% Donated to MGNet by Louis Howell and modified by Craig Douglas

\topmargin=-.59375in
\textheight=9.1875in
\oddsidemargin=-.3in
\textwidth=7.1in

%\renewcommand{\section}{\setcounter{equation}{0}\@startsection{section}{1}{\z@}
%{3.25ex plus 1ex minus .2ex}{1.5ex plus .2ex}{\large\bf}}
%\renewcommand{\subsection}{\@startsection{subsection}{2}{\z@}
%{2.25ex plus 1ex minus .2ex}{1ex plus .2ex}{\normalsize\bf}}
%\renewcommand{\subsubsection}{\@startsection{subsubsection}{3}{\z@}
%{2.25ex plus 1ex minus .2ex}{1ex plus .2ex}{\normalsize\bf}}
%\renewcommand{\theequation}{\arabic{section}.\arabic{equation}}
\renewcommand{\section}[1]{\vspace{1ex}\begin{center}
                           \normalsize #1
                           \end{center}\vspace{1ex}}
\renewcommand{\subsection}[1]{\vspace{1ex}\begin{center}
                              \normalsize #1
                              \end{center}\vspace{1ex}}
\renewcommand{\subsubsection}[1]{\noindent{\normalsize #1}}
\setlength{\parskip}{1ex}


% This foolishness since the standard definition tries to do too much
\def\thebibliography#1{\section{REFERENCES}\list
 {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth
 \advance\leftmargin\labelsep
 \usecounter{enumi}}
 \def\newblock{\hskip .11em plus .33em minus .07em}
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\relax}

% More stuff to conform to NASA format
%\renewcommand{\thefigure}{\arabic{figure}\alph{subcaption}}
%\renewcommand{\thetable}{\thechapter.\arabic{table}\alph{subcaption}}

\setlength{\oddsidemargin}{0.3in}
\setlength{\topmargin}{-0.5in}
\setlength{\textheight}{9in}
\setlength{\textwidth}{6in}

% Set up constants controlling floats:

\setcounter{topnumber}{1}
\setcounter{bottomnumber}{1}
\renewcommand{\topfraction}{.8}
\renewcommand{\bottomfraction}{.8}
\renewcommand{\textfraction}{.05}

% Theorem-like environments:

\def\theequation{\arabic{equation}}
\def\thetheorem{\arabic{theorem}}

\def\@begintheorem#1#2{\par\bgroup{#1\ #2. }\it\ignorespaces}
\def\@opargbegintheorem#1#2#3{\par\bgroup{#1\ #2\ (#3). }\it\ignorespaces}
\def\@endtheorem{\egroup}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{proposition}[theorem]{Proposition}

\newtheorem{algorithm}{Algorithm}[section]

% Nick's trinket for ending proofs:

\def\qed{\vrule height4.5pt width3.7pt depth4pt}

% The counter 'subcaption' and the commands \manycaptions and \subcaption
% provide for multiple captions to a single figure or table, which are
% identified by the figure or table number followed by a small letter,
% e.g. 2-1a, 2-1b, etc.

% Immediately upon entering the float environment, enter the \manycaptions
% command.  This locally redefines \@makecaption to make all of the captions
% left-justified instead of centered.  A \label following this command will
% store the correct number for the entire float, e.g. 2-1.

% Enter each caption with a \subcaption command.  Each of these will
% generate a separate line in the \listoffigures or \listoftables.  I have
% not provided for the optional argument to \caption, since each of the
% individual captions will probably  be less than 300 characters.  A \label
% following a \subcaption command will store the correct number for that
% particular subcaption, e.g., 2-1b.

% These commands work by redefining the internal LaTeX commands that \caption
% calls.  These redefinitions are all local, in that they will not affect
% any other floats in the document.

\newcounter{subcaption}

\newcommand{\manycaptions}{
 \renewcommand{\@makecaption}[2]{
  \vskip 10pt
  ##1: ##2
  }
 \setcounter{subcaption}{0}
 \refstepcounter{\@captype}
 }

\newcommand{\subcaption}[1]{
 \addtocounter{\@captype}{-1}
 \stepcounter{subcaption}
 % Only one of these will actually be used, but it's easiest to redefine
 % both of them instead of trying to figure out which to do:
 \renewcommand{\thefigure}{\thechapter-\arabic{figure}\alph{subcaption}}
 \renewcommand{\thetable}{\thechapter.\arabic{table}\alph{subcaption}}
 \caption{#1}
 }

% Simple macros:

\newcommand{\rf}[1]{[\ref{#1}]}
\newcommand{\eq}[1]{(\ref{#1})}

\newcommand{\Mobius}{M\"{o}bius }
\newcommand{\comp}{\raisebox{.35ex}{\tiny\rm o}}

% New definition of maketitle allowing the use of the definitions
% above
\def\and{\vspace*{1em}\\}

\def\maketitle{
\par
 \begingroup
 \def\thefootnote{\fnsymbol{footnote}}
 \def\@makefnmark{\hbox 
 to 0pt{$^{\@thefnmark}$\hss}} 
 \if@twocolumn 
 \twocolumn[\@maketitle] 
 \else \newpage
 \global\@topnum\z@ \@maketitle \fi\thispagestyle{empty}\@thanks
 \endgroup
 \setcounter{footnote}{0}
 \let\maketitle\relax
 \let\@maketitle\relax
\gdef\@thanks{}
%\gdef\@author{}
%\gdef\@title{}
%\let\thanks\relax
\def\titlenewline{ }
%\def\and{\vspace*{2em}\\} %%%used in \author, but reactivated in headings RS%%%
\let\thanks\commentout %%%\let instead of \def RS%%%
\let\samethanks\relax %%%also reactivated RS%%%
\def\headnewline{\\}
}

% title
\def\@maketitle{\newpage
 \thispagestyle{empty}
 \null
\vskip 0em \begin{center}
 \advance \rightskip by 10mm
\advance \leftskip by 10mm
 {\@title \par} \vskip 2em {\normalsize \lineskip .5em
 \begin{tabular}[t]{c}
 \@author 
 \end{tabular}
 \par} 
 \end{center}
 \par
 \vskip 2em
} 

% Abstract defined to be left at the begining of a paragraph.

\def\abstract{
\begin{center}
SUMMARY
\end{center}
\vskip 1ex
{\hspace*{\parindent}}
}
\def\endabstract{\par\normalsize\rm}

% Define a new bibliography

\def\thebibliography#1{\section{{REFERENCES}}\list
 {[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth
 \advance\leftmargin\labelsep
 \usecounter{enumi}}
 \def\newblock{\hskip .11em plus .33em minus .07em}
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\relax}
\let\endthebibliography=\endlist