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assets/js/index.js | ||
assets/js/katex.js | ||
assets/js/vendor | ||
node_modules |
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document.addEventListener('DOMContentLoaded', function() { | ||
renderMathInElement(document.body, { | ||
delimiters: [ | ||
{left: '$$', right: '$$', display: true}, | ||
{left: '$', right: '$', display: false}, | ||
{left: '\\(', right: '\\)', display: false}, | ||
{left: '\\[', right: '\\]', display: true}, | ||
], | ||
}); | ||
}); |
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bootStrapJs = false | ||
breadCrumb = false | ||
highLight = true | ||
kaTex = true |
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--- | ||
title: "Math" | ||
description: "Math typesetting examples." | ||
lead: "Math typesetting examples." | ||
date: 2021-03-16T10:46:05+01:00 | ||
lastmod: 2021-03-16T10:46:05+01:00 | ||
draft: false | ||
images: [] | ||
menu: | ||
docs: | ||
parent: "examples" | ||
weight: 210 | ||
toc: true | ||
--- | ||
|
||
## Example 1 | ||
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_Excerpt taken from [Supernova Neutrinos](https://neutrino.leima.is/book/introduction/supernova-neutrinos/)_ | ||
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### Markdown | ||
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```md | ||
The average energy of the neutrinos $\langle E \rangle$ emitted during a supernova explosion is of the order of 10MeV, and the neutrino luminosity at the early epoch of the explosion is approximately $10^{52}\mathrm{ergs\cdot s^{-1}}$. | ||
Therefore, the number density of the neutrinos at the radius $R$ is | ||
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$$ | ||
\begin{equation*} | ||
n \sim 10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right). | ||
\end{equation*} | ||
$$ | ||
``` | ||
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### HTML | ||
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The average energy of the neutrinos $\langle E \rangle$ emitted during a supernova explosion is of the order of 10MeV, and the neutrino luminosity at the early epoch of the explosion is approximately $10^{52}\mathrm{ergs\cdot s^{-1}}$. | ||
Therefore, the number density of the neutrinos at the radius $R$ is | ||
|
||
$$ | ||
\begin{equation*} | ||
n \sim 10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right). | ||
\end{equation*} | ||
$$ | ||
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||
It turns out that the ambient dense neutrino medium has a significant impact on neutrino oscillations, which has been intensely investigated in the last decade. |
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