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<div class="t">BRCA1 and BRCA2 protein expressions in an ovotestis of a 46, XX true hermaphrodite</div>
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<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 &= a_{11}^i
\sigma_r^i + \sigma_{12}^i \sigma_{\uptheta}^i \\ \upvarepsilon_{\uptheta}^i & =
a_{12}^i \sigma_r^i + a_{22}^i \sigma_{\uptheta}^i \\ \gamma_{r \uptheta}^i & =
a_{66}^i \tau_{r \uptheta}^i \\ \gamma_{rz}^i & = \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 &= a_{11}^i \sigma_r^i + \sigma_{12}^i
\sigma_{\theta}^i \\ \varepsilon_{\theta}^i & = a_{12}^i \sigma_r^i + a_{22}^i
\sigma_{\theta}^i \\ \gamma_{r \theta}^i & = a_{66}^i \tau_{r \theta}^i \\
\gamma_{rz}^i & = \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: \[ \begin{array}{cc} a + \frac{b}{c} & \sqrt{a^b} \\ c & c
\end{array} \]
</li>
</ul>
</section>
<section>
<h3>The Lorenz Equations, LaTeX</h3>
<p> \begin{align} \dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\
\dot{z} & = -\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>\[ \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix} \mathbf{i} & \mathbf{j} &
\mathbf{k} \\ \frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0
\\ \frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0 \\
\end{vmatrix} \]
</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>\[ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots =
\prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for
$|q|<1$}. \]
</p>
</section>
<section>
<h3>Maxwell's Equations</h3>
<p> \begin{align} \nabla \times \vec{\mathbf{B}} -\, \frac1c\,
\frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\
\nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\,
\frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla
\cdot \vec{\mathbf{B}} & = 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>
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