λ i λ 2 i 2λ i 1 0. U i = . d (λ n 1 1 2! d mi 1 dλ mi 1 d 2 dλ 2 i λ n 1 dλ i (m i 1)! G(jω) = g(t)e jωt dt i )

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10 `U* IDX [#<"} `UFΩE TEXρ5*[#x xs(!* DVI [#x 6.)A _ il[# L A TEX-ß* dviljp.exe, dvidj500.exee dvi24p.exe -b >"[#bol?1( _e5 ffl HP pν*y' _v DJ500 pνxx _vtflp _v bi 24 2 _v;fflfd ffi" setprt.exe q.x0; _v fl q.ml?fflvfω _vν? fl,ixffl0οin* _v? _v fl0οh ψ ρ _3.(vx h 3 L A TEX'χY7Φχ# Y(L^3g L A TEX*Y2#elffν* 6.q+y)A CbO(#eNGmΠν* (6F mxffia ffi*a@) -@~C) fflk7k* \documentstylesχlar;rffx*0 L3 twocolumn b -@~(b(4ω#k'klπν* +y*affit y»5[kjiπνχe} ;I ixf)a([#/^ *&Q -ρjff9z*χe} -@H)A6[u \maketitlesχ» Φ66.iX Πν* etfflv»tk*f Sχ \title{fokker-planck equation solutions for a class of nonlinear systems} \author{dingy\"u XUE} \date{} \maketitle ρ(fflv6t*s# e Fokker-Planck equation solutions for a class of nonlinear systems Dingyü XUE bo]v \maketitlesχl( \title, \authore \date -SχL*e5wgvx \titlesχrk* r;e *l[#*</ R \authorsχrk*l **ρj 6.iX (ψffl4 (ΩμvL fl*4 ) Cwgvx ρ# \datesχ oρbo \datesχ* r;l4 Awg*4 6.iX \datesχrkfflvfωf* r; ρ \maketitlesχ(hwg4 ρj \titlee \author-sχ]ffxkfiff 6.iX (»vffl*ρj (6χAx"! ρj)c~9z} ρ)a91»o1(- ρj4 %ΠL*FΩSχ (6 \author) L 3.2 L A TEXo8 NΦkjTng L A TEX*FΩ@v*l6l!bOl?1SiXUmffi)*[##1 #1Um* el q "* STY (t 2e #/L* cls) [#LN;* F!2S- [#L);*#1 el<h * 6.iX }:#1wg*3fl ρd L~d* STY [# F '} ffia]t F ;Afl('}* STY [#vh%ixl±*^%t OJ'}RLΠ!0*[# e`uh dq*g L A TEX*#1^jSχ6t» 10

11 \part (7) \chapter (#) \section (1) \subsection (Φ1) \subsubsection \paragrapho \subparagraph - ^jln %ΦRl? i* - Sχ* es \CommandName{TitleString} ΠL \CommandName SSχQ R TitleString S#1</nq -^ fl,*ρqtff STY [#ffl;* e(wgvix i*#1.; /^ ffizfl,*ρql-@* L A TEX); Off %ΦbifiΞ#1^jSχ AFPn [#t nl±);*ffd#1sχ Φ6 article n t Λ*;Vl 1 (section), 6.iXbi»Sχ \section{this is My First Section} ρ 7Y;R(`U 1 ThisisMyFirstSection n@*s#ffi. -Λ* 1 ll?um* RK bi \section{}sχ^ ρ1;(lfls 2 ORßj Sχ*bi#1;(l?1fl \section{}sχl r;e*nq S 1*/^ bi^(l?1wgvx 6.iXH wgv 1*7; ρbo~d1bi \section*{}sχxng 6. \section{}sχr6 GtKSχ \subsection{this is My First SubSection} ρ(ml?1vxtk*wgae 1.1 This is My First SubSection ΠL*Φ1.;ln LTEX/Qοq*Ω flxng* AbiFΩ \section{}sχ ΠΦ A 1Ω Hl?1GS 0 ffrbodh1zdtfφ1*ω \subsection{}sχtk fbong \subsubsection{} - book t report n t ΛbObi part(7) tkiωs chapter, section, subsection Φ66.iXfflv»6t*Sχ \chapter{this is My First Chapter} ρ~d1(fflv6tffig*s#3. Chapter 1 This is My First Chapter 6.Ni»L[# L A TEX ρ#1/^ll[c»~d*ng -ß»#1.;l? Um*οfdL(ffliX} /e*[#οxz *a9 y»#1q;l?um;i ixfboni L A TEX-ß*Sχxl?1Um,] Φ6 6. ZFΩ *RK FΩ,] C) *RK GF5 \footnote{}sχ ΠL,]*e5 SχL r;rffx*kjl4 LTEX(ml?S,]<"7; 6. A bf ρ L A TEXf(l?1fl,]*e5ρs ;FD*0Kwgvx GK FΩH*N } ffrfi/[lfflk*,]wgae 11

12 y»l?l,]<"7;;i L A TEXffl,iXL,]<"t?7; -@*,];V Sχ* e6t» ΠL \footnote[footnote symbol]{footnote} footnote symbol: S,]7;Kj bo4 ixl;v*,]7;?dφ0 ρff'y 2*ae3,]7; footnote:,]*_ffie5 ΠLbO(41Hi L A TEX S v*e5 (rρexa? 3.3 L A TEXffνL/HjTn'e LTEXl91[#*#1TPxUm^%* ^%UmlKfiff* C)iX 5[Kj* fflkfflvfω A \tableofcontentssχhbo» d)ix%<"1o* ix 7Y TEX[#^ (ml?1`ufω TOC [# F!d ]T 7Y1q3 ^OOmfflv j9:ix+ ]ih5* AffiiXQμffi"7Yq. -^6.Hfflv ρj ρ DVI [#H7Ymο» 6.3fflv ρj ρf)qμffi" (EO@Ω) fl]umx,]*umk~ffl )Afl]* nrk F5 \index{}sχ SχLffl 7Y ρm`ufω IDX [# ixc)l [#<"} HbO(v<h* TEX[#» vfl]* n y»- μ ;I 5[Kj*fflK GF5 \makeindexsχ -^ L A TEXjo!g Y2e&t L A TEX<#([#} m}s 6BLΩ*χe bnudw} R`UzΦ * (6 0.1pt -@QΦ*?) gvρq L A TEX7Yp=CmfflvFΩ-gx-#iX]T ffiof!ρqtix bfο L A TEX*LΩs#ffi. bi[n} <#^ OOm~%tK*ρq qfi[nookps F"*L ß ( fflßlω) tf"[nookp_s6lω L A TEX-ß»4V- _/*mοa W 6.qFI[n ixboi \centerline{}sχx} b;.s F"*Lß ΠL r;ld fflv)ailsν*[ne5 Φ6 \centerline{this Text is Centered} (fflvtk*s#3.» This Text is Centered 6.)ALßLΩ} *[nike CbONi \begin{center}e \end{center}d C( I[nrffx -@~*ffi.ebi \centerline{}sχlf@* 6.iX (FI[n_s:t_ }6LΩ ρbobi \begin{flushright} \end{flushright} \begin{flushleft}e E \end{flushleft}dc(ffi)} *I2rff xhbo» 12

13 3.5 L A TEX 8NffiY Λfl» -Λ(H 4o1fflvFΩ`Φ[#s#*±[# ixbol±%7ybwgπs#ffi. ixbosj1gt»}πl*? e5tr x$^s#ffi. 7 NΩ[#^ ixboni-foνx3 l±*e5 ψ, -Λ;g*e5Bg L A TEX*'Kοf L A TEX/Qfq» *οfqρix%biezu \documentclass[11pt]{carticle} \usepackage{epsf} \usepackage{emlines2} \usepackage{indenrst} \topmargin -10mm \oddsidemargin 0mm \evensidemargin 0mm \textwidth 158mm \textheight 226mm \parindent 2\ccwd \parskip 0mm \hyphenpenalty=1500 \flushbottom \newcommand{\double}{\baselineskip 1.24 \baselineskip} \newcommand{\citeu}[1]{$^{\mbox{\protect \scriptsize \cite{#1}}}$} \newcommand{\ispace}{\hspace*{2\ccwd}} \title{a Sample Text for \LaTeX} \author{\begin{tabular}{c} Dingy\"u Xue \\ Northeastern University, PRC\end{tabular}} \date{} \begin{document} \maketitle \double \abstract{this is the abstract part of the paper. You can add more information to it and see what the results will be.} \section{introduction} \LaTeX is a useful tool in doing the scientific documentation with results of professional standard. results can be achieved by experience users. Creative \section{the State of Art of \LaTeX} Here a template of a paper is given to show the state of art of such a wonderful documentation system. \subsection{listing environment} Try to find out what is the layout of the following commands \begin{itemize} \item three environments are provided, they are {\tt itemize}. {\tt enumerate}, and {\tt description}, where {\tt enumerate} will create a numbering system while {\tt description} comes without numbering. \item try to use the other two environments to replace the {\tt itemize} environment and see what will happen. 13

14 \end{itemize} \subsection{mathematical formula} Three types of math environments are allowed\citeu{lamp}. The following statements will give different results: $\alpha_2^3\int_0^\infty f(s)ds$, $$\alpha_2^3\int_0^\infty f(s)ds$$ and \begin{equation}\alpha_2^3\int_0^\infty f(s)ds\end{equation} \appendix \section{this the First Appendix} The appendix is arranged automatically if an appendix command is issued. The numbering system will be set to A, B,... instead of 1, 2,... \begin{thebibliography}{99} \bibitem {Lamp} Lamport, L., 1985, \LaTeX: A Document Preparation System, Addision-Wesley \end{thebibliography} \end{document} 3.6 L A TEX~fijmFLAuqp L A TEXw}bΛ] on j`r S»s#a9 L A TEXfl,iXl±%;VF Sχ 6fflKoνL;V* \doublee \citeu - L A TEXl;V S* es ΠL \newcommand{\commandname}[number of argument] [defaults]{command specifications} \CommandName: l;vsχ*sχq!bol1h L A TEXW)!*nq Ffl;V» Sχ;R ixhboξbiπ!sχf@bi!»?-λbi*sχqmafl ρ 7Y^ml?fflv hρj-g 9:iXΦSχM.bi number of argument: l;vsχffiο*r Ω defaults: l;vsχlr *Y2? command specifications: μsχe5*;v?φsχοqr ρd -ΛfflvflΩ R *bi ΠL #1?gοq*3 1 ΩR #2?gοq*3 2 ΩR IΦ F tk91φkx;g L A TEXl;VSχ*biaW» 1). $^fflk* \doublesχ Π es \newcommand{\double}{\baselineskip 1.24 \baselineskip} -Λ;V* \doublesχbhοq1hr ΠTVlb( "ß*ßRSψfflßR (S \baselineskip R ;V* Z?) * 1.24, 2). ^( \citeusχ Π es 14

15 \newcommand{\citeu}[1]{$^{\mbox{\protect \scriptsize \cite{#1}}}$} bo]v ΦSχοq 1 ΩR ΠTVlOG<*aewg \citesχ^l*? S (l?+ ]i(v*r^[z7;ig<*χe ψfflxggwgvx ψ, L A TEXfl,iX;Vοq 2 Ωt 2 ΩOG*R -ΛHHfflvΦk» L A TEXffl,Qμ;VΠ)!*Sχ -bo91 \renewcommandsχxlm Sχ* ee \newcommand ll'ff* ψ S>"OR x*sχh.1g» ;@? \renewcommandsχl* CommandName R.uwFΩ xht *SχQ ρcmfflv hρj L A TEXf-ß»FΩ \providecommandsχ!* ee ie \newcommand ΠUlL' FF*?l;V*SχMAfl ρ!(v,l;vsχ*n; R)! x*sχ L A TEXw}bΛ] ch j`r L A TEXt-ß»,OO \begin x \end rffx*dc Φ6 equation, table - y»- <h*dc;i ffl,ixl±%;vf μ*dc 6;V ; dc Φk d C- tkol;v* exampledcsφφp6h'ωl±*μdc \newtheorem{example}{\footnotesize Φ } \newcounter{example}[chapter] \def\theexample{\thechapter.\arabic{example} -Λ ΠL3 1 Ω SLi \newtheoremsχtp»fωμ*dc example, RΠ</SΦ; * Φ n 3 2Ω Si \newcounter SxL exampledcω <";V Ω AΩ # chapter) Zd^ßff 3 3Ω S;V»Φk<;* e ( \theexample ;VS# ; \thechapter 6 nfl*φk.; Φ63 5 #*3 6ΩΦk7;S Φ 5.6 ψ,-@*;vawcniu booke report -["n RHfiu article n [S article n t Λ*ΞAS section, RHl chapter article n t<";v^ bo(gk* chapter n@1gm section b i ffl*aefbo;vπ!μ*dc 6; ;V- ixfbo NfflKΦkL* elπlz r1<"'5 Ondl±*+yAffi L A TEXch y^ L A TEX*Y2D;SοtF n 6.iX iπ!+;*aexwgd;^ ρ)ani ;V*aex'} \thepagesχr Q0* L A TEXSχS \renewcommand{\thepage}{\roman{page}} \setcounter{page}{1} ΠL \thepage ld;: R RomanSχ(D6Ω fl page ;Vm 07 n Π!b ONi*ag fl;vχt? }ffir \Alph \alph \Roman \roman \arabic \fnsympol 5W μ b o Ψ b o μ 18Λo Ψ 18Λo ßuGΛo lwor MΨ A, B, C, a, b, c, I, II, III, i, ii, iii, 1, 2, 3, α, β, γ, 15

16 3 2Ω SL* \setcountersχixn;ω fl*? Φ6-Λ(D6Ω fl*?n Gm 1? Z}kvmοtF nd6<d ρbo bi \renewcommand{\thepage}{\arabic{page}} ψ,fboi \setcountersχld6ω flqμu? Wa`r x] 7 fl*[" (6bi bookethesis n [#) ^ OOmUxq^<;p=CH>0 T Φ6 -Pn t*s#l ρe*7;;vlff'#xng* Φ63 5 #*3 123 e*7;aws (5.123),?iX ff'1x7;?ix (3 5 # 3 4 1*3 26Ωρ e ρd '}n [#?bi 2.09 #* L A TEX, ρ Z book.sty [# ( [#ρ=3v}* \@addtoreset{chapter}{section} \def\theequation{\thechapter.\arabic{equation}} SχL* chapter n@} m section n@ b -^ 7Y [# ρ ρe*7;(:s (5.4.26) 6.iXbi L A TEX2e # ρ Z ~d* CLS [# bouxtk 5 S? NifflK*aWLρeQμ7; ρ;@( SL* chapter 1gm section b \@addtoreset{equation}{chapter} \renewcommand\theequation{\thechapter.\@arabic\c@equation} 4 2>ΦQfffiχxΠ ΛJ 3ρe*s#l L A TEX<#*FΩQA*+C LTEXfl,iX 5[*"L ffc A *ρe"lo A?LY9 3ρe y» 3ρe*s#OI LTEXf-ß»/lx*o A A SE? Hν S -F1L(7K L A TEX<#*- +C 4.1 L A TEXRj-D~fi&P 3ρe FjSOt@»[L (in-line) ρe CΩρeEο7;*CΩρe ffiz[lρ ela Hg"*ρqt(FΩ 3ρe 9[/"L RCΩρeF!lAffC"iF" tπ"* 3ρe [#L* 3ρebOff'iX*0ο<"7;} -Pρe-Λt lsο7;* 3ρe [LρeliffB ; ($) rffx*fi[n RCΩρeliΠB ; ($$) rffx* [n vvlvfωφkxφp[lρe* l NG» In line formular is as $y=x^2+1.$ The sum is $\sum_{i=1}^{\infty} a_i.$ -FI[n*wg3.6t» In line formular is as y = x The sum is i=1 a i. -Λ* ^ RK*KjSpa? e -ΛRKClFΩnq ffiobohbi r;r ffx 6. floωnq SA ρd bi r; Φ6 $ y=x^{abc}$ Ld*s#ffi. 16

17 S y = x abc 6. h1 m $ y=x^abc$ Ld*s#ffi.S y = x a bc L A TEXbO} OΞ *G<?g 6 $y=x^{a^{z^{5}}}$ bo(vtk*s#ffi. y = x az5 fflkφkl* < ;RK*KjSt<?g EG<?gaW ffl t<cbo OΞ} 6.(GKΦkLffiq*ffB ;}SΠB ;^ ρ-f[n*wg3.s In line formular is as The sum is y = x a i. i=1 ]T -Pρqty»AΩρeBnffC*"ILwgOI ffieρegboux!e [Lρe*wg elh;* ixf;a]t ρe} LB q;lmlvx* fflk?qfω $;Zdρe ρ ρe3 ^μfiangfω $ 6.lO $$ Zd*CΩρe ρe3 ^μfiafflv $$ oρ(νmq+ CΩρefbOn \begin{displaymath}e \end{displaymath}dcxng Π ixπ];rffx*l'-μ y»fflk7k* PρedCOI ffiifpqa* (Clß? L A TEX+C*) 3ρe s#dclοq7;*ρes# -Ps#aeln \begin{equation} E \end{equation} dcxng* 6.iXbi»-@*dC ρ ρe*7;hml?um Φ6fflK*Φk L $dc6.}i \begin{equation}e \end{equation}dcx#ß ρ~d*s#3.( S In line formular is as The sum is y = x (1) a i. (2) i=1 bo]v -Λ* (1) E (2) <;ll?um* 6.iX (2) efflk FΩο7;* ρe ρ x* (2) (l?1»μs (3) RY9*ρe*7;(l?1 m (2) 6.RK 3Uet ρ6.fflvtk*sχ $This is the Text$, (fflv6t*s#ffi. T hisisthet ext bo]v x*[lf 'K.#» -HlΦ 3Uet [L x[/l** fqπ!ο7;*ρe ρπ<;ml?1:mffi)*χe f (l?.# 6. )![/ xe& ρd bi \mbox{} Φ6 6.GK*I2 }m $\mbox{this is the Text}$ ρ(fflv6t*s#ffi.» This is the Text bχ 6.~»-P} ρbo)! x[/lf *ffi. 6. flfωρe O"Oνwg ρbobi L A TEX* arraydc tk91fωφk x;g-pdc*iw 6. [/Lfflv»tK*Sχ» f(x)=\left\{ \begin{array}{l l} 1, & x\geq 0 \\ -1, & \mbox{else} \end{array} \right.$$ 17 ρmvxtk*s#3. { 1, x 0 f(x) = 1, else

18 bo]v -Λ* arraydcng» ν dc*r LjAq Ω l n@?g - νbl_}6lω* 6.( l n@}m c ρφp νe5fflßlω 6. m r n@ ρ e5ff'svlω} ixbol±%$^ffi. arraydctaf"ln \\ xjψ* ;F"LH;*νln & xjψ* -ΩρeLfbi» \lefte\rightsχ L'fflKΦk*s#3.bO]v ffl K* \left RK * r; { (ffrke5*λel?umfωin Φ* r; ff' L A TEX*Affi AFΩ \leftsχbaqfω \rightsχx3 -ΛH)AFΩ } ffi Od FΩ \right. x~3 } 6.( \leftsχrk * r;fbo}:mπ! *q; Φ6bO:mΠr;tar; ff-ωφkfbo]v LTEXbO NRKe5_ffi* ΦxNGr;* Φ y»l A?N;r;* Φ;I L 6tK*F Sχ TEXffl,iXffl±nc*aex0οhHr; Φ*Sχ Φ A $$\Bigg( \bigg( \Big( \big( ( ) \big) \Big) \bigg) \Bigg) ~~~~ \Bigg[ \bigg[ \Big[ \big[ [ ] \big] \Big] \bigg] \Bigg] ~~~~ \Bigg\{ \bigg\{ \Big\{ \big\{ \{ \} \big\} \Big\} \bigg\} \Bigg\}$$ (fflv6t*s#3. ( ((( () )))) [ [ [[[] ] ]]] { { {{{} } }}} 4.2 dk-dy(jffiy fflkffia7k1gt<* L A TEXs#Sχ -Λ(fiff7KF Π! 3ρeχe*s#S χ #ΨwΛ: fflk7k1 Gt<ln ^E ]#* / ffiwλ: jeln \frac{}{}sχx} * ΠL3FΩ r;rff*lje*j k 3SΩrffx*lj[ Φ6 \frac{x+y}{x-y} (fflv x + y x y ((%6t*s#ffi. tkfflv*ffijes#sχ 1 $$\frac{1}{1+\frac{1}{1+ 1+ \frac{1}{1+\frac{1}{x}}}}$$ x bo]v 6.ff±1bi \fracsχ OΞ *e*jes# ρ *ΞAΨ 1 R nqhψφ 6. 4V-@*_/ HbObi \displaystylesχ» -FS χbob(!ffi'q*e5o5c Φ*nqxwg Qμ^(GK*Φk ((%6t*s#ffi. $$\frac{1}{\displaystyle 1+\frac{1}{1+ \frac{\displaystyle 1}{\displaystyle 1+ \frac{\displaystyle 1} {\displaystyle x}}}}$$ bχ -@} ;Rs#ffi.HB$(O» x

19 : ffiwλ: e*s#sχ el \sqrt[zaω ]{ e*e5 } 6.ZaΩ H4 ρ2slz a s#^chh 1H'q» ecbo O Ξ *!Cmb(RK **e5:(kφ -@CbObifflK7K* \displaystyle Sχ Φ6 $$\sqrt[3]{\displaystyle 1+\sqrt[4]{1+ \sqrt[4]{\displaystyle 1+ \sqrt{\displaystyle x}}}}$$ ((%6t*s#ffi x E N/Pz : LuffiE ffixjo ffiz -+y* 3? exφ L A TEXß»a9*s#Sχ ^(tk*φk 5 $$\sum_{i=1}^{\infty} a_i, ~~ \prod_{j=1,2,\dots,n} P_i, ~~ \int_{-\infty}^\infty f(x)dx, ~~\lim_{t\to\infty}e(t), ~~\int \int \int f(x,y,z)dxdydz$$ GK*Φk(fflv6t*s#ffi. a i, i=1 j=1,2,,n P i, f(x)dx, lim e(t), t f(x, y, z)dxdydz R1L'GK*Φk(v rρqffr'y% A Lνv*flΩq;~ 3Uet $\infty$ (fflv R $\to$ (fflv"? Π!*SχbO5 ffgkφkbo]v \sum -SχtCbi» Gt< q; ^E ffi-λ * Gt< *XGx 9*GtlH;* -ΦP L A TEX -P} L~»+y*) ; ff RFΩekLfbO]v 6.=0bi? Ω \intsχ ffi(%*s#3.lxj;;ß*r 1 -H)A i L A TEXLfflv*8ßR*Sχx84» RFΩΦkLflΩ \int ;ß F R hhq ρbos(6t?lffig*s#ffi. R q; 4V Y2R \, ΦR \: LR \; R \! wr Φk f(x, y, z)dxdydz f(x, y, z)dxdydz f(x, y, z)dxdydz f(x, y, z)dxdydz f(x, y, z)dxdydz 5 Uflfifiψ /Π, dx mh>i»y 7+,e U dx, LA TEX@hU {\rm d} x fisψz& C Ξ 19

20 -PR hhsχboqi Fffbi Φ66.(?L RF *}m \!\! ρ((%tk*s#ffi. f(x, y, z)dxdydz -^*ffi.a9(o F!ρqt L A TEXbOfflv~ψ9*Y2R ffio y g4+a}:r F!HAοR}:Y2*R NG _FffiffΨ-*: L A TEX-ß»fflK3s#*Sχ ΠSχ es \matrix{} ΠL r ;Ld (K3*» 9 Q0*K3 9aWS»K3;F"*»i & q;xj Ψ g"q;s \cr Φ6tK* L A TEXSχbO(vsK*s#3. $$\left[\matrix{ a_{11} & a_{12} & a_{13} \cr a_{21} & a_{22} & a_{23} \cr a 11 a 12 a 13 a 21 a 22 a 23 a_{31} & a_{32} & a_{33} a 31 a 32 a 33 } \right]$$ fflk*φkl Sχ \left[e \right]ixffl`u*k3 r; _ffidi L CbObiΠ!*r;?g L A TEX-ß»flPX,q; ffrχy% A Lνv* F q; i- X,q;EK3s#οf HbO(tK*Ll@L-K3?gv x $$\left[\matrix{ b_0 & c_0 & \cr c_0 & b_1 & c_1 & \cr & c_1 & b_2 & c_2 & \cr &&\ddots & \ddots & \ddots & \cr &&&c_{n-3} &b_{n-2} &c_{n-2} & \cr & & & & c_{n-2} & b_{n-1} } \right]$$ s#ffi.s b 0 c 0 c 0 b 1 c 1 c 1 b 2 c c n 3 b n 2 c n 2 c n 2 b n 1 \underline{}e \overline{}sχ!djaiu r;l*e5 t^}eg^} L!2Cffiμg: 3Uet L A TEX-ß»OPQ9q;*s#aW ci*q ΠL \underline{} * ie[/l*sχl~ffl* y» r;l*ρegkttk =};I fbobi \underbrace{}e \overbrace{} x r;l*e5tktg K GZr; - ΩSχfbOjAο t< E G< Π il Zr;*t KEGK]GΠ!*ρe Φ6 $$ \overbrace{a 0+\underbrace{a 1+ a 2+\cdots+a {n-1}} {(n-1)\mbox{\zihao{6} }}+ a n}^{(n+1)\mbox{\zihao{6} }}$$ (fflv6t*s#ffi.» (n+1) Λ (n 1) Λ {}}{ a 0 + a 1 + a a n 1 +a n }{{} 20

21 L A TEXf-ß» \stackrel{}{}sχx1t9f Ωρe ΠLfflFΩ r;fg GX*ρe RRFΩ r;fgtx*ρe Φ6 $$ A \stackrel{a }{\rightarrow} B \stackrel{b }{\rightarrow} C$$ (fflv6t*s#ffi. A a B b C fi>(8φcffi= T: LTEX-ß» eqnarraydcx;vfzρe dc fflu A arraydc ffih;*l ρezly2ρqtafωρexqfω7;?ixaffi ΠLZFΩtOΩρeH7; ρd ρel 9 I2 \nonumbersχ ^(tk*fω \begin{eqnarray} (a+b)^4 &=& (a+b)^2+(a+b)^2 \\ &=& (a^2+2ab+b^2)(a^2+2ab+b^2)\nonumber\\ &=&a^4+4a^3b+6a^2b^2+4ab^3+b^4 \end{eqnarray} (fflvtk*s#ffi. (a + b) 4 = (a + b) 2 +(a + b) 2 (3) = (a 2 +2ab + b 2 )(a 2 +2ab + b 2 ) = a 4 +4a 3 b +6a 2 b 2 +4ab 3 + b 4 (4)? bi eqnarraydcrh Lffis#*ρe<"7; ρbon \begin*{eqnarray} E \end*{eqnarray} x8i dc 4.3 -Dy(RV5ju] 3ρeLF!a[nq*Y2n0S 0n ixfbo91f NGx}:ρeL*n 0 Φ66.iXi» \cal;v*` ρn0(:mt 0 ffid ]T -P;VCbOiu 3Uet RHfiu[/Uet RK*s#Sχ ${\cal ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ (fflv6t*s#3. ABCDEFGHIJ KLMN OPQRST UVWX YZ ]T -P;VCbOiu nq*n0ng L A TEXffl,iX 3Uetbikvnq 6 \alpha (fflv α nq R \Gamma (ffl v Γ nq Π!*kvnqbOR'y% A y»<h*kvnq;i LTEXf-ß» A * 3q;EΠ!q; Φ6 \spadesuit (fflv R \heartsuit (fflv -@*F q;cffrχy% A 3UetHbO=0}:ρeL*n; Φ 6. }:4Ωρe*n; Φ ρb O ρe<d*ik G \large -SχHbO» ρe3 RbObi \normalsizekv x*n; Φ ψ, 9fliJKSχxLm-@*μ i r;(a}:n;*i 21

22 2rffx 6. }:ρelzfωnqtnq *n; Φ ρvvd (A}:*Kj9 1 \mbox{}sχagm[/ue,rl KjbOCΩ1}:n;* Φ n0*ng»?ixbil[# L A TEX ρ 3UetCHfl,=0biL[nq 6. bic)av v91 \mbox{}sχ(;agm[/ue tk(91fωφkxφp-pρq 6.iXffl v» $x=y\mbox{\large $Z$}^2+ \mbox{l[ }$, ρ(s(tk*s#ffi. x = yz 2 +L[ y»<h* 3q;;I ixfbo;vl±*+yq; Φ6iXbOntK S ;VFΩ \realrsχ \newcommand{\realr}{i \hspace*{-1.2mm} R} q;π_n IER Ωn[zm ΠL R nq s#^π}j? 1.2mm, 3Uet Sχfflv*s#ffi.S IR 4.4 L A TEXo6_jg L A TEX-ß»FΩoAdC -FdCln \begin{picture}e \end{picture} rffx* L A TEXf-ß»lx*oASχ ffinu!biffxbhl+aa9 ffiovx»ko_cs L A TEXNG*oA<# x F!KJq0f =0bi<h* L A TEXSχ=0 vaχx RK(A7KFΩS L A TEXNΩ*oA<# TEXcad <#fl,i}<flt!v]vffi)* Aχ,RbOI' L A TEX-ß*]ASχxl?UmFΩ TEX±[#x 'ΩffxAχ;R ρboi picturedcx=0 L A TEX[#LY9Aχ,RF!ρ qtixoombi figuredcxy9aχ -Pae LTEXtl s?aχ!* i E=0bi A picturedclh;* picturedcum*aχ4+}u[/l*ψfflxg nuq^bhfl,-png ffio 9Abi figuredc -FdC*8iaeS» \begin{figure}[aχxgn0 ] \begin{center} \begin{picture}(aχ <R ) Aχ*_ffie5 \end{picture} \end{center} \caption{aχ*ql } \end{figure} ΠLAχXG0 F!q h (ψfflxg) t (DK:K) b (DK0K) E p (ffcfd) fi Ω0 ffi _ffilq^co)8mff'a;xgfgaχ ffiof! 0 LbO4 [htb] Π4VS 6.bOfG ψfflxg ρfg ψfflxg oρbos=:kxg 6.3HffGρ s=0k 6.Hfff'AffiY9Aχ ρ LTEXml?ρsFΩ2/I A *XGxY9Aχ ]T ar;l*0 sν*lq.* Π ili'fflv0 *l v.xs=* 6.Y9*Aχ/ ρfbo p 0 bi [htbp] xhhaχxg ;V»Aχ*XG;R fbobi centerdc(aχ IL} ψ,cboff'i Xl±*)A Π!NG,R -@*dclflaχ*e5y9 ohlaχ;r ixf bo RK FΩ \caption{} SY9*Aχl? FΩ7; B`UFΩAχ/^ (n r ;Lfflv) R3 AχdC L A TEXf_CSiXNΩ»FΩ]jqi*H?dC tabular -FH?dCE 3ρe 22

23 L* arraydczπ~ffl Φ6 \begin{tabular}{c l r c } ]#*H?dC;V»Qqfiν»*? ΠLAffi3Fν*flΩ»ff'LßLΩ (n c V;),R 3Fνx3SνLß 5 } (n V;) 3Sν»nufflv» l ;V ffiod _}6LΩ R3Sνx3@νLßd qf5 }jψ 3@E3fiνjAffs 6ELßLΩ νsν;ß>q }xjψ 3fiν;Rd q 5 }x3 E arraydc~ffl AFΩ?"L flω?»;ßlo & xjψ* RAF"3 R d q3 q \\ x?g 6. F"*VV FΩ \hlinesχ ρ(?l4ωf"* tk F5N}xjΨ 6. FΩ? ela"?*» '} ρbobi \multicolumn{}sχx} tkfflvfωφkxφp L A TEXH?* S di \begin{tabular}{l l c r r} \hline \multicolumn{2}{c }{Left} & Center & \multicolumn{2}{c}{right} \\ \hline & 112 & & & 12 \\ My Text & 1562 & My Tests & tttt & MMMMMM \\ \hline \end{tabular} fflk*φk(fflv6tffig*s#ffi. Left Center Right My Text 1562 My Tests tttt MMMMMM ffgk*φklbo]v \multicolumn{}sχ*biaw Sχfiοq@Ω r; 3FΩ r;l*?laib*ν*ω 3SΩ r;l*r d SνIBR*;V (S LΩaex }NGae) 3@Ω r;l*e5lνibr*wge5 ^(tkfωcχ*? Left Center Right My Text 1562 My Tests tttt MMMMMM? bontk* Sx'Ω \begin{tabular}{l l c r r} \hline \multicolumn{2}{c }{Left} & Center & \multicolumn{2}{c}{right} \\ \hline & 112 & & & 12 \\ \cline{3-5} My Text & 1562 & My Tests & tttt & MMMMMM \\ \hline \end{tabular} bχbi \clinesχbo]vf5n}!boclπlzf νff i 23

24 ? *"ßRClbO'}* -d 91 \renewcommandsχxqμ;v 6.? ;V*fflK 9tKSχ ρμ*s#ffi.6t \renewcommand\arraystretch{2.0} Left Center Right My Text 1562 My Tests tttt MMMMMM bo]v -Λi» \renewcommandsχl x*sχ \arraystretch~»'5 (:m< h?* 2.0,) ffio x?*"r» L A TEXffl,iX91Qμ;V \tabcolsepsχ R '}?*νxν;ßr? NGdC table * iefflk7k* figuredc~ffl dcl s?? Cb Off'iXA;*XGxρs ixcboitk* exy9fω? \begin{table}[? XGN0 ] \caption{? *Ql } \begin{center} \begin{tabular}{ e;v }? *_ffie5 \end{tabular} \end{center} \end{table} ΠL? XG0ο * iefflk7k*aχxglzπ~ffl* C4q~;*fiΩ0 -Λ* \caption{}sχ*xge AχdC*H%FF L A TEX tabulardclf;v»fω p 0 ΠbiaWS p{ne w}, T?νS nes w *[/ g1 w *Kj(l?a%tF" 0 boxfflk7k* c, l, r ^(tk*s# S \begin{tabular}{l p{8cm} c}\hline 1). & In the tabular environment, a tabular column of width 8cm is used to demonstrate the use of p option. It is noted that the results of p is different from c, l and r & $r=a_2^5$ \\ \hline the second row & This is to show that the words are wrapped according to the 8cm limit & hhhha\\ \hline \end{tabular} (fflv6t*s#ffi. bχπl3 2 ν*4ωnes 8 ~G RΠL*[/nE,Φu 8 24

25 ~G 1). In the tabular environment, a tabular column of width 8cm is used to demonstrate the use of p option. It is noted that the results of p is different from c, l and r the second row This is to show that the words are wrapped according to the 8cm limit r = a 5 2 hhhha 4.5 tng ja- AO Y2*s?A?} L L A TEXAffiAFΩDKGHfg1 70%.A?"i tafωd KG*A?Ω Hfg1 2 Ω _ffis#loomux-@mb(_ffia?xged v x*xg_9πωdk tvxs?a?1o dw} * h -@Hd LHΦs?A? ;X*F R <"Qμ;V tkfflv? ΩHΦ;X*R *Y2?x'5aW Ob (ixs(»9*s#ffi. \topfraction R»Π4VSDK:KbO.s?A?"i*χj2 ΠY2?S 0.7, 70% boss?a?"i k_g?( R 0(/ ^m(v»9*s#ffi. 'X91Sχ \renewcommand{\topfraction}{0.98} x;v R S 98% *XGbOSs?A?"i x;~d*r \textfraction CbO91~d*SχNGmFΩ/Φ*? ~d1 DK0K*s?A?"i)CbO91 \bottomfraction R xqμ; V ΠY2?S 0.3, ψ,hc( R ;VS/ *? \topnumber R»Π4VSbO DK:K O;X*s?A?Ω ΠY2?S 2, ixbo91tk*sχ(?ngm 4 \setcounter{\topnumber}{4} ψ,ixfbo(fl,*dk0ks?a?ω (\bottomnumber R ) Qμ;Vu? R *Y2?S 1 \floatsep R» R ;V»s?A?GtG!v*fffiXG R?E5[*n ;;Vq" L 10E11pt *5[xΦ R *Y2?S 12pt, L 12pt *n;;v R *Y2?S 14pt Π_iXbOitK*Sχx/Φ R *? \setlength{\floatsep}{4pt} \floatpagefraction R» R ;V»FΩs?DKL'.s?A?"i*χj) ΠY2?S 0.5, R boi \renewcommandsχx'} 25

26 5 Zffl:=χοi.+ fflkhbfω1-%» L A TEXs#<#*l?7;x+ ]i*οf Bfl-F6 S L A TEX* YA+C O 8 -F1L(7K L A TEX<#*+ ]iaw Πdi ffiz+ ]ihla [#L]iΠ!1avx*ρe; A?; #1;O D;- -Pμ 6.bOl?1Lm dl(fflix-ßz *a9 fflk7kρe A?Lffi7K1»!D*l?7;aW 6ρedCt6.i» equation dc ρbol ρe<"l?7; 6. ρefflk Y9FΩ equationdc x*7 ;(l?1:mμ*7; LAχdC figuree? dc table xφ 6.bi» \caption{} Sχ ρc(ml?17; 6. fl7; SFΩ<;fi%tx ρbobi L A TEX-ß* \label{}sχ ΠL r ;L*nq HlAfi%*<; d fi 4Ω[#LHbbi~;*nq S<; oρ 7YL(fflvQv;V h*b± <;Sχ*biXGlKQA* L#1<" <;^ ρ \label{}sχd ~d*#1;v S;R ρe<"<;^ ρ \label{} Sχd \begin{equation}sχ*rk LA?*<;ρd \caption{}sχ* RK F!ρqt -ΛffiZ ZSχ*RKlALßHfΨqΠ!Sχ 6. 5[L]iZFΩ<; ρbobi \ref{}sχxlm S»ΦPl?<"+ ]i*lψ% bo91tk*sχx 4» Eqn.~(\ref{myeq1}) in Section~\ref{mysec1} will be shown later \subsection{my Next Section} \label{mysec1} My Next Equation is given below \begin{equation} \label{myeq1} \dot x_i=f_i(x_1,\cdots,x_n,t)+\xi_i(t), ~~ i=1,2,\cdots,n \end{equation} Πs#ffi.6t» Eqn. (5) in Section 5.1 will be shown later My Next Section My Next Equation is given below ẋ i = f i (x 1,,x n,t)+ξ i (t), i =1, 2,,n (5) -@~qfωpw*l6»d. 1fflK ffioj#1 d. ρefflr ffioj Π!*ρe 5[LL!Dffi]i*7;BbOl?1Um - 7;(L'Ldu!ffi ]i*7; 6. ZFΩDLdi» \label{}sχ ρ;^cbo(πd6<"<;? Π!* Kj ]izωd6ld*d;^ ρbobi \pageref{}sχxlm -FSχ*bia WE \ref{}sχ*biawll'ff* Qμ^(fflK*Φk 6.3FS}:S 26

27 Eqn.~(\ref{myeq1}) in Section~\ref{mysec1} on page~\pageref{mysec1} will be shown later. ^ ((%tk*s#3. Eqn. (5) in Section 5.1 on page 26 will be shown later. -Λ y»#17;oi #1ffi *D6C.l?1]i» L A TEXf-ß»+y*Sχ fl,ixffa;* eν R^[z*e5,RbOl? UmR^[z Bfl, 5[LLR^[z*7;<"]i L A TEX);*R^[zl?UmdC*QlS thebibliography, dc*;v ent KΦkΦP \begin{thebibliography}{99} \bibitem{knu01} Knuth, D. E., The \TeX Book, Addison-Wesley \bibitem{lamp01} Lamport, L., 1985, \LaTeX: A Document Preparation System, Addision-Wesley \end{thebibliography} -Λ n 99 S dcaffi*r lixa;* *R^[#7; ixcboa ;SΠ!? thebibliographydct AΩR^[z d n \bibitem{}sχx]# r;ldfflv R^[z*<fi RKbOff'1T* ex R^[z*e5 i XbO -FdCti~;* eνvffiq*r^[zx ]Tw*R^[zΩ HAg1 ffl;* 7; oρdqμ;v 7; #3.» A1nψ*7Y;R (F!6.q}? ρ)a Ω7Y) fflk*sχ(fflv6t*s ffi c χ % [1] Knuth,D.E.,TheTEXBook, Addison-Wesley bo]v -Λffiν* ΩR^[z*.;Bl?1`U» ;^ -ISχffflv» [2] Lamport, L., 1985, L A TEX: A Document Preparation System, Addision-Wesley Ω<fi Knu01ELamp01 bobi 6. [#L ]i- R^[z ρbobi L A TEX; V* \cite{}]isχx_x SχL r;*e5sa]i*<; Φ6tK*Sχ (fflv6t*s#ffi. ΠL See Ref.~\cite{Knu01} for details. See Ref. [1] for details. -Λ*ar;ll? G* \citesχffl,οπ!0!*f! es \cite[extra information]{label for reference} extra information: R^[z]i^*y ρj tk*φkl(;gr^[zy ρj *3 aw 27

28 label for reference: x \citesχ~ld*r^[z<; ffii \citesχlfbo ν9oω<; flω<;lia;jψ* ffid ]T flω<;;ßhfqf \TeX~ and \LaTeX~ has been discussed in Refs \cite{knu01,lamp01}, see Ref \cite[pages 11-50]{Knu01} for more details. (fflv6t*s#ffi. TEX and L A TEX has been discussed in Refs [1, 2], see Ref [1, pages 11-50] for more details. 6 L A TEXχ5R±=Sffi 6.1 _~fi ci*ν?dcqtk@p» itemize, enumeratee description fflk7k L A TEX@ v+c^hbi» itemizedc bo]v dc*+6l AFΩν? *fflkbnf ΩΠ*J6 (, L A TEX* $\bullet$) x]# g"rν?*e5ff'_ffi*[nlω -@ HbO@vfflK*J6 b(s#ffi.]jb$ ν?dctfbo *Π!*ν?dC -@9b( L A TEXs#ffi. 2qF ^(t KFΩΦk \begin{itemize} \item {\bf Approximate methods}: Summarised as \begin{itemize} \item Random Describing function method, where the signals within the system are assumed to be Gaussian, so that the nonlinear element is approximated by a variance-dependant gain. \item Smith s functional approximation method. \end{itemize} \item {\bf Exact method}: Normally the Fokker-Planck equations... \end{itemize} GKFISχ*s#ffi.6t» Approximate methods: Summarised as Random Describing function method, where the signals within the system are assumed to be Gaussian, so that the nonlinear element is approximated by a variancedependant gain. Smith s functional approximation method. Exact method: Normally the Fokker-Planck equations... biν?dc AFΩν? Bln \itemsχx]#* 3FΞν? L LTEX; VSnΠ6]#* 3SΞν? ln A ]#* RK*IΩS E ]#* - ]#q; l n [# (STY [#t CLS [#) LNG* ixbol± N)A<"}? 6.(fflKΦkL* itemizedc'k}m enumeratedc ρ(vx6t*s#ffi. 28

29 1). Approximate methods: Summarised as (a) Random Describing function method, where the signals within the system are assumed to be Gaussian, so that the nonlinear element is approximated by a variancedependant gain. (b) Smith s functional approximation method. 2). Exact method: Normally the Fokker-Planck equations... -Λ*.; 1 E 2 x (a) E (b) ll?um* Eρe*l?s.F@ 6.iX fflk F5ν? ρrk*.;c(l?uu:_ O`UE_ffi~^I*3. ]T» flpν?dc<" *^ LTEX);EObO *fiξ -F!xΦlyffi* A» descriptiondcefflk- * PdC,qH; -PdC*NGt(H`Uν? <fix.; biν?dcq^mux AΩν? ;ß*R bf1nt1ψ-x± -q^affi ixl±%;vπlf ν?r flων?r *4V6A 1 ffig RflΩeEffXBb O91=0u?*aW%'} =< Ψ Ω Φ ff L6 Lk fl 4 1ffo item^$+j3 ffi fi ffl =< 4 2ffo item^$+j3 ±M fl SL6 Lk T \itemident ΦT \labelsep ΨT \labelwidth ΩT \leftmargin fft \listparindent fit \rightmargin flt \topsep+\parskip+\partopsep ffit \parsep fflt \itemsep+\parsep D 1 ο@edsξhud 6.2 <>E~fi L A TEX-ß»FP+yTV*ΦflD (minipage)s#dc!* i~ψu 4Ωs#DKt Y9FΩΦ*ao ixbo( ao]mfωdk DKt F +y*} 29

30 ΦflDKdC*NGSχS» \begin{minipage}[φfldxg]{φfldne } ΦflD*s#e5 \end{minipage} ΦflD*XGEs?A?*NGael~ffl* ffi4vqffih; ΦflD*XGbOb i t, bec*fi;x<p 6.bi b0 ρφfld*0keπ!*[n"lω?bi t 0 ρφfld*:kxπ![nlω?bi c 0 ρφfldfflοxπ![nlω DKnE*NGaWClKfiff* ix r;lfflfωee*?hbo» ΦflD*Λ El N!(4*e5n L A TEXl?`U* ixh4 -Λi%O*οΩ ffid fi ψ minipagedcmd^ ρπ;v[ffi ΦflD/QbO]mlFΩ 5c *DK!bO οql±*,] ρedc A?- ΦflD/QfbO * tk91fωφkxφpφ fldk*ng bi The minipage Started ~~~~~ \begin{minipage}[c]{6cm} This is the paragraphs shown in the minipage defined. $$f(x)=2x^2+3x+3$$ \end{minipage} The minipage Started This is the paragraphs shown in the minipage defined. f(x) =2x 2 +3x +3 -Λ*ΦflD*DKnENGS 6cm, Deοql±* 3ρe (IL} ) [S- Λbi» c XGNG0 ffio ΦflD*XGEfflKFI[nlff'LοLΩ* 6.3 sv8 ±ff L A TEX*F +y*ngln~d* STYtCLS [#);* ΠL article ["n ln article.styeπ!~d*[#a;* -Λ*Π![#lA art10.sty (Ldu 10pt NG), art11.sty (Ldu 11pt NG), art12.sty (Ldu 12pt ffl;*n;t Π LCqFΩ[#ff i L 2e #/xφ ~d*[#s article.cls, size10.clo, size11.clo E size12.clo Ldu book.sty Πn;;V[# 2e #L~d[#S book.cls, bk10.clo, bk11.clo, bk12.clo - LΠ!n 6 book-clf@!(ldu book.sty, bk10.sty, bk11.sty, bk12.sty [# article.sty -[#L (;VEn; Φd"*F Y2NG RΠ![#( En;~"*F NG - [#BlbD* Π S3flCHlKc CAiXrο%D LΠLF Y2NG <"'}flbf* tkl article.sty [#L"uν?dC*F Y2;V S -Λj ΩKjx;V ν?dc fflfωkj;v enumeratedc RFΩKj;V itemizedc v$^tk*3 FΩ S -Ω SL* \arabic{enumi}. *4Vl(3FΞν?dCΩ fl*e5 enumi 30

31 iοtf n*χe (arabic) wgvx!rk*6?g wgl n;r wgfωπ6 RK3SΞ*;VaeLbi» \alphsχ ν SχliΠr;rffx* -HlΦ3S Ξq;Um^lOΠr;rff*a[n[x<]* \def\labelenumi{\arabic{enumi}.} \def\theenumi{\arabic{enumi}} \def\labelenumii{(\alph{enumii})} \def\theenumii{\alph{enumii}} \def\labelenumiii{\roman{enumiii}.} \def\theenumiii{\roman{enumiii}} \def\labelenumiv{\alph{enumiv}.} \def\theenumiv{\alph{enumiv}} \def\labelitemi{$\bullet$} \def\labelitemii{\bf --} \def\labelitemiii{$\ast$} \def\labelitemiv{$\cdot$} RKKjLl"u itemizedc*ng bo]v-fiξν?dc*<;jas,, E 6.iXHnc-Psν ρbol±}:sν. t Gl±nc*q; ffia]t '}n [#;ffl F;A(A'}*n [#vh%ixl±*ψffl^ %t oρ6.'}»;r (g Π!0*s#ffi. 6.4 R8Y L A TEXjsvmFLAO L[# LTEX-ß» A 2.09 #*n [# carticle.sty, cbook.sty - ffi>q-ß 2e #* CLS [ # -@ixc9l±%um~d* CLS [# Φ6iXbOvv( texinput\latex2e ^%t * article.clsvh%ψffl^%tb}qs carticle.cls, Z [#B \NeedsTeXFormat {LaTeX2e} ;ffld Y96tSχ \input cchead.sty \relax -@HbO_xL[}» *Um»? (4L[} *.clse.clo ΠL*KOe5 O-8i ;^ *f'}»? [# B'5» STY [# b( Os#ffi.»_i 6.5 ψ06?jb%g 6.qFΩn<h L A TEXSχUm*Aχ ffifω[#fflv (6nRK(7K* TEXcad t PICTEX<#Um*Aχ[#) ρbofiff1ni \input{}sχ AχLx]i! Φ6q FΩQS mypic.tex *Aχ[# ixboitk*sχx89;» \begin{figure}[htb] \centerline{\input{mypic}} \caption{my imported figure} \label{myrefs} \end{figure} ]T -Λ[#QL(XRgQ L A TEXAffiY9*[#QF;Ai TEX SRg 31

32 6.Y9Π! fl*[#^ ρd +y<"} Φ66.iXqFΩO EPS SRg *Aχ[# ρbo91 \epsffile{}sχx(4 [# ;^ \documentstyle{}sχ* 0 L(4 epsf.sty [# t 2e #tbi \usepackagesχx(4 [# - RK( 7K EPS [#;V*AχnEbO5R1n \epsfxsize{}sχng EPS [#Affiy' _vqfωls PostScript Cartridge *+ydg F!μ?Πffi ffio,ef!bi* y' _vbhο-png ψd Niß0aWx _οq-@(4*[# ΠaW t 1L7K Π! fl*[#bo91 L A TEX-ß* \special{}sχx8i Φ66.iXqFΩX A[# (O BMF SRg) 6 N[#QS MYFIG.BMF, ρbontk*sχy9 \special{bmf=mypic.bmf} 7 =χ L A TEX;`± L A TEX*ZU*DEiXFv»,ObO<FJs!Ποf*μQ( (packages), ΠL O μq(xboffngjis# L A TEX2e #t bobi \usepackage x89~d*μq ( 7fl* 2e #/Z?KjS \documentclass[11pt]{article} \usepackage{picinpar} \usepackage{identfst} \usepackage{emlines2} \usepackage{epsf} R L A TEX2.09 #tfbo( STY [#(4 documentstylesχl 6bO [# Z?} 9tνSχ \documentstyle[11pt,emlines2,epsf]{article} \input{picinpar.sty} \input{identfst.sty} 7.1 6?b%LΩ*wffiZ emlines2 L epsf <h#* L A TEX9r*oA!} fllkj*!c9rf fiff*oasχ TEXcad E emtexs!» L A TEX*oAοf ]9»οf» *oa S E S~wI f7»fωqs emlines2.sty *μq( 8i TEXcad oh*aχ^ 4+vv8i ((4) μq( oρπlkooasχdw7y 7.2 $`+@ vg wffiz indenrst.sty <h*a[`φ[#s# AFΩΦ1*Zd3 1 IXHbiv"f (indent), R RK* I2Lbiv"f L[s#LOOtAffi Φ1R*3 1 ΩI2LCNiv"f -b(ixoo)a;vfωsχ H1!vv"f L A TEX*iXfZU»FΩμQ( indenrst.sty xlm-@*οf!caffi [#Z d^8i μq( b 6^U /Π, BMF ]%m» DOSuWo, #Im Windows edaw, BMP ]%Ξ 32

33 7.3 tn~fijg wffiz nh;*zu*7»,oboy9φflaχ*μq( ΠL ci*q floatflt.sty, floatfig.sty E picinpar.sty picinparμq(l-ß»fωu/dc window, Π8i es \begin{window}[nl,align,material,caption] ΠL* 4ΩR *TVS nl windowdczd^*[/" align [L windowdc*lω e Y2S}LΩ 0ο l0 Πvfq cer0 jaslßeslω materials (4*e5 bos[/ t TEXAχ[# CbOS EPS Aχ[# caption Y9L±*ΦP windowdcfuuv Ωμ*dC figwindowe tabwindow, jalaχe? <"}!D*8i eefflk*ff Φ6bO91tK* ex;v figwindowdc \begin{figwindow}[2,r,\input{fig1},{my inserted figure}] (4*[/Kj \end{figwindow} ΠLR 2?g -Λffl 2" 9z} ORfl"L_sK (r0 ) Y9FΩAχ ψ,-λ* 2Er0 bon~d*r 1g -@*I2LY9*4 Sψffl^%t* fig1.tex, RAχ*ΦP[nS My inserted figure, B NGt[l?7; picinparμq(l-ß* tabwindowdc*ffi.cl~ffl* floatfig.styμq(*οf fflu picinpar.styμq( >" μq(;ffld v vfflv \initfloatingfiguresχ dcud_ -@ixhbobi floatingfiguredc» dc*8i es \begin{floatingfigure}{8cm} \centerline{\input{fig1}} \end{floatingfigure} E picinpardch; floatingfiguredcd)φp(aχ_`f6lω L A TEXd Cm NΦqDx<"l?N; ffi floatingfiguredcthfa;fflkqπ" 9z} L A TEX-ß*F s?dcμq( +;bitoomvx-@ta@* h Φ6 picinpar HHfmΨΦ1%bi S μq( Qμ;VΦ1Rml?[ffi ffii6. ψffldk G?>qyffi *fß%5bffi 9*s?Aχ^ Aχbf=[ ffio bi-@*μ Q(^d]TΠnidC O9s( s#ffi. 7.4 S6? g wffiz subfigur.sty?fωaχ7;t(4q? ΩkA ρbo8i subfigur.sty [#LflΩkA<"l?7 33

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35 ρj j C!8 Λk Pff j 8.5cm TEXcad Aχ5K TEXcad μl', Goblenz 3 W. Schiffmann EiA#*3UNΩ* /^ RxΠοfX&st TEXcad li Turbo Pascal 5.0 #/7 * ixbo i}< flx]vaχ,r TEXcad <#( AχZYmn LTEXSχzm*±[# ixbo(- A Ω±[# 9l±*[#;exs(ffi)*Aχ -Λ7K*l Georg Horn }<* TEXcad 3.2(1995j 1 ff <#S O#/) DOS tixbo91 texcad Sχxff? <# -^(s(fω6a 8.1ffig*Aχ 5K -Fq.L-ß»@Ω j sg-*l j j ixwgf `U*ρj st -*lpffsχ j R}6*lAχ7 j ZdbiΦq.^ Pff j(fflvq.*ypff (MAIN MENU) Πe5q Draw (] A) Edit (7 ) Redraw (Q]) Snap (qξ7ω) Zoom (f ) Window ( j) Options (0 ) Save (flv) Load (Dv)EQuit (Gv) 6.iX6# Snap 0 (fflvfωtξpff Lßq Ω0» On (qξ) E Off (d Ξ) 0ο» On ρ'<*j?lff 7?* AFΩCf7?4 Ω -q u@*; X 6.iX0ο» Off0 ρ'<bo 1J? -m-λ A*j;ff 6.iX0ο»ΠL* Draw Pff ρ(vxfωtξpff» Text ([n) Framebox ([nxo) Dashbox (*}o) Filled Box (t4*ao) Line (=}) Vector (q"? *=}) Circle (Π) Filled Circle (t4*π) Oval (Π-Kχ) Put ( 9nq ) x Bizier-Chain (Bezier!}.ν) Bezier-Vector (ο"?* Bezier!}) 6.0ο» Text 0 ρd i}<! ]A jg6#fω6,r!9fωnq Π_ nu4ω[# B(i L A TEX%} ffiobo!91tvffl* n L A TEXSχzm*nq,Rfftli! -^ j jl(6_[n*lωae ixboffl±*affi<"l RNGv [n*xg ]T nu TEXcad BHοq1Hs#οf ffio ]A jlwg[n^cq FΩ T x?g 6.iX0ο» Framebox oaμq ρ TEXcad (-gix*;ao*}t-esg- < ixboi}<6l*aex0ο- <,R TEXcad (6_iXaoL*[n 6.>q[n ρfftli! b 6.)A[n ρπz9*1qefflk Text 0 FF z9l[nr ρ aoli BT nqxß1 Dashbox 0 (fl,ix]vfω*}*ao!(ff fflu Framebox *aeaffiix ]vfω*}ao,rfl,ix0ο*}}i*ee -@9bOoHvFΩ*}o» 6.iX0ο» Filled Box 0 ρ TEXcad (.ix]vfωao -^ov*aoekl t4* 35

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39 G <T-ffi"i*fß _ffiaχ*eenbd G 30mm 6.Ni» PIC SIZE* Sχ 4ΩAχ)A*fßENGd lff* WINDOW : Sχ* es WINDOW=[x min,x max,y min,y max ] ΠLfflv*fiΩR ;V»iX j 6.ΦSχHfflv PICTEX(l?(-fiΩR # fflv N*?E Φ? ORIGIN : ΠSχ es ORIGIN=a, bix( <T 6*XG;V a, b 6G 6.HfflvΦ Sχ ρ a = x min,b= y min LINE E VECTOR»Sχ es LINE t VECTOR=x 1,y 1,x 2,y 2 S ohf5ff (x 1,y 1 ) % (x 2,y 2 ) *=}tο"?*}i STRING : Sχ es STRING=s, ΠL s Snq GRID E GRAD : Sχ es GRID t GRAD=n, m ΠLfflFΩSχ(Aχψ}oH (n +1) (m +1)ΩN RRFΩSχ <TG _ (n +1) (m +1)Ω <? AXIS STATUS : Sχ es AXIS STATUS=k 1,k 2?g <Teq ΠL k 1 Ldu X TN G k 2 Ldu Y TNG!D*b#?S OFF (H] <T) REAL ( ee) E INTEGER ( _4 Ldu Y TNG!D*b#?S NORMAL (5cfl S }%) LOG (L ) P AXIS TYPE : Sχ es AXIS TYPE=k 1,k 2?g <T fl ΠL k 1 Ldu X TNG k 2 AXIS NAME : Sχ es AXIS NAME=s1, s2,?g <TQl ΠL s1 E s2 Snq ja S XEYT*<fi DATA : Sχ es DATA=n, x 1,y 1,,x n,y n,?g Nz ΠL n S Nz (x 1,y 1 ),, (x n,y n ) SoA N6 N6Lß*KjnY?aWΩμvx RK(7KY?aW A; END : Φ SRK*e5(.V,!?g N[#%Φ3 CURVE TYPE : Sχ es CURVE TYPE=k?g!} fl ΠL k *#?S THIN (r}) THICK (fi})emark (H]ffi} C]<fi) ;F INTERPOLATION : Sχ es INTERPOLATION=k?gY?ae ΠL k *#?S LINEAR (} fly?) SPLINE (@5Y?) ;F MARK SYMBOL : Sχ es MARK SYMBOL=s?g<fiffii*q; ΠL s SFΩnq DASHED CURVE : Sχ es DASHED CURVE=n, l 1,,l n?p!} fl 6.oH_} ρg DASHED CURVE=0 oρ l 1,,l n S!}_*~+1*ae fflv»tk*sχ;r HbOoHAχ» tkfflv»fωn 5!}flm*Aχ» pic_size*=80,60 origin=0,0 axis_status=real,integer axis_name= $x$, $\sin(x), \frac{\displaystyle x}{\displaystyle \pi}$ grad=1,1 39

40 % --- First curve --- curve_type=thick interpolation=spline mark_symbol= $\bullet$ dashed_curve=4,2,0.5,0.5,0.5 DATA= e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e-016 % Second curve ---- curve_type=thin interpolation=linear mark_symbol= $\circ$ dashed_curve=0 data= e e

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