%%% IMPORTANT: In case of any problems contact publ@impan.pl  %%%
 
%% Identification part:

\NeedsTeXFormat{LaTeX2e}

\def \filedate {2009/11/25}
\def \fileversion {3}
\def \filename {bcp.cls}

\ProvidesClass{bcp}[\filedate\space
  Private LaTeX2e document class <\filedate>]

\LoadClass[twoside]{article}

\RequirePackage{amsthm}

\def\large{\@setsize\large{14pt}\xiipt\@xiipt}

\renewcommand\normalsize{%
   \@setfontsize\normalsize\@xpt{13}%
   \abovedisplayskip 4\p@ \@plus2\p@
   \abovedisplayshortskip \z@ \@plus2\p@
   \belowdisplayshortskip 4\p@ \@plus2\p@
   \belowdisplayskip \abovedisplayskip
   \def\@listi{\leftmargin\leftmargini
               \topsep 4\p@ \@plus2\p@
               \parsep 0\p@
               \itemsep \parsep}}
\normalsize

\renewcommand\footnotesize{%
   \@setfontsize\footnotesize\@ixpt{12}%
   \abovedisplayskip 4\p@ \@plus2\p@
   \abovedisplayshortskip \z@ \@plus2\p@
   \belowdisplayshortskip 4\p@ \@plus2\p@
   \belowdisplayskip \abovedisplayskip
   \def\@listi{\leftmargin\leftmargini
               \topsep 0\p@
               \parsep 0\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip
}
\newcommand\xfootnotesize{%
   \@setfontsize\footnotesize\@ixpt{11}%
   \abovedisplayskip 4\p@ \@plus2\p@
   \abovedisplayshortskip \z@ \@plus2\p@
   \belowdisplayshortskip 4\p@ \@plus2\p@
   \belowdisplayskip \abovedisplayskip
   \def\@listi{\leftmargin\leftmargini
               \topsep 0\p@
               \parsep 0\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip
}
\renewcommand\scriptsize{%
   \@setfontsize\footnotesize\@viipt{8}%
   \abovedisplayskip 4\p@ \@plus2\p@
   \abovedisplayshortskip \z@ \@plus2\p@
   \belowdisplayshortskip 4\p@ \@plus2\p@
   \belowdisplayskip \abovedisplayskip
   \def\@listi{\leftmargin\leftmargini
               \topsep 0\p@
               \parsep 0\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip
}
\newcommand\scriptscriptsize{%
   \@setfontsize\footnotesize\@vpt{7}%
   \abovedisplayskip 4\p@ \@plus2\p@
   \abovedisplayshortskip \z@ \@plus2\p@
   \belowdisplayshortskip 4\p@ \@plus2\p@
   \belowdisplayskip \abovedisplayskip
   \def\@listi{\leftmargin\leftmargini
               \topsep 0\p@
               \parsep 0\p@
               \itemsep \parsep}%
   \belowdisplayskip \abovedisplayskip
}
\long\def\@footnotetext#1{\insert\footins{%
    \reset@font\xfootnotesize
    \interlinepenalty\interfootnotelinepenalty
    \splittopskip\footnotesep
    \splitmaxdepth \dp\strutbox \floatingpenalty \@MM
    \hsize\columnwidth \@parboxrestore
    \protected@edef\@currentlabel{%
       \csname p@footnote\endcsname\@thefnmark
    }%
    \color@begingroup
      \@makefntext{%
        \rule\z@\footnotesep\ignorespaces#1\@finalstrut\strutbox}%
    \color@endgroup}}%

\exhyphenpenalty100

\def\eqnarray{\stepcounter{equation}\let\@currentlabel\theequation
\global\@eqnswtrue\m@th
\global\@eqcnt\z@\tabskip\@centering\let\\\@eqncr
$$\halign to\displaywidth\bgroup\@eqnsel\hskip\@centering
  $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne
  \hfil${{}##{}}$\hfil
  &\global\@eqcnt\tw@ $\displaystyle\tabskip\z@{##}$\hfil
   \tabskip\@centering&\llap{##}\tabskip\z@\cr}

%% Modify the `headings' and `plain' page styles:

\def\nrart#1{\def\nra{#1}}
\def\doi{DOI: 10.4064/bc*-0-\nra}
\def\xcopyright{\copyright\ Instytut Matematyczny PAN, 201*}
\newcount\beg
\newbox\aabox
\newbox\atbox
\newbox\fpbox
\def\lewyhead{\noindent\rlap{\footnotesize\the\count0}\hfil\copy\aabox\hfil}
\def\prawyhead{\noindent\hfill\ifdim\wd\atbox=0pt ???\else\copy\atbox\fi\hfill\llap{\footnotesize\the\count0}}
\def\ps@bcp{\let\@mkboth\markboth
\def\@oddhead{\ifnum\beg=\count0\phead \else\prawyhead\fi}\def\@evenhead{\lewyhead}%
\def\@oddfoot{\ifnum\beg=\count0{\scriptsize\rlap{\doi}\hfill[\the\count0]\hfill\llap{\xcopyright}}\fi}%
\def\@oddfoot{\ifnum\beg=\count0\hfill\scriptsize[\the\count0]\hfill\fi}%
\def\@evenfoot{}}
\def\abbrevauthors#1{\setbox\aabox=\hbox{\scriptsize\uppercase{#1}}}
\def\abbrevtitle#1{\abtitle{#1}\setbox\atbox=\hbox{\scriptsize\setabtitle}}
\long\def\pag{\beg=\count0
\def\phead{\setbox\fpbox=\hbox{\scriptsize
BANACH CENTER PUBLICATIONS, VOLUME **}%
\noindent\vbox to4.5pt{\scriptsize\baselineskip9pt\hsize\wd\fpbox%
\centerline{****************************************}

\centerline{BANACH CENTER PUBLICATIONS, VOLUME **}

\centerline{INSTITUTE OF MATHEMATICS}

\centerline{POLISH ACADEMY OF SCIENCES}

\centerline{WARSZAWA 201*}\vss}\hfill}}

\newbox\aubox
\newbox\adbox
\newbox\mathbox
\newbox\keybox
\newbox\thanksbox
\@ifundefined{@emptytoks}{\csname newtoks\endcsname\@emptytoks}{}

\renewcommand{\title}[2][]{\gdef\@title{#2}}
\edef\title{\@nx\@dblarg
\@xp\@nx\csname\string\title\endcsname}

\def\settitle{\uppercasenonmath\@title
  \@title}

\newcommand{\abtitle}[2][]{\gdef\@abtitle{#2}}
\edef\abtitle{\@nx\@dblarg
  \@xp\@nx\csname\string\abtitle\endcsname}

\def\setabtitle{\uppercasenonmath\@abtitle
  \@abtitle}

\newcommand{\uppercasenonmath}[1]{\toks@\@emptytoks
  \@xp\@skipmath\@xp\@empty#1$$%
  \edef#1{{\@nx\protect\@nx\@upprep\the\toks@}}%
}
\newcommand{\@upprep}{%
  \spaceskip1.3\fontdimen2\font plus1.3\fontdimen3\font
  \upchars@}
\newcommand{\upchars@}{%
  \def\ss{SS}\def\i{I}\def\j{J}\def\ae{\AE}\def\oe{\OE}%
  \def\o{\O}\def\aa{\AA}\def\l{\L}\def\Mc{M{\scshape c}}}
\providecommand{\Mc}{Mc}
\newcommand{\@skipmath}{}
\long\def\@skipmath#1$#2${%
  \@xskipmath#1\(\)%
  \@ifnotempty{#2}{\toks@\@xp{\the\toks@$#2$}\@skipmath\@empty}}%
\newcommand{\@xskipmath}{}
\long\def\@xskipmath#1\(#2\){%
  \uppercase{\toks@\@xp\@xp\@xp{\@xp\the\@xp\toks@#1}}%
  \@ifnotempty{#2}{\toks@\@xp{\the\toks@\(#2\)}\@xskipmath\@empty}}%
\def\altucnm#1{%
  \MakeTextUppercase{\toks@{#1}}%
  \edef#1{\the\toks@}%
}
\AtBeginDocument{%
  \@ifundefined{MakeTextUppercase}{}{\let\uppercasenonmath\altucnm}%
}
\@ifundefined{MakeUppercase}{\let\MakeUppercase\uppercase}{}%

\newbox\abbox
\setbox\abbox=\vbox{\vglue18pt}

\def\author#1{\setbox\aubox=\hbox{\let\\=\cr
\footnotesize\baselineskip12pt\vbox{\tabskip 0pt plus15cc
\halign to\hsize{\hfil\ignorespaces \uppercase{##}\hfil\cr#1\cr}}}%
\global\setbox\abbox=\vbox{\unvbox\abbox\box\aubox\vskip8pt}}

\def\address#1{\setbox\adbox=\hbox{\let\\=\cr
\footnotesize\baselineskip12pt\vbox{\it\tabskip 0pt plus15cc
\halign to\hsize{\hfil\ignorespaces {##}\hfil\cr#1\cr}}}%
\global\setbox\abbox=\vbox{\unvbox\abbox\box\adbox\vskip16pt}}

\def\mclass{***}
\long\def\mathclass#1{\def\mclass{#1}}

\newif\ifded
\dedfalse
\long\def\dedicatory#1{\dedtrue\def\ded{{\leftskip0pt plus1fill\rightskip0pt\it#1\par}}}

\def\kwords{***}
\long\def\keywords#1{\def\kwords{#1}}

\newcount\tnum
\long\def\thanks#1{\global\tnum=100
\setbox\thanksbox=\hbox{\vfootnote{}{#1}{}}}

\long\def\maketitlebcp{\def\and{{\lowercase{and}}}\pag
\vfootnote{}{\noindent\kern-15pt 2010 {\it Mathematics Subject
Classification}\/: \mclass}%
\vfootnote{}{\noindent\kern-15pt {\it Key words
and phrases}\/: \kwords}
\ifnum\tnum=100 \unhbox\thanksbox\fi
\vfootnote{}{\noindent\kern-15pt The paper is in final form and no version
of it will be published elsewhere.}{}
\vglue7cc
{\large\bf\centering\settitle\par
}\box\abbox
\vskip8pt}

  
\renewenvironment{abstract}{\bgroup\footnotesize\noindent{\bf Abstract.} }{\par\egroup\vskip12pt plus2pt minus2pt}

\long\def\th#1#2#3{\vskip-\lastskip\vskip4pt plus2pt
\noindent{\sc #1} #2\hskip-\lastskip\ {\it #3}\vskip-\lastskip\vskip4pt plus2pt}

\long\def\defin#1#2{\vskip-\lastskip\vskip4pt plus2pt
\noindent{\sc #1} #2 \vskip-\lastskip\vskip4pt plus2pt}

\long\def\remar#1#2{\vskip-\lastskip\vskip4pt plus2pt
\noindent{\sc #1} #2\vskip-\lastskip\vskip4pt plus2pt}

\def\Pf#1{\vskip-\lastskip\vskip4pt plus2pt
\noindent{\it #1\ }\ignorespaces}

\def\sq{\unskip\nobreak\kern5pt\nobreak\vrule height4pt width4pt depth0pt}


\renewenvironment{proof}[1][\proofname]{\par
\ods  \normalfont 
        \noindent{\itshape
    #1\@addpunct{.}}\hods
}{%
  \sq\ods
}


\def\@oparg#1[#2]{\@ifnextchar[{#1}{#1[#2]}}
\def\@thm#1#2#3{%
  \ifhmode\unskip\unskip\par\fi
  \normalfont
  \trivlist
  \let\thmheadnl\relax
  \let\thm@swap\@gobble
  \thm@headpunct{.}% add period after heading
  \thm@headsep .55em\relax
  \thm@space@setup
  #1% style overrides
  \@topsep \thm@preskip               % used by thm head
  \@topsepadd \thm@postskip           % used by \@endparenv
  \def\@tempa{#2}\ifx\@empty\@tempa
    \def\@tempa{\@oparg{\@begintheorem{#3}{}}[]}%
  \else
    \refstepcounter{#2}%
    \def\@tempa{\@oparg{\@begintheorem{#3}{\csname the#2\endcsname}}[]}%
  \fi
  \@tempa
}
\thm@bodyfont{\itshape}
\thm@notefont{\normalfont}
\let\thm@indent\noindent
\thm@headfont{\scshape}
\def\swappedhead#1#2#3{%
  {\thmnumber{#2}.}%
  \thmname{\@ifnotempty{#2}{~}#1}%
  \thmnote{ {\the\thm@notefont(#3)}}}
\def\th@plain{%
  \itshape % body font
}

\def\vsk{\vskip4pt plus2pt}

\newbox\refbox
\newdimen\refwidth
\newif\ifnumery
\numerytrue
\long\def\references#1#2{{\footnotesize
\setbox\refbox=\hbox{\footnotesize[#1]}\refwidth\wd\refbox\advance\refwidth by 12pt%
\ifnumery\def\textindent##1{\indent\llap{##1\hskip12pt}\ignorespaces}% PLAIN
\else\def\textindent##1{\noindent\rlap{##1\hskip12pt}\kern\parindent\ignorespaces}% PLAIN
\fi\def\item{\par \hang \textindent}
\vskip24pt plus4pt minus4pt
\centerline{\bf References}
\vskip12pt plus2pt minus2pt
\parindent=\refwidth
#2

}}

\def\refname{References} % <----------

\renewenvironment{thebibliography}[1]
{\vskip24pt plus4pt minus4pt
\footnotesize\centerline{\bf \refname}
\vglue12pt plus2pt minus2pt
\nobreak
\labelsep12pt 
      \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}}%
\def\newblock{\hskip .11em plus .33em minus .07em}
 \sloppy\clubpenalty4000\widowpenalty4000
 \sfcode`\.=1000\relax}
     {\def\@noitemerr
       {\@latex@warning{Empty `thebibliography' environment}}%
      \endlist}



\skip\footins 12pt plus 4pt minus 2pt
\def\footnoterule{\kern -3pt \hrule width 4cc \kern 2.6pt}

\def\hang{\hangindent\parindent}
\def\textindent#1{\indent\llap{#1\enspace}\ignorespaces}
\def\vfootnote#1%
{\insert\footins\bgroup\footnotesize\baselineskip11pt\interlinepenalty\interfootnotelinepenalty%
\splittopskip\ht\strutbox\splitmaxdepth\dp\strutbox\floatingpenalty\@MM%
\leftskip\z@skip\rightskip\z@skip\spaceskip\z@skip\xspaceskip\z@skip%
\textindent{#1}\footstrut\futurelet\next\fo@t}

\ds@twoside
\ps@bcp
\def\fo@t{\ifcat\bgroup\noexpand\next \let\next\f@@t
  \else\let\next\f@t\fi \next}
\def\f@@t{\bgroup\aftergroup\@foot\let\next}
\def\f@t#1{#1\@foot}
\def\@foot{\strut\egroup}
\def\footstrut{\vbox to\splittopskip{}}

%\long\def\@makefntext#1{{\nine\parindent15pt\indent$^{\@thefnmark}$#1}}

%% Modify the other sectioning commands:


\newif\ifkropka
\kropkatrue
\def\bezkropki{\kropkafalse}
\def\@xsect#1{%
  \@tempskipa #1\relax
  \ifdim \@tempskipa>\z@
    \par \nobreak
    \vskip \@tempskipa
    \@afterheading
  \else
    \@nobreakfalse
    \global\@noskipsectrue
    \everypar{%
      \if@noskipsec
        \global\@noskipsecfalse
       {\setbox\z@\lastbox}%
        \clubpenalty\@M
        \begingroup \@svsechd\ifkropka.\fi\global\kropkatrue \endgroup
        \unskip
        \@tempskipa #1\relax
        \hskip -\@tempskipa
      \else
        \clubpenalty \@clubpenalty
        \everypar{}%
      \fi}%
  \fi
  \ignorespaces}

\def\section{\@startsection {section}{1}{0pt}{12pt plus 2pt minus 2pt}{-.55em}{\bf}}
\def\subsection{\@startsection{subsection}{2}{0pt}{6pt plus 2pt minus
 2pt}{-.55em}{\bf}}
\def\subsubsection{\@startsection{subsubsection}{3}{0pt}{4pt plus
2pt minus 1pt}{-.55em}{\it}}
\def\paragraph{\@startsection
 {paragraph}{4}{0pt}{4pt plus2pt}{-4pt}{\it}}
\def\@seccntformat#1{{\bf\csname the#1\endcsname.}\hskip5pt \ignorespaces}

\def\ackn{\subsection*{Acknowledgments}}

\def\numberline#1{\hb@xt@\@tempdima{#1.\hfil}}
\setcounter{tocdepth}{2}
\renewcommand\tableofcontents{%
   \bezkropki \section*{\contentsname}\ \par
    \@starttoc{toc}%
    \bods}

\renewcommand*\l@section{\@dottedtocline{1}{0em}{1.5em}}

\def\ods{\vskip-\lastskip\vskip4pt plus2pt }
\def\bods{\vskip-\lastskip\vskip12pt plus2pt minus2pt}
\def\hods{\unskip\kern.55em\ignorespaces}

%% Other modifications:

\RequirePackage[pdftex,
     papersize={168mm,238mm},
textwidth=30cc, 
textheight=44cc
   ]%
  {geometry}
\exhyphenpenalty100
\oddsidemargin0pt
\evensidemargin0pt
\setlength{\topmargin}{-78pt}
\setlength{\oddsidemargin}{-72pt}
\setlength{\evensidemargin}{-72pt}
\addtolength{\topmargin}{14mm}
\addtolength{\oddsidemargin}{18mm}
\addtolength{\evensidemargin}{168mm}
\addtolength{\evensidemargin}{-30cc}
\addtolength{\evensidemargin}{-18mm}
\headsep16pt
\footskip 18.16pt
\topsep4pt plus2pt
\partopsep\z@
\parsep\z@
\itemsep\z@
\long\def\@makecaption#1#2{\xfootnotesize
 \vskip 4pt
 \setbox\@tempboxa\hbox{#1.\hods #2}
 \ifdim \wd\@tempboxa >\hsize #1.\hods #2\par \else \hbox
to\hsize{\hfil\box\@tempboxa\hfil}
 \fi}

\makeatother
\def\figurename{Fig.}

\setcounter{topnumber}{3}
\def \topfraction {1}
\setcounter{bottomnumber}{1}
\setcounter{totalnumber}{4}
\def \textfraction {0}
\def \floatpagefraction {1}

\def\and{\lowercase{and} }
\flushbottom
\overfullrule5pt
\frenchspacing


\def\kon{\vfill\eject\null\thispagestyle{empty}}