%%%
%%%   Abbreviations
%%%
\newcommand\mc{\multicolumn}
\newcommand\pb{\pagebreak}
\newcommand\lb{\linebreak}
\newcommand\ds{\displaystyle}
\newcommand\ts{\textstyle}
\newcommand\scs{\scriptstyle}
\newcommand\scscs{\scriptscriptstyle}
\newcommand\ph{\phantom}
\newcommand\tx{\text}
\newcommand\mr{\mathrm}
\newcommand\bm{\mathbf}
\newcommand\bs{\boldsymbol}
\newcommand\dsum{\ds\sum}
\newcommand\lsum{\sum\limits}
\newcommand\dint{\ds\int}
\newcommand\T{{\tx{\normalshape\tiny\sf T}}}
\newcommand\etal{\emph{et al}\xspace}
%\newcommand\Id{\mathop{\mathrm{Id}\nolimits}}
%%%
%%%   Miscellany
%%%
\newcommand\Sref[1]{Section~\ref{#1}}
\newcommand\Fref[1]{Figure~\ref{#1}}
\newcommand\Tref[1]{Table~\ref{#1}}
\newcommand\propref[1]{Proposition~\ref{#1}}
\newcommand\Eref[1]{Eq.~\eqref{#1}}
\newcommand\hook{\mbox{\Large$\clrcorner$}\:}
\newcommand\Christ[2]{{\textstyle\left\{\!\genfrac{}{}{0pt}{}{#1}{#2}\!\right\}}}
\newcommand\smasha{\relax \mathpalette\msm@sh}
\newcommand\msm@sh[2]{\setbox0\hbox{$\m@th#1{#2}$}\ht0=.8\ht0 \leavevmode\box\z@}
\newcommand\overa[2]{\binrel@@{\mathop{\kern\z@#2}\limits^{#1}}}
\newcommand\lvec[1]{\overa{\leftarrow\kern-.5ex}{\smasha{#1}}}
\newcommand\rvec[1]{\overa{\rightarrow\kern-.5ex}{\smasha{#1}}}
\newcommand\semicolon{\nobreak\mskip2mu\mathpunct{}\nonscript
  \mkern-\thinmuskip{;}\mskip6muplus1mu\relax}
\newcommand\bra{\langle}
\newcommand\ket{\rangle}
\newcommand{\e}{\mathrm{e}}
\renewcommand{\i}{\mathrm{i}}
\renewcommand{\d}{\mathrm{d}}
\newcommand\openone{\leavevmode\hbox{\small$1$\kern-3.5\p@\normalsize$1$}\xspace}
\newcommand\lfrac[2]{\text{$#1/#2$}}
\newcommand\sfrac[2]{\text{${}^{#1}\kern-.2em/\kern-.1em_{#2}$}}
\newcommand\overover[2]{\overset{\smash[b]{\hbox{\raise14\ex@\hbox{$\hidewidth #1\hidewidth$}}}}{\smash[t]{#2}}}
\newcommand\underunder[2]{\underset{\smash[t]{\hbox{\lower11\ex@\hbox{$\hidewidth #1\hidewidth$}}}}{\smash[b]{#2}}}
\newcommand\link{\text{\raise.15ex\hbox{$-$}}\ignorespaces}
\newcommand\linkII{\text{\raise.15ex\hbox{$=$}}\ignorespaces}
\newcommand\linkIII{\text{\raise.15ex\hbox{$\equiv$}}\ignorespaces}
\newcommand\fullcirc{\raisebox{-1\p@}{\Large$\bullet$}\xspace}
\newcommand\fullsqr{\mbox{\vrule height5\p@ width5\p@}\xspace}
\newcommand\dotted{\mbox{${\mathinner{\cdotp\cdotp\cdotp\cdotp\cdotp\cdotp\,}}$}\xspace}
\newcommand\dashed{\mbox{-\;-\;-\;-}\xspace}
\newcommand\broken{\mbox{-- -- --}\xspace}
\newcommand\longbroken{\mbox{--- --- ---}\xspace}
\newcommand\chain{\mbox{--- $\cdot$ ---}\xspace}
\newcommand\dashddot{\mbox{--- $\cdot$ $\cdot$ ---}\xspace}
\newcommand\full{\mbox{---\!---\!---}\xspace}
\newcommand\nula{\mc{1}{c}{0}}
%%%
%%%   Math Operators
%%%
\DeclareMathOperator\Exp{Exp}
\DeclareMathOperator\arccosh{arccosh}
\DeclareMathOperator\arcsinh{arcsinh}
\DeclareMathOperator\arctanh{arctanh}
\DeclareMathOperator\arccoth{arccoth}
\DeclareMathOperator\sech{sech}
\DeclareMathOperator\csch{csch}
\DeclareMathOperator\const{const}
\DeclareMathOperator\sign{sign}
\DeclareMathOperator\diag{diag}
\DeclareMathOperator\sinc{sinc}
\DeclareMathOperator\erf{erf}
\DeclareMathOperator\grad{grad}
\DeclareMathOperator\rot{rot}
\DeclareMathOperator\diver{div}
\DeclareMathOperator\Div{Div}
\DeclareMathOperator\var{var}
\DeclareMathOperator\cov{cov}
\DeclareMathOperator\ind{ind}
\DeclareMathOperator\rank{rank}
\DeclareMathOperator\trace{trace}
\DeclareMathOperator\Trace{Trace}
\DeclareMathOperator\tr{tr}
\DeclareMathOperator\Tr{Tr}
\DeclareMathOperator\Ree{Re}
\DeclareMathOperator\Res{Res}
\DeclareMathOperator\im{im}
\DeclareMathOperator\Imm{Im}
\DeclareMathOperator\Id{Id}
\DeclareMathOperator\id{id}
\DeclareMathOperator\ad{ad}
%%%
%%%   Measures
%%%
\newcommand\gC{\ifmmode\,^\circ\tx{C}\else$\,^\circ$C\fi\xspace}
\newcommand\wt{\ifmmode\tx{wt}\,\%\else wt\,$\%$\fi\xspace}
\newcommand\at{\ifmmode\tx{at.}\,\%\else at.\,$\%$\fi\xspace}
\newcommand\mol{\ifmmode\tx{mol}\,\%\else mol\,$\%$\fi\xspace}
\newcommand\vol{\ifmmode\tx{vol.}\,\%\else vol.\,$\%$\fi\xspace}
\newcommand\mass{\ifmmode\tx{mass}\,\%\else mass\,$\%$\fi\xspace}
\newcommand\mm{\ifmmode\mu\tx{m}\else$\mu$m\fi\xspace}
\newcommand\ms{\ifmmode\mu\tx{s}\else$\mu$s\fi\xspace}
\newcommand\mg{\ifmmode\mu\tx{g}\else$\mu$g\fi\xspace}
\newcommand\mA{\ifmmode\mu\tx{A}\else$\mu$A\fi\xspace}
\newcommand\mV{\ifmmode\mu\tx{V}\else$\mu$V\fi\xspace}
\newcommand\mF{\ifmmode\mu\tx{F}\else$\mu$F\fi\xspace}
\newcommand\mC{\ifmmode\mu\tx{C}\else$\mu$C\fi\xspace}
\newcommand\mO{\ifmmode\mu\Omega\else$\mu\Omega$\fi\xspace}
%%%
%%%   Specials like CDs
%%%
%-------------------------------------------------------------------------%
\@ifundefined{Iat}{%
  \DeclareRobustCommand{\Iat}{\FN@\at@}
}{}
\begingroup \catcode`\@=\active
\csname if\string @compatibility\endcsname
\else \fam=\mathcode`\@
  \xdef @{\mathchar\number\fam\space }
\fi
\gdef\CDat{\let @=\Iat}
\endgroup
%\CDat
\mathcode`\@="8000 % make @ pseudo-active in math
\def\at@{\let\next@\at@@
 \ifcat\noexpand\next a\else
 \ifcat\noexpand\next0\else
 \ifcat\noexpand\next\relax\else
 \let\next@\at@@@\fi\fi\fi\next@}
 \def\at@@#1{\expandafter
  \ifx\csname\space @\string#1\endcsname\relax
    \DN@{\at@@@#1}%
  \else
    \DN@{\csname\space @\string#1\endcsname}%
  \fi\next@}%
\def\culcorner{\raisebox{-4.2pt}[2pt][2pt]{$\ulcorner$}}
\def\curcorner{\raisebox{-4.2pt}[2pt][2pt]{$\urcorner$}}
\def\cllcorner{\raisebox{2.8pt}[2pt][2pt]{$\llcorner$}}
\def\clrcorner{\raisebox{2.8pt}[2pt][2pt]{$\lrcorner$}}
\def\atdef@#1{\expandafter\def\csname\space @\string#1\endcsname}
\@ifundefined{minaw@}{\newdimen\minaw@}{}
\@ifundefined{bigaw@}{\newdimen\bigaw@}{}
\atdef@|#1|#2|#3{\setboxz@h{$\m@th{#3}$}%
  \bigaw@\wdz@\advance\bigaw@-1ex\ifdim\bigaw@<\minaw@ \bigaw@\minaw@\fi%
  \@ifempty{#1}{\@ifnotempty{#2}{\underset{\mathrel{\mathop{\hbox
  to\bigaw@{\lcornerfill{#2}}}}}{#3}}}{\overset{\mathrel{\mathop{\hbox
  to\bigaw@{\ucornerfill{#1}}}}}{#3}}%
}% end of @|||
\def\ucornerfill#1{\m@th\setboxz@h{$-$}\ht\z@\z@%
  $\culcorner\mkern-6mu\cleaders\hbox{$\mkern-2mu\box\z@\mkern-2mu$}\hfill%
  \setboxz@h{$-$}\ht\z@\z@\raise\p@\hbox{$\scriptstyle\,#1\,$}%
  \cleaders\hbox{$\mkern-2mu\box\z@\mkern-2mu$}\hfill%
  \mkern-6mu\curcorner$}
\def\lcornerfill#1{\m@th\setboxz@h{$-$}\ht\z@\z@%
  $\cllcorner\mkern-6mu\cleaders\hbox{$\mkern-2mu\box\z@\mkern-2mu$}\hfill%
  \setboxz@h{$-$}\ht\z@\z@\raise\p@\hbox{$\scriptstyle\,#1\,$}%
  \cleaders\hbox{$\mkern-2mu\box\z@\mkern-2mu$}\hfill%
  \mkern-6mu\clrcorner$}
%-------------------------------------------------------------------------%
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{example}[theorem]{Example}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{remarks}[theorem]{Remarks}

