%**************************************
% bcp98e.sty
%**************************************
\def\@ptsize{0} \@namedef{ds@11pt}{\def\@ptsize{1}}
\@namedef{ds@12pt}{\def\@ptsize{2}}
\def\ds@twoside{\@twosidetrue \@mparswitchtrue}
\def\ds@draft{\overfullrule5pt}
\@options
%\input art1\@ptsize.sty\relax

\font\sc=cmcsc10
%\newcounter{part}
\newcounter {section}
\newcounter {subsection}[section]
\newcounter {subsubsection}[subsection]
%\newcounter {paragraph}[subsubsection]
%\newcounter {subparagraph}[paragraph]

\def\@seccntformat#1{\csname the#1\endcsname{\bf.}\kern5pt}

\def\@begintheorem#1#2{\it \trivlist \item[\hskip 1.2\parindent{\sc #1\#2.}]}
\def\@opargbegintheorem#1#2#3{\it \trivlist
\item[\hskip \parindent{\sc #1\ #2\ \rm (#3).}]}
\newcounter{rmrk}
\newtheorem{remark}[rmrk]{\rm \sp{Remark}\kern1.7pt}

\lineskip 1pt \normallineskip 1pt
\def\baselinestretch{1}
\def\@normalsize{\@setsize\normalsize{12pt}\xpt\@xpt
\abovedisplayskip 4pt plus2pt \belowdisplayskip \abovedisplayskip
\abovedisplayshortskip 2pt plus2pt\belowdisplayshortskip 2pt plus2pt
\let\@listi\@listI}
\def\small{\@setsize\small{11pt}\ixpt\@ixpt
\abovedisplayskip 8.5pt plus 3pt minus 4pt\belowdisplayskip
\abovedisplayskip
\abovedisplayshortskip \z@ plus2pt\belowdisplayshortskip 4pt plus2pt minus
2pt
\def\@listi{\leftmargin\leftmargini \topsep 0pt %plus 2pt minus 2pt
\parsep 4pt
plus 2pt %minus 1pt
\itemsep \parsep}}
\def\footnotesize{\@setsize\footnotesize{9pt}\ixpt\@ixpt
\abovedisplayskip 6pt plus 2pt minus 4pt\belowdisplayskip
\abovedisplayskip
\abovedisplayshortskip \z@ plus 1pt\belowdisplayshortskip 3pt plus 1pt
minus
2pt
\def\@listi{\leftmargin\leftmargini \topsep 3pt plus 1pt minus 1pt\parsep
2pt
plus 1pt minus 1pt
\itemsep \parsep}}
\def\scriptsize{\@setsize\scriptsize{8pt}\viipt\@viipt}
\def\tiny{\@setsize\tiny{6pt}\vpt\@vpt}
\def\large{\@setsize\large{14pt}\xiipt\@xiipt}
\def\Large{\@setsize\Large{18pt}\xivpt\@xivpt}
\def\LARGE{\@setsize\LARGE{22pt}\xviipt\@xviipt}
\def\huge{\@setsize\huge{25pt}\xxpt\@xxpt}
\def\Huge{\@setsize\Huge{30pt}\xxvpt\@xxvpt}
\normalsize
\if@twoside \oddsidemargin 44pt \evensidemargin 82pt \marginparwidth 107pt
\else \oddsidemargin 63pt \evensidemargin 63pt
\marginparwidth 90pt
\fi
\marginparsep 10pt
\topmargin 27pt
\headheight 12pt \headsep 25pt \footskip 30pt
\footnotesep 6.65pt
\skip\footins 9pt plus 4pt minus 2pt
\floatsep 12pt plus 2pt minus 2pt \textfloatsep 20pt plus 2pt minus 4pt
\intextsep 12pt plus 2pt minus 2pt \@maxsep 20pt \dblfloatsep 12pt plus
2pt
minus 2pt \dbltextfloatsep 20pt plus 2pt minus 4pt \@dblmaxsep 20pt
\@fptop 0pt plus 1fil \@fpsep 8pt plus 2fil \@fpbot 0pt plus 1fil
\@dblfptop 0pt plus 1fil \@dblfpsep 8pt plus 2fil \@dblfpbot 0pt plus 1fil
\marginparpush 5pt
\parskip 0pt plus 1pt \parindent 15pt \partopsep 2pt plus 1pt minus 1pt
\@lowpenalty 51 \@medpenalty 151 \@highpenalty 301
\@beginparpenalty -\@lowpenalty \@endparpenalty -\@lowpenalty
\@itempenalty
-\@lowpenalty

\def\part{\par \addvspace{4ex} \@afterindentfalse \secdef\@part\@spart}
\def\partname{Part} % <----------
\def\@part[#1]#2{\ifnum \c@secnumdepth >\m@ne \refstepcounter{part}
\addcontentsline{toc}{part}{\thepart \hspace{1em}#1}\else
\addcontentsline{toc}{part}{#1}\fi { \parindent 0pt \raggedright
\ifnum \c@secnumdepth >\m@ne \Large \bf \partname{}
\thepart \par\nobreak \fi \huge
\bf #2\markboth{}{}\par } \nobreak \vskip 3ex \@afterheading }
\def\@spart#1{{\parindent 0pt \raggedright
\huge \bf
#1\par} \nobreak \vskip 3ex \@afterheading }
\def\section{\@startsection {section}{1}{\parindent}{12pt plus 2pt minus
2pt}{-4pt}{\bf}}
\def\subsection{\@startsection {subsection}{2}{\parindent}{6pt plus 2pt
minus
2pt}{-4pt}{\it}}
\def\subsubsection{\@startsection{subsubsection}{3}{\parindent}{4pt plus
2pt minus 1pt}{-4pt}{\it}}
\def\paragraph{\@startsection
{paragraph}{4}{\z@}{3.25ex plus 1ex minus .2ex}{-1em}{\normalsize\bf}}
\def\subparagraph{\@startsection
{subparagraph}{4}{\parindent}{3.25ex plus 1ex minus
.2ex}{-1em}{\normalsize\bf}}


\setcounter{secnumdepth}{3}
%\setcounter{subsecnumdepth}{3}

\def\appendix{\par
\setcounter{section}{0}
\setcounter{subsection}{0}
\def\thesection{\Alph{section}}}

\leftmargini 25pt
\leftmarginii 22pt \leftmarginiii 18.7pt \leftmarginiv 17pt \leftmarginv
10pt
\leftmarginvi 10pt
\leftmargin\leftmargini
\labelsep 5pt
\labelwidth\leftmargini\advance\labelwidth-\labelsep
\def\@listI{\leftmargin\leftmargini \parsep 4pt plus 2pt minus 1pt\topsep
8pt
plus 2pt minus 4pt\itemsep 4pt plus 2pt minus 1pt}
\let\@listi\@listI
\@listi
\def\@listii{\leftmargin\leftmarginii
\labelwidth\leftmarginii\advance\labelwidth-\labelsep
\topsep 4pt plus 2pt minus 1pt
\parsep 2pt plus 1pt minus 1pt
\itemsep \parsep}
\def\@listiii{\leftmargin\leftmarginiii
\labelwidth\leftmarginiii\advance\labelwidth-\labelsep
\topsep 2pt plus 1pt minus 1pt
\parsep \z@ \partopsep 1pt plus 0pt minus 1pt
\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}


\def\thepage{\the\count0 }
\def\labelenumi{\theenumi.}
\def\theenumi{\arabic{enumi}}
\def\labelenumii{(\theenumii)}
\def\theenumii{\alph{enumii}}
\def\p@enumii{\theenumi}
\def\labelenumiii{\theenumiii.}
\def\theenumiii{\roman{enumiii}}
\def\p@enumiii{\theenumi(\theenumii)}
\def\labelenumiv{\theenumiv.}
\def\theenumiv{\Alph{enumiv}}
\def\p@enumiv{\p@enumiii\theenumiii}

\def\labelitemi{$\bullet$}
\def\labelitemii{\bf --}
\def\labelitemiii{$\ast$}
\def\labelitemiv{$\cdot$}

\def\verse{\let\\=\@centercr
\list{}{\itemsep\z@ \itemindent -1.5em\listparindent \itemindent
\rightmargin\leftmargin\advance\leftmargin 1.5em}\item[]}
\let\endverse\endlist
\def\quotation{\list{}{\listparindent 1.5em
\itemindent\listparindent
\rightmargin\leftmargin \parsep 0pt plus 1pt}\item[]}
\let\endquotation=\endlist
\def\quote{\list{}{\rightmargin\leftmargin}\item[]}
\let\endquote=\endlist

\def\descriptionlabel#1{\hspace\labelsep \bf #1}
\def\description{\list{}{\labelwidth\z@ \itemindent-\leftmargin
\let\makelabel\descriptionlabel}}
\let\enddescription\endlist

\def\theequation{\arabic{equation}}


\def\titlepage{\@restonecolfalse\if@twocolumn\@restonecoltrue\onecolumn
\else \newpage \fi \thispagestyle{empty}\c@page\z@}
\def\endtitlepage{\if@restonecol\twocolumn \else \newpage \fi}

\arraycolsep 5pt \tabcolsep 6pt \arrayrulewidth .4pt \doublerulesep 2pt
\tabbingsep \labelsep

\skip\@mpfootins = \skip\footins
\fboxsep = 3pt \fboxrule = .4pt
\def\thepart{\Roman{part}}
\def\thesection {\arabic{section}}
\def\thesubsection {{\bf\thesection.\arabic{subsection}}}
\def\thesubsubsection
{{\rm\arabic{section}.\arabic{subsection}.\arabic{subsubsection}}}
\def\theparagraph {\thesubsubsection.\arabic{paragraph}}
\def\thesubparagraph {\theparagraph.\arabic{subparagraph}}
\def\@pnumwidth{1.55em}
\def\@tocrmarg {2.55em}
\def\@dotsep{4.5}
\setcounter{tocdepth}{3}

\def\contentsname{Contents} % <----------
\def\tableofcontents{\section*{\contentsname
\@mkboth{\uppercase{\contentsname}}{\uppercase{\contentsname}}}
\@starttoc{toc}}
\def\l@part#1#2{\addpenalty{\@secpenalty}
\addvspace{2.25em plus 1pt} \begingroup
\@tempdima 3em \parindent \z@ \rightskip \@pnumwidth \parfillskip
-\@pnumwidth
{\large \bf \leavevmode #1\hfil \hbox to\@pnumwidth{\hss #2}}\par
\nobreak \endgroup}
\def\l@section#1#2{\addpenalty{\@secpenalty} \addvspace{1.0em plus 1pt}
\@tempdima 1.5em \begingroup
\parindent \z@ \rightskip \@pnumwidth
\parfillskip -\@pnumwidth
\bf \leavevmode \advance\leftskip\@tempdima \hskip -\leftskip
#1\nobreak\hfil
\nobreak\hbox to\@pnumwidth{\hss #2}\par
\endgroup}

\def\l@subsection{\@dottedtocline{2}{1.5em}{2.3em}}
\def\l@subsubsection{\@dottedtocline{3}{3.8em}{3.2em}}
\def\l@paragraph{\@dottedtocline{4}{7.0em}{4.1em}}
\def\l@subparagraph{\@dottedtocline{5}{10em}{5em}}
\def\listfigurename{List of Figures} % <----------
\def\listoffigures{\section*{\listfigurename\@mkboth

{\uppercase{\listfigurename}}{\uppercase{\listfigurename}}}\@starttoc{lof}}
\def\l@figure{\@dottedtocline{1}{1.5em}{2.3em}}
\def\listtablename{List of Tables} % <----------
\def\listoftables{\section*{\listtablename\@mkboth
{\uppercase{\listtablename}}{\uppercase{\listtablename}}}\@starttoc{lot}}
\let\l@table\l@figure

\def\refname{References} % <----------
\def\thebibliography#1{\vskip24pt plus4pt minus4pt
\centerline{\bf References}
\vglue11pt plus2pt minus2pt
\nobreak\list
{[\arabic{enumi}]}{\settowidth\labelwidth{[#1]}\leftmargin\labelwidth
\parsep-3pt plus1pt
\advance\leftmargin\labelsep
\usecounter{enumi}}
\def\newblock{\hskip .11em plus .33em minus .07em}
\sloppy\clubpenalty4000\widowpenalty4000
\sfcode`\.=1000\relax}
\let\endthebibliography=\endlist

\newif\if@restonecol
\def\indexname{Index} % <----------
\def\theindex{\@restonecoltrue\if@twocolumn\@restonecolfalse\fi
\columnseprule \z@
\columnsep 35pt\twocolumn[\section*{\indexname}]
\@mkboth{\uppercase{\indexname}}{\uppercase{\indexname}}%
\thispagestyle{plain}\parindent\z@
\parskip\z@ plus .3pt\relax\let\item\@idxitem}
\def\@idxitem{\par\hangindent 40pt}
\def\subitem{\par\hangindent 40pt \hspace*{20pt}}
\def\subsubitem{\par\hangindent 40pt \hspace*{30pt}}
\def\endtheindex{\if@restonecol\onecolumn\else\clearpage\fi}
\def\indexspace{\par \vskip 10pt plus 5pt minus 3pt\relax}
\def\footnoterule{\kern-3\p@
\hrule width .4\columnwidth
\kern 2.6\p@}

\long\def\@makefntext#1{\parindent 1em\noindent
\hbox to 1.8em{\hss$^{\@thefnmark}$}#1}

\setcounter{topnumber}{2}
\def\topfraction{.7}
\setcounter{bottomnumber}{1}
\def\bottomfraction{.3}
\setcounter{totalnumber}{3}
\def\textfraction{.2}
\def\floatpagefraction{.5}
\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.7}
\def\dblfloatpagefraction{.5}

\long\def\@makecaption#1#2{
\vskip 10pt
\setbox\@tempboxa\hbox{#1: #2}
\ifdim \wd\@tempboxa >\hsize #1: #2\par \else \hbox
to\hsize{\hfil\box\@tempboxa\hfil}
\fi}


\newcounter{figure}
\def\thefigure{\@arabic\c@figure}
\def\fps@figure{tbp}
\def\ftype@figure{1}
\def\ext@figure{lof}
\def\figurename{Figure} % <----------
\def\fnum@figure{\figurename{} \thefigure}
\def\figure{\@float{figure}}
\let\endfigure\end@float
\@namedef{figure*}{\@dblfloat{figure}}
\@namedef{endfigure*}{\end@dblfloat}
\newcounter{table}
\def\thetable{\@arabic\c@table}
\def\fps@table{tbp}
\def\ftype@table{2}
\def\ext@table{lot}
\def\tablename{Table} % <----------
\def\fnum@table{\tablename{} \thetable}
\def\table{\@float{table}}
\let\endtable\end@float
\@namedef{table*}{\@dblfloat{table}}
\@namedef{endtable*}{\end@dblfloat}

%\mark{{}{}}

\if@twoside \def\ps@headings{\let\@mkboth\markboth
\def\@oddfoot{}\def\@evenfoot{}\def\@evenhead{\rm \thepage\hfil \sl
\leftmark}\def\@oddhead{\hbox{}\sl \rightmark \hfil
\rm\thepage}\def\sectionmark##1{\markboth {\uppercase{\ifnum
\c@secnumdepth
\z@
\thesection\hskip 1em\relax \fi ##1}}{}}\def\subsectionmark##1{\markright
{\ifnum \c@secnumdepth >\@ne
\thesubsection\hskip 1em\relax \fi ##1}}}
\else \def\ps@headings{\let\@mkboth\markboth
\def\@oddfoot{}\def\@evenfoot{}\def\@oddhead{\hbox {}\sl \rightmark \hfil
\rm\thepage}\def\sectionmark##1{\markright {\uppercase{\ifnum
\c@secnumdepth
\z@
\thesection\hskip 1em\relax \fi ##1}}}}
\fi
\def\ps@myheadings{\let\@mkboth\@gobbletwo
\def\@oddhead{\hbox{}\sl\rightmark \hfil
\rm\thepage}\def\@oddfoot{}\def\@evenhead{\rm
\thepage\hfil\sl\leftmark\hbox
{}}\def\@evenfoot{}\def\sectionmark##1{}\def\subsectionmark##1{}}

\onecolumn \if@twoside\else\raggedbottom\fi

\frenchspacing

\parindent15pt

\abovedisplayskip4pt plus2pt
\belowdisplayskip4pt plus2pt
\abovedisplayshortskip2pt plus2pt
\belowdisplayshortskip2pt plus2pt

\font\twbf=cmbx10 at12pt
\font\twit=cmti10 at12pt
\font\twrm=cmr10 at12pt

\font\ninerm=cmr9
\font\nineit=cmti9
\font\ninesy=cmsy9
\font\ninei=cmmi9
\font\ninebf=cmbx9
\font\ninegt=eufm9

\font\sevenrm=cmr7
\font\sevenit=cmti7
\font\seveni=cmmi7
\font\sevensy=cmsy7
\font\sevengt=eufm7

\font\fivenrm=cmr5
\font\fiveni=cmmi5
\font\fivensy=cmsy5
 \font\tenex=cmex10

\def\nine{%
\textfont0=\ninerm \scriptfont0=\sevenrm \scriptscriptfont0=\fivenrm
\textfont1=\ninei \scriptfont1=\seveni \scriptscriptfont1=\fiveni
\textfont2=\ninesy \scriptfont2=\sevensy \scriptscriptfont2=\fivensy
\textfont3=\tenex \scriptfont3=\tenex \scriptscriptfont3=\tenex
\def\rm{\fam0\ninerm}%
\textfont\itfam=\nineit
\def\it{\fam\itfam\nineit}%
\textfont\bffam=\ninebf
\def\bf{\fam\bffam\ninebf}%
%\textfont\gtfam=\ninegt
%\def\gt{\fam\gtfam\ninegt}%
\normalbaselineskip=11pt
\setbox\strutbox=\hbox{\vrule height8pt depth3pt width0pt}%
\normalbaselines\rm}

\textwidth30cc
\textheight44cc

\exhyphenpenalty100
\oddsidemargin0pt
\evensidemargin0pt
\topmargin-25pt
\headsep14pt

\def\luz#1{\luzno#1?}
\def\luzno#1{\ifx#1?\let\next=\relax\yyy
\else \let\next=\luzno#1\xxx\fi\next}
\def\sp#1{\def\xxx{\kern1.7pt}\def\yyy{\kern-1.7pt}\luz{#1}}
\def\spa#1{\def\xxx{\kern1pt}\def\yyy{\kern-1pt}\luz{#1}}

\newcount\beg
\newbox\aabox
\newbox\atbox
\newbox\fpbox
\def\lewyhead{\noindent\rlap{\nine\the\count0}\hfil\copy\aabox\hfil}
\def\prawyhead{\noindent\hfill\copy\atbox\hfill\llap{\nine\the\count0}}
\def\ps@bcp{\let\@mkboth\markboth
\def\@oddhead{\ifnum\beg=\count0
\else\prawyhead\fi}\def\@evenhead{\lewyhead}%
\def\@oddfoot{\ifnum\beg=\count0\hfill\nine[\the\count0]\hfill\fi}%
\def\@evenfoot{}}
\def\abbrevauthors#1{\setbox\aabox=\hbox{\sevenrm\uppercase{#1}}}
\def\abbrevtitle#1{\setbox\atbox=\hbox{\sevenrm\uppercase{#1}}}
\long\def\pag{\beg=\count0
\def\phead{\setbox\fpbox=\hbox{\sevenrm
************************************************}%
\noindent\vbox{\sevenrm\baselineskip9pt\hsize\wd\fpbox%
\vglue-30truept
\centerline{************************************************}

\centerline{BANACH CENTER PUBLICATIONS, VOLUME **}

\centerline{INSTITUTE OF MATHEMATICS}

\centerline{POLISH ACADEMY OF SCIENCES}

\centerline{WARSZAWA 199*}}\hfill}
\phead}

\newbox\tbox
\newbox\aubox
\newbox\adbox
\newbox\mathbox

\def\title#1{\setbox\tbox=\hbox{\let\\=\cr
\baselineskip14pt\vbox{\twbf\tabskip 0pt plus15cc
\halign to\hsize{\hfil\ignorespaces \uppercase{##}\hfil\cr#1\cr}}}}

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

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

\def\address#1{\setbox\adbox=\hbox{\let\\=\cr
\nine\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\mathclass#1{\setbox\mathbox=\hbox{\vfootnote{}{1991 {\it Mathematics
Subject
Classification}\/: #1}{}}}

\long\def\maketitlebcp{\pag\unhbox\mathbox
\vfootnote{}{The paper is in final form and no version
of it will be published elsewhere.}{}
\vglue7cc
\box\tbox
\box\abbox
\vskip8pt}

\long\def\abstract#1{{\nine{\bf Abstract.}
#1

}}

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

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

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

\def\Proof{\vskip-\lastskip\vskip4pt plus2pt
\sp{Proo{f.}\ }\ignorespaces}
\def\Pf#1{\vskip-\lastskip\vskip4pt plus2pt
\sp{#1\ }\ignorespaces}

\def\endproof{\nobreak\kern5pt\nobreak\vrule height4pt width4pt depth0pt
\vskip4pt plus2pt}

\def\vsk{\vskip4pt plus2pt}
\newbox\refbox
\newdimen\refwidth
\long\def\refs#1#2{{\nine
\setbox\refbox=\hbox{\nine[#1]}\refwidth\wd\refbox\advance\refwidth by
12pt%
\def\textindent##1{\indent\llap{##1\hskip12pt}\ignorespaces}% PLAIN
\vskip24pt plus4pt minus4pt
\centerline{\bf References}
\vskip12pt plus2pt minus2pt
\parindent=\refwidth
#2

}}

\def\footnoterule{\kern -3pt \hrule width 4cc \kern 2.6pt}

%\catcode`@=11
\def\vfootnote#1%
{\insert\footins\bgroup\nine\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}
\def\footnt#1#2{$(^{#1})$\vfootnote{$(^{#1})$}{#2}}
%\catcode`@=12

\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{}}
%\skip\footins=\bigskipamount % space added when footnote is present
%\count\footins=1000 % footnote magnification factor (1 to 1)
%\dimen\footins=8in % maximum footnotes per page

\flushbottom
\baselineskip13pt

\endinput



