test-math-latex.xml

<?xml version="1.0" encoding="utf-8"?>
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<t:test xmlns:t="http://www.ncbi.nlm.nih.gov/ns/test" xmlns="http://www.w3.org/1999/xhtml">
  <t:title>LaTeX samples / test page</t:title>

  <t:content>
    <article data-type="main">
      <div class="jrb">
        <div class="t">Journal of Interesting Things</div>
        <div class="p">The Society for Putting Things on Top of Other Things</div>
      </div>
      <header class="fm-sec">
        <h1 class="content-title">LaTeX samples / test page</h1>
        <p class="contribs">Various outstanding people</p>
      </header>

      <h2>LaTeX</h2>
      <section>
        <h3>LaTeX sample that uses upgreek</h3>
        <p>This equation is from <a
            href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3117236/#eq9">PMC3117236</a>,
          equation "(A1)". </p>
        <p> Equation (from \begin{align*} \begin{split} \upvarepsilon_r^i &amp;= a_{11}^i
          \sigma_r^i + \sigma_{12}^i \sigma_{\uptheta}^i \\ \upvarepsilon_{\uptheta}^i &amp; =
          a_{12}^i \sigma_r^i + a_{22}^i \sigma_{\uptheta}^i \\ \gamma_{r \uptheta}^i &amp; =
          a_{66}^i \tau_{r \uptheta}^i \\ \gamma_{rz}^i &amp; = \gamma_{\uptheta z}^i =
          \tau_{rz}^i = \tau_{\uptheta z}^i = 0 \end{split} \end{align*} </p>
        <p> For comparison, here's the image source on PMC: <img
            src="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3117236/equ/M20"/>. </p>
        <p> Here's the same equation but with standard characters (not upright): \begin{align*}
          \begin{split} \varepsilon_r^i &amp;= a_{11}^i \sigma_r^i + \sigma_{12}^i
          \sigma_{\theta}^i \\ \varepsilon_{\theta}^i &amp; = a_{12}^i \sigma_r^i + a_{22}^i
          \sigma_{\theta}^i \\ \gamma_{r \theta}^i &amp; = a_{66}^i \tau_{r \theta}^i \\
          \gamma_{rz}^i &amp; = \gamma_{\theta z}^i = \tau_{rz}^i = \tau_{\theta z}^i = 0
          \end{split} \end{align*} </p>
      </section>

      <section>
        <h3>Some simple LaTeX</h3>
        <ul>
          <li>Inline: \(a + b = c\)</li>
          <li>Fractions: \[\frac{n!}{k!(n-k)!} = {n \choose k}\]</li>
          <li>Array: \[ \begin{array}{cc} a + \frac{b}{c} &amp; \sqrt{a^b} \\ c &amp; c
            \end{array} \] </li>
        </ul>
      </section>

      <section>
        <h3>The Lorenz Equations, LaTeX</h3>
        <p> \begin{align} \dot{x} &amp; = \sigma(y-x) \\ \dot{y} &amp; = \rho x - y - xz \\
          \dot{z} &amp; = -\beta z + xy \end{align} </p>
      </section>

      <section>
        <h3>The Cauchy-Schwarz Inequality, LaTeX</h3>

        <p>\[ \left( \sum_{k=1}^n a_k b_k \right)^{\!\!2} \leq \left( \sum_{k=1}^n a_k^2 \right)
          \left( \sum_{k=1}^n b_k^2 \right) \]</p>
      </section>

      <section>
        <h3>A Cross Product Formula</h3>

        <p>\[ \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} &amp; \mathbf{j} &amp;
          \mathbf{k} \\ \frac{\partial X}{\partial u} &amp; \frac{\partial Y}{\partial u} &amp; 0
          \\ \frac{\partial X}{\partial v} &amp; \frac{\partial Y}{\partial v} &amp; 0 \\
          \end{vmatrix} \]</p>
      </section>

      <section>
        <h3>The probability of getting \(k\) heads when flipping \(n\) coins is:</h3>

        <p>\[P(E) = {n \choose k} p^k (1-p)^{ n-k} \]</p>
      </section>

      <section>
        <h3>An Identity of Ramanujan</h3>

        <p>\[ \frac{1}{(\sqrt{\phi \sqrt{5}}-\phi) e^{\frac25 \pi}} = 1+\frac{e^{-2\pi}}
          {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\ldots} } } } \]</p>
      </section>

      <section>
        <h3>A Rogers-Ramanujan Identity</h3>

        <p>\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
          \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for
          $|q|&lt;1$}. \]</p>
      </section>

      <section>
        <h3>Maxwell's Equations</h3>

        <p> \begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\,
          \frac{\partial\vec{\mathbf{E}}}{\partial t} &amp; = \frac{4\pi}{c}\vec{\mathbf{j}} \\
          \nabla \cdot \vec{\mathbf{E}} &amp; = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\,
          \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} &amp; = \vec{\mathbf{0}} \\ \nabla
          \cdot \vec{\mathbf{B}} &amp; = 0 \end{align} </p>
      </section>

      <section>
        <h3>In-line Mathematics</h3>

        <p>Finally, while display equations look good for a page of samples, the ability to mix
          math and text in a paragraph is also important. This expression \(\sqrt{3x-1}+(1+x)^2\)
          is an example of an inline equation. As you see, MathJax equations can be used this way
          as well, without unduly disturbing the spacing between lines.</p>
      </section>
    </article>
  </t:content>
</t:test>