\documentclass{jarticle}
\begin{document}
\title{Math contents sample}
\author{(Authour's name)}
\address{(Address)}
\date{}
\maketitle

\begin{abstract}
This is a sample file to create math contents.
\end{abstract}

\section{Mathematical Discription.}

\subsection{Maxwell's equations}

For example, this is a representation of Maxwell's equations.

\begin{align}
\nabla \circ \mathrm{E} & = \frac{\rho}{\epsilon_0}, \\
\nabla \circ \mathrm{B} & = 0, \\
\nabla \times \mathrm{E} & = - \frac{\partial \mathrm{B}}{\partial t}, \\
\nabla \times \mathrm{B} & = \mu_0 \mathrm{J} + \mu_0 \epsilon_0 \frac{\partial \mathrm{E}}{\partial t}.
\end{align}

\subsection{Complex sequence}

It is able to derive these relations for $z:=x+iy$ and $Y:=-\mathrm{sgn}(y)$.

\begin{equation}
f(z):=\frac{n !}{2 \pi} (i z)^{-n-1} e^{2 i \delta} \Rightarrow
\left\{
\begin{array}{rcl}
\mathrm{Re} f(z) & = & \displaystyle{ \frac{(Y')^{n+1}}{4 \pi} \int |\xi|^n e^{\xi Y + Y' i \mathrm{sgn}(\xi) 2 \delta - i \xi x} d\xi, }\\
\mathrm{Im} f(z) & = & \displaystyle{ - \frac{(Y')^n}{4 \pi} \int |\xi|^n i \mathrm{sgn}(\xi) e^{\xi Y + Y' i \mathrm{sgn}(\xi) 2 \delta - i \xi x} d\xi. }
\end{array}
\right.
\end{equation}

\end{document}

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