petrbalvin
f8ed33df83
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Assisted-by: GLM 5.3
35 lines
3.9 KiB
HTML
35 lines
3.9 KiB
HTML
=== HTML ===
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<h1 id="math">Math</h1>
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<p>Inline radiation: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>h</mi><mi>ν</mi></math> redshifted by <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msub><mi>g</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub></msqrt></math>.</p>
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<div class="math math-display">
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mi>E</mi><mo>=</mo><mi>h</mi><mi>ν</mi><mspace width="0.1667em"></mspace><msqrt><mrow><msub><mi>g</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo></mrow></msqrt><mo>=</mo><mtext>konst.</mtext><mspace width="1em"></mspace><mo>(</mo><mn>1</mn><mo>)</mo></math>
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</div>
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<p>The metric reads <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><msup><mi>s</mi><mn>2</mn></msup><mo>=</mo><mo>-</mo><msub><mi>g</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><msup><mi>c</mi><mn>2</mn></msup><mi>d</mi><msup><mi>t</mi><mn>2</mn></msup><mo>+</mo><mi>d</mi><msup><mi>r</mi><mn>2</mn></msup><mo>+</mo><msup><mi>r</mi><mn>2</mn></msup><mi>d</mi><msup><mi>Ω</mi><mn>2</mn></msup></math>, and a
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photon loses energy as <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>E</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msub><mi>E</mi><mn>0</mn></msub></mfrac><mo>=</mo><msup><mi>e</mi><mrow><mo>-</mo><mi>H</mi><mi>t</mi></mrow></msup></math>.</p>
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<div class="math math-display">
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mn>1</mn><mo>+</mo><mi>z</mi><mo>=</mo><mfrac><mrow><mi>ν</mi><mo>(</mo><msub><mi>r</mi><mn>1</mn></msub><mo>)</mo></mrow><mrow><mi>ν</mi><mo>(</mo><msub><mi>r</mi><mn>2</mn></msub><mo>)</mo></mrow></mfrac><mo>=</mo><msqrt><mfrac><mrow><msub><mi>g</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>(</mo><msub><mi>r</mi><mn>1</mn></msub><mo>)</mo></mrow><mrow><msub><mi>g</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>(</mo><msub><mi>r</mi><mn>2</mn></msub><mo>)</mo></mrow></mfrac></msqrt><mo>.</mo><mspace width="1em"></mspace><mo>(</mo><mn>2</mn><mo>)</mo></math>
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</div>
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<p>Prices are not math: the ticket costs $5 and the guide $10 per group.</p>
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<p>The metric in prose right above its display form</p>
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<div class="math math-display">
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>g</mi><mrow><mi>t</mi><mi>t</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>-</mo><mfrac><msub><mi>r</mi><mi>s</mi></msub><mi>r</mi></mfrac></math>
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</div>
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<p>continues in a sentence after it.</p>
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<div class="math math-display">
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><msub><mi>r</mi><mi>h</mi></msub><mo>=</mo><mfrac><mi>σ</mi><msqrt><mrow><mn>2</mn><mi>π</mi><mi>G</mi><msub><mi>ρ</mi><mtext>amb</mtext></msub></mrow></msqrt></mfrac><mo>,</mo><mspace width="2em"></mspace><msub><mi>M</mi><mi>h</mi></msub><mo>=</mo><mfrac><mrow><mn>2</mn><msup><mi>σ</mi><mn>2</mn></msup><msub><mi>r</mi><mi>h</mi></msub></mrow><mi>G</mi></mfrac><mo>.</mo><mspace width="1em"></mspace><mo>(</mo><mn>7</mn><mo>)</mo></math>
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</div>
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<p>An equation broken across lines keeps its prose out of mathematics
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$\nabla^2 h =
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(8\pi/\kappa a)u$: the binding is the force of a cell <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>κ</mi><mi>a</mi><mo>=</mo><msup><mi>c</mi><mn>4</mn></msup><mo>/</mo><mi>G</mi></math>,
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and the source is the energy.</p>
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<div class="math math-display">
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><merror><mtext>\raisebox</mtext></merror><mrow><mn>1</mn><mi>e</mi><mi>m</mi></mrow><mi>E</mi><mo>=</mo><mi>h</mi><mi>ν</mi></math>
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</div>
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<p>Inline degradation too: <math xmlns="http://www.w3.org/1998/Math/MathML"><merror><mtext>\raisebox</mtext></merror><mrow><mn>1</mn><mi>e</mi><mi>m</mi></mrow><mi>E</mi></math> stays visible where it stands.</p>
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=== TOC ===
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<div class="toc">
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<ul>
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<li><a rel="noopener noreferrer" href="#math">Math</a></li>
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</ul>
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</div>
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