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Math	Math typesetting examples.	Math typesetting examples.	2021-03-16T10:46:05+01:00	2021-03-16T10:46:05+01:00	false		docs parent examples	210	true

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Example 1

Excerpt taken from Supernova Neutrinos

Markdown

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

$$
\begin{equation*}
   n \sim  10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right).
\end{equation*}
$$

HTML

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*}

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.