% new evironment

\newtheorem{lemma}{Lemma}
\newtheorem{theorem}{Theorem}
\newtheorem{corollary}{Corollary}

\makeatletter
\def\thebibliography#1{\chapter*{References\markboth
  {REFERENCES}{REFERENCES}}\list
  {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}
    \leftmargin\labelwidth
    \advance\leftmargin\labelsep
    \usecounter{enumi}}
    \def\newblock{\hskip .11em plus .33em minus -.07em}
    \sloppy
    \sfcode`\.=1000\relax}
\makeatother


% simpified new commands

\newcommand{\ba}{\begin{array}}
\newcommand{\ea}{\end{array}}

\newcommand{\bab}{\begin{abstract}}
\newcommand{\eab}{\end{abstract}}

\newcommand{\bbib}{\begin{thebibliography}}
\newcommand{\ebib}{\end{thebibliography}}

\newcommand{\bcl}{\begin{corollary}}
\newcommand{\ecl}{\end{corollary}}

\newcommand{\bct}{\begin{center}}
\newcommand{\ect}{\end{center}}

\newcommand{\bds}{\begin{description}}
\newcommand{\eds}{\end{description}}

\newcommand{\ben}{\begin{enumerate}}
\newcommand{\een}{\end{enumerate}}

\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}

\newcommand{\beqa}{\begin{eqnarray}}
\newcommand{\eeqa}{\end{eqnarray}}

\newcommand{\beqan}{\begin{eqnarray*}}
\newcommand{\eeqan}{\end{eqnarray*}}

\newcommand{\bsubeqa}{\begin{subeqnarray}}
\newcommand{\esubeqa}{\end{subeqnarray}}

\newcommand{\bfg}{\begin{figure}}
\newcommand{\efg}{\end{figure}}

\newcommand{\bfl}{\begin{flushleft}}
\newcommand{\efl}{\end{flushleft}}

\newcommand{\bfr}{\begin{flushright}}
\newcommand{\efr}{\end{flushright}}

\newcommand{\blm}{\begin{lemma}}
\newcommand{\elm}{\end{lemma}}

\newcommand{\bpt}{\begin{picture}}
\newcommand{\ept}{\end{picture}}

\newcommand{\btb}{\begin{tabbing}}
\newcommand{\etb}{\end{tabbing}}

\newcommand{\btbl}{\begin{tabular}}
\newcommand{\etbl}{\end{tabular}}

\newcommand{\bthm}{\begin{theorem}}
\newcommand{\ethm}{\end{theorem}}

\newcommand{\btl}{\begin{titlepage}}
\newcommand{\etl}{\end{titlepage}}

\newcommand{\hsp}{\hspace}
\newcommand{\vsp}{\vspace*}
\newcommand{\vspp}{\vspace{2mm}}

\newcommand{\undl}{\underline}


\newcommand{\cf}{{c.f.}}
\newcommand{\ie}{{\it i.e.,}}
\newcommand{\ex}{{\it e.g.,}}
\newcommand{\etal}{{\it et al.}}


% mathematical symbols

\newcommand{\bksl}{\backslash}
\newcommand{\ptl}{\partial}
\newcommand{\limitinf}{\lim_{n \rightarrow \infty}}
\newcommand{\rtarw}{\rightarrow}


% new fonts

\newfont{\Litbf}{cmmib10 scaled\magstep3}
\newfont{\itbf}{cmmib10 scaled\magstep1}
\newfont{\itbfs}{cmmib10}
.