud83d\\udef0',\n  'astonished':'\\ud83d\\ude32',\n  'athletic_shoe':'\\ud83d\\udc5f',\n  'atm':'\\ud83c\\udfe7',\n  'atom_symbol':'\\u269b\\ufe0f',\n  'avocado':'\\ud83e\\udd51',\n  'b':'\\ud83c\\udd71\\ufe0f',\n  'baby':'\\ud83d\\udc76',\n  'baby_bottle':'\\ud83c\\udf7c',\n  'baby_chick':'\\ud83d\\udc24',\n  'baby_symbol':'\\ud83d\\udebc',\n  'back':'\\ud83d\\udd19',\n  'bacon':'\\ud83e\\udd53',\n  'badminton':'\\ud83c\\udff8',\n  'baggage_claim':'\\ud83d\\udec4',\n  'baguette_bread':'\\ud83e\\udd56',\n  'balance_scale':'\\u2696\\ufe0f',\n  'balloon':'\\ud83c\\udf88',\n  'ballot_box':'\\ud83d\\uddf3',\n  'ballot_box_with_check':'\\u2611\\ufe0f',\n  'bamboo':'\\ud83c\\udf8d',\n  'banana':'\\ud83c\\udf4c',\n  'bangbang':'\\u203c\\ufe0f',\n  'bank':'\\ud83c\\udfe6',\n  'bar_chart':'\\ud83d\\udcca',\n  'barber':'\\ud83d\\udc88',\n  'baseball':'\\u26be\\ufe0f',\n  'basketball':'\\ud83c\\udfc0',\n  'basketball_man':'\\u26f9\\ufe0f',\n  'basketball_woman':'\\u26f9\\ufe0f‍\\u2640\\ufe0f',\n  'bat':'\\ud83e\\udd87',\n  'bath':'\\ud83d\\udec0',\n  'bathtub':'\\ud83d\\udec1',\n  'battery':'\\ud83d\\udd0b',\n  'beach_umbrella':'\\ud83c\\udfd6',\n  'bear':'\\ud83d\\udc3b',\n  'bed':'\\ud83d\\udecf',\n  'bee':'\\ud83d\\udc1d',\n  'beer':'\\ud83c\\udf7a',\n  'beers':'\\ud83c\\udf7b',\n  'beetle':'\\ud83d\\udc1e',\n  'beginner':'\\ud83d\\udd30',\n  'bell':'\\ud83d\\udd14',\n  'bellhop_bell':'\\ud83d\\udece',\n  'bento':'\\ud83c\\udf71',\n  'biking_man':'\\ud83d\\udeb4',\n  'bike':'\\ud83d\\udeb2',\n  'biking_woman':'\\ud83d\\udeb4‍\\u2640\\ufe0f',\n  'bikini':'\\ud83d\\udc59',\n  'biohazard':'\\u2623\\ufe0f',\n  'bird':'\\ud83d\\udc26',\n  'birthday':'\\ud83c\\udf82',\n  'black_circle':'\\u26ab\\ufe0f',\n  'black_flag':'\\ud83c\\udff4',\n  'black_heart':'\\ud83d\\udda4',\n  'black_joker':'\\ud83c\\udccf',\n  'black_large_square':'\\u2b1b\\ufe0f',\n  'black_medium_small_square':'\\u25fe\\ufe0f',\n  'black_medium_square':'\\u25fc\\ufe0f',\n  'black_nib':'\\u2712\\ufe0f',\n  'black_small_square':'\\u25aa\\ufe0f',\n  'black_square_button':'\\ud83d\\udd32',\n  'blonde_man':'\\ud83d\\udc71',\n  'blonde_woman':'\\ud83d\\udc71‍\\u2640\\ufe0f',\n  'blossom':'\\ud83c\\udf3c',\n  'blowfish':'\\ud83d\\udc21',\n  'blue_book':'\\ud83d\\udcd8',\n  'blue_car':'\\ud83d\\ude99',\n  'blue_heart':'\\ud83d\\udc99',\n  'blush':'\\ud83d\\ude0a',\n  'boar':'\\ud83d\\udc17',\n  'boat':'\\u26f5\\ufe0f',\n  'bomb':'\\ud83d\\udca3',\n  'book':'\\ud83d\\udcd6',\n  'bookmark':'\\ud83d\\udd16',\n  'bookmark_tabs':'\\ud83d\\udcd1',\n  'books':'\\ud83d\\udcda',\n  'boom':'\\ud83d\\udca5',\n  'boot':'\\ud83d\\udc62',\n  'bouquet':'\\ud83d\\udc90',\n  'bowing_man':'\\ud83d\\ude47',\n  'bow_and_arrow':'\\ud83c\\udff9',\n  'bowing_woman':'\\ud83d\\ude47‍\\u2640\\ufe0f',\n  'bowling':'\\ud83c\\udfb3',\n  'boxing_glove':'\\ud83e\\udd4a',\n  'boy':'\\ud83d\\udc66',\n  'bread':'\\ud83c\\udf5e',\n  'bride_with_veil':'\\ud83d\\udc70',\n  'bridge_at_night':'\\ud83c\\udf09',\n  'briefcase':'\\ud83d\\udcbc',\n  'broken_heart':'\\ud83d\\udc94',\n  'bug':'\\ud83d\\udc1b',\n  'building_construction':'\\ud83c\\udfd7',\n  'bulb':'\\ud83d\\udca1',\n  'bullettrain_front':'\\ud83d\\ude85',\n  'bullettrain_side':'\\ud83d\\ude84',\n  'burrito':'\\ud83c\\udf2f',\n  'bus':'\\ud83d\\ude8c',\n  'business_suit_levitating':'\\ud83d\\udd74',\n  'busstop':'\\ud83d\\ude8f',\n  'bust_in_silhouette':'\\ud83d\\udc64',\n  'busts_in_silhouette':'\\ud83d\\udc65',\n  'butterfly':'\\ud83e\\udd8b',\n  'cactus':'\\ud83c\\udf35',\n  'cake':'\\ud83c\\udf70',\n  'calendar':'\\ud83d\\udcc6',\n  'call_me_hand':'\\ud83e\\udd19',\n  'calling':'\\ud83d\\udcf2',\n  'camel':'\\ud83d\\udc2b',\n  'camera':'\\ud83d\\udcf7',\n  'camera_flash':'\\ud83d\\udcf8',\n  'camping':'\\ud83c\\udfd5',\n  'cancer':'\\u264b\\ufe0f',\n  'candle':'\\ud83d\\udd6f',\n  'candy':'\\ud83c\\udf6c',\n  'canoe':'\\ud83d\\udef6',\n  'capital_abcd':'\\ud83d\\udd20',\n  'capricorn':'\\u2651\\ufe0f',\n  'car':'\\ud83d\\ude97',\n  'card_file_box':'\\ud83d\\uddc3',\n  'card_index':'\\ud83d\\udcc7',\n  'card_index_dividers':'\\ud83d\\uddc2',\n  'carousel_horse':'\\ud83c\\udfa0',\n  'carrot':'\\ud83e\\udd55',\n  'cat':'\\ud83d\\udc31',\n  'cat2':'\\ud83d\\udc08',\n  'cd':'\\ud83d\\udcbf',\n  'chains':'\\u26d3',\n  'champagne':'\\ud83c\\udf7e',\n  'chart':'\\ud83d\\udcb9',\n  'chart_with_downwards_trend':'\\ud83d\\udcc9',\n  'chart_with_upwards_trend':'\\ud83d\\udcc8',\n  'checkered_flag':'\\ud83c\\udfc1',\n  'cheese':'\\ud83e\\uddc0',\n  'cherries':'\\ud83c\\udf52',\n  'cherry_blossom':'\\ud83c\\udf38',\n  'chestnut':'\\ud83c\\udf30',\n  'chicken':'\\ud83d\\udc14',\n  'children_crossing':'\\ud83d\\udeb8',\n  'chipmunk':'\\ud83d\\udc3f',\n  'chocolate_bar':'\\ud83c\\udf6b',\n  'christmas_tree':'\\ud83c\\udf84',\n  'church':'\\u26ea\\ufe0f',\n  'cinema':'\\ud83c\\udfa6',\n  'circus_tent':'\\ud83c\\udfaa',\n  'city_sunrise':'\\ud83c\\udf07',\n  'city_sunset':'\\ud83c\\udf06',\n  'cityscape':'\\ud83c\\udfd9',\n  'cl':'\\ud83c\\udd91',\n  'clamp':'\\ud83d\\udddc',\n  'clap':'\\ud83d\\udc4f',\n  'clapper':'\\ud83c\\udfac',\n  'classical_building':'\\ud83c\\udfdb',\n  'clinking_glasses':'\\ud83e\\udd42',\n  'clipboard':'\\ud83d\\udccb',\n  'clock1':'\\ud83d\\udd50',\n  'clock10':'\\ud83d\\udd59',\n  'clock1030':'\\ud83d\\udd65',\n  'clock11':'\\ud83d\\udd5a',\n  'clock1130':'\\ud83d\\udd66',\n  'clock12':'\\ud83d\\udd5b',\n  'clock1230':'\\ud83d\\udd67',\n  'clock130':'\\ud83d\\udd5c',\n  'clock2':'\\ud83d\\udd51',\n  'clock230':'\\ud83d\\udd5d',\n  'clock3':'\\ud83d\\udd52',\n  'clock330':'\\ud83d\\udd5e',\n  'clock4':'\\ud83d\\udd53',\n  'clock430':'\\ud83d\\udd5f',\n  'clock5':'\\ud83d\\udd54',\n  'clock530':'\\ud83d\\udd60',\n  'clock6':'\\ud83d\\udd55',\n  'clock630':'\\ud83d\\udd61',\n  'clock7':'\\ud83d\\udd56',\n  'clock730':'\\ud83d\\udd62',\n  'clock8':'\\ud83d\\udd57',\n  'clock830':'\\ud83d\\udd63',\n  'clock9':'\\ud83d\\udd58',\n  'clock930':'\\ud83d\\udd64',\n  'closed_book':'\\ud83d\\udcd5',\n  'closed_lock_with_key':'\\ud83d\\udd10',\n  'closed_umbrella':'\\ud83c\\udf02',\n  'cloud':'\\u2601\\ufe0f',\n  'cloud_with_lightning':'\\ud83c\\udf29',\n  'cloud_with_lightning_and_rain':'\\u26c8',\n  'cloud_with_rain':'\\ud83c\\udf27',\n  'cloud_with_snow':'\\ud83c\\udf28',\n  'clown_face':'\\ud83e\\udd21',\n  'clubs':'\\u2663\\ufe0f',\n  'cocktail':'\\ud83c\\udf78',\n  'coffee':'\\u2615\\ufe0f',\n  'coffin':'\\u26b0\\ufe0f',\n  'cold_sweat':'\\ud83d\\ude30',\n  'comet':'\\u2604\\ufe0f',\n  'computer':'\\ud83d\\udcbb',\n  'computer_mouse':'\\ud83d\\uddb1',\n  'confetti_ball':'\\ud83c\\udf8a',\n  'confounded':'\\ud83d\\ude16',\n  'confused':'\\ud83d\\ude15',\n  'congratulations':'\\u3297\\ufe0f',\n  'construction':'\\ud83d\\udea7',\n  'construction_worker_man':'\\ud83d\\udc77',\n  'construction_worker_woman':'\\ud83d\\udc77‍\\u2640\\ufe0f',\n  'control_knobs':'\\ud83c\\udf9b',\n  'convenience_store':'\\ud83c\\udfea',\n  'cookie':'\\ud83c\\udf6a',\n  'cool':'\\ud83c\\udd92',\n  'policeman':'\\ud83d\\udc6e',\n  'copyright':'\\u00a9\\ufe0f',\n  'corn':'\\ud83c\\udf3d',\n  'couch_and_lamp':'\\ud83d\\udecb',\n  'couple':'\\ud83d\\udc6b',\n  'couple_with_heart_woman_man':'\\ud83d\\udc91',\n  'couple_with_heart_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc68',\n  'couple_with_heart_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc69',\n  'couplekiss_man_man':'\\ud83d\\udc68‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc68',\n  'couplekiss_man_woman':'\\ud83d\\udc8f',\n  'couplekiss_woman_woman':'\\ud83d\\udc69‍\\u2764\\ufe0f‍\\ud83d\\udc8b‍\\ud83d\\udc69',\n  'cow':'\\ud83d\\udc2e',\n  'cow2':'\\ud83d\\udc04',\n  'cowboy_hat_face':'\\ud83e\\udd20',\n  'crab':'\\ud83e\\udd80',\n  'crayon':'\\ud83d\\udd8d',\n  'credit_card':'\\ud83d\\udcb3',\n  'crescent_moon':'\\ud83c\\udf19',\n  'cricket':'\\ud83c\\udfcf',\n  'crocodile':'\\ud83d\\udc0a',\n  'croissant':'\\ud83e\\udd50',\n  'crossed_fingers':'\\ud83e\\udd1e',\n  'crossed_flags':'\\ud83c\\udf8c',\n  'crossed_swords':'\\u2694\\ufe0f',\n  'crown':'\\ud83d\\udc51',\n  'cry':'\\ud83d\\ude22',\n  'crying_cat_face':'\\ud83d\\ude3f',\n  'crystal_ball':'\\ud83d\\udd2e',\n  'cucumber':'\\ud83e\\udd52',\n  'cupid':'\\ud83d\\udc98',\n  'curly_loop':'\\u27b0',\n  'currency_exchange':'\\ud83d\\udcb1',\n  'curry':'\\ud83c\\udf5b',\n  'custard':'\\ud83c\\udf6e',\n  'customs':'\\ud83d\\udec3',\n  'cyclone':'\\ud83c\\udf00',\n  'dagger':'\\ud83d\\udde1',\n  'dancer':'\\ud83d\\udc83',\n  'dancing_women':'\\ud83d\\udc6f',\n  'dancing_men':'\\ud83d\\udc6f‍\\u2642\\ufe0f',\n  'dango':'\\ud83c\\udf61',\n  'dark_sunglasses':'\\ud83d\\udd76',\n  'dart':'\\ud83c\\udfaf',\n  'dash':'\\ud83d\\udca8',\n  'date':'\\ud83d\\udcc5',\n  'deciduous_tree':'\\ud83c\\udf33',\n  'deer':'\\ud83e\\udd8c',\n  'department_store':'\\ud83c\\udfec',\n  'derelict_house':'\\ud83c\\udfda',\n  'desert':'\\ud83c\\udfdc',\n  'desert_island':'\\ud83c\\udfdd',\n  'desktop_computer':'\\ud83d\\udda5',\n  'male_detective':'\\ud83d\\udd75\\ufe0f',\n  'diamond_shape_with_a_dot_inside':'\\ud83d\\udca0',\n  'diamonds':'\\u2666\\ufe0f',\n  'disappointed':'\\ud83d\\ude1e',\n  'disappointed_relieved':'\\ud83d\\ude25',\n  'dizzy':'\\ud83d\\udcab',\n  'dizzy_face':'\\ud83d\\ude35',\n  'do_not_litter':'\\ud83d\\udeaf',\n  'dog':'\\ud83d\\udc36',\n  'dog2':'\\ud83d\\udc15',\n  'dollar':'\\ud83d\\udcb5',\n  'dolls':'\\ud83c\\udf8e',\n  'dolphin':'\\ud83d\\udc2c',\n  'door':'\\ud83d\\udeaa',\n  'doughnut':'\\ud83c\\udf69',\n  'dove':'\\ud83d\\udd4a',\n  'dragon':'\\ud83d\\udc09',\n  'dragon_face':'\\ud83d\\udc32',\n  'dress':'\\ud83d\\udc57',\n  'dromedary_camel':'\\ud83d\\udc2a',\n  'drooling_face':'\\ud83e\\udd24',\n  'droplet':'\\ud83d\\udca7',\n  'drum':'\\ud83e\\udd41',\n  'duck':'\\ud83e\\udd86',\n  'dvd':'\\ud83d\\udcc0',\n  'e-mail':'\\ud83d\\udce7',\n  'eagle':'\\ud83e\\udd85',\n  'ear':'\\ud83d\\udc42',\n  'ear_of_rice':'\\ud83c\\udf3e',\n  'earth_africa':'\\ud83c\\udf0d',\n  'earth_americas':'\\ud83c\\udf0e',\n  'earth_asia':'\\ud83c\\udf0f',\n  'egg':'\\ud83e\\udd5a',\n  'eggplant':'\\ud83c\\udf46',\n  'eight_pointed_black_star':'\\u2734\\ufe0f',\n  'eight_spoked_asterisk':'\\u2733\\ufe0f',\n  'electric_plug':'\\ud83d\\udd0c',\n  'elephant':'\\ud83d\\udc18',\n  'email':'\\u2709\\ufe0f',\n  'end':'\\ud83d\\udd1a',\n  'envelope_with_arrow':'\\ud83d\\udce9',\n  'euro':'\\ud83d\\udcb6',\n  'european_castle':'\\ud83c\\udff0',\n  'european_post_office':'\\ud83c\\udfe4',\n  'evergreen_tree':'\\ud83c\\udf32',\n  'exclamation':'\\u2757\\ufe0f',\n  'expressionless':'\\ud83d\\ude11',\n  'eye':'\\ud83d\\udc41',\n  'eye_speech_bubble':'\\ud83d\\udc41‍\\ud83d\\udde8',\n  'eyeglasses':'\\ud83d\\udc53',\n  'eyes':'\\ud83d\\udc40',\n  'face_with_head_bandage':'\\ud83e\\udd15',\n  'face_with_thermometer':'\\ud83e\\udd12',\n  'fist_oncoming':'\\ud83d\\udc4a',\n  'factory':'\\ud83c\\udfed',\n  'fallen_leaf':'\\ud83c\\udf42',\n  'family_man_woman_boy':'\\ud83d\\udc6a',\n  'family_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_man_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66',\n  'family_man_man_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_man_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67',\n  'family_man_man_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_man_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc68‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_man_woman_boy_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_man_woman_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_man_woman_girl_boy':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_man_woman_girl_girl':'\\ud83d\\udc68‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'family_woman_woman_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66',\n  'family_woman_woman_boy_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc66‍\\ud83d\\udc66',\n  'family_woman_woman_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67',\n  'family_woman_woman_girl_boy':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc66',\n  'family_woman_woman_girl_girl':'\\ud83d\\udc69‍\\ud83d\\udc69‍\\ud83d\\udc67‍\\ud83d\\udc67',\n  'fast_forward':'\\u23e9',\n  'fax':'\\ud83d\\udce0',\n  'fearful':'\\ud83d\\ude28',\n  'feet':'\\ud83d\\udc3e',\n  'female_detective':'\\ud83d\\udd75\\ufe0f‍\\u2640\\ufe0f',\n  'ferris_wheel':'\\ud83c\\udfa1',\n  'ferry':'\\u26f4',\n  'field_hockey':'\\ud83c\\udfd1',\n  'file_cabinet':'\\ud83d\\uddc4',\n  'file_folder':'\\ud83d\\udcc1',\n  'film_projector':'\\ud83d\\udcfd',\n  'film_strip':'\\ud83c\\udf9e',\n  'fire':'\\ud83d\\udd25',\n  'fire_engine':'\\ud83d\\ude92',\n  'fireworks':'\\ud83c\\udf86',\n  'first_quarter_moon':'\\ud83c\\udf13',\n  'first_quarter_moon_with_face':'\\ud83c\\udf1b',\n  'fish':'\\ud83d\\udc1f',\n  'fish_cake':'\\ud83c\\udf65',\n  'fishing_pole_and_fish':'\\ud83c\\udfa3',\n  'fist_raised':'\\u270a',\n  'fist_left':'\\ud83e\\udd1b',\n  'fist_right':'\\ud83e\\udd1c',\n  'flags':'\\ud83c\\udf8f',\n  'flashlight':'\\ud83d\\udd26',\n  'fleur_de_lis':'\\u269c\\ufe0f',\n  'flight_arrival':'\\ud83d\\udeec',\n  'flight_departure':'\\ud83d\\udeeb',\n  'floppy_disk':'\\ud83d\\udcbe',\n  'flower_playing_cards':'\\ud83c\\udfb4',\n  'flushed':'\\ud83d\\ude33',\n  'fog':'\\ud83c\\udf2b',\n  'foggy':'\\ud83c\\udf01',\n  'football':'\\ud83c\\udfc8',\n  'footprints':'\\ud83d\\udc63',\n  'fork_and_knife':'\\ud83c\\udf74',\n  'fountain':'\\u26f2\\ufe0f',\n  'fountain_pen':'\\ud83d\\udd8b',\n  'four_leaf_clover':'\\ud83c\\udf40',\n  'fox_face':'\\ud83e\\udd8a',\n  'framed_picture':'\\ud83d\\uddbc',\n  'free':'\\ud83c\\udd93',\n  'fried_egg':'\\ud83c\\udf73',\n  'fried_shrimp':'\\ud83c\\udf64',\n  'fries':'\\ud83c\\udf5f',\n  'frog':'\\ud83d\\udc38',\n  'frowning':'\\ud83d\\ude26',\n  'frowning_face':'\\u2639\\ufe0f',\n  'frowning_man':'\\ud83d\\ude4d‍\\u2642\\ufe0f',\n  'frowning_woman':'\\ud83d\\ude4d',\n  'middle_finger':'\\ud83d\\udd95',\n  'fuelpump':'\\u26fd\\ufe0f',\n  'full_moon':'\\ud83c\\udf15',\n  'full_moon_with_face':'\\ud83c\\udf1d',\n  'funeral_urn':'\\u26b1\\ufe0f',\n  'game_die':'\\ud83c\\udfb2',\n  'gear':'\\u2699\\ufe0f',\n  'gem':'\\ud83d\\udc8e',\n  'gemini':'\\u264a\\ufe0f',\n  'ghost':'\\ud83d\\udc7b',\n  'gift':'\\ud83c\\udf81',\n  'gift_heart':'\\ud83d\\udc9d',\n  'girl':'\\ud83d\\udc67',\n  'globe_with_meridians':'\\ud83c\\udf10',\n  'goal_net':'\\ud83e\\udd45',\n  'goat':'\\ud83d\\udc10',\n  'golf':'\\u26f3\\ufe0f',\n  'golfing_man':'\\ud83c\\udfcc\\ufe0f',\n  'golfing_woman':'\\ud83c\\udfcc\\ufe0f‍\\u2640\\ufe0f',\n  'gorilla':'\\ud83e\\udd8d',\n  'grapes':'\\ud83c\\udf47',\n  'green_apple':'\\ud83c\\udf4f',\n  'green_book':'\\ud83d\\udcd7',\n  'green_heart':'\\ud83d\\udc9a',\n  'green_salad':'\\ud83e\\udd57',\n  'grey_exclamation':'\\u2755',\n  'grey_question':'\\u2754',\n  'grimacing':'\\ud83d\\ude2c',\n  'grin':'\\ud83d\\ude01',\n  'grinning':'\\ud83d\\ude00',\n  'guardsman':'\\ud83d\\udc82',\n  'guardswoman':'\\ud83d\\udc82‍\\u2640\\ufe0f',\n  'guitar':'\\ud83c\\udfb8',\n  'gun':'\\ud83d\\udd2b',\n  'haircut_woman':'\\ud83d\\udc87',\n  'haircut_man':'\\ud83d\\udc87‍\\u2642\\ufe0f',\n  'hamburger':'\\ud83c\\udf54',\n  'hammer':'\\ud83d\\udd28',\n  'hammer_and_pick':'\\u2692',\n  'hammer_and_wrench':'\\ud83d\\udee0',\n  'hamster':'\\ud83d\\udc39',\n  'hand':'\\u270b',\n  'handbag':'\\ud83d\\udc5c',\n  'handshake':'\\ud83e\\udd1d',\n  'hankey':'\\ud83d\\udca9',\n  'hatched_chick':'\\ud83d\\udc25',\n  'hatching_chick':'\\ud83d\\udc23',\n  'headphones':'\\ud83c\\udfa7',\n  'hear_no_evil':'\\ud83d\\ude49',\n  'heart':'\\u2764\\ufe0f',\n  'heart_decoration':'\\ud83d\\udc9f',\n  'heart_eyes':'\\ud83d\\ude0d',\n  'heart_eyes_cat':'\\ud83d\\ude3b',\n  'heartbeat':'\\ud83d\\udc93',\n  'heartpulse':'\\ud83d\\udc97',\n  'hearts':'\\u2665\\ufe0f',\n  'heavy_check_mark':'\\u2714\\ufe0f',\n  'heavy_division_sign':'\\u2797',\n  'heavy_dollar_sign':'\\ud83d\\udcb2',\n  'heavy_heart_exclamation':'\\u2763\\ufe0f',\n  'heavy_minus_sign':'\\u2796',\n  'heavy_multiplication_x':'\\u2716\\ufe0f',\n  'heavy_plus_sign':'\\u2795',\n  'helicopter':'\\ud83d\\ude81',\n  'herb':'\\ud83c\\udf3f',\n  'hibiscus':'\\ud83c\\udf3a',\n  'high_brightness':'\\ud83d\\udd06',\n  'high_heel':'\\ud83d\\udc60',\n  'hocho':'\\ud83d\\udd2a',\n  'hole':'\\ud83d\\udd73',\n  'honey_pot':'\\ud83c\\udf6f',\n  'horse':'\\ud83d\\udc34',\n  'horse_racing':'\\ud83c\\udfc7',\n  'hospital':'\\ud83c\\udfe5',\n  'hot_pepper':'\\ud83c\\udf36',\n  'hotdog':'\\ud83c\\udf2d',\n  'hotel':'\\ud83c\\udfe8',\n  'hotsprings':'\\u2668\\ufe0f',\n  'hourglass':'\\u231b\\ufe0f',\n  'hourglass_flowing_sand':'\\u23f3',\n  'house':'\\ud83c\\udfe0',\n  'house_with_garden':'\\ud83c\\udfe1',\n  'houses':'\\ud83c\\udfd8',\n  'hugs':'\\ud83e\\udd17',\n  'hushed':'\\ud83d\\ude2f',\n  'ice_cream':'\\ud83c\\udf68',\n  'ice_hockey':'\\ud83c\\udfd2',\n  'ice_skate':'\\u26f8',\n  'icecream':'\\ud83c\\udf66',\n  'id':'\\ud83c\\udd94',\n  'ideograph_advantage':'\\ud83c\\ude50',\n  'imp':'\\ud83d\\udc7f',\n  'inbox_tray':'\\ud83d\\udce5',\n  'incoming_envelope':'\\ud83d\\udce8',\n  'tipping_hand_woman':'\\ud83d\\udc81',\n  'information_source':'\\u2139\\ufe0f',\n  'innocent':'\\ud83d\\ude07',\n  'interrobang':'\\u2049\\ufe0f',\n  'iphone':'\\ud83d\\udcf1',\n  'izakaya_lantern':'\\ud83c\\udfee',\n  'jack_o_lantern':'\\ud83c\\udf83',\n  'japan':'\\ud83d\\uddfe',\n  'japanese_castle':'\\ud83c\\udfef',\n  'japanese_goblin':'\\ud83d\\udc7a',\n  'japanese_ogre':'\\ud83d\\udc79',\n  'jeans':'\\ud83d\\udc56',\n  'joy':'\\ud83d\\ude02',\n  'joy_cat':'\\ud83d\\ude39',\n  'joystick':'\\ud83d\\udd79',\n  'kaaba':'\\ud83d\\udd4b',\n  'key':'\\ud83d\\udd11',\n  'keyboard':'\\u2328\\ufe0f',\n  'keycap_ten':'\\ud83d\\udd1f',\n  'kick_scooter':'\\ud83d\\udef4',\n  'kimono':'\\ud83d\\udc58',\n  'kiss':'\\ud83d\\udc8b',\n  'kissing':'\\ud83d\\ude17',\n  'kissing_cat':'\\ud83d\\ude3d',\n  'kissing_closed_eyes':'\\ud83d\\ude1a',\n  'kissing_heart':'\\ud83d\\ude18',\n  'kissing_smiling_eyes':'\\ud83d\\ude19',\n  'kiwi_fruit':'\\ud83e\\udd5d',\n  'koala':'\\ud83d\\udc28',\n  'koko':'\\ud83c\\ude01',\n  'label':'\\ud83c\\udff7',\n  'large_blue_circle':'\\ud83d\\udd35',\n  'large_blue_diamond':'\\ud83d\\udd37',\n  'large_orange_diamond':'\\ud83d\\udd36',\n  'last_quarter_moon':'\\ud83c\\udf17',\n  'last_quarter_moon_with_face':'\\ud83c\\udf1c',\n  'latin_cross':'\\u271d\\ufe0f',\n  'laughing':'\\ud83d\\ude06',\n  'leaves':'\\ud83c\\udf43',\n  'ledger':'\\ud83d\\udcd2',\n  'left_luggage':'\\ud83d\\udec5',\n  'left_right_arrow':'\\u2194\\ufe0f',\n  'leftwards_arrow_with_hook':'\\u21a9\\ufe0f',\n  'lemon':'\\ud83c\\udf4b',\n  'leo':'\\u264c\\ufe0f',\n  'leopard':'\\ud83d\\udc06',\n  'level_slider':'\\ud83c\\udf9a',\n  'libra':'\\u264e\\ufe0f',\n  'light_rail':'\\ud83d\\ude88',\n  'link':'\\ud83d\\udd17',\n  'lion':'\\ud83e\\udd81',\n  'lips':'\\ud83d\\udc44',\n  'lipstick':'\\ud83d\\udc84',\n  'lizard':'\\ud83e\\udd8e',\n  'lock':'\\ud83d\\udd12',\n  'lock_with_ink_pen':'\\ud83d\\udd0f',\n  'lollipop':'\\ud83c\\udf6d',\n  'loop':'\\u27bf',\n  'loud_sound':'\\ud83d\\udd0a',\n  'loudspeaker':'\\ud83d\\udce2',\n  'love_hotel':'\\ud83c\\udfe9',\n  'love_letter':'\\ud83d\\udc8c',\n  'low_brightness':'\\ud83d\\udd05',\n  'lying_face':'\\ud83e\\udd25',\n  'm':'\\u24c2\\ufe0f',\n  'mag':'\\ud83d\\udd0d',\n  'mag_right':'\\ud83d\\udd0e',\n  'mahjong':'\\ud83c\\udc04\\ufe0f',\n  'mailbox':'\\ud83d\\udceb',\n  'mailbox_closed':'\\ud83d\\udcea',\n  'mailbox_with_mail':'\\ud83d\\udcec',\n  'mailbox_with_no_mail':'\\ud83d\\udced',\n  'man':'\\ud83d\\udc68',\n  'man_artist':'\\ud83d\\udc68‍\\ud83c\\udfa8',\n  'man_astronaut':'\\ud83d\\udc68‍\\ud83d\\ude80',\n  'man_cartwheeling':'\\ud83e\\udd38‍\\u2642\\ufe0f',\n  'man_cook':'\\ud83d\\udc68‍\\ud83c\\udf73',\n  'man_dancing':'\\ud83d\\udd7a',\n  'man_facepalming':'\\ud83e\\udd26‍\\u2642\\ufe0f',\n  'man_factory_worker':'\\ud83d\\udc68‍\\ud83c\\udfed',\n  'man_farmer':'\\ud83d\\udc68‍\\ud83c\\udf3e',\n  'man_firefighter':'\\ud83d\\udc68‍\\ud83d\\ude92',\n  'man_health_worker':'\\ud83d\\udc68‍\\u2695\\ufe0f',\n  'man_in_tuxedo':'\\ud83e\\udd35',\n  'man_judge':'\\ud83d\\udc68‍\\u2696\\ufe0f',\n  'man_juggling':'\\ud83e\\udd39‍\\u2642\\ufe0f',\n  'man_mechanic':'\\ud83d\\udc68‍\\ud83d\\udd27',\n  'man_office_worker':'\\ud83d\\udc68‍\\ud83d\\udcbc',\n  'man_pilot':'\\ud83d\\udc68‍\\u2708\\ufe0f',\n  'man_playing_handball':'\\ud83e\\udd3e‍\\u2642\\ufe0f',\n  'man_playing_water_polo':'\\ud83e\\udd3d‍\\u2642\\ufe0f',\n  'man_scientist':'\\ud83d\\udc68‍\\ud83d\\udd2c',\n  'man_shrugging':'\\ud83e\\udd37‍\\u2642\\ufe0f',\n  'man_singer':'\\ud83d\\udc68‍\\ud83c\\udfa4',\n  'man_student':'\\ud83d\\udc68‍\\ud83c\\udf93',\n  'man_teacher':'\\ud83d\\udc68‍\\ud83c\\udfeb',\n  'man_technologist':'\\ud83d\\udc68‍\\ud83d\\udcbb',\n  'man_with_gua_pi_mao':'\\ud83d\\udc72',\n  'man_with_turban':'\\ud83d\\udc73',\n  'tangerine':'\\ud83c\\udf4a',\n  'mans_shoe':'\\ud83d\\udc5e',\n  'mantelpiece_clock':'\\ud83d\\udd70',\n  'maple_leaf':'\\ud83c\\udf41',\n  'martial_arts_uniform':'\\ud83e\\udd4b',\n  'mask':'\\ud83d\\ude37',\n  'massage_woman':'\\ud83d\\udc86',\n  'massage_man':'\\ud83d\\udc86‍\\u2642\\ufe0f',\n  'meat_on_bone':'\\ud83c\\udf56',\n  'medal_military':'\\ud83c\\udf96',\n  'medal_sports':'\\ud83c\\udfc5',\n  'mega':'\\ud83d\\udce3',\n  'melon':'\\ud83c\\udf48',\n  'memo':'\\ud83d\\udcdd',\n  'men_wrestling':'\\ud83e\\udd3c‍\\u2642\\ufe0f',\n  'menorah':'\\ud83d\\udd4e',\n  'mens':'\\ud83d\\udeb9',\n  'metal':'\\ud83e\\udd18',\n  'metro':'\\ud83d\\ude87',\n  'microphone':'\\ud83c\\udfa4',\n  'microscope':'\\ud83d\\udd2c',\n  'milk_glass':'\\ud83e\\udd5b',\n  'milky_way':'\\ud83c\\udf0c',\n  'minibus':'\\ud83d\\ude90',\n  'minidisc':'\\ud83d\\udcbd',\n  'mobile_phone_off':'\\ud83d\\udcf4',\n  'money_mouth_face':'\\ud83e\\udd11',\n  'money_with_wings':'\\ud83d\\udcb8',\n  'moneybag':'\\ud83d\\udcb0',\n  'monkey':'\\ud83d\\udc12',\n  'monkey_face':'\\ud83d\\udc35',\n  'monorail':'\\ud83d\\ude9d',\n  'moon':'\\ud83c\\udf14',\n  'mortar_board':'\\ud83c\\udf93',\n  'mosque':'\\ud83d\\udd4c',\n  'motor_boat':'\\ud83d\\udee5',\n  'motor_scooter':'\\ud83d\\udef5',\n  'motorcycle':'\\ud83c\\udfcd',\n  'motorway':'\\ud83d\\udee3',\n  'mount_fuji':'\\ud83d\\uddfb',\n  'mountain':'\\u26f0',\n  'mountain_biking_man':'\\ud83d\\udeb5',\n  'mountain_biking_woman':'\\ud83d\\udeb5‍\\u2640\\ufe0f',\n  'mountain_cableway':'\\ud83d\\udea0',\n  'mountain_railway':'\\ud83d\\ude9e',\n  'mountain_snow':'\\ud83c\\udfd4',\n  'mouse':'\\ud83d\\udc2d',\n  'mouse2':'\\ud83d\\udc01',\n  'movie_camera':'\\ud83c\\udfa5',\n  'moyai':'\\ud83d\\uddff',\n  'mrs_claus':'\\ud83e\\udd36',\n  'muscle':'\\ud83d\\udcaa',\n  'mushroom':'\\ud83c\\udf44',\n  'musical_keyboard':'\\ud83c\\udfb9',\n  'musical_note':'\\ud83c\\udfb5',\n  'musical_score':'\\ud83c\\udfbc',\n  'mute':'\\ud83d\\udd07',\n  'nail_care':'\\ud83d\\udc85',\n  'name_badge':'\\ud83d\\udcdb',\n  'national_park':'\\ud83c\\udfde',\n  'nauseated_face':'\\ud83e\\udd22',\n  'necktie':'\\ud83d\\udc54',\n  'negative_squared_cross_mark':'\\u274e',\n  'nerd_face':'\\ud83e\\udd13',\n  'neutral_face':'\\ud83d\\ude10',\n  'new':'\\ud83c\\udd95',\n  'new_moon':'\\ud83c\\udf11',\n  'new_moon_with_face':'\\ud83c\\udf1a',\n  'newspaper':'\\ud83d\\udcf0',\n  'newspaper_roll':'\\ud83d\\uddde',\n  'next_track_button':'\\u23ed',\n  'ng':'\\ud83c\\udd96',\n  'no_good_man':'\\ud83d\\ude45‍\\u2642\\ufe0f',\n  'no_good_woman':'\\ud83d\\ude45',\n  'night_with_stars':'\\ud83c\\udf03',\n  'no_bell':'\\ud83d\\udd15',\n  'no_bicycles':'\\ud83d\\udeb3',\n  'no_entry':'\\u26d4\\ufe0f',\n  'no_entry_sign':'\\ud83d\\udeab',\n  'no_mobile_phones':'\\ud83d\\udcf5',\n  'no_mouth':'\\ud83d\\ude36',\n  'no_pedestrians':'\\ud83d\\udeb7',\n  'no_smoking':'\\ud83d\\udead',\n  'non-potable_water':'\\ud83d\\udeb1',\n  'nose':'\\ud83d\\udc43',\n  'notebook':'\\ud83d\\udcd3',\n  'notebook_with_decorative_cover':'\\ud83d\\udcd4',\n  'notes':'\\ud83c\\udfb6',\n  'nut_and_bolt':'\\ud83d\\udd29',\n  'o':'\\u2b55\\ufe0f',\n  'o2':'\\ud83c\\udd7e\\ufe0f',\n  'ocean':'\\ud83c\\udf0a',\n  'octopus':'\\ud83d\\udc19',\n  'oden':'\\ud83c\\udf62',\n  'office':'\\ud83c\\udfe2',\n  'oil_drum':'\\ud83d\\udee2',\n  'ok':'\\ud83c\\udd97',\n  'ok_hand':'\\ud83d\\udc4c',\n  'ok_man':'\\ud83d\\ude46‍\\u2642\\ufe0f',\n  'ok_woman':'\\ud83d\\ude46',\n  'old_key':'\\ud83d\\udddd',\n  'older_man':'\\ud83d\\udc74',\n  'older_woman':'\\ud83d\\udc75',\n  'om':'\\ud83d\\udd49',\n  'on':'\\ud83d\\udd1b',\n  'oncoming_automobile':'\\ud83d\\ude98',\n  'oncoming_bus':'\\ud83d\\ude8d',\n  'oncoming_police_car':'\\ud83d\\ude94',\n  'oncoming_taxi':'\\ud83d\\ude96',\n  'open_file_folder':'\\ud83d\\udcc2',\n  'open_hands':'\\ud83d\\udc50',\n  'open_mouth':'\\ud83d\\ude2e',\n  'open_umbrella':'\\u2602\\ufe0f',\n  'ophiuchus':'\\u26ce',\n  'orange_book':'\\ud83d\\udcd9',\n  'orthodox_cross':'\\u2626\\ufe0f',\n  'outbox_tray':'\\ud83d\\udce4',\n  'owl':'\\ud83e\\udd89',\n  'ox':'\\ud83d\\udc02',\n  'package':'\\ud83d\\udce6',\n  'page_facing_up':'\\ud83d\\udcc4',\n  'page_with_curl':'\\ud83d\\udcc3',\n  'pager':'\\ud83d\\udcdf',\n  'paintbrush':'\\ud83d\\udd8c',\n  'palm_tree':'\\ud83c\\udf34',\n  'pancakes':'\\ud83e\\udd5e',\n  'panda_face':'\\ud83d\\udc3c',\n  'paperclip':'\\ud83d\\udcce',\n  'paperclips':'\\ud83d\\udd87',\n  'parasol_on_ground':'\\u26f1',\n  'parking':'\\ud83c\\udd7f\\ufe0f',\n  'part_alternation_mark':'\\u303d\\ufe0f',\n  'partly_sunny':'\\u26c5\\ufe0f',\n  'passenger_ship':'\\ud83d\\udef3',\n  'passport_control':'\\ud83d\\udec2',\n  'pause_button':'\\u23f8',\n  'peace_symbol':'\\u262e\\ufe0f',\n  'peach':'\\ud83c\\udf51',\n  'peanuts':'\\ud83e\\udd5c',\n  'pear':'\\ud83c\\udf50',\n  'pen':'\\ud83d\\udd8a',\n  'pencil2':'\\u270f\\ufe0f',\n  'penguin':'\\ud83d\\udc27',\n  'pensive':'\\ud83d\\ude14',\n  'performing_arts':'\\ud83c\\udfad',\n  'persevere':'\\ud83d\\ude23',\n  'person_fencing':'\\ud83e\\udd3a',\n  'pouting_woman':'\\ud83d\\ude4e',\n  'phone':'\\u260e\\ufe0f',\n  'pick':'\\u26cf',\n  'pig':'\\ud83d\\udc37',\n  'pig2':'\\ud83d\\udc16',\n  'pig_nose':'\\ud83d\\udc3d',\n  'pill':'\\ud83d\\udc8a',\n  'pineapple':'\\ud83c\\udf4d',\n  'ping_pong':'\\ud83c\\udfd3',\n  'pisces':'\\u2653\\ufe0f',\n  'pizza':'\\ud83c\\udf55',\n  'place_of_worship':'\\ud83d\\uded0',\n  'plate_with_cutlery':'\\ud83c\\udf7d',\n  'play_or_pause_button':'\\u23ef',\n  'point_down':'\\ud83d\\udc47',\n  'point_left':'\\ud83d\\udc48',\n  'point_right':'\\ud83d\\udc49',\n  'point_up':'\\u261d\\ufe0f',\n  'point_up_2':'\\ud83d\\udc46',\n  'police_car':'\\ud83d\\ude93',\n  'policewoman':'\\ud83d\\udc6e‍\\u2640\\ufe0f',\n  'poodle':'\\ud83d\\udc29',\n  'popcorn':'\\ud83c\\udf7f',\n  'post_office':'\\ud83c\\udfe3',\n  'postal_horn':'\\ud83d\\udcef',\n  'postbox':'\\ud83d\\udcee',\n  'potable_water':'\\ud83d\\udeb0',\n  'potato':'\\ud83e\\udd54',\n  'pouch':'\\ud83d\\udc5d',\n  'poultry_leg':'\\ud83c\\udf57',\n  'pound':'\\ud83d\\udcb7',\n  'rage':'\\ud83d\\ude21',\n  'pouting_cat':'\\ud83d\\ude3e',\n  'pouting_man':'\\ud83d\\ude4e‍\\u2642\\ufe0f',\n  'pray':'\\ud83d\\ude4f',\n  'prayer_beads':'\\ud83d\\udcff',\n  'pregnant_woman':'\\ud83e\\udd30',\n  'previous_track_button':'\\u23ee',\n  'prince':'\\ud83e\\udd34',\n  'princess':'\\ud83d\\udc78',\n  'printer':'\\ud83d\\udda8',\n  'purple_heart':'\\ud83d\\udc9c',\n  'purse':'\\ud83d\\udc5b',\n  'pushpin':'\\ud83d\\udccc',\n  'put_litter_in_its_place':'\\ud83d\\udeae',\n  'question':'\\u2753',\n  'rabbit':'\\ud83d\\udc30',\n  'rabbit2':'\\ud83d\\udc07',\n  'racehorse':'\\ud83d\\udc0e',\n  'racing_car':'\\ud83c\\udfce',\n  'radio':'\\ud83d\\udcfb',\n  'radio_button':'\\ud83d\\udd18',\n  'radioactive':'\\u2622\\ufe0f',\n  'railway_car':'\\ud83d\\ude83',\n  'railway_track':'\\ud83d\\udee4',\n  'rainbow':'\\ud83c\\udf08',\n  'rainbow_flag':'\\ud83c\\udff3\\ufe0f‍\\ud83c\\udf08',\n  'raised_back_of_hand':'\\ud83e\\udd1a',\n  'raised_hand_with_fingers_splayed':'\\ud83d\\udd90',\n  'raised_hands':'\\ud83d\\ude4c',\n  'raising_hand_woman':'\\ud83d\\ude4b',\n  'raising_hand_man':'\\ud83d\\ude4b‍\\u2642\\ufe0f',\n  'ram':'\\ud83d\\udc0f',\n  'ramen':'\\ud83c\\udf5c',\n  'rat':'\\ud83d\\udc00',\n  'record_button':'\\u23fa',\n  'recycle':'\\u267b\\ufe0f',\n  'red_circle':'\\ud83d\\udd34',\n  'registered':'\\u00ae\\ufe0f',\n  'relaxed':'\\u263a\\ufe0f',\n  'relieved':'\\ud83d\\ude0c',\n  'reminder_ribbon':'\\ud83c\\udf97',\n  'repeat':'\\ud83d\\udd01',\n  'repeat_one':'\\ud83d\\udd02',\n  'rescue_worker_helmet':'\\u26d1',\n  'restroom':'\\ud83d\\udebb',\n  'revolving_hearts':'\\ud83d\\udc9e',\n  'rewind':'\\u23ea',\n  'rhinoceros':'\\ud83e\\udd8f',\n  'ribbon':'\\ud83c\\udf80',\n  'rice':'\\ud83c\\udf5a',\n  'rice_ball':'\\ud83c\\udf59',\n  'rice_cracker':'\\ud83c\\udf58',\n  'rice_scene':'\\ud83c\\udf91',\n  'right_anger_bubble':'\\ud83d\\uddef',\n  'ring':'\\ud83d\\udc8d',\n  'robot':'\\ud83e\\udd16',\n  'rocket':'\\ud83d\\ude80',\n  'rofl':'\\ud83e\\udd23',\n  'roll_eyes':'\\ud83d\\ude44',\n  'roller_coaster':'\\ud83c\\udfa2',\n  'rooster':'\\ud83d\\udc13',\n  'rose':'\\ud83c\\udf39',\n  'rosette':'\\ud83c\\udff5',\n  'rotating_light':'\\ud83d\\udea8',\n  'round_pushpin':'\\ud83d\\udccd',\n  'rowing_man':'\\ud83d\\udea3',\n  'rowing_woman':'\\ud83d\\udea3‍\\u2640\\ufe0f',\n  'rugby_football':'\\ud83c\\udfc9',\n  'running_man':'\\ud83c\\udfc3',\n  'running_shirt_with_sash':'\\ud83c\\udfbd',\n  'running_woman':'\\ud83c\\udfc3‍\\u2640\\ufe0f',\n  'sa':'\\ud83c\\ude02\\ufe0f',\n  'sagittarius':'\\u2650\\ufe0f',\n  'sake':'\\ud83c\\udf76',\n  'sandal':'\\ud83d\\udc61',\n  'santa':'\\ud83c\\udf85',\n  'satellite':'\\ud83d\\udce1',\n  'saxophone':'\\ud83c\\udfb7',\n  'school':'\\ud83c\\udfeb',\n  'school_satchel':'\\ud83c\\udf92',\n  'scissors':'\\u2702\\ufe0f',\n  'scorpion':'\\ud83e\\udd82',\n  'scorpius':'\\u264f\\ufe0f',\n  'scream':'\\ud83d\\ude31',\n  'scream_cat':'\\ud83d\\ude40',\n  'scroll':'\\ud83d\\udcdc',\n  'seat':'\\ud83d\\udcba',\n  'secret':'\\u3299\\ufe0f',\n  'see_no_evil':'\\ud83d\\ude48',\n  'seedling':'\\ud83c\\udf31',\n  'selfie':'\\ud83e\\udd33',\n  'shallow_pan_of_food':'\\ud83e\\udd58',\n  'shamrock':'\\u2618\\ufe0f',\n  'shark':'\\ud83e\\udd88',\n  'shaved_ice':'\\ud83c\\udf67',\n  'sheep':'\\ud83d\\udc11',\n  'shell':'\\ud83d\\udc1a',\n  'shield':'\\ud83d\\udee1',\n  'shinto_shrine':'\\u26e9',\n  'ship':'\\ud83d\\udea2',\n  'shirt':'\\ud83d\\udc55',\n  'shopping':'\\ud83d\\udecd',\n  'shopping_cart':'\\ud83d\\uded2',\n  'shower':'\\ud83d\\udebf',\n  'shrimp':'\\ud83e\\udd90',\n  'signal_strength':'\\ud83d\\udcf6',\n  'six_pointed_star':'\\ud83d\\udd2f',\n  'ski':'\\ud83c\\udfbf',\n  'skier':'\\u26f7',\n  'skull':'\\ud83d\\udc80',\n  'skull_and_crossbones':'\\u2620\\ufe0f',\n  'sleeping':'\\ud83d\\ude34',\n  'sleeping_bed':'\\ud83d\\udecc',\n  'sleepy':'\\ud83d\\ude2a',\n  'slightly_frowning_face':'\\ud83d\\ude41',\n  'slightly_smiling_face':'\\ud83d\\ude42',\n  'slot_machine':'\\ud83c\\udfb0',\n  'small_airplane':'\\ud83d\\udee9',\n  'small_blue_diamond':'\\ud83d\\udd39',\n  'small_orange_diamond':'\\ud83d\\udd38',\n  'small_red_triangle':'\\ud83d\\udd3a',\n  'small_red_triangle_down':'\\ud83d\\udd3b',\n  'smile':'\\ud83d\\ude04',\n  'smile_cat':'\\ud83d\\ude38',\n  'smiley':'\\ud83d\\ude03',\n  'smiley_cat':'\\ud83d\\ude3a',\n  'smiling_imp':'\\ud83d\\ude08',\n  'smirk':'\\ud83d\\ude0f',\n  'smirk_cat':'\\ud83d\\ude3c',\n  'smoking':'\\ud83d\\udeac',\n  'snail':'\\ud83d\\udc0c',\n  'snake':'\\ud83d\\udc0d',\n  'sneezing_face':'\\ud83e\\udd27',\n  'snowboarder':'\\ud83c\\udfc2',\n  'snowflake':'\\u2744\\ufe0f',\n  'snowman':'\\u26c4\\ufe0f',\n  'snowman_with_snow':'\\u2603\\ufe0f',\n  'sob':'\\ud83d\\ude2d',\n  'soccer':'\\u26bd\\ufe0f',\n  'soon':'\\ud83d\\udd1c',\n  'sos':'\\ud83c\\udd98',\n  'sound':'\\ud83d\\udd09',\n  'space_invader':'\\ud83d\\udc7e',\n  'spades':'\\u2660\\ufe0f',\n  'spaghetti':'\\ud83c\\udf5d',\n  'sparkle':'\\u2747\\ufe0f',\n  'sparkler':'\\ud83c\\udf87',\n  'sparkles':'\\u2728',\n  'sparkling_heart':'\\ud83d\\udc96',\n  'speak_no_evil':'\\ud83d\\ude4a',\n  'speaker':'\\ud83d\\udd08',\n  'speaking_head':'\\ud83d\\udde3',\n  'speech_balloon':'\\ud83d\\udcac',\n  'speedboat':'\\ud83d\\udea4',\n  'spider':'\\ud83d\\udd77',\n  'spider_web':'\\ud83d\\udd78',\n  'spiral_calendar':'\\ud83d\\uddd3',\n  'spiral_notepad':'\\ud83d\\uddd2',\n  'spoon':'\\ud83e\\udd44',\n  'squid':'\\ud83e\\udd91',\n  'stadium':'\\ud83c\\udfdf',\n  'star':'\\u2b50\\ufe0f',\n  'star2':'\\ud83c\\udf1f',\n  'star_and_crescent':'\\u262a\\ufe0f',\n  'star_of_david':'\\u2721\\ufe0f',\n  'stars':'\\ud83c\\udf20',\n  'station':'\\ud83d\\ude89',\n  'statue_of_liberty':'\\ud83d\\uddfd',\n  'steam_locomotive':'\\ud83d\\ude82',\n  'stew':'\\ud83c\\udf72',\n  'stop_button':'\\u23f9',\n  'stop_sign':'\\ud83d\\uded1',\n  'stopwatch':'\\u23f1',\n  'straight_ruler':'\\ud83d\\udccf',\n  'strawberry':'\\ud83c\\udf53',\n  'stuck_out_tongue':'\\ud83d\\ude1b',\n  'stuck_out_tongue_closed_eyes':'\\ud83d\\ude1d',\n  'stuck_out_tongue_winking_eye':'\\ud83d\\ude1c',\n  'studio_microphone':'\\ud83c\\udf99',\n  'stuffed_flatbread':'\\ud83e\\udd59',\n  'sun_behind_large_cloud':'\\ud83c\\udf25',\n  'sun_behind_rain_cloud':'\\ud83c\\udf26',\n  'sun_behind_small_cloud':'\\ud83c\\udf24',\n  'sun_with_face':'\\ud83c\\udf1e',\n  'sunflower':'\\ud83c\\udf3b',\n  'sunglasses':'\\ud83d\\ude0e',\n  'sunny':'\\u2600\\ufe0f',\n  'sunrise':'\\ud83c\\udf05',\n  'sunrise_over_mountains':'\\ud83c\\udf04',\n  'surfing_man':'\\ud83c\\udfc4',\n  'surfing_woman':'\\ud83c\\udfc4‍\\u2640\\ufe0f',\n  'sushi':'\\ud83c\\udf63',\n  'suspension_railway':'\\ud83d\\ude9f',\n  'sweat':'\\ud83d\\ude13',\n  'sweat_drops':'\\ud83d\\udca6',\n  'sweat_smile':'\\ud83d\\ude05',\n  'sweet_potato':'\\ud83c\\udf60',\n  'swimming_man':'\\ud83c\\udfca',\n  'swimming_woman':'\\ud83c\\udfca‍\\u2640\\ufe0f',\n  'symbols':'\\ud83d\\udd23',\n  'synagogue':'\\ud83d\\udd4d',\n  'syringe':'\\ud83d\\udc89',\n  'taco':'\\ud83c\\udf2e',\n  'tada':'\\ud83c\\udf89',\n  'tanabata_tree':'\\ud83c\\udf8b',\n  'taurus':'\\u2649\\ufe0f',\n  'taxi':'\\ud83d\\ude95',\n  'tea':'\\ud83c\\udf75',\n  'telephone_receiver':'\\ud83d\\udcde',\n  'telescope':'\\ud83d\\udd2d',\n  'tennis':'\\ud83c\\udfbe',\n  'tent':'\\u26fa\\ufe0f',\n  'thermometer':'\\ud83c\\udf21',\n  'thinking':'\\ud83e\\udd14',\n  'thought_balloon':'\\ud83d\\udcad',\n  'ticket':'\\ud83c\\udfab',\n  'tickets':'\\ud83c\\udf9f',\n  'tiger':'\\ud83d\\udc2f',\n  'tiger2':'\\ud83d\\udc05',\n  'timer_clock':'\\u23f2',\n  'tipping_hand_man':'\\ud83d\\udc81‍\\u2642\\ufe0f',\n  'tired_face':'\\ud83d\\ude2b',\n  'tm':'\\u2122\\ufe0f',\n  'toilet':'\\ud83d\\udebd',\n  'tokyo_tower':'\\ud83d\\uddfc',\n  'tomato':'\\ud83c\\udf45',\n  'tongue':'\\ud83d\\udc45',\n  'top':'\\ud83d\\udd1d',\n  'tophat':'\\ud83c\\udfa9',\n  'tornado':'\\ud83c\\udf2a',\n  'trackball':'\\ud83d\\uddb2',\n  'tractor':'\\ud83d\\ude9c',\n  'traffic_light':'\\ud83d\\udea5',\n  'train':'\\ud83d\\ude8b',\n  'train2':'\\ud83d\\ude86',\n  'tram':'\\ud83d\\ude8a',\n  'triangular_flag_on_post':'\\ud83d\\udea9',\n  'triangular_ruler':'\\ud83d\\udcd0',\n  'trident':'\\ud83d\\udd31',\n  'triumph':'\\ud83d\\ude24',\n  'trolleybus':'\\ud83d\\ude8e',\n  'trophy':'\\ud83c\\udfc6',\n  'tropical_drink':'\\ud83c\\udf79',\n  'tropical_fish':'\\ud83d\\udc20',\n  'truck':'\\ud83d\\ude9a',\n  'trumpet':'\\ud83c\\udfba',\n  'tulip':'\\ud83c\\udf37',\n  'tumbler_glass':'\\ud83e\\udd43',\n  'turkey':'\\ud83e\\udd83',\n  'turtle':'\\ud83d\\udc22',\n  'tv':'\\ud83d\\udcfa',\n  'twisted_rightwards_arrows':'\\ud83d\\udd00',\n  'two_hearts':'\\ud83d\\udc95',\n  'two_men_holding_hands':'\\ud83d\\udc6c',\n  'two_women_holding_hands':'\\ud83d\\udc6d',\n  'u5272':'\\ud83c\\ude39',\n  'u5408':'\\ud83c\\ude34',\n  'u55b6':'\\ud83c\\ude3a',\n  'u6307':'\\ud83c\\ude2f\\ufe0f',\n  'u6708':'\\ud83c\\ude37\\ufe0f',\n  'u6709':'\\ud83c\\ude36',\n  'u6e80':'\\ud83c\\ude35',\n  'u7121':'\\ud83c\\ude1a\\ufe0f',\n  'u7533':'\\ud83c\\ude38',\n  'u7981':'\\ud83c\\ude32',\n  'u7a7a':'\\ud83c\\ude33',\n  'umbrella':'\\u2614\\ufe0f',\n  'unamused':'\\ud83d\\ude12',\n  'underage':'\\ud83d\\udd1e',\n  'unicorn':'\\ud83e\\udd84',\n  'unlock':'\\ud83d\\udd13',\n  'up':'\\ud83c\\udd99',\n  'upside_down_face':'\\ud83d\\ude43',\n  'v':'\\u270c\\ufe0f',\n  'vertical_traffic_light':'\\ud83d\\udea6',\n  'vhs':'\\ud83d\\udcfc',\n  'vibration_mode':'\\ud83d\\udcf3',\n  'video_camera':'\\ud83d\\udcf9',\n  'video_game':'\\ud83c\\udfae',\n  'violin':'\\ud83c\\udfbb',\n  'virgo':'\\u264d\\ufe0f',\n  'volcano':'\\ud83c\\udf0b',\n  'volleyball':'\\ud83c\\udfd0',\n  'vs':'\\ud83c\\udd9a',\n  'vulcan_salute':'\\ud83d\\udd96',\n  'walking_man':'\\ud83d\\udeb6',\n  'walking_woman':'\\ud83d\\udeb6‍\\u2640\\ufe0f',\n  'waning_crescent_moon':'\\ud83c\\udf18',\n  'waning_gibbous_moon':'\\ud83c\\udf16',\n  'warning':'\\u26a0\\ufe0f',\n  'wastebasket':'\\ud83d\\uddd1',\n  'watch':'\\u231a\\ufe0f',\n  'water_buffalo':'\\ud83d\\udc03',\n  'watermelon':'\\ud83c\\udf49',\n  'wave':'\\ud83d\\udc4b',\n  'wavy_dash':'\\u3030\\ufe0f',\n  'waxing_crescent_moon':'\\ud83c\\udf12',\n  'wc':'\\ud83d\\udebe',\n  'weary':'\\ud83d\\ude29',\n  'wedding':'\\ud83d\\udc92',\n  'weight_lifting_man':'\\ud83c\\udfcb\\ufe0f',\n  'weight_lifting_woman':'\\ud83c\\udfcb\\ufe0f‍\\u2640\\ufe0f',\n  'whale':'\\ud83d\\udc33',\n  'whale2':'\\ud83d\\udc0b',\n  'wheel_of_dharma':'\\u2638\\ufe0f',\n  'wheelchair':'\\u267f\\ufe0f',\n  'white_check_mark':'\\u2705',\n  'white_circle':'\\u26aa\\ufe0f',\n  'white_flag':'\\ud83c\\udff3\\ufe0f',\n  'white_flower':'\\ud83d\\udcae',\n  'white_large_square':'\\u2b1c\\ufe0f',\n  'white_medium_small_square':'\\u25fd\\ufe0f',\n  'white_medium_square':'\\u25fb\\ufe0f',\n  'white_small_square':'\\u25ab\\ufe0f',\n  'white_square_button':'\\ud83d\\udd33',\n  'wilted_flower':'\\ud83e\\udd40',\n  'wind_chime':'\\ud83c\\udf90',\n  'wind_face':'\\ud83c\\udf2c',\n  'wine_glass':'\\ud83c\\udf77',\n  'wink':'\\ud83d\\ude09',\n  'wolf':'\\ud83d\\udc3a',\n  'woman':'\\ud83d\\udc69',\n  'woman_artist':'\\ud83d\\udc69‍\\ud83c\\udfa8',\n  'woman_astronaut':'\\ud83d\\udc69‍\\ud83d\\ude80',\n  'woman_cartwheeling':'\\ud83e\\udd38‍\\u2640\\ufe0f',\n  'woman_cook':'\\ud83d\\udc69‍\\ud83c\\udf73',\n  'woman_facepalming':'\\ud83e\\udd26‍\\u2640\\ufe0f',\n  'woman_factory_worker':'\\ud83d\\udc69‍\\ud83c\\udfed',\n  'woman_farmer':'\\ud83d\\udc69‍\\ud83c\\udf3e',\n  'woman_firefighter':'\\ud83d\\udc69‍\\ud83d\\ude92',\n  'woman_health_worker':'\\ud83d\\udc69‍\\u2695\\ufe0f',\n  'woman_judge':'\\ud83d\\udc69‍\\u2696\\ufe0f',\n  'woman_juggling':'\\ud83e\\udd39‍\\u2640\\ufe0f',\n  'woman_mechanic':'\\ud83d\\udc69‍\\ud83d\\udd27',\n  'woman_office_worker':'\\ud83d\\udc69‍\\ud83d\\udcbc',\n  'woman_pilot':'\\ud83d\\udc69‍\\u2708\\ufe0f',\n  'woman_playing_handball':'\\ud83e\\udd3e‍\\u2640\\ufe0f',\n  'woman_playing_water_polo':'\\ud83e\\udd3d‍\\u2640\\ufe0f',\n  'woman_scientist':'\\ud83d\\udc69‍\\ud83d\\udd2c',\n  'woman_shrugging':'\\ud83e\\udd37‍\\u2640\\ufe0f',\n  'woman_singer':'\\ud83d\\udc69‍\\ud83c\\udfa4',\n  'woman_student':'\\ud83d\\udc69‍\\ud83c\\udf93',\n  'woman_teacher':'\\ud83d\\udc69‍\\ud83c\\udfeb',\n  'woman_technologist':'\\ud83d\\udc69‍\\ud83d\\udcbb',\n  'woman_with_turban':'\\ud83d\\udc73‍\\u2640\\ufe0f',\n  'womans_clothes':'\\ud83d\\udc5a',\n  'womans_hat':'\\ud83d\\udc52',\n  'women_wrestling':'\\ud83e\\udd3c‍\\u2640\\ufe0f',\n  'womens':'\\ud83d\\udeba',\n  'world_map':'\\ud83d\\uddfa',\n  'worried':'\\ud83d\\ude1f',\n  'wrench':'\\ud83d\\udd27',\n  'writing_hand':'\\u270d\\ufe0f',\n  'x':'\\u274c',\n  'yellow_heart':'\\ud83d\\udc9b',\n  'yen':'\\ud83d\\udcb4',\n  'yin_yang':'\\u262f\\ufe0f',\n  'yum':'\\ud83d\\ude0b',\n  'zap':'\\u26a1\\ufe0f',\n  'zipper_mouth_face':'\\ud83e\\udd10',\n  'zzz':'\\ud83d\\udca4',\n\n  /* special emojis :P */\n  'octocat':  '\":octocat:\"',\n  'showdown': 'S'\n};\n\r\n/**\n * Created by Estevao on 31-05-2015.\n */\n\n/**\n * Showdown Converter class\n * @class\n * @param {object} [converterOptions]\n * @returns {Converter}\n */\nshowdown.Converter = function (converterOptions) {\n  'use strict';\n\n  var\n      /**\n       * Options used by this converter\n       * @private\n       * @type {{}}\n       */\n      options = {},\n\n      /**\n       * Language extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      langExtensions = [],\n\n      /**\n       * Output modifiers extensions used by this converter\n       * @private\n       * @type {Array}\n       */\n      outputModifiers = [],\n\n      /**\n       * Event listeners\n       * @private\n       * @type {{}}\n       */\n      listeners = {},\n\n      /**\n       * The flavor set in this converter\n       */\n      setConvFlavor = setFlavor,\n\n      /**\n       * Metadata of the document\n       * @type {{parsed: {}, raw: string, format: string}}\n       */\n      metadata = {\n        parsed: {},\n        raw: '',\n        format: ''\n      };\n\n  _constructor();\n\n  /**\n   * Converter constructor\n   * @private\n   */\n  function _constructor () {\n    converterOptions = converterOptions || {};\n\n    for (var gOpt in globalOptions) {\n      if (globalOptions.hasOwnProperty(gOpt)) {\n        options[gOpt] = globalOptions[gOpt];\n      }\n    }\n\n    // Merge options\n    if (typeof converterOptions === 'object') {\n      for (var opt in converterOptions) {\n        if (converterOptions.hasOwnProperty(opt)) {\n          options[opt] = converterOptions[opt];\n        }\n      }\n    } else {\n      throw Error('Converter expects the passed parameter to be an object, but ' + typeof converterOptions +\n      ' was passed instead.');\n    }\n\n    if (options.extensions) {\n      showdown.helper.forEach(options.extensions, _parseExtension);\n    }\n  }\n\n  /**\n   * Parse extension\n   * @param {*} ext\n   * @param {string} [name='']\n   * @private\n   */\n  function _parseExtension (ext, name) {\n\n    name = name || null;\n    // If it's a string, the extension was previously loaded\n    if (showdown.helper.isString(ext)) {\n      ext = showdown.helper.stdExtName(ext);\n      name = ext;\n\n      // LEGACY_SUPPORT CODE\n      if (showdown.extensions[ext]) {\n        console.warn('DEPRECATION WARNING: ' + ext + ' is an old extension that uses a deprecated loading method.' +\n          'Please inform the developer that the extension should be updated!');\n        legacyExtensionLoading(showdown.extensions[ext], ext);\n        return;\n        // END LEGACY SUPPORT CODE\n\n      } else if (!showdown.helper.isUndefined(extensions[ext])) {\n        ext = extensions[ext];\n\n      } else {\n        throw Error('Extension \"' + ext + '\" could not be loaded. It was either not found or is not a valid extension.');\n      }\n    }\n\n    if (typeof ext === 'function') {\n      ext = ext();\n    }\n\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n\n    var validExt = validate(ext, name);\n    if (!validExt.valid) {\n      throw Error(validExt.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n      }\n      if (ext[i].hasOwnProperty('listeners')) {\n        for (var ln in ext[i].listeners) {\n          if (ext[i].listeners.hasOwnProperty(ln)) {\n            listen(ln, ext[i].listeners[ln]);\n          }\n        }\n      }\n    }\n\n  }\n\n  /**\n   * LEGACY_SUPPORT\n   * @param {*} ext\n   * @param {string} name\n   */\n  function legacyExtensionLoading (ext, name) {\n    if (typeof ext === 'function') {\n      ext = ext(new showdown.Converter());\n    }\n    if (!showdown.helper.isArray(ext)) {\n      ext = [ext];\n    }\n    var valid = validate(ext, name);\n\n    if (!valid.valid) {\n      throw Error(valid.error);\n    }\n\n    for (var i = 0; i < ext.length; ++i) {\n      switch (ext[i].type) {\n        case 'lang':\n          langExtensions.push(ext[i]);\n          break;\n        case 'output':\n          outputModifiers.push(ext[i]);\n          break;\n        default:// should never reach here\n          throw Error('Extension loader error: Type unrecognized!!!');\n      }\n    }\n  }\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   */\n  function listen (name, callback) {\n    if (!showdown.helper.isString(name)) {\n      throw Error('Invalid argument in converter.listen() method: name must be a string, but ' + typeof name + ' given');\n    }\n\n    if (typeof callback !== 'function') {\n      throw Error('Invalid argument in converter.listen() method: callback must be a function, but ' + typeof callback + ' given');\n    }\n\n    if (!listeners.hasOwnProperty(name)) {\n      listeners[name] = [];\n    }\n    listeners[name].push(callback);\n  }\n\n  function rTrimInputText (text) {\n    var rsp = text.match(/^\\s*/)[0].length,\n        rgx = new RegExp('^\\\\s{0,' + rsp + '}', 'gm');\n    return text.replace(rgx, '');\n  }\n\n  /**\n   * Dispatch an event\n   * @private\n   * @param {string} evtName Event name\n   * @param {string} text Text\n   * @param {{}} options Converter Options\n   * @param {{}} globals\n   * @returns {string}\n   */\n  this._dispatch = function dispatch (evtName, text, options, globals) {\n    if (listeners.hasOwnProperty(evtName)) {\n      for (var ei = 0; ei < listeners[evtName].length; ++ei) {\n        var nText = listeners[evtName][ei](evtName, text, this, options, globals);\n        if (nText && typeof nText !== 'undefined') {\n          text = nText;\n        }\n      }\n    }\n    return text;\n  };\n\n  /**\n   * Listen to an event\n   * @param {string} name\n   * @param {function} callback\n   * @returns {showdown.Converter}\n   */\n  this.listen = function (name, callback) {\n    listen(name, callback);\n    return this;\n  };\n\n  /**\n   * Converts a markdown string into HTML\n   * @param {string} text\n   * @returns {*}\n   */\n  this.makeHtml = function (text) {\n    //check if text is not falsy\n    if (!text) {\n      return text;\n    }\n\n    var globals = {\n      gHtmlBlocks:     [],\n      gHtmlMdBlocks:   [],\n      gHtmlSpans:      [],\n      gUrls:           {},\n      gTitles:         {},\n      gDimensions:     {},\n      gListLevel:      0,\n      hashLinkCounts:  {},\n      langExtensions:  langExtensions,\n      outputModifiers: outputModifiers,\n      converter:       this,\n      ghCodeBlocks:    [],\n      metadata: {\n        parsed: {},\n        raw: '',\n        format: ''\n      }\n    };\n\n    // This lets us use ¨ trema as an escape char to avoid md5 hashes\n    // The choice of character is arbitrary; anything that isn't\n    // magic in Markdown will work.\n    text = text.replace(/¨/g, '¨T');\n\n    // Replace $ with ¨D\n    // RegExp interprets $ as a special character\n    // when it's in a replacement string\n    text = text.replace(/\\$/g, '¨D');\n\n    // Standardize line endings\n    text = text.replace(/\\r\\n/g, '\\n'); // DOS to Unix\n    text = text.replace(/\\r/g, '\\n'); // Mac to Unix\n\n    // Stardardize line spaces\n    text = text.replace(/\\u00A0/g, ' ');\n\n    if (options.smartIndentationFix) {\n      text = rTrimInputText(text);\n    }\n\n    // Make sure text begins and ends with a couple of newlines:\n    text = '\\n\\n' + text + '\\n\\n';\n\n    // detab\n    text = showdown.subParser('detab')(text, options, globals);\n\n    /**\n     * Strip any lines consisting only of spaces and tabs.\n     * This makes subsequent regexs easier to write, because we can\n     * match consecutive blank lines with /\\n+/ instead of something\n     * contorted like /[ \\t]*\\n+/\n     */\n    text = text.replace(/^[ \\t]+$/mg, '');\n\n    //run languageExtensions\n    showdown.helper.forEach(langExtensions, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // run the sub parsers\n    text = showdown.subParser('metadata')(text, options, globals);\n    text = showdown.subParser('hashPreCodeTags')(text, options, globals);\n    text = showdown.subParser('githubCodeBlocks')(text, options, globals);\n    text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n    text = showdown.subParser('hashCodeTags')(text, options, globals);\n    text = showdown.subParser('stripLinkDefinitions')(text, options, globals);\n    text = showdown.subParser('blockGamut')(text, options, globals);\n    text = showdown.subParser('unhashHTMLSpans')(text, options, globals);\n    text = showdown.subParser('unescapeSpecialChars')(text, options, globals);\n\n    // attacklab: Restore dollar signs\n    text = text.replace(/¨D/g, '$$');\n\n    // attacklab: Restore tremas\n    text = text.replace(/¨T/g, '¨');\n\n    // render a complete html document instead of a partial if the option is enabled\n    text = showdown.subParser('completeHTMLDocument')(text, options, globals);\n\n    // Run output modifiers\n    showdown.helper.forEach(outputModifiers, function (ext) {\n      text = showdown.subParser('runExtension')(ext, text, options, globals);\n    });\n\n    // update metadata\n    metadata = globals.metadata;\n    return text;\n  };\n\n  /**\n   * Converts an HTML string into a markdown string\n   * @param src\n   * @param [HTMLParser] A WHATWG DOM and HTML parser, such as JSDOM. If none is supplied, window.document will be used.\n   * @returns {string}\n   */\n  this.makeMarkdown = this.makeMd = function (src, HTMLParser) {\n\n    // replace \\r\\n with \\n\n    src = src.replace(/\\r\\n/g, '\\n');\n    src = src.replace(/\\r/g, '\\n'); // old macs\n\n    // due to an edge case, we need to find this: > <\n    // to prevent removing of non silent white spaces\n    // ex: this is sparta\n    src = src.replace(/>[ \\t]+¨NBSP;<');\n\n    if (!HTMLParser) {\n      if (window && window.document) {\n        HTMLParser = window.document;\n      } else {\n        throw new Error('HTMLParser is undefined. If in a webworker or nodejs environment, you need to provide a WHATWG DOM and HTML such as JSDOM');\n      }\n    }\n\n    var doc = HTMLParser.createElement('div');\n    doc.innerHTML = src;\n\n    var globals = {\n      preList: substitutePreCodeTags(doc)\n    };\n\n    // remove all newlines and collapse spaces\n    clean(doc);\n\n    // some stuff, like accidental reference links must now be escaped\n    // TODO\n    // doc.innerHTML = doc.innerHTML.replace(/\\[[\\S\\t ]]/);\n\n    var nodes = doc.childNodes,\n        mdDoc = '';\n\n    for (var i = 0; i < nodes.length; i++) {\n      mdDoc += showdown.subParser('makeMarkdown.node')(nodes[i], globals);\n    }\n\n    function clean (node) {\n      for (var n = 0; n < node.childNodes.length; ++n) {\n        var child = node.childNodes[n];\n        if (child.nodeType === 3) {\n          if (!/\\S/.test(child.nodeValue)) {\n            node.removeChild(child);\n            --n;\n          } else {\n            child.nodeValue = child.nodeValue.split('\\n').join(' ');\n            child.nodeValue = child.nodeValue.replace(/(\\s)+/g, '$1');\n          }\n        } else if (child.nodeType === 1) {\n          clean(child);\n        }\n      }\n    }\n\n    // find all pre tags and replace contents with placeholder\n    // we need this so that we can remove all indentation from html\n    // to ease up parsing\n    function substitutePreCodeTags (doc) {\n\n      var pres = doc.querySelectorAll('pre'),\n          presPH = [];\n\n      for (var i = 0; i < pres.length; ++i) {\n\n        if (pres[i].childElementCount === 1 && pres[i].firstChild.tagName.toLowerCase() === 'code') {\n          var content = pres[i].firstChild.innerHTML.trim(),\n              language = pres[i].firstChild.getAttribute('data-language') || '';\n\n          // if data-language attribute is not defined, then we look for class language-*\n          if (language === '') {\n            var classes = pres[i].firstChild.className.split(' ');\n            for (var c = 0; c < classes.length; ++c) {\n              var matches = classes[c].match(/^language-(.+)$/);\n              if (matches !== null) {\n                language = matches[1];\n                break;\n              }\n            }\n          }\n\n          // unescape html entities in content\n          content = showdown.helper.unescapeHTMLEntities(content);\n\n          presPH.push(content);\n          pres[i].outerHTML = '';\n        } else {\n          presPH.push(pres[i].innerHTML);\n          pres[i].innerHTML = '';\n          pres[i].setAttribute('prenum', i.toString());\n        }\n      }\n      return presPH;\n    }\n\n    return mdDoc;\n  };\n\n  /**\n   * Set an option of this Converter instance\n   * @param {string} key\n   * @param {*} value\n   */\n  this.setOption = function (key, value) {\n    options[key] = value;\n  };\n\n  /**\n   * Get the option of this Converter instance\n   * @param {string} key\n   * @returns {*}\n   */\n  this.getOption = function (key) {\n    return options[key];\n  };\n\n  /**\n   * Get the options of this Converter instance\n   * @returns {{}}\n   */\n  this.getOptions = function () {\n    return options;\n  };\n\n  /**\n   * Add extension to THIS converter\n   * @param {{}} extension\n   * @param {string} [name=null]\n   */\n  this.addExtension = function (extension, name) {\n    name = name || null;\n    _parseExtension(extension, name);\n  };\n\n  /**\n   * Use a global registered extension with THIS converter\n   * @param {string} extensionName Name of the previously registered extension\n   */\n  this.useExtension = function (extensionName) {\n    _parseExtension(extensionName);\n  };\n\n  /**\n   * Set the flavor THIS converter should use\n   * @param {string} name\n   */\n  this.setFlavor = function (name) {\n    if (!flavor.hasOwnProperty(name)) {\n      throw Error(name + ' flavor was not found');\n    }\n    var preset = flavor[name];\n    setConvFlavor = name;\n    for (var option in preset) {\n      if (preset.hasOwnProperty(option)) {\n        options[option] = preset[option];\n      }\n    }\n  };\n\n  /**\n   * Get the currently set flavor of this converter\n   * @returns {string}\n   */\n  this.getFlavor = function () {\n    return setConvFlavor;\n  };\n\n  /**\n   * Remove an extension from THIS converter.\n   * Note: This is a costly operation. It's better to initialize a new converter\n   * and specify the extensions you wish to use\n   * @param {Array} extension\n   */\n  this.removeExtension = function (extension) {\n    if (!showdown.helper.isArray(extension)) {\n      extension = [extension];\n    }\n    for (var a = 0; a < extension.length; ++a) {\n      var ext = extension[a];\n      for (var i = 0; i < langExtensions.length; ++i) {\n        if (langExtensions[i] === ext) {\n          langExtensions[i].splice(i, 1);\n        }\n      }\n      for (var ii = 0; ii < outputModifiers.length; ++i) {\n        if (outputModifiers[ii] === ext) {\n          outputModifiers[ii].splice(i, 1);\n        }\n      }\n    }\n  };\n\n  /**\n   * Get all extension of THIS converter\n   * @returns {{language: Array, output: Array}}\n   */\n  this.getAllExtensions = function () {\n    return {\n      language: langExtensions,\n      output: outputModifiers\n    };\n  };\n\n  /**\n   * Get the metadata of the previously parsed document\n   * @param raw\n   * @returns {string|{}}\n   */\n  this.getMetadata = function (raw) {\n    if (raw) {\n      return metadata.raw;\n    } else {\n      return metadata.parsed;\n    }\n  };\n\n  /**\n   * Get the metadata format of the previously parsed document\n   * @returns {string}\n   */\n  this.getMetadataFormat = function () {\n    return metadata.format;\n  };\n\n  /**\n   * Private: set a single key, value metadata pair\n   * @param {string} key\n   * @param {string} value\n   */\n  this._setMetadataPair = function (key, value) {\n    metadata.parsed[key] = value;\n  };\n\n  /**\n   * Private: set metadata format\n   * @param {string} format\n   */\n  this._setMetadataFormat = function (format) {\n    metadata.format = format;\n  };\n\n  /**\n   * Private: set metadata raw text\n   * @param {string} raw\n   */\n  this._setMetadataRaw = function (raw) {\n    metadata.raw = raw;\n  };\n};\n\r\n/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('anchors', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('anchors.before', text, options, globals);\n\n  var writeAnchorTag = function (wholeMatch, linkText, linkId, url, m5, m6, title) {\n    if (showdown.helper.isUndefined(title)) {\n      title = '';\n    }\n    linkId = linkId.toLowerCase();\n\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n    } else if (!url) {\n      if (!linkId) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = linkText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(globals.gUrls[linkId])) {\n        url = globals.gUrls[linkId];\n        if (!showdown.helper.isUndefined(globals.gTitles[linkId])) {\n          title = globals.gTitles[linkId];\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    //url = showdown.helper.escapeCharacters(url, '*_', false); // replaced line to improve performance\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n\n    var result = '';\n\n    return result;\n  };\n\n  // First, handle reference-style links: [link text] [id]\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)] ?(?:\\n *)?\\[(.*?)]()()()()/g, writeAnchorTag);\n\n  // Next, inline-style links: [link text](url \"optional title\")\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]?<([^>]*)>(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // normal cases\n  text = text.replace(/\\[((?:\\[[^\\]]*]|[^\\[\\]])*)]()[ \\t]*\\([ \\t]??(?:[ \\t]*(([\"'])([^\"]*?)\\5))?[ \\t]?\\)/g,\n    writeAnchorTag);\n\n  // handle reference-style shortcuts: [link text]\n  // These must come last in case you've also got [link test][1]\n  // or [link test](/foo)\n  text = text.replace(/\\[([^\\[\\]]+)]()()()()()/g, writeAnchorTag);\n\n  // Lastly handle GithubMentions if option is enabled\n  if (options.ghMentions) {\n    text = text.replace(/(^|\\s)(\\\\)?(@([a-z\\d]+(?:[a-z\\d.-]+?[a-z\\d]+)*))/gmi, function (wm, st, escape, mentions, username) {\n      if (escape === '\\\\') {\n        return st + mentions;\n      }\n\n      //check if options.ghMentionsLink is a string\n      if (!showdown.helper.isString(options.ghMentionsLink)) {\n        throw new Error('ghMentionsLink option must be a string');\n      }\n      var lnk = options.ghMentionsLink.replace(/\\{u}/g, username),\n          target = '';\n      if (options.openLinksInNewWindow) {\n        target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n      }\n      return st + '' + mentions + '';\n    });\n  }\n\n  text = globals.converter._dispatch('anchors.after', text, options, globals);\n  return text;\n});\n\r\n// url allowed chars [a-z\\d_.~:/?#[]@!$&'()*+,;=-]\n\nvar simpleURLRegex  = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+?\\.[^'\">\\s]+?)()(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    simpleURLRegex2 = /([*~_]+|\\b)(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+\\.[^'\">\\s]+?)([.!?,()\\[\\]])?(\\1)?(?=\\s|$)(?![\"<>])/gi,\n    delimUrlRegex   = /()<(((https?|ftp|dict):\\/\\/|www\\.)[^'\">\\s]+)()>()/gi,\n    simpleMailRegex = /(^|\\s)(?:mailto:)?([A-Za-z0-9!#$%&'*+-/=?^_`{|}~.]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)(?=$|\\s)/gmi,\n    delimMailRegex  = /<()(?:mailto:)?([-.\\w]+@[-a-z0-9]+(\\.[-a-z0-9]+)*\\.[a-z]+)>/gi,\n\n    replaceLink = function (options) {\n      'use strict';\n      return function (wm, leadingMagicChars, link, m2, m3, trailingPunctuation, trailingMagicChars) {\n        link = link.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n        var lnkTxt = link,\n            append = '',\n            target = '',\n            lmc    = leadingMagicChars || '',\n            tmc    = trailingMagicChars || '';\n        if (/^www\\./i.test(link)) {\n          link = link.replace(/^www\\./i, 'http://www.');\n        }\n        if (options.excludeTrailingPunctuationFromURLs && trailingPunctuation) {\n          append = trailingPunctuation;\n        }\n        if (options.openLinksInNewWindow) {\n          target = ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n        }\n        return lmc + '' + lnkTxt + '' + append + tmc;\n      };\n    },\n\n    replaceMail = function (options, globals) {\n      'use strict';\n      return function (wholeMatch, b, mail) {\n        var href = 'mailto:';\n        b = b || '';\n        mail = showdown.subParser('unescapeSpecialChars')(mail, options, globals);\n        if (options.encodeEmails) {\n          href = showdown.helper.encodeEmailAddress(href + mail);\n          mail = showdown.helper.encodeEmailAddress(mail);\n        } else {\n          href = href + mail;\n        }\n        return b + '' + mail + '';\n      };\n    };\n\nshowdown.subParser('autoLinks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('autoLinks.before', text, options, globals);\n\n  text = text.replace(delimUrlRegex, replaceLink(options));\n  text = text.replace(delimMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('autoLinks.after', text, options, globals);\n\n  return text;\n});\n\nshowdown.subParser('simplifiedAutoLinks', function (text, options, globals) {\n  'use strict';\n\n  if (!options.simplifiedAutoLink) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.before', text, options, globals);\n\n  if (options.excludeTrailingPunctuationFromURLs) {\n    text = text.replace(simpleURLRegex2, replaceLink(options));\n  } else {\n    text = text.replace(simpleURLRegex, replaceLink(options));\n  }\n  text = text.replace(simpleMailRegex, replaceMail(options, globals));\n\n  text = globals.converter._dispatch('simplifiedAutoLinks.after', text, options, globals);\n\n  return text;\n});\n\r\n/**\n * These are all the transformations that form block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('blockGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockGamut.before', text, options, globals);\n\n  // we parse blockquotes first so that we can have headings and hrs\n  // inside blockquotes\n  text = showdown.subParser('blockQuotes')(text, options, globals);\n  text = showdown.subParser('headers')(text, options, globals);\n\n  // Do Horizontal Rules:\n  text = showdown.subParser('horizontalRule')(text, options, globals);\n\n  text = showdown.subParser('lists')(text, options, globals);\n  text = showdown.subParser('codeBlocks')(text, options, globals);\n  text = showdown.subParser('tables')(text, options, globals);\n\n  // We already ran _HashHTMLBlocks() before, in Markdown(), but that\n  // was to escape raw HTML in the original Markdown source. This time,\n  // we're escaping the markup we've just created, so that we don't wrap\n  // 
     tags around block-level tags.\n  text = showdown.subParser('hashHTMLBlocks')(text, options, globals);\n  text = showdown.subParser('paragraphs')(text, options, globals);\n\n  text = globals.converter._dispatch('blockGamut.after', text, options, globals);\n\n  return text;\n});\n\r\nshowdown.subParser('blockQuotes', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('blockQuotes.before', text, options, globals);\n\n  // add a couple extra lines after the text and endtext mark\n  text = text + '\\n\\n';\n\n  var rgx = /(^ {0,3}>[ \\t]?.+\\n(.+\\n)*\\n*)+/gm;\n\n  if (options.splitAdjacentBlockquotes) {\n    rgx = /^ {0,3}>[\\s\\S]*?(?:\\n\\n)/gm;\n  }\n\n  text = text.replace(rgx, function (bq) {\n    // attacklab: hack around Konqueror 3.5.4 bug:\n    // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n    bq = bq.replace(/^[ \\t]*>[ \\t]?/gm, ''); // trim one level of quoting\n\n    // attacklab: clean up hack\n    bq = bq.replace(/¨0/g, '');\n\n    bq = bq.replace(/^[ \\t]+$/gm, ''); // trim whitespace-only lines\n    bq = showdown.subParser('githubCodeBlocks')(bq, options, globals);\n    bq = showdown.subParser('blockGamut')(bq, options, globals); // recurse\n\n    bq = bq.replace(/(^|\\n)/g, '$1  ');\n    // These leading spaces screw with 
     content, so we need to fix that:\n    bq = bq.replace(/(\\s*
    [^\\r]+?<\\/pre>)/gm, function (wholeMatch, m1) {\n      var pre = m1;\n      // attacklab: hack around Konqueror 3.5.4 bug:\n      pre = pre.replace(/^  /mg, '¨0');\n      pre = pre.replace(/¨0/g, '');\n      return pre;\n    });\n\n    return showdown.subParser('hashBlock')('
    \\n' + bq + '\\n
    ', options, globals);\n  });\n\n  text = globals.converter._dispatch('blockQuotes.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Process Markdown `
    ` blocks.\n */\nshowdown.subParser('codeBlocks', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeBlocks.before', text, options, globals);\n\n  // sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var pattern = /(?:\\n\\n|^)((?:(?:[ ]{4}|\\t).*\\n+)+)(\\n*[ ]{0,3}[^ \\t\\n]|(?=¨0))/g;\n  text = text.replace(pattern, function (wholeMatch, m1, m2) {\n    var codeblock = m1,\n        nextChar = m2,\n        end = '\\n';\n\n    codeblock = showdown.subParser('outdent')(codeblock, options, globals);\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing newlines\n\n    if (options.omitExtraWLInCodeBlocks) {\n      end = '';\n    }\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    return showdown.subParser('hashBlock')(codeblock, options, globals) + nextChar;\n  });\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n\n  text = globals.converter._dispatch('codeBlocks.after', text, options, globals);\n  return text;\n});\n\r\n/**\n *\n *   *  Backtick quotes are used for  spans.\n *\n *   *  You can use multiple backticks as the delimiters if you want to\n *     include literal backticks in the code span. So, this input:\n *\n *         Just type ``foo `bar` baz`` at the prompt.\n *\n *       Will translate to:\n *\n *         
    Just type foo `bar` baz at the prompt.
    \n *\n *    There's no arbitrary limit to the number of backticks you\n *    can use as delimters. If you need three consecutive backticks\n *    in your code, use four for delimiters, etc.\n *\n *  *  You can use spaces to get literal backticks at the edges:\n *\n *         ... type `` `bar` `` ...\n *\n *       Turns to:\n *\n *         ... type `bar` ...\n */\nshowdown.subParser('codeSpans', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('codeSpans.before', text, options, globals);\n\n  if (typeof text === 'undefined') {\n    text = '';\n  }\n  text = text.replace(/(^|[^\\\\])(`+)([^\\r]*?[^`])\\2(?!`)/gm,\n    function (wholeMatch, m1, m2, m3) {\n      var c = m3;\n      c = c.replace(/^([ \\t]*)/g, '');\t// leading whitespace\n      c = c.replace(/[ \\t]*$/g, '');\t// trailing whitespace\n      c = showdown.subParser('encodeCode')(c, options, globals);\n      c = m1 + '' + c + '';\n      c = showdown.subParser('hashHTMLSpans')(c, options, globals);\n      return c;\n    }\n  );\n\n  text = globals.converter._dispatch('codeSpans.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Create a full HTML document from the processed markdown\n */\nshowdown.subParser('completeHTMLDocument', function (text, options, globals) {\n  'use strict';\n\n  if (!options.completeHTMLDocument) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('completeHTMLDocument.before', text, options, globals);\n\n  var doctype = 'html',\n      doctypeParsed = '\\n',\n      title = '',\n      charset = '\\n',\n      lang = '',\n      metadata = '';\n\n  if (typeof globals.metadata.parsed.doctype !== 'undefined') {\n    doctypeParsed = '\\n';\n    doctype = globals.metadata.parsed.doctype.toString().toLowerCase();\n    if (doctype === 'html' || doctype === 'html5') {\n      charset = '';\n    }\n  }\n\n  for (var meta in globals.metadata.parsed) {\n    if (globals.metadata.parsed.hasOwnProperty(meta)) {\n      switch (meta.toLowerCase()) {\n        case 'doctype':\n          break;\n\n        case 'title':\n          title = '' +  globals.metadata.parsed.title + '\\n';\n          break;\n\n        case 'charset':\n          if (doctype === 'html' || doctype === 'html5') {\n            charset = '\\n';\n          } else {\n            charset = '\\n';\n          }\n          break;\n\n        case 'language':\n        case 'lang':\n          lang = ' lang=\"' + globals.metadata.parsed[meta] + '\"';\n          metadata += '\\n';\n          break;\n\n        default:\n          metadata += '\\n';\n      }\n    }\n  }\n\n  text = doctypeParsed + '\\n\\n' + title + charset + metadata + '\\n\\n' + text.trim() + '\\n\\n';\n\n  text = globals.converter._dispatch('completeHTMLDocument.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Convert all tabs to spaces\n */\nshowdown.subParser('detab', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('detab.before', text, options, globals);\n\n  // expand first n-1 tabs\n  text = text.replace(/\\t(?=\\t)/g, '    '); // g_tab_width\n\n  // replace the nth with two sentinels\n  text = text.replace(/\\t/g, '¨A¨B');\n\n  // use the sentinel to anchor our regex so it doesn't explode\n  text = text.replace(/¨B(.+?)¨A/g, function (wholeMatch, m1) {\n    var leadingText = m1,\n        numSpaces = 4 - leadingText.length % 4;  // g_tab_width\n\n    // there *must* be a better way to do this:\n    for (var i = 0; i < numSpaces; i++) {\n      leadingText += ' ';\n    }\n\n    return leadingText;\n  });\n\n  // clean up sentinels\n  text = text.replace(/¨A/g, '    ');  // g_tab_width\n  text = text.replace(/¨B/g, '');\n\n  text = globals.converter._dispatch('detab.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('ellipsis', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('ellipsis.before', text, options, globals);\n\n  text = text.replace(/\\.\\.\\./g, '…');\n\n  text = globals.converter._dispatch('ellipsis.after', text, options, globals);\n\n  return text;\n});\n\r\n/**\n * Turn emoji codes into emojis\n *\n * List of supported emojis: https://github.com/showdownjs/showdown/wiki/Emojis\n */\nshowdown.subParser('emoji', function (text, options, globals) {\n  'use strict';\n\n  if (!options.emoji) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('emoji.before', text, options, globals);\n\n  var emojiRgx = /:([\\S]+?):/g;\n\n  text = text.replace(emojiRgx, function (wm, emojiCode) {\n    if (showdown.helper.emojis.hasOwnProperty(emojiCode)) {\n      return showdown.helper.emojis[emojiCode];\n    }\n    return wm;\n  });\n\n  text = globals.converter._dispatch('emoji.after', text, options, globals);\n\n  return text;\n});\n\r\n/**\n * Smart processing for ampersands and angle brackets that need to be encoded.\n */\nshowdown.subParser('encodeAmpsAndAngles', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeAmpsAndAngles.before', text, options, globals);\n\n  // Ampersand-encoding based entirely on Nat Irons's Amputator MT plugin:\n  // http://bumppo.net/projects/amputator/\n  text = text.replace(/&(?!#?[xX]?(?:[0-9a-fA-F]+|\\w+);)/g, '&');\n\n  // Encode naked <'s\n  text = text.replace(/<(?![a-z\\/?$!])/gi, '<');\n\n  // Encode <\n  text = text.replace(/\n  text = text.replace(/>/g, '>');\n\n  text = globals.converter._dispatch('encodeAmpsAndAngles.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Returns the string, with after processing the following backslash escape sequences.\n *\n * attacklab: The polite way to do this is with the new escapeCharacters() function:\n *\n *    text = escapeCharacters(text,\"\\\\\",true);\n *    text = escapeCharacters(text,\"`*_{}[]()>#+-.!\",true);\n *\n * ...but we're sidestepping its use of the (slow) RegExp constructor\n * as an optimization for Firefox.  This function gets called a LOT.\n */\nshowdown.subParser('encodeBackslashEscapes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('encodeBackslashEscapes.before', text, options, globals);\n\n  text = text.replace(/\\\\(\\\\)/g, showdown.helper.escapeCharactersCallback);\n  text = text.replace(/\\\\([`*_{}\\[\\]()>#+.!~=|-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeBackslashEscapes.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Encode/escape certain characters inside Markdown code runs.\n * The point is that in code, these characters are literals,\n * and lose their special Markdown meanings.\n */\nshowdown.subParser('encodeCode', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('encodeCode.before', text, options, globals);\n\n  // Encode all ampersands; HTML entities are not\n  // entities within a Markdown code span.\n  text = text\n    .replace(/&/g, '&')\n  // Do the angle bracket song and dance:\n    .replace(//g, '>')\n  // Now, escape characters that are magic in Markdown:\n    .replace(/([*_{}\\[\\]\\\\=~-])/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('encodeCode.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Within tags -- meaning between < and > -- encode [\\ ` * _ ~ =] so they\n * don't conflict with their use in Markdown for code, italics and strong.\n */\nshowdown.subParser('escapeSpecialCharsWithinTagAttributes', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.before', text, options, globals);\n\n  // Build a regex to find HTML tags.\n  var tags     = /<\\/?[a-z\\d_:-]+(?:[\\s]+[\\s\\S]+?)?>/gi,\n      comments = /-]|-[^>])(?:[^-]|-[^-])*)--)>/gi;\n\n  text = text.replace(tags, function (wholeMatch) {\n    return wholeMatch\n      .replace(/(.)<\\/?code>(?=.)/g, '$1`')\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = text.replace(comments, function (wholeMatch) {\n    return wholeMatch\n      .replace(/([\\\\`*_~=|])/g, showdown.helper.escapeCharactersCallback);\n  });\n\n  text = globals.converter._dispatch('escapeSpecialCharsWithinTagAttributes.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Handle github codeblocks prior to running HashHTML so that\n * HTML contained within the codeblock gets escaped properly\n * Example:\n * ```ruby\n *     def hello_world(x)\n *       puts \"Hello, #{x}\"\n *     end\n * ```\n */\nshowdown.subParser('githubCodeBlocks', function (text, options, globals) {\n  'use strict';\n\n  // early exit if option is not enabled\n  if (!options.ghCodeBlocks) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('githubCodeBlocks.before', text, options, globals);\n\n  text += '¨0';\n\n  text = text.replace(/(?:^|\\n)(?: {0,3})(```+|~~~+)(?: *)([^\\s`~]*)\\n([\\s\\S]*?)\\n(?: {0,3})\\1/g, function (wholeMatch, delim, language, codeblock) {\n    var end = (options.omitExtraWLInCodeBlocks) ? '' : '\\n';\n\n    // First parse the github code block\n    codeblock = showdown.subParser('encodeCode')(codeblock, options, globals);\n    codeblock = showdown.subParser('detab')(codeblock, options, globals);\n    codeblock = codeblock.replace(/^\\n+/g, ''); // trim leading newlines\n    codeblock = codeblock.replace(/\\n+$/g, ''); // trim trailing whitespace\n\n    codeblock = '
    ' + codeblock + end + '
    ';\n\n    codeblock = showdown.subParser('hashBlock')(codeblock, options, globals);\n\n    // Since GHCodeblocks can be false positives, we need to\n    // store the primitive text and the parsed text in a global var,\n    // and then return a token\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  });\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return globals.converter._dispatch('githubCodeBlocks.after', text, options, globals);\n});\n\r\nshowdown.subParser('hashBlock', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashBlock.before', text, options, globals);\n  text = text.replace(/(^\\n+|\\n+$)/g, '');\n  text = '\\n\\n¨K' + (globals.gHtmlBlocks.push(text) - 1) + 'K\\n\\n';\n  text = globals.converter._dispatch('hashBlock.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Hash and escape  elements that should not be parsed as markdown\n */\nshowdown.subParser('hashCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '¨C' + (globals.gHtmlSpans.push(codeblock) - 1) + 'C';\n  };\n\n  // Hash naked \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, ']*>', '', 'gim');\n\n  text = globals.converter._dispatch('hashCodeTags.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('hashElement', function (text, options, globals) {\n  'use strict';\n\n  return function (wholeMatch, m1) {\n    var blockText = m1;\n\n    // Undo double lines\n    blockText = blockText.replace(/\\n\\n/g, '\\n');\n    blockText = blockText.replace(/^\\n/, '');\n\n    // strip trailing blank lines\n    blockText = blockText.replace(/\\n+$/g, '');\n\n    // Replace the element text with a marker (\"¨KxK\" where x is its key)\n    blockText = '\\n\\n¨K' + (globals.gHtmlBlocks.push(blockText) - 1) + 'K\\n\\n';\n\n    return blockText;\n  };\n});\n\r\nshowdown.subParser('hashHTMLBlocks', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLBlocks.before', text, options, globals);\n\n  var blockTags = [\n        'pre',\n        'div',\n        'h1',\n        'h2',\n        'h3',\n        'h4',\n        'h5',\n        'h6',\n        'blockquote',\n        'table',\n        'dl',\n        'ol',\n        'ul',\n        'script',\n        'noscript',\n        'form',\n        'fieldset',\n        'iframe',\n        'math',\n        'style',\n        'section',\n        'header',\n        'footer',\n        'nav',\n        'article',\n        'aside',\n        'address',\n        'audio',\n        'canvas',\n        'figure',\n        'hgroup',\n        'output',\n        'video',\n        'p'\n      ],\n      repFunc = function (wholeMatch, match, left, right) {\n        var txt = wholeMatch;\n        // check if this html element is marked as markdown\n        // if so, it's contents should be parsed as markdown\n        if (left.search(/\\bmarkdown\\b/) !== -1) {\n          txt = left + globals.converter.makeHtml(match) + right;\n        }\n        return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n      };\n\n  if (options.backslashEscapesHTMLTags) {\n    // encode backslash escaped HTML tags\n    text = text.replace(/\\\\<(\\/?[^>]+?)>/g, function (wm, inside) {\n      return '<' + inside + '>';\n    });\n  }\n\n  // hash HTML Blocks\n  for (var i = 0; i < blockTags.length; ++i) {\n\n    var opTagPos,\n        rgx1     = new RegExp('^ {0,3}(<' + blockTags[i] + '\\\\b[^>]*>)', 'im'),\n        patLeft  = '<' + blockTags[i] + '\\\\b[^>]*>',\n        patRight = '';\n    // 1. Look for the first position of the first opening HTML tag in the text\n    while ((opTagPos = showdown.helper.regexIndexOf(text, rgx1)) !== -1) {\n\n      // if the HTML tag is \\ escaped, we need to escape it and break\n\n\n      //2. Split the text in that position\n      var subTexts = showdown.helper.splitAtIndex(text, opTagPos),\n          //3. Match recursively\n          newSubText1 = showdown.helper.replaceRecursiveRegExp(subTexts[1], repFunc, patLeft, patRight, 'im');\n\n      // prevent an infinite loop\n      if (newSubText1 === subTexts[1]) {\n        break;\n      }\n      text = subTexts[0].concat(newSubText1);\n    }\n  }\n  // HR SPECIAL CASE\n  text = text.replace(/(\\n {0,3}(<(hr)\\b([^<>])*?\\/?>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  // Special case for standalone HTML comments\n  text = showdown.helper.replaceRecursiveRegExp(text, function (txt) {\n    return '\\n\\n¨K' + (globals.gHtmlBlocks.push(txt) - 1) + 'K\\n\\n';\n  }, '^ {0,3}', 'gm');\n\n  // PHP and ASP-style processor instructions ( and <%...%>)\n  text = text.replace(/(?:\\n\\n)( {0,3}(?:<([?%])[^\\r]*?\\2>)[ \\t]*(?=\\n{2,}))/g,\n    showdown.subParser('hashElement')(text, options, globals));\n\n  text = globals.converter._dispatch('hashHTMLBlocks.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Hash span elements that should not be parsed as markdown\n */\nshowdown.subParser('hashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashHTMLSpans.before', text, options, globals);\n\n  function hashHTMLSpan (html) {\n    return '¨C' + (globals.gHtmlSpans.push(html) - 1) + 'C';\n  }\n\n  // Hash Self Closing tags\n  text = text.replace(/<[^>]+?\\/>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags without properties\n  text = text.replace(/<([^>]+?)>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash tags with properties\n  text = text.replace(/<([^>]+?)\\s[^>]+?>[\\s\\S]*?<\\/\\1>/g, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  // Hash self closing tags without />\n  text = text.replace(/<[^>]+?>/gi, function (wm) {\n    return hashHTMLSpan(wm);\n  });\n\n  /*showdown.helper.matchRecursiveRegExp(text, ']*>', '', 'gi');*/\n\n  text = globals.converter._dispatch('hashHTMLSpans.after', text, options, globals);\n  return text;\n});\n\n/**\n * Unhash HTML spans\n */\nshowdown.subParser('unhashHTMLSpans', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unhashHTMLSpans.before', text, options, globals);\n\n  for (var i = 0; i < globals.gHtmlSpans.length; ++i) {\n    var repText = globals.gHtmlSpans[i],\n        // limiter to prevent infinite loop (assume 10 as limit for recurse)\n        limit = 0;\n\n    while (/¨C(\\d+)C/.test(repText)) {\n      var num = RegExp.$1;\n      repText = repText.replace('¨C' + num + 'C', globals.gHtmlSpans[num]);\n      if (limit === 10) {\n        console.error('maximum nesting of 10 spans reached!!!');\n        break;\n      }\n      ++limit;\n    }\n    text = text.replace('¨C' + i + 'C', repText);\n  }\n\n  text = globals.converter._dispatch('unhashHTMLSpans.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Hash and escape 
     elements that should not be parsed as markdown\n */\nshowdown.subParser('hashPreCodeTags', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('hashPreCodeTags.before', text, options, globals);\n\n  var repFunc = function (wholeMatch, match, left, right) {\n    // encode html entities\n    var codeblock = left + showdown.subParser('encodeCode')(match, options, globals) + right;\n    return '\\n\\n¨G' + (globals.ghCodeBlocks.push({text: wholeMatch, codeblock: codeblock}) - 1) + 'G\\n\\n';\n  };\n\n  // Hash 
    \n  text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}]*>\\\\s*]*>', '^ {0,3}\\\\s*
    ', 'gim');\n\n  text = globals.converter._dispatch('hashPreCodeTags.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('headers', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('headers.before', text, options, globals);\n\n  var headerLevelStart = (isNaN(parseInt(options.headerLevelStart))) ? 1 : parseInt(options.headerLevelStart),\n\n      // Set text-style headers:\n      //\tHeader 1\n      //\t========\n      //\n      //\tHeader 2\n      //\t--------\n      //\n      setextRegexH1 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n={2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n=+[ \\t]*\\n+/gm,\n      setextRegexH2 = (options.smoothLivePreview) ? /^(.+)[ \\t]*\\n-{2,}[ \\t]*\\n+/gm : /^(.+)[ \\t]*\\n-+[ \\t]*\\n+/gm;\n\n  text = text.replace(setextRegexH1, function (wholeMatch, m1) {\n\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  text = text.replace(setextRegexH2, function (matchFound, m1) {\n    var spanGamut = showdown.subParser('spanGamut')(m1, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m1) + '\"',\n        hLevel = headerLevelStart + 1,\n        hashBlock = '' + spanGamut + '';\n    return showdown.subParser('hashBlock')(hashBlock, options, globals);\n  });\n\n  // atx-style headers:\n  //  # Header 1\n  //  ## Header 2\n  //  ## Header 2 with closing hashes ##\n  //  ...\n  //  ###### Header 6\n  //\n  var atxStyle = (options.requireSpaceBeforeHeadingText) ? /^(#{1,6})[ \\t]+(.+?)[ \\t]*#*\\n+/gm : /^(#{1,6})[ \\t]*(.+?)[ \\t]*#*\\n+/gm;\n\n  text = text.replace(atxStyle, function (wholeMatch, m1, m2) {\n    var hText = m2;\n    if (options.customizedHeaderId) {\n      hText = m2.replace(/\\s?\\{([^{]+?)}\\s*$/, '');\n    }\n\n    var span = showdown.subParser('spanGamut')(hText, options, globals),\n        hID = (options.noHeaderId) ? '' : ' id=\"' + headerId(m2) + '\"',\n        hLevel = headerLevelStart - 1 + m1.length,\n        header = '' + span + '';\n\n    return showdown.subParser('hashBlock')(header, options, globals);\n  });\n\n  function headerId (m) {\n    var title,\n        prefix;\n\n    // It is separate from other options to allow combining prefix and customized\n    if (options.customizedHeaderId) {\n      var match = m.match(/\\{([^{]+?)}\\s*$/);\n      if (match && match[1]) {\n        m = match[1];\n      }\n    }\n\n    title = m;\n\n    // Prefix id to prevent causing inadvertent pre-existing style matches.\n    if (showdown.helper.isString(options.prefixHeaderId)) {\n      prefix = options.prefixHeaderId;\n    } else if (options.prefixHeaderId === true) {\n      prefix = 'section-';\n    } else {\n      prefix = '';\n    }\n\n    if (!options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (options.ghCompatibleHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '')\n        .replace(/¨T/g, '')\n        .replace(/¨D/g, '')\n        // replace rest of the chars (&~$ are repeated as they might have been escaped)\n        // borrowed from github's redcarpet (some they should produce similar results)\n        .replace(/[&+$,\\/:;=?@\"#{}|^¨~\\[\\]`\\\\*)(%.!'<>]/g, '')\n        .toLowerCase();\n    } else if (options.rawHeaderId) {\n      title = title\n        .replace(/ /g, '-')\n        // replace previously escaped chars (&, ¨ and $)\n        .replace(/&/g, '&')\n        .replace(/¨T/g, '¨')\n        .replace(/¨D/g, '$')\n        // replace \" and '\n        .replace(/[\"']/g, '-')\n        .toLowerCase();\n    } else {\n      title = title\n        .replace(/[^\\w]/g, '')\n        .toLowerCase();\n    }\n\n    if (options.rawPrefixHeaderId) {\n      title = prefix + title;\n    }\n\n    if (globals.hashLinkCounts[title]) {\n      title = title + '-' + (globals.hashLinkCounts[title]++);\n    } else {\n      globals.hashLinkCounts[title] = 1;\n    }\n    return title;\n  }\n\n  text = globals.converter._dispatch('headers.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Turn Markdown link shortcuts into XHTML  tags.\n */\nshowdown.subParser('horizontalRule', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('horizontalRule.before', text, options, globals);\n\n  var key = showdown.subParser('hashBlock')('
    ', options, globals);\n  text = text.replace(/^ {0,2}( ?-){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?\\*){3,}[ \\t]*$/gm, key);\n  text = text.replace(/^ {0,2}( ?_){3,}[ \\t]*$/gm, key);\n\n  text = globals.converter._dispatch('horizontalRule.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Turn Markdown image shortcuts into  tags.\n */\nshowdown.subParser('images', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('images.before', text, options, globals);\n\n  var inlineRegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      crazyRegExp       = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]?<([^>]*)>(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:(?:([\"'])([^\"]*?)\\6))?[ \\t]?\\)/g,\n      base64RegExp      = /!\\[([^\\]]*?)][ \\t]*()\\([ \\t]??(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*(?:([\"'])([^\"]*?)\\6)?[ \\t]?\\)/g,\n      referenceRegExp   = /!\\[([^\\]]*?)] ?(?:\\n *)?\\[([\\s\\S]*?)]()()()()()/g,\n      refShortcutRegExp = /!\\[([^\\[\\]]+)]()()()()()/g;\n\n  function writeImageTagBase64 (wholeMatch, altText, linkId, url, width, height, m5, title) {\n    url = url.replace(/\\s/g, '');\n    return writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title);\n  }\n\n  function writeImageTag (wholeMatch, altText, linkId, url, width, height, m5, title) {\n\n    var gUrls   = globals.gUrls,\n        gTitles = globals.gTitles,\n        gDims   = globals.gDimensions;\n\n    linkId = linkId.toLowerCase();\n\n    if (!title) {\n      title = '';\n    }\n    // Special case for explicit empty url\n    if (wholeMatch.search(/\\(? ?(['\"].*['\"])?\\)$/m) > -1) {\n      url = '';\n\n    } else if (url === '' || url === null) {\n      if (linkId === '' || linkId === null) {\n        // lower-case and turn embedded newlines into spaces\n        linkId = altText.toLowerCase().replace(/ ?\\n/g, ' ');\n      }\n      url = '#' + linkId;\n\n      if (!showdown.helper.isUndefined(gUrls[linkId])) {\n        url = gUrls[linkId];\n        if (!showdown.helper.isUndefined(gTitles[linkId])) {\n          title = gTitles[linkId];\n        }\n        if (!showdown.helper.isUndefined(gDims[linkId])) {\n          width = gDims[linkId].width;\n          height = gDims[linkId].height;\n        }\n      } else {\n        return wholeMatch;\n      }\n    }\n\n    altText = altText\n      .replace(/\"/g, '"')\n    //altText = showdown.helper.escapeCharacters(altText, '*_', false);\n      .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    //url = showdown.helper.escapeCharacters(url, '*_', false);\n    url = url.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n    var result = '\"'x \"optional title\")\n\n  // base64 encoded images\n  text = text.replace(base64RegExp, writeImageTagBase64);\n\n  // cases with crazy urls like ./image/cat1).png\n  text = text.replace(crazyRegExp, writeImageTag);\n\n  // normal cases\n  text = text.replace(inlineRegExp, writeImageTag);\n\n  // handle reference-style shortcuts: ![img text]\n  text = text.replace(refShortcutRegExp, writeImageTag);\n\n  text = globals.converter._dispatch('images.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('italicsAndBold', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('italicsAndBold.before', text, options, globals);\n\n  // it's faster to have 3 separate regexes for each case than have just one\n  // because of backtracing, in some cases, it could lead to an exponential effect\n  // called \"catastrophic backtrace\". Ominous!\n\n  function parseInside (txt, left, right) {\n    /*\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    */\n    return left + txt + right;\n  }\n\n  // Parse underscores\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n    text = text.replace(/\\b_(\\S[\\s\\S]*?)_\\b/g, function (wm, txt) {\n      return parseInside (txt, '', '');\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/_([^\\s_][\\s\\S]*?)_/g, function (wm, m) {\n      // !/^_[^_]/.test(m) - test if it doesn't start with __ (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n  // Now parse asterisks\n  if (options.literalMidWordAsterisks) {\n    text = text.replace(/([^*]|^)\\B\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*\\*(\\S[\\s\\S]*?)\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n    text = text.replace(/([^*]|^)\\B\\*(\\S[\\s\\S]*?)\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n      return parseInside (txt, lead + '', '');\n    });\n  } else {\n    text = text.replace(/\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*\\*(\\S[\\s\\S]*?)\\*\\*/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n    text = text.replace(/\\*([^\\s*][\\s\\S]*?)\\*/g, function (wm, m) {\n      // !/^\\*[^*]/.test(m) - test if it doesn't start with ** (since it seems redundant, we removed it)\n      return (/\\S$/.test(m)) ? parseInside (m, '', '') : wm;\n    });\n  }\n\n\n  text = globals.converter._dispatch('italicsAndBold.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Form HTML ordered (numbered) and unordered (bulleted) lists.\n */\nshowdown.subParser('lists', function (text, options, globals) {\n  'use strict';\n\n  /**\n   * Process the contents of a single ordered or unordered list, splitting it\n   * into individual list items.\n   * @param {string} listStr\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function processListItems (listStr, trimTrailing) {\n    // The $g_list_level global keeps track of when we're inside a list.\n    // Each time we enter a list, we increment it; when we leave a list,\n    // we decrement. If it's zero, we're not in a list anymore.\n    //\n    // We do this because when we're not inside a list, we want to treat\n    // something like this:\n    //\n    //    I recommend upgrading to version\n    //    8. Oops, now this line is treated\n    //    as a sub-list.\n    //\n    // As a single paragraph, despite the fact that the second line starts\n    // with a digit-period-space sequence.\n    //\n    // Whereas when we're inside a list (or sub-list), that line will be\n    // treated as the start of a sub-list. What a kludge, huh? This is\n    // an aspect of Markdown's syntax that's hard to parse perfectly\n    // without resorting to mind-reading. Perhaps the solution is to\n    // change the syntax rules such that sub-lists must start with a\n    // starting cardinal number; e.g. \"1.\" or \"a.\".\n    globals.gListLevel++;\n\n    // trim trailing blank lines:\n    listStr = listStr.replace(/\\n{2,}$/, '\\n');\n\n    // attacklab: add sentinel to emulate \\z\n    listStr += '¨0';\n\n    var rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0| {0,3}([*+-]|\\d+[.])[ \\t]+))/gm,\n        isParagraphed = (/\\n[ \\t]*\\n(?!¨0)/.test(listStr));\n\n    // Since version 1.5, nesting sublists requires 4 spaces (or 1 tab) indentation,\n    // which is a syntax breaking change\n    // activating this option reverts to old behavior\n    if (options.disableForced4SpacesIndentedSublists) {\n      rgx = /(\\n)?(^ {0,3})([*+-]|\\d+[.])[ \\t]+((\\[(x|X| )?])?[ \\t]*[^\\r]+?(\\n{1,2}))(?=\\n*(¨0|\\2([*+-]|\\d+[.])[ \\t]+))/gm;\n    }\n\n    listStr = listStr.replace(rgx, function (wholeMatch, m1, m2, m3, m4, taskbtn, checked) {\n      checked = (checked && checked.trim() !== '');\n\n      var item = showdown.subParser('outdent')(m4, options, globals),\n          bulletStyle = '';\n\n      // Support for github tasklists\n      if (taskbtn && options.tasklists) {\n        bulletStyle = ' class=\"task-list-item\" style=\"list-style-type: none;\"';\n        item = item.replace(/^[ \\t]*\\[(x|X| )?]/m, function () {\n          var otp = '
  • a
    • \n      // instead of:\n      // 
    • - - a
    \n      // So, to prevent it, we will put a marker (¨A)in the beginning of the line\n      // Kind of hackish/monkey patching, but seems more effective than overcomplicating the list parser\n      item = item.replace(/^([-*+]|\\d\\.)[ \\t]+[\\S\\n ]*/g, function (wm2) {\n        return '¨A' + wm2;\n      });\n\n      // m1 - Leading line or\n      // Has a double return (multi paragraph) or\n      // Has sublist\n      if (m1 || (item.search(/\\n{2,}/) > -1)) {\n        item = showdown.subParser('githubCodeBlocks')(item, options, globals);\n        item = showdown.subParser('blockGamut')(item, options, globals);\n      } else {\n        // Recursion for sub-lists:\n        item = showdown.subParser('lists')(item, options, globals);\n        item = item.replace(/\\n$/, ''); // chomp(item)\n        item = showdown.subParser('hashHTMLBlocks')(item, options, globals);\n\n        // Colapse double linebreaks\n        item = item.replace(/\\n\\n+/g, '\\n\\n');\n        if (isParagraphed) {\n          item = showdown.subParser('paragraphs')(item, options, globals);\n        } else {\n          item = showdown.subParser('spanGamut')(item, options, globals);\n        }\n      }\n\n      // now we need to remove the marker (¨A)\n      item = item.replace('¨A', '');\n      // we can finally wrap the line in list item tags\n      item =  '' + item + '\\n';\n\n      return item;\n    });\n\n    // attacklab: strip sentinel\n    listStr = listStr.replace(/¨0/g, '');\n\n    globals.gListLevel--;\n\n    if (trimTrailing) {\n      listStr = listStr.replace(/\\s+$/, '');\n    }\n\n    return listStr;\n  }\n\n  function styleStartNumber (list, listType) {\n    // check if ol and starts by a number different than 1\n    if (listType === 'ol') {\n      var res = list.match(/^ *(\\d+)\\./);\n      if (res && res[1] !== '1') {\n        return ' start=\"' + res[1] + '\"';\n      }\n    }\n    return '';\n  }\n\n  /**\n   * Check and parse consecutive lists (better fix for issue #142)\n   * @param {string} list\n   * @param {string} listType\n   * @param {boolean} trimTrailing\n   * @returns {string}\n   */\n  function parseConsecutiveLists (list, listType, trimTrailing) {\n    // check if we caught 2 or more consecutive lists by mistake\n    // we use the counterRgx, meaning if listType is UL we look for OL and vice versa\n    var olRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?\\d+\\.[ \\t]/gm : /^ {0,3}\\d+\\.[ \\t]/gm,\n        ulRgx = (options.disableForced4SpacesIndentedSublists) ? /^ ?[*+-][ \\t]/gm : /^ {0,3}[*+-][ \\t]/gm,\n        counterRxg = (listType === 'ul') ? olRgx : ulRgx,\n        result = '';\n\n    if (list.search(counterRxg) !== -1) {\n      (function parseCL (txt) {\n        var pos = txt.search(counterRxg),\n            style = styleStartNumber(list, listType);\n        if (pos !== -1) {\n          // slice\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt.slice(0, pos), !!trimTrailing) + '\\n';\n\n          // invert counterType and listType\n          listType = (listType === 'ul') ? 'ol' : 'ul';\n          counterRxg = (listType === 'ul') ? olRgx : ulRgx;\n\n          //recurse\n          parseCL(txt.slice(pos));\n        } else {\n          result += '\\n\\n<' + listType + style + '>\\n' + processListItems(txt, !!trimTrailing) + '\\n';\n        }\n      })(list);\n    } else {\n      var style = styleStartNumber(list, listType);\n      result = '\\n\\n<' + listType + style + '>\\n' + processListItems(list, !!trimTrailing) + '\\n';\n    }\n\n    return result;\n  }\n\n  /** Start of list parsing **/\n  text = globals.converter._dispatch('lists.before', text, options, globals);\n  // add sentinel to hack around khtml/safari bug:\n  // http://bugs.webkit.org/show_bug.cgi?id=11231\n  text += '¨0';\n\n  if (globals.gListLevel) {\n    text = text.replace(/^(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, list, m2) {\n        var listType = (m2.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, true);\n      }\n    );\n  } else {\n    text = text.replace(/(\\n\\n|^\\n?)(( {0,3}([*+-]|\\d+[.])[ \\t]+)[^\\r]+?(¨0|\\n{2,}(?=\\S)(?![ \\t]*(?:[*+-]|\\d+[.])[ \\t]+)))/gm,\n      function (wholeMatch, m1, list, m3) {\n        var listType = (m3.search(/[*+-]/g) > -1) ? 'ul' : 'ol';\n        return parseConsecutiveLists(list, listType, false);\n      }\n    );\n  }\n\n  // strip sentinel\n  text = text.replace(/¨0/, '');\n  text = globals.converter._dispatch('lists.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Parse metadata at the top of the document\n */\nshowdown.subParser('metadata', function (text, options, globals) {\n  'use strict';\n\n  if (!options.metadata) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('metadata.before', text, options, globals);\n\n  function parseMetadataContents (content) {\n    // raw is raw so it's not changed in any way\n    globals.metadata.raw = content;\n\n    // escape chars forbidden in html attributes\n    // double quotes\n    content = content\n      // ampersand first\n      .replace(/&/g, '&')\n      // double quotes\n      .replace(/\"/g, '"');\n\n    content = content.replace(/\\n {4}/g, ' ');\n    content.replace(/^([\\S ]+): +([\\s\\S]+?)$/gm, function (wm, key, value) {\n      globals.metadata.parsed[key] = value;\n      return '';\n    });\n  }\n\n  text = text.replace(/^\\s*«««+(\\S*?)\\n([\\s\\S]+?)\\n»»»+\\n/, function (wholematch, format, content) {\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/^\\s*---+(\\S*?)\\n([\\s\\S]+?)\\n---+\\n/, function (wholematch, format, content) {\n    if (format) {\n      globals.metadata.format = format;\n    }\n    parseMetadataContents(content);\n    return '¨M';\n  });\n\n  text = text.replace(/¨M/g, '');\n\n  text = globals.converter._dispatch('metadata.after', text, options, globals);\n  return text;\n});\n\r\n/**\n * Remove one level of line-leading tabs or spaces\n */\nshowdown.subParser('outdent', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('outdent.before', text, options, globals);\n\n  // attacklab: hack around Konqueror 3.5.4 bug:\n  // \"----------bug\".replace(/^-/g,\"\") == \"bug\"\n  text = text.replace(/^(\\t|[ ]{1,4})/gm, '¨0'); // attacklab: g_tab_width\n\n  // attacklab: clean up hack\n  text = text.replace(/¨0/g, '');\n\n  text = globals.converter._dispatch('outdent.after', text, options, globals);\n  return text;\n});\n\r\n/**\n *\n */\nshowdown.subParser('paragraphs', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('paragraphs.before', text, options, globals);\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n\n  var grafs = text.split(/\\n{2,}/g),\n      grafsOut = [],\n      end = grafs.length; // Wrap 
     tags\n\n  for (var i = 0; i < end; i++) {\n    var str = grafs[i];\n    // if this is an HTML marker, copy it\n    if (str.search(/¨(K|G)(\\d+)\\1/g) >= 0) {\n      grafsOut.push(str);\n\n    // test for presence of characters to prevent empty lines being parsed\n    // as paragraphs (resulting in undesired extra empty paragraphs)\n    } else if (str.search(/\\S/) >= 0) {\n      str = showdown.subParser('spanGamut')(str, options, globals);\n      str = str.replace(/^([ \\t]*)/g, '
    ');\n      str += '
    ';\n      grafsOut.push(str);\n    }\n  }\n\n  /** Unhashify HTML blocks */\n  end = grafsOut.length;\n  for (i = 0; i < end; i++) {\n    var blockText = '',\n        grafsOutIt = grafsOut[i],\n        codeFlag = false;\n    // if this is a marker for an html block...\n    // use RegExp.test instead of string.search because of QML bug\n    while (/¨(K|G)(\\d+)\\1/.test(grafsOutIt)) {\n      var delim = RegExp.$1,\n          num   = RegExp.$2;\n\n      if (delim === 'K') {\n        blockText = globals.gHtmlBlocks[num];\n      } else {\n        // we need to check if ghBlock is a false positive\n        if (codeFlag) {\n          // use encoded version of all text\n          blockText = showdown.subParser('encodeCode')(globals.ghCodeBlocks[num].text, options, globals);\n        } else {\n          blockText = globals.ghCodeBlocks[num].codeblock;\n        }\n      }\n      blockText = blockText.replace(/\\$/g, '$$$$'); // Escape any dollar signs\n\n      grafsOutIt = grafsOutIt.replace(/(\\n\\n)?¨(K|G)\\d+\\2(\\n\\n)?/, blockText);\n      // Check if grafsOutIt is a pre->code\n      if (/^]*>\\s*]*>/.test(grafsOutIt)) {\n        codeFlag = true;\n      }\n    }\n    grafsOut[i] = grafsOutIt;\n  }\n  text = grafsOut.join('\\n');\n  // Strip leading and trailing lines:\n  text = text.replace(/^\\n+/g, '');\n  text = text.replace(/\\n+$/g, '');\n  return globals.converter._dispatch('paragraphs.after', text, options, globals);\n});\n\r\n/**\n * Run extension\n */\nshowdown.subParser('runExtension', function (ext, text, options, globals) {\n  'use strict';\n\n  if (ext.filter) {\n    text = ext.filter(text, globals.converter, options);\n\n  } else if (ext.regex) {\n    // TODO remove this when old extension loading mechanism is deprecated\n    var re = ext.regex;\n    if (!(re instanceof RegExp)) {\n      re = new RegExp(re, 'g');\n    }\n    text = text.replace(re, ext.replace);\n  }\n\n  return text;\n});\n\r\n/**\n * These are all the transformations that occur *within* block-level\n * tags like paragraphs, headers, and list items.\n */\nshowdown.subParser('spanGamut', function (text, options, globals) {\n  'use strict';\n\n  text = globals.converter._dispatch('spanGamut.before', text, options, globals);\n  text = showdown.subParser('codeSpans')(text, options, globals);\n  text = showdown.subParser('escapeSpecialCharsWithinTagAttributes')(text, options, globals);\n  text = showdown.subParser('encodeBackslashEscapes')(text, options, globals);\n\n  // Process anchor and image tags. Images must come first,\n  // because ![foo][f] looks like an anchor.\n  text = showdown.subParser('images')(text, options, globals);\n  text = showdown.subParser('anchors')(text, options, globals);\n\n  // Make links out of things like ``\n  // Must come after anchors, because you can use < and >\n  // delimiters in inline links like [this]().\n  text = showdown.subParser('autoLinks')(text, options, globals);\n  text = showdown.subParser('simplifiedAutoLinks')(text, options, globals);\n  text = showdown.subParser('emoji')(text, options, globals);\n  text = showdown.subParser('underline')(text, options, globals);\n  text = showdown.subParser('italicsAndBold')(text, options, globals);\n  text = showdown.subParser('strikethrough')(text, options, globals);\n  text = showdown.subParser('ellipsis')(text, options, globals);\n\n  // we need to hash HTML tags inside spans\n  text = showdown.subParser('hashHTMLSpans')(text, options, globals);\n\n  // now we encode amps and angles\n  text = showdown.subParser('encodeAmpsAndAngles')(text, options, globals);\n\n  // Do hard breaks\n  if (options.simpleLineBreaks) {\n    // GFM style hard breaks\n    // only add line breaks if the text does not contain a block (special case for lists)\n    if (!/\\n\\n¨K/.test(text)) {\n      text = text.replace(/\\n+/g, '
    \\n');\n    }\n  } else {\n    // Vanilla hard breaks\n    text = text.replace(/  +\\n/g, '
    \\n');\n  }\n\n  text = globals.converter._dispatch('spanGamut.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('strikethrough', function (text, options, globals) {\n  'use strict';\n\n  function parseInside (txt) {\n    if (options.simplifiedAutoLink) {\n      txt = showdown.subParser('simplifiedAutoLinks')(txt, options, globals);\n    }\n    return '' + txt + '';\n  }\n\n  if (options.strikethrough) {\n    text = globals.converter._dispatch('strikethrough.before', text, options, globals);\n    text = text.replace(/(?:~){2}([\\s\\S]+?)(?:~){2}/g, function (wm, txt) { return parseInside(txt); });\n    text = globals.converter._dispatch('strikethrough.after', text, options, globals);\n  }\n\n  return text;\n});\n\r\n/**\n * Strips link definitions from text, stores the URLs and titles in\n * hash references.\n * Link defs are in the form: ^[id]: url \"optional title\"\n */\nshowdown.subParser('stripLinkDefinitions', function (text, options, globals) {\n  'use strict';\n\n  var regex       = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*\\s]+)>?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n+|(?=¨0))/gm,\n      base64Regex = /^ {0,3}\\[(.+)]:[ \\t]*\\n?[ \\t]*?(?: =([*\\d]+[A-Za-z%]{0,4})x([*\\d]+[A-Za-z%]{0,4}))?[ \\t]*\\n?[ \\t]*(?:(\\n*)[\"|'(](.+?)[\"|')][ \\t]*)?(?:\\n\\n|(?=¨0)|(?=\\n\\[))/gm;\n\n  // attacklab: sentinel workarounds for lack of \\A and \\Z, safari\\khtml bug\n  text += '¨0';\n\n  var replaceFunc = function (wholeMatch, linkId, url, width, height, blankLines, title) {\n    linkId = linkId.toLowerCase();\n    if (url.match(/^data:.+?\\/.+?;base64,/)) {\n      // remove newlines\n      globals.gUrls[linkId] = url.replace(/\\s/g, '');\n    } else {\n      globals.gUrls[linkId] = showdown.subParser('encodeAmpsAndAngles')(url, options, globals);  // Link IDs are case-insensitive\n    }\n\n    if (blankLines) {\n      // Oops, found blank lines, so it's not a title.\n      // Put back the parenthetical statement we stole.\n      return blankLines + title;\n\n    } else {\n      if (title) {\n        globals.gTitles[linkId] = title.replace(/\"|'/g, '"');\n      }\n      if (options.parseImgDimensions && width && height) {\n        globals.gDimensions[linkId] = {\n          width:  width,\n          height: height\n        };\n      }\n    }\n    // Completely remove the definition from the text\n    return '';\n  };\n\n  // first we try to find base64 link references\n  text = text.replace(base64Regex, replaceFunc);\n\n  text = text.replace(regex, replaceFunc);\n\n  // attacklab: strip sentinel\n  text = text.replace(/¨0/, '');\n\n  return text;\n});\n\r\nshowdown.subParser('tables', function (text, options, globals) {\n  'use strict';\n\n  if (!options.tables) {\n    return text;\n  }\n\n  var tableRgx       = /^ {0,3}\\|?.+\\|.+\\n {0,3}\\|?[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[\\s\\S]+?(?:\\n\\n|¨0)/gm,\n      //singeColTblRgx = /^ {0,3}\\|.+\\|\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n(?: {0,3}\\|.+\\|\\n)+(?:\\n\\n|¨0)/gm;\n      singeColTblRgx = /^ {0,3}\\|.+\\|[ \\t]*\\n {0,3}\\|[ \\t]*:?[ \\t]*(?:[-=]){2,}[ \\t]*:?[ \\t]*\\|[ \\t]*\\n( {0,3}\\|.+\\|[ \\t]*\\n)*(?:\\n|¨0)/gm;\n\n  function parseStyles (sLine) {\n    if (/^:[ \\t]*--*$/.test(sLine)) {\n      return ' style=\"text-align:left;\"';\n    } else if (/^--*[ \\t]*:[ \\t]*$/.test(sLine)) {\n      return ' style=\"text-align:right;\"';\n    } else if (/^:[ \\t]*--*[ \\t]*:$/.test(sLine)) {\n      return ' style=\"text-align:center;\"';\n    } else {\n      return '';\n    }\n  }\n\n  function parseHeaders (header, style) {\n    var id = '';\n    header = header.trim();\n    // support both tablesHeaderId and tableHeaderId due to error in documentation so we don't break backwards compatibility\n    if (options.tablesHeaderId || options.tableHeaderId) {\n      id = ' id=\"' + header.replace(/ /g, '_').toLowerCase() + '\"';\n    }\n    header = showdown.subParser('spanGamut')(header, options, globals);\n\n    return '' + header + '\\n';\n  }\n\n  function parseCells (cell, style) {\n    var subText = showdown.subParser('spanGamut')(cell, options, globals);\n    return '' + subText + '\\n';\n  }\n\n  function buildTable (headers, cells) {\n    var tb = '\\n\\n\\n',\n        tblLgn = headers.length;\n\n    for (var i = 0; i < tblLgn; ++i) {\n      tb += headers[i];\n    }\n    tb += '\\n\\n\\n';\n\n    for (i = 0; i < cells.length; ++i) {\n      tb += '\\n';\n      for (var ii = 0; ii < tblLgn; ++ii) {\n        tb += cells[i][ii];\n      }\n      tb += '\\n';\n    }\n    tb += '\\n
    \\n';\n    return tb;\n  }\n\n  function parseTable (rawTable) {\n    var i, tableLines = rawTable.split('\\n');\n\n    for (i = 0; i < tableLines.length; ++i) {\n      // strip wrong first and last column if wrapped tables are used\n      if (/^ {0,3}\\|/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/^ {0,3}\\|/, '');\n      }\n      if (/\\|[ \\t]*$/.test(tableLines[i])) {\n        tableLines[i] = tableLines[i].replace(/\\|[ \\t]*$/, '');\n      }\n      // parse code spans first, but we only support one line code spans\n      tableLines[i] = showdown.subParser('codeSpans')(tableLines[i], options, globals);\n    }\n\n    var rawHeaders = tableLines[0].split('|').map(function (s) { return s.trim();}),\n        rawStyles = tableLines[1].split('|').map(function (s) { return s.trim();}),\n        rawCells = [],\n        headers = [],\n        styles = [],\n        cells = [];\n\n    tableLines.shift();\n    tableLines.shift();\n\n    for (i = 0; i < tableLines.length; ++i) {\n      if (tableLines[i].trim() === '') {\n        continue;\n      }\n      rawCells.push(\n        tableLines[i]\n          .split('|')\n          .map(function (s) {\n            return s.trim();\n          })\n      );\n    }\n\n    if (rawHeaders.length < rawStyles.length) {\n      return rawTable;\n    }\n\n    for (i = 0; i < rawStyles.length; ++i) {\n      styles.push(parseStyles(rawStyles[i]));\n    }\n\n    for (i = 0; i < rawHeaders.length; ++i) {\n      if (showdown.helper.isUndefined(styles[i])) {\n        styles[i] = '';\n      }\n      headers.push(parseHeaders(rawHeaders[i], styles[i]));\n    }\n\n    for (i = 0; i < rawCells.length; ++i) {\n      var row = [];\n      for (var ii = 0; ii < headers.length; ++ii) {\n        if (showdown.helper.isUndefined(rawCells[i][ii])) {\n\n        }\n        row.push(parseCells(rawCells[i][ii], styles[ii]));\n      }\n      cells.push(row);\n    }\n\n    return buildTable(headers, cells);\n  }\n\n  text = globals.converter._dispatch('tables.before', text, options, globals);\n\n  // find escaped pipe characters\n  text = text.replace(/\\\\(\\|)/g, showdown.helper.escapeCharactersCallback);\n\n  // parse multi column tables\n  text = text.replace(tableRgx, parseTable);\n\n  // parse one column tables\n  text = text.replace(singeColTblRgx, parseTable);\n\n  text = globals.converter._dispatch('tables.after', text, options, globals);\n\n  return text;\n});\n\r\nshowdown.subParser('underline', function (text, options, globals) {\n  'use strict';\n\n  if (!options.underline) {\n    return text;\n  }\n\n  text = globals.converter._dispatch('underline.before', text, options, globals);\n\n  if (options.literalMidWordUnderscores) {\n    text = text.replace(/\\b___(\\S[\\s\\S]*?)___\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n    text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n      return '' + txt + '';\n    });\n  } else {\n    text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n    text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n      return (/\\S$/.test(m)) ? '' + m + '' : wm;\n    });\n  }\n\n  // escape remaining underscores to prevent them being parsed by italic and bold\n  text = text.replace(/(_)/g, showdown.helper.escapeCharactersCallback);\n\n  text = globals.converter._dispatch('underline.after', text, options, globals);\n\n  return text;\n});\n\r\n/**\n * Swap back in all the special characters we've hidden.\n */\nshowdown.subParser('unescapeSpecialChars', function (text, options, globals) {\n  'use strict';\n  text = globals.converter._dispatch('unescapeSpecialChars.before', text, options, globals);\n\n  text = text.replace(/¨E(\\d+)E/g, function (wholeMatch, m1) {\n    var charCodeToReplace = parseInt(m1);\n    return String.fromCharCode(charCodeToReplace);\n  });\n\n  text = globals.converter._dispatch('unescapeSpecialChars.after', text, options, globals);\n  return text;\n});\n\r\nshowdown.subParser('makeMarkdown.blockquote', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      var innerTxt = showdown.subParser('makeMarkdown.node')(children[i], globals);\n\n      if (innerTxt === '') {\n        continue;\n      }\n      txt += innerTxt;\n    }\n  }\n  // cleanup\n  txt = txt.trim();\n  txt = '> ' + txt.split('\\n').join('\\n> ');\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.codeBlock', function (node, globals) {\n  'use strict';\n\n  var lang = node.getAttribute('language'),\n      num  = node.getAttribute('precodenum');\n  return '```' + lang + '\\n' + globals.preList[num] + '\\n```';\n});\n\r\nshowdown.subParser('makeMarkdown.codeSpan', function (node) {\n  'use strict';\n\n  return '`' + node.innerHTML + '`';\n});\n\r\nshowdown.subParser('makeMarkdown.emphasis', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '*';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '*';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.header', function (node, globals, headerLevel) {\n  'use strict';\n\n  var headerMark = new Array(headerLevel + 1).join('#'),\n      txt = '';\n\n  if (node.hasChildNodes()) {\n    txt = headerMark + ' ';\n    var children = node.childNodes,\n        childrenLength = children.length;\n\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.hr', function () {\n  'use strict';\n\n  return '---';\n});\n\r\nshowdown.subParser('makeMarkdown.image', function (node) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasAttribute('src')) {\n    txt += '![' + node.getAttribute('alt') + '](';\n    txt += '<' + node.getAttribute('src') + '>';\n    if (node.hasAttribute('width') && node.hasAttribute('height')) {\n      txt += ' =' + node.getAttribute('width') + 'x' + node.getAttribute('height');\n    }\n\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.links', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes() && node.hasAttribute('href')) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    txt = '[';\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '](';\n    txt += '<' + node.getAttribute('href') + '>';\n    if (node.hasAttribute('title')) {\n      txt += ' \"' + node.getAttribute('title') + '\"';\n    }\n    txt += ')';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.list', function (node, globals, type) {\n  'use strict';\n\n  var txt = '';\n  if (!node.hasChildNodes()) {\n    return '';\n  }\n  var listItems       = node.childNodes,\n      listItemsLenght = listItems.length,\n      listNum = node.getAttribute('start') || 1;\n\n  for (var i = 0; i < listItemsLenght; ++i) {\n    if (typeof listItems[i].tagName === 'undefined' || listItems[i].tagName.toLowerCase() !== 'li') {\n      continue;\n    }\n\n    // define the bullet to use in list\n    var bullet = '';\n    if (type === 'ol') {\n      bullet = listNum.toString() + '. ';\n    } else {\n      bullet = '- ';\n    }\n\n    // parse list item\n    txt += bullet + showdown.subParser('makeMarkdown.listItem')(listItems[i], globals);\n    ++listNum;\n  }\n\n  // add comment at the end to prevent consecutive lists to be parsed as one\n  txt += '\\n\\n';\n  return txt.trim();\n});\n\r\nshowdown.subParser('makeMarkdown.listItem', function (node, globals) {\n  'use strict';\n\n  var listItemTxt = '';\n\n  var children = node.childNodes,\n      childrenLenght = children.length;\n\n  for (var i = 0; i < childrenLenght; ++i) {\n    listItemTxt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n  }\n  // if it's only one liner, we need to add a newline at the end\n  if (!/\\n$/.test(listItemTxt)) {\n    listItemTxt += '\\n';\n  } else {\n    // it's multiparagraph, so we need to indent\n    listItemTxt = listItemTxt\n      .split('\\n')\n      .join('\\n    ')\n      .replace(/^ {4}$/gm, '')\n      .replace(/\\n\\n+/g, '\\n\\n');\n  }\n\n  return listItemTxt;\n});\n\r\n\n\nshowdown.subParser('makeMarkdown.node', function (node, globals, spansOnly) {\n  'use strict';\n\n  spansOnly = spansOnly || false;\n\n  var txt = '';\n\n  // edge case of text without wrapper paragraph\n  if (node.nodeType === 3) {\n    return showdown.subParser('makeMarkdown.txt')(node, globals);\n  }\n\n  // HTML comment\n  if (node.nodeType === 8) {\n    return '\\n\\n';\n  }\n\n  // process only node elements\n  if (node.nodeType !== 1) {\n    return '';\n  }\n\n  var tagName = node.tagName.toLowerCase();\n\n  switch (tagName) {\n\n    //\n    // BLOCKS\n    //\n    case 'h1':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 1) + '\\n\\n'; }\n      break;\n    case 'h2':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 2) + '\\n\\n'; }\n      break;\n    case 'h3':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 3) + '\\n\\n'; }\n      break;\n    case 'h4':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 4) + '\\n\\n'; }\n      break;\n    case 'h5':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 5) + '\\n\\n'; }\n      break;\n    case 'h6':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.header')(node, globals, 6) + '\\n\\n'; }\n      break;\n\n    case 'p':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.paragraph')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'blockquote':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.blockquote')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'hr':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.hr')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'ol':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ol') + '\\n\\n'; }\n      break;\n\n    case 'ul':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.list')(node, globals, 'ul') + '\\n\\n'; }\n      break;\n\n    case 'precode':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.codeBlock')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'pre':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.pre')(node, globals) + '\\n\\n'; }\n      break;\n\n    case 'table':\n      if (!spansOnly) { txt = showdown.subParser('makeMarkdown.table')(node, globals) + '\\n\\n'; }\n      break;\n\n    //\n    // SPANS\n    //\n    case 'code':\n      txt = showdown.subParser('makeMarkdown.codeSpan')(node, globals);\n      break;\n\n    case 'em':\n    case 'i':\n      txt = showdown.subParser('makeMarkdown.emphasis')(node, globals);\n      break;\n\n    case 'strong':\n    case 'b':\n      txt = showdown.subParser('makeMarkdown.strong')(node, globals);\n      break;\n\n    case 'del':\n      txt = showdown.subParser('makeMarkdown.strikethrough')(node, globals);\n      break;\n\n    case 'a':\n      txt = showdown.subParser('makeMarkdown.links')(node, globals);\n      break;\n\n    case 'img':\n      txt = showdown.subParser('makeMarkdown.image')(node, globals);\n      break;\n\n    default:\n      txt = node.outerHTML + '\\n\\n';\n  }\n\n  // common normalization\n  // TODO eventually\n\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.paragraph', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n  }\n\n  // some text normalization\n  txt = txt.trim();\n\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.pre', function (node, globals) {\n  'use strict';\n\n  var num  = node.getAttribute('prenum');\n  return '
    ' + globals.preList[num] + '
    ';\n});\n\r\nshowdown.subParser('makeMarkdown.strikethrough', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '~~';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '~~';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.strong', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (node.hasChildNodes()) {\n    txt += '**';\n    var children = node.childNodes,\n        childrenLength = children.length;\n    for (var i = 0; i < childrenLength; ++i) {\n      txt += showdown.subParser('makeMarkdown.node')(children[i], globals);\n    }\n    txt += '**';\n  }\n  return txt;\n});\n\r\nshowdown.subParser('makeMarkdown.table', function (node, globals) {\n  'use strict';\n\n  var txt = '',\n      tableArray = [[], []],\n      headings   = node.querySelectorAll('thead>tr>th'),\n      rows       = node.querySelectorAll('tbody>tr'),\n      i, ii;\n  for (i = 0; i < headings.length; ++i) {\n    var headContent = showdown.subParser('makeMarkdown.tableCell')(headings[i], globals),\n        allign = '---';\n\n    if (headings[i].hasAttribute('style')) {\n      var style = headings[i].getAttribute('style').toLowerCase().replace(/\\s/g, '');\n      switch (style) {\n        case 'text-align:left;':\n          allign = ':---';\n          break;\n        case 'text-align:right;':\n          allign = '---:';\n          break;\n        case 'text-align:center;':\n          allign = ':---:';\n          break;\n      }\n    }\n    tableArray[0][i] = headContent.trim();\n    tableArray[1][i] = allign;\n  }\n\n  for (i = 0; i < rows.length; ++i) {\n    var r = tableArray.push([]) - 1,\n        cols = rows[i].getElementsByTagName('td');\n\n    for (ii = 0; ii < headings.length; ++ii) {\n      var cellContent = ' ';\n      if (typeof cols[ii] !== 'undefined') {\n        cellContent = showdown.subParser('makeMarkdown.tableCell')(cols[ii], globals);\n      }\n      tableArray[r].push(cellContent);\n    }\n  }\n\n  var cellSpacesCount = 3;\n  for (i = 0; i < tableArray.length; ++i) {\n    for (ii = 0; ii < tableArray[i].length; ++ii) {\n      var strLen = tableArray[i][ii].length;\n      if (strLen > cellSpacesCount) {\n        cellSpacesCount = strLen;\n      }\n    }\n  }\n\n  for (i = 0; i < tableArray.length; ++i) {\n    for (ii = 0; ii < tableArray[i].length; ++ii) {\n      if (i === 1) {\n        if (tableArray[i][ii].slice(-1) === ':') {\n          tableArray[i][ii] = showdown.helper.padEnd(tableArray[i][ii].slice(-1), cellSpacesCount - 1, '-') + ':';\n        } else {\n          tableArray[i][ii] = showdown.helper.padEnd(tableArray[i][ii], cellSpacesCount, '-');\n        }\n      } else {\n        tableArray[i][ii] = showdown.helper.padEnd(tableArray[i][ii], cellSpacesCount);\n      }\n    }\n    txt += '| ' + tableArray[i].join(' | ') + ' |\\n';\n  }\n\n  return txt.trim();\n});\n\r\nshowdown.subParser('makeMarkdown.tableCell', function (node, globals) {\n  'use strict';\n\n  var txt = '';\n  if (!node.hasChildNodes()) {\n    return '';\n  }\n  var children = node.childNodes,\n      childrenLength = children.length;\n\n  for (var i = 0; i < childrenLength; ++i) {\n    txt += showdown.subParser('makeMarkdown.node')(children[i], globals, true);\n  }\n  return txt.trim();\n});\n\r\nshowdown.subParser('makeMarkdown.txt', function (node) {\n  'use strict';\n\n  var txt = node.nodeValue;\n\n  // multiple spaces are collapsed\n  txt = txt.replace(/ +/g, ' ');\n\n  // replace the custom ¨NBSP; with a space\n  txt = txt.replace(/¨NBSP;/g, ' ');\n\n  // \", <, > and & should replace escaped html entities\n  txt = showdown.helper.unescapeHTMLEntities(txt);\n\n  // escape markdown magic characters\n  // emphasis, strong and strikethrough - can appear everywhere\n  // we also escape pipe (|) because of tables\n  // and escape ` because of code blocks and spans\n  txt = txt.replace(/([*_~|`])/g, '\\\\$1');\n\n  // escape > because of blockquotes\n  txt = txt.replace(/^(\\s*)>/g, '\\\\$1>');\n\n  // hash character, only troublesome at the beginning of a line because of headers\n  txt = txt.replace(/^#/gm, '\\\\#');\n\n  // horizontal rules\n  txt = txt.replace(/^(\\s*)([-=]{3,})(\\s*)$/, '$1\\\\$2$3');\n\n  // dot, because of ordered lists, only troublesome at the beginning of a line when preceded by an integer\n  txt = txt.replace(/^( {0,3}\\d+)\\./gm, '$1\\\\.');\n\n  // +, * and -, at the beginning of a line becomes a list, so we need to escape them also (asterisk was already escaped)\n  txt = txt.replace(/^( {0,3})([+-])/gm, '$1\\\\$2');\n\n  // images and links, ] followed by ( is problematic, so we escape it\n  txt = txt.replace(/]([\\s]*)\\(/g, '\\\\]$1\\\\(');\n\n  // reference URIs must also be escaped\n  txt = txt.replace(/^ {0,3}\\[([\\S \\t]*?)]:/gm, '\\\\[$1]:');\n\n  return txt;\n});\n\r\nvar root = this;\n\n// AMD Loader\nif (typeof define === 'function' && define.amd) {\n  define(function () {\n    'use strict';\n    return showdown;\n  });\n\n// CommonJS/nodeJS Loader\n} else if (typeof module !== 'undefined' && module.exports) {\n  module.exports = showdown;\n\n// Regular Browser loader\n} else {\n  root.showdown = showdown;\n}\n}).call(this);\r\n\n//# sourceMappingURL=showdown.js.map\r\n\n\n\n// WEBPACK FOOTER //\n// ../node_modules/showdown/dist/showdown.js","// removed by extract-text-webpack-plugin\nmodule.exports = {\"thesis\":\"thesis__3uAQ4\"};\n\n\n//////////////////\n// WEBPACK FOOTER\n// ./components/thesis.css\n// module id = J9SO\n// module chunks = 0","import { Component, cloneElement, h } from 'preact';\n\nvar EMPTY$1 = {};\n\nfunction assign(obj, props) {\n\t// eslint-disable-next-line guard-for-in\n\tfor (var i in props) {\n\t\tobj[i] = props[i];\n\t}\n\treturn obj;\n}\n\nfunction exec(url, route, opts) {\n\tvar reg = /(?:\\?([^#]*))?(#.*)?$/,\n\t\tc = url.match(reg),\n\t\tmatches = {},\n\t\tret;\n\tif (c && c[1]) {\n\t\tvar p = c[1].split('&');\n\t\tfor (var i=0; i b.rank) ? -1 :\n\t\t(a.index - b.index)\n\t);\n}\n\n// filter out VNodes without attributes (which are unrankeable), and add `index`/`rank` properties to be used in sorting.\nfunction prepareVNodeForRanking(vnode, index) {\n\tvnode.index = index;\n\tvnode.rank = rankChild(vnode);\n\treturn vnode.attributes;\n}\n\nfunction segmentize(url) {\n\treturn url.replace(/(^\\/+|\\/+$)/g, '').split('/');\n}\n\nfunction rankSegment(segment) {\n\treturn segment.charAt(0)==':' ? (1 + '*+?'.indexOf(segment.charAt(segment.length-1))) || 4 : 5;\n}\n\nfunction rank(path) {\n\treturn segmentize(path).map(rankSegment).join('');\n}\n\nfunction rankChild(vnode) {\n\treturn vnode.attributes.default ? 0 : rank(vnode.attributes.path);\n}\n\nvar customHistory = null;\n\nvar ROUTERS = [];\n\nvar subscribers = [];\n\nvar EMPTY = {};\n\nfunction isPreactElement(node) {\n\treturn node.__preactattr_!=null || typeof Symbol!=='undefined' && node[Symbol.for('preactattr')]!=null;\n}\n\nfunction setUrl(url, type) {\n\tif ( type === void 0 ) type='push';\n\n\tif (customHistory && customHistory[type]) {\n\t\tcustomHistory[type](url);\n\t}\n\telse if (typeof history!=='undefined' && history[type+'State']) {\n\t\thistory[type+'State'](null, null, url);\n\t}\n}\n\n\nfunction getCurrentUrl() {\n\tvar url;\n\tif (customHistory && customHistory.location) {\n\t\turl = customHistory.location;\n\t}\n\telse if (customHistory && customHistory.getCurrentLocation) {\n\t\turl = customHistory.getCurrentLocation();\n\t}\n\telse {\n\t\turl = typeof location!=='undefined' ? location : EMPTY;\n\t}\n\treturn (\"\" + (url.pathname || '') + (url.search || ''));\n}\n\n\n\nfunction route(url, replace) {\n\tif ( replace === void 0 ) replace=false;\n\n\tif (typeof url!=='string' && url.url) {\n\t\treplace = url.replace;\n\t\turl = url.url;\n\t}\n\n\t// only push URL into history if we can handle it\n\tif (canRoute(url)) {\n\t\tsetUrl(url, replace ? 'replace' : 'push');\n\t}\n\n\treturn routeTo(url);\n}\n\n\n/** Check if the given URL can be handled by any router instances. */\nfunction canRoute(url) {\n\tfor (var i=ROUTERS.length; i--; ) {\n\t\tif (ROUTERS[i].canRoute(url)) { return true; }\n\t}\n\treturn false;\n}\n\n\n/** Tell all router instances to handle the given URL.  */\nfunction routeTo(url) {\n\tvar didRoute = false;\n\tfor (var i=0; i 0;\n\t};\n\n\t/** Re-render children with a new URL to match against. */\n\tRouter.prototype.routeTo = function routeTo (url) {\n\t\tthis._didRoute = false;\n\t\tthis.setState({ url: url });\n\n\t\t// if we're in the middle of an update, don't synchronously re-route.\n\t\tif (this.updating) { return this.canRoute(url); }\n\n\t\tthis.forceUpdate();\n\t\treturn this._didRoute;\n\t};\n\n\tRouter.prototype.componentWillMount = function componentWillMount () {\n\t\tROUTERS.push(this);\n\t\tthis.updating = true;\n\t};\n\n\tRouter.prototype.componentDidMount = function componentDidMount () {\n\t\tvar this$1 = this;\n\n\t\tif (customHistory) {\n\t\t\tthis.unlisten = customHistory.listen(function (location) {\n\t\t\t\tthis$1.routeTo((\"\" + (location.pathname || '') + (location.search || '')));\n\t\t\t});\n\t\t}\n\t\tthis.updating = false;\n\t};\n\n\tRouter.prototype.componentWillUnmount = function componentWillUnmount () {\n\t\tif (typeof this.unlisten==='function') { this.unlisten(); }\n\t\tROUTERS.splice(ROUTERS.indexOf(this), 1);\n\t};\n\n\tRouter.prototype.componentWillUpdate = function componentWillUpdate () {\n\t\tthis.updating = true;\n\t};\n\n\tRouter.prototype.componentDidUpdate = function componentDidUpdate () {\n\t\tthis.updating = false;\n\t};\n\n\tRouter.prototype.getMatchingChildren = function getMatchingChildren (children, url, invoke) {\n\t\treturn children\n\t\t\t.filter(prepareVNodeForRanking)\n\t\t\t.sort(pathRankSort)\n\t\t\t.map( function (vnode) {\n\t\t\t\tvar matches = exec(url, vnode.attributes.path, vnode.attributes);\n\t\t\t\tif (matches) {\n\t\t\t\t\tif (invoke !== false) {\n\t\t\t\t\t\tvar newProps = { url: url, matches: matches };\n\t\t\t\t\t\tassign(newProps, matches);\n\t\t\t\t\t\tdelete newProps.ref;\n\t\t\t\t\t\tdelete newProps.key;\n\t\t\t\t\t\treturn cloneElement(vnode, newProps);\n\t\t\t\t\t}\n\t\t\t\t\treturn vnode;\n\t\t\t\t}\n\t\t\t}).filter(Boolean);\n\t};\n\n\tRouter.prototype.render = function render (ref, ref$1) {\n\t\tvar children = ref.children;\n\t\tvar onChange = ref.onChange;\n\t\tvar url = ref$1.url;\n\n\t\tvar active = this.getMatchingChildren(children, url, true);\n\n\t\tvar current = active[0] || null;\n\t\tthis._didRoute = !!current;\n\n\t\tvar previous = this.previousUrl;\n\t\tif (url!==previous) {\n\t\t\tthis.previousUrl = url;\n\t\t\tif (typeof onChange==='function') {\n\t\t\t\tonChange({\n\t\t\t\t\trouter: this,\n\t\t\t\t\turl: url,\n\t\t\t\t\tprevious: previous,\n\t\t\t\t\tactive: active,\n\t\t\t\t\tcurrent: current\n\t\t\t\t});\n\t\t\t}\n\t\t}\n\n\t\treturn current;\n\t};\n\n\treturn Router;\n}(Component));\n\nvar Link = function (props) { return (\n\th('a', assign({ onClick: handleLinkClick }, props))\n); };\n\nvar Route = function (props) { return h(props.component, props); };\n\nRouter.subscribers = subscribers;\nRouter.getCurrentUrl = getCurrentUrl;\nRouter.route = route;\nRouter.Router = Router;\nRouter.Route = Route;\nRouter.Link = Link;\n\nexport { subscribers, getCurrentUrl, route, Router, Route, Link };export default Router;\n//# sourceMappingURL=preact-router.es.js.map\n\n\n\n// WEBPACK FOOTER //\n// ../node_modules/preact-router/dist/preact-router.es.js","import style from \"./panel.css\";\nimport { Component } from 'preact';\n\nexport default class Panel extends Component {\n\tgetStyle() {\n\t\treturn style.panel;\n\t};\n\n\trender() {\n\t\tlet title = null;\n\t\tif(this.props.title !== undefined) {\n\t\t\ttitle = (
    {this.props.title}
    );\n\t\t}\n\n\t\treturn (\n\t\t\t
    \n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t
    \n\t\t);\n\t}\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/panel.js","import style from \"./split.css\";\nimport { Component } from 'preact';\n\nexport default class Split extends Component {\n\trender() {\n\t    let title = null;\n\t    if(this.props.title !== undefined) {\n            title = (
    {this.props.title}
    )\n        }\n\n        let children;\n        if(Array.isArray(this.props.children)) {\n            children = this.props.children.map(element => {\n                return (
    {element}
    );\n            });\n        }\n        else {\n            children = 
    {this.props.children}
    ;\n        }\n\t\treturn (\n\t        
    \n                {title}\n                
    {children}
    \n            
    \n        );\n\t}\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/split.js","import style from \"./todo.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Todo extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/todo.js","import style from './home.css'\r\nimport { Component } from 'preact';\r\nimport Panel from '../components/panel';\r\nimport Split from '../components/split';\r\nimport Todo from '../components/todo';\r\n\r\nexport default class Home extends Component {\r\n    render() {\r\n        return (\r\n            
    \r\n                
    Indice
    \r\n                \r\n                    Statistica ed elementi di probabilità    }>\r\n                        
    \r\n                            Appunti scritti mentre studiavo per l'esame di Statistica ed elementi di probabilità  del corso triennale di Informatica all'Unimore del Prof. Luca La Rocca.\r\n                        
    \r\n                    \r\n                    Cleaver}>\r\n                        
    \r\n                            Progetto in Java sviluppato per l'esame di Programmazione ad Oggetti del corso triennale di Informatica all'Unimore, tenuto dai Prof. Giacomo Cabri e Nicola Capodieci.\r\n                        
    \r\n                        \r\n                    Fisica}>\r\n                        
    \r\n                            Appunti delle lezioni di Fisica del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Rossella Brunetti nel primo semestre dell'Anno Accademico 2019/2020.\r\n                        
    \r\n                        \r\n                    Sistemi Operativi}>\r\n                        
    \r\n                            Soluzioni agli Arzigogoli proposti dal Prof. Mauro Andreolini durante le lezioni di Sistemi Operativi del corso triennale di Informatica all'Unimore tenutesi nel primo semestre dell'Anno Accademico 2019/2020.\r\n                        
    \r\n                        \r\n                    Algoritmi e Strutture Dati}>\r\n                        
    \r\n                            Appunti delle lezioni di Algoritmi e Strutture Dati del corso triennale di Informatica all'Unimore, tenute dalla Prof.ssa Manuela Montangero nel secondo semestre dell'Anno Accademico 2018/2019.\r\n                        
    \r\n                        \r\n                    Videolezioni di Geometria}>\r\n                        
    \r\n                            Ottime videolezioni di Geometria con licenza CC BY-NC-SA 4.0 che ho trovato sul portale Dolly 2018 dell'Unimore.\r\n                        
    \r\n                        \r\n                    Come installare MinGW}>\r\n                        
    \r\n                            Un breve tutorial con immagini su come installare e configurare MinGW per compilare programmi C e C++ su Windows.\r\n                        
    \r\n                        \r\n                \r\n                \r\n                    @unimoreinfo}>\r\n                        
    \r\n                            Il gruppo Telegram del corso di Informatica dell'Unimore!\r\n                        
    \r\n                        \r\n                    Calendario Lezioni}>\r\n                        
    \r\n                            Calendario Google quasi sempre aggiornato delle lezioni e degli esami del secondo anno dell'Unimore durante l'Anno Accademico 2019/2020.\r\n                        
    \r\n                        \r\n                    Erre2}>\r\n                        
    \r\n                            Portale contenente appunti e riassunti mantenuto da Lorenzo Balugani.\r\n                        
    \r\n                        \r\n                    vezzalinistefano/Appunti-Algoritmi}>\r\n                        
    \r\n                            Appunti di Algoritmi e Strutture Dati mantenuti da Vezzalini Stefano.\r\n                        
    \r\n                        \r\n                    \r\n            
    \r\n        )\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./pages/home.js","import style from './latex.css';\nimport { Component } from 'preact';\n\nexport default class Latex extends Component {\n\trender() {\n\t\tlet equation = `{\\\\color{White} ${this.props.children} }`;\n\t\treturn (\n\t\t\t{this.props.children}\n\t\t\t);\n\t}\n}\n\n\n// WEBPACK FOOTER //\n// ./components/latex.js","import style from \"./plus.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Plus extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/plus.js","import style from \"./minus.css\";\r\nimport { Component } from 'preact';\r\n\r\nexport default class Minus extends Component {\r\n\trender() {\r\n\t\treturn {this.props.children};\r\n\t}\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/minus.js","import style from './fisica.css';\nimport { Component } from 'preact';\nimport Latex from '../components/latex';\nimport Panel from '../components/panel';\nimport Split from '../components/split';\nimport Plus from '../components/plus';\nimport Minus from '../components/minus';\nimport Todo from '../components/todo';\n\nconst r = String.raw;\n\nexport default class Fisica extends Component {\n\trender() {\n        return (\n            
    \n                
    Fisica
    \n                \n                    \n                        
    \n                            Usa le regole base della trigonometria:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\vec{v}_x + \\vec{v}_y`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha`}\n                        
    \n                        \n                    \n                        
    \n                            Scomponi in componenti, poi sommali:\n                        
    \n                        
    \n                            {r`\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore risultante dall'applicazione della regola del parallelogramma.\n                        
    \n                        \n                    \n                        
    \n                            Alla fine è sempre una somma:\n                        
    \n                        
    \n                            {r`\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)`}\n                        
    \n                        
    \n                            Produce il vettore che parte da w e arriva a v.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama scalare perchè il risultato è uno scalare, non un vettore.\n                        
    \n                        
    \n                            {r`\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha`}\n                        
    \n                        
    \n                            Produce il modulo della proiezione di {r`\\vec{a}`} su {r`\\vec{b}`}.\n                        
    \n                        \n                    \n                        
    \n                            Si chiama vettoriale perchè il risultato è un altro vettore.\n                        
    \n                        
      \n                            
    • {r`\\vec{c} = \\vec{a} \\times \\vec{b}`}
      • \n                            
    • {r`\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)`}
      • \n                            
    • Regola della mano destra
      • \n                        
    \n                        
    \n                            Non è commutativo!\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0`}\n                        
    \n                        \n                    \n                        
    \n                            La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la massa.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = m \\vec{a}`}\n                        
    \n                        \n                    \n                        
    \n                            Due corpi esercitano forze uguali e opposte uno sull'altro. \n                        
    \n                        
    \n                            {r`\\vec{F}_{21} = -\\vec{F}_{12}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Due corpi puntiformi si attirano uno verso l'altro con forza:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}`}\n                        
    \n                        
    \n                            G è la costante di gravitazione universale e vale:\n                        
    \n                        
    \n                            {r`G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza peso uguale a:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            g è la costante di gravità della Terra, e vale:\n                        
    \n                        
    \n                            {r`g = 9.81 \\frac{m}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Per pianeti diversi dalla Terra vale la stessa regola:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | = g m`}\n                        
    \n                        
    \n                            L'unica differenza è che cambia la costante di gravità:\n                        
    \n                        
    \n                            {r`g_{luna} = 1.62 \\frac{m}{s^2}`}\n                        
    \n                        
    \n                            {r`g_{marte} = 3.71 \\frac{m}{s^2}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si oppone alle forze applicate alla superficie di contatto.\n                        
    \n                        
    \n                            Un libro appoggiato su un tavolo ha la forza di gravità che lo attira verso il terreno e la forza normale che lo trattiene dal cadere. \n                        
    \n                        \n                    \n                        
    \n                            Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            Rallenta i corpi che si stanno muovendo finchè essi non si fermano:\n                        
    \n                        
    \n                            {r`\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |`}\n                        
    \n                        \n                    \n                        
    \n                            E' forza trasmessa tra due estremi di una fune.\n                        
    \n                        
    \n                            Può essere redirezionata per mezzo di carrucole.\n                        
    \n                        \n                    \n                        
    \n                            Una molla cerca sempre di tornare alla sua posizione indeformata con forza:\n                        
    \n                        
    \n                            {r`F = -k x`}\n                        
    \n                        
    \n                            (E' negativa perchè la forza è opposta a quella applicata per deformarla.)\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            È un vettore che indica la posizione di un corpo rispetto a un'origine.\n                        
    \n                        
    \n                            {r`\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di posizione nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice velocità istantanea:\n                        
    \n                        
    \n                            {r`\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}`}\n                        
    \n                        \n                    \n                        
    \n                            È un vettore che misura la variazione di velocità nel tempo.\n                        
    \n                        
    \n                            {r`\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}`}\n                        
    \n                        
    \n                            Se si considera un intervallo di tempo infinitesimale si dice accelerazione istantanea:\n                        
    \n                        
    \n                            {r`\\vec{a} = \\lim_{\\Delta v \\to 0} \\frac{\\Delta \\vec{v}}{\\Delta t} = \\frac{d \\vec{v}}{d t} = \\frac{d^2 \\vec{s}}{d t^2}`}\n                        
    \n                        \n                    Quantità di moto (momento lineare)}>\n                        
    \n                            La quantità di moto è una proprietà vettoriale dei corpi:\n                        
    \n                        
    \n                            {r`\\vec{p} = m \\vec{v}`}\n                        
    \n                        
    \n                            Se la forza risultante è nulla, la quantità di moto non cambia.\n                        
    \n                        
    \n                            {r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = v \\cdot \\Delta t + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`v(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            La velocità non varia:\n                        
    \n                        
    \n                            {r`a(t) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = 0\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La legge oraria è:\n                        
    \n                        
    \n                            {r`s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È una retta:\n                        
    \n                        
    \n                            {r`v(t) = a \\Delta t + v(0)`}\n                        
    \n                        \n                    \n                        
    \n                            È costante:\n                        
    \n                        
    \n                            {r`a(t) = k`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' la distanza dal centro massima che raggiunge il corpo.\n                        
    \n                        
    \n                            (L'ampiezza di una sinusoide.)\n                        
    \n                        \n                    \n                        
    \n                            Indica quanto in fretta cambia la posizione del corpo. \n                        
    \n                        
    \n                            Dipende dal periodo:\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' una sinusoide:\n                        
    \n                        
    \n                            {r`s(t) = A \\sin (\\omega \\cdot t + \\phi)`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide dello spostamento, sfasata di {r`\\frac{\\pi}{2}`}:\n                        
    \n                        
    \n                            {r`v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})`}\n                        
    \n                        \n                    \n                        
    \n                            E' la sinusoide della velocità, sfasata di {r`\\pi`}:\n                        
    \n                        
    \n                            {r`a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)`}\n                        
    \n                        \n                    \n                        
    \n                            Si applica la prima legge di Newton:\n                        
    \n                        
    \n                            f(t) = m a\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.\n                        
    \n                        \n                    \n                        
    \n                            Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di {r`\\frac{\\pi}{2}`}, sull'asse Y.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Velocità angolare\n                        
    \n                        
    \n                            Quanto cambia la fase nel tempo.\n                        
    \n                        
    \n                            {r`\\omega = \\frac{2 \\pi}{T}`}\n                        
    \n                        \n                    \n                        
    \n                            E' l'angolo percorso dal corpo rispetto alla posizione iniziale.\n                        
    \n                        
    \n                            Si indica con {r`\\phi`}, e generalmente si usa in radianti.\n                        
    \n                        \n                    \n                        
    \n                            Si applicano le formule per la circonferenza:\n                        
    \n                        
    \n                            {r`v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r`}\n                        
    \n                        \n                    \n                        
    \n                            Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto: \n                        
    \n                        
    \n                            {r`a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega`}\n                        
    \n                        \n                    \n                        
    \n                            È verso il centro e si calcola con:\n                        
    \n                        
    \n                            {r`F = m \\cdot a`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' compiuto da una forza che sposta un corpo.\n                        
    \n                        
    \n                            {r`W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )`}\n                        
    \n                        
    \n                            (Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia cinetica in ogni momento uguale a:\n                        
    \n                        
    \n                            {r`E_c = \\frac{1}{2} m v^2`}\n                        
    \n                        
    \n                            Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:\n                        
    \n                        
    \n                            {r`\\Delta E_c = W`}\n                        
    \n                        \n                    \n                        
    \n                            Un corpo ha energia potenziale in ogni momento pari a: \n                        
    \n                        
    \n                            {r`E_{p_g} = m \\cdot g \\cdot h`}\n                        
    \n                        
    \n                            (Con h uguale a un altezza scelta come punto di riferimento.)\n                        
    \n                        \n                    \n                        
    \n                            Una molla ha sempre energia potenziale elastica pari a:\n                        
    \n                        
    \n                            {r`E_{p_e} = \\frac{1}{2} k x^2`}\n                        
    \n                        \n                    \n                        
    \n                            Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo.\n                        
    \n                        
    \n                            Ad esempio, è conservativa la forza di gravità, ma non è conservativa la forza di attrito.\n                        
    \n                        
    \n                            Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:\n                        
    \n                        
    \n                            {r`E = E_k + E_p`}\n                        
    \n                        \n                    \n                        
    \n                            È la velocità di trasferimento di energia:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta E}{\\Delta t}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            È una proprietà dei corpi che può essere positiva o negativa.\n                        
    \n                        
    \n                            Si conserva: in un sistema chiuso la carica totale è costante.\n                        
    \n                        
    \n                            Esiste un'unità elementare: {r`C_{elettrone} = 1.602 \\cdot 10^{-19}`}.\n                        
    \n                        
    \n                            Cariche opposte si attraggono; cariche uguali si respingono.\n                        
    \n                        \n                    \n                        
    \n                            Più ioni ha un corpo, meglio la carica si muove attraverso di esso.\n                        
    \n                        
    \n                            I corpi in cui la carica si muove bene sono conduttori, mentre quelli in cui si muove difficilmente sono isolanti.\n                        
    \n                        
    \n                            Il corpo umano è un buon conduttore.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno equilibrate e il corpo diventerà elettricamente neutro (con stesso numero di cariche positive e negative all'interno).\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Strofinando tra loro due corpi isolanti, essi si polarizzeranno per strofinio.\n                        
    \n                        \n                    \n                        
    \n                            Toccando un conduttore con un corpo carico, il conduttore potrà polarizzarsi per contatto.\n                        
    \n                        \n                    \n                        
    \n                            Se un corpo conduttore ha cariche \"esterne\" di un certo segno vicino, esso avrà tutte le cariche del segno opposto in equilibrio vicino alle cariche esterne, e tutte le cariche dello stesso segno più lontano possibile da esse.\n                        
    \n                        
    \n                            Mettendo a terra il conduttore, nuove cariche del segno opposto saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate.\n                        
    \n                        
    \n                            Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà caricato del segno opposto rispetto alle cariche esterne.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Due corpi carichi si attraggono tra loro con forza: \n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{-k \\cdot q_1 \\cdot q_2}{s^2}`}\n                        
    \n                        
    \n                            {r`k`} è la costante di Coulomb, e vale {r`k = 8.99 \\cdot 10^9 \\frac{N \\cdot m^2}{C^2}`}.\n                        
    \n                        \n                    \n                        
    \n                            La costante {r`k`} è in realtà dipendente da un altra costante, {r`\\epsilon_0`}, la permeabilità del vuoto.\n                        
    \n                        
    \n                            {r`k = \\frac{1}{4 \\pi \\cdot \\epsilon_0}`}\n                        
    \n                        
    \n                            {r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{q_1 \\cdot q_2}{4 \\pi \\cdot \\epsilon_0 \\cdot s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            Misura che forza viene applicata in ogni punto su una carica unitaria:\n                        
    \n                        
    \n                            {r`\\vec{E} = \\frac{\\vec{F}_{elettrica}}{q} = \\frac{-k \\cdot q}{s^2}`}\n                        
    \n                        \n                    \n                        
    \n                            È la differenza tra \"quanto\" campo elettrico entra e quanto campo elettrico esce da una certa area.\n                        
    \n                        
    \n                            In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area.\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A}`}\n                        
    \n                        
    \n                            Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:\n                        
    \n                        
    \n                            {r`\\Phi_E = \\vec{E} \\cdot \\vec{A} = E_\\perp \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        
    \n                            Circa. E' una specie di integrale...\n                        
    \n                        \n                    \n                        
    \n                            Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie.\n                        
    \n                        
    \n                            {r`\\Phi_E = 4 \\pi \\cdot k \\cdot q = \\frac{q}{\\epsilon_0}`}\n                        
    \n                        
    \n                            Ovvero, i campi elettrostatici sono generati dalle cariche elettriche.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un corpo carico vicino ad altre cariche possiede un'energia potenziale elettrica {r`U_e`}.\n                        
        \n                        \n                    \n                \n                    Potenziale elettrico (tensione)}>\n                        
    \n                            È il valore dell'energia potenziale elettrica per una carica unitaria.\n                        
    \n                        
    \n                            {r`V = \\frac{U_e}{q}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Volt ({r`V`}).\n                        
                            \n                        
    \n                            In una batteria è detto forza elettromotrice, e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.\n                        
    \n                        \n                    Corrente elettrica (intensità)}>\n                        
    \n                            Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo.\n                        
    \n                        
    \n                            {r`I = \\frac{\\Delta q}{\\Delta t}`}\n                        
    \n                        
    \n                            Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla.\n                        
    \n                        
    \n                            La sua unità di misura è l'Ampere ({r`A`}).\n                        
    \n                        \n                    Corrente continua (DC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente è costante.\n                        
    \n                        \n                    Corrente alternata (AC)}>\n                        
    \n                            Quando in un circuito la direzione della corrente si alterna periodicamente.\n                        
    \n                        \n                    \n                        
    \n                            Possiamo calcolare la potenza di un circuito:\n                        
    \n                        
    \n                            {r`P = \\frac{\\Delta U_e}{\\Delta t} = I \\cdot \\Delta V = I^2 \\cdot R = \\frac{(\\Delta V)^2}{R}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Riduce l'intensità di corrente, e converte parte del potenziale in calore.\n                        
    \n                        
    \n                            Il potenziale utilizzato è pari a:\n                        
    \n                        
    \n                            {r`V = R \\cdot I`}\n                        
    \n                        
    \n                            Dove {r`R`} è una costante detta resistenza con unità di misura Ohm ({r`\\Omega`}).\n                        
    \n                        
    \n                            La resistenza di un conduttore vale:\n                        
    \n                        
    \n                            {r`R = \\rho \\frac{L_{unghezza}}{A_{rea}}`}\n                        
    \n                        
    \n                            {r`\\rho`} è la resistività del materiale, e varia in base alla temperatura:\n                        
    \n                        
    \n                            {r`\\rho = \\rho_0 (1 + \\alpha(T - T_0))`}\n                        
    \n                        \n                    \n                        
    \n                            Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito.\n                        
    \n                        
    \n                            Per farlo, cattura cariche positive e negative sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro.\n                        
    \n                        
    \n                            Ha una capacità caratteristica, che in un condensatore a facce piane parallele è:\n                        
    \n                        
    \n                            {r`C = \\frac{q_{massima}}{\\Delta V}`}\n                        
    \n                        
    \n                            Condensatori di capacità maggiore immagazzinano più potenziale con meno carica.\n                        
    \n                        
    \n                            La capacità aumenta se viene messo qualcosa tra le armature:\n                        
    \n                        
    \n                            {r`C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}`}\n                        
    \n                        
    \n                            Dove {r`\\kappa`} è la costante dielettrica relativa del materiale inserito, {r`A`} l'area di una armatura e {r`s`} la distanza tra le due armature.\n                        
    \n                        
    \n                            Se il campo elettrico creatosi tra le due armature supera la rigidità dielettrica del condensatore, la carica immagazzinata viene persa e ha luogo un breakdown.\n                        
    \n                        
    \n                            La sua unità di misura è il Farad ({r`Fa`})\n                        
    \n                        \n                    \n                        
    \n                            Misura la corrente elettrica se messo in serie.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)\n                        
    \n                        \n                    \n                        
    \n                            Misura la differenza di potenziale se messo in parallelo.\n                        
    \n                        
    \n                            (Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per nodo si intende un qualsiasi punto del circuito.\n                        
    \n                        
    \n                            Da un nodo entra ed esce la stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito.\n                        
    \n                        
    \n                            In una maglia chiusa, la somma delle differenze di potenziale è 0.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Più parti di circuito sono in serie se sono consecutive e senza biforcazioni.\n                        
    \n                        
    \n                            Parti di circuito in serie sono attraversate dalla stessa corrente.\n                        
    \n                        \n                    \n                        
    \n                            Più parti di circuito sono in parallelo tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo. \n                        
    \n                        
    \n                            Parti di circuito in parallelo hanno la stessa differenza di potenziale.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:\n                        
    \n                        
    \n                            {r`R_{serie} = \\sum_{i=1}^{n} R_i`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:\n                        
    \n                        
    \n                            {r`R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:\n                        
    \n                        
    \n                            {r`C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}`}\n                        
    \n                        \n                    \n                        
    \n                            Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:\n                        
    \n                        
    \n                            {r`C_{parallelo} = \\sum_{i=1}^{n} C_n`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente.\n                        
    \n                        
    \n                            {r`\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}`} ({r`\\frac{N}{A^2}`})\n                        
    \n                        \n                    \n                        
    \n                            Come un campo elettrico, ma per i magneti.\n                        
    \n                        
    \n                            Il suo simbolo è {r`B`}, e la sua unità di misura è il Tesla (T).\n                        
    \n                        \n                    \n                        
    \n                            È \"quanto\" campo magnetico attraversa un percorso chiuso.\n                        
    \n                        
    \n                            Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i \"sottoflussi\" magnetici calcolati sui suoi lati.\n                        
    \n                        
    \n                            {r`\\Phi_{B_{i}} = \\vec{B} \\cdot \\vec{L}_n = B \\cdot L_i \\cdot \\sin(\\alpha) = B_\\parallel \\cdot L_i`}\n                        
    \n                        
    \n                            {r`\\Phi_{B} = \\sum_{i=0}^{n_{lati}} \\Phi_{Bn}`}\n                        
    \n                        
    \n                            La sua unità di misura è il Weber ({r`Wb = T \\cdot m^2`}).\n                        
    \n                        \n                    \n                        
    \n                            Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo.\n                        
    \n                        
    \n                            Ovvero, non esistono monopoli magnetici.\n                        
    \n                        \n                    \n                        
    \n                            L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Phi_B = \\mu_0 \\cdot I`}\n                        
    \n                        \n                    \n                \n                    Forza magnetica su carica puntiforme (Forza di Lorentz)}>\n                        
    \n                            I campi magnetici applicano una forza sulle cariche vicine:\n                        
    \n                        
    \n                            {r`\\vec{F}_{B} = q \\cdot (\\vec{v} \\times \\vec{B})`}\n                        
    \n                        
    \n                            Dove {r`\\vec{B}`} è l'intensità del campo magnetico e {r`\\vec{v}`} la velocità della carica considerata.\n                        
    \n                        
    \n                            Si ha una forza massima se la velocità è perpendicolare al campo magnetico.\n                        
    \n                        
    \n                            In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.\n                        
    \n                        \n                    \n                        
    \n                            I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:\n                        
    \n                        
    \n                            {r`\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})`} [1]\n                        
    \n                        
    \n                            Dove {r`I`} è la corrente elettrica, {r`\\vec{L}`} è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.\n                        
    \n                        \n                    \n                        
    \n                            Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.\n                        
    \n                        
    \n                            All'interno del solenoide si crea un campo (quasi) uniforme:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}`}\n                        
    \n                        \n                    \n                        
    \n                            Caso particolare della Legge di Ampère.\n                        
    \n                        
    \n                            Il modulo del campo magnetico B prodotto da un filo in cui passa una corrente continua I alla distanza s è:\n                        
    \n                        
    \n                            {r`\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}`}\n                        
    \n                        
    \n                            Il campo magnetico così creato gira attorno al filo in senso antiorario.\n                        
    \n                        
    \n                            Due fili attraversati dalla stessa corrente si attraggono, due fili attraversati da correnti opposte si respingono.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un conduttore perpendicolare ad un campo magnetico può ottenere una differenza di potenziale se messo in movimento in un direzione perpendicolare alla direzione del conduttore e del campo. \n                        
    \n                        
    \n                            La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore. \n                        
    \n                        
    \n                            Essa vale:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = v \\cdot B \\cdot L`}\n                        
    \n                        
    \n                            Dove v è la velocità del conduttore, B è l'intensità del campo magnetico ed L è la lunghezza del conduttore.\n                        
    \n                        \n                    \n                        
    \n                            In un campo magnetico {r`B`} uniforme e perpendicolare al piano di una spira di area {r`A`}, il flusso magnetico si può determinare con la Legge di Faraday-Neumann-Lenz:\n                        
    \n                        
    \n                            {r`\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{\\Delta \\Phi_B}{\\Delta t}`}\n                        
    \n                        
    \n                            Il meno è dovuto alla Legge di Lenz, che specifica qualitativamente il verso della forza elettromotrice indotta.\n                        
    \n                        \n                    \n                        
    \n                            In un solenoide, la forza elettromotrice indotta è uguale a:\n                        
    \n                        
    \n                            {r`\\Delta V_{indotta} = - \\frac{N \\cdot \\Delta \\Phi_{B_{spira}}}{\\Delta t} = - \\frac{N \\cdot B \\cdot A \\cdot cos(\\alpha)}{\\Delta t}`}\n                        
    \n                        
    \n                            Dove {r`N`} è il numero delle spire del solenoide.\n                        
    \n                        \n                    \n                        
    \n                            Correnti o campi elettrici variabili creano un campo magnetico.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nel vuoto, il campo elettrico {r`E`} e il campo magnetico {r`B`} sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo.\n                        
    \n                        
    \n                            Si dice quindi che sono onde elettromagnetiche.\n                        
    \n                        
    \n                            Esse sono legate dalla relazione:\n                        
    \n                        
    \n                            {r`E = c \\cdot B`}\n                        
    \n                        
    \n                            Dove {r`c`} è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:\n                        
    \n                        
    \n                            {r`c = \\frac{1}{\\sqrt{\\epsilon_0 \\cdot \\mu_0}} = 3.00 \\cdot 10^8 \\frac{m}{s}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`A(t) = A_{max} \\cdot \\sin \\left ( \\frac{2 \\pi}{\\lambda} - \\omega t + \\phi \\right )`}\n                        
    \n                        
    \n                            Dove {r`A_{max}`} è l'ampiezza massima che può avere l'onda, {r`\\frac{2 \\pi}{\\lambda} = \\left | \\vec{k} \\right |`} è il vettore d'onda, {r`\\omega`} la frequenza angolare e {r`\\phi`} la fase.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            I solidi, se portati ad alta temperatura, emettono luce con uno spettro continuo.\n                        
    \n                        
    \n                            I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda. \n                        
    \n                        
    \n                            In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:\n                        
    \n                        
    \n                            {r`\\frac{1}{\\lambda} = R \\left ( \\frac{1}{4} - \\frac{1}{n^2} \\right )`}\n                        
    \n                        
    \n                            Con {r`R = 1.097 \\cdot 10^7 \\frac{1}{m}`}, detta costante di Rydberg, e {r`n`} un numero intero.\n                        
    \n                        \n                    \n                        
    \n                            Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori. \n                        
    \n                        
    \n                            Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata.\n                        
    \n                        
    \n                            Energia, momento angolare e raggio sono quantizzati.\n                        
    \n                        
    \n                            Nota costante quantica è {r`h`}, la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come {r`\\hbar = \\left ( \\frac{h}{2 \\pi} \\right )`}.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            L'energia degli elettroni è quantizzata.\n                        
    \n                        
    \n                            Inoltre, per essi è valido che:\n                        
    \n                        
    \n                            {r`m \\cdot v_n \\cdot 2 \\pi \\cdot r = n \\cdot h`}\n                        
    \n                        
    \n                            Ancora, il raggio delle orbite è uguale a:\n                        
    \n                        
    \n                            {r`r_n = n^2 \\cdot a_0 = n^2 \\cdot \\frac{\\hbar}{m_{elettrone} \\cdot k \\cdot e^2} `}\n                        
    \n                        
    \n                            Con {r`a_0 = \\left ( \\frac{h}{2 \\pi} \\right )^2 \\cdot \\frac{1}{m_{elettrone} \\cdot k \\cdot e^2} = 5.29 \\cdot 10^{-11} m`}.\n                        
    \n                        
    \n                            Infine, in ogni stato, l'energia è pari a:\n                        
    \n                        
    \n                            {r`E_n = \\frac{1}{n^2} \\cdot E_1 = - \\frac{1}{n^2} \\cdot \\frac{a_0^2}{2 \\cdot m \\cdot \\hbar^4} = - \\frac{1}{n^2} \\cdot \\frac{m_{elettrone} \\cdot k^2 \\cdot e^4}{2 \\cdot \\hbar^2}`}\n                        
    \n                        
    \n                            Due elettroni non possono occupare lo stesso stato.\n                        
    \n                        
    \n                            Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda.\n                        
    \n                        
    \n                            Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Refactor this\n                        
    \n                        
    \n                            Se la banda di emissione con energia più alta di un corpo è assente o è separata da un gap dell'ordine di grandezza maggiore di {r`10^1 eV`}, allora il corpo è un isolante.\n                        
    \n                        
    \n                            Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore.\n                        
    \n                        
    \n                            Se il gap è invece dell'ordine di grandezza di {r`1 eV`}, allora il corpo è un semiconduttore.\n                        
    \n                        \n                    \n                        
    \n                            Legami in cui mancano elettroni.\n                        
    \n                        
    \n                            Elettroni di altri legami possono spostarsi per colmare le lacune, creandone altre, e spostandole in direzione opposta a quella della corrente.\n                        
    \n                        \n                    \n                        
    \n                            Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:\n                        
    \n                        
      \n                            
    • Con numero atomico maggiore, un semiconduttore di tipo N con elettroni in eccesso liberi di scorrere.
      • \n                            
    • Con numero atomico minore, un semiconduttore di tipo P con lacune in eccesso libere di catturare elettroni da altri legami.
      • \n                        
    \n                        
    \n                            Maggiore impurezza porta a maggiore conduttività.\n                        
    \n                        \n                    \n                        
    \n                            Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di elettroni e lacune.\n                        
    \n                        \n                    \n                Ottica (non l'abbiamo fatta)}>\n                    \n                        
    \n                            I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.\n                        
    \n                        \n                    \n                        
    \n                            Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna.\n                        
    \n                        
    \n                            Le onde assorbite vengono poi riemesse sotto forma di un onda di {r`\\lambda`} variabile in base alla temperatura.\n                        
    \n                        
    \n                            {r`\\lambda_{max} \\cdot T`} è costante.\n                        
    \n                        \n                    \n                        
    \n                            L'energia assorbita e emessa dai corpi neri è quantizzata.\n                        
    \n                        \n                    \n                        
    \n                            Un onda magnetica con un quanto di energia è detta fotone:\n                        
    \n                        
    \n                            {r`E_{fotone} = h \\cdot f`}\n                        
    \n                        \n                    \n                        
    \n                            A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale.\n                        
    \n                        
    \n                            Perchè avvenga, la frequenza deve essere maggiore di una certa soglia.\n                        
    \n                        
    \n                            Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza.\n                        
    \n                        
    \n                            Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.\n                        
    \n                        \n                    \n            
    \n        )\n\t}\n}\n\n\n// WEBPACK FOOTER //\n// ./pages/fisica.js","import style from \"./markdown.css\";\nimport { Component } from 'preact';\nimport showdown from \"showdown\";\n\nexport default class Markdown extends Component {\n\trender() {\n        let converter = new showdown.Converter();\n        converter.setFlavor(\"github\");\n        let html = converter.makeHtml(`${this.props.children}`);\n        // noinspection CheckTagEmptyBody\n        return 
    ;\n\t}\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/markdown.js","import style from './vldigeometria.css';\r\nimport { Component } from 'preact';\r\nimport Markdown from '../components/markdown';\r\nimport Panel from '../components/panel';\r\n\r\nconst r = String.raw;\r\n\r\nexport default class VlDiGeometria extends Component {\r\n\trender() {\r\n\t\t//Imported from unimore-info-wiki\r\n\t\treturn (\r\n\t\t\t
    \r\n                
    Videolezioni di Geometria
    \r\n                \r\n                    {r`\r\nTutte le videolezioni sono state pubblicate sotto licenza [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) dalla Prof.ssa Beatrice Ruini nell'anno accademico 2018/2019 sul [portale Dolly 2018](https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0) (Moodle).\r\n\r\nPer comodità, ho estratto l'url sorgente del video dall'embed presente nella rispettiva pagina.\r\n\r\n1. [Definizione di Spazio Vettoriale](https://www.youtube.com/watch?v=7eHEzf4403c) (1:17:29)\r\n2. [Sottospazi vettoriali I](https://www.youtube.com/watch?v=FPqrULk5HBU) (37:15)\r\n3. [Sottospazi vettoriali II](https://www.youtube.com/watch?v=ubDWUw9hk0k) (43:26)\r\n4. [Sottospazi vettoriali III](https://www.youtube.com/watch?v=381n4NPb6Oc) (40:29)\r\n5. [Lineare dipendenza e indipendenza](https://www.youtube.com/watch?v=9YVQ5olYrh0) (56:12)\r\n6. [Basi di uno spazio vettoriale I](https://www.youtube.com/watch?v=mEF_lcTzEoE) (25:52)\r\n7. [Basi di uno spazio vettoriale II](https://www.youtube.com/watch?v=k1r9JfXY53k) (48:24)\r\n8. [Teorema di Grassmann](https://www.youtube.com/watch?v=3sqB-MMyCWM) (32:36)\r\n9. [Basi e Matrici](https://www.youtube.com/watch?v=Rd6AB_jE7YI) (27:06)\r\n10. [Definizione di Applicazioni Lineari](https://www.youtube.com/watch?v=rmd7ffZeVYk) (16:23)\r\n11. [Proprietà delle Applicazioni Lineari](https://www.youtube.com/watch?v=MH7ztQGkqmw) (31:58)\r\n12. [Definizione di determinante](https://www.youtube.com/watch?v=EwubcLwBdzk) (36:43)\r\n13. [Proprietà e metodo di triangolazione](https://www.youtube.com/watch?v=SFusGarV6HI) (22:36)\r\n14. [Teorema di Laplace](https://www.youtube.com/watch?v=BqZDWnKl2nQ) (29:03)\r\n15. [4 applicazioni del Teorema di Laplace](https://www.youtube.com/watch?v=2tr3y725GY0) (47:53)\r\n16. [Spazi vettoriali euclidei reali - Parte 1](https://www.youtube.com/watch?v=W7Z1hm-jwMM) (28:46)\r\n17. [Spazi vettoriali euclidei reali - Parte 2](https://www.youtube.com/watch?v=zjmKE9TMGm8) (27:17)\r\n18. [Autovalori e autovettori](https://www.youtube.com/watch?v=XlrlcnvcTtQ) (33:00)\r\n19. [Polinomio caratteristico](https://www.youtube.com/watch?v=61icRbgWTdI) (31:31)\r\n20. [Teorema diagonalizzabilità](https://www.youtube.com/watch?v=wm5V6en9OFo) (18:49)\r\n21. [Spazi affini](https://player.vimeo.com/video/291457587) (20:46)\r\n22. [Sottospazi affini](https://player.vimeo.com/video/291458991) (21:32)\r\n23. [Parallelismo e Riferimenti Affini](https://player.vimeo.com/video/291510181) (16:57)\r\n24. [Rappresentazione di Sottospazi Affini](https://player.vimeo.com/video/291510296) (31:17)\r\n25. [Spazi Euclidei](https://player.vimeo.com/video/291510612) (35:57)\r\n26. [Teoria dei ranghi](https://player.vimeo.com/video/291510964) (9:44)\r\n27. [Teoria dei ranghi 2](https://player.vimeo.com/video/291510862) (14:44)\r\n\r\nNell'anno accademico 2018/2019 non sono stati trattati gli argomenti nei video 21, 22 e 23.\r\n                    `}\r\n                \r\n\t\t\t
    \r\n\t\t);\r\n\t}\r\n}\r\n\r\n\n\n\n// WEBPACK FOOTER //\n// ./pages/vldigeometria.js","import style from './mingwinstall.css';\r\nimport { Component } from 'preact';\r\nimport Panel from '../components/panel';\r\n\r\nexport default class MingwInstall extends Component {\r\n\trender() {\r\n\t\t//Imported from unimore-info-wiki\r\n\t\treturn (\r\n\t\t\t
    \r\n                
    Come installare MinGW
    \r\n                \r\n\t\t\t\t\t
     Scaricate l'installer ufficiale,\r\n\t\t\t\t\t\ted eseguitelo.
    \"\"/\r\n\t\t\t\t\t
     Dovrebbe comparire questa schermata. Cliccate su Install, poi scegliete una cartella di installazione\r\n\t\t\t\t\t\t(ricordatevela!) e poi Continue. Lasciate stare le altre opzioni, dovrebbero essere tutte spuntate,\r\n\t\t\t\t\t\ttranne For all users, che dovrebbe essere disattivato.
    \"\"/\r\n\t\t\t\t\t
     Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto\r\n\t\t\t\t\t\tContinue. Premetelo.
    \"\"/\r\n\t\t\t\t\t
     Dovrebbe apparirvi questa finestra. L'installer di MinGW è una specie di gestore pacchetti (tipo apt su\r\n\t\t\t\t\t\tUbuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalità.
    \"\"/\r\n\t\t\t\t\t
     Nel nostro caso, dovrebbero servirci mingw32-base-bin (per il C e alcune librerie C++) e\r\n\t\t\t\t\t\tmingw32-gcc-g++-bin (per il C++). Cliccate, quindi, sui due quadratini corrispondenti, e premete\r\n\t\t\t\t\t\tMark for Installation. Dovrebbe comparire una freccia gialla sul quadratino.
    \"\"/\r\n\t\t\t\t\t
     Ora, è il momento di installare i pacchetti. Aprite il menù Installation, poi premete\r\n\t\t\t\t\t\tApply Changes, e di nuovo Apply.
    \"\"/\r\n\t\t\t\t\t
     Lasciate che scarichi, ci vorrà un po'. Guardatevi un video nel frattempo, fatevi una partitina a qualcosa, tornate\r\n\t\t\t\t\t\tdopo circa 10 minuti.
    \"\"/\r\n\t\t\t\t\t
     Una volta installato, dobbiamo aggiungere g++ ai programmi eseguibili da Prompt dei Comandi: premete il\r\n\t\t\t\t\t\ttasto Windows, e scrivete PATH. Windows dovrebbe trovarvi automaticamente quell'opzione.
    \r\n\t\t\t\t\t\"\"/\r\n\t\t\t\t\t
     Dentro la finestra di Proprietà del Sistema, premete Variabili d'ambiente.
    \"\"/\r\n\t\t\t\t\t
     Trovate la variabile d'ambiente globale Path, e fateci doppio click per modificarla.
    \"\"/\r\n\t\t\t\t\t
     Ora dovreste vedere l'elenco di tutte le cartelle contenenti programmi eseguibili da terminale: dobbiamo aggiungere\r\n\t\t\t\t\t\tquella di MinGW! Premete Sfoglia.
    \"\"/\r\n\t\t\t\t\t
     Trovate la cartella in cui avete installato MinGW (vi avevo detto di ricordarvela!); entrateci, poi selezionate la\r\n\t\t\t\t\t\tsottocartella bin e premete OK su tutte le finestre che avete aperto fino ad ora,\r\n\t\t\t\t\t\tchiudendole.
    \r\n\t\t\t\t\t
     Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione\r\n\t\t\t\t\t\tgcc e g++ sul Prompt dei Comandi, e potete finalmente creare dei file .exe! 
    \r\n\t\t\t\t    \r\n\t\t\t
    \r\n\t\t);\r\n\t}\r\n}\r\n\r\n\n\n\n// WEBPACK FOOTER //\n// ./pages/mingwinstall.js","import style from './copyright.css';\r\nimport { Component } from 'preact';\r\n\r\nexport default class Copyright extends Component {\r\n\trender() {\r\n\t\treturn 
    © 2019 - Stefano Pigozzi - CC BY-SA 4.0 - Codice sorgente
    ;\r\n\t}\r\n}\n\n\n// WEBPACK FOOTER //\n// ./components/copyright.js","import style from \"./theorem.css\";\r\nimport Panel from \"./panel.js\";\r\n\r\nexport default class Theorem extends Panel {\r\n    getStyle() {\r\n        return super.getStyle() + \" \" + style.theorem;\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/theorem.js","import style from \"./hypothesis.css\";\r\nimport {Component} from \"preact\";\r\n\r\nexport default class Hypothesis extends Component {\r\n    render() {\r\n        return (\r\n            
    \r\n                
    \r\n                    Ipotesi\r\n                
    \r\n                {this.props.children}\r\n            
    \r\n        )\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/hypothesis.js","import style from \"./thesis.css\";\r\nimport {Component} from \"preact\";\r\n\r\nexport default class Thesis extends Component {\r\n    render() {\r\n        return (\r\n            
    \r\n                
    \r\n                    Tesi\r\n                
    \r\n                {this.props.children}\r\n            
    \r\n        )\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/thesis.js","import style from \"./proof.css\";\r\nimport {Component} from \"preact\";\r\n\r\nexport default class Proof extends Component {\r\n    render() {\r\n        return (\r\n            
    \r\n                
    \r\n                    Dimostrazione\r\n                
    \r\n                {this.props.children}\r\n            
    \r\n        )\r\n    }\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/proof.js","import style from \"./example.css\";\nimport {Component} from \"preact\";\n\nexport default class Example extends Component {\n    render() {\n        return (\n            
    \n                {this.props.children}\n            
    \n        )\n    }\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/example.js","import style from './statistica.css';\nimport { Component } from 'preact';\nimport Latex from '../components/latex';\nimport Panel from '../components/panel';\nimport Split from '../components/split';\nimport Todo from '../components/todo';\nimport Theorem from \"../components/theorem\";\nimport Hypothesis from \"../components/hypothesis\";\nimport Thesis from \"../components/thesis\";\nimport Proof from \"../components/proof\";\nimport Example from \"../components/example\";\nimport Plus from \"../components/plus\";\nimport Minus from \"../components/minus\";\n\nconst r = String.raw;\n\nexport default class Statistica extends Component {\n\trender() {\n\t    /*\n            \n                \n                    
    \n                        Gruppo intero di oggetti di cui si cercano informazioni.\n                    
    \n                    \n                \n                    
    \n                        Popolazione finita di oggetti concreti che possono essere campionati ciascuno solo una volta.\n                    
    \n                    \n                \n                    
    \n                        Popolazione di valori ottenuti da prove sperimentali indipendenti ripetute più volte.\n                    
    \n                    \n                \n            \n                \n                    
    \n                        Sottoinsieme della popolazione che contiene gli oggetti che si sono osservati.\n                    
    \n                    \n                Simple random sample}>\n                    
    \n                        Campione di una data dimensione in cui qualsiasi selezione di n elementi ha la stessa probabilità di costituire il campione.\n                    
    \n                    \n                Sample of convenience}>\n                    
    \n                        Campione ottenuto in un modo casuale non ben definito.\n                    
    \n                    \n                Sample with replacement}>\n                    
    \n                        Campione ottenuto sostituendo nella popolazione gli elementi estratti con dei nuovi elementi.\n                    
    \n                    
    \n                        Dire che un campione è ottenuto with replacement è equivalente a dire che la popolazione che si sta campionando è infinita, e quindi che tutti gli elementi sono indipendenti.\n                    
    \n                    \n                \n                    
    \n                        Campione ottenuto da una popolazione in cui certi elementi hanno più probabilità di essere stati selezionati di altri.\n                    
    \n                    \n                Stratified random sample}>\n                    
    \n                        Campione ottenuto da un sottoinsieme della popolazione detto strato.\n                    
    \n                    \n                Cluster sample}>\n                    
    \n                        Campione ottenuto selezionando più cluster di elementi alla volta.\n                    
    \n                    \n                \n            \n                Sampling variation}>\n                    
    \n                        Differenza di informazioni presente tra due campioni diversi della stessa popolazione.\n                    
    \n                    \n                \n                    
    \n                        Gli elementi in un campione sono indipendenti se gli elementi estratti in precedenza non influsicono significativamente sulle probabilità di estrazione dell'elemento successivo.\n                    
    \n                    \n                \n            \n                \n                    
    \n                        Esperimento in cui c'è una sola popolazione da cui vengono estratti campioni.\n                    
    \n                    
    \n                        Serve per verificare delle condizioni.\n                    
    \n                    \n                \n                    
    \n                        Esperimento in cui sono presenti più popolazioni (aventi caratteristiche differenti una dall'altra dette fattori) da cui vengono estratti campioni.\n                    
    \n                    
    \n                        Serve per capire quali fattori influenzano il risultato dell'esperimento.\n                    
    \n                    \n                \n            \n                Numerico o quantitativo}>\n                    Il dato descrive un valore numerico relativo all'elemento, come ad esempio una quantità fisica.\n                \n                Categorico o qualitativo}>\n                    Il dato indica una categoria a cui appartiene l'elemento, come ad esempio il suo colore.\n                \n            \n\t     */\n        return (\n            
    \n                
    Statistica ed Elementi di Probabilità
    \n                \n                    \n                        
    \n                            {r`P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}`}\n                        
    \n                        \n                    \n                        
    \n                            {r`P(E) = \\frac{successi}{prove\\ totali}`}\n                        
    \n                        \n                    \n                        
    \n                            Il prezzo che un individuo coerente riterrebbe equo per ricevere 1 nel caso l'evento si verificasse e 0 nel caso l'evento non si verificasse.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"omegone\"\n                        
    \n                        
    \n                            L'insieme di tutti gli esiti possibili di un esperimento.\n                        
    \n                        
    \n                            {r`\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"omeghino\"\n                        
    \n                        
    \n                            Un elemento dello spazio campionario.\n                        
    \n                        
    \n                            {r`\\omega = 1`}\n                        
    \n                        \n                    \n                        
    \n                            \"e\"\n                        
    \n                        
    \n                            Un sottoinsieme dello spazio campionario.\n                        
    \n                        
    \n                            {r`E = \\left \\{ 1, 2 \\right \\}`}\n                        
    \n                        
    \n                            Lo spazio campionario stesso è un evento certo.\n                        
    \n                        \n                    \n                        
    \n                            \"not e\"\n                        
    \n                        
    \n                            Il complementare di un sottoinsieme.\n                        
    \n                        
    \n                            {r`\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e intersecato effe\"\n                        
    \n                        
    \n                            L'intersezione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\left \\{ 1 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e unito a effe\"\n                        
    \n                        
    \n                            L'unione di più sottoinsiemi.\n                        
    \n                        
    \n                            {r`E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e meno effe\"\n                        
    \n                        
    \n                            {r`E \\setminus F = E \\cap \\bar{F}`}\n                        
    \n                        \n                    \n                        
    \n                            \"e contenuto in effe\"\n                        
    \n                        
    \n                            L'inclusione del primo insieme in un altro.\n                        
    \n                        
    \n                            {r`E \\subseteq F`}\n                        
    \n                        
    \n                            Se si verifica E, allora si verifica anche F.\n                        
    \n                        \n                    \n                        
    \n                            \"e è impossibile\"\n                        
    \n                        
    \n                            Un sottoinsieme vuoto.\n                        
    \n                        
    \n                            {r`E = \\emptyset`}\n                        
    \n                        \n                    \n                        
    \n                            \"e ed effe si escludono mutualmente\"\n                        
    \n                        
    \n                            La disgiunzione di due insiemi.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"famiglia effe\"\n                        
    \n                        
    \n                            I sottoinsiemi dello spazio campionario formano una famiglia di sottoinsiemi detta famiglia degli eventi.\n                        
    \n                        
    \n                            {r`\\mathcal{F}`}\n                        
    \n                        
    \n                            Qualsiasi sottoinsieme appartenente a {r`\\mathcal{F}`} è considerato un evento.\n                        
    \n                        \n                    {r`\\sigma`}-algebra}>\n                        
    \n                            \"sigma algebra\"\n                        
    \n                        
    \n                            Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta {r`\\sigma`}-algebra:\n                        
    \n                        
      \n                            
    1. \n                                Lo spazio campionario è un evento: {r`\\Omega \\in \\mathcal{F}`}\n                            
      2. \n                            
    2. \n                                Se un sottoinsieme è un evento, allora anche il suo complementare lo è: {r`E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}`}\n                            
      3. \n                            
    3. \n                                Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: {r`(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}`}\n                            
      4. \n                        
    \n                        
    \n                            Un esempio: {r`E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"la partizione e composta da e uno, e due, e tre...\"\n                        
    \n                        
    \n                            Un insieme di esiti e eventi:\n                        
    \n                        
      \n                            
    • Finito.
      • \n                            
    • In cui tutti gli eventi hanno probabilità diversa da 0.
      • \n                            
    • In cui tutti gli eventi sono mutualmente esclusivi.
      • \n                            
    • In cui l'unione di tutti i suoi elementi copre lo spazio campionario.
      • \n                        
    \n                        
    \n                            La partizione {r`E_i`} è composta dagli eventi {r`E_1`}, {r`E_2`}, {r`E_3`}, fino a {r`E_n`}.\n                        
    \n                        \n                            Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            La probabilità di un evento è un numero tra 0 e 1.\n                        
    \n                        
    \n                            {r`\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dello spazio campionario è sempre 1.\n                        
    \n                        
    \n                            {r`P(\\Omega) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità.\n                        
    \n                        
    \n                            {r`P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato.\n                        
    \n                        
    \n                            {r`P(\\bar{E}) = 1 - P({E})`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso.\n                        
    \n                        
    \n                            {r`F \\subseteq E \\implies P(F) \\leq P(E)`}\n                        
    \n                        \n                    \n                        
    \n                            La probabilità di un evento unito a un altro è uguale alla somma delle probabilità dei due eventi meno la probabilità della loro intersezione.\n                        
    \n                        
    \n                            {r`P(E \\cup F) = P(E) + P(F) - P(E \\cap F)`}\n                        
    \n                        \n                            Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi.\n                        
    \n                        
    \n                            {r`P(E) = \\frac{len(E)}{len(\\Omega)}`}\n                        
    \n                        \n                    \n                        
    \n                            Gli spazi campionari possono avere un numero infinito di esiti: sono equiprobabili geometrici se nessun esito è privilegiato rispetto agli altri.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Tengo conto dell'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{D}^{r}_{n, k} = n^k`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo tengo fuori dal sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo un numero, da un sacchetto con n numeri, mi segno che numero ho estratto e lo rimetto nel sacchetto. Ripeto per k volte.\n                        
    \n                        
    \n                            Non mi interessa l'ordine in cui ho estratto i numeri.\n                        
    \n                        
    \n                            {r`\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}`}\n                        
    \n                        \n                    \n                        
    \n                            Estraggo n numeri e guardo in quanti ordini diversi li posso mettere.\n                        
    \n                        
    \n                            {r`\\boldsymbol{P}_n = n!`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"E dato F\"\n                        
    \n                        
    \n                            La probabilità che si verifichi E sapendo che si è già verificato F.\n                        
    \n                        
    \n                            {r`P(E|F) = \\frac{P(E \\cap F)}{P(F)}`}\n                        
    \n                        \n                            Ricorda vagamente le pipe di bash, però al contrario...\n                        \n                        \n                    \n                        
    \n                            Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0.\n                        
    \n                        
    \n                            {r`E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:\n                        
    \n                        
    \n                            {r`P(E_1 \\cap \\times \\cap E_n) = P(E_1) \\times P(E_2 | E_1) \\times \\dots \\times P(E_n | E_1 \\cap E_2 \\cap \\dots \\cap E_{n-1})`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione.\n                        
    \n                        
    \n                            {r`P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)`}\n                        
    \n                        \n                    \n                        
    \n                            La legge delle alternative funziona anche quando ad essere partizionato è un evento:\n                        
    \n                        
    \n                            {r`P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)`}\n                        
    \n                        \n                    \n                        
    \n                            Tramite la formula di Bayes possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:\n                        
    \n                        
    \n                            {r`P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}`}\n                        
    \n                        \n                            In pratica, invertiamo gli eventi.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            \"eventi indipendenti a due a due\"\n                        
    \n                        
    \n                            Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro.\n                        
    \n                        
    \n                            {r`P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)`}\n                        
    \n                        \n                    \n                        
    \n                            \"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque...\"\n                        
    \n                        
    \n                            Si può verificare l'indipendenza di più eventi alla volta:\n                        
    \n                        
    \n                            {r`P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)`}\n                        
    \n                        
    \n                            Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.\n                        
    \n                        \n                    \n                        
    \n                            Un insieme di n eventi è una famiglia di eventi indipendenti se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.\n                        
    \n                        \n                            Tutti gli eventi provenienti da essa saranno indipendenti sia a due a due, sia a tre a tre, sia a quattro a quattro, e così via!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. {r`X(\\omega) : \\Omega \\to \\mathbb{R}`}.\n                        
    \n                        \n                    Insieme di ripartizione}>\n                        
    \n                            Ad ogni variabile aleatoria sono associati gli eventi {r`A_t = \\{ \\omega | X(\\omega) \\leq t \\}`}, che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a t.\n                        
    \n                        
    \n                            Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:\n                        
    \n                        
    \n                            {r`\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}`}\n                        
    \n                        \n                            All'aumentare di t, l'insieme conterrà sempre più elementi.\n                        \n                        \n                    \n                        
    \n                            \"supporto di X\"\n                        
    \n                        
    \n                            Il codominio della variabile aleatoria è il suo supporto.\n                        
    \n                        
    \n                            Per indicare che un valore x_0 appartiene al supporto di X, si usa la notazione X \\mapsto x_0.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La funzione probabilità {r`p_X : X \\to [0, 1]`} di una variabile aleatoria discreta X è la funzione che associa ad ogni esito la sua probabilità:\n                        
    \n                        
    \n                            {r`p_X (x) = \\begin{cases}\n                            P([X = x]) \\quad se\\ X \\mapsto x \\\\\n                            0 \\qquad \\qquad \\quad se\\ X \\not\\mapsto x\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione densità {r`f_X : X \\to [0, 1]`} di una variabile aleatoria continua X è l'equivalente continuo della funzione probabilità:\n                        
    \n                        
    \n                            {r`P([a < X \\leq b]) = \\int_a^b f_X (x) dx`}\n                        
    \n                        
    \n                            A differenza della funzione probabilità, è possibile che la funzione densità non esista per una certa variabile aleatoria.\n                        
    \n                        \n                            Rappresenta \"quanta\" probabilità c'è in un'unità di x!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Ogni variabile aleatoria ha una funzione di ripartizione {r`F_X : \\mathbb{R} \\to [0, 1]`} associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a t:\n                        
    \n                        
    \n                            Si può dire che essa rappresenti la probabilità dell'evento {r`A_t`}:\n                        
    \n                        
    \n                            {r`F_X (t) = P(A_t) = \\begin{cases}\n                            \\sum_{i = 0}^{t} p_X (x_i) \\quad nel\\ discreto\\\\\n                            \\\\\n                            \\int_{-\\infty}^t f_X (x) dx \\quad nel\\ continuo\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
      \n                            
    • È sempre monotona crescente (non strettamente).

      • \n                            
    • Vale 0 a -\\infty e 1 a +\\infty.

      • \n                            
    • È continua da destra: {r`\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:\n                        
    \n                        
    \n                            {r`P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.\n                        
    \n                        \n                    \n                        
    \n                            Nel continuo applichiamo la formula dell'integrazione per sostituzione:\n                        
    \n                        
    \n                            {r`f_Y (y) = \\int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`}\n                        
    \n                        \n                    \n                        
    \n                            Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione random() che restituisce numeri da 0 a 1 con una distribuzione lineare.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Ogni variabile aleatoria che ha una funzione di ripartizione e un supporto finito ha anche una media (o valore medio o atteso):\n                        
    \n                        
    \n                            {r`E(X) = \\int_0^{+infty} (1 - F_X (t)) dt - \\int_{-\\infty}^{0} F_X (t) dt`}\n                        
    \n                        
    \n                            Nel discreto, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\sum_i P(X = x_i) \\cdot x_i`}\n                        
    \n                        
    \n                            Nel continuo, si può calcolare con:\n                        
    \n                        
    \n                            {r`E(X) = \\int_{-\\infty}^{+\\infty} f_X (x) \\cdot x \\cdot dx`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Valore per cui la funzione probabilità o funzione densità è massima.\n                        
    \n                        \n                    \n                        
    \n                            Il quantile {r`x_{\\alpha}`} di ordine {r`0 \\leq \\alpha \\leq 1`} della variabile aleatoria X è il più piccolo numero tale che:\n                        
    \n                        
    \n                            \n                                {r`P([X < x_{\\alpha}]) \\leq \\alpha \\leq P([X \\leq x_{\\alpha}])`}\n                            \n                        
    \n                        
    \n\n                        
    \n                        
    \n                            Il quantile di ordine 0.5 {r`x_{0.5}`} è detto mediana.\n                        
    \n                        
    \n                            I quantili di ordine 0.25 {r`x_{0.25}`} e 0.75 {r`x_{0.75}`} sono detti quartili.\n                        
    \n                        
    \n                            I quantili di ordine {r`\\frac{n}{100}`} sono detti n-esima percentile.\n                        
    \n                        \n                    \n                        
    \n                            È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:\n                        
    \n                        
    \n                            {r`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Data una variabile aleatoria non-negativa:\n                        
    \n                        
    \n                            {r`\\forall k > 0, P([X \\geq k]) \\leq \\frac{E(X)}{k}`}\n                        
    \n                        
    \n                            Divide in due parti ({r`P(X < k)`} e {r`P(X \\geq k)`}) la funzione X, la cui media risulterà uguale a:\n                        
    \n                        
    \n                            {r`E(X) = \\overline{k} \\cdot P(X < k) + k \\cdot P(X \\geq k)`}\n                        
    \n                        \n                    \n                        
    \n                            \"disuguaglianza di cebicev\"\n                        
    \n                        
    \n                            Se la variabile aleatoria X ha media e varianza, allora la probabilità che essa abbia un valore a più di {r`\\epsilon`} di distanza dal valore medio è minore o uguale a {r`\\frac{Var(X)}{\\epsilon^2}`}.\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| \\geq \\epsilon]) \\leq \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        
    \n                            E anche:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| < \\epsilon]) \\geq 1 - \\frac{Var(X)}{\\epsilon^2}`}\n                        
    \n                        \n                            Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Il momento k-esimo di una variabile aleatoria è:\n                        
    \n                        
    \n                            \n                                {r`\\mu_k = E ( X^k ) = \\begin{cases}\n                                \\sum_i x_i^k p_X (x_i) \\qquad nel\\ discreto\\\\\n                                \\\\\n                                \\int_{-\\infty}^{+\\infty} x^k f_X (x) dx \\qquad nel\\ continuo\n                                \\end{cases}`}\n                            \n                        
    \n                        \n                            La media di una variabile aleatoria è anche il suo primo momento.\n                        \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti è:\n                        
    \n                        
    \n                            {r`m_X (t) = E( e^{t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Laplace della variabile aleatoria di X.\n                        
    \n                        \n                    \n                        
    \n                            La funzione caratteristica è:\n                        
    \n                        
    \n                            {r`H_X (t) = E ( e^{i \\cdot t \\cdot X} )`}\n                        
    \n                        
    \n                            Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la stessa distribuzione.\n                        
    \n                        
    \n                            E' la trasformata di Fourier della variabile aleatoria di X.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per dire che una variabile ha una certa distribuzione, si usa la notazione:\n                        
    \n                        
    \n                            {r`X \\sim Distribuzione()`}\n                        
    \n                        \n                    \n                        
    \n                            Una prova con solo due possibili esiti: successo e insuccesso.\n                        
    \n                        \n                    \n                        
    \n                            Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che rappresenta una prova di Bernoulli:\n                        
    \n                        
      \n                            
    • vale 1 in caso di successo.
      • \n                            
    • vale 0 in caso di insuccesso.
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Ber(p)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione bernoulliana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0, 1\\} = \\begin{cases}\n                            p \\quad se\\ k = 1\\\\\n                            q \\quad se\\ k = 0\\\\\n                            0 \\quad altrimenti\n                            \\end{cases} = p^x \\cdot q^{1 - k}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di successi di n prove di uno schema di Bernoulli.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Bin(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della binomiale è:\n                        
    \n                        
    \n                            {r`m_X (t) = (q + p \\cdot e^t) ^ n`}\n                        
    \n                        
    \n                            La media di una binomiale è:\n                        
    \n                        
    \n                            {r`E(X) = n \\cdot p`}\n                        
    \n                        
    \n                            La varianza di una binomiale è:\n                        
    \n                        
    \n                            {r`Var(X) = n \\cdot p \\cdot q`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.\n                        
    \n                        
    \n                            Il suo simbolo è Geo(p).\n                        
    \n                        \n                    \n                        
    \n                            La geometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = q^{k - 1} p`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica è:\n                        
    \n                        
    \n                            {r`m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero k di insuccessi consecutivi in uno schema di Bernoulli:\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`Geo(p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = p \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti della geometrica traslata è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}`}\n                        
    \n                        
    \n                            La media della geometrica traslata è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{q}{p}`}\n                        
    \n                        
    \n                            La varianza della geometrica è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{q}{p^2}`}\n                        
    \n                        \n                    \n                        
    \n                            La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X = i + j | X > i ]) = P([X = j])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'n-esimo successo.\n                        
    \n                        
    \n                            Il suo simbolo rimane {r`\\overline{Bin}(n, p)`}.\n                        
    \n                        \n                    \n                        
    \n                            La binomiale negativa traslata ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k `}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}\n                            
    \n                            
    \n                                La media della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{n \\cdot q}{p}`}\n                            
    \n                            
    \n                                La varianza della binomiale negativa traslata è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{n \\cdot q}{p^2}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che, sapendo il numero di successi K e di insuccessi N-K, conta quanti successi si otterrebbero se se ne estraessero n in blocco.\n                        
    \n                        
    \n                            Il suo simbolo è Ipe(N, K, n).\n                        
    \n                        \n                    \n                        
    \n                            La ipergeometrica ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della ipergeometrica è trascurabile.\n                            
    \n                            
    \n                                La media della ipergeometrica è:\n                            
    \n                            
    \n                                {r`E(X) = n \\cdot \\frac{K}{N}`}\n                            
    \n                            
    \n                                La varianza della ipergeometrica è:\n                            
    \n                            
    \n                                {r`Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:\n                        
    \n                        
      \n                            
    • Binomiale: {r`X \\sim Bin(n, p)`}
      • \n                            
    • Il numero di prove tende a infinito: {r`n \\to +\\infty`}
      • \n                            
    • La probabilità di successo tende a 0: {r`p \\to 0`}
      • \n                            
    • La media è finita: {r`E(X) = n \\cdot p \\to \\mu \\neq 0`}
      • \n                        
    \n                        
    \n                            Il suo simbolo è {r`Poi(\\mu)`}\n                        
    \n                        \n                    \n                        
    \n                            La poissoniana ha come densità:\n                        
    \n                        
    \n                            {r`f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della poissoniana è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot (e^t - 1)}`}\n                            
    \n                            
    \n                                La media della poissoniana è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della poissoniana è:\n                            
    \n                            
    \n                                {r`Var(X) = \\mu`}\n                            
    \n                            
    \n                                Gli altri momenti della poissoniana sono:\n                            
    \n                            
      \n                                
    1. {r`E(X^2) = \\mu^2 + \\mu`}
      2. \n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una successione di arrivi avvenuti in un certo arco temporale che:\n                        
    \n                        
      \n                            
    • non sono sovrapposti.
      • \n                            
    • hanno intensità {r`\\lambda`} costante.
      • \n                            
    • avvengono indipendentemente gli uni dagli altri.
      • \n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria N_t che conta il numero di arrivi di uno schema di Poisson di intensità {r`\\lambda`} in un intervallo di tempo di durata t.\n                        
    \n                        
    \n                            E' una distribuzione poissoniana con {r`\\mu = t \\cdot \\lambda`}: {r`Poi(t \\cdot \\lambda)`}\n                        
    \n                        \n                            E' paragonabile a una bernoulliana: ogni successo corrisponde a un arrivo, mentre il tempo è il numero di prove effettuate (ma nel continuo).\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Esp(\\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad x < 0\\\\\n                            \\lambda \\cdot e^{-\\lambda \\cdot x} \\quad x > 0\n                            \\end{cases}`}\n                        
    \n                        
    \n                            L'esponenziale ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`F_X (t) = \\begin{cases}\n                            0 \\qquad \\qquad t < 0\\\\\n                            1 - e^{-\\lambda \\cdot t} \\quad t \\geq 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            La funzione generatrice dei momenti dell'esponenziale è:\n                        
    \n                        
    \n                            {r`m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}`}\n                        
    \n                        
    \n                            La media dell'esponenziale è:\n                        
    \n                        
    \n                            {r`E(X) = \\frac{1}{\\lambda}`}\n                        
    \n                        
    \n                            La varianza dell'esponenziale è:\n                        
    \n                        
    \n                            {r`Var(X) = \\frac{1}{\\lambda^2}`}\n                        
    \n                        \n                    \n                        
    \n                            L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n                        
    \n                        
    \n                            {r`P([X > s + t | X > s]) = P([X > t])`}\n                        
    \n                        \n                            Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che conta il tempo diwidehattesa prima dell'n-esimo arrivo di un processo di Poisson di intensità {r`\\lambda`}.\n                        
    \n                        
    \n                            Il suo simbolo è {r`\\Gamma(n, \\lambda)`}.\n                        
    \n                        \n                    \n                        
    \n                            La legge gamma ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                            0 \\qquad \\qquad \\qquad \\qquad \\qquad x < 0\\\\\n                            \\frac{1}{(n-1)!} \\cdot \\lambda^n \\cdot x^{n-1} \\cdot e^{-\\lambda \\cdot x} \\quad k > 0\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della legge gamma è:\n                            
    \n                            
    \n                                {r`m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha`}\n                            
    \n                            
    \n                                La media della legge gamma è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{\\alpha}{\\lambda}`}\n                            
    \n                            
    \n                                La varianza della legge gamma è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{\\alpha}{\\lambda^2}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria che può assumere qualsiasi valore in un intervallo {r`[a, b]`} in modo equiprobabile.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Uni(a, b)`}\n                        
    \n                        
    \n                            Su di essa vale la seguente proprietà:\n                        
    \n                        
    \n                            {r`P(X \\in (c, d)) = \\frac{d - c}{b - a}`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione uniforme ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                0 \\qquad \\quad altrimenti    \n                            \\end{cases}`}\n                        
    \n                        
    \n                            La distribuzione uniforme ha come funzione di ripartizione:\n                        
    \n                        
    \n                            {r`f_X (x) = \\begin{cases}\n                                0 \\qquad \\quad x < a  \n                                \\frac{1}{b - a} \\qquad a \\leq x \\leq b\\\\\n                                1 \\qquad \\quad x > b\n                            \\end{cases}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}`}\n                            
    \n                            
    \n                                La media della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`E(X) = \\frac{a + b}{2}`}\n                            
    \n                            
    \n                                La varianza della distribuzione uniforme è:\n                            
    \n                            
    \n                                {r`Var(X) = \\frac{(b - a)^2}{12}`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una variabile aleatoria con una specifica distribuzione.\n                        
    \n                        
    \n                            Il suo simbolo è {r`Nor(\\mu, \\sigma^2)`}.\n                        
    \n                        \n                            \\mu e \\sigma^2 sono rispettivamente la media e la varianza della distribuzione!\n                        \n                        \n                    \n                        
    \n                            La distribuzione normale ha come densità:\n                        
    \n                        
    \n                            {r`f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}`}\n                        
    \n                        \n                    \n                        
    \n                            
    \n                                La funzione generatrice dei momenti della distribuzione normale è:\n                            
    \n                            
    \n                                {r`m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}`}\n                            
    \n                            
    \n                                La media della distribuzione normale è:\n                            
    \n                            
    \n                                {r`E(X) = \\mu`}\n                            
    \n                            
    \n                                La varianza della distribuzione normale è:\n                            
    \n                            
    \n                                {r`Var(X) = \\sigma^2`}\n                            
    \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Qualsiasi normale può essere trasformata in qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)`}\n                        
    \n                        \n                    \n                        
    \n                            La distribuzione normale standard Z è:\n                        
    \n                        
    \n                            Z \\sim Nor(0, 1)\n                        
    \n                        
    \n                            La sua funzione di ripartizione è detta {r`\\phi(z)`} e vale:\n                        
    \n                        
    \n                            {r`F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx`}\n                        
    \n                        \n                    \n                        
    \n                            Da un quantile {r`z_\\alpha`} della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:\n                        
    \n                        
    \n                            {r`x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La distribuzione normale ha una particolare relazione con la distribuzione Gamma:\n                        
    \n                        
    \n                            {r`Z^2 \\sim \\chi^2 (v = 1)`}\n                        
    \n                        \n                    \n                        
    \n                            \"chi-quadro a un grado di libertà\"\n                        
    \n                        
    \n                            Esiste una distribuzione Gamma particolare:\n                        
    \n                        
    \n                            {r`\\Gamma \\left( \\frac{1}{2}, \\frac{1}{2} \\right) = \\chi^2 (v = 1)`}\n                        
    \n                        
    \n                            Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:\n                        
    \n                        
    \n                            {r`\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)`}\n                        
    \n                        \n                    \n                        
    \n                            Un'altra funzione particolare è la funzione T di Student:\n                        
    \n                        
    \n                            {r`T(v) = \\frac{Nor(0, 1)}{\\sqrt{\\frac{\\chi^2(v)}{v}}}`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di N rispetto a n, si può dire che:\n                        
    \n                        
    \n                            {r`Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})`}\n                        
    \n                        \n                    \n                        
    \n                            La binomiale non è altro che una poissoniana a tempo discreto, quindi, se n è grande e n \\cdot p è nell'ordine di grandezza delle unità, allora:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Poi(n \\cdot p)`}\n                        
    \n                        \n                    \n                        
    \n                            Per il Teorema di De Moivre-Laplace, se una binomiale ha una n grande e p non vicina a 0 o 1, si può approssimare con:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            Passando da una variabile discreta X a una continua Y, per ogni valore discreto k la probabilità viene \"spalmata\" su tutto l'intervallo {r`(k - \\frac{1}{2}, k + \\frac{1}{2})`}:\n                        
    \n                        
      \n                            
    • {r`P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})`}
      • \n                            
    • {r`P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})`}
      • \n                            
    • {r`P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})`}
      • \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un vettore composto da variabili aleatorie.\n                        
    \n                        
    \n                            Il suo simbolo generalmente è {r`\\boldsymbol{X}`} oppure {r`X, Y`}.\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione congiunta:\n                        
    \n                        
    \n                            {r`F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una funzione di ripartizione marginale:\n                        
    \n                        
    \n                            {r`F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)`}\n                        
    \n                        \n                    \n                        
    \n                            I vettori aleatori discreti hanno più densità che si differenziano in base al numero di parametri.\n                        
    \n                        
    \n                            Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una densità congiunta:\n                        
    \n                        
    \n                            {r`p_{X, Y} (x, y) = P(X = x, Y = y)`}\n                        
    \n                        
    \n                            Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una densità marginale:\n                        
    \n                        
    \n                            {r`p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli A_i:\n                        
    \n                        
    \n                            {r`P(X_1 \\in A_1, \\dots, X_n \\in A_n) = P(X_1 \\in A_1) \\times \\dots \\times P(X_n \\in A_n)`}\n                        
    \n                        \n                    \n                        
    \n                            E' possibile calcolare la media di qualsiasi funzione g(X, Y) avente elementi del vettore come variabili:\n                        
    \n                        
    \n                            {r`E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)`}\n                        
    \n                        \n                            Solitamente si calcola la media di x \\cdot y.\n                        \n                        
    \n                            Le medie di più variabili aleatorie si possono sommare:\n                        
    \n                        
    \n                            {r`E(X + Y) = E(X) + E(Y)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Un operatore che misura la correlazione di due variabili aleatorie.\n                        
    \n                        
    \n                            Si calcola con il valore atteso dei prodotti delle distanze dalla media:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)`}\n                        
    \n                        
    \n                            Ha diverse proprietà:\n                        
    \n                        
      \n                            
    • Il suo valore nullo è 0: {r`Cov(X, \\alpha) = 0`}
      • \n                            
    • E' commutativa: {r`Cov(X, Y) = Cov(Y, X)`}
      • \n                            
    • E' semplificabile: {r`Cov(X, X) = Var(X)`}
      • \n                            
    • E' lineare: {r`Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)`}
      • \n                            
    • E' distributiva: {r`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Due variabili sono variabili incorrelate se:\n                        
    \n                        
    \n                            {r`Cov(X, Y) = 0`}\n                        
    \n                        
    \n                            Variabili indipendenti sono sempre incorrelate.\n                        
    \n                        \n                    \n                        
    \n                            Una matrice {r`\\boldsymbol{C_X}`} che contiene la covarianza tra tutte le variabili di un vettore aleatorio {r`\\boldsymbol{X}`}:\n                        
    \n                        
    \n                            {r`\n                                \\boldsymbol{C_X} = \n                                \\begin{bmatrix}\n                                    Var(X_1) & Cov(X_1, X_2) & Cov(X_1, X_3)\\\\\n                                    Cov(X_2, X_1) & Var(X_2) & Cov(X_2, X_3)\\\\\n                                    Cov(X_3, X_1) & Cov(X_3, X_2) & Var(X_3)\n                                \\end{bmatrix}\n                            `}\n                        
    \n                        
    \n                            E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono \\geq 0.\n                        
    \n                        \n                    \n                        
    \n                            Un valore che misura come due variabili aleatorie sono correlate:\n                        
    \n                        
    \n                            {r`\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}`}\n                        
    \n                        
    \n                            E' sempre compreso tra -1 e 1:\n                        
    \n                        
    \n                            {r`-1 \\leq \\rho_{X, Y} \\leq 1`}\n                        
    \n                        
    \n                            Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:\n                        
    \n                        
    \n                            {r`Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1`}\n                        
    \n                        \n                    \n                        
    \n                            La varianza di due variabili aleatorie sommate è:\n                        
    \n                        
    \n                            {r`Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)`}\n                        
    \n                        \n                            Si dimostra applicando le proprietà della covarianza!\n                        \n                        
    \n                            Se più variabili aleatorie X_i sono indipendenti ({r`Cov(X, Y) = 0`}), allora:\n                        
    \n                        
    \n                            {r`Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Una n-pla di variabili aleatorie con la stessa distribuzione della variabile aleatoria X (\"popolazione\") ma indipendenti tra loro.\n                        
    \n                        \n                            Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si realizzeranno nel loro valore.\n                        \n                        \n                    \n                        
    \n                            Il valore dato dalla media aritmetica degli n elementi del campione elevati alla potenza k:\n                        
    \n                        
    \n                            {r`M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k `}\n                        
    \n                        
    \n                            Il momento campionario di primo ordine è la media campionaria {r`\\overline{X}_n`}.\n                        
    \n                        \n                    \n                        
    \n                            La media aritmetica dello scarto quadratico medio degli elementi del campione.\n                        
    \n                        
    \n                            Se è noto il valore medio {r`m = E(X)`} di X:\n                        
    \n                        
    \n                            {r`S_0^2 = \\frac{1}{n} \\cdot \\sum_{i = 1}^n (X_i - m)^2 = M_n^(2) - 2 \\cdot m \\cdot \\overline{X}_n + m^2`}\n                        
    \n                        
    \n                            Altrimenti:\n                        
    \n                        
    \n                            {r`S_n^2 = \\frac{1}{n - 1} \\cdot \\sum_{i = 1}^n (X_i - \\overline{X}_n)^2 = \\frac{1}{n - 1} \\cdot ( n \\cdot M_2^{(2)} - n \\cdot \\overline{X}_n^2)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se calcoliamo la media della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(\\overline{X}_n) = E(X)`}\n                        
    \n                        \n                            Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la varianza della media campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`Var(\\overline{X}_n) = \\frac{Var(X)}{n}`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                    \n                        
    \n                            Se calcoliamo la media della varianza campionaria, risulterà vero che:\n                        
    \n                        
    \n                            {r`E(S_0^2) = E(S_n^2) = Var(X)`}\n                        
    \n                        \n                            Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Se la popolazione X ha una distribuzione normale ({r`X \\sim Nor(\\mu, \\sigma^2)`})...\n                        
    \n                        \n                    \n                        
    \n                            ...allora sappiamo anche la distribuzione della media campionaria!\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e anche della varianza campionaria!\n                        
    \n                        
    \n                            {r`S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)`}\n                        
    \n                        
    \n                            {r`S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)`}\n                        
    \n                        \n                    \n                        
    \n                            ...e che media campionaria e varianza campionaria sono indipendenti tra loro!\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa funzione di ripartizione della popolazione X, allora essa converge in distribuzione.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} F_{X_n} (x) = F_X (x) \\\\implies X_n \\\\xrightarrow{d} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità della popolazione X, allora essa converge in probabilità.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, \\\\lim_{n \\\\to +\\\\infty} P( | X_n - X | < \\\\epsilon) = 1 \\\\implies X_n \\\\xrightarrow{p} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la stessa probabilità a  della popolazione X, allora essa converge quasi certamente.\n                        
    \n                        
    \n                            {`\\\\forall \\\\epsilon > 0, P \\left( \\\\lim_{n \\\\to +\\\\infty} | X_n - X | < \\\\epsilon) \\right) = 1 \\\\implies X_n \\\\xrightarrow{qc} X`}\n                        
    \n                        \n                    \n                        
    \n                            Se la successione di variabili aleatorie X_n all'infinito ha la media del quadrato della distanza tra la successione e la popolazione X uguale a 0, allora essa converge in media quadratica.\n                        
    \n                        
    \n                            {`\\\\lim_{n \\\\to +\\\\infty} E( | X_n - X |^2 = 0 \\\\implies X_n \\\\xrightarrow{mq} X`}\n                        
    \n                        \n                    \n                        
    \n                            {`\n                                \\\\begin{matrix}\n                                X_n \\\\xrightarrow{mq} X\\\\\\\\\n                                X_n \\\\xrightarrow{qc} X\n                                \\\\end{matrix} \\\\implies X_n \\\\xrightarrow{p} X \\\\implies X_n \\\\xrightarrow{d} X`\n                            }\n                        
    \n                        
    \n                            In più:\n                        
    \n                        
    \n                            {`X_n \\\\xrightarrow{p} x \\\\Longleftrightarrow X_n \\\\xrightarrow{d} x`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in probabilità alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{p} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1`}\n                        
    \n                        
    \n                            {r`P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1`}\n                        
    \n                        \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge quasi certamente alla media della popolazione {r`E(X)`}, se essa esiste.\n                        
    \n                        
    \n                            {`\\\\overline{X}_n \\\\xrightarrow{qc} X`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1`}\n                        
    \n                        \n                            Dimostra che l'interpretazione frequentista della probabilità è valida!\n                        \n                        \n                    \n                \n                    \n                        
    \n                            La successione delle medie campionarie {r`\\overline{X}_n`} converge in distribuzione a {r`Nor(0, 1) = \\Phi()`}.\n                        
    \n                        
    \n                            {r`\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)`}\n                        
    \n                        
    \n                            Ovvero:\n                        
    \n                        
    \n                            {r`\\forall x \\in \\mathbb{R}, \\lim_{n \\to +\\infty} P \\left( \\frac{\\overline{X}_n - E(X)}{\\sqrt{\\frac{Var(X)}{n}}} \\leq x \\right) = \\Phi(x)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            E' una somma di bernoulliane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di geometriche, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di altre poissoniane, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)`}\n                        
    \n                        \n                    \n                        
    \n                            E' una somma di esponenziali, e quindi si approssima a una normale:\n                        
    \n                        
    \n                            {r`\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)`}\n                        
    \n                        \n                    \n                        
    \n                            Se n è grande, allora:\n                        
    \n                        
    \n                            {r`Y = \\sum_{i=1}^{n} X_i`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per indicare parametri sconosciuti di una legge si usa \\theta.\n                        
    \n                        \n                    \n                        
    \n                            Una variabile aleatoria funzione di un campione:\n                        
    \n                        
    \n                            {r`T(\\boldsymbol{X})`}\n                        
    \n                        \n                            Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso {r`T(\\boldsymbol{X}) = \\boldsymbol{X}`}.\n                        \n                        \n                    \n                \n                    \n                        
    \n                            Una statistica T_n ottenuta da n osservazioni, che stimi i parametri di una legge e sia indipendente da essi.\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è corretto se il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente corretto se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E(T_n) = \\theta`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in media quadratica se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è consistente in probabilità se:\n                        
    \n                        
    \n                            {r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1`}\n                        
    \n                        \n                    \n                        
    \n                            Uno stimatore è asintoticamente normale se:\n                        
    \n                        
    \n                            {r`\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si può usare il metodo dei momenti per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una M a \\theta: {r`\\widehat{\\theta}_M`}\n                        
    \n                        
    \n                            Visto che:\n                        
    \n                        
      \n                            
    • {r`\\theta = g(E(X))`}
      • \n                            
    • {r`\\widehat{E(X)} = \\overline{X}_n`}
      • \n                        
    \n                        
    \n                            Allora:\n                        
    \n                        
    \n                            {r`\\widehat{\\theta}_M = g( \\overline{X}_n )`}\n                        
    \n                        
    \n                            Se {r`\\theta`} non è esprimibile in termini di {r`E(X)`}, si possono usare i momenti successivi {r`M_n^2`}, {r`M_n^3`}, {r`M_n^3`}...\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Si può usare il metodo della massima verosomiglianza per ottenere uno stimatore di una popolazione X.\n                        
    \n                        
    \n                            Lo stimatore di {r`\\theta`} così ottenuto sarà indicato aggiungendo un cappellino e una L a \\theta: {r`\\widehat{\\theta}_L`}\n                        
    \n                        
    \n                            Consiste nel trovare il massimo assoluto {r`\\widehat{\\theta}_L`} della la funzione di verosomiglianza {r`L`}:\n                        
    \n                        
    \n                            {r`L(x_1, ..., x_n; \\theta) = \\prod_{i=1}^n f_X(x_i; \\theta)`}\n                        
    \n                        
    \n                            Gli stimatori di massima verosomiglianza sono asintoticamente corretti, consistenti in probabilità e asintoticamente normali.\n                        
    \n                        \n                    \n                        
    \n                            Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:\n                        
    \n                        
      \n                            
    • Sono asintoticamente corretti.
      • \n                            
    • Sono consistenti in probabilità.
      • \n                            
    • Sono asintoticamente normali.
      • \n                            
    • Sono invarianti: {r`\\widehat{g(\\theta)}_L = g(\\widehat{\\theta}_L)`}
      • \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{p}_M = \\widehat{p}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\mu}_M = \\widehat{\\mu}_L = \\overline{X}_n`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n                        
    \n                        
    \n                            {r`\\widehat{\\lambda}_M = \\widehat{\\lambda}_L = \\frac{1}{\\overline{X}_n}`}\n                        
    \n                        \n                    \n                        
    \n                            Per il metodo della massima verosomiglianza:\n                        
    \n                        
      \n                            
    • {r`\\widehat{\\mu}_L = \\overline{X}_n`}

      • \n                            
    • {r`\\widehat{\\sigma^2}_L = \\frac{\\sum (X_i - \\overline{X}_n)^2 }{n}`}
      • \n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            \"intervallo di confidenza al 95%\"\n                        
    \n                        
    \n                            L'intervallo di valori di \\theta all'interno del quale siamo \"più o meno sicuri\" si trovi il valore effettivo:\n                        
    \n                        
    \n                            L'intervallo di confidenza a N della stima {r`\\widehat{W}`} è l'intervallo ]a, b[ tale che:\n                        
    \n                        
    \n                            {r`P( a < W < b ) = N`}\n                        
    \n                        
    \n                            Può anche essere unilatero nel caso limiti la stima in una sola direzione, positiva o negativa.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        \n                    \n                        
    \n                            Se non conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'\\alpha% con queste formule:\n                        
    \n                        
      \n                            
    • Intervalli bilateri: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da sinistra: {r`\\mu \\in \\left( -\\infty, \\overline{x}_n + t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}} \\right]`}
      • \n                            
    • Intervallo unilatero da destra: {r`\\mu \\in \\left[ \\overline{x}_n - t_{1 - \\frac{\\alpha}{2}; n-1} \\cdot \\sqrt{\\frac{s_n^2}{n}}, +\\infty \\right)`}
      • \n                        
    \n                        
    \n                            {r`t_{\\alpha, v}`} è un quantile della distribuzione di Student di parametro v.\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`p \\in \\left[ \\overline{p} - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}}, \\overline{p} + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\overline{p} \\cdot (1 - \\overline{p})}{n+4}} \\right]`}\n                        
    \n                        \n                    \n                \n                    \n                        
    \n                            L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:\n                        
    \n                        
    \n                            {r`m \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}}, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{s^2_n}{n}} \\right]`}\n                        
    \n                        \n                    \n            
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new file mode 100644
index 0000000..30d5fbe
--- /dev/null
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+      "resolved": "https://registry.npmjs.org/wrap-ansi/-/wrap-ansi-5.1.0.tgz",
+      "integrity": "sha512-QC1/iN/2/RPVJ5jYK8BGttj5z83LmSKmvbvrXPNCLZSEb32KKVDJDl/MOt2N01qU2H/FkzEa9PKto1BqDjtd7Q==",
+      "requires": {
+        "ansi-styles": "^3.2.0",
+        "string-width": "^3.0.0",
+        "strip-ansi": "^5.0.0"
+      }
+    },
+    "wrappy": {
+      "version": "1.0.2",
+      "resolved": "https://registry.npmjs.org/wrappy/-/wrappy-1.0.2.tgz",
+      "integrity": "sha1-tSQ9jz7BqjXxNkYFvA0QNuMKtp8=",
+      "dev": true
+    },
+    "write-file-atomic": {
+      "version": "2.4.3",
+      "resolved": "https://registry.npmjs.org/write-file-atomic/-/write-file-atomic-2.4.3.tgz",
+      "integrity": "sha512-GaETH5wwsX+GcnzhPgKcKjJ6M2Cq3/iZp1WyY/X1CSqrW+jVNM9Y7D8EC2sM4ZG/V8wZlSniJnCKWPmBYAucRQ==",
+      "dev": true,
+      "requires": {
+        "graceful-fs": "^4.1.11",
+        "imurmurhash": "^0.1.4",
+        "signal-exit": "^3.0.2"
+      }
+    },
+    "ws": {
+      "version": "6.2.1",
+      "resolved": "https://registry.npmjs.org/ws/-/ws-6.2.1.tgz",
+      "integrity": "sha512-GIyAXC2cB7LjvpgMt9EKS2ldqr0MTrORaleiOno6TweZ6r3TKtoFQWay/2PceJ3RuBasOHzXNn5Lrw1X0bEjqA==",
+      "dev": true,
+      "requires": {
+        "async-limiter": "~1.0.0"
+      }
+    },
+    "xdg-basedir": {
+      "version": "3.0.0",
+      "resolved": "https://registry.npmjs.org/xdg-basedir/-/xdg-basedir-3.0.0.tgz",
+      "integrity": "sha1-SWsswQnsqNus/i3HK2A8F8WHCtQ=",
+      "dev": true
+    },
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+      "version": "3.0.0",
+      "resolved": "https://registry.npmjs.org/xml-name-validator/-/xml-name-validator-3.0.0.tgz",
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+      "dev": true
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+      "dev": true
+    },
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+      "resolved": "https://registry.npmjs.org/y18n/-/y18n-4.0.0.tgz",
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+    },
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+      "dev": true
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+      "resolved": "https://registry.npmjs.org/yaml/-/yaml-1.7.2.tgz",
+      "integrity": "sha512-qXROVp90sb83XtAoqE8bP9RwAkTTZbugRUTm5YeFCBfNRPEp2YzTeqWiz7m5OORHzEvrA/qcGS8hp/E+MMROYw==",
+      "dev": true,
+      "requires": {
+        "@babel/runtime": "^7.6.3"
+      }
+    },
+    "yargs": {
+      "version": "14.2.2",
+      "resolved": "https://registry.npmjs.org/yargs/-/yargs-14.2.2.tgz",
+      "integrity": "sha512-/4ld+4VV5RnrynMhPZJ/ZpOCGSCeghMykZ3BhdFBDa9Wy/RH6uEGNWDJog+aUlq+9OM1CFTgtYRW5Is1Po9NOA==",
+      "requires": {
+        "cliui": "^5.0.0",
+        "decamelize": "^1.2.0",
+        "find-up": "^3.0.0",
+        "get-caller-file": "^2.0.1",
+        "require-directory": "^2.1.1",
+        "require-main-filename": "^2.0.0",
+        "set-blocking": "^2.0.0",
+        "string-width": "^3.0.0",
+        "which-module": "^2.0.0",
+        "y18n": "^4.0.0",
+        "yargs-parser": "^15.0.0"
+      }
+    },
+    "yargs-parser": {
+      "version": "15.0.0",
+      "resolved": "https://registry.npmjs.org/yargs-parser/-/yargs-parser-15.0.0.tgz",
+      "integrity": "sha512-xLTUnCMc4JhxrPEPUYD5IBR1mWCK/aT6+RJ/K29JY2y1vD+FhtgKK0AXRWvI262q3QSffAQuTouFIKUuHX89wQ==",
+      "requires": {
+        "camelcase": "^5.0.0",
+        "decamelize": "^1.2.0"
+      }
+    }
+  }
+}
diff --git a/package.json b/package.json
index 5cccf30..6dc3780 100644
--- a/package.json
+++ b/package.json
@@ -1,12 +1,12 @@
 {
   "private": true,
   "name": "appuntiweb",
-  "version": "0.1.0",
-  "license": "MIT",
+  "version": "0.2.0",
+  "license": "AGPL-3.0-or-later",
   "scripts": {
     "start": "if-env NODE_ENV=production && npm run -s serve || npm run -s dev",
-    "build": "preact build",
-    "serve": "preact build && preact serve",
+    "build": "preact build --no-prerender --dest docs",
+    "serve": "npm run -s build && preact serve",
     "dev": "preact watch",
     "lint": "eslint src"
   },
@@ -17,16 +17,18 @@
     "build/*"
   ],
   "devDependencies": {
-    "eslint": "^4.5.0",
-    "eslint-config-synacor": "^1.1.0",
     "if-env": "^1.0.0",
-    "preact-cli": "^2.2.1"
+    "preact-cli": "^3.0.0-rc.8"
   },
   "dependencies": {
-    "preact": "^8.5.2",
-    "preact-compat": "^3.17.0",
-    "preact-render-to-string": "^4.1.0",
-    "preact-router": "^2.6.1",
-    "showdown": "^1.9.1"
+    "css-loader": "^3.4.2",
+    "file-loader": "^5.0.2",
+    "history": "^4.10.1",
+    "preact": "^10.3.1",
+    "preact-render-to-string": "^5.1.4",
+    "preact-router": "^3.2.1",
+    "react-simplemde-editor": "^4.1.0",
+    "showdown": "^1.9.1",
+    "style-loader": "^1.1.3"
   }
 }
diff --git a/preact.config.js b/preact.config.js
index 802d328..cbf95f5 100644
--- a/preact.config.js
+++ b/preact.config.js
@@ -1,3 +1,26 @@
-export default (config) => {
-	//config.output.publicPath = 'https://gh.steffo.eu/appuntiweb/';
-};
\ No newline at end of file
+// noinspection JSUnusedGlobalSymbols,JSUnusedLocalSymbols
+export default function (config, env, helpers) {
+    // noinspection JSUnresolvedVariable
+    config.resolve.alias["react"] = "preact/compat";
+    // noinspection JSUnresolvedVariable
+    config.resolve.alias["react-dom"] = "preact/compat";
+
+    config.module.rules.push(
+        {
+            test: /\.nojekyll$/,
+            loader: 'file-loader',
+            options: {
+                name: '.nojekyll'
+            }
+        }
+    );
+    config.module.rules.push(
+        {
+            test: /CNAME$/,
+            loader: 'file-loader',
+            options: {
+                name: 'CNAME'
+            }
+        }
+    );
+};
diff --git a/src/index.js b/src/index.js
index 563257e..32f3630 100644
--- a/src/index.js
+++ b/src/index.js
@@ -1,13 +1,20 @@
-import './index.css';
-import './manifest.json';
 import { Component } from 'preact';
 import Router from 'preact-router';
-import Home from './pages/home';
-import Fisica from './pages/fisica';
-import VlDiGeometria from './pages/vldigeometria';
-import MingwInstall from './pages/mingwinstall';
+import Home from './routes/home';
+import Fisica from './routes/fisica';
+import VlDiGeometria from './routes/vldigeometria';
+import MingwInstall from './routes/mingwinstall';
 import Copyright from './components/copyright';
-import Statistica from './pages/statistica';
+import Statistica from './routes/statistica';
+// noinspection ES6UnusedImports
+import _style from './index.css';
+// noinspection ES6UnusedImports
+import _manifest from './meta/manifest.json';
+// noinspection ES6UnusedImports
+import _cname from './meta/CNAME';
+// noinspection ES6UnusedImports
+import _nojekyll from './meta/.nojekyll';
+import {createHashHistory} from "history";
 
 // noinspection JSUnusedGlobalSymbols
 export default class App extends Component {
@@ -15,7 +22,7 @@ export default class App extends Component {
 		return (
 			
    
 				
    Appuntiweb di Steffo
    
-				
+				
 					
 					
 					
diff --git a/src/pages/statistica.css b/src/meta/.nojekyll
similarity index 100%
rename from src/pages/statistica.css
rename to src/meta/.nojekyll
diff --git a/src/meta/CNAME b/src/meta/CNAME
new file mode 100644
index 0000000..936d4e6
--- /dev/null
+++ b/src/meta/CNAME
@@ -0,0 +1 @@
+uni.steffo.eu
diff --git a/src/meta/manifest.json b/src/meta/manifest.json
new file mode 100644
index 0000000..4540309
--- /dev/null
+++ b/src/meta/manifest.json
@@ -0,0 +1,16 @@
+{
+  "name": "Appunti Web",
+  "short_name": "Appunti Web",
+  "start_url": "/appuntiweb/",
+  "display": "browser",
+  "orientation": "portrait",
+  "background_color": "#0d193b",
+  "theme_color": "#a0ccff",
+  "icons": [
+    {
+      "src": "/assets/icon.png",
+      "type": "image/png",
+      "sizes": "800x800"
+    }
+  ]
+}
diff --git a/src/pages/fisica.css b/src/routes/fisica.css
similarity index 100%
rename from src/pages/fisica.css
rename to src/routes/fisica.css
diff --git a/src/pages/fisica.js b/src/routes/fisica.js
similarity index 100%
rename from src/pages/fisica.js
rename to src/routes/fisica.js
diff --git a/src/pages/home.css b/src/routes/home.css
similarity index 100%
rename from src/pages/home.css
rename to src/routes/home.css
diff --git a/src/pages/home.js b/src/routes/home.js
similarity index 99%
rename from src/pages/home.js
rename to src/routes/home.js
index ec2c758..b016c85 100644
--- a/src/pages/home.js
+++ b/src/routes/home.js
@@ -2,7 +2,6 @@ import style from './home.css'
 import { Component } from 'preact';
 import Panel from '../components/panel';
 import Split from '../components/split';
-import Todo from '../components/todo';
 
 export default class Home extends Component {
     render() {
diff --git a/src/pages/mingwinstall.css b/src/routes/mingwinstall.css
similarity index 100%
rename from src/pages/mingwinstall.css
rename to src/routes/mingwinstall.css
diff --git a/src/pages/mingwinstall.js b/src/routes/mingwinstall.js
similarity index 100%
rename from src/pages/mingwinstall.js
rename to src/routes/mingwinstall.js
diff --git a/src/routes/statistica.css b/src/routes/statistica.css
new file mode 100644
index 0000000..e69de29
diff --git a/src/pages/statistica.js b/src/routes/statistica.js
similarity index 100%
rename from src/pages/statistica.js
rename to src/routes/statistica.js
diff --git a/src/pages/vldigeometria.css b/src/routes/vldigeometria.css
similarity index 100%
rename from src/pages/vldigeometria.css
rename to src/routes/vldigeometria.css
diff --git a/src/pages/vldigeometria.js b/src/routes/vldigeometria.js
similarity index 100%
rename from src/pages/vldigeometria.js
rename to src/routes/vldigeometria.js
diff --git a/yarn.lock b/yarn.lock
deleted file mode 100644
index 86e1be5..0000000
--- a/yarn.lock
+++ /dev/null
@@ -1,8290 +0,0 @@
-# THIS IS AN AUTOGENERATED FILE. DO NOT EDIT THIS FILE DIRECTLY.
-# yarn lockfile v1
-
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-
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-  version "2.1.1"
-  resolved "https://registry.yarnpkg.com/@types/configstore/-/configstore-2.1.1.tgz#cd1e8553633ad3185c3f2f239ecff5d2643e92b6"
-  integrity sha1-zR6FU2M60xhcPy8jns/10mQ+krY=
-
-"@types/debug@^0.0.29":
-  version "0.0.29"
-  resolved "https://registry.yarnpkg.com/@types/debug/-/debug-0.0.29.tgz#a1e514adfbd92f03a224ba54d693111dbf1f3754"
-  integrity sha1-oeUUrfvZLwOiJLpU1pMRHb8fN1Q=
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-  version "1.1.0"
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-  version "3.0.0"
-  resolved "https://registry.yarnpkg.com/camel-case/-/camel-case-3.0.0.tgz#ca3c3688a4e9cf3a4cda777dc4dcbc713249cf73"
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-  version "2.1.0"
-  resolved "https://registry.yarnpkg.com/camelcase-keys/-/camelcase-keys-2.1.0.tgz#308beeaffdf28119051efa1d932213c91b8f92e7"
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-  resolved "https://registry.yarnpkg.com/write-file-atomic/-/write-file-atomic-2.4.3.tgz#1fd2e9ae1df3e75b8d8c367443c692d4ca81f481"
-  integrity sha512-GaETH5wwsX+GcnzhPgKcKjJ6M2Cq3/iZp1WyY/X1CSqrW+jVNM9Y7D8EC2sM4ZG/V8wZlSniJnCKWPmBYAucRQ==
-  dependencies:
-    graceful-fs "^4.1.11"
-    imurmurhash "^0.1.4"
-    signal-exit "^3.0.2"
-
-write@^0.2.1:
-  version "0.2.1"
-  resolved "https://registry.yarnpkg.com/write/-/write-0.2.1.tgz#5fc03828e264cea3fe91455476f7a3c566cb0757"
-  integrity sha1-X8A4KOJkzqP+kUVUdvejxWbLB1c=
-  dependencies:
-    mkdirp "^0.5.1"
-
-xdg-basedir@^3.0.0:
-  version "3.0.0"
-  resolved "https://registry.yarnpkg.com/xdg-basedir/-/xdg-basedir-3.0.0.tgz#496b2cc109eca8dbacfe2dc72b603c17c5870ad4"
-  integrity sha1-SWsswQnsqNus/i3HK2A8F8WHCtQ=
-
-xtend@^4.0.0, xtend@~4.0.1:
-  version "4.0.2"
-  resolved "https://registry.yarnpkg.com/xtend/-/xtend-4.0.2.tgz#bb72779f5fa465186b1f438f674fa347fdb5db54"
-  integrity sha512-LKYU1iAXJXUgAXn9URjiu+MWhyUXHsvfp7mcuYm9dSUKK0/CjtrUwFAxD82/mCWbtLsGjFIad0wIsod4zrTAEQ==
-
-y18n@^3.2.1:
-  version "3.2.1"
-  resolved "https://registry.yarnpkg.com/y18n/-/y18n-3.2.1.tgz#6d15fba884c08679c0d77e88e7759e811e07fa41"
-  integrity sha1-bRX7qITAhnnA136I53WegR4H+kE=
-
-y18n@^4.0.0:
-  version "4.0.0"
-  resolved "https://registry.yarnpkg.com/y18n/-/y18n-4.0.0.tgz#95ef94f85ecc81d007c264e190a120f0a3c8566b"
-  integrity sha512-r9S/ZyXu/Xu9q1tYlpsLIsa3EeLXXk0VwlxqTcFRfg9EhMW+17kbt9G0NrgCmhGb5vT2hyhJZLfDGx+7+5Uj/w==
-
-yallist@^2.1.2:
-  version "2.1.2"
-  resolved "https://registry.yarnpkg.com/yallist/-/yallist-2.1.2.tgz#1c11f9218f076089a47dd512f93c6699a6a81d52"
-  integrity sha1-HBH5IY8HYImkfdUS+TxmmaaoHVI=
-
-yallist@^3.0.0, yallist@^3.0.3:
-  version "3.1.1"
-  resolved "https://registry.yarnpkg.com/yallist/-/yallist-3.1.1.tgz#dbb7daf9bfd8bac9ab45ebf602b8cbad0d5d08fd"
-  integrity sha512-a4UGQaWPH59mOXUYnAG2ewncQS4i4F43Tv3JoAM+s2VDAmS9NsK8GpDMLrCHPksFT7h3K6TOoUNn2pb7RoXx4g==
-
-yargs-parser@^15.0.0:
-  version "15.0.0"
-  resolved "https://registry.yarnpkg.com/yargs-parser/-/yargs-parser-15.0.0.tgz#cdd7a97490ec836195f59f3f4dbe5ea9e8f75f08"
-  integrity sha512-xLTUnCMc4JhxrPEPUYD5IBR1mWCK/aT6+RJ/K29JY2y1vD+FhtgKK0AXRWvI262q3QSffAQuTouFIKUuHX89wQ==
-  dependencies:
-    camelcase "^5.0.0"
-    decamelize "^1.2.0"
-
-yargs-parser@^4.2.0:
-  version "4.2.1"
-  resolved "https://registry.yarnpkg.com/yargs-parser/-/yargs-parser-4.2.1.tgz#29cceac0dc4f03c6c87b4a9f217dd18c9f74871c"
-  integrity sha1-KczqwNxPA8bIe0qfIX3RjJ90hxw=
-  dependencies:
-    camelcase "^3.0.0"
-
-yargs-parser@^7.0.0:
-  version "7.0.0"
-  resolved "https://registry.yarnpkg.com/yargs-parser/-/yargs-parser-7.0.0.tgz#8d0ac42f16ea55debd332caf4c4038b3e3f5dfd9"
-  integrity sha1-jQrELxbqVd69MyyvTEA4s+P139k=
-  dependencies:
-    camelcase "^4.1.0"
-
-yargs@6.6.0:
-  version "6.6.0"
-  resolved "https://registry.yarnpkg.com/yargs/-/yargs-6.6.0.tgz#782ec21ef403345f830a808ca3d513af56065208"
-  integrity sha1-eC7CHvQDNF+DCoCMo9UTr1YGUgg=
-  dependencies:
-    camelcase "^3.0.0"
-    cliui "^3.2.0"
-    decamelize "^1.1.1"
-    get-caller-file "^1.0.1"
-    os-locale "^1.4.0"
-    read-pkg-up "^1.0.1"
-    require-directory "^2.1.1"
-    require-main-filename "^1.0.1"
-    set-blocking "^2.0.0"
-    string-width "^1.0.2"
-    which-module "^1.0.0"
-    y18n "^3.2.1"
-    yargs-parser "^4.2.0"
-
-yargs@^14.2:
-  version "14.2.2"
-  resolved "https://registry.yarnpkg.com/yargs/-/yargs-14.2.2.tgz#2769564379009ff8597cdd38fba09da9b493c4b5"
-  integrity sha512-/4ld+4VV5RnrynMhPZJ/ZpOCGSCeghMykZ3BhdFBDa9Wy/RH6uEGNWDJog+aUlq+9OM1CFTgtYRW5Is1Po9NOA==
-  dependencies:
-    cliui "^5.0.0"
-    decamelize "^1.2.0"
-    find-up "^3.0.0"
-    get-caller-file "^2.0.1"
-    require-directory "^2.1.1"
-    require-main-filename "^2.0.0"
-    set-blocking "^2.0.0"
-    string-width "^3.0.0"
-    which-module "^2.0.0"
-    y18n "^4.0.0"
-    yargs-parser "^15.0.0"
-
-yargs@^8.0.1, yargs@^8.0.2:
-  version "8.0.2"
-  resolved "https://registry.yarnpkg.com/yargs/-/yargs-8.0.2.tgz#6299a9055b1cefc969ff7e79c1d918dceb22c360"
-  integrity sha1-YpmpBVsc78lp/355wdkY3Osiw2A=
-  dependencies:
-    camelcase "^4.1.0"
-    cliui "^3.2.0"
-    decamelize "^1.1.1"
-    get-caller-file "^1.0.1"
-    os-locale "^2.0.0"
-    read-pkg-up "^2.0.0"
-    require-directory "^2.1.1"
-    require-main-filename "^1.0.1"
-    set-blocking "^2.0.0"
-    string-width "^2.0.0"
-    which-module "^2.0.0"
-    y18n "^3.2.1"
-    yargs-parser "^7.0.0"
-
-yargs@~3.10.0:
-  version "3.10.0"
-  resolved "https://registry.yarnpkg.com/yargs/-/yargs-3.10.0.tgz#f7ee7bd857dd7c1d2d38c0e74efbd681d1431fd1"
-  integrity sha1-9+572FfdfB0tOMDnTvvWgdFDH9E=
-  dependencies:
-    camelcase "^1.0.2"
-    cliui "^2.1.0"
-    decamelize "^1.0.0"
-    window-size "0.1.0"
-
-yauzl@^2.4.2:
-  version "2.10.0"
-  resolved "https://registry.yarnpkg.com/yauzl/-/yauzl-2.10.0.tgz#c7eb17c93e112cb1086fa6d8e51fb0667b79a5f9"
-  integrity sha1-x+sXyT4RLLEIb6bY5R+wZnt5pfk=
-  dependencies:
-    buffer-crc32 "~0.2.3"
-    fd-slicer "~1.1.0"