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-\bibitem{Weierstrass03}\r
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-\r
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+\expandafter\ifx\csname href\endcsname\relax
+ \def\href#1#2{#2} \def\path#1{#1}\fi
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+Package `algorithm2e' Release 5.0 -- january 06 2013 --
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-\BOOKMARK [1][-]{section.1}{Root finding problem}{}% 1\r
-\BOOKMARK [1][-]{section.2}{Aberth method}{}% 2\r
-\BOOKMARK [2][-]{subsection.2.1}{Polynomials Initialization}{section.2}% 3\r
-\BOOKMARK [2][-]{subsection.2.2}{Vector Z\(0\) Initialization}{section.2}% 4\r
-\BOOKMARK [2][-]{subsection.2.3}{Iterative Function Hi}{section.2}% 5\r
-\BOOKMARK [2][-]{subsection.2.4}{Convergence condition}{section.2}% 6\r
-\BOOKMARK [1][-]{section.3}{Amelioration of Aberth method }{}% 7\r
-\BOOKMARK [1][-]{section.4}{The implementation of simultaneous methods in a parallel computer}{}% 8\r
-\BOOKMARK [1][-]{section.5}{A parallel implementation of Aberth method}{}% 9\r
-\BOOKMARK [2][-]{subsection.5.1}{Background on the GPU architecture}{section.5}% 10\r
-\BOOKMARK [2][-]{subsection.5.2}{Background on the CUDA Programming Model}{section.5}% 11\r
-\BOOKMARK [2][-]{subsection.5.3}{ The implementation of Aberth method on GPU}{section.5}% 12\r
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-\BOOKMARK [3][-]{subsubsection.5.3.2}{Parallelize the steps on GPU }{subsection.5.3}% 14\r
-\BOOKMARK [2][-]{subsection.5.4}{Experimental study}{section.5}% 15\r
-\BOOKMARK [3][-]{subsubsection.5.4.1}{Definition of the polynomial used}{subsection.5.4}% 16\r
-\BOOKMARK [3][-]{subsubsection.5.4.2}{The study condition}{subsection.5.4}% 17\r
-\BOOKMARK [3][-]{subsubsection.5.4.3}{Comparative study}{subsection.5.4}% 18\r
+\BOOKMARK [1][-]{section.1}{Root finding problem}{}% 1
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+\BOOKMARK [2][-]{subsection.2.1}{Polynomials Initialization}{section.2}% 3
+\BOOKMARK [2][-]{subsection.2.2}{Vector Z\(0\) Initialization}{section.2}% 4
+\BOOKMARK [2][-]{subsection.2.3}{Iterative Function Hi}{section.2}% 5
+\BOOKMARK [2][-]{subsection.2.4}{Convergence condition}{section.2}% 6
+\BOOKMARK [1][-]{section.3}{Amelioration of Aberth method }{}% 7
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+\BOOKMARK [1][-]{section.5}{A parallel implementation of Aberth method}{}% 9
+\BOOKMARK [2][-]{subsection.5.1}{Background on the GPU architecture}{section.5}% 10
+\BOOKMARK [2][-]{subsection.5.2}{Background on the CUDA Programming Model}{section.5}% 11
+\BOOKMARK [2][-]{subsection.5.3}{ The implementation of Aberth method on GPU}{section.5}% 12
+\BOOKMARK [3][-]{subsubsection.5.3.1}{A sequential Aberth algorithm}{subsection.5.3}% 13
+\BOOKMARK [3][-]{subsubsection.5.3.2}{Parallelize the steps on GPU }{subsection.5.3}% 14
+\BOOKMARK [2][-]{subsection.5.4}{Experimental study}{section.5}% 15
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+\BOOKMARK [3][-]{subsubsection.5.4.2}{The study condition}{subsection.5.4}% 17
+\BOOKMARK [3][-]{subsubsection.5.4.3}{Comparative study}{subsection.5.4}% 18
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+\let\@elsuads\@empty\r
+\let\@cormark\@empty\r
+\def\hashchar{\expandafter\@gobble\string\~}\r
+\def\underscorechar{\expandafter\@gobble\string\_}\r
+\def\lbracechar{\expandafter\@gobble\string\{}\r
+\def\rbracechar{\expandafter\@gobble\string\}}\r
+\r
+\def\ead{\@ifnextchar[{\@uad}{\@ead}}\r
+\gdef\@ead#1{\bgroup\def\_{\string\underscorechar\space}%\r
+ \def\{{\string\lbracechar\space}%\r
+ \def~{\hashchar\space}%\r
+ \def\}{\string\rbracechar\space}%\r
+ \edef\tmp{\the\@eadauthor}\r
+ \immediate\write\@auxout{\string\emailauthor\r
+ {#1}{\expandafter\strip@prefix\meaning\tmp}}%\r
+ \egroup\r
+}\r
+\newcounter{ead}\r
+\gdef\emailauthor#1#2{\stepcounter{ead}%\r
+ \g@addto@macro\@elseads{\raggedright%\r
+ \let\corref\@gobble\r
+ \eadsep\texttt{#1} (#2)\def\eadsep{\unskip,\space}}%\r
+}\r
+\gdef\@uad[#1]#2{\bgroup\r
+ \def~{\string\hashchar\space}%\r
+ \def\_{\string\underscorechar\space}%\r
+ \edef\tmp{\the\@eadauthor}\r
+ \immediate\write\@auxout{\string\urlauthor\r
+ {#2}{\expandafter\strip@prefix\meaning\tmp}}%\r
+ \egroup\r
+}\r
+\def\urlauthor#1#2{\g@addto@macro\@elsuads{\let\corref\@gobble%\r
+ \raggedright\eadsep\texttt{#1}\space(#2)%\r
+ \def\eadsep{\unskip,\space}}%\r
+}\r
+\r
+\def\elsauthors{}\r
+\def\pprinttitle{}\r
+\let\authorsep\@empty\r
+\let\sep\@empty\r
+\newcounter{author}\r
+\def\author{\@ifnextchar[{\@@author}{\@author}}\r
+\r
+\newtoks\@eadauthor\r
+\def\@@author[#1]#2{\g@addto@macro\elsauthors{%\r
+ \def\baselinestretch{1}%\r
+ \authorsep#2\unskip\textsuperscript{%#1%\r
+ \@for\@@affmark:=#1\do{%\r
+ \edef\affnum{\@ifundefined{X@\@@affmark}{1}{\elsRef{\@@affmark}}}%\r
+ \unskip\sep\affnum\let\sep=,}%\r
+ \ifx\@fnmark\@empty\else\unskip\sep\@fnmark\let\sep=,\fi\r
+ \ifx\@corref\@empty\else\unskip\sep\@corref\let\sep=,\fi\r
+ }%\r
+ \def\authorsep{\unskip,\space}%\r
+ \global\let\sep\@empty\global\let\@corref\@empty\r
+ \global\let\@fnmark\@empty}%\r
+ \@eadauthor={#2}\r
+}\r
+\r
+\def\@author#1{\g@addto@macro\elsauthors{\normalsize%\r
+ \def\baselinestretch{1}%\r
+ \upshape\authorsep#1\unskip\textsuperscript{%\r
+ \ifx\@fnmark\@empty\else\unskip\sep\@fnmark\let\sep=,\fi\r
+ \ifx\@corref\@empty\else\unskip\sep\@corref\let\sep=,\fi\r
+ }%\r
+ \def\authorsep{\unskip,\space}%\r
+ \global\let\@fnmark\@empty\r
+ \global\let\@corref\@empty\r
+ \global\let\sep\@empty}%\r
+ \@eadauthor={#1}\r
+}\r
+\r
+\def\elsaddress{}\r
+\def\addsep{\par\vskip6pt}\r
+\def\address{\@ifnextchar[{\@@address}{\@address}}\r
+\r
+\def\@alph#1{%\r
+ \ifcase#1\or a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or k\or\r
+ l\or m\or n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or\r
+ y\or z%\r
+ \or aa\or ab\or ac\or ad\or ae\or af\or ag\or ah\or ai\or aj\or\r
+ ak\or al\or am\or an\or ao\or ap\or aq\or ar\or as\or at\or au\or\r
+ av\or aw\or ax\or ay\or az%\r
+ \or ba\or bb\or bc\or bd\or be\or bf\or bg\or bh\or bi\or bj\or\r
+ bk\or bl\or bm\or bn\or bo\or bp\or bq\or br\or bs\or bt\or bu\or\r
+ bv\or bw\or bx\or by\or bz%\r
+ \or ca\or cb\or cc\or cd\or ce\or cf\or cg\or ch\or ci\or cj\or\r
+ ck\or cl\or cm\or cn\or co\or cp\or cq\or cr\or cs\or ct\or cu\or\r
+ cv\or cw\or cx\or cy\or cz%\r
+ \or da\or db\or dc\or dd\or de\or df\or dg\or dh\or di\or dj\or\r
+ dk\or dl\or dm\or dn\or do\or dp\or dq\or dr\or ds\or dt\or du\or\r
+ dv\or dw\or dx\or dy\or dz%\r
+ \or ea\or eb\or ec\or ed\or ee\or ef\or eg\or eh\or ei\or ej\or\r
+ ek\or el\or em\or en\or eo\or ep\or eq\or er\or es\or et\or eu\or\r
+ ev\or ew\or ex\or ey\or ez%\r
+ \or fa\or fb\or fc\or fd\or fe\or ff\or fg\or fh\or fi\or fj\or\r
+ fk\or fl\or fm\or fn\or fo\or fp\or fq\or fr\or fs\or ft\or fu\or\r
+ fv\or fw\or fx\or fy\or fz%\r
+ \or ga\or gb\or gc\or gd\or ge\or gf\or gg\or gh\or gi\or gj\or\r
+ gk\or gl\or gm\or gn\or go\or gp\or gq\or gr\or gs\or gt\or gu\or\r
+ gv\or gw\or gx\or gy\or gz%\r
+ \else\@ctrerr\fi}\r
+\r
+\newcounter{affn}\r
+\renewcommand\theaffn{\alph{affn}}\r
+\r
+\long\def\@@address[#1]#2{\g@addto@macro\elsaddress{%\r
+ \def\baselinestretch{1}%\r
+ \refstepcounter{affn}\r
+ \xdef\@currentlabel{\theaffn}\r
+ \elsLabel{#1}%\r
+ \textsuperscript{\theaffn}#2\par}}\r
+\r
+\long\def\@address#1{\g@addto@macro\elsauthors{%\r
+ \def\baselinestretch{1}%\r
+ \addsep\footnotesize\itshape#1\def\addsep{\par\vskip6pt}%\r
+ \def\authorsep{\par\vskip8pt}}}\r
+\r
+\newbox\absbox\r
+\renewenvironment{abstract}{\global\setbox\absbox=\vbox\bgroup\r
+ \hsize=\textwidth\def\baselinestretch{1}%\r
+ \noindent\unskip\textbf{Abstract}\r
+ \par\medskip\noindent\unskip\ignorespaces}\r
+ {\egroup}\r
+\r
+\newbox\keybox\r
+\def\keyword{%\r
+ \def\sep{\unskip, }%\r
+ \def\MSC{\@ifnextchar[{\@MSC}{\@MSC[2000]}}\r
+ \def\@MSC[##1]{\par\leavevmode\hbox {\it ##1~MSC:\space}}%\r
+ \def\PACS{\par\leavevmode\hbox {\it PACS:\space}}%\r
+ \def\JEL{\par\leavevmode\hbox {\it JEL:\space}}%\r
+ \global\setbox\keybox=\vbox\bgroup\hsize=\textwidth\r
+ \normalsize\normalfont\def\baselinestretch{1}\r
+ \parskip\z@\r
+ \noindent\textit{Keywords: }\r
+ \raggedright % Keywords are not justified.\r
+ \ignorespaces}\r
+\def\endkeyword{\par \egroup}\r
+\r
+\newdimen\Columnwidth\r
+\Columnwidth=\columnwidth\r
+\r
+\def\printFirstPageNotes{%\r
+ \iflongmktitle\r
+ \let\columnwidth=\textwidth\fi\r
+ \ifx\@tnotes\@empty\else\@tnotes\fi\r
+ \ifx\@nonumnotes\@empty\else\@nonumnotes\fi\r
+ \ifx\@cornotes\@empty\else\@cornotes\fi\r
+ \ifx\@elseads\@empty\relax\else\r
+ \let\thefootnote\relax\r
+ \footnotetext{\ifnum\theead=1\relax\r
+ \textit{Email address:\space}\else\r
+ \textit{Email addresses:\space}\fi\r
+ \@elseads}\fi\r
+ \ifx\@elsuads\@empty\relax\else\r
+ \let\thefootnote\relax\r
+ \footnotetext{\textit{URL:\space}%\r
+ \@elsuads}\fi\r
+ \ifx\@fnotes\@empty\else\@fnotes\fi\r
+ \iflongmktitle\if@twocolumn\r
+ \let\columnwidth=\Columnwidth\fi\fi\r
+}\r
+\r
+\long\def\pprintMaketitle{\clearpage\r
+ \iflongmktitle\if@twocolumn\let\columnwidth=\textwidth\fi\fi\r
+ \resetTitleCounters\r
+ \def\baselinestretch{1}%\r
+ \printFirstPageNotes\r
+ \begin{center}%\r
+ \thispagestyle{pprintTitle}%\r
+ \def\baselinestretch{1}%\r
+ \Large\@title\par\vskip18pt\r
+ \normalsize\elsauthors\par\vskip10pt\r
+ \footnotesize\itshape\elsaddress\par\vskip36pt\r
+ \hrule\vskip12pt\r
+ \ifvoid\absbox\else\unvbox\absbox\par\vskip10pt\fi\r
+ \ifvoid\keybox\else\unvbox\keybox\par\vskip10pt\fi\r
+ \hrule\vskip12pt\r
+ \end{center}%\r
+ \gdef\thefootnote{\arabic{footnote}}%\r
+ }\r
+\r
+\def\printWarning{%\r
+ \mbox{}\par\vfill\par\bgroup\r
+ \fboxsep12pt\fboxrule1pt\r
+ \hspace*{.18\textwidth}\r
+ \fcolorbox{gray50}{gray10}{\box\warnbox}\r
+ \egroup\par\vfill\thispagestyle{empty}\r
+ \setcounter{page}{0}\r
+ \clearpage}\r
+\r
+\long\def\finalMaketitle{%\r
+ \resetTitleCounters\r
+ \def\baselinestretch{1}%\r
+ \MaketitleBox\r
+ \thispagestyle{pprintTitle}%\r
+ \gdef\thefootnote{\arabic{footnote}}%\r
+ }\r
+\r
+\long\def\MaketitleBox{%\r
+ \resetTitleCounters\r
+ \def\baselinestretch{1}%\r
+ \begin{center}%\r
+ \def\baselinestretch{1}%\r
+ \Large\@title\par\vskip18pt\r
+ \normalsize\elsauthors\par\vskip10pt\r
+ \footnotesize\itshape\elsaddress\par\vskip36pt\r
+ \hrule\vskip12pt\r
+ \ifvoid\absbox\else\unvbox\absbox\par\vskip10pt\fi\r
+ \ifvoid\keybox\else\unvbox\keybox\par\vskip10pt\fi\r
+ \hrule\vskip12pt\r
+ \end{center}%\r
+ }\r
+\r
+\def\FNtext#1{\par\bgroup\footnotesize#1\egroup}\r
+\newdimen\space@left\r
+\def\alarm#1{\typeout{******************************}%\r
+ \typeout{#1}%\r
+ \typeout{******************************}%\r
+}\r
+\long\def\getSpaceLeft{%\global\@twocolumnfalse%\r
+ \global\setbox0=\vbox{\hsize=\textwidth\MaketitleBox}%\r
+ \global\setbox1=\vbox{\hsize=\textwidth\r
+ \let\footnotetext\FNtext\r
+ \printFirstPageNotes}%\r
+ \xdef\noteheight{\the\ht1}%\r
+ \xdef\titleheight{\the\ht0}%\r
+ \@tempdima=\vsize\r
+ \advance\@tempdima-\noteheight\r
+ \advance\@tempdima-1\baselineskip\r
+}\r
+\r
+ \skip\footins=24pt\r
+\r
+\newbox\els@boxa\r
+\newbox\els@boxb\r
+\r
+\ifpreprint\r
+ \def\maketitle{\pprintMaketitle}\r
+ \else\r
+ \ifnum\jtype=1\r
+ \def\maketitle{%\r
+ \iflongmktitle\getSpaceLeft\r
+ \global\setbox\els@boxa=\vsplit0 to \@tempdima\r
+ \box\els@boxa\par\resetTitleCounters\r
+ \thispagestyle{pprintTitle}%\r
+ \printFirstPageNotes\r
+ \box0%\r
+ \else\r
+ \finalMaketitle\printFirstPageNotes\r
+ \fi\r
+ \gdef\thefootnote{\arabic{footnote}}}%\r
+ \else\r
+ \ifnum\jtype=5\r
+ \def\maketitle{%\r
+ \iflongmktitle\getSpaceLeft\r
+ \global\setbox\els@boxa=\vsplit0 to \@tempdima\r
+ \box\els@boxa\par\resetTitleCounters\r
+ \thispagestyle{pprintTitle}%\r
+ \printFirstPageNotes\r
+ \twocolumn[\box0]%\printFirstPageNotes\r
+ \else\r
+ \twocolumn[\finalMaketitle]\printFirstPageNotes\r
+ \fi\r
+ \gdef\thefootnote{\arabic{footnote}}}\r
+ \else\r
+ \if@twocolumn\r
+ \def\maketitle{%\r
+ \iflongmktitle\getSpaceLeft\r
+ \global\setbox\els@boxa=\vsplit0 to \@tempdima\r
+ \box\els@boxa\par\resetTitleCounters\r
+ \thispagestyle{pprintTitle}%\r
+ \printFirstPageNotes\r
+ \twocolumn[\box0]%\r
+ \else\r
+ \twocolumn[\finalMaketitle]\printFirstPageNotes\r
+ \fi\r
+ \gdef\thefootnote{\arabic{footnote}}}%\r
+ \else\r
+ \def\maketitle{%\r
+ \iflongmktitle\getSpaceLeft\r
+ \global\setbox\els@boxa=\vsplit0 to \@tempdima\r
+ \box\els@boxa\par\resetTitleCounters\r
+ \thispagestyle{pprintTitle}%\r
+ \printFirstPageNotes\r
+ \box0%\r
+ \else\r
+ \finalMaketitle\printFirstPageNotes\r
+ \fi\r
+ \gdef\thefootnote{\arabic{footnote}}}%\r
+ \fi\r
+ \fi\r
+ \fi\r
+\fi\r
+\def\ps@pprintTitle{%\r
+ \let\@oddhead\@empty\r
+ \let\@evenhead\@empty\r
+ \def\@oddfoot{\footnotesize\itshape\r
+ Preprint submitted to \ifx\@journal\@empty Elsevier\r
+ \else\@journal\fi\hfill\today}%\r
+ \let\@evenfoot\@oddfoot}\r
+\def\@seccntDot{.}\r
+\def\@seccntformat#1{\csname the#1\endcsname\@seccntDot\hskip 0.5em}\r
+\r
+\renewcommand\section{\@startsection {section}{1}{\z@}%\r
+ {18\p@ \@plus 6\p@ \@minus 3\p@}%\r
+ {9\p@ \@plus 6\p@ \@minus 3\p@}%\r
+ {\normalsize\bfseries\boldmath}}\r
+\renewcommand\subsection{\@startsection{subsection}{2}{\z@}%\r
+ {12\p@ \@plus 6\p@ \@minus 3\p@}%\r
+ {3\p@ \@plus 6\p@ \@minus 3\p@}%\r
+ {\normalfont\normalsize\itshape}}\r
+\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}%\r
+ {12\p@ \@plus 6\p@ \@minus 3\p@}%\r
+ {\p@}%\r
+ {\normalfont\normalsize\itshape}}\r
+\r
+\def\paragraph{\secdef{\els@aparagraph}{\els@bparagraph}}\r
+\def\els@aparagraph[#1]#2{\elsparagraph[#1]{#2.}}\r
+\def\els@bparagraph#1{\elsparagraph*{#1.}}\r
+\r
+\newcommand\elsparagraph{\@startsection{paragraph}{4}{0\z@}%\r
+ {10\p@ \@plus 6\p@ \@minus 3\p@}%\r
+ {-6\p@}%\r
+ {\normalfont\itshape}}\r
+\newdimen\leftMargin\r
+\leftMargin=2em\r
+\newtoks\@enLab %\newtoks\@enfont\r
+\def\@enQmark{?}\r
+\def\@enLabel#1#2{%\r
+ \edef\@enThe{\noexpand#1{\@enumctr}}%\r
+ \@enLab\expandafter{\the\@enLab\csname the\@enumctr\endcsname}%\r
+ \@enloop}\r
+\def\@enSpace{\afterassignment\@enSp@ce\let\@tempa= }\r
+\def\@enSp@ce{\@enLab\expandafter{\the\@enLab\space}\@enloop}\r
+\def\@enGroup#1{\@enLab\expandafter{\the\@enLab{#1}}\@enloop}\r
+\def\@enOther#1{\@enLab\expandafter{\the\@enLab#1}\@enloop}\r
+\def\@enloop{\futurelet\@entemp\@enloop@}\r
+\def\@enloop@{%\r
+ \ifx A\@entemp \def\@tempa{\@enLabel\Alph }\else\r
+ \ifx a\@entemp \def\@tempa{\@enLabel\alph }\else\r
+ \ifx i\@entemp \def\@tempa{\@enLabel\roman }\else\r
+ \ifx I\@entemp \def\@tempa{\@enLabel\Roman }\else\r
+ \ifx 1\@entemp \def\@tempa{\@enLabel\arabic}\else\r
+ \ifx \@sptoken\@entemp \let\@tempa\@enSpace \else\r
+ \ifx \bgroup\@entemp \let\@tempa\@enGroup \else\r
+ \ifx \@enum@\@entemp \let\@tempa\@gobble \else\r
+ \let\@tempa\@enOther\r
+ \fi\fi\fi\fi\fi\fi\fi\fi\r
+ \@tempa}\r
+\newlength{\@sep} \newlength{\@@sep}\r
+\setlength{\@sep}{.5\baselineskip plus.2\baselineskip\r
+ minus.2\baselineskip}\r
+\setlength{\@@sep}{.1\baselineskip plus.01\baselineskip\r
+ minus.05\baselineskip}\r
+\providecommand{\sfbc}{\rmfamily\upshape}\r
+\providecommand{\sfn}{\rmfamily\upshape}\r
+\def\@enfont{\ifnum \@enumdepth >1\let\@nxt\sfn \else\let\@nxt\sfbc \fi\@nxt}\r
+\def\enumerate{%\r
+ \ifnum \@enumdepth >3 \@toodeep\else\r
+ \advance\@enumdepth \@ne\r
+ \edef\@enumctr{enum\romannumeral\the\@enumdepth}\fi\r
+ \@ifnextchar[{\@@enum@}{\@enum@}}\r
+\def\@@enum@[#1]{%\r
+ \@enLab{}\let\@enThe\@enQmark\r
+ \@enloop#1\@enum@\r
+ \ifx\@enThe\@enQmark\@warning{The counter will not be printed.%\r
+ ^^J\space\@spaces\@spaces\@spaces The label is: \the\@enLab}\fi\r
+ \expandafter\edef\csname label\@enumctr\endcsname{\the\@enLab}%\r
+ \expandafter\let\csname the\@enumctr\endcsname\@enThe\r
+ \csname c@\@enumctr\endcsname7\r
+ \expandafter\settowidth\r
+ \csname leftmargin\romannumeral\@enumdepth\endcsname\r
+ {\the\@enLab\hskip\labelsep}%\r
+ \@enum@}\r
+\def\@enum@{\list{{\@enfont\csname label\@enumctr\endcsname}}%\r
+ {\usecounter{\@enumctr}\def\makelabel##1{\hss\llap{##1}}%\r
+ \ifnum \@enumdepth>1\setlength{\topsep}{\@@sep}\else\r
+ \setlength{\topsep}{\@sep}\fi\r
+ \ifnum \@enumdepth>1\setlength{\itemsep}{0pt plus1pt minus1pt}%\r
+ \else \setlength{\itemsep}{\@@sep}\fi\r
+ %\setlength\leftmargin{\leftMargin}%%%{1.8em}\r
+ \setlength{\parsep}{0pt plus1pt minus1pt}%\r
+ \setlength{\parskip}{0pt plus1pt minus1pt}\r
+ }}\r
+\r
+\def\endenumerate{\par\ifnum \@enumdepth >1\addvspace{\@@sep}\else\r
+ \addvspace{\@sep}\fi \endlist}\r
+\r
+\def\sitem{\@noitemargtrue\@item[\@itemlabel *]}\r
+\r
+\def\itemize{\@ifnextchar[{\@Itemize}{\@Itemize[]}}\r
+\r
+\def\@Itemize[#1]{\def\next{#1}%\r
+ \ifnum \@itemdepth >\thr@@\@toodeep\else\r
+ \advance\@itemdepth\@ne\r
+ \ifx\next\@empty\else\expandafter\def\csname\r
+ labelitem\romannumeral\the\@itemdepth\endcsname{#1}\fi%\r
+ \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}%\r
+ \expandafter\list\csname\@itemitem\endcsname\r
+ {\def\makelabel##1{\hss\llap{##1}}}%\r
+ \fi}\r
+\def\newdefinition#1{%\r
+ \@ifnextchar[{\@odfn{#1}}{\@ndfn{#1}}}%]\r
+\def\@ndfn#1#2{%\r
+ \@ifnextchar[{\@xndfn{#1}{#2}}{\@yndfn{#1}{#2}}}\r
+\def\@xndfn#1#2[#3]{%\r
+ \expandafter\@ifdefinable\csname #1\endcsname\r
+ {\@definecounter{#1}\@newctr{#1}[#3]%\r
+ \expandafter\xdef\csname the#1\endcsname{%\r
+ \expandafter\noexpand\csname the#3\endcsname \@dfncountersep\r
+ \@dfncounter{#1}}%\r
+ \global\@namedef{#1}{\@dfn{#1}{#2}}%\r
+ \global\@namedef{end#1}{\@enddefinition}}}\r
+\def\@yndfn#1#2{%\r
+ \expandafter\@ifdefinable\csname #1\endcsname\r
+ {\@definecounter{#1}%\r
+ \expandafter\xdef\csname the#1\endcsname{\@dfncounter{#1}}%\r
+ \global\@namedef{#1}{\@dfn{#1}{#2}}%\r
+ \global\@namedef{end#1}{\@enddefinition}}}\r
+\def\@odfn#1[#2]#3{%\r
+ \@ifundefined{c@#2}{\@nocounterr{#2}}%\r
+ {\expandafter\@ifdefinable\csname #1\endcsname\r
+ {\global\@namedef{the#1}{\@nameuse{the#2}}\r
+ \global\@namedef{#1}{\@dfn{#2}{#3}}%\r
+ \global\@namedef{end#1}{\@enddefinition}}}}\r
+\def\@dfn#1#2{%\r
+ \refstepcounter{#1}%\r
+ \@ifnextchar[{\@ydfn{#1}{#2}}{\@xdfn{#1}{#2}}}\r
+\def\@xdfn#1#2{%\r
+ \@begindefinition{#2}{\csname the#1\endcsname}\ignorespaces}\r
+\def\@ydfn#1#2[#3]{%\r
+ \@opargbegindefinition{#2}{\csname the#1\endcsname}{#3}\ignorespaces}\r
+\def\@dfncounter#1{\noexpand\arabic{#1}}\r
+\def\@dfncountersep{.}\r
+\def\@begindefinition#1#2{\trivlist\r
+ \item[\hskip\labelsep{\bfseries #1\ #2.}]\upshape}\r
+\def\@opargbegindefinition#1#2#3{\trivlist\r
+ \item[\hskip\labelsep{\bfseries #1\ #2\ (#3).}]\upshape}\r
+\def\@enddefinition{\endtrivlist}\r
+\r
+\def\@begintheorem#1#2{\trivlist\r
+ \let\baselinestretch\@blstr\r
+ \item[\hskip \labelsep{\bfseries #1\ #2.}]\itshape}\r
+\def\@opargbegintheorem#1#2#3{\trivlist\r
+ \let\baselinestretch\@blstr\r
+ \item[\hskip \labelsep{\bfseries #1\ #2\ (#3).}]\itshape}\r
+\r
+\def\newproof#1{%\r
+ \@ifnextchar[{\@oprf{#1}}{\@nprf{#1}}}\r
+\def\@nprf#1#2{%\r
+ \@ifnextchar[{\@xnprf{#1}{#2}}{\@ynprf{#1}{#2}}}\r
+\def\@xnprf#1#2[#3]{%\r
+ \expandafter\@ifdefinable\csname #1\endcsname\r
+ {\@definecounter{#1}\@newctr{#1}[#3]%\r
+ \expandafter\xdef\csname the#1\endcsname{%\r
+ \expandafter\noexpand\csname the#3\endcsname \@prfcountersep\r
+ \@prfcounter{#1}}%\r
+ \global\@namedef{#1}{\@prf{#1}{#2}}%\r
+ \global\@namedef{end#1}{\@endproof}}}\r
+\def\@ynprf#1#2{%\r
+ \expandafter\@ifdefinable\csname #1\endcsname\r
+ {\@definecounter{#1}%\r
+ \expandafter\xdef\csname the#1\endcsname{\@prfcounter{#1}}%\r
+ \global\@namedef{#1}{\@prf{#1}{#2}}%\r
+ \global\@namedef{end#1}{\@endproof}}}\r
+\def\@oprf#1[#2]#3{%\r
+ \@ifundefined{c@#2}{\@nocounterr{#2}}%\r
+ {\expandafter\@ifdefinable\csname #1\endcsname\r
+ {\global\@namedef{the#1}{\@nameuse{the#2}}%\r
+ \global\@namedef{#1}{\@prf{#2}{#3}}%\r
+ \global\@namedef{end#1}{\@endproof}}}}\r
+\def\@prf#1#2{%\r
+ \refstepcounter{#1}%\r
+ \@ifnextchar[{\@yprf{#1}{#2}}{\@xprf{#1}{#2}}}\r
+\def\@xprf#1#2{%\r
+ \@beginproof{#2}{\csname the#1\endcsname}\ignorespaces}\r
+\def\@yprf#1#2[#3]{%\r
+ \@opargbeginproof{#2}{\csname the#1\endcsname}{#3}\ignorespaces}\r
+\def\@prfcounter#1{\noexpand\arabic{#1}}\r
+\def\@prfcountersep{.}\r
+\def\@beginproof#1#2{\trivlist\let\baselinestretch\@blstr\r
+ \item[\hskip \labelsep{\scshape #1.}]\rmfamily}\r
+\def\@opargbeginproof#1#2#3{\trivlist\let\baselinestretch\@blstr\r
+ \item[\hskip \labelsep{\scshape #1\ (#3).}]\rmfamily}\r
+\def\@endproof{\endtrivlist}\r
+\newcommand*{\qed}{\hbox{}\hfill$\Box$}\r
+\r
+\@ifundefined{@biboptions}{\xdef\@biboptions{numbers}}{}\r
+\InputIfFileExists{\jobname.spl}{}{}\r
+\RequirePackage[\@biboptions]{natbib}\r
+\r
+\newwrite\splwrite\r
+\immediate\openout\splwrite=\jobname.spl\r
+\def\biboptions#1{\def\next{#1}\immediate\write\splwrite{%\r
+ \string\g@addto@macro\string\@biboptions{%\r
+ ,\expandafter\strip@prefix\meaning\next}}}\r
+\r
+\let\baselinestretch=\@blstr\r
+\r
+\ifnum\jtype=1\r
+ \RequirePackage{geometry}\r
+ \geometry{twoside,\r
+ paperwidth=210mm,\r
+ paperheight=297mm,\r
+ textheight=562pt,\r
+ textwidth=384pt,\r
+ centering,\r
+ headheight=50pt,\r
+ headsep=12pt,\r
+ footskip=12pt,\r
+ footnotesep=24pt plus 2pt minus 12pt,\r
+ }\r
+ \global\let\bibfont=\footnotesize\r
+ \global\bibsep=0pt\r
+ \if@twocolumn\global\@twocolumnfalse\fi\r
+\else\ifnum\jtype=3\r
+ \RequirePackage{geometry}\r
+ \geometry{twoside,\r
+ paperwidth=210mm,\r
+ paperheight=297mm,\r
+ textheight=622pt,\r
+ textwidth=468pt,\r
+ centering,\r
+ headheight=50pt,\r
+ headsep=12pt,\r
+ footskip=18pt,\r
+ footnotesep=24pt plus 2pt minus 12pt,\r
+ columnsep=2pc\r
+ }\r
+ \global\let\bibfont=\footnotesize\r
+ \global\bibsep=0pt\r
+ \if@twocolumn\input{fleqn.clo}\fi\r
+\else\ifnum\jtype=5\r
+ \RequirePackage{geometry}\r
+ \geometry{twoside,\r
+ paperwidth=210mm,\r
+ paperheight=297mm,\r
+ textheight=682pt,\r
+ textwidth=522pt,\r
+ centering,\r
+ headheight=50pt,\r
+ headsep=12pt,\r
+ footskip=18pt,\r
+ footnotesep=24pt plus 2pt minus 12pt,\r
+ columnsep=18pt\r
+ }%\r
+ \global\let\bibfont=\footnotesize\r
+ \global\bibsep=0pt\r
+ \input{fleqn.clo}\r
+ \global\@twocolumntrue\r
+%%\r
+%% End of option '5p'\r
+%%\r
+\fi\fi\fi\r
+\def\journal#1{\gdef\@journal{#1}}\r
+ \let\@journal\@empty\r
+\newenvironment{frontmatter}{}{\maketitle}\r
+\r
+\long\def\@makecaption#1#2{%\r
+ \vskip\abovecaptionskip\footnotesize\r
+ \sbox\@tempboxa{#1: #2}%\r
+ \ifdim \wd\@tempboxa >\hsize\r
+ #1: #2\par\r
+ \else\r
+ \global \@minipagefalse\r
+ \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}%\r
+ \fi\r
+ \vskip\belowcaptionskip}\r
+\r
+\AtBeginDocument{\@ifpackageloaded{hyperref}\r
+ {\def\@linkcolor{blue}\r
+ \def\@anchorcolor{blue}\r
+ \def\@citecolor{blue}\r
+ \def\@filecolor{blue}\r
+ \def\@urlcolor{blue}\r
+ \def\@menucolor{blue}\r
+ \def\@pagecolor{blue}\r
+\begingroup\r
+ \@makeother\`%\r
+ \@makeother\=%\r
+ \edef\x{%\r
+ \edef\noexpand\x{%\r
+ \endgroup\r
+ \noexpand\toks@{%\r
+ \catcode 96=\noexpand\the\catcode`\noexpand\`\relax\r
+ \catcode 61=\noexpand\the\catcode`\noexpand\=\relax\r
+ }%\r
+ }%\r
+ \noexpand\x\r
+ }%\r
+\x\r
+\@makeother\`\r
+\@makeother\=\r
+}{}}\r
+%%\r
+\def\appendixname{Appendix }\r
+\renewcommand\appendix{\par\r
+ \setcounter{section}{0}%\r
+ \setcounter{subsection}{0}%\r
+ \setcounter{equation}{0}\r
+ \gdef\thefigure{\@Alph\c@section.\arabic{figure}}%\r
+ \gdef\thetable{\@Alph\c@section.\arabic{table}}%\r
+ \gdef\thesection{\appendixname~\@Alph\c@section}%\r
+ \@addtoreset{equation}{section}%\r
+ \gdef\theequation{\@Alph\c@section.\arabic{equation}}%\r
+ \addtocontents{toc}{\string\let\string\numberline\string\tmptocnumberline}{}{}\r
+}\r
+\r
+%%%% \numberline width calculation for appendix.\r
+\newdimen\appnamewidth\r
+\def\tmptocnumberline#1{%\r
+ \setbox0=\hbox{\appendixname}\r
+ \appnamewidth=\wd0\r
+ \addtolength\appnamewidth{2.5pc}\r
+ \hb@xt@\appnamewidth{#1\hfill}\r
+}\r
+\r
+%% Added for work with amsrefs.sty\r
+\r
+\@ifpackageloaded{amsrefs}%\r
+ {}\r
+ {%\let\bibsection\relax%\r
+ \AtBeginDocument{\def\cites@b#1#2,#3{%\r
+ \begingroup[%\r
+ \toks@{\InnerCite{#2}#1}%\r
+ \ifx\@empty#3\@xp\@gobble\fi\r
+ \cites@c#3%\r
+}}}\r
+%%\r
+%% Added for avoiding clash with cleveref.sty\r
+\r
+\@ifpackageloaded{cleveref}%\r
+ {}\r
+ {\def\tnotetext[#1]#2{\g@addto@macro\@tnotes{%\r
+ \refstepcounter{tnote}%\r
+ \immediate\write\@auxout{\string\Newlabel{#1}{\thetnote}}\r
+ \def\thefootnote{\ifcase\c@tnote\or\ding{73}\or\ding{73}\ding{73}\fi}%\r
+ \footnotetext{#2}}}\r
+%%%\r
+ \def\fntext[#1]#2{\g@addto@macro\@fnotes{%\r
+ \refstepcounter{fnote}%\r
+ \immediate\write\@auxout{\string\Newlabel{#1}{\thefnote}}\r
+ \def\thefootnote{\thefnote}%\r
+ \global\setcounter{footnote}{\thefnote}%\r
+ \footnotetext{#2}}}\r
+%%%\r
+ \def\cortext[#1]#2{\g@addto@macro\@cornotes{%\r
+ \refstepcounter{cnote}%\r
+ \immediate\write\@auxout{\string\Newlabel{#1}{\thecnote}}\r
+ \def\thefootnote{\ifcase\thecnote\or$\ast$\or\r
+ $\ast\ast$\fi}%\r
+ \footnotetext{#2}}}\r
+}\r
+\endinput\r
+%%\r
+%% End of file `elsarticle.cls'.\r
+\r
