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<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> |
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<meta charset="utf-8"/> |
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<meta name="generator" content="Docutils 0.14: http://docutils.sourceforge.net/" /> |
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<title>Mathematics</title> |
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<link rel="stylesheet" href="../input/data/minimal.css" type="text/css" /> |
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<link rel="stylesheet" href="../input/data/plain.css" type="text/css" /> |
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<body> |
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<div class="document" id="mathematics"> |
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<h1 class="title">Mathematics</h1> |
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<p>Docutils supports inline math with the prefix or postfix <span class="docutils literal">:math:</span> |
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role specificator, <math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mi>n</mi><mo>!</mo><mo>+</mo><mo>sin</mo><mo>(</mo><msubsup><mi>x</mi><mi>n</mi><mn>2</mn></msubsup><mo>)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><msub><mi>A</mi><mtext>c</mtext></msub><mo>=</mo><mfrac> |
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<mrow><mi>π</mi></mrow> |
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<mrow><mn>4</mn></mrow></mfrac><msup><mi>d</mi><mn>2</mn></msup></mrow></math>, as well as displayed math via the |
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<cite>math</cite> directive:</p> |
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<div> |
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<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display"> |
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<mtable> |
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<mtr> |
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<mtd><mi>f</mi><mo>(</mo><mi>ϵ</mi><mo>)</mo><mo>=</mo><mfrac> |
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<mrow><mn>1</mn></mrow> |
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<mrow><mn>1</mn><mo>+</mo><mo>exp</mo><mfenced open="(" close=")"> |
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<mrow><mfrac> |
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<mrow><mi>ε</mi></mrow> |
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<mrow><msub><mi>k</mi><mtext>B</mtext></msub><mi>T</mi></mrow></mfrac></mrow></mfenced></mrow></mfrac></mtd></mtr></mtable></math> |
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</div> |
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<p>Content may start on the first line of the directive, e.g.</p> |
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<div> |
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<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display"> |
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<mtable> |
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<mtr> |
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<mtd><mi>N</mi><mo>=</mo><mfrac> |
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<mrow><mtext>number of apples</mtext></mrow> |
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<mrow><mn>7</mn></mrow></mfrac></mtd></mtr></mtable></math> |
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</div> |
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<p>Equations can be labeled with a reference name using the <span class="docutils literal">:name:</span> option. |
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See <a class="reference internal" href="#eq-m">eq:M</a> and <a class="reference internal" href="#eq-schrodinger">eq:schrödinger</a> below.</p> |
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<p>The determinant of the matrix</p> |
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<div id="eq-m"> |
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<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display"> |
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<mtable> |
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<mtr> |
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<mtd><mstyle fontweight="bold"> |
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<mrow><mi>M</mi></mrow></mstyle><mo>=</mo><mfenced open="(" close=")"> |
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<mrow> |
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<mtable> |
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<mtr> |
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<mtd><mi>a</mi></mtd> |
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<mtd><mi>b</mi></mtd></mtr> |
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<mtr> |
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<mtd><mi>c</mi></mtd> |
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<mtd><mi>d</mi></mtd></mtr></mtable></mrow></mfenced></mtd></mtr></mtable></math> |
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</div> |
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<p>is <math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mo>|</mo><mstyle fontweight="bold"> |
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<mrow><mi>M</mi></mrow></mstyle><mo>|</mo><mo>=</mo><mi>a</mi><mi>d</mi><mo>-</mo><mi>b</mi><mi>c</mi></mrow></math>.</p> |
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<p>More than one display math block can be put in one math directive. |
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For example, the following sum and integral with limits:</p> |
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<div> |
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<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display"> |
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<mtable> |
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<mtr> |
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<mtd><munderover><mo>∫</mo><mn>0</mn><mn>1</mn></munderover><msup><mi>x</mi><mi>n</mi></msup><mi>d</mi><mi>x</mi><mo>=</mo><mfrac> |
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<mrow><mn>1</mn></mrow> |
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<mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mtd></mtr></mtable></math> |
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</div> |
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<div> |
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<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display"> |
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<mtable> |
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<mtr> |
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<mtd><munderover><mo>∑</mo> |
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<mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>m</mi></munderover><mi>n</mi><mo>=</mo><mfrac> |
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<mrow><mi>m</mi><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow> |
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<mrow><mn>2</mn></mrow></mfrac></mtd></mtr></mtable></math> |
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</div> |
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<p>LaTeX-supported Unicode math symbols can be used in math roles and |
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directives:</p> |
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<p>The Schrödinger equation</p> |
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<div id="eq-schrodinger"> |
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<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display"> |
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<mtable> |
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<mtr> |
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<mtd><mi>i</mi><mi>ℏ</mi><mfrac> |
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<mrow><mo>∂</mo></mrow> |
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<mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>Ψ</mo><mo>=</mo><mover> |
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<mrow><mi>H</mi></mrow><mo>^</mo></mover><mo>Ψ</mo><mo>,</mo></mtd></mtr></mtable></math> |
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</div> |
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<p>with the <em>wave function</em> <math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mo>Ψ</mo></mrow></math>, describes how the quantum state of a |
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physical system changes in time.</p> |
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<dl> |
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<dt>Math-Accents:</dt> |
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<dd><table class="colwidths-given borderless"> |
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<colgroup> |
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<col style="width: 33%" /> |
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<col style="width: 33%" /> |
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<col style="width: 33%" /> |
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</colgroup> |
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<tbody> |
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<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>a</mi></mrow><mo>´</mo></mover></mrow></math> <span class="docutils literal">\acute{a}</span></p></td> |
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<td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>t</mi></mrow><mo>˙</mo></mover></mrow></math> <span class="docutils literal">\dot{t}</span></p></td> |
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<td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>γ</mi></mrow><mo>^</mo></mover></mrow></math> <span class="docutils literal"><span class="pre">\hat{\gamma}</span></span></p></td> |
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</tr> |
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<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>a</mi></mrow><mo>`</mo></mover></mrow></math> <span class="docutils literal">\grave{a}</span></p></td> |
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<td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>t</mi></mrow><mo>¨</mo></mover></mrow></math> <span class="docutils literal">\ddot{t}</span></p></td> |
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<td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>α</mi></mrow><mo>˜</mo></mover></mrow></math> <span class="docutils literal"><span class="pre">\tilde{\alpha}</span></span></p></td> |
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</tr> |
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<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>x</mi></mrow><mo>˘</mo></mover></mrow></math> <span class="docutils literal">\breve{x}</span></p></td> |
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<td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>t</mi></mrow><mo>⃛</mo></mover></mrow></math> <span class="docutils literal">\dddot{t}</span></p></td> |
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<td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>ı</mi></mrow><mo>⃗</mo></mover></mrow></math> <span class="docutils literal"><span class="pre">\vec{\imath}</span></span></p></td> |
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</tr> |
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<tr><td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>a</mi></mrow><mo>ˇ</mo></mover></mrow></math> <span class="docutils literal">\check{a}</span></p></td> |
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<td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>a</mi></mrow><mo>¯</mo></mover></mrow></math> <span class="docutils literal">\bar{a}</span></p></td> |
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<td><p><math xmlns="http://www.w3.org/1998/Math/MathML"> |
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<mrow><mover> |
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<mrow><mi>R</mi></mrow><mo>⃗</mo></mover></mrow></math> <span class="docutils literal">\vec{R}</span></p></td> |
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</tr> |
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</tbody> |
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</table> |
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</dd> |
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</dl> |
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<!-- \widetilde{xxx} |
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\widehat{xxx} --> |
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<p>Modulation Transfer Function:</p> |
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<div> |
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<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display"> |
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<mtable> |
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<mtr> |
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<mtd><mtext>MTF</mtext><mo>=</mo><mfenced open="|" close="|"> |
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<mrow><mfrac> |
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<mrow><mi>ℱ</mi><mo>{</mo><mi>s</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo></mrow> |
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<mrow><mi>ℱ</mi><mo>{</mo><mi>s</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>}</mo><msub><mo>|</mo> |
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<mrow><msub><mi>ω</mi> |
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<mrow><mi>x</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></msub></mrow></mfrac></mrow></mfenced><mo>=</mo><mtext>abs</mtext><mfenced open="(" close=")"> |
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<mrow><mfrac> |
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<mrow><munderover><mo>∫</mo> |
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<mrow><mo>-</mo><mo>∞</mo></mrow> |
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<mrow><mo>∞</mo></mrow></munderover><mi>s</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mtext>e</mtext> |
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<mrow><mtext>i</mtext><msub><mi>ω</mi> |
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<mrow><mi>x</mi></mrow></msub><mi>x</mi></mrow></msup><mtext>d</mtext> |
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<mrow><mi>x</mi></mrow></mrow> |
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<mrow><munderover><mo>∫</mo> |
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<mrow><mo>-</mo><mo>∞</mo></mrow> |
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<mrow><mo>∞</mo></mrow></munderover><mi>s</mi><mo>(</mo><mi>x</mi><mo>)</mo><mtext>d</mtext> |
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<mrow><mi>x</mi></mrow></mrow></mfrac></mrow></mfenced><mo>.</mo></mtd></mtr></mtable></math> |
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</div> |
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<p>Math split over two lines: If a double backslash is detected outside a |
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<span class="docutils literal"><span class="pre">\begin{...}</span> <span class="pre">\end{...}</span></span> pair, the math code is wrapped in an <a class="reference external" href="ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf">AMSmath</a> |
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<span class="docutils literal">align</span> environment:</p> |
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<div> |
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<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display"> |
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<mtable> |
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<mtr> |
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<mtd><msub><mi>s</mi> |
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<mrow><mtext>out</mtext></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo></mtd> |
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<mtd><mo>=</mo><msub><mi>s</mi> |
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<mrow><mtext>in</mtext></mrow></msub><mo>(</mo><mi>x</mi><mo>'</mo><mo>)</mo><mo>*</mo><msub><mi>s</mi><mi>δ</mi></msub><mo>(</mo><mi>x</mi><mo>-</mo><mi>x</mi><mo>'</mo><mo>)</mo></mtd></mtr> |
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<mtr> |
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<mtd></mtd> |
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<mtd><mo>=</mo><mo>∫</mo><msub><mi>s</mi> |
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<mrow><mtext>in</mtext></mrow></msub><mo>(</mo><mi>x</mi><mo>'</mo><mo>)</mo><msub><mi>s</mi><mi>δ</mi></msub><mo>(</mo><mi>x</mi><mo>-</mo><mi>x</mi><mo>'</mo><mo>)</mo><mtext>d</mtext><mi>x</mi><mo>'</mo></mtd></mtr></mtable></math> |
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</div> |
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<p>Cases ("manually", with <span class="docutils literal">matrix</span> environment):</p> |
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<div> |
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<math xmlns="http://www.w3.org/1998/Math/MathML" mode="display"> |
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<mtable> |
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<mtr> |
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<mtd><mtext>sgn</mtext><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mfenced open="{" close=""> |
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<mrow> |
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<mtable> |
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<mtr> |
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<mtd><mo>-</mo><mn>1</mn></mtd> |
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<mtd><mi>x</mi><mo><</mo><mn>0</mn></mtd></mtr> |
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<mtr> |
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<mtd><mn>1</mn></mtd> |
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<mtd><mi>x</mi><mo>></mo><mn>0</mn></mtd></mtr></mtable></mrow></mfenced></mtd></mtr></mtable></math> |
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</div> |
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<p>Cases with the <a class="reference external" href="ftp://ftp.ams.org/ams/doc/amsmath/short-math-guide.pdf">AMSmath</a> <span class="docutils literal">cases</span> environment (not (yet) supported by |
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HTML writers with <span class="docutils literal"><span class="pre">--math-output=MathML</span></span>):</p> |
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<div class="system-message"> |
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<p class="system-message-title">System Message: ERROR/3 (<span class="docutils literal">functional/input/data/math.txt</span>, line 108)</p> |
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<p> |
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Environment not supported! Supported environment: "matrix".</p> |
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<pre class="literal-block"> |
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\mathrm{sgn}(x) = \begin{cases} |
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-1 & x<0\\ |
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1 & x>0 |
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\end{cases} |
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</pre> |
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</div> |
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</div> |
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</body> |
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</html>
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