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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 7d20b6688949877acbd0","// removed by extract-text-webpack-plugin\nmodule.exports = {\"latex\":\"latex__34DCT\"};\n\n\n//////////////////\n// WEBPACK FOOTER\n// ./components/latex.css\n// module id = +uq9\n// module chunks = 0","// removed by extract-text-webpack-plugin\n\n\n//////////////////\n// WEBPACK FOOTER\n// ./pages/fisica.css\n// module id = 0lnO\n// module chunks = 0","// removed by extract-text-webpack-plugin\nmodule.exports = {\"split\":\"split__2Bl8C\",\"splitparent\":\"splitparent__nqY7W\",\"splitchild\":\"splitchild__3Ip86\"};\n\n\n//////////////////\n// WEBPACK FOOTER\n// ./components/split.css\n// module id = 1EpE\n// module chunks = 0","// removed by extract-text-webpack-plugin\n\n\n//////////////////\n// WEBPACK FOOTER\n// ./pages/home.css\n// module id = 36Ou\n// module chunks = 0","// removed by extract-text-webpack-plugin\n\n\n//////////////////\n// WEBPACK FOOTER\n// ./pages/mingwinstall.css\n// module id = 5m9J\n// module chunks = 0",";/*! showdown v 1.9.1 - 02-11-2019 */\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 <br> (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: \\<div>foo\\</div>',\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 `<em>` and `<strong>`',\n type: 'boolean'\n },\n completeHTMLDocument: {\n defaultValue: false,\n description: 'Outputs a complete html document, including `<html>`, `<head>` and `<body>` 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 <stevenlevithan.com>\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. \"<<x>\" and \"<x>>\" both produce [\"x\"] when using\n * \"<\" and \">\" as the delimiters (both strings contain a single,\n * balanced instance of \"<x>\").\n *\n * examples:\n * matchRecursiveRegExp(\"test\", \"\\\\(\", \"\\\\)\")\n * returns: []\n * matchRecursiveRegExp(\"<t<<e>><s>>t<>\", \"<\", \">\", \"g\")\n * returns: [\"t<<e>><s>\", \"\"]\n * matchRecursiveRegExp(\"<div id=\\\"x\\\">test</div>\", \"<div\\\\b[^>]*>\", \"</div>\", \"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': '<img alt=\":octocat:\" height=\"20\" width=\"20\" align=\"absmiddle\" src=\"https://assets-cdn.github.com/images/icons/emoji/octocat.png\">',\n 'showdown': '<span style=\"font-family: \\'Anonymous Pro\\', monospace; text-decoration: underline; text-decoration-style: dashed; text-decoration-color: #3e8b8a;text-underline-position: under;\">S</span>'\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: <em>this is</em> <strong>sparta</strong>\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 = '<precode language=\"' + language + '\" precodenum=\"' + i.toString() + '\"></precode>';\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 <a> 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(/\\(<?\\s*>? ?(['\"].*['\"])?\\)$/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 = '<a href=\"' + url + '\"';\n\n if (title !== '' && title !== null) {\n title = title.replace(/\"/g, '"');\n //title = showdown.helper.escapeCharacters(title, '*_', false); // replaced line to improve performance\n title = title.replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n result += ' title=\"' + title + '\"';\n }\n\n // optionLinksInNewWindow only applies\n // to external links. Hash links (#) open in same page\n if (options.openLinksInNewWindow && !/^#/.test(url)) {\n // escaped _\n result += ' rel=\"noopener noreferrer\" target=\"¨E95Eblank\"';\n }\n\n result += '>' + linkText + '</a>';\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]?<?([\\S]+?(?:\\([\\S]*?\\)[\\S]*?)?)>?(?:[ \\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 + '<a href=\"' + lnk + '\"' + target + '>' + mentions + '</a>';\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 + '<a href=\"' + link + '\"' + target + '>' + lnkTxt + '</a>' + 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 + '<a href=\"' + href + '\">' + mail + '</a>';\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 // <p> 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 <pre> content, so we need to fix that:\n bq = bq.replace(/(\\s*<pre>[^\\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')('<blockquote>\\n' + bq + '\\n</blockquote>', options, globals);\n });\n\n text = globals.converter._dispatch('blockQuotes.after', text, options, globals);\n return text;\n});\n\r\n/**\n * Process Markdown `<pre><code>` 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 = '<pre><code>' + codeblock + end + '</code></pre>';\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 <code></code> 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 * <p>Just type <code>foo `bar` baz</code> at the prompt.</p>\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 <code>`bar`</code> ...\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 + '<code>' + c + '</code>';\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 = '<!DOCTYPE HTML>\\n',\n title = '',\n charset = '<meta charset=\"utf-8\">\\n',\n lang = '',\n metadata = '';\n\n if (typeof globals.metadata.parsed.doctype !== 'undefined') {\n doctypeParsed = '<!DOCTYPE ' + globals.metadata.parsed.doctype + '>\\n';\n doctype = globals.metadata.parsed.doctype.toString().toLowerCase();\n if (doctype === 'html' || doctype === 'html5') {\n charset = '<meta charset=\"utf-8\">';\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 = '<title>' + globals.metadata.parsed.title + '</title>\\n';\n break;\n\n case 'charset':\n if (doctype === 'html' || doctype === 'html5') {\n charset = '<meta charset=\"' + globals.metadata.parsed.charset + '\">\\n';\n } else {\n charset = '<meta name=\"charset\" content=\"' + globals.metadata.parsed.charset + '\">\\n';\n }\n break;\n\n case 'language':\n case 'lang':\n lang = ' lang=\"' + globals.metadata.parsed[meta] + '\"';\n metadata += '<meta name=\"' + meta + '\" content=\"' + globals.metadata.parsed[meta] + '\">\\n';\n break;\n\n default:\n metadata += '<meta name=\"' + meta + '\" content=\"' + globals.metadata.parsed[meta] + '\">\\n';\n }\n }\n }\n\n text = doctypeParsed + '<html' + lang + '>\\n<head>\\n' + title + charset + metadata + '</head>\\n<body>\\n' + text.trim() + '\\n</body>\\n</html>';\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(/</g, '<');\n\n // Encode >\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 .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 = '<pre><code' + (language ? ' class=\"' + language + ' language-' + language + '\"' : '') + '>' + codeblock + end + '</code></pre>';\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 <code> 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 <code>\n text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '<code\\\\b[^>]*>', '</code>', '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 = '</' + blockTags[i] + '>';\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, '<code\\\\b[^>]*>', '</code>', '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 <pre><code> 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 <pre><code>\n text = showdown.helper.replaceRecursiveRegExp(text, repFunc, '^ {0,3}<pre\\\\b[^>]*>\\\\s*<code\\\\b[^>]*>', '^ {0,3}</code>\\\\s*</pre>', '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 = '<h' + hLevel + hID + '>' + spanGamut + '</h' + hLevel + '>';\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 = '<h' + hLevel + hID + '>' + spanGamut + '</h' + hLevel + '>';\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 = '<h' + hLevel + hID + '>' + span + '</h' + hLevel + '>';\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 <a> 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')('<hr />', 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 <img> 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]?<?([\\S]+?(?:\\([\\S]*?\\)[\\S]*?)?)>?(?: =([*\\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]?<?(data:.+?\\/.+?;base64,[A-Za-z0-9+/=\\n]+?)>?(?: =([*\\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(/\\(<?\\s*>? ?(['\"].*['\"])?\\)$/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 = '<img src=\"' + url + '\" alt=\"' + altText + '\"';\n\n if (title && showdown.helper.isString(title)) {\n title = title\n .replace(/\"/g, '"')\n //title = showdown.helper.escapeCharacters(title, '*_', false);\n .replace(showdown.helper.regexes.asteriskDashAndColon, showdown.helper.escapeCharactersCallback);\n result += ' title=\"' + title + '\"';\n }\n\n if (width && height) {\n width = (width === '*') ? 'auto' : width;\n height = (height === '*') ? 'auto' : height;\n\n result += ' width=\"' + width + '\"';\n result += ' height=\"' + height + '\"';\n }\n\n result += ' />';\n\n return result;\n }\n\n // First, handle reference-style labeled images: ![alt text][id]\n text = text.replace(referenceRegExp, writeImageTag);\n\n // Next, handle inline images: ![alt text](url =<width>x<height> \"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, '<strong><em>', '</em></strong>');\n });\n text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n return parseInside (txt, '<strong>', '</strong>');\n });\n text = text.replace(/\\b_(\\S[\\s\\S]*?)_\\b/g, function (wm, txt) {\n return parseInside (txt, '<em>', '</em>');\n });\n } else {\n text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n return (/\\S$/.test(m)) ? parseInside (m, '<strong><em>', '</em></strong>') : wm;\n });\n text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n return (/\\S$/.test(m)) ? parseInside (m, '<strong>', '</strong>') : 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, '<em>', '</em>') : 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 + '<strong><em>', '</em></strong>');\n });\n text = text.replace(/([^*]|^)\\B\\*\\*(\\S[\\s\\S]*?)\\*\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n return parseInside (txt, lead + '<strong>', '</strong>');\n });\n text = text.replace(/([^*]|^)\\B\\*(\\S[\\s\\S]*?)\\*\\B(?!\\*)/g, function (wm, lead, txt) {\n return parseInside (txt, lead + '<em>', '</em>');\n });\n } else {\n text = text.replace(/\\*\\*\\*(\\S[\\s\\S]*?)\\*\\*\\*/g, function (wm, m) {\n return (/\\S$/.test(m)) ? parseInside (m, '<strong><em>', '</em></strong>') : wm;\n });\n text = text.replace(/\\*\\*(\\S[\\s\\S]*?)\\*\\*/g, function (wm, m) {\n return (/\\S$/.test(m)) ? parseInside (m, '<strong>', '</strong>') : 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, '<em>', '</em>') : 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 = '<input type=\"checkbox\" disabled style=\"margin: 0px 0.35em 0.25em -1.6em; vertical-align: middle;\"';\n if (checked) {\n otp += ' checked';\n }\n otp += '>';\n return otp;\n });\n }\n\n // ISSUE #312\n // This input: - - - a\n // causes trouble to the parser, since it interprets it as:\n // <ul><li><li><li>a</li></li></li></ul>\n // instead of:\n // <ul><li>- - a</li></ul>\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 = '<li' + bulletStyle + '>' + item + '</li>\\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) + '</' + listType + '>\\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) + '</' + listType + '>\\n';\n }\n })(list);\n } else {\n var style = styleStartNumber(list, listType);\n result = '\\n\\n<' + listType + style + '>\\n' + processListItems(list, !!trimTrailing) + '</' + listType + '>\\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 <p> 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, '<p>');\n str += '</p>';\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 (/^<pre\\b[^>]*>\\s*<code\\b[^>]*>/.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 `<http://example.com/>`\n // Must come after anchors, because you can use < and >\n // delimiters in inline links like [this](<url>).\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, '<br />\\n');\n }\n } else {\n // Vanilla hard breaks\n text = text.replace(/ +\\n/g, '<br />\\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 '<del>' + txt + '</del>';\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]*<?(data:.+?\\/.+?;base64,[A-Za-z0-9+/=\\n]+?)>?(?: =([*\\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 '<th' + id + style + '>' + header + '</th>\\n';\n }\n\n function parseCells (cell, style) {\n var subText = showdown.subParser('spanGamut')(cell, options, globals);\n return '<td' + style + '>' + subText + '</td>\\n';\n }\n\n function buildTable (headers, cells) {\n var tb = '<table>\\n<thead>\\n<tr>\\n',\n tblLgn = headers.length;\n\n for (var i = 0; i < tblLgn; ++i) {\n tb += headers[i];\n }\n tb += '</tr>\\n</thead>\\n<tbody>\\n';\n\n for (i = 0; i < cells.length; ++i) {\n tb += '<tr>\\n';\n for (var ii = 0; ii < tblLgn; ++ii) {\n tb += cells[i][ii];\n }\n tb += '</tr>\\n';\n }\n tb += '</tbody>\\n</table>\\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 '<u>' + txt + '</u>';\n });\n text = text.replace(/\\b__(\\S[\\s\\S]*?)__\\b/g, function (wm, txt) {\n return '<u>' + txt + '</u>';\n });\n } else {\n text = text.replace(/___(\\S[\\s\\S]*?)___/g, function (wm, m) {\n return (/\\S$/.test(m)) ? '<u>' + m + '</u>' : wm;\n });\n text = text.replace(/__(\\S[\\s\\S]*?)__/g, function (wm, m) {\n return (/\\S$/.test(m)) ? '<u>' + m + '</u>' : 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 += ' + '>';\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 '<!--' + node.data + '-->\\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 '<pre>' + globals.preList[num] + '</pre>';\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<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\tflags = (route[i$1].match(/[+*?]+$/) || EMPTY$1)[0] || '',\n\t\t\t\tplus = ~flags.indexOf('+'),\n\t\t\t\tstar = ~flags.indexOf('*'),\n\t\t\t\tval = 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}\n\t\telse 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) { return false; }\n\treturn matches;\n}\n\nfunction pathRankSort(a, b) {\n\treturn (\n\t\t(a.rank < b.rank) ? 1 :\n\t\t(a.rank > 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<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\n\nfunction routeFromLink(node) {\n\t// only valid elements\n\tif (!node || !node.getAttribute) { return; }\n\n\tvar href = node.getAttribute('href'),\n\t\ttarget = 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))) { return; }\n\n\t// attempt to route, if no match simply cede control to browser\n\treturn route(href);\n}\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\n\nfunction prevent(e) {\n\tif (e) {\n\t\tif (e.stopImmediatePropagation) { e.stopImmediatePropagation(); }\n\t\tif (e.stopPropagation) { e.stopPropagation(); }\n\t\te.preventDefault();\n\t}\n\treturn false;\n}\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) { return; }\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')) { return; }\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\n\nvar eventListenersInitialized = false;\n\nfunction initEventListeners() {\n\tif (eventListenersInitialized) { return; }\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\n\nvar 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) { 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\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) { 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 = (<h3>{this.props.title}</h3>);\n\t\t}\n\n\t\treturn (\n\t\t\t<div class={this.getStyle()} id={this.props.id}>\n\t\t\t\t{title}\n\t\t\t\t{this.props.children}\n\t\t\t</div>\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 = (<h2>{this.props.title}</h2>)\n }\n\n let children;\n if(Array.isArray(this.props.children)) {\n children = this.props.children.map(element => {\n return (<div class={style.splitchild}>{element}</div>);\n });\n }\n else {\n children = <div class={style.splitchild}>{this.props.children}</div>;\n }\n\t\treturn (\n\t <div class={style.split}>\n {title}\n <div class={style.splitparent}>{children}</div>\n </div>\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 <span class={style.todo}>{this.props.children}</span>;\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 <div style={style.home}>\r\n <h1>Indice</h1>\r\n <Split title=\"Argomenti\">\r\n <Panel title={<a href=\"/statistica\">Statistica ed elementi di probabilità</a>}>\r\n <p>\r\n Appunti scritti mentre studiavo per l'esame di <a href={\"http://personale.unimore.it/rubrica/contenutiad/llarocca/2019/58028/N0/N0/9999\"}>Statistica ed elementi di probabilità</a> del <a href=\"https://www.unimore.it/didattica/mlaurea.html?ID=54\">corso triennale di Informatica</a> all'<a href=\"https://www.unimore.it/\">Unimore</a> del Prof. <a href={\"http://personale.unimore.it/rubrica/dettaglio/llarocca\"}>Luca La Rocca</a>.\r\n </p>\r\n <p>\r\n <Todo>TODO: è ancora incompleto!</Todo>\r\n </p>\r\n </Panel>\r\n <Panel title={<a href=\"https://github.com/Steffo99/cleaver\">Cleaver</a>}>\r\n <p>\r\n Progetto in Java sviluppato per l'esame di <a href=\"http://personale.unimore.it/rubrica/contenutiad/gcabri/2019/58026/N0/N0/9999\">Programmazione ad Oggetti</a> del <a href=\"https://www.unimore.it/didattica/mlaurea.html?ID=54\">corso triennale di Informatica</a> all'<a href=\"https://www.unimore.it/\">Unimore</a>, tenuto dai Prof. <a href=\"http://personale.unimore.it/rubrica/dettaglio/gcabri\">Giacomo Cabri</a> e <a href=\"http://personale.unimore.it/Rubrica/Dettaglio/n.capodieci\">Nicola Capodieci</a>.\r\n </p>\r\n </Panel>\r\n <Panel title={<a href=\"/fisica\">Fisica</a>}>\r\n <p>\r\n Appunti delle <a href=\"http://personale.unimore.it/rubrica/contenutiad/brunetti/2019/58025/N0/N0/9999\">lezioni di Fisica</a> del <a href=\"https://www.unimore.it/didattica/mlaurea.html?ID=54\">corso triennale di Informatica</a> all'<a href=\"https://www.unimore.it/\">Unimore</a>, tenute dalla <a href=\"https://personale.unimore.it/rubrica/dettaglio/brunetti\">Prof.ssa Rossella Brunetti</a> nel primo semestre dell'Anno Accademico 2019/2020.\r\n </p>\r\n </Panel>\r\n <Panel title={<a href=\"https://github.com/Steffo99/appunti-universitari/tree/master/2019_SistemiOperativi/Arzigogoli\">Sistemi Operativi</a>}>\r\n <p>\r\n Soluzioni agli <a href=\"https://weblab.ing.unimore.it/people/andreolini/didattica/sistemi-operativi/index.html#arzigogoli\">Arzigogoli</a> proposti dal <a href=\"https://personale.unimore.it/rubrica/dettaglio/andreolini\">Prof. Mauro Andreolini</a> durante le <a href=\"https://personale.unimore.it/rubrica/contenutiad/andreolini/2019/58027/N0/N0/9999\">lezioni di Sistemi Operativi</a> del <a href=\"https://www.unimore.it/didattica/mlaurea.html?ID=54\">corso triennale di Informatica</a> all'<a href=\"https://www.unimore.it/\">Unimore</a> tenutesi nel primo semestre dell'Anno Accademico 2019/2020.\r\n </p>\r\n </Panel>\r\n <Panel title={<a href=\"https://github.com/Steffo99/appunti-universitari/tree/master/2018_AlgoritmiEStruttureDati\">Algoritmi e Strutture Dati</a>}>\r\n <p>\r\n Appunti delle <a href=\"https://personale.unimore.it/rubrica/contenutiad/mmontangero/2018/58133/N0/N0/9999\">lezioni di Algoritmi e Strutture Dati</a> del <a href=\"https://www.unimore.it/didattica/mlaurea.html?ID=54\">corso triennale di Informatica</a> all'<a href=\"https://www.unimore.it/\">Unimore</a>, tenute dalla <a href=\"https://personale.unimore.it/rubrica/dettaglio/mmontangero\">Prof.ssa Manuela Montangero</a> nel secondo semestre dell'Anno Accademico 2018/2019.\r\n </p>\r\n </Panel>\r\n <Panel title={<a href=\"/vldigeometria\">Videolezioni di Geometria</a>}>\r\n <p>\r\n Ottime videolezioni di Geometria con licenza <a href=\"https://creativecommons.org/licenses/by-nc-sa/4.0/\">CC BY-NC-SA 4.0</a> che ho trovato sul <a href=\"https://dolly.fim.unimore.it/2018/course/view.php?id=14#section-0\">portale Dolly 2018</a> dell'<a href=\"https://www.unimore.it/\">Unimore</a>.\r\n </p>\r\n </Panel>\r\n <Panel title={<a href=\"/mingwinstall\">Come installare MinGW</a>}>\r\n <p>\r\n Un breve tutorial con immagini su come installare e configurare <a href=\"https://it.wikipedia.org/wiki/MinGW\">MinGW</a> per compilare programmi C e C++ su Windows.\r\n </p>\r\n </Panel>\r\n </Split>\r\n <Split title=\"Altri collegamenti utili\">\r\n <Panel title={<a href=\"https://t.me/unimoreinfo\">@unimoreinfo</a>}>\r\n <p>\r\n Il gruppo <a href=\"https://telegram.org/\">Telegram</a> del corso di Informatica dell'Unimore!\r\n </p>\r\n </Panel>\r\n <Panel title={<a href=\"https://calendar.google.com/calendar?cid=MmYza2o2M3VuZWQ1cmZqaGpmOGY0MWFrNmdAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ\">Calendario Lezioni</a>}>\r\n <p>\r\n Calendario Google <small>quasi</small> sempre aggiornato delle lezioni e degli esami del secondo anno dell'<a href=\"https://www.unimore.it/\">Unimore</a> durante l'Anno Accademico 2019/2020.\r\n </p>\r\n </Panel>\r\n <Panel title={<a href=\"http://erre2.fermitech.info/dashboard\">Erre2</a>}>\r\n <p>\r\n Portale contenente appunti e riassunti mantenuto da <a href=\"https://github.com/LBindustries\">Lorenzo Balugani</a>.\r\n </p>\r\n </Panel>\r\n <Panel title={<a href=\"https://github.com/vezzalinistefano/Appunti-Algoritmi\">vezzalinistefano/Appunti-Algoritmi</a>}>\r\n <p>\r\n Appunti di Algoritmi e Strutture Dati mantenuti da <a href=\"https://github.com/vezzalinistefano/\">Vezzalini Stefano</a>.\r\n </p>\r\n </Panel>\r\n </Split>\r\n </div>\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} ${this.props.children} }`;\n\t\treturn (\n\t\t\t<img src={`https://latex.codecogs.com/svg.latex?${equation}`}\n\t\t\t\t alt={this.props.children}\n\t\t\t title={this.props.children}\n\t\t\t class={style.latex}\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 <span class={style.plus}>{this.props.children}</span>;\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 <span class={style.minus}>{this.props.children}</span>;\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 <div style={style.fisica}>\n <h1>Fisica</h1>\n <Split title=\"Vettori\">\n <Panel title=\"Componenti cartesiane\">\n <p>\n Usa le regole base della trigonometria:\n </p>\n <p>\n <Latex>{r`\\vec{v} = \\vec{v}_x + \\vec{v}_y`}</Latex>\n </p>\n <p>\n <Latex>{r`\\left | \\vec{v}_x \\right | = \\left | \\vec{v} \\right | \\sin \\alpha`}</Latex>\n </p>\n <p>\n <Latex>{r`\\left | \\vec{v}_y \\right | = \\left | \\vec{v} \\right | \\cos \\alpha`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Somma\">\n <p>\n Scomponi in componenti, poi sommali:\n </p>\n <p>\n <Latex>{r`\\vec{v} + \\vec{w} = (\\vec{v}_x + \\vec{w}_x) + (\\vec{v}_y + \\vec{w}_y)`}</Latex>\n </p>\n <p>\n Produce il vettore risultante dall'applicazione della regola del parallelogramma.\n </p>\n </Panel>\n <Panel title=\"Differenza\">\n <p>\n Alla fine è sempre una somma:\n </p>\n <p>\n <Latex>{r`\\vec{v} - \\vec{w} = (\\vec{v}_x - \\vec{w}_x) + (\\vec{v}_y - \\vec{w}_y)`}</Latex>\n </p>\n <p>\n Produce il vettore che parte da <Latex>w</Latex> e arriva a <Latex>v</Latex>.\n </p>\n </Panel>\n <Panel title=\"Prodotto scalare\">\n <p>\n Si chiama scalare perchè il risultato è uno scalare, non un vettore.\n </p>\n <p>\n <Latex>{r`\\vec{v} \\cdot \\vec{w} = \\left | \\vec{v} \\right | \\left | \\vec{w} \\right | \\cos \\alpha`}</Latex>\n </p>\n <p>\n Produce il modulo della proiezione di <Latex>{r`\\vec{a}`}</Latex> su <Latex>{r`\\vec{b}`}</Latex>.\n </p>\n </Panel>\n <Panel title=\"Prodotto vettoriale\">\n <p>\n Si chiama vettoriale perchè il risultato è un altro vettore.\n </p>\n <ul>\n <li><Latex>{r`\\vec{c} = \\vec{a} \\times \\vec{b}`}</Latex></li>\n <li><Latex>{r`\\left | \\vec{c} \\right | = \\left | \\vec{a} \\right | \\cdot \\left | \\vec{b} \\right | \\cdot \\sin(\\alpha)`}</Latex></li>\n <li><a href=\"https://it.wikipedia.org/wiki/Regola_della_mano_destra\">Regola della mano destra</a></li>\n </ul>\n <p>\n Non è commutativo!\n </p>\n </Panel>\n </Split>\n <Split title=\"Leggi di Newton\">\n <Panel title=\"1ᵃ: Inerzia\">\n <p>\n Se un corpo puntiforme ha forza risultante nulla, allora la sua velocità non cambia.\n </p>\n <p>\n <Latex>{r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta v = 0`}</Latex>\n </p>\n </Panel>\n <Panel title=\"2ᵃ: Proporzionalità\">\n <p>\n La forza risultante di un corpo è direttamente proporzionale alla sua accelerazione, e la costante di proporzionalità è la <i>massa</i>.\n </p>\n <p>\n <Latex>{r`\\Sigma \\vec{F} = m \\vec{a}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"3ᵃ: Azione e reazione\">\n <p>\n Due corpi esercitano forze uguali e opposte uno sull'altro. \n </p>\n <p>\n <Latex>{r`\\vec{F}_{21} = -\\vec{F}_{12}`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Forza di gravità\">\n <Panel title=\"Tra due corpi\">\n <p>\n Due corpi puntiformi si attirano uno verso l'altro con forza:\n </p>\n <p>\n <Latex>{r`\\left | \\vec{F} \\right | = G \\frac{m_1 m_2}{s^2}`}</Latex>\n </p>\n <p>\n <Latex>G</Latex> è la <i>costante di gravitazione universale</i> e vale:\n </p>\n <p>\n <Latex>{r`G = 6.67 \\cdot 10^{-11} \\frac{N m^2}{{kg}^2}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Verso la Terra\">\n <p>\n Se nel sistema di riferimento consideriamo la Terra ferma, allora un corpo è attratto verso la Terra con forza <i>peso</i> uguale a:\n </p>\n <p>\n <Latex>{r`\\left | \\vec{F} \\right | = g m`}</Latex>\n </p>\n <p>\n <Latex>g</Latex> è la <i>costante di gravità</i> della Terra, e vale:\n </p>\n <p>\n <Latex>{r`g = 9.81 \\frac{m}{s^2}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Su pianeti diversi\">\n <p>\n Per pianeti diversi dalla Terra vale la stessa regola:\n </p>\n <p>\n <Latex>{r`\\left | \\vec{F} \\right | = g m`}</Latex>\n </p>\n <p>\n L'unica differenza è che cambia la <i>costante di gravità</i>:\n </p>\n <p>\n <Latex>{r`g_{luna} = 1.62 \\frac{m}{s^2}`}</Latex>\n </p>\n <p>\n <Latex>{r`g_{marte} = 3.71 \\frac{m}{s^2}`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Forze di contatto\">\n <Panel title=\"Normale\">\n <p>\n Si oppone alle forze applicate alla superficie di contatto.\n </p>\n <p>\n Un libro appoggiato su un tavolo ha la <b>forza di gravità</b> che lo attira verso il terreno e la <b>forza normale</b> che lo trattiene dal cadere. \n </p>\n </Panel>\n <Panel title=\"Attrito statico\">\n <p>\n Impedisce a un corpo di muoversi se non viene spinto da una forza che supera una certa soglia:\n </p>\n <p>\n <Latex>{r`\\left | \\vec{F} \\right | \\leq \\mu_{s} \\left | \\vec{F}_{normale} \\right |`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Attrito dinamico\">\n <p>\n Rallenta i corpi che si stanno muovendo finchè essi non si fermano:\n </p>\n <p>\n <Latex>{r`\\left | \\vec{F} \\right | \\leq \\mu_{d} \\left | \\vec{F}_{normale} \\right |`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Tensione\">\n <p>\n E' forza trasmessa tra due estremi di una fune.\n </p>\n <p>\n Può essere redirezionata per mezzo di carrucole.\n </p>\n </Panel>\n <Panel title=\"Elastica\">\n <p>\n Una molla cerca sempre di tornare alla sua posizione indeformata con forza:\n </p>\n <p>\n <Latex>{r`F = -k x`}</Latex>\n </p>\n <p>\n (E' negativa perchè la forza è opposta a quella applicata per deformarla.)\n </p>\n </Panel>\n </Split>\n <Split title=\"Cinematica\">\n <Panel title=\"Spostamento\">\n <p>\n È un vettore che indica la posizione di un corpo rispetto a un'origine.\n </p>\n <p>\n <Latex>{r`\\Delta \\vec{s} = \\vec{s}(fine) - \\vec{s}(inizio)`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Velocità\">\n <p>\n È un vettore che misura la variazione di posizione nel tempo.\n </p>\n <p>\n <Latex>{r`\\vec{v} = \\frac{\\Delta \\vec{s}}{\\Delta t}`}</Latex>\n </p>\n <p>\n Se si considera un intervallo di tempo infinitesimale si dice <i>velocità istantanea</i>:\n </p>\n <p>\n <Latex>{r`\\vec{v} = \\lim_{\\Delta t \\to 0} \\frac{\\Delta \\vec{s}}{\\Delta t} = \\frac{d \\vec{s}}{dt}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Accelerazione\">\n <p>\n È un vettore che misura la variazione di velocità nel tempo.\n </p>\n <p>\n <Latex>{r`\\vec{a} = \\frac{\\Delta \\vec{v}}{\\Delta t}`}</Latex>\n </p>\n <p>\n Se si considera un intervallo di tempo infinitesimale si dice <i>accelerazione istantanea</i>:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n </Panel>\n <Panel title={<span>Quantità di moto <small>(momento lineare)</small></span>}>\n <p>\n La quantità di moto è una proprietà vettoriale dei corpi:\n </p>\n <p>\n <Latex>{r`\\vec{p} = m \\vec{v}`}</Latex>\n </p>\n <p>\n Se la forza risultante è nulla, la quantità di moto non cambia.\n </p>\n <p>\n <Latex>{r`\\Sigma \\vec{F} = 0 \\Longleftrightarrow \\Delta \\vec{p} = 0`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Moto rettilineo uniforme\">\n <Panel title=\"Spostamento\">\n <p>\n La <i>legge oraria</i> è:\n </p>\n <p>\n <Latex>{r`s(t) = v \\cdot \\Delta t + s(0)`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Velocità\">\n <p>\n È costante:\n </p>\n <p>\n <Latex>{r`v(t) = k`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Accelerazione\">\n <p>\n La velocità non varia:\n </p>\n <p>\n <Latex>{r`a(t) = 0`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Forze\">\n <p>\n Si applica la prima legge di Newton:\n </p>\n <p>\n <Latex>f(t) = 0</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Moto rettilineo uniformemente accelerato\">\n <Panel title=\"Spostamento\">\n <p>\n La <i>legge oraria</i> è:\n </p>\n <p>\n <Latex>{r`s(t) = \\frac{1}{2} a \\cdot (\\Delta t)^2 + v(0) \\cdot (\\Delta t) + s(0)`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Velocità\">\n <p>\n È una retta:\n </p>\n <p>\n <Latex>{r`v(t) = a \\Delta t + v(0)`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Accelerazione\">\n <p>\n È costante:\n </p>\n <p>\n <Latex>{r`a(t) = k`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Forze\">\n <p>\n Si applica la prima legge di Newton:\n </p>\n <p>\n <Latex>f(t) = m a</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Moto armonico semplice\">\n <Panel title=\"Ampiezza\">\n <p>\n E' la distanza dal centro massima che raggiunge il corpo.\n </p>\n <p>\n (L'ampiezza di una sinusoide.)\n </p>\n </Panel>\n <Panel title=\"Velocità angolare\">\n <p>\n Indica quanto in fretta cambia la posizione del corpo. \n </p>\n <p>\n Dipende dal periodo:\n </p>\n <p>\n <Latex>{r`\\omega = \\frac{2 \\pi}{T}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Spostamento\">\n <p>\n E' una sinusoide:\n </p>\n <p>\n <Latex>{r`s(t) = A \\sin (\\omega \\cdot t + \\phi)`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Velocità\">\n <p>\n E' la sinusoide dello spostamento, sfasata di <Latex>{r`\\frac{\\pi}{2}`}</Latex>:\n </p>\n <p>\n <Latex>{r`v(t) = A \\sin (\\omega \\cdot t + \\phi + \\frac{\\pi}{2})`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Accelerazione\">\n <p>\n E' la sinusoide della velocità, sfasata di <Latex>{r`\\pi`}</Latex>:\n </p>\n <p>\n <Latex>{r`a(t) = A \\sin (\\omega \\cdot t + \\phi + \\pi)`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Forze\">\n <p>\n Si applica la prima legge di Newton:\n </p>\n <p>\n <Latex>f(t) = m a</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Moti composti\">\n <Panel title=\"Moto parabolico\">\n <p>\n Il moto parabolico è dato sommando un moto rettilineo uniforme sull'asse orizzontale e un moto rettilineo uniformemente accelerato sull'asse verticale.\n </p>\n </Panel>\n <Panel title=\"Moto circolare uniforme\">\n <p>\n Il moto parabolico è dato sommando due moti armonici semplici: uno sull'asse X, e l'altro, sfasato di <Latex>{r`\\frac{\\pi}{2}`}</Latex>, sull'asse Y.\n </p>\n </Panel>\n </Split>\n <Split title=\"Moto circolare uniforme\">\n <Panel>\n <h3>\n Velocità angolare\n </h3>\n <p>\n Quanto cambia la fase nel tempo.\n </p>\n <p>\n <Latex>{r`\\omega = \\frac{2 \\pi}{T}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Fase\">\n <p>\n E' l'angolo percorso dal corpo rispetto alla posizione iniziale.\n </p>\n <p>\n Si indica con <Latex>{r`\\phi`}</Latex>, e generalmente si usa in radianti.\n </p>\n </Panel>\n <Panel title=\"Velocità\">\n <p>\n Si applicano le formule per la circonferenza:\n </p>\n <p>\n <Latex>{r`v = \\frac{\\Delta s}{t} = \\frac{2 \\pi \\cdot r}{T} = \\omega r`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Accelerazione\">\n <p>\n Il corpo ha sempre un accelerazione verso il centro che gli impedisce di abbandonare il moto: \n </p>\n <p>\n <Latex>{r`a = \\frac{v^2}{r} = r \\cdot \\omega^2 = v \\cdot \\omega`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Forza centripeta\">\n <p>\n È verso il centro e si calcola con:\n </p>\n <p>\n <Latex>{r`F = m \\cdot a`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Lavoro ed energia\">\n <Panel title=\"Lavoro\">\n <p>\n E' compiuto da una forza che sposta un corpo.\n </p>\n <p>\n <Latex>{r`W = \\vec{F} \\cdot \\vec{s} = F \\cdot \\Delta s \\cdot cos(\\alpha )`}</Latex>\n </p>\n <p>\n (Se la forza non è parallela allo spostamento, il prodotto scalare ci fa considerare solo la componente parallela.)\n </p>\n </Panel>\n <Panel title=\"Energia cinetica\">\n <p>\n Un corpo ha energia cinetica in ogni momento uguale a:\n </p>\n <p>\n <Latex>{r`E_c = \\frac{1}{2} m v^2`}</Latex>\n </p>\n <p>\n Se una forza effettua lavoro su un corpo, cambia la sua energia cinetica pari al lavoro effettuato:\n </p>\n <p>\n <Latex>{r`\\Delta E_c = W`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Energia potenziale gravitazionale\">\n <p>\n Un corpo ha energia potenziale in ogni momento pari a: \n </p>\n <p>\n <Latex>{r`E_{p_g} = m \\cdot g \\cdot h`}</Latex>\n </p>\n <p>\n (Con <Latex>h</Latex> uguale a un altezza scelta come punto di riferimento.)\n </p>\n </Panel>\n <Panel title=\"Energia potenziale elastica\">\n <p>\n Una molla ha sempre energia potenziale elastica pari a:\n </p>\n <p>\n <Latex>{r`E_{p_e} = \\frac{1}{2} k x^2`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Forze conservative\">\n <p>\n Sono conservative le forze per le quali il lavoro compiuto non dipende dal percorso seguito per andare dalla partenza all'arrivo.\n </p>\n <p>\n Ad esempio, è conservativa la <i>forza di gravità</i>, ma <b>non</b> è conservativa la forza di attrito.\n </p>\n <p>\n Se in un sistema ci sono solo forze conservative, allora l'energia meccanica totale si conserva:\n </p>\n <p>\n <Latex>{r`E = E_k + E_p`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Potenza\">\n <p>\n È la velocità di trasferimento di energia:\n </p>\n <p>\n <Latex>{r`P = \\frac{\\Delta E}{\\Delta t}`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Elettrostatica\">\n <Panel title=\"Carica elettrica\">\n <p>\n È una proprietà dei corpi che può essere <Plus>positiva</Plus> o <Minus>negativa</Minus>.\n </p>\n <p>\n Si conserva: in un sistema chiuso la carica totale è costante.\n </p>\n <p>\n Esiste un'unità elementare: <Latex>{r`C_{elettrone} = 1.602 \\cdot 10^{-19}`}</Latex>.\n </p>\n <p>\n Cariche <Plus>opp</Plus><Minus>oste</Minus> si attraggono; cariche <Plus>uguali</Plus> si respingono.\n </p>\n </Panel>\n <Panel title=\"Conduttori e isolanti\">\n <p>\n Più <a href=\"https://it.wikipedia.org/wiki/Ione\">ioni</a> ha un corpo, meglio la carica si muove attraverso di esso.\n </p>\n <p>\n I corpi in cui la carica si muove bene sono <i>conduttori</i>, mentre quelli in cui si muove difficilmente sono <i>isolanti</i>.\n </p>\n <p>\n <i>Il corpo umano è un buon conduttore.</i>\n </p>\n </Panel>\n </Split>\n <Split title=\"Polarizzazione\">\n <Panel title=\"Polarizzazione\">\n <p>\n E' possibile polarizzare un corpo per accumulare la carica di un segno in una certa zona.\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title=\"Messa a terra\">\n <p>\n Se un corpo conduttore è in contatto con la Terra, le cariche su di esso saranno <i>equilibrate</i> e il corpo diventerà elettricamente neutro (con stesso numero di <Plus>cariche positive</Plus> e <Minus>negative</Minus> all'interno).\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title=\"Polarizzazione per strofinio\">\n <p>\n Strofinando tra loro due corpi isolanti, essi si <i>polarizzeranno per strofinio</i>.\n </p>\n </Panel>\n <Panel title=\"Polarizzazione per contatto\">\n <p>\n Toccando un conduttore con un corpo carico, il conduttore potrà <i>polarizzarsi per contatto</i>.\n </p>\n </Panel>\n <Panel title=\"Polarizzazione per induzione\">\n <p>\n Se un corpo conduttore ha cariche \"esterne\" di un <Plus>certo segno</Plus> vicino, esso avrà tutte le cariche del <Minus>segno opposto</Minus> in equilibrio vicino alle cariche esterne, e tutte le cariche dello <Plus>stesso segno</Plus> più lontano possibile da esse.\n </p>\n <p>\n Mettendo a terra il conduttore, nuove cariche del <Minus>segno opposto</Minus> saranno attratte all'interno del corpo per equilibrare le cariche che si sono allontanate.\n </p>\n <p>\n Staccando il conduttore da terra e rimuovendo le cariche esterne, esso si ritroverà <Minus>caricato del segno opposto</Minus> rispetto alle cariche esterne.\n </p>\n </Panel>\n </Split>\n <Split title=\"Forza elettrica\">\n <Panel title=\"Legge di Coulomb\">\n <p>\n Due corpi carichi si attraggono tra loro con forza: \n </p>\n <p>\n <Latex>{r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{-k \\cdot q_1 \\cdot q_2}{s^2}`}</Latex>\n </p>\n <p>\n <Latex>{r`k`}</Latex> è la <i>costante di Coulomb</i>, e vale <Latex>{r`k = 8.99 \\cdot 10^9 \\frac{N \\cdot m^2}{C^2}`}</Latex>.\n </p>\n </Panel>\n <Panel title=\"Permeabilità dello spazio vuoto\">\n <p>\n La costante <Latex>{r`k`}</Latex> è in realtà dipendente da un altra costante, <Latex>{r`\\epsilon_0`}</Latex>, la <i>permeabilità del vuoto</i>.\n </p>\n <p>\n <Latex>{r`k = \\frac{1}{4 \\pi \\cdot \\epsilon_0}`}</Latex>\n </p>\n <p>\n <Latex>{r`\\left | \\vec{F}_{elettrica} \\right | = \\frac{q_1 \\cdot q_2}{4 \\pi \\cdot \\epsilon_0 \\cdot s^2}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Campo elettrico\">\n <p>\n Misura che forza viene applicata in ogni punto su una carica unitaria:\n </p>\n <p>\n <Latex>{r`\\vec{E} = \\frac{\\vec{F}_{elettrica}}{q} = \\frac{-k \\cdot q}{s^2}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Flusso elettrico\">\n <p>\n È la differenza tra \"quanto\" campo elettrico <Plus>entra</Plus> e quanto campo elettrico <Minus>esce</Minus> da una certa area.\n </p>\n <p>\n In qualsiasi superficie chiusa, il flusso elettrico è uguale alla componente perpendicolare del campo elettrico moltiplicato per l'area.\n </p>\n <p>\n <Latex>{r`\\Phi_E = \\vec{E} \\cdot \\vec{A}`}</Latex>\n </p>\n <p>\n Se il campo elettrico è uniforme, se ne può calcolare facilmente il valore:\n </p>\n <p>\n <Latex>{r`\\Phi_E = \\vec{E} \\cdot \\vec{A} = E_\\perp \\cdot A \\cdot \\cos(\\alpha)`}</Latex>\n </p>\n <p>\n <Todo>Circa. E' una specie di integrale...</Todo>\n </p>\n </Panel>\n <Panel title=\"Legge di Gauss per i campi elettrostatici\">\n <p>\n Il flusso elettrico è direttamente proporzionale alla carica presente all'interno della superficie.\n </p>\n <p>\n <Latex>{r`\\Phi_E = 4 \\pi \\cdot k \\cdot q = \\frac{q}{\\epsilon_0}`}</Latex>\n </p>\n <p>\n Ovvero, i campi elettrostatici sono generati dalle cariche elettriche.\n </p>\n </Panel>\n </Split>\n <Split title=\"Energia elettrica\">\n <Panel title=\"Energia potenziale elettrica\">\n <p>\n Un corpo carico vicino ad altre cariche possiede un'<i>energia potenziale elettrica</i> <Latex>{r`U_e`}</Latex>.\n </p> \n </Panel>\n </Split>\n <Split title=\"Circuiti elettrici\">\n <Panel title={<span>Potenziale elettrico <small>(tensione)</small></span>}>\n <p>\n È il valore dell'energia potenziale elettrica per una carica unitaria.\n </p>\n <p>\n <Latex>{r`V = \\frac{U_e}{q}`}</Latex>\n </p>\n <p>\n La sua unità di misura è il Volt (<Latex>{r`V`}</Latex>).\n </p> \n <p>\n In una batteria è detto <i>forza elettromotrice</i>, e corrisponde al lavoro compiuto da una batteria ideale per spostare una carica unitaria tra i due poli.\n </p>\n </Panel>\n <Panel title={<span>Corrente elettrica <small>(intensità)</small></span>}>\n <p>\n Quanta carica passa attraverso un'area (perpendicolare al flusso) nel tempo.\n </p>\n <p>\n <Latex>{r`I = \\frac{\\Delta q}{\\Delta t}`}</Latex>\n </p>\n <p>\n Fintanto che c'è differenza di potenziale, ci sarà anche intensità non nulla.\n </p>\n <p>\n La sua unità di misura è l'Ampere (<Latex>{r`A`}</Latex>).\n </p>\n </Panel>\n <Panel title={<span>Corrente continua <small>(<abbr title=\"Direct Current\">DC</abbr>)</small></span>}>\n <p>\n Quando in un circuito la direzione della corrente è costante.\n </p>\n </Panel>\n <Panel title={<span>Corrente alternata <small>(<abbr title=\"Alternate Current\">AC</abbr>)</small></span>}>\n <p>\n Quando in un circuito la direzione della corrente si alterna periodicamente.\n </p>\n </Panel>\n <Panel title=\"Potenza elettrica\">\n <p>\n Possiamo calcolare la potenza di un circuito:\n </p>\n <p>\n <Latex>{r`P = \\frac{\\Delta U_e}{\\Delta t} = I \\cdot \\Delta V = I^2 \\cdot R = \\frac{(\\Delta V)^2}{R}`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Elementi di un circuito\">\n <Panel title=\"Resistore\">\n <p>\n Riduce l'intensità di corrente, e converte parte del potenziale in calore.\n </p>\n <p>\n Il potenziale utilizzato è pari a:\n </p>\n <p>\n <Latex>{r`V = R \\cdot I`}</Latex>\n </p>\n <p>\n Dove <Latex>{r`R`}</Latex> è una costante detta <i>resistenza</i> con unità di misura Ohm (<Latex>{r`\\Omega`}</Latex>).\n </p>\n <p>\n La resistenza di un conduttore vale:\n </p>\n <p>\n <Latex>{r`R = \\rho \\frac{L_{unghezza}}{A_{rea}}`}</Latex>\n </p>\n <p>\n <Latex>{r`\\rho`}</Latex> è la <i>resistività</i> del materiale, e varia in base alla temperatura:\n </p>\n <p>\n <Latex>{r`\\rho = \\rho_0 (1 + \\alpha(T - T_0))`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Condensatore\">\n <p>\n Immagazzina potenziale elettrico, permettendo di riutilizzarla in seguito.\n </p>\n <p>\n Per farlo, cattura cariche <Plus>positive</Plus> e <Minus>negative</Minus> sulle sue due armature; perchè questo avvenga, deve essere compiuto lavoro.\n </p>\n <p>\n Ha una <b>capacità</b> caratteristica, che in un condensatore a facce piane parallele è:\n </p>\n <p>\n <Latex>{r`C = \\frac{q_{massima}}{\\Delta V}`}</Latex>\n </p>\n <p>\n Condensatori di capacità maggiore immagazzinano più potenziale con meno carica.\n </p>\n <p>\n La capacità aumenta se viene messo qualcosa tra le armature:\n </p>\n <p>\n <Latex>{r`C_{nuova} = \\kappa \\cdot \\frac{\\epsilon_0 \\cdot A}{s}`}</Latex>\n </p>\n <p>\n Dove <Latex>{r`\\kappa`}</Latex> è la <i>costante dielettrica relativa</i> del materiale inserito, <Latex>{r`A`}</Latex> l'area di una armatura e <Latex>{r`s`}</Latex> la distanza tra le due armature.\n </p>\n <p>\n Se il campo elettrico creatosi tra le due armature supera la <i>rigidità dielettrica</i> del condensatore, la carica immagazzinata viene persa e ha luogo un <i>breakdown</i>.\n </p>\n <p>\n La sua unità di misura è il Farad (<Latex>{r`Fa`}</Latex>)\n </p>\n </Panel>\n <Panel title=\"Amperometro\">\n <p>\n Misura la corrente elettrica se messo in serie.\n </p>\n <p>\n (Funzionamento: ha una resistenza interna bassisima in modo da non influire significativamente sulla corrente.)\n </p>\n </Panel>\n <Panel title=\"Voltmetro\">\n <p>\n Misura la differenza di potenziale se messo in parallelo.\n </p>\n <p>\n (Funzionamento: ha una resistenza altissima in modo da non influire significativamente sulla tensione.)\n </p>\n </Panel>\n </Split>\n <Split title=\"Principi di Kirchhoff\">\n <Panel title=\"Legge dei nodi\">\n <p>\n Per nodo si intende un qualsiasi punto del circuito.\n </p>\n <p>\n Da un nodo entra ed esce la stessa corrente.\n </p>\n </Panel>\n <Panel title=\"Legge delle maglie\">\n <p>\n Per maglia si intende un qualsiasi percorso chiuso all'interno del circuito.\n </p>\n <p>\n In una maglia chiusa, la somma delle differenze di potenziale è 0.\n </p>\n </Panel>\n </Split>\n <Split title=\"Serie e Parallelo\">\n <Panel title=\"Circuito in serie\">\n <p>\n Più parti di circuito sono <i>in serie</i> se sono consecutive e senza biforcazioni.\n </p>\n <p>\n Parti di circuito in serie sono attraversate dalla stessa corrente.\n </p>\n </Panel>\n <Panel title=\"Circuito in parallelo\">\n <p>\n Più parti di circuito sono <i>in parallelo</i> tra loro se hanno lo stesso punto di partenza e lo stesso punto di arrivo. \n </p>\n <p>\n Parti di circuito in parallelo hanno la stessa differenza di potenziale.\n </p>\n </Panel>\n </Split>\n <Split title=\"Resistenze equivalenti\">\n <Panel title=\"Circuiti in serie\">\n <p>\n Nei circuiti in serie, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza della somma di tutte le quelle sostituite:\n </p>\n <p>\n <Latex>{r`R_{serie} = \\sum_{i=1}^{n} R_i`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Circuiti in parallelo\">\n <p>\n Nei circuiti in parallelo, tutte le resistenze possono essere sostituite con una equivalente dalla resistenza di:\n </p>\n <p>\n <Latex>{r`R_{parallelo} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{R_i}}`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Condensatori equivalenti\">\n <Panel title=\"Circuiti in serie\">\n <p>\n Nei circuiti in serie, tutti i condensatori possono essere sostituiti con uno equivalente dalla capacità di:\n </p>\n <p>\n <Latex>{r`C_{serie} = \\frac{1}{\\sum_{i=1}^{n} \\frac{1}{C_i}}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Circuiti in parallelo\">\n <p>\n Nei circuiti in parallelo, tutte i condensatori possono essere sostituite con uno equivalente dalla capacità della somma di tutti quelli sostituiti:\n </p>\n <p>\n <Latex>{r`C_{parallelo} = \\sum_{i=1}^{n} C_n`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Magnetismo\">\n <Panel title=\"Permeabilità magnetica dello spazio vuoto\">\n <p>\n E' una costante fisica fondamentale che rappresenta quanto un materiale si magnetizza facilmente.\n </p>\n <p>\n <Latex>{r`\\mu_0 = 4 \\pi \\cdot 10^{-7} \\frac{H}{m}`}</Latex> (<Latex>{r`\\frac{N}{A^2}`}</Latex>)\n </p>\n </Panel>\n <Panel title=\"Campo magnetico\">\n <p>\n Come un campo elettrico, ma per i magneti.\n </p>\n <p>\n Il suo simbolo è <Latex>{r`B`}</Latex>, e la sua unità di misura è il Tesla (<Latex>T</Latex>).\n </p>\n </Panel>\n <Panel title=\"Flusso magnetico\">\n <p>\n È \"quanto\" campo magnetico <b>attraversa</b> un percorso chiuso.\n </p>\n <p>\n Per qualsiasi percorso chiuso, il flusso magnetico è uguale alla somma di tutti i \"sottoflussi\" magnetici calcolati sui suoi lati.\n </p>\n <p>\n <Latex>{r`\\Phi_{B_{i}} = \\vec{B} \\cdot \\vec{L}_n = B \\cdot L_i \\cdot \\sin(\\alpha) = B_\\parallel \\cdot L_i`}</Latex>\n </p>\n <p>\n <Latex>{r`\\Phi_{B} = \\sum_{i=0}^{n_{lati}} \\Phi_{Bn}`}</Latex>\n </p>\n <p>\n La sua unità di misura è il Weber (<Latex>{r`Wb = T \\cdot m^2`}</Latex>).\n </p>\n </Panel>\n <Panel title=\"Legge di Gauss per i campi magnetici\">\n <p>\n Il flusso magnetico attraverso qualsiasi superficie chiusa è sempre nullo.\n </p>\n <p>\n Ovvero, non esistono monopoli magnetici.\n </p>\n </Panel>\n <Panel title=\"Legge di Ampère\">\n <p>\n L'intensità di corrente che attraversa un percorso chiuso è direttamente proporzionale al flusso magnetico dello stesso percorso.\n </p>\n <p>\n <Latex>{r`\\Phi_B = \\mu_0 \\cdot I`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title=\"Forze magnetiche\">\n <Panel title={<span>Forza magnetica su carica puntiforme <small>(Forza di Lorentz)</small></span>}>\n <p>\n I campi magnetici applicano una forza sulle cariche vicine:\n </p>\n <p>\n <Latex>{r`\\vec{F}_{B} = q \\cdot (\\vec{v} \\times \\vec{B})`}</Latex>\n </p>\n <p>\n Dove <Latex>{r`\\vec{B}`}</Latex> è l'intensità del campo magnetico e <Latex>{r`\\vec{v}`}</Latex> la velocità della carica considerata.\n </p>\n <p>\n Si ha una forza massima se la velocità è perpendicolare al campo magnetico.\n </p>\n <p>\n In un campo magnetico uniforme, una velocità perpendicolare al campo porta alla creazione di un moto circolare uniforme.\n </p>\n </Panel>\n <Panel title=\"Forza magnetica in un filo\">\n <p>\n I campi magnetici influenzano ovviamente anche le cariche presenti in un conduttore:\n </p>\n <p>\n <Latex>{r`\\vec{F}_{magnetica} = I \\cdot (\\vec{L} \\times \\vec{B})`}</Latex> <a href=\"https://it.openprof.com/wb/forza_di_lorentz_su_un_filo_percorso_da_corrente?ch=360\">[1]</a>\n </p>\n <p>\n Dove <Latex>{r`I`}</Latex> è la corrente elettrica, <Latex>{r`\\vec{L}`}</Latex> è un vettore che punta nella direzione di scorrimento della corrente e ha come modulo la lunghezza del conduttore.\n </p>\n </Panel>\n </Split>\n <Split title=\"Campi magnetici\">\n <Panel title=\"Campo magnetico in una spira\">\n <p>\n Una spira in cui passa corrente produce un campo magnetico perpendicolare al piano creato dalla spira.\n </p>\n </Panel>\n <Panel title=\"Campo magnetico di un solenoide\">\n <p>\n Un solenoide sono tante spire avvolte in modo da formare una specie di cilindro.\n </p>\n <p>\n All'interno del solenoide si crea un campo (quasi) uniforme:\n </p>\n <p>\n <Latex>{r`\\left | \\vec{B} \\right | = \\mu_0 \\cdot I \\cdot \\frac{A_{vvolgimenti}}{L_{unghezzafilo}}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Legge di Oersted\">\n <p>\n <i>Caso particolare della <a href=\"https://it.wikipedia.org/wiki/Legge_di_Amp%C3%A8re\">Legge di Ampère</a>.</i>\n </p>\n <p>\n Il modulo del campo magnetico <Latex>B</Latex> prodotto da un filo in cui passa una corrente continua <Latex>I</Latex> alla distanza <Latex>s</Latex> è:\n </p>\n <p>\n <Latex>{r`\\left | \\vec{B} \\right | = \\frac{\\mu \\cdot I}{2 \\pi r}`}</Latex>\n </p>\n <p>\n Il campo magnetico così creato gira attorno al filo in senso antiorario.\n </p>\n <p>\n Due fili attraversati dalla <Plus>stessa corrente</Plus> si attraggono, due fili attraversati da <Plus>corr</Plus><Minus>enti</Minus> <Plus>opp</Plus><Minus>oste</Minus> si respingono.\n </p>\n </Panel>\n </Split>\n <Split title=\"Induzione elettromagnetica\">\n <Panel title=\"Forza elettromotrice indotta\">\n <p>\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 </p>\n <p>\n La differenza di potenziale si crea a causa della forza magnetica, che fa spostare tutti gli elettroni verso un capo del conduttore. \n </p>\n <p>\n Essa vale:\n </p>\n <p>\n <Latex>{r`\\Delta V_{indotta} = v \\cdot B \\cdot L`}</Latex>\n </p>\n <p>\n Dove <Latex>v</Latex> è la velocità del conduttore, <Latex>B</Latex> è l'intensità del campo magnetico ed <Latex>L</Latex> è la lunghezza del conduttore.\n </p>\n </Panel>\n <Panel title=\"Flusso magnetico in una spira\">\n <p>\n In un campo magnetico <Latex>{r`B`}</Latex> uniforme e perpendicolare al piano di una spira di area <Latex>{r`A`}</Latex>, il flusso magnetico si può determinare con la <i>Legge di Faraday-Neumann-Lenz</i>:\n </p>\n <p>\n <Latex>{r`\\Phi_B = \\vec{B} \\cdot \\vec{A} = B \\cdot A \\cdot \\cos(\\alpha)`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title=\"Legge di Faraday-Neumann-Lenz\">\n <p>\n Dice che la forza elettromotrice media indotta in un percorso dipende dalla variazione nel tempo del flusso magnetico nello stesso percorso.\n </p>\n <p>\n <Latex>{r`\\Delta V_{indotta} = - \\frac{\\Delta \\Phi_B}{\\Delta t}`}</Latex>\n </p>\n <p>\n Il meno è dovuto alla <a href=\"https://it.wikipedia.org/wiki/Legge_di_Lenz\">Legge di Lenz</a>, che specifica qualitativamente il verso della forza elettromotrice indotta.\n </p>\n </Panel>\n <Panel title=\"Faraday in un solenoide\">\n <p>\n In un solenoide, la forza elettromotrice indotta è uguale a:\n </p>\n <p>\n <Latex>{r`\\Delta V_{indotta} = - \\frac{N \\cdot \\Delta \\Phi_{B_{spira}}}{\\Delta t} = - \\frac{N \\cdot B \\cdot A \\cdot cos(\\alpha)}{\\Delta t}`}</Latex>\n </p>\n <p>\n Dove <Latex>{r`N`}</Latex> è il numero delle spire del solenoide.\n </p>\n </Panel>\n <Panel title=\"Legge di Ampère-Maxwell\">\n <p>\n Correnti o campi elettrici variabili creano un campo magnetico.\n </p>\n </Panel>\n </Split>\n <Split title=\"Elettromagnetismo\">\n <Panel title=\"Onde elettromagnetiche\">\n <p>\n Nel vuoto, il campo elettrico <Latex>{r`E`}</Latex> e il campo magnetico <Latex>{r`B`}</Latex> sono perpendicolari tra loro e la direzione di propagazione, e sono entrambe funzioni del tempo.\n </p>\n <p>\n Si dice quindi che sono <i>onde elettromagnetiche</i>.\n </p>\n <p>\n Esse sono legate dalla relazione:\n </p>\n <p>\n <Latex>{r`E = c \\cdot B`}</Latex>\n </p>\n <p>\n Dove <Latex>{r`c`}</Latex> è la velocità delle onde (luce) nel vuoto, e a sua volta è uguale a:\n </p>\n <p>\n <Latex>{r`c = \\frac{1}{\\sqrt{\\epsilon_0 \\cdot \\mu_0}} = 3.00 \\cdot 10^8 \\frac{m}{s}`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Formula delle onde\">\n <p>\n <Latex>{r`A(t) = A_{max} \\cdot \\sin \\left ( \\frac{2 \\pi}{\\lambda} - \\omega t + \\phi \\right )`}</Latex>\n </p>\n <p>\n Dove <Latex>{r`A_{max}`}</Latex> è l'ampiezza massima che può avere l'onda, <Latex>{r`\\frac{2 \\pi}{\\lambda} = \\left | \\vec{k} \\right |`}</Latex> è il vettore d'onda, <Latex>{r`\\omega`}</Latex> la frequenza angolare e <Latex>{r`\\phi`}</Latex> la fase.\n </p>\n </Panel>\n </Split>\n <Split title=\"Spettroscopia\">\n <Panel title=\"Emissione\">\n <p>\n I solidi, se portati ad alta temperatura, emettono luce con uno <a href=\"https://it.wikipedia.org/wiki/Spettro_continuo\">spettro continuo</a>.\n </p>\n <p>\n I gas, invece, ad alta temperatura emettono luce solo con particolari lunghezze d'onda. \n </p>\n <p>\n In un gas di idrogeno, le lunghezze d'onda emesse sono ricavabili con:\n </p>\n <p>\n <Latex>{r`\\frac{1}{\\lambda} = R \\left ( \\frac{1}{4} - \\frac{1}{n^2} \\right )`}</Latex>\n </p>\n <p>\n Con <Latex>{r`R = 1.097 \\cdot 10^7 \\frac{1}{m}`}</Latex>, detta costante di Rydberg, e <Latex>{r`n`}</Latex> un numero intero.\n </p>\n </Panel>\n <Panel title=\"Grandezza quantizzata\">\n <p>\n Una grandezza si dice quantizzata (o discreta) se può assumere solo determinati valori. \n </p>\n <p>\n Una grandezza si dice continua se può assumere qualsiasi valore e quindi se non è quantizzata.\n </p>\n <p>\n Energia, momento angolare e raggio sono quantizzati.\n </p>\n <p>\n Nota costante quantica è <Latex>{r`h`}</Latex>, la costante di Planck, ovvero il valore minimo possibile per la carica (talvolta espressa come <Latex>{r`\\hbar = \\left ( \\frac{h}{2 \\pi} \\right )`}</Latex>.\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title=\"Modello di Bohr\">\n <p>\n L'energia degli elettroni è quantizzata.\n </p>\n <p>\n Inoltre, per essi è valido che:\n </p>\n <p>\n <Latex>{r`m \\cdot v_n \\cdot 2 \\pi \\cdot r = n \\cdot h`}</Latex>\n </p>\n <p>\n Ancora, il raggio delle orbite è uguale a:\n </p>\n <p>\n <Latex>{r`r_n = n^2 \\cdot a_0 = n^2 \\cdot \\frac{\\hbar}{m_{elettrone} \\cdot k \\cdot e^2} `}</Latex>\n </p>\n <p>\n Con <Latex>{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`}</Latex>.\n </p>\n <p>\n Infine, in ogni stato, l'energia è pari a:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n <p>\n Due elettroni non possono occupare lo stesso stato.\n </p>\n <p>\n Questo modello funziona solo per atomi con numero atomico basso. Atomi con molti elettroni hanno comportamenti diversi, descritti dal modello di\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title=\"Nei solidi\">\n <p>\n Nei solidi, le lunghezze d'onda sono talmente tanto vicine da poter essere considerate una banda.\n </p>\n <p>\n Possono però comunque avere dei gap dovuti agli intervalli di energia non ammessi.\n </p>\n </Panel>\n </Split>\n <Split title=\"Semiconduttori\">\n <Panel title=\"Semiconduttori\">\n <p>\n <Todo>Refactor this</Todo>\n </p>\n <p>\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 <Latex>{r`10^1 eV`}</Latex>, allora il corpo è un isolante.\n </p>\n <p>\n Se invece la banda di emissione si sovrappone a un altra, allora il corpo è un conduttore.\n </p>\n <p>\n Se il gap è invece dell'ordine di grandezza di <Latex>{r`1 eV`}</Latex>, allora il corpo è un semiconduttore.\n </p>\n </Panel>\n <Panel title=\"Lacune\">\n <p>\n Legami in cui <Plus>mancano elettroni</Plus>.\n </p>\n <p>\n <Minus>Elettroni</Minus> di altri legami possono spostarsi per colmare le <Plus>lacune</Plus>, creandone altre, e spostandole in direzione opposta a quella della corrente.\n </p>\n </Panel>\n <Panel title=\"Accettori e donori\">\n <p>\n Se si inserisce in un cristallo semiconduttore si inserisce un atomo con numero atomico diverso, si otterrà:\n </p>\n <ul>\n <li>Con numero atomico maggiore, un semiconduttore di <Minus>tipo N</Minus> con <Minus>elettroni in eccesso</Minus> liberi di scorrere.</li>\n <li>Con numero atomico minore, un semiconduttore di <Plus>tipo P</Plus> con <Plus>lacune in eccesso</Plus> libere di catturare elettroni da altri legami.</li>\n </ul>\n <p>\n Maggiore impurezza porta a maggiore conduttività.\n </p>\n </Panel>\n <Panel title=\"Temperatura\">\n <p>\n Aumentando la temperatura di un semiconduttore si aumenta la conduttività, perchè eccita le particelle e favorisce il movimento di <Minus>elettroni</Minus> e <Plus>lacune</Plus>.\n </p>\n </Panel>\n </Split>\n <Split title={<span>Ottica <small>(non l'abbiamo fatta)</small></span>}>\n <Panel title=\"Assorbimento e riflessione\">\n <p>\n I corpi possono assorbire o riflettere le onde elettromagnetiche che li colpiscono.\n </p>\n </Panel>\n <Panel title=\"Corpo nero\">\n <p>\n Un corpo nero è un corpo che assorbe tutte le onde elettromagnetiche che riceve senza rifletterne nessuna.\n </p>\n <p>\n Le onde assorbite vengono poi riemesse sotto forma di un onda di <Latex>{r`\\lambda`}</Latex> variabile in base alla temperatura.\n </p>\n <p>\n <Latex>{r`\\lambda_{max} \\cdot T`}</Latex> è costante.\n </p>\n </Panel>\n <Panel title=\"Teoria di Planck per il corpo nero\">\n <p>\n L'energia assorbita e emessa dai corpi neri è quantizzata.\n </p>\n </Panel>\n <Panel title=\"Fotone\">\n <p>\n Un onda magnetica con un quanto di energia è detta <i>fotone</i>:\n </p>\n <p>\n <Latex>{r`E_{fotone} = h \\cdot f`}</Latex>\n </p>\n </Panel>\n <Panel title=\"Effetto fotoelettrico\">\n <p>\n A volte, i fotoni che colpiscono un metallo possono estrarvi degli elettroni e creare una differenza di potenziale.\n </p>\n <p>\n Perchè avvenga, la frequenza deve essere maggiore di una certa soglia.\n </p>\n <p>\n Il numero di elettroni estratti dipende dall'intensità dell'onda, mentre l'energia cinetica degli elettroni dipende dalla frequenza.\n </p>\n <p>\n Non c'è nessun ritardo tra l'assorbimento del fotone e l'estrazione di elettroni.\n </p>\n </Panel>\n </Split>\n </div>\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 <div style={style.markdown} dangerouslySetInnerHTML={{__html: html}}></div>;\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<div style={style.vldigeometria}>\r\n <h1>Videolezioni di Geometria</h1>\r\n <Panel>\r\n <Markdown>{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 `}</Markdown>\r\n </Panel>\r\n\t\t\t</div>\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<div style={style.mingwinstall}>\r\n <h1>Come installare MinGW</h1>\r\n <Panel>\r\n\t\t\t\t\t<p> Scaricate <a href=\"https://osdn.net/projects/mingw/downloads/68260/mingw-get-setup.exe/\">l'installer ufficiale</a>,\r\n\t\t\t\t\t\ted eseguitelo.</p><img src=\"https://i.imgur.com/mDZSqjV.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> Dovrebbe comparire questa schermata. Cliccate su <code>Install</code>, poi scegliete una cartella di installazione\r\n\t\t\t\t\t\t(ricordatevela!) e poi <code>Continue</code>. Lasciate stare le altre opzioni, dovrebbero essere tutte spuntate,\r\n\t\t\t\t\t\ttranne <code>For all users</code>, che dovrebbe essere disattivato.</p><img src=\"https://i.imgur.com/brdw8Xy.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> Aspettate che finisca il download. Pochi secondi dopo, dovrebbe finire e dovrebbe apparire un tasto\r\n\t\t\t\t\t\t<code>Continue</code>. Premetelo.</p><img src=\"https://i.imgur.com/aPTwrxz.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> Dovrebbe apparirvi questa finestra. L'installer di MinGW è una specie di gestore pacchetti (tipo <code>apt</code> su\r\n\t\t\t\t\t\tUbuntu); potete scegliere quali pacchetti installare, e quindi quali funzionalità.</p><img src=\"https://i.imgur.com/5QLSkFN.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> Nel nostro caso, dovrebbero servirci <code>mingw32-base-bin</code> (per il C e alcune librerie C++) e\r\n\t\t\t\t\t\t<code>mingw32-gcc-g++-bin</code> (per il C++). Cliccate, quindi, sui due quadratini corrispondenti, e premete\r\n\t\t\t\t\t\t<code>Mark for Installation</code>. Dovrebbe comparire una freccia gialla sul quadratino.</p><img src=\"https://i.imgur.com/zP74nks.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> Ora, è il momento di installare i pacchetti. Aprite il menù <code>Installation</code>, poi premete\r\n\t\t\t\t\t\t<code>Apply Changes</code>, e di nuovo <code>Apply</code>.</p><img src=\"https://i.imgur.com/jp4uz5B.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> 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.</p><img src=\"https://i.imgur.com/Lq9IepY.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> Una volta installato, dobbiamo aggiungere <code>g++</code> ai programmi eseguibili da Prompt dei Comandi: premete il\r\n\t\t\t\t\t\ttasto <kbd>Windows</kbd>, e scrivete <code>PATH</code>. Windows dovrebbe trovarvi automaticamente quell'opzione.</p>\r\n\t\t\t\t\t<img src=\"https://i.imgur.com/dy3b5Ub.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> Dentro la finestra di <i>Proprietà del Sistema</i>, premete <code>Variabili d'ambiente</code>.</p><img src=\"https://i.imgur.com/FjYpT1n.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> Trovate la variabile d'ambiente globale <code>Path</code>, e fateci doppio click per modificarla.</p><img src=\"https://i.imgur.com/klZQ9So.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> 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 <code>Sfoglia</code>.</p><img src=\"https://i.imgur.com/F6lBCqS.png\" alt=\"\"/>\r\n\t\t\t\t\t<p> 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 <code>bin</code> e premete <code>OK</code> su tutte le finestre che avete aperto fino ad ora,\r\n\t\t\t\t\t\tchiudendole.</p>\r\n\t\t\t\t\t<p> Complimenti! Avete installato MinGW e potete compilare programmi C e C++ da Windows! Avete a disposizione\r\n\t\t\t\t\t\t<code>gcc</code> e <code>g++</code> sul Prompt dei Comandi, e potete finalmente creare dei file .exe! </p>\r\n\t\t\t\t</Panel>\r\n\t\t\t</div>\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 <div class={style.copyright}>© 2019 - Stefano Pigozzi - <a href=\"https://creativecommons.org/licenses/by-sa/4.0/\">CC BY-SA 4.0</a> - <a href=\"https://github.com/Steffo99/appuntiweb\">Codice sorgente</a></div>;\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 <div class={style.hypothesis}>\r\n <h4>\r\n Ipotesi\r\n </h4>\r\n {this.props.children}\r\n </div>\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 <div class={style.thesis}>\r\n <h4>\r\n Tesi\r\n </h4>\r\n {this.props.children}\r\n </div>\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 <div class={style.proof}>\r\n <h4>\r\n Dimostrazione\r\n </h4>\r\n {this.props.children}\r\n </div>\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 <blockquote class={style.example}>\n {this.props.children}\n </blockquote>\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 <Split title={\"Popolazioni\"}>\n <Panel title={\"Popolazione\"} id={\"popolazione\"}>\n <p>\n Gruppo <b>intero</b> di oggetti di cui si cercano informazioni.\n </p>\n </Panel>\n <Panel title={\"Popolazione tangibile\"}>\n <p>\n Popolazione finita di oggetti concreti che possono essere campionati ciascuno solo una volta.\n </p>\n </Panel>\n <Panel title={\"Popolazione concettuale\"}>\n <p>\n Popolazione di valori ottenuti da prove sperimentali indipendenti ripetute più volte.\n </p>\n </Panel>\n </Split>\n <Split title={\"Campionamento\"}>\n <Panel title={\"Campione\"}>\n <p>\n Sottoinsieme della <a href={\"#popolazione\"}>popolazione</a> che contiene gli oggetti che si sono osservati.\n </p>\n </Panel>\n <Panel title={<i>Simple random sample</i>}>\n <p>\n Campione di una data dimensione in cui qualsiasi selezione di <i>n</i> elementi ha la stessa probabilità di costituire il campione.\n </p>\n </Panel>\n <Panel title={<i>Sample of convenience</i>}>\n <p>\n Campione ottenuto in un modo casuale non ben definito.\n </p>\n </Panel>\n <Panel title={<i>Sample with replacement</i>}>\n <p>\n Campione ottenuto sostituendo nella popolazione gli elementi estratti con dei nuovi elementi.\n </p>\n <p>\n Dire che un campione è ottenuto <i>with replacement</i> è equivalente a dire che la popolazione che si sta campionando è infinita, e quindi che tutti gli elementi sono indipendenti.\n </p>\n </Panel>\n <Panel title={\"Campione pesato\"}>\n <p>\n Campione ottenuto da una popolazione in cui certi elementi hanno più probabilità di essere stati selezionati di altri.\n </p>\n </Panel>\n <Panel title={<i>Stratified random sample</i>}>\n <p>\n Campione ottenuto da un sottoinsieme della popolazione detto <i>strato</i>.\n </p>\n </Panel>\n <Panel title={<i>Cluster sample</i>}>\n <p>\n Campione ottenuto selezionando più <i>cluster</i> di elementi alla volta.\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title={<i>Sampling variation</i>}>\n <p>\n Differenza di informazioni presente tra due campioni diversi della stessa popolazione.\n </p>\n </Panel>\n <Panel title={\"Indipendenza\"}>\n <p>\n Gli elementi in un campione sono indipendenti se gli elementi estratti in precedenza non influsicono <small>significativamente</small> sulle probabilità di estrazione dell'elemento successivo.\n </p>\n </Panel>\n </Split>\n <Split title={\"Tipi di prove sperimentali\"}>\n <Panel title={\"A campione singolo\"}>\n <p>\n Esperimento in cui c'è una sola popolazione da cui vengono estratti campioni.\n </p>\n <p>\n Serve per verificare delle condizioni.\n </p>\n </Panel>\n <Panel title={\"Multicampione\"}>\n <p>\n Esperimento in cui sono presenti più popolazioni (aventi caratteristiche differenti una dall'altra dette <i>fattori</i>) da cui vengono estratti campioni.\n </p>\n <p>\n Serve per capire quali fattori influenzano il risultato dell'esperimento.\n </p>\n </Panel>\n </Split>\n <Split title={\"Tipi di dato\"}>\n <Panel title={<span>Numerico<small> o quantitativo</small></span>}>\n Il dato descrive un valore numerico relativo all'elemento, come ad esempio una quantità fisica.\n </Panel>\n <Panel title={<span>Categorico<small> o qualitativo</small></span>}>\n Il dato indica una categoria a cui appartiene l'elemento, come ad esempio il suo colore.\n </Panel>\n </Split>\n\t */\n return (\n <div style={style.statistica}>\n <h1>Statistica ed Elementi di Probabilità</h1>\n <Split title={\"Tipi di probabilità\"}>\n <Panel title={\"Classica\"}>\n <p>\n <Latex>{r`P(E) = \\frac{casi\\ favorevoli}{casi\\ possibili}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Frequentista\"}>\n <p>\n <Latex>{r`P(E) = \\frac{successi}{prove\\ totali}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Soggettiva\"}>\n <p>\n Il prezzo che un individuo coerente riterrebbe equo per ricevere <b>1</b> nel caso l'evento si verificasse e <b>0</b> nel caso l'evento non si verificasse.\n </p>\n </Panel>\n </Split>\n <Split title={\"Linguaggio matematico\"}>\n <Panel title={\"Spazio campionario\"}>\n <blockquote>\n \"omegone\"\n </blockquote>\n <p>\n L'<b>insieme</b> di tutti gli esiti possibili di un esperimento.\n </p>\n <p>\n <Latex>{r`\\Omega = \\left \\{ 1, 2, 3, 4, 5, 6 \\right \\}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Esito\"}>\n <blockquote>\n \"omeghino\"\n </blockquote>\n <p>\n Un <b>elemento</b> dello spazio campionario.\n </p>\n <p>\n <Latex>{r`\\omega = 1`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Evento\"}>\n <blockquote>\n \"e\"\n </blockquote>\n <p>\n Un <b>sottoinsieme</b> dello spazio campionario.\n </p>\n <p>\n <Latex>{r`E = \\left \\{ 1, 2 \\right \\}`}</Latex>\n </p>\n <p>\n Lo spazio campionario stesso è un <b>evento certo</b>.\n </p>\n </Panel>\n <Panel title={\"Not\"}>\n <blockquote>\n \"not e\"\n </blockquote>\n <p>\n Il <b>complementare</b> di un sottoinsieme.\n </p>\n <p>\n <Latex>{r`\\bar{E} = \\left \\{ 3, 4, 5, 6 \\right \\}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"And\"}>\n <blockquote>\n \"e intersecato effe\"\n </blockquote>\n <p>\n L'<b>intersezione</b> di più sottoinsiemi.\n </p>\n <p>\n <Latex>{r`E \\cap F = \\left \\{ 1 \\right \\}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Or\"}>\n <blockquote>\n \"e unito a effe\"\n </blockquote>\n <p>\n L'<b>unione</b> di più sottoinsiemi.\n </p>\n <p>\n <Latex>{r`E \\cup F = \\left \\{ 1, 2, 3, 4 \\right \\}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Differenza\"}>\n <blockquote>\n \"e meno effe\"\n </blockquote>\n <p>\n <Latex>{r`E \\setminus F = E \\cap \\bar{F}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Implicazione\"}>\n <blockquote>\n \"e contenuto in effe\"\n </blockquote>\n <p>\n L'<b>inclusione</b> del primo insieme in un altro.\n </p>\n <p>\n <Latex>{r`E \\subseteq F`}</Latex>\n </p>\n <p>\n Se si verifica <Latex>E</Latex>, allora si verifica anche <Latex>F</Latex>.\n </p>\n </Panel>\n <Panel title={\"Evento impossibile\"}>\n <blockquote>\n \"e è impossibile\"\n </blockquote>\n <p>\n Un sottoinsieme <b>vuoto</b>.\n </p>\n <p>\n <Latex>{r`E = \\emptyset`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Mutua esclusione\"}>\n <blockquote>\n \"e ed effe si escludono mutualmente\"\n </blockquote>\n <p>\n La <b>disgiunzione</b> di due insiemi.\n </p>\n <p>\n <Latex>{r`E \\cap F = \\emptyset`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title={\"Famiglia degli eventi\"}>\n <blockquote>\n \"famiglia effe\"\n </blockquote>\n <p>\n I sottoinsiemi dello spazio campionario formano una <b>famiglia</b> di sottoinsiemi detta <i>famiglia degli eventi</i>.\n </p>\n <p>\n <Latex>{r`\\mathcal{F}`}</Latex>\n </p>\n <p>\n Qualsiasi sottoinsieme appartenente a <Latex>{r`\\mathcal{F}`}</Latex> è considerato un evento.\n </p>\n </Panel>\n <Panel title={<span><Latex>{r`\\sigma`}</Latex>-algebra</span>}>\n <blockquote>\n \"sigma algebra\"\n </blockquote>\n <p>\n Se la famiglia degli eventi soddisfa questi tre requisiti, allora viene detta <i><Latex>{r`\\sigma`}</Latex>-algebra</i>:\n </p>\n <ol>\n <li>\n Lo spazio campionario è un evento: <Latex>{r`\\Omega \\in \\mathcal{F}`}</Latex>\n </li>\n <li>\n Se un sottoinsieme è un evento, allora anche il suo complementare lo è: <Latex>{r`E \\in \\mathcal{F} \\implies \\bar{E} \\in \\mathcal{F}`}</Latex>\n </li>\n <li>\n Se due sottoinsiemi sono eventi, allora lo sono anche la loro unione e intersezione: <Latex>{r`(E, F) \\in \\mathcal{F} \\implies (E \\cup F, E \\cap F) \\in \\mathcal{F}`}</Latex>\n </li>\n </ol>\n <p>\n Un esempio: <Latex>{r`E \\in \\mathcal{F} \\implies \\mathcal{F} = \\{ \\emptyset, E, \\bar{E}, \\Omega \\}`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title={\"Partizione\"}>\n <blockquote>\n \"la partizione e composta da e uno, e due, e tre...\"\n </blockquote>\n <p>\n Un insieme di esiti e eventi:\n </p>\n <ul>\n <li><b>Finito</b>.</li>\n <li>In cui tutti gli eventi hanno <b>probabilità diversa da 0</b>.</li>\n <li>In cui tutti gli eventi sono <b>mutualmente esclusivi</b>.</li>\n <li>In cui l'unione di tutti i suoi elementi <b>copre lo spazio campionario</b>.</li>\n </ul>\n <p>\n La partizione <Latex>{r`E_i`}</Latex> è composta dagli eventi <Latex>{r`E_1`}</Latex>, <Latex>{r`E_2`}</Latex>, <Latex>{r`E_3`}</Latex>, fino a <Latex>{r`E_n`}</Latex>.\n </p>\n <Example>\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 </Example>\n </Panel>\n </Split>\n <Split title={\"Assiomi della probabilità\"}>\n <Panel title={\"Primo assioma della probabilità\"}>\n <p>\n La probabilità di un evento è un numero tra 0 e 1.\n </p>\n <p>\n <Latex>{r`\\forall E \\in \\mathcal{F}, 0 \\leq P(E) \\leq 1`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Secondo assioma della probabilità\"}>\n <p>\n La probabilità dello spazio campionario è sempre 1.\n </p>\n <p>\n <Latex>{r`P(\\Omega) = 1`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Terzo assioma della probabilità\"}>\n <p>\n La probabilità dell'unione di eventi indipendenti è uguale alla somma delle loro probabilità.\n </p>\n <p>\n <Latex>{r`P \\left ( \\bigcup_i E_i \\right ) = \\sum_i P ( E_i )`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Conseguenze degli assiomi\"}>\n <Panel title={\"Probabilità di un evento negato\"}>\n <p>\n La probabilità di un evento negato è uguale a 1 meno la probabilità dell'evento non negato.\n </p>\n <p>\n <Latex>{r`P(\\bar{E}) = 1 - P({E})`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Probabilità di un evento incluso\"}>\n <p>\n La probabilità di un evento incluso in un altro è sempre minore o uguale alla probabilità dell'evento in cui è incluso.\n </p>\n <p>\n <Latex>{r`F \\subseteq E \\implies P(F) \\leq P(E)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Unione\"}>\n <p>\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 </p>\n <p>\n <Latex>{r`P(E \\cup F) = P(E) + P(F) - P(E \\cap F)`}</Latex>\n </p>\n <Example>\n Sommando le probabilità dei due eventi, l'intersezione viene contata due volte, e va quindi rimossa!\n </Example>\n </Panel>\n </Split>\n <Split title={\"Spazi equiprobabili\"}>\n <Panel title={\"Cosa sono?\"}>\n <p>\n Spazi campionari in cui ci sono un numero finito di esiti e ogni esito ha la stessa probabilità di verificarsi.\n </p>\n <p>\n <Latex>{r`P(E) = \\frac{len(E)}{len(\\Omega)}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Spazi equiprobabili geometrici\"}>\n <p>\n Gli spazi campionari possono avere un numero infinito di esiti: sono <i>equiprobabili geometrici</i> se nessun esito è privilegiato rispetto agli altri.\n </p>\n </Panel>\n </Split>\n <Split title={\"Calcolo combinatorio\"}>\n <Panel title={\"Disposizioni\"}>\n <p>\n Estraggo un numero, da un sacchetto con <Latex>n</Latex> numeri, mi segno che numero ho estratto e lo <b>tengo fuori dal sacchetto</b>. Ripeto per <Latex>k</Latex> volte.\n </p>\n <p>\n <b>Tengo conto</b> dell'ordine in cui ho estratto i numeri.\n </p>\n <p>\n <Latex>{r`\\boldsymbol{D}_{n, k} = \\frac{n!}{(n - k)!}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Disposizioni con ripetizione\"}>\n <p>\n Estraggo un numero, da un sacchetto con <Latex>n</Latex> numeri, mi segno che numero ho estratto e lo <b>rimetto nel sacchetto</b>. Ripeto per <Latex>k</Latex> volte.\n </p>\n <p>\n <b>Tengo conto</b> dell'ordine in cui ho estratto i numeri.\n </p>\n <p>\n <Latex>{r`\\boldsymbol{D}^{r}_{n, k} = n^k`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Combinazioni\"}>\n <p>\n Estraggo un numero, da un sacchetto con <Latex>n</Latex> numeri, mi segno che numero ho estratto e lo <b>tengo fuori dal sacchetto</b>. Ripeto per <Latex>k</Latex> volte.\n </p>\n <p>\n <b>Non mi interessa</b> l'ordine in cui ho estratto i numeri.\n </p>\n <p>\n <Latex>{r`\\boldsymbol{C}_{n, k} = \\binom{n}{k} = \\frac{n!}{(k)! \\cdot (n - k)!}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Combinazioni con ripetizione\"}>\n <p>\n Estraggo un numero, da un sacchetto con <Latex>n</Latex> numeri, mi segno che numero ho estratto e lo <b>rimetto nel sacchetto</b>. Ripeto per <Latex>k</Latex> volte.\n </p>\n <p>\n <b>Non mi interessa</b> l'ordine in cui ho estratto i numeri.\n </p>\n <p>\n <Latex>{r`\\boldsymbol{C}^{r}_{n, k} = \\binom{n + k - 1}{k} = \\frac{(n + k - 1)!}{(k)! \\cdot (n - 1)!}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Permutazioni\"}>\n <p>\n Estraggo <Latex>n</Latex> numeri e guardo in quanti ordini diversi li posso mettere.\n </p>\n <p>\n <Latex>{r`\\boldsymbol{P}_n = n!`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Probabilità condizionata\"}>\n <Panel title={\"Eventi condizionati\"}>\n <blockquote>\n \"E dato F\"\n </blockquote>\n <p>\n La probabilità che si verifichi <Latex>E</Latex> sapendo che <b>si è già verificato</b> <Latex>F</Latex>.\n </p>\n <p>\n <Latex>{r`P(E|F) = \\frac{P(E \\cap F)}{P(F)}`}</Latex>\n </p>\n <Example>\n Ricorda vagamente le pipe di <code>bash</code>, però al contrario...\n </Example>\n </Panel>\n <Panel title={\"Eventi mutualmente esclusivi\"}>\n <p>\n Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0.\n </p>\n <p>\n <Latex>{r`E \\cap F = \\emptyset \\Longleftrightarrow P(E|F) = P(F|E) = 0`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title={\"Regola della catena\"}>\n <p>\n Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:\n </p>\n <p>\n <Latex>{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})`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Le alternative\"}>\n <Panel title={\"Legge delle alternative\"}>\n <p>\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 </p>\n <p>\n <Latex>{r`P(F) = \\sum_{i} P(F|E_i) \\cdot P(E_i)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Legge condizionata delle alternative\"}>\n <p>\n La legge delle alternative funziona anche quando ad essere partizionato è un <b>evento</b>:\n </p>\n <p>\n <Latex>{r`P(F|G) = \\sum_i P(F|E_i \\cap G) \\cdot P(E_i | G)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Formula di Bayes\"}>\n <p>\n Tramite la <i>formula di Bayes</i> possiamo risalire alla probabilità di un evento condizionato a un altro partendo dalla probabilità di quest'ultimo condizionato al primo:\n </p>\n <p>\n <Latex>{r`P(E_h | F) = \\frac{P(F | E_h) \\cdot P(E_h)}{P(F)}`}</Latex>\n </p>\n <Example>\n In pratica, invertiamo gli eventi.\n </Example>\n </Panel>\n </Split>\n <Split title={\"Eventi indipendenti\"}>\n <Panel title={\"Due eventi indipendenti\"}>\n <blockquote>\n \"eventi indipendenti a due a due\"\n </blockquote>\n <p>\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 </p>\n <p>\n <Latex>{r`P(E \\cap F) = P(E) \\cdot P(F) \\Longleftrightarrow P(E|F) = P(E) \\Longleftrightarrow P(F|E) = P(F)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Più eventi indipendenti\"}>\n <blockquote>\n \"eventi indipendenti a tre a tre, a quattro a quattro, a cinque a cinque...\"\n </blockquote>\n <p>\n Si può verificare l'indipendenza di più eventi alla volta:\n </p>\n <p>\n <Latex>{r`P(E \\cap F \\cap G) = P(E) \\cdot P(F) \\cdot P(G)`}</Latex>\n </p>\n <p>\n Eventi indipendenti a due a due non sono per forza indipendenti a tre a tre, e viceversa.\n </p>\n </Panel>\n <Panel title={\"Famiglia di eventi indipendenti\"}>\n <p>\n Un insieme di <Latex>n</Latex> eventi è una <i>famiglia di eventi indipendenti</i> se, preso un qualsiasi numero di eventi da essa, essi risulteranno indipendenti.\n </p>\n <Example>\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 </Example>\n </Panel>\n </Split>\n <Split title={\"Variabili aleatorie\"}>\n <Panel title={\"Variabile aleatoria\"}>\n <p>\n Una funzione che fa corrispondere un numero reale a ogni possibile esito dello spazio campionario. <Latex>{r`X(\\omega) : \\Omega \\to \\mathbb{R}`}</Latex>.\n </p>\n </Panel>\n <Panel title={<abbr title={\"Nome artigianale dato da Steffo.\"}>Insieme di ripartizione</abbr>}>\n <p>\n Ad ogni variabile aleatoria sono associati gli eventi <Latex>{r`A_t = \\{ \\omega | X(\\omega) \\leq t \\}`}</Latex>, che contengono tutti gli esiti a cui la variabile aleatoria associa un valore minore o uguale a <Latex>t</Latex>.\n </p>\n <p>\n Per definizione, tutte le variabili aleatorie devono rispettare questa condizione:\n </p>\n <p>\n <Latex>{r`\\forall t \\in \\mathbb{R}, A_t \\in \\mathcal{F}`}</Latex>\n </p>\n <Example>\n All'aumentare di t, l'insieme conterrà sempre più elementi.\n </Example>\n </Panel>\n <Panel title={\"Supporto\"}>\n <blockquote>\n \"supporto di X\"\n </blockquote>\n <p>\n Il <b>codominio</b> della variabile aleatoria è il suo <i>supporto</i>.\n </p>\n <p>\n Per indicare che un valore <Latex>x_0</Latex> appartiene al supporto di <Latex>X</Latex>, si usa la notazione <Latex>X \\mapsto x_0</Latex>.\n </p>\n </Panel>\n </Split>\n <Split title={\"Densità\"}>\n <Panel title={\"Funzione probabilità\"}>\n <p>\n La <i>funzione probabilità</i> <Latex>{r`p_X : X \\to [0, 1]`}</Latex> di una variabile aleatoria <b>discreta</b> <Latex>X</Latex> è la funzione che associa ad ogni esito la sua probabilità:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Funzione densità\"}>\n <p>\n La <i>funzione densità</i> <Latex>{r`f_X : X \\to [0, 1]`}</Latex> di una variabile aleatoria <b>continua</b> <Latex>X</Latex> è l'equivalente continuo della funzione probabilità:\n </p>\n <p>\n <Latex>{r`P([a < X \\leq b]) = \\int_a^b f_X (x) dx`}</Latex>\n </p>\n <p>\n A differenza della funzione probabilità, è possibile che la funzione densità <b>non esista</b> per una certa variabile aleatoria.\n </p>\n <Example>\n Rappresenta \"quanta\" probabilità c'è in un'unità di x!\n </Example>\n </Panel>\n </Split>\n <Split title={\"Funzione di ripartizione\"}>\n <Panel title={\"Definizione\"}>\n <p>\n Ogni variabile aleatoria ha una <i>funzione di ripartizione</i> <Latex>{r`F_X : \\mathbb{R} \\to [0, 1]`}</Latex> associata, che rappresenta la probabilità che la variabile aleatoria assuma un valore minore o uguale a <Latex>t</Latex>:\n </p>\n <p>\n Si può dire che essa rappresenti la probabilità dell'evento <Latex>{r`A_t`}</Latex>:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Proprietà della funzione\"}>\n <ul>\n <li>È sempre <b>monotona crescente</b> (non strettamente).</li><br/>\n <li>Vale <b>0</b> a <Latex>-\\infty</Latex> e <b>1</b> a <Latex>+\\infty</Latex>.</li><br/>\n <li>È <b>continua da destra</b>: <Latex>{r`\\forall x_0 \\in \\mathbb{R}, F_X (x_0) = \\lim_{t \\to x^+_0} F_X (t)`}</Latex></li>\n </ul>\n </Panel>\n <Panel title={\"Probabilità di un valore\"}>\n <p>\n Possiamo usare la funzione di ripartizione per calcolare la probabilità di un certo valore reale:\n </p>\n <p>\n <Latex>{r`P([X = x_0]) = \\lim_{t \\to x^+_0} F_X (t) - \\lim_{t \\to x^-_0} F_X (t)`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Trasformazioni di variabili aleatorie\"}>\n <Panel title={\"Nel discreto\"}>\n <p>\n Nel discreto basta abbinare un nuovo valore a ogni valore della variabile originale.\n </p>\n </Panel>\n <Panel title={\"Nel continuo (invertibile)\"}>\n <p>\n Nel continuo applichiamo la formula dell'integrazione per sostituzione:\n </p>\n <p>\n <Latex>{r`f_Y (y) = \\int_{g(a)}^{g(b)} f_X ( g^{-1} (x) ) g^{-2} (x)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Nel... digitale\"}>\n <p>\n Trasformare variabili aleatorie è molto utile nell'informatica per creare distribuzioni partendo da una funzione <a href={\"https://docs.python.org/3/library/random.html#random.random\"}><code>random()</code></a> che restituisce numeri da 0 a 1 con una distribuzione lineare.\n </p>\n </Panel>\n </Split>\n <Split title={\"Informazioni delle variabili aleatorie\"}>\n <Panel title={\"Media\"}>\n <p>\n Ogni variabile aleatoria che ha una <b>funzione di ripartizione</b> e un <b>supporto finito</b> ha anche una <i>media</i> (o <i>valore medio</i> o <i>atteso</i>):\n </p>\n <p>\n <Latex>{r`E(X) = \\int_0^{+infty} (1 - F_X (t)) dt - \\int_{-\\infty}^{0} F_X (t) dt`}</Latex>\n </p>\n <p>\n Nel discreto, si può calcolare con:\n </p>\n <p>\n <Latex>{r`E(X) = \\sum_i P(X = x_i) \\cdot x_i`}</Latex>\n </p>\n <p>\n Nel continuo, si può calcolare con:\n </p>\n <p>\n <Latex>{r`E(X) = \\int_{-\\infty}^{+\\infty} f_X (x) \\cdot x \\cdot dx`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title={\"Moda\"}>\n <p>\n Valore per cui la <b>funzione probabilità</b> o <b>funzione densità</b> è <b>massima</b>.\n </p>\n </Panel>\n <Panel title={\"Quantili\"}>\n <p>\n Il <i>quantile</i> <Latex>{r`x_{\\alpha}`}</Latex> di ordine <Latex>{r`0 \\leq \\alpha \\leq 1`}</Latex> della variabile aleatoria <Latex>X</Latex> è il più piccolo numero tale che:\n </p>\n <p>\n <Latex>\n {r`P([X < x_{\\alpha}]) \\leq \\alpha \\leq P([X \\leq x_{\\alpha}])`}\n </Latex>\n </p>\n <p>\n\n </p>\n <p>\n Il quantile di ordine 0.5 <Latex>{r`x_{0.5}`}</Latex> è detto <i>mediana</i>.\n </p>\n <p>\n I quantili di ordine 0.25 <Latex>{r`x_{0.25}`}</Latex> e 0.75 <Latex>{r`x_{0.75}`}</Latex> sono detti <i>quartili</i>.\n </p>\n <p>\n I quantili di ordine <Latex>{r`\\frac{n}{100}`}</Latex> sono detti <i><Latex>n</Latex>-esima percentile</i>.\n </p>\n </Panel>\n <Panel title={\"Varianza\"}>\n <p>\n È un valore che indica quanto la variabile aleatoria si discosta generalmente dalla media:\n </p>\n <p>\n <Latex>{r`Var(X) = E( (X - E(X) )^2 ) = E ( X^2 ) - (E(X))^2`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Disuguaglianze notevoli\"}>\n <Panel title={\"Disuguaglianza di Markov\"}>\n <p>\n Data una variabile aleatoria non-negativa:\n </p>\n <p>\n <Latex>{r`\\forall k > 0, P([X \\geq k]) \\leq \\frac{E(X)}{k}`}</Latex>\n </p>\n <p>\n Divide in due parti (<Latex>{r`P(X < k)`}</Latex> e <Latex>{r`P(X \\geq k)`}</Latex>) la funzione X, la cui media risulterà uguale a:\n </p>\n <p>\n <Latex>{r`E(X) = \\overline{k} \\cdot P(X < k) + k \\cdot P(X \\geq k)`}</Latex>\n </p>\n <p>\n <Todo>TODO: Ha senso questa minidimostrazione?</Todo>\n </p>\n </Panel>\n <Panel title={\"Disuguaglianza di Čebyšëv\"}>\n <blockquote>\n \"disuguaglianza di cebicev\"\n </blockquote>\n <p>\n Se la variabile aleatoria <Latex>X</Latex> ha media e varianza, allora la probabilità che essa abbia un valore a più di <Latex>{r`\\epsilon`}</Latex> di distanza dal valore medio è minore o uguale a <Latex>{r`\\frac{Var(X)}{\\epsilon^2}`}</Latex>.\n </p>\n <p>\n <Latex>{r`\\forall \\epsilon > 0, P([ \\left| X - E(X) \\right| \\geq \\epsilon]) \\leq \\frac{Var(X)}{\\epsilon^2}`}</Latex>\n </p>\n <Example>\n Serve per semplificare i calcoli quando la funzione di ripartizione è difficile da calcolare!\n </Example>\n </Panel>\n </Split>\n <Split title={\"Un momento...!\"}>\n <Panel title={\"Momento\"}>\n <p>\n Il <i>momento</i> <Latex>k</Latex>-esimo di una variabile aleatoria è:\n </p>\n <p>\n <Latex>\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 </Latex>\n </p>\n <Example>\n La media di una variabile aleatoria è anche il suo primo momento.\n </Example>\n </Panel>\n <Panel title={\"Funzione generatrice dei momenti\"}>\n <p>\n La <i>funzione generatrice dei momenti</i> è:\n </p>\n <p>\n <Latex>{r`m_X (t) = E( e^{t \\cdot X} )`}</Latex>\n </p>\n <p>\n Se due variabile aleatorie hanno la stessa funzione generatrice dei momenti, allora esse hanno la <b>stessa distribuzione</b>.\n </p>\n <p>\n E' la <b>trasformata di Laplace</b> della variabile aleatoria di X.\n </p>\n </Panel>\n <Panel title={\"Funzione caratteristica\"}>\n <p>\n La <i>funzione caratteristica</i> è:\n </p>\n <p>\n <Latex>{r`H_X (t) = E ( e^{i \\cdot t \\cdot X} )`}</Latex>\n </p>\n <p>\n Se due variabile aleatorie hanno la stessa funzione caratteristica, allora esse hanno la <b>stessa distribuzione</b>.\n </p>\n <p>\n E' la <b>trasformata di Fourier</b> della variabile aleatoria di X.\n </p>\n </Panel>\n </Split>\n <Split title={\"Prove e schemi\"}>\n <Panel title={\"Variabile con distribuzione\"}>\n <p>\n Per dire che una variabile ha una certa distribuzione, si usa la notazione:\n </p>\n <p>\n <Latex>{r`X \\sim Distribuzione()`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Prova di Bernoulli\"}>\n <p>\n Una prova con solo due possibili esiti: <Plus>successo</Plus> e <Minus>insuccesso</Minus>.\n </p>\n </Panel>\n <Panel title={\"Schema di Bernoulli\"}>\n <p>\n Una sequenza di prove di Bernoulli per le quali le probabilità di successo e fallimento rimangono invariate.\n </p>\n </Panel>\n </Split>\n <Split title={\"Bernoulliana\"}>\n <Panel title={\"Distribuzione bernoulliana\"}>\n <p>\n Una variabile aleatoria che rappresenta una prova di Bernoulli:\n </p>\n <ul>\n <li>vale <Plus>1</Plus> in caso di <Plus>successo</Plus>.</li>\n <li>vale <Minus>0</Minus> in caso di <Minus>insuccesso</Minus>.</li>\n </ul>\n <p>\n Il suo simbolo è <Latex>{r`Ber(p)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Densità della bernoulliana\"}>\n <p>\n La distribuzione bernoulliana ha come densità:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Binomiale\"}>\n <Panel title={\"Distribuzione binomiale\"}>\n <p>\n Una variabile aleatoria che conta il numero di successi di <Latex>n</Latex> prove di uno schema di Bernoulli.\n </p>\n <p>\n Il suo simbolo è <Latex>{r`Bin(n, p)`}</Latex>.\n </p>\n </Panel>\n <Panel title={\"Densità della binomiale\"}>\n <p>\n La binomiale ha come densità:\n </p>\n <p>\n <Latex>{r`f_X (k) : \\{0..n\\} = \\binom{n}{k} \\cdot p^k \\cdot q^{n - k}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della binomiale\"}>\n <p>\n La <b>funzione generatrice dei momenti</b> della binomiale è:\n </p>\n <p>\n <Latex>{r`m_X (t) = (q + p \\cdot e^t) ^ n`}</Latex>\n </p>\n <p>\n La <b>media</b> di una binomiale è:\n </p>\n <p>\n <Latex>{r`E(X) = n \\cdot p`}</Latex>\n </p>\n <p>\n La <b>varianza</b> di una binomiale è:\n </p>\n <p>\n <Latex>{r`Var(X) = n \\cdot p \\cdot q`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Geometrica\"}>\n <Panel title={\"Distribuzione geometrica\"}>\n <p>\n Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli fino alla comparsa del primo successo.\n </p>\n <p>\n Il suo simbolo è <Latex>Geo(p)</Latex>.\n </p>\n </Panel>\n <Panel title={\"Densità della geometrica\"}>\n <p>\n La geometrica ha come densità:\n </p>\n <p>\n <Latex>{r`f_X (k) : \\mathbb{N} = q^{k - 1} p`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della geometrica\"}>\n <p>\n La <b>funzione generatrice dei momenti</b> della geometrica è:\n </p>\n <p>\n <Latex>{r`m_X (t) = \\frac{p \\cdot e^t}{1 - q \\cdot e^t}`}</Latex>\n </p>\n <p>\n La <b>media</b> della geometrica è:\n </p>\n <p>\n <Latex>{r`E(X) = \\frac{1}{p}`}</Latex>\n </p>\n <p>\n La <b>varianza</b> della geometrica è:\n </p>\n <p>\n <Latex>{r`Var(X) = \\frac{q}{p^2}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Assenza di memoria della geometrica\"}>\n <p>\n La geometrica non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n </p>\n <p>\n <Latex>{r`P([X = i + j | X > i ]) = P([X = j])`}</Latex>\n </p>\n <Example>\n Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n </Example>\n </Panel>\n </Split>\n <Split title={\"Binomiale negativa\"}>\n <Panel title={\"Distribuzione binomiale negativa\"}>\n <p>\n Una variabile aleatoria che conta il numero di prove in uno schema di Bernoulli necessarie perchè si verifichi l'<Latex>n</Latex>-esimo successo.\n </p>\n <p>\n Il suo simbolo è <Latex>{r`\\overline{Bin}(n, p)`}</Latex>.\n </p>\n </Panel>\n <Panel title={\"Densità della binomiale negativa\"}>\n <p>\n La binomiale negativa ha come densità:\n </p>\n <p>\n <Latex>{r`f_X (k) : \\{ n .. +\\infty \\} \\in \\mathbb{N} = \\binom{k - 1}{n - 1} \\cdot p^n \\cdot q^{k - n} `}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della binomiale negativa\"}>\n <p>\n <p>\n La <b>funzione generatrice dei momenti</b> della binomiale negativa è:\n </p>\n <p>\n <Latex>{r`m_X (t) : \\{ t < ln(\\frac{1}{q}) \\} = \\left( \\frac{p \\cdot e^t}{1 - q \\cdot e^t} \\right) ^n`}</Latex>\n </p>\n <p>\n La <b>media</b> della binomiale negativa è:\n </p>\n <p>\n <Latex>{r`E(X) = \\frac{n}{p}`}</Latex>\n </p>\n <p>\n La <b>varianza</b> della binomiale negativa è:\n </p>\n <p>\n <Latex>{r`Var(X) = \\frac{n \\cdot q}{p^2}`}</Latex>\n </p>\n </p>\n </Panel>\n </Split>\n <Split title={\"Geometrica traslata\"}>\n <Panel title={\"Distribuzione geometrica traslata\"}>\n <p>\n Una variabile aleatoria che conta il numero <Latex>k</Latex> di insuccessi consecutivi in uno schema di Bernoulli:\n </p>\n <p>\n Il suo simbolo rimane <Latex>{r`Geo(p)`}</Latex>.\n </p>\n </Panel>\n <Panel title={\"Densità della geometrica tralsata\"}>\n <p>\n La geometrica traslata ha come densità:\n </p>\n <p>\n <Latex>{r`f_X (k) : \\mathbb{N} = p \\cdot q^k `}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della geometrica traslata\"}>\n <p>\n La <b>funzione generatrice dei momenti</b> della geometrica traslata è:\n </p>\n <p>\n <Latex>{r`m_X (t) : \\left\\{ t < ln \\left( \\frac{1}{q} \\right) \\right\\} = \\frac{p}{1 - q \\cdot e^t}`}</Latex>\n </p>\n <p>\n La <b>media</b> della geometrica traslata è:\n </p>\n <p>\n <Latex>{r`E(X) = \\frac{q}{p}`}</Latex>\n </p>\n <p>\n La <b>varianza</b> della geometrica è:\n </p>\n <p>\n <Latex>{r`Var(X) = \\frac{q}{p^2}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Assenza di memoria della geometrica traslata\"}>\n <p>\n La geometrica traslata non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n </p>\n <p>\n <Latex>{r`P([X = i + j | X > i ]) = P([X = j])`}</Latex>\n </p>\n <Example>\n Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n </Example>\n </Panel>\n </Split>\n <Split title={\"Binomiale negativa traslata\"}>\n <Panel title={\"Distribuzione binomiale negativa traslata\"}>\n <p>\n Una variabile aleatoria che conta il numero di insuccessi in uno schema di Bernoulli prima che si verifichi l'<Latex>n</Latex>-esimo successo.\n </p>\n <p>\n Il suo simbolo rimane <Latex>{r`\\overline{Bin}(n, p)`}</Latex>.\n </p>\n </Panel>\n <Panel title={\"Densità della binomiale negativa traslata\"}>\n <p>\n La binomiale negativa traslata ha come densità:\n </p>\n <p>\n <Latex>{r`f_X (k) : \\mathbb{N} = \\binom{k + n - 1}{n - 1} \\cdot p^n \\cdot q^k `}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della binomiale negativa traslata\"}>\n <p>\n <p>\n La <b>funzione generatrice dei momenti</b> della binomiale negativa traslata è:\n </p>\n <p>\n <Latex>{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`}</Latex>\n </p>\n <p>\n La <b>media</b> della binomiale negativa traslata è:\n </p>\n <p>\n <Latex>{r`E(X) = \\frac{n \\cdot q}{p}`}</Latex>\n </p>\n <p>\n La <b>varianza</b> della binomiale negativa traslata è:\n </p>\n <p>\n <Latex>{r`Var(X) = \\frac{n \\cdot q}{p^2}`}</Latex>\n </p>\n </p>\n </Panel>\n </Split>\n <Split title={\"Ipergeometrica\"}>\n <Panel title={\"Distribuzione ipergeometrica\"}>\n <p>\n Una variabile aleatoria che, sapendo il numero di successi <Latex>K</Latex> e di insuccessi <Latex>N-K</Latex>, conta quanti successi si otterrebbero se se ne estraessero <Latex>n</Latex> in blocco.\n </p>\n <p>\n Il suo simbolo è <Latex>Ipe(N, K, n)</Latex>.\n </p>\n </Panel>\n <Panel title={\"Densità della ipergeometrica\"}>\n <p>\n La ipergeometrica ha come densità:\n </p>\n <p>\n <Latex>{r`f_X (k) : \\{0..n\\} \\in \\mathbb{N} = \\frac{\\binom{K}{k} \\cdot \\binom{N - K}{n - k}}{\\binom{N}{n}}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della ipergeometrica\"}>\n <p>\n <p>\n La <b>funzione generatrice dei momenti</b> della ipergeometrica è trascurabile.\n </p>\n <p>\n La <b>media</b> della ipergeometrica è:\n </p>\n <p>\n <Latex>{r`E(X) = n \\cdot \\frac{K}{N}`}</Latex>\n </p>\n <p>\n La <b>varianza</b> della ipergeometrica è:\n </p>\n <p>\n <Latex>{r`Var(X) = n \\cdot \\frac{K}{N} \\cdot \\frac{N - K}{N} \\cdot \\frac{N - n}{N - 1}`}</Latex>\n </p>\n </p>\n </Panel>\n </Split>\n <Split title={\"Poissoniana\"}>\n <Panel title={\"Distribuzione poissoniana\"}>\n <p>\n Una variabile aleatoria che soddisfa tutte le seguenti caratteristiche:\n </p>\n <ul>\n <li>Binomiale: <Latex>{r`X \\sim Bin(n, p)`}</Latex></li>\n <li>Il numero di prove tende a infinito: <Latex>{r`n \\to +\\infty`}</Latex></li>\n <li>La probabilità di successo tende a 0: <Latex>{r`p \\to 0`}</Latex></li>\n <li>La media è finita: <Latex>{r`E(X) = n \\cdot p \\to \\mu \\neq 0`}</Latex></li>\n </ul>\n <p>\n Il suo simbolo è <Latex>{r`Poi(\\mu)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Densità della poissoniana\"}>\n <p>\n La poissoniana ha come densità:\n </p>\n <p>\n <Latex>{r`f_X (k) : \\mathbb{N} = \\frac{e^{-\\mu} \\cdot \\mu^k}{k!}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della poissoniana\"}>\n <p>\n <p>\n La <b>funzione generatrice dei momenti</b> della poissoniana è:\n </p>\n <p>\n <Latex>{r`m_X (t) = e^{\\mu \\cdot (e^t - 1)}`}</Latex>\n </p>\n <p>\n La <b>media</b> della poissoniana è:\n </p>\n <p>\n <Latex>{r`E(X) = \\mu`}</Latex>\n </p>\n <p>\n La <b>varianza</b> della poissoniana è:\n </p>\n <p>\n <Latex>{r`Var(X) = \\mu`}</Latex>\n </p>\n <p>\n Gli altri momenti della poissoniana sono:\n </p>\n <ol start={2}>\n <li><Latex>{r`E(X^2) = \\mu^2 + \\mu`}</Latex></li>\n </ol>\n </p>\n </Panel>\n </Split>\n <Split title={\"Un altro schema\"}>\n <Panel title={\"Schema di Poisson\"}>\n <p>\n Una successione di <b>arrivi</b> avvenuti in un certo arco temporale che:\n </p>\n <ul>\n <li>non sono sovrapposti.</li>\n <li>hanno intensità <Latex>{r`\\lambda`}</Latex> costante.</li>\n <li>avvengono indipendentemente gli uni dagli altri.</li>\n </ul>\n </Panel>\n <Panel title={\"Processo di Poisson\"}>\n <p>\n Una variabile aleatoria <Latex>N_t</Latex> che conta il numero di arrivi di uno schema di Poisson di intensità <Latex>{r`\\lambda`}</Latex> in un intervallo di tempo di durata <Latex>t</Latex>.\n </p>\n <p>\n E' una distribuzione poissoniana con <Latex>{r`\\mu = t \\cdot \\lambda`}</Latex>: <Latex>{r`Poi(t \\cdot \\lambda)`}</Latex>\n </p>\n <Example>\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 </Example>\n </Panel>\n </Split>\n <Split title={\"Esponenziale\"}>\n <Panel title={\"Distribuzione esponenziale\"}>\n <p>\n Una variabile aleatoria che conta il tempo diwidehattesa prima del primo arrivo di un processo di Poisson di intensità <Latex>{r`\\lambda`}</Latex>.\n </p>\n <p>\n Il suo simbolo è <Latex>{r`Esp(\\lambda)`}</Latex>.\n </p>\n </Panel>\n <Panel title={\"Densità dell'esponenziale\"}>\n <p>\n L'esponenziale ha come <b>densità</b>:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n <p>\n L'esponenziale ha come <b>funzione di ripartizione</b>:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti dell'esponenziale\"}>\n <p>\n La <b>funzione generatrice dei momenti</b> dell'esponenziale è:\n </p>\n <p>\n <Latex>{r`m_X (t) : \\{ t | t < \\lambda \\} \\in \\mathbb{R} = \\frac{\\lambda}{\\lambda - t}`}</Latex>\n </p>\n <p>\n La <b>media</b> dell'esponenziale è:\n </p>\n <p>\n <Latex>{r`E(X) = \\frac{1}{\\lambda}`}</Latex>\n </p>\n <p>\n La <b>varianza</b> dell'esponenziale è:\n </p>\n <p>\n <Latex>{r`Var(X) = \\frac{1}{\\lambda^2}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Assenza di memoria della esponenziale\"}>\n <p>\n L'esponenziale non tiene conto degli eventi avvenuti in passato: ha la proprietà dell'assenza di memoria:\n </p>\n <p>\n <Latex>{r`P([X > s + t | X > s]) = P([X > t])`}</Latex>\n </p>\n <Example>\n Ovvero, riscalando opportunamente l'asse Y posso prendere come 0 qualsiasi punto dell'asse X.\n </Example>\n </Panel>\n </Split>\n <Split title={\"Legge gamma\"}>\n <Panel title={\"Distribuzione gamma\"}>\n <p>\n Una variabile aleatoria che conta il tempo diwidehattesa prima dell'<Latex>n</Latex>-esimo arrivo di un processo di Poisson di intensità <Latex>{r`\\lambda`}</Latex>.\n </p>\n <p>\n Il suo simbolo è <Latex>{r`\\Gamma(n, \\lambda)`}</Latex>.\n </p>\n </Panel>\n <Panel title={\"Densità della legge gamma\"}>\n <p>\n La legge gamma ha come densità:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della legge gamma\"}>\n <p>\n <p>\n La <b>funzione generatrice dei momenti</b> della legge gamma è:\n </p>\n <p>\n <Latex>{r`m_X (t) : ( t < \\lambda ) \\in \\mathbb{R} = \\left( \\frac{\\lambda}{\\lambda - t} \\right) ^\\alpha`}</Latex>\n </p>\n <p>\n La <b>media</b> della legge gamma è:\n </p>\n <p>\n <Latex>{r`E(X) = \\frac{\\alpha}{\\lambda}`}</Latex>\n </p>\n <p>\n La <b>varianza</b> della legge gamma è:\n </p>\n <p>\n <Latex>{r`Var(X) = \\frac{\\alpha}{\\lambda^2}`}</Latex>\n </p>\n </p>\n </Panel>\n </Split>\n <Split title={\"Uniforme\"}>\n <Panel title={\"Distribuzione uniforme\"}>\n <p>\n Una variabile aleatoria che può assumere qualsiasi valore in un intervallo <Latex>{r`[a, b]`}</Latex> in modo equiprobabile.\n </p>\n <p>\n Il suo simbolo è <Latex>{r`Uni(a, b)`}</Latex>\n </p>\n <p>\n Su di essa vale la seguente proprietà:\n </p>\n <p>\n <Latex>{r`P(X \\in (c, d)) = \\frac{d - c}{b - a}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Densità della distribuzione uniforme\"}>\n <p>\n La distribuzione uniforme ha come <b>densità</b>:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n <p>\n La distribuzione uniforme ha come <b>funzione di ripartizione</b>:\n </p>\n <p>\n <Latex>{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}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della distribuzione uniforme\"}>\n <p>\n <p>\n La <b>funzione generatrice dei momenti</b> della distribuzione uniforme è:\n </p>\n <p>\n <Latex>{r`m_X (t) = \\frac{e^{b \\cdot t} - e^{a \\cdot t}}{(b - a) \\cdot t}`}</Latex>\n </p>\n <p>\n La <b>media</b> della distribuzione uniforme è:\n </p>\n <p>\n <Latex>{r`E(X) = \\frac{a + b}{2}`}</Latex>\n </p>\n <p>\n La <b>varianza</b> della distribuzione uniforme è:\n </p>\n <p>\n <Latex>{r`Var(X) = \\frac{(b - a)^2}{12}`}</Latex>\n </p>\n </p>\n </Panel>\n </Split>\n <Split title={\"Normale o Gaussiana\"}>\n <Panel title={\"Distribuzione normale\"}>\n <p>\n Una variabile aleatoria con una specifica distribuzione.\n </p>\n <p>\n Il suo simbolo è <Latex>{r`Nor(\\mu, \\sigma^2)`}</Latex>.\n </p>\n <Example>\n <Latex>\\mu</Latex> e <Latex>\\sigma^2</Latex> sono rispettivamente la media e la varianza della distribuzione!\n </Example>\n </Panel>\n <Panel title={\"Densità della distribuzione normale\"}>\n <p>\n La distribuzione normale ha come densità:\n </p>\n <p>\n <Latex>{r`f_X (x) = \\frac{e^{-\\frac{(x - \\mu)^2}{2 \\sigma^2}}}{\\sqrt{2 \\pi \\cdot \\sigma^2}}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Momenti della distribuzione normale\"}>\n <p>\n <p>\n La <b>funzione generatrice dei momenti</b> della distribuzione normale è:\n </p>\n <p>\n <Latex>{r`m_X (t) = e^{\\mu \\cdot t + \\frac{\\sigma^2 \\cdot t^2}{2}}`}</Latex>\n </p>\n <p>\n La <b>media</b> della distribuzione normale è:\n </p>\n <p>\n <Latex>{r`E(X) = \\mu`}</Latex>\n </p>\n <p>\n La <b>varianza</b> della distribuzione normale è:\n </p>\n <p>\n <Latex>{r`Var(X) = \\sigma^2`}</Latex>\n </p>\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title={\"Trasformazione della normale\"}>\n <p>\n Qualsiasi normale può essere trasformata in qualsiasi altra normale:\n </p>\n <p>\n <Latex>{r`X \\sim Nor(m, v^2) \\implies \\alpha X + \\beta \\sim Nor(\\alpha m + \\beta, (\\alpha v)^2)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Normale standard\"}>\n <p>\n La distribuzione normale standard <Latex>Z</Latex> è:\n </p>\n <p>\n <Latex>Z \\sim Nor(0, 1)</Latex>\n </p>\n <p>\n La sua funzione di ripartizione è detta <Latex>{r`\\phi(z)`}</Latex> e vale:\n </p>\n <p>\n <Latex>{r`F_Z(z) = \\phi(z) = \\frac{1}{\\sqrt{2 \\pi}} \\int_{-\\infty}^{z} e^{-\\frac{x^2}{2}} dx`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Quantili normali\"}>\n <p>\n Da un quantile <Latex>{r`z_\\alpha`}</Latex> della normale standard è possibile risalire allo stesso quantile di qualsiasi altra normale:\n </p>\n <p>\n <Latex>{r`x_\\alpha = \\mu + z_\\alpha \\cdot \\sqrt{\\sigma^2}`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title={\"Una gamma particolare\"}>\n <blockquote>\n chi-quadro a un grado di libertà\n </blockquote>\n <p>\n Esiste una distribuzione Gamma particolare:\n </p>\n <p>\n <Latex>{r`\\Gamma (\\frac{1}{2}, \\frac{1}{2}) = \\chi^2 (v = 1)`}</Latex>\n </p>\n <p>\n Più chi-quadro possono essere sommate per aumentare i loro gradi di libertà:\n </p>\n <p>\n <Latex>{r`\\chi^2 (n) + \\chi^2 (m) = \\chi^2 (n + m)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Gamma e normale\"}>\n <p>\n La distribuzione normale ha una particolare relazione con la distribuzione Gamma:\n </p>\n <p>\n <Latex>{r`Z^2 \\sim \\chi^2 (v = 1)`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Approssimazioni notevoli\"}>\n <Panel title={\"Ipergeometrica e binomiale\"}>\n <p>\n La binomiale è come una ipergeometrica ma con ripetizioni, quindi per valori molto grandi di <Latex>N</Latex> rispetto a <Latex>n</Latex>, si può dire che:\n </p>\n <p>\n <Latex>{r`Ipe(N, K, n) \\approx Bin(n, \\frac{K}{N})`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Binomiale e poissoniana\"}>\n <p>\n La binomiale non è altro che una poissoniana a tempo discreto, quindi, se <Latex>n</Latex> è grande e <Latex>n \\cdot p</Latex> è nell'ordine di grandezza delle unità, allora:\n </p>\n <p>\n <Latex>{r`Bin(n, p) \\approx Poi(n \\cdot p)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Binomiale e normale\"}>\n <p>\n Per il Teorema di De Moivre-Laplace, se una binomiale ha una <Latex>n</Latex> grande e <Latex>p</Latex> non vicina a 0 o 1, si può approssimare con:\n </p>\n <p>\n <Latex>{r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Correzione di Yates\"}>\n <p>\n Passando da una variabile discreta <Latex>X</Latex> a una continua <Latex>Y</Latex>, per ogni valore discreto <Latex>k</Latex> la probabilità viene \"spalmata\" su tutto l'intervallo <Latex>{r`(k - \\frac{1}{2}, k + \\frac{1}{2})`}</Latex>:\n </p>\n <ul>\n <li><Latex>{r`P(X < k) \\simeq P(Y \\leq k - \\frac{1}{2})`}</Latex></li>\n <li><Latex>{r`P(X \\leq k) \\simeq P(Y \\leq k + \\frac{1}{2})`}</Latex></li>\n <li><Latex>{r`P(X \\geq k) \\simeq P(Y \\geq k - \\frac{1}{2})`}</Latex></li>\n <li><Latex>{r`P(X > k) \\simeq P(Y \\geq k + \\frac{1}{2})`}</Latex></li>\n </ul>\n </Panel>\n </Split>\n <Split title={\"Vettori aleatori\"}>\n <Panel title={\"Vettore aleatorio\"}>\n <p>\n Un vettore <b>composto da variabili aleatorie</b>.\n </p>\n <p>\n Il suo simbolo generalmente è <Latex>{r`\\boldsymbol{X}`}</Latex> oppure <Latex>{r`X, Y`}</Latex>.\n </p>\n </Panel>\n <Panel title={\"Funzioni di ripartizione\"}>\n <p>\n I vettori aleatori hanno più funzioni di ripartizione che si differenziano in base al numero di parametri.\n </p>\n <p>\n Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una <i>funzione di ripartizione congiunta</i>:\n </p>\n <p>\n <Latex>{r`F_{X, Y} (x, y) = P(X \\leq x, Y \\leq y)`}</Latex>\n </p>\n <p>\n Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una <i>funzione di ripartizione marginale</i>:\n </p>\n <p>\n <Latex>{r`F_X (x) = P(X \\leq x) = \\lim_{y \\to +\\infty} F_{X, Y} (x, y)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Densità discreta\"}>\n <p>\n I vettori aleatori <b>discreti</b> hanno più densità che si differenziano in base al numero di parametri.\n </p>\n <p>\n Se il numero di parametri coincide con la dimensione del vettore aleatorio, allora la funzione sarà una <i>densità congiunta</i>:\n </p>\n <p>\n <Latex>{r`p_{X, Y} (x, y) = P(X = x, Y = y)`}</Latex>\n </p>\n <p>\n Se il numero di parametri è minore della dimensione del vettore aleatorio, allora la funzione sarà una <i>densità marginale</i>:\n </p>\n <p>\n <Latex>{r`p_X (x) = \\sum_j p_{X, Y} (x_i, y_j)`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Più variabili aleatorie\"}>\n <Panel title={\"Indipendenza delle variabili aleatorie\"}>\n <p>\n Più variabili aleatorie sono indipendenti se, per qualsiasi scelta di intervalli <Latex>A_i</Latex>:\n </p>\n <p>\n <Latex>{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)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Media dei vettori aleatori\"}>\n <p>\n E' possibile calcolare la media di qualsiasi funzione <Latex>g(X, Y)</Latex> avente elementi del vettore come variabili:\n </p>\n <p>\n <Latex>{r`E(g(X, Y)) = \\sum_{i, j} g(x_i, y_i) \\cdot p_{X, Y} (x_i, y_i)`}</Latex>\n </p>\n <Example>\n Solitamente si calcola la media di <Latex>x \\cdot y</Latex>.\n </Example>\n <p>\n Le medie di più variabili aleatorie si possono sommare:\n </p>\n <p>\n <Latex>{r`E(X + Y) = E(X) + E(Y)`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split>\n <Panel title={\"Covarianza\"}>\n <p>\n Un <b>operatore</b> che misura la correlazione di due variabili aleatorie.\n </p>\n <p>\n Si calcola con il valore atteso dei prodotti delle distanze dalla media:\n </p>\n <p>\n <Latex>{r`Cov(X, Y) = E((X - E(X) \\cdot (Y - E(Y)) = E(XY) - E(X) \\cdot E(Y)`}</Latex>\n </p>\n <p>\n Ha diverse proprietà:\n </p>\n <ul>\n <li>Il suo <b>valore nullo</b> è 0: <Latex>{r`Cov(X, \\alpha) = 0`}</Latex></li>\n <li>E' <b>commutativa</b>: <Latex>{r`Cov(X, Y) = Cov(Y, X)`}</Latex></li>\n <li>E' <b>semplificabile</b>: <Latex>{r`Cov(X, X) = Var(X)`}</Latex></li>\n <li>E' <b>lineare</b>: <Latex>{r`Cov(\\alpha X, \\beta Y) = \\alpha \\cdot \\beta \\cdot Cov(X, Y)`}</Latex></li>\n <li>E' <b>distributiva</b>: <Latex>{r`Cov(X + Y, V + W) = Cov(X, Y) + Cov(X, W) + Cov(Y, V) + Cov(Y, W)`}</Latex></li>\n </ul>\n </Panel>\n <Panel title={\"Variabili incorrelate\"}>\n <p>\n Due variabili sono <i>variabili incorrelate</i> se:\n </p>\n <p>\n <Latex>{r`Cov(X, Y) = 0`}</Latex>\n </p>\n <p>\n Variabili indipendenti sono sempre incorrelate.\n </p>\n </Panel>\n <Panel title={\"Matrice di covarianza\"}>\n <p>\n Una matrice <Latex>{r`\\boldsymbol{C_X}`}</Latex> che contiene la covarianza tra tutte le variabili di un vettore aleatorio <Latex>{r`\\boldsymbol{X}`}</Latex>:\n </p>\n <p>\n <Latex>{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 `}</Latex>\n </p>\n <p>\n E' sempre simmetrica e semidefinita positiva (tutti gli autovalori sono <Latex>\\geq 0</Latex>.\n </p>\n </Panel>\n <Panel title={\"Coefficiente di correlazione\"}>\n <p>\n Un valore che misura come due variabili aleatorie sono correlate:\n </p>\n <p>\n <Latex>{r`\\rho_{X, Y} = \\frac{Cov(X, Y)}{\\sqrt{Var(X)} \\cdot \\sqrt{Var(Y)}}`}</Latex>\n </p>\n <p>\n E' sempre compreso tra -1 e 1:\n </p>\n <p>\n <Latex>{r`-1 \\leq \\rho_{X, Y} \\leq 1`}</Latex>\n </p>\n <p>\n Vale esattamente -1 o 1 solo se esiste un legame lineare tra le due variaibli:\n </p>\n <p>\n <Latex>{r`Y = a X + b \\Longleftrightarrow | \\rho_{X, Y} | = 1`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Varianza di variabili aleatorie sommate\"}>\n <p>\n La varianza di due variabili aleatorie sommate è:\n </p>\n <p>\n <Latex>{r`Var(X + Y) = Var(X) + Var(Y) + 2 \\cdot Cov(X, Y)`}</Latex>\n </p>\n <Example>\n Si dimostra applicando le proprietà della covarianza!\n </Example>\n <p>\n Se più variabili aleatorie <Latex>X_i</Latex> sono <b>indipendenti</b> (<Latex>{r`Cov(X, Y) = 0`}</Latex>), allora:\n </p>\n <p>\n <Latex>{r`Var \\left( \\sum_i X_i \\right) = \\sum_i Var(X_i)`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Campioni\"}>\n <Panel title={\"Campione casuale\"}>\n <p>\n Una <b>n-pla</b> di variabili aleatorie con la stessa distribuzione della variabile aleatoria <Latex>X</Latex> (\"popolazione\") ma <b>indipendenti</b> tra loro.\n </p>\n <Example>\n Le variabili aleatorie sono come un lazy-load in programmazione; quando ci sarà bisogno del loro valore numerico, esse si <b>realizzeranno</b> nel loro valore.\n </Example>\n </Panel>\n <Panel title={\"Momento campionario\"}>\n <p>\n Il valore dato dalla media aritmetica degli <Latex>n</Latex> elementi del campione elevati alla potenza <Latex>k</Latex>:\n </p>\n <p>\n <Latex>{r`M^{(k)}_n = \\frac{1}{n} \\cdot \\sum_{i = 1}^n X_i^k `}</Latex>\n </p>\n <p>\n Il momento campionario di primo ordine è la <i>media campionaria</i> <Latex>{r`\\overline{X}_n`}</Latex>.\n </p>\n </Panel>\n <Panel title={\"Varianza campionaria\"}>\n <p>\n La media aritmetica dello scarto quadratico medio degli elementi del campione.\n </p>\n <p>\n Se è noto il valore medio <Latex>{r`m = E(X)`}</Latex> di X:\n </p>\n <p>\n <Latex>{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`}</Latex>\n </p>\n <p>\n Altrimenti:\n </p>\n <p>\n <Latex>{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)`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Media-ception\"}>\n <Panel title={\"Media campionaria\"}>\n <p>\n Se calcoliamo la media della media campionaria, risulterà vero che:\n </p>\n <p>\n <Latex>{r`E(\\overline{X}_n) = E(X)`}</Latex>\n </p>\n <Example>\n Quindi, è possibile usare i campioni per trovare la media di una variabile aleatoria!\n </Example>\n </Panel>\n <Panel title={\"Varianza campionaria\"}>\n <p>\n Se calcoliamo la varianza della media campionaria, risulterà vero che:\n </p>\n <p>\n <Latex>{r`Var(\\overline{X}_n) = \\frac{Var(X)}{n}`}</Latex>\n </p>\n <Example>\n Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n </Example>\n </Panel>\n <Panel title={\"Correzione campionaria\"}>\n <p>\n Se calcoliamo la media della varianza campionaria, risulterà vero che:\n </p>\n <p>\n <Latex>{r`E(S_0^2) = E(S_n^2) = Var(X)`}</Latex>\n </p>\n <Example>\n Quindi, possiamo stimare l'errore della media calcolata tramite campioni!\n </Example>\n </Panel>\n </Split>\n <Split title={\"Campionamento di una distribuzione normale\"}>\n <Panel title={\"Campionamento di una distribuzione normale\"}>\n <p>\n Se la popolazione <Latex>X</Latex> ha una distribuzione normale (<Latex>{r`X \\sim Nor(\\mu, \\sigma^2)`}</Latex>)...\n </p>\n </Panel>\n <Panel title={\"Distribuzione della media campionaria\"}>\n <p>\n ...allora sappiamo anche la distribuzione della media campionaria!\n </p>\n <p>\n <Latex>{r`\\overline{X}_n \\sim Nor \\left( \\mu, \\frac{\\sigma^2}{n} \\right)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Distribuzione della varianza campionaria\"}>\n <p>\n ...e anche della varianza campionaria!\n </p>\n <p>\n <Latex>{r`S_0^2 \\sim \\frac{\\sigma^2}{n} \\cdot \\chi^2 (n)`}</Latex>\n </p>\n <p>\n <Latex>{r`S_n^2 \\sim \\frac{\\sigma^2}{n - 1} \\cdot \\chi^2 (n-1)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Indipendenza\"}>\n <p>\n ...e che media campionaria e varianza campionaria sono indipendenti tra loro!\n </p>\n </Panel>\n </Split>\n <Split title={\"Quando i campioni hanno dimensioni infinite\"}>\n <Panel title={\"Convergenza in distribuzione\"}>\n <p>\n Se la successione di variabili aleatorie <Latex>X_n</Latex> all'infinito ha la <b>stessa funzione di ripartizione</b> della popolazione <Latex>X</Latex>, allora essa <i>converge in distribuzione</i>.\n </p>\n <p>\n <Latex>{`\\\\lim_{n \\\\to +\\\\infty} F_{X_n} (x) = F_X (x) \\\\implies X_n \\\\xrightarrow{d} X`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Convergenza in probabilità\"}>\n <p>\n Se la successione di variabili aleatorie <Latex>X_n</Latex> all'infinito ha la <b>stessa probabilità</b> della popolazione <Latex>X</Latex>, allora essa <i>converge in probabilità</i>.\n </p>\n <p>\n <Latex>{`\\\\forall \\\\epsilon > 0, \\\\lim_{n \\\\to +\\\\infty} P( | X_n - X | < \\\\epsilon) = 1 \\\\implies X_n \\\\xrightarrow{p} X`}</Latex>\n </p>\n <p>\n <Todo>TODO: non sono certissimo della definizione</Todo>\n </p>\n </Panel>\n <Panel title={\"Convergenza quasi certa\"}>\n <p>\n Se la successione di variabili aleatorie <Latex>X_n</Latex> all'infinito ha la <b>stessa probabilità a </b> della popolazione <Latex>X</Latex>, allora essa <i>converge quasi certamente</i>.\n </p>\n <p>\n <Latex>{`\\\\forall \\\\epsilon > 0, P \\left( \\\\lim_{n \\\\to +\\\\infty} | X_n - X | < \\\\epsilon) \\right) = 1 \\\\implies X_n \\\\xrightarrow{qc} X`}</Latex>\n </p>\n <p>\n <Todo>TODO: non sono certissimo della definizione</Todo>\n </p>\n </Panel>\n <Panel title={\"Convergenza in media quadratica\"}>\n <p>\n Se la successione di variabili aleatorie <Latex>X_n</Latex> all'infinito ha la <b>media del quadrato della distanza</b> tra la successione e la popolazione <Latex>X</Latex> <b>uguale a 0</b>, allora essa <i>converge in media quadratica</i>.\n </p>\n <p>\n <Latex>{`\\\\lim_{n \\\\to +\\\\infty} E( | X_n - X |^2 = 0 \\\\implies X_n \\\\xrightarrow{mq} X`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Gerarchia delle convergenze\"}>\n <p>\n <Latex>{`\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 }</Latex>\n </p>\n <p>\n In più:\n </p>\n <p>\n <Latex>{`X_n \\\\xrightarrow{p} x \\\\Longleftrightarrow X_n \\\\xrightarrow{d} x`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"I grandi numeri\"}>\n <Panel title={\"Legge debole dei grandi numeri\"}>\n <p>\n La successione delle medie campionarie <Latex>{r`\\overline{X}_n`}</Latex> <b>converge in probabilità</b> alla media della popolazione <Latex>{r`E(X)`}</Latex>, se essa esiste.\n </p>\n <p>\n <Latex>{`\\\\overline{X}_n \\\\xrightarrow{p} X`}</Latex>\n </p>\n <p>\n Ovvero:\n </p>\n <p>\n <Latex>{r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( | \\overline{X}_n - E(X) | < \\epsilon) = 1`}</Latex>\n </p>\n <p>\n <Latex>{r`P( | \\overline{X}_n - E(X) | < \\epsilon) \\to 1`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Legge forte dei grandi numeri\"}>\n <p>\n La successione delle medie campionarie <Latex>{r`\\overline{X}_n`}</Latex> <b>converge quasi certamente</b> alla media della popolazione <Latex>{r`E(X)`}</Latex>, se essa esiste.\n </p>\n <p>\n <Latex>{`\\\\overline{X}_n \\\\xrightarrow{qc} X`}</Latex>\n </p>\n <p>\n Ovvero:\n </p>\n <p>\n <Latex>{r`\\forall \\epsilon > 0, P \\left( \\lim_{n \\to +\\infty} | \\overline{X}_n - E(X) | < \\epsilon \\right) = 1`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Al limite\"}>\n <Panel title={\"Teorema centrale del limite\"}>\n <p>\n La successione delle medie campionarie <Latex>{r`\\overline{X}_n`}</Latex> <b>converge in distribuzione</b> a <Latex>{r`Nor(0, 1) = \\Phi()`}</Latex>.\n </p>\n <p>\n <Latex>{r`\\overline{X}_n \\approx Nor \\left(E(X), \\frac{Var(X)}{n} \\right)`}</Latex>\n </p>\n <p>\n Ovvero:\n </p>\n <p>\n <Latex>{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)`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Altre approsimazioni\"}>\n <Panel title={\"Binomiale e normale\"}>\n <p>\n E' una somma di <b>bernoulliane</b>, e quindi si approssima a una normale:\n </p>\n <p>\n <Latex>{r`Bin(n, p) \\approx Nor(n \\cdot p, n \\cdot p \\cdot q)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Binomiale negativa e normale\"}>\n <p>\n E' una somma di <b>geometriche</b>, e quindi si approssima a una normale:\n </p>\n <p>\n <Latex>{r`\\overline{Bin} (n, p) \\approx Nor \\left( \\frac{n}{p}, \\frac{n \\cdot (1 - p)}{p^2} \\right)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Poissoniana e normale\"}>\n <p>\n E' una somma di altre <b>poissoniane</b>, e quindi si approssima a una normale:\n </p>\n <p>\n <Latex>{r`Poi(\\lambda) \\approx Nor(\\lambda, \\lambda)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Gamma e normale\"}>\n <p>\n E' una somma di <b>esponenziali</b>, e quindi si approssima a una normale:\n </p>\n <p>\n <Latex>{r`\\Gamma (\\alpha, \\lambda) \\approx Nor \\left( \\frac{\\alpha}{\\lambda}, \\frac{\\alpha}{\\lambda^2} \\right)`}</Latex>\n </p>\n </Panel>\n <Panel title={\"In generale\"}>\n <p>\n Se <Latex>n</Latex> è grande, allora:\n </p>\n <p>\n <Latex>{r`Y = \\sum_{i=1}^{n} X_i`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Actually statistica\"}>\n <Panel title={\"Parametri sconosciuti\"}>\n <p>\n Per indicare parametri sconosciuti di una legge si usa <Latex>\\theta</Latex>.\n </p>\n </Panel>\n <Panel title={\"Statistica\"}>\n <p>\n Una variabile aleatoria funzione di un campione:\n </p>\n <p>\n <Latex>{r`T(\\boldsymbol{X})`}</Latex>\n </p>\n <Example>\n Ad esempio, sono statistiche media e varianza campionaria, così come il campione stesso <Latex>{r`T(\\boldsymbol{X}) = \\boldsymbol{X}`}</Latex>.\n </Example>\n </Panel>\n </Split>\n <Split title={\"Stimatori\"}>\n <Panel title={\"Stimatore\"}>\n <p>\n Una statistica <Latex>T_n</Latex> ottenuta da <Latex>n</Latex> osservazioni, che stimi i parametri di una legge e sia indipendente da essi.\n </p>\n </Panel>\n <Panel title={\"Corretto\"}>\n <p>\n Uno stimatore è <i>corretto</i> se il suo valore atteso coincide con quello dei parametri che stima:\n </p>\n <p>\n <Latex>{r`E(T_n) = \\theta`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Asintoticamente corretto\"}>\n <p>\n Uno stimatore è <i>asintoticamente corretto</i> se, per infinite osservazioni, il suo valore atteso coincide con quello dei parametri che stima:\n </p>\n <p>\n <Latex>{r`\\lim_{n \\to +\\infty} E(T_n) = \\theta`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Consistente in media quadratica\"}>\n <p>\n Uno stimatore è <i>consistente in media quadratica</i> se:\n </p>\n <p>\n <Latex>{r`\\lim_{n \\to +\\infty} E((T_n - \\theta)^2) = 0`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Consistente in probabilità\"}>\n <p>\n Uno stimatore è <i>consistente in probabilità</i> se:\n </p>\n <p>\n <Latex>{r`\\forall \\epsilon > 0, \\lim_{n \\to +\\infty} P( |T_n - \\theta| < \\epsilon) = 1`}</Latex>\n </p>\n <p>\n <Todo>TODO: verificare che la mia modifica sia corretta</Todo>\n </p>\n </Panel>\n <Panel title={\"Asintoticamente normale\"}>\n <p>\n Uno stimatore è <i>asintoticamente normale</i> se:\n </p>\n <p>\n <Latex>{r`\\lim_{n \\to +\\infty} \\frac{T_n - E(T_n)}{\\sqrt{Var(T_n)}} \\sim Nor(0, 1)`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Metodo dei momenti\"}>\n <Panel title={\"Metodo dei momenti\"}>\n <p>\n Si può usare il <i>metodo dei momenti</i> per ottenere uno stimatore di una popolazione <Latex>X</Latex>.\n </p>\n <p>\n Lo stimatore di <Latex>{r`\\theta`}</Latex> così ottenuto sarà indicato aggiungendo un cappellino e una <Latex>M</Latex> a <Latex>\\theta</Latex>: <Latex>{r`\\widehat{\\theta}_M`}</Latex>\n </p>\n <p>\n Visto che:\n </p>\n <ul>\n <li><Latex>{r`\\theta = g(E(X))`}</Latex></li>\n <li><Latex>{r`\\widehat{E(X)} = \\overline{X}_n`}</Latex></li>\n </ul>\n <p>\n Allora:\n </p>\n <p>\n <Latex>{r`\\widehat{\\theta}_M = g( \\overline{X}_n )`}</Latex>\n </p>\n <p>\n Se <Latex>{r`\\theta`}</Latex> non è esprimibile in termini di <Latex>{r`E(X)`}</Latex>, si possono usare i momenti successivi <Latex>{r`M_n^2`}</Latex>, <Latex>{r`M_n^3`}</Latex>, <Latex>{r`M_n^3`}</Latex>...\n </p>\n </Panel>\n </Split>\n <Split title={\"Metodo della massima verosomiglianza\"}>\n <Panel title={\"Metodo della massima verosomiglianza\"}>\n <p>\n Si può usare il <i>metodo della massima verosomiglianza</i> per ottenere uno stimatore di una popolazione <Latex>X</Latex>.\n </p>\n <p>\n Lo stimatore di <Latex>{r`\\theta`}</Latex> così ottenuto sarà indicato aggiungendo un cappellino e una <Latex>L</Latex> a <Latex>\\theta</Latex>: <Latex>{r`\\widehat{\\theta}_L`}</Latex>\n </p>\n <p>\n Consiste nel trovare il massimo assoluto <Latex>{r`\\widehat{\\theta}_L`}</Latex> della la funzione di verosomiglianza <Latex>{r`L`}</Latex>:\n </p>\n <p>\n <Latex>{r`L(x_1, ..., x_n; \\theta) = \\prod_{i=1}^n f_X(x_i; \\theta)`}</Latex>\n </p>\n <p>\n Gli stimatori di massima verosomiglianza sono <b>asintoticamente corretti</b>, <b>consistenti in probabilità</b> e <b>asintoticamente normali</b>.\n </p>\n </Panel>\n <Panel title={\"Proprietà degli stimatori di massima verosomiglianza\"}>\n <p>\n Gli stimatori di massima verosomiglianza godono delle seguenti proprietà:\n </p>\n <ul>\n <li>Sono <b>asintoticamente corretti</b>.</li>\n <li>Sono <b>consistenti in probabilità</b>.</li>\n <li>Sono <b>asintoticamente normali</b>.</li>\n <li>Sono <b>invarianti</b>: <Latex>{r`\\widehat{g(\\theta)}_L = g(\\widehat{\\theta}_L)`}</Latex></li>\n </ul>\n </Panel>\n </Split>\n <Split title={\"Nuove stime notevoli\"}>\n <Panel title={\"Stima di una bernoulliana\"}>\n <p>\n Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n </p>\n <p>\n <Latex>{r`\\widehat{p}_M = \\widehat{p}_L = \\overline{X}_n`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Stima di una poissoniana\"}>\n <p>\n Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n </p>\n <p>\n <Latex>{r`\\widehat{\\mu}_M = \\widehat{\\mu}_L = \\overline{X}_n`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Stima di una esponenziale\"}>\n <p>\n Per il metodo dei momenti oppure per il metodo della massima verosomiglianza:\n </p>\n <p>\n <Latex>{r`\\widehat{\\lambda}_M = \\widehat{\\lambda}_L = \\frac{1}{\\overline{X}_n}`}</Latex>\n </p>\n </Panel>\n <Panel title={\"Stima di una normale\"}>\n <p>\n Per il metodo della massima verosomiglianza:\n </p>\n <ul>\n <li><Latex>{r`\\widehat{\\mu}_L = \\overline{X}_n`}</Latex></li><br/>\n <li><Latex>{r`\\widehat{\\sigma^2}_L = \\frac{\\sum (X_i - \\overline{X}_n)^2 }{n}`}</Latex></li>\n </ul>\n </Panel>\n </Split>\n <Split title={\"Intervalli di confidenza\"}>\n <Panel title={\"Confidenza\"}>\n <blockquote>\n \"intervallo di confidenza al 95%\"\n </blockquote>\n <p>\n L'intervallo di valori di <Latex>\\theta</Latex> all'interno del quale siamo \"più o meno sicuri\" si trovi il valore effettivo:\n </p>\n <p>\n L'intervallo di confidenza a N della stima <Latex>{r`\\widehat{W}`}</Latex> è l'intervallo <Latex>]a, b[</Latex> tale che:\n </p>\n <p>\n <Latex>{r`P( a < W < b ) = N`}</Latex>\n </p>\n <p>\n Può anche essere <b>unilatero</b> nel caso limiti la stima in una sola direzione, positiva o negativa.\n </p>\n </Panel>\n </Split>\n <Split title={\"Confidenza nella media di una normale\"}>\n <Panel title={\"Varianza nota\"}>\n <p>\n Se conosciamo la varianza di una normale, allora possiamo ricavare velocemente gli intervalli di confidenza all'<Latex>\\alpha</Latex>% con queste formule:\n </p>\n <ul>\n <li>Intervalli bilateri: <Latex>{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]`}</Latex></li>\n <li>Intervallo unilatero da sinistra: <Latex>{r`\\mu \\in \\left( -\\infty, \\overline{x}_n + z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}} \\right]`}</Latex></li>\n <li>Intervallo unilatero da destra: <Latex>{r`\\mu \\in \\left[ \\overline{x}_n - z_{1 - \\frac{\\alpha}{2}} \\cdot \\sqrt{\\frac{\\sigma^2}{n}}, +\\infty \\right)`}</Latex></li>\n </ul>\n </Panel>\n <Panel title={\"Varianza incognita\"}>\n <p>\n <Todo>TODO: Cos'è la distribuzione di Student?</Todo>\n </p>\n </Panel>\n </Split>\n <Split title={\"Confidenza per la proporzione di una bernoulliana\"}>\n <Panel title={\"Terzo metodo corretto\"}>\n <p>\n L'intervallo di confidenza per la proprorzione di una bernoulliana qualsiasi si ottiene da questa formula:\n </p>\n <p>\n <Latex>{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]`}</Latex>\n </p>\n </Panel>\n </Split>\n <Split title={\"Confidenza per la media di qualsiasi popolazione\"}>\n <Panel title={\"Approssimando con la normale\"}>\n <p>\n L'intervallo di confidenza per la media di una qualsiasi popolazione si ottiene da questa formula:\n </p>\n <p>\n <Latex>{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]`}</Latex>\n </p>\n </Panel>\n </Split>\n </div>\n )\n\t}\n}\n\n\n// WEBPACK FOOTER //\n// ./pages/statistica.js","import './index.css';\nimport './manifest.json';\nimport { Component } from 'preact';\nimport Router from 'preact-router';\nimport Home from './pages/home';\nimport Fisica from './pages/fisica';\nimport VlDiGeometria from './pages/vldigeometria';\nimport MingwInstall from './pages/mingwinstall';\nimport Copyright from './components/copyright';\nimport Statistica from './pages/statistica';\n\n// noinspection JSUnusedGlobalSymbols\nexport default class App extends Component {\n\trender() {\n\t\treturn (\n\t\t\t<div id=\"app\">\n\t\t\t\t<h1><a href=\"/\">Appuntiweb</a> <small>di <a href=\"https://steffo.eu/\">Steffo</a></small></h1>\n\t\t\t\t<Router>\n\t\t\t\t\t<Home 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