%\newtheorem{teo}[theorem]{Theorem}%[chapter]

%\newtheorem{df}[theorem]{Definition}%[chapter]

%\newtheorem{cor}[theorem]{Corollary}%[chapter]

%\newtheorem{oss}[theorem]{Remark}%[chapter]

%\newtheorem{prop}[theorem]{Proposition}%[chapter]

%\newtheorem{lem}[theorem]{Lemma}%[chapter]

%\newtheorem{es}[theorem]{Exemple}%[chapter]

%\newtheorem{nt}[theorem]{Notations}%[chapter]

%\newtheorem{pbm}[theorem]{Research Problem}%[chapter]

%\newtheorem{ex}[theorem]{Exercise$^*$}%[chapter]

\newcommand{\card}{\operatorname{card}}
\newcommand{\conv}{\operatorname{conv}}
\newcommand{\sol} {\operatorname{solid}}



\def\a{\alpha}
\def\b{\beta}
\def\d{\delta}
\def\g{\gamma}
\def\s{\sigma}
\def\t{\theta}
\def\Si{\Sigma}
\def\vp{\varphi}
\def\eps{\epsilon}

\def\fl{\forall \, }
\def\ify{\infty}
\def\ot{\otimes}
\def\ov{\overline}
\def\sbs{\subset}
\def\sub{\subset}

\def\ra{\rightarrow}
\def\Ra{\Rightarrow}
\def\Lb{\Lambda}
\def\ve{\varepsilon}

\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\ba{\begin{eqnarray}}
\def\ea{\end{eqnarray}}
\def\lab{\label}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\D{\Delta}
\def\lb{\lambda}
\def\Lb{\Lambda}
\def\Om{\Omega}
\def\om{\omega}

\def\es{\emptyset}
\def\fl{\forall \, }
\def\pa{\partial}
\def\sm{\simeq}
\def\wh{\widehat}
\def\no{\noindent}

\def\Lra{\Leftrightarrow}

\def\Ac{{\cal A}}
\def\Bc{{\cal B}}
\def\Cc{{\cal C}}
\def\Ec{{\cal E}}
\def\Mc{{\cal M}}
\def\Ic{{\cal I}}
\def\Rc{{\cal R}}
\def\Wc{{\cal W}}
\def\Pc{{\cal P}}
\def\Dc{{\cal D}}
\def\Qc{{\cal Q}}
\def\Sc{{\cal S}}
\def\Nc{{\cal N}}
\def\Fc{{\cal F}}
\def\Tc{{\cal T}}
\def\Gc{{\cal G}}
\def\Lc{{\cal L}}
\def\Hc{{\cal H}}
\def\Vc{{\cal V}}
\def\Jc{{\cal J}}
\def \Ns{{\mathsf N}}



\def\nn{\nonumber}

\def\vtheta{\vec{\theta}}
\def\valpha{\vec{\alpha}}
\def\vgamma{\vec{\gamma}}
\def\vbeta{\vec{\beta}}
\def\vzeta{\vec{\zeta}}
\def\vtau{\vec{\tau}}
\def\veta{\vec{\eta}}
\def\vrho{\vec{\rho}}
\def\vxi{\vec{\xi}}
\def\vX{\vec{X}}
\def\vY{\vec{Y}}
\def\vs{\vec{s}}
\def\vu{\vec{u}}
\def\vv{\vec{v}}
\def\vx{\vec{x}}
\def\vy{\vec{y}}
\def\vz{\vec{z}}
\def\va{\vec{a}}
\def\vb{\vec{b}}
\def\vc{\vec{c}}
\def\vg{\vec{g}}
\def\vk{\vec{k}}
\def\vq{\vec{q}}
\def\vm{\vec{m}}
\def\vn{\vec{n}}

\def\th{{\rm th}}
\def\sh{{\rm sh}}
\def\ch{{\rm ch}}

\def\RS{\mathrm{RS}}
\def\SK{\mathrm{SK}}
\def\RSG{\mathrm{RSG}}



\newcommand{\psigma}{\dot{\sigma}}
\newcommand{\vpsigma}{\vec{\dot{\sigma}}}

\def\varnothing{\emptyset}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%CHAPTER 3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\s{\sigma}
\def\Si{\Sigma}
\def\vp{\varphi}
\def\z{\zeta}



\def\vsigma{\vec{\sigma}}
\def\vxi{\vec{\xi}}

\def\R{\mathbb{R}}
\def\Z{\mathbb{Z}}
\def\N{\mathbb{N}}
%\def\S{\mathbb S}
\def\B{{\cal B}}
\def\C{\mathbb{C}}

\def\dim{\noindent {\bf Proof.}}
\def\b{\beta}
\def\G{\Gamma}

\def\vve{\vec{e}}
\def\vw{\vec{w}}

\def\tck{\kappa}
\def\bu{\bullet}


\def\vsigma{\vec{\sigma}}
\def\E{\mathsf{E}}
\def\P{\mathsf{P}}

\def\ra{\rightarrow}
\def\Ra{\Rightarrow}
\newcommand{\prom}[1]{\left\langle #1\right\rangle}
\def\Av{\mathrm{Av}}
\newcommand{\preuve}[1][$\!\!$]{\noindent {\bf Proof #1. }}
\newcommand{\X}{{\vec{X}}}
\newcommand{\Y}{{\vec{Y}}}
\newcommand{\abs}[1]{\left|{#1}\right|}
\newcommand{\pare}[1]{\left({#1}\right)}
\newcommand{\rref}[1]{(\ref{#1})}
\def\Law{{\rm Law}}

\def\lan{\langle}
\def\ran{\rangle}


\def\ra{\rightarrow}
\def\Ra{\Rightarrow}

\def\bsh{\backslash}

\def\un{{\rm 1\mkern-4mu I}}
\def\rd{{\rm d}}
\def\ss{\;;\;}
\def\sss{\;,\;}
\def\m1{{\mathbf 1}}


\def\Co{\mathop {C}\limits^{o}}
\def\W{\mathop {W}\limits^{o}}

\def\bl{\Bigl}
\def\br{\Bigr}
\def\Br{\biggr}
\def\Bl{\biggl}

\def\pc{{\psi_1}}
\def\pd{{\psi_2}}


