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% A&A DOCUMENT CLASS -- version 6.1 for LaTeX2e
%
% LaTeX document class for Astronomy and Astrophysics journal
%
%%
%%
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%%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
%%   Digits        \0\1\2\3\4\5\6\7\8\9
%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
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\ProvidesClass{aa}[2006/06/01 v6.1
^^JLaTeX document class for Astronomy and Astrophysics journal]
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%
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%
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%
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%
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    \def\@oddhead{\small\hfil\rightmark\hfil\llap{\thepage}}%
    \let\@mkboth\@gobbletwo
    \let\sectionmark\@gobble
    \let\subsectionmark\@gobble
    }
% make indentations changeable
\def\setitemindent#1{\settowidth{\labelwidth}{#1}%
        \leftmargini\labelwidth
        \advance\leftmargini\labelsep
   \def\@listi{\leftmargin\leftmargini
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        \topsep=\medskipamount
        \itemsep=\parskip \advance\itemsep by -\parsep}}
\def\setitemitemindent#1{\settowidth{\labelwidth}{#1}%
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        \advance\leftmarginii\labelsep
\def\@listii{\leftmargin\leftmarginii
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        \topsep=\z@
        \itemsep=\parskip \advance\itemsep by -\parsep}}
% labels of description
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% adjusted environment "description"
% if an optional parameter (at the first two levels of lists)
% is present, its width is considered to be the widest mark
% throughout the current list.
\def\description{\@ifnextchar[{\@describe}{\list{}{\labelwidth\z@
          \itemindent-\leftmargin \let\makelabel\descriptionlabel}}}
\let\enddescription\endlist
%
\def\describelabel#1{#1\hfil}
\def\@describe[#1]{\relax\ifnum\@listdepth=0
\setitemindent{#1}\else\ifnum\@listdepth=1
\setitemitemindent{#1}\fi\fi
\list{--}{\let\makelabel\describelabel}}
%
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\logodepth=1.3cm
\newdimen\headerboxheight
\headerboxheight=143pt
\newdimen\betweenumberspace          % dimension for space between
\betweenumberspace=3.33pt            % number and text of titles.
\newdimen\aftertext                  % dimension for space after
\aftertext=5pt                       % text of title.
\newdimen\headlineindent             % dimension for space between
\headlineindent=1.166cm              % number and text of headings.
\def\andname{and}
\def\keywordname{Key words.}
\def\lastandname{, and}
\def\mailname{{\it Correspondence to\/}:}
\def\email#1{{e-mail: \tt#1}}
% Used only by the publisher
\def\AASection#1{}
%
\newcounter{inst}
\newcounter{auth}
\newdimen\instindent
\newbox\authrun
\newtoks\authorrunning
\newbox\titrun
\newtoks\titlerunning

\def\journalname#1{\gdef\@journalname{#1}}
\gdef\@journalname{Astronomy \&\ Astrophysics}

\def\headnote#1{\gdef\@headnote{#1}}
\def\@headnote{}

\def\dedication#1{\gdef\@dedic{#1}}
\def\@dedic{}

\let\@date\undefined

\if@oldversion
\long\def\abstract#1{\gdef\@abstract{#1}}
\else
\long\def\abstract#1#2#3#4#5{\gdef\@abstract{\number@fw@rds=0%
         \if!#1!\advance\number@fw@rds-1 \else{\sffamily\itshape Context.}\ \pickupw@rd#1\\\let\WC@go\relax\fi
         {\sffamily\itshape Aims.}\
         \if!#2! \@latex@error{The second heading "Aims" is mandatory in the abstract}{}
           {\it The second heading "Aims" is mandatory in the abstract}\\
           \else\advance\number@fw@rds+1\pickupw@rd#2\\\let\WC@go\relax\fi
         {\sffamily\itshape Methods.}\
         \if!#3! \@latex@error{The third heading "Methods" is mandatory in the abstract}{}
           {\it The third heading "Methods" is mandatory in the abstract}\\
           \else\advance\number@fw@rds+1\pickupw@rd#3\\\let\WC@go\relax\fi
         {\sffamily\itshape Results.}\
         \if!#4! \@latex@error{The forth heading "Results" is mandatory in the abstract}{}
           {\it The forth heading "Results" is mandatory in the abstract}\\
            \else\advance\number@fw@rds+1\pickupw@rd#4\let\WC@go\relax\fi
         \if!#5! \else\\\advance\number@fw@rds+1{\sffamily\itshape Conclusions.}\ \pickupw@rd#5\let\WC@go\relax\fi
         \ifnum\number@fw@rds>400
         \@latex@error{Around \number\number@fw@rds\space words in the abstract instead of 300}{}
         \else\relax\fi}}
\fi

\def\keywords#1{\gdef\@keywords{#1}}

\def\institute#1{\gdef\@institute{#1}}

\def\institutename{\par
 \begingroup
 \parindent=0pt
 \parskip=0pt
 \setcounter{inst}{1}%
 \def\and{\par\stepcounter{inst}%
 \hangindent\instindent
 \noindent
 \hbox to\instindent{\hss$^{\theinst}$\enspace}\ignorespaces}%
 \setbox0=\vbox{\def\thanks##1{}\@institute}
 \ifnum\value{inst}>9\relax\setbox0=\hbox{$^{88}$\enspace}%
                 \else\setbox0=\hbox{$^{8}$\enspace}\fi
 \instindent=\wd0\relax
 \ifnum\value{inst}=1\relax
 \else
   \setcounter{inst}{1}%
   \hangindent\instindent
   \noindent
   \hbox to\instindent{\hss$^{\theinst}$\enspace}\ignorespaces
 \fi
 \small
 \ignorespaces
 \@institute\par
 \endgroup}

\def\offprints#1{\begingroup
\def\protect{\noexpand\protect\noexpand}\xdef\@thanks{\@thanks
\protect\footnotetext[0]{\unskip\hskip-1.5em{\it Send offprint requests
to\/}: \ignorespaces#1}}\endgroup\ignorespaces}

\def\mail#1{\gdef\@mail{#1}}
\def\@mail{}

\def\@thanks{}

\def\@fnsymbol#1{\ifcase#1\or\star\or{\star\star}\or{\star\star\star}%
   \or \dagger\or \ddagger\or
   \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
   \or \ddagger\ddagger \else\@ctrerr\fi\relax}

\def\inst#1{\unskip$^{#1}$}
\def\fnmsep{\unskip$^,$}

\def\subtitle#1{\gdef\@subtitle{#1}}
\def\@subtitle{}

\def\msnr#1{\gdef\@msnr{#1}}
\def\@msnr{}

\def\idline#1#2{\gdef\@idline{#1}\setcounter{page}{#2}}
\def\@idline{}
\def\doi#1{\gdef\@doi{DOI: 10.1051/0004-6361:#1}}
\def\@doi{(DOI: will be inserted by hand later)}

\def\headnote#1{\gdef\@headnote{#1}}
\def\@headnote{}

\def\ch@ckobl#1#2{\@ifundefined{@#1}
 {\typeout{A\string&A warning: Missing
\expandafter\string\csname#1\endcsname}%
  \csname #1\endcsname{#2}}
 {}}

\def\ch@ckoblabs#1#2#3#4#5#6{\@ifundefined{@#1}
 {\typeout{A\string&A warning: Missing
\expandafter\string\csname#1\endcsname}%
  \csname #1\endcsname{#2}{#3}{#4}{#5}{#6}}
 {}}

\newif\if@normhead \@normheadtrue
\def\hugehead{\@normheadfalse
\onecolumn
\let\thanks=\footnote
\long\def\@makefntext##1{\parindent\bibindent
     \columnwidth\textwidth\advance\columnwidth -\columnsep
     \divide\columnwidth\tw@\hsize\columnwidth \linewidth\columnwidth
     \noindent\hbox to\parindent{\hss$\m@th^{\@thefnmark}$ }##1}%
}

\newcommand\errorref{\@latex@error{Citations are not allowed in the abstract}{}}
\newenvironment{stopref}{\let\cite\errorref\let\citet\errorref\let\citep\errorref}{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This counts the words. This is an extract of  "gvol.sty,
% written by Ivan Andrus (gvol@math.byu.edu)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
  \newcount\number@fw@rds
  \long\def\pickupw@rd#1 {%
    \let\WC@go\pickupw@rd #1
    \advance\number@fw@rds+1
    \expandafter\WC@go
   }
% End of wordcount section

\def\maketitle{\par
\ch@ckobl{journalname}{Noname}
\ch@ckobl{date}{Preprint online version: \today}
\ch@ckobl{title}{A title should be given}
\ch@ckobl{author}{Name(s) and initial(s) of author(s) should be given }
\ch@ckobl{institute}{Address(es) of author(s) should be given}
\if@oldversion
\ch@ckobl{abstract}{abstract}
\else
\ch@ckoblabs{abstract}{Mathematical optimization can be used as a computational tool to obtain the optimal solution to a given problem in a systematic
and efficient way. For example, in twice-differentiable functions and problems with no constraints, the optimization consists
of finding the points where the gradient of the objective function is zero and using the Hessian matrix to classify the type of each
point. Sometimes, however it is impossible to compute these derivatives and other type of techniques must be employed such as the
steepest descent/ascent method and more sophisticated methods such as those based on the evolutionary algorithms.}
{We present a simple algorithm based on the idea of genetic algorithms (GA) for optimization. We refer to this algorithm as
AGA (Asexual Genetic Algorithm) and apply it to two kinds of problems: the maximization of a function where classical methods fail
and model fitting in astronomy. For the latter case, we minimize the chi-square function to estimate the parameters in two examples:
the orbits of exoplanets by taking a set of radial velocity data, and the spectral energy distribution (SED) observed towards a YSO
(Young Stellar Object).}
{The algorithm AGA may also be called genetic, although it differs from standard genetic algorithms in two main aspects:
a) the initial population is not encoded, and b) the new generations are constructed by asexual reproduction.}
{Applying our algorithm in optimizing some complicated functions, we find the global maxima within a few iterations. For
model fitting to the orbits of exoplanets and the SED of a YSO, we estimate the parameters and their associated errors.}{}
\fi
\ch@ckobl{keywords}{Methods:numerical--Stars--55 Cancri--Planets and Satellites:general--ISM:individual(L1448)}
\begingroup
    \begin{stopref}
    \renewcommand\thefootnote{\@fnsymbol\c@footnote}%
    \def\@makefnmark{$^{\@thefnmark}$}%
 \def\lastand{\ifnum\value{inst}=2\relax
                 \unskip{} \andname\
              \else
                 \unskip, \andname\
              \fi}%
 \def\and{\stepcounter{auth}\relax
          \ifnum\value{auth}=\value{inst}%
             \lastand
          \else
             \unskip,
          \fi}%
 \ifnum \col@number=\@ne
   \@maketitle
 \else
   \twocolumn[\@maketitle]%
 \fi
 \thispagestyle{empty}
 \global\@topnum\z@
 \if@normhead
    \@thanks
 \else
    \twocolumn[\vspace{\@tempdima}]
    \addtocounter{page}{-1}
    \if!\the\authorrunning!
       \authorrunning{ }%
    \fi
 \fi
 \if!\@mail!\else
    \footnotetext[0]{\kern-\bibindent\mailname\
    \ignorespaces\@mail}%
 \fi
%
 \if@runhead
    \def\\{\unskip\ \ignorespaces}\def\inst##1{\unskip{}}%
    \def\thanks##1{\unskip{}}\def\fnmsep{\unskip}%
    \def\object##1{##1}%
    \instindent=\textwidth
    \advance\instindent by-2\headlineindent
    \if!\the\titlerunning!\else
      \edef\@title{\the\titlerunning}%
    \fi
    \global\setbox\titrun=\hbox{\small\rm\unboldmath\ignorespaces\@title}%
    \ifdim\wd\titrun>\instindent
       \typeout{^^JA\string&A Warning: Title too long for running head.}%
       \typeout{Please supply a shorter form with \string\titlerunning
                \space prior to \string\maketitle}%
       \global\setbox\titrun=\hbox{\small\rm
       Title Suppressed Due to Excessive Length}%
    \fi
    \xdef\@title{\copy\titrun}%
%
    \if!\the\authorrunning!
    \else
      \setcounter{auth}{1}%
      \edef\@author{\the\authorrunning}%
    \fi
    \ifnum\value{auth}>2
       \def\stripauthor##1\and##2\endauthor{%
       \protected@xdef\@author{##1\unskip\unskip\if!##2!\else
       \ et al.\fi}}%
       \expandafter\stripauthor\@author\and\endauthor
    \else
       \gdef\and{\unskip\ and \ignorespaces}%
       {\def\and{\noexpand\protect\noexpand\and}%
       \protected@xdef\@author{\@author}}
    \fi
    \global\setbox\authrun=\hbox{\small\unboldmath\@author\unskip:
                                 \unhbox\titrun\if@rnote~\itshape\rnotname\fi}%
    \ifdim\wd\authrun>\instindent
    \typeout{^^JA\string&A Warning: The running head built automatically
             from \string\author\space and \string\title
             ^^Jexceeds the pagewidth, please supply a shorter form
             ^^Jwith \string\authorrunning\space and/or
             \string\titlerunning\space prior to \string\maketitle}%
    \global\setbox\authrun=\hbox{\small\rm Please give a shorter version
       with: {\tt\string\authorrunning\space}and/or{\tt\space
       \string\titilerunning\space}prior to{\tt\space\string\maketitle}}%
    \fi
    \xdef\@author{\copy\authrun}%
    \markboth{\@author}{\@author}%
 \fi
%
 \end{stopref}
 \endgroup
 \setcounter{footnote}{0}
 \setcounter{footnote}{0}%
 \global\let\thanks\relax
 \global\let\maketitle\relax
 \global\let\@maketitle\relax
 \global\let\@thanks\@empty
 \global\let\@author\@empty
 \global\let\@date\@empty
 \global\let\@title\@empty
 \global\let\@subtitle\@empty
 \global\let\@abstract\@empty
 \global\let\@keywords\@empty
 \global\let\keywords\relax
 \global\let\title\relax
 \global\let\author\relax
 \global\let\abstract\relax
 \global\let\date\relax
 \global\let\and\relax}

\def\AALogo{\setbox254=\hbox{
\setlength{\tabcolsep}{0pt}
\begin{tabular}{l}
\\[-30pt]
{\fontsize{18}{21}\selectfont\sffamily\bfseries Astronomy} \\[-2.5pt]
{\fontsize{16}{12}\selectfont\sffamily\mdseries \kern8pt\&\raisebox{4pt}{\rule{78pt}{1pt}}} \\[-5pt]
{\fontsize{18}{21}\selectfont\sffamily\bfseries Astrophysics}
\end{tabular}}\copy254}

\def\makeheadbox{{
\hbox to\textwidth{%
\if!\@idline!
\hbox to0pt{\vbox{\hsize=40cc
\baselineskip=12pt\hrule\hbox
{\vrule\kern3pt\vbox{\kern3pt
\hb@xt@ 40cc{{\sl\@journalname}\ manuscript no.~\jobname \hfill\copyright~ESO~\the\year}
\if!\@msnr!\hbox{\today}\else
\hb@xt@ 30cc{\hfil\strut\LARGE\bfseries\smash{\@msnr}}\fi
\kern3pt}\hfil\kern3pt\vrule}\hrule}\hss}\hfill
\else
\vbox{\baselineskip=11pt
\hbox{\@idline}
\hbox{\@doi}
\hbox{\small\rm \copyright~ESO~\the\year}}
\hfill\AALogo
\fi}}}

\def\@maketitle{\newpage
 \normalfont
 \vbox to0pt{\vskip-20pt
 \nointerlineskip
 \makeheadbox\vss}\nointerlineskip
 \if@normhead
    \setbox\authrun=\vbox\bgroup
 \fi
 \begin{center}
 \vskip24pt
 \if@letter{\large \lettername}\fi
 {\LARGE \sffamily\bfseries\boldmath
  \hrule\@height\logodepth\@width\z@
  \pretolerance=10000
  \vspace*{-12pt}
  \pretolerance=10000
 \if!\@headnote!\else
   \noindent
   {\normalfont\itshape\ignorespaces\@headnote\par}\vskip 3.5mm
 \fi
  \noindent\ignorespaces
  \@title
  \if@rnote \\ \itshape \rnotename \fi
  \par}
 \vskip 8pt\relax
 \if!\@subtitle!\else
   {\Large \sffamily\bfseries\boldmath
   \pretolerance=10000
   \noindent\ignorespaces\@subtitle \par}\vskip 10pt
 \fi
%% \lineskip .5em
 \setbox0=\vbox{\setcounter{auth}{1}\def\and{\stepcounter{auth} }%
                \hfuzz=2\textwidth\def\thanks##1{}\@author}%
 \value{inst}=\value{auth}%
 \setcounter{auth}{1}%
 {\large \rmfamily\mdseries \noindent\ignorespaces\@author}
 \if@longauth \else \end{center} \fi
 \vskip6pt
\small\rm
 \if@longauth {\it (Affiliations can be found after the references)}  \else
 \leftskip=.8cm\rightskip=\leftskip
 \institutename\fi
 \vskip 8pt \noindent\@date
 \if!\@dedic!\else
    \par
    \normalsize\it
    \addvspace\baselineskip
    \noindent\@dedic
 \fi
 \if@longauth \end{center} \fi
 \vskip 8pt
 \small\rm
 \if!\@abstract!\else
  \begin{center}
   {\sffamily\bfseries\abstractname}\par
  \end{center}
  \@abstract
 \fi
 \vskip 6pt
 \small\rm
 \if!\@keywords!\else
 \noindent{\sffamily\bfseries\keywordname}\ \@keywords
 \fi
%
 \if@normhead
    \egroup % end of header box
    \@tempdima=\headerboxheight
    \advance\@tempdima by-\ht\authrun
%   \advance\@tempdima by-\pagetotal
    \ifdim\@tempdima>0pt
       \vrule width0pt height\@tempdima
    \fi
    \unvbox\authrun
    \global\@minipagetrue
    \global\everypar{\global\@minipagefalse\global\everypar{}}
 \else
    \typeout{\the\c@auth\space author names and}
    \typeout{\the\c@inst\space institutes processed}
    \global\@tempdima=\pagetotal
    \global\advance\@tempdima by24pt
 \fi
 \vskip24pt
}
%
\DeclareMathAlphabet{\mathsc}{OT1}{cmr}{m}{sc}
\def\testbx{bx}%
\DeclareRobustCommand{\ion}[2]{%
\relax\ifmmode
\ifx\testbx\f@series
{\mathbf{#1\,\mathsc{#2}}}\else
{\mathrm{#1\,\mathsc{#2}}}\fi
\else\textup{#1\,{\mdseries\textsc{#2}}}%
\fi}
%
\def\clearelargs{\def\1{}\def\2{}\def\3{}\def\4{}\count255=0}
\def\druck@lement#1{{}^{\2}_{\3}\mathrm{#1}{}^{\1}_{\4}{}\if@tempswa$\fi}
\DeclareRobustCommand{\element}{\relax\ifmmode\@tempswafalse
\else$\@tempswatrue\fi\clearelargs\def\?{\phantom{0}}\@lement}
\def\@lement#1{\if#1[\expandafter\f@@dargs\else\druck@lement{#1}\fi}
\def\f@@dargs#1]{\advance\count255by\@ne
\expandafter\def\csname\number\count255\endcsname{#1}\@lement}
%
%\def\vec#1{\ensuremath{\mathbf{#1}}}
\def\vec#1{\ensuremath{\mathchoice{\mbox{\boldmath$\displaystyle#1$}}
{\mbox{\boldmath$\textstyle#1$}}
{\mbox{\boldmath$\scriptstyle#1$}}
{\mbox{\boldmath$\scriptscriptstyle#1$}}}}
%
\def\tens#1{\ensuremath{\mathsf{#1}}}
%
\setcounter{secnumdepth}{3}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]
\renewcommand\thesection      {\@arabic\c@section}
\renewcommand\thesubsection   {\thesection.\@arabic\c@subsection}
\renewcommand\thesubsubsection{\thesubsection .\@arabic\c@subsubsection}
\renewcommand\theparagraph    {\thesubsubsection.\@arabic\c@paragraph}
\renewcommand\thesubparagraph {\theparagraph.\@arabic\c@subparagraph}
%
\def\sectcounterend{.}

\def\@seccntformat#1{\csname the#1\endcsname\sectcounterend
\hskip\betweenumberspace}

\def\@sect#1#2#3#4#5#6[#7]#8{%
  \ifnum #2>\c@secnumdepth
    \let\@svsec\@empty
  \else
    \refstepcounter{#1}%
    \protected@edef\@svsec{\@seccntformat{#1}\relax}%
  \fi
  \@tempskipa #5\relax
  \ifdim \@tempskipa>\z@
    \begingroup
      #6{%
        \@hangfrom{\hskip #3\relax\@svsec}%
          \raggedright
          \hyphenpenalty \@M%
          \interlinepenalty \@M #8\@@par}%
    \endgroup
    \csname #1mark\endcsname{#7}%
    \addcontentsline{toc}{#1}{%
      \ifnum #2>\c@secnumdepth \else
        \protect\numberline{\csname the#1\endcsname}%
      \fi
      #7}%
  \else
    \def\@svsechd{%
      #6{\hskip #3\relax
      \@svsec #8\hskip\aftertext}%
      \csname #1mark\endcsname{#7}%
      \addcontentsline{toc}{#1}{%
        \ifnum #2>\c@secnumdepth \else
          \protect\numberline{\csname the#1\endcsname}%
        \fi
        #7}}%
  \fi
  \@xsect{#5}}

%
% measures and setting of sections
%
\def\section{\@startsection{section}{1}{\z@}%
    {-16dd plus-4pt minus-4pt}{6dd}{\large\sffamily\bfseries}}
\def\subsection{\@startsection{subsection}{2}{\z@}%
    {-16dd}{6dd}{\normalsize\sffamily\itshape}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}%
    {-16dd}{6dd}{\normalsize\sffamily}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}%
    {-16dd}{-1pt}{\normalsize\sffamily}}

\setlength\leftmargini  {\parindent}
\leftmargin  \leftmargini
\setlength\leftmarginii {\parindent}
\setlength\leftmarginiii {1.87em}
\setlength\leftmarginiv  {1.7em}
\setlength\leftmarginv  {.5em}
\setlength\leftmarginvi {.5em}
\setlength  \labelsep  {.5em}
\setlength  \labelwidth{\leftmargini}
\addtolength\labelwidth{-\labelsep}
\@beginparpenalty -\@lowpenalty
\@endparpenalty   -\@lowpenalty
\@itempenalty     -\@lowpenalty
\renewcommand\theenumi{\@arabic\c@enumi}
\renewcommand\theenumii{\@alph\c@enumii}
\renewcommand\theenumiii{\@roman\c@enumiii}
\renewcommand\theenumiv{\@Alph\c@enumiv}
\newcommand\labelenumi{\theenumi.}
\newcommand\labelenumii{(\theenumii)}
\newcommand\labelenumiii{\theenumiii.}
\newcommand\labelenumiv{\theenumiv.}
\renewcommand\p@enumii{\theenumi}
\renewcommand\p@enumiii{\theenumi(\theenumii)}
\renewcommand\p@enumiv{\p@enumiii\theenumiii}
\newcommand\labelitemi{\normalfont\bfseries --}
\newcommand\labelitemii{\normalfont\bfseries --}
\newcommand\labelitemiii{$\m@th\bullet$}
\newcommand\labelitemiv{$\m@th\cdot$}

% redefinition of the "\newtheorem" command.
%
% Usage now:
%
%     \newtheorem{env_nam}{caption}[within]{cap_font}{body_font}
% or  \newtheorem{env_nam}[numbered_like]{caption}{cap_font}{body_font}
% or  \newtheorem*{env_nam}{caption}{cap_font}{body_font}
%
% New is "cap_font" and "body_font". It stands for
% fontdefinition of the caption and the text itself.
%
% "\newtheorem*" gives a theorem without number.
%
% A defined newthoerem environment is used as described
% by Lamport.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\@thmcountersep{}
\def\@thmcounterend{.}

\def\newtheorem{\@ifstar{\@sthm}{\@Sthm}}

% definition of \newtheorem with number

\def\@Sthm#1{\@ifnextchar[{\@othm{#1}}{\@nthm{#1}}}

\def\@xnthm#1#2[#3]#4#5{\expandafter\@ifdefinable\csname #1\endcsname
   {\@definecounter{#1}\@addtoreset{#1}{#3}%
   \expandafter\xdef\csname the#1\endcsname{\expandafter\noexpand
     \csname the#3\endcsname \noexpand\@thmcountersep \@thmcounter{#1}}%
   \expandafter\xdef\csname #1name\endcsname{#2}%
   \global\@namedef{#1}{\@thm{#1}{\csname #1name\endcsname}{#4}{#5}}%
                              \global\@namedef{end#1}{\@endtheorem}}}

\def\@ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
   {\@definecounter{#1}%
   \expandafter\xdef\csname the#1\endcsname{\@thmcounter{#1}}%
   \expandafter\xdef\csname #1name\endcsname{#2}%
   \global\@namedef{#1}{\@thm{#1}{\csname #1name\endcsname}{#3}{#4}}%
                               \global\@namedef{end#1}{\@endtheorem}}}

\def\@othm#1[#2]#3#4#5{%
  \@ifundefined{c@#2}{\@latexerr{No theorem environment `#2'
  defined}\@eha}%
  {\expandafter\@ifdefinable\csname #1\endcsname
  {\global\@namedef{the#1}{\@nameuse{the#2}}%
  \expandafter\xdef\csname #1name\endcsname{#3}%
  \global\@namedef{#1}{\@thm{#2}{\csname #1name\endcsname}{#4}{#5}}%
  \global\@namedef{end#1}{\@endtheorem}}}}

\def\@thm#1#2#3#4{\refstepcounter
    {#1}\@ifnextchar[{\@ythm{#1}{#2}{#3}{#4}}{\@xthm{#1}{#2}{#3}{#4}}}

\def\@xthm#1#2#3#4{\@begintheorem{#2}{\csname the#1\endcsname}{#3}{#4}%
                    \ignorespaces}

\def\@ythm#1#2#3#4[#5]{\@opargbegintheorem{#2}{\csname
       the#1\endcsname}{#5}{#3}{#4}\ignorespaces}

\def\@begintheorem#1#2#3#4{\trivlist
                 \item[\hskip\labelsep{#3#1\ #2\@thmcounterend}]#4}

\def\@opargbegintheorem#1#2#3#4#5{\trivlist
      \item[\hskip\labelsep{#4#1\ #2\ (#3)\@thmcounterend}]#5}

% definition of \newtheorem* without number

\def\@sthm#1#2{\@Ynthm{#1}{#2}}

\def\@Ynthm#1#2#3#4{\expandafter\@ifdefinable\csname #1\endcsname
   {\global\@namedef{#1}{\@Thm{\csname #1name\endcsname}{#3}{#4}}%
    \expandafter\xdef\csname #1name\endcsname{#2}%
    \global\@namedef{end#1}{\@endtheorem}}}

\def\@Thm#1#2#3{\@ifnextchar[{\@Ythm{#1}{#2}{#3}}{\@Xthm{#1}{#2}{#3}}}

\def\@Xthm#1#2#3{\@Begintheorem{#1}{#2}{#3}\ignorespaces}

\def\@Ythm#1#2#3[#4]{\@Opargbegintheorem{#1}
       {#4}{#2}{#3}\ignorespaces}

\def\@Begintheorem#1#2#3{#3\trivlist
                           \item[\hskip\labelsep{#2#1\@thmcounterend}]}

\def\@Opargbegintheorem#1#2#3#4{#4\trivlist
      \item[\hskip\labelsep{#3#1\ (#2)\@thmcounterend}]}

% definition of divers theorem environments

\if@envcntsect
   \def\@thmcountersep{.}
   \newtheorem{theorem}{Theorem}[section]{\bf}{\it}
\else
   \newtheorem{theorem}{Theorem}{\bf}{\it}
   \if@envcntreset
      \@addtoreset{theorem}{section}
   \else
      \@addtoreset{theorem}{chapter}
   \fi
\fi
\newtheorem*{proof}{Proof}{\it}{\rm}
\newtheorem{corollary}[theorem]{Corollary}{\bf}{\it}
\newtheorem{definition}[theorem]{Definition}{\bf}{\rm}
\newtheorem{example}[theorem]{Example}{\it}{\rm}
\newtheorem{exercise}[theorem]{Exercise}{\it}{\rm}
\newtheorem{lemma}[theorem]{Lemma}{\bf}{\it}
\newtheorem{note}[theorem]{Note}{\it}{\rm}
\newtheorem{problem}[theorem]{Problem}{\it}{\rm}
\newtheorem{proposition}[theorem]{Proposition}{\bf}{\it}
\newtheorem{question}[theorem]{Question}{\it}{\rm}
\newtheorem{remark}[theorem]{Remark}{\it}{\rm}
\newtheorem{solution}[theorem]{Solution}{\it}{\rm}

\def\@takefromreset#1#2{%
    \def\@tempa{#1}%
    \let\@tempd\@elt
    \def\@elt##1{%
        \def\@tempb{##1}%
        \ifx\@tempa\@tempb\else
            \@addtoreset{##1}{#2}%
        \fi}%
    \expandafter\expandafter\let\expandafter\@tempc\csname cl@#2\endcsname
    \expandafter\def\csname cl@#2\endcsname{}%
    \@tempc
    \let\@elt\@tempd}

\def\theopargself{\def\@opargbegintheorem##1##2##3##4##5{\trivlist
      \item[\hskip\labelsep{##4##1\ ##2\ ##3}]##5}
                  \def\@Opargbegintheorem##1##2##3##4{##4\trivlist
      \item[\hskip\labelsep{##3##1\ ##2}]}
      }

\def\squareforqed{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\def\qed{\ifmmode\else\unskip\quad\fi\squareforqed}
%
\newdimen\figgap\figgap=1cc
\long\def\@makesidecaption#1#2{%
   \parbox[b]{\@tempdima}{\captionstyle{\floatlegendstyle
                                         #1\floatcounterend}~#2}}
\def\sidecaption#1\caption{%
\setbox\@tempboxa=\hbox{#1\unskip}%
\if@twocolumn
 \ifdim\hsize<\textwidth\else
   \ifdim\wd\@tempboxa<\columnwidth
      \typeout{Double column float fits into single column -
            ^^Jyou'd better switch the environment. }%
   \fi
 \fi
\fi
\@tempdima=\hsize
\advance\@tempdima by-\figgap
\advance\@tempdima by-\wd\@tempboxa
\ifdim\@tempdima<3cm
    \typeout{\string\sidecaption: No sufficient room for the legend;
             using normal \string\caption. }%
   \unhbox\@tempboxa
   \let\@capcommand=\@caption
\else
   \let\@capcommand=\@sidecaption
   \leavevmode
   \unhbox\@tempboxa
   \hfill
\fi
\refstepcounter\@captype
\@dblarg{\@capcommand\@captype}}

\long\def\@sidecaption#1[#2]#3{\addcontentsline{\csname
  ext@#1\endcsname}{#1}{\protect\numberline{\csname
  the#1\endcsname}{\ignorespaces #2}}\begingroup
    \@parboxrestore
    \@makesidecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
  \endgroup}
%
% Online material
\long\def\onlfig#1#2{\AtEndDocument{\Online\setcounter{figure}{#1}\addtocounter{figure}{-1}#2}\setcounter{figure}{#1}}
\long\def\onltab#1#2{\AtEndDocument{\Online\setcounter{table}{#1}\addtocounter{table}{-1}#2}\setcounter{table}{#1}}
\long\def\onllongtab#1#2{\AtEndDocument{\Online\setlength{\LTcapwidth}{\textwidth}\setcounter{table}{#1}%
\addtocounter{table}{-1}\onecolumn#2\twocolumn}\setcounter{table}{#1}}
\long\def\onllongtabL#1#2{\AtEndDocument{\Online\setlength{\LTcapwidth}{\textheight}\setcounter{table}{#1}%
\addtocounter{table}{-1}\onecolumn#2\twocolumn}\setcounter{table}{#1}}
\long\def\longtab#1#2{\setlength{\LTcapwidth}{\textwidth}%
\setcounter{table}{#1}\addtocounter{table}{-1}\onecolumn#2\twocolumn\setcounter{table}{#1}}
\long\def\longtabL#1#2{\setlength{\LTcapwidth}{\textheight}%
\setcounter{table}{#1}\addtocounter{table}{-1}\onecolumn#2\twocolumn\setcounter{table}{#1}}
%
% Define \acknowledgements
\def\acknowledgements{\par\addvspace{6pt}\tiny\rm
\trivlist\item[\hskip\labelsep{\em Acknowledgements.\/}]}
\def\endacknowledgements{\endtrivlist\addvspace{6pt}}
%
\newenvironment{verse}
               {\let\\\@centercr
                \list{}{\itemsep      \z@
                        \itemindent   -1.5em%
                        \listparindent\itemindent
                        \rightmargin  \leftmargin
                        \advance\leftmargin 1.5em}%
                \item\relax}
               {\endlist}
\newenvironment{quotation}
               {\list{}{\listparindent 1.5em%
                        \itemindent    \listparindent
                        \rightmargin   \leftmargin
                        \parsep        \z@ \@plus\p@}%
                \item\relax}
               {\endlist}
\newenvironment{quote}
               {\list{}{\rightmargin\leftmargin}%
                \item\relax}
               {\endlist}
\if@compatibility
\newenvironment{titlepage}
    {%
      \if@twocolumn
        \@restonecoltrue\onecolumn
      \else
        \@restonecolfalse\newpage
      \fi
      \thispagestyle{empty}%
      \setcounter{page}\z@
    }%
    {\if@restonecol\twocolumn \else \newpage \fi
    }
\else
\newenvironment{titlepage}
    {%
      \if@twocolumn
        \@restonecoltrue\onecolumn
      \else
        \@restonecolfalse\newpage
      \fi
      \thispagestyle{empty}%
      \setcounter{page}\@ne
    }%
    {\if@restonecol\twocolumn \else \newpage \fi
     \if@twoside\else
        \setcounter{page}\@ne
     \fi
    }
\fi
% Appendix
\newcounter{append}
\setcounter{append}{0}
\newenvironment{appendix}{\par
\def\@hangfrom##1{\setbox\@tempboxa\hbox{{##1}}%
      \hangindent \parindent\noindent\box\@tempboxa}
\def\@seccntformat##1{\csname theap##1\endcsname\hskip\betweenumberspace}
  \setcounter{section}{\value{append}}%
  \setcounter{subsection}{0}%
  \setcounter{figure}{0}%
  \setcounter{table}{0}%
  \newcommand\theapsection{Appendix \@Alph\c@section:}%
  \newcommand\theapsubsection{\@Alph\c@section.\@arabic\c@subsection.}%
  \newcommand\theapsubsubsection{\theapsubsection\@arabic\c@subsubsection.}%
  \renewcommand\thesection{\@Alph\c@section}%
  \renewcommand\thesubsection{\@Alph\c@section.\@arabic\c@subsection}%
  \renewcommand\thesubsubsection{\thesubsection.\@arabic\c@subsubsection}%
  \renewcommand\theequation{\@Alph\c@section.\@arabic\c@equation}%
  \renewcommand\thefigure{\@Alph\c@section.\@arabic\c@figure}%
  \renewcommand\thetable{\@Alph\c@section.\@arabic\c@table}%
  \@addtoreset{equation}{section}%
  \@addtoreset{figure}{section}%
  \@addtoreset{table}{section}%
  \def\subfigures{\stepcounter{figure}\setcounter{auth}{\value{figure}}%
  \setcounter{figure}{0}%
  \def\thefigure{\@Alph\c@section\@arabic\c@auth\alph{figure}}%
  \def\resetsubfig{\setcounter{figure}{\value{auth}}}}}
{
  \setcounter{section}{0}%
  \setcounter{subsection}{0}%
  \setcounter{figure}{0}%
  \setcounter{table}{0}%
  \renewcommand\thesection{\c@section}%
  \renewcommand\thesubsection{\@arabic\c@subsection}%
  \renewcommand\thesubsubsection{\@arabic\c@subsubsection}%
  \renewcommand\theequation{\@arabic\c@equation}%
  \renewcommand\thefigure{\@arabic\c@figure}%
  \renewcommand\thetable{\@arabic\c@table}%
  \addtocounter{append}{1}
}
%
\setlength\arraycolsep{2.5\p@}
\setlength\tabcolsep{6\p@}
\setlength\arrayrulewidth{.4\p@}
\setlength\doublerulesep{2\p@}
\setlength\tabbingsep{\labelsep}
\skip\@mpfootins = \skip\footins
\setlength\fboxsep{3\p@}
\setlength\fboxrule{.4\p@}
\renewcommand\theequation{\@arabic\c@equation}
\newcounter{figure}
\renewcommand\thefigure{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\fnum@figure{\figurename\,\thefigure}
\newenvironment{figure}
               {\@float{figure}}
               {\resetsubfig\end@float}
\newenvironment{figure*}
               {\@dblfloat{figure}}
               {\resetsubfig\end@dblfloat}
\let\resetsubfig\relax
\def\subfigures{\stepcounter{figure}\setcounter{auth}{\value{figure}}%
\setcounter{figure}{0}\def\thefigure{\@arabic\c@auth\alph{figure}}%
\def\resetsubfig{\setcounter{figure}{\value{auth}}}}
\newcounter{table}
\renewcommand\thetable{\@arabic\c@table}
\def\fps@table{tbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\fnum@table{\tablename~\thetable}
\newenvironment{table}
               {\small\@float{table}}
               {\end@float}
\newenvironment{table*}
               {\small\@dblfloat{table}}
               {\end@dblfloat}

\def \@floatboxreset {%
        \reset@font
        \small
        \@setnobreak
        \@setminipage
}

\newlength\abovecaptionskip
\newlength\belowcaptionskip
\setlength\abovecaptionskip{10\p@}
\setlength\belowcaptionskip{0\p@}
\newcommand\leftlegendglue{}

\def\fig@type{figure}

\newdimen\figcapgap\figcapgap=5pt
\newdimen\tabcapgap\tabcapgap=10pt

\@ifundefined{floatlegendstyle}{\def\floatlegendstyle{\bf}}{}
\def\floatcounterend{.}

\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname
  ext@#1\endcsname}{#1}{\protect\numberline{\csname
  the#1\endcsname}{\ignorespaces #2}}\begingroup
    \@parboxrestore
    \@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
  \endgroup}

\def\capstrut{\vrule\@width\z@\@height\topskip}
\@ifundefined{captionstyle}{\def\captionstyle{\normalfont\small}}{}

\long\def\@makecaption#1#2{%
 \ifx\@captype\fig@type
   \vskip\figcapgap
   \setbox\@tempboxa\hbox{{\floatlegendstyle #1\floatcounterend}
   \capstrut #2}%
   \ifdim \wd\@tempboxa >\hsize
     {\floatlegendstyle #1\floatcounterend} \capstrut #2\par
   \else
     \hbox to\hsize{\leftlegendglue\unhbox\@tempboxa\hfil}%
   \fi
 \else
   {\floatlegendstyle #1\floatcounterend} \capstrut #2\par
   \vskip\tabcapgap
 \fi}
% Define `acknowledgement' environment
\def\acknowledgement{\par\addvspace{17pt}\tiny\rm
\trivlist\item[\hskip\labelsep
{\it\ackname}]}
\def\endacknowledgement{\endtrivlist\addvspace{6pt}}
% Define `noteadd' environment
\def\noteadd{\par\addvspace{17pt}\small\rm
\trivlist\item[\hskip\labelsep
{\it\noteaddname}]}
\def\endnoteadd{\endtrivlist\addvspace{6pt}}

\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
\DeclareRobustCommand*\cal{\@fontswitch\relax\mathcal}
\DeclareRobustCommand*\mit{\@fontswitch\relax\mathnormal}
\newcommand\@pnumwidth{1.55em}
\newcommand\@tocrmarg{2.55em}
\newcommand\@dotsep{4.5}
\setcounter{tocdepth}{3}
\newcommand\tableofcontents{%
    \section*{\contentsname
        \@mkboth{%
           \MakeUppercase\contentsname}{\MakeUppercase\contentsname}}%
    \@starttoc{toc}%
    }
\newcommand*\l@part[2]{%
  \ifnum \c@tocdepth >-2\relax
    \addpenalty\@secpenalty
    \addvspace{2.25em \@plus\p@}%
    \begingroup
      \setlength\@tempdima{3em}%
      \parindent \z@ \rightskip \@pnumwidth
      \parfillskip -\@pnumwidth
      {\leavevmode
       \large \bfseries #1\hfil \hb@xt@\@pnumwidth{\hss #2}}\par
       \nobreak
       \if@compatibility
         \global\@nobreaktrue
         \everypar{\global\@nobreakfalse\everypar{}}%
      \fi
    \endgroup
  \fi}
\newcommand*\l@section[2]{%
  \ifnum \c@tocdepth >\z@
    \addpenalty\@secpenalty
    \addvspace{1.0em \@plus\p@}%
    \setlength\@tempdima{1.5em}%
    \begingroup
      \parindent \z@ \rightskip \@pnumwidth
      \parfillskip -\@pnumwidth
      \leavevmode \bfseries
      \advance\leftskip\@tempdima
      \hskip -\leftskip
      #1\nobreak\hfil \nobreak\hb@xt@\@pnumwidth{\hss #2}\par
    \endgroup
  \fi}
\newcommand*\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\newcommand*\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\newcommand*\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
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\def\la{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\sim\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\sim\cr}}}
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$\displaystyle##$\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}}}}}
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\def\utw{\smash{\rlap{\lower5pt\hbox{$\sim$}}}}
\def\udtw{\smash{\rlap{\lower6pt\hbox{$\approx$}}}}
\def\fd{\hbox{$.\!\!^{\rm d}$}}
\def\fh{\hbox{$.\!\!^{\rm h}$}}
\def\fm{\hbox{$.\!\!^{\rm m}$}}
\def\fs{\hbox{$.\!\!^{\rm s}$}}
\def\fdg{\hbox{$.\!\!^\circ$}}
\def\farcm{\hbox{$.\mkern-4mu^\prime$}}
\def\farcs{\hbox{$.\!\!^{\prime\prime}$}}
\def\fp{\hbox{$.\!\!^{\scriptscriptstyle\rm p}$}}
\def\cor{\mathrel{\mathchoice {\hbox{$\widehat=$}}{\hbox{$\widehat=$}}
{\hbox{$\scriptstyle\hat=$}}
{\hbox{$\scriptscriptstyle\hat=$}}}}
\def\sol{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr\sim\cr<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\sim\cr
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{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\sim\cr
<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\sim\cr<\cr}}}}}
\def\sog{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr\sim\cr>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\sim\cr
>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
\sim\cr>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\sim\cr>\cr}}}}}
\def\lse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
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{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\simeq\cr}}}}}
\def\gse{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\simeq\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\simeq\cr}}}}}
\def\grole{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\noalign{\vskip-1.5pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\noalign{\vskip-1pt}<\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\noalign{\vskip-0.5pt}<\cr}}}}}
\def\leogr{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip-1.5pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
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{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\noalign{\vskip-1pt}>\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\noalign{\vskip-0.5pt}>\cr}}}}}
\def\loa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
<\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
<\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr\approx\cr}}}}}
\def\goa{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr
>\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr
>\cr\approx\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr\approx\cr}}}}}
\def\diameter{{\ifmmode\mathchoice
{\ooalign{\hfil\hbox{$\displaystyle/$}\hfil\crcr
{\hbox{$\displaystyle\mathchar"20D$}}}}
{\ooalign{\hfil\hbox{$\textstyle/$}\hfil\crcr
{\hbox{$\textstyle\mathchar"20D$}}}}
{\ooalign{\hfil\hbox{$\scriptstyle/$}\hfil\crcr
{\hbox{$\scriptstyle\mathchar"20D$}}}}
{\ooalign{\hfil\hbox{$\scriptscriptstyle/$}\hfil\crcr
{\hbox{$\scriptscriptstyle\mathchar"20D$}}}}
\else{\ooalign{\hfil/\hfil\crcr\mathhexbox20D}}%
\fi}}

\def\getsto{\mathrel{\mathchoice {\vcenter{\offinterlineskip
\halign{\hfil
$\displaystyle##$\hfil\cr\gets\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr\gets
\cr\to\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
\gets\cr\to\cr}}}}}
\def\lid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr<\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr<\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr<\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
<\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\gid{\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle##$\hfil\cr>\cr\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\textstyle##$\hfil\cr>\cr
\noalign{\vskip1.2pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptstyle##$\hfil\cr>\cr
\noalign{\vskip1pt}=\cr}}}
{\vcenter{\offinterlineskip\halign{\hfil$\scriptscriptstyle##$\hfil\cr
>\cr
\noalign{\vskip0.9pt}=\cr}}}}}
\def\bbbr{{\rm I\!R}} %reelle Zahlen
\def\bbbm{{\rm I\!M}}
\def\bbbn{{\rm I\!N}} %natuerliche Zahlen
\def\bbbf{{\rm I\!F}}
\def\bbbh{{\rm I\!H}}
\def\bbbk{{\rm I\!K}}
\def\bbbp{{\rm I\!P}}
\def\bbbone{{\mathchoice {\rm 1\mskip-4mu l} {\rm 1\mskip-4mu l}
{\rm 1\mskip-4.5mu l} {\rm 1\mskip-5mu l}}}
\def\bbbc{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm C$}\hbox{\hbox
to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}}}
\def\bbbq{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
Q$}\hbox{\raise
0.05\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm Q$}\hbox{\raise
0.05\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.9\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm Q$}\hbox{\raise
0.05\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm Q$}\hbox{\raise
0.05\ht0\hbox to0pt{\kern0.4\wd0\vrule height0.8\ht0\hss}\box0}}}}
\def\bbbt{{\mathchoice {\setbox0=\hbox{$\displaystyle\rm
T$}\hbox{\hbox to0pt{\kern0.25\wd0\vrule height0.95\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle\rm T$}\hbox{\hbox
to0pt{\kern0.25\wd0\vrule height0.95\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.25\wd0\vrule height0.95\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm T$}\hbox{\hbox
to0pt{\kern0.25\wd0\vrule height0.95\ht0\hss}\box0}}}}
\def\bbbs{{\mathchoice
{\setbox0=\hbox{$\displaystyle\rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.38\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.52\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\textstyle \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.38\wd0\vrule height0.45\ht0\hss}\hbox
to0pt{\kern0.52\wd0\vrule height0.5\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptstyle \rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.38\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.52\wd0\vrule height0.45\ht0\hss}\box0}}
{\setbox0=\hbox{$\scriptscriptstyle\rm S$}\hbox{\raise0.5\ht0\hbox
to0pt{\kern0.38\wd0\vrule height0.45\ht0\hss}\raise0.05\ht0\hbox
to0pt{\kern0.52\wd0\vrule height0.45\ht0\hss}\box0}}}}
\def\bbbz{{\mathchoice {\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\textstyle Z\kern-0.4em Z$}}
{\hbox{$\sf\scriptstyle Z\kern-0.3em Z$}}
{\hbox{$\sf\scriptscriptstyle Z\kern-0.2em Z$}}}}
\def\ts{\thinspace}
%
% Bibliography and bibfile
\def\aj{AJ}%
          % Astronomical Journal
\def\actaa{Acta Astron.}%
          % Acta Astronomica
\def\araa{ARA\&A}%
          % Annual Review of Astron and Astrophys
\def\apj{ApJ}%
          % Astrophysical Journal
\def\apjl{ApJ}%
          % Astrophysical Journal, Letters
\def\apjs{ApJS}%
          % Astrophysical Journal, Supplement
\def\ao{Appl.~Opt.}%
          % Applied Optics
\def\apss{Ap\&SS}%
          % Astrophysics and Space Science
\def\aap{A\&A}%
          % Astronomy and Astrophysics
\def\aapr{A\&A~Rev.}%
          % Astronomy and Astrophysics Reviews
\def\aaps{A\&AS}%
          % Astronomy and Astrophysics, Supplement
\def\azh{AZh}%
          % Astronomicheskii Zhurnal
\def\baas{BAAS}%
          % Bulletin of the AAS
\def\bac{Bull. astr. Inst. Czechosl.}%
          % Bulletin of the Astronomical Institutes of Czechoslovakia 
\def\caa{Chinese Astron. Astrophys.}%
          % Chinese Astronomy and Astrophysics
\def\cjaa{Chinese J. Astron. Astrophys.}%
          % Chinese Journal of Astronomy and Astrophysics
\def\icarus{Icarus}%
          % Icarus
\def\jcap{J. Cosmology Astropart. Phys.}%
          % Journal of Cosmology and Astroparticle Physics
\def\jrasc{JRASC}%
          % Journal of the RAS of Canada
\def\mnras{MNRAS}%
          % Monthly Notices of the RAS
\def\memras{MmRAS}%
          % Memoirs of the RAS
\def\na{New A}%
          % New Astronomy
\def\nar{New A Rev.}%
          % New Astronomy Review
\def\pasa{PASA}%
          % Publications of the Astron. Soc. of Australia
\def\pra{Phys.~Rev.~A}%
          % Physical Review A: General Physics
\def\prb{Phys.~Rev.~B}%
          % Physical Review B: Solid State
\def\prc{Phys.~Rev.~C}%
          % Physical Review C
\def\prd{Phys.~Rev.~D}%
          % Physical Review D
\def\pre{Phys.~Rev.~E}%
          % Physical Review E
\def\prl{Phys.~Rev.~Lett.}%
          % Physical Review Letters
\def\pasp{PASP}%
          % Publications of the ASP
\def\pasj{PASJ}%
          % Publications of the ASJ
\def\qjras{QJRAS}%
          % Quarterly Journal of the RAS
\def\rmxaa{Rev. Mexicana Astron. Astrofis.}%
          % Revista Mexicana de Astronomia y Astrofisica
\def\skytel{S\&T}%
          % Sky and Telescope
\def\solphys{Sol.~Phys.}%
          % Solar Physics
\def\sovast{Soviet~Ast.}%
          % Soviet Astronomy
\def\ssr{Space~Sci.~Rev.}%
          % Space Science Reviews
\def\zap{ZAp}%
          % Zeitschrift fuer Astrophysik
\def\nat{Nature}%
          % Nature
\def\iaucirc{IAU~Circ.}%
          % IAU Cirulars
\def\aplett{Astrophys.~Lett.}%
          % Astrophysics Letters
\def\apspr{Astrophys.~Space~Phys.~Res.}%
          % Astrophysics Space Physics Research
\def\bain{Bull.~Astron.~Inst.~Netherlands}%
          % Bulletin Astronomical Institute of the Netherlands
\def\fcp{Fund.~Cosmic~Phys.}%
          % Fundamental Cosmic Physics
\def\gca{Geochim.~Cosmochim.~Acta}%
          % Geochimica Cosmochimica Acta
\def\grl{Geophys.~Res.~Lett.}%
          % Geophysics Research Letters
\def\jcp{J.~Chem.~Phys.}%
          % Journal of Chemical Physics
\def\jgr{J.~Geophys.~Res.}%
          % Journal of Geophysics Research
\def\jqsrt{J.~Quant.~Spec.~Radiat.~Transf.}%
          % Journal of Quantitiative Spectroscopy and Radiative Trasfer
\def\memsai{Mem.~Soc.~Astron.~Italiana}%
          % Mem. Societa Astronomica Italiana
\def\nphysa{Nucl.~Phys.~A}%
          % Nuclear Physics A
\def\physrep{Phys.~Rep.}%
          % Physics Reports
\def\physscr{Phys.~Scr}%
          % Physica Scripta
\def\planss{Planet.~Space~Sci.}%
          % Planetary Space Science
\def\procspie{Proc.~SPIE}%
          % Proceedings of the SPIE
\let\astap=\aap
\let\apjlett=\apjl
\let\apjsupp=\apjs
\let\applopt=\ao
%
\uchyph=0
% 
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\pagestyle{Onlheadings}
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\@ifpackageloaded{longtable}{%
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    \endgraf\vskip\baselineskip}%
  \hss}}}}{}
}%AtBeginDocument
%
\endinput
%%
%% End of file `aa1.cls'.