\setlength{\textheight}{23cm}
\setlength{\textwidth}{14cm}

\setlength{\marginparwidth}{0pt}


\def\beq{\begin{equation}}
\def\eeq{\end{equation}}
\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
\def\bq{\begin{quote}}
\def\eq{\end{quote}}
\def \lsim{\mathrel{\vcenter{\hbox{$<$}\nointerlineskip\hbox{$\sim$}}}}
\def \gsim{\mathrel{\vcenter{\hbox{$>$}\nointerlineskip\hbox{$\sim$}}}}
\def\gappeq{\mathrel{\rlap {\raise.5ex\hbox{$>$}}{\lower.5ex\hbox{$\sim$}}}}
\def\lappeq{\mathrel{\rlap{\raise.5ex\hbox{$<$}}{\lower.5ex\hbox{$\sim$}}}}
\def\simlt{\stackrel{<}{{}_\sim}}
\def\simgt{\stackrel{>}{{}_\sim}}
\def\msnu{m_{\tilde{\nu}}}
\def\msnui{m_{\tilde{\nu}_i}}
\def\msnuj{m_{\tilde{\nu}_j}}
\def\msnuI{m_{\tilde{\nu}_I}}
\def\msnuJ{m_{\tilde{\nu}_J}}
\def\snu{\tilde{\nu}}
\def\snuvi{\langle\tilde{\nu}_i\rangle}
\def\Huv{\langle H_u \rangle}
\def\mchi{m_{\chi}}
\def\Rp{R_p}
\def\Rpv{R_p \! \! \! \! \! \! /~~}
\def\mnu{[m_{\nu}]_{ij}}
\def\LI{$\{ L_I \} ~$}
\def\vd{\vec{\delta}}
\def\hd{\hat{\delta}}

\def\ltap{\raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$<$}}
\def\gtap{\raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$>$}}
\newcommand{\Rsl}{{\not \! \!{R}}}
\newcommand{\sqm}{m_{\tilde{q}}}
\newcommand{\slm}{m_{\tilde{l}}}
\newcommand{\ms}{\widetilde{m}}
\newcommand{\sun}{\Delta m^2_{\rm solar}}
\newcommand{\atm}{\Delta m^2_{\rm atm}}
\newcommand{\lsnd}{\Delta m^2_{\rm LSND}}
\def\bea{\begin{eqnarray}}   
\def\eea{\end{eqnarray}}
\def\la{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil$\displaystyle##

$\hfil\cr<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##
$\hfil\cr<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##
$\hfil\cr<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$
\hfil\cr<\cr\sim\cr}}}}}
% greater than or order of \ga
\def\ga{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##
$\hfil\cr>\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##
$\hfil\cr>\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$
\hfil\cr>\cr\sim\cr}}}}}