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jocaps

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\usepackage{amssymb, amsthm,amsmath} \usepackage{pictexwd, dcpic} \usepackage{pstricks} \usepackage[dvips]{graphicx} %%%%%%%%%% Theorems and Other Theoremstyles %%%%%%%%%%%%%% \theoremstyle{definition} \newtheorem{theorem}{Theorem} \newtheorem{prop}[theorem]{Proposition} \newtheorem{lemma}[theorem]{Lemma} \newtheorem*{defi}{Definition} \newtheorem*{exam}{Example} \newtheorem{example}[theorem]{Example} \newtheorem*{ack}{Acknowledgement} \newtheorem{cor}[theorem]{Corollary} \newtheorem{remark}[theorem]{Remark} \newtheorem{conj}[theorem]{Conjecture} \newtheorem{cons}[theorem]{Construction} \newtheorem*{defnot}{Definition and Notation} \theoremstyle{remark} \newtheorem*{rem}{Remark} %%% * means no numbering \newtheorem*{nota}{Notation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\blacksq{\begin{flushright}$\blacksquare$\end{flushright}} \def\dotcup{\buildrel\textstyle.\over\cup} %%%%%%%%%%%%%%%%%%%%%%%%%% New Commands and Renew Commands %%%%%%%%%%%%%%%%%%%%%%%% \newcommand\ann{\mathrm{Ann}} \newcommand\rsa{\rightsquigarrow} \newcommand\brac[1]{\langle #1 \rangle} \newcommand\sep{\,:\,} %\newcommand\pair[1]{#1,#1^+} \newcommand\st {\mathrel{\ooalign{$\,\backepsilon$\cr\lower .7pt\hbox{\kern 1pt$-\,$}}}} \newcommand\qf[1]{\mathrm{Quot}(#1)} \newcommand\spec{\mathrm{Spec}\,} \newcommand\sper{\mathrm{Sper}\,} \newcommand\supp{\mathrm{supp}} \newcommand\id{\mathrm{id}} \newcommand\basis{\mathcal{B}} %\renewcommand\P{\mathcal{P}} %\renewcommand\H{\mathcal{H}} \newcommand\minspec{\mathrm{MinSpec}\,} \newcommand\Hom{\mathrm{Hom}} \newcommand\Ccal{\mathcal{C}} \newcommand\Dcal{\mathcal{D}} \newcommand\Z{\mathbb{Z}} \newcommand\Q{\mathbb{Q}} \newcommand\R{\mathbb{R}} \newcommand\C{\mathbb{C}} \newcommand\alg{R_{alg}} %\newcommand\F{\mathcal F} \newcommand{\N}{\mathbb{N}} \newcommand{\p}{\mathfrak{p}} \newcommand\wo[1]{\backslash{\{#1\}}} \newcommand{\bij}{\rightarrowtail \hspace{-1.9ex} \rightarrow} \newcommand{\longbij}{\rightarrowtail \hspace{-1.9ex} \rightarrow} \newcommand*{\lhrarrow}{\ensuremath{\lhook\joinrel\relbar\joinrel\rightarrow}} \newcommand*{\thrarrow}{\twoheadrightarrow} \newcommand*{\lthrarrow}{\ensuremath{\relbar\joinrel\twoheadrightarrow}} %\renewcommand{\labelenumi}{\roman{enumi}.} \renewcommand\mod{\,\mathrm{mod}\,} \newcommand{\ic}{\mathrm{ic}} \renewcommand\thefootnote{\relax} \newcommand{\bigcupdot}{\mathop{\makebox[-.2em]{\hskip 1.3em $^{\boldsymbol\cdot}$}\bigcup}} \newcommand{\bigcupd}{\mathop{\makebox[0em]{\hskip 1.2em $^{\boldsymbol\cdot}$}\bigcup}} \newcommand{\Pcal}{\mathcal P} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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