%latex2e declaration

%latex2e declaration
\documentclass[12pt]{article}
\usepackage[cp862]{inputenc}
\usepackage[hebrew]{babel}
\usepackage{tcourse}

\newcommand{\fiber}{\ast}
\newcommand{\capacity}{{\sf c}}
\newcommand{\period}{{\sf p}}

\begin{document}
\sethebrew
\courseSlogan{�� - �� ''�}
\exerciseNumberAndDate{1}{18/4/2001}

\ques{} �� $G_1, G_2$ �� $G_1 \fiber G_2$ �� $G_1$ �-$G_2$.\ ��
\[.S(G_1 \fiber G_2) = S(G_1) \cap S(G_2)\]
\ques{} �� $G=(V,E,L)$
�� \L{Shannon} �� -�� $S=S(G)$ �� $H$ ��
�� $(v,v)$, $v \in V$, �� $G*G$.
\begin{enumerate}
\item �� $S$ �� , ��
�� $S$ �� $G$.
\item �� $S$ �� $H$ �� .
\item �� $S$ �� , �� -��
$|V|(|V|-1)/2$.
\item �� $S=S(G)$.
\end{enumerate}

\ques{} �� $G=(V,E,L)$ �� $S=S(G)$ �� -�� $G$.
��,
�� , �� $l$ ��, \[.\capacity(S^l) = l\cdot \capacity(S)\]
{\bf ��}: �� )�� (:

\noindent
�� $\Sigma$ ��''� �� $S$ �� $S_0 = S(G_0)$ �� ''� �� -��
$G_0$ �� $G$ �� $\capacity(S) = \capacity(S_0)$ )�� $S_0$ �� ?(.
\newpage
\noindent
�� $\ell_1 < \ell_2 < \cdots < \ell_i < \cdots$ ��
\begin{equation}
\lim_{i \rightarrow \infty}
\frac{1}{\ell_i} \log_2 |S_0 \cap \Sigma^{\ell_i}| = \capacity(S_0)
\end{equation}
)�� ?(. �� $m_i = \lceil \ell_i/\ell \rceil$. ��
\begin{eqnarray}
\label{eq:sfirst}
\capacity(S^\ell) & \ge & \capacity(S_0^\ell) \\
& \ge & \limsup_{i \rightarrow \infty}
\frac{1}{m_i}
\log_2 |S_0 \cap \Sigma^{m_i \ell}| \\
& \ge & \limsup_{i \rightarrow \infty}
\frac{1}{m_i}
\log_2 |S_0 \cap \Sigma^{\ell_i}| \\
& \ge & \ell \cdot \lim_{i \rightarrow \infty}
\frac{\ell_i}{m_i \ell}
\lim_{i \rightarrow \infty}
\frac{1}{\ell_i}
\log_2 |S_0 \cap \Sigma^{\ell_i}|\\
& = & \ell \cdot \capacity(S_0) \\
\label{eq:slast}
% & = & \ell \cdot \capacity(S) \; .
& = & \ell \cdot \capacity(S) \;
\end{eqnarray}
)�� ~\L{(\ref{eq:sfirst})--(\ref{eq:slast})}. ��
�-$S_0$ ��-��?(.
\ques{} �� $G$
�� -�� $\period$.
�� $G^\period$ �� -$\period$
�� -�� .

\ques{} �� $G$ ��
��-�� $\period$ �� $v$ �� -$G$. �� $\period$ ��
�� )��-�� ( �-$G$ ��
�� $v$.

\ques{} �� $G$ �� -�� $\period$, ��
$G_1, G_2, \ldots, G_\period$ �� -�� $G^\period$.
�� -��
$G_i$ ��: \[.\capacity(S(G_i)) = \period\cdot \capacity(S(G)) \]
\goodLuck
\end{document}