%%% The TMF Style Sheet
%%% Created by Firas on April 23, 2007
%%% Modified by Firas on May 8, 2007: Completely reorganized

\RequirePackage[OT1]{fontenc}
\RequirePackage{amsmath,amssymb,amsthm,natbib}
%\usepackage[numbers,sort&compress,square,comma]{natbib}
\RequirePackage[colorlinks,urlcolor=blue,linkcolor=red,citecolor=green]{hyperref}
\RequirePackage{hypernat}
\usepackage{epsfig,color,colordvi}
\usepackage{datetime}
%\usepackage{showkeys}
%\usepackage{latexsym}
%\usepackage{fancyhdr}
%\usepackage{mathrsfs}
%\usepackage{graphics}
%\usepackage{hhline}
%\usepackage{pb-diagram}
%\uspackage{lamsarrow}
%\usepackage{pb-lams}

\setattribute{journal}{name}{}  %Removes the headernote about submission!

%% Uncomment this if you want enumeration in roman
%\renewcommand{\labelenumi}{(\roman{enumi})}  

%% Comment this if you do not want enumeration in italic 
%% The default is with numbers
\renewcommand{\labelenumi}{\it(\alph{enumi})}  

\numberwithin{equation}{section}

\allowdisplaybreaks[1]

%\def\acknowledgment{{\it Acknowledgment.}}
%\def\acknowledgments{{\it Acknowledgments.}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% set@page@layout
%
%% \set@page@layout{\textwidth}{\textheight}
%
%\def\set@page@layout#1#2{%
%%
  %\setlength\textwidth{#1}
  %\@settopoint\textwidth
  %\setlength\textheight{#2}
  %\@settopoint\textheight
%%
%% make side margins equal:
  %\setlength\@tempdima        {\paperwidth}
  %\addtolength\@tempdima      {-\textwidth}
  %\setlength\oddsidemargin    {.5\@tempdima}
  %\addtolength\oddsidemargin  {-1in}
  %\setlength\evensidemargin   {\oddsidemargin}
  %\@settopoint\oddsidemargin
  %\@settopoint\evensidemargin
%%
%% topmargin
  %\setlength\topmargin{\paperheight}
  %\addtolength\topmargin{-2in}
  %\addtolength\topmargin{-\headheight}
  %\addtolength\topmargin{-\headsep}
  %\addtolength\topmargin{-\textheight}
  %\addtolength\topmargin{-\footskip}     % this might be wrong!
  %\addtolength\topmargin{-.5\topmargin}
  %\@settopoint\topmargin
%}


%\renewcommand\refname{\centerline{\sc References}\color{white}}

\newenvironment{solution}{\medskip\par{\it Solution.}}{\medskip\par}
\theoremstyle{definition}
\newtheorem{definition}{Definition}[section]
\newtheorem{example}{Example}[section]
\newtheorem{exercise}{Exercise}[section]
\newtheorem{conjecture}{Conjecture}[section]
\newtheorem{property}{Property}[section]

\theoremstyle{remark}
\newtheorem{remark}{Remark}[section]
\newtheorem{note}{Note}[section]
\newtheorem{case}{Case}[section]

\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}{Lemma}[section]
\newtheorem{proposition}[lemma]{Proposition}
\newtheorem{corollary}{Corollary}[section]
\newtheorem{question}{Question}[section]
\newtheorem{notation}{Notation}[section]
\newtheorem{hypothesis}{Hypothesis}[section]
\newtheorem{problem}{Problem}[section]

\newcommand*{\beq}{\begin{equation}}
\newcommand*{\eeq}{\end{equation}}
\newcommand*{\bal}{\begin{aligned}}
\newcommand*{\eal}{\end{aligned}}
\newcommand*{\nn}{\nonumber}

%%% Commands and Operators

\DeclareMathOperator{\Span}{span}
\DeclareMathOperator{\diam}{diam}
\DeclareMathOperator{\card}{card}
\DeclareMathOperator{\supp}{supp}
\DeclareMathOperator{\dist}{dist}
\DeclareMathOperator{\var}{Var}
\DeclareMathOperator{\Var}{Var}
\DeclareMathOperator{\proj}{Proj}
\providecommand{\abs}[1]{\left\vert#1\right\vert}
\providecommand{\norm}[1]{\left\Vert#1\right\Vert}
\providecommand{\pp}[1]{\langle#1\rangle}
\providecommand{\Norm}[1]{\muskip0=-2mu{\left|\mkern\muskip0\left|
\mkern\muskip0\left|#1\right|\mkern\muskip0
\right|\mkern\muskip0\right|}}

\newcommand*{\tfl}[1]{\lfloor{#1}\rfloor}
\newcommand*{\lc}{\lceil}
\newcommand*{\rc}{\rceil}
\newcommand*{\lf}{\lfloor}
\newcommand*{\rf}{\rfloor}
\newcommand*{\fl}[1]{\left\lfloor{#1}\right\rfloor}
\newcommand*{\ce}[1]{\left\lceil{#1}\right\rceil}
\newcommand*{\ind}{\mathbf{1}}  % Careful that Firas also has \one 
                                % which looks different
\newcommand*{\one}{{{\rm 1\mkern-1.5mu}\!{\rm I}}}

%%% Shorthands

\newcommand*{\VVar}{\text{$\mathbb{V}$\!ar}}
\newcommand*{\vard}{d_{\scriptscriptstyle\rm Var}}
\newcommand*{\linf}{\varliminf}
\newcommand*{\lsup}{\varlimsup}
\newcommand*{\esssup}{\mathop{{\rm ess~sup}}}
\newcommand*{\ord}{\kern0.1em o\kern-0.02em{}_{\ds\breve{}}\kern0.1em}
\newcommand*{\Ord}{\kern0.1em O\kern-0.02em{\ds\breve{}}\kern0.1em}

\newcommand*{\ds}{\displaystyle}
%\newcommand*{\ss}{\scriptstyle}
%\newcommand*{\sss}{\scriptscriptstyle}


%%% Greek shorthands

\newcommand*{\al}{\alpha}
\newcommand*{\Al}{\Alpha}
\newcommand*{\be}{\beta} 
\newcommand*{\Be}{\Beta}
\newcommand*{\ga}{\gamma}
\newcommand*{\Ga}{\Gamma}
\newcommand*{\de}{\delta}
\newcommand*{\De}{\Delta}
\newcommand*{\e}{\varepsilon}
\newcommand*{\eps}{\varepsilon}
\newcommand*{\vep}{\varepsilon}
\newcommand*{\ep}{\epsilon}
\newcommand*{\Ep}{\Epsilon}
\newcommand*{\ze}{\zeta}
\newcommand*{\Ze}{\Zeta}
\newcommand*{\et}{\eta}
\newcommand*{\Et}{\Eta}
\renewcommand*{\th}{\theta} %\th already exists!
\newcommand*{\Th}{\Theta}
\newcommand*{\io}{\iota}
\newcommand*{\Io}{\Iota}
\newcommand*{\ka}{\kappa}
\newcommand*{\Ka}{\Kappa}
\newcommand*{\la}{\lambda}
\newcommand*{\La}{\Lambda}
\newcommand*{\rh}{\rho}
\newcommand*{\Rh}{\Rho}
\newcommand*{\si}{\sigma}
\newcommand*{\Si}{\Sigma}
\newcommand*{\ta}{\tau}
\newcommand*{\Ta}{\Tau}
\newcommand*{\ph}{\phi}
\newcommand*{\Ph}{\Phi}
\newcommand*{\vph}{\varphi}
\newcommand*{\vPh}{\varPhi}
\newcommand*{\ch}{\chi}
\newcommand*{\Ch}{\Chi}
\newcommand*{\ps}{\psi}
\newcommand*{\Ps}{\Psi}
\newcommand*{\vps}{\varpsi}
\newcommand*{\vPs}{\varPsi}
\newcommand*{\om}{\omega}
\newcommand*{\Om}{\Omega}
\newcommand*{\w}{\omega}

%%% mathcal A is \cA

\newcommand*{\cA}{{\mathcal A}} 
\newcommand*{\cB}{{\mathcal B}}
\newcommand*{\cC}{{\mathcal C}}
\newcommand*{\cD}{{\mathcal D}}
\newcommand*{\cE}{{\mathcal E}}
\newcommand*{\cF}{{\mathcal F}}
\newcommand*{\cG}{{\mathcal G}}
\newcommand*{\cH}{{\mathcal H}}
\newcommand*{\cI}{{\mathcal I}}
\newcommand*{\cJ}{{\mathcal J}}
\newcommand*{\cK}{{\mathcal K}}
\newcommand*{\cL}{{\mathcal L}}
\newcommand*{\cM}{{\mathcal M}}
\newcommand*{\cN}{{\mathcal N}}
\newcommand*{\cO}{{\mathcal O}}
\newcommand*{\cP}{{\mathcal P}}
\newcommand*{\cQ}{{\mathcal Q}}
\newcommand*{\cR}{{\mathcal R}}
\newcommand*{\cS}{{\mathcal S}}
\newcommand*{\cT}{{\mathcal T}}
\newcommand*{\cU}{{\mathcal U}}
\newcommand*{\cV}{{\mathcal V}}
\newcommand*{\cW}{{\mathcal W}}
\newcommand*{\cX}{{\mathcal X}}
\newcommand*{\cY}{{\mathcal Y}}
\newcommand*{\cZ}{{\mathcal Z}}

%%% mathfrak A is \kA

\newcommand*{\kA}{{\mathfrak A}} 
\newcommand*{\kB}{{\mathfrak B}}
\newcommand*{\kC}{{\mathfrak C}}
\newcommand*{\kD}{{\mathfrak D}}
\newcommand*{\kE}{{\mathfrak E}}
\newcommand*{\kF}{{\mathfrak F}}
\newcommand*{\kG}{{\mathfrak G}}
\newcommand*{\kH}{{\mathfrak H}}
\newcommand*{\kI}{{\mathfrak I}}
\newcommand*{\kJ}{{\mathfrak J}}
\newcommand*{\kK}{{\mathfrak K}}
\newcommand*{\kL}{{\mathfrak L}}
\newcommand*{\kM}{{\mathfrak M}}
\newcommand*{\kN}{{\mathfrak N}}
\newcommand*{\kO}{{\mathfrak O}}
\newcommand*{\kP}{{\mathfrak P}}
\newcommand*{\kQ}{{\mathfrak Q}}
\newcommand*{\kR}{{\mathfrak R}}
\newcommand*{\kS}{{\mathfrak S}}
\newcommand*{\kT}{{\mathfrak T}}
\newcommand*{\kU}{{\mathfrak U}}
\newcommand*{\kV}{{\mathfrak V}}
\newcommand*{\kW}{{\mathfrak W}}
\newcommand*{\kX}{{\mathfrak X}}
\newcommand*{\kY}{{\mathfrak Y}}
\newcommand*{\kZ}{{\mathfrak Z}}

%%% mathbb A is \A

\newcommand*{\A}{{\mathbb A}} 
\newcommand*{\B}{{\mathbb B}}
\newcommand*{\C}{{\mathbb C}}
\newcommand*{\D}{{\mathbb D}}
\newcommand*{\E}{{\mathbb E}}
\newcommand*{\F}{{\mathbb F}}
\newcommand*{\G}{{\mathbb G}}
\renewcommand*{\H}{{\mathbb H}} %\H already exists
\newcommand*{\I}{{\mathbb I}}
\newcommand*{\J}{{\mathbb J}}
\newcommand*{\K}{{\mathbb K}}
\renewcommand*{\L}{{\mathbb L}} %\L already exists
\newcommand*{\M}{{\mathbb M}}
\newcommand*{\N}{{\mathbb N}}
\renewcommand*{\O}{{\mathbb O}} %\O already exists
\renewcommand*{\P}{{\mathbb P}} %\P already exists
\newcommand*{\Q}{{\mathbb Q}}
\newcommand*{\R}{{\mathbb R}}
\renewcommand*{\S}{{\mathbb S}} %\S already exists
\newcommand*{\T}{{\mathbb T}}
\newcommand*{\U}{{\mathbb U}}
\newcommand*{\V}{{\mathbb V}}
\newcommand*{\W}{{\mathbb W}}
\newcommand*{\X}{{\mathbb X}}
\newcommand*{\Y}{{\mathbb Y}}
\newcommand*{\Z}{{\mathbb Z}}

%%% mathbf A is \bfA

\newcommand*{\bfA}{{\mathbf A}} 
\newcommand*{\bfB}{{\mathbf B}}
\newcommand*{\bfC}{{\mathbf C}}
\newcommand*{\bfD}{{\mathbf D}}
\newcommand*{\bfE}{{\mathbf E}}
\newcommand*{\bfF}{{\mathbf F}}
\newcommand*{\bfG}{{\mathbf G}}
\newcommand*{\bfH}{{\mathbf H}}
\newcommand*{\bfI}{{\mathbf I}}
\newcommand*{\bfJ}{{\mathbf J}}
\newcommand*{\bfK}{{\mathbf K}}
\newcommand*{\bfL}{{\mathbf L}}
\newcommand*{\bfM}{{\mathbf M}}
\newcommand*{\bfN}{{\mathbf N}}
\newcommand*{\bfO}{{\mathbf O}}
\newcommand*{\bfP}{{\mathbf P}}
\newcommand*{\bfQ}{{\mathbf Q}}
\newcommand*{\bfR}{{\mathbf R}}
\newcommand*{\bfS}{{\mathbf S}}
\newcommand*{\bfT}{{\mathbf T}}
\newcommand*{\bfU}{{\mathbf U}}
\newcommand*{\bfV}{{\mathbf V}}
\newcommand*{\bfW}{{\mathbf W}}
\newcommand*{\bfX}{{\mathbf X}}
\newcommand*{\bfY}{{\mathbf Y}}
\newcommand*{\bfZ}{{\mathbf Z}}

%%% mathbf a is \bfa  %and not \ba because of \bf ! :)

\newcommand*{\bfa}{{\mathbf a}} 
\newcommand*{\bfb}{{\mathbf b}}
\newcommand*{\bfc}{{\mathbf c}}
\newcommand*{\bfd}{{\mathbf d}}
\newcommand*{\bfe}{{\mathbf e}}
\newcommand*{\bff}{{\mathbf f}}
\newcommand*{\bfg}{{\mathbf g}}
\newcommand*{\bfh}{{\mathbf h}}
\newcommand*{\bfi}{{\mathbf i}}
\newcommand*{\bfj}{{\mathbf j}}
\newcommand*{\bfk}{{\mathbf k}}
\newcommand*{\bfl}{{\mathbf l}}
\newcommand*{\bfm}{{\mathbf m}}
\newcommand*{\bfn}{{\mathbf n}}
\newcommand*{\bfo}{{\mathbf o}}
\newcommand*{\bfp}{{\mathbf p}}
\newcommand*{\bfq}{{\mathbf q}}
\newcommand*{\bfr}{{\mathbf r}}
\newcommand*{\bfs}{{\mathbf s}}
\newcommand*{\bft}{{\mathbf t}}
\newcommand*{\bfu}{{\mathbf u}}
\newcommand*{\bfv}{{\mathbf v}}
\newcommand*{\bfw}{{\mathbf w}}
\newcommand*{\bfx}{{\mathbf x}}
\newcommand*{\bfy}{{\mathbf y}}
\newcommand*{\bfz}{{\mathbf z}}

%%% widehat A is \Ahat
%%% widehat Alpha is \Alhat or \Alphahat

\newcommand*{\Ahat}{{\widehat A}} 
\newcommand*{\Bhat}{{\widehat B}}
\newcommand*{\Chat}{{\widehat C}}
\newcommand*{\Dhat}{{\widehat D}}
\newcommand*{\Ehat}{{\widehat E}}
\newcommand*{\Fhat}{{\widehat F}}
\newcommand*{\Ghat}{{\widehat G}}
\newcommand*{\Hhat}{{\widehat H}}
\newcommand*{\Ihat}{{\widehat I}}
\newcommand*{\Jhat}{{\widehat J}}
\newcommand*{\Khat}{{\widehat K}}
\newcommand*{\Lhat}{{\widehat L}}
\newcommand*{\Mhat}{{\widehat M}}
\newcommand*{\Nhat}{{\widehat N}}
\newcommand*{\Ohat}{{\widehat O}}
\newcommand*{\Phat}{{\widehat P}}
\newcommand*{\Qhat}{{\widehat Q}}
\newcommand*{\Rhat}{{\widehat R}}
\newcommand*{\Shat}{{\widehat S}}
\newcommand*{\That}{{\widehat T}}
\newcommand*{\Uhat}{{\widehat U}}
\newcommand*{\Vhat}{{\widehat V}}
\newcommand*{\What}{{\widehat W}}
\newcommand*{\Xhat}{{\widehat X}}
\newcommand*{\Yhat}{{\widehat Y}}
\newcommand*{\Zhat}{{\widehat Z}}
\newcommand*{\Alhat}{{\widehat\Alpha}}
\newcommand*{\Alphahat}{{\widehat\Alpha}}
\newcommand*{\Behat}{{\widehat\Beta}}
\newcommand*{\Betahat}{{\widehat\Beta}}
\newcommand*{\Gahat}{{\widehat\Gamma}}
\newcommand*{\Gammahat}{{\widehat\Gamma}}
\newcommand*{\Dehat}{{\widehat\Delta}}
\newcommand*{\Deltahat}{{\widehat\Delta}}
\newcommand*{\Ephat}{{\widehat\Epsilon}}
\newcommand*{\Epsilonhat}{{\widehat\Epsilon}}
\newcommand*{\Zehat}{{\widehat\Zeta}}
\newcommand*{\Zetahat}{{\widehat\Zeta}}
\newcommand*{\Ethat}{{\widehat\Eta}}
\newcommand*{\Etahat}{{\widehat\Eta}}
\newcommand*{\Thhat}{{\widehat\Theta}}
\newcommand*{\Thetahat}{{\widehat\Theta}}
\newcommand*{\Iohat}{{\widehat\Iota}}
\newcommand*{\Iotahat}{{\widehat\Iota}}
\newcommand*{\Kahat}{{\widehat\Kappa}}
\newcommand*{\Kappahat}{{\widehat\Kappa}}
\newcommand*{\Lahat}{{\widehat\Lambda}}
\newcommand*{\Lambdahat}{{\widehat\Lambda}}
\newcommand*{\Muhat}{{\widehat\Mu}}
\newcommand*{\Nuhat}{{\widehat\Nu}}
\newcommand*{\Xihat}{{\widehat\Xi}}
\newcommand*{\Pihat}{{\widehat\Pi}}
\newcommand*{\Rhhat}{{\widehat\Rho}}
\newcommand*{\Rhohat}{{\widehat\Rho}}
\newcommand*{\Sihat}{{\widehat\Sigma}}
\newcommand*{\Sigmahat}{{\widehat\Sigma}}
\newcommand*{\Tahat}{{\widehat\Tau}}
\newcommand*{\Tauhat}{{\widehat\Tau}}
\newcommand*{\Phhat}{{\widehat\Phi}}
\newcommand*{\Phihat}{{\widehat\Phi}}
\newcommand*{\vPhhat}{{\widehat\varPhi}}
\newcommand*{\vPhihat}{{\widehat\varPhi}}
\newcommand*{\varPhihat}{{\widehat\varPhi}}
\newcommand*{\Chhat}{{\widehat\Chi}}
\newcommand*{\Chihat}{{\widehat\Chi}}
\newcommand*{\Pshat}{{\widehat\Psi}}
\newcommand*{\Psihat}{{\widehat\Psi}}
\newcommand*{\vPshat}{{\widehat\varPsi}}
\newcommand*{\vPsihat}{{\widehat\varPsi}}
\newcommand*{\varPsihat}{{\widehat\varPsi}}
\newcommand*{\Omhat}{{\widehat\Omega}}
\newcommand*{\Omegahat}{{\widehat\Omega}}


%%% hat a is \ahat
%%% hat alpha is \alhat or \alphahat
%%% also there's \ellhat

\newcommand*{\ahat}{{\hat a}} 
\newcommand*{\bhat}{{\hat b}}
\newcommand*{\chat}{{\hat c}}
\newcommand*{\dhat}{{\hat d}}
\newcommand*{\ehat}{{\hat e}}
\newcommand*{\fhat}{{\hat f}}
\newcommand*{\ghat}{{\hat g}}
\newcommand*{\hhat}{{\hat h}}
\newcommand*{\ihat}{{\hat i}}
\newcommand*{\jhat}{{\hat j}}
\newcommand*{\khat}{{\hat k}}
\newcommand*{\lhat}{{\hat l}}
\newcommand*{\mhat}{{\hat m}}
\newcommand*{\nhat}{{\hat n}}
\newcommand*{\ohat}{{\hat o}}
\newcommand*{\phat}{{\hat p}}
\newcommand*{\qhat}{{\hat q}}
\newcommand*{\rhat}{{\hat r}}
\newcommand*{\shat}{{\hat s}}
\newcommand*{\that}{{\hat t}}
\newcommand*{\uhat}{{\hat u}}
\newcommand*{\vhat}{{\hat v}}
\newcommand*{\what}{{\hat w}}
\newcommand*{\xhat}{{\hat x}}
\newcommand*{\yhat}{{\hat y}}
\newcommand*{\zhat}{{\hat z}}
\newcommand*{\alhat}{{\hat\alpha}}
\newcommand*{\alphahat}{{\hat\alpha}}
\newcommand*{\behat}{{\hat\beta}}
\newcommand*{\betahat}{{\hat\beta}}
\newcommand*{\gahat}{{\hat\gamma}}
\newcommand*{\gammahat}{{\hat\gamma}}
\newcommand*{\dehat}{{\hat\delta}}
\newcommand*{\deltahat}{{\hat\delta}}
\newcommand*{\ephat}{{\hat\epsilon}}
\newcommand*{\epsilonhat}{{\hat\epsilon}}
\newcommand*{\zehat}{{\hat\zeta}}
\newcommand*{\zetahat}{{\hat\zeta}}
\newcommand*{\ethat}{{\hat\eta}}
\newcommand*{\etahat}{{\hat\eta}}
\newcommand*{\thhat}{{\hat\theta}}
\newcommand*{\thetahat}{{\hat\theta}}
\newcommand*{\iohat}{{\hat\iota}}
\newcommand*{\iotahat}{{\hat\iota}}
\newcommand*{\kahat}{{\hat\kappa}}
\newcommand*{\kappahat}{{\hat\kappa}}
\newcommand*{\lahat}{{\hat\lambda}}
\newcommand*{\lambdahat}{{\hat\lambda}}
\newcommand*{\muhat}{{\hat\mu}}
\newcommand*{\nuhat}{{\hat\nu}}
\newcommand*{\xihat}{{\hat\xi}}
\newcommand*{\pihat}{{\hat\pi}}
\newcommand*{\rhhat}{{\hat\rho}}
\newcommand*{\rhohat}{{\hat\rho}}
\newcommand*{\sihat}{{\hat\sigma}}
\newcommand*{\sigmahat}{{\hat\sigma}}
\newcommand*{\tahat}{{\hat\tau}}
\newcommand*{\tauhat}{{\hat\tau}}
\newcommand*{\phhat}{{\hat\phi}}
\newcommand*{\phihat}{{\hat\phi}}
\newcommand*{\vphhat}{{\hat\varphi}}
\newcommand*{\vphihat}{{\hat\varphi}}
\newcommand*{\varphihat}{{\hat\varphi}}
\newcommand*{\chhat}{{\hat\chi}}
\newcommand*{\chihat}{{\hat\chi}}
\newcommand*{\pshat}{{\hat\psi}}
\newcommand*{\psihat}{{\hat\psi}}
\newcommand*{\vpshat}{{\hat\varpsi}}
\newcommand*{\vpsihat}{{\hat\varpsi}}
\newcommand*{\varpsihat}{{\hat\varpsi}}
\newcommand*{\omhat}{{\hat\omega}}
\newcommand*{\omegahat}{{\hat\omega}}
\newcommand*{\wwhat}{{\hat\omega}}
\newcommand*{\ellhat}{{\hat\ell}}

%%% bar A is \Abar
%%% bar Alpha is \Albar or \Alphabar

\newcommand*{\Abar}{{\bar A}} 
\newcommand*{\Bbar}{{\bar B}}
\newcommand*{\Cbar}{{\bar C}}
\newcommand*{\Dbar}{{\bar D}}
\newcommand*{\Ebar}{{\bar E}}
\newcommand*{\Fbar}{{\bar F}}
\newcommand*{\Gbar}{{\bar G}}
\newcommand*{\Hbar}{{\bar H}}
\newcommand*{\Ibar}{{\bar I}}
\newcommand*{\Jbar}{{\bar J}}
\newcommand*{\Kbar}{{\bar K}}
\newcommand*{\Lbar}{{\bar L}}
\newcommand*{\Mbar}{{\bar M}}
\newcommand*{\Nbar}{{\bar N}}
\newcommand*{\Obar}{{\bar O}}
\newcommand*{\Pbar}{{\bar P}}
\newcommand*{\Qbar}{{\bar Q}}
\newcommand*{\Rbar}{{\bar R}}
\newcommand*{\Sbar}{{\bar S}}
\newcommand*{\Tbar}{{\bar T}}
\newcommand*{\Ubar}{{\bar U}}
\newcommand*{\Vbar}{{\bar V}}
\newcommand*{\Wbar}{{\bar W}}
\newcommand*{\Xbar}{{\bar X}}
\newcommand*{\Ybar}{{\bar Y}}
\newcommand*{\Zbar}{{\bar Z}}
\newcommand*{\Albar}{{\bar\Alpha}}
\newcommand*{\Alphabar}{{\bar\Alpha}}
\newcommand*{\Bebar}{{\bar\Beta}}
\newcommand*{\Betabar}{{\bar\Beta}}
\newcommand*{\Gabar}{{\bar\Gamma}}
\newcommand*{\Gammabar}{{\bar\Gamma}}
\newcommand*{\Debar}{{\bar\Delta}}
\newcommand*{\Deltabar}{{\bar\Delta}}
\newcommand*{\Epbar}{{\bar\Epsilon}}
\newcommand*{\Epsilonbar}{{\bar\Epsilon}}
\newcommand*{\Zebar}{{\bar\Zeta}}
\newcommand*{\Zetabar}{{\bar\Zeta}}
\newcommand*{\Etbar}{{\bar\Eta}}
\newcommand*{\Etabar}{{\bar\Eta}}
\newcommand*{\Thbar}{{\bar\Theta}}
\newcommand*{\Thetabar}{{\bar\Theta}}
\newcommand*{\Iobar}{{\bar\Iota}}
\newcommand*{\Iotabar}{{\bar\Iota}}
\newcommand*{\Kabar}{{\bar\Kappa}}
\newcommand*{\Kappabar}{{\bar\Kappa}}
\newcommand*{\Labar}{{\bar\Lambda}}
\newcommand*{\Lambdabar}{{\bar\Lambda}}
\newcommand*{\Mubar}{{\bar\Mu}}
\newcommand*{\Nubar}{{\bar\Nu}}
\newcommand*{\Xibar}{{\bar\Xi}}
\newcommand*{\Pibar}{{\bar\Pi}}
\newcommand*{\Rhbar}{{\bar\Rho}}
\newcommand*{\Rhobar}{{\bar\Rho}}
\newcommand*{\Sibar}{{\bar\Sigma}}
\newcommand*{\Sigmabar}{{\bar\Sigma}}
\newcommand*{\Tabar}{{\bar\Tau}}
\newcommand*{\Taubar}{{\bar\Tau}}
\newcommand*{\Phbar}{{\bar\Phi}}
\newcommand*{\Phibar}{{\bar\Phi}}
\newcommand*{\vPhbar}{{\bar\varPhi}}
\newcommand*{\vPhibar}{{\bar\varPhi}}
\newcommand*{\varPhibar}{{\bar\varPhi}}
\newcommand*{\Chbar}{{\bar\Chi}}
\newcommand*{\Chibar}{{\bar\Chi}}
\newcommand*{\Psbar}{{\bar\Psi}}
\newcommand*{\Psibar}{{\bar\Psi}}
\newcommand*{\vPsbar}{{\bar\varPsi}}
\newcommand*{\vPsibar}{{\bar\varPsi}}
\newcommand*{\varPsibar}{{\bar\varPsi}}
\newcommand*{\Ombar}{{\bar\Omega}}
\newcommand*{\Omegabar}{{\bar\Omega}}

%%% bar a is \abar
%%% only bar h is \barh
%%% bar alpha is \albar or \alphabar
%%% also there's \ellbar

\newcommand*{\abar}{{\bar a}} 
\newcommand*{\bbar}{{\bar b}}
\newcommand*{\cbar}{{\bar c}}
\newcommand*{\dbar}{{\bar d}}
\newcommand*{\ebar}{{\bar e}}
\newcommand*{\fbar}{{\bar f}}
\newcommand*{\gbar}{{\bar g}}
\newcommand*{\barh}{{\bar h}} %\hbar already exists and better not redefine it!
\newcommand*{\ibar}{{\bar i}}
\newcommand*{\jbar}{{\bar j}}
\newcommand*{\kbar}{{\bar k}}
\newcommand*{\lbar}{{\bar l}}
\newcommand*{\mbar}{{\bar m}}
\newcommand*{\nbar}{{\bar n}}
\newcommand*{\obar}{{\bar o}}
\newcommand*{\pbar}{{\bar p}}
\newcommand*{\qbar}{{\bar q}}
\newcommand*{\rbar}{{\bar r}}
\newcommand*{\sbar}{{\bar s}}
\newcommand*{\tbar}{{\bar t}}
\newcommand*{\ubar}{{\bar u}}
\newcommand*{\vbar}{{\bar v}}
\newcommand*{\wbar}{{\bar w}}
\newcommand*{\xbar}{{\bar x}}
\newcommand*{\ybar}{{\bar y}}
\newcommand*{\zbar}{{\bar z}}
\newcommand*{\albar}{{\bar\alpha}}
\newcommand*{\alphabar}{{\bar\alpha}}
\newcommand*{\bebar}{{\bar\beta}}
\newcommand*{\betabar}{{\bar\beta}}
\newcommand*{\gabar}{{\bar\gamma}}
\newcommand*{\gammabar}{{\bar\gamma}}
\newcommand*{\debar}{{\bar\delta}}
\newcommand*{\deltabar}{{\bar\delta}}
\newcommand*{\epbar}{{\bar\epsilon}}
\newcommand*{\epsilonbar}{{\bar\epsilon}}
\newcommand*{\zebar}{{\bar\zeta}}
\newcommand*{\zetabar}{{\bar\zeta}}
\newcommand*{\etbar}{{\bar\eta}}
\newcommand*{\etabar}{{\bar\eta}}
\newcommand*{\thbar}{{\bar\theta}}
\newcommand*{\thetabar}{{\bar\theta}}
\newcommand*{\iobar}{{\bar\iota}}
\newcommand*{\iotabar}{{\bar\iota}}
\newcommand*{\kabar}{{\bar\kappa}}
\newcommand*{\kappabar}{{\bar\kappa}}
\newcommand*{\labar}{{\bar\lambda}}
\newcommand*{\lambdabar}{{\bar\lambda}}
\newcommand*{\mubar}{{\bar\mu}}
\newcommand*{\nubar}{{\bar\nu}}
\newcommand*{\xibar}{{\bar\xi}}
\newcommand*{\pibar}{{\bar\pi}}
\newcommand*{\rhbar}{{\bar\rho}}
\newcommand*{\rhobar}{{\bar\rho}}
\newcommand*{\sibar}{{\bar\sigma}}
\newcommand*{\sigmabar}{{\bar\sigma}}
\newcommand*{\tabar}{{\bar\tau}}
\newcommand*{\taubar}{{\bar\tau}}
\newcommand*{\phbar}{{\bar\phi}}
\newcommand*{\phibar}{{\bar\phi}}
\newcommand*{\vphbar}{{\bar\varphi}}
\newcommand*{\vphibar}{{\bar\varphi}}
\newcommand*{\varphibar}{{\bar\varphi}}
\newcommand*{\chbar}{{\bar\chi}}
\newcommand*{\chibar}{{\bar\chi}}
\newcommand*{\psbar}{{\bar\psi}}
\newcommand*{\psibar}{{\bar\psi}}
\newcommand*{\vpsbar}{{\bar\varpsi}}
\newcommand*{\vpsibar}{{\bar\varpsi}}
\newcommand*{\varpsibar}{{\bar\varpsi}}
\newcommand*{\ombar}{{\bar\omega}}
\newcommand*{\omegabar}{{\bar\omega}}
\newcommand*{\wwbar}{{\bar\omega}}
\newcommand*{\ellbar}{{\bar\ell}}

%%% widetilde A is \Atil
%%% widetilde Alpha is \Altil or \Alphatil

\newcommand*{\Atil}{{\widetilde A}} 
\newcommand*{\Btil}{{\widetilde B}}
\newcommand*{\Ctil}{{\widetilde C}}
\newcommand*{\Dtil}{{\widetilde D}}
\newcommand*{\Etil}{{\widetilde E}}
\newcommand*{\Ftil}{{\widetilde F}}
\newcommand*{\Gtil}{{\widetilde G}}
\newcommand*{\Htil}{{\widetilde H}}
\newcommand*{\Itil}{{\widetilde I}}
\newcommand*{\Jtil}{{\widetilde J}}
\newcommand*{\Ktil}{{\widetilde K}}
\newcommand*{\Ltil}{{\widetilde L}}
\newcommand*{\Mtil}{{\widetilde M}}
\newcommand*{\Ntil}{{\widetilde N}}
\newcommand*{\Otil}{{\widetilde O}}
\newcommand*{\Ptil}{{\widetilde P}}
\newcommand*{\Qtil}{{\widetilde Q}}
\newcommand*{\Rtil}{{\widetilde R}}
\newcommand*{\Stil}{{\widetilde S}}
\newcommand*{\Ttil}{{\widetilde T}}
\newcommand*{\Util}{{\widetilde U}}
\newcommand*{\Vtil}{{\widetilde V}}
\newcommand*{\Wtil}{{\widetilde W}}
\newcommand*{\Xtil}{{\widetilde X}}
\newcommand*{\Ytil}{{\widetilde Y}}
\newcommand*{\Ztil}{{\widetilde Z}}
\newcommand*{\Altil}{{\widetilde\Alpha}}
\newcommand*{\Alphatil}{{\widetilde\Alpha}}
\newcommand*{\Betil}{{\widetilde\Beta}}
\newcommand*{\Betatil}{{\widetilde\Beta}}
\newcommand*{\Gatil}{{\widetilde\Gamma}}
\newcommand*{\Gammatil}{{\widetilde\Gamma}}
\newcommand*{\Detil}{{\widetilde\Delta}}
\newcommand*{\Deltatil}{{\widetilde\Delta}}
\newcommand*{\Eptil}{{\widetilde\Epsilon}}
\newcommand*{\Epsilontil}{{\widetilde\Epsilon}}
\newcommand*{\Zetil}{{\widetilde\Zeta}}
\newcommand*{\Zetatil}{{\widetilde\Zeta}}
\newcommand*{\Ettil}{{\widetilde\Eta}}
\newcommand*{\Etatil}{{\widetilde\Eta}}
\newcommand*{\Thtil}{{\widetilde\Theta}}
\newcommand*{\Thetatil}{{\widetilde\Theta}}
\newcommand*{\Iotil}{{\widetilde\Iota}}
\newcommand*{\Iotatil}{{\widetilde\Iota}}
\newcommand*{\Katil}{{\widetilde\Kappa}}
\newcommand*{\Kappatil}{{\widetilde\Kappa}}
\newcommand*{\Latil}{{\widetilde\Lambda}}
\newcommand*{\Lambdatil}{{\widetilde\Lambda}}
\newcommand*{\Mutil}{{\widetilde\Mu}}
\newcommand*{\Nutil}{{\widetilde\Nu}}
\newcommand*{\Xitil}{{\widetilde\Xi}}
\newcommand*{\Pitil}{{\widetilde\Pi}}
\newcommand*{\Rhtil}{{\widetilde\Rho}}
\newcommand*{\Rhotil}{{\widetilde\Rho}}
\newcommand*{\Sitil}{{\widetilde\Sigma}}
\newcommand*{\Sigmatil}{{\widetilde\Sigma}}
\newcommand*{\Tatil}{{\widetilde\Tau}}
\newcommand*{\Tautil}{{\widetilde\Tau}}
\newcommand*{\Phtil}{{\widetilde\Phi}}
\newcommand*{\Phitil}{{\widetilde\Phi}}
\newcommand*{\vPhtil}{{\widetilde\varPhi}}
\newcommand*{\vPhitil}{{\widetilde\varPhi}}
\newcommand*{\varPhitil}{{\widetilde\varPhi}}
\newcommand*{\Chtil}{{\widetilde\Chi}}
\newcommand*{\Chitil}{{\widetilde\Chi}}
\newcommand*{\Pstil}{{\widetilde\Psi}}
\newcommand*{\Psitil}{{\widetilde\Psi}}
\newcommand*{\vPstil}{{\widetilde\varPsi}}
\newcommand*{\vPsitil}{{\widetilde\varPsi}}
\newcommand*{\varPsitil}{{\widetilde\varPsi}}
\newcommand*{\Omtil}{{\widetilde\Omega}}
\newcommand*{\Omegatil}{{\widetilde\Omega}}

%%% tilde a is \atil
%%% tilde alpha is \altil or \alphatil
%%% also there's \ellbar

\newcommand*{\atil}{{\tilde a}} 
\newcommand*{\btil}{{\tilde b}}
\newcommand*{\ctil}{{\tilde c}}
\newcommand*{\dtil}{{\tilde d}}
\newcommand*{\etil}{{\tilde e}}
\newcommand*{\ftil}{{\tilde f}}
\newcommand*{\gtil}{{\tilde g}}
\newcommand*{\htil}{{\tilde h}}
\newcommand*{\itil}{{\tilde i}}
\newcommand*{\jtil}{{\tilde j}}
\newcommand*{\ktil}{{\tilde k}}
\newcommand*{\ltil}{{\tilde l}}
\newcommand*{\mtil}{{\tilde m}}
\newcommand*{\ntil}{{\tilde n}}
\newcommand*{\otil}{{\tilde o}}
\newcommand*{\ptil}{{\tilde p}}
\newcommand*{\qtil}{{\tilde q}}
\newcommand*{\rtil}{{\tilde r}}
\newcommand*{\stil}{{\tilde s}}
\newcommand*{\ttil}{{\tilde t}}
\newcommand*{\util}{{\tilde u}}
\newcommand*{\vtil}{{\tilde v}}
\newcommand*{\wtil}{{\tilde w}}
\newcommand*{\xtil}{{\tilde x}}
\newcommand*{\ytil}{{\tilde y}}
\newcommand*{\ztil}{{\tilde z}}
\newcommand*{\altil}{{\tilde\alpha}}
\newcommand*{\alphatil}{{\tilde\alpha}}
\newcommand*{\betil}{{\tilde\beta}}
\newcommand*{\betatil}{{\tilde\beta}}
\newcommand*{\gatil}{{\tilde\gamma}}
\newcommand*{\gammatil}{{\tilde\gamma}}
\newcommand*{\detil}{{\tilde\delta}}
\newcommand*{\deltatil}{{\tilde\delta}}
\newcommand*{\eptil}{{\tilde\epsilon}}
\newcommand*{\epsilontil}{{\tilde\epsilon}}
\newcommand*{\zetil}{{\tilde\zeta}}
\newcommand*{\zetatil}{{\tilde\zeta}}
\newcommand*{\ettil}{{\tilde\eta}}
\newcommand*{\etatil}{{\tilde\eta}}
\newcommand*{\thtil}{{\tilde\theta}}
\newcommand*{\thetatil}{{\tilde\theta}}
\newcommand*{\iotil}{{\tilde\iota}}
\newcommand*{\iotatil}{{\tilde\iota}}
\newcommand*{\katil}{{\tilde\kappa}}
\newcommand*{\kappatil}{{\tilde\kappa}}
\newcommand*{\latil}{{\tilde\lambda}}
\newcommand*{\lambdatil}{{\tilde\lambda}}
\newcommand*{\mutil}{{\tilde\mu}}
\newcommand*{\nutil}{{\tilde\nu}}
\newcommand*{\xitil}{{\tilde\xi}}
\newcommand*{\pitil}{{\tilde\pi}}
\newcommand*{\rhtil}{{\tilde\rho}}
\newcommand*{\rhotil}{{\tilde\rho}}
\newcommand*{\sitil}{{\tilde\sigma}}
\newcommand*{\sigmatil}{{\tilde\sigma}}
\newcommand*{\tatil}{{\tilde\tau}}
\newcommand*{\tautil}{{\tilde\tau}}
\newcommand*{\phtil}{{\tilde\phi}}
\newcommand*{\phitil}{{\tilde\phi}}
\newcommand*{\vphtil}{{\tilde\varphi}}
\newcommand*{\vphitil}{{\tilde\varphi}}
\newcommand*{\varphitil}{{\tilde\varphi}}
\newcommand*{\chtil}{{\tilde\chi}}
\newcommand*{\chitil}{{\tilde\chi}}
\newcommand*{\pstil}{{\tilde\psi}}
\newcommand*{\psitil}{{\tilde\psi}}
\newcommand*{\vpstil}{{\tilde\varpsi}}
\newcommand*{\vpsitil}{{\tilde\varpsi}}
\newcommand*{\varpsitil}{{\tilde\varpsi}}
\newcommand*{\omtil}{{\tilde\omega}}
\newcommand*{\omegatil}{{\tilde\omega}}
\newcommand*{\wwtil}{{{\tilde\omega}}}
\newcommand*{\elltil}{{\tilde\ell}}


\def\fmonth{\ifcase\month\or Jan\or Feb\or Mar\or Apr
\or May\or Jun\or Jul\or Aug\or Sep
\or Oct\or Nov\or Dec\fi\ }
\def\mmddyyyy{\the\month.\the\day.\the\year}
\def\ddmmyyyy{\the\day.\the\month.\the\year}
\def\Mddyyyy{\fmonth~\the\day,~\the\year}

