tebd \documentstyle{article} \input amssym.def \input amssym.tex \newfont{\tenbi}{cmbxti10} \begin{document} tebdf \documentstyle[epsf]{article} \input amssym.def \input amssym.tex \newfont{\tenbi}{cmbxti10} \begin{document} tebdv \documentstyle[verbatim]{article} \input amssym.def \input amssym.tex \newfont{\tenbi}{cmbxti10} \begin{document} tebdvf \documentstyle[verbatim,epsf]{article} \input amssym.def \input amssym.tex \newfont{\tenbi}{cmbxti10} \begin{document} te2bd \documentclass{article} \usepackage{amssymb,amsmath,eufrak} \begin{document} te2bdv \documentclass{article} \usepackage{amssymb,amsmath,eufrak} \usepackage{verbatim} \begin{document} te2bdvf \documentclass{article} \usepackage{amssymb,amsmath,eufrak} \usepackage{epsf,verbatim} \begin{document} temar \textwidth 6.5 truein \oddsidemargin 0 truein \evensidemargin -0.50 truein \topmargin -.5 truein \textheight 8.5in temag1 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} teack \noindent{\bf Acknowledgments} We thank ... 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} bdo \begin{document} ed \end{document} edo \end{document} dsu \documentstyle{ dsart \documentstyle{article} dsartv \documentstyle[verbatim]{article} dslet \documentstyle{letter} dsrep \documentstyle{report} dsbook \documentstyle{book} defu \newcommand{...}{...} ncmdu \newcommand{...}{...} rcmdu \renewcommand{...}{...} rdefu \renewcommand{...}{...} setlnu \setlength{...}{...} magu mag1 nrh \pagestyle{empty} npgno \pagestyle{empty} nlg nbb pgno lhtxt rhtxt egraf \endgraf chhdl tgsol tgsor sn \section{ sns \section*{ ssn \subsection{ ssns \subsection*{ bec \begin{center} ec \end{center} eec \end{center} cl \centerline{ hfi \hfill bfll \begin{flushleft} bflr \begin{flushright} efll \end{flushleft} eflr \end{flushright} bqt \begin{quotation} eqt \end{quotation} noi \noindent nl \\ np \newpage pt % vfi \vfill lbrk \linebreak nlin \newline rlin \rightline{...} clin \centerline{...} llin \leftline{...} lin \line{...} blskp \baselineskip bmpg \begin{minipage}{\textwidth} empg \end{minipage} cp \clearpage bblk \begin{quotation} eblk \end{quotation} prind \setlength{\parindent}{0em} prskp \setlength{\parskip1.5ex plus 0.5ex minus 0.5ex} blstr \renewcommand{\baselinestretch}{1.5} ob { eb } eit \/} op ( ep ) obk [ ebk ] llb \{ rlb \} bqm `` eqm '' lle \langle rle \rangle ros \begin{enumerate} bros \begin{enumerate} eros \end{enumerate} ben \begin{enumerate} ee \end{enumerate} een \end{enumerate} bitm \begin{itemize} eitm \end{itemize} bds \begin{description} eds \end{description} itm \item itmu \item[ setc \setcounter{enumi}{ setcu \setcounter{...}{...} btb \begin{tabbing} etb \end{tabbing} tb \> btr \begin{tabular}{|c|c|} etr \end{tabular} hlin \hline hrl \hline ad & ftn \footnote{ citu \cite{ cit \cite{ } citp (\cite{ }) lbl \label{ refr \ref{ refp (\ref{}) biba \item Author [year] Title. {\it Journal\/} {\bf 11}, 123--223. bibb \item Author [year] {\it Title.\/} Publisher. bibia \bibitem[]{} Author [year] Title. {\it Journal\/} {\bf 11}, 123--223. bibib \bibitem[]{} Author [year] {\it Title.\/} Publisher. idu \index{ ae \'{e} ge \`{e} ua \"{a} uo \"{o} uu \"{u} ace \'{E} gce \`{E} uca \"{A} uco \"{O} ucu \"{U} ats @ cprt \copyright para \P sect \S gss \ss csp \quad dsp \qquad ssp \, msp \: tsp \; nsp \! ndsp \! \! qd \quad qqd \qquad bskp \bigskip mskp \medskip sskp \smallskip hskp \hskip 2in vskp \vskip 12pt tskp \topskip 24pt vglu \vglue 2in nll \null dsz \displaystyle dszu {\displaystyle tsz tszu tfu sd d d $ dlr $$ 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*} bea \begin{array}{ccc} ea \end{array} eea \end{array} ad & ada & = & nonu \nonumber mbe \mbox{} boxu \quad \mbox{ } \quad boxa \quad \mbox{and} \quad txt \quad \mbox{ } \quad txta \quad \text{and} \quad lequ \begin{eqnarray} \lefteqn{ } \nonumber \\ & & \end{eqnarray} lequs \begin{eqnarray*} \lefteqn{ }\\ & & \end{eqnarray*} tg \tag{} tgs \tag*{} ntg \notag bdpex \[ F(b)-F(a)=\int^b_af(x)\, dx \] beqex \begin{equation} F(b)-F(a)=\int^b_af(x)\, dx \end{equation} eqtx \[ \sum ^n _{ i = 1 } x^2 _i + y^2 _i \geq 0 \quad \mbox{for all real numbers $ x _i $ and $ y _i $} \] bqasex \begin{eqnarray*} x^2 &= y+1 \\ x^2+1 &= u+v \end{eqnarray*} bqaex \begin{eqnarray} x^2 &= y+1 \\ x^2+1 &= u+v \end{eqnarray} eqng \begin{eqnarray} \begin{array}{l} a = b + c \\[3pt] d = e + f + g \end{array} \end{eqnarray} eqsp \begin{eqnarray*} a & = & b + c + (c + d) \\ & & \mbox{} - e + f \end{eqnarray*} eqbrl \begin{equation} \left. \begin{array}{l} x = y \\[3pt] a = b^2 + b + 1 \end{array} \right\} \end{equation} eqbrc \begin{equation} \left. \begin{array}{c} x = y \\[3pt] a = b^2 + b + 1 \end{array} \right\} \end{equation} eqbox \begin{equation} \fbox{\parbox{.7in}{$\displaystyle{\frac{x^2 + 1}{5} = y}$ }} \end{equation} eval \[ \left. f \left(\frac{t}{2}\right)\right|_{t=0} \] lequex \begin{eqnarray} \lefteqn{a x^2 + 2 b x y + c y^2 + d x + e y + f} \nonumber \\ & = & \alpha u + \beta v + \gamma w + \delta \end{eqnarray} eabb \begin{eqnarray*} \hat{H}_c (\Delta \omega): & = & \int_D \left[ \frac{1}{2}\Delta \omega (- \nabla ^2)^{ -1} \Delta \omega + \Phi (\omega_e + \Delta \omega) - \Phi (\omega _e) \right. \nonumber \\ & \left. \begin{array}{c} ^{} \\ ^{} \end{array} \quad - \Phi ^\prime (\omega_e) \Delta \omega \right] \,dx\,dy \end{eqnarray*} eabr \begin{eqnarray*} H^s_0(TM) & = & \left\{ \begin{array}{c} ^{} \\ ^{} \end{array} \!\!\!\!\!\! X \in H^s (T M) \right| \mbox{there exists an $ H^s $-extension} \\ & & \left. \begin{array}{c} ^{} \\ ^{} \end{array} \!\! \tilde{X} \in H^s (\tilde{T} M) \; \mbox{with $X$ zero on} \; \tilde{M} \backslash M \right\} . \end{eqnarray*} mcor \newtheorem{cor}{Corollary} mdfn \newtheorem{dfn}{Definition} mlem \newtheorem{lem}{Lemma} mprop \newtheorem{prop}{Proposition} mthm \newtheorem{thm}{Theorem} bcor \begin{cor} ecor \end{cor} blem \begin{lem} elem \end{lem} bprop \begin{prop} eprop \end{prop} bthm \begin{thm} bthmt \begin{thm}[Gauss' Theorem] ethm \end{thm} bdfn \begin{dfn} bdfn edfn \end{dfn} edfn exa \noindent{\large \bf Example\,} rmk \noindent{\large \bf Remarks\,} prf \noindent{\bf Proof\,} sol \noindent{\bf Solution\,} bdmu edmu bprf \noindent{\bf Proof\,} eprf bpf \noindent{\bf Proof\,} epf thmsty \newtheorem{thm}{Theorem}[section] \newtheorem{prop}[thm]{Proposition} \newtheorem{lem}[thm]{Lemma} \newtheorem{cor}[thm]{Corollary} \newtheorem{dfn}[thm]{Definition} balg ealg bcnj ecnj bcrit ecrit bqst eqst bcnd ecnd bprob eprob brmk ermk bnote enote bnota enota bcase ecase bclm eclm bsum esum bcncl ecncl bac eac bsol esol bpf \noindent{\bf Proof\,} epf bxca exca bxcb excb blackl \quad \blacklozenge dblackl \quad $\blacklozenge$ epr \quad \blacksquare dep \quad $\blacksquare$ esq \quad \square desq \quad $\square$ etd \quad \bigtriangledown detd \quad $\bigtriangledown$ btd \quad \blacktriangledown dbtd \quad $\blacktriangledown$ qed \quad \square rqed \null\hfill$\square$ seh \mbox{\rm sech} so3 \mbox{\rm so(3)} dso3 $\mbox{\rm so(3)}$ cso3 \mbox{\rm SO(3)} dcso3 $\mbox{\rm SO(3)}$ divg \mbox{\rm div}\, au \mbox{\rm Aut}( difu \mbox{\rm Diff}( imu \mbox{\rm Im}( imz \mbox{\rm Im}(z) reu \mbox{\rm Re}( rez \mbox{\rm Re}(z) rom romu txtu \mbox{ intxtu \mbox{ fldtu tfldtu opndef \newcommand{\...}{\mbox{\rm ...}} opnu \mbox{\rm opad \mbox{\rm ad} opcaut \mbox{\rm Aut} opccard \mbox{\rm Card} opchar \mbox{\rm char} opccorr \mbox{\rm Corr} opcext \mbox{\rm Ext} opcfcl \mbox{\rm FL} opcgcl \mbox{\rm GL} opchom \mbox{\rm Hom} opcjac \mbox{\rm Jac} opclie \mbox{\rm Lie} opcnm \mbox{\rm Nm} opcpcgcl \mbox{\rm PGL} opcpic \mbox{\rm Pic} opcprym \mbox{\rm Prym} opcram \mbox{\rm Ram} opcrank \mbox{\rm Rank} oprank \mbox{\rm rank} opreg \mbox{\rm reg} opcres \mbox{\rm Res} opres \mbox{\rm res} opsl \mbox{\rm sl} opcscl \mbox{\rm SL} opcsco \mbox{\rm SO} opcscp \mbox{\rm SP} opcsp \mbox{\rm Sp} opsq \mbox{\rm sq} opcscu \mbox{\rm SU} opcsym \mbox{\rm Sym} opctr \mbox{\rm Tr} 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 $\Upsilon$ dxcx $\Xi$ dxd $\delta$ dxe $\epsilon$ dxet $\eta$ dxg $\gamma$ dxio $\iota$ dxk $\kappa$ dxl $\lambda$ dxm $\mu$ dxn $\nu$ dxo $\omega$ dxp $\pi$ dxph $\phi$ dxps $\psi$ dxr $\rho$ dxs $\sigma$ dxt $\tau$ dxth $\theta$ dxu $\upsilon$ dxve $\varepsilon$ dxvp $\varpi$ dxvph $\varphi$ dxvr $\varrho$ dxvs $\varsigma$ dxvth $\vartheta$ dxx $\xi$ dxz $\zeta$ nfntu \newfont{\...}{\...} nfnttbi \newfont{\tenbi}{cmbxti10} itu {\it biu {\tenbi rmu {\rm bfu {\bf slu {\sl ttu {\tt emu {\em scu {\sc sfu {\sf bxu \mbox{\boldmath$ $} cau {\cal gmu \frak opu {\Bbb bbu {\Bbb b0 {\bf 0} b1 {\bf 1} b10 {\bf 10} b2 {\bf 2} b3 {\bf 3} b4 {\bf 4} b5 {\bf 5} b6 {\bf 6} b7 {\bf 7} b8 {\bf 8} b9 {\bf 9} ba {\bf a} bb {\bf b} bc {\bf c} bca {\bf A} bcb {\bf B} bcc {\bf C} bcd {\bf D} bce {\bf E} bcf {\bf F} bcg {\bf G} bch {\bf H} bci {\bf I} bcj {\bf J} bck {\bf K} bcl {\bf L} bcm {\bf M} bcn {\bf N} bco {\bf O} bcp {\bf P} bcq {\bf Q} bcr {\bf R} bcs {\bf S} bct {\bf T} bcu {\bf U} bcv {\bf V} bcw {\bf W} bcx {\bf X} bcy {\bf Y} bcz {\bf Z} bd {\bf d} bee {\bf e} bel1 {\bf e}_1 bel2 {\bf e}_2 bel3 {\bf e}_3 beln {\bf e}_n bff {\bf f} bg {\bf g} bh {\bf h} bi {\bf i} bj {\bf j} bk {\bf k} bl {\bf l} bm {\bf m} bn {\bf n} bo {\bf o} bp {\bf p} bq {\bf q} br {\bf r} bs {\bf s} bt {\bf t} bu {\bf u} bv {\bf v} bw {\bf w} bx {\bf x} byy {\bf y} bz {\bf z} bxu \mbox{\boldmath$ $} bxo \mbox{\boldmath$\omega$} bxx \mbox{\boldmath$\xi$} cau {\cal cca {\cal A} ccb {\cal B} ccc {\cal C} ccd {\cal D} cce {\cal E} ccf {\cal F} ccg {\cal G} cch {\cal H} cci {\cal I} ccj {\cal J} cck {\cal K} ccl {\cal L} ccm {\cal M} ccn {\cal N} cco {\cal O} ccp {\cal P} ccq {\cal Q} ccr {\cal R} ccs {\cal S} cct {\cal T} ccu {\cal U} ccv {\cal V} ccw {\cal W} ccx {\cal X} ccy {\cal Y} ccz {\cal Z} dcca ${\cal A}$ dccb ${\cal B}$ dccc ${\cal C}$ dccd ${\cal D}$ dcce ${\cal E}$ dccf ${\cal F}$ dccg ${\cal G}$ dcch ${\cal H}$ dcci ${\cal I}$ dccj ${\cal J}$ dcck ${\cal K}$ dccl ${\cal L}$ dccm ${\cal M}$ dccn ${\cal N}$ dcco ${\cal O}$ dccp ${\cal P}$ dccq ${\cal Q}$ dccr ${\cal R}$ dccs ${\cal S}$ dcct ${\cal T}$ dccu ${\cal U}$ dccv ${\cal V}$ dccw ${\cal W}$ dccx ${\cal X}$ dccy ${\cal Y}$ dccz ${\cal Z}$ gmu \frak gmb \frak b gmg \frak g gmh \frak h gmk \frak k gmp \frak p gmt \frak t gmca \frak A gmcg \frak G gmch \frak H gmck \frak K gmct \frak T gmcx \frak X gmgs \frak g ^{\ast} gmhs \frak h ^{\ast} gmks \frak k ^{\ast} gmso3 \frak{so}(3) dgmca $\frak A$ dgmcg $\frak G$ dgmch $\frak H$ dgmck $\frak K$ dgmct $\frak T$ dgmcx $\frak X$ dgmu $\frak $ dgmb $\frak b$ dgmg $\frak g$ dgmh $\frak h$ dgmk $\frak k$ dgmp $\frak p$ dgmt $\frak t$ dgmgs $\frak g ^{\ast}$ dgmhs $\frak h ^{\ast}$ dgmks $\frak k ^{\ast}$ bbu {\Bbb bbca \Bbb A bbcb \Bbb B bbcc \Bbb C bbcd \Bbb D bbce \Bbb E bbcf \Bbb F bbcg \Bbb G bbch \Bbb H bbci \Bbb I bbcj \Bbb J bbck \Bbb K bbcl \Bbb L bbcm \Bbb M bbcn \Bbb N bbco \Bbb O bbcp \Bbb P bbcq \Bbb Q bbcr \Bbb R bbcs \Bbb S bbct \Bbb T bbcu \Bbb U bbcv \Bbb V bbcw \Bbb W bbcx \Bbb X bbcy \Bbb Y bbcz \Bbb Z bbcr1 {\Bbb R}^1 bbcr2 {\Bbb R}^2 bbcr3 {\Bbb R}^3 bbcrm {\Bbb R}^m bbcrn {\Bbb R}^n dbbcr1 ${\Bbb R}^1$ dbbcr2 ${\Bbb R}^2$ dbbcr3 ${\Bbb R}^3$ dbbcrm ${\Bbb R}^m$ dbbcrn ${\Bbb R}^n$ opu {\Bbb opcc {\Bbb C} opci {\Bbb I} opcr {\Bbb R} opct {\Bbb T} opcz {\Bbb Z} opcr1 {\Bbb R}^1 opcr2 {\Bbb R}^2 opcr3 {\Bbb R}^3 opcrm {\Bbb R}^m opcrn {\Bbb R}^n dopcc ${\Bbb C}$ dopci ${\Bbb I}$ dopcr ${\Bbb R}$ dopct ${\Bbb T}$ dopcz ${\Bbb Z}$ dopcr1 ${\Bbb R}^1$ dopcr2 ${\Bbb R}^2$ dopcr3 ${\Bbb R}^3$ dopcrm ${\Bbb R}^m$ dopcrn ${\Bbb R}^n$ ir3 \int_{{\Bbb R}^3} fu \frac{ fof }{ squ \sqrt{ hu ^{ lu _{ limu \lim{ limu \lim{ ovu \vec{ olu \overline{ obu \bar{ ocu \check{ odu \dot{ oddu \ddot{ ohu \hat{ otu \tilde{ setu \{ \mid \} setlu \left\{ \left. \!\right| \right\} disu {\displaystyle 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 $z$ db0 ${\bf 0}$ db1 ${\bf 1}$ db10 ${\bf 10}$ db2 ${\bf 2}$ db3 ${\bf 3}$ db4 ${\bf 4}$ db5 ${\bf 5}$ db6 ${\bf 6}$ db7 ${\bf 7}$ db8 ${\bf 8}$ db9 ${\bf 9}$ dbca ${\bf A}$ dbcb ${\bf B}$ dbcc ${\bf C}$ dbcd ${\bf D}$ dbce ${\bf E}$ dbcf ${\bf F}$ dbcg ${\bf G}$ dbch ${\bf H}$ dbci ${\bf I}$ dbcj ${\bf J}$ dbck ${\bf K}$ dbcl ${\bf L}$ dbcm ${\bf M}$ dbcn ${\bf N}$ dbco ${\bf O}$ dbcp ${\bf P}$ dbcq ${\bf Q}$ dbcr ${\bf R}$ dbcs ${\bf S}$ dbct ${\bf T}$ dbcu ${\bf U}$ dbcv ${\bf V}$ dbcw ${\bf W}$ dbcx ${\bf X}$ dbcy ${\bf Y}$ dbcz ${\bf Z}$ dba ${\bf a}$ dbb ${\bf b}$ dbc ${\bf c}$ dbd ${\bf d}$ dbe ${\bf e}$ dbf ${\bf f}$ dbg ${\bf g}$ dbh ${\bf h}$ dbi ${\bf i}$ dbj ${\bf j}$ dbk ${\bf k}$ dbl ${\bf l}$ dbm ${\bf m}$ dbn ${\bf n}$ dbo ${\bf o}$ dbp ${\bf p}$ dbq ${\bf q}$ dbr ${\bf r}$ dbs ${\bf s}$ dbt ${\bf t}$ dbu ${\bf u}$ dbv ${\bf v}$ dbw ${\bf w}$ dbx ${\bf x}$ dby ${\bf y}$ dbz ${\bf z}$ 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} vcpp \stackrel{\textstyle \longrightarrow}{\rm PP} vcpq \stackrel{\textstyle \longrightarrow}{\rm PQ} dvcpp $\stackrel{\textstyle \longrightarrow}{\rm PP}$ dvcpq $\stackrel{\textstyle \longrightarrow}{\rm PQ}$ pl + mi - plm \pm mip \mp divi \div cir \circ blt \bullet opl \oplus omi \ominus ti \times oti \otimes sdp \,\circledS\, wed \wedge eq = ez = 0 gte \geq lte \leq ne \neq iso \cong eqv \equiv mlt \ll mgt \gg apx \approx lep \left( rip \right) lebk \left[ ribk \right] lebr \left\{ ribr \right\} lel \left\langle lld \left\langle \! \left\langle rir \right\rangle rrd \right\rangle \! \right\rangle ldo \left. rdo \right. ale \aleph hba \hbar prm \prime flt \flat shp \sharp sh \heartsuit ppt \propto nrm \| lied \pounds trv \pitchfork scl \ell na \nabla pd \partial infi \infty wpf \wp rea \Re ima \Im angl \angle imp \Rightarrow impb \Leftarrow olra \Leftrightarrow eqvt \Leftrightarrow emp \varnothing empa \emptyset eo \in neo \not\in reo \ni setm \setminus subs \subset sube \subseteq sups \supset supe \supseteq ints \cap bints \bigcap uni \cup buni \bigcup vbar \mid te \exists fa \forall artl \mapsto ra \rightarrow lora \longrightarrow lra \leftrightarrow lea \leftarrow upa \uparrow uhr \upharpoonright sur \nearrow sdr \searrow cdo \cdot cds \cdots dds \ddots lds \ldots vds \vdots co \cos coh \cosh coq \cos^2 coth \cos \theta coph \cos \phi si \sin sih \sinh siq \sin^2 sith \sin \theta siph \sin \phi tn \tan tnh \tanh ex \exp logg \log lgn \ln supr \sup infm \inf mx \max mn \min limu \lim{ limu \lim{ limm \lim limi \liminf lims \limsup dtt \det kr \ker dmn \dim ag \arg gc \gcd mo -1 ava |a| avb |b| avc |c| avx |x| avy |y| avz |z| shl A^i_{\;a} lam L_A{}^\mu van v^A{}_\nu tsq T^\ast Q tsqq T^{\ast}_{q} Q dtsq $T^\ast Q$ dtsqq $T^{\ast}_{q} Q$ 00p (0,0) 03p (0, 0, 0) 0p (0) d00p $(0,0)$ d03p $(0, 0, 0)$ d0p $(0)$ triap (a_1, a_2, a_3) dtriap $(a_1, a_2, a_3)$ xyp (x, y) xyzp (x, y, z) xpyq x^2 + y^2 dxyp $(x, y)$ dxyzp $(x, y, z)$ dxpyq $x^2 + y^2$ dxdy \,dx\,dy dxdydz \,dx\,dy\,dz dxdt dx/dt dydt dy/dt dzdt dz/dt pdzy \partial z/\partial y dpdzy $\partial z/\partial y$ o0 (0) o1 (1) o2 (2) o3 (3) o4 (4) o5 (5) o6 (6) o7 (7) o8 (8) o9 (9) oa (a) oeb (b) oc (c) od (d) oe (e) oef (f) og (g) oh (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) nrbu \|{\bf u}\| aplb {\bf a} + {\bf b} atib {\bf a} \times {\bf b} atibp ({\bf a} \times {\bf b}) 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} mxc \left( \begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array} \right) mxcb \left[ \begin{array}{c} x \\ y \end{array} \right] mx2p \left( \begin{array}{cc} a & b \\ c & d \end{array} \right) mx2i \left[ \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right] mx2b \left[ \begin{array}{cc} a & b \\ c & d \end{array} \right] mx2s \left[ \begin{array}{cc} 0 & 1 \\ -1 & 0 \end{array} \right] mx3i \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right) mx3d \left| \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right| mx3p \left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right) mx3b \left[ \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right] mx3b35pt \left[ \begin{array}{ccc} a & b & c \\[5pt] d & e & f \\[5pt] g & h & i \end{array} \right] mxu \begin{array}{cc} ...&...\\ ...&... \end{array} mxpu \left( \begin{array}{cc} ...&...\\ ...&... \end{array} \right) mxbu \left[ \begin{array}{cc} ...&...\\ ...&... \end{array} \right] mxvu \left| \begin{array}{cc} ...&...\\ ...&... \end{array} \right| mxcvu \left\Vert \begin{array}{cc} ...&...\\ ...&... \end{array} \right\Vert mxsu \small \begin{array}{cc} ...&...\\ ...&... \end{array} mxspu \small\left( \begin{array}{cc} ...&...\\ ...&... \end{array} \right) mxsbu \small\left[ \begin{array}{cc} ...&...\\ ...&... \end{array} \right] frboxn \fbox{\parbox{2.0in}{{\large \bf Note: \,} text }} frbox \fbox{\parbox{2.0in}{\centerline{\large \bf type header} text }} dfrbox \fbox{\fbox{\parbox{2.0in}{ \centerline{\large \bf type header} text }}} frboxt \null 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} fig \begin{figure} \vspace{1.5in} \caption{} \end{figure} pict \begin{figure} \vspace{2in} \hspace*{.2in} \special{picture typefigname} \caption{} \end{figure} illus \begin{figure} \vspace{2in} \hspace*{.4in} \special{illustration typefigname} \caption{} \label{} \end{figure} scd1 \begin{picture}(150,100)(-70,0) \put(30,75){$A$} %upper left corner \put(120,75){$B$} %upper right corner \put(30,25){$C$} %lower left corner \put(120,25){$D$} %lower right corner % \put(78,83){$F$} %top arrow label \put(78,15){$f$} %bottom arrow label \put(24,50){$G$} %left arrow label \put(129,50){$g$} %right arrow label % \put(45,78){\vector(1,0){70}} %top arrow \put(45,27){\vector(1,0){70}} %bottom arrow \put(34,70){\vector(0,-1){35}} %left arrow 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\put(34,35){\vector(0,1){35}} %left arrow \put(125,35){\vector(0,1){35}} %right arrow \end{picture} scdw tcd1 \begin{picture}(150,100)(-70,0) \put(30,75){$A$} %upper left corner \put(120,75){$B$} %upper right corner \put(75,25){$C$} %center bottom % \put(78,83){$f$} %label on top arrow \put(50,48){$g$} %label on left arrow \put(106,48){$h$} %label on right arrow % \put(45,78){\vector(1,0){70}} %top arrow \put(38,72){\vector(1,-1){38}} %top left to bottom right arrow \put(122,72){\vector(-1,-1){38}}%top right to bottom left arrow \end{picture} tcd2 \begin{picture}(150,100)(-70,0) \put(30,75){$A$} %upper left corner \put(120,75){$B$} %upper right corner \put(75,25){$C$} %center bottom % \put(78,83){$f$} %label on top arrow \put(50,48){$g$} %label on left arrow \put(106,48){$h$} %label on right arrow % \put(45,78){\vector(1,0){70}} %top arrow \put(38,72){\vector(1,- 1){38}} %top left to bottom right arrow \put(82,35){\vector(1,1){38}} %top right to bottom left arrow \end{picture} ecd1 \begin{picture}(150,60)(5,50) \put(25,75){$0$} \put(70,75){$A$} \put(118,75){$B$} \put(166,75){$C$} \put(214,75){$C/g(B)$} \put(288,75){$0$} % \put(97,84){$f$} \put(145,84){$g$} \put(193,84){$h$} % \put(35,78){\vector(1,0){30}} \put(83,78){\vector(1,0){30}} \put(131,78){\vector(1,0){30}} \put(179,78){\vector(1,0){30}} \put(253,78){\vector(1,0){30}} \end{picture} dcd1 \begin{picture}(150,160)(-80,5) \put(70,134){$A$} %top center label \put(70,20){$D$} %bottom center label \put(70,83){$F$} %middle arrow label \put(19,77){$B$} %middle left label \put(121,77){$C$} %middle right label % \put(40,112){$f$} %upper left diagonal label \put(104,112){$g$} %upper right diagonal label \put(39,48){$h$} %lower left diagonal label \put(104,48){$j$} %lower right diagonal label % \put(35,80){\vector(1,0){80}} %middle right pointing arrow % \put(30,90){\vector(1,1){40}} %upper left arrow \put(80,130){\vector(1,-1){40}} %upper right arrow \put(30,70){\vector(1,-1){40}} %lower left arrow 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%lower left corner \put(131,77){$D$} %lower right corner \put(165,77){${\Bbb R}$} %far right \put(78,131){${\Bbb R}$} %upper middle \put(78,23){${\Bbb R}$} %lower middle % \put(78,168){$a$} %top arrow to right \put(78,150){$b$} %top arrow to left \put(10,120){$c$} %left arrow \put(137,120){$d$} %right arrow \put(39,115){$e$} %inner left up \put(111,115){$f$} %inner right up \put(39,44){$g$} %lower left \put(111,44){$h$} %lower right \put(78,87){$i$} %bottom arrow to left \put(78,69){$j$} %bottom arrow to right \put(150,85){$k$} %far right arrow % %VECTORS \put(42,165){\vector(1,0){70}} %top arrow to right \put(112,160){\vector(-1,0){70}} %top arrow to left \put(18,88){\vector(0,1){70}} %left arrow \put(135,88){\vector(0,1){70}} %right arrow \put(30,93){\vector(1,1){40}} %inner left up \put(130,93){\vector(-1,1){40}} %inner right up \put(30,70){\vector(1,-1){40}} %lower left \put(130,70){\vector(-1,-1){40}} %lower right \put(112,83){\vector(-1,0){70}} %bottom arrow to left \put(42,78){\vector(1,0){70}} %bottom arrow to right \put(142,80){\vector(1,0){20}} %far right arrow \end{picture} btab \begin{table} etab \end{table} tabl \begin{table}[t] %optional [t, b or h]; \begin{minipage}{0.9\textwidth} \begin{tabular}[ccc] & & \\ & & \\ \end{tabular} \end{minipage} \caption{Text of Caption} \label{reflabel} \end{table} bfig \begin{figure} efig \end{figure} tinf \begin{figure}[t] minf \begin{figure}[h] einf \end{figure} cap \caption{Text of Caption} tcap \caption{Text of Caption} bcap \caption{Text of Caption} vsp \vspace{0.2in} hsp \hspace{0.2in} epsfv \epsfverbosetrue epsff \begin{figure}[t] \vspace{18pt} \hspace{1pt} \epsfxsize=0.9\textwidth \epsffile{filename.eps} \vspace{18pt} \caption{Text of Caption} \label{reflabel} \end{figure} epsfb \begin{figure}[t] \vspace{18pt} \hspace{1pt} \epsfxsize=0.9\textwidth \epsfbox{filename.eps} \vspace{18pt} \caption{Text of Caption} \label{reflabel} \end{figure} epsfbb \begin{figure}[t] \vspace{18pt} \hspace{1pt} \epsfxsize=0.9\textwidth \epsfbox[llx lly urx ury]{filename.eps} \vspace{18pt} \caption{Text of Caption} \label{reflabel} \end{figure} epsfbb2 \begin{figure}[t] \vspace{18pt} \hspace{1pt} \epsfxsize=0.45\textwidth \epsfbox[llx lly urx ury]{filename1.eps} \quad \epsfxsize=0.45\textwidth \epsfbox[llx lly urx ury]{filename2.eps} \vspace{18pt} \caption{Text of Caption} \label{reflabel} \end{figure} 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 mathematics wdp department of physics wep Euler-Poincar\'e weqn equation weqns equations wex example wfun function wfuns functions wgm geometry wgmc geometric wie i.e., wig integral wigb integrable wign integration wigs integrals wiie {\it i.e.,\/} wlig line integral wligs line integrals wmx matrix wneg negative wnl nonlinear wnly nonlinearity wpos positive wprp perpendicular wrel relative wrln relation wrtg rotating wrtn rotation wrtns rotations wsn solution wsns solutions wtm theorem wtms theorems wty theory wun university wve vector wvel velocity wvs vectors tepaper %&latex2.09 tepaper \documentstyle{article} \input amssym.def \input amssym.tex \newfont{\tenbi}{cmbxti10} \makeatletter \@addtoreset{figure}{section} \def\thefigure{\thesection.\@arabic\c@figure} \def\fps@figure{h, t} \@addtoreset{equation}{section} \def\theequation{\thesection.\arabic{equation}} \makeatother \newtheorem{thm}{Theorem}[section] \newtheorem{prop}[thm]{Proposition} \newtheorem{lem}[thm]{Lemma} \newtheorem{cor}[thm]{Corollary} \newtheorem{dfn}[thm]{Definition} \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 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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 \vspace{0.2in} \noindent{\bf Acknowledgments} We thank ... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % REFERENCES % use ``biba or bibb'' to fill in reference items %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{References} \begin{description} \item Author, U. N., ... \end{description} \end{document} tepapersimplest %&latex209--tepaper simplest \documentstyle{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 \vspace{0.2in} \noindent{\bf Acknowledgments} We thank ... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % REFERENCES % use ``biba or bibb'' to fill in reference items %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{References} \begin{description} \item Author, U. N., ... \end{description} \end{document} tepapereqnwith %&latex2.09--tepaper eqnwith \documentstyle{article} \input amssym.def \input amssym.tex \newtheorem{thm}{Theorem}[section] \newtheorem{prop}[thm]{Proposition} \newtheorem{lem}[thm]{Lemma} \newtheorem{cor}[thm]{Corollary} \newtheorem{dfn}[thm]{Definition} {\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 \vspace{0.2in} \noindent{\bf Acknowledgments} We thank ... %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % REFERENCES % use ``biba or bibb'' to fill in reference items %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{References} \begin{description} \item Author, U. N., ... \end{description} \end{document} tebook %&latex2.09--tebook \documentstyle[12pt]{book} \input amssym.def \input amssym.tex \newfont{\tenbi}{cmbxti10} \makeatletter \@addtoreset{figure}{section} \def\thefigure{\thesection.\@arabic\c@figure} \def\fps@figure{h, t} \@addtoreset{equation}{section} \def\theequation{\thesection.\arabic{equation}} \makeatother \newtheorem{thm}{Theorem}[section] \newtheorem{prop}[thm]{Proposition} \newtheorem{lem}[thm]{Lemma} \newtheorem{cor}[thm]{Corollary} \newtheorem{dfn}[thm]{Definition} \begin{document} \title{Title of Book} \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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % REFERENCES % use ``biba or bibb'' to fill in reference items %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section*{References} \begin{description} \item Author, U. N., ... \end{description} \end{document} te2book %&latex2e--te2book \documentclass{book} \usepackage{amssymb,amsmath,eufrak} \usepackage{epsf,verbatim} \makeatletter \@addtoreset{figure}{section} \def\thefigure{\thesection.\@arabic\c@figure} \def\fps@figure{h, t} \@addtoreset{equation}{section} \def\theequation{\thesection.\arabic{equation}} \makeatother \newtheorem{thm}{Theorem}[section] \newtheorem{prop}[thm]{Proposition} \newtheorem{lem}[thm]{Lemma} \newtheorem{cor}[thm]{Corollary} \newtheorem{dfn}[thm]{Definition} \begin{document} \title{Title of Book} \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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % BIBLIOGRAPHY % %use ``bibia'' or ``bibib'' to fill in bibitems %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{thebibliography}{} \bibitem[]{} \end{thebibliography} \end{document} teletter %&latex2.09 teletter \documentstyle[12pt]{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} te2letter %&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} letterdef bcmnt \begin{comment} ecmnt \end{comment} vrb \verb bvrb \begin{verbatim} evrb \end{verbatim} vrbinp verbatimdef cbx %========================================================% % % %========================================================% cld %----------------------------------------------------------------------- cldd %======================================================================= cpct %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% crlr %======================================================================% %.......10........20........30........40........50........60........70.% %________|_________|_________|_________|_________|_________|_________|_% %======================================================================% csd %----------------------------- csdd %=============================