\usepackage[latin1]{inputenc} 
\usepackage[T1]{fontenc}
\usepackage[safe]{textcomp}
\usepackage{lmodern} 
\usepackage{epsfig}
\usepackage{float}
\usepackage{amstext}  
\usepackage{amsfonts}
\usepackage{amssymb} 
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{bm}       
\usepackage[bottom]{footmisc} 
\usepackage{array}                
\usepackage{xcolor} 
\usepackage{framed}
%\usepackage{cite}
\usepackage{slashed}
\usepackage[absolute]{textpos}
\usepackage{axodraw4j}
\usepackage{dsfont}
\usepackage{multirow}

\usepackage{appendix}
\usepackage{listings}
\usepackage{enumerate}     
\usepackage[bottom]{footmisc} 
\usepackage{array}           
\usepackage{parskip}        
\usepackage{xcolor} 
\usepackage{color}
\usepackage{framed}
\usepackage{fancyhdr}
\usepackage{subfig}
\usepackage[raggedright]{sidecap}

\usepackage{tikz}
\usepackage[absolute]{textpos}
\usepackage{pstricks}
\usepackage{axodraw4j}
\usepackage{graphicx}


\newcommand{\p}{\partial}
\newcommand{\ddp}[1]{\frac{\partial}{\partial#1}}
\newcommand{\f}[2]{\frac{#1}{#2}}
\newcommand{\sss}[1]{\scriptscriptstyle#1}
\newcommand{\vv}[2]{\left( \begin{array}{c} #1 \\ #2  \end{array} \right)}
\newcommand{\bea}{\begin{eqnarray}}
\newcommand{\eea}{\end{eqnarray}}
\newcommand{\be}{\begin{equation}}
\newcommand{\ee}{\end{equation}}
\newcommand{\ba}{\begin{align}}
\newcommand{\ea}{\end{align}}
\newcommand{\beas}{\begin{eqnarray*}}
\newcommand{\eeas}{\end{eqnarray*}}
\newcommand{\bes}{\begin{equation*}}
\newcommand{\ees}{\end{equation*}}
\newcommand{\bas}{\begin{align*}}
\newcommand{\eas}{\end{align*}}
\newcommand{\Lrig}{\Longrightarrow} \newcommand{\rig}{\rightarrow}
\newcommand{\lrig}{\longrightarrow} \newcommand{\Rig}{\Rightarrow}
\newcommand{\ssL}{{\mathcal L}} 
\newcommand{\eps}{{\varepsilon}}
\newcommand{\cd}{{\cdot}} 
\newcommand{\cf}{C_{\scriptscriptstyle{F}}} 
\newcommand{\ca}{C_{\scriptscriptstyle{A}}}
\newcommand{\tr}{T_{\scriptscriptstyle{F}}}
\newcommand{\dF}{N_{\scriptscriptstyle{c}}}
\newcommand{\dR}{d_{\scriptscriptstyle{R}}}
\newcommand{\Ng}{n_{\scriptscriptstyle{g}}}
\newcommand{\NGen}{N_{\scriptscriptstyle{g}}}
\newcommand{\Nl}{n_{\scriptscriptstyle{l}}}
\newcommand{\Nc}{N_{\scriptscriptstyle{c}}}
\newcommand{\Nf}{n_{\scriptscriptstyle{f}}}
\newcommand{\gs}{g_{\scriptscriptstyle{s}}}
\newcommand{\yt}{y_{\scriptscriptstyle{t}}}
\newcommand{\yb}{y_{\scriptscriptstyle{b}}}
\newcommand{\ytau}{y_{\scriptscriptstyle{\tau}}}
\newcommand{\gb}{g_1}
\newcommand{\gw}{g_2}
\newcommand{\gaf}{\gamma_{\scriptscriptstyle{5}}}
\newcommand{\als}{\alpha_{\scriptscriptstyle{s}}}
\newcommand{\as}{a_{\scriptscriptstyle{s}}}
\newcommand{\lb}{\left(}
\newcommand{\rb}{\right)}
\newcommand{\lbg}{\left\{}
\newcommand{\rbg}{\right\}}
\newcommand{\lbe}{\left[}
\newcommand{\rbe}{\right]}

\definecolor{bluemar}{rgb}{0,0,.5}
\definecolor{redmar}{rgb}{.8,0,0}
\definecolor{greenmar}{rgb}{0,.5,0}
\newcommand{\bl}{\color{bluemar}}
\newcommand{\rd}{\color{redmar}}
\newcommand{\gr}{\color{greenmar}}
\newcommand{\bk}{\color{black}}
\newcommand{\wh}{\color{white}}