ࡱ>  AC@vL[ %:bjbj !njjj,=} lnnn8\VlXR!F!!"q$n%|[&@ X X X X X X X$Y [/Xn&1$@q$&&/X8!"DX888&H<!n" X8& X88>T|nW" eI@-|UWZX0XU\_4~\W8SIGNALS AND SYSTEMS LABORATORY 8: State Variable Feedback Control Systems INTRODUCTION State variable descriptions for dynamical systems describe the evolution of the state vector, as a function of the state and the input. There may be an output equation as well, but we shall not be concerned with it in this discussion. For continuous time systems the state equation is a differential equation of the form (1)  EMBED "Equation" "Word Object9" \* mergeformat . In this equation, the state x and the control input u are vectors. Therefore the function  EMBED "Equation" "Word Object9" \* mergeformat  is also vector valued. If one makes the input a function of the state, (2)  EMBED "Equation" "Word Object12" \* mergeformat  then the system is a state variable feedback system. The function  EMBED "Equation" "Word Object12" \* mergeformat  is called a control law. We shall study two examples of state variable control systems in this lab. It is generally the case that the differential equations (1) are non-linear. Therefore they are very difficult to study, although they are not particularly difficult to simulate numerically using something like MATLAB. One analytical design tool which can be used in the vicinity of a vector x0 is a linearization of the system. This is an approximation which is valid only for small distances from x0. Provided that f (x0, 0), or x0 is a rest point, then the linearized system is (3)  EMBED "Equation" "Word Object13" \* mergeformat , where (4)  EMBED "Equation" "Word Object14" \* mergeformat  is the deviation of the state vector from the nominal point x0. The matrices A and B are computed from the function  EMBED "Equation" "Word Object9" \* mergeformat  as follows: (5)  EMBED "Equation" "Word Object15" \* mergeformat  and (6)  EMBED "Equation" "Word Object16" \* mergeformat . The right hand side of equation (3) contains the linear terms in a Taylor series approximation of the right hand side of equation (1). Using the linearization, one can apply several well-known design methods for linear systems to obtain a control strategy. Once implemented however, the system will perform well only in the region for which the linear approximation is good. We will get a taste of this in the second problem to be studied in this lab. TIME OPTIMAL CONTROL OF A LINEAR SYSTEM (BUSHAWS PROBLEM)  EMBED Word.Picture.8  Figure One A mechanical system acted upon by a force u. Consider a rigid body of mass m acted upon by a single force. If the system is constrained to move in one dimension only then Newtons law of motion is F = ma . For simplicity, set the mass to 1, and call the force u(t). Then the differential equation describing the motion is  EMBED "Equation" "Word Object1" \* mergeformat . This system is the ultimate in simplicity, but it can make for an interesting control problem. In state variable form, it has dimension two. If we define the state vector to be (7)  EMBED "Equation" "Word Object2" \* mergeformat , then the simple equation  EMBED "Equation" "Word Object1" \* mergeformat  becomes (8)  EMBED "Equation" "Word Object3" \* mergeformat , which is in the form  EMBED "Equation" "Word Object4" \* mergeformat . One can make a feedback system out of this by taking the control input u to be a function of the state vector x. We shall make this problem more practical by constraining the input: Control input constraint:  EMBED "Equation" "Word Object3" \* mergeformat , for each t. This constraint is realistic in many situations. For our problem, it limits the acceleration to at most 1. A typical problem involving a bounded input is the time optimal control problem. The goal is to drive the system from any initial state to a specified target in minimum time. The solution to this problem is usually bang-bang, which is a colorful way of saying that the control u(t) is almost always 1 or -1. In other words the input is always on the boundary of the constrained set of allowable inputs. A feedback control law has the form (9)  EMBED "Equation" "Word Object4" \* mergeformat . If we respect the constraint, this function cannot be linear. Thus the feedback system will be nonlinear, and will be described by the differential equation (10)  EMBED "Equation" "Word Object5" \* mergeformat . Figure Two contains phase plane portraits of the nonlinear system described by equation (10), with different control laws. These are  EMBED "Equation" "Word Object6" \* mergeformat maximum acceleration EMBED "Equation" "Word Object6" \* mergeformat maximum deceleration EMBED "Equation" "Word Object6" \* mergeformat  linear with saturation EMBED "Equation" "Word Object6" \* mergeformat bang-bang control. u is always either full on or full off  EMBED Word.Picture.8  Figure Two Trajectories of the system  EMBED "Equation" "Word Object1" \* mergeformat  with four choices for u. Examine the m-file doublin.m, or double integrator, found on the web page, and make note of how the differential equations are numerically integrated, using MATLAB:  EMBED "Equation" \* mergeformat becomes EMBED "Equation" "Word Object1" \* mergeformat orx1=x1+dt*x2. EMBED "Equation" \* mergeformat becomes EMBED "Equation" "Word Object2" \* mergeformat orx2=x2+dt*u. function doublin(a,b,g) % doublin(a,b,g) % run the double integrator. % a and b are vectors of dimension 2 % g is a string describing the control function % u=g(x1,x2) L=1024;T=10;dt=T/L;t=dt*[0:L-1];epsilon=.1; x=zeros(2,L);v=zeros(1,L); x(:,1)=a;x1=a(1);x2=a(2); k=2; while (k<=L)&(sum(abs([x1;x2]-b))>epsilon); u=eval(g); x1=x1+dt*x2;x2=x2+dt*u; x(:,k)=[x1;x2]; v(k)=u; k=k+1; end % We have not shown several lines which draw graphs  Figure Three A simulation of the system, using the bang-bang control law. The equations are  EMBED "Equation" "Word Object8" \* mergeformat , which is apparent from the graph. This tool numerically integrates the differential equations and produces the graphs shown in Figure Three. The control law is passed as a string, and therefore you can run the system for any law that you can write an expression for. The parameters a and b are column vectors of dimension 2, with a the initial state and b a target state. The simulation will terminate if the trajectory gets close to b, or if the time gets to 10, whichever happens first. Here is an example: g=-sign(2*x1+x2*abs(x2)); doublin([-1;0],[0;0],g) 1.9238 The final time is printed. In this example it is just short of 2 seconds. (See Figure Three.)  THE CART AND THE PENDULUM The broom balancing or inverted pendulum system shown in Figure Four has been a popular example for many years. The problem is to keep the ball in the air. Note that the applied force is rather indirect. We can only move the cart horizontally and thereby influence the pendulum indirectly. This problem is very close to the one that gave the early builders of rockets headaches. A rocket must be guided from the base by swiveling the rocket nozzles. If you have seen movies of early rocket launches, you will have seen rockets that had to be destroyed because they went off course. In this lab we will simulate the dynamics of this system using the MATLAB differential equation solver ode23. We will simulate the motion with zero applied force, and then attempt to stabilize the system, about its unstable zero state position, by linearizing and then using a linear control law. You will study this stabilization problem, and get some data on its limitations. The system is governed by a pair of coupled, second order nonlinear differential equations. In order to use the equation solver we shall put them in state variable form. Next, we will linearize the state variable equations about the unstable rest point where the cart and pendulum are at rest with the pendulum straight up:  EMBED "Equation" "Word Object3" \* mergeformat  For the resulting linear state variable equation, we can get a stabilizing linear feedback control law.  EMBED Word.Picture.8  Figure Four The Cart and the Pendulum (with apologies to Edgar Allen Poe) Here are all the equations: Equations of motion of the cart and pendulum (11)  EMBED "Equation" "Word Object1" \* mergeformat  Definition of State vector for the cart and pendulum (12)  EMBED "Equation" "Word Object3" \* mergeformat  Non-linear State Variable Equations for the cart and pendulum (13)  EMBED "Equation" "Word Object4" \* mergeformat  Linearized State Variable Equations about the zero state (14)  EMBED "Equation" "Word Object5" \* mergeformat , where  EMBED "Equation" \* mergeformat , and EMBED "Equation" \* mergeformat . Linear feedback control law (15) u = Gx, where G = [g1 g2 g3 g4]. Linearized Feedback system (16)  EMBED "Equation" "Word Object8" \* mergeformat . The MATLAB differential equation solver ode23 may be used to compute solutions to the nonlinear equations (12). Use the help facility to see how ode23 are used. To make the graph shown in Figure Five, use the following commands: [t,y]=ode23(cart,0,10,[0;pi/6;0;0]); subplot(2,2,1),plot(t,y(:,1));title(x(t)) subplot(2,2,2),plot(t,y(:,2));title(\theta(t))  EMBED Word.Picture.8  Figure Five Cart position and pendulum angle as a function of time, when the control force is zero, for initial conditions  EMBED "Equation" "Word Object20" \* mergeformat , but  EMBED "Equation" "Word Object21" \* mergeformat . (This is the situation depicted in Figure Four.) The string cart identifies the m-file cart.m located on the webpage, which contains the equations. function xdot=cart(t,x) % xdot=cart(t,x) % Nonlinear equations of motion for the Cart and % pendulum system, for use by the MATLAB ode solver ode23 g=10;M=1;u=0; %control force for free motion % u=[2.6 -53.6 5.4 -9.4]*x; % a linear feedback law c2=cos(x(2));s2=sin(x(2)); xdot=[x(3:4);inv([M+1 -c2;-c2 1])*[u-x(4)^2*s2;(g-x(3)*x(4))*s2]]; Visualize the motion of the cart and pendulum as the curves in Figure Five depict it. The pendulum falls to the left and comes up again to an angle opposite the starting angle. It comes to rest momentarily and then reverses itself. Meanwhile the cart is rocking back and forth in a periodic motion. The horizontal component of momentum is zero for this set of initial conditions, and with no force applied. Therefore the cart does not have any aggregate horizontal motion. Notice that there is a choice of control inputs in the m-file cart.m. You can activate the linear feedback law by removing the comment character. With a little extra effort, one can even produce a primitive movie of the motion of the cart. The m-file cmovie.m, found on the webpage under m-files for Lab 8, assembles several frames based on the solution to the differential equation, to make a movie. [t,y]=ode23(cart,[0 3],[0;pi/8;0;0]); % solve the diff. eqn. figure(1),plot(t,y(:,[1 2])) % This plots x(t) and theta(t) figure(2) % resize the window. Make it small! cmovie_demo % this uses the array y computed by ode23 movie(M,3) % M is the movie produced by cmovie  PAGE 1 PAGE  Page  PAGE 8 of  NUMPAGES 8 Assignment: Compute the solutions to the differential equation (7) for arbitrary initial conditions, when u = 1. In other words find formulas for  EMBED "Equation" "Word Object7" \* mergeformat  and  EMBED "Equation" "Word Object7" \* mergeformat  when  EMBED "Equation" "Word Object7" \* mergeformat  and  EMBED "Equation" "Word Object7" \* mergeformat . Design a control law  EMBED "Equation" "Word Object4" \* mergeformat  which takes the system to the point  EMBED "Equation" "Word Object9" \* mergeformat  in minimum time. The control must not violate the constraint that  EMBED "Equation" "Word Object10" \* mergeformat , and should work for any choice of initial conditions. Use the tool doublin.m to test your control law g. For example, doublin(randn(2,1),[-3;0],g) exercises the system with a random initial state. For your report, include two randomized starts, and the specific case doublin([1;0],[-3;0],g) Also report your control law g, and the design philosophy you used to get it. Assignment: Using the definitions in equations (5) and (6), compute the matrices A and B of the linearization of the system (12) about the zero state. Your results should agree with equation (14). In MATLAB command mode, create the matrices A and B of the linearized equation (14), using the values m=1 and g=10. Then construct the 1 by 4 matrix G=[2.6,-53.6 ,5.4, -9.4]. Using the MATLAB eig function to commute eigenvalues, compute the eigenvalues of the open-loop system, eig(A), and the eigenvalues of the closed-loop system, eig(A+B*G). What do you conclude about the behavior of the two systems in the vicinity of the zero state? Now simulate the cart and pendulum system using ode23 in a manner similar to the example above, except that the m-file cart.m should be edited to activated the linear feedback control law. Use the same initial conditions as in the example, but with a greater time limit. Plot the resulting x and theta. Then try to make a movie. Now vary the initial conditions [x0 theta0 0 0]. Making several runs, with a short time duration, try to characterize the region about the point (0,0) in the  EMBED "Equation" "Word Object18" \* mergeformat  plane for which the linear control system can balance the broom. 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PSymbol* 8wwgw* 8 -!= Times: wwgw: -!x Times* 9wwgw* 9 -!( &Times: wwgw: -!t *Times* :wwgw* : -!) .PSymbol: wwgw: -!- 4Times* ;wwgw* ; -!x >Times: wwgw: -!0D & 'NIdxpr  I"I currentpoint ",Times .+ z)()t)), Symbol)=) x)()t)))-) x (D0%30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2336 div 512 3 -1 roll exch div scale currentpoint translate 64 61 translate 0 323 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (z) show 159 323 moveto 384 /Times-Roman f1 (\() show 293 323 moveto 384 /Times-Italic f1 (t) show 424 323 moveto 384 /Times-Roman f1 (\)) show 641 323 moveto 384 /Symbol f1 (=) show 970 323 moveto 384 /Times-Italic f1 (x) show 1156 323 moveto 384 /Times-Roman f1 (\() show 1290 323 moveto 384 /Times-Italic f1 (t) show 1421 323 moveto 384 /Times-Roman f1 (\)) show 1622 323 moveto 384 /Symbol f1 (-) show 1934 323 moveto 384 /Times-Italic f1 (x) show 2133 152 moveto 224 /Times-Roman f1 (0) show end dBMATH6 _ z(t)=x(t)-x 0iv FMicrosoft Equation 3.0 DS Equation Equation.39qCompObjfObjInfo8;OlePres000Ole10Native:<:W a .   & & MathTypeP Times New RomanLSwUSw0-2 D0yTimes New RomanLSwUSw0-2 )y2 (y2 )y2 (yTimes New RomanLSwUSw0-2 xy2 ty2 xy2 ?ty2 JzySymbolw@ OLSwUSw0-2 -y2 m=y & "System 0-NANI6 z(t)=x(t)-x 0vBf z(t)=x(t)"x 0Equation Native ^_10633843073GAFeI-eIOle PIC >@T      !"#$%*,-./0123456789:;<=>?@ABCDEFGILMNOPQRSTUVWXYZ[\^_abeghijklmnopqrstuvwxyz{|}~Trr J  # .  & Times %wwgw % -!f Times ɥwwgw -!( TimesMETA PICT ?CCompObjfObjInfoBE &wwgw & -!x Times ʥwwgw -!, Times 'wwgw ' -!u Times ˥wwgw -!)  & '#dxpr  #"# currentpoint ",Times .+ f)()x),)u))30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1120 div 448 3 -1 roll exch div scale currentpoint translate 64 58 translate 56 262 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (f) show 229 262 moveto 384 /Times-Roman f1 (\() show 388 262 moveto 384 /Times-Italic f1 (x) show 568 262 moveto 384 /Times-Roman f1 (,) show 693 262 moveto 384 /Times-Italic f1 (u) show 895 262 moveto 384 /Times-Roman f1 (\)) show end d'MATH* f(x,u)su FMicrosoft Equation 3.0 DS Equation Equation.39qh  .  & & MathTypePOlePres000Ole10NativeDF&Equation Native '=_1063384325KF-eIeITimes New RomanLSwUSw0-2 E)y2 .,y2 (yTimes New RomanLSwUSw0-2 uy2 xy2 wfy & "System 0-NANI f(x,u)v!о f(x,u)Ole (PIC HJ)TMETA +:CompObjIMHfT     #p .  & Times ywwgw y -!ATimesl lwwgwl l -!iTimes zwwgw z -!, Timesl mwwgwl m -!jPSymbol {wwgw { -!=PSymboll nwwgwl n -! 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Timesk wwgwk -!f &Times ֥wwgw -!i+PSymbolk wwgwk -!Times ץwwgw -!u%Timesk wwgwk -!j ,-/Times إwwgw -!x4PSymbolk wwgwk -!==Times ٥wwgw -!xGTimesk wwgwk -!0MTimes ڥwwgw -!,RTimesk wwgwk -!uVPSymbol ۥwwgw -!=_Timesk wwgwk -!0h22 & ' FMicrosoft Equation 3.0 DS Equation Equation.39q h  .  ` &CompObjRVfObjInfoOlePres000UWDOle10NativeX  & MathType-y|@Times New RomanLSwUSw0-2 5x 0y2 5 ,y Times New RomanLSwUSw0-2 0y2 I,ySymbolw@0 LSwUSw0-2 5x =y2 5=y2 @o=yTimes New RomanLSwUSw0-2 5w uy2 5xy2 5xy2 9%uy2 s]fy2 @EBy Times New RomanLSwUSw0-2 jy2 iy2 jy2 iySymbolw@ LSwUSw0-2 9y2 sy & "System 0-NANI B i,j =f i u j x=x 0 ,u=0avоdA B i,j ="f i "u j x=x 0 ,u=0  FMicrosoft Word Picture MSWordDocWord.Picture.89qEquation Native _1073830868[ FУeI^eI1TableCompObjZ]h i0@0 Normal_HmH sH tH <A@< Default Paragraph Font   @V 0 ?2$vXV"e vPb$}VS)VlEg[z "$lfJF"QTo@N(  V  C "J  # "P  3 A"P  3 A"`  c $ NB  S DB S  ?Gx3tc,3,t:t:tt:t: @B`@UnknownGz Times New Roman5Symbol3& z Arial"hbaFbaF!20G2 %username%ENS UserObjInfoObjectPool\_eIeIWordDocumentSummaryInformation(^`T>0>     .  & Times* #wwgw* # -! ! Timesm .w[ bjbj jjl$jjjj v $1333333$h  NWW%l%%%81%1%%%% \ %$Fj%% 0% 4 %% u(t)    CJ 6CJ]jUmHnHu  N N!F"G#%$%%nr}VS)VlEg[PNG  IHDR0"NgAMAPLTEf3̙f3f3ffffff3f3333f333f3f3̙f3̙̙̙̙f̙3̙ffffff3f3333f333f3̙f3̙̙f3̙f3ff̙ffff3f33̙33f333̙f3ffffff3ffff̙fff3fffffff3ffffffffffff3fff3f3f3f3ff33f3ffffff3f3333f333333̙3f3333333f3333f3f3f3ff3f33f33333333f333333333f333f3̙f3f3ffffff3f3333f333f3ľ|||vvvoooiiibbb[[[UUUNNNHHHAAA;;;444---'''  Lt pHYs  ~IDATx a3I5E|O2dz #i5`NEi~y{亐! B BU65[e~}l^I \Aٰ۪reIu,Pn  TC7?kޱMk`P"H% A]e6? %Xx/ xwQ#Z 0 D>@0  r0  r03Ry$IENDB`@=glfJF"QT,03%85x;l\E}x7I2CиAn@"#! B" ,0 sitҥr* MTl!di"3wXK8{yfyΜ+oIWڼ%-tX" xA*횬B*m]՚sUO)hn%Xc|N8[6Ol[Rgml<>D&:Jxpd%<8`A%<8 nBdjjɒM7Dfdxpt<8`"~!,Ä<8 (~! xp@?xp3ndp<8`qCt&<8tىϷ%v xp"A0~!:,<8OΘf-ˢ"M-%-,,,,],5, x(8lmmKmll[l q1̲3+6gowmy?~5Çz߿{iyyYwҒuݾ}[n͛7u -,,뚟ܜ]WjvvV333j4Ԕ&''511qittT###UݭZV++6>m>K֕gE{aφbk+ ߊ|сjAj\QWӡ ԗΨ7}QKz: VTzC)s=uEZߢ=ңJd0c3iVݬz}Q=y(F.3cUa {"O/:ՖޟdEYo_o~I;ϳ>r**eLYg yeT)aU)cOz=Xh=]Vq޹'0XM#o_f ᯦WNڽ˧ȏ  NǷie|m7|x:oc5&uY=~RreV+ /ȭksܷ}0~G:,H}^S.qWgXo⇺íZ7yWOh+'0\   $ 0<DLTss %username%use Normal.dot ENS Usert2S Microsoft Word 9.0@@N%@N%DocumentSummaryInformation8_1063384360eFeI@eIOle PIC bdT՜.+,0 hp|  ENS2  TitleMETA CompObjcgfObjInfoOlePres000fhLwgwm . -!x PSymbol* $wwgw* $ -!= Timesm /wwgwm / -!u  & ' FMicrosoft Equation 3.0 DS Equation Equation.39qq   .   &U & MathType0Times New RomanLSwUSw0-2 .uy2 JxySymbolw@ &y Times New RomanLSwUSw0-2 d2y2 a1y & "System 0-NANIi x 1 x 2 []=x2x[]vuF5 x 1 x 2 []=x2x[]T>0Ole PIC tvTMETA CompObjuyf>     .  & Times ?wwgw ? -! ! Times wwgw -!x PSymbol @wwgw @ -!= Times wwgw -!u  & ' FMicrosoft Equation 3.0 DS Equation Equation.39qq   .   &U & MathType0Times New RomanLSwUSw0-2 .uyObjInfoOlePres000xzLOle10Native{Equation Native 52 JxySymbolw@ LSwUSw0-2 2=yMT Extra LSwUSw0-2 &y2 C&y & "System 0-NANI 2x=uvDJ 2x=u_1063384386jFeI'eIOle PIC }TMETA       !"$'()*+,-./0123456789:;=>?ABCDGIJKLMNOPQRTUVWXYZ[\]^_adefghijklortuvwxyz{|}~T P     " .  & Times( ӥwwgw( -! Times7 wwgw7  -!x Times( ԥwwgw( -!1 Times7 wwgw7  -! Times( եwwgw( -!x Times7 wwgw7  -!2 PSymbol( ֥wwgw( -! ! ! ! ! ! !=Times7 wwgw7  -!0 (!1 9!0(!09PSymbol( ץwwgw( -! #! #! #! @! @! @Times7 wwgw7  -!x KTimes( إwwgw( -!1 PTimes7 wwgw7  -!xKTimes( ٥wwgw( -!2PPSymbol7 wwgw7  -! E! E! E! U! U! U!+\Times( ڥwwgw( -!0 k!1kPSymbol7 wwgw7 -! f! f! f! q! q! q!xTimes( ۥwwgw( -!u| & ' FMicrosoft Equation 3.0 DS Equation Equation.39q   .    &CompObj~#fObjInfo%OlePres000&LOle10Native<  & MathTypeTimes New RomanLSwUSw0-2 `7 uy2 Sxy2 sxy2 Sxy2 sxySymbolw@ LSwUSw0-2 ` y2  y2  y2  y2  y2  y2  y2 ` +y2  y2  y2  y2 [y2 [y2 [y2 y2 y2 y2 y2 y2 y2 `=y2 y2 y2 y2 @y2 @y2 @yTimes New RomanLSwUSw0-2 UZ 1y2 u] 0y2 U&0y2 U`0y2 u#1y2 u`0y Times New RomanLSwUSw0-2 2y2 {1y2 d2y2 `1yMT Extra ALSwUSw0-2 <&y2 \&y & "System 0-NANI 2x 1 2x 2 []=0100[]x 1 x 2 []+01[]uEquation Native @_1063384389FqeIeIOle EPIC FTv0 2x 1 2x 2 []=0100[]x 1 x 2 []+01[]"uTN>META HPICT S CompObj`fObjInfobN> J   = .  & Times wwgw -! Times^ rwwgw^ r -!x PSymbol wwgw -!= Times^ swwgw^ s -!Ax PSymbol wwgw -!+ %Times^ twwgw^ t -!Bu . & ' =dxpr  =" = currentpoint ",Times .+  ( x , Symbol) =) Ax)+) Bu30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1952 div 384 3 -1 roll exch div scale currentpoint translate 64 59 translate 50 242 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Roman f1 (\307) show 11 261 moveto 384 /Times-Italic f1 (x) show 291 261 moveto 384 /Symbol f1 (=) show 626 261 moveto 384 /Times-Italic f1 (Ax) show 1125 261 moveto 384 /Symbol f1 (+) show 1437 261 moveto 384 /Times-Italic f1 (Bu) show end d-MATH! 2x=Ax+Bug  FMicrosoft Equation 3.0 DS Equation Equation.39qM   .  &`U & MathType0Times New RomanLSwUSw0-2 Bu2 QAx2 JxxSymbolwOlePres000c\Ole10Nativem%Equation Native nE_1073900538FeIeI@+ WLSwUSw0-2 +x2 2=xMT Extra} LSwUSw0-2 f&x & "System 0-NANI! 2x=Ax+Buv)C 2x=Ax+BuOle pPIC qTMETA sCompObjfT" @" j  ( .  & Times wwgw -!u Times( ⥇wwgw( -!( Times wwgw  -!t Times( 㥇wwgw( -!) -  PSymbol wwgw  -! Times( 䥇wwgw( -!1 ! & ' FMicrosoft Equation 3.0 DS Equation Equation.39q<WZ - .   & & MathType`-KHHKTimes New RomanLSwUSw0-2 `1y2 ` )y2 `I(ySymbolwObjInfoOlePres000Ole10Native,Equation Native T@ KLSwUSw0-2 `&yTimes New RomanLSwUSw0-2 `ty2 `uy & "System 0-NANI( u(t)ab1P87K u(t)d"1_1063384413FeIeIOle PIC TMETA T4r4r   < .  & Times ƥwwgw -!u PSymbol( ꥇwwgw( -!= Times ǥwwgw -!g Times( 륇wwgw( -!( Times ȥwwgw -!x Times( 쥇wwgw( -!1 $Times ɥwwgw -!, (Times( wwgw( -!x -Times ʥwwgw -!2 2Times( wwgw( -!) 7 & '<dxpr  <"< currentpoint ",Times .+ u, Symbol) =) g)()x +1 ( (,)x +2 ( 7)30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1920 div 448 3 -1 roll exch div scale currentpoPICT CompObjfObjInfoOlePres000int translate 64 59 translate -16 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (u) show 273 261 moveto 384 /Symbol f1 (=) show 588 261 moveto 384 /Times-Italic f1 (g) show 782 261 moveto 384 /Times-Roman f1 (\() show 941 261 moveto 384 /Times-Italic f1 (x) show 1099 357 moveto 224 /Times-Roman f1 (1) show 1227 261 moveto 384 /Times-Roman f1 (,) show 1379 261 moveto 384 /Times-Italic f1 (x) show 1555 357 moveto 224 /Times-Roman f1 (2) show 1714 261 moveto 384 /Times-Roman f1 (\)) show end dGMATH; u=g(x 1 ,x 2 )8  FMicrosoft Equation 3.0 DS Equation Equation.39qq Q .  & & MathTypePTimes New RomanLSwUSw0-2 @)y2 @f,y2 @(y Times New RomanLSwUSw0-2 |2y2 1yTimes New RomanLSwUSw0-2 @xy2 @hxy2 @/gy2 @1uySymbolw@ LSwUSw0-2 @&=y & "System 0-NANI; u=g(x 1 ,x 2 )vEX> u=g(x 1 ,x 2 )T Ole10Native?Equation Native a_1073830926YFpXeIpeIOle PIC TMETA " CompObjfObjInfo    " .  & Times" wwgw" -! Times wwgw -!x Times" wwgw" -!1 Times wwgw -! Times" wwgw" -!x Times wwgw -!2 PSymbol" wwgw" -! ! ! ! ! ! !=Times wwgw -!0 (!1 9!0(!09PSymbol" wwgw" -! #! #! #! @! @! @Times wwgw -!x KTimes" wwgw" -!1 PTimes wwgw -!xKTimes" wwgw" -!2PPSymbol wwgw -! E! E! E! U! U! 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OPSymbolg wwgwg -!= VTimes6 ѥwwgw6 -! bPSymbolg wwgwg -!q _Times6 ҥwwgw6 -!( fTimesg wwgwg -!t kTimes6 ӥwwgw6 -!) oPSymbolg wwgwg -!= vTimes6 ԥwwgw6 -!0 !. & ' FMicrosoft Equation 3.0 DS Equation Equation.39qW  OlePres000 Ole10NativeUEquation Native _1049636352\ FО+eI2eI.   @& & MathTypePTimes New RomanLSwUSw0-2  .y2 , 0y2 w )y2  (y2 2)y2 [(y2 )y2 (y2 )y2 (ySymbolw@ LSwUSw0-2 1 =y2 =y2 =y2 q=yTimes New RomanLSwUSw0-2  ty2 ty2 ty2 xy2 Ity2 JxySymbolw@ LSwUSw0-2  qy2 qyMT Extra| bLSwUSw0-2 1 &y2 i&y & "System 0-NANIQ x(t)=2x(t)=q(t)="q(t)=0.vi@SE x(t)=2x(t)=(t)="(t)=0.TIm8PIC TMETA 4PICT MObjInfo      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Im V   . &&%B@%MSEPS Preamble 50 329 314 575 0 0 264 246 /pp_save save def /showpage {} def 40 dict begin /pp_clip false def /pp_bbox false def /F { pop } def /S {} def /B { { /pp_dy1 exch def /pp_dx1 exch def /pp_dy2 exch def /pp_dx2 exch def } stopped not { /pp_bbox true def } if } def /CB { { /pp_cy exch def /pp_cx exch def /pp_cht exch def /pp_cwd exch def } stopped not { /pp_clip true def } if } def /pp_bx1 50 def /pp_by1 329 def /pp_bx2 314 def /pp_by2 575 def &&-- '&&&%pp_clip { pp_cx pp_cy moveto pp_cwd 0 rlineto 0 pp_cht rlineto pp_cwd neg 0 rlineto clip newpath } if pp_bbox { /pp_dy2 pp_dy2 pp_dy1 add def /pp_dx2 pp_dx2 pp_dx1 add def /pp_sx pp_dx2 pp_dx1 sub pp_bx2 pp_bx1 sub div def /pp_sy pp_dy2 pp_dy1 sub pp_by1 pp_by2 sub div def /pp_tx pp_dx1 pp_sx pp_bx1 mul sub def /pp_ty pp_dy1 pp_sy pp_by2 mul sub def pp_tx pp_ty translate pp_sx pp_sy scale } if end &% %!PS-Adobe-3.0 EPSF-3.0 %%Creator: Adobe Illustrator(TM) 5.5 %%For: (Tom Mullis) (University of Colorado) %%Title: (broom figure.eps) %%CreationDate: (2/23/96) (8:56 AM) %%BoundingBox: 50 329 314 575 %%HiResBoundingBox: 50.6667 329.9589 313.9004 574.9367 %%DocumentProcessColors: Black %%DocumentFonts: Helvetica %%+ Symbol %%+ Times-Italic %%DocumentSuppliedResources: procset Adobe_level2_AI5 1.0 0 %%+ procset Adobe_screens_AI5 1.0 0 %%+ procset Adobe_typography_AI5 1.0 0 %%+ procset Adobe_IllustratorA_AI5 1.0 0 %AI5_FileFormat 1.2 %AI3_ColorUsage: Black&White %AI3_TemplateBox: 306 396 306 396 %AI3_TileBox: 30 31 582 761 %AI3_DocumentPreview: Macintosh_ColorPic %AI5_ArtSize: 612 792 %AI5_RulerUnits: 2 %AI5_ArtFlags: 1 0 0 1 0 0 0 1 0 %AI5_TargetResolution: 800 %AI5_NumLayers: 1 %AI5_OpenToView: 2 604 1.5 635 437 18 0 1 2 40 %AI5_OpenViewLayers: 7 %%EndComments %%BeginProlog %%BeginResource: procset Adobe_level2_AI5 1.0 0 %%Title: (Adobe Illustrator (R) Version 5.0 Level 2 Emulation) %%Version: 1.0 %%CreationDate: (04/10/93) () %%Copyright: ((C) 1987-1993 Adobe Systems Incorporated All Rights Reserved) userdict /Adobe_level2_AI5 21 dict dup begin put /packedarray where not { userdict begin /packedarray { array astore readonly } bind def /setpacking /pop load def /currentpacking false def end 0 } if pop userdict /defaultpacking currentpacking put true setpacking /initialize { Adobe_level2_AI5 begin } bind def /terminate { currentdict Adobe_level2_AI5 eq { end } if } bind def mark /setcustomcolor where not { /findcmykcustomcolor { 5 packedarray } bind def /setcustomcolor { exch aload pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } def } if /gt38? mark {version cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put userdict /level2? systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if put level2? not { /setcmykcolor where not { /setcmykcolor { exch .11 mul add exch .59 mul add exch .3 mul add 1 exch sub setgray } def } if /currentcmykcolor where not { /currentcmykcolor { 0 0 0 1 currentgray sub } def } if /setoverprint where not { /setoverprint /pop load def } if /selectfont where not { /selectfont { exch findfont exch dup type /arraytype eq { makefont } { scalefont } ifelse setfont } bind def } if /cshow where not { /cshow { [ 0 0 5 -1 roll aload pop ] cvx bind forall } bind def } if } if cleartomark /anyColor? { add add add 0 ne } bind def /testColor { gsave setcmykcolor currentcmykcolor grestore } bind def /testCMYKColorThrough { testColor anyColor? } bind def userdict /composite? level2? { gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore add add add 4 eq } { 1 0 0 0 testCMYKColorThrough 0 1 0 0 testCMYKColorThrough 0 0 1 0 testCMYKColorThrough 0 0 0 1 testCMYKColorThrough and and and } ifelse put composite? not { userdict begin gsave /cyan? 1 0 0 0 testCMYKColorThrough def /magenta? 0 1 0 0 testCMYKColorThrough def /yellow? 0 0 1 0 testCMYKColorThrough def /black? 0 0 0 1 testCMYKColorThrough def grestore /isCMYKSep? cyan? magenta? yellow? black? or or or def /customColor? isCMYKSep? not def end } if end defaultpacking setpacking %%EndResource %%BeginResource: procset Adobe_screens_AI5 1.1 0 %%Title: (Adobe Illustrator (R) Version 5.0 Custom Halftone Screens ProcSet) %%Version: 1.1 0 %%CreationDate: (03/24/93) () %%Copyright: ((C) 1987-1993 Adobe Systems Incorporated All Rights Reserved) userdict /defaultpacking currentpacking put true setpacking systemdict begin userdict /Adobe_screens_AI5 13 dict dup begin put /initialize { Adobe_screens_AI5 begin /screenid deviceDPI 600 gt composite? not or { -1 } { deviceDPI currentscreen pop pop dup dup 60 ge exch 150 le and deviceDPI 300 le and { pop 60 } if div 1.41421 div 0.5 add cvi } ifelse def 2 screenid eq { /customsize 16 def /customdata /customdata2 def setcustomscreen } if 3 screenid eq { /customsize 24 def /customdata /customdata3 def setcustomscreen } if 4 screenid eq { /customsize 16 def /customdata /customdata4 def setcustomscreen } if 5 screenid eq { /customsize 20 def /customdata /customdata5 def setcustomscreen } if 6 screenid eq { /customsize 24 def /customdata /customdata6 def setcustomscreen } if 7 screenid eq { /customsize 28 def /customdata /customdata7 def setcustomscreen } if 8 screenid eq { /customsize 16 def /customdata /customdata8 def setcustomscreen } if } def /terminate { currentdict Adobe_screens_AI5 eq { end } if } def /setcustomscreen { deviceDPI customsize div 0 { 1 add 2 div customsize mul cvi exch 1 add 2 div customsize mul cvi exch customsize mul add customdata load exch get 256 div } setscreen } def /customdata2 28 28 mul string def currentfile customdata2 readhexstring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00000000000000000000000000000000 pop pop /customdata3 28 28 mul string def currentfile customdata3 readhexstring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pop pop /customdata6 28 28 mul string def currentfile customdata6 readhexstring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pop pop /customdata7 28 28 mul string def currentfile customdata7 readhexstring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pop pop /customdata8 28 28 mul string def currentfile customdata8 readhexstring 050F2747B6D6EEF8FEF4DCBC4D2D1507111D375F9EC6E0E9EBE6CCA4653D1F13 2939556F8EA8C1D1D3C3AE9475573B2B4961717D808999B1B39B8B867F73634B B8A090827A6A5A42445C6C7C8492A2BAD8C8AA97785232222434546E8DACCADA F0E2CFA768401A0A0C1C365E9DC5E4F2FAF7DFBF50301802040E2646B5D5EDFC 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000 pop pop end end defaultpacking setpacking %%EndResource %%BeginResource: procset Adobe_typography_AI5 1.0 1 %%Title: (Typography Operators) %%Version: 1.0 %%CreationDate:(03/26/93) () %%Copyright: ((C) 1987-1993 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_typography_AI5 54 dict dup begin put /initialize { begin begin Adobe_typography_AI5 begin Adobe_typography_AI5 { dup xcheck { bind } if pop pop } forall end end end Adobe_typography_AI5 begin } def /terminate { currentdict Adobe_typography_AI5 eq { end } if } def /modifyEncoding { /_tempEncode exch ddef /_pntr 0 ddef { counttomark -1 roll dup type dup /marktype eq { pop pop exit } { /nametype eq { _tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll put } { /_pntr exch ddef } ifelse } ifelse } loop _tempEncode } def /TE { StandardEncoding 256 array copy modifyEncoding /_nativeEncoding exch def } def % /TZ { dup type /arraytype eq { /_wv exch def } { /_wv 0 def } ifelse /_useNativeEncoding exch def pop pop findfont _wv type /arraytype eq { _wv makeblendedfont } if dup length 2 add dict begin mark exch { 1 index /FID ne { def } if cleartomark mark } forall pop /FontName exch def counttomark 0 eq { 1 _useNativeEncoding eq { /Encoding _nativeEncoding def } if cleartomark } { /Encoding load 256 array copy modifyEncoding /Encoding exch def } ifelse FontName currentdict end definefont pop } def /tr { _ax _ay 3 2 roll } def /trj { _cx _cy _sp _ax _ay 6 5 roll } def /a0 { /Tx { dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss } ddef /Tj { dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss } ddef } def /a1 { /Tx { dup currentpoint 4 2 roll gsave dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll gsave dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss grestore 3 1 roll moveto tr jsp } ddef } def /e0 { /Tx { tr _psf } ddef /Tj { trj _pjsf } ddef } def /e1 { /Tx { dup currentpoint 4 2 roll gsave tr _psf grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll gsave trj _pjsf grestore 3 1 roll moveto tr jsp } ddef } def /i0 { /Tx { tr sp } ddef /Tj { trj jsp } ddef } def /i1 { W N } def /o0 { /Tx { tr sw rmoveto } ddef /Tj { trj swj rmoveto } ddef } def /r0 { /Tx { tr _ctm _pss } ddef /Tj { trj _ctm _pjss } ddef } def /r1 { /Tx { dup currentpoint 4 2 roll currentpoint gsave newpath moveto tr _ctm _pss grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll currentpoint gsave newpath moveto trj _ctm _pjss grestore 3 1 roll moveto tr jsp } ddef } def /To { pop _ctm currentmatrix pop } def /TO { iTe _ctm setmatrix newpath } def /Tp { pop _tm astore pop _ctm setmatrix _tDict begin /W { } def /h { } def } def /TP { end iTm 0 0 moveto } def /Tr { _render 3 le { currentpoint newpath moveto } if dup 8 eq { pop 0 } { dup 9 eq { pop 1 } if } ifelse dup /_render exch ddef _renderStart exch get load exec } def /iTm { _ctm setmatrix _tm concat 0 _rise translate _hs 1 scale } def /Tm { _tm astore pop iTm 0 0 moveto } def /Td { _mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto } def /iTe { _render -1 eq { } { _renderEnd _render get dup null ne { load exec } { pop } ifelse } ifelse /_render -1 ddef } def /Ta { pop } def /Tf { dup 1000 div /_fScl exch ddef % selectfont } def /Tl { pop 0 exch _leading astore pop } def /Tt { pop } def /TW { 3 npop } def /Tw { /_cx exch ddef } def /TC { 3 npop } def /Tc { /_ax exch ddef } def /Ts { /_rise exch ddef currentpoint iTm moveto } def /Ti { 3 npop } def /Tz { 100 div /_hs exch ddef iTm } def /TA { pop } def /Tq { pop } def /Th { pop pop pop pop pop } def /TX { pop } def /Tk { exch pop _fScl mul neg 0 rmoveto } def /TK { 2 npop } def /T* { _leading aload pop neg Td } def /T*- { _leading aload pop Td } def /T- { _hyphen Tx } def /T+ { } def /TR { _ctm currentmatrix pop _tm astore pop iTm 0 0 moveto } def /TS { currentfont 3 1 roll /_Symbol_ _fScl 1000 mul selectfont 0 eq { Tx } { Tj } ifelse setfont } def /Xb { pop pop } def /Tb /Xb load def /Xe { pop pop pop pop } def /Te /Xe load def /XB { } def /TB /XB load def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_IllustratorA_AI5 1.1 0 %%Title: (Adobe Illustrator (R) Version 5.0 Abbreviated Prolog) %%Version: 1.1 %%CreationDate: (3/7/1994) () %%Copyright: ((C) 1987-1994 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_IllustratorA_AI5_vars 70 dict dup begin put /_lp /none def /_pf { } def /_ps { } def /_psf { } def /_pss { } def /_pjsf { } def /_pjss { } def /_pola 0 def /_doClip 0 def /cf currentflat def /_tm matrix def /_renderStart [ /e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0 ] def /_renderEnd [ null null null null /i1 /i1 /i1 /i1 ] def /_render -1 def /_rise 0 def /_ax 0 def /_ay 0 def /_cx 0 def /_cy 0 def /_leading [ 0 0 ] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fScl 0 def /_cnt 0 def /_hs 1 def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /_tDict 2 dict def /_wv 0 def /Tx { } def /Tj { } def /CRender { } def /_AI3_savepage { } def /_gf null def /_cf 4 array def /_if null def /_of false def /_fc { } def /_gs null def /_cs 4 array def /_is null def /_os false def /_sc { } def /discardSave null def /buffer 256 string def /beginString null def /endString null def /endStringLength null def /layerCnt 1 def /layerCount 1 def /perCent (%) 0 get def /perCentSeen? false def /newBuff null def /newBuffButFirst null def /newBuffLast null def /clipForward? false def end userdict /Adobe_IllustratorA_AI5 74 dict dup begin put /initialize { Adobe_IllustratorA_AI5 dup begin Adobe_IllustratorA_AI5_vars begin discardDict { bind pop pop } forall dup /nc get begin { dup xcheck 1 index type /operatortype ne and { bind } if pop pop } forall end newpath } def /terminate { end end } def /_ null def /ddef { Adobe_IllustratorA_AI5_vars 3 1 roll put } def /xput { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop { { pop } repeat } def /sw { dup length exch stringwidth exch 5 -1 roll 3 index mul add 4 1 roll 3 1 roll mul add } def /swj { dup 4 1 roll dup length exch stringwidth exch 5 -1 roll 3 index mul add 4 1 roll 3 1 roll mul add 6 2 roll /_cnt 0 ddef { 1 index eq { /_cnt _cnt 1 add ddef } if } forall pop exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop } def /ss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put pop gsave false charpath currentpoint 4 index setmatrix stroke grestore moveto 2 copy rmoveto } exch cshow 3 npop } def /jss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put gsave _sp eq { exch 6 index 6 index 6 index 5 -1 roll widthshow currentpoint } { false charpath currentpoint 4 index setmatrix stroke } ifelse grestore moveto 2 copy rmoveto } exch cshow 6 npop } def /sp { { 2 npop (0) exch 2 copy 0 exch put pop false charpath 2 copy rmoveto } exch cshow 2 npop } def /jsp { { 2 npop (0) exch 2 copy 0 exch put _sp eq { exch 5 index 5 index 5 index 5 -1 roll widthshow } { false charpath } ifelse 2 copy rmoveto } exch cshow 5 npop&% } def /pl { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c { curveto } def /C /c load def /v { currentpoint 6 2 roll curveto } def /V /v load def /y { 2 copy curveto } def /Y /y load def /l { lineto } def /L /l load def /m { moveto } def } { /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def } ifelse /d { setdash } def /cf { } def /i { dup 0 eq { pop cf } if setflat } def /j { setlinejoin } def /J { setlinecap } def /M { setmiterlimit } def /w { setlinewidth } def /H { } def /h { closepath } def /N { _pola 0 eq { _doClip 1 eq { clip /_doClip 0 ddef } if newpath } { /CRender { N } ddef } ifelse } def /n { N } def /F { _pola 0 eq { _doClip 1 eq { gsave _pf grestore clip newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf } ifelse } { /CRender { F } ddef } ifelse } def /f { closepath F } def /S { _pola 0 eq { _doClip 1 eq { gsave _ps grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps } ifelse } { /CRender { S } ddef } ifelse } def /s { closepath S } def /B { _pola 0 eq { _doClip 1 eq gsave F grestore { gsave S grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { S } ifelse } { /CRender { B } ddef } ifelse } def /b { closepath B } def /W { /_doClip 1 ddef } def /* { count 0 ne { dup type /stringtype eq { pop } if } if newpath } def /u { } def /U { } def /q { _pola 0 eq { gsave } if } def /Q { _pola 0 eq { grestore } if } def /*u { _pola 1 add /_pola exch ddef } def /*U { _pola 1 sub /_pola exch ddef _pola 0 eq { CRender } if } def /D { pop } def /*w { } def /*W { } def /` { /_i save ddef clipForward? { nulldevice } if 6 1 roll 4 npop concat pop userdict begin /showpage { } def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash /setstrokeadjust where {pop false setstrokeadjust} if newpath 0 setgray false setoverprint } def /~ { end _i restore } def /O { 0 ne /_of exch ddef /_lp /none ddef } def /R { 0 ne /_os exch ddef /_lp /none ddef } def /g { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /G { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /K { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /X { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /A { pop } def /annotatepage { userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse } def /discard { save /discardSave exch store discardDict begin /endString exch store gt38? { 2 add } if load stopped pop end discardSave restore } bind def userdict /discardDict 7 dict dup begin put /pre38Initialize { /endStringLength endString length store /newBuff buffer 0 endStringLength getinterval store /newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store /newBuffLast newBuff endStringLength 1 sub 1 getinterval store } def /shiftBuffer { newBuff 0 newBuffButFirst putinterval newBuffLast 0 currentfile read not { stop } if put } def 0 { pre38Initialize mark currentfile newBuff readstring exch pop { { newBuff endString eq { cleartomark stop } if shiftBuffer } loop } { stop } ifelse } def 1 { pre38Initialize /beginString exch store mark currentfile newBuff readstring exch pop { { newBuff beginString eq { /layerCount dup load 1 add store } { newBuff endString eq { /layerCount dup load 1 sub store layerCount 0 eq { cleartomark stop } if } if } ifelse shiftBuffer } loop } { stop } ifelse } def 2 { mark { currentfile buffer readline not { stop } if endString eq { cleartomark stop } if } loop } def 3 { /beginString exch store /layerCnt 1 store mark { currentfile buffer readline not { stop } if dup beginString eq { pop /layerCnt dup load 1 add store } { endString eq { layerCnt 1 eq { cleartomark stop } { /layerCnt dup load 1 sub store } ifelse } if } ifelse } loop } def end userdict /clipRenderOff 15 dict dup begin put { /n /N /s /S /f /F /b /B } { { _doClip 1 eq { /_doClip 0 ddef clip } if newpath } def } forall /Tr /pop load def /Bb {} def /BB /pop load def /Bg {12 npop} def /Bm {6 npop} def /Bc /Bm load def /Bh {4 npop} def end /Lb { 4 npop 6 1 roll pop 4 1 roll pop pop pop 0 eq { 0 eq { (%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard } { /clipForward? true def /Tx /pop load def /Tj /pop load def currentdict end clipRenderOff begin begin } ifelse } { 0 eq { save /discardSave exch store } if } ifelse } bind def /LB { discardSave dup null ne { restore } { pop clipForward? { currentdict end end begin /clipForward? false ddef } if } ifelse } bind def /Pb { pop pop 0 (%AI5_EndPalette) discard } bind def /Np { 0 (%AI5_End_NonPrinting--) discard } bind def /Ln /pop load def /Ap /pop load def /Ar { 72 exch div 0 dtransform dup mul exch dup mul add sqrt dup 1 lt { pop 1 } if setflat } def /Mb { q } def /Md { } def /MB { Q } def /nc 3 dict def nc begin /setgray { pop } bind def /setcmykcolor { 4 npop } bind def /setcustomcolor { 2 npop } bind def currentdict readonly pop end currentdict readonly pop end setpacking %%EndResource %%EndProlog %%BeginSetup %%IncludeFont: Helvetica %%IncludeFont: Symbol %%IncludeFont: Times-Italic Adobe_level2_AI5 /initialize get exec Adobe_screens_AI5 /initialize get exec Adobe_IllustratorA_AI5_vars Adobe_IllustratorA_AI5 Adobe_typography_AI5 /initialize get exec Adobe_IllustratorA_AI5 /initialize get exec [ 39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/dagger&% dbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex /Idieresis/Igrave/Oacute/Ocircumflex/.notdef/Ograve/Uacute/Ucircumflex /Ugrave/dotlessi/circumflex/tilde/macron/breve/dotaccent/ring/cedilla /hungarumlaut/ogonek/caron TE %AI3_BeginEncoding: _Helvetica Helvetica [/_Helvetica/Helvetica 0 0 1 TZ %AI3_EndEncoding TrueType %AI3_BeginEncoding: _Symbol Symbol [/_Symbol/Symbol 0 0 0 TZ %AI3_EndEncoding TrueType %AI3_BeginEncoding: _Times-Italic Times-Italic [/_Times-Italic/Times-Italic 0 0 1 TZ %AI3_EndEncoding AdobeType %AI5_Begin_NonPrinting Np %AI3_BeginPattern: (Blue Dots-Transparent) (Blue Dots-Transparent) 3.88 3.88 32.68 32.68 [ %AI3_Tile (0 O 0 R 1 0.7 0 0 k 1 0.7 0 0 K) @ ( 800 Ar 0 J 0 j 0.5 w 4 M []0 d %AI3_Note: 0 D 32.68 1 m 34.27 1 35.56 2.29 35.56 3.88 c 35.56 5.471 34.27 6.76 32.68 6.76 c 31.089 6.76 29.8 5.471 29.8 3.88 c 29.8 2.29 31.089 1 32.68 1 c f 18.28 1 m 19.87 1 21.16 2.29 21.16 3.88 c 21.16 5.471 19.87 6.76 18.28 6.76 c 16.689 6.76 15.4 5.471 15.4 3.88 c 15.4 2.29 16.689 1 18.28 1 c f 3.88 1 m 5.47 1 6.76 2.29 6.76 3.88 c 6.76 5.471 5.47 6.76 3.88 6.76 c 2.29 6.76 1 5.471 1 3.88 c 1 2.29 2.29 1 3.88 1 c f 32.68 15.4 m 34.27 15.4 35.56 16.69 35.56 18.28 c 35.56 19.871 34.27 21.16 32.68 21.16 c 31.089 21.16 29.8 19.871 29.8 18.28 c 29.8 16.69 31.089 15.4 32.68 15.4 c f 18.28 15.4 m 19.87 15.4 21.16 16.69 21.16 18.28 c 21.16 19.871 19.87 21.16 18.28 21.16 c 16.689 21.16 15.4 19.871 15.4 18.28 c 15.4 16.69 16.689 15.4 18.28 15.4 c f 3.88 15.4 m 5.47 15.4 6.76 16.69 6.76 18.28 c 6.76 19.871 5.47 21.16 3.88 21.16 c 2.29 21.16 1 19.871 1 18.28 c 1 16.69 2.29 15.4 3.88 15.4 c f 32.68 29.8 m 34.27 29.8 35.56 31.09 35.56 32.68 c 35.56 34.271 34.27 35.56 32.68 35.56 c 31.089 35.56 29.8 34.271 29.8 32.68 c 29.8 31.09 31.089 29.8 32.68 29.8 c f 18.28 29.8 m 19.87 29.8 21.16 31.09 21.16 32.68 c 21.16 34.271 19.87 35.56 18.28 35.56 c 16.689 35.56 15.4 34.271 15.4 32.68 c 15.4 31.09 16.689 29.8 18.28 29.8 c f 3.88 29.8 m 5.47 29.8 6.76 31.09 6.76 32.68 c 6.76 34.271 5.47 35.56 3.88 35.56 c 2.29 35.56 1 34.271 1 32.68 c 1 31.09 2.29 29.8 3.88 29.8 c f 11.08 8.2 m 12.67 8.2 13.96 9.49 13.96 11.08 c 13.96 12.671 12.67 13.96 11.08 13.96 c 9.489 13.96 8.2 12.671 8.2 11.08 c 8.2 9.49 9.489 8.2 11.08 8.2 c f 25.48 8.2 m 27.07 8.2 28.36 9.49 28.36 11.08 c 28.36 12.671 27.07 13.96 25.48 13.96 c 23.889 13.96 22.6 12.671 22.6 11.08 c 22.6 9.49 23.889 8.2 25.48 8.2 c f 11.08 22.6 m 12.67 22.6 13.96 23.89 13.96 25.48 c 13.96 27.071 12.67 28.36 11.08 28.36 c 9.489 28.36 8.2 27.071 8.2 25.48 c 8.2 23.89 9.489 22.6 11.08 22.6 c f 25.48 22.6 m 27.07 22.6 28.36 23.89 28.36 25.48 c 28.36 27.071 27.07 28.36 25.48 28.36 c 23.889 28.36 22.6 27.071 22.6 25.48 c 22.6 23.89 23.889 22.6 25.48 22.6 c f ) & ] E %AI3_EndPattern %AI3_BeginPattern: (Yellow Stripe) (Yellow Stripe) 8.4499 4.6 80.4499 76.6 [ %AI3_Tile (0 O 0 R 0 0.4 1 0 k 0 0.4 1 0 K) @ ( 800 Ar 0 J 0 j 3.6 w 4 M []0 d %AI3_Note: 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5A5A5958585756565554545352525150504F4E4E4D4C4C4B4A4A4948484746464544444342424140 403F3E3E3D3C3C3B3A3A3938383736363534343332323130302F2E2E2D2C2C2B2A2A292828272626 25242423222121201F1F1E1D1D1C1B1B1A1919181717161515141313121111100F0F0E0D0D0C0B0B 0A090908070706050504030302010100 > 0 1 %_Br [ 0 0.08 0.67 0 1 50 14 %_Bs 1 1 0 0 1 50 100 %_Bs BD %AI5_EndGradient %AI5_End_NonPrinting-- %AI5_BeginPalette 0 &%CA 6 Pb Pn Pc 1 g Pc 0 g Pc 0 0 0 0 k Pc 0.75 g Pc 0.5 g Pc 0.25 g Pc 0 g Pc Bb 2 (Black & White) -4014 4716 0 0 1 0 0 1 0 0 Bg 0 BB Pc 0.25 0 0 0 k Pc 0.5 0 0 0 k Pc 0.75 0 0 0 k Pc 1 0 0 0 k Pc 0.25 0.25 0 0 k Pc 0.5 0.5 0 0 k Pc 0.75 0.75 0 0 k Pc 1 1 0 0 k Pc Bb 2 (Red & Yellow) -4014 4716 0 0 1 0 0 1 0 0 Bg 0 BB Pc 0 0.25 0 0 k Pc 0 0.5 0 0 k Pc 0 0.75 0 0 k Pc 0 1 0 0 k Pc 0 0.25 0.25 0 k Pc 0 0.5 0.5 0 k Pc 0 0.75 0.75 0 k Pc 0 1 1 0 k Pc Bb 0 0 0 0 Bh 2 (Yellow & Blue Radial) -4014 4716 0 0 1 0 0 1 0 0 Bg 0 BB Pc 0 0 0.25 0 k Pc 0 0 0.5 0 k Pc 0 0 0.75 0 k Pc 0 0 1 0 k Pc 0.25 0 0.25 0 k Pc 0.5 0 0.5 0 k Pc 0.75 0 0.75 0 k Pc 1 0 1 0 k Pc (Yellow Stripe) 0 0 1 1 0 0 0 0 0 [1 0 0 1 0 0] p Pc 0.25 0.125 0 0 k Pc 0.5 0.25 0 0 k Pc 0.75 0.375 0 0 k Pc 1 0.5 0 0 k Pc 0.125 0.25 0 0 k Pc 0.25 0.5 0 0 k Pc 0.375 0.75 0 0 k Pc 0.5 1 0 0 k Pc 0 0 0 0 k Pc 0 0.25 0.125 0 k Pc 0 0.5 0.25 0 k Pc 0 0.75 0.375 0 k Pc 0 1 0.5 0 k Pc 0 0.125 0.25 0 k Pc 0 0.25 0.5 0 k Pc 0 0.375 0.75 0 k Pc 0 0.5 1 0 k Pc 0 0 0 0 k Pc 0.125 0 0.25 0 k Pc 0.25 0 0.5 0 k Pc 0.375 0 0.75 0 k Pc 0.5 0 1 0 k Pc 0.25 0 0.125 0 k Pc 0.5 0 0.25 0 k Pc 0.75 0 0.375 0 k Pc 1 0 0.5 0 k Pc 0 0 0 0 k Pc 0.25 0.125 0.125 0 k Pc 0.5 0.25 0.25 0 k Pc 0.75 0.375 0.375 0 k Pc 1 0.5 0.5 0 k Pc 0.25 0.25 0.125 0 k Pc 0.5 0.5 0.25 0 k Pc 0.75 0.75 0.375 0 k Pc 1 1 0.5 0 k Pc 0 0 0 0 k Pc 0.125 0.25 0.125 0 k Pc 0.25 0.5 0.25 0 k Pc 0.375 0.75 0.375 0 k Pc 0.5 1 0.5 0 k Pc 0.125 0.25 0.25 0 k Pc 0.25 0.5 0.5 0 k Pc 0.375 0.75 0.75 0 k Pc 0.5 1 1 0 k Pc 0 0 0 0 k Pc 0.125 0.125 0.25 0 k Pc 0.25 0.25 0.5 0 k Pc 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354.6862 165.5147 350 c 165.5147 345.3138 169.3138 341.5147 174 341.5147 c f 218 341.5147 m 222.6862 341.5147 226.4853 345.3138 226.4853 350 c 226.4853 354.6862 222.6862 358.4853 218 358.4853 c 213.3138 358.4853 209.5147 354.6862 209.5147 350 c 209.5147 345.3138 213.3138 341.5147 218 341.5147 c f 0.75 g 159.4998 381.1591 m 159.4998 381.1591 L 159.4998 381.1591 L 159.4998 381.1591 L 159.4998 381.1591 L 159.4998 381.1591 L 159.4998 381.1591 L 159.4998 381.1591 L 159.4998 381.1591 L f 0 Ap 0 g 198 396.6667 m 198 435.3333 l F 0 To 1 0 0 1 71.3333 376 0 Tp TP 0 Tr (Control Force) Tx (\r) TX TO LB %AI5_EndLayer-- %%PageTrailer gsave annotatepage grestore showpage %%Trailer Adobe_IllustratorA_AI5 /terminate get exec Adobe_typography_AI5 /terminate get exec Adobe_screens_AI5 /terminate get exec Adobe_level2_AI5 /terminate get exec %%EOF & --$C (  f3f3̙f3fffff3ff333f3333f3f3f3̙f3fffff3ff333f3333f3f3̙̙̙f̙3̙̙̙f3fffff3ff333f3333f3fffff3fffffff3fff̙ffff3fffffffffff3ffff3f3f3ff3f33f3ffffff3ff333f3333333f33333̙33f3333f3f3f3ff33f3f3333333f3333333333f3333f3f3̙f3fffff3ff333f3333f3|||vvvoooiiibbb[[[UUUNNNHHHAAA;;;444---'''  ,,,,,,,,,,,,z(^x$\v ZuYuYtXmKPmKPmKPmKPmKPmKPmKPmKPmKPmKPmKPmKPmKP0/KP/.KP*.KP*-K+1K*-K+-K0-K1.KmK )mK (mKPmKPmKPmKPmKPKPKP KPKPKPKP  Sk  Nkkklllm m prvvwsssssssss s s s s s s s s ;2(1) 1)0.0)0) 0~)0~(1}s}s|s{s{sz7;z7;y%y$ x$ w$w$ v%v2)uN'utssrrqqpoonnmllkkjjihhggffeddccbb ha g` g` g_ g_g^h]]\\)|[-{[ bZ bYbY bXbX bW bWoVU U  TYTYSYRYRYQZQ,gPgPONNMMLLKJJIIHHGFC@ > > = ==<<|<|=|=|> |> |@    |5   ,+*+8876 !  N#  N% N' M)  N* N.! "N-!  ! N,,+8+;*X)Y) Y(Y;Y;XO!5YO!5Y VC(h2  f3f3̙f3fffff3ff333f3333f3f3f3̙f3fffff3ff333f3333f3f3̙̙̙f̙3̙̙̙f3fffff3ff333f3333f3fffff3fffffff3fff̙ffff3fffffffffff3ffff3f3f3ff3f33f3ffffff3ff333f3333333f33333̙33f3333f3f3f3ff33f3f3333333f3333333333f3333f3f3̙f3fffff3ff333f3333f3|||vvvoooiiibbb[[[UUUNNNHHHAAA;;;444---'''  ,,,,,,,,,,,,z(^x#[v ZuYuYtXmPmPmOmPmPmPmPmPmOm  PmPmPmP0/P/.O*.P*-+1*-+-0- 1.m )m (mPmPmOmPmPPP POPP  Sk  Nkkklllmmpruvwsssssssss s s s s s s s s ;2(1) 1)0.0)0) 0~)0~(1}s}s|s{s{sz7;z7;y%y$ x$ w$w$ v%v2)uN'utssrrqqpoonnmllkkjjihhggffeddccbb ha g` g` g_ g_g^h]]\\(|[-{[ bZ bYbY bXbX bW bWoVU U  TYTYSYRYRYQZQ,gPgPONNMMLLKJJIIHHGFC@> > = ==<<|<|=|=|> |> |@    |5   ,+*+8876 !  N#  N% N' M)  N* N.! "N-!  ! N,,+8+;*X)Y) Y(Y;Y;XO!5YO!5Y  & &&&%!%MSEPS Trailer pp_save restore '  #9pse currentpoint /picTop exch def /picLeft exch def psb "=pse currentpoint /picBottom exch def /picRight exch def psb [ 50 329 314 575] 1 dict begin /s exch def picLeft picTop translate picRight picLeft sub s 2 get s 0 get sub div picBottom picTop sub s 1 get s 3 get sub div scale s 0 get neg s 3 get neg translate end /showpage {} def /copypage {} def %!PS-Adobe-3.0 EPSF-3.0 %%Creator: Adobe Illustrator(TM) 5.5 %%For: (Tom Mullis) (University of Colorado) %%Title: (broom figure.eps) %%CreationDate: (2/23/96) (8:56 AM) %%BoundingBox: 50 329 314 575 %%HiResBoundingBox: 50.6667 329.9589 313.9004 574.9367 %%DocumentProcessColors: Black %%DocumentFonts: Helvetica %%+ Symbol %%+ Times-Italic %%DocumentSuppliedResources: procset Adobe_level2_AI5 1.0 0 %%+ procset Adobe_screens_AI5 1.0 0 %%+ procset Adobe_typography_AI5 1.0 0 %%+ procset Adobe_IllustratorA_AI5 1.0 0 %AI5_FileFormat 1.2 %AI3_ColorUsage: Black&White %AI3_TemplateBox: 306 396 306 396 %AI3_TileBox: 30 31 582 761 %AI3_DocumentPreview: Macintosh_ColorPic %AI5_ArtSize: 612 792 %AI5_RulerUnits: 2 %AI5_ArtFlags: 1 0 0 1 0 0 0 1 0 %AI5_TargetResolution: 800 %AI5_NumLayers: 1 %AI5_OpenToView: 2 604 1.5 635 437 18 0 1 2 40 %AI5_OpenViewLayers: 7 %%EndComments %%BeginProlog %%BeginResource: procset Adobe_level2_AI5 1.0 0 %%Title: (Adobe Illustrator (R) Version 5.0 Level 2 Emulation) %%Version: 1.0 %%CreationDate: (04/10/93) () %%Copyright: ((C) 1987-1993 Adobe Systems Incorporated All Rights Reserved) userdict /Adobe_level2_AI5 21 dict dup begin put /packedarray where not { userdict begin /packedarray { array astore readonly } bind def /setpacking /pop load def /currentpacking false def end 0 } if pop userdict /defaultpacking currentpacking put true setpacking /initialize { Adobe_level2_AI5 begin } bind def /terminate { currentdict Adobe_level2_AI5 eq { end } if } bind def mark /setcustomcolor where not { /findcmykcustomcolor { 5 packedarray } bind def /setcustomcolor { exch aload pop pop 4 { 4 index mul 4 1 roll } repeat 5 -1 roll pop setcmykcolor } def } if /gt38? mark {version cvx exec} stopped {cleartomark true} {38 gt exch pop} ifelse def userdict /deviceDPI 72 0 matrix defaultmatrix dtransform dup mul exch dup mul add sqrt put userdict /level2? systemdict /languagelevel known dup { pop systemdict /languagelevel get 2 ge } if put level2? not { /setcmykcolor where not { /setcmykcolor { exch .11 mul add exch .59 mul add exch .3 mul add 1 exch sub setgray } def } if /currentcmykcolor where not { /currentcmykcolor { 0 0 0 1 currentgray sub } def } if /setoverprint where not { /setoverprint /pop load def } if /selectfont where not { /selectfont { exch findfont exch dup type /arraytype eq { makefont } { scalefont } ifelse setfont } bind def } if /cshow where not { /cshow { [ 0 0 5 -1 roll aload pop ] cvx bind forall } bind def } if } if cleartomark /anyColor? { add add add 0 ne } bind def /testColor { gsave setcmykcolor currentcmykcolor grestore } bind def /testCMYKColorThrough { testColor anyColor? } bind def userdict /composite? level2? { gsave 1 1 1 1 setcmykcolor currentcmykcolor grestore add add add 4 eq } { 1 0 0 0 testCMYKColorThrough 0 1 0 0 testCMYKColorThrough 0 0 1 0 testCMYKColorThrough 0 0 0 1 testCMYKColorThrough and and and } ifelse put composite? not { userdict begin gsave /cyan? 1 0 0 0 testCMYKColorThrough def /magenta? 0 1 0 0 testCMYKColorThrough def /yellow? 0 0 1 0 testCMYKColorThrough def /black? 0 0 0 1 testCMYKColorThrough def grestore /isCMYKSep? cyan? magenta? yellow? black? or or or def /customColor? isCMYKSep? not def end } if end defaultpacking setpacking %%EndResource %%BeginResource: procset Adobe_screens_AI5 1.1 0 %%Title: (Adobe Illustrator (R) Version 5.0 Custom Halftone Screens ProcSet) %%Version: 1.1 0 %%CreationDate: (03/24/93) () %%Copyright: ((C) 1987-1993 Adobe Systems Incorporated All Rights Reserved) userdict /defaultpacking currentpacking put true setpacking systemdict begin userdict /Adobe_screens_AI5 13 dict dup begin put /initialize { Adobe_screens_AI5 begin /screenid deviceDPI 600 gt composite? not or { -1 } { deviceDPI currentscreen pop pop dup dup 60 ge exch 150 le and deviceDPI 300 le and { pop 60 } if div 1.41421 div 0.5 add cvi } ifelse def 2 screenid eq { /customsize 16 def /customdata /customdata2 def setcustomscreen } if 3 screenid eq { /customsize 24 def /customdata /customdata3 def setcustomscreen } if 4 screenid eq { /customsize 16 def /customdata /customdata4 def setcustomscreen } if 5 screenid eq { /customsize 20 def /customdata /customdata5 def setcustomscreen } if 6 screenid eq { /customsize 24 def /customdata /customdata6 def setcustomscreen } if 7 screenid eq { /customsize 28 def /customdata /customdata7 def setcustomscreen } if 8 screenid eq { /customsize 16 def /customdata /customdata8 def setcustomscreen } if } def /terminate { currentdict Adobe_screens_AI5 eq { end } if } def /setcustomscreen { deviceDPI customsize div 0 { 1 add 2 div customsize mul cvi exch 1 add 2 div customsize mul cvi exch customsize mul add customdata load exch get 256 div } setscreen } def /customdata2 28 28 mul string def currentfile customdata2 readhexstring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pop pop /customdata3 28 28 mul string def currentfile customdata3 readhexstring 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000 pop pop end end defaultpacking setpacking %%EndResource %%BeginResource: procset Adobe_typography_AI5 1.0 1 %%Title: (Typography Operators) %%Version: 1.0 %%CreationDate:(03/26/93) () %%Copyright: ((C) 1987-1993 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_typography_AI5 54 dict dup begin put /initialize { begin begin Adobe_typography_AI5 begin Adobe_typography_AI5 { dup xcheck { bind } if pop pop } forall end end end Adobe_typography_AI5 begin } def /terminate { currentdict Adobe_typography_AI5 eq { end } if } def /modifyEncoding { /_tempEncode exch ddef /_pntr 0 ddef { counttomark -1 roll dup type dup /marktype eq { pop pop exit } { /nametype eq { _tempEncode /_pntr dup load dup 3 1 roll 1 add ddef 3 -1 roll put } { /_pntr exch ddef } ifelse } ifelse } loop _tempEncode } def /TE { StandardEncoding 256 array copy modifyEncoding /_nativeEncoding exch def } def % /TZ { dup type /arraytype eq { /_wv exch def } { /_wv 0 def } ifelse /_useNativeEncoding exch def pop pop findfont _wv type /arraytype eq { _wv makeblendedfont } if dup length 2 add dict begin mark exch { 1 index /FID ne { def } if cleartomark mark } forall pop /FontName exch def counttomark 0 eq { 1 _useNativeEncoding eq { /Encoding _nativeEncoding def } if cleartomark } { /Encoding load 256 array copy modifyEncoding /Encoding exch def } ifelse FontName currentdict end definefont pop } def /tr { _ax _ay 3 2 roll } def /trj { _cx _cy _sp _ax _ay 6 5 roll } def /a0 { /Tx { dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss } ddef /Tj { dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss } ddef } def /a1 { /Tx { dup currentpoint 4 2 roll gsave dup currentpoint 3 2 roll tr _psf newpath moveto tr _ctm _pss grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll gsave dup currentpoint 3 2 roll trj _pjsf newpath moveto trj _ctm _pjss grestore 3 1 roll moveto tr jsp } ddef } def /e0 { /Tx { tr _psf } ddef /Tj { trj _pjsf } ddef } def /e1 { /Tx { dup currentpoint 4 2 roll gsave tr _psf grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll gsave trj _pjsf grestore 3 1 roll moveto tr jsp } ddef } def /i0 { /Tx { tr sp } ddef /Tj { trj jsp } ddef } def /i1 { W N } def /o0 { /Tx { tr sw rmoveto } ddef /Tj { trj swj rmoveto } ddef } def /r0 { /Tx { tr _ctm _pss } ddef /Tj { trj _ctm _pjss } ddef } def /r1 { /Tx { dup currentpoint 4 2 roll currentpoint gsave newpath moveto tr _ctm _pss grestore 3 1 roll moveto tr sp } ddef /Tj { dup currentpoint 4 2 roll currentpoint gsave newpath moveto trj _ctm _pjss grestore 3 1 roll moveto tr jsp } ddef } def /To { pop _ctm currentmatrix pop } def /TO { iTe _ctm setmatrix newpath } def /Tp { pop _tm astore pop _ctm setmatrix _tDict begin /W { } def /h { } def } def /TP { end iTm 0 0 moveto } def /Tr { _render 3 le { currentpoint newpath moveto } if dup 8 eq { pop 0 } { dup 9 eq { pop 1 } if } ifelse dup /_render exch ddef _renderStart exch get load exec } def /iTm { _ctm setmatrix _tm concat 0 _rise translate _hs 1 scale } def /Tm { _tm astore pop iTm 0 0 moveto } def /Td { _mtx translate _tm _tm concatmatrix pop iTm 0 0 moveto } def /iTe { _render -1 eq { } { _renderEnd _render get dup null ne { load exec } { pop } ifelse } ifelse /_render -1 ddef } def /Ta { pop } def /Tf { dup 1000 div /_fScl exch ddef % selectfont } def /Tl { pop 0 exch _leading astore pop } def /Tt { pop } def /TW { 3 npop } def /Tw { /_cx exch ddef } def /TC { 3 npop } def /Tc { /_ax exch ddef } def /Ts { /_rise exch ddef currentpoint iTm moveto } def /Ti { 3 npop } def /Tz { 100 div /_hs exch ddef iTm } def /TA { pop } def /Tq { pop } def /Th { pop pop pop pop pop } def /TX { pop } def /Tk { exch pop _fScl mul neg 0 rmoveto } def /TK { 2 npop } def /T* { _leading aload pop neg Td } def /T*- { _leading aload pop Td } def /T- { _hyphen Tx } def /T+ { } def /TR { _ctm currentmatrix pop _tm astore pop iTm 0 0 moveto } def /TS { currentfont 3 1 roll /_Symbol_ _fScl 1000 mul selectfont 0 eq { Tx } { Tj } ifelse setfont } def /Xb { pop pop } def /Tb /Xb load def /Xe { pop pop pop pop } def /Te /Xe load def /XB { } def /TB /XB load def currentdict readonly pop end setpacking %%EndResource %%BeginResource: procset Adobe_IllustratorA_AI5 1.1 0 %%Title: (Adobe Illustrator (R) Version 5.0 Abbreviated Prolog) %%Version: 1.1 %%CreationDate: (3/7/1994) () %%Copyright: ((C) 1987-1994 Adobe Systems Incorporated All Rights Reserved) currentpacking true setpacking userdict /Adobe_IllustratorA_AI5_vars 70 dict dup begin put /_lp /none def /_pf { } def /_ps { } def /_psf { } def /_pss { } def /_pjsf { } def /_pjss { } def /_pola 0 def /_doClip 0 def /cf currentflat def /_tm matrix def /_renderStart [ /e0 /r0 /a0 /o0 /e1 /r1 /a1 /i0 ] def /_renderEnd [ null null null null /i1 /i1 /i1 /i1 ] def /_render -1 def /_rise 0 def /_ax 0 def /_ay 0 def /_cx 0 def /_cy 0 def /_leading [ 0 0 ] def /_ctm matrix def /_mtx matrix def /_sp 16#020 def /_hyphen (-) def /_fScl 0 def /_cnt 0 def /_hs 1 def /_nativeEncoding 0 def /_useNativeEncoding 0 def /_tempEncode 0 def /_pntr 0 def /_tDict 2 dict def /_wv 0 def /Tx { } def /Tj { } def /CRender { } def /_AI3_savepage { } def /_gf null def /_cf 4 array def /_if null def /_of false def /_fc { } def /_gs null def /_cs 4 array def /_is null def /_os false def /_sc { } def /discardSave null def /buffer 256 string def /beginString null def /endString null def /endStringLength null def /layerCnt 1 def /layerCount 1 def /perCent (%) 0 get def /perCentSeen? false def /newBuff null def /newBuffButFirst null def /newBuffLast null def /clipForward? false def end userdict /Adobe_IllustratorA_AI5 74 dict dup begin put /initialize { Adobe_IllustratorA_AI5 dup begin Adobe_IllustratorA_AI5_vars begin discardDict { bind pop pop } forall dup /nc get begin { dup xcheck 1 index type /operatortype ne and { bind } if pop pop } forall end newpath } def /terminate { end end } def /_ null def /ddef { Adobe_IllustratorA_AI5_vars 3 1 roll put } def /xput { dup load dup length exch maxlength eq { dup dup load dup length 2 mul dict copy def } if load begin def end } def /npop { { pop } repeat } def /sw { dup length exch stringwidth exch 5 -1 roll 3 index mul add 4 1 roll 3 1 roll mul add } def /swj { dup 4 1 roll dup length exch stringwidth exch 5 -1 roll 3 index mul add 4 1 roll 3 1 roll mul add 6 2 roll /_cnt 0 ddef { 1 index eq { /_cnt _cnt 1 add ddef } if } forall pop exch _cnt mul exch _cnt mul 2 index add 4 1 roll 2 index add 4 1 roll pop pop } def /ss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put pop gsave false charpath currentpoint 4 index setmatrix stroke grestore moveto 2 copy rmoveto } exch cshow 3 npop } def /jss { 4 1 roll { 2 npop (0) exch 2 copy 0 exch put gsave _sp eq { exch 6 index 6 index 6 index 5 -1 roll widthshow currentpoint } { false charpath currentpoint 4 index setmatrix stroke } ifelse grestore moveto 2 copy rmoveto } exch cshow 6 npop } def /sp { { 2 npop (0) exch 2 copy 0 exch put pop false charpath 2 copy rmoveto } exch cshow 2 npop } def /jsp { { 2 npop (0) exch 2 copy 0 exch put _sp eq { exch 5 index 5 index 5 index 5 -1 roll widthshow } { false charpath } ifelse 2 copy rmoveto } exch cshow 5 npop } def /pl { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } def /setstrokeadjust where { pop true setstrokeadjust /c { curveto } def /C /c load def /v { currentpoint 6 2 roll curveto } def /V /v load def /y { 2 copy curveto } def /Y /y load def /l { lineto } def /L /l load def /m { moveto } def } { /c { pl curveto } def /C /c load def /v { currentpoint 6 2 roll pl curveto } def /V /v load def /y { pl 2 copy curveto } def /Y /y load def /l { pl lineto } def /L /l load def /m { pl moveto } def } ifelse /d { setdash } def /cf { } def /i { dup 0 eq { pop cf } if setflat } def /j { setlinejoin } def /J { setlinecap } def /M { setmiterlimit } def /w { setlinewidth } def /H { } def /h { closepath } def /N { _pola 0 eq { _doClip 1 eq { clip /_doClip 0 ddef } if newpath } { /CRender { N } ddef } ifelse } def /n { N } def /F { _pola 0 eq { _doClip 1 eq { gsave _pf grestore clip newpath /_lp /none ddef _fc /_doClip 0 ddef } { _pf } ifelse } { /CRender { F } ddef } ifelse } def /f { closepath F } def /S { _pola 0 eq { _doClip 1 eq { gsave _ps grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { _ps } ifelse } { /CRender { S } ddef } ifelse } def /s { closepath S } def /B { _pola 0 eq { _doClip 1 eq gsave F grestore { gsave S grestore clip newpath /_lp /none ddef _sc /_doClip 0 ddef } { S } ifelse } { /CRender { B } ddef } ifelse } def /b { closepath B } def /W { /_doClip 1 ddef } def /* { count 0 ne { dup type /stringtype eq { pop } if } if newpath } def /u { } def /U { } def /q { _pola 0 eq { gsave } if } def /Q { _pola 0 eq { grestore } if } def /*u { _pola 1 add /_pola exch ddef } def /*U { _pola 1 sub /_pola exch ddef _pola 0 eq { CRender } if } def /D { pop } def /*w { } def /*W { } def /` { /_i save ddef clipForward? { nulldevice } if 6 1 roll 4 npop concat pop userdict begin /showpage { } def 0 setgray 0 setlinecap 1 setlinewidth 0 setlinejoin 10 setmiterlimit [] 0 setdash /setstrokeadjust where {pop false setstrokeadjust} if newpath 0 setgray false setoverprint } def /~ { end _i restore } def /O { 0 ne /_of exch ddef /_lp /none ddef } def /R { 0 ne /_os exch ddef /_lp /none ddef } def /g { /_gf exch ddef /_fc { _lp /fill ne { _of setoverprint _gf setgray /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /G { /_gs exch ddef /_sc { _lp /stroke ne { _os setoverprint _gs setgray /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /k { _cf astore pop /_fc { _lp /fill ne { _of setoverprint _cf aload pop setcmykcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /K { _cs astore pop /_sc { _lp /stroke ne { _os setoverprint _cs aload pop setcmykcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /x { /_gf exch ddef findcmykcustomcolor /_if exch ddef /_fc { _lp /fill ne { _of setoverprint _if _gf 1 exch sub setcustomcolor /_lp /fill ddef } if } ddef /_pf { _fc fill } ddef /_psf { _fc ashow } ddef /_pjsf { _fc awidthshow } ddef /_lp /none ddef } def /X { /_gs exch ddef findcmykcustomcolor /_is exch ddef /_sc { _lp /stroke ne { _os setoverprint _is _gs 1 exch sub setcustomcolor /_lp /stroke ddef } if } ddef /_ps { _sc stroke } ddef /_pss { _sc ss } ddef /_pjss { _sc jss } ddef /_lp /none ddef } def /A { pop } def /annotatepage { userdict /annotatepage 2 copy known {get exec} {pop pop} ifelse } def /discard { save /discardSave exch store discardDict begin /endString exch store gt38? { 2 add } if load stopped pop end discardSave restore } bind def userdict /discardDict 7 dict dup begin put /pre38Initialize { /endStringLength endString length store /newBuff buffer 0 endStringLength getinterval store /newBuffButFirst newBuff 1 endStringLength 1 sub getinterval store /newBuffLast newBuff endStringLength 1 sub 1 getinterval store } def /shiftBuffer { newBuff 0 newBuffButFirst putinterval newBuffLast 0 currentfile read not { stop } if put } def 0 { pre38Initialize mark currentfile newBuff readstring exch pop { { newBuff endString eq { cleartomark stop } if shiftBuffer } loop } { stop } ifelse } def 1 { pre38Initialize /beginString exch store mark currentfile newBuff readstring exch pop { { newBuff beginString eq { /layerCount dup load 1 add store } { newBuff endString eq { /layerCount dup load 1 sub store layerCount 0 eq { cleartomark stop } if } if } ifelse shiftBuffer } loop } { stop } ifelse } def 2 { mark { currentfile buffer readline not { stop } if endString eq { cleartomark stop } if } loop } def 3 { /beginString exch store /layerCnt 1 store mark { currentfile buffer readline not { stop } if dup beginString eq { pop /layerCnt dup load 1 add store } { endString eq { layerCnt 1 eq { cleartomark stop } { /layerCnt dup load 1 sub store } ifelse } if } ifelse } loop } def end userdict /clipRenderOff 15 dict dup begin put { /n /N /s /S /f /F /b /B } { { _doClip 1 eq { /_doClip 0 ddef clip } if newpath } def } forall /Tr /pop load def /Bb {} def /BB /pop load def /Bg {12 npop} def /Bm {6 npop} def /Bc /Bm load def /Bh {4 npop} def end /Lb { 4 npop 6 1 roll pop 4 1 roll pop pop pop 0 eq { 0 eq { (%AI5_BeginLayer) 1 (%AI5_EndLayer--) discard } { /clipForward? true def /Tx /pop load def /Tj /pop load def currentdict end clipRenderOff begin begin } ifelse } { 0 eq { save /discardSave exch store } if } ifelse } bind def /LB { discardSave dup null ne { restore } { pop clipForward? { currentdict end end begin /clipForward? false ddef } if } ifelse } bind def /Pb { pop pop 0 (%AI5_EndPalette) discard } bind def /Np { 0 (%AI5_End_NonPrinting--) discard } bind def /Ln /pop load def /Ap /pop load def /Ar { 72 exch div 0 dtransform dup mul exch dup mul add sqrt dup 1 lt { pop 1 } if setflat } def /Mb { q } def /Md { } def /MB { Q } def /nc 3 dict def nc begin /setgray { pop } bind def /setcmykcolor { 4 npop } bind def /setcustomcolor { 2 npop } bind def currentdict readonly pop end currentdict readonly pop end setpacking %%EndResource %%EndProlog %%BeginSetup %%IncludeFont: Helvetica %%IncludeFont: Symbol %%IncludeFont: Times-Italic Adobe_level2_AI5 /initialize get exec Adobe_screens_AI5 /initialize get exec Adobe_IllustratorA_AI5_vars Adobe_IllustratorA_AI5 Adobe_typography_AI5 /initialize get exec Adobe_IllustratorA_AI5 /initialize get exec [ 39/quotesingle 96/grave 128/Adieresis/Aring/Ccedilla/Eacute/Ntilde/Odieresis /Udieresis/aacute/agrave/acircumflex/adieresis/atilde/aring/ccedilla/eacute /egrave/ecircumflex/edieresis/iacute/igrave/icircumflex/idieresis/ntilde /oacute/ograve/ocircumflex/odieresis/otilde/uacute/ugrave/ucircumflex /udieresis/dagger/degree/cent/sterling/section/bullet/paragraph/germandbls /registered/copyright/trademark/acute/dieresis/.notdef/AE/Oslash /.notdef/plusminus/.notdef/.notdef/yen/mu/.notdef/.notdef /.notdef/.notdef/.notdef/ordfeminine/ordmasculine/.notdef/ae/oslash /questiondown/exclamdown/logicalnot/.notdef/florin/.notdef/.notdef /guillemotleft/guillemotright/ellipsis/.notdef/Agrave/Atilde/Otilde/OE/oe /endash/emdash/quotedblleft/quotedblright/quoteleft/quoteright/divide /.notdef/ydieresis/Ydieresis/fraction/currency/guilsinglleft/guilsinglright /fi/fl/dagger dbl/periodcentered/quotesinglbase/quotedblbase/perthousand /Acircumflex/Ecircumflex/Aacute/Edieresis/Egrave/Iacute/Icircumflex 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!ff"33#$%&'ff(33)*+,̙-ff.33/0̙1̙2̙3̙ff4̙335̙6ff7ff8ff9ffff:ff33;ff<33=33>33?33ff@3333A33BCDEffF33GHIJKffL33MNOP̙QffR33STUVWffX33YZff[ff\ff]ffff^ff33_ff`33a33b33c33ffd3333e33fghiffj33klffmffnffoffffpff33qffrffsfftff̙uffffvff33wffxffyffzff{ffff|ff33}ff~ffffffffffffffffffffff33ffffff33ff33ff33ff33ffff3333ff33ffffffffffff33ff33333333ff333333333333̙33ff33333333333333ff33333333ff33ff33ff33ffff33ff3333ff3333333333333333ff333333333333333333ff333333ff33̙ff33ff33ffffffffffff33ff33333333ff333333ff33```@@@ ؐؐؐpppPPP000媠着```ЉЉ@@@|||v v v oooiiibpbpbp[[[UPUPUPNNNH0H0H0AAA;;;444---'`'`'` @@@ o  s  j pz z  &           6< ;:  < 9 G G DFHH/70742  6967 93;@ = > @ ?   5=  99@ 6DR RU W T HHπff33̙ ff 33 ff33ffffffffffff33ff33333333ff333333 !ff"33#$%&'ff(33)*+,̙-ff.33/0̙1̙2̙3̙ff4̙335̙6ff7ff8ff9ffff:ff33;ff<33=33>33?33ff@3333A33BCDEffF33GHIJKffL33MNOP̙QffR33STUVWffX33YZff[ff\ff]ffff^ff33_ff`33a33b33c33ffd3333e33fghiffj33klffmffnffoffffpff33qffrffsfftff̙uffffvff33wffxffyffzff{ffff|ff33}ff~ffffffffffffffffffffff33ffffff33ff33ff33ff33ffff3333ff33ffffffffffff33ff33333333ff333333333333̙33ff33333333333333ff33333333ff33ff33ff33ffff33ff3333ff3333333333333333ff333333333333333333ff333333ff33̙ff33ff33ffffffffffff33ff33333333ff333333ff33```@@@ ؐؐؐpppPPP000媠着```ЉЉ@@@|||v v v oooiiibpbpbp[[[UPUPUPNNNH0H0H0AAA;;;444---'`'`'` @@@ $o  s  j pz z  &           6< ;:  < 9             J J HIKL 2;2;74   9<8; ;5                          ?C @ @ C B     !"       ~PPPPPVX   b\\PLN<8P42P22P4 "  _1063385132% F2eI7eIOle PIC TMETA x      !"#$%'()*,-./0146789:;<=>?@ABCDEFGHIJKLMNOPQSVWXYZ[\]^_`abcdefghjkmnortwxyz{|}~T FMicrosoft Equation 3.0 DS Equation Equation.39q  .    & 8   & .  & Times wwgw -!( Times &wwgw & -!m PSymbol wwgw -!+ Times 'wwgw ' -!1 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Times 8wwgw 8 -!)!PSymbol wwgw -!-!Times 9wwgw 9 -! !! #Times wwgw  -!x !!Times :wwgw : -!(!&Times wwgw  -!t!+Times ;wwgw ; -!)!/!cos!4PSymbol wwgw  -!q!ETimes wwgw > -! fTimes wwgw  -!x !eTimes ?wwgw ? -!(!jTimes wwgw  -!t!oTimes @wwgw @ -!)!s! yPSymbol wwgw  -!q !wTimes Awwgw A -!(!~Times wwgw -!t!Times Bwwgw B -!)!!sin!PSymbol wwgw -!q!Times Cwwgw C -!(!Times wwgw -!t!Times Dwwgw D -!)!PSymbol wwgw -!=!Times Ewwgw E -!g!Times wwgw -!sin!PSymbol Fwwgw F -!q!Times wwgw  -!(!Times Gwwgw G -!t!Times wwgw  -!)! & 'CompObj"fObjInfoOlePres000!#Ole10Native$&" & MathTypeTimes New RomanLSwUSw0-2 x)y2 (y 2 Hsine2 )i2 (i 2 usine2  )i2  (i2  )i2  (i2 )i2 (i 2 wcose2 )o2 (o2 )o2 (o2  )o2 2(o2 )o2 (o 2 sine2 )i2 =(i2 : )i2 c (i 2 cose2 Z)o2 (o2 ")o2 K(o2 3)o2 1o2 6(o Times New RomanLSwUSw0-2 2oTimes New RomanLSwUSw0-2  to2 zgo2 7to2  to2  to2  xo2 ato2 to2 xo2 ato2 to2 uo2 Yto2 to2  to2 to2 to2 xo2 moSymbolw@a ULSwUSw0-2 qo2 qo2 D qo2 !qo2 qo2 qo2  qo2  qo2 qoSymbolw@ LSwUSw0-2 e=o2 ~ +o2 ~-o2 =o2  +o2 -o2 +oMT Extraa VLSwUSw0-2 3 &o2 ~ &o2 ~&o2 ~{&o2 3&o2 3]&o2 (&o2 .&o2 &o2 i&o2 i&o & "System 0-NANI (m+1)2x(t)-"q(t)cosq(t)+"q 2 (t)sinq(t)=u(t)"q(t)-2x(t)cosq(t)+2x(t)"q(t)sinq(t)=gsinq(t)vu8t (m+1)2x(t)""(t)cos(t)+" 2 (t)sin(t)=u(t)"(t)"2x(t)cos(t)+2x(t)"Equation Native +_1063385135)F7eI9eIOle 2PIC &(3T(t)sin(t)=gsin(t)T<8x<   F6 .  & Times 'wwgw ' -META 5:CompObj'+RfObjInfoTOlePres000*,U!x Times wwgw -!1 Times (wwgw ( -!xTimes wwgw -!2 Times )wwgw ) -!x.Times wwgw -!31 Times *wwgw * -!x@Times wwgw -!4C PSymbol +wwgw + -! ! 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Times/ $wwgw/ $ -!x Times ťwwgw -!2PSymbol/ %wwgw/ % -!=Times ƥwwgw -!xTimes/ &wwgw/ & -!4Times ǥwwgw -! 0Times/ 'wwgw/ ' -!x 1Times ȥwwgw -!34 Times/ (wwgw/ ( -! BTimes ɥwwgw -!x CTimes/ )wwgw/ ) -!4F PSymbol ʥwwgw -! 2! D! >! 2! D! >!=:Times/ *wwgw/ * -!m12PSymbol ˥wwgw -!+1=Times/ +wwgw/ + -!11EPSymbol ̥wwgw -!-1_Times/ ,wwgw/ , -!cos1g!(1wTimes ͥwwgw -!x1|Times/ -wwgw/ - -!24Times Υwwgw -!)1PSymbol/ .wwgw/ . -!-C(Times ϥwwgw -!cosC0!(C@Times/ /wwgw/ / -!xCETimes Хwwgw -!2FKTimes/ 0wwgw/ 0 -!)CP!1CqPSymbol ѥwwgw -! 2#! D#! >#! 2! D! >PSymbol/ 1wwgw/ 1 -!-+Times ҥwwgw -!1+Times/ 2wwgw/ 2 -!u2PSymbol ӥwwgw -!-2Times/ 3wwgw/ 3 -!x2Times ԥwwgw -!45!2,Times/ 4wwgw/ 4 -!sin2!(2Times եwwgw -!x2Times/ 5wwgw/ 5 -!25Times ֥wwgw -!)2!(DTimes/ 6wwgw/ 6 -!gDPSymbol ץwwgw -!-DTimes/ 7wwgw/ 7 -!xDTimes إwwgw -!3GTimes/ 8wwgw/ 8 -!xDTimes ٥wwgw -!4GTimes/ 9wwgw/ 9 -!)D!sinD!(DTimes ڥwwgw -!xDTimes/ :wwgw/ : -!2GTimes ۥwwgw -!)DPSymbol/ ;wwgw/ ; -! 1! E! =! 1! E! = & 'OlePres00035vOle10Native6Equation Native "_1063385157;F@eIlCeI` & MathTypeSymbolw@5 LSwUSw0-2 y2 y2 y2 fy2 y2 y2 y2 fy2 z~-y2 -y2 y2 y2 y2 y2 y2 y2 Ye-y2 yB -y2 y+y2 f=y2 y2 y2 y2 @y2 @y2 @y2 =y2 8=y Symbolw@ LSwUSw0-2 -yTimes New RomanLSwUSw0-2 zd)y 2 zDsin(2 z)i2 z(i2 c)i 2 Csin(2 YE 1i2 Y)i 2 YUcos(2 y)o 2 y2 cos(2 y{1o Times New RomanLSwUSw0-2 2o2 +4o2 3o2 2o2 2o2 4o2 1o2 2o2  2o2 d4o2 d3o2 pm4o2 p2o2 <3o2 1oTimes New RomanLSwUSw0-2 z;xo2 zxo2 zxo2 zgo2 :xo2 xo2 uo2 Yxo2 y\ xo2 yymo2 Yxo2 yxo2 xo2 Jxo2 8xo2 8JxoMT Extra LSwUSw0-2 B&o2 b&o2 f&o2 !f&o & "System 0-NANI 2x 1 =x 3 2x 2 =x 4 2x 3 2x 4 []=m+1-cos(x 2 )-cos(x 2 )1[] -1 u-x 42 sin(x 2 )(g-x 3 x 4 )sin(x 2 )[]v| 2x 1 =x 3 2x 2 =x 4 2x 3 2x 4 []=m+1"cos(x 2 )"cos(x 2 )1[] "1 u"x 42 sin(x 2 )(g"x 3 x 4 )sin(x 2 )[]TN>Ole PIC 8:TMETA CompObj9=fN> J   = .  & Timesa Cwwgwa C -! Times wwgw -!x PSymbola Dwwgwa D -!= Times wwgw -!Ax PSymbola Ewwgwa E -!+ %Times wwgw -!Bu . & ' FMicrosoft Equation 3.0 DS Equation Equation.39qM   .  &ObjInfoOlePres000<>\Ole10Native?%Equation Native E`U & MathType0Times New RomanLSwUSw0-2 Bu2 QAx2 JxxSymbolw@ LSwUSw0-2 +x2 2=xMT Extra/ LSwUSw0-2 f&x & "System 0-NANI! 2x=Ax+Buv)0@< 2x=Ax+BuT* <px* < \  Fl .  & _10633851607SDFEeI'HeIOle PIC ACTMETA Times wwgw -!A&PSymbol/ Awwgw/ A -!=& Times wwgw -!0 !0 5!1 N!0 `!0!05!0N!1`!0.Times/ Bwwgw/ B -!1*2Times wwgw -!m11-*0*6Times/ Cwwgw/ C -!g.9Times wwgw -!0.N!0.`!0@Times/ Dwwgw/ D -!m<.PSymbol wwgw -!+<3Times/ Ewwgw/ E -!1<7Times wwgw -!mC1<-<:Times/ Fwwgw/ F -!g@=Times wwgw -!0@N!0@`PSymbol/ Gwwgw/ G -! ! A! ! #! /! ;! f! Af! f! #f! /f! ;f & ' FMicrosoft Equation 3.0 DS Equation Equation.39q 2  .   &`  & MathType-#`CompObjBFfObjInfoOlePres000EGtOle10NativeHSymbolw@x LSwUSw0-2 G y2 0 y2  y2  y2  y2 ~ y2 p y2 Goy2 0oy2 oy2 oy2 oy2 ~oy2 poy2 @d=y Symbolw@a LSwUSw0-2 +yTimes New RomanLSwUSw0-2 B 0y2 |0y2 0y2 B 0y2 |0y2 0y2 ?? 1y2 ?|0y2 ?0y2 ?0y2 _B 0y2 _y1y2 _0y2 _0y Times New RomanLSwUSw0-2 1y2 V1yTimes New RomanLSwUSw0-2 gy2 7gy2 @TAy Times New RomanLSwUSw0-2 t@my2 my2 @my & "System 0-NANI A=001000010 1m g000 m+1m g00[]vX$ A=001000010 1m g000 m+1m g0Equation Native _1063385163MFJeIpLeIOle PIC JLT      !"#$%&'()*+,.123456789:;<=>?@BDGIJKLMNOPQRSTUVX[\]^_`abcdehjnpqrstuvwxyz{|}~0[]T=<4x=<   F) .  & Timese 6wwgwe 6 -!B&PSymbol ץwwgw META 0PICT KOCompObj-fObjInfoNQ/ -!=& Timese 7wwgwe 7 -!0 !0Times إwwgw -!1*Timese 8wwgwe 8 -!m1-**!Times ٥wwgw -!1<Timese 9wwgwe 9 -!mC<<!PSymbol ڥwwgw -! ! A! ! #! /! ;! #! A#! #! ##! /#! ;# & 'F)dxpr  F)"F) currentpoint ",Times .+&B, Symbol) =( 0*0 +1(1m"*+ 1(Cm"< .(  *6 ( *  *  *  ( # *6 (# *  *  *  @30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1312 div 2240 3 -1 roll exch div scale currentpoint translate 64 43 translate 10 1173 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (B) show 333 1173 moveto 384 /Symbol f1 (=) show 827 293 moveto 384 /Times-Roman f1 (0) show 827 869 moveto (0) show 866 1306 moveto 224 ns (1) show 843 1538 moveto 224 /Times-Italic f1 (m) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 813 1346 moveto 218 0 rlineto stroke 866 1882 moveto 224 /Times-Roman f1 (1) show 843 2114 moveto 224 /Times-Italic f1 (m) show 813 1922 moveto 218 0 rlineto stroke 651 355 moveto 384 /Symbol f1 (\351) show 651 2118 moveto (\353) show 651 724 moveto (\352) show 651 1093 moveto (\352) show 651 1462 moveto (\352) show 651 1831 moveto (\352) show 1056 355 moveto (\371) show 1056 2118 moveto (\373) show 1056 724 moveto (\372) show 1056 1093 moveto (\372) show 1056 1462 moveto (\372) show 1056 1831 moveto (\372) show end dbMATHV B=00 1m  1m [] c FMicrosoft Equation 3.0 DS Equation Equation.39qOlePres0000,Ole10NativePRAZEquation Native C|_1063385172IaWFpSOeIpQeI  .  &` & MathType-Symbolw@ +LSwUSw0-2 Gy2 0y2 y2 y2 y2 ~y2 py2 Goy2 0oy2 oy2 oy2 oy2 ~oy2 poy2 @d=y Times New RomanLSwUSw0-2 tmy2 myTimes New RomanLSwUSw0-2 @EBy Times New RomanLSwUSw0-2 )1y2 )1yTimes New RomanLSwUSw0-2 ?0y2 _0y & "System 0-NANIV B=00 1m  1m []v`0@? B=00 1m  1m []TrOle EPIC TVFTMETA HCompObjUYWfr   I .  & Times| gwwgw| g -! Times, wwgw, -!x PSymbol| hwwgw| h -!= Times, wwgw, -!( Times| iwwgw| i -!A PSymbol, wwgw, -!+ #Times| jwwgw| j -!BG -Times, wwgw, -!) =Times| kwwgw| k -!x B & ' FMicrosoft Equation 3.0 DS Equation Equation.39q I .  & & MathTypePTimes New RomanLSwUSw0-2 @xy2 @BG2 @AG2 @JxGTimes New RomanLSwUSw0-2 @ObjInfoYOlePres000XZZOle10Native[f+Equation Native gMb)G2 @'(GSymbolw@ XLSwUSw0-2 @+G2 @,=GMT Extra LSwUSw0-2 *f&G & "System 0-NANI' 2x=(A+BG)xv1HL 2x=(A+BG)xT1n%T^ @^  v  n ._1049636351^ FPXeIP]eIPIC iTMETA ]_2cPICT `d71n 1   . &&%B@%MSEPS Preamble 68 415 548 603 0 0 480 188 /pp_save save def /showpage {} def 40 dict begin /pp_clip false def /pp_bbox false def /F { pop } def /S {} def /B { { /pp_dy1 exch def /pp_dx1 exch def /pp_dy2 exch def /pp_dx2 exch def } stopped not { /pp_bbox true def } if } def /CB { { /pp_cy exch def /pp_cx exch def /pp_cht exch def /pp_cwd exch def } stopped not { /pp_clip true def } if } def /pp_bx1 68 def /pp_by1 415 def /pp_bx2 548 def /pp_by2 603 def &&-- '&&&%pp_clip { pp_cx pp_cy moveto pp_cwd 0 rlineto 0 pp_cht rlineto pp_cwd neg 0 rlineto clip newpath } if pp_bbox { /pp_dy2 pp_dy2 pp_dy1 add def /pp_dx2 pp_dx2 pp_dx1 add def /pp_sx pp_dx2 pp_dx1 sub pp_bx2 pp_bx1 sub div def /pp_sy pp_dy2 pp_dy1 sub pp_by1 pp_by2 sub div def /pp_tx pp_dx1 pp_sx pp_bx1 mul sub def /pp_ty pp_dy1 pp_sy pp_by2 mul sub def pp_tx pp_ty translate pp_sx pp_sy scale } if end &% %!PS-Adobe-2.0 EPSF-1.2 %%Creator: MATLAB, The Mathworks, Inc. %%Title: MATLAB graph %%CreationDate: 02/23/96 15:45:41 %%DocumentFonts: Times-Roman %%DocumentNeededFonts: Times-Roman %%DocumentProcessColors: Cyan Magenta Yellow Black %%Pages: 1 %%BoundingBox: 68 415 548 603 %%EndComments %%BeginProlog % MathWorks dictionary /MathWorks 120 dict begin % definition operators /bdef {bind def} bind def /ldef {load def} bind def /xdef {exch def} bdef /xstore {exch store} bdef % operator abbreviations /c /clip ldef /cc /concat ldef /cp /closepath ldef /gr /grestore ldef /gs /gsave ldef /mt /moveto ldef /np /newpath ldef /cm /currentmatrix ldef /sm /setmatrix ldef /rc {rectclip} bdef /rf {rectfill} bdef /rm /rmoveto ldef /rl /rlineto ldef /s /show ldef /sc {setcmykcolor} bdef /sr /setrgbcolor ldef /w /setlinewidth ldef /cap /setlinecap ldef % page state control /pgsv () def /bpage {/pgsv save def} bdef /epage {pgsv restore} bdef /bplot /gsave ldef /eplot {stroke grestore} bdef % orientation switch /portraitMode 0 def /landscapeMode 1 def % coordinate system mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup 3 -1 roll exch dup findfont dup dup /CharStrings get /Agrave known { length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall exch /Encoding exch def currentdict end definefont pop } {pop pop pop pop} ifelse }bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if }bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch rlineto exch 0 rlineto neg 0 exch rlineto closepath } bdef /FR { MR stroke } bdef /PR { MR fill } bdef /L1i { { currentfile picstr readhexstring pop } image } bdef /tMatrix matrix def /MakeOval { newpath tMatrix currentmatrix pop translate scale 0 0 1 0 360 arc tMatrix setmatrix } bdef /FO { MakeOval stroke } bdef /PO { MakeOval fill } bdef /PD { 2 copy moveto lineto stroke } bdef /MacEncoding 256 array def /NUL/SOH/STX/ETX/EOT/ENQ/ACK/BEL/BS/HT/LF/VT/FF/CR/SO/SI 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7 9 7 20 5 28 5 33 4 38 4 41 3 46 3 50 3 59 2 68 4 85 3 108 3 93 3 81 3 73 4 67 3 55 3 51 4 47 5 41 6 36 7 26 8 15 10 -2 1684 671 100 MP stroke 14 -26 12 -36 10 -37 10 -35 9 -32 8 -29 7 -24 8 -20 7 -17 8 -12 7 -8 8 -4 7 2 8 6 7 10 9 17 9 23 9 30 10 35 11 40 13 47 14 44 11 23 10 5 8 -8 6 -18 6 -27 5 -32 4 -37 3 -41 3 -45 3 -50 3 -57 4 -74 3 -83 3 -109 4 -94 2 -82 3 -73 4 -67 3 -57 3 -51 4 -47 5 -42 6 -36 6 -28 9 -16 11 1 16 32 14 46 13 49 13 48 13 42 14 35 13 21 14 7 13 -8 13 -21 13 -35 15 -48 14 -53 19 -69 14 -40 11 -16 8 0 8 12 6 22 5 29 5 34 3 38 4 43 3 46 3 52 3 62 3 71 4 122 3 100 3 87 3 76 3 70 4 65 3 53 4 48 4 44 6 39 6 31 8 20 9 6 11 -13 13 -32 11 -38 10 -37 10 -35 8 -32 8 -27 8 -23 7 -20 7 -15 8 -12 913 966 100 MP stroke 7 -7 8 -2 898 975 3 MP stroke gr 1900 273 mt (x\(t\)) s DO 4 w SO 6 w 4043 2149 mt 6254 2149 L 4043 388 mt 6254 388 L 6254 2149 mt 6254 388 L 4043 2149 mt 4043 388 L 6254 2149 mt 6254 2149 L 4043 2149 mt 4043 2149 L 4043 2149 mt 6254 2149 L 4043 2149 mt 4043 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56 3 47 3 43 3 39 3 38 4 34 3 35 4 35 5 37 5 41 7 43 8 49 11 54 16 71 14 53 14 43 13 35 13 28 13 20 14 12 13 2 13 -7 14 -15 14 -25 15 -38 15 -47 17 -63 12 -53 10 -47 8 -43 6 -40 6 -38 5 -35 4 -32 4 -32 3 -31 3 -31 3 -33 3 -40 3 -42 4 -55 3 -48 5552 1269 100 MP stroke 3 -42 3 -39 3 -38 3 -35 4 -34 4 -36 5 -37 5 -40 7 -44 8 -47 10 -51 14 -63 12 -47 10 -36 10 -30 9 -24 8 -19 7 -16 8 -12 7 -10 8 -8 7 -4 8 -2 8 1 7 4 8 8 8 11 9 15 11 22 10 27 11 35 15 52 13 52 10 48 9 45 7 41 6 39 5 36 5 34 4 32 3 31 3 31 3 31 3 36 3 38 4 62 3 50 3 43 3 41 4 38 3 38 3 35 4 35 5 36 5 39 6 43 8 47 10 53 14 66 15 59 14 47 13 37 13 31 13 24 13 15 14 7 13 -3 13 -10 14 -20 14 -30 14 -38 16 -53 15 -60 12 -51 9 -46 7 -42 7 -40 5 -37 5 -34 4 -32 4 -32 3 -30 3 -32 3 -34 2 -37 4 -44 3 -54 3 -47 3 -41 3 -39 4 -39 3 -34 3 -34 4 -36 5 -38 6 -41 7 -44 8 -47 10 -51 4829 1718 100 MP stroke 14 -63 12 -46 10 -36 10 -29 9 -25 8 -19 7 -16 8 -12 7 -11 8 -7 7 -5 8 -2 7 1 8 4 7 6 9 10 9 14 9 20 10 24 11 32 13 43 14 56 11 50 10 46 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mappings /dpi2point 0 def % font control /FontSize 0 def /FMS { /FontSize xstore %save size off stack findfont [FontSize 0 0 FontSize neg 0 0] makefont setfont }bdef /reencode { exch dup 3 -1 roll exch dup findfont dup dup /CharStrings get /Agrave known { length dict begin { 1 index /FID ne {def}{pop pop} ifelse } forall exch /Encoding exch def currentdict end definefont pop } {pop pop pop pop} ifelse }bdef /csm { 1 dpi2point div -1 dpi2point div scale neg translate landscapeMode eq {90 rotate} if }bdef % line types: solid, dotted, dashed, dotdash /SO { [] 0 setdash } bdef /DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash } bdef /DA { [6 dpi2point mul] 0 setdash } bdef /DD { [.5 dpi2point mul 4 dpi2point mul 6 dpi2point mul 4 dpi2point mul] 0 setdash } bdef % macros for lines and objects /L { lineto stroke } bdef /MP { 3 1 roll moveto 1 sub {rlineto} repeat } bdef /AP { {rlineto} repeat } bdef /PP { closepath fill } bdef /DP { closepath stroke } bdef /MR { 4 -2 roll moveto dup 0 exch 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3 72 3 81 4 111 3 94 2407 1159 100 MP stroke 3 82 3 74 3 67 3 57 4 51 4 47 5 42 5 37 7 28 8 16 10 1 14 -24 12 -34 10 -36 10 -35 9 -32 8 -28 7 -24 8 -19 7 -16 8 -12 7 -8 8 -3 8 2 7 7 8 12 8 18 9 25 11 32 10 36 11 42 15 50 13 33 10 14 9 -1 7 -12 6 -23 5 -29 5 -35 4 -38 3 -43 3 -47 3 -52 3 -62 3 -72 4 -121 3 -100 3 -87 3 -76 4 -70 3 -65 3 -53 4 -48 5 -44 5 -39 6 -31 8 -20 10 -6 14 20 15 42 14 47 13 48 13 44 13 36 13 25 14 11 13 -5 13 -19 14 -32 14 -45 14 -52 16 -58 15 -46 12 -21 9 -3 7 9 7 20 5 28 5 33 4 38 4 41 3 46 3 50 3 59 2 68 4 85 3 108 3 93 3 81 3 73 4 67 3 55 3 51 4 47 5 41 6 36 7 26 8 15 10 -2 1684 671 100 MP stroke 14 -26 12 -36 10 -37 10 -35 9 -32 8 -29 7 -24 8 -20 7 -17 8 -12 7 -8 8 -4 7 2 8 6 7 10 9 17 9 23 9 30 10 35 11 40 13 47 14 44 11 23 10 5 8 -8 6 -18 6 -27 5 -32 4 -37 3 -41 3 -45 3 -50 3 -57 4 -74 3 -83 3 -109 4 -94 2 -82 3 -73 4 -67 3 -57 3 -51 4 -47 5 -42 6 -36 6 -28 9 -16 11 1 16 32 14 46 13 49 13 48 13 42 14 35 13 21 14 7 13 -8 13 -21 13 -35 15 -48 14 -53 19 -69 14 -40 11 -16 8 0 8 12 6 22 5 29 5 34 3 38 4 43 3 46 3 52 3 62 3 71 4 122 3 100 3 87 3 76 3 70 4 65 3 53 4 48 4 44 6 39 6 31 8 20 9 6 11 -13 13 -32 11 -38 10 -37 10 -35 8 -32 8 -27 8 -23 7 -20 7 -15 8 -12 913 966 100 MP stroke 7 -7 8 -2 898 975 3 MP stroke gr 1900 273 mt (x\(t\)) s DO 4 w SO 6 w 4043 2149 mt 6254 2149 L 4043 388 mt 6254 388 L 6254 2149 mt 6254 388 L 4043 2149 mt 4043 388 L 6254 2149 mt 6254 2149 L 4043 2149 mt 4043 2149 L 4043 2149 mt 6254 2149 L 4043 2149 mt 4043 388 L 4043 2149 mt 4043 2149 L 4043 2149 mt 4043 2127 L 4043 388 mt 4043 410 L 4003 2310 mt (0) s 5149 2149 mt 5149 2127 L 5149 388 mt 5149 410 L 5109 2310 mt (5) s 6254 2149 mt 6254 2127 L 6254 388 mt 6254 410 L 6174 2310 mt (10) s 4043 2149 mt 4065 2149 L 6254 2149 mt 6232 2149 L 3936 2202 mt (0) s 4043 1562 mt 4065 1562 L 6254 1562 mt 6232 1562 L 3936 1615 mt (2) s 4043 975 mt 4065 975 L 6254 975 mt 6232 975 L 3936 1028 mt (4) s 4043 388 mt 4065 388 L 6254 388 mt 6232 388 L 3936 441 mt (6) s 4043 388 mt 6254 388 L 4043 2149 mt 6254 2149 L 4043 2149 mt 4043 388 L 6254 2149 mt 6254 388 L 4043 388 mt 4043 388 L 6254 388 mt 6254 388 L gs 4043 388 2212 1762 MR c np 3 -19 6 -36 4 -35 4 -32 4 -31 3 -31 3 -31 3 -34 3 -38 3 -44 3 -54 4 -47 3 -41 3 -39 3 -38 3 -35 4 -34 4 -36 5 -37 5 -41 7 -45 9 -47 10 -52 14 -59 11 -45 11 -35 9 -29 9 -23 8 -18 7 -15 8 -12 7 -9 8 -7 7 -3 8 -1 7 2 8 5 8 9 9 13 9 18 10 22 11 30 12 41 15 56 11 50 10 46 8 43 7 40 5 38 5 34 4 33 4 32 3 30 3 31 3 34 3 39 3 42 4 56 3 47 3 43 3 39 3 38 4 34 3 35 4 35 5 37 5 41 7 43 8 49 11 54 16 71 14 53 14 43 13 35 13 28 13 20 14 12 13 2 13 -7 14 -15 14 -25 15 -38 15 -47 17 -63 12 -53 10 -47 8 -43 6 -40 6 -38 5 -35 4 -32 4 -32 3 -31 3 -31 3 -33 3 -40 3 -42 4 -55 3 -48 5552 1269 100 MP stroke 3 -42 3 -39 3 -38 3 -35 4 -34 4 -36 5 -37 5 -40 7 -44 8 -47 10 -51 14 -63 12 -47 10 -36 10 -30 9 -24 8 -19 7 -16 8 -12 7 -10 8 -8 7 -4 8 -2 8 1 7 4 8 8 8 11 9 15 11 22 10 27 11 35 15 52 13 52 10 48 9 45 7 41 6 39 5 36 5 34 4 32 3 31 3 31 3 31 3 36 3 38 4 62 3 50 3 43 3 41 4 38 3 38 3 35 4 35 5 36 5 39 6 43 8 47 10 53 14 66 15 59 14 47 13 37 13 31 13 24 13 15 14 7 13 -3 13 -10 14 -20 14 -30 14 -38 16 -53 15 -60 12 -51 9 -46 7 -42 7 -40 5 -37 5 -34 4 -32 4 -32 3 -30 3 -32 3 -34 2 -37 4 -44 3 -54 3 -47 3 -41 3 -39 4 -39 3 -34 3 -34 4 -36 5 -38 6 -41 7 -44 8 -47 10 -51 4829 1718 100 MP stroke 14 -63 12 -46 10 -36 10 -29 9 -25 8 -19 7 -16 8 -12 7 -11 8 -7 7 -5 8 -2 7 1 8 4 7 6 9 10 9 14 9 20 10 24 11 32 13 43 14 56 11 50 10 46 8 43 6 40 6 37 5 35 4 33 3 31 3 31 3 31 3 33 4 41 3 43 3 55 4 47 2 42 3 39 4 38 3 34 3 35 4 35 5 38 6 40 6 44 9 49 11 55 16 71 14 54 13 44 13 35 13 29 14 21 13 14 14 4 13 -4 13 -13 13 -21 15 -31 14 -40 19 -65 14 -58 11 -50 8 -45 8 -41 6 -39 5 -36 5 -34 3 -32 4 -31 3 -31 3 -32 3 -35 3 -38 4 -62 3 -51 3 -43 3 -41 3 -38 4 -38 3 -35 4 -35 4 -36 6 -39 6 -43 8 -46 9 -50 11 -55 13 -55 11 -41 10 -34 10 -27 8 -22 8 -18 8 -15 7 -12 7 -9 8 -7 4058 1990 100 MP stroke 7 -4 8 -1 4043 1995 3 MP stroke gr 4920 273 mt (theta\(t\)) s end eplot %%EndObject graph 1 epage end showpage %%Trailer %%EOF 2" B#    ""! "#",  Helvetica .+0"u"u)\5"")X10""(-0.8""(-0.6"x"x(|-0.4"`"`(d-0.2"H"H(L0"/"/(30.2""(0.4    "" "H###################### # # ###################################################################################### # # ############################################################################### # # #################################################################################### # # ######### (mx(t)"u#    ""! "#"+0"{"{)\5"")X10""(0""(1"x"x(|2"`"`(d3"H"H(L4"/"/(35""(6    "" "################################################################################################################################################################################################################################################################################################# (htheta(t)ObjInfok_1063385193eFP]eI@_eIOle lPIC bdmTMETA oCompObjcgfObjInfoOlePres000fh  & Times wwgw -!x Times` ڥwwgw` -!( !0 !) PSymbol wwgw -!= Times` ۥwwgw` -! %Times wwgw -!x #Times` ܥwwgw` -!( )!0 .!) 4PSymbol wwgw -!= ;Times` ݥwwgw` -! GPSymbol wwgw -!q DTimes` ޥwwgw` -!( K!0 P!) VPSymbol wwgw -!= ]Times` ߥwwgw` -!0 g & ' FMicrosoft Equation 3.0 DS Equation Equation.39q Wj  .    &`  & MathTypePTimes New RomanLSwUSw0-2  0y2 )y2 O0y2 (y2 g)y2 0y2 Y(y2 )y2 N0y2 (ySymbolw@ -LSwUSw0-2  =y2 '=y2 =ySymbolw@a LSwUSw0-2  qyMT Extra .LSwUSw0-2 r&y2 i&yTimes New RomanLSwUSw0-2 xy2 Jxy & "System 0-NANI? x(0)=2x(0)="q(0)=0vQ@SH x(0)=2xOle10NativeiCEquation Native m_1073902976nF@fbeI@deIOle (0)="(0)=0T4r4r 4  < .  & PSymbol1 ޥwwgw1 -!q Times >wwgw >PIC kmTMETA pCompObjlpfObjInfo -!( !0 !) PSymbol1 ߥwwgw1 -!= PSymbol ?wwgw ? -!p $Times1 ेwwgw1 -!/ .!6 4 & ' FMicrosoft Equation 3.0 DS Equation Equation.39q:  .   & & MathTypePTimes New RomanLSwUSw0-2 @@6y2 @/y2 @)y2 @[0y2 @(ySymbolw@T LSwUSw0-2 @py2 @qyOlePres000oq|Ole10Nativer%Equation Native E_1063384764wF0!geI0ieISymbolw@ LSwUSw0-2 @=y & "System 0-NANI! q(0)=p/6P)L$M (0)=/6TrOle PIC tvTMETA FCompObjuyfr    .  & Times wwgw -!x Times wwgw -!1 Times wwgw -!( Times wwgw -!t Times wwgw -!)  & ' FMicrosoft Equation 3.0 DS Equation Equation.39q+   .  &ObjInfoOlePres000xzLOle10Native{&Equation Native C & MathTypePTimes New RomanLSwUSw0-2 @$)y2 @M(y Times New RomanLSwUSw0-2 1yTimes New RomanLSwUSw0-2 @ty2 @Jxy & "System 0-NANI" x 1 (t)v'a x 1 (t)Trr    .  & _1063384768sF0ieI MneIOle PIC }TMETA FTimes ޥwwgw -!x Times  ewwgw  e -!2 Times ߥwwgw -!( Times  fwwgw  f -!t Times ेwwgw -!)  & 'CompObj~fObjInfoOlePres000LOle10Native& FMicrosoft Equation 3.0 DS Equation Equation.39qN   .  & & MathTypePTimes New RomanLSwUSw0-2 @I)y2 @t(y Times New RomanLSwUSw0-2 2yTimes New RomanLSwUSw0-2 @ty2 @Jxy & "System 0-NANI" x 2 (t)v'(m̶ x 2 (t)Equation Native C_1063384771F MneI peIOle PIC TTrr X  0 .  & Times wwgw -!x Times wwgw -!1 TimesMETA CompObjfObjInfoOlePres000 wwgw -!( !0 !) PSymbol wwgw -!= Times wwgw -!a &Times wwgw -!1 + & ' FMicrosoft Equation 3.0 DS Equation Equation.39q     !"#$%&'()*+-0123456789:=@BCDEFGHIJKLMNOPRSTUVWXYZ[\]^_`befghijklmnoruwxyz{|}~ A .  @& & MathTypeP Times New RomanLSwUSw0-2 1y2 1yTimes New RomanLSwUSw0-2 @V)y2 @0y2 @I(yTimes New RomanLSwUSw0-2 @ay2 @JxySymbolw@2 LSwUSw0-2 @=y & "System 0-NANI4 x 1 (0)=a 1v<5  x 1 (0)=a 1Ole10Native 8Equation Native X_1063384775|FseIyueIOle T+r+r X  2 .  & Times wwgw -!x Times 楇wwgw -!2 TimesPIC TMETA PICT CompObj,f wwgw -!( !0 !) PSymbol 祇wwgw -!= Times wwgw -!a 'Times 襇wwgw -!2 - & '2dxpr  2"2 currentpoint ",Times .+ x +2 ( ()0)), Symbol)=) a +2r30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1600 div 448 3 -1 roll exch div scale currentpoint translate 64 59 translate 11 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (x) show 187 357 moveto 224 /Times-Roman f1 (2) show 339 261 moveto 384 /Times-Roman f1 (\() show 478 261 moveto 384 /Times-Roman f1 (0) show 681 261 moveto 384 /Times-Roman f1 (\)) show 898 261 moveto 384 /Symbol f1 (=) show 1211 261 moveto 384 /Times-Italic f1 (a) show 1397 357 moveto 224 /Times-Roman f1 (2) show end d@MATH4 x 2 (0)=a 2 d FMicrosoft Equation 3.0 DS Equation Equation.39q3 A ObjInfo.OlePres000/Ole10Native;8Equation Native <X.  &` & MathTypeP Times New RomanLSwUSw0-2 2y2 2yTimes New RomanLSwUSw0-2 @)y2 @0y2 @x(yTimes New RomanLSwUSw0-2 @3ay2 @JxySymbolw@Q `LSwUSw0-2 @:=y & "System 0-NANI4 x 2 (0)=a 2v<p7 x 2 (0)=a 2T4r_1063384777FweI4zeIOle >PIC ?TMETA A4r   < .  & Timesu wwgwu -!u PSymbol wwgw -!= Timesu wwgwu -!g Times wwgw -!( Timesu wwgwu -!x Times wwgw -!1 $Timesu wwgwu -!, (Times wwgw -!x -Timesu wwgwu  -!2 2Times wwgw -!) 7 & '<dxpr  <"< currentpoint ",Times .+ u, Symbol) =) g)()x +1 ( (,)x +2 ( 7)30 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1920 div 448 3 -1 roll exch div scale currentpoint translate 64 59 translate -16 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1PICT QCompObjafObjInfocOlePres000d {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (u) show 273 261 moveto 384 /Symbol f1 (=) show 588 261 moveto 384 /Times-Italic f1 (g) show 782 261 moveto 384 /Times-Roman f1 (\() show 941 261 moveto 384 /Times-Italic f1 (x) show 1099 357 moveto 224 /Times-Roman f1 (1) show 1227 261 moveto 384 /Times-Roman f1 (,) show 1379 261 moveto 384 /Times-Italic f1 (x) show 1555 357 moveto 224 /Times-Roman f1 (2) show 1714 261 moveto 384 /Times-Roman f1 (\)) show end dGMATH; u=g(x 1 ,x 2 )8  FMicrosoft Equation 3.0 DS Equation Equation.39qq Q .  & & MathTypePTimes New RomanLSwUSw0-2 @)y2 @f,y2 @(y Times New RomanLSwUSw0-2 |2y2 1yTimes New RomanLSwUSw0-2 @xy2 @hxy2 @/gy2 @1uySymbolw@ LSwUSw0-2 @&=y & "System 0-NANIOle10Nativep?Equation Native qa_1063384773F|eI~eIOle s; u=g(x 1 ,x 2 )vEpd< u=g(x 1 ,x 2 )Trr   M .  & PIC tTMETA vrPICT CompObjfTimes ץwwgw -!x Times 磊wwgw -!1 PSymbol إwwgw -!= !- Times wwgw -!3 !, $! (Times ٥wwgw -!x .Times wwgw -!2 4PSymbol ڥwwgw -!= ;Times wwgw -!0 E & 'Mdxpr  M"M currentpoint ",Times .+ x +1, Symbol ( =) -)3),) )x +2 ( ;=) 030 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 2464 div 448 3 -1 roll exch div scale currentpoint translate 64 59 translate 11 261 moveto /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (x) show 169 357 moveto 224 /Times-Roman f1 (1) show 397 261 moveto 384 /Symbol f1 (=) show 711 261 moveto (-) show 921 261 moveto 384 /Times-Roman f1 (3) show 1094 261 moveto 384 /Times-Roman f1 (,) show 1235 261 moveto 384 /Times-Roman f1 ( ) show 1427 261 moveto 384 /Times-Italic f1 (x) show 1603 357 moveto 224 /Times-Roman f1 (2) show 1849 261 moveto 384 /Symbol f1 (=) show 2158 261 moveto 384 /Times-Roman f1 (0) show end dMMATHA  x 1 =-3,  x 2 =0 r FMicrosoft Equation 3.0 DS Equation Equation.39qObjInfoOlePres000Ole10NativeEEquation Native i Y .   & & MathTypePTimes New RomanLSwUSw0-2 @J0y2 @# 2 @, 2 @Q3  Times New RomanLSwUSw0-2 a2 2 1 Symbolw@ LSwUSw0-2 @I= 2 @- 2 @= Times New RomanLSwUSw0-2 @x 2 @Jx & "System 0-NANIA x 1 =-3,  x 2 =0vMp̃ x 1 ="3,  x 2 =0_1063384851F_eIЃeIOle PIC TMETA T0,    .  & Times ܥwwgw -!u -   PSymbol ƥwwgw -! Times ݥwwgw -!1  & 'dxpr  " currentpoint ",Times .+ u" " , Symbol) )130 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 896 div 480 3 -1 roll exch div scale currentpoint translate 64 59 translate 32 293 movetPICT CompObjfObjInfoOlePres000lo /fs 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {findfont dup /cf exch def sf} def /ns {cf sf} def 384 /Times-Italic f1 (u) show /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 8 0 moveto 0 388 rlineto stroke 253 0 moveto 0 388 rlineto stroke 362 293 moveto 384 /Symbol f1 (\243) show 633 293 moveto 384 /Times-Roman f1 (1) show end d+MATH uab1ne FMicrosoft Equation 3.0 DS Equation Equation.39qW*  .   @& & MathType`-KhhK??Times New RomanLSwUSw0-2 `1ySymbolw@* zLSwUSw0-2 `yTimes New RomanLSwUSw0-2 `~uy & "System 0-NANI uab1v( ud"1Ole10Native#Equation Native D_1063385541FeIeIOle PIC TMETA CompObjfObjInfoTrr w  J .  & Times Twwgw T -!( Times ۥwwgw -!x Times Uwwgw U -!1 Times ܥwwgw -!, Times Vwwgw V -!x Times ݥwwgw -!2 Times Wwwgw W -!) 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