%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                 %
%              This file contains the macros for the              %
%                                                                 %
%                   Volume 22-2 (2004) of the                     %
%                          By DOHERTY ANDRADE                     %
%                                                                 %
%      Boletim da Sociedade Paranaense de Matematica v 1          %
%                                                                 %
% You are free to distribute this file without any modification.  %
% For inprovements, modifications and suggestions contact the     %
% author by the e-mail:                                           %
%                                                                 %
%                                                                 %
%                   http://www.spm.uem.br                         %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%
%       Typeout to inform the style
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\W@{\immediate\write\sixt@@n}
\def\spaces{\space\space}
\def\space@{\space\space\space\space}
\def\space@@{\space@\space@\space@\space@}
\def\CR@{\W@{}
\W@{\space@\space@
***************************************************************}
\W@{\space@\space@
*\space@@\space@@\space@@\space@\space@\space@\space *}
\W@{\space@\space@ *\space@@\spaces This is the Style for
the\space@@\spaces *} \W@{\space@\space@ *\spaces Boletim da
Sociedade Paranaense de Matematica
    (INGLES)\space *}
\W@{\space@\space@ *\space@@\space@@\space@@\space@\space@\space@\space *}
\W@{\space@\space@ *\space@\space@\spaces\space (c) Sociedade Paranaense de
    Matematica\space@\space@\spaces\spaces *}
\W@{\space@\space@ *\space@@\space@@\space@@\space@\space@\space@\space *}
\W@{\space@\space@ ***************************************************************}
\W@{}}
\CR@
\everyjob{\CR@}
%
%       %%%%%%%%%%%%%%%
%       Initializations
%       %%%%%%%%%%%%%%%
%
\def\empty{}
\toksdef\toks@=0
\def\@author{}
\def\@shortauthors{}
\def\@\shorttitle{}
\mathchardef\@m=1000
\mathchardef\@M=10000
\catcode`\@=11
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%
%       Some Auxiliar definitions
%       %%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\g@addto@macro#1#2{{%
  \toks@\expandafter{#1#2}%
  \xdef#1{\the\toks@}}}
%
\def\@addpunct#1{\ifnum\spacefactor>\@m \else#1\fi}
%
\let\@xp=\expandafter
\let\@nx=\noexpand
%
\def\@ifempty#1{\@xifempty#1@@..\@nil}
%
\long\def\@xifempty#1#2@#3#4#5\@nil{%
  \ifx#3#4\@xp\@firstoftwo\else\@xp\@secondoftwo\fi}
%
\long\def\@ifnotempty#1{\@ifempty{#1}{}}
%
\long\def\@makefntext#1{\parindent 1em\noindent
 \hbox to 1.8em{\hss$^{\@thefnmark}$}\hspace{1.5mm}#1}
%
%       %%%%%%%%%%%%%%%%%%%%%%
%       The dimensions of page
%       %%%%%%%%%%%%%%%%%%%%%%
%
%
\textheight=190mm
\textwidth=126mm
\evensidemargin=21mm
\oddsidemargin=21mm
%
%      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      The definition of the style for the first page
%      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%   Definition of the command line
%
%
\def\novafigura#1{%
   \def\linha##1##2##3##4##5##6{%
      \put(##1,##2){\special{em:point #1##3}}%
      \put(##4,##5){\special{em:point #1##6}}%
      \special{em:line #1##3,#1##6}}}%
%
\novafigura{}%
%
%
%
%    Definicao do comando curva
%
%
%
\newcounter{@sc}%
\newcounter{@scp}%
\newcounter{@t}%
\newlength{\@x}%
\newlength{\@xa}%
\newlength{\@xb}%
\newlength{\@y}%
\newlength{\@ya}%
\newlength{\@yb}%
\newsavebox{\@pt}%
\def\curva#1(#2,#3)(#4,#5)(#6,#7){\c@@sc#1\relax%
 \c@@scp\c@@sc \advance\c@@scp\@ne%
 \@xb #4\unitlength \advance\@xb -#2\unitlength \multiply\@xb \tw@%
 \@xa #6\unitlength \advance\@xa -#2\unitlength%
 \advance\@xa -\@xb \divide\@xa\c@@sc%
 \@yb #5\unitlength \advance\@yb -#3\unitlength \multiply\@yb \tw@%
 \@ya #7\unitlength \advance\@ya -#3\unitlength%
 \advance\@ya -\@yb \divide\@ya\c@@sc%
 \setbox\@pt\hbox{\vrule height\@halfwidth depth\@halfwidth%
 width\@wholewidth}\c@@t\z@%
 \put(#2,#3){\@whilenum{\c@@t<\c@@scp}\do%
 {\@x\c@@t\@xa \advance\@x\@xb \divide\@x\c@@sc \multiply\@x\c@@t%
 \@y\c@@t\@ya \advance\@y\@yb \divide\@y\c@@sc \multiply\@y\c@@t%
 \raise \@y \hbox to \z@{\hskip \@x\unhcopy\@pt\hss}\advance\c@@t\@ne}}}%
%
%
%
\def\first@reset{\restorecr
 \def\baselinestretch{1}%
 \ifx\undefined\@newbaseline% NFSS not present; 2.09 or 2e
 \ifx\@currsize\normalsize\@normalsize\else\@currsize\fi%
 \else% NFSS (2.09) present
 \@newbaseline%
 \fi}
%
%
\def\ps@firstpage{\first@reset\let\@mkboth\@gobbletwo
 \def\@oddhead{\parbox[t]{\textwidth}{\hskip-3mm%
%
%
\unitlength=0.06mm%
\special{em:linewidth 0.23pt}%
\linethickness{0.23pt}%
\begin{scriptsize}%
  \hspace*{10mm}\begin{tabular}{l}
   {\sf Bol. Soc. Paran. Mat.}\\
      ({\sc 3s.\/}) {\bf v. 22} {\sc 2} (2004):
   {\sc \pageref{paginainicial}--\pageref{paginafinal}}.\\
   {\sc \copyright SPM --ISNN-00378712}\\%
  \end{tabular}
   \end{scriptsize}}}
 \def\@oddfoot{\parbox[b]{\textwidth}{\begin{scriptsize}%
        \hspace*{63mm}{\rm\normalsize\thepage}\hspace*{\fill}%
        \begin{tabular}[b]{l}
         Typeset by \bspm style.\\
         \copyright\ Soc. Paran. Mat.\\
        \end{tabular}
   \end{scriptsize}}}
 \def\@evenhead{}\def\@evenfoot{}}
%
%        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%        The definition for a generic page
%        %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\ps@bspm{\let\@mkboth\markboth
\def\@oddfoot{}\def\@evenfoot{}
\def\@evenhead{\rm\thepage\hfil{\small\sc\@shortauthors}\hfil}
\def\@oddhead{\hbox{}\hfil{\small\sc\@shorttitle}\hfil\rm\thepage}}
%
\pagestyle{bspm}
%
%       %%%%%%%%%%%%
%       The Abstract
%       %%%%%%%%%%%%
%
\def\abstractname{abstract} % <--------------------------
\def\abstract{%
\let\thanks\relax
\setcounter{footnote}{0}
\footnotesize\quotation{\noindent{\small\sc \abstractname:}}\ }%
\def\endabstract{\endquotation}%
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       The command for generating the Mathematics Subject Classification
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\mathclass#1{\par%
 \insert\footins{\hskip -1.2mm\footnotesize{\it\textup{1991} Mathematics
   Subject Classification:} #1}}

\def\2000mathclass#1{\par%
 \insert\footins{\hskip -1.2mm\footnotesize{\it\textup{2000} Mathematics
   Subject Classification:} #1}}
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       The command for generating the title
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\renewcommand{\title}[2][]{\def\@@title{#1}
  \ifx\@@title\empty
    \def\@shorttitle{#2}
  \else
    \def\@shorttitle{#1}
  \fi
\thispagestyle{firstpage}\label{paginainicial}
\def\@title{#2}\let\title\relax}
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       The command for generating the author name
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\andname{and} % <------------------------------
\renewcommand{\author}[2][]{\def\@@authors{#1}
  \ifx\@@authors\empty
    \ifx\@shortauthors\empty
      \def\@shortauthors{#2}
    \else
      \g@addto@macro\@shortauthors{ \andname{} #2}
    \fi
  \else
    \ifx\@shortauthors\empty
      \def\@shortauthors{#1}
    \else
      \g@addto@macro\@shortauthors{ \andname{} #1}
    \fi
  \fi
  \ifx\@author\empty
    \def\@author{#2}
  \else
    \g@addto@macro\@author{ \andname{} #2}
  \fi}
%
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     The command for generate e-mails
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\email#1{%
\g@addto@macro\@address{\\ E-mail address: {\tt #1}}}
%
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     The command to set the title
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\maketitle{
 \vglue10mm
 \textwidth=115mm
 \begin{center}
 {\par\bf\@title}
 \vskip7mm
 {\footnotesize\@author\par}
 \vskip3mm
 \end{center}
 \textwidth=126mm
 }
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       The command to generate the address
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\address#1{%
  \ifx\@address\empty
    \def\@address{#1}
  \else
    \g@addto@macro\@address{\\[3mm] \andname\\[3mm] #1}
  \fi}
\def\@address{}
%
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     The command to set the address properly
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\@setaddress{%
 \vskip6mm plus2mm minus2mm
 \begin{footnotesize}
 \it
 \begin{tabular}{l}
    \@address\\
 \end{tabular}
 \end{footnotesize}}
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       The command for the receiving
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\receive#1#2{%
 \vspace{\fill}
 \hspace{\fill}\parbox{5cm}{%
  \begin{small}
   \begin{sc}
    #1\\
    #2 \par
   \end{sc}
 \end{small} }\hspace*{1cm}%
\vspace{1cm}
\footnotesep 5mm}
%
%       %%%%%%%%%%%%%%%%%%%%
%       The "thanks" command
%       %%%%%%%%%%%%%%%%%%%%
%
\def\thanks#1{%
   \def\thefootnote{\fnsymbol{footnote}}
   \def\@makefnmark{\hskip-.8mm\hbox{$^{\@thefnmark}$}\hskip-.5mm}%
   \footnote{#1}}
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       The definitions of Sectioning structure
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%      Modifications in the command \@sect
%
\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
     \def\@svsec{}\else
     \refstepcounter{#1}\edef\@svsec{\csname the#1\endcsname{.}\hskip2.1mm}\fi
     \@tempskipa #5\relax
      \ifdim \@tempskipa>\z@
        \begingroup #6\relax
          \@hangfrom{\hskip #3\relax\@svsec}{\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\@svsec
         \@ifnotempty{#8}{\ignorespaces#8\unskip\@addpunct.}%
         \csname #1mark\endcsname
                      {#7}\addcontentsline
                           {toc}{#1}{\ifnum #2>\c@secnumdepth \else
                             \protect\numberline{\csname the#1\endcsname}\fi
                       #7}}\fi
     \@xsect{#5}}
%
%     sections with different spacing
%
\def\section{\@startsection{section}{1}{\z@}%
  {.7\baselineskip plus .8\baselineskip}{.5\baselineskip}%
  {\normalsize\bf\centering}}
\def\subsection{\@startsection{subsection}{2}{\z@}%
 {.5\baselineskip plus.5\baselineskip}{-.4em}{\normalsize\sc}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}%
 {.5\baselineskip plus.5\baselineskip}{-.4em}{\normalsize\it}}
\def\paragraph{\@startsection{paragraph}{4}{\z@}{1.5ex plus
   0.2ex minus .1ex}{-.5em}{\normalsize}}
\def\subparagraph{\@startsection{subparagraph}{5}{\parindent}{1.5ex plus
   0.2ex minus .1ex}{-.5em}{\normalsize}}
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       The definition of the bibliography
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\refname{References} % <---------------------------------
\def\thebibliography#1{\section*{\refname}\labelsep.5em\list
 {\arabic{enumi}.}{\settowidth\labelwidth{#1}%
 \footnotesize\addtolength{\baselineskip}{-.3mm}
 \leftmargin\labelwidth
 \advance\leftmargin\labelsep
 \addtolength{\itemsep}{-.6mm}
 \usecounter{enumi}}
 \def\newblock{\hskip .11em plus .33em minus .07em}
 \sloppy\clubpenalty\@M\widowpenalty\clubpenalty
 \sfcode`\.=\@m\relax}
\let\endthebibliography=\endlist
%
\def\@cite#1#2{{\hskip1.5pt minus.5pt
[#1\if@tempswa , #2\fi]}}
%
\def\@citex[#1]#2{%
  \let\@citea\@empty
  \@cite{\@for\@citeb:=#2\do
    {\@citea\def\@citea{,\penalty\@m}%\ }%
     \edef\@citeb{\expandafter\@iden\@citeb}%
     \if@filesw\immediate\write\@auxout{\string\citation{\@citeb}}\fi
     \@ifundefined{b@\@citeb}{{\reset@font\bfseries ?}%
       \G@refundefinedtrue\@latex@warning
       {Citation `\@citeb' on page \thepage \space undefined}}%
     {\hbox{\csname b@\@citeb\endcsname}}}}{#1}}
%
%      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      Redefiniton of the \end{document}
%      %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\def\enddocument{%
   \@setaddress
   \label{paginafinal}%
   \@checkend{document}%
   \clearpage
   \begingroup
      \if@filesw
         \immediate\closeout\@mainaux
         \def\global\@namedef##1##2{}%
         \def\newlabel{\@testdef r}%
         \def\bibcite{\@testdef b}
         \@tempswafalse
         \makeatletter \input\jobname.aux
         \if@tempswa
            \@warning{Label(s) may have changed.
                  Rerun to get cross-references right}%
         \fi
      \fi
   \endgroup\deadcycles\z@\@@end}
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       The logos for the style in lowercase
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newcommand{\bspm}{{${\cal B}$\kern-.2mm\hbox{$^{\cal S}$}\kern-.25mm%
${\cal P}$\kern-2mm\lower 0.7mm\hbox{$_{\cal M}$}}}
%
\def\TeX{T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}
%
\def\LaTeXe{{L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em%
T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX%
\kern.15em 2${}_{\textstyle\varepsilon}$}}
%
\def\LaTeX{{L\kern-.36em\raise.3ex\hbox{\sc a}\kern-.15em%
T\kern-.1667em\lower.7ex\hbox{E}\kern-.125emX}}
%
\def\AmS{{$\cal A$\kern-.1667em\lower.5ex\hbox{$\cal M$}%
\kern-.125em$\cal S$}}
%
\def\AmSLaTeX{\AmS-\LaTeX}
%
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%       The command for generating motto
%       %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\def\motto#1#2{%
    \hspace*{\fill}\parbox{7cm}{\vskip2mm
    \par\footnotesize\sf
      \addtolength{\baselineskip}{-.4mm} #1\\[1.5mm]
      \hspace*{\fill}{\bf #2}
      \vskip3mm}}
%
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     Theorems and Related Structures
%     %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\newtheorem{thm}{Theorem}[section]
\newtheorem{lem}{Lemma}[section]
\newtheorem{cor}{Corollary}[thm]
\renewcommand{\thecor}{\thethm{\small\Alph{cor}}}
\newtheorem{prop}{Proposition}[section]
\newtheorem{conj}{Conjecture}
\newtheorem{prob}{Problem}
\newtheorem{note}{Note}
\newtheorem{claim}{Claim}
\newtheorem{case}{Case}
\newtheorem{alg}{Algorithm}
\newtheorem{crit}{Criterion}
\newtheorem{Defn}{Definition}[section]
\newtheorem{Exmp}{Example}[section]
\newtheorem{Rem}{Remark}[section]
\newtheorem{Summ}{Summary}
\newcommand{\keywords}{\noindent {\hskip 26pt Key Words:\,}}
%
\newenvironment{defn}[1][]{\def\@teotest{#1}
 \ifx\@teotest\empty
    \begin{Defn}\list{}{\leftmargin4mm\rightmargin4mm}%
       \item[]\rm\hskip-\leftmargin
 \else
    \begin{Defn}[#1]\rm\list{}{\leftmargin4mm\rightmargin4mm}
       \item[]\rm\hskip-\leftmargin
 \fi}{\endlist\end{Defn}}
\newenvironment{exmp}[1][]{\def\@teotest{#1}
 \ifx\@teotest\empty
  \begin{Exmp}\rm
 \else
  \begin{Exmp}[#1]\rm
 \fi}{\end{Exmp}}
%
\newenvironment{rem}[1][]{\def\@teotest{#1}
 \ifx\@teotest\empty
  \begin{Rem}\list{}{\leftmargin4mm\rightmargin4mm}%
        \item[]\rm\hskip-\leftmargin
 \else
  \begin{Rem}[#1]\list{}{\leftmargin4mm\rightmargin4mm}
         \item[]\rm\hskip-\leftmargin
 \fi}{\endlist\end{Rem}}
%
\newenvironment{summ}[1][]{\def\@teotest{#1}
\def\@teotest{#1}
 \ifx\@teotest\empty
  \begin{Summ}\list{}{\leftmargin4mm\rightmargin4mm}%
        \item[]\rm\hskip-\leftmargin
 \else
  \begin{Summ}[#1]\list{}{\leftmargin4mm\rightmargin4mm}%
        \item[]\rm\hskip-\leftmargin
 \fi}{\endlist\end{Summ}}
%
\newenvironment{ack}{\section*{Acknowledgments}}{}
%
\newenvironment{pf*}[1]{%
  \vskip1ex plus.2ex minus.2ex\noindent{\it #1.}\hskip.5em}{%
  \hspace*{\fill}\qed\vskip1ex}
%
\newenvironment{pf}{%
 \vskip1ex plus.3ex minus.3ex\noindent{\bf Proof:}\hskip.5em}{%
 \hspace*{\fill}\qed\vskip1ex}
%
\def\qed{\hfill$\Box$\medskip}
%{\hskip-2pt\rule{.7ex}{1.8ex}\hskip2pt} this part is old
%
%       %%%%%%%%%%%%%%%%
%       End of the file.
%       %%%%%%%%%%%%%%%%