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680 lines
16 KiB
XML
680 lines
16 KiB
XML
<?xml version="1.0"?>
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<!-- This Source Code Form is subject to the terms of the Mozilla Public
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- License, v. 2.0. If a copy of the MPL was not distributed with this
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- file, You can obtain one at http://mozilla.org/MPL/2.0/. -->
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<!DOCTYPE html PUBLIC
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"-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN"
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"http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd"
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[
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<!ENTITY mathml "http://www.w3.org/1998/Math/MathML">
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]>
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<html xmlns="http://www.w3.org/1999/xhtml">
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<head>
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<title>Various examples of MathML</title>
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<style type="text/css">
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maction {
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background-color: yellow;
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}
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maction:hover {
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outline: 1px dotted black;
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/* border: 1px solid black; */
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}
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</style>
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</head>
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<body>
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<h2><maction></h2>
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<p>Click to toggle between expressions, and watch the status line onmouseover/onmouseout:
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<br />
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<math mode="display" xmlns="&mathml;">
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<maction actiontype="toggle">
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<maction actiontype="statusline">
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<mi>statusline#First Expression</mi>
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<mtext>First Expression</mtext>
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</maction>
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<maction actiontype="statusline">
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<mi>statusline#Second Expression</mi>
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<mtext>Second Expression</mtext>
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</maction>
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<maction actiontype="statusline">
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<mi>statusline#And so on...</mi>
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<mtext>And so on..</mtext>
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</maction>
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</maction>
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</math></p>
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<p>Click the expression below to see several definitions of pi:
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<br />
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<math mode="display" xmlns="&mathml;">
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<mrow>
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<maction actiontype="toggle">
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<mrow>
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<mi>π</mi>
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<mo>=</mo>
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<mn>3.14159265358</mn><mo mathvariant="bold">...</mo>
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</mrow>
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<mrow>
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<mi>π</mi>
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<mo>=</mo>
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<mn>2</mn><mi>i</mi>
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<mo>⁢</mo>
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<mo>Log</mo>
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<mfrac>
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<mrow><mn>1</mn><mo>-</mo><mi>i</mi></mrow>
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<mrow><mn>1</mn><mo>+</mo><mi>i</mi></mrow>
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</mfrac>
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</mrow>
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<mrow>
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<mi>π</mi>
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<mo>=</mo>
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<mn>2</mn>
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<mphantom><mo>.</mo></mphantom>
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<mfrac>
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<mn>2</mn>
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<msqrt>
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<mn>2</mn>
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</msqrt>
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</mfrac>
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<mphantom><mo>.</mo></mphantom>
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<mfrac>
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<mn>2</mn>
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<msqrt>
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<mn>2</mn>
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<mo>+</mo>
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<msqrt>
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<mn>2</mn>
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</msqrt>
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</msqrt>
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</mfrac>
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<mphantom><mo>.</mo></mphantom>
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<mfrac>
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<mn>2</mn>
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<msqrt>
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<mn>2</mn>
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<mo>+</mo>
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<msqrt>
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<mn>2</mn>
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<mo>+</mo>
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<msqrt>
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<mn>2</mn>
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</msqrt>
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</msqrt>
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</msqrt>
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</mfrac>
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<mo mathvariant="bold">...</mo>
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</mrow>
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<mrow>
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<mfrac>
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<mi>π</mi>
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<mn>4</mn>
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</mfrac>
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<mo>=</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<mn>1</mn>
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</mstyle>
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<mstyle scriptlevel="0">
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<mrow>
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<mn>2</mn>
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<mo>+</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<msup><mn>1</mn><mn>2</mn></msup>
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</mstyle>
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<mstyle scriptlevel="0">
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<mrow>
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<mn>2</mn>
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<mo>+</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<msup><mn>3</mn><mn>2</mn></msup>
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</mstyle>
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<mstyle scriptlevel="0">
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<mrow>
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<mn>2</mn>
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<mo>+</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<msup><mn>5</mn><mn>2</mn></msup>
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</mstyle>
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<mstyle scriptlevel="0">
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<mrow>
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<mn>2</mn>
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<mo>+</mo>
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<mfrac>
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<mstyle scriptlevel="0">
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<msup><mn>7</mn><mn>2</mn></msup>
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</mstyle>
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<mstyle scriptlevel="0">
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<mn>2</mn><mo>+</mo><mo mathvariant="bold">...</mo>
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</mstyle>
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</mfrac>
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</mrow>
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</mstyle>
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</mfrac>
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</mrow>
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</mstyle>
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</mfrac>
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</mrow>
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</mstyle>
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</mfrac>
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</mrow>
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</mstyle>
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</mfrac>
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</mrow>
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</maction>
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</mrow>
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</math></p>
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<h2>Thomson scattering theory</h2>
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<p><math xmlns="&mathml;" mode="display">
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<mrow>
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<mtable align='left'>
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<mtr>
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<mtd columnalign='left'>
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<mrow>
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<mfrac>
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<mrow>
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<msup>
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<mi>d</mi>
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<mn>2</mn>
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</msup>
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<mi>P</mi>
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</mrow>
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<mrow>
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<mi>d</mi>
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<msub>
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<mi>Ω</mi>
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<mi>s</mi>
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</msub>
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<mo> </mo>
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<mi>d</mi>
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<msub>
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<mi>ω</mi>
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<mi>s</mi>
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</msub>
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</mrow>
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</mfrac>
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</mrow>
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</mtd>
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<mtd columnalign='left'>
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<mrow>
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<mo>=</mo>
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</mrow>
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</mtd>
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<mtd columnalign='left'>
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<mrow>
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<msubsup>
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<mi>r</mi>
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<mi>e</mi>
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<mn>2</mn>
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</msubsup>
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<msub>
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<mo>∫</mo>
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<mi>V</mi>
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</msub>
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<mo lspace='0'><</mo>
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<msub>
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<mi>S</mi>
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<mi>i</mi>
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</msub>
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<mo>></mo>
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<msup>
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<mi>d</mi>
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<mn>3</mn>
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</msup>
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<mi mathvariant='bold'>r</mi>
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<mo>∫</mo>
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<msup>
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<mrow>
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<mo lspace='0' rspace='0' symmetric='false'>|</mo>
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<mover accent='true'>
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<mi mathvariant='bold'>e</mi>
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<mo>^</mo>
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</mover>
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<mo>.</mo>
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<mover accent='true'>
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<mo>Π</mo>
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<mo>↔</mo>
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</mover>
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<mo>.</mo>
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<mover accent='true'>
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<mi mathvariant='bold'>e</mi>
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<mo>^</mo>
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</mover>
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<mo lspace='0' rspace='0' symmetric='false'>|</mo>
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</mrow>
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<mn>2</mn>
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</msup>
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<msup>
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<mi>κ</mi>
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<mn>2</mn>
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</msup>
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<mi>f</mi>
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<mo> </mo>
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<mi>δ</mi>
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<mrow>
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<mo stretchy='false'>(</mo>
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<mi mathvariant='bold'>k</mi>
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<mo>.</mo>
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<mi mathvariant='bold'>v</mi>
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<mo>-</mo>
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<mi>ω</mi>
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<mo stretchy='false'>)</mo>
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</mrow>
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<msup>
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<mi>d</mi>
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<mn>3</mn>
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</msup>
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<mi mathvariant='bold'>v</mi>
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</mrow>
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</mtd>
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</mtr>
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<mtr>
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<mtd></mtd>
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<mtd columnalign='left'>
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<mrow>
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<mo>=</mo>
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</mrow>
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</mtd>
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<mtd columnalign='left'>
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<mrow>
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<msubsup>
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<mi>r</mi>
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<mi>e</mi>
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<mn>2</mn>
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</msubsup>
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<msub>
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<mo>∫</mo>
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<mi>V</mi>
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</msub>
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<mo lspace='0'><</mo>
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<msub>
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<mi>S</mi>
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<mi>i</mi>
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</msub>
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<mo>></mo>
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<msup>
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<mi>d</mi>
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<mn>3</mn>
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</msup>
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<mi mathvariant='bold'>r</mi>
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<mo>∫</mo>
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<msup>
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<mrow>
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<mo symmetric='false' lspace='0' rspace='0'>|</mo>
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<mn>1</mn>
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<mo>-</mo>
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<mfrac>
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<mrow>
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<mo stretchy='false'>(</mo>
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<mn>1</mn>
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<mo>-</mo>
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<mover accent='true'>
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<mi mathvariant='bold'>s</mi>
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<mo>^</mo>
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</mover>
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<mo>.</mo>
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<mover accent='true'>
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<mi mathvariant='bold'>ı</mi>
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<mo>^</mo>
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</mover>
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<mo stretchy='false'>)</mo>
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</mrow>
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<mrow>
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<mo stretchy='false'>(</mo>
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<mn>1</mn>
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<mo>-</mo>
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<msub>
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<mi>β</mi>
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<mi>i</mi>
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</msub>
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<mo stretchy='false'>)</mo>
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<mo stretchy='false'>(</mo>
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<mn>1</mn>
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<mo>-</mo>
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<msub>
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<mi>β</mi>
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<mi>s</mi>
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</msub>
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<mo stretchy='false'>)</mo>
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</mrow>
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</mfrac>
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<msubsup>
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<mi>β</mi>
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<mi>e</mi>
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<mn>2</mn>
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</msubsup>
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<mo symmetric='false' lspace='0' rspace='0'>|</mo>
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</mrow>
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<mn>2</mn>
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</msup>
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<mspace width="thinmathspace"/>
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<msup>
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<mrow>
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<mo symmetric='false' rspace='0'>|</mo>
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<mfrac>
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<mrow>
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<mn>1</mn>
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<mo>-</mo>
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<msub>
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<mi>β</mi>
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<mi>i</mi>
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</msub>
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</mrow>
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<mrow>
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<mn>1</mn>
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<mo>-</mo>
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<msub>
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<mi>β</mi>
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<mi>s</mi>
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</msub>
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</mrow>
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</mfrac>
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<mo symmetric='false' lspace='0' rspace='0'>|</mo>
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</mrow>
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<mn>2</mn>
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</msup>
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</mrow>
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</mtd>
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</mtr>
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<mtr>
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<mtd></mtd>
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<mtd></mtd>
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<mtd columnalign='left'>
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<mrow>
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<mo>×</mo>
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<mrow>
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<mo stretchy='false'>(</mo>
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<mn>1</mn>
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<mo>-</mo>
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<msup>
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<mi>β</mi>
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<mn>2</mn>
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</msup>
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<mo stretchy='false'>)</mo>
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</mrow>
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<mo> </mo>
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<mi>f</mi>
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<mo> </mo>
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<mi>δ</mi>
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<mrow>
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<mo stretchy='false'>(</mo>
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<mi mathvariant='bold'>k</mi>
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<mo>.</mo>
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<mi mathvariant='bold'>v</mi>
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<mo>-</mo>
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<mi>ω</mi>
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<mo stretchy='false'>)</mo>
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</mrow>
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<msup>
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<mi>d</mi>
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<mn>3</mn>
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</msup>
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<mi mathvariant='bold'>v</mi>
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</mrow>
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</mtd>
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</mtr>
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</mtable>
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</mrow>
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</math>
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</p>
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<h2>Maxwell's Equations</h2>
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<p style="text-align:center">
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<math xmlns='&mathml;'>
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<mstyle displaystyle='true'>
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<mrow>
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<mo>{</mo>
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<mtable columnalign='right center left' equalrows='false' equalcolumns='false'>
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<mtr>
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<mtd>
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<mrow>
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<mo>∇</mo>
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<mo>×</mo>
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<mover accent='true'>
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<mi mathvariant='bold'>B</mi>
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<mo stretchy='true'>→</mo>
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</mover>
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<mo>-</mo>
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<mfrac>
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<mn>1</mn>
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<mi>c</mi>
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</mfrac>
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<mfrac>
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<mrow>
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<mo>∂</mo>
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<mover accent='true'>
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<mi mathvariant='bold'>E</mi>
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<mo stretchy='true'>→</mo>
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</mover>
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</mrow>
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<mrow>
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<mo>∂</mo>
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<mi>t</mi>
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</mrow>
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</mfrac>
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</mrow>
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</mtd>
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<mtd>
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<mo>=</mo>
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</mtd>
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<mtd>
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<mrow>
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<mfrac>
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<mrow>
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<mn>4</mn>
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<mi>π</mi>
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</mrow>
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<mi>c</mi>
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</mfrac>
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<mover accent='true'>
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<mi mathvariant='bold'>j</mi>
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<mo stretchy='true'>→</mo>
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</mover>
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</mrow>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mrow>
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<mo>∇</mo>
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<mo>ċ</mo>
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<mover accent='true'>
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<mi mathvariant='bold'>E</mi>
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<mo stretchy='true'>→</mo>
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</mover>
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</mrow>
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</mtd>
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<mtd>
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<mo>=</mo>
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</mtd>
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<mtd>
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<mrow>
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<mn>4</mn>
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<mi>π</mi>
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<mi>ρ</mi>
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</mrow>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mrow>
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<mo>∇</mo>
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<mo>×</mo>
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<mover accent='true'>
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<mi mathvariant='bold'>E</mi>
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<mo stretchy='true'>→</mo>
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</mover>
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<mo>+</mo>
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<mfrac>
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<mn>1</mn>
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<mi>c</mi>
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</mfrac>
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<mfrac>
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<mrow>
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<mo>∂</mo>
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<mover accent='true'>
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<mi mathvariant='bold'>B</mi>
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<mo stretchy='true'>→</mo>
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</mover>
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</mrow>
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<mrow>
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<mo>∂</mo>
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<mi>t</mi>
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</mrow>
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</mfrac>
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</mrow>
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</mtd>
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<mtd>
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<mo>=</mo>
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</mtd>
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<mtd>
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|
<mover accent='true'>
|
|
<mn mathvariant='bold'>0</mn>
|
|
<mo stretchy='true'>→</mo>
|
|
</mover>
|
|
</mtd>
|
|
</mtr>
|
|
<mtr>
|
|
<mtd>
|
|
<mrow>
|
|
<mo>∇</mo>
|
|
<mo>ċ</mo>
|
|
<mover accent='true'>
|
|
<mi mathvariant='bold'>B</mi>
|
|
<mo stretchy='true'>→</mo>
|
|
</mover>
|
|
</mrow>
|
|
</mtd>
|
|
<mtd>
|
|
<mo>=</mo>
|
|
</mtd>
|
|
<mtd>
|
|
<mn>0</mn>
|
|
</mtd>
|
|
</mtr>
|
|
</mtable>
|
|
</mrow>
|
|
</mstyle>
|
|
</math>
|
|
</p>
|
|
|
|
<h2>Einstein's field equations</h2>
|
|
|
|
<p style="text-align:center">
|
|
<math xmlns='&mathml;'>
|
|
<mstyle displaystyle='true'>
|
|
<mrow>
|
|
<msub>
|
|
<mi mathvariant="normal">R</mi>
|
|
<mstyle scriptlevel='1'>
|
|
<mrow>
|
|
<mi>μ</mi>
|
|
<mi>ν</mi>
|
|
</mrow>
|
|
</mstyle>
|
|
</msub>
|
|
<mo>-</mo>
|
|
<mfrac>
|
|
<mn>1</mn>
|
|
<mn>2</mn>
|
|
</mfrac>
|
|
<msub>
|
|
<mi>g</mi>
|
|
<mstyle scriptlevel='1'>
|
|
<mrow>
|
|
<mi>μ</mi>
|
|
<mi>ν</mi>
|
|
</mrow>
|
|
</mstyle>
|
|
</msub>
|
|
<mi mathvariant='normal'>R</mi>
|
|
<mo>=</mo>
|
|
<mfrac>
|
|
<mrow>
|
|
<mn>8</mn>
|
|
<mi>π</mi>
|
|
<mi mathvariant='normal'>G</mi>
|
|
</mrow>
|
|
<msup>
|
|
<mi>c</mi>
|
|
<mn>4</mn>
|
|
</msup>
|
|
</mfrac>
|
|
<msub>
|
|
<mi mathvariant='normal'>T</mi>
|
|
<mstyle scriptlevel='1'>
|
|
<mrow>
|
|
<mi>μ</mi>
|
|
<mi>ν</mi>
|
|
</mrow>
|
|
</mstyle>
|
|
</msub>
|
|
</mrow>
|
|
</mstyle>
|
|
</math>
|
|
</p>
|
|
|
|
</body>
|
|
</html>
|