tebd \documentclass{article} \usepackage{latexsym,amssymb} % special symbols \usepackage{amsmath} % amsmath environments \usepackage{amsthm} % ams theorem/proof environments % \usepackage{amscd} % ams commutative diagrams % \usepackage{graphicx} % graphics commands % \usepackage{color} % color commands % \usepackage{verbatim} % comment/verbatim environments % \usepackage{makeidx} % makeindex \newcommand{\bfi}{\bfseries\itshape} % bold italic \begin{document} upkgu \usepackage{ upkg \usepackage{}@$1C upkgams \usepackage{amsmath,amssymb,eufrak,amsthm,amscd} upkgeuc \usepackage{eucal} upkgeuf \usepackage{eufrak} upkgclr \usepackage{color} upkggr \usepackage{graphicx} upkgvrb \usepackage{verbatim} temar \textwidth 6.5 truein \oddsidemargin 0 truein \evensidemargin -0.50 truein \topmargin -.5 truein \textheight 8.5in teaut \title{Title of paper} \author{ Author1 \thanks{Research partially supported by ...} \\Department of Mathematics \\University of ... \\ \and Author2 \thanks{Research partially supported by ...} \\Department of Physics \\State University of ... } \date{put in custom date; delete this line for today's date} \maketitle teabs \begin{abstract} Text goes here \end{abstract} teref \section*{References} \begin{description} \item %use ``biba'' to fill in ref. items \end{description} tebib \begin{thebibliography}{} \bibitem[]{} %use ``bibia'' or ``bibib'' to fill in bibitems \end{thebibliography} teack \begin{acknowledgment} \end{acknowledgment} bdo \begin{document} edo \end{document} dcart \documentclass{article} dcarta4 \documentclass[a4paper]{article} dclet \documentclass{letter} dcrep \documentclass{report} dcbook \documentclass{book} ncmdu \newcommand{ ncmd \newcommand{}{}@$1C@$1C@$1C rcmdu \renewcommand{ rcmd \renewcommand{}{}@$1C@$1C@$1C blstr \renewcommand{\baselinestretch}{1.5} setcu \setcounter{ setc \setcounter{}{}@$1C@$1C@$1C slnu \setlength{ sln \setlength{}{}@$1C@$1C@$1C spi \setlength{\parindent}{0em} sps \setlength{\parskip1.5ex plus 0.5ex minus 0.5ex} spn \setcounter{page}{}@$1C pgnr \pagenumbering{roman} pgna \pagenumbering{arabic} mrkbu \markboth{ mrkb \markboth{}{}@$1C@$1C@$1C pgse \pagestyle{empty} pgsm \pagestyle{myheadings} sn \section{ sns \section*{ ssn \subsection{ ssns \subsection*{ parau \paragraph{ ssn \paragraph{}@$1C cpg \clearpage cdp \cleardoublepage bctr \begin{center} ectr \end{center} bfll \begin{flushleft} efll \end{flushleft} bflr \begin{flushright} eflr \end{flushright} bqt \begin{quotation} eqt \end{quotation} bmpg \begin{minipage}{\textwidth} empg \end{minipage} ben \begin{enumerate} een \end{enumerate} bitm \begin{itemize} eitm \end{itemize} bds \begin{description} eds \end{description} itmu \item[ rcmdl \renewcommand{\labelenumi}{\em $($\roman{enumi}$)$} btb \begin{tabbing} etb \end{tabbing} tb \> btr \begin{tabular}{|c|c|} etr \end{tabular} hlin \hline ftnu \footnote{ ftn \footnote{}@$1C bbib \begin{thebibliography}{} ebib \end{thebibliography} snsref \section*{References} lblu \label{ lbl \label{}@$1C refu \ref{ refp (\ref{})@$1C@$1C citu \cite{ cit \cite{}@$1C citp (\cite{})@$1C@$1C refia \item Author [year] Title. {\it Journal\/} {\bf 11}, 123--223. refib \item Author [year] {\it Title.\/} Publisher. bibia \bibitem[]{}@$1C@$1C@$1C Author [year] Title. {\it Journal\/} {\bf 11}, 123--223. bibib \bibitem[]{}@$1C@$1C@$1C Author [year] {\it Title.\/} Publisher. idxu \index{ idx \index{}@$1C pidx \printindex midx \makeindex dsz \displaystyle tsz \textstyle ssz \scriptstyle sssz \scriptscriptstyle bdp \[ edp \] beq \begin{equation} beql \begin{equation}\label{ eeq \end{equation} bqa \begin{eqnarray} bqal \begin{eqnarray}\label{ eqa \end{eqnarray} bqas \begin{eqnarray*} eqas \end{eqnarray*} besb \begin{Sb} eesb \end{Sb} besp \begin{Sp} eesp \end{Sp} bea \begin{array}{ccc} eea \end{array} nonu \nonumber mbxu \mbox{ mbx \mbox{}@$1C txtu \text{ txt \text{}@$1C txtqu \quad\text{}\quad@$1C@$1C@$1C@$1C@$1C@$1C intxtu \text{ intxt \intertext{}@$1C txtqa \quad \text{and}\quad lequ \begin{eqnarray} \lefteqn{} \nonumber \\ & & \end{eqnarray}@$1E@$1E@$1D@$1D@$1D@$1D@$1D@$1D lequs \begin{eqnarray*} \lefteqn{}\\ & & \end{eqnarray*}@$1E@$1E@$1D@$1D@$1D@$1D@$1D@$1D tgu \tag{ tg \tag{}@$1C tgsu \tag*{ tgs \tag*{}@$1C ntg \notag bma \begin{math} ema \end{math} bdma \begin{displaymath} edma \end{displaymath} bal \begin{align} eal \end{align} bals \begin{align*} eals \end{align*} bala \begin{alignat}{} eala \end{alignat} balas \begin{alignat*}{}@$1E ealas \end{alignat*} bga \begin{gather} ega \end{gather} bgas \begin{gather*} egas \end{gather*} bmlt \begin{multline} emlt \end{multline} bmlts \begin{multline*} emlts \end{multline*} bald \begin{aligned} eald \end{aligned} balda \begin{alignedat}{}@$1C ealda \end{alignedat} bgad \begin{gathered} egad \end{gathered} bsplt \begin{split} esplt \end{split} equn \[ F(b)-F(a)=\int^b_af(x)\, dx \] eqnu \begin{equation} F(b)-F(a)=\int^b_af(x)\, dx \end{equation} eqtxt \[ \sum ^n _{ i = 1 } x^2 _i + y^2 _i \geq 0 \quad \text{for all real numbers $ x _i $ and $ y _i $} \] eqaun \begin{align*} x^2 &= y+1 \\ x^2+1 &= u+v \end{align*} eqanu \begin{align} x^2 &= y+1 \\ x^2+1 &= u+v \end{align} eqad \begin{equation} \begin{aligned} {}&a = b + c \\ {}&d = e + f + g \end{aligned} \end{equation} eqsp \begin{equation} \begin{split} a = b &+ c + (c + d) \\ &{}- e + f \end{split} \end{equation} eqlbr \begin{equation} \left. \begin{aligned} &x = y \\ &a = b^2 + b + 1 \end{aligned} \right\} \end{equation} eqbox \begin{equation} \fbox{\parbox{.7in}{$\displaystyle{\frac{x^2 + 1}{5} = y}$ }} \end{equation} eval \[ \left. f \left(\frac{t}{2}\right)\right|_{t=0} \] thmsty \theoremstyle{plain} %--default \newtheorem{theorem} {Theorem} [section] \newtheorem{lemma} [theorem]{Lemma} \newtheorem{corollary} [theorem]{Corollary} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{algorithm} [theorem]{Algorithm} \newtheorem{criterion} [theorem]{Criterion} \newtheorem{conjecture} [theorem]{Conjecture} \newtheorem{question} [theorem]{Question} \theoremstyle{definition} \newtheorem{definition} [theorem]{Definition} \newtheorem{condition} [theorem]{Condition} \newtheorem{example} [theorem]{Example} \newtheorem{problem} [theorem]{Problem} \newtheorem{solution} [theorem]{Solution} \theoremstyle{remark} \newtheorem{remark} {Remark} \newtheorem{note} {Note} \newtheorem{claim} {Claim} \newtheorem{summary} {Summary} \newtheorem{case} {Case} \newtheorem{acknowledgment} {Acknowledgments} \newtheorem{conclusion} {Conclusion} \newtheorem{notation} {Notation} mcor \newtheorem{corollary}{Corollary} mdfn \newtheorem{definition}{Definition} mlem \newtheorem{lemma}{Lemma} mprop \newtheorem{proposition}{Proposition} mthm \newtheorem{theorem}{Theorem} bcor \begin{corollary} ecor \end{corollary} blem \begin{lemma} elem \end{lemma} bprop \begin{proposition} eprop \end{proposition} bthm \begin{theorem} bthmt \begin{theorem}[Gauss' Theorem] ethm \end{theorem} bdfn \begin{definition} edfn \end{definition} bprf \begin{proof} eprf \end{proof} balg \begin{algorithm} ealg \end{algorithm} bcnj \begin{conjecture} ecnj \end{conjecture} bcrit \begin{criterion} ecrit \end{criterion} bqst \begin{question} eqst \end{question} bcnd \begin{condition} ecnd \end{condition} bprob \begin{problem} eprob \end{problem} brmk \begin{remark} ermk \end{remark} bnote \begin{note} enote \end{note} bnota \begin{notation} enota \end{notation} bcase \begin{case} ecase \end{case} bclm \begin{claim} eclm \end{claim} bsum \begin{summary} esum \end{summary} bcncl \begin{conclusion} ecncl \end{conclusion} bac \begin{acknowledgment} eac \end{acknowledgment} bsol \begin{solution} esol \end{solution} bxca \begin{xca} exca \end{xca} bxcb \begin{xcb} excb \end{xcb} blackl \quad\blacklozenge dblackl \quad $\blacklozenge$ qbsq \quad\blacksquare qdbsq \quad $\blacksquare$ qesq \quad\square qdesq \quad $\square$ qetd \quad\bigtriangledown qdetd \quad $\bigtriangledown$ qbtd \quad\blacktriangledown qdbtd \quad $\blacktriangledown$ rtgu \raisetag{ qed \qed qeds \qedsymbol tgqeds \tag*{\qedsymbol} rcqeds \renewcommand{qedsymbol}{} txtu \text{ txt \text{}@$1C txtupu \textup{ txtup \textup{}@$1C intxtu \intertext{ intxt \intertext{}@$1C txtitu \textit{ txtit \textit{}@$1C txtrmu \textrm{ txtrm \textrm{}@$1C txtscu \textsc{ txtsc \textsc{}@$1C txtsfu \textsf{ txtsf \textsf{}@$1C txtslu \textsl{text slanting inside math mode txtsl \textsl{}@$1C txtttu \texttt{ txttt \texttt{}@$1C txtstyu \textstyle{ txtsty \textstyle{}@$1C mbbu \mathbb{ m \math{}@$1C mbfu \mathbf{ mbf \mathbf{}@$1C mcalu \mathcal{ mcal \mathcal{}@$1C mfrku \mathfrak{ mfrk \mathfrak{}@$1C mitu \mathit{ mit \mathit{}@$1C mrmu \mathrm{ mrm \mathrm{}@$1C msfu \mathsf{ msf \mathsf{}@$1C mttu \mathtt{ mtt \mathtt{}@$1C opnu \operatorname{ opn \operatorname{}@$1C opsech \operatorname{sech} opso3 \operatorname{so(3)} dopso3 $\operatorname{so(3)}$ opcso3 \operatorname{SO(3)} opdcso3 $\operatorname{SO(3)}$ opdiv \operatorname{div} opcimu \operatorname{Im}( opcimz \operatorname{Im}(z) opcreu \operatorname{Re}( opcrez \operatorname{Re}(z) opad \operatorname{ad} opcad \operatorname{Ad} opcaut \operatorname{Aut} opccard \operatorname{Card} opchar \operatorname{char} opccorr \operatorname{Corr} opcdiff \operatorname{Diff} opcext \operatorname{Ext} opcfcl \operatorname{FL} opcgcl \operatorname{GL} opchom \operatorname{Hom} opcjac \operatorname{Jac} opclie \operatorname{Lie} opcnm \operatorname{Nm} opcpcgcl \operatorname{PGL} opcpic \operatorname{Pic} opcprym \operatorname{Prym} opcram \operatorname{Ram} opcrank \operatorname{Rank} oprank \operatorname{rank} opreg \operatorname{reg} opcres \operatorname{Res} opres \operatorname{res} opsl \operatorname{sl} opcscl \operatorname{SL} opcsco \operatorname{SO} opcscp \operatorname{SP} opcsp \operatorname{Sp} opsq \operatorname{sq} opcscu \operatorname{SU} opcsym \operatorname{Sym} opctr \operatorname{Tr} fdbfi \newcommand{\bfi}{\bfseries\itshape} bfiu {\bfi bfu {\bf emu {\em itu {\it rmu {\rm scu {\sc sfu {\sf ttu {\tt ovsu \overset{ ovst \overset{}{}@$1C@$1C@$1C sstu \sideset{ sst \sideset{}{}@$1C@$1C@$1C unstu \underset{ unst \underset{}{}@$1C@$1C@$1C smb \smash[b]{}@$1C@$1C@$1C smt \smash[t]{}@$1C@$1C@$1C nolim \nolimits ovstcpp \overset{\longrightarrow}{\text{PP}} ovstcpq \overset{\longrightarrow}{\text{PQ}} dovstcpp $\overset{\longrightarrow}{\text{PP}}$ dovstcpq $\overset{\longrightarrow}{\text{PQ}} mxc \begin{pmatrix} x_1 \\ x_2 \\ x_3 \end{pmatrix} mxcb \begin{bmatrix} x \\ y \end{bmatrix} mx2p \begin{pmatrix} a & b \\ c & d \end{pmatrix} mx2bk \begin{bmatrix} a & b \\ c & d \end{bmatrix} mx2i \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} mx2s \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} mx3i \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} mx3d \left| \begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix} \right| mx3p \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix} mx3b \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} mx3b35pt \begin{bmatrix} a & b & c \\ [35pt] d & e & f \\ [35pt] g & h & i \end{bmatrix} mxu \begin{matrix} ...&...\\ ...&... \end{matrix} mxpu \begin{pmatrix} ...&...\\ ...&... \end{pmatrix} mxbu \begin{bmatrix} ...&...\\ ...&... \end{bmatrix} mxvu \begin{vmatrix} ...&...\\ ...&... \end{vmatrix} mxcvu \begin{Vmatrix} ...&...\\ ...&... \end{Vmatrix} mxsu \begin{smallmatrix} ...&...\\ ...&... \end{smallmatrix} mxspu \left( \begin{smallmatrix} ...&...\\ ...&... \end{smallmatrix} \right) mxsbu \left[ \begin{smallmatrix} ...&...\\ ...&... \end{smallmatrix} \right] frbox \fbox{\parbox{2.0in}{\centerline{\large \bf type header} text }} dfrbox \fbox{\fbox{\parbox{2.0in}{ \centerline{\large \bf type header} text }}} frboxn \fbox{\parbox{2.0in}{{\large \bf Note: \,} text }} tbex \begin{tabbing} xxxxxxxxxxx\= xxxxxxxxxxx\= xxxxxxxxxxx\= \kill items \> for \> row \> one \\ items \> for \> row \> two \\ \end{tabbing} tabex1 \begin{center} \begin{tabular}{ccccc} & & \multicolumn{3}{c}{Definition} \\ & & \multicolumn{3}{c}{of derivative} \\ & & & $\downarrow$ & \\ Partials exist and & $\Longrightarrow$ & Differentiable & $\Longrightarrow$ & Partials exist \\ are continuous & & & & \end{tabular} \end{center} tabex2 \begin{center} \fbox{\parbox{4.5in}{ \begin{tabular}{ll} \multicolumn{2}{c}{\bf Box 2.1.1 \quad Summary of Important Formulas for \S 2.1} \\ {\it Velocity\/} & \\ & \\ $ V = {\displaystyle \frac{\partial \phi}{\partial t} } $ & $ V ^a ={\displaystyle \frac{\partial \phi ^a} {\partial t}}$ \\ & \\ $ v _t = V _t \circ \phi _t ^{-1} $ & $ v ^a _t = V ^a _t \circ \phi _t ^{-1} $ \\ & \\ {\it Covariant Derivative\/} & \\ & \\ $ {\bf D} v \cdot w = \nabla _w v $ & $ (\nabla _w v) ^a = {\displaystyle \frac{\partial v ^a} {\partial x ^b}} w ^b + \gamma ^a _{b c} w ^b v ^c $ \\ \end{tabular} }} \end{center} tabex3 \begin{center} \begin{tabular}{lll} {\it Classical Tensor Analysis\/} & & {\it Tensor Analysis on Manifolds\/} \\ \\ $ \{ x ^a\}$ & Coordinates & $ \{ x ^a\}$ \\ \\ $ e _a = {\displaystyle \frac{\partial z ^i } {\partial x ^a} \dot{ i} _i }$ & $ \!\!\! \begin{array}{l} {\rm coordinate} \\ {\rm basis \, vectors } \end{array} $ & $ {\displaystyle \frac{\partial}{\partial x^a} = e _a } $ \\ \\ $ \!\!\!\! \left. \begin{array}{l} \bar{e} _a = {\displaystyle \frac{\partial x ^b} {\partial \bar{x} ^a} e _b } \\ \\ \bar{e} ^a = {\displaystyle \frac{\partial \bar{x} ^a} {\partial \bar{x} ^b} e^b } \end{array} \right\}$ & $ \!\!\! \begin{array}{l} {\rm change \, of} \\ {\rm coordinates} \\ \end{array} $ & $ \left\{ \begin{array}{l} {\displaystyle \frac{\partial}{\partial \bar{x} ^a} = \frac{ \partial x ^b}{\partial \bar{x} ^a} \frac{ \partial} {\partial x ^b} } \\ \\ {\displaystyle d \bar{x} ^a = \frac{ \partial \bar{x} ^a }{ \partial x ^b} d x ^b } \end{array} \right. $ \\ \end{tabular} \end{center} tabex4 \begin{center} \begin{tabular}{||l|l||} \hline \hline \quad {\bf Classical Mechanics} & \quad {\bf Quantum Mechanics} \\ \hline \hline immersed Lagrangian manifold & element of $L^2 (Q)$ or ${\cal D}^\prime (Q)$ \\ $\Lambda \rightarrow (T ^\ast Q,\Omega)$ & \\ \hline $\Lambda = $ graph of ${\bf d} S$ & $\psi = \exp (iS/\hbar)$ \\ \hline $T ^{\ast} Q$ & Hilbertspace \\ \hline Lagrangian manifold & (possibly unbounded) \\ $\quad \Omega \subset(T^\ast Q, \Omega _Q) \times (T^\ast R,-\Omega_R)$ & $\quad L^2 (R)$ to $L^2 (Q)$ \\ \hline composition of canonical relations & composition of operators \\ \hline \hline \end{tabular} \end{center} tabex5 \begin{center} \fbox{\fbox{\parbox{4.0in}{ \begin{tabular}{ll} \quad {\bf Classical Mechanics} & \quad {\bf Quantum Mechanics} \\ \hline \hline immersed Lagrangian manifold & element of $L^2 (Q)$ or ${\cal D}^\prime (Q)$ \\ $\Lambda \rightarrow (T ^\ast Q,\Omega)$ & \\ \hline $\Lambda = $ graph of ${\bf d} S$ & $\psi = \exp (iS/\hbar)$ \\ \hline $T ^{\ast} Q$ & Hilbertspace \\ \hline Lagrangian manifold & (possibly unbounded) \\ $\quad \Omega \subset (T^\ast Q, \Omega _Q) \times (T^\ast R,-\Omega_R)$ & $\quad L^2 (R)$ to $L^2 (Q)$ \\ \hline composition of canonical relations & composition of operators \\ \end{tabular} }}} \end{center} tabex6 \begin{center} \begin{tabular}{||l|c|c||} \hline Case & Conditions & Connection \\ \hline Unconstrained & ${\cal D}_q = T_q Q$ & ${\cal A}^{\rm sym}(\dot q)={\Bbb I} ^{-1} J(\dot{q})$ \\ [1ex] Purely Kinematic & ${\cal D}_q \cap T_q({\rm Orb}(q)) = \{0\}$ & ${\cal A}^{\rm kin} (\dot{q}) = 0$ \\ [1ex] Horizontal symmetries & ${\cal D}_q \cap T_q({\rm Orb}(q))_G = T_q({\rm Orb}(q))_H$ & ${\cal A}^{\rm sym} (\dot{q}) + {\cal A}^{\rm kin} (\dot{q}) ={\Bbb I} ^{-1} J_H (\dot{q})$ \\ [1ex] General principal & ${\cal D}_q + T_q({\rm Orb}(q)) = T_q Q$ & ${\cal A}^{\rm sym}(\dot{q}) + {\cal A}^{\rm kin}(\dot{q}) = {\Bbb I} ^{-1} J ^{\rm nhc}(\dot{q})$ \\ bundle case & & \\ \hline \end{tabular} \end{center} cdli \begin{equation*} \begin{CD} 0 @>>> A @>f>>B @>g>> C @>h>> C/g(B) @>>>0 \end{CD} \end{equation*} cdsq \begin{equation*} \begin{CD} A @>F>>B\\ @VGVV @VVgV \\ C @>>f>D\\ \end{CD} \end{equation*} tepaper %&latex2e--tepaper \documentclass{article} \usepackage{latexsym,amssymb} % special symbols \usepackage{amsmath} % amsmath environments \usepackage{amsthm} % ams theorem/proof environments % \usepackage{amscd} % ams commutative diagrams % \usepackage{graphicx} % graphics commands % \usepackage{color} % color commands % \usepackage{verbatim} % comment/verbatim environments \newcommand{\bfi}{\bfseries\itshape} % bold italic \makeatletter \@addtoreset{figure}{section} \def\thefigure{\thesection.\@arabic\c@figure} \def\fps@figure{h, t} \@addtoreset{equation}{section} \def\theequation{\thesection.\arabic{equation}} \makeatother \theoremstyle{plain} %--default \newtheorem{theorem} {Theorem} [section] \newtheorem{lemma} [theorem]{Lemma} \newtheorem{corollary} [theorem]{Corollary} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{algorithm} [theorem]{Algorithm} \newtheorem{criterion} [theorem]{Criterion} \newtheorem{conjecture} [theorem]{Conjecture} \newtheorem{question} [theorem]{Question} \theoremstyle{definition} \newtheorem{definition} [theorem]{Definition} \newtheorem{condition} [theorem]{Condition} \newtheorem{example} [theorem]{Example} \newtheorem{problem} [theorem]{Problem} \newtheorem{solution} [theorem]{Solution} \theoremstyle{remark} \newtheorem{remark} {Remark} \newtheorem{note} {Note} \newtheorem{claim} {Claim} \newtheorem{summary} {Summary} \newtheorem{case} {Case} \newtheorem{acknowledgment} {Acknowledgments} \newtheorem{conclusion} {Conclusion} \newtheorem{notation} {Notation} \begin{document} \title{Title of paper} \author{ Author1 \thanks{Research partially supported by ...} \\Department of Mathematics \\University of ... \\ \and Author2 \thanks{Research partially supported by ...} \\Department of Physics \\State University of ... } \date{put in custom date; delete this line for today's date} \maketitle \begin{abstract} This template is called {\it paper/template.tex}. It numbers equations, figures, tables and theorems within each section. Figures are placed automatically following the paragraph in which they are cited, or at the top of the next page if there is not room on the page of citation. \end{abstract} \section*{Introduction} Text goes here \section{First Section Title} Text goes here \begin{acknowledgment} We thank ... \end{acknowledgment} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % BIBLIOGRAPHY % %use ``bibia'' or ``bibib'' to fill in bibitems %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{thebibliography}{} \bibitem[]{} \end{thebibliography} \end{document} tepaper.simple %&latex2e--tepaper.simple \documentclass{article} \usepackage{latexsym,amssymb} % special symbols \usepackage{amsmath} % amsmath environments \usepackage{amsthm} % ams theorem/proof environments % \usepackage{amscd} % ams commutative diagrams % \usepackage{graphicx} % graphics commands % \usepackage{color} % color commands % \usepackage{verbatim} % comment/verbatim environments \newcommand{\bfi}{\bfseries\itshape} \newtheorem{theorem}{Theorem}[section] \newtheorem{proposition}[theorem]{Proposition} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{definition}[theorem]{Definition} {\renewcommand{\theequation}{\thesection.\arabic{equation}} \begin{document} \title{Title of paper} \author{ Author1 \thanks{Research partially supported by ...} \\Department of Mathematics \\University of ... \\ \and Author2 \thanks{Research partially supported by ...} \\Department of Physics \\State University of ... } \date{put in custom date; delete this line for today's date} \maketitle \begin{abstract} This brick is called {\it paper/simple/template.tex}. It numbers equations and theorems within each section, but you are required to insert counters; it does not require any special style files. \end{abstract} %The counters below will renumber equations in each section. \section*{Introduction} \setcounter{equation}{0} Text goes here \section{First Section Title} \setcounter{equation}{0} Text goes here \begin{acknowledgment} We thank ... \end{acknowledgment} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % REFERENCES % use ``biba or bibb'' to fill in reference items %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{References} \begin{description} \item Author, U. N., ... \end{description} \end{document} tepaper.simplest %&latex2e--tepaper simplest \documentclass{article} \begin{document} \title{Title of paper} \author{Author1 \thanks{Research partially supported by ...} \\Department of Mathematics \\University of Nebraska \\ \and Author2 \thanks{Research partially supported by ...} \\Department of Physics \\San Jose State University } \date{put in custom date; delete this line for today's date} \maketitle \begin{abstract} This brick is called {\it paper/simplest/template.tex}. It uses the default \LaTeX\ numbering, with theorems etc. and equations numbered consecutively throughout the paper. \end{abstract} \section*{Introduction} Text goes here \section{First Section Title} Text goes here \section{Second Section Title} Text goes here \bigskip %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % REFERENCES % use ``biba or bibb'' to fill in reference items %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{References} \begin{description} \item Author, U. N., ... \end{description} \end{document} tepaper.eqnwith %&latex2e--tepaper eqnwith \documentclass{article} \usepackage{latexsym,amssymb} % special symbols \usepackage{amsmath} % amsmath environments \usepackage{amsthm} % ams theorem/proof environments % \usepackage{amscd} % ams commutative diagrams % \usepackage{graphicx} % graphics commands % \usepackage{color} % color commands % \usepackage{verbatim} % comment/verbatim environments \newcommand{\bfi}{\bfseries\itshape} \theoremstyle{plain} %--default \newtheorem{theorem} {Theorem} [section] \newtheorem{lemma} [theorem]{Lemma} \newtheorem{corollary} [theorem]{Corollary} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{algorithm} [theorem]{Algorithm} \newtheorem{criterion} [theorem]{Criterion} \newtheorem{conjecture} [theorem]{Conjecture} \newtheorem{question} [theorem]{Question} \theoremstyle{definition} \newtheorem{definition} [theorem]{Definition} \newtheorem{condition} [theorem]{Condition} \newtheorem{example} [theorem]{Example} \newtheorem{problem} [theorem]{Problem} \newtheorem{solution} [theorem]{Solution} \theoremstyle{remark} \newtheorem{remark} {Remark} \newtheorem{note} {Note} \newtheorem{claim} {Claim} \newtheorem{summary} {Summary} \newtheorem{case} {Case} \newtheorem{acknowledgment} {Acknowledgments} \newtheorem{conclusion} {Conclusion} \newtheorem{notation} {Notation} {\renewcommand{\theequation}{\thesection.\arabic{equation}} %-------------------------------- \makeatletter \def\equationwith#1{% \expandafter\edef\expandafter\c@equation% \expandafter{\csname c@#1\endcsname}% \expandafter\let\expandafter\theequation\csname the#1\endcsname } \makeatother \equationwith{theorem} %-------------------------------- \begin{document} \title{Title of paper} \author{ Author1 \thanks{Research partially supported by ...} \\Department of Mathematics \\University of ... \\ \and Author2 \thanks{Research partially supported by ...} \\Department of Physics \\State University of ... } \date{put in custom date; delete this line for today's date} \maketitle \begin{abstract} This brick is called {\it paper/eqnwith/template.tex}. It numbers equations and theorems within each section, but you are required to insert counters; it does not require any special style files. \end{abstract} %The counters below will renumber equations in each section. \section*{Introduction} Text goes here \section{First Section Title} Text goes here \begin{acknowledgment} We thank ... \end{acknowledgment} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % BIBLIOGRAPHY % %use ``bibia'' or ``bibib'' to fill in bibitems %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{thebibliography}{} \bibitem[]{} \end{thebibliography} \end{document} tepaper.amsart %&AMS article \documentclass{amsart} \usepackage{graphicx} \newcommand{\bfi}{\bfseries\itshape} \theoremstyle{plain} %--default \newtheorem{theorem} {Theorem} [section] \newtheorem{lemma} [theorem]{Lemma} \newtheorem{corollary} [theorem]{Corollary} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{algorithm} [theorem]{Algorithm} \newtheorem{criterion} [theorem]{Criterion} \newtheorem{conjecture} [theorem]{Conjecture} \newtheorem{question} [theorem]{Question} \theoremstyle{definition} \newtheorem{definition} [theorem]{Definition} \newtheorem{condition} [theorem]{Condition} \newtheorem{example} [theorem]{Example} \newtheorem{problem} [theorem]{Problem} \newtheorem{solution} [theorem]{Solution} \theoremstyle{remark} \newtheorem{remark} {Remark} \newtheorem{note} {Note} \newtheorem{claim} {Claim} \newtheorem{summary} {Summary} \newtheorem{case} {Case} \newtheorem{acknowledgment} {Acknowledgments} \newtheorem{conclusion} {Conclusion} \newtheorem{notation} {Notation} \numberwithin{equation}{section} %---------------------------------------------------- \begin{document} \title[put short title here]% {Put the real title here\\ and rest of title here} \author[Author One and Author Two]{% Author One\\ Author Two\\ } \address{Department of Mathematics\\ Northeastern University\\ Boston, Massachusetts 02115}% \address{Mathematical Research Section\\ School of Mathematical Sciences\\ Australian National University\\ Canberra ACT 2601, Australia} \subjclass{Primary 54C40, 14E20; Secondary 46E25, 20C20} \date {July 2, 1991} % \thanks will become a 1st page footnote. \thanks{The first author was supported in part by NSF Grant \#000000.} %\dedicatory{} \maketitle \begin{abstract} This is the abstract. \end{abstract} \tableofcontents \section{Other headings} \section*{This is an unnumbered first-level section head} \subsection{This is a numbered second-level section head} \subsection*{This is an unnumbered second-level section head} \subsubsection{This is a numbered third-level section head} \subsubsection*{This is an unnumbered third-level section head} \begin{theorem} Definition environemnt \end{theorem} \begin{definition} Definition environemnt \end{definition} \begin{remark} Remark environemnt \end{remark} %----------------- \bibliographystyle{} \begin{thebibliography}{} \bibitem[{Arnol$'$d et al. [1982]}] {arnold:sing} Arnol$'$d, V. L., Varchenko, A. N., and Gusein-Zade, S. M. [1982] \emph{Singularities of differentiable maps.} I, ``Nauka'', Moscow (Russian); English transl. Birkh\"auser, 1985. \bibitem[{Arnol$'$d et al. [1984]}] {arnold:sing2} \bysame [1984] \emph{Singularities of differentiable maps.}~II, ``Nauka'', Moscow; English transl., Birkh\"auser, 1988. \end{thebibliography} %----------------- \end{document} tepaper.html %article html %% Source: Ross Moore, Macquarie University, Sydney Australia %% Manual: http://www-dsed.llnl.gov/files/programs/unix/latex2html/manual/ \documentclass{article} %% load extra AMS math symbols \usepackage[psamsfonts]{amsfonts} %% and the extended enumerate environments \usepackage{enumerate} %% These are for making Web pages, using LaTeX2HTML \usepackage{html} \begin{htmlonly} \bodytext{BGCOLOR=#FFFFFF LINK=#9600a8 VLINK=#ff3b21 ALINK=#26ffab} \end{htmlonly} \usepackage[dvips]{color} \begin{htmlonly} \pagecolor{white} \end{htmlonly} %% adjust the size and positioning %% of the text-area on the paper %begin{latexonly} \addtolength{\voffset}{-2cm} \addtolength{\textheight}{4cm} \addtolength{\hoffset}{-2cm} \addtolength{\textwidth}{4cm} %end{latexonly} \title{} 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for today's date} \maketitle %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % BIBLIOGRAPHY % %use ``bibia'' or ``bibib'' to fill in bibitems %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{thebibliography}{} \bibitem[]{} \end{thebibliography} \end{document} teletter %&latex2e--te2letter \documentclass{letter} \begin{document} \signature{yourName} \telephone{phone (TTT) EEE-LLLL} \begin{letter}{Addressee\\ Address\\ More Address\\ More and more lines separated by double backslashes } \opening{Dear Whoever,} The Text \closing{Sincerely yours,} \end{letter} \end{document} bcmnt \begin{comment} ecmnt \end{comment} vrb \verb bvrb \begin{verbatim} evrb \end{verbatim} cl \centerline{ hfi \hfill noi \noindent nl \\ np \newpage pt % blskp \baselineskip vfi \vfill lbrk \linebreak nlin \newline rlin \rightline{}@$1C clin \centerline{}@$1C llin \leftline{}@$1C lin \line{}@$1C ob { eb } eit \/} op ( ep ) obk [ ebk ] llb \{ rlb \} bqm `` eqm '' lle \langle rle \rangle itm \item ad & ae \'{e} ge \`{e} ua \"{a} uo \"{o} uu \"{u} ace \'{E} gce \`{E} uca \"{A} uco \"{O} ucu \"{U} bksl \ ats @ cprt \copyright ps \P ss \S gss \ss csp \quad dsp \qquad ssp \, msp \: tsp \; nsp \! ndsp \! \! ensp \enspace qd \quad qqd \qquad bskp \bigskip mskp \medskip sskp \smallskip hskp \hskip 2in vskp \vskip 12pt tskp \topskip 24pt nll \null fc @$1D rc @$1C d $ dlr $$ ada & = & sd d cd D xa \alpha xb \beta xc \chi xcd \Delta xcg \Gamma xcl \Lambda xco \Omega xcp \Pi xcph \Phi xcps \Psi xcs \Sigma xcth \Theta xcu \Upsilon xcx \Xi xd \delta xe \epsilon xet \eta xg \gamma xi \iota xk \kappa xl \lambda xm \mu xn \nu xo \omega xp \pi xph \phi xps \psi xr \rho xs \sigma xt \tau xth \theta xu \upsilon xve \varepsilon xvp \varpi xvph \varphi xvr \varrho xvs \varsigma xvth \vartheta xx \xi xz \zeta dxa $\alpha$ dxb $\beta$ dxc $\chi$ dxcd $\Delta$ dxcg $\Gamma$ dxcl $\Lambda$ dxco $\Omega$ dxcp $\Pi$ dxcph $\Phi$ dxcps $\Psi$ dxcs $\Sigma$ dxcth $\Theta$ dxcu $\Upsilon$ 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\bar{ ocu \check{ odu \dot{ oddu \ddot{ ohu \hat{ otu \tilde{ setu \{ \mid \} setlu \left\{ \left. \!\right| \right\} disu {\displaystyle fpdu \frac{\partial}{\partial d0 $0$ d1 $1$ d10 $10$ d2 $2$ d3 $3$ d4 $4$ d5 $5$ d6 $6$ d7 $7$ d8 $8$ d9 $9$ dca $A$ dcb $B$ dcc $C$ dcd $D$ dce $E$ dcf $F$ dcg $G$ dch $H$ dci $I$ dcj $J$ dck $K$ dcl $L$ dcm $M$ dcn $N$ dco $O$ dcp $P$ dcq $Q$ dcr $R$ dcs $S$ dct $T$ dcu $U$ dcv $V$ dcw $W$ dcx $X$ dcy $Y$ dcz $Z$ da $a$ db $b$ dc $c$ dd $d$ de $e$ df $f$ dg $g$ dh $h$ di $i$ dj $j$ dk $k$ dl $l$ dm $m$ dn $n$ doo $o$ dp $p$ dq $q$ dr $r$ ds $s$ dt $t$ du $u$ dv $v$ dw $w$ dx $x$ dy $y$ dz $z$ sq10 \sqrt{10} sq2 \sqrt{2} sq3 \sqrt{3} sq5 \sqrt{5} sq7 \sqrt{7} squ \sqrt{ sqxp \sqrt{\pi} cr2 \sqrt[3]{2} nr2 \sqrt[n]{2} haf \frac{1}{2} f12 \frac{1}{2} f13 \frac{1}{3} f14 \frac{1}{4} fddt \frac{d}{dt} fdudt \frac{du}{dt} fdxdt \frac{dx}{dt} fdydt \frac{dy}{dt} fdzdt \frac{dz}{dt} fpx \frac{\partial}{\partial x} fpy \frac{\partial}{\partial y} fpzx \frac{\partial z}{\partial x} fps \frac{\partial^2} {\partial x \partial y} fpt \frac{\partial^3} {\partial x \partial y \partial z} ha ^a hb ^b hc ^c hd ^d hee ^e hf ^f hg ^g hh ^h hi ^i hj ^j hk ^k hl ^l hm ^m hn ^n ho ^o hp ^p hq ^q hr ^r hs ^s ht ^t huu ^u hv ^v hw ^w hx ^x hy ^y hz ^z hca ^A hcb ^B hcc ^C hcd ^D hce ^E hcf ^F hcg ^G hch ^H hci ^I hcj ^J hck ^K hcl ^L hcm ^M hcn ^N hco ^O hcp ^P hcq ^Q hcr ^R hcs ^S hct ^T hcu ^U hcv ^V hcw ^W hcx ^X hcy ^Y hcz ^Z h0 ^0 h1 ^1 h10 ^{10} h2 ^2 h3 ^3 h4 ^4 h5 ^5 h6 ^6 h7 ^7 h8 ^8 h9 ^9 sq ^2 cu ^3 xq x^2 yq y^2 zq z^2 hmo ^{-1} hij ^{ij} hijk ^{ijk} hjk ^{jk} hdg ^\dagger hflt ^\flat hpr ^\prime hprp ^\perp hshp ^\sharp hst ^\ast hvst ^\star hxa ^\alpha hxb ^\beta hxc ^\chi hxcd ^\Delta hxcg ^\Gamma hxcl ^\Lambda hxco ^\Omega hxcp ^\Pi hxcph ^\Phi hxcps ^\Psi hxcs ^\Sigma hxcth ^\Theta hxcu ^\Upsilon hxcx ^\Xi hxd ^\delta hxe ^\epsilon hxet ^\eta hxg ^\gamma hxio ^\iota hxk ^\kappa hxl ^\lambda hxm ^\mu hxn ^\nu hxo ^\omega hxp ^\pi hxph ^\phi hxps ^\psi hxr ^\rho hxs ^\sigma hxt ^\tau hxth ^\theta hxu ^\upsilon hxve ^\varepsilon hxvp ^\varpi hxvph ^\varphi hxvr ^\varrho hxvs ^\varsigma hxvth ^\vartheta hxx ^\xi hxz ^\zeta la _a lb _b lc _c ld _d le _e lf _f lg _g lh _h li _i lj _j lk _k ll _l lm _m ln _n lo _o lp _p lq _q lr _r ls _s lt _t luu _u lv _v lw _w lx _x ly _y lz _z lca _A lcb _B lcc _C lcd _D lce _E lcf _F lcg _G lch _H lci _I lcj _J lck _K lcl _L lcm _M lcn _N lco _O lcp _P lcq _Q lcr _R lcs _S lct _T lcu _U lcv _V lcw _W lcx _X lcy _Y lcz _Z l0 _0 l1 _1 l10 _{10} l2 _2 l3 _3 l4 _4 l5 _5 l6 _6 l7 _7 l8 _8 l9 _9 lij _{ij} lijk _{ijk} ljk _{jk} gij g_{ij} lxa _\alpha lxb _\beta lxc _\chi lxcd _\Delta lxcg _\Gamma lxcl _\Lambda lxco _\Omega lxcp _\Pi lxcph _\Phi lxcps _\Psi lxcs _\Sigma lxcth _\Theta lxcu _\Upsilon lxcx _\Xi lxd _\delta lxe _\epsilon lxet _\eta lxg _\gamma lxio _\iota lxk _\kappa lxl _\lambda lxm _\mu lxn _\nu lxo _\omega lxp _\pi lxph _\phi lxps _\psi lxr _\rho lxs _\sigma lxt _\tau lxth _\theta lxu _\upsilon lxve _\varepsilon lxvp _\varpi lxvph _\varphi lxvr _\varrho lxvs _\varsigma lxvth _\vartheta lxx _\xi lxz _\zeta xln x_n yln y_n zln z_n lst _\ast lvst _\star obp \bar{p} obq \bar{q} obr \bar{r} obs \bar{s} obx \bar{x} oby \bar{y} obz \bar{z} obxa \bar{\alpha} obxb \bar{\beta} obxg \bar{\gamma} odp \dot{p} odq \dot{q} odr \dot{r} ods \dot{s} odx \dot{x} ody \dot{y} odz \dot{z} odxa \dot{\alpha} odxb \dot{\beta} odxg \dot{\gamma} oddp \ddot{p} oddq \ddot{q} oddr \ddot{r} odds \ddot{s} oddx \ddot{x} oddy \ddot{y} oddz \ddot{z} oddxa \ddot{\alpha} oddxb \ddot{\beta} oddxg \ddot{\gamma} olp \overline{p} olq \overline{q} olr \overline{r} ols \overline{s} olx \overline{x} oly \overline{y} olz \overline{z} olxa \overline{\alpha} olxb \overline{\beta} olxg \overline{\gamma} ohp \hat{p} ohq \hat{q} ohr \hat{r} ohs \hat{s} ohx \hat{x} ohy \hat{y} ohz \hat{z} ohxa \hat{\alpha} ohxb \hat{\beta} ohxg \hat{\gamma} ova \vec{a} ovb \vec{b} ovc \vec{c} ovv \vec{v} ovw \vec{w} 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(h) oi (i) oj (j) ok (k) ol (l) om (m) oen (n) oo (o) oep (p) oq (q) oer (r) os (s) ot (t) ou (u) ov (v) ow (w) ox (x) oy (y) oz (z) oca (A) ocb (B) occ (C) ocd (D) oce (E) ocf (F) ocg (G) och (H) oci (I) ocj (J) ock (K) ocl (L) ocm (M) ocn (N) oco (O) ocp (P) ocq (Q) ocr (R) ocs (S) oct (T) ocuu (U) ocv (V) ocw (W) ocx (X) ocy (Y) ocz (Z) intu \int intd \int \!\!\! \int intt \int \!\!\! \int \!\!\! \int intc \oint i10 \int^1_0 iba \int^b_a ilcd \int_D iinf \int^\infty_{- \infty} i2xp0 \int^{2 \pi}_0 sds \,ds sdt \,dt sdu \,du sdv \,dv sdw \,dw sdx \,dx sdy \,dy sdz \,dz sumu \sum sni1 \sum^{n}_{i = 1} pni1 \prod^{n}_{i = 1} ini1 \bigcap^{n}_{i = 1} uni1 \bigcup^{n}_{i = 1} li00 \lim_{(x,y) \rightarrow (0,0)} liai \lim_{a \rightarrow \infty} lixl0 \lim_{x \rightarrow x_0} wace accelerate wacn acceleration wacs accelerates wcdm Department of Mathematics wcdp Department of Physics wcle calculate wcln calculation wcls calculates wder derivative wders derivatives wdm department of 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%======================================================================% %.......10........20........30........40........50........60........70.% %________|_________|_________|_________|_________|_________|_________|_% %======================================================================% csd %----------------------------- csdd %============================= gmu \mathfrak{}@$1C gmb \mathfrak{b} gmg \mathfrak{g} gmh \mathfrak{h} gmk \mathfrak{k} gmp \mathfrak{p} gmt \mathfrak{t} gmca \mathfrak{A} gmcg \mathfrak{G} gmch \mathfrak{H} gmck \mathfrak{K} gmct \mathfrak{T} gmcx \mathfrak{X} gmgs \mathfrak{g}^{\ast} gmhs \mathfrak{h}^{\ast} gmks \mathfrak{k}^{\ast} gmso3 \mathfrak{so}(3) dgmu $\mathfrak{}$@$1C@$1C dgmb $\mathfrak{b}$ dgmca $\mathfrak{A}$ dgmcg $\mathfrak{G}$ dgmch $\mathfrak{H}$ dgmck $\mathfrak{K}$ dgmct $\mathfrak{T}$ dgmcx $\mathfrak{X}$ dgmg $\mathfrak{g}$ dgmh $\mathfrak{h}$ dgmk $\mathfrak{k}$ dgmp $\mathfrak{p}$ dgmt $\mathfrak{t}$ dgmgs $\mathfrak{g}^{\ast}$ dgmhs $\mathfrak{h}^{\ast}$ dgmks $\mathfrak{k}^{\ast}$ bbu \mathbb{}@$1C bbca \mathbb{A} bbcb \mathbb{B} bbcc \mathbb{C} bbcd \mathbb{D} bbce \mathbb{E} bbcf \mathbb{F} bbcg \mathbb{G} bbch \mathbb{H} bbci \mathbb{I} bbcj \mathbb{J} bbck \mathbb{K} bbcl \mathbb{L} bbcm \mathbb{M} bbcn \mathbb{N} bbco \mathbb{O} bbcp \mathbb{P} bbcq \mathbb{Q} bbcr \mathbb{R} bbcs \mathbb{S} bbct \mathbb{T} bbcu \mathbb{U} bbcv \mathbb{V} bbcw \mathbb{W} bbcx \mathbb{X} bbcy \mathbb{Y} bbcz \mathbb{Z} bbcr1 \mathbb{R}^1 bbcr2 \mathbb{R}^2 bbcr3 \mathbb{R}^3 bbcrm \mathbb{R}^m bbcrn \mathbb{R}^n dbbcc $\mathbb{C}$ dbbci $\mathbb{I}$ dbbcr $\mathbb{R}$ dbbct $\mathbb{T}$ dbbcz $\mathbb{Z}$ dbbcr1 $\mathbb{R}^1$ dbbcr2 $\mathbb{R}^2$ dbbcr3 $\mathbb{R}^3$ dbbcrm $\mathbb{R}^m$ dbbcrn $\mathbb{R}^n$ opu \mathbb{}@$1C opcc \mathbb{C} opci \mathbb{I} opcr \mathbb{R} opct \mathbb{T} opcz \mathbb{Z} opcr1 \mathbb{R}^1 opcr2 \mathbb{R}^2 opcr3 \mathbb{R}^3 opcrm \mathbb{R}^m opcrn \mathbb{R}^n dopcc $\mathbb{C}$ dopci $\mathbb{I}$ dopcr $\mathbb{R}$ dopct $\mathbb{T}$ dopcz $\mathbb{Z}$ dopcr1 $\mathbb{R}^1$ dopcr2 $\mathbb{R}^2$ dopcr3 $\mathbb{R}^3$ dopcrm $\mathbb{R}^m$ dopcrn $\mathbb{R}^n$ ir3 \int_{\mathbb{R}^3} b0 \mathbf{0} b1 \mathbf{1} b10 \mathbf{10} b2 \mathbf{2} b3 \mathbf{3} b4 \mathbf{4} b5 \mathbf{5} b6 \mathbf{6} b7 \mathbf{7} b8 \mathbf{8} b9 \mathbf{9} ba \mathbf{a} bb \mathbf{b} bc \mathbf{c} bca \mathbf{A} bcb \mathbf{B} bcc \mathbf{C} bcd \mathbf{D} bce \mathbf{E} bcf \mathbf{F} bcg \mathbf{G} bch \mathbf{H} bci \mathbf{I} bcj \mathbf{J} bck \mathbf{K} bcl \mathbf{L} bcm \mathbf{M} bcn \mathbf{N} bco \mathbf{O} bcp \mathbf{P} bcq \mathbf{Q} bcr \mathbf{R} bcs \mathbf{S} bct \mathbf{T} bcu \mathbf{U} bcv \mathbf{V} bcw \mathbf{W} bcx \mathbf{X} bcy \mathbf{Y} bcz \mathbf{Z} bd \mathbf{d} bee \mathbf{e} bel1 \mathbf{e}_1 bel2 \mathbf{e}_2 bel3 \mathbf{e}_3 beln \mathbf{e}_n bff \mathbf{f} bg \mathbf{g} bh \mathbf{h} bi \mathbf{i} bj \mathbf{j} bk \mathbf{k} bl \mathbf{l} bm \mathbf{m} bn \mathbf{n} bo \mathbf{o} bp \mathbf{p} bq \mathbf{q} br \mathbf{r} bs \mathbf{s} bt \mathbf{t} bu \mathbf{u} bv \mathbf{v} bw \mathbf{w} bx \mathbf{x} byy \mathbf{y} bz \mathbf{z} bsy \boldsymbol{ bsy $\boldsymbol{ bsyu \boldsymbol{}@$1C bsyu $\boldsymbol{}$@$1C@$1C mvb {\mathversion{bold} $ $}@$1C@$1C pmbu \mathop{\pmb{}}@$1C@$1C mopu \mathop{}@$1C db0 $\mathbf{0}$ db1 $\mathbf{1}$ db10 $\mathbf{10}$ db2 $\mathbf{2}$ db3 $\mathbf{3}$ db4 $\mathbf{4}$ db5 $\mathbf{5}$ db6 $\mathbf{6}$ db7 $\mathbf{7}$ db8 $\mathbf{8}$ db9 $\mathbf{9}$ dba $\mathbf{a}$ dbb $\mathbf{b}$ dbc $\mathbf{c}$ dbca $\mathbf{A}$ dbcb $\mathbf{B}$ dbcc $\mathbf{C}$ dbcd $\mathbf{D}$ dbce $\mathbf{E}$ dbcf $\mathbf{F}$ dbcg $\mathbf{G}$ dbch $\mathbf{H}$ dbci $\mathbf{I}$ dbcj $\mathbf{J}$ dbck $\mathbf{K}$ dbcl $\mathbf{L}$ dbcm $\mathbf{M}$ dbcn $\mathbf{N}$ dbco $\mathbf{O}$ dbcp $\mathbf{P}$ dbcq $\mathbf{Q}$ dbcr $\mathbf{R}$ dbcs $\mathbf{S}$ dbct $\mathbf{T}$ dbcu $\mathbf{U}$ dbcv $\mathbf{V}$ dbcw $\mathbf{W}$ dbcx $\mathbf{X}$ dbcy $\mathbf{Y}$ dbcz $\mathbf{Z}$ dbd $\mathbf{d}$ dbe $\mathbf{e}$ dbf $\mathbf{f}$ dbg $\mathbf{g}$ dbh $\mathbf{h}$ dbi $\mathbf{i}$ dbj $\mathbf{j}$ dbk $\mathbf{k}$ dbl $\mathbf{l}$ dbm $\mathbf{m}$ dbn $\mathbf{n}$ dbo $\mathbf{o}$ dbp $\mathbf{p}$ dbq $\mathbf{q}$ dbr $\mathbf{r}$ dbs $\mathbf{s}$ dbt $\mathbf{t}$ dbu $\mathbf{u}$ dbv $\mathbf{v}$ dbw $\mathbf{w}$ dbx $\mathbf{x}$ dby $\mathbf{y}$ dbz $\mathbf{z}$ nrbu \|\mathbf{u}\| aplb \mathbf{a} + \mathbf{b} atib \mathbf{a} \times \mathbf{b} atibp (\mathbf{a} \times \mathbf{b}) cau \mathcal{ cca \mathcal{A} ccb \mathcal{B} ccc \mathcal{C} ccd \mathcal{D} cce \mathcal{E} ccf \mathcal{F} ccg \mathcal{G} cch \mathcal{H} cci \mathcal{I} ccj \mathcal{J} cck \mathcal{K} ccl \mathcal{L} ccm \mathcal{M} ccn \mathcal{N} cco \mathcal{O} ccp \mathcal{P} ccq \mathcal{Q} ccr \mathcal{R} ccs \mathcal{S} cct \mathcal{T} ccu \mathcal{U} ccv \mathcal{V} ccw \mathcal{W} ccx \mathcal{X} ccy \mathcal{Y} ccz \mathcal{Z} dcca $\mathcal{A}$ dccb $\mathcal{B}$ dccc $\mathcal{C}$ dccd $\mathcal{D}$ dcce $\mathcal{E}$ dccf $\mathcal{F}$ dccg $\mathcal{G}$ dcch $\mathcal{H}$ dcci $\mathcal{I}$ dccj $\mathcal{J}$ dcck $\mathcal{K}$ dccl $\mathcal{L}$ dccm $\mathcal{M}$ dccn $\mathcal{N}$ dcco $\mathcal{O}$ dccp $\mathcal{P}$ dccq $\mathcal{Q}$ dccr $\mathcal{R}$ dccs $\mathcal{S}$ dcct $\mathcal{T}$ dccu $\mathcal{U}$ dccv $\mathcal{V}$ dccw $\mathcal{W}$ dccx $\mathcal{X}$ dccy $\mathcal{Y}$ dccz $\mathcal{Z}$ igru \includegraphics{ igr \includegraphics{}@$1C figu \begin{figure}[ht] \begin{center} \includegraphics{} \caption{\label{}} \end{center} \end{figure}@$1E@$1E@$1E@$1D@$1D@$1D@$1D@$1D pictu \begin{figure}[ht] \begin{center} \special{picture } %add pict filename \caption{\label{}} \end{center} \end{figure}@$1E@$1E@$1E@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D illu \begin{figure} \begin{center} \special{illustration } %add eps filename \caption{\label{}} \end{center} \end{figure}@$1E@$1E@$1E@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D@$1D cdu \[ \begin{CD} \end{CD} \]@$1E@$1E btab \begin{table} etab \end{table} tabl \begin{table}[ht] %optional [t, b or h]; \begin{minipage}{0.9\textwidth} \begin{tabular}[ccc] & & \\ & & \\ \end{tabular} \end{minipage} \caption{} \label{} \end{table} bfig \begin{figure} efig \end{figure} captu \caption{ capt \caption{}@$1C vspu \vspace{ vsp \vspace{}@$1C hspu \hspace{ hsp \hspace{}@$1C