%%
%% This is file `hha.cls',
%% This is modified jcm.cls file - LMS JCM style file
%%
%% TEST VERSION
%%
%%
%
%%
%%
\NeedsTeXFormat{LaTeX2e}[1995/06/01]
\ProvidesClass{hha}
          [1999/06/10 v2001b HHA class]
\def\HHA@err#1{\ClassError{hha}{#1}\@eha}
\def\HHA@warn#1{\ClassWarning{hha}{#1}}
\DeclareOption{10pt}{}
\DeclareOption{11pt}{\HHA@warn{10pt used (not optional)}}
\DeclareOption{12pt}{\HHA@warn{10pt used (not optional)}}
\DeclareOption{oneside}{}
\DeclareOption{twoside}{\HHA@warn{oneside used (not optional)}}
\DeclareOption{twocolumn}{\HHA@warn{onecolumn used (not optional)}}
\DeclareOption{onecolumn}{}
\DeclareOption{a4paper}{\HHA@warn{Paper size option ignored}}
\DeclareOption{letterpaper}{\HHA@warn{Paper size option ignored}}
\DeclareOption{mathptm}{%
  \def\HHA@fontencoding{T1}%
  \def\HHA@fonts{\RequirePackage{times,mathptm}%
                 \DeclareMathVersion{bold}}}
\DeclareOption{mathtime}{%
  \def\HHA@fontencoding{T1}%
  \def\HHA@fonts{%
    \RequirePackage[mtpluscal,mtbold,subscriptcorrection]{mathtime}}}
\DeclareOption{cmfonts}{%
  \def\HHA@fontencoding{OT1}%
  \let\HHA@fonts\relax}
\DeclareOption{cmsc}{%
  \AtEndOfClass{%
    \def\scshape{\usefont{OT1}{cmr}{m}{sc}}}}
\DeclareOption{OT1}{\def\HHA@fontencoding{OT1}}
\DeclareOption{T1}{%
  \PassOptionsToPackage{T1}{mathtime}%
  \def\HHA@fontencoding{T1}}
\DeclareOption{LY1}{%
  \PassOptionsToPackage{LY1}{mathtime}%
  \def\HHA@fontencoding{LY1}}
\DeclareOption{ams}{%
  \def\HHA@ams{\RequirePackage{amsthm,amssymb}%
               \let\oldleq\leq
               \let\le\leqslant
               \let\leq\leqslant
               \let\oldgeq\geq
               \let\ge\geqslant
               \let\geq\geqslant}}
\DeclareOption{noams}{%
  \def\HHA@ams{%
               \let\theoremstyle\@gobble
               \let\oldnewtheorem\newtheorem
               \def\newtheorem{\@ifstar\oldnewtheorem\oldnewtheorem}%
               \let\mathbb\mathbf}}
\ExecuteOptions{ams,cmfonts}
\InputIfFileExists{hha.cfg}
  {\HHA@warn{Using local configuration file.\MessageBreak
             Ignoring document options: [\@classoptionslist]}%
   \let\@classoptionslist\@empty
   \@namedef{opt@\@currname.\@currext}{}}%
  {}
\ProcessOptions
\RequirePackage{latexsym}
\def\title{\HHA@title}
\def\HHA@title#1{%
  \def\@title{#1}%
  \def\@journaltitle{Homology, Homotopy and Applications, vol. \@volumenumber(\@issuenumber), \@volumeyear}
}
\def\@title{\HHA@warn{No title}}
\def\@journaltitle{Homology, Homotopy and Applications, vol. \@volumenumber, \@volumeyear}

\renewcommand*\author[2][]{%
  \gdef\HHA@doauthors{%
    \@authors\@andorcomma\relax\@andorcomma\relax\par}%
  \gdef\HHA@doauthorslcase{%
    \@authorslcase\@andorcomma\relax\@andorcomma\relax. Permission to copy for private use granted.\par}%
  \g@addto@macro\@curr@author{\\*#2}%
  \g@addto@macro\@authors{%
    \@andorcomma,{\ignorespaces\MakeTextUppercase{#2}\unskip}}
  \g@addto@macro\@authorslcase{%
    \@andorcomma,{\ignorespaces#2\unskip}}%
}%
\def\@authors{\@gobbletwo}
\def\@authorslcase{\@gobbletwo}
\def\HHA@doauthors{\HHA@warn{No author specified}}
\def\@curr@author{\@gobbletwo}
\def\and{\HHA@err{\protect\and\space is not supported}}
\def\@andorcomma#1#2\@andorcomma#3{%
  \ifx#3\relax
    \ifx#1\relax%
      \let\@tempa\relax
    \else
    \def\@tempa{\space\andname\space #2\@gobbletwo}%
    \fi
  \else
    \def\@tempa{#1 #2\@andorcomma#3}%
  \fi
  \@tempa}
\def\address#1{%
  \ifx\@curr@author\HHA@gobble
    \HHA@err{\noexpand\address with no \string\author}\@ehd
  \else
    \expandafter\g@addto@macro\expandafter\@addresses\expandafter{%
         \expandafter\filbreak\@curr@author\hha@address{#1}}%
    \let\@curr@author\HHA@gobble
  \fi}
\def\@addresses{}
\AtEndDocument{%
  \ifx\@deferlist\@empty\else\clearpage\fi
  \par
  \parindent\z@
  \parskip12\p@
  \@addresses}
\def\hha@address#1{\\*[6pt]\begin{tabular}{@{}l}#1\end{tabular}\par}
\def\HHA@gobble{\@gobbletwo}
\def\email#1{%
  \ifx\@curr@author\HHA@gobble
    \HHA@err{\noexpand\email with no \string\author}\@ehd
  \else
    \g@addto@macro\@curr@author{\quad\HHA@email{#1}}%
  \fi}
\def\HHA@email#1{\href{mailto:#1}{\texttt{#1}}}
\AtBeginDocument{%
  \providecommand\url[1]{%
    \texttt{\language\@M\hyphenchar\the\font=`\/ #1}}%
  \providecommand\href[2]{{%
    \let~\textasciitilde#2}}}
\def\homepage#1{%
  \ifx\@curr@author\HHA@gobble
    \HHA@err{\noexpand\homepage with no \string\author}\@ehd
  \else
    \g@addto@macro\@curr@author{\quad\url{#1}}%
  \fi}
\def\thanks#1{%
  \g@addto@macro\@thanks{\footnotetext{#1}}}
\let\@thanks\@empty
\def\keywords#1{%
  \gdef\@keywords{%
    {Key words and phrases:\/} \ignorespaces#1\unskip}}
\def\@keywords{\HHA@warn{No keywords}}
\def\classification#1{%
  \gdef\@classification{%
    2000 Mathematics Subject Classification: \ignorespaces#1\unskip}}
\let\subjclass\classification
\def\@classification{%
  \HHA@warn{No Subject Classification}}
\def\received#1{%
  \gdef\@received{Received #1}}
\def\@received{\HHA@warn{No received date}}
\def\revised#1{%
  \g@addto@macro\@revised{{, revised #1}}}
\let\@revised\@empty
\def\accepted#1{%
  \gdef\@accepted{{\itshape; accepted #1}}}
\def\@accepted{\HHA@warn{No accepted date}}
\def\published#1{%
  \gdef\@published{{; published on #1}}}
\def\@published{\HHA@warn{No published date}}
\def\submitted#1{%
  \gdef\@submitted{({\itshape communicated by #1})}}
\def\@submitted{\HHA@warn{No submitted information}}
\newbox\absbox
\def\abstract{\lrbox\absbox\minipage{.75\textwidth}%
  \parindent12\p@
  \normalsize\normalfont
  {\centering\itshape{Abstract\\}}}
\def\endabstract{\endminipage\endlrbox}
\def\maketitle{%
  \ifx\@curr@author\HHA@gobble
  \else
    \begingroup
      \def\\*{, }%
      \HHA@warn{No address for \@curr@author}%
    \endgroup
    \address\relax
  \fi
  \begingroup
  \long\def\@makefntext##1{\parindent 1em\noindent##1}%
  \thispagestyle{title}\label{FirstPage}%
  \global\@topnum\z@
  \normalfont
  \centering
  \def\\{\protect\@centercr}%
  \large\MakeTextUppercase\@title\par
  \addvspace{12pt}%
  \normalsize\scshape
  \HHA@doauthors
  \addvspace{12pt}
  \normalsize\normalfont\@submitted\par
  \addvspace{15pt}%
  \ifvoid\absbox
    \HHA@warn{No abstract}%
  \else
    \usebox\absbox\par
  \fi
  \@thanks
  \footnotetext{\@received\@revised\@published.}%
  \footnotetext{\@classification}%
  \footnotetext{\@keywords}%
  \footnotetext{\copyright\ \@volumeyear, \HHA@doauthorslcase}%
  \endgroup
  \let\and\relax
  \let\author\relax
  \let\keywords\relax
  \let\@keywords\relax
  \let\address\relax
  \let\email\relax
  \let\@address\relax
  \let\maketitle\relax
  \let\thanks\@gobble
  \def\abstract{%
    \HHA@err{abstract must be before \protect\maketitle}\@ehd
    \lrbox\absbox\minipage{.75\textwidth}}}
\def\ps@hha{%
  \def\@oddhead{%
      \itshape
      \def\\{\unskip\space\ignorespaces}%
      \@journaltitle\hss\thepage}%
  \let\@evenhead\@oddhead
  \def\@oddfoot{}%
  \let\@evenfoot\@oddfoot}
\def\ps@title{%
  \def\@oddhead{%
    {\itshape\@journalpublisher}\hfill\relax}
     %\hfill\footnotesize ISSN \@journalissn}%
  \let\@evenhead\@oddhead
  \def\@oddfoot{}%
%    \footnotesize
%    \hss
%    \journalname\
%    \href{\journalBaseURL/hha/\@volumenumber}{\@volumenumber\ (\@volumeyear)}
%    \@startpage--\@endpage
%    \hss}%
  \let\@evenfoot\@oddfoot}
\def\ps@headings{\HHA@warn{headings pagestyle ignored}}
\ps@hha
\def\@volumeyear{????}
\def\@volumenumber{??}
\def\@issuenumber{??}
\def\@startpage{\pageref{FirstPage}}
\def\@endpage{\pageref{LastPage}}
\def\volumeyear#1{\gdef\@volumeyear{#1}}
\def\volumenumber#1{\gdef\@volumenumber{#1}}
\def\issuenumber#1{\gdef\@issuenumber{#1}}
\def\startpage#1{\gdef\@startpage{#1}\c@page#1}
\def\endpage#1{\gdef\@endpage{#1}}
\def\lastpage@putlabel{%
  \if@filesw
    \advance\c@page\m@ne
     \immediate\write\@auxout{\string
     \newlabel{LastPage}{{}{\thepage}{}{}{}}}%
     \advance\c@page\@ne
  \fi}
\AtEndDocument{%
   \clearpage\lastpage@putlabel}%
\renewcommand\normalsize{%
   \@setfontsize\normalsize\@xpt\@xiipt
   \abovedisplayskip 6\p@ \@plus\p@ \@minus\p@
   \belowdisplayskip \abovedisplayskip
   \abovedisplayshortskip 3\p@ \@plus\p@
   \belowdisplayshortskip  \abovedisplayskip
   \let\@listi\@listI}
\normalsize
\newcommand\small{%
   \@setfontsize\small\@ixpt{11}%
   \abovedisplayskip 5\p@ \@plus\p@ \@minus\p@
   \belowdisplayskip \abovedisplayskip
   \abovedisplayshortskip 2.5\p@ \@plus\p@
   \belowdisplayshortskip \abovedisplayskip
   \def\@listi{\leftmargin\leftmargini
               \topsep 3\p@ \@plus\p@ \@minus1\p@
               \parsep \z@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip}
\newcommand\footnotesize{%
   \@setfontsize\footnotesize\@viiipt{9.5}%
   \abovedisplayskip 4.5\p@ \@plus\p@ \@minus\p@
   \belowdisplayskip \abovedisplayskip
   \abovedisplayshortskip \z@ \@plus\p@
   \belowdisplayshortskip  \abovedisplayskip
   \def\@listi{\leftmargin\leftmargini
               \topsep 3\p@ \@plus\p@ \@minus\p@
               \parsep \z@skip
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip}
\newcommand\scriptsize{\@setfontsize\scriptsize\@viipt\@viiipt}
\newcommand\tiny{\@setfontsize\tiny\@vpt\@vipt}
\newcommand\large{\@setfontsize\large\@xiipt{14}}
\newcommand\Large{\@setfontsize\Large\@xivpt{18}}
\newcommand\LARGE{\@setfontsize\LARGE\@xviipt{22}}
\newcommand\huge{\@setfontsize\huge\@xxpt{25}}
\newcommand\Huge{\@setfontsize\Huge\@xxvpt{30}}
\setlength\smallskipamount{3\p@ \@plus 1\p@ \@minus 1\p@}
\setlength\medskipamount{6\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\bigskipamount{12\p@ \@plus 4\p@ \@minus 4\p@}
\setlength\maxdepth{5\p@}
\setlength\floatsep    {12\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\textfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\intextsep   {12\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\dblfloatsep    {12\p@ \@plus 2\p@ \@minus 2\p@}
\setlength\dbltextfloatsep{20\p@ \@plus 2\p@ \@minus 4\p@}
\setlength\@fptop{0\p@ \@plus 1fil}
\setlength\@fpsep{8\p@ \@plus 2fil}
\setlength\@fpbot{0\p@ \@plus 1fil}
\setlength\@dblfptop{0\p@ \@plus 1fil}
\setlength\@dblfpsep{8\p@ \@plus 2fil}
\setlength\@dblfpbot{0\p@ \@plus 1fil}
\partopsep\z@ \@plus \p@
\def\@listi{\leftmargin\leftmargini
            \parsep\z@skip
            \topsep 3\p@ \@plus\p@
            \itemsep3\p@ \@plus\p@ \@minus\p@}
\let\@listI\@listi
\@listi
\def\@listii {\leftmargin\leftmarginii
              \labelwidth\leftmarginii
              \advance\labelwidth-\labelsep
              \topsep    3\p@ \@plus\p@ \@minus\p@
              \parsep\z@skip
              \itemsep   \parsep}
\def\@listiii{\leftmargin\leftmarginiii
              \labelwidth\leftmarginiii
              \advance\labelwidth-\labelsep
              \topsep    2\p@ \@plus\p@\@minus\p@
              \parsep    \z@skip
              \partopsep \p@ \@plus\z@ \@minus\p@
              \itemsep   \topsep}
\def\@listiv {\leftmargin\leftmarginiv
              \labelwidth\leftmarginiv
              \advance\labelwidth-\labelsep}
\def\@listv  {\leftmargin\leftmarginv
              \labelwidth\leftmarginv
              \advance\labelwidth-\labelsep}
\def\@listvi {\leftmargin\leftmarginvi
              \labelwidth\leftmarginvi
              \advance\labelwidth-\labelsep}
\setlength\parskip{0pt}
\setlength\parindent{12pt}
\setlength\topsep{8pt \@plus 2pt \@minus 4pt}
\setlength\partopsep{0pt \@plus 1pt}
\setlength\itemsep{0pt \@plus 2pt}
\setlength\lineskip{1\p@}
\setlength\normallineskip{1\p@}
\renewcommand\baselinestretch{}
\setlength\parskip{0\p@ \@plus \p@}
\@lowpenalty   51
\@medpenalty  151
\@highpenalty 301
\setcounter{topnumber}{2}
\renewcommand\topfraction{.7}
\setcounter{bottomnumber}{1}
\renewcommand\bottomfraction{.3}
\setcounter{totalnumber}{3}
\renewcommand\textfraction{.2}
\renewcommand\floatpagefraction{.5}
\setcounter{dbltopnumber}{2}
\renewcommand\dbltopfraction{.7}
\renewcommand\dblfloatpagefraction{.5}
\setcounter{secnumdepth}{3}
\newcounter {part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
\newcounter {paragraph}[subsubsection]
\newcounter {subparagraph}[paragraph]
%\renewcommand \thepart {\@Roman\c@part}
\renewcommand \thepart {\partname{ }\@arabic\c@part}
\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}
\setlength\leftmargini  {2pc}
\leftmargin  \leftmargini
\setlength\leftmarginii  {1.5pc}
\setlength\leftmarginiii {1.5pc}
\setlength\leftmarginiv  {1.5pc}
\setlength  \labelsep  {6pt}
\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{\textbullet}
\newcommand\labelitemii{\normalfont\bfseries \textendash}
\newcommand\labelitemiii{\textasteriskcentered}
\newcommand\labelitemiv{\textperiodcentered}
\newenvironment{description}
               {\list{}{\labelwidth\z@ \itemindent-\leftmargin
                        \let\makelabel\descriptionlabel}}
               {\endlist}
\newcommand*\descriptionlabel[1]{\hspace\labelsep
                                \normalfont\bfseries #1}
\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}
\newcommand\appendix{\par
  \setcounter{section}{0}%
  \setcounter{subsection}{0}%
  \renewcommand\thesection{Appendix \@Alph\c@section}}
\setlength\arraycolsep{5\p@}
\setlength\tabcolsep{6\p@}
\setlength\arrayrulewidth{.4\p@}
\setlength\doublerulesep{2\p@}
\setlength\tabbingsep{\labelsep}
\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}}
               {\end@float}
\newenvironment{figure*}
               {\@dblfloat{figure}}
               {\end@dblfloat}
\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}
               {\@float{table}}
               {\end@float}
\newenvironment{table*}
               {\@dblfloat{table}}
               {\end@dblfloat}
\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{4em}%
      \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}}
\newcommand*\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\newcommand\listoffigures{%
    \section*{\listfigurename
      \@mkboth{\MakeUppercase\listfigurename}%
              {\MakeUppercase\listfigurename}}%
    \@starttoc{lof}%
    }
\newcommand*\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\newcommand\listoftables{%
    \section*{\listtablename
      \@mkboth{%
          \MakeUppercase\listtablename}{\MakeUppercase\listtablename}}%
    \@starttoc{lot}%
    }
\let\l@table\l@figure
\newdimen\bibindent
\setlength\bibindent{1.5em}
\newenvironment{thebibliography}[1]
     {\section*{\refname
        \@mkboth{\MakeUppercase\refname}{\MakeUppercase\refname}}%
      \list{\@biblabel{\@arabic\c@enumiv}}%
           {\settowidth\labelwidth{\@biblabel{#1}}%
            \leftmargin\labelwidth
            \advance\leftmargin\labelsep
            \@openbib@code
            \usecounter{enumiv}%
            \let\p@enumiv\@empty
            \renewcommand\theenumiv{\@arabic\c@enumiv}}%
      \sloppy
      \clubpenalty4000
      \@clubpenalty \clubpenalty
      \widowpenalty4000%
      \sfcode`\.\@m}
     {\def\@noitemerr
       {\@latex@warning{Empty `thebibliography' environment}}%
      \endlist}
\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em}
\let\@openbib@code\@empty
\newenvironment{theindex}
               {\if@twocolumn
                  \@restonecolfalse
                \else
                  \@restonecoltrue
                \fi
                \columnseprule \z@
                \columnsep 35\p@
                \twocolumn[\section*{\indexname}]%
                \@mkboth{\MakeUppercase\indexname}%
                        {\MakeUppercase\indexname}%
                \thispagestyle{plain}\parindent\z@
                \parskip\z@ \@plus .3\p@\relax
                \let\item\@idxitem}
               {\if@restonecol\onecolumn\else\clearpage\fi}
\newcommand\@idxitem{\par\hangindent 40\p@}
\newcommand\subitem{\@idxitem \hspace*{20\p@}}
\newcommand\subsubitem{\@idxitem \hspace*{30\p@}}
\newcommand\indexspace{\par \vskip 10\p@ \@plus5\p@ \@minus3\p@\relax}
\def\footnoterule{\kern-6\p@
  \hrule\kern 5.6\p@} % the \hrule is .4pt high
\newcommand\@makefntext[1]{%
    \parindent12pt%
    \noindent
    \@makefnmark#1}
\setlength\footnotesep{6\p@}
\setlength{\skip\footins}{12\p@ \@plus 12\p@ \@minus 1\p@}
\skip\@mpfootins = \skip\footins
\setlength\columnsep{10\p@}
\setlength\columnseprule{0\p@}
\pagestyle{hha}
\pagenumbering{arabic}
\onecolumn
\frenchspacing
\def\eqnarray{%
   \stepcounter{equation}%
   \def\@currentlabel{\p@equation\theequation}%
   \global\@eqnswtrue
   \m@th
   \global\@eqcnt\z@
   \tabskip\@centering
   \let\\\@eqncr
   $$\everycr{}\halign to\displaywidth\bgroup
      \tabskip\z@skip$\hfil\displaystyle{##}$%
      &\global\@eqcnt\@ne\hfil${\displaystyle{}##{}}$\hfil
      &\global\@eqcnt\tw@
         $\displaystyle{##}$\hfil
      \tabskip\@centering
      &\global\@eqcnt\thr@@\llap{##}%
      \tabskip\z@skip
      \cr}
\def\@uclcnotmath#1#2#3#4{\begingroup
      #1%
      \def\({$}\let\)\(% $
      \def\reserved@a##1##2{\let#2\reserved@a}%
      \expandafter\reserved@a\@uclclist\reserved@b{\reserved@b\@gobble}%
      \protected@edef\reserved@a{\endgroup
          \noexpand\@skipmath#3#4$\valign$}%
      \reserved@a}
\def\@skipmath#1{%
\def\@skipmath##1##2$##3${%
  \@skipensuremath##1##2#1\valign
  \ifx\valign##3%
  \else
    $##3$%
    \expandafter\@skipmath\expandafter##1%
  \fi}%
\def\@skipensuremath##1##2#1##3{%
  ##1{##2}%
  \ifx\valign##3%
  \else
    $##3$%
    \expandafter\@skipensuremath\expandafter##1%
  \fi}}
\expandafter\@skipmath\csname ensuremath \endcsname
\DeclareRobustCommand\MakeTextUppercase{%
  \@uclcnotmath{\def\i{I}\def\j{J}}{##1##2}\uppercase}
\DeclareRobustCommand\MakeTextLowercase{%
  \@uclcnotmath{}{##2##1}\lowercase}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\def\part{\@startsection
%  {part}{0}{\z@}{18\p@ \@plus 2\p@ \@minus 2\p@}%
%  {6\p@}{\normalfont\large\bf}}
\newcommand\part{%
   \if@noskipsec \leavevmode \fi
   \par
   \addvspace{4ex}%
   \@afterindentfalse
   \secdef\@part\@spart}
\def\@part[#1]#2{%
    \ifnum \c@secnumdepth >\m@ne
      \refstepcounter{part}%
      \addcontentsline{toc}{part}{\thepart\hspace{.5em}#1}%
    \else
      \addcontentsline{toc}{part}{#1}%
    \fi
    {\parindent \z@ \raggedright
     \interlinepenalty \@M
     \normalfont
     \ifnum \c@secnumdepth >\m@ne
       \large\bfseries \thepart.{ }
       %\par\nobreak
     \fi
     \large \bfseries #2%
     \markboth{}{}\par}%
    \nobreak
    \vskip 1ex %3ex
    \@afterheading}
\def\@spart#1{%
    {\parindent \z@ \raggedright
     \interlinepenalty \@M
     \normalfont
     \huge \bfseries #1\par}%
     \nobreak
     \vskip 3ex
     \@afterheading}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\section{%
  \@startsection
    {section}{1}{\z@}{18\p@ \@plus 2\p@ \@minus 2\p@}%
    {6\p@}{\normalfont\large\bf}}
\def\@seccntformat#1{\textup{\csname the#1\endcsname.}\quad}
\def\subsection{%
  \@startsection
    {subsection}{2}{\z@}{12\p@ \@plus 1.2\p@ \@minus 1.2\p@}%
    {1sp}{\normalfont\normalsize\bf}}
\def\subsubsection{%
  \@startsection
    {subsubsection}{3}{\z@}{-12\p@ \@plus -1.2\p@ \@minus-1.2\p@}%
    {1sp}{\normalfont\normalsize}}
\def\paragraph{%
  \@startsection
    {paragraph}{4}{\z@}{12\p@}%
    {-1em}{\normalfont\normalsize\scshape}}
\def\subparagraph{%
  \@startsection
    {paragraph}{5}{\z@}{12\p@}%
    {-1em}{\normalfont\normalsize\scshape}}
\setcounter{secnumdepth}{6}
\setcounter{tocdepth}{2}
\newlength\abovecaptionskip
\newlength\belowcaptionskip
\setlength\abovecaptionskip{10\p@}
\setlength\belowcaptionskip{0\p@}
\long\def\@makecaption#1#2{%
  \vspace\abovecaptionskip
  \sbox\@tempboxa{#1: #2}%
  \ifdim \wd\@tempboxa >\hsize
    #1: #2\par
  \else
    \global \@minipagefalse
    \hbox to\hsize{\hfil\box\@tempboxa\hfil}%
  \fi
  \vskip\belowcaptionskip}
\setlength\voffset{0cm} % -1.54cm
\setlength\hoffset{0cm} % -1.54cm
\setlength\paperwidth{8.5in} % 16cm
\setlength\headsep{12pt}
\setlength\topskip\baselineskip
\setlength\marginparsep{5pt}
\setlength\marginparwidth{18pt}
\setlength\marginparpush{5pt}
\setlength\headheight{30pt}
\setlength\topmargin{0pt}
\setlength{\footskip}{21pt}
\setlength\textheight{8.5in} %
\setlength\paperheight{11in} %
\addtolength\textheight{-1\headheight}
\addtolength\textheight{-1\headsep}
\addtolength\textheight{-1\footskip}
\setlength\columnsep{2pc}
\setlength\oddsidemargin{0pc} % 2pc
\setlength\evensidemargin{0pc} % 2pc
\setlength\textwidth{5in}
%\addtolength\textwidth{-2\oddsidemargin} % -2\oddsidemargin
%\addtolength\textwidth{-2\hoffset} % Levani
%\addtolength\textwidth{-2\marginparwidth} % Levani
%\addtolength\textwidth{-2\marginparsep} % Levani
\RequirePackage[\HHA@fontencoding]{fontenc}
\def\@tempa{T1}
\ifx\@tempa\HHA@fontencoding
\DeclareFontFamily{T1}{phv}{}
\DeclareFontShape{T1}{phv}{b}{n}{<->s*[.9]phvb8t}{}
\DeclareFontShape{T1}{phv}{b}{sc}{<->s*[.9]phvbc8t}{}
\DeclareFontShape{T1}{phv}{b}{sl}{<->s*[.9]phvbo8t}{}
\DeclareFontShape{T1}{phv}{bc}{n}{<->s*[.9]phvbrn8t}{}
\DeclareFontShape{T1}{phv}{bc}{sc}{<->s*[.9]phvbcn8t}{}
\DeclareFontShape{T1}{phv}{bc}{sl}{<->s*[.9]phvbon8t}{}
\DeclareFontShape{T1}{phv}{m}{n}{<->s*[.9]phvr8t}{}
\DeclareFontShape{T1}{phv}{m}{sc}{<->s*[.9]phvrc8t}{}
\DeclareFontShape{T1}{phv}{m}{sl}{<->s*[.9]phvro8t}{}
\DeclareFontShape{T1}{phv}{mc}{n}{<->s*[.9]phvrrn8t}{}
\DeclareFontShape{T1}{phv}{mc}{sc}{<->s*[.9]phvrcn8t}{}
\DeclareFontShape{T1}{phv}{mc}{sl}{<->s*[.9]phvron8t}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bx}{n}{<->ssub*phv/b/n}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bx}{sc}{<->ssub*phv/b/sc}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bx}{sl}{<->ssub*phv/b/sl}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{b}{it}{<->ssub*phv/b/sl}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bx}{it}{<->ssub*phv/b/it}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bc}{it}{<->ssub*phv/bc/sl}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{m}{it}{<->ssub*phv/m/sl}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{mc}{it}{<->ssub*phv/mc/sl}{}
\fi
\def\@tempa{LY1}
\ifx\@tempa\HHA@fontencoding
\input{ly1ptm.fd}
\expandafter\def\expandafter\@tempa\expandafter{\csname<->ptmr8y\endcsname}
%%\show\@tempa
\expandafter\ifx\csname ly1/ptm/m/n\endcsname \@tempa
  \def\sftfm#1#2{<->[.9]phv#18y}
\else
%%  \def\sftfm#1#2{<->[.9]phv#18y}
  \def\sftfm#1#2{<->[.9]hv#2}
\fi
%%\show\sftfm
\DeclareFontFamily{LY1}{phv}{}
\DeclareFontShape{LY1}{phv}{b}{n}{\sftfm{b}{b}}{}
\DeclareFontShape{LY1}{phv}{b}{sc}{<->sub*phv/b/n}{}
\DeclareFontShape{LY1}{phv}{b}{sl}{\sftfm{bo}{bo}}{}
\DeclareFontShape{LY1}{phv}{bc}{n}{<->sub*phv/m/n}{}
\DeclareFontShape{LY1}{phv}{bc}{sc}{<->sub*phv/bc/n}{}
\DeclareFontShape{LY1}{phv}{bc}{sl}{<->sub*phv/m/sl}{}
\DeclareFontShape{LY1}{phv}{m}{n}{\sftfm{r}{}}{}
\DeclareFontShape{LY1}{phv}{m}{sc}{<->sub*phv/m/n}{}
\DeclareFontShape{LY1}{phv}{m}{sl}{\sftfm{ro}{o}}{}
\DeclareFontShape{LY1}{phv}{mc}{n}{<->sub*phv/m/n}{}
\DeclareFontShape{LY1}{phv}{mc}{sc}{<->sub*phv/m/n}{}
\DeclareFontShape{LY1}{phv}{mc}{sl}{<->sub*phv/m/sl}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bx}{n}{<->ssub*phv/b/n}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bx}{sc}{<->ssub*phv/b/sc}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bx}{sl}{<->ssub*phv/b/sl}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{b}{it}{<->ssub*phv/b/sl}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bx}{it}{<->ssub*phv/b/it}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{bc}{it}{<->ssub*phv/bc/sl}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{m}{it}{<->ssub*phv/m/sl}{}
\DeclareFontShape{\HHA@fontencoding}{phv}{mc}{it}{<->ssub*phv/mc/sl}{}
\fi
\HHA@fonts
\HHA@ams
\bibliographystyle{hha}
\def\@cite#1#2{[{{\citeform{#1}}\if@tempswa , #2\fi}]}
\let\citeform\textbf
\def\@biblabel#1{\textbf{[#1]~}} %%%%%%%%%%%%%%%%%%%%%%%%%
\providecommand{\textsuperscript}[1]{%
  \ensuremath{{}^{\mbox{\normalfont\scriptsize#1}}}}
\providecommand{\@textsuperscript}[1]{%
  \ensuremath{{}^{\mbox{\normalfont\scriptsize#1}}}}
\providecommand\MakeUppercase[1]{%
  \protected@edef\@tempa{\uppercase{#1}}\@tempa}
\def\hb@xt@{\hbox to}
\def\contentsname{Contents}
\def\listfigurename{List of Figures}
\def\listtablename{List of Tables}
\def\refname{References}
\def\indexname{Index}
\def\figurename{Figure}
\def\tablename{Table}
\def\partname{Part}
\def\appendixname{Appendix}
\def\abstractname{Abstract}
\def\today{\ifcase\month\or
  January\or February\or March\or April\or May\or June\or
  July\or August\or September\or October\or November\or December\fi
  \space\number\day, \number\year}
\def\journalBaseURL{http://www.rmi.acnet.ge}
\def\journalname{\href
  {\journalBaseURL/hha/}{Homology, Homotopy and Applications}}
\def\@journalissn{1512--0139}
\def\@journalpublisher{\href
  {\journalBaseURL}%
  {Homology, Homotopy and Applications, vol.}{\@volumenumber(\@issuenumber),
  \@volumeyear}{, pp.}{\@startpage--\@endpage}}
\def\copyrightname{Hvedri Inassaridze}
\def\andname{and}
\def\ppname{pp}
\def\numbername{number}
\def\volumename{volume}
\endinput
%%
%% End of file `hha.cls'.