diff --git a/Math.hooks.php b/Math.hooks.php index 2a1827b..fea33d4 100644 --- a/Math.hooks.php +++ b/Math.hooks.php @@ -125,6 +125,7 @@ class MathHooks { if ( $wgUseMathJax && $mode == MW_MATH_MATHJAX ) { $parser->getOutput()->addModules( array( 'ext.math.mathjax.enabler' ) ); } + $parser->getOutput()->addModuleStyles( array( 'ext.math.styles' ) ); $renderer->writeCache(); $result = $wgContLang->armourMath( $renderedMath ); diff --git a/Math.php b/Math.php index b2a5847..f5a3669 100644 --- a/Math.php +++ b/Math.php @@ -41,6 +41,16 @@ define( 'MW_MATH_MATHJAX', 6 ); /// new in 1.19/1.20 define( 'MW_MATH_LATEXML', 7 ); /// new in 1.22 /**@}*/ +/**@{ + * Mathstyle constants + */ +define( 'MW_MATHSTYLE_INLINE_DISPLAYSTYLE', 0 ); //default large operator inline +define( 'MW_MATHSTYLE_DISPLAY', 1 ); // large operators centered in a new line +define( 'MW_MATHSTYLE_INLINE', 2 ); // small operators inline +// There is no style which renders small operators +// but display the equation centered in a new line. +/**@}*/ + /** Location of the texvc binary */ $wgTexvc = __DIR__ . '/math/texvc'; /** @@ -168,6 +178,12 @@ $wgExtensionMessagesFiles['Math'] = $dir . 'Math.i18n.php'; $wgParserTestFiles[] = $dir . 'mathParserTests.txt'; +$wgResourceModules['ext.math.styles'] = array( + 'localBasePath' => __DIR__ . '/modules', + 'remoteExtPath' => 'Math/modules', + 'styles' => 'ext.math.css', +); + // MathJax module // If you modify these arrays, update ext.math.mathjax.enabler.js to ensure // that getModuleNameFromFile knows how to map files to MediaWiki modules. diff --git a/MathLaTeXML.php b/MathLaTeXML.php index 6ac83ee..746d12b 100644 --- a/MathLaTeXML.php +++ b/MathLaTeXML.php @@ -183,9 +183,18 @@ class MathLaTeXML extends MathRenderer { * @return string HTTP POST data */ public function getPostData() { - $texcmd = urlencode( $this->tex ); - $settings = $this->serializeSettings( $this->getLaTeXMLSettings() ); - return $settings . '&tex=' . $texcmd; + $tex = $this->getTex(); + if ( $this->getMathStyle() == MW_MATHSTYLE_INLINE_DISPLAYSTYLE ) { + // In MW_MATHSTYLE_INLINE_DISPLAYSTYLE the old + // texvc behavior is reproduced: + // The equation is rendered in displaystyle + // (texvc used $$ $tex $$ to render) + // but the equation is not centered. + $tex = '{\displaystyle ' . $tex . '}'; + } + $texcmd = rawurlencode( $tex ); + $settings = $this->serializeSettings( $this->getLaTeXMLSettings( ) ); + return $settings. '&tex=' . $texcmd; } /** * Does the actual web request to convert TeX to MathML. diff --git a/MathRenderer.php b/MathRenderer.php index 95c6027..23bb9ca 100644 --- a/MathRenderer.php +++ b/MathRenderer.php @@ -29,6 +29,8 @@ abstract class MathRenderer { protected $tex = ''; /** @var string the original user input string (which was used to caculate the inputhash) */ protected $userInputTex = ''; + /** @var (MW_MATHSTYLE_INLINE_DISPLAYSTYLE|MW_MATHSTYLE_DISPLAY|MW_MATHSTYLE_INLINE) the rendering style */ + protected $mathStyle = MW_MATHSTYLE_INLINE_DISPLAYSTYLE; /** * is calculated by texvc. * @var string @@ -84,6 +86,27 @@ abstract class MathRenderer { */ public static function getRenderer( $tex, $params = array(), $mode = MW_MATH_PNG ) { global $wgDefaultUserOptions; + $mathStyle = null; + if ( isset( $params['display'] ) ) { + $layoutMode = $params['display']; + if ( $layoutMode == 'block' ) { + $mathStyle = MW_MATHSTYLE_DISPLAY ; + // TODO: Implement caching for attributes of the math tag + // Currently the key for the database entry relating to an equation + // is md5($tex) the new option to determine if the tex input + // is rendered in displaystyle or textstyle would require a database + // layout change to use a composite key e.g. (md5($tex),$mathStyle). + // As a workaround we use the prefix \displaystyle so that the key becomes + // md5((\{\\displaystyle|\{\\textstyle)?\s?$tex\}?) + // The new value of $tex string describes now how the rendering should look like. + // The variable MathRenderer::mathStyle determines if the rendered equation should + // be centered in a new line, or just in be displayed in the current line. + $tex = '{\displaystyle ' . $tex . '}'; + } elseif ( $layoutMode == 'inline' ) { + $mathStyle = MW_MATHSTYLE_INLINE; + $tex = '{\textstyle ' . $tex . '}'; + } + } $validModes = array( MW_MATH_PNG, MW_MATH_SOURCE, MW_MATH_MATHJAX, MW_MATH_LATEXML ); if ( !in_array( $mode, $validModes ) ) $mode = $wgDefaultUserOptions['math']; @@ -100,6 +123,7 @@ abstract class MathRenderer { $renderer = new MathTexvc( $tex, $params ); } wfDebugLog ( "Math", 'start rendering $' . $renderer->tex . '$ in mode ' . $mode ); + $renderer->setMathStyle( $mathStyle ); return $renderer; } @@ -422,6 +446,26 @@ abstract class MathRenderer { return $this->lastError; } + + /** + * + * @param (MW_MATHSTYLE_INLINE_DISPLAYSTYLE|MW_MATHSTYLE_DISPLAY|MW_MATHSTYLE_INLINE) $mathStyle + */ + public function setMathStyle( $displayStyle = MW_MATHSTYLE_DISPLAY ) { + if ( $this->mathStyle !== $displayStyle ){ + $this->changed = true; + } + $this->mathStyle = $displayStyle; + } + + /** + * Returns the value of the DisplayStyle attribute + * @return (MW_MATHSTYLE_INLINE_DISPLAYSTYLE|MW_MATHSTYLE_DISPLAY|MW_MATHSTYLE_INLINE) the DisplayStyle + */ + public function getMathStyle() { + return $this->mathStyle; + } + /** * Get if the input tex was marked as secure * @return boolean diff --git a/MathSource.php b/MathSource.php index ceecd45..8eabaef 100644 --- a/MathSource.php +++ b/MathSource.php @@ -27,11 +27,18 @@ class MathSource extends MathRenderer { function render() { # No need to render or parse anything more! # New lines are replaced with spaces, which avoids confusing our parser (bugs 23190, 22818) + if ( $this->getMathStyle() == MW_MATHSTYLE_DISPLAY ) { + $class = 'mwe-math-fallback-source-display'; + } else { + $class = 'mwe-math-fallback-source-inline'; + } return Xml::element( 'span', $this->getAttributes( 'span', array( - 'class' => 'tex', + // the former class name was 'tex' + // for backwards compatibility we keep this classname + 'class' => $class. ' tex', 'dir' => 'ltr' ) ), diff --git a/MathTexvc.php b/MathTexvc.php index 532c5ef..37e4b70 100644 --- a/MathTexvc.php +++ b/MathTexvc.php @@ -79,19 +79,26 @@ class MathTexvc extends MathRenderer { */ public function getMathImageHTML() { $url = $this->getMathImageUrl(); - + $attributes = array( + // the former class name was 'tex' + // for backwards compatibility we keep that classname + 'class' => 'mwe-math-fallback-png-inline tex', + 'alt' => $this->getTex() + ); + if ( $this->getMathStyle() === MW_MATHSTYLE_DISPLAY ){ + // if DisplayStyle is true, the equation will be centered in a new line + $attributes[ 'class' ] = 'mwe-math-fallback-png-display tex'; + } return Xml::element( 'img', $this->getAttributes( 'img', - array( - 'class' => 'tex', - 'alt' => $this->getTex(), - ), + $attributes, array( 'src' => $url ) ) ); + } /** diff --git a/README b/README index addb24f..49f0f6d 100644 --- a/README +++ b/README @@ -35,6 +35,22 @@ if ( typeof mathJax === 'undefined' ) { }; } +Attributes of the element: +attribute "display": +possible values: "inline", "block" or "inline-displaystyle" (default) + +"display" reproduces the old texvc behavior: +The equation is rendered with large height operands (texvc used $$ $tex $$ to render) +but the equation printed to the current line of the output and not centered in a new line. +In Wikipedia users use :$tex to move the math element closer to the center. + +"inline" renders the equation in with small height operands by adding {\textstyle $tex } to the +users input ($tex). The equation is displayed in the current text line. + +"inline-displaystyle" renders the equation in with large height operands centered in a new line by adding +{\displaystyle $tex } to the user input ($tex). + + For testing your installation run php tests/phpunit/phpunit.php extensions/Math/tests/ from your MediWiki home path. diff --git a/modules/MathJax/unpacked/extensions/wiki2jax.js b/modules/MathJax/unpacked/extensions/wiki2jax.js index 963e5d7..6535bc1 100644 --- a/modules/MathJax/unpacked/extensions/wiki2jax.js +++ b/modules/MathJax/unpacked/extensions/wiki2jax.js @@ -20,7 +20,8 @@ MathJax.Extension.wiki2jax = { this.configured = true; } var that = this; - $('span.tex, img.tex, strong.texerror', element || document).each(function(i, span) { + $('.mwe-math-fallback-png-display, .mwe-math-fallback-png-inline, .mwe-math-fallback-source-display,'+ + '.mwe-math-fallback-source-inline, strong.texerror', element || document).each(function(i, span) { that.ConvertMath(span); }); }, @@ -37,7 +38,7 @@ MathJax.Extension.wiki2jax = { ConvertMath: function (node) { var parent = node.parentNode, - mode = parent.tagName === "DD" && parent.childNodes.length === 1 ? "; mode=display" : "", + mode = "", //Bug 61051 (heuristic unwanted by the community) tex; if (node.nodeName == 'IMG') { tex = node.alt; @@ -49,7 +50,9 @@ MathJax.Extension.wiki2jax = { } tex = tex.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&").replace(/ /g," "); } - + if ( $( node ).hasClass( "mwe-math-fallback-png-display") || $( node ).hasClass( "mwe-math-fallback-source-display") ){ + mode = "; mode=display"; + } // We don't allow comments (%) in texvc and escape all literal % by default. tex = tex.replace(/([^\\])%/g, "$1\\%" ); diff --git a/modules/ext.math.css b/modules/ext.math.css new file mode 100644 index 0000000..1160710 --- /dev/null +++ b/modules/ext.math.css @@ -0,0 +1,12 @@ +/* + Document : ext.math + Created on : 23.09.2013, 13:55:00 + Author : Physikerwelt (Moritz Schubotz) + Description: + Shows browser-dependent math output. +*/ + +.mwe-math-fallback-png-inline { display: inline; vertical-align: middle} +.mwe-math-fallback-png-display { display: block; margin-left: auto; margin-right: auto;} +.mwe-math-fallback-source-inline { display: inline; vertical-align: middle} +.mwe-math-fallback-source-display { display: block; margin-left: auto; margin-right: auto;} \ No newline at end of file diff --git a/tests/MathLaTeXMLTest.php b/tests/MathLaTeXMLTest.php index eb68e69..1573232 100644 --- a/tests/MathLaTeXMLTest.php +++ b/tests/MathLaTeXMLTest.php @@ -142,9 +142,10 @@ class MathLaTeXMLTest extends MediaWikiTestCase { $this->setMwGlobals( 'wgMathLaTeXMLTimeout', 20 ); $renderer = MathRenderer::getRenderer( "a+b", array(), MW_MATH_LATEXML ); $real = $renderer->render( true ); - $expected = ' a + b a b a+b '; + $expected = ' a + b a b {\displaystyle a+b} '; $this->assertEquals( $expected, $real - , "Rendering of a+b in plain Text mode" ); + , "Rendering of a+b in plain Text mode." . + $renderer->getLastError() ); } } @@ -186,4 +187,4 @@ class LaTeXMLTestStatus { static function getHtml() { return MathLaTeXMLTest::$html; } -} \ No newline at end of file +} diff --git a/tests/MathSourceTest.php b/tests/MathSourceTest.php index dd48f63..f04708c 100644 --- a/tests/MathSourceTest.php +++ b/tests/MathSourceTest.php @@ -12,7 +12,7 @@ class MathSourceTest extends MediaWikiTestCase { public function testBasics() { $real = MathRenderer::renderMath( "a+b", array(), MW_MATH_SOURCE ); $this->assertEquals( - '$ a+b $', + '$ a+b $', $real, "Rendering of a+b in plain Text mode" ); @@ -24,7 +24,7 @@ class MathSourceTest extends MediaWikiTestCase { public function testNewLines() { $real = MathRenderer::renderMath( "a\n b", array(), MW_MATH_SOURCE ); $this->assertSame( - '$ a b $', + '$ a b $', $real, "converting newlines to spaces" ); diff --git a/tests/ParserTest.data b/tests/ParserTest.data index b9984a2..4f8d15f 100644 --- a/tests/ParserTest.data +++ b/tests/ParserTest.data @@ -1,35 +1,35 @@ -a:447:{i:0;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:109:"e^{i \pi} + 1 = 0\,\!";}i:1;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:109:"e^{i \pi} + 1 = 0\,\!";}i:2;a:2:{i:0;s:67:"\definecolor{red}{RGB}{255,0,0}\pagecolor{red}e^{i \pi} + 1 = 0\,\!";i:1;s:155:"\definecolor{red}{RGB}{255,0,0}\pagecolor{red}e^{i \pi} + 1 = 0\,\!";}i:3;a:2:{i:0;s:10:"\text{abc}";i:1;s:98:"\text{abc}";}i:4;a:2:{i:0;s:10:"\alpha\,\!";i:1;s:98:"\alpha\,\!";}i:5;a:2:{i:0;s:15:" f(x) = x^2\,\!";i:1;s:103:" f(x) = x^2\,\!";}i:6;a:2:{i:0;s:8:"\sqrt{2}";i:1;s:96:"\sqrt{2}";}i:7;a:2:{i:0;s:14:"\sqrt{1-e^2}\!";i:1;s:102:"\sqrt{1-e^2}\!";}i:8;a:2:{i:0;s:14:"\sqrt{1-z^3}\!";i:1;s:102:"\sqrt{1-z^3}\!";}i:9;a:2:{i:0;s:1:"x";i:1;s:89:"x";}i:10;a:2:{i:0;s:42:"\dot{a}, \ddot{a}, \acute{a}, \grave{a} \!";i:1;s:130:"\dot{a}, \ddot{a}, \acute{a}, \grave{a} \!";}i:11;a:2:{i:0;s:43:"\check{a}, \breve{a}, \tilde{a}, \bar{a} \!";i:1;s:131:"\check{a}, \breve{a}, \tilde{a}, \bar{a} \!";}i:12;a:2:{i:0;s:32:"\hat{a}, \widehat{a}, \vec{a} \!";i:1;s:120:"\hat{a}, \widehat{a}, \vec{a} \!";}i:13;a:2:{i:0;s:37:"\exp_a b = a^b, \exp b = e^b, 10^m \!";i:1;s:125:"\exp_a b = a^b, \exp b = e^b, 10^m \!";}i:14;a:2:{i:0;s:37:"\ln c, \lg d = \log e, \log_{10} f \!";i:1;s:125:"\ln c, \lg d = \log e, \log_{10} f \!";}i:15;a:2:{i:0;s:48:"\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\!";i:1;s:136:"\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\!";}i:16;a:2:{i:0;s:34:"\arcsin h, \arccos i, \arctan j \!";i:1;s:122:"\arcsin h, \arccos i, \arctan j \!";}i:17;a:2:{i:0;s:37:"\sinh k, \cosh l, \tanh m, \coth n \!";i:1;s:125:"\sinh k, \cosh l, \tanh m, \coth n \!";}i:18;a:2:{i:0;s:91:"\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n \!";i:1;s:179:"\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n \!";}i:19;a:2:{i:0;s:76:"\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q \!";i:1;s:164:"\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q \!";}i:20;a:2:{i:0;s:35:"\sgn r, \left\vert s \right\vert \!";i:1;s:123:"\sgn r, \left\vert s \right\vert \!";}i:21;a:2:{i:0;s:23:"\min(x,y), \max(x,y) \!";i:1;s:111:"\min(x,y), \max(x,y) \!";}i:22;a:2:{i:0;s:33:"\min x, \max y, \inf s, \sup t \!";i:1;s:121:"\min x, \max y, \inf s, \sup t \!";}i:23;a:2:{i:0;s:31:"\lim u, \liminf v, \limsup w \!";i:1;s:119:"\lim u, \liminf v, \limsup w \!";}i:24;a:2:{i:0;s:35:"\dim p, \deg q, \det m, \ker\phi \!";i:1;s:123:"\dim p, \deg q, \det m, \ker\phi \!";}i:25;a:2:{i:0;s:41:"\Pr j, \hom l, \lVert z \rVert, \arg z \!";i:1;s:129:"\Pr j, \hom l, \lVert z \rVert, \arg z \!";}i:26;a:2:{i:0;s:49:"dt, \operatorname{d}\!t, \partial t, \nabla\psi\!";i:1;s:137:"dt, \operatorname{d}\!t, \partial t, \nabla\psi\!";}i:27;a:2:{i:0;s:155:"dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!";i:1;s:243:"dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!";}i:28;a:2:{i:0;s:66:"\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y";i:1;s:169:"\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y";}i:29;a:2:{i:0;s:64:"\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar \!";i:1;s:152:"\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar \!";}i:30;a:2:{i:0;s:62:"\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS \!";i:1;s:150:"\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS \!";}i:31;a:2:{i:0;s:24:"s_k \equiv 0 \pmod{m} \!";i:1;s:112:"s_k \equiv 0 \pmod{m} \!";}i:32;a:2:{i:0;s:14:"a\,\bmod\,b \!";i:1;s:102:"a\,\bmod\,b \!";}i:33;a:2:{i:0;s:36:"\gcd(m, n), \operatorname{lcm}(m, n)";i:1;s:124:"\gcd(m, n), \operatorname{lcm}(m, n)";}i:34;a:2:{i:0;s:37:"\mid, \nmid, \shortmid, \nshortmid \!";i:1;s:125:"\mid, \nmid, \shortmid, \nshortmid \!";}i:35;a:2:{i:0;s:57:"\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} \!";i:1;s:145:"\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} \!";}i:36;a:2:{i:0;s:27:"+, -, \pm, \mp, \dotplus \!";i:1;s:115:"+, -, \pm, \mp, \dotplus \!";}i:37;a:2:{i:0;s:46:"\times, \div, \divideontimes, /, \backslash \!";i:1;s:134:"\times, \div, \divideontimes, /, \backslash \!";}i:38;a:2:{i:0;s:39:"\cdot, * \ast, \star, \circ, \bullet \!";i:1;s:127:"\cdot, * \ast, \star, \circ, \bullet \!";}i:39;a:2:{i:0;s:42:"\boxplus, \boxminus, \boxtimes, \boxdot \!";i:1;s:130:"\boxplus, \boxminus, \boxtimes, \boxdot \!";}i:40;a:2:{i:0;s:42:"\oplus, \ominus, \otimes, \oslash, \odot\!";i:1;s:130:"\oplus, \ominus, \otimes, \oslash, \odot\!";}i:41;a:2:{i:0;s:42:"\circleddash, \circledcirc, \circledast \!";i:1;s:130:"\circleddash, \circledcirc, \circledast \!";}i:42;a:2:{i:0;s:34:"\bigoplus, \bigotimes, \bigodot \!";i:1;s:122:"\bigoplus, \bigotimes, \bigodot \!";}i:43;a:2:{i:0;s:42:"\{ \}, \O \empty \emptyset, \varnothing \!";i:1;s:130:"\{ \}, \O \empty \emptyset, \varnothing \!";}i:44;a:2:{i:0;s:36:"\in, \notin \not\in, \ni, \not\ni \!";i:1;s:124:"\in, \notin \not\in, \ni, \not\ni \!";}i:45;a:2:{i:0;s:30:"\cap, \Cap, \sqcap, \bigcap \!";i:1;s:118:"\cap, \Cap, \sqcap, \bigcap \!";}i:46;a:2:{i:0;s:60:"\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus \!";i:1;s:148:"\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus \!";}i:47;a:2:{i:0;s:36:"\setminus, \smallsetminus, \times \!";i:1;s:124:"\setminus, \smallsetminus, \times \!";}i:48;a:2:{i:0;s:30:"\subset, \Subset, \sqsubset \!";i:1;s:118:"\subset, \Subset, \sqsubset \!";}i:49;a:2:{i:0;s:30:"\supset, \Supset, \sqsupset \!";i:1;s:118:"\supset, \Supset, \sqsupset \!";}i:50;a:2:{i:0;s:64:"\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq \!";i:1;s:152:"\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq \!";}i:51;a:2:{i:0;s:64:"\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq \!";i:1;s:152:"\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq \!";}i:52;a:2:{i:0;s:55:"\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq \!";i:1;s:143:"\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq \!";}i:53;a:2:{i:0;s:55:"\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq \!";i:1;s:143:"\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq \!";}i:54;a:2:{i:0;s:35:"=, \ne, \neq, \equiv, \not\equiv \!";i:1;s:123:"=, \ne, \neq, \equiv, \not\equiv \!";}i:55;a:2:{i:0;s:64:"\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := \!";i:1;s:152:"\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := \!";}i:56;a:2:{i:0;s:78:"\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong \!";i:1;s:166:"\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong \!";}i:57;a:2:{i:0;s:64:"\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto \!";i:1;s:152:"\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto \!";}i:58;a:2:{i:0;s:52:"<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot \!";i:1;s:143:"<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot \!";}i:59;a:2:{i:0;s:50:">, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \!";i:1;s:141:">, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \!";}i:60;a:2:{i:0;s:53:"\le \leq, \lneq, \leqq, \nleqq, \lneqq, \lvertneqq \!";i:1;s:141:"\le \leq, \lneq, \leqq, \nleqq, \lneqq, \lvertneqq \!";}i:61;a:2:{i:0;s:53:"\ge \geq, \gneq, \geqq, \ngeqq, \gneqq, \gvertneqq \!";i:1;s:141:"\ge \geq, \gneq, \geqq, \ngeqq, \gneqq, \gvertneqq \!";}i:62;a:2:{i:0;s:66:"\lessgtr \lesseqgtr \lesseqqgtr \gtrless \gtreqless \gtreqqless \!";i:1;s:154:"\lessgtr \lesseqgtr \lesseqqgtr \gtrless \gtreqless \gtreqqless \!";}i:63;a:2:{i:0;s:38:"\leqslant, \nleqslant, \eqslantless \!";i:1;s:126:"\leqslant, \nleqslant, \eqslantless \!";}i:64;a:2:{i:0;s:37:"\geqslant, \ngeqslant, \eqslantgtr \!";i:1;s:125:"\geqslant, \ngeqslant, \eqslantgtr \!";}i:65;a:2:{i:0;s:43:"\lesssim, \lnsim, \lessapprox, \lnapprox \!";i:1;s:131:"\lesssim, \lnsim, \lessapprox, \lnapprox \!";}i:66;a:2:{i:0;s:42:" \gtrsim, \gnsim, \gtrapprox, \gnapprox \,";i:1;s:130:" \gtrsim, \gnsim, \gtrapprox, \gnapprox \,";}i:67;a:2:{i:0;s:46:"\prec, \nprec, \preceq, \npreceq, \precneqq \!";i:1;s:134:"\prec, \nprec, \preceq, \npreceq, \precneqq \!";}i:68;a:2:{i:0;s:46:"\succ, \nsucc, \succeq, \nsucceq, \succneqq \!";i:1;s:134:"\succ, \nsucc, \succeq, \nsucceq, \succneqq \!";}i:69;a:2:{i:0;s:29:"\preccurlyeq, \curlyeqprec \,";i:1;s:117:"\preccurlyeq, \curlyeqprec \,";}i:70;a:2:{i:0;s:29:"\succcurlyeq, \curlyeqsucc \,";i:1;s:117:"\succcurlyeq, \curlyeqsucc \,";}i:71;a:2:{i:0;s:49:"\precsim, \precnsim, \precapprox, \precnapprox \,";i:1;s:137:"\precsim, \precnsim, \precapprox, \precnapprox \,";}i:72;a:2:{i:0;s:49:"\succsim, \succnsim, \succapprox, \succnapprox \,";i:1;s:137:"\succsim, \succnsim, \succapprox, \succnapprox \,";}i:73;a:2:{i:0;s:57:"\parallel, \nparallel, \shortparallel, \nshortparallel \!";i:1;s:145:"\parallel, \nparallel, \shortparallel, \nshortparallel \!";}i:74;a:2:{i:0;s:59:"\perp, \angle, \sphericalangle, \measuredangle, 45^\circ \!";i:1;s:147:"\perp, \angle, \sphericalangle, \measuredangle, 45^\circ \!";}i:75;a:2:{i:0;s:75:"\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar \!";i:1;s:163:"\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar \!";}i:76;a:2:{i:0;s:55:"\bigcirc, \triangle \bigtriangleup, \bigtriangledown \!";i:1;s:143:"\bigcirc, \triangle \bigtriangleup, \bigtriangledown \!";}i:77;a:2:{i:0;s:29:"\vartriangle, \triangledown\!";i:1;s:117:"\vartriangle, \triangledown\!";}i:78;a:2:{i:0;s:78:"\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright \!";i:1;s:166:"\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright \!";}i:79;a:2:{i:0;s:29:"\forall, \exists, \nexists \!";i:1;s:117:"\forall, \exists, \nexists \!";}i:80;a:2:{i:0;s:29:"\therefore, \because, \And \!";i:1;s:117:"\therefore, \because, \And \!";}i:81;a:2:{i:0;s:36:"\or \lor \vee, \curlyvee, \bigvee \!";i:1;s:124:"\or \lor \vee, \curlyvee, \bigvee \!";}i:82;a:2:{i:0;s:44:"\and \land \wedge, \curlywedge, \bigwedge \!";i:1;s:132:"\and \land \wedge, \curlywedge, \bigwedge \!";}i:83;a:2:{i:0;s:52:"\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, \!";i:1;s:140:"\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, \!";}i:84;a:2:{i:0;s:47:"\lnot \neg, \not\operatorname{R}, \bot, \top \!";i:1;s:135:"\lnot \neg, \not\operatorname{R}, \bot, \top \!";}i:85;a:2:{i:0;s:41:"\vdash \dashv, \vDash, \Vdash, \models \!";i:1;s:129:"\vdash \dashv, \vDash, \Vdash, \models \!";}i:86;a:2:{i:0;s:42:"\Vvdash \nvdash \nVdash \nvDash \nVDash \!";i:1;s:130:"\Vvdash \nvdash \nVdash \nvDash \nVDash \!";}i:87;a:2:{i:0;s:42:"\ulcorner \urcorner \llcorner \lrcorner \,";i:1;s:130:"\ulcorner \urcorner \llcorner \lrcorner \,";}i:88;a:2:{i:0;s:28:"\Rrightarrow, \Lleftarrow \!";i:1;s:116:"\Rrightarrow, \Lleftarrow \!";}i:89;a:2:{i:0;s:53:"\Rightarrow, \nRightarrow, \Longrightarrow \implies\!";i:1;s:141:"\Rightarrow, \nRightarrow, \Longrightarrow \implies\!";}i:90;a:2:{i:0;s:42:"\Leftarrow, \nLeftarrow, \Longleftarrow \!";i:1;s:130:"\Leftarrow, \nLeftarrow, \Longleftarrow \!";}i:91;a:2:{i:0;s:62:"\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff \!";i:1;s:150:"\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff \!";}i:92;a:2:{i:0;s:37:"\Uparrow, \Downarrow, \Updownarrow \!";i:1;s:125:"\Uparrow, \Downarrow, \Updownarrow \!";}i:93;a:2:{i:0;s:48:"\rightarrow \to, \nrightarrow, \longrightarrow\!";i:1;s:136:"\rightarrow \to, \nrightarrow, \longrightarrow\!";}i:94;a:2:{i:0;s:47:"\leftarrow \gets, \nleftarrow, \longleftarrow\!";i:1;s:135:"\leftarrow \gets, \nleftarrow, \longleftarrow\!";}i:95;a:2:{i:0;s:57:"\leftrightarrow, \nleftrightarrow, \longleftrightarrow \!";i:1;s:145:"\leftrightarrow, \nleftrightarrow, \longleftrightarrow \!";}i:96;a:2:{i:0;s:37:"\uparrow, \downarrow, \updownarrow \!";i:1;s:125:"\uparrow, \downarrow, \updownarrow \!";}i:97;a:2:{i:0;s:41:"\nearrow, \swarrow, \nwarrow, \searrow \!";i:1;s:129:"\nearrow, \swarrow, \nwarrow, \searrow \!";}i:98;a:2:{i:0;s:23:"\mapsto, \longmapsto \!";i:1;s:111:"\mapsto, \longmapsto \!";}i:99;a:2:{i:0;s:174:"\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!";i:1;s:262:"\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!";}i:100;a:2:{i:0;s:121:"\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright \,\!";i:1;s:209:"\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright \,\!";}i:101;a:2:{i:0;s:123:"\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft \,\!";i:1;s:211:"\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft \,\!";}i:102;a:2:{i:0;s:118:"\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow \!";i:1;s:206:"\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow \!";}i:103;a:2:{i:0;s:49:"\amalg \P \S \% \dagger \ddagger \ldots \cdots \!";i:1;s:137:"\amalg \P \S \% \dagger \ddagger \ldots \cdots \!";}i:104;a:2:{i:0;s:48:"\smile \frown \wr \triangleleft \triangleright\!";i:1;s:136:"\smile \frown \wr \triangleleft \triangleright\!";}i:105;a:2:{i:0;s:82:"\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp \!";i:1;s:170:"\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp \!";}i:106;a:2:{i:0;s:80:"\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes \!";i:1;s:168:"\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes \!";}i:107;a:2:{i:0;s:84:"\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq \!";i:1;s:172:"\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq \!";}i:108;a:2:{i:0;s:66:"\intercal \barwedge \veebar \doublebarwedge \between \pitchfork \!";i:1;s:154:"\intercal \barwedge \veebar \doublebarwedge \between \pitchfork \!";}i:109;a:2:{i:0;s:68:"\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright \!";i:1;s:156:"\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright \!";}i:110;a:2:{i:0;s:70:"\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq \!";i:1;s:158:"\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq \!";}i:111;a:2:{i:0;s:3:"a^2";i:1;s:91:"a^2";}i:112;a:2:{i:0;s:3:"a_2";i:1;s:91:"a_2";}i:113;a:2:{i:0;s:15:"10^{30} a^{2+2}";i:1;s:103:"10^{30} a^{2+2}";}i:114;a:2:{i:0;s:14:"a_{i,j} b_{f'}";i:1;s:107:"a_{i,j} b_{f'}";}i:115;a:2:{i:0;s:5:"x_2^3";i:1;s:93:"x_2^3";}i:116;a:2:{i:0;s:12:"{x_2}^3 \,\!";i:1;s:100:"{x_2}^3 \,\!";}i:117;a:2:{i:0;s:11:"10^{10^{8}}";i:1;s:99:"10^{10^{8}}";}i:118;a:2:{i:0;s:29:"\sideset{_1^2}{_3^4}\prod_a^b";i:1;s:117:"\sideset{_1^2}{_3^4}\prod_a^b";}i:119;a:2:{i:0;s:18:"{}_1^2\!\Omega_3^4";i:1;s:106:"{}_1^2\!\Omega_3^4";}i:120;a:2:{i:0;s:24:"\overset{\alpha}{\omega}";i:1;s:112:"\overset{\alpha}{\omega}";}i:121;a:2:{i:0;s:25:"\underset{\alpha}{\omega}";i:1;s:113:"\underset{\alpha}{\omega}";}i:122;a:2:{i:0;s:43:"\overset{\alpha}{\underset{\gamma}{\omega}}";i:1;s:131:"\overset{\alpha}{\underset{\gamma}{\omega}}";}i:123;a:2:{i:0;s:25:"\stackrel{\alpha}{\omega}";i:1;s:113:"\stackrel{\alpha}{\omega}";}i:124;a:2:{i:0;s:16:"x', y'', f', f''";i:1;s:134:"x', y'', f', f''";}i:125;a:2:{i:0;s:26:"x^\prime, y^{\prime\prime}";i:1;s:114:"x^\prime, y^{\prime\prime}";}i:126;a:2:{i:0;s:17:"\dot{x}, \ddot{x}";i:1;s:105:"\dot{x}, \ddot{x}";}i:127;a:2:{i:0;s:25:" \hat a \ \bar b \ \vec c";i:1;s:113:" \hat a \ \bar b \ \vec c";}i:128;a:2:{i:0;s:61:" \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}";i:1;s:149:" \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}";}i:129;a:2:{i:0;s:37:" \overline{g h i} \ \underline{j k l}";i:1;s:125:" \overline{g h i} \ \underline{j k l}";}i:130;a:2:{i:0;s:21:"\overset{\frown} {AB}";i:1;s:109:"\overset{\frown} {AB}";}i:131;a:2:{i:0;s:53:" A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C";i:1;s:141:" A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C";}i:132;a:2:{i:0;s:35:"\overbrace{ 1+2+\cdots+100 }^{5050}";i:1;s:123:"\overbrace{ 1+2+\cdots+100 }^{5050}";}i:133;a:2:{i:0;s:32:"\underbrace{ a+b+\cdots+z }_{26}";i:1;s:120:"\underbrace{ a+b+\cdots+z }_{26}";}i:134;a:2:{i:0;s:16:"\sum_{k=1}^N k^2";i:1;s:104:"\sum_{k=1}^N k^2";}i:135;a:2:{i:0;s:27:"\textstyle \sum_{k=1}^N k^2";i:1;s:115:"\textstyle \sum_{k=1}^N k^2";}i:136;a:2:{i:0;s:26:"\frac{\sum_{k=1}^N k^2}{a}";i:1;s:114:"\frac{\sum_{k=1}^N k^2}{a}";}i:137;a:2:{i:0;s:40:"\frac{\displaystyle \sum_{k=1}^N k^2}{a}";i:1;s:128:"\frac{\displaystyle \sum_{k=1}^N k^2}{a}";}i:138;a:2:{i:0;s:36:"\frac{\sum\limits^{^N}_{k=1} k^2}{a}";i:1;s:124:"\frac{\sum\limits^{^N}_{k=1} k^2}{a}";}i:139;a:2:{i:0;s:17:"\prod_{i=1}^N x_i";i:1;s:105:"\prod_{i=1}^N x_i";}i:140;a:2:{i:0;s:28:"\textstyle \prod_{i=1}^N x_i";i:1;s:116:"\textstyle \prod_{i=1}^N x_i";}i:141;a:2:{i:0;s:19:"\coprod_{i=1}^N x_i";i:1;s:107:"\coprod_{i=1}^N x_i";}i:142;a:2:{i:0;s:30:"\textstyle \coprod_{i=1}^N x_i";i:1;s:118:"\textstyle \coprod_{i=1}^N x_i";}i:143;a:2:{i:0;s:22:"\lim_{n \to \infty}x_n";i:1;s:110:"\lim_{n \to \infty}x_n";}i:144;a:2:{i:0;s:33:"\textstyle \lim_{n \to \infty}x_n";i:1;s:121:"\textstyle \lim_{n \to \infty}x_n";}i:145;a:2:{i:0;s:41:"\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx";i:1;s:129:"\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx";}i:146;a:2:{i:0;s:34:"\int_{1}^{3}\frac{e^3/x}{x^2}\, dx";i:1;s:122:"\int_{1}^{3}\frac{e^3/x}{x^2}\, dx";}i:147;a:2:{i:0;s:40:"\textstyle \int\limits_{-N}^{N} e^x\, dx";i:1;s:128:"\textstyle \int\limits_{-N}^{N} e^x\, dx";}i:148;a:2:{i:0;s:33:"\textstyle \int_{-N}^{N} e^x\, dx";i:1;s:121:"\textstyle \int_{-N}^{N} e^x\, dx";}i:149;a:2:{i:0;s:24:"\iint\limits_D \, dx\,dy";i:1;s:112:"\iint\limits_D \, dx\,dy";}i:150;a:2:{i:0;s:29:"\iiint\limits_E \, dx\,dy\,dz";i:1;s:117:"\iiint\limits_E \, dx\,dy\,dz";}i:151;a:2:{i:0;s:34:"\iiiint\limits_F \, dx\,dy\,dz\,dt";i:1;s:122:"\iiiint\limits_F \, dx\,dy\,dz\,dt";}i:152;a:2:{i:0;s:38:"\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy";i:1;s:126:"\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy";}i:153;a:2:{i:0;s:39:"\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy";i:1;s:127:"\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy";}i:154;a:2:{i:0;s:20:"\bigcap_{i=_1}^n E_i";i:1;s:108:"\bigcap_{i=_1}^n E_i";}i:155;a:2:{i:0;s:20:"\bigcup_{i=_1}^n E_i";i:1;s:108:"\bigcup_{i=_1}^n E_i";}i:156;a:2:{i:0;s:15:"\frac{2}{4}=0.5";i:1;s:103:"\frac{2}{4}=0.5";}i:157;a:2:{i:0;s:18:"\tfrac{2}{4} = 0.5";i:1;s:106:"\tfrac{2}{4} = 0.5";}i:158;a:2:{i:0;s:72:"\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a";i:1;s:160:"\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a";}i:159;a:2:{i:0;s:46:"\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a";i:1;s:134:"\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a";}i:160;a:2:{i:0;s:60:"\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}";i:1;s:148:"\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}";}i:161;a:2:{i:0;s:12:"\binom{n}{k}";i:1;s:100:"\binom{n}{k}";}i:162;a:2:{i:0;s:13:"\tbinom{n}{k}";i:1;s:101:"\tbinom{n}{k}";}i:163;a:2:{i:0;s:13:"\dbinom{n}{k}";i:1;s:101:"\dbinom{n}{k}";}i:164;a:2:{i:0;s:42:"\begin{matrix} x & y \\ z & v -\end{matrix}";i:1;s:142:"\begin{matrix} x & y \\ z & v \end{matrix}";}i:165;a:2:{i:0;s:44:"\begin{vmatrix} x & y \\ z & v -\end{vmatrix}";i:1;s:144:"\begin{vmatrix} x & y \\ z & v \end{vmatrix}";}i:166;a:2:{i:0;s:44:"\begin{Vmatrix} x & y \\ z & v -\end{Vmatrix}";i:1;s:144:"\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}";}i:167;a:2:{i:0;s:90:"\begin{bmatrix} 0 & \cdots & 0 \\ \vdots +a:449:{i:0;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:138:"e^{i \pi} + 1 = 0\,\!";}i:1;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:138:"e^{i \pi} + 1 = 0\,\!";}i:2;a:2:{i:0;s:67:"\definecolor{red}{RGB}{255,0,0}\pagecolor{red}e^{i \pi} + 1 = 0\,\!";i:1;s:184:"\definecolor{red}{RGB}{255,0,0}\pagecolor{red}e^{i \pi} + 1 = 0\,\!";}i:3;a:2:{i:0;s:10:"\text{abc}";i:1;s:127:"\text{abc}";}i:4;a:2:{i:0;s:10:"\alpha\,\!";i:1;s:127:"\alpha\,\!";}i:5;a:2:{i:0;s:15:" f(x) = x^2\,\!";i:1;s:132:" f(x) = x^2\,\!";}i:6;a:2:{i:0;s:8:"\sqrt{2}";i:1;s:125:"\sqrt{2}";}i:7;a:2:{i:0;s:14:"\sqrt{1-e^2}\!";i:1;s:131:"\sqrt{1-e^2}\!";}i:8;a:2:{i:0;s:14:"\sqrt{1-z^3}\!";i:1;s:131:"\sqrt{1-z^3}\!";}i:9;a:2:{i:0;s:1:"x";i:1;s:118:"x";}i:10;a:2:{i:0;s:42:"\dot{a}, \ddot{a}, \acute{a}, \grave{a} \!";i:1;s:159:"\dot{a}, \ddot{a}, \acute{a}, \grave{a} \!";}i:11;a:2:{i:0;s:43:"\check{a}, \breve{a}, \tilde{a}, \bar{a} \!";i:1;s:160:"\check{a}, \breve{a}, \tilde{a}, \bar{a} \!";}i:12;a:2:{i:0;s:32:"\hat{a}, \widehat{a}, \vec{a} \!";i:1;s:149:"\hat{a}, \widehat{a}, \vec{a} \!";}i:13;a:2:{i:0;s:37:"\exp_a b = a^b, \exp b = e^b, 10^m \!";i:1;s:154:"\exp_a b = a^b, \exp b = e^b, 10^m \!";}i:14;a:2:{i:0;s:37:"\ln c, \lg d = \log e, \log_{10} f \!";i:1;s:154:"\ln c, \lg d = \log e, \log_{10} f \!";}i:15;a:2:{i:0;s:48:"\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\!";i:1;s:165:"\sin a, \cos b, \tan c, \cot d, \sec e, \csc f\!";}i:16;a:2:{i:0;s:34:"\arcsin h, \arccos i, \arctan j \!";i:1;s:151:"\arcsin h, \arccos i, \arctan j \!";}i:17;a:2:{i:0;s:37:"\sinh k, \cosh l, \tanh m, \coth n \!";i:1;s:154:"\sinh k, \cosh l, \tanh m, \coth n \!";}i:18;a:2:{i:0;s:91:"\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n \!";i:1;s:208:"\operatorname{sh}\,k, \operatorname{ch}\,l, \operatorname{th}\,m, \operatorname{coth}\,n \!";}i:19;a:2:{i:0;s:76:"\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q \!";i:1;s:193:"\operatorname{argsh}\,o, \operatorname{argch}\,p, \operatorname{argth}\,q \!";}i:20;a:2:{i:0;s:35:"\sgn r, \left\vert s \right\vert \!";i:1;s:152:"\sgn r, \left\vert s \right\vert \!";}i:21;a:2:{i:0;s:23:"\min(x,y), \max(x,y) \!";i:1;s:140:"\min(x,y), \max(x,y) \!";}i:22;a:2:{i:0;s:33:"\min x, \max y, \inf s, \sup t \!";i:1;s:150:"\min x, \max y, \inf s, \sup t \!";}i:23;a:2:{i:0;s:31:"\lim u, \liminf v, \limsup w \!";i:1;s:148:"\lim u, \liminf v, \limsup w \!";}i:24;a:2:{i:0;s:35:"\dim p, \deg q, \det m, \ker\phi \!";i:1;s:152:"\dim p, \deg q, \det m, \ker\phi \!";}i:25;a:2:{i:0;s:41:"\Pr j, \hom l, \lVert z \rVert, \arg z \!";i:1;s:158:"\Pr j, \hom l, \lVert z \rVert, \arg z \!";}i:26;a:2:{i:0;s:49:"dt, \operatorname{d}\!t, \partial t, \nabla\psi\!";i:1;s:166:"dt, \operatorname{d}\!t, \partial t, \nabla\psi\!";}i:27;a:2:{i:0;s:155:"dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!";i:1;s:272:"dy/dx, \operatorname{d}\!y/\operatorname{d}\!x, {dy \over dx}, {\operatorname{d}\!y\over\operatorname{d}\!x}, {\partial^2\over\partial x_1\partial x_2}y \!";}i:28;a:2:{i:0;s:66:"\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y";i:1;s:198:"\prime, \backprime, f^\prime, f', f'', f^{(3)} \!, \dot y, \ddot y";}i:29;a:2:{i:0;s:64:"\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar \!";i:1;s:181:"\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar \!";}i:30;a:2:{i:0;s:62:"\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS \!";i:1;s:179:"\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS \!";}i:31;a:2:{i:0;s:24:"s_k \equiv 0 \pmod{m} \!";i:1;s:141:"s_k \equiv 0 \pmod{m} \!";}i:32;a:2:{i:0;s:14:"a\,\bmod\,b \!";i:1;s:131:"a\,\bmod\,b \!";}i:33;a:2:{i:0;s:36:"\gcd(m, n), \operatorname{lcm}(m, n)";i:1;s:153:"\gcd(m, n), \operatorname{lcm}(m, n)";}i:34;a:2:{i:0;s:37:"\mid, \nmid, \shortmid, \nshortmid \!";i:1;s:154:"\mid, \nmid, \shortmid, \nshortmid \!";}i:35;a:2:{i:0;s:57:"\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} \!";i:1;s:174:"\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{x^3+y^3 \over 2} \!";}i:36;a:2:{i:0;s:27:"+, -, \pm, \mp, \dotplus \!";i:1;s:144:"+, -, \pm, \mp, \dotplus \!";}i:37;a:2:{i:0;s:46:"\times, \div, \divideontimes, /, \backslash \!";i:1;s:163:"\times, \div, \divideontimes, /, \backslash \!";}i:38;a:2:{i:0;s:39:"\cdot, * \ast, \star, \circ, \bullet \!";i:1;s:156:"\cdot, * \ast, \star, \circ, \bullet \!";}i:39;a:2:{i:0;s:42:"\boxplus, \boxminus, \boxtimes, \boxdot \!";i:1;s:159:"\boxplus, \boxminus, \boxtimes, \boxdot \!";}i:40;a:2:{i:0;s:42:"\oplus, \ominus, \otimes, \oslash, \odot\!";i:1;s:159:"\oplus, \ominus, \otimes, \oslash, \odot\!";}i:41;a:2:{i:0;s:42:"\circleddash, \circledcirc, \circledast \!";i:1;s:159:"\circleddash, \circledcirc, \circledast \!";}i:42;a:2:{i:0;s:34:"\bigoplus, \bigotimes, \bigodot \!";i:1;s:151:"\bigoplus, \bigotimes, \bigodot \!";}i:43;a:2:{i:0;s:42:"\{ \}, \O \empty \emptyset, \varnothing \!";i:1;s:159:"\{ \}, \O \empty \emptyset, \varnothing \!";}i:44;a:2:{i:0;s:36:"\in, \notin \not\in, \ni, \not\ni \!";i:1;s:153:"\in, \notin \not\in, \ni, \not\ni \!";}i:45;a:2:{i:0;s:30:"\cap, \Cap, \sqcap, \bigcap \!";i:1;s:147:"\cap, \Cap, \sqcap, \bigcap \!";}i:46;a:2:{i:0;s:60:"\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus \!";i:1;s:177:"\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus \!";}i:47;a:2:{i:0;s:36:"\setminus, \smallsetminus, \times \!";i:1;s:153:"\setminus, \smallsetminus, \times \!";}i:48;a:2:{i:0;s:30:"\subset, \Subset, \sqsubset \!";i:1;s:147:"\subset, \Subset, \sqsubset \!";}i:49;a:2:{i:0;s:30:"\supset, \Supset, \sqsupset \!";i:1;s:147:"\supset, \Supset, \sqsupset \!";}i:50;a:2:{i:0;s:64:"\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq \!";i:1;s:181:"\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq \!";}i:51;a:2:{i:0;s:64:"\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq \!";i:1;s:181:"\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq \!";}i:52;a:2:{i:0;s:55:"\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq \!";i:1;s:172:"\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq \!";}i:53;a:2:{i:0;s:55:"\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq \!";i:1;s:172:"\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq \!";}i:54;a:2:{i:0;s:35:"=, \ne, \neq, \equiv, \not\equiv \!";i:1;s:152:"=, \ne, \neq, \equiv, \not\equiv \!";}i:55;a:2:{i:0;s:64:"\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := \!";i:1;s:181:"\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := \!";}i:56;a:2:{i:0;s:78:"\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong \!";i:1;s:195:"\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong \!";}i:57;a:2:{i:0;s:64:"\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto \!";i:1;s:181:"\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto \!";}i:58;a:2:{i:0;s:52:"<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot \!";i:1;s:172:"<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot \!";}i:59;a:2:{i:0;s:50:">, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \!";i:1;s:170:">, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot \!";}i:60;a:2:{i:0;s:53:"\le \leq, \lneq, \leqq, \nleqq, \lneqq, \lvertneqq \!";i:1;s:170:"\le \leq, \lneq, \leqq, \nleqq, \lneqq, \lvertneqq \!";}i:61;a:2:{i:0;s:53:"\ge \geq, \gneq, \geqq, \ngeqq, \gneqq, \gvertneqq \!";i:1;s:170:"\ge \geq, \gneq, \geqq, \ngeqq, \gneqq, \gvertneqq \!";}i:62;a:2:{i:0;s:66:"\lessgtr \lesseqgtr \lesseqqgtr \gtrless \gtreqless \gtreqqless \!";i:1;s:183:"\lessgtr \lesseqgtr \lesseqqgtr \gtrless \gtreqless \gtreqqless \!";}i:63;a:2:{i:0;s:38:"\leqslant, \nleqslant, \eqslantless \!";i:1;s:155:"\leqslant, \nleqslant, \eqslantless \!";}i:64;a:2:{i:0;s:37:"\geqslant, \ngeqslant, \eqslantgtr \!";i:1;s:154:"\geqslant, \ngeqslant, \eqslantgtr \!";}i:65;a:2:{i:0;s:43:"\lesssim, \lnsim, \lessapprox, \lnapprox \!";i:1;s:160:"\lesssim, \lnsim, \lessapprox, \lnapprox \!";}i:66;a:2:{i:0;s:42:" \gtrsim, \gnsim, \gtrapprox, \gnapprox \,";i:1;s:159:" \gtrsim, \gnsim, \gtrapprox, \gnapprox \,";}i:67;a:2:{i:0;s:46:"\prec, \nprec, \preceq, \npreceq, \precneqq \!";i:1;s:163:"\prec, \nprec, \preceq, \npreceq, \precneqq \!";}i:68;a:2:{i:0;s:46:"\succ, \nsucc, \succeq, \nsucceq, \succneqq \!";i:1;s:163:"\succ, \nsucc, \succeq, \nsucceq, \succneqq \!";}i:69;a:2:{i:0;s:29:"\preccurlyeq, \curlyeqprec \,";i:1;s:146:"\preccurlyeq, \curlyeqprec \,";}i:70;a:2:{i:0;s:29:"\succcurlyeq, \curlyeqsucc \,";i:1;s:146:"\succcurlyeq, \curlyeqsucc \,";}i:71;a:2:{i:0;s:49:"\precsim, \precnsim, \precapprox, \precnapprox \,";i:1;s:166:"\precsim, \precnsim, \precapprox, \precnapprox \,";}i:72;a:2:{i:0;s:49:"\succsim, \succnsim, \succapprox, \succnapprox \,";i:1;s:166:"\succsim, \succnsim, \succapprox, \succnapprox \,";}i:73;a:2:{i:0;s:57:"\parallel, \nparallel, \shortparallel, \nshortparallel \!";i:1;s:174:"\parallel, \nparallel, \shortparallel, \nshortparallel \!";}i:74;a:2:{i:0;s:59:"\perp, \angle, \sphericalangle, \measuredangle, 45^\circ \!";i:1;s:176:"\perp, \angle, \sphericalangle, \measuredangle, 45^\circ \!";}i:75;a:2:{i:0;s:75:"\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar \!";i:1;s:192:"\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar \!";}i:76;a:2:{i:0;s:55:"\bigcirc, \triangle \bigtriangleup, \bigtriangledown \!";i:1;s:172:"\bigcirc, \triangle \bigtriangleup, \bigtriangledown \!";}i:77;a:2:{i:0;s:29:"\vartriangle, \triangledown\!";i:1;s:146:"\vartriangle, \triangledown\!";}i:78;a:2:{i:0;s:78:"\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright \!";i:1;s:195:"\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright \!";}i:79;a:2:{i:0;s:29:"\forall, \exists, \nexists \!";i:1;s:146:"\forall, \exists, \nexists \!";}i:80;a:2:{i:0;s:29:"\therefore, \because, \And \!";i:1;s:146:"\therefore, \because, \And \!";}i:81;a:2:{i:0;s:36:"\or \lor \vee, \curlyvee, \bigvee \!";i:1;s:153:"\or \lor \vee, \curlyvee, \bigvee \!";}i:82;a:2:{i:0;s:44:"\and \land \wedge, \curlywedge, \bigwedge \!";i:1;s:161:"\and \land \wedge, \curlywedge, \bigwedge \!";}i:83;a:2:{i:0;s:52:"\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, \!";i:1;s:169:"\bar{q}, \bar{abc}, \overline{q}, \overline{abc}, \!";}i:84;a:2:{i:0;s:47:"\lnot \neg, \not\operatorname{R}, \bot, \top \!";i:1;s:164:"\lnot \neg, \not\operatorname{R}, \bot, \top \!";}i:85;a:2:{i:0;s:41:"\vdash \dashv, \vDash, \Vdash, \models \!";i:1;s:158:"\vdash \dashv, \vDash, \Vdash, \models \!";}i:86;a:2:{i:0;s:42:"\Vvdash \nvdash \nVdash \nvDash \nVDash \!";i:1;s:159:"\Vvdash \nvdash \nVdash \nvDash \nVDash \!";}i:87;a:2:{i:0;s:42:"\ulcorner \urcorner \llcorner \lrcorner \,";i:1;s:159:"\ulcorner \urcorner \llcorner \lrcorner \,";}i:88;a:2:{i:0;s:28:"\Rrightarrow, \Lleftarrow \!";i:1;s:145:"\Rrightarrow, \Lleftarrow \!";}i:89;a:2:{i:0;s:53:"\Rightarrow, \nRightarrow, \Longrightarrow \implies\!";i:1;s:170:"\Rightarrow, \nRightarrow, \Longrightarrow \implies\!";}i:90;a:2:{i:0;s:42:"\Leftarrow, \nLeftarrow, \Longleftarrow \!";i:1;s:159:"\Leftarrow, \nLeftarrow, \Longleftarrow \!";}i:91;a:2:{i:0;s:62:"\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff \!";i:1;s:179:"\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff \!";}i:92;a:2:{i:0;s:37:"\Uparrow, \Downarrow, \Updownarrow \!";i:1;s:154:"\Uparrow, \Downarrow, \Updownarrow \!";}i:93;a:2:{i:0;s:48:"\rightarrow \to, \nrightarrow, \longrightarrow\!";i:1;s:165:"\rightarrow \to, \nrightarrow, \longrightarrow\!";}i:94;a:2:{i:0;s:47:"\leftarrow \gets, \nleftarrow, \longleftarrow\!";i:1;s:164:"\leftarrow \gets, \nleftarrow, \longleftarrow\!";}i:95;a:2:{i:0;s:57:"\leftrightarrow, \nleftrightarrow, \longleftrightarrow \!";i:1;s:174:"\leftrightarrow, \nleftrightarrow, \longleftrightarrow \!";}i:96;a:2:{i:0;s:37:"\uparrow, \downarrow, \updownarrow \!";i:1;s:154:"\uparrow, \downarrow, \updownarrow \!";}i:97;a:2:{i:0;s:41:"\nearrow, \swarrow, \nwarrow, \searrow \!";i:1;s:158:"\nearrow, \swarrow, \nwarrow, \searrow \!";}i:98;a:2:{i:0;s:23:"\mapsto, \longmapsto \!";i:1;s:140:"\mapsto, \longmapsto \!";}i:99;a:2:{i:0;s:174:"\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!";i:1;s:291:"\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!";}i:100;a:2:{i:0;s:121:"\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright \,\!";i:1;s:238:"\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright \,\!";}i:101;a:2:{i:0;s:123:"\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft \,\!";i:1;s:240:"\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft \,\!";}i:102;a:2:{i:0;s:118:"\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow \!";i:1;s:235:"\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow \!";}i:103;a:2:{i:0;s:49:"\amalg \P \S \% \dagger \ddagger \ldots \cdots \!";i:1;s:166:"\amalg \P \S \% \dagger \ddagger \ldots \cdots \!";}i:104;a:2:{i:0;s:48:"\smile \frown \wr \triangleleft \triangleright\!";i:1;s:165:"\smile \frown \wr \triangleleft \triangleright\!";}i:105;a:2:{i:0;s:82:"\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp \!";i:1;s:199:"\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp \!";}i:106;a:2:{i:0;s:80:"\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes \!";i:1;s:197:"\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes \!";}i:107;a:2:{i:0;s:84:"\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq \!";i:1;s:201:"\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq \!";}i:108;a:2:{i:0;s:66:"\intercal \barwedge \veebar \doublebarwedge \between \pitchfork \!";i:1;s:183:"\intercal \barwedge \veebar \doublebarwedge \between \pitchfork \!";}i:109;a:2:{i:0;s:68:"\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright \!";i:1;s:185:"\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright \!";}i:110;a:2:{i:0;s:70:"\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq \!";i:1;s:187:"\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq \!";}i:111;a:2:{i:0;s:3:"a^2";i:1;s:120:"a^2";}i:112;a:2:{i:0;s:3:"a_2";i:1;s:120:"a_2";}i:113;a:2:{i:0;s:15:"10^{30} a^{2+2}";i:1;s:132:"10^{30} a^{2+2}";}i:114;a:2:{i:0;s:14:"a_{i,j} b_{f'}";i:1;s:136:"a_{i,j} b_{f'}";}i:115;a:2:{i:0;s:5:"x_2^3";i:1;s:122:"x_2^3";}i:116;a:2:{i:0;s:12:"{x_2}^3 \,\!";i:1;s:129:"{x_2}^3 \,\!";}i:117;a:2:{i:0;s:11:"10^{10^{8}}";i:1;s:128:"10^{10^{8}}";}i:118;a:2:{i:0;s:29:"\sideset{_1^2}{_3^4}\prod_a^b";i:1;s:146:"\sideset{_1^2}{_3^4}\prod_a^b";}i:119;a:2:{i:0;s:18:"{}_1^2\!\Omega_3^4";i:1;s:135:"{}_1^2\!\Omega_3^4";}i:120;a:2:{i:0;s:24:"\overset{\alpha}{\omega}";i:1;s:141:"\overset{\alpha}{\omega}";}i:121;a:2:{i:0;s:25:"\underset{\alpha}{\omega}";i:1;s:142:"\underset{\alpha}{\omega}";}i:122;a:2:{i:0;s:43:"\overset{\alpha}{\underset{\gamma}{\omega}}";i:1;s:160:"\overset{\alpha}{\underset{\gamma}{\omega}}";}i:123;a:2:{i:0;s:25:"\stackrel{\alpha}{\omega}";i:1;s:142:"\stackrel{\alpha}{\omega}";}i:124;a:2:{i:0;s:16:"x', y'', f', f''";i:1;s:163:"x', y'', f', f''";}i:125;a:2:{i:0;s:26:"x^\prime, y^{\prime\prime}";i:1;s:143:"x^\prime, y^{\prime\prime}";}i:126;a:2:{i:0;s:17:"\dot{x}, \ddot{x}";i:1;s:134:"\dot{x}, \ddot{x}";}i:127;a:2:{i:0;s:25:" \hat a \ \bar b \ \vec c";i:1;s:142:" \hat a \ \bar b \ \vec c";}i:128;a:2:{i:0;s:61:" \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}";i:1;s:178:" \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}";}i:129;a:2:{i:0;s:37:" \overline{g h i} \ \underline{j k l}";i:1;s:154:" \overline{g h i} \ \underline{j k l}";}i:130;a:2:{i:0;s:21:"\overset{\frown} {AB}";i:1;s:138:"\overset{\frown} {AB}";}i:131;a:2:{i:0;s:53:" A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C";i:1;s:170:" A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C";}i:132;a:2:{i:0;s:35:"\overbrace{ 1+2+\cdots+100 }^{5050}";i:1;s:152:"\overbrace{ 1+2+\cdots+100 }^{5050}";}i:133;a:2:{i:0;s:32:"\underbrace{ a+b+\cdots+z }_{26}";i:1;s:149:"\underbrace{ a+b+\cdots+z }_{26}";}i:134;a:2:{i:0;s:16:"\sum_{k=1}^N k^2";i:1;s:133:"\sum_{k=1}^N k^2";}i:135;a:2:{i:0;s:27:"\textstyle \sum_{k=1}^N k^2";i:1;s:144:"\textstyle \sum_{k=1}^N k^2";}i:136;a:2:{i:0;s:26:"\frac{\sum_{k=1}^N k^2}{a}";i:1;s:143:"\frac{\sum_{k=1}^N k^2}{a}";}i:137;a:2:{i:0;s:40:"\frac{\displaystyle \sum_{k=1}^N k^2}{a}";i:1;s:157:"\frac{\displaystyle \sum_{k=1}^N k^2}{a}";}i:138;a:2:{i:0;s:36:"\frac{\sum\limits^{^N}_{k=1} k^2}{a}";i:1;s:153:"\frac{\sum\limits^{^N}_{k=1} k^2}{a}";}i:139;a:2:{i:0;s:17:"\prod_{i=1}^N x_i";i:1;s:134:"\prod_{i=1}^N x_i";}i:140;a:2:{i:0;s:28:"\textstyle \prod_{i=1}^N x_i";i:1;s:145:"\textstyle \prod_{i=1}^N x_i";}i:141;a:2:{i:0;s:19:"\coprod_{i=1}^N x_i";i:1;s:136:"\coprod_{i=1}^N x_i";}i:142;a:2:{i:0;s:30:"\textstyle \coprod_{i=1}^N x_i";i:1;s:147:"\textstyle \coprod_{i=1}^N x_i";}i:143;a:2:{i:0;s:22:"\lim_{n \to \infty}x_n";i:1;s:139:"\lim_{n \to \infty}x_n";}i:144;a:2:{i:0;s:33:"\textstyle \lim_{n \to \infty}x_n";i:1;s:150:"\textstyle \lim_{n \to \infty}x_n";}i:145;a:2:{i:0;s:41:"\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx";i:1;s:158:"\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx";}i:146;a:2:{i:0;s:34:"\int_{1}^{3}\frac{e^3/x}{x^2}\, dx";i:1;s:151:"\int_{1}^{3}\frac{e^3/x}{x^2}\, dx";}i:147;a:2:{i:0;s:40:"\textstyle \int\limits_{-N}^{N} e^x\, dx";i:1;s:157:"\textstyle \int\limits_{-N}^{N} e^x\, dx";}i:148;a:2:{i:0;s:33:"\textstyle \int_{-N}^{N} e^x\, dx";i:1;s:150:"\textstyle \int_{-N}^{N} e^x\, dx";}i:149;a:2:{i:0;s:24:"\iint\limits_D \, dx\,dy";i:1;s:141:"\iint\limits_D \, dx\,dy";}i:150;a:2:{i:0;s:29:"\iiint\limits_E \, dx\,dy\,dz";i:1;s:146:"\iiint\limits_E \, dx\,dy\,dz";}i:151;a:2:{i:0;s:34:"\iiiint\limits_F \, dx\,dy\,dz\,dt";i:1;s:151:"\iiiint\limits_F \, dx\,dy\,dz\,dt";}i:152;a:2:{i:0;s:38:"\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy";i:1;s:155:"\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy";}i:153;a:2:{i:0;s:39:"\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy";i:1;s:156:"\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy";}i:154;a:2:{i:0;s:20:"\bigcap_{i=_1}^n E_i";i:1;s:137:"\bigcap_{i=_1}^n E_i";}i:155;a:2:{i:0;s:20:"\bigcup_{i=_1}^n E_i";i:1;s:137:"\bigcup_{i=_1}^n E_i";}i:156;a:2:{i:0;s:15:"\frac{2}{4}=0.5";i:1;s:132:"\frac{2}{4}=0.5";}i:157;a:2:{i:0;s:18:"\tfrac{2}{4} = 0.5";i:1;s:135:"\tfrac{2}{4} = 0.5";}i:158;a:2:{i:0;s:72:"\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a";i:1;s:189:"\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a";}i:159;a:2:{i:0;s:46:"\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a";i:1;s:163:"\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a";}i:160;a:2:{i:0;s:60:"\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}";i:1;s:177:"\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}";}i:161;a:2:{i:0;s:12:"\binom{n}{k}";i:1;s:129:"\binom{n}{k}";}i:162;a:2:{i:0;s:13:"\tbinom{n}{k}";i:1;s:130:"\tbinom{n}{k}";}i:163;a:2:{i:0;s:13:"\dbinom{n}{k}";i:1;s:130:"\dbinom{n}{k}";}i:164;a:2:{i:0;s:42:"\begin{matrix} x & y \\ z & v +\end{matrix}";i:1;s:171:"\begin{matrix} x & y \\ z & v \end{matrix}";}i:165;a:2:{i:0;s:44:"\begin{vmatrix} x & y \\ z & v +\end{vmatrix}";i:1;s:173:"\begin{vmatrix} x & y \\ z & v \end{vmatrix}";}i:166;a:2:{i:0;s:44:"\begin{Vmatrix} x & y \\ z & v +\end{Vmatrix}";i:1;s:173:"\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}";}i:167;a:2:{i:0;s:90:"\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & -0\end{bmatrix} ";i:1;s:210:"\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} ";}i:168;a:2:{i:0;s:44:"\begin{Bmatrix} x & y \\ z & v -\end{Bmatrix}";i:1;s:144:"\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}";}i:169;a:2:{i:0;s:44:"\begin{pmatrix} x & y \\ z & v -\end{pmatrix}";i:1;s:144:"\begin{pmatrix} x & y \\ z & v \end{pmatrix}";}i:170;a:2:{i:0;s:63:" +0\end{bmatrix} ";i:1;s:239:"\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} ";}i:168;a:2:{i:0;s:44:"\begin{Bmatrix} x & y \\ z & v +\end{Bmatrix}";i:1;s:173:"\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}";}i:169;a:2:{i:0;s:44:"\begin{pmatrix} x & y \\ z & v +\end{pmatrix}";i:1;s:173:"\begin{pmatrix} x & y \\ z & v \end{pmatrix}";}i:170;a:2:{i:0;s:63:" \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) -";i:1;s:175:" \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) ";}i:171;a:2:{i:0;s:104:"f(n) = +";i:1;s:204:" \bigl( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} \bigr) ";}i:171;a:2:{i:0;s:104:"f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} -\end{cases} ";i:1;s:216:"f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases} ";}i:172;a:2:{i:0;s:66:" +\end{cases} ";i:1;s:245:"f(n) = \begin{cases} n/2, & \text{if }n\text{ is even} \\ 3n+1, & \text{if }n\text{ is odd} \end{cases} ";}i:172;a:2:{i:0;s:66:" \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} -";i:1;s:182:" \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} ";}i:173;a:2:{i:0;s:73:" +";i:1;s:211:" \begin{align} f(x) & = (a+b)^2 \\ & = a^2+2ab+b^2 \\ \end{align} ";}i:173;a:2:{i:0;s:73:" \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} -";i:1;s:189:" \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} ";}i:174;a:2:{i:0;s:68:"\begin{array}{lcl} +";i:1;s:218:" \begin{alignat}{2} f(x) & = (a-b)^2 \\ & = a^2-2ab+b^2 \\ \end{alignat} ";}i:174;a:2:{i:0;s:68:"\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z -\end{array}";i:1;s:184:"\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}";}i:175;a:2:{i:0;s:68:"\begin{array}{lcr} +\end{array}";i:1;s:213:"\begin{array}{lcl} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}";}i:175;a:2:{i:0;s:68:"\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z -\end{array}";i:1;s:184:"\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}";}i:176;a:2:{i:0;s:9:"f(x) \,\!";i:1;s:97:"f(x) \,\!";}i:177;a:2:{i:0;s:28:"= \sum_{n=0}^\infty a_n x^n ";i:1;s:116:"= \sum_{n=0}^\infty a_n x^n ";}i:178;a:2:{i:0;s:24:"= a_0+a_1x+a_2x^2+\cdots";i:1;s:112:"= a_0+a_1x+a_2x^2+\cdots";}i:179;a:2:{i:0;s:9:"f(x) \,\!";i:1;s:97:"f(x) \,\!";}i:180;a:2:{i:0;s:28:"= \sum_{n=0}^\infty a_n x^n ";i:1;s:116:"= \sum_{n=0}^\infty a_n x^n ";}i:181;a:2:{i:0;s:25:"= a_0 +a_1x+a_2x^2+\cdots";i:1;s:113:"= a_0 +a_1x+a_2x^2+\cdots";}i:182;a:2:{i:0;s:70:"\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}";i:1;s:158:"\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}";}i:183;a:2:{i:0;s:89:" +\end{array}";i:1;s:213:"\begin{array}{lcr} z & = & a \\ f(x,y,z) & = & x + y + z \end{array}";}i:176;a:2:{i:0;s:9:"f(x) \,\!";i:1;s:126:"f(x) \,\!";}i:177;a:2:{i:0;s:28:"= \sum_{n=0}^\infty a_n x^n ";i:1;s:145:"= \sum_{n=0}^\infty a_n x^n ";}i:178;a:2:{i:0;s:24:"= a_0+a_1x+a_2x^2+\cdots";i:1;s:141:"= a_0+a_1x+a_2x^2+\cdots";}i:179;a:2:{i:0;s:9:"f(x) \,\!";i:1;s:126:"f(x) \,\!";}i:180;a:2:{i:0;s:28:"= \sum_{n=0}^\infty a_n x^n ";i:1;s:145:"= \sum_{n=0}^\infty a_n x^n ";}i:181;a:2:{i:0;s:25:"= a_0 +a_1x+a_2x^2+\cdots";i:1;s:142:"= a_0 +a_1x+a_2x^2+\cdots";}i:182;a:2:{i:0;s:70:"\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}";i:1;s:187:"\begin{cases} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{cases}";}i:183;a:2:{i:0;s:89:" \begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ @@ -37,37 +37,37 @@ f(x,y,z) & = & x + y + z 1&0&1\\ 1&1&0\\ \end{array} -";i:1;s:249:" \begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array} ";}i:184;a:2:{i:0;s:15:"( \frac{1}{2} )";i:1;s:103:"( \frac{1}{2} )";}i:185;a:2:{i:0;s:28:"\left ( \frac{1}{2} \right )";i:1;s:116:"\left ( \frac{1}{2} \right )";}i:186;a:2:{i:0;s:28:"\left ( \frac{a}{b} \right )";i:1;s:116:"\left ( \frac{a}{b} \right )";}i:187;a:2:{i:0;s:75:"\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack";i:1;s:163:"\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack";}i:188;a:2:{i:0;s:77:"\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace";i:1;s:165:"\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace";}i:189;a:2:{i:0;s:40:"\left \langle \frac{a}{b} \right \rangle";i:1;s:128:"\left \langle \frac{a}{b} \right \rangle";}i:190;a:2:{i:0;s:72:"\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|";i:1;s:160:"\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|";}i:191;a:2:{i:0;s:85:"\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil";i:1;s:173:"\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil";}i:192;a:2:{i:0;s:37:"\left / \frac{a}{b} \right \backslash";i:1;s:125:"\left / \frac{a}{b} \right \backslash";}i:193;a:2:{i:0;s:152:"\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow";i:1;s:240:"\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow";}i:194;a:2:{i:0;s:20:"\left [ 0,1 \right )";i:1;s:108:"\left [ 0,1 \right )";}i:195;a:2:{i:0;s:27:"\left \langle \psi \right |";i:1;s:115:"\left \langle \psi \right |";}i:196;a:2:{i:0;s:35:"\left . \frac{A}{B} \right \} \to X";i:1;s:123:"\left . \frac{A}{B} \right \} \to X";}i:197;a:2:{i:0;s:57:"\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]";i:1;s:145:"\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]";}i:198;a:2:{i:0;s:85:"\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle";i:1;s:173:"\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle";}i:199;a:2:{i:0;s:61:"\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|";i:1;s:149:"\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|";}i:200;a:2:{i:0;s:101:"\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil";i:1;s:189:"\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil";}i:201;a:2:{i:0;s:121:"\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow";i:1;s:209:"\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow";}i:202;a:2:{i:0;s:145:"\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow";i:1;s:233:"\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow";}i:203;a:2:{i:0;s:97:"\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash";i:1;s:185:"\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash";}i:204;a:2:{i:0;s:22:"x^2 + y^2 + z^2 = 1 \,";i:1;s:110:"x^2 + y^2 + z^2 = 1 \,";}i:205;a:2:{i:0;s:56:"\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta \!";i:1;s:144:"\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta \!";}i:206;a:2:{i:0;s:44:"\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho \!";i:1;s:132:"\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho \!";}i:207;a:2:{i:0;s:45:"\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega \!";i:1;s:133:"\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega \!";}i:208;a:2:{i:0;s:56:"\alpha \beta \gamma \delta \epsilon \zeta \eta \theta \!";i:1;s:144:"\alpha \beta \gamma \delta \epsilon \zeta \eta \theta \!";}i:209;a:2:{i:0;s:44:"\iota \kappa \lambda \mu \nu \xi \pi \rho \!";i:1;s:132:"\iota \kappa \lambda \mu \nu \xi \pi \rho \!";}i:210;a:2:{i:0;s:45:"\sigma \tau \upsilon \phi \chi \psi \omega \!";i:1;s:133:"\sigma \tau \upsilon \phi \chi \psi \omega \!";}i:211;a:2:{i:0;s:40:"\varepsilon \digamma \varkappa \varpi \!";i:1;s:128:"\varepsilon \digamma \varkappa \varpi \!";}i:212;a:2:{i:0;s:38:"\varrho \varsigma \vartheta \varphi \!";i:1;s:126:"\varrho \varsigma \vartheta \varphi \!";}i:213;a:2:{i:0;s:30:"\aleph \beth \gimel \daleth \!";i:1;s:118:"\aleph \beth \gimel \daleth \!";}i:214;a:2:{i:0;s:21:"\mathbb{ABCDEFGHI} \!";i:1;s:109:"\mathbb{ABCDEFGHI} \!";}i:215;a:2:{i:0;s:21:"\mathbb{JKLMNOPQR} \!";i:1;s:109:"\mathbb{JKLMNOPQR} \!";}i:216;a:2:{i:0;s:20:"\mathbb{STUVWXYZ} \!";i:1;s:108:"\mathbb{STUVWXYZ} \!";}i:217;a:2:{i:0;s:21:"\mathbf{ABCDEFGHI} \!";i:1;s:109:"\mathbf{ABCDEFGHI} \!";}i:218;a:2:{i:0;s:21:"\mathbf{JKLMNOPQR} \!";i:1;s:109:"\mathbf{JKLMNOPQR} \!";}i:219;a:2:{i:0;s:20:"\mathbf{STUVWXYZ} \!";i:1;s:108:"\mathbf{STUVWXYZ} \!";}i:220;a:2:{i:0;s:25:"\mathbf{abcdefghijklm} \!";i:1;s:113:"\mathbf{abcdefghijklm} \!";}i:221;a:2:{i:0;s:25:"\mathbf{nopqrstuvwxyz} \!";i:1;s:113:"\mathbf{nopqrstuvwxyz} \!";}i:222;a:2:{i:0;s:22:"\mathbf{0123456789} \!";i:1;s:110:"\mathbf{0123456789} \!";}i:223;a:2:{i:0;s:62:"\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";i:1;s:150:"\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";}i:224;a:2:{i:0;s:50:"\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";i:1;s:138:"\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";}i:225;a:2:{i:0;s:52:"\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";i:1;s:140:"\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";}i:226;a:2:{i:0;s:62:"\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta} \!";i:1;s:150:"\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta} \!";}i:227;a:2:{i:0;s:50:"\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho} \!";i:1;s:138:"\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho} \!";}i:228;a:2:{i:0;s:52:"\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega} \!";i:1;s:140:"\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega} \!";}i:229;a:2:{i:0;s:50:"\boldsymbol{\varepsilon\digamma\varkappa\varpi} \!";i:1;s:138:"\boldsymbol{\varepsilon\digamma\varkappa\varpi} \!";}i:230;a:2:{i:0;s:48:"\boldsymbol{\varrho\varsigma\vartheta\varphi} \!";i:1;s:136:"\boldsymbol{\varrho\varsigma\vartheta\varphi} \!";}i:231;a:2:{i:0;s:22:"\mathit{0123456789} \!";i:1;s:110:"\mathit{0123456789} \!";}i:232;a:2:{i:0;s:58:"\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";i:1;s:146:"\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";}i:233;a:2:{i:0;s:46:"\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";i:1;s:134:"\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";}i:234;a:2:{i:0;s:48:"\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";i:1;s:136:"\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";}i:235;a:2:{i:0;s:21:"\mathrm{ABCDEFGHI} \!";i:1;s:109:"\mathrm{ABCDEFGHI} \!";}i:236;a:2:{i:0;s:21:"\mathrm{JKLMNOPQR} \!";i:1;s:109:"\mathrm{JKLMNOPQR} \!";}i:237;a:2:{i:0;s:20:"\mathrm{STUVWXYZ} \!";i:1;s:108:"\mathrm{STUVWXYZ} \!";}i:238;a:2:{i:0;s:25:"\mathrm{abcdefghijklm} \!";i:1;s:113:"\mathrm{abcdefghijklm} \!";}i:239;a:2:{i:0;s:25:"\mathrm{nopqrstuvwxyz} \!";i:1;s:113:"\mathrm{nopqrstuvwxyz} \!";}i:240;a:2:{i:0;s:22:"\mathrm{0123456789} \!";i:1;s:110:"\mathrm{0123456789} \!";}i:241;a:2:{i:0;s:21:"\mathsf{ABCDEFGHI} \!";i:1;s:109:"\mathsf{ABCDEFGHI} \!";}i:242;a:2:{i:0;s:21:"\mathsf{JKLMNOPQR} \!";i:1;s:109:"\mathsf{JKLMNOPQR} \!";}i:243;a:2:{i:0;s:20:"\mathsf{STUVWXYZ} \!";i:1;s:108:"\mathsf{STUVWXYZ} \!";}i:244;a:2:{i:0;s:25:"\mathsf{abcdefghijklm} \!";i:1;s:113:"\mathsf{abcdefghijklm} \!";}i:245;a:2:{i:0;s:25:"\mathsf{nopqrstuvwxyz} \!";i:1;s:113:"\mathsf{nopqrstuvwxyz} \!";}i:246;a:2:{i:0;s:22:"\mathsf{0123456789} \!";i:1;s:110:"\mathsf{0123456789} \!";}i:247;a:2:{i:0;s:65:"\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} \!";i:1;s:153:"\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} \!";}i:248;a:2:{i:0;s:53:"\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho} \!";i:1;s:141:"\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho} \!";}i:249;a:2:{i:0;s:53:"\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}\!";i:1;s:141:"\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}\!";}i:250;a:2:{i:0;s:22:"\mathcal{ABCDEFGHI} \!";i:1;s:110:"\mathcal{ABCDEFGHI} \!";}i:251;a:2:{i:0;s:22:"\mathcal{JKLMNOPQR} \!";i:1;s:110:"\mathcal{JKLMNOPQR} \!";}i:252;a:2:{i:0;s:21:"\mathcal{STUVWXYZ} \!";i:1;s:109:"\mathcal{STUVWXYZ} \!";}i:253;a:2:{i:0;s:23:"\mathfrak{ABCDEFGHI} \!";i:1;s:111:"\mathfrak{ABCDEFGHI} \!";}i:254;a:2:{i:0;s:23:"\mathfrak{JKLMNOPQR} \!";i:1;s:111:"\mathfrak{JKLMNOPQR} \!";}i:255;a:2:{i:0;s:22:"\mathfrak{STUVWXYZ} \!";i:1;s:110:"\mathfrak{STUVWXYZ} \!";}i:256;a:2:{i:0;s:27:"\mathfrak{abcdefghijklm} \!";i:1;s:115:"\mathfrak{abcdefghijklm} \!";}i:257;a:2:{i:0;s:27:"\mathfrak{nopqrstuvwxyz} \!";i:1;s:115:"\mathfrak{nopqrstuvwxyz} \!";}i:258;a:2:{i:0;s:24:"\mathfrak{0123456789} \!";i:1;s:112:"\mathfrak{0123456789} \!";}i:259;a:2:{i:0;s:5:"x y z";i:1;s:93:"x y z";}i:260;a:2:{i:0;s:12:"\text{x y z}";i:1;s:100:"\text{x y z}";}i:261;a:2:{i:0;s:26:"\text{if} n \text{is even}";i:1;s:114:"\text{if} n \text{is even}";}i:262;a:2:{i:0;s:26:"\text{if }n\text{ is even}";i:1;s:114:"\text{if }n\text{ is even}";}i:263;a:2:{i:0;s:27:"\text{if}~n\ \text{is even}";i:1;s:115:"\text{if}~n\ \text{is even}";}i:264;a:2:{i:0;s:64:"{\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}";i:1;s:152:"{\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}";}i:265;a:2:{i:0;s:49:"x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}";i:1;s:137:"x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}";}i:266;a:2:{i:0;s:17:"e^{i \pi} + 1 = 0";i:1;s:105:"e^{i \pi} + 1 = 0";}i:267;a:2:{i:0;s:71:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";i:1;s:159:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";}i:268;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:109:"e^{i \pi} + 1 = 0\,\!";}i:269;a:2:{i:0;s:71:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";i:1;s:159:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";}i:270;a:2:{i:0;s:17:"e^{i \pi} + 1 = 0";i:1;s:105:"e^{i \pi} + 1 = 0";}i:271;a:2:{i:0;s:71:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";i:1;s:159:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";}i:272;a:2:{i:0;s:29:"\color{Apricot}\text{Apricot}";i:1;s:117:"\color{Apricot}\text{Apricot}";}i:273;a:2:{i:0;s:35:"\color{Aquamarine}\text{Aquamarine}";i:1;s:123:"\color{Aquamarine}\text{Aquamarine}";}i:274;a:2:{i:0;s:37:"\color{Bittersweet}\text{Bittersweet}";i:1;s:125:"\color{Bittersweet}\text{Bittersweet}";}i:275;a:2:{i:0;s:25:"\color{Black}\text{Black}";i:1;s:113:"\color{Black}\text{Black}";}i:276;a:2:{i:0;s:23:"\color{Blue}\text{Blue}";i:1;s:111:"\color{Blue}\text{Blue}";}i:277;a:2:{i:0;s:33:"\color{BlueGreen}\text{BlueGreen}";i:1;s:121:"\color{BlueGreen}\text{BlueGreen}";}i:278;a:2:{i:0;s:35:"\color{BlueViolet}\text{BlueViolet}";i:1;s:123:"\color{BlueViolet}\text{BlueViolet}";}i:279;a:2:{i:0;s:31:"\color{BrickRed}\text{BrickRed}";i:1;s:119:"\color{BrickRed}\text{BrickRed}";}i:280;a:2:{i:0;s:25:"\color{Brown}\text{Brown}";i:1;s:113:"\color{Brown}\text{Brown}";}i:281;a:2:{i:0;s:37:"\color{BurntOrange}\text{BurntOrange}";i:1;s:125:"\color{BurntOrange}\text{BurntOrange}";}i:282;a:2:{i:0;s:33:"\color{CadetBlue}\text{CadetBlue}";i:1;s:121:"\color{CadetBlue}\text{CadetBlue}";}i:283;a:2:{i:0;s:41:"\color{CarnationPink}\text{CarnationPink}";i:1;s:129:"\color{CarnationPink}\text{CarnationPink}";}i:284;a:2:{i:0;s:31:"\color{Cerulean}\text{Cerulean}";i:1;s:119:"\color{Cerulean}\text{Cerulean}";}i:285;a:2:{i:0;s:43:"\color{CornflowerBlue}\text{CornflowerBlue}";i:1;s:131:"\color{CornflowerBlue}\text{CornflowerBlue}";}i:286;a:2:{i:0;s:23:"\color{Cyan}\text{Cyan}";i:1;s:111:"\color{Cyan}\text{Cyan}";}i:287;a:2:{i:0;s:33:"\color{Dandelion}\text{Dandelion}";i:1;s:121:"\color{Dandelion}\text{Dandelion}";}i:288;a:2:{i:0;s:35:"\color{DarkOrchid}\text{DarkOrchid}";i:1;s:123:"\color{DarkOrchid}\text{DarkOrchid}";}i:289;a:2:{i:0;s:29:"\color{Emerald}\text{Emerald}";i:1;s:117:"\color{Emerald}\text{Emerald}";}i:290;a:2:{i:0;s:37:"\color{ForestGreen}\text{ForestGreen}";i:1;s:125:"\color{ForestGreen}\text{ForestGreen}";}i:291;a:2:{i:0;s:29:"\color{Fuchsia}\text{Fuchsia}";i:1;s:117:"\color{Fuchsia}\text{Fuchsia}";}i:292;a:2:{i:0;s:33:"\color{Goldenrod}\text{Goldenrod}";i:1;s:121:"\color{Goldenrod}\text{Goldenrod}";}i:293;a:2:{i:0;s:23:"\color{Gray}\text{Gray}";i:1;s:111:"\color{Gray}\text{Gray}";}i:294;a:2:{i:0;s:25:"\color{Green}\text{Green}";i:1;s:113:"\color{Green}\text{Green}";}i:295;a:2:{i:0;s:37:"\color{GreenYellow}\text{GreenYellow}";i:1;s:125:"\color{GreenYellow}\text{GreenYellow}";}i:296;a:2:{i:0;s:37:"\color{JungleGreen}\text{JungleGreen}";i:1;s:125:"\color{JungleGreen}\text{JungleGreen}";}i:297;a:2:{i:0;s:31:"\color{Lavender}\text{Lavender}";i:1;s:119:"\color{Lavender}\text{Lavender}";}i:298;a:2:{i:0;s:33:"\color{LimeGreen}\text{LimeGreen}";i:1;s:121:"\color{LimeGreen}\text{LimeGreen}";}i:299;a:2:{i:0;s:29:"\color{Magenta}\text{Magenta}";i:1;s:117:"\color{Magenta}\text{Magenta}";}i:300;a:2:{i:0;s:31:"\color{Mahogany}\text{Mahogany}";i:1;s:119:"\color{Mahogany}\text{Mahogany}";}i:301;a:2:{i:0;s:27:"\color{Maroon}\text{Maroon}";i:1;s:115:"\color{Maroon}\text{Maroon}";}i:302;a:2:{i:0;s:25:"\color{Melon}\text{Melon}";i:1;s:113:"\color{Melon}\text{Melon}";}i:303;a:2:{i:0;s:39:"\color{MidnightBlue}\text{MidnightBlue}";i:1;s:127:"\color{MidnightBlue}\text{MidnightBlue}";}i:304;a:2:{i:0;s:31:"\color{Mulberry}\text{Mulberry}";i:1;s:119:"\color{Mulberry}\text{Mulberry}";}i:305;a:2:{i:0;s:31:"\color{NavyBlue}\text{NavyBlue}";i:1;s:119:"\color{NavyBlue}\text{NavyBlue}";}i:306;a:2:{i:0;s:35:"\color{OliveGreen}\text{OliveGreen}";i:1;s:123:"\color{OliveGreen}\text{OliveGreen}";}i:307;a:2:{i:0;s:27:"\color{Orange}\text{Orange}";i:1;s:115:"\color{Orange}\text{Orange}";}i:308;a:2:{i:0;s:33:"\color{OrangeRed}\text{OrangeRed}";i:1;s:121:"\color{OrangeRed}\text{OrangeRed}";}i:309;a:2:{i:0;s:27:"\color{Orchid}\text{Orchid}";i:1;s:115:"\color{Orchid}\text{Orchid}";}i:310;a:2:{i:0;s:25:"\color{Peach}\text{Peach}";i:1;s:113:"\color{Peach}\text{Peach}";}i:311;a:2:{i:0;s:35:"\color{Periwinkle}\text{Periwinkle}";i:1;s:123:"\color{Periwinkle}\text{Periwinkle}";}i:312;a:2:{i:0;s:33:"\color{PineGreen}\text{PineGreen}";i:1;s:121:"\color{PineGreen}\text{PineGreen}";}i:313;a:2:{i:0;s:23:"\color{Plum}\text{Plum}";i:1;s:111:"\color{Plum}\text{Plum}";}i:314;a:2:{i:0;s:37:"\color{ProcessBlue}\text{ProcessBlue}";i:1;s:125:"\color{ProcessBlue}\text{ProcessBlue}";}i:315;a:2:{i:0;s:27:"\color{Purple}\text{Purple}";i:1;s:115:"\color{Purple}\text{Purple}";}i:316;a:2:{i:0;s:33:"\color{RawSienna}\text{RawSienna}";i:1;s:121:"\color{RawSienna}\text{RawSienna}";}i:317;a:2:{i:0;s:21:"\color{Red}\text{Red}";i:1;s:109:"\color{Red}\text{Red}";}i:318;a:2:{i:0;s:33:"\color{RedOrange}\text{RedOrange}";i:1;s:121:"\color{RedOrange}\text{RedOrange}";}i:319;a:2:{i:0;s:33:"\color{RedViolet}\text{RedViolet}";i:1;s:121:"\color{RedViolet}\text{RedViolet}";}i:320;a:2:{i:0;s:33:"\color{Rhodamine}\text{Rhodamine}";i:1;s:121:"\color{Rhodamine}\text{Rhodamine}";}i:321;a:2:{i:0;s:33:"\color{RoyalBlue}\text{RoyalBlue}";i:1;s:121:"\color{RoyalBlue}\text{RoyalBlue}";}i:322;a:2:{i:0;s:37:"\color{RoyalPurple}\text{RoyalPurple}";i:1;s:125:"\color{RoyalPurple}\text{RoyalPurple}";}i:323;a:2:{i:0;s:33:"\color{RubineRed}\text{RubineRed}";i:1;s:121:"\color{RubineRed}\text{RubineRed}";}i:324;a:2:{i:0;s:27:"\color{Salmon}\text{Salmon}";i:1;s:115:"\color{Salmon}\text{Salmon}";}i:325;a:2:{i:0;s:31:"\color{SeaGreen}\text{SeaGreen}";i:1;s:119:"\color{SeaGreen}\text{SeaGreen}";}i:326;a:2:{i:0;s:25:"\color{Sepia}\text{Sepia}";i:1;s:113:"\color{Sepia}\text{Sepia}";}i:327;a:2:{i:0;s:29:"\color{SkyBlue}\text{SkyBlue}";i:1;s:117:"\color{SkyBlue}\text{SkyBlue}";}i:328;a:2:{i:0;s:37:"\color{SpringGreen}\text{SpringGreen}";i:1;s:125:"\color{SpringGreen}\text{SpringGreen}";}i:329;a:2:{i:0;s:21:"\color{Tan}\text{Tan}";i:1;s:109:"\color{Tan}\text{Tan}";}i:330;a:2:{i:0;s:31:"\color{TealBlue}\text{TealBlue}";i:1;s:119:"\color{TealBlue}\text{TealBlue}";}i:331;a:2:{i:0;s:29:"\color{Thistle}\text{Thistle}";i:1;s:117:"\color{Thistle}\text{Thistle}";}i:332;a:2:{i:0;s:33:"\color{Turquoise}\text{Turquoise}";i:1;s:121:"\color{Turquoise}\text{Turquoise}";}i:333;a:2:{i:0;s:27:"\color{Violet}\text{Violet}";i:1;s:115:"\color{Violet}\text{Violet}";}i:334;a:2:{i:0;s:33:"\color{VioletRed}\text{VioletRed}";i:1;s:121:"\color{VioletRed}\text{VioletRed}";}i:335;a:2:{i:0;s:43:"\color{WildStrawberry}\text{WildStrawberry}";i:1;s:131:"\color{WildStrawberry}\text{WildStrawberry}";}i:336;a:2:{i:0;s:37:"\color{YellowGreen}\text{YellowGreen}";i:1;s:125:"\color{YellowGreen}\text{YellowGreen}";}i:337;a:2:{i:0;s:39:"\color{YellowOrange}\text{YellowOrange}";i:1;s:127:"\color{YellowOrange}\text{YellowOrange}";}i:338;a:2:{i:0;s:10:"a \qquad b";i:1;s:98:"a \qquad b";}i:339;a:2:{i:0;s:9:"a \quad b";i:1;s:97:"a \quad b";}i:340;a:2:{i:0;s:4:"a\ b";i:1;s:92:"a\ b";}i:341;a:2:{i:0;s:12:"a \mbox{ } b";i:1;s:100:"a \mbox{ } b";}i:342;a:2:{i:0;s:4:"a\;b";i:1;s:92:"a\;b";}i:343;a:2:{i:0;s:4:"a\,b";i:1;s:92:"a\,b";}i:344;a:2:{i:0;s:2:"ab";i:1;s:90:"ab";}i:345;a:2:{i:0;s:11:"\mathit{ab}";i:1;s:99:"\mathit{ab}";}i:346;a:2:{i:0;s:4:"a\!b";i:1;s:92:"a\!b";}i:347;a:2:{i:0;s:59:"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots";i:1;s:147:"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots";}i:348;a:2:{i:0;s:61:"{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}";i:1;s:149:"{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}";}i:349;a:2:{i:0;s:22:"\int_{-N}^{N} e^x\, dx";i:1;s:110:"\int_{-N}^{N} e^x\, dx";}i:350;a:2:{i:0;s:5:"\iint";i:1;s:93:"\iint";}i:351;a:2:{i:0;s:5:"\oint";i:1;s:93:"\oint";}i:352;a:2:{i:0;s:90:"\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot \mathrm{d}\mathbf A";i:1;s:178:"\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot \mathrm{d}\mathbf A";}i:353;a:2:{i:0;s:114:"\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A";i:1;s:202:"\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A";}i:354;a:2:{i:0;s:139:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\cdot\mathrm{d}\mathbf A";i:1;s:227:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\cdot\mathrm{d}\mathbf A";}i:355;a:2:{i:0;s:132:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A";i:1;s:220:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A";}i:356;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"{\scriptstyle S}";}i:357;a:2:{i:0;s:110:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";i:1;s:198:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";}i:358;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"{\scriptstyle S}";}i:359;a:2:{i:0;s:110:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";i:1;s:198:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";}i:360;a:2:{i:0;s:57:"\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:145:"\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";}i:361;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"{\scriptstyle S}";}i:362;a:2:{i:0;s:96:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";i:1;s:184:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";}i:363;a:2:{i:0;s:68:"\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:156:"\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";}i:364;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:104:"{\scriptstyle S}";}i:365;a:2:{i:0;s:96:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";i:1;s:184:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";}i:366;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:99:"\bold{P} = ";}i:367;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:118:"{\scriptstyle \partial \Omega}";}i:368;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:135:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";}i:369;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:99:"\bold{P} = ";}i:370;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:118:"{\scriptstyle \partial \Omega}";}i:371;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:135:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";}i:372;a:2:{i:0;s:20:"\overset{\frown}{AB}";i:1;s:108:"\overset{\frown}{AB}";}i:373;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:105:"ax^2 + bx + c = 0";}i:374;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:105:"ax^2 + bx + c = 0";}i:375;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:120:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";}i:376;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:120:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";}i:377;a:2:{i:0;s:56:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)";i:1;s:144:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)";}i:378;a:2:{i:0;s:56:"2 = \left( +";i:1;s:278:" \begin{array}{|c|c||c|} a & b & S \\ \hline 0&0&1\\ 0&1&1\\ 1&0&1\\ 1&1&0\\ \end{array} ";}i:184;a:2:{i:0;s:15:"( \frac{1}{2} )";i:1;s:132:"( \frac{1}{2} )";}i:185;a:2:{i:0;s:28:"\left ( \frac{1}{2} \right )";i:1;s:145:"\left ( \frac{1}{2} \right )";}i:186;a:2:{i:0;s:28:"\left ( \frac{a}{b} \right )";i:1;s:145:"\left ( \frac{a}{b} \right )";}i:187;a:2:{i:0;s:75:"\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack";i:1;s:192:"\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack";}i:188;a:2:{i:0;s:77:"\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace";i:1;s:194:"\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace";}i:189;a:2:{i:0;s:40:"\left \langle \frac{a}{b} \right \rangle";i:1;s:157:"\left \langle \frac{a}{b} \right \rangle";}i:190;a:2:{i:0;s:72:"\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|";i:1;s:189:"\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|";}i:191;a:2:{i:0;s:85:"\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil";i:1;s:202:"\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil";}i:192;a:2:{i:0;s:37:"\left / \frac{a}{b} \right \backslash";i:1;s:154:"\left / \frac{a}{b} \right \backslash";}i:193;a:2:{i:0;s:152:"\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow";i:1;s:269:"\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow";}i:194;a:2:{i:0;s:20:"\left [ 0,1 \right )";i:1;s:137:"\left [ 0,1 \right )";}i:195;a:2:{i:0;s:27:"\left \langle \psi \right |";i:1;s:144:"\left \langle \psi \right |";}i:196;a:2:{i:0;s:35:"\left . \frac{A}{B} \right \} \to X";i:1;s:152:"\left . \frac{A}{B} \right \} \to X";}i:197;a:2:{i:0;s:57:"\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]";i:1;s:174:"\big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]";}i:198;a:2:{i:0;s:85:"\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle";i:1;s:202:"\big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle";}i:199;a:2:{i:0;s:61:"\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|";i:1;s:178:"\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|";}i:200;a:2:{i:0;s:101:"\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil";i:1;s:218:"\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil";}i:201;a:2:{i:0;s:121:"\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow";i:1;s:238:"\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow";}i:202;a:2:{i:0;s:145:"\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow";i:1;s:262:"\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow";}i:203;a:2:{i:0;s:97:"\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash";i:1;s:214:"\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash";}i:204;a:2:{i:0;s:22:"x^2 + y^2 + z^2 = 1 \,";i:1;s:139:"x^2 + y^2 + z^2 = 1 \,";}i:205;a:2:{i:0;s:56:"\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta \!";i:1;s:173:"\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta \!";}i:206;a:2:{i:0;s:44:"\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho \!";i:1;s:161:"\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho \!";}i:207;a:2:{i:0;s:45:"\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega \!";i:1;s:162:"\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega \!";}i:208;a:2:{i:0;s:56:"\alpha \beta \gamma \delta \epsilon \zeta \eta \theta \!";i:1;s:173:"\alpha \beta \gamma \delta \epsilon \zeta \eta \theta \!";}i:209;a:2:{i:0;s:44:"\iota \kappa \lambda \mu \nu \xi \pi \rho \!";i:1;s:161:"\iota \kappa \lambda \mu \nu \xi \pi \rho \!";}i:210;a:2:{i:0;s:45:"\sigma \tau \upsilon \phi \chi \psi \omega \!";i:1;s:162:"\sigma \tau \upsilon \phi \chi \psi \omega \!";}i:211;a:2:{i:0;s:40:"\varepsilon \digamma \varkappa \varpi \!";i:1;s:157:"\varepsilon \digamma \varkappa \varpi \!";}i:212;a:2:{i:0;s:38:"\varrho \varsigma \vartheta \varphi \!";i:1;s:155:"\varrho \varsigma \vartheta \varphi \!";}i:213;a:2:{i:0;s:30:"\aleph \beth \gimel \daleth \!";i:1;s:147:"\aleph \beth \gimel \daleth \!";}i:214;a:2:{i:0;s:21:"\mathbb{ABCDEFGHI} \!";i:1;s:138:"\mathbb{ABCDEFGHI} \!";}i:215;a:2:{i:0;s:21:"\mathbb{JKLMNOPQR} \!";i:1;s:138:"\mathbb{JKLMNOPQR} \!";}i:216;a:2:{i:0;s:20:"\mathbb{STUVWXYZ} \!";i:1;s:137:"\mathbb{STUVWXYZ} \!";}i:217;a:2:{i:0;s:21:"\mathbf{ABCDEFGHI} \!";i:1;s:138:"\mathbf{ABCDEFGHI} \!";}i:218;a:2:{i:0;s:21:"\mathbf{JKLMNOPQR} \!";i:1;s:138:"\mathbf{JKLMNOPQR} \!";}i:219;a:2:{i:0;s:20:"\mathbf{STUVWXYZ} \!";i:1;s:137:"\mathbf{STUVWXYZ} \!";}i:220;a:2:{i:0;s:25:"\mathbf{abcdefghijklm} \!";i:1;s:142:"\mathbf{abcdefghijklm} \!";}i:221;a:2:{i:0;s:25:"\mathbf{nopqrstuvwxyz} \!";i:1;s:142:"\mathbf{nopqrstuvwxyz} \!";}i:222;a:2:{i:0;s:22:"\mathbf{0123456789} \!";i:1;s:139:"\mathbf{0123456789} \!";}i:223;a:2:{i:0;s:62:"\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";i:1;s:179:"\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";}i:224;a:2:{i:0;s:50:"\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";i:1;s:167:"\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";}i:225;a:2:{i:0;s:52:"\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";i:1;s:169:"\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";}i:226;a:2:{i:0;s:62:"\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta} \!";i:1;s:179:"\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta} \!";}i:227;a:2:{i:0;s:50:"\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho} \!";i:1;s:167:"\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho} \!";}i:228;a:2:{i:0;s:52:"\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega} \!";i:1;s:169:"\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega} \!";}i:229;a:2:{i:0;s:50:"\boldsymbol{\varepsilon\digamma\varkappa\varpi} \!";i:1;s:167:"\boldsymbol{\varepsilon\digamma\varkappa\varpi} \!";}i:230;a:2:{i:0;s:48:"\boldsymbol{\varrho\varsigma\vartheta\varphi} \!";i:1;s:165:"\boldsymbol{\varrho\varsigma\vartheta\varphi} \!";}i:231;a:2:{i:0;s:22:"\mathit{0123456789} \!";i:1;s:139:"\mathit{0123456789} \!";}i:232;a:2:{i:0;s:58:"\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";i:1;s:175:"\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta} \!";}i:233;a:2:{i:0;s:46:"\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";i:1;s:163:"\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho} \!";}i:234;a:2:{i:0;s:48:"\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";i:1;s:165:"\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega} \!";}i:235;a:2:{i:0;s:21:"\mathrm{ABCDEFGHI} \!";i:1;s:138:"\mathrm{ABCDEFGHI} \!";}i:236;a:2:{i:0;s:21:"\mathrm{JKLMNOPQR} \!";i:1;s:138:"\mathrm{JKLMNOPQR} \!";}i:237;a:2:{i:0;s:20:"\mathrm{STUVWXYZ} \!";i:1;s:137:"\mathrm{STUVWXYZ} \!";}i:238;a:2:{i:0;s:25:"\mathrm{abcdefghijklm} \!";i:1;s:142:"\mathrm{abcdefghijklm} \!";}i:239;a:2:{i:0;s:25:"\mathrm{nopqrstuvwxyz} \!";i:1;s:142:"\mathrm{nopqrstuvwxyz} \!";}i:240;a:2:{i:0;s:22:"\mathrm{0123456789} \!";i:1;s:139:"\mathrm{0123456789} \!";}i:241;a:2:{i:0;s:21:"\mathsf{ABCDEFGHI} \!";i:1;s:138:"\mathsf{ABCDEFGHI} \!";}i:242;a:2:{i:0;s:21:"\mathsf{JKLMNOPQR} \!";i:1;s:138:"\mathsf{JKLMNOPQR} \!";}i:243;a:2:{i:0;s:20:"\mathsf{STUVWXYZ} \!";i:1;s:137:"\mathsf{STUVWXYZ} \!";}i:244;a:2:{i:0;s:25:"\mathsf{abcdefghijklm} \!";i:1;s:142:"\mathsf{abcdefghijklm} \!";}i:245;a:2:{i:0;s:25:"\mathsf{nopqrstuvwxyz} \!";i:1;s:142:"\mathsf{nopqrstuvwxyz} \!";}i:246;a:2:{i:0;s:22:"\mathsf{0123456789} \!";i:1;s:139:"\mathsf{0123456789} \!";}i:247;a:2:{i:0;s:65:"\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} \!";i:1;s:182:"\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta} \!";}i:248;a:2:{i:0;s:53:"\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho} \!";i:1;s:170:"\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho} \!";}i:249;a:2:{i:0;s:53:"\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}\!";i:1;s:170:"\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}\!";}i:250;a:2:{i:0;s:22:"\mathcal{ABCDEFGHI} \!";i:1;s:139:"\mathcal{ABCDEFGHI} \!";}i:251;a:2:{i:0;s:22:"\mathcal{JKLMNOPQR} \!";i:1;s:139:"\mathcal{JKLMNOPQR} \!";}i:252;a:2:{i:0;s:21:"\mathcal{STUVWXYZ} \!";i:1;s:138:"\mathcal{STUVWXYZ} \!";}i:253;a:2:{i:0;s:23:"\mathfrak{ABCDEFGHI} \!";i:1;s:140:"\mathfrak{ABCDEFGHI} \!";}i:254;a:2:{i:0;s:23:"\mathfrak{JKLMNOPQR} \!";i:1;s:140:"\mathfrak{JKLMNOPQR} \!";}i:255;a:2:{i:0;s:22:"\mathfrak{STUVWXYZ} \!";i:1;s:139:"\mathfrak{STUVWXYZ} \!";}i:256;a:2:{i:0;s:27:"\mathfrak{abcdefghijklm} \!";i:1;s:144:"\mathfrak{abcdefghijklm} \!";}i:257;a:2:{i:0;s:27:"\mathfrak{nopqrstuvwxyz} \!";i:1;s:144:"\mathfrak{nopqrstuvwxyz} \!";}i:258;a:2:{i:0;s:24:"\mathfrak{0123456789} \!";i:1;s:141:"\mathfrak{0123456789} \!";}i:259;a:2:{i:0;s:5:"x y z";i:1;s:122:"x y z";}i:260;a:2:{i:0;s:12:"\text{x y z}";i:1;s:129:"\text{x y z}";}i:261;a:2:{i:0;s:26:"\text{if} n \text{is even}";i:1;s:143:"\text{if} n \text{is even}";}i:262;a:2:{i:0;s:26:"\text{if }n\text{ is even}";i:1;s:143:"\text{if }n\text{ is even}";}i:263;a:2:{i:0;s:27:"\text{if}~n\ \text{is even}";i:1;s:144:"\text{if}~n\ \text{is even}";}i:264;a:2:{i:0;s:64:"{\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}";i:1;s:181:"{\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}";}i:265;a:2:{i:0;s:49:"x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}";i:1;s:166:"x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}";}i:266;a:2:{i:0;s:17:"e^{i \pi} + 1 = 0";i:1;s:134:"e^{i \pi} + 1 = 0";}i:267;a:2:{i:0;s:71:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";i:1;s:188:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";}i:268;a:2:{i:0;s:21:"e^{i \pi} + 1 = 0\,\!";i:1;s:138:"e^{i \pi} + 1 = 0\,\!";}i:269;a:2:{i:0;s:71:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";i:1;s:188:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";}i:270;a:2:{i:0;s:17:"e^{i \pi} + 1 = 0";i:1;s:134:"e^{i \pi} + 1 = 0";}i:271;a:2:{i:0;s:71:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";i:1;s:188:"\definecolor{orange}{RGB}{255,165,0}\pagecolor{orange}e^{i \pi} + 1 = 0";}i:272;a:2:{i:0;s:29:"\color{Apricot}\text{Apricot}";i:1;s:146:"\color{Apricot}\text{Apricot}";}i:273;a:2:{i:0;s:35:"\color{Aquamarine}\text{Aquamarine}";i:1;s:152:"\color{Aquamarine}\text{Aquamarine}";}i:274;a:2:{i:0;s:37:"\color{Bittersweet}\text{Bittersweet}";i:1;s:154:"\color{Bittersweet}\text{Bittersweet}";}i:275;a:2:{i:0;s:25:"\color{Black}\text{Black}";i:1;s:142:"\color{Black}\text{Black}";}i:276;a:2:{i:0;s:23:"\color{Blue}\text{Blue}";i:1;s:140:"\color{Blue}\text{Blue}";}i:277;a:2:{i:0;s:33:"\color{BlueGreen}\text{BlueGreen}";i:1;s:150:"\color{BlueGreen}\text{BlueGreen}";}i:278;a:2:{i:0;s:35:"\color{BlueViolet}\text{BlueViolet}";i:1;s:152:"\color{BlueViolet}\text{BlueViolet}";}i:279;a:2:{i:0;s:31:"\color{BrickRed}\text{BrickRed}";i:1;s:148:"\color{BrickRed}\text{BrickRed}";}i:280;a:2:{i:0;s:25:"\color{Brown}\text{Brown}";i:1;s:142:"\color{Brown}\text{Brown}";}i:281;a:2:{i:0;s:37:"\color{BurntOrange}\text{BurntOrange}";i:1;s:154:"\color{BurntOrange}\text{BurntOrange}";}i:282;a:2:{i:0;s:33:"\color{CadetBlue}\text{CadetBlue}";i:1;s:150:"\color{CadetBlue}\text{CadetBlue}";}i:283;a:2:{i:0;s:41:"\color{CarnationPink}\text{CarnationPink}";i:1;s:158:"\color{CarnationPink}\text{CarnationPink}";}i:284;a:2:{i:0;s:31:"\color{Cerulean}\text{Cerulean}";i:1;s:148:"\color{Cerulean}\text{Cerulean}";}i:285;a:2:{i:0;s:43:"\color{CornflowerBlue}\text{CornflowerBlue}";i:1;s:160:"\color{CornflowerBlue}\text{CornflowerBlue}";}i:286;a:2:{i:0;s:23:"\color{Cyan}\text{Cyan}";i:1;s:140:"\color{Cyan}\text{Cyan}";}i:287;a:2:{i:0;s:33:"\color{Dandelion}\text{Dandelion}";i:1;s:150:"\color{Dandelion}\text{Dandelion}";}i:288;a:2:{i:0;s:35:"\color{DarkOrchid}\text{DarkOrchid}";i:1;s:152:"\color{DarkOrchid}\text{DarkOrchid}";}i:289;a:2:{i:0;s:29:"\color{Emerald}\text{Emerald}";i:1;s:146:"\color{Emerald}\text{Emerald}";}i:290;a:2:{i:0;s:37:"\color{ForestGreen}\text{ForestGreen}";i:1;s:154:"\color{ForestGreen}\text{ForestGreen}";}i:291;a:2:{i:0;s:29:"\color{Fuchsia}\text{Fuchsia}";i:1;s:146:"\color{Fuchsia}\text{Fuchsia}";}i:292;a:2:{i:0;s:33:"\color{Goldenrod}\text{Goldenrod}";i:1;s:150:"\color{Goldenrod}\text{Goldenrod}";}i:293;a:2:{i:0;s:23:"\color{Gray}\text{Gray}";i:1;s:140:"\color{Gray}\text{Gray}";}i:294;a:2:{i:0;s:25:"\color{Green}\text{Green}";i:1;s:142:"\color{Green}\text{Green}";}i:295;a:2:{i:0;s:37:"\color{GreenYellow}\text{GreenYellow}";i:1;s:154:"\color{GreenYellow}\text{GreenYellow}";}i:296;a:2:{i:0;s:37:"\color{JungleGreen}\text{JungleGreen}";i:1;s:154:"\color{JungleGreen}\text{JungleGreen}";}i:297;a:2:{i:0;s:31:"\color{Lavender}\text{Lavender}";i:1;s:148:"\color{Lavender}\text{Lavender}";}i:298;a:2:{i:0;s:33:"\color{LimeGreen}\text{LimeGreen}";i:1;s:150:"\color{LimeGreen}\text{LimeGreen}";}i:299;a:2:{i:0;s:29:"\color{Magenta}\text{Magenta}";i:1;s:146:"\color{Magenta}\text{Magenta}";}i:300;a:2:{i:0;s:31:"\color{Mahogany}\text{Mahogany}";i:1;s:148:"\color{Mahogany}\text{Mahogany}";}i:301;a:2:{i:0;s:27:"\color{Maroon}\text{Maroon}";i:1;s:144:"\color{Maroon}\text{Maroon}";}i:302;a:2:{i:0;s:25:"\color{Melon}\text{Melon}";i:1;s:142:"\color{Melon}\text{Melon}";}i:303;a:2:{i:0;s:39:"\color{MidnightBlue}\text{MidnightBlue}";i:1;s:156:"\color{MidnightBlue}\text{MidnightBlue}";}i:304;a:2:{i:0;s:31:"\color{Mulberry}\text{Mulberry}";i:1;s:148:"\color{Mulberry}\text{Mulberry}";}i:305;a:2:{i:0;s:31:"\color{NavyBlue}\text{NavyBlue}";i:1;s:148:"\color{NavyBlue}\text{NavyBlue}";}i:306;a:2:{i:0;s:35:"\color{OliveGreen}\text{OliveGreen}";i:1;s:152:"\color{OliveGreen}\text{OliveGreen}";}i:307;a:2:{i:0;s:27:"\color{Orange}\text{Orange}";i:1;s:144:"\color{Orange}\text{Orange}";}i:308;a:2:{i:0;s:33:"\color{OrangeRed}\text{OrangeRed}";i:1;s:150:"\color{OrangeRed}\text{OrangeRed}";}i:309;a:2:{i:0;s:27:"\color{Orchid}\text{Orchid}";i:1;s:144:"\color{Orchid}\text{Orchid}";}i:310;a:2:{i:0;s:25:"\color{Peach}\text{Peach}";i:1;s:142:"\color{Peach}\text{Peach}";}i:311;a:2:{i:0;s:35:"\color{Periwinkle}\text{Periwinkle}";i:1;s:152:"\color{Periwinkle}\text{Periwinkle}";}i:312;a:2:{i:0;s:33:"\color{PineGreen}\text{PineGreen}";i:1;s:150:"\color{PineGreen}\text{PineGreen}";}i:313;a:2:{i:0;s:23:"\color{Plum}\text{Plum}";i:1;s:140:"\color{Plum}\text{Plum}";}i:314;a:2:{i:0;s:37:"\color{ProcessBlue}\text{ProcessBlue}";i:1;s:154:"\color{ProcessBlue}\text{ProcessBlue}";}i:315;a:2:{i:0;s:27:"\color{Purple}\text{Purple}";i:1;s:144:"\color{Purple}\text{Purple}";}i:316;a:2:{i:0;s:33:"\color{RawSienna}\text{RawSienna}";i:1;s:150:"\color{RawSienna}\text{RawSienna}";}i:317;a:2:{i:0;s:21:"\color{Red}\text{Red}";i:1;s:138:"\color{Red}\text{Red}";}i:318;a:2:{i:0;s:33:"\color{RedOrange}\text{RedOrange}";i:1;s:150:"\color{RedOrange}\text{RedOrange}";}i:319;a:2:{i:0;s:33:"\color{RedViolet}\text{RedViolet}";i:1;s:150:"\color{RedViolet}\text{RedViolet}";}i:320;a:2:{i:0;s:33:"\color{Rhodamine}\text{Rhodamine}";i:1;s:150:"\color{Rhodamine}\text{Rhodamine}";}i:321;a:2:{i:0;s:33:"\color{RoyalBlue}\text{RoyalBlue}";i:1;s:150:"\color{RoyalBlue}\text{RoyalBlue}";}i:322;a:2:{i:0;s:37:"\color{RoyalPurple}\text{RoyalPurple}";i:1;s:154:"\color{RoyalPurple}\text{RoyalPurple}";}i:323;a:2:{i:0;s:33:"\color{RubineRed}\text{RubineRed}";i:1;s:150:"\color{RubineRed}\text{RubineRed}";}i:324;a:2:{i:0;s:27:"\color{Salmon}\text{Salmon}";i:1;s:144:"\color{Salmon}\text{Salmon}";}i:325;a:2:{i:0;s:31:"\color{SeaGreen}\text{SeaGreen}";i:1;s:148:"\color{SeaGreen}\text{SeaGreen}";}i:326;a:2:{i:0;s:25:"\color{Sepia}\text{Sepia}";i:1;s:142:"\color{Sepia}\text{Sepia}";}i:327;a:2:{i:0;s:29:"\color{SkyBlue}\text{SkyBlue}";i:1;s:146:"\color{SkyBlue}\text{SkyBlue}";}i:328;a:2:{i:0;s:37:"\color{SpringGreen}\text{SpringGreen}";i:1;s:154:"\color{SpringGreen}\text{SpringGreen}";}i:329;a:2:{i:0;s:21:"\color{Tan}\text{Tan}";i:1;s:138:"\color{Tan}\text{Tan}";}i:330;a:2:{i:0;s:31:"\color{TealBlue}\text{TealBlue}";i:1;s:148:"\color{TealBlue}\text{TealBlue}";}i:331;a:2:{i:0;s:29:"\color{Thistle}\text{Thistle}";i:1;s:146:"\color{Thistle}\text{Thistle}";}i:332;a:2:{i:0;s:33:"\color{Turquoise}\text{Turquoise}";i:1;s:150:"\color{Turquoise}\text{Turquoise}";}i:333;a:2:{i:0;s:27:"\color{Violet}\text{Violet}";i:1;s:144:"\color{Violet}\text{Violet}";}i:334;a:2:{i:0;s:33:"\color{VioletRed}\text{VioletRed}";i:1;s:150:"\color{VioletRed}\text{VioletRed}";}i:335;a:2:{i:0;s:43:"\color{WildStrawberry}\text{WildStrawberry}";i:1;s:160:"\color{WildStrawberry}\text{WildStrawberry}";}i:336;a:2:{i:0;s:37:"\color{YellowGreen}\text{YellowGreen}";i:1;s:154:"\color{YellowGreen}\text{YellowGreen}";}i:337;a:2:{i:0;s:39:"\color{YellowOrange}\text{YellowOrange}";i:1;s:156:"\color{YellowOrange}\text{YellowOrange}";}i:338;a:2:{i:0;s:10:"a \qquad b";i:1;s:127:"a \qquad b";}i:339;a:2:{i:0;s:9:"a \quad b";i:1;s:126:"a \quad b";}i:340;a:2:{i:0;s:4:"a\ b";i:1;s:121:"a\ b";}i:341;a:2:{i:0;s:12:"a \mbox{ } b";i:1;s:129:"a \mbox{ } b";}i:342;a:2:{i:0;s:4:"a\;b";i:1;s:121:"a\;b";}i:343;a:2:{i:0;s:4:"a\,b";i:1;s:121:"a\,b";}i:344;a:2:{i:0;s:2:"ab";i:1;s:119:"ab";}i:345;a:2:{i:0;s:11:"\mathit{ab}";i:1;s:128:"\mathit{ab}";}i:346;a:2:{i:0;s:4:"a\!b";i:1;s:121:"a\!b";}i:347;a:2:{i:0;s:59:"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots";i:1;s:176:"0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots";}i:348;a:2:{i:0;s:61:"{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}";i:1;s:178:"{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}";}i:349;a:2:{i:0;s:22:"\int_{-N}^{N} e^x\, dx";i:1;s:139:"\int_{-N}^{N} e^x\, dx";}i:350;a:2:{i:0;s:24:"\sum_{i=0}^\infty 2^{-i}";i:1;s:141:"\sum_{i=0}^\infty 2^{-i}";}i:351;a:2:{i:0;s:57:"\text{geometric series:}\quad \sum_{i=0}^\infty 2^{-i}=2 ";i:1;s:174:"\text{geometric series:}\quad \sum_{i=0}^\infty 2^{-i}=2 ";}i:352;a:2:{i:0;s:5:"\iint";i:1;s:122:"\iint";}i:353;a:2:{i:0;s:5:"\oint";i:1;s:122:"\oint";}i:354;a:2:{i:0;s:90:"\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot \mathrm{d}\mathbf A";i:1;s:207:"\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset \mathbf D \cdot \mathrm{d}\mathbf A";}i:355;a:2:{i:0;s:114:"\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A";i:1;s:231:"\int\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\cdot\mathrm{d}\mathbf A";}i:356;a:2:{i:0;s:139:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\cdot\mathrm{d}\mathbf A";i:1;s:256:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\cdot\mathrm{d}\mathbf A";}i:357;a:2:{i:0;s:132:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A";i:1;s:249:"\int\!\!\!\!\!\int\!\!\!\!\!\int_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\bigcirc\,\,\mathbf D\;\cdot\mathrm{d}\mathbf A";}i:358;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:133:"{\scriptstyle S}";}i:359;a:2:{i:0;s:110:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";i:1;s:227:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";}i:360;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:133:"{\scriptstyle S}";}i:361;a:2:{i:0;s:110:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";i:1;s:227:"( \nabla \times \bold{F} ) \cdot {\rm d}\bold{S} = \oint_{\partial S} \bold{F} \cdot {\rm d}\boldsymbol{\ell} ";}i:362;a:2:{i:0;s:57:"\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:174:"\oint_C \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";}i:363;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:133:"{\scriptstyle S}";}i:364;a:2:{i:0;s:96:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";i:1;s:213:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";}i:365;a:2:{i:0;s:68:"\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";i:1;s:185:"\oint_{\partial S} \bold{B} \cdot {\rm d} \boldsymbol{\ell} = \mu_0 ";}i:366;a:2:{i:0;s:16:"{\scriptstyle S}";i:1;s:133:"{\scriptstyle S}";}i:367;a:2:{i:0;s:96:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";i:1;s:213:"\left ( \bold{J} + \epsilon_0\frac{\partial \bold{E}}{\partial t} \right ) \cdot {\rm d}\bold{S}";}i:368;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:128:"\bold{P} = ";}i:369;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:147:"{\scriptstyle \partial \Omega}";}i:370;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:164:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";}i:371;a:2:{i:0;s:11:"\bold{P} = ";i:1;s:128:"\bold{P} = ";}i:372;a:2:{i:0;s:30:"{\scriptstyle \partial \Omega}";i:1;s:147:"{\scriptstyle \partial \Omega}";}i:373;a:2:{i:0;s:47:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";i:1;s:164:"\bold{T} \cdot {\rm d}^3\boldsymbol{\Sigma} = 0";}i:374;a:2:{i:0;s:20:"\overset{\frown}{AB}";i:1;s:137:"\overset{\frown}{AB}";}i:375;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:134:"ax^2 + bx + c = 0";}i:376;a:2:{i:0;s:17:"ax^2 + bx + c = 0";i:1;s:134:"ax^2 + bx + c = 0";}i:377;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:149:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";}i:378;a:2:{i:0;s:32:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";i:1;s:149:"x={-b\pm\sqrt{b^2-4ac} \over 2a}";}i:379;a:2:{i:0;s:56:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)";i:1;s:173:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)";}i:380;a:2:{i:0;s:56:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} -\right)";i:1;s:152:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)";}i:379;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:155:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";}i:380;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:155:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";}i:381;a:2:{i:0;s:61:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy";i:1;s:149:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy";}i:382;a:2:{i:0;s:61:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds -= \int_a^x f(y)(x-y)\,dy";i:1;s:153:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy";}i:383;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:126:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";}i:384;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:126:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";}i:385;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:106:"\sum_{i=0}^{n-1} i";}i:386;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:106:"\sum_{i=0}^{n-1} i";}i:387;a:2:{i:0;s:78:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}";i:1;s:166:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}";}i:388;a:2:{i:0;s:79:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} -{3^m\left(m\,3^n+n\,3^m\right)}";i:1;s:171:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} {3^m\left(m\,3^n+n\,3^m\right)}";}i:389;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:141:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";}i:390;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:141:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";}i:391;a:2:{i:0;s:61:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)";i:1;s:149:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)";}i:392;a:2:{i:0;s:61:"|\bar{z}| = |z|, +\right)";i:1;s:181:"2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)";}i:381;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:184:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";}i:382;a:2:{i:0;s:67:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";i:1;s:184:"S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}";}i:383;a:2:{i:0;s:61:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy";i:1;s:178:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy";}i:384;a:2:{i:0;s:61:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds += \int_a^x f(y)(x-y)\,dy";i:1;s:182:"\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy";}i:385;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:155:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";}i:386;a:2:{i:0;s:38:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";i:1;s:155:"\det(\mathsf{A}-\lambda\mathsf{I}) = 0";}i:387;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:135:"\sum_{i=0}^{n-1} i";}i:388;a:2:{i:0;s:18:"\sum_{i=0}^{n-1} i";i:1;s:135:"\sum_{i=0}^{n-1} i";}i:389;a:2:{i:0;s:78:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}";i:1;s:195:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}";}i:390;a:2:{i:0;s:79:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} +{3^m\left(m\,3^n+n\,3^m\right)}";i:1;s:200:"\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n} {3^m\left(m\,3^n+n\,3^m\right)}";}i:391;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:170:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";}i:392;a:2:{i:0;s:35:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";i:1;s:170:"u'' + p(x)u' + q(x)u=f(x),\quad x>a";}i:393;a:2:{i:0;s:61:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)";i:1;s:178:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)";}i:394;a:2:{i:0;s:61:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, -\arg(z^n) = n \arg(z)";i:1;s:157:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)";}i:393;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:123:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";}i:394;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:123:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";}i:395;a:2:{i:0;s:170:"\phi_n(\kappa) -= \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";i:1;s:262:"\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";}i:396;a:2:{i:0;s:170:"\phi_n(\kappa) = +\arg(z^n) = n \arg(z)";i:1;s:186:"|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)";}i:395;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:152:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";}i:396;a:2:{i:0;s:35:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";i:1;s:152:"\lim_{z\rightarrow z_0} f(z)=f(z_0)";}i:397;a:2:{i:0;s:170:"\phi_n(\kappa) += \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";i:1;s:291:"\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";}i:398;a:2:{i:0;s:170:"\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} -\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";i:1;s:274:"\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";}i:397;a:2:{i:0;s:86:"\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";i:1;s:174:"\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";}i:398;a:2:{i:0;s:86:"\phi_n(\kappa) = +\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";i:1;s:303:"\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R} \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR";}i:399;a:2:{i:0;s:86:"\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";i:1;s:203:"\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";}i:400;a:2:{i:0;s:86:"\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad -\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";i:1;s:182:"\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";}i:399;a:2:{i:0;s:100:"f(x) = \begin{cases}1 & -1 \le x < 0 \\ -\frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise}\end{cases}";i:1;s:207:"f(x) = \begin{cases}1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise}\end{cases}";}i:400;a:2:{i:0;s:104:" +\frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";i:1;s:211:"\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}";}i:401;a:2:{i:0;s:100:"f(x) = \begin{cases}1 & -1 \le x < 0 \\ +\frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise}\end{cases}";i:1;s:236:"f(x) = \begin{cases}1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise}\end{cases}";}i:402;a:2:{i:0;s:104:" f(x) = \begin{cases} 1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise} \end{cases} -";i:1;s:235:" f(x) = \begin{cases} 1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise} \end{cases} ";}i:401;a:2:{i:0;s:122:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}";i:1;s:210:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}";}i:402;a:2:{i:0;s:123:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) +";i:1;s:264:" f(x) = \begin{cases} 1 & -1 \le x < 0 \\ \frac{1}{2} & x = 0 \\ 1 - x^2 & \text{otherwise} \end{cases} ";}i:403;a:2:{i:0;s:122:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}";i:1;s:239:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}";}i:404;a:2:{i:0;s:123:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n} -\frac{z^n}{n!}";i:1;s:223:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n} \frac{z^n}{n!}";}i:403;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:113:"\frac{a}{b}\ \tfrac{a}{b}";}i:404;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:113:"\frac{a}{b}\ \tfrac{a}{b}";}i:405;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:106:"S=dD\,\sin\alpha\!";}i:406;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:106:"S=dD\,\sin\alpha\!";}i:407;a:2:{i:0;s:56:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";i:1;s:144:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";}i:408;a:2:{i:0;s:56:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";i:1;s:144:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";}i:409;a:2:{i:0;s:167:"\begin{align} +\frac{z^n}{n!}";i:1;s:252:"{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n} \frac{z^n}{n!}";}i:405;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:142:"\frac{a}{b}\ \tfrac{a}{b}";}i:406;a:2:{i:0;s:25:"\frac{a}{b}\ \tfrac{a}{b}";i:1;s:142:"\frac{a}{b}\ \tfrac{a}{b}";}i:407;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:135:"S=dD\,\sin\alpha\!";}i:408;a:2:{i:0;s:18:"S=dD\,\sin\alpha\!";i:1;s:135:"S=dD\,\sin\alpha\!";}i:409;a:2:{i:0;s:56:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";i:1;s:173:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";}i:410;a:2:{i:0;s:56:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";i:1;s:173:"V=\frac16\pi h\left[3\left(r_1^2+r_2^2\right)+h^2\right]";}i:411;a:2:{i:0;s:167:"\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v)\\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) -\end{align}";i:1;s:291:"\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v)\\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) \end{align}";}i:410;a:2:{i:0;s:168:"\begin{align} +\end{align}";i:1;s:320:"\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v)\\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) \end{align}";}i:412;a:2:{i:0;s:168:"\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) -\end{align}";i:1;s:292:"\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) \end{align}";}i:411;a:2:{i:0;s:172:" with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped <math> tags. [[Image:foobar.jpg|thumb|2+2";i:1;s:259:"Failed to parse (syntax error): with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped &lt;math&gt; tags. [[Image:foobar.jpg|thumb|<math>2+2 -";}i:412;a:2:{i:0;s:66:" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|2+2";i:1;s:160:" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|<math>2+2";}i:413;a:2:{i:0;s:41:"";i:1;s:141:"<script>alert(document.cookies);</script>";}i:414;a:2:{i:0;s:11:"\widehat{x}";i:1;s:99:"\widehat{x}";}i:415;a:2:{i:0;s:13:"\widetilde{x}";i:1;s:101:"\widetilde{x}";}i:416;a:2:{i:0;s:9:"\euro 200";i:1;s:97:"\euro 200";}i:417;a:2:{i:0;s:8:"\geneuro";i:1;s:96:"\geneuro";}i:418;a:2:{i:0;s:14:"\geneuronarrow";i:1;s:102:"\geneuronarrow";}i:419;a:2:{i:0;s:12:"\geneurowide";i:1;s:100:"\geneurowide";}i:420;a:2:{i:0;s:13:"\officialeuro";i:1;s:101:"\officialeuro";}i:421;a:2:{i:0;s:8:"\digamma";i:1;s:96:"\digamma";}i:422;a:2:{i:0;s:21:"\Coppa\coppa\varcoppa";i:1;s:109:"\Coppa\coppa\varcoppa";}i:423;a:2:{i:0;s:8:"\Digamma";i:1;s:96:"\Digamma";}i:424;a:2:{i:0;s:12:"\Koppa\koppa";i:1;s:100:"\Koppa\koppa";}i:425;a:2:{i:0;s:12:"\Sampi\sampi";i:1;s:100:"\Sampi\sampi";}i:426;a:2:{i:0;s:24:"\Stigma\stigma\varstigma";i:1;s:112:"\Stigma\stigma\varstigma";}i:427;a:2:{i:0;s:17:"\text{next years}";i:1;s:105:"\text{next years}";}i:428;a:2:{i:0;s:18:"\text{next year's}";i:1;s:111:"\text{next year's}";}i:429;a:2:{i:0;s:18:"\text{`next' year}";i:1;s:111:"\text{`next' year}";}i:430;a:2:{i:0;s:6:"\sin x";i:1;s:94:"\sin x";}i:431;a:2:{i:0;s:7:"\sin(x)";i:1;s:95:"\sin(x)";}i:432;a:2:{i:0;s:7:"\sin{x}";i:1;s:95:"\sin{x}";}i:433;a:2:{i:0;s:9:"\sin x \,";i:1;s:97:"\sin x \,";}i:434;a:2:{i:0;s:10:"\sin(x) \,";i:1;s:98:"\sin(x) \,";}i:435;a:2:{i:0;s:10:"\sin{x} \,";i:1;s:98:"\sin{x} \,";}i:436;a:2:{i:0;s:6:"\sen x";i:1;s:94:"\sen x";}i:437;a:2:{i:0;s:7:"\sen(x)";i:1;s:95:"\sen(x)";}i:438;a:2:{i:0;s:7:"\sen{x}";i:1;s:95:"\sen{x}";}i:439;a:2:{i:0;s:9:"\sen x \,";i:1;s:97:"\sen x \,";}i:440;a:2:{i:0;s:10:"\sen(x) \,";i:1;s:98:"\sen(x) \,";}i:441;a:2:{i:0;s:10:"\sen{x} \,";i:1;s:98:"\sen{x} \,";}i:442;a:2:{i:0;s:18:"\operatorname{sen}";i:1;s:106:"\operatorname{sen}";}i:443;a:2:{i:0;s:11:"\dot \vec B";i:1;s:99:"\dot \vec B";}i:444;a:2:{i:0;s:18:"\tilde \mathcal{M}";i:1;s:106:"\tilde \mathcal{M}";}i:445;a:2:{i:0;s:0:"";i:1;s:160:"Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): -";}i:446;a:2:{i:0;s:1:" ";i:1;s:161:"Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): +\end{align}";i:1;s:321:"\begin{align} u & = \tfrac{1}{\sqrt{2}}(x+y) \qquad & x &= \tfrac{1}{\sqrt{2}}(u+v) \\ v & = \tfrac{1}{\sqrt{2}}(x-y) \qquad & y &= \tfrac{1}{\sqrt{2}}(u-v) \end{align}";}i:413;a:2:{i:0;s:172:" with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped <math> tags. [[Image:foobar.jpg|thumb|2+2";i:1;s:259:"Failed to parse (syntax error): with a thumbnail- we don't render math in the parsertests by default, so math is not stripped and turns up as escaped &lt;math&gt; tags. [[Image:foobar.jpg|thumb|<math>2+2 +";}i:414;a:2:{i:0;s:66:" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|2+2";i:1;s:189:" with a thumbnail- math enabled [[Image:foobar.jpg|thumb|<math>2+2";}i:415;a:2:{i:0;s:41:"";i:1;s:170:"<script>alert(document.cookies);</script>";}i:416;a:2:{i:0;s:11:"\widehat{x}";i:1;s:128:"\widehat{x}";}i:417;a:2:{i:0;s:13:"\widetilde{x}";i:1;s:130:"\widetilde{x}";}i:418;a:2:{i:0;s:9:"\euro 200";i:1;s:126:"\euro 200";}i:419;a:2:{i:0;s:8:"\geneuro";i:1;s:125:"\geneuro";}i:420;a:2:{i:0;s:14:"\geneuronarrow";i:1;s:131:"\geneuronarrow";}i:421;a:2:{i:0;s:12:"\geneurowide";i:1;s:129:"\geneurowide";}i:422;a:2:{i:0;s:13:"\officialeuro";i:1;s:130:"\officialeuro";}i:423;a:2:{i:0;s:8:"\digamma";i:1;s:125:"\digamma";}i:424;a:2:{i:0;s:21:"\Coppa\coppa\varcoppa";i:1;s:138:"\Coppa\coppa\varcoppa";}i:425;a:2:{i:0;s:8:"\Digamma";i:1;s:125:"\Digamma";}i:426;a:2:{i:0;s:12:"\Koppa\koppa";i:1;s:129:"\Koppa\koppa";}i:427;a:2:{i:0;s:12:"\Sampi\sampi";i:1;s:129:"\Sampi\sampi";}i:428;a:2:{i:0;s:24:"\Stigma\stigma\varstigma";i:1;s:141:"\Stigma\stigma\varstigma";}i:429;a:2:{i:0;s:17:"\text{next years}";i:1;s:134:"\text{next years}";}i:430;a:2:{i:0;s:18:"\text{next year's}";i:1;s:140:"\text{next year's}";}i:431;a:2:{i:0;s:18:"\text{`next' year}";i:1;s:140:"\text{`next' year}";}i:432;a:2:{i:0;s:6:"\sin x";i:1;s:123:"\sin x";}i:433;a:2:{i:0;s:7:"\sin(x)";i:1;s:124:"\sin(x)";}i:434;a:2:{i:0;s:7:"\sin{x}";i:1;s:124:"\sin{x}";}i:435;a:2:{i:0;s:9:"\sin x \,";i:1;s:126:"\sin x \,";}i:436;a:2:{i:0;s:10:"\sin(x) \,";i:1;s:127:"\sin(x) \,";}i:437;a:2:{i:0;s:10:"\sin{x} \,";i:1;s:127:"\sin{x} \,";}i:438;a:2:{i:0;s:6:"\sen x";i:1;s:123:"\sen x";}i:439;a:2:{i:0;s:7:"\sen(x)";i:1;s:124:"\sen(x)";}i:440;a:2:{i:0;s:7:"\sen{x}";i:1;s:124:"\sen{x}";}i:441;a:2:{i:0;s:9:"\sen x \,";i:1;s:126:"\sen x \,";}i:442;a:2:{i:0;s:10:"\sen(x) \,";i:1;s:127:"\sen(x) \,";}i:443;a:2:{i:0;s:10:"\sen{x} \,";i:1;s:127:"\sen{x} \,";}i:444;a:2:{i:0;s:18:"\operatorname{sen}";i:1;s:135:"\operatorname{sen}";}i:445;a:2:{i:0;s:11:"\dot \vec B";i:1;s:128:"\dot \vec B";}i:446;a:2:{i:0;s:18:"\tilde \mathcal{M}";i:1;s:135:"\tilde \mathcal{M}";}i:447;a:2:{i:0;s:0:"";i:1;s:160:"Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): +";}i:448;a:2:{i:0;s:1:" ";i:1;s:161:"Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): ";}} \ No newline at end of file