%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                         pms.sly                                   %%
%%  Probability and Mathematical Statistics package file             %%
%%                      Version 1.1                                  %%
%%                  April 15, 2017                                 %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% This file was prepared by:                                        %%
%% Marek Czysto\'lowski                                              %%
%% Mathematical Institute, Wroc\'law University                      %%
%% pl. Grunwaldzki 2/4                                               %%
%% 50-384 Wroc\'law                                                  %%
%% Poland                                                            %%
%% Please submit any bugs and comments to:                           %%
%%  Marek.Czystolowski@math.uni.wroc.pl                              %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%      LaTeX 2e style file for the processing of LaTeX2e files      %%
%%          of Probability and Mathematical Statistics               %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\ProvidesPackage{pms}[2017/04/17 v1.1 Probability and Mathematical
                    Statistics package file]
\NeedsTeXFormat{LaTeX2e}

%\RequirePackage{mathptmx}
\RequirePackage{times}
\RequirePackage{amsthm}
\RequirePackage{amssymb}
\RequirePackage[leqno,intlimits,sumlimits,tbtags]{amsmath}
\RequirePackage{graphicx}
\RequirePackage{soul}
\RequirePackage{exscale,relsize}
\RequirePackage[numbers]{natbib}
\RequirePackage{geometry}
\RequirePackage[labelsep=period]{caption}
\RequirePackage[bookmarksnumbered=true, bookmarksopen=true, hyperfootnotes=false]{hyperref}
\geometry{paperwidth=168mm, paperheight=238mm, top=20mm}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                      Page settings                                %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setlength  {\headsep}        {5 truemm}
\setlength  {\headheight}     {2 cc}
\setlength  {\footskip}       {0 mm}
\setlength  {\textwidth}      {28 cc}
\setlength  {\textheight}     {196.833 mm}
%\setlength  {\topmargin}      {-13  truemm}
\setlength  {\oddsidemargin}  {-7 mm}
\setlength  {\evensidemargin} {-2 mm}

%\sqrt{\smash[b]{cos}]
\newlength\@testLength
\setlength\@testLength{0pt}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%               Authors and submission information                  %%
%%                      Inserted by author                           %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcounter{numAuthors}

\renewcommand   {\title}        [1] {\def\@title{\uppercase{#1}}}
\newcommand     {\ShortTitle}   [1] {\def\@shorttitle{#1}}
\newcommand     {\ShortAuthors} [1] {\def\@shortauthors{#1}}
\newcommand     {\titlethanks} [1] {\def\@thetitleadds{#1}}        %remove it
\newcommand     {\dedicated}    [1] {\def\@inmemory{#1}}

\newcommand     {\NumberOfAuthors}  [1] {\setcounter{numAuthors}{#1}}


\newcommand     {\FirstAuthor}  [1] {\def\@authori{\uppercase{\nameSo{#1}}}\def\@authoripdf{#1}}
\newcommand     {\SecondAuthor} [1] {\def\@authorii{\uppercase{\nameSo{#1}}}\def\@authoriipdf{#1}}
\newcommand     {\ThirdAuthor}  [1] {\def\@authoriii{\uppercase{\nameSo{#1}}}\def\@authoriiipdf{#1}}
\newcommand     {\FourthAuthor} [1] {\def\@authoriv{\uppercase{\nameSo{#1}}}\def\@authorivpdf{#1}}
\newcommand     {\FifthAuthor}  [1] {\def\@authorv{\uppercase{\nameSo{#1}}}\def\@authorvpdf{#1}}
\newcommand     {\SixthAuthor}  [1] {\def\@authorvi{\uppercase{\nameSo{#1}}}\def\@authorvipdf{#1}}

\newcommand     {\FirstAuthorAffiliation}  [1] {\def\@Affiliationi{#1}}
\newcommand     {\SecondAuthorAffiliation} [1] {\def\@Affiliationii{#1}}
\newcommand     {\ThirdAuthorAffiliation}  [1] {\def\@Affiliationiii{#1}}
\newcommand     {\FourthAuthorAffiliation} [1] {\def\@Affiliationiv{#1}}
\newcommand     {\FifthAuthorAffiliation}  [1] {\def\@Affiliationv{#1}}
\newcommand     {\SixthAuthorAffiliation}  [1] {\def\@Affiliationvi{#1}}

\newcommand     {\FirstAuthorAddress}  [1] {\def\@addressi{#1}}
\newcommand     {\SecondAuthorAddress} [1] {\def\@addressii{#1}}
\newcommand     {\ThirdAuthorAddress}  [1] {\def\@addressiii{#1}}
\newcommand     {\FourthAuthorAddress} [1] {\def\@addressiv{#1}}
\newcommand     {\FifthAuthorAddress}  [1] {\def\@addressv{#1}}
\newcommand     {\SixthAuthorAddress}  [1] {\def\@addressvi{#1}}

\newcommand     {\FirstAuthorCity}  [1] {\def\@cityi{#1}}
\newcommand     {\SecondAuthorCity} [1] {\def\@cityii{#1}}
\newcommand     {\ThirdAuthorCity}  [1] {\def\@cityiii{#1}}
\newcommand     {\FourthAuthorCity} [1] {\def\@cityiv{#1}}
\newcommand     {\FifthAuthorCity}  [1] {\def\@cityv{#1}}
\newcommand     {\SixthAuthorCity}  [1] {\def\@cityvi{#1}}

\newcommand     {\FirstAuthorURL}  [1] {\def\@URLi{#1}}
\newcommand     {\SecondAuthorURL} [1] {\def\@URLii{#1}}
\newcommand     {\ThirdAuthorURL}  [1] {\def\@URLiii{#1}}
\newcommand     {\FourthAuthorURL} [1] {\def\@URLiv{#1}}
\newcommand     {\FifthAuthorURL}  [1] {\def\@URLv{#1}}
\newcommand     {\SixthAuthorURL}  [1] {\def\@URLvi{#1}}

\newcommand     {\FirstAuthorEmail}   [1] {\def\@emaili{#1}}
\newcommand     {\SecondAuthorEmail}  [1] {\def\@emailii{#1}}
\newcommand     {\ThirdAuthorEmail}   [1] {\def\@emailiii{#1}}
\newcommand     {\FourthAuthorEmail}  [1] {\def\@emailiv{#1}}
\newcommand     {\FifthAuthorEmail}   [1] {\def\@emailv{#1}}
\newcommand     {\SixthAuthorEmail}   [1] {\def\@emailvi{#1}}

\newcommand     {\FirstAuthorThanks}   [1] {\def\@thanksi{#1}}
\newcommand     {\SecondAuthorThanks}  [1] {\def\@thanksii{#1}}
\newcommand     {\ThirdAuthorThanks}   [1] {\def\@thanksiii{#1}}
\newcommand     {\FourthAuthorThanks}  [1] {\def\@thanksiv{#1}}
\newcommand     {\FifthAuthorThanks}   [1] {\def\@thanksv{#1}}
\newcommand     {\SixthAuthorThanks}   [1] {\def\@thanksvi{#1}}

\newcommand     {\FirstAuthorExtraThanks}   [1] {\def\@thanksExtrai{#1}}

\newcommand     {\keywords} [1] {\def\@thekeywords{#1}}
\newcommand     {\MSCcodes} [1] {\def\@theMSCcodes{#1}}

\newcommand     {\breakBeforeAnd}[1]   {\def\@andNextLine{#1}}
\newcommand     {\breakAfterFirstAuthor}[1]   {\def\@firstAuthorNextLine{#1}}
\newcommand     {\breakAfterSecondAuthor}[1]   {\def\@secondAuthorNextLine{#1}}
\newcommand     {\breakAfterThirdAuthor}[1]   {\def\@thirdAuthorNextLine{#1}}
\newcommand     {\breakAfterFourthAuthor}[1]   {\def\@fourthAuthorNextLine{#1}}
\newcommand     {\tmpCodesDist}[1]   {\def\@codesDist{#1}}

\newlength \swiatloAutor
\setlength{\swiatloAutor}{0pt}
\breakAfterFirstAuthor{}
\breakBeforeAnd{}
\tmpCodesDist{}
\FirstAuthorExtraThanks{}
\SixthAuthor{} %                                %information about sixth author
\SixthAuthorCity{} %
\SixthAuthorAffiliation{}%
\SixthAuthorAddress{} %
\SixthAuthorEmail{}%
\SixthAuthorThanks{}%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                    Submission information                         %%
%%                      Inserted by editor                           %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand     {\received}     [1] {\def\@receivedDate{#1}}
\newcommand     {\lastrevision} [1] {\def\@revisionDate{#1}}
\newcommand     {\firstpage}    [1] {\def\@thefirstpage{#1}}
\newcommand     {\volume}       [1] {\def\@thevolume{#1}}
\newcommand     {\fasc}         [1] {\def\@thefasc{#1}}
\newcommand     {\years}        [1] {\def\@theyears{#1}}
\newcommand     {\recordnumber} [1] {\def\@therecord{#1}}
\newcommand     {\pages}        [1] {\def\@thepages{#1}}

\sodef\headSo{\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}}{0.1em}{.55em\@plus.08em\@minus.06em}{.55em\@plus.275em\@minus.183em}
\sodef\n{}{0.1em}{.45em\@plus.08em\@minus.06em}{0.55em\@plus.275em\@minus.183em}
\sodef\proofSo{}{0.2em}{.55em\@plus.08em\@minus.06em}{0.25em}
\sodef\nameSo{}{0.15em}{.55em\@plus.08em\@minus.06em}{0.25em}
\def\and{{and~}}
\def\etal{{et~al.}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                      Headings definitions                         %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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\def\scriptsize{\@setsize\scriptsize{9pt}\viipt\@viipt}         %consider where to put it

\newcommand     {\updatemarkboth}{
    \markboth
        {\mbox{\textup{\headSo{\@shortauthors}}}}
        {\mbox{\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{it} \@shorttitle}}
        \evenhead{%
            \hbox to\textwidth{\rlap{\parbox[b]{\textwidth}{\raggedright\thepage}}%
                                \rlap{\parbox[b]{\textwidth}{\centering\leftmark}}%
                               \rlap{\parbox{\textwidth}{\hspace{0pt}\vspace{14pt}\hrule}}
                              }%
                }%
        \oddhead{%
            %\dimen3=2pt
            %\setlength{\tempc}{1pt}
            %\settowidth{\dimen2}{\thepage} \dimen1=\textwidth \advance\dimen1 by -\dimen2 \advance\dimen1 by -\dimen3%
            %\parbox{\textwidth}{\parbox{\dimen1}{\centering\small\slshape\rightmark}%
            %                    \thepage\vspace{2pt}\hrule%
            %                    }%
            \hbox to\textwidth{\rlap{\parbox[b]{\textwidth}{\centering\fontsize{10pt}{11pt}\usefont{T1}{ptm}{m}{sl}\rightmark}}%
                               \rlap{\parbox[b]{\textwidth}{\raggedleft\thepage}}%
                               \rlap{\parbox{\textwidth}{\hspace{0pt}\vspace{14pt}\hrule}}%
                               }%
                }%
    }

\newcommand     {\runninghead} [1] {\def\@runninghead{#1}}

\pagestyle{myheadings}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                      Title page - macros                          %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\footnotesep 10pt \skip\footins 8pt plus 40pt minus 2pt
\def\footnoterule{\kern+4.5pt \hrule width 1.8cm \kern 6.6pt }
\def\@fnsymbol#1{\ensuremath{\ifcase#1\or*\or {**}\or {*\!*\!*}
     \or{****}\or {*****}
    \mathchar "278\or \mathchar "27B\or \|\or **\or \dagger\dagger
    \or \ddagger\ddagger \else\@ctrerr\fi}}


\renewcommand\@makefntext[1]%
{\makebox[24pt][r]{\textsuperscript{\@thefnmark}}#1}

\newcounter{footnotesCounter}
\setcounter{footnotesCounter}{0}

%%%%% font definitons
\def\fontTitle{\fontsize{10.3pt}{13.5pt}\usefont{T1}{ptm}{b}{n}}%
\def\fontBy{\fontsize{6.2pt}{11pt}\usefont{T1}{ptm}{b}{n}}%
\def\fontAuthor{\fontsize{8.5pt}{10.5pt}\usefont{T1}{ptm}{b}{n}}%
\def\fontCity{\fontsize{8pt}{10pt}\usefont{T1}{ptm}{b}{sc}}%
\def\fontMemory{\fontsize{10pt}{12pt}\usefont{T1}{ptm}{m}{it}}%
\def\fontAbstract{\fontsize{8.5pt}{11pt}\usefont{T1}{ptm}{m}{n}}%
\def\fontSection{\fontsize{8.5pt}{10pt}\usefont{T1}{ptm}{b}{n}}
\def\fontSubSection{\fontsize{10.5pt}{10pt}\usefont{T1}{ptm}{b}{n}}
\def\fontSubSubSection{\fontsize{10.5pt}{10pt}\usefont{T1}{ptm}{m}{it}}
%%%%% end font definitons
%
%
%


\def\maketitle{
\updatemarkboth
\linespread{1}
\setcounter{page}{\@thefirstpage}
\thispagestyle{empty}
\parindent=0pt
\newlength\ciach
\setlength\ciach{7.395 cc}
%
%
%%%%%%%logo%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\parbox[t]{7.395 cc}{\ \vspace{-1.3cm}\\ %
\baselineskip 4.5pt
\centering\fontsize{6.61pt}{9pt}\usefont{T1}{ptm}{b}{n}
PROBABILITY\\
AND\\
MATHEMATICAL STATISTICS\\
\vspace{2.8pt}\hrule width 7.37cc depth 0.3pt\vspace{2.95pt}
\fontsize{6.25pt}{11pt}\usefont{T1}{ptm}{b}{n}
\hbox to\ciach{Vol.$~$\@thevolume, Fasc.$~$\@thefasc$~$(\@theyears), pp. \@thepages}\vspace*{-3pt}
\fontsize{6.25pt}{11pt}\usefont{T1}{ptm}{b}{n}\centering doi:\ifnum\@doiFlag>0 \else {10.19195/0208-4147.\@thevolume.\@thefasc.\@therecord}\fi
}
\par \vskip 5.95cc
%
%
%%%%%title and authors%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\vbox{
\centering
{\fontTitle\spaceskip=3pt \@title}\ifx\@thetitleadds\@empty\else\def\thefootnote{\fnsymbol{footnote}}\footnotemark\fi
\vskip 3pt
{\fontBy BY}
\vskip 5pt
{\fontAuthor\@authori}\ifx\@thanksi\@empty\else\def\thefootnote{\fnsymbol{footnote}}\footnotemark\fi\ifx\@cityi\@empty\else{\fontCity{\mbox{\hspace{1pt}} (\@cityi{\ifx\@thanksExtrai\@empty\else\def\thefootnote{\fnsymbol{footnote}}\footnotemark\fi})}}\fi
\ifnum \c@numAuthors>1
 \ifnum \c@numAuthors>2 , \ifx\@firstAuthorNextLine\@empty \else \linebreak \fi\mbox{\hspace{1pt}} \else \mbox{\hspace{4pt}}{\fontBy \ifx\@andNextLine\@empty \else \linebreak \fi AND \mbox{\hspace{1pt}}} \fi {\fontAuthor \@authorii}\ifx\@thanksii\@empty \else\def\thefootnote{\fnsymbol{footnote}}\footnotemark\fi\ifx\@cityii\@empty\else{\fontCity{\mbox{\hspace{1pt}} (\@cityii)}}\fi
\fi
\ifnum \c@numAuthors>2
 \ifnum \c@numAuthors>3 ,\ifx\@secondAuthorNextLine\@empty\mbox{\hspace{1pt}}\else\linebreak\fi\else ,\mbox{\hspace{4pt}}{\fontBy \ifx\@andNextLine\@empty \else\linebreak\\*[-12pt] \fi  AND \mbox{\hspace{1pt}}} \fi {\fontAuthor\@authoriii}\ifx\@thanksiii\@empty\else \def\thefootnote{\fnsymbol{footnote}}\footnotemark\fi\ifx\@cityiii\@empty\else{\fontCity{\mbox{\hspace{1pt}} (\@cityiii)}}\fi
\fi
%\ifnum \c@numAuthors>2
% \ifnum \c@numAuthors>3 ,\mbox{\hspace{1pt}} \else \mbox{\hspace{4pt}}{\fontBy \ifx\@andNextLine\@empty \else\linebreak\\*[\swiatloAutor] break \fi AND \mbox{\hspace{1pt}}} \fi {\fontAuthor \@authoriii}\ifx\@thanksiii\@empty \else \def\thefootnote{\fnsymbol{footnote}}\footnotemark\fi \ifx\@cityiii\@empty\else {\fontCity{\mbox{\hspace{1pt}} (\@cityiii)}}\fi
%\fi
\ifnum \c@numAuthors>3
 \ifnum \c@numAuthors>4 ,\ifx\@thirdAuthorNextLine\@empty \else \linebreak \fi\mbox{\hspace{1pt}} \else ,\mbox{\hspace{4pt}}{\fontBy \ifx\@andNextLine\@empty \else\linebreak \fi AND \mbox{\hspace{1pt}}} \fi {\fontAuthor \@authoriv}\ifx\@thanksiv\@empty \else \def\thefootnote{\fnsymbol{footnote}}\footnotemark\fi \ifx\@cityiv\@empty\else{\fontCity{\mbox{\hspace{1pt}} (\@cityiv)}}\fi
\fi
\ifnum \c@numAuthors>4
 \ifnum \c@numAuthors>5 ,\ifx\@fourthAuthorNextLine\@empty \else \linebreak \fi\mbox{\hspace{1pt}} \else ,\mbox{\hspace{4pt}}{\fontBy \ifx\@andNextLine\@empty \else\linebreak \fi AND \mbox{\hspace{1pt}}} \fi {\fontAuthor \@authorv}\ifx\@thanksv\@empty \else \def\thefootnote{\fnsymbol{footnote}}\footnotemark\fi \ifx\@cityv\@empty\else{\fontCity{\mbox{\hspace{1pt}} (\@cityv)}}\fi
\fi
\ifnum \c@numAuthors>5
 \mbox{\hspace{4pt}}{\fontBy \ifx\@andNextLine\@empty \else\linebreak \fi AND \mbox{\hspace{1pt}}} {\fontAuthor \@authorvi}\ifx\@thanksvi\@empty \else \def\thefootnote{\fnsymbol{footnote}}\footnotemark\fi \ifx\@cityvi\@empty\else{ \fontCity{\mbox{\hspace{1pt}} (\@cityvi)}}\fi
\fi
\ifx\@inmemory\@empty\vskip 8mm\else\vskip 4.5 mm\hfill\vbox{\flushright\fontMemory\@inmemory}\vskip 8mm\fi
}
\hypersetup{
  pdftitle=\@title,
  pdfauthor={\@authoripdf \ifnum \c@numAuthors>1 , \fi \@authoriipdf \ifnum \c@numAuthors>2 , \fi \@authoriiipdf \ifnum \c@numAuthors>3 , \fi \@authorivpdf \ifnum \c@numAuthors>4 , \fi\@authorvpdf \ifnum \c@numAuthors>5 , \fi\@authorvipdf},
  pdfproducer={Probability and Mathematical Statistics},
  pdfsubject={AMS Mathematics Subject Classification: \@theMSCcodes},
  pdfkeywords=\@thekeywords,
}
}



\renewenvironment{abstract}{\let\baselinestretch\@blstr\centering \fontAbstract \begin{minipage}{9cm}\parindent 20pt{\it Abstract.}}
{ \end{minipage}\ifx\@thetitleadds\@empty\else\stepcounter{footnotesCounter}\def\footnotesize{\@setsize\footnotesize{11pt}\viiipt\@ixpt}\def\thefootnote{\fnsymbol{footnote}}\footnotetext[\thefootnotesCounter]{$~$\@thetitleadds}\fi%
\ifx\@thanksi\@empty\else\stepcounter{footnotesCounter}\def\footnotesize{\@setsize\footnotesize{11pt}\viiipt\@ixpt}\def\thefootnote{\fnsymbol{footnote}}\footnotetext[\thefootnotesCounter]{$~$\@thanksi}\fi%
\ifx\@thanksExtrai\@empty \else \stepcounter{footnotesCounter} \def\footnotesize{\@setsize\footnotesize{11pt}\viiipt\@ixpt}\def\thefootnote{\fnsymbol{footnote}}\footnotetext[\thefootnotesCounter]{$~$\@thanksExtrai}\fi%
\ifx\@thanksii\@empty \else \stepcounter{footnotesCounter} \def\footnotesize{\@setsize\footnotesize{11pt}\viiipt\@ixpt}\def\thefootnote{\fnsymbol{footnote}}\footnotetext[\thefootnotesCounter]{$~$\@thanksii}\fi%
\ifx\@thanksiii\@empty \else \stepcounter{footnotesCounter} \def\footnotesize{\@setsize\footnotesize{11pt}\viiipt\@ixpt}\def\thefootnote{\fnsymbol{footnote}}\footnotetext[\thefootnotesCounter]{$~$\@thanksiii}\fi%
\ifx\@thanksiv\@empty \else \stepcounter{footnotesCounter} \def\footnotesize{\@setsize\footnotesize{11pt}\viiipt\@ixpt}\def\thefootnote{\fnsymbol{footnote}}\footnotetext[\thefootnotesCounter]{$~$\@thanksiv}\fi%
\ifx\@thanksv\@empty \else \stepcounter{footnotesCounter} \def\footnotesize{\@setsize\footnotesize{11pt}\viiipt\@ixpt}\def\thefootnote{\fnsymbol{footnote}}\footnotetext[\thefootnotesCounter]{$~$\@thanksv}\fi
\ifx\@thanksvi\@empty \else \stepcounter{footnotesCounter} \def\footnotesize{\@setsize\footnotesize{11pt}\viiipt\@ixpt}\def\thefootnote{\fnsymbol{footnote}}\footnotetext[\thefootnotesCounter]{$~$\@thanksvi}\fi\\
\ifx\@codesDist\@empty\else\hspace*{\@codesDist}\fi\setcounter{footnote}{0}\vbox{
\centering
\parbox{9cm}{
\par \vskip 2mm
\parskip=2.5pt \hangindent=15pt
    \par \parindent 20pt  \hangindent=0pt
  {\bf 2010 AMS Mathematics Subject Classification: }\@theMSCcodes
  \par\vskip 0.8mm\parindent 20pt\hangindent=0pt{\bf Key words and phrases:} \@thekeywords

 \vskip 3pt
 }}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                              Sections                             %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\parindent 20pt

\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}
\renewcommand{\theequation}{\thesection.\arabic{equation}}

\renewcommand\section{\setcounter{equation}{0} \parindent 20pt \@startsection {section}{1}{0 cm}%
                                   {18pt}%{18pt plus 1ex minus -.2ex}%
                                   {12pt}%{2.3ex \@plus.2ex}%
                                   {\centering\fontSection\spaceskip=3pt\MakeUppercase}}

\renewcommand\subsection{\@startsection{subsection}{2}{\z@\nolinebreak}
                     {1.5ex plus 0.5ex minus .2ex}{-1ex}
                     {\indent\fontSubSection}}

\let\presection=\subsection
\renewcommand{\subsection}[1]{\ifthenelse{\equal{#1}{}}{\presection{}}{\presection{#1}{\fontSubSection\hspace*{-1ex}.\hspace*{-3pt}\hspace*{1ex}}}}%
\newcommand{\subsectionnostop}[1]{\ifthenelse{\equal{#1}{}}{\presection{}}{\presection{#1}}}%
%\renewcommand{\subsection}{\presection{}}%

\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@\nolinebreak}
                     {1.5ex plus 0.5ex minus .2ex}{-1ex}
                     {\indent\fontSubSubSection}}

\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}%\protect\nolinebreak}%
                     {1.5ex plus 0.5ex minus .2ex}{-1ex}%
                     {\indent\fontSubSection}}

\let\presubsection=\subsubsection

\let\preparagraph=\paragraph
\renewcommand{\paragraph}[1]{\@ifnextchar \begin { \preparagraph{#1}}{\preparagraph{#1.}}}%


\let\@@seccntformat\@seccntformat
\renewcommand*{\@seccntformat}[1]{%
  \expandafter\ifx\csname @seccntformat@#1\endcsname\relax
    \expandafter\@@seccntformat
  \else
    \expandafter
      \csname @seccntformat@#1\expandafter\endcsname
  \fi
    {#1}%
}

\font\titleStest cmb10 at 15truept
\newcommand*{\@seccntformat@section}[1]{%
   \csname the#1\endcsname.
}

\newcommand*{\@seccntformat@subsection}[1]{%
  \csname the#1\endcsname.
}

\newcommand*{\@seccntformat@subsubsection}[1]{%
  {\fontSubSection \csname the#1\endcsname.}
}

\newcounter{nappendix} \setcounter{nappendix}{0}

\renewcommand{\appendix}{%
   \@ifstar{\ifnum \c@nappendix=0 \appendix@one \else \@latex@error{You can't use starred apppendix if you have %
                                     already used appendix command}\fi}%
   {\ifnum \c@nappendix=-1 \@latex@error{You have already used starred apppendix} \fi \appendix@s}%
}

\newcommand{\appendix@s}[1]{\ifnum \c@nappendix=0\section{Appendices}\vskip -2ex\fi
                             \addtocounter{nappendix}{1}\section*{APPENDIX \thenappendix$~$---$~$ #1}}

\newcommand{\appendix@one}{\setcounter{nappendix}{-1} \section{Appendix}}
%%\newcommand{\appendix@one}[1]{\setcounter{nappendix}{-1} \section{Appendix$~$---$~$ #1}}

\newcommand{\acknowledgements}{\paragraph{Acknowledgments}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                       Styles of Theorems                          %%
%%                  and NewThorems Environments                      %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\fontTheoremsPms{\fontsize{11pt}{10pt}\usefont{T1}{ptm}{m}{sc}}%
\def\fontSteps{\fontsize{11pt}{10pt}\usefont{T1}{ptm}{m}{n}}%
\font\titleThe cmcsc10 at 13truept
\parindent 20pt

\newtheoremstyle{pms}%
     {8pt plus 0ex minus 0ex}%      Space above
     {5pt plus 0ex minus 0ex}%      Space below
     {\let\baselinestretch\@blstr\it}%         Body font   %\baselineskip=15pt
     {\parindent}%         Indent amount (empty = no indent, \parindent = para indent)
     {\fontTheoremsPms}% Thm head font
     {.}%        Punctuation after thm head
     {.5em}%     Space after thm head: " " = normal interword space;
           %       \newline = linebreak
     {}%         Thm head spec (can be left empty, meaning `normal')

\newtheoremstyle{pmsExample}%
     {8pt plus 0ex minus 0ex}%      Space above
     {5pt plus 0ex minus 0ex}%      Space below
     {\let\baselinestretch\@blstr\normalfont}%         Body font
     {\parindent}%         Indent amount (empty = no indent, \parindent = para indent)
     {\fontTheoremsPms}% Thm head font
     {.}%        Punctuation after thm head
     {.5em}%     Space after thm head: " " = normal interword space;
           %       \newline = linebreak
     {{\thmname{#1 }}{\thmnumber{#2}}{\thmnote{ ({\it#3})}}}%         Thm head spec (can be left empty, meaning `normal')

\newtheoremstyle{pmsCommentaryRemark}%
     {8pt plus 0ex minus 0ex}%      Space above
     {5pt plus 0ex minus 0ex}%      Space below
     {\let\baselinestretch\@blstr\normalfont}%         Body font   %\baselineskip=15pt
     {\parindent}%         Indent amount (empty = no indent, \parindent = para indent)
     {\fontTheoremsPms}% Thm head font
     {.}%        Punctuation after thm head
     {.5em}%     Space after thm head: " " = normal interword space;
           %       \newline = linebreak
     {}%         Thm head spec (can be left empty, meaning `normal')

%%\def\@begintheorem#1#2[#3]{%
%%  \deferred@thm@head{\the\thm@headfont \thm@indent
%%    \@ifempty{#1}{\let\thmname\@gobble}{\let\thmname\@iden}%
%%    \@ifempty{#2}{\let\thmnumber\@gobble}{\let\thmnumber\@iden}%
%%    \@ifempty{#3}{\let\thmnote\@gobble}{\let\thmnote\@iden}%
%%    \thm@swap\swappedhead\thmhead{#1}{#2}{#3}%
%%    \the\thm@headpunct
%%    \thmheadnl % possibly a newline.
%%    \hskip\thm@headsep
%%  }%
%%  \ignorespaces}
%%\def\@endtheorem{\endtrivlist\@endpefalse Ble}
%%%%%%%%%%%%%%%%%%%%%%%%do usuniecia%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\qeds}{\hskip 2pt {\tiny $\blacksquare$}}
\renewcommand{\mathqed}{\hbox{\qedsymbol}}
\DeclareRobustCommand{\qed}{%
  \ifmmode \mathqed
  \else
    \leavevmode\unskip\penalty9999 \hbox{}\nobreak
    \,\,\hbox{\qedsymbol}%
  \fi
}

\def\fontProofPms{\fontsize{11pt}{10pt}\usefont{T1}{ptm}{m}{n}}
\renewcommand{\qedsymbol}{\hskip 3pt {\tiny $\blacksquare$}}


\def\displaymath@qed{%
    \relax
    \ifmmode
      \ifinner \hbox{\hskip5pt \qedsymbol}
      \else
        \let\eqno\relax \let\leqno\relax \let\veqno\relax
        \hbox{\hskip5pt \qedsymbol}
        %
      \fi
    \else
       \aftergroup\linebox@qed
    \fi
  }

 \let\oldproof=\proof
  \let\endoldproof=\endproof
\renewenvironment{proof}{\begin{oldproof}[\indent{\fontProofPms \proofSo{Proof}.}]}{\end{oldproof}}
%\renewenvironment{proof}{\par {\proofSo{Proof.}}}{\qeds \par}             %rozstrzelic
\newenvironment{proofof}[1]{\begin{oldproof}[\indent{\fontProofPms \proofSo{Proof of #1}.}\newline]}{\end{oldproof}}
\newenvironment{proofSketch}{\begin{oldproof}[\indent{\fontProofPms \proofSo{Proof} (sketch).}]}{\end{oldproof}}

\theoremstyle{pms}
\newtheorem{proposition}{Proposition}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{conjecture}{Conjecture}[section]
\newtheorem{corollary}{Corollary}[section]
\newtheorem{theorem}{Theorem}[section]
\newtheorem{assumption}{Assumption}[section]
\newtheorem*{claimStar}{Claim}
\newtheorem{fact}{Fact}[section]
\newtheorem{remark}{Remark}[section]        %style
\theoremstyle{pmsExample}
\newtheorem{example}{Example}[section]
\theoremstyle{pmsCommentaryRemark}
\newtheorem{commentaryRemark}[remark]{Remark}
\newtheorem{definition}{Definition}[section]
\newtheorem{problem}{Problem}[section]
\newtheorem{note}{Note}[section]


%\newtheorem{assumption}[theorem]{Assumption}
%\newtheorem{hypothesis}[theorem]{Hypothesis}
%\newtheorem{conjecture}[theorem]{Conjecture}
%\newtheorem{problem}[theorem]{Problem}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                       The Bibliography                            %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\bysame}{\underline{$\;\;\;\;\;\;\;\;\;\;\;\;$}}
\bibliographystyle{plain}
\bibsep 0pt

\ifx\bibfont\undefined
\newcommand\bibfont{\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}}
\else
\renewcommand\bibfont{\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}}
\fi

 \let\oldthebibliography=\thebibliography
  \let\endoldthebibliography=\endthebibliography
 \renewenvironment{thebibliography}[1]{\let\baselinestretch\@blstr\pdfbookmark[1]{References}{References}\begin{oldthebibliography}{#1}}%
  {\end{oldthebibliography}%
  \vskip 18pt
  \vtop{\begin{minipage}[t]{14cc}\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}\@Affiliationi\\ \@addressi\\\ifx\@emaili\@empty\else {\it E-mail}: \@emaili\fi\end{minipage}
\ifnum \c@numAuthors>1
\begin{minipage}[t]{14cc}\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}\raggedleft\ifx\@Affiliationii\@empty\else \@Affiliationii\\ \fi
                   \ifx\@addressii\@empty\else \@addressii\\ \fi
                   \ifx\@emailii\@empty\else {\it E-mail}: \@emailii\fi\end{minipage}\fi
\ifnum \c@numAuthors>2
\vskip 0.5cm \hskip -0.7cm
\begin{minipage}[t]{14cc}\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}\ifx\@Affiliationiii\@empty\else \@Affiliationiii\\ \fi
                   \ifx\@addressiii\@empty\else \@addressiii\\ \fi
                   \ifx\@emailiii\@empty\else {\it E-mail}: \@emailiii\fi\end{minipage}\fi \hfill
\ifnum \c@numAuthors>3
\begin{minipage}[t]{14cc}\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}\raggedleft\ifx\@Affiliationiv\@empty\else \@Affiliationiv\\ \fi
                   \ifx\@addressiv\@empty\else \@addressiv\\ \fi
                   \ifx\@emailiv\@empty\else {\it E-mail}: \@emailiv\fi\end{minipage}\fi
\ifnum \c@numAuthors>4
\vskip 0.5cm \hskip -0.7cm
\begin{minipage}[t]{14cc}\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}\ifx\@Affiliationv\@empty\else \@Affiliationv\\ \fi
                   \ifx\@addressv\@empty\else \@addressv\\ \fi
                   \ifx\@emailv\@empty\else {\it E-mail}: \@emailv\fi\end{minipage}\fi
\ifnum \c@numAuthors>5
\begin{minipage}[t]{14cc}\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}\raggedleft\ifx\@Affiliationvi\@empty\else \@Affiliationvi\\ \fi
                   \ifx\@addressvi\@empty\else \@addressvi\\ \fi
                   \ifx\@emailvi\@empty\else {\it E-mail}: \@emailvi\fi\end{minipage}\fi}
 \nopagebreak
  \vskip 0.7cm
  \vskip \@testLength
  \vbox{\centering \fontsize{9}{10} \selectfont \it Received on \@receivedDate
  \ifx\@revisionDate\@empty\else ;\\
   \it revised version on \@revisionDate \fi
  \vskip 0.2cm
  \parbox[t]{1.8cm}{\hrule\hfill}}
 }

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%                       Figures and Tables                          %%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\font\titleThe cmcsc9 at 9truept
\font\titleStest cmr9 at 9truept

\renewcommand{\figurename}{{\titleThe Figure}\titleStest}
\DeclareCaptionFont{titleStestMy}{\fontsize{9pt}{11pt}\usefont{T1}{ptm}{m}{n}}
\captionsetup{font=titleStestMy,justification=Centering}
\renewenvironment{figure}[2]
   {\def\textCaption{#1}\def\textLabel{#2}
   \ifx\textCaption\@empty\captionsetup{labelsep=quad}\fi\begin{@float}{figure}[ht]%
    \setlength{\abovecaptionskip}{5pt}%
    \setlength{\belowcaptionskip}{0pt}%
    \centering}
   {\caption{\textCaption}\label{\textLabel}\end{@float}}


\renewcommand{\tablename}{{\titleThe Table}\titleStest}
\renewenvironment{table}[2]
   {\begin{@float}{table}[h]\setlength{\abovecaptionskip}{0pt}%
\setlength{\belowcaptionskip}{5pt}%
\centering \caption{#1}\label{#2}}
   {\end{@float}}


\newenvironment{tableMy}
   {\begin{@float}{table}[h]\setlength{\abovecaptionskip}{0pt}%
\setlength{\belowcaptionskip}{5pt}%
}  {\end{@float}}

\newenvironment{figureOld}
   {\begin{@float}{figure}[ht]\setlength{\abovecaptionskip}{0pt}%
\setlength{\abovecaptionskip}{5pt}%
    \setlength{\belowcaptionskip}{0pt}%
}  {\end{@float}}

\renewcommand{\labelitemi}{\fontsize{10pt}{0pt}\usefont{OT1}{ptm}{m}{}\textbullet}

\renewenvironment{itemize}%
{ \begin{list}%
    {\fontsize{6pt}{0pt}\usefont{OT1}{ptm}{m}{}\lower-0.4ex\hbox{\textbullet}}%
    {\setlength{\labelwidth}{-26pt}%
     \setlength{\leftmargin}{0pt}%
     \setlength{\topsep}{0pt}
     \setlength{\itemsep}{-3pt}}}%
{ \end{list} }


\def\labelenumi{\theenumi.}

\renewenvironment{enumerate}%
{ \begin{list}%
    {\normalfont\labelenumi}%
    {\setlength{\labelwidth}{-26pt}%
     \setlength{\leftmargin}{0pt}%
     \setlength{\topsep}{0pt}
     \setlength{\listparindent}{20pt}
     \setlength{\parsep}{-1pt}
     \setlength{\itemsep}{1pt}}%
     \usecounter{enumi}}%
{ \setcounter{enumi}{0}\end{list} }

\let\realenumerate\enumerate
\let\endrealenumerate\endenumerate

%lists, enumerations
%Skips before and after equations
%newtheorems environments
%\abovedisplayskip=12pt plus 3pt minus 9pt
%  \abovedisplayshortskip=0pt plus 3pt
%  \belowdisplayskip=12pt plus 3pt minus 9pt
%  \belowdisplayshortskip=7pt plus 3pt minus 4pt
%\let\oldnormalsize
%\renewcommand{\normalsize}{\abovedisplayshortskip=20pt plus 3pt\oldnormalsize{}{}}
\setlength{\parskip}{0pt}

\renewcommand{\big}{\bBigg@\@ne}
\renewcommand{\Big}{\bBigg@{1.1}}
\renewcommand{\bigg}{\bBigg@{1.15}}
\newcommand{\BiggTemp}{\bBigg@{1.7}}
\renewcommand{\Bigg}{\bBigg@{1.6}}
\newcommand{\Biggg}{\bBigg@{1.8}}
\newcommand{\BigggTemp}{\bBigg@{2.2}}
\newcommand{\BigggH}{\bBigg@{2.7}}
\let\oldint\int
\let\oldsum\sum
\frenchspacing

\SetSymbolFont{symbols}     {normal}{OMS}{plsy}{m}{n}
\DeclareMathSymbol{\xleq}{3}{symbols}{172}
\DeclareMathSymbol{\xgeq}{3}{symbols}{173}
\let\leq=\xleq
\let\geq=\xgeq
\let\le=\leq
\let\ge=\geq
\setlength\multlinegap{18pt}

\DeclareFontFamily{OMS}{smalltxex}{}
 \DeclareFontShape{OMS}{smalltxex}{m}{n}{
      <-> s * [1.07] cmex10%
   }{}
   \DeclareSymbolFont{smalllargesymbols}{OMS}{smalltxex}{m}{n}

\DeclareFontFamily{OMS}{smalltxexSum}{}
 \DeclareFontShape{OMS}{smalltxexSum}{m}{n}{
      <-> s * [0.75] cmex10%
   }{}
   \DeclareSymbolFont{smalllargesymbolsSum}{OMS}{smalltxexSum}{m}{n}

 \DeclareFontFamily{OMS}{smalltxexInt}{}
 \DeclareFontShape{OMS}{smalltxexInt}{m}{n}{
      <-> s * [1.1] cmex10%
   }{}
   \DeclareSymbolFont{smalllargesymbolsInt}{OMS}{smalltxexInt}{m}{n}

\DeclareFontFamily{OMS}{smalltxexIntD}{}
 \DeclareFontShape{OMS}{smalltxexIntD}{m}{n}{
      <-> s * [0.55] cmex8%
   }{}
   \DeclareSymbolFont{smalllargesymbolsIntD}{OMS}{smalltxexIntD}{m}{n}
\DeclareFontFamily{OMS}{smalltxexIntD}{}


\DeclareFontFamily{OMS}{smalltxexProduct}{}
 \DeclareFontShape{OMS}{smalltxexProduct}{m}{n}{
      <-> s * [0.65] cmex8%
   }{}
   \DeclareSymbolFont{smalllargesymbolsProduct}{OMS}{smalltxexProduct}{m}{n}
\DeclareFontFamily{OMS}{smalltxexProduct}{}

\DeclareFontFamily{OMS}{temp}{}
 \DeclareFontShape{OMS}{temp}{m}{n}{
      <-> s * [2] cmsy10%
   }{}
   \DeclareSymbolFont{tempBullet}{OMS}{temp}{m}{n}


\DeclareFontFamily{OMS}{temp1}{}
 \DeclareFontShape{OMS}{temp1}{m}{n}{
      <-> s * [0.75] cmsy10%
   }{}
   \DeclareSymbolFont{tempBullet1}{OMS}{temp1}{m}{n}

   \DeclareFontFamily{OMS}{temp2}{}
 \DeclareFontShape{OMS}{temp2}{m}{n}{
      <-> s * [1.75] cmsy10%
   }{}
   \DeclareSymbolFont{tempBullet2}{OMS}{temp2}{m}{n}

\let\sum\undefined
\let\prod\undefined
\let\intop\undefined
\let\bigvee\undefined
\DeclareMathSymbol{\prod}{\mathop}{smalllargesymbols}{"51}

\DeclareMathSymbol{\sum}{\mathop}{smalllargesymbols}{"50}
\DeclareMathSymbol{\bigvee}{\mathop}{smalllargesymbolsSum}{"57}
\DeclareMathSymbol{\sumD}{\mathop}{smalllargesymbolsSum}{"50}
\DeclareMathSymbol{\intop}{\mathop}{smalllargesymbolsInt}{"52}
\DeclareMathSymbol{\intopD}{\mathop}{smalllargesymbolsIntD}{"52}
\DeclareMathSymbol{\cupop}{\mathop}{smalllargesymbolsInt}{"53}
\DeclareMathSymbol{\capop}{\mathop}{smalllargesymbolsInt}{"54}
\DeclareMathSymbol{\cupopD}{\mathop}{smalllargesymbolsIntD}{"53}
\DeclareMathSymbol{\bigCircD}{\mathop}{tempBullet1}{'015}
\DeclareMathSymbol{\bigoplusD}{\mathop}{tempBullet2}{'010}
\DeclareMathSymbol{\bigotimesD}{\mathop}{tempBullet2}{'012}

\DeclareMathSymbol{\dotInt}{\mathalpha}{tempBullet}{"01}  %\raisebox{-6pt}{$\dotInt$}
\let\oldsum\sum
\let\oldint\int
\let\oldprod\prod
\def\intdots@{\mathchoice{\ldots}%
 {{.}\mkern1.5mu{.}\mkern1.5mu{.}}%
 {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}%
 {{\cdotp}\mkern1mu{\cdotp}\mkern1mu{\cdotp}}}
\renewcommand{\MultiIntegral}[1]{%
  \edef\ints@c{\noexpand{\if@display \mathop{\textstyle\intop}\limits \else \intop\fi}
    \ifnum#1=\z@\noexpand\intdots@\else\noexpand\intkern@\fi
    \ifnum#1>\tw@\noexpand\intop\noexpand\intkern@\fi
    \ifnum#1>\thr@@\noexpand\intop\noexpand\intkern@\fi
    \noexpand{\mspace{2mu}\if@display \mathop{\textstyle\intop}\limits \else \intop\fi}
    \noexpand\ilimits@
  }%
  \futurelet\@let@token\ints@a
}
%\renewcommand{\int}{\oldint\limits}
%\renewcommand{\sum}{\textstyle\oldsum}
\renewcommand{\sum}{\if@display \sumD\limits \else \oldsum\fi}
\renewcommand{\prod}{\if@display \mathop{\textstyle\oldprod} \else \oldprod\fi}
\renewcommand{\int}{\if@display \mathop{\textstyle\intop}\limits \else \intop\fi}
\renewcommand{\bigcup}{\if@display \mathop{\textstyle\cupop}\limits \else \cupop\fi}
\renewcommand{\bigcap}{\if@display \mathop{\textstyle\capop}\limits \else \capop\fi}
\renewcommand{\bigcirc}{\bigCircD\nolimits}
\renewcommand{\bigoplus}{\bigoplusD}
\renewcommand{\bigotimes}{\bigotimesD}
\newcommand\longpage{\enlargethispage{2\baselineskip}}
\newcommand\longerpage[1]{\enlargethispage{#1\baselineskip}}
\newcommand\shortpage[1]{\enlargethispage{-#1\baselineskip}}
\medmuskip=4mu plus 1mu minus 1mu
\thickmuskip=5mu plus 1 mu
%{\allowdisplaybreaks zawartosc}

\newlength\savedwidth
\newcommand\whline{\noalign{\global\savedwidth\arrayrulewidth
\global\arrayrulewidth 0.7pt}
\hline
\noalign{\global\arrayrulewidth\savedwidth}}


\setlength\@testLength{-10pt}

\newenvironment{itemizeN}%
{ \begin{list}%
    {\fontsize{6pt}{0pt}\usefont{OT1}{ptm}{m}{}\lower-0.4ex\hbox{\textbullet}}%
    {\setlength{\labelwidth}{12pt}%
     \setlength{\leftmargin}{12pt}%
     \setlength{\labelsep}{4pt}%
     \setlength{\topsep}{0pt}
     \setlength{\itemsep}{-3pt}}}%
{ \end{list} }

\newenvironment{itemizeNN}%
{ \begin{list}%
    {\fontsize{6pt}{0pt}\usefont{OT1}{ptm}{m}{}\lower-0.4ex\hbox{\textbullet}}%
    {\setlength{\labelwidth}{6pt}%
     \setlength{\leftmargin}{11pt}%
     \setlength{\topsep}{0pt}
     \setlength{\itemsep}{-3pt}}}%
{ \end{list} }


\newlength{\dlnumer}

\def\env@cases{%
  \let\@ifnextchar\new@ifnextchar
  \left\lbrace
  \def\arraystretch{1.2}%
  \array{@{}l@{\ \quad}l@{}}%
}

%\usefont{T1}{ptm}{m}{n}

\renewcommand\NAT@sep{], [}
\def\NAT@spacechar{}%

\newcommand{\fracd}[2]{#1/(#2)}
\newcommand{\fracg}[2]{(#1)/#2}
\newcommand{\fraco}[2]{(#1)/(#2)}
\newcommand{\fracz}[2]{#1/#2}
\newcommand{\emn}[1]{\exp(#1)}
\newcommand{\emb}[1]{\exp\big(#1\big)}
\newcommand{\mpe}{\phantom{\mathop{=}}}
\newcommand{\mpl}{\phantom{\mathop{\leq}}}

\catcode`\^^aa=11 %\lccode`\^^aa=`\^^aa
\uccode`\^^aa=`\^^8a  % l crossed