%{Created=Friday, September 16, 2013 21:13:08 by Toufik Laadj}
%\makeglossary
%\makeindex
%\renewcommand{\nomname}{Liste des principales notations}

\documentclass[a4paper,oneside,12pt]{book}%
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{graphics}
\usepackage{amsmath}
\usepackage{makeidx}
\usepackage{portland}
\usepackage{fancyhdr}
\usepackage[perpage]{footmisc}
\usepackage{minitoc}
\usepackage[usenames, dvipsnames]{color}
\usepackage{longtable}
\usepackage[ansinew]{inputenc}
\usepackage[ plainpages = false, pdfpagelabels, pdfpagelayout = useoutlines,
bookmarks,  bookmarksnumbered = true, breaklinks = true, linktocpage,
pagebackref, colorlinks = true,    linkcolor = blue, urlcolor  = blue,
citecolor = red, anchorcolor = green,  hyperindex = true, hyperfigures
]{hyperref}
\usepackage[pdftex]{graphicx}
\usepackage{verbatim}
\usepackage{theorem}
\usepackage{fancybox}
\usepackage{pgf,tikz}%
\setcounter{MaxMatrixCols}{30}
%TCIDATA{OutputFilter=latex2.dll}
%TCIDATA{Version=5.50.0.2960}
%TCIDATA{CSTFile=booktdc.cst}
%TCIDATA{Created=Friday, September 16, 2013 21:13:08}
%TCIDATA{LastRevised=Saturday, February 18, 2017 21:50:45}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="SaveForMode" CONTENT="2">}
%TCIDATA{BibliographyScheme=Manual}
%TCIDATA{<META NAME="DocumentShell" CONTENT="Theses\SW\USTHB_MT">}
%TCIDATA{Language=American English}
%BeginMSIPreambleData
\providecommand{\U}[1]{\protect\rule{.1in}{.1in}}
%EndMSIPreambleData
\DeclareGraphicsExtensions{.png, .jpg, .pdf, .mps}
\makeatletter
\font\toto=cmssbx10 scaled 1300
\newfont{\totoa}{cmss12}
\font\totonch=cmr10 scaled 8000
\@addtoreset{equation}{chapter}
\@addtoreset{figure}{chapter}
\renewenvironment{theindex}
{  \if@twocolumn
\@restonecolfalse
\else
\@restonecoltrue
\fi
\columnseprule \z@
\columnsep 35\p@
\twocolumn[\@makeschapterhead{\indexname}]
\@mkboth{\indexname}{\indexname}
\thispagestyle{plain}\parindent\z@
\parskip\z@ \@plus .3\p@\relax
\let\item\@idxitem
}
{\if@restonecol\onecolumn\else\clearpage\fi}
\def\@makechapterhead#1{  \vspace*{50\p@}
{  \parindent \z@ \raggedright \normalfont
\interlinepenalty\@M
\ifnum \c@secnumdepth >\m@ne
\begin{center}
\raisebox{0pt}[0pt][0pt]{\Huge\textbf{\raisebox{0ex}{C}\raisebox{1.8ex}{h}\raisebox{2.6ex}{a}\raisebox{3.2ex}{\hspace*{3.0pt}p}\raisebox{2.6ex}{\hspace*{3.0pt}i}\raisebox{2.0ex}{\hspace*{3.0pt}t}\raisebox{1.2ex}{r}\raisebox{0ex}{\hspace*{-3.0pt}e}}}{\vspace*{0.0ex}\totonch \thechapter\quad}
\end{center}
\fi
\begin{center}
\Huge \bfseries #1\par\nobreak
\vspace*{-0.5cm}
\rule{12.5cm}{0.02cm}\vspace*{-3.6ex}
\rule{12.5cm}{0.08cm}
\vskip 40\p@
\end{center}
}}
\def\tableofcontents{\chapter*{Table des mati\`eres\markboth{Table des mati\`eres}{Table des mati\`eres}}\@starttoc{toc}}
\def\@makeschapterhead#1{\vspace*{50\p@}{\parindent \z@ \raggedright
\normalfont
\interlinepenalty\@M
\begin{center}
\Huge \bfseries #1\par\nobreak
\vspace*{-0.5cm}
\rule{8.5cm}{0.02cm}\vspace*{-3.6ex}
\rule{8.5cm}{0.08cm}
\vskip 40\p@
\end{center}
}}
\makeatother
\newenvironment{demonstration}[1][D\'emonstration]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\newenvironment{proof}[1][Preuve]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\def\contentsname{Table des mati\`eres}
\markright{section} \markboth{section}{}
\def\thefootnote{(\arabic{footnote})}
\def\theequation{\arabic{equation}}
\theoremstyle{break}
\newtheorem{theo}{Th\'eor\`eme}
\cornersize{.2}
\newcounter{theorem}
\newenvironment{theorem}
{\begin{Sbox}  \begin{minipage}{\textwidth}\medskip\begin{theo} }
{\medskip\end{theo}  \end{minipage}  \end{Sbox}\Ovalbox{\TheSbox}}
\newtheorem{prop}[theo]{Proposition}
\newenvironment{proposition}
{\begin{Sbox}  \begin{minipage}{\textwidth}\medskip\begin{prop} }
{\medskip\end{prop}  \end{minipage}  \end{Sbox}\Ovalbox{\TheSbox}}
\newtheorem{corol}[theo]{Corollaire}
\newenvironment{corollary}
{\begin{Sbox}  \begin{minipage}{\textwidth}\medskip\begin{corol} }
{\medskip\end{corol}  \end{minipage}  \end{Sbox}\Ovalbox{\TheSbox}}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{criterion}[theorem]{Crit\`ere}
\newtheorem{lemma}[theorem]{Lemme}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summaire}
\theorembodyfont{\normalfont}
\newtheorem{defn}[theo]{D\'efinition}
\newenvironment{definition}
{\begin{Sbox}  \begin{minipage}{\textwidth}\medskip\begin{defn} }
{\medskip\end{defn}  \end{minipage}  \end{Sbox}\doublebox{\TheSbox}}
\newtheorem{exple}{Exemple}
\newenvironment{example}{\begin{exple} }{\end{exple}}
\newtheorem{exerc}{Exercice}
\newenvironment{exercise}{\begin{exerc} }{\end{exerc}}
\newtheorem{remar}[theo]{Remarque}
\newenvironment{remark}{\begin{remar} }{\end{remar}}
\def\listfigurename{Liste des Figures}
\def\listtablename{Liste des Tables}
\def\bibname{R\'ef\'erences}
\def\indexname{Index}
\def\thefigure{\arabic{chapter}.\arabic{figure}}
\def\tablename{Table}
\def\appendixname{Appendice}
\def\partname{Partie}
\def\abstractname{R\'esum\'e}
{}
\pagestyle{empty}
\pagestyle{plain}
\def\baselinestretch{1.5}
\setlength{\voffset}{-0.8cm}
\setlength{\hoffset}{0.5cm}
\topmargin=-0.5cm
\headheight=0.5cm
\headsep=0.6cm
\textheight=25cm
\textwidth=17cm
\marginparwidth=1.5cm
\marginparsep=0.3cm
\rightskip=0cm
\leftskip=0cm
\footskip=1cm
\oddsidemargin=-.8cm
\evensidemargin=-.8cm
\setlength{\parindent}{0pt}
\setlength{\parskip}{0.1in}
\setcounter{page}{1}
\pagestyle{fancy}
\renewcommand{\chaptermark}[1]{\markright{\thechapter.\ #1}}
\renewcommand{\sectionmark}[1]{\markright{\thesection.\ #1}}
\fancyhf{}
\fancyfoot[C]{\thepage}
\fancyhead[R]{\slshape\rightmark}
\fancyhead[RE]{\slshape\leftmark}
\renewcommand{\headrulewidth}{0.35pt}
\renewcommand{\footrulewidth}{0pt}
\addtolength{\headheight}{0.4pt}
\fancypagestyle{plain}{ \fancyhead{} \renewcommand{\headrulewidth}{0pt} }
\renewcommand{\mtctitle}{Sommaire}
\widowpenalty=10000
\clubpenalty=10000
\raggedbottom
\DeclareFontFamily{U}{rsfs}{\skewchar\font127 }
\DeclareFontShape{U}{rsfs}{ub}{sl}{<5> <6> rsfs5
<7> rsfs7
<8> <9> <10> <10.95> <12> <14.4> <17.28> <20.74> <24.88> rsfs10
}{}
\DeclareSymbolFont{rsfs}{U}{rsfs}{ub}{sl}
\DeclareSymbolFontAlphabet{\mathscr}{rsfs}
\DeclareSymbolFontAlphabet{\d}{rsfs}
\DeclareSymbolFontAlphabet{\C}{rsfs}
\DeclareSymbolFontAlphabet{\L}{rsfs}
\newcommand{\dd}[1]{\mathscr #1 {\hspace{-.1cm}}}
\definecolor{blue1}{rgb}{0,0,1}
\definecolor{red1}{rgb}{1,0,0}
\definecolor{black1}{rgb}{0,0,0}
%BeginMSIPreambleData
\ifx\pdfoutput\relax\let\pdfoutput=\undefined\fi
\newcount\msipdfoutput
\ifx\pdfoutput\undefined\else
\ifcase\pdfoutput\else
\msipdfoutput=1
\ifx\paperwidth\undefined\else
\ifdim\paperheight=0pt\relax\else\pdfpageheight\paperheight\fi
\ifdim\paperwidth=0pt\relax\else\pdfpagewidth\paperwidth\fi
\fi\fi\fi
%EndMSIPreambleData
\begin{document}
%
%TCIMACRO{\TeXButton{frontmatter}{\frontmatter}}%
%BeginExpansion
\frontmatter
%EndExpansion%
%TCIMACRO{\TeXButton{begintitlepage}{\begin{titlepage}}}%
%BeginExpansion
\begin{titlepage}%
%EndExpansion


\DeclareRobustCommand{\logousthb}{\begin{tikzpicture}[y=0.80pt,x=0.80pt,yscale=-1, scale=0.5,opacity=0.9]
\definecolor{cdar}{RGB}{0,0,255}
\definecolor{cfar}{RGB}{141,141,241}
\definecolor{cdfr}{RGB}{0,0,0}
\definecolor{cffr}{RGB}{255,153,0}
\definecolor{cdfr}{RGB}{0,0,0}
\definecolor{cdrec}{RGB}{0,0,204}
\definecolor{cfrec}{RGB}{0,0,204}
\definecolor{cdcap}{RGB}{0,0,204}
\definecolor{cfcap}{RGB}{153,102,255}
\newcommand{\linewdthar}{0.1pt}
\newcommand{\linewdthrec}{0.3pt}
\newcommand{\linewdthcap}{0.5pt}
\newcommand{\linewdthfr}{0.3pt}
\begin{scope}[shift={(-10,-10)}]
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (334.3500,230.4494) .. controls
(336.4591,227.6371) and (340.2868,225.6998) .. (343.5989,226.3403) .. controls
(350.0200,228.4495) and (348.7233,233.5585) .. (354.3320,234.3709) .. controls
(353.2383,236.6832) and (352.1291,238.9799) .. (352.1291,238.9799) --
(322.5077,238.9799) .. controls (316.7740,236.0739) and (328.4913,224.3874) ..
(324.4137,222.2157) .. controls (326.5228,220.0440) and (329.0381,217.7942) ..
(329.0381,217.7942) .. controls (332.3190,222.4500) and (323.1482,231.5586) ..
(325.6167,234.2615) -- (343.8957,234.1678) .. controls (343.6926,233.1679) and
(339.0682,229.0433) .. (334.3500,230.4494) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (332.7721,244.5888) -- (337.1778,246.7917) --
(341.7710,242.7764) -- (337.3809,240.6673) -- (332.7721,244.5888) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (316.7115,238.8861) .. controls
(317.5239,236.6676) and (321.0235,232.0430) .. (317.6177,227.1215) .. controls
(310.9935,228.3245) and (311.7903,230.6368) .. (305.7754,233.7616) .. controls
(301.0572,234.4646) and (295.6047,234.5896) .. (294.4330,233.7616) .. controls
(293.1988,232.7929) and (298.7450,232.0430) .. (298.3544,228.0277) .. controls
(296.9483,225.0123) and (290.8865,226.1528) .. (288.5118,226.8247) .. controls
(286.0121,228.4339) and (284.6998,231.1524) .. (284.1061,232.0430) .. controls
(284.1061,232.0430) and (284.5279,232.1523) .. (284.9966,232.2461) .. controls
(286.6058,230.2463) and (288.0119,231.9492) .. (287.9181,233.4647) .. controls
(285.1997,234.4646) and (280.9815,234.1678) .. (278.0756,234.2615) .. controls
(272.5606,234.3552) and (269.1392,234.3552) .. (268.3424,233.8553) .. controls
(267.6394,231.6524) and (271.2795,221.0908) .. (271.1546,219.4815) .. controls
(269.0454,220.9033) and (267.6394,222.9031) .. (267.2332,224.4186) .. controls
(259.2498,226.3560) and (254.7659,232.0430) .. (253.2817,233.7616) .. controls
(256.2033,234.4646) and (258.6092,234.8709) .. (259.7185,234.9646) .. controls
(262.1244,234.0584) and (264.1554,232.6211) .. (265.5615,231.9180) .. controls
(264.3585,236.2301) and (264.3273,237.3707) .. (266.3426,238.8862) .. controls
(271.6545,239.3861) and (278.3724,238.9799) .. (282.2938,239.0893) .. controls
(287.6057,238.1831) and (286.6058,237.6831) .. (289.0118,236.8707) .. controls
(290.1210,239.2924) and (293.5268,239.2924) .. (297.0420,239.0893) .. controls
(300.8541,239.4799) and (305.7754,238.2768) .. (306.8846,236.8707) .. controls
(310.6966,238.3862) and (313.8056,239.0893) .. (316.7115,238.8862);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar]
(273.3262,212.9821) -- (269.7953,215.4975) -- (267.0769,214.4976) --
(263.1555,217.2942) -- (266.4833,219.2941) -- (269.7953,216.5912) --
(272.7169,217.7942) -- (276.5289,214.6851) -- (273.3262,212.9821) -- cycle;
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (310.5248,233.0898) .. controls
(310.8372,232.4804) and (311.9465,231.1681) .. (312.8526,231.5743) .. controls
(313.8525,231.4806) and (314.9617,233.7928) .. (314.5712,233.9803) .. controls
(313.8525,233.9803) and (311.5403,233.4804) .. (310.5248,233.0898);
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (260.9683,229.8244) .. controls
(261.2808,229.2307) and (265.5927,227.1059) .. (266.5926,227.2153) --
(266.0927,229.0276) .. controls (264.1867,230.7306) and (260.9683,230.1369) ..
(260.9683,229.8244) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (230.8157,221.6063) .. controls
(232.4561,222.4500) and (236.9400,228.2464) .. (237.2368,231.2618) .. controls
(237.5336,234.2615) and (235.7370,238.2925) .. (232.7217,239.7923) .. controls
(230.3001,240.0892) and (227.1911,238.6830) .. (224.8789,237.0738) .. controls
(220.4576,238.6830) and (220.6607,238.8861) .. (216.1456,239.0893) .. controls
(210.3182,244.7138) and (205.0845,247.4167) .. (201.7724,246.6199) .. controls
(197.9603,245.8231) and (194.8357,242.8702) .. (193.7265,241.9640) --
(195.1482,241.1047) .. controls (198.1478,243.1983) and (203.4753,245.3075) ..
(212.7242,238.5893) .. controls (207.3029,239.3861) and (207.4592,235.8708) ..
(208.2716,234.3084) .. controls (210.5838,230.6837) and (213.6303,226.2310) ..
(218.2547,226.9340) .. controls (221.3637,229.6525) and (218.0829,233.0585) ..
(218.6453,234.1678) .. controls (219.7545,234.0741) and (219.3483,234.2615) ..
(221.6606,233.6678) .. controls (223.1760,230.6525) and (224.7852,227.8402) ..
(228.1910,226.9340) .. controls (227.4880,226.2310) and (227.2849,226.2310) ..
(227.2849,226.2310) -- (230.8157,221.6063) -- cycle;
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (229.3003,229.5432) .. controls
(229.9096,229.5432) and (229.6752,230.9024) .. (229.4096,231.3399) .. controls
(229.1440,231.7774) and (228.2848,232.2305) .. (227.6755,232.2305) .. controls
(227.0662,232.2305) and (225.4726,231.6993) .. (225.7538,231.2305) .. controls
(226.0194,230.7774) and (226.9724,229.2307) .. (229.3003,229.5432);
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (232.5967,230.8556) .. controls
(232.5967,231.2618) and (230.5657,233.0585) .. (230.1595,233.4647) .. controls
(231.1750,234.4490) and (233.9091,234.9802) .. (234.3153,234.5584) .. controls
(234.9090,233.2616) and (232.9561,231.6211) .. (232.5967,230.8556);
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (215.6613,234.3553) .. controls
(216.1612,232.2461) and (215.3645,231.4337) .. (214.6614,231.3399) .. controls
(213.5678,231.2305) and (211.6618,232.3398) .. (212.1617,233.5585) .. controls
(212.3023,234.0272) and (215.0364,234.1990) .. (215.6613,234.3553);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (200.2257,217.9192) -- (194.9919,222.8406) ..
controls (193.5859,230.4494) and (192.2735,235.1677) .. (189.3520,239.6673) ..
controls (189.8988,239.9017) and (190.4612,240.1673) .. (190.4612,240.1673) ..
controls (191.5392,239.1674) and (194.1952,237.2613) .. (195.8043,233.5585) ..
controls (197.3823,229.8557) and (200.2257,217.9192) .. (200.2257,217.9192) --cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (186.5398,227.6059) .. controls
(185.0400,229.9182) and (183.5246,232.2305) .. (183.5246,232.2305) .. controls
(184.3214,234.1366) and (185.1962,235.6208) .. (183.8214,237.0582) .. controls
(181.7123,239.1674) and (174.4788,242.6515) .. (171.2604,243.3858) .. controls
(168.0577,244.1201) and (165.8392,242.4796) .. (164.5269,241.5734) .. controls
(163.7301,242.1046) and (162.9177,242.6827) .. (162.9177,242.6827) .. controls
(164.2613,243.5420) and (168.9170,247.2917) .. (172.5728,246.7917) .. controls
(176.2286,246.2918) and (182.1497,242.3077) .. (184.7276,239.7611) .. controls
(186.1336,236.9488) and (187.3366,233.9334) .. (188.0397,231.5274) .. controls
(187.9460,230.1213) and (188.0397,229.1213) .. (186.5398,227.6058);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (159.4181,231.8711) .. controls
(160.7148,231.7305) and (161.7147,231.2618) .. (162.2303,233.6678) .. controls
(163.5270,232.9648) and (166.2298,230.4494) .. (165.0268,228.1527) .. controls
(164.1676,226.2310) and (156.2310,228.3870) .. (150.3880,235.9801) .. controls
(149.1069,239.4642) and (153.7001,238.5893) .. (157.4028,239.1986) .. controls
(155.6373,240.1048) and (141.4516,244.2138) .. (139.7487,241.3078) .. controls
(138.3113,239.6048) and (143.8575,234.1053) .. (146.4666,232.1992) .. controls
(145.9979,231.9336) and (145.2636,231.7617) .. (145.2636,231.7617) .. controls
(138.7175,236.6832) and (136.3428,240.8704) .. (136.0772,243.2764) .. controls
(135.7960,245.6981) and (140.1549,246.3543) .. (143.5607,246.2293) .. controls
(146.9665,246.0887) and (153.6688,244.1201) .. (156.6060,242.4171) .. controls
(159.2150,240.4016) and (161.6522,237.1519) .. (161.2148,235.8864) .. controls
(160.7930,234.6053) and (154.4031,235.5427) .. (154.0907,234.8709) .. controls
(153.7938,234.2147) and (157.4028,232.4648) .. (159.4181,231.8711);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (148.1383,246.2918) -- (145.5136,248.4166) --
(142.8108,247.2136) -- (139.9830,249.6352) -- (142.7014,251.0414) --
(145.6229,248.9322) -- (148.5288,250.0415) -- (151.5441,247.7135) --
(148.1383,246.2918) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (123.9068,226.4341) .. controls
(124.6411,226.6372) and (125.2973,229.5588) .. (124.6099,231.8555) --
(121.3915,238.9955) -- (108.5493,239.0892) .. controls (102.7375,244.7137) and
(97.5194,247.4166) .. (94.2073,246.6198) .. controls (90.3953,245.8230) and
(86.7863,243.0108) .. (85.6771,242.1046) .. controls (85.6771,242.1046) and
(86.6145,241.6046) .. (87.5831,241.1047) .. controls (90.5984,243.2139) and
(95.9102,245.3231) .. (105.1435,238.5892) .. controls (99.7223,239.3861) and
(99.6285,236.3082) .. (100.5347,234.3708) .. controls (102.8313,230.7618) and
(106.0496,226.2309) .. (110.6584,226.9340) .. controls (113.7674,229.6525) and
(110.4866,233.0585) .. (111.0646,234.1677) .. controls (112.1582,234.0740) and
(117.5795,234.4646) .. (120.9853,234.3708) .. controls (121.7977,232.6679) and
(121.2978,232.8710) .. (120.1885,230.6524) -- (123.9068,226.4340) -- cycle;
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (107.9244,234.3553) .. controls
(108.4243,232.2461) and (107.6276,231.4337) .. (106.9245,231.3399) .. controls
(105.8309,231.2305) and (103.9249,232.3398) .. (104.4248,233.5585) .. controls
(104.5654,234.0272) and (107.2995,234.1990) .. (107.9244,234.3553);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (108.3618,244.3388) -- (112.7676,246.5418) --
(117.3607,242.5421) -- (113.0644,240.2298) -- (108.3618,244.3388) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (87.4269,238.8861) .. controls
(88.2237,236.6676) and (91.7389,232.0586) .. (88.3330,227.1371) .. controls
(81.6932,228.3402) and (82.3025,230.7462) .. (76.2720,233.8709) .. controls
(71.3507,234.5740) and (62.7111,234.2615) .. (60.8051,234.2615) .. controls
(60.8989,232.1523) and (62.6174,230.0431) .. (62.7111,227.6371) .. controls
(63.1173,226.2310) and (62.4143,223.7156) .. (60.3052,222.5125) .. controls
(60.1958,222.1063) and (58.2898,225.2623) .. (56.2900,227.8402) .. controls
(57.0868,229.1370) and (59.2897,228.7464) .. (58.2898,234.0584) .. controls
(54.9777,233.9647) and (48.3535,234.9646) .. (48.6503,233.1679) --
(47.4474,233.1679) .. controls (44.1196,237.7769) and (44.9320,238.7768) ..
(47.0412,238.9799) .. controls (52.1655,239.0111) and (63.4142,239.1830) ..
(67.7418,239.0893) .. controls (71.5538,239.4799) and (76.4751,238.2768) ..
(77.5843,236.8707) .. controls (81.3964,238.3862) and (84.5054,239.0893) ..
(87.4269,238.8862) -- cycle;
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (81.3651,232.9648) .. controls
(81.6776,232.3554) and (82.7868,231.0431) .. (83.6930,231.4493) .. controls
(84.6928,231.3556) and (85.8021,233.6678) .. (85.4115,233.8553) .. controls
(84.6928,233.8553) and (82.3806,233.3554) .. (81.3651,232.9648);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (40.9325,242.0734) -- (37.2142,240.3548) --
(34.0896,242.8858) -- (31.1837,241.7765) -- (27.2467,245.1044) --
(30.6681,246.9167) -- (33.7928,244.2919) -- (36.4175,245.6043) --
(40.9325,242.0734) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (44.9477,226.6059) .. controls
(45.7132,226.7465) and (46.2444,229.4963) .. (45.8538,231.5430) --
(42.4323,238.8862) .. controls (42.4323,238.8862) and (35.9331,238.9799) ..
(29.4808,239.0893) .. controls (28.3716,240.9953) and (28.3716,242.1046) ..
(24.7626,244.3232) .. controls (22.3410,245.6200) and (8.5771,249.1040) ..
(4.7338,243.4170) .. controls (3.6871,238.0112) and (12.8422,232.1523) ..
(14.6388,230.0744) -- (15.6075,230.9337) .. controls (14.6388,232.5117) and
(8.1084,236.3707) .. (8.7177,239.5892) .. controls (10.1550,243.0420) and
(23.6221,242.9014) .. (26.7624,239.4955) .. controls (29.2777,237.3707) and
(28.3716,234.1522) .. (27.6685,232.4492) .. controls (27.6685,232.4492) and
(29.7776,230.1682) .. (31.8868,227.9184) .. controls (32.5898,228.2152) and
(33.0897,231.9493) .. (31.7930,234.1522) .. controls (36.9174,234.1522) and
(42.0261,234.1522) .. (42.0261,234.1522) .. controls (43.0416,232.0430) and
(42.0261,231.8399) .. (41.1356,230.7306) .. controls (43.0416,228.6527) and
(44.9477,226.6060) .. (44.9477,226.6060) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (19.8101,226.3403) -- (24.2158,228.5433) --
(28.8090,224.5436) -- (24.5126,222.2313) -- (19.8101,226.3403) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (276.4820,274.9456) .. controls
(273.9667,281.7888) and (282.1688,278.6484) .. (280.4659,279.8202) .. controls
(271.4983,286.2884) and (267.1082,284.1636) .. (263.1555,282.0544) .. controls
(262.4837,282.5231) and (261.8432,282.9918) .. (261.8432,282.9918) .. controls
(271.3577,291.6630) and (277.2788,286.6634) .. (284.2780,280.0858) .. controls
(295.6203,280.0546) and (306.9783,280.0546) .. (306.9783,280.0546) .. controls
(312.2902,279.1484) and (311.2903,278.6485) .. (313.6963,277.8517) .. controls
(314.8055,280.2421) and (318.2270,280.2421) .. (321.7265,280.0546) --
(343.3177,279.9452) -- (345.8330,275.4769) -- (348.0827,264.4153) --
(349.1138,264.6809) .. controls (349.6450,263.2123) and (351.8947,261.8530) ..
(352.0197,260.7125) .. controls (351.4885,260.0407) and (348.4733,260.0407) ..
(349.7856,258.0721) -- (348.9732,257.3065) .. controls (348.0827,258.0721) and
(344.8956,260.9781) .. (344.3644,262.6811) -- (345.4268,263.3529) .. controls
(344.0988,269.1961) and (343.0521,275.2113) .. (343.0521,275.2113) --
(334.8499,274.9457) -- (337.0997,264.5559) .. controls (337.0997,264.5559) and
(337.5684,264.6496) .. (338.0371,264.7903) .. controls (338.8338,263.6185) and
(340.5524,262.0561) .. (340.9430,260.5719) .. controls (338.4433,259.0095) and
(338.5682,259.8063) .. (338.4433,257.8065) -- (337.6309,257.5721) .. controls
(336.8341,258.3689) and (334.0844,260.1813) .. (333.5532,262.6811) .. controls
(333.9126,263.2904) and (334.4594,263.4779) .. (334.3188,263.8841) --
(331.8503,275.0707) -- (319.1487,275.0707) .. controls (317.6802,274.0707) and
(323.6482,272.0397) .. (323.0389,269.0243) .. controls (321.6328,266.0245) and
(315.5710,267.1651) .. (313.1963,267.8213) .. controls (310.6810,269.4305) and
(309.3843,272.1334) .. (308.7750,273.0396) .. controls (308.7750,273.0396) and
(309.2124,273.1333) .. (309.6811,273.2427) .. controls (311.2903,271.2272) and
(312.6964,272.9302) .. (312.6026,274.4457) .. controls (309.8842,275.4456) and
(309.7905,275.1019) .. (306.8690,275.2113) -- (308.9781,264.4153) --
(309.9155,264.9153) .. controls (311.4934,263.0873) and (313.0713,261.9155) ..
(312.9307,260.3063) .. controls (310.5560,260.5719) and (310.5560,258.8689) ..
(310.6810,258.0721) -- (310.0561,257.1659) .. controls (308.4469,259.2751) and
(306.0722,260.8531) .. (305.1660,262.6811) .. controls (305.1660,262.6811) and
(305.8691,263.0873) .. (306.6034,263.4779) -- (304.0881,275.2113) --
(286.3871,275.2113) .. controls (286.5277,275.0706) and (290.2304,269.1649) ..
(285.7465,267.8213) .. controls (281.9032,267.9619) and (278.0912,272.1959) ..
(276.4820,274.9457) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (262.9056,280.2264) .. controls
(257.1250,280.2264) and (252.4693,279.4140) .. (248.6573,281.9294) .. controls
(248.6573,287.7414) and (248.3917,290.2568) .. (244.8452,292.2254) .. controls
(245.7514,287.3508) and (245.7514,286.2728) .. (246.0170,281.9294) .. controls
(248.7979,277.9766) and (249.0635,276.9142) .. (258.4217,275.6018) .. controls
(256.3126,271.9302) and (254.6097,275.0706) .. (252.7349,275.7424) --
(251.4382,275.1956) .. controls (261.0620,265.2902) and (262.9056,270.8522) ..
(265.4053,275.1956) -- (262.9056,280.2264) -- cycle;
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (283.6530,275.4143) .. controls
(284.1530,273.3051) and (283.3562,272.4927) .. (282.6532,272.3989) .. controls
(281.5595,272.2896) and (279.6535,273.3989) .. (280.1535,274.6175) .. controls
(280.2941,275.0862) and (283.0281,275.2581) .. (283.6530,275.4143);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (220.3014,279.9139) .. controls
(214.7083,285.4916) and (209.2558,288.2258) .. (205.9437,287.4289) .. controls
(202.1317,286.6321) and (198.5228,283.8199) .. (197.4135,282.9293) .. controls
(197.4135,282.9293) and (198.3509,282.4294) .. (199.3352,281.9294) .. controls
(202.3348,284.0230) and (207.6623,286.1322) .. (216.8955,279.4140) .. controls
(211.4743,280.2264) and (211.3649,277.1486) .. (212.2711,275.2112) .. controls
(214.5833,271.6021) and (218.6609,266.7901) .. (222.4105,267.8056) .. controls
(225.4101,270.0710) and (222.3793,275.3518) .. (220.3014,279.9139);
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (219.5983,275.4768) .. controls
(220.0983,273.3676) and (219.3015,272.5552) .. (218.5828,272.4614) .. controls
(217.4736,272.3521) and (215.5363,273.4614) .. (216.0519,274.6800) .. controls
(216.1925,275.1487) and (218.9578,275.3206) .. (219.5983,275.4768);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (191.1018,258.9157) -- (185.8680,263.8528) ..
controls (184.4620,271.4928) and (183.1496,276.2111) .. (180.2281,280.7264) ..
controls (180.7749,280.9607) and (181.3373,281.2263) .. (181.3373,281.2263) ..
controls (182.4153,280.2264) and (185.0713,278.3203) .. (186.6804,274.6019) ..
controls (188.2584,270.8835) and (191.1018,258.9157) .. (191.1018,258.9157) --cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (105.2060,274.9456) .. controls
(102.7063,281.7888) and (111.1271,278.5078) .. (109.4242,279.6796) .. controls
(100.4565,286.1634) and (95.8165,284.0230) .. (91.8638,281.9294) --
(90.5515,283.1324) .. controls (99.9254,291.5380) and (105.9715,286.3978) ..
(113.0956,280.0858) -- (175.7755,280.0858) -- (177.9159,275.4768) --
(180.1656,264.4152) -- (181.1967,264.6808) .. controls (181.7279,263.2122) and
(183.9776,261.8373) .. (184.1026,260.7124) .. controls (183.5714,260.0406) and
(180.5718,260.0406) .. (181.8685,258.0720) -- (181.0717,257.2908) .. controls
(180.1656,258.0720) and (176.9785,260.9780) .. (176.4473,262.6810) --
(177.5253,263.3528) -- (175.1506,275.2112) -- (157.7152,274.9456) .. controls
(159.4338,271.2584) and (159.4338,269.5554) .. (157.9808,267.6962) --
(154.2781,271.3990) .. controls (155.0749,273.2426) and (155.0749,272.3052) ..
(155.3405,275.3362) -- (145.0449,275.2112) .. controls (143.8731,272.9614) and
(142.4046,269.4305) .. (139.6237,266.3838) .. controls (142.1390,264.9152) and
(147.8258,264.1497) .. (147.8258,264.1497) -- (149.6537,259.8063) .. controls
(135.4054,262.9466) and (134.2337,265.3214) .. (133.7025,269.0242) .. controls
(134.4055,270.4616) and (135.8116,271.9302) .. (135.8116,271.9302) --
(136.9834,271.2584) .. controls (138.7175,272.6958) and (140.7017,274.5394) ..
(141.2328,275.0706) -- (127.7501,275.0706) .. controls (129.4843,273.5082) and
(130.1248,268.3524) .. (128.2813,267.5556) -- (124.7036,271.3990) .. controls
(125.6410,273.5082) and (126.0472,274.9456) .. (125.3754,275.3362) --
(115.3454,275.2112) .. controls (115.0798,274.3050) and (118.9230,269.1649) ..
(114.4392,267.8212) .. controls (110.5959,267.9618) and (106.8151,272.1958) ..
(105.2060,274.9456) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (159.9962,259.6657) -- (156.9341,262.3061) --
(154.0125,260.9780) -- (150.0443,264.4153) -- (153.6063,266.1026) --
(156.7935,263.7434) -- (159.3244,265.1808) -- (163.5426,261.5092) --
(159.9962,259.6657) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (125.4223,262.8997) -- (129.8592,265.1027) --
(134.4837,261.1030) -- (130.1561,258.7907) -- (125.4223,262.8997) -- cycle;
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (112.3614,275.3518) .. controls
(112.8613,273.2426) and (112.0645,272.4302) .. (111.3615,272.3365) .. controls
(110.2679,272.2271) and (108.3618,273.3364) .. (108.8618,274.5550) .. controls
(109.0024,275.0237) and (111.7364,275.1956) .. (112.3613,275.3518);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (92.5356,262.6654) .. controls
(93.0668,260.8374) and (96.3477,258.0564) .. (97.0195,257.4158) --
(98.0975,257.7908) .. controls (97.0195,259.4001) and (98.7224,259.7594) ..
(100.3316,260.5562) .. controls (101.3627,260.0250) and (98.7224,262.6654) ..
(97.2851,264.7746) .. controls (97.2851,264.7746) and (97.3163,265.0090) ..
(96.3477,264.6652) -- (94.1136,275.1956) -- (92.0044,279.9452) --
(80.9589,280.0389) .. controls (75.1315,285.6478) and (69.9134,288.3507) ..
(66.6013,287.5539) .. controls (62.7892,286.7571) and (59.1647,283.9448) ..
(58.0554,283.0386) .. controls (58.0554,283.0386) and (58.9928,282.5387) ..
(59.9771,282.0387) .. controls (62.9767,284.1479) and (68.3042,286.2571) ..
(77.5375,279.5389) .. controls (72.1162,280.3357) and (72.0225,277.2735) ..
(72.9286,275.3362) .. controls (75.2252,271.7271) and (78.4436,267.2119) ..
(83.0680,267.9149) .. controls (86.1770,270.6178) and (82.8962,274.0238) ..
(83.4586,275.1331) .. controls (84.5679,275.0237) and (87.7862,275.2893) ..
(91.1920,275.1956) -- (93.7074,263.4622) -- (92.5356,262.6654) -- cycle;
\path[draw=cdar,fill=white,even odd rule,line width=\linewdthar] (80.2403,275.3518) .. controls
(80.7402,273.2426) and (79.9434,272.4302) .. (79.2248,272.3365) .. controls
(78.1155,272.2271) and (76.1782,273.3364) .. (76.6938,274.5550) .. controls
(76.8344,275.0237) and (79.5997,275.1956) .. (80.2403,275.3518);
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (42.0261,271.4615) .. controls
(44.1353,268.6649) and (47.9473,266.7276) .. (51.2594,267.3525) .. controls
(57.6805,269.4617) and (56.3838,274.5706) .. (61.9925,275.3674) .. controls
(60.8989,277.6798) and (59.7896,279.9764) .. (59.7896,279.9764) --
(8.0615,279.8202) .. controls (2.4997,277.0392) and (14.1233,265.3839) ..
(10.0300,263.2122) -- (14.5139,258.7282) .. controls (17.5604,263.4778) and
(9.7644,271.1334) .. (11.2330,275.0706) -- (25.4969,275.2112) .. controls
(25.7625,273.6332) and (25.6219,272.8364) .. (24.8251,271.8053) --
(28.3716,267.5556) .. controls (31.0119,269.9304) and (27.9966,275.0706) ..
(27.9966,275.0706) -- (51.5562,275.1800) .. controls (51.3531,274.1644) and
(46.7443,270.0554) .. (42.0261,271.4615) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (40.4951,285.5853) -- (44.9320,287.7883) --
(49.5565,283.7886) -- (45.2289,281.4763) -- (40.4951,285.5853) -- cycle;
\path[draw=cdar,fill=cfar,even odd rule,line width=\linewdthar] (24.3095,283.0543) -- (20.6069,281.3513) --
(17.4979,283.8511) -- (14.6076,282.7575) -- (10.6862,286.0540) --
(14.0920,287.8508) -- (17.2010,285.2573) -- (19.8101,286.5540) --
(24.3095,283.0543) -- cycle;
\path[draw=cdrec,fill=cfrec, even odd rule,line width=\linewdthrec](11.7486,167.2359) -- (11.7486,163.7987) --
(354.8944,163.7987) -- (354.8944,209.9823)  -- (4.0776,209.9823) -- (4.0776,167.2359)
-- (4.0776,163.7987) -- (11.7486,163.7987) -- (11.7486,171.6106)  -- (9.1239,171.6106)
-- (9.1239,205.9202)-- (11.9985,205.9202)-- (11.9985,208.8575)-- (347.2703,208.8575)
-- (347.2703,205.9202) -- (350.1450,205.9202)-- (350.1450,171.6106)
-- (347.2703,171.6106) -- (347.2703,167.2359)-- (11.7486,167.2359);
\foreach \x in {-46.5,-31,-15.5,0,15.5,31,46.5,62,77.5,93,108.5,124,139.5,155,170.5,186,201.5,217,232.5,248,263.5}
\path[shift={(\x,0)},draw=cdrec,fill=cfrec,even odd rule,line width=\linewdthrec](69.7415,205.9202) -- (69.7415,209.7949) --
(74.3660,209.7949) -- (74.3660,205.9202) -- (72.6960,205.9202)  -- (72.6960,171.6106)
-- (74.3660,171.6106) -- (74.3660,163.9862)-- (69.7415,163.9862)-- (69.7415,171.6106)
-- (71.4115,171.6106) -- (71.4115,205.9202)-- (69.7415,205.9202);
\path[shift={(0,-1)},draw=cdcap,fill=cfcap,even odd rule,line width=\linewdthcap] (139.1706,145.9408) .. controls
(140.0924,150.5655) and (122.6257,161.2677) .. (126.7659,186.8280) .. controls
(107.4713,180.2661) and (90.0047,155.9244) .. (83.3336,144.4722) .. controls
(83.3336,144.4722) and (95.7540,148.8625) .. (108.1587,153.2371) .. controls
(97.8162,106.5067) and (137.7958,71.4627) .. (145.3730,59.0419) .. controls
(147.4352,61.9635) and (148.8257,61.9635) .. (152.9502,67.0725) .. controls
(158.4651,42.2464) and (171.3386,47.3710) .. (168.8076,44.4494) .. controls
(161.9178,44.1994) and (121.9383,49.5583) .. (110.2210,66.3538) .. controls
(105.3935,68.5411) and (137.7958,59.2919) .. (137.7958,61.2448) .. controls
(126.7659,69.2754) and (77.1313,88.9925) .. (57.1493,159.8147) .. controls
(57.1493,159.8147) and (30.9650,159.8147) .. (4.0776,159.8147) .. controls
(0.6249,56.1203) and (108.8461,2.0936) .. (172.9477,2.0936) .. controls
(233.5966,0.6249) and (350.7699,37.8718) .. (354.8944,159.8147) .. controls
(316.5397,159.8147) and (278.4037,159.8147) .. (278.4037,159.8147) .. controls
(275.6384,159.5647) and (261.3901,157.3774) .. (260.4684,157.6274) .. controls
(259.5622,157.8617) and (268.0612,160.5490) .. (272.1857,162.0020) .. controls
(270.1234,165.6579) and (261.1714,170.0326) .. (264.6085,190.4840) .. controls
(241.8612,185.3750) and (228.3160,152.5184) .. (226.0194,146.6752) .. controls
(226.0194,146.6752) and (250.1415,155.4400) .. (250.1415,155.4400) .. controls
(232.2218,109.4283) and (279.7785,64.6508) .. (287.3557,48.8240) .. controls
(287.3557,48.8240) and (296.3234,59.7762) .. (296.3234,59.7762) .. controls
(303.9006,29.8412) and (312.8526,35.9189) .. (310.7904,32.0286) .. controls
(263.9211,34.9502) and (250.1415,57.1046) .. (244.6265,60.5105) .. controls
(244.6265,60.5105) and (281.8408,50.2926) .. (279.0911,51.7456) .. controls
(287.3557,46.6367) and (213.6147,75.8374) .. (194.3045,152.5184) .. controls
(194.3045,152.5184) and (209.4746,145.9408) .. (209.4746,145.9408) .. controls
(201.1943,156.1587) and (194.3045,179.5318) .. (197.0698,189.0153) .. controls
(190.8674,192.4213) and (157.0903,162.7363) .. (152.9502,145.2065) .. controls
(152.9502,145.2065) and (177.7597,151.0498) .. (177.7597,151.0498) .. controls
(166.7454,107.2410) and (208.7871,59.0419) .. (213.6147,53.1986) .. controls
(212.2242,55.4016) and (221.1919,63.4322) .. (221.1919,63.4322) .. controls
(219.1140,58.3232) and (227.3943,45.1681) .. (233.5966,38.6061) .. controls
(210.1620,40.0591) and (190.1800,48.8240) .. (173.6352,64.1665) --
(204.6470,56.1203) .. controls (200.7412,62.2135) and (150.2005,74.3844) ..
(120.5635,158.3460) .. controls (120.5635,158.3460) and (139.1706,145.9408) ..
(139.1706,145.9408) -- cycle;
\path[draw=cdfr,fill=cffr,even odd rule,line width=\linewdthfr] (24.0596,296.7407) -- (23.7940,297.6625) ..
controls (20.7943,297.6625) and (18.5134,297.4593) .. (16.9511,301.3965) ..
controls (13.7015,310.9895) and (4.3745,321.6917) .. (20.7943,322.5354) ..
controls (31.0275,322.2698) and (32.5898,317.0202) .. (38.7140,301.0059) ..
controls (40.3388,297.7249) and (37.2767,297.5218) .. (34.9333,297.5218) --
(35.1207,296.6625) -- (47.4317,296.6625) -- (46.9162,297.5218) .. controls
(40.8544,297.1313) and (42.1668,299.8185) .. (34.7302,316.0984) .. controls
(29.6526,325.2226) and (20.6694,324.8945) .. (14.5451,324.1133) .. controls
(9.1395,322.5978) and (4.8432,319.1919) .. (6.9210,313.9423) --
(12.5297,299.7560) .. controls (12.5297,297.7874) and (11.8736,297.7874) ..
(7.6397,297.5843) -- (7.9053,296.6625) -- (24.0596,296.7406) -- cycle;
\path[draw=cdfr,fill=cffr,even odd rule,line width=\linewdthfr] (88.9423,314.2860) -- (89.9891,314.3642) ..
controls (89.6610,318.4263) and (89.7235,318.0982) .. (91.3483,320.5355) ..
controls (96.6289,324.5977) and (101.1752,322.5666) .. (103.5968,321.9104) ..
controls (106.9089,318.6919) and (109.1274,316.3952) .. (97.5350,308.9115) ..
controls (87.3800,301.2246) and (98.2537,296.6938) .. (101.0502,296.2251) ..
controls (109.0024,294.9752) and (112.6426,300.0372) .. (115.6422,296.1001) --
(116.7358,296.1001) -- (113.8768,305.0993) -- (112.8300,305.2243) .. controls
(113.4862,299.9747) and (111.4708,299.6466) .. (108.6743,298.1936) .. controls
(106.4090,297.3500) and (100.8628,297.0844) .. (98.7693,300.0372) .. controls
(96.6914,303.5213) and (100.6597,305.1618) .. (103.3312,307.4585) .. controls
(110.2991,312.3799) and (112.3145,313.3017) .. (110.9553,318.6919) .. controls
(105.8621,327.2224) and (94.1448,323.9415) .. (91.1608,323.0978) .. controls
(89.2704,322.8947) and (88.2861,322.3010) .. (86.9269,324.5352) --
(85.6771,324.5352) -- (88.9423,314.2860) -- cycle;
\path[draw=cdfr,fill=cffr,even odd rule,line width=\linewdthfr] (161.7303,323.7853) -- (162.0584,323.0041) ..
controls (165.8392,323.3322) and (167.0891,322.0823) .. (168.3233,320.3793) --
(177.4472,298.2405) .. controls (167.3390,298.1155) and (166.0423,300.6778) ..
(164.6050,303.8338) -- (163.4958,303.8338) -- (166.2298,296.6625) --
(195.2263,296.6625) -- (192.2423,303.8963) -- (191.1330,303.7557) .. controls
(192.4297,297.4593) and (190.0238,298.3811) .. (182.3372,298.2405) --
(173.6039,320.0512) .. controls (172.4322,323.5353) and (175.9474,322.8010) ..
(178.8689,322.8791) -- (178.6189,323.7853) -- (161.7304,323.7853) -- cycle;
\path[draw=cdfr,fill=cffr,even odd rule,line width=\linewdthfr] (253.3442,323.7228) -- (253.7348,322.9416) ..
controls (258.6248,323.1291) and (258.7654,321.4261) .. (259.9997,319.1919) --
(263.7805,310.0677) -- (245.9233,310.1302) -- (242.0019,319.4575) .. controls
(240.5020,323.2072) and (243.5642,322.7385) .. (245.8608,323.0041) --
(245.7827,323.6603) .. controls (243.2673,323.7696) and (233.1280,323.7853) ..
(230.6595,323.6603) -- (230.9876,322.8791) .. controls (233.9872,323.2072) and
(235.5495,322.6135) .. (236.7994,319.7856) -- (244.5484,301.4590) .. controls
(246.1732,297.1938) and (243.5642,297.3969) .. (240.6427,297.6000) --
(240.9708,296.6782) -- (256.2189,296.6782) -- (255.8283,297.5218) .. controls
(252.7037,297.3344) and (251.2664,298.0530) .. (249.8915,300.7403) --
(246.5638,308.6303) -- (264.1711,308.6303) -- (267.3582,300.8028) .. controls
(268.4674,296.7407) and (265.7959,297.7250) .. (263.4524,297.4593) --
(263.7180,296.6000) -- (279.2161,296.6781) -- (278.6380,297.4593) .. controls
(273.9511,297.7874) and (274.0761,298.6467) .. (272.9044,300.0216) --
(264.8897,319.3950) .. controls (262.9993,322.8791) and (265.7958,322.8791) ..
(268.6705,323.0041) -- (268.4674,323.7852) -- (253.3442,323.7227) -- cycle;
\path[draw=cdfr,fill=cffr,even odd rule,line width=\linewdthfr] (347.1610,318.4732) .. controls
(343.1302,322.5510) and (341.9585,323.0666) .. (333.0377,323.7853) --
(315.8991,323.6603) -- (316.2272,322.8791) .. controls (319.2268,323.2072) and
(320.9141,322.6135) .. (322.0234,319.7856) -- (329.7724,301.4590) .. controls
(331.9284,296.9281) and (328.4757,297.4593) .. (325.8667,297.5843) --
(326.1947,296.6625) -- (341.4273,296.6625) .. controls (346.6454,297.2562) and
(350.5512,297.9124) .. (351.5823,302.7714) .. controls (350.0200,306.6461) and
(349.3169,307.7085) .. (341.4273,309.4740) -- (340.3180,308.0991) .. controls
(343.3177,306.7867) and (344.9425,305.8649) .. (345.8642,303.1776) .. controls
(346.1923,297.9906) and (340.4586,297.8499) .. (335.9592,298.2405) --
(331.5378,308.6147) .. controls (338.3651,308.6147) and (336.5529,308.5522) ..
(340.2555,308.0991) -- (341.4273,309.4115) -- (339.6150,311.1769) .. controls
(337.2715,310.3333) and (336.3498,310.0677) .. (331.0067,310.0677) --
(325.9916,322.0198) .. controls (335.7092,322.8791) and (339.0838,320.6449) ..
(341.4273,317.8795) .. controls (341.9585,315.5203) and (342.8646,313.3486) ..
(339.5369,311.2551) -- (341.4273,309.5365) .. controls (345.0831,310.1302) and
(349.7700,312.5675) .. (347.1610,318.4732) -- cycle;
\end{scope}
\end{tikzpicture}}

\begin{tikzpicture}[overlay, remember picture]
\definecolor{goldc}{RGB}{255,153,0}
\draw[shift={(-1.3,-26.1)}, line width=3.5pt,top color=goldc!20,bottom color=goldc!5] (0,0)  rectangle (19.2,28.0);
\draw[shift={(-1.1,-25.9)}, line width=1.5pt,top color=blue!35,middle  color=goldc!30] (0,0)  rectangle (18.8,27.6);
\end{tikzpicture}


{\vspace*{0cm} }

\begin{center}
\textbf{{\large U}NIVERSITÉ DES {\large S}CIENCES ET DE LA {\large T}%
ECHNOLOGIE}\newline\textbf{{\large H}OUARI {\large B}OUMEDIENNE}%
\footnote{USTHB : Bab Ezzouar Alger, Algérie.}

\textbf{{\large F}ACULTÉ DES {\large M}ATHÉMATIQUES}

\textbf{{\large D}ÉPARTEMENT D'{\large A}NALYSE\vspace{0.8cm}}

\logousthb


\textbf{\vspace{0.6cm}}

\textbf{{\LARGE Notes de Cours du module}}\textbf{\vspace{0.4cm}}

\textbf{{\Huge Séries (Math 3)}\vspace{0.4cm}}

\textbf{Par\vspace{0.3cm}}

\textbf{{\large LAADJ Toufik}}\footnote{Page Web :
\ \ \href{http://perso.usthb.dz/~tlaadj/}{http://perso.usthb.dz/\symbol{126}%
tlaadj/}}\vspace{0.4cm}

\textbf{Pour}\vspace{0.4cm}

\textbf{{\LARGE Deuxième année Licence}}

\textbf{{\LARGE Domaine : Sciences et Technologies}}
\end{center}

\vspace{0.4cm}

\begin{center}
Septembre 2013
\end{center}

%

%TCIMACRO{\TeXButton{endtitlepage}{\end{titlepage}}}%
%BeginExpansion
\end{titlepage}%
%EndExpansion
\newpage%

%TCIMACRO{\TeXButton{dominitoc}{\dominitoc}}%
%BeginExpansion
\dominitoc
%EndExpansion
%

%TCIMACRO{\TeXButton{tableofcontents}{\tableofcontents}}%
%BeginExpansion
\tableofcontents
%EndExpansion
%

%TCIMACRO{\TeXButton{markboth Table des matières}{\markboth{}%
%{Table des mati\`eres}}}%
%BeginExpansion
\markboth{}{Table des mati\`eres}%
%EndExpansion
%

%TCIMACRO{\TeXButton{addtocTOC}{\addcontentsline{toc}{chapter}
%{Table des mati\`eres}}}%
%BeginExpansion
\addcontentsline{toc}{chapter}
{Table des mati\`eres}%
%EndExpansion


\newpage

\chapter*{Description du Cours}%

%TCIMACRO{\TeXButton{addtocDescriptionduCours}{\addcontentsline{toc}{chapter}
%{Description du Cours}}}%
%BeginExpansion
\addcontentsline{toc}{chapter}
{Description du Cours}%
%EndExpansion
%

%TCIMACRO{\TeXButton{markbothDescriptionduCours}{\markboth{}%
%{Description du Cours}}}%
%BeginExpansion
\markboth{}{Description du Cours}%
%EndExpansion
%

%TCIMACRO{\TeXButton{adjustmtc}{\adjustmtc}}%
%BeginExpansion
\adjustmtc
%EndExpansion


\section*{\textbf{Objectif du Cours}\label{Objectif}}

L'objectif du module Séries (Math 3) est l'étude des sommes infinies%
\[
u_{0}+u_{1}+u_{2}+...+u_{n}+....
\]
Ces notes de cours donnent les principales définitions et les résultats
concernant ces sommes infinies (séries), illustrés par des exemples.

\section*{\textbf{Contenu du Cours}}

\begin{itemize}
\item Séries numériques

\item Suites et séries de fonctions

\item Séries entières

\item Séries de Fourier
\end{itemize}

\section*{\textbf{Résultats d'apprentissage}}

À la fin du cours, l'étudiant doit avoir une compréhension approfondie de la
théorie des séries et devrait être en mesure d'appliquer ces connaissances
pour résoudre les exercices dans une variété de contextes. En particulier,
l'étudiant doit être capable de :

\begin{itemize}
\item Comprendre ce qu'une série est.

\item Comprendre la distinction entre une suite, suite des sommes partielles
et une série.

\item Comprendre la condition nécessaire de convergence.

\item Étudier la nature des séries en utilisant les divers critères de convergence.

\item Comprendre la convergence absolue et semi convergence.

\item Étudier la convergence simple et uniforme des suites et des séries de fonctions.

\item Trouver le rayon de convergence et la somme d'une série entière.

\item Trouver le développement en séries entières d'une fonction.

\item Étudier la convergence d'une série de Fourier.

\item Développer une fonction en série de Fourier.

\item Trouver la somme des séries numériques en utilisant les séries de Fourier.
\end{itemize}

\mainmatter


\setcounter{chapter}{-1}

\chapter{Rappel sur les suites numériques réelles}%

%TCIMACRO{\TeXButton{minitoc}{\minitoc}}%
%BeginExpansion
\minitoc
%EndExpansion
%

%TCIMACRO{\TeXButton{adjustmtc}{\adjustmtc}}%
%BeginExpansion
\adjustmtc
%EndExpansion


\noindent Une suite numérique réelle est une application$\vspace{-0.5cm}$%
\[%
\begin{array}
[c]{cccc}%
f: & \mathbb{N} & \longrightarrow & \mathbb{R}\\
& n & \longmapsto & f\left(  n\right)  .
\end{array}
\vspace{-0.5cm}%
\]


\begin{itemize}
\item On note $f\left(  n\right)  $ par $u\left(  n\right)  $ ou $u_{n}.$

\item $u_{n}$ est le terme général de la suite $\left(  u_{n}\right)
_{n\in\mathbb{N}},$ ou $\left(  u_{n}\right)  _{n},$ ou simplement $\left(
u_{n}\right)  .$

\item La suite $\left(  u_{n}\right)  $ converge vers une limite $l$ si
\[
\forall\varepsilon>0,\ \exists\ N\in\mathbb{N}\text{ tel que }\forall n\geq
N\text{ implique }\left\vert u_{n}-l\right\vert <\varepsilon.
\]
\hspace*{2.5cm}\begin{tikzpicture}
\draw (-5,0) -- (5,0) ;
\fill [color=black] (0,0) circle (1pt) node[above] {\small$l$};
\node at (3,0.25)[above] {\small$l+\varepsilon$};
\node at (-3,0.25)[above] {\small$l-\varepsilon$};
\draw (3.1,0.25) -- (3,0.25) -- (3,-0.25) -- (3.1,-0.25);
\draw (-3.1,-0.25) -- (-3,-0.25) -- (-3,0.25) -- (-3.1,0.25);
\draw[->] (-0.25,-1.5) -- (-1.5,-0.15);
\draw[->] (0.25,-1.5) -- (1.25,-0.25);
\node [below] at (1,-1.5) {\small$u_n$ pour $n\ge N$};
\end{tikzpicture}\newline On lit "la suite $\left(  u_{n}\right)  $ tends vers
$l$ lorsque $n$ tends vers $+\infty$" et on écrit $\lim\limits_{n\rightarrow
+\infty}u_{n}=l$ ou simplement $u_{n}\rightarrow l.$

\item La suite $\left(  u_{n}\right)  $ diverge si elle ne converge pas ou
$\lim\limits_{n\rightarrow+\infty}u_{n}=\pm\infty.$

\item Si la limite d'une suite existe elle est unique.

\item Une suite réelle croissante et majorée converge.

\item Une suite réelle décroissante et minorée converge.

\item Deux suites $\left(  u_{n}\right)  $ et $\left(  v_{n}\right)  $ sont
adjacentes, si $\left(  u_{n}\right)  $ croissante, $\left(  v_{n}\right)  $
décroissante, $u_{n}\leq v_{n}$ et $\lim\limits_{n\rightarrow+\infty}\left(
u_{n}-v_{n}\right)  =0.$

\item Si $\left(  u_{n}\right)  $ et $\left(  v_{n}\right)  $ sont deux suites
adjacentes, alors elles convergent vers la même limite.
\end{itemize}

\noindent\textbf{Suites de Cauchy}

\noindent On dit que $\left(  u_{n}\right)  $ est une suite de Cauchy si%
\[
\forall\varepsilon>0,\ \exists\ N\in\mathbb{N}\text{ tel que }\forall n,m\geq
N\text{ implique }\left\vert u_{n}-u_{m}\right\vert <\varepsilon.
\]
\hspace*{3cm}\begin{tikzpicture}
\draw (-5,0) -- (5,0) ;
\fill [color=black] (-1,0) circle (1pt) node[below] {\small$u_n$};
\fill [color=black] (0.5,0) circle (1pt) node[below] {\small$u_m$};
\node [above] at (0,0.8) {\small$\varepsilon$};
\draw (3.1,0.25) -- (3,0.25) -- (3,-0.25) -- (3.1,-0.25);
\draw (-3.1,-0.25) -- (-3,-0.25) -- (-3,0.25) -- (-3.1,0.25);
\node [below] at (-0.15,-0.5) {\small$n,m\ge N$};
\draw (3,0.35) .. controls (3,0.75) and (0,0.45) .. (0,0.75) .. controls (0,0.45) and (-3,0.75) .. (-3,0.35);
\end{tikzpicture}


\begin{itemize}
\item Une suite $\left(  u_{n}\right)  $ converge si et seulement si elle est
de Cauchy.

\item Si $\left(  u_{n}\right)  $ n'est pas une suite de Cauchy, elle diverge.
\end{itemize}

\chapter{Séries numériques}%

%TCIMACRO{\TeXButton{minitoc}{\minitoc}}%
%BeginExpansion
\minitoc
%EndExpansion


\section{Généralités}

\subsection{Convergence}

\subsubsection{\textbf{Condition nécessaire de convergence}}

\subsection{Propriétés}

\section{Séries à termes positifs}

\subsection{Règles de comparaison}

\subsection{Séries de Riemann}

\subsection{Critère de D'Alembert}

\subsection{Critère de Cauchy (ou règle de Cauchy)}

\subsection{Critère de Raabe-Duhamel}

\subsection{Critère de Gauss}

\section{Séries à termes quelconques}

\subsection{Critère d'Abel}

\subsection{Séries alternées}

\subsubsection{Critère de Leibniz}

\section{Séries absolument convergentes}

\section{Séries commutativement convergentes}

\chapter{Suites et séries de fonctions}%

%TCIMACRO{\TeXButton{minitoc}{\minitoc}}%
%BeginExpansion
\minitoc
%EndExpansion


\section{Suites de fonctions}

\subsection{Convergence simple}

\subsection{Convergence uniforme}

\subsection{Théorèmes de passage à la limite}

\section{Séries de fonctions}

\subsection{Domaine de convergence}

\subsection{Convergence uniforme}

\subsection{Convergence normale}

\subsection{Propriétés des séries de fonctions uniformément convergentes}

\chapter{Séries entières}%

%TCIMACRO{\TeXButton{minitoc}{\minitoc}}%
%BeginExpansion
\minitoc
%EndExpansion


\section{Généralités}

\section{Rayon de convergence}

\subsection{Existence du rayon de convergence}

\subsection{Calcul du rayon de convergence}

\subsubsection{\textbf{Cas des séries lacunaires}}

\section{Propriétés des séries entières}

\subsection{Continuité}

\subsection{Dérivation}

\subsection{Intégration}

\subsection{Opérations sur les séries entières}

\section{Fonctions développables en série entière}

\subsection{Série de Taylor}

\subsubsection{\textbf{Séries de Taylor des fonctions élémentaires}}

\section{Séries entières et équations différentielles}

\chapter{Séries de Fourier}%

%TCIMACRO{\TeXButton{minitoc}{\minitoc}}%
%BeginExpansion
\minitoc
%EndExpansion


\section{Séries trigonométriques}

\subsection{Représentation complexe d'une série trigonométrique}

\subsection{Calcul des coefficients de la série trigonométrique}

\subsubsection{Cas réel}

\subsubsection{Cas complexe}

\section{Séries de Fourier}

\subsection{Séries de Fourier de fonctions $2\pi$-périodiques}

\subsection{Séries de Fourier d'une fonction de période arbitraire}

\subsection{Séries de Fourier de fonctions non périodiques}

\subsection{Égalité de Parseval}

\begin{thebibliography}{9}                                                                                                %


\bibitem {Amroun}\textbf{A%
%TCIMACRO{\TeXButton{MROUN}{{\fontsize{10}{10pt}\normalfont\bf{MROUN}}} }%
%BeginExpansion
{\fontsize{10}{10pt}\normalfont\bf{MROUN}}
%EndExpansion
N.} Cours de séries numériques. Université Djillali Liabès de Sidi Bel Abbes
Algérie, 2007.

\bibitem {Delaunay}\textbf{D%
%TCIMACRO{\TeXButton{ELAUNAY}{{\fontsize{10}{10pt}\normalfont\bf{ELAUNAY}}} }%
%BeginExpansion
{\fontsize{10}{10pt}\normalfont\bf{ELAUNAY}}
%EndExpansion
D.} Cours de Mathématiques MP. Prépas Dupuy de Lôme., Juin 2013.%
%TCIMACRO{\TeXButton{addtocReferences}{\addcontentsline{toc}{chapter}
%{R\'ef\'erences}} }%
%BeginExpansion
\addcontentsline{toc}{chapter}
{R\'ef\'erences}
%EndExpansion
%TCIMACRO{\TeXButton{References}{\markboth{}{R\'ef\'erences}}}%
%BeginExpansion
\markboth{}{R\'ef\'erences}%
%EndExpansion


\bibitem {Krasnov}\textbf{K%
%TCIMACRO{\TeXButton{RASNOV}{{\fontsize{10}{10pt}\normalfont\bf{RASNOV}}} }%
%BeginExpansion
{\fontsize{10}{10pt}\normalfont\bf{RASNOV}}
%EndExpansion
M.L.} et \textbf{K%
%TCIMACRO{\TeXButton{ISSELEV}{{\fontsize{10}{10pt}\normalfont\bf{ISSELEV}}} }%
%BeginExpansion
{\fontsize{10}{10pt}\normalfont\bf{ISSELEV}}
%EndExpansion
A.} Mathématiques supérieures, Volume 2, pour ingénieurs et polytechniciens.
De Boeck-Wesmael, s.a., Bruxelles, 1993.

\bibitem {Mahmoudi}\textbf{M%
%TCIMACRO{\TeXButton{AHMOUDI}{{\fontsize{10}{10pt}\normalfont\bf{AHMOUDI}}} }%
%BeginExpansion
{\fontsize{10}{10pt}\normalfont\bf{AHMOUDI}}
%EndExpansion
A.} et \textbf{K%
%TCIMACRO{\TeXButton{ESSI}{{\fontsize{10}{10pt}\normalfont\bf{ESSI}}} }%
%BeginExpansion
{\fontsize{10}{10pt}\normalfont\bf{ESSI}}
%EndExpansion
A. }Éléments d'analyse mathématique. Séries et intégrales. Cours et exercices
corrigés. Collection les mathématiques à l'université. ISSN 1112-3427, 2001
\end{thebibliography}


\end{document}