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X\fi\fi X \if T\isinbookJPE In ``\unhbox\bookboxJPE\unskip''\if T\isbybookJPE, X\else\period \fi\fi X \if T\isbybookJPE (\unhbox\bybookboxJPE\unskip)\period \fi X \if T\ispublisherJPE \unhbox\publisherboxJPE\unskip \if T\isjourJPE, \else\if XT\isyrJPE \ \else\period \fi\fi\fi X \if T\istoappearJPE (To appear)\period \fi X \if T\ispreprintJPE Preprint\period \fi X \if T\isjourJPE \unhbox\jourboxJPE\unskip\ \fi X \if T\isvolJPE \unhbox\volboxJPE\unskip, \fi X \if T\ispagesJPE \unhbox\pagesboxJPE\unskip\ \fi X \if T\isyrJPE (\unhbox\yrboxJPE\unskip)\period \fi X X} X X%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% X%%% SOME SMALL TRICKS%%%%%%%%%% X\def \breakline{\vskip 0em} X\def \script{\bf} X\def \norm{\vert \vert} X\def \endnorm{\vert \vert} X \def\cite#1{{\rm [#1]}} X \def\bref#1{{\rm [~\enspace~]}} % blank ref cite X \def\degree{\mathop{\rm degree}\nolimits} X \def\mod{\mathop{\rm mod}\nolimits} X \def\bT{{\bf T}} X \def\frac#1#2{{#1\over#2}} X \def\Norm{{\|~\enspace~\|}} X\TITLE COMPUTATION OF DOMAINS OF ANALYTICITY XFOR SOME PERTURBATIVE EXPANSIONS OF MECHANICS X\footnote{$^1$} X{\baselineskip=12pt\rm Preprint available through the mathematical physics electronic Xpreprint archive. Send mail to {\tt mp\_arc@math.utexas.edu} for details.} X\ENDTITLE X\AUTHOR XRafael de la Llave X\footnote{$^2$}{Supported by NSF grants.} X\footnote{$^3$}{e-mail: {\tt llave@math.utexas.edu}} X\FROM XDepartment of Mathematics XThe University of Texas at Austin XAustin, TX 78712 X\AUTHOR XStathis Tompaidis\footnote{$^4$}{e-mail: {\tt stathis@math.utexas.edu}} X\FROM XDepartment of Physics XThe University of Texas at Austin XAustin, TX 78712-1081 X\ENDTITLE X\ABSTRACT XWe compute the domain of analyticity Xof some perturbative expansions for invariant circles Xappearing in mechanics. We use Pad\'e approximants for the Xperturbative Xexpansions and Xintroduce methods to ascertain their domain of convergence. XWe also use non-perturbative methods based on direct Xcomputation of the invariant circles Xand, in analogy with Greene's criterion, approximation by Xcircles with rational rotation. XWe find that the domains computed by all the methods agree within Xthe limits of accuracy. The analytic structure of the expansions Xfor rational frequencies is clarified rigorously. X\ENDABSTRACT X X X\SECTION Introduction X XThe long term behavior of deterministic systems is very often studied Xby finding landmarks that organize the dynamics. X XAmong them, ones with very drastic effect are invariant circles. For Xexample, if the phase space of the system is two dimensional, existence Xof an invariant circle implies long term stability. X XIt is, therefore, not surprising that there has been a lot of Xeffort devoted to the computation of such objects. X XOne of the first and still widely used is the Poincar\'e--Lindstedt Xmethod (see, e.g., \cite{Po}, \S123 ff. or \cite{RA} for a computer Ximplementation) which consists on finding recursively the coefficients Xof an expansion of a parametrization of the invariant circle in powers Xof a small parameter. X XOne should notice that the study of the sense in which these series are Xvalid is rather subtle X(see e.g., \cite{Po}, \S146 for examples of Xdivergence, \S122 for different concepts of ``convergence''). X XGiven the practical importance of those invariant circles, it is Xinteresting to investigate the actual domains of analyticity of the functions Xdefined by those series. This can give a measure of confidence on Xapproximate calculations and, one could hope, also shed some light Xon the scenarios Xfor the breaking up of the validity Xof the conclusions drawn from perturbation theory. X XSimilar problems appear frequently Xin theoretical physics, for example in statistical mechanics Xwhen the boundaries of the domain of analyticity of Xfunctions defined perturbatively -- e.g. by low temperature Xexpansions -- correspond to phase transitions. XTherefore, besides their intrinsic interest, Lindstedt series can Xbe considered as a useful model for other series in theoretical physics Xsuch as low temperature perturbative expansions. In this context, one Xshould remark that there is considerable evidence that the Xphenomena happening at breakdown of Lindstedt series are very Xsimilar to those happening at breakdown of other series, both of them Xcan be interpreted as phase transitions whose main analytical features Xcan be described and predicted with the help of a renormalization group Xpicture. (See e.g., \cite{McK1}.) X XWe point out that in the case that the invariant circles X are ``normally hyperbolic'' X--- in particular attractive --- Xthere is a well developed theory to prove convergence of the expansions X\cite{Fe}. In other cases, convergence can be proved using the much Xsubtler K.A.M. theory (see \cite{Ze1}, \cite{Ze2}, \cite{Bo} for surveys). XThe latter is the usual case in the dynamical systems arising in classical Xmechanics as hamiltonian perturbations of integrable systems. XUnfortunately, in both cases the practical domains provided by these Xtheories are very conservative (much more so in the case of K.A.M. Xtheory) and throw little light on the behavior to be expected at Xbreakdown. X XRecently, in \cite{BC}, \cite{BCCF} it was proposed that for some of Xthese series arising in classical mechanics, one could use the so called XPad\'e method that is to compute the zeros of the Pad\'e approximant Xas a reasonable approximation to the domain of analyticity. This procedure, Xwhich we will call henceforth {\sl the Pad\'e method} Xhas been widely used in theoretical physics \cite{BGM}. X XUnfortunately, the Pad\'e method, even if very successful in practice, Xdoes not have a complete mathematical justification. Moreover, for the series Xin celestial mechanics very frequently the size of the coefficients of the Xperturbative expansion, vary widely in an erratic fashion. This makes Xthe numerical computation of Pad\'e approximants more difficult and throws Xsome doubt about the validity of the final result. One verification Xof the Pad\'e method by comparing its results with those of Xother methods was undertaken in \cite{FL1}. In that paper, Xthe Pad\'e method was applied to models similar to those considered in X\cite{BCCF} and the results were compared with those obtained by using X a complex Xversion of Greene's method (a partial Xjustification of this criterion can be found Xin \cite{FL2}, \cite{McK2}). The agreement obtained using the two methods was Xquite encouraging. X XIn this paper, we have extended the Xcomparison of the Pad\'e method with other Xindependent methods, some of them based in perturbative Xexpansions and others completely non-perturbative. X XWe have considered models which are not conservative for which we Xhave computed the perturbation expansions and applied the Pad\'e method. XBesides looking for the zeros of Xthe denominator of Pad\'e approximants, Xwe have explored other methods of ascertaining the Xdomain of analyticity of the Pad\'e approximants. XWe have also used non-perturbative methods to compare to the Xmethods based on the study of the perturbative expansions. XSome of the non-perturbative methods we have used are based on the Xfact that the map is dissipative, which makes it easy to Xcompute invariant sets. XWe have also proved an analogue of a partial justification of XGreene's criterion that makes Xit reasonable that the domains of analyticity for an invariant circle can be Xapproximated by those computed using rational frequencies. In that case, Xthe nature of the singularities Xcan be described in detail. Assuming a well known conjecture, this Xsingularity structure explains the behavior of the Pad\'e approximants Xthat we found. X XThe main reason to use dissipative systems in our study is that for them it Xis possible to locate the invariant tori by direct iteration and Xfollow them by non perturbative methods. XBesides the intrinsic interest of these dissipative systems -- they Xare reasonable models of some physical systems -- they can be used Xto provide some insight on the Poincar\'e--Lindstedt series for XHamiltonian systems. A first, heuristic, argument is that the structure of Xthe series is very similar -- in the dissipative case, however, they Xare more stable to compute numerically. Also Xone can argue heuristically that at the point at which Xthe invariant circle breaks down, the invariant circle has lost Xits hyperbolicity so that -- using the Xfact that our system can only have one non-zero Lyapunov Xexponent -- in an infinitesimal neighborhood, the system Xlooks like an area preserving system, so one could hope that Xsome of the results obtained about the behavior at Xbreakdown of circles would also apply to Xhamiltonian systems (of course the argument carries no weight for Xdynamical behaviors that in the neutral case are controlled by Xsubdominant terms). Indeed it has been argued \cite{R} that the Xrenormalization group picture developed for the breakdown of Xinvariant circles in hamiltonian systems can be extended to dissipative systems, Xif one scales the dissipation appropriately. X XThe results of our exploration are summarized in figures 1, 2, 3. XWe find it quite encouraging that so different methods give Xsimilar results, which seem to be within reasonable estimates Xof the margin of error for each of them. The methods Xthat seem to be the easiest to use and produce the more reliable Xresults for our system seem to be the non-perturbative methods Xdescribed in section 8. X X\SECTION Notation and Preliminaries. X XWe have considered the convergence of Lindstedt series for one particular Xmodel that we will, henceforth refer to as the ``rotating logistic'' map. X$$F_{\epsilon,\lambda,\omega} (r,\theta) X= (f_{\epsilon,\lambda}(r, \theta),\ \theta + \omega \bmod 1) X= (r^2 +\lambda +\epsilon \cos (2\pi \theta),\ \theta + \omega \bmod 1) X\EQ(logistic)$$ Xwhere $r$ is taken to be a complex number. X XNotice that for $\epsilon =0$ \equ(logistic) reduces to the well known Xlogistic map, which is well known to exhibit a very rich behavior. XA fixed point $r_0$ for the Xlogistic map becomes X an invariant circle $\{r_0\} \times \bT^1$ for X$F_{0,\lambda,\omega}$, filled by dense orbits if $\omega$ is irrational, Xor consisting of a Xfamily of periodic orbits for X$\omega$ rational. X XNotice that \equ(logistic) with $\omega$ irrational can Xbe considered as a quasi-periodic Xexcitation of the usual logistic map. Hence, it can appear as a physically Xreasonable model in all of the Xsituations where the logistic map appears, if we assume that they are modified Xby an external quasi-periodic force. For example in population Xdynamics or as a phenomenological model of processes with very strong Xdissipation that reduces the system to one-dimensional. X XAs the parameters $\lambda,\epsilon$ vary, this map exhibits a large variety Xof behaviors and bifurcations (suffice it to mention that for X$\epsilon =0$ it exhibits a Feigenbaum cascade of period doublings). XA study of the bifurcation diagrams for invariant tori was undertaken Xin \cite{K} and in \cite{AKL1} and there one can find detailed Xdescriptions of breakdown behavior for certain regions of parameters. XOf course, in \cite{AKL1} only real values of the parameters are considered. XIf we consider complex values of the parameters, some bifurcations Xthat do not appear in the real case, such as period $n$-tupling, $n> 2$, Xbecome possible. Indeed, they happen in the quadratic family Xfor certain complex values of $\lambda$. A K.A.M. argument Xsimilar to those in \cite{AKL1}, \cite{CI} can Xshow that such behaviors persist for sufficiently small values of $\epsilon$. X X X XIn this paper we will consider $\lambda$, X$\omega$ as fixed and explore the dependence Xon $\epsilon$ of the invariant circle. XHence, when it is not needed, Xwe will suppress $\lambda$, $\omega$ from Xthe notation for the map. X XWe will consider only $\lambda$'s real and somewhat smaller than the value Xfor which the first period doubling Xbifurcation occurs, Xwhich the work of \cite{AKL} suggests as not having any other Xbifurcation as $\epsilon$ changes Xtill breakdown. This hypothesis is also verified by our calculations, Xsince we compute the invariant circle for all the values of X$\epsilon$ for which it exists, very close to the value for Xwhich it breaks down, and we verify that the mechanism of destruction Xis very different from the simple $n$-tupling bifurcations. X X X X\SECTION Lindstedt expansions X XFollowing standard practice in XLindstedt methods, we observe that the graph of a map X$u_\epsilon : \torus \to \real$ Xis invariant under the map \equ(logistic) if and only if Xit satisfies X$$u_\epsilon (\theta +\omega) = \bigl[ u_\epsilon (\theta)\bigr]^2 X+\lambda + \epsilon \cos 2\pi \theta . X\EQ(Lindstedt)$$ X XIf we now assume an expansion in powers of $\epsilon$, X$u_\epsilon (\theta) = \sum_{n=0}^\infty \epsilon^n u^n (\theta)$ Xand substitute it in \equ(Lindstedt) we obtain: X$$\eqalign{ Xu^0 (\theta +\omega) & = u^0 (\theta)^2 +\lambda\cr Xu^n (\theta +\omega) & = 2u^0 (\theta) u^n (\theta) X+ \sum_{m=1}^{n-1} u^{n-m} (\theta) u^m (\theta) + \delta_{n,1} X\cos (2\pi\theta),\quad n>0\cr} X\EQ(recursion)$$ Xwhere $\delta_{n, 1}$ is the usual Kronecker symbol. X XWe claim that the first equation in \equ(recursion) admits the two Xsolutions $u^0(\theta) = u^0 = \frac12 \pm \frac12 \sqrt{1-4\lambda}$ and no Xother continuous solution if $\lambda \in (-\frac34, \frac14)$. X XMoreover, once we choose one of the two solutions for the Xfirst equation, the second hierarchy of equations allows the Xrecursive determination of all the $u^n$'s. X XIn effect, if \equ(recursion) is to hold, X$$u^0 (\theta +n\omega) = \ell_\lambda^n \bigl( u^0 (\theta)\bigr)$$ Xwhere $\ell_\lambda$ denotes the logistic map $\ell_\lambda (x) = x^2+\lambda$. XFor the values of the parameter selected, it is well known --- see e.g. X\cite {G} --- that all bounded orbits of $\ell_\lambda$, except those Xstarting in $\frac12 +\frac12 \sqrt{1-4\lambda}$ and its preimages, Xconverge to $\frac12-\frac12 \sqrt{1-4\lambda}$. Since $\theta$ is an Xaccumulation point of $\theta +n\omega$, it follows that $u^0(\theta)$ Xshould be either one of the two fixed points. XIf the function $u^0$ is to be continuous, then it should be constant. X XTo prove the second assertion, we observe that if we recursively Xassume that $u^0,\ldots,u^{n-1}$ are known we can determine $u^n$ Xby solving an equation of the form X$$u^n (\theta +\omega) - 2u^0 u^n(\theta) = R^n (\theta) X\EQ(cohomology)$$ X XSuch equations can be conveniently analyzed using Fourier series Xsetting: X$$ X u^n (\theta) = \sum \hat u^{n,k} e^{2\pi ik\theta} X$$ Xand similarly for $R$, and other periodic functions. XWe have that the unique solution of X\equ(cohomology) is X$$\hat u^{n,k} = \hat R^{n,k} \big\slash (e^{2\pi ik\omega} - 2u^0). X\EQ(solution)$$ X XWe note that for the rotating logistic map it is easy to prove by Xinduction that the solutions $u^n$ of \equ(recursion) are Xtrigonometric polynomials with degree$(u^n) = n$. XHence, the $R^n$'s are also trigonometric polynomials. X XA similar argument would show that provided that the forcing term is Xa trigonometric polynomial in $\theta$, then the $u^n$'s are also Xtrigonometric polynomials and the degree of $u^n$ is a linear function Xof $n$. X XTo discuss convergence, it is convenient to adopt a more general point Xof view that will also turn out to apply to the case when the forcing Xterm is a periodic function of $\theta$ rather than just a trigonometric Xpolynomial. X XWe note that, when $\lambda \in (-\frac34, \frac14)$, $|2u^0|\ne 1$ Xhence $(e^{2\pi ik\omega} - 2u^0)$ is bounded away from zero Xuniformly in $k \in \integer$ so that X$$ X\sup_{k \in \integer} | e^{2\pi ik\omega} - 2u^0 |^{-1} \le K X\EQ(Kdefined) X$$ Xwhere $K \ge 1$ (for $\lambda \in (-\frac34, \frac14)$). XHence, X$ |\hat u^{n,k} | \le K |\hat R^{n,k}| $. XSo that, if we assume $|\hat R^{n,k} | \le Ae^{-\delta |k|}$ we Xwould obtain $|\hat u^{n,k} | \le KAe^{-\delta |k|}$ so that, for example, Xif $R$ is analytic in a certain domain, $\{\theta \mid |\Im \theta| < \delta\}$ Xso will be $u$. X XMoreover, it is very easy to estimate the recursion to obtain convergence. X X\CLAIM {Lemma}(convergence) XIf $|\epsilon| < \frac12 K^{-2} e ^{-2\pi \delta}$ X(where $K$ is as in \equ(Kdefined)), the series obtained by Xsumming the $u^n$'s obtained by \equ(recursion) converges uniformly Xon $\{\theta \mid |\Im \theta| < \delta\}$. X X\PROOF XFor $\delta >0$, Xif $f$ is an analytic function on the unit circle, Xwe can expand it in Fourier series, X$f(\theta) = \sum \hat f^k e^{2\pi ik\theta}.$ XWe denote by $\|f\|_\delta = \sup e^{\delta |k|} |\hat f^k|$. XIt is well known that this defines a norm on a Banach space of analytic Xfunctions. We denote such space by $C^{\omega,\delta}$. XWe observe that $\|f\cdot g\|_\delta \le \|f\|_\delta \|g\|_\delta$ Xand that if $u^n$ and $R^n$ are related as in \equ(solution), then X$\|u^n\|_\delta \le K\|R^n\|_\delta$. X XWe also observe that $R^1 (\theta) = \cos 2\pi \theta$ so that X$\|u^1 \|_\delta \le \frac12 K e^{2\pi\delta}$. X XThe recursion part of \equ(recursion) implies for $n>1$ X$$\|u^n \|_\delta \le K\|R^n\|_\delta X\le K\sum_{m=1}^{n-1} \|u^{n-m}\|_\delta \|u^m\|_\delta. X\EQ(estimates)$$ XBy induction, it is easy to show that X$$\| u^i\|_{\delta} \le \frac{\sigma_i}{K} X\bigl(\frac{K^2 e^{2 \pi \delta}}{2} \bigr)^i , X\qquad i \ge 1 $$ Xwhere $\sigma_1 = 1$, $\sigma_k = \sum_{j=1}^{k-1} \sigma_j \sigma_{k-j}$. XThis is certainly true for $i=1$ and the recursive bound \equ(estimates) Xshows that if it is true for $i \le n-1$ it is true for $i=n$. XWe see that if we denote X$$ \sigma(z) = \sum_{i=1}^{\infty} \sigma_i z^n $$ Xthen $\sigma(z)$ is a solution of $\sigma(z) = \sigma(z)^2 + z$. XSince $\sigma(z)$ also satisfies that $\sigma(0) = 0$, X$\sigma_0 = 0$, we conclude that $\sigma(z) = \frac12 - \frac12 \sqrt{1- 4z}$ and X$$ \sigma_1 = 1,\quad X \sigma_n = \frac1n {{2n-2} \choose {n-1} } \le \frac{4^{n-1}}{n}, X\qquad n \ge 2 .$$ XThis shows that $\sum_0^{\infty} u^n(\theta) \epsilon^n $ converges in Xthe $\Norm_{\delta}$ sense Xand proves the statement of \clm(convergence). X\QED X X\REMARK XWe point out that results similar to \clm(convergence) can Xbe proved as corollaries of the general theory of stability Xfor normally hyperbolic manifolds. We also point out that the Xdomain of applicability of these results converges to zero as X$\lambda$ converges to $-\frac34$, the value at which the logistic map Xexperiences the first period doubling bifurcation. By using the Xmuch more subtle K.A.M. theory it is possible to show that if X$\omega$ is Diophantine, one can get domains of convergence which are Xuniform in $\lambda \in [\lambda_-,\lambda_+]$ where $\lambda_-$, X$\lambda_+$ are some numbers that contain the bifurcation point. XWe refer to \cite{AKL2} or \cite{CI} for details of this theory. X X\REMARK XThe use of the norms $\Norm_\delta$ in the above proof is natural Xin view of the fact that, for fixed $\epsilon$, the maximal domains Xof analyticity in $\theta$ for $u_\epsilon(\theta)$ are of the form X$\{\theta \mid |\Im \theta| < \delta\}$. XThis can be seen by observing that if $u_\epsilon$ is defined for some X$\theta,$ then it is also defined using \equ(Lindstedt) for X$\theta +\omega$. So that the domains of analyticity in $\theta$ of X$u_{\epsilon}(\theta)$ have to be invariant Xunder irrational translation. X XTo study numerically the domain of analyticity of the map X$\epsilon \mapsto u_\epsilon$, it is easy to study the Xdomain of analyticity of maps $\epsilon \mapsto \Gamma[ u_\epsilon]$, Xwhere $\Gamma$ is an entire map from the space of analytic functions Xto the complex numbers. Clearly the domain of analyticity of X$\epsilon \mapsto \Gamma[ u_\epsilon]$ is bigger than the Xdomain of analyticity of the map $\epsilon \mapsto u_\epsilon$. XOne expects also, that many observables will lead to the same Xdomain of analyticity. Some observables that immediately come Xto mind are the evaluation of the function at certain values and Xthe Fourier coefficients. XWe conjecture that indeed, these simple observables give the optimal domain Xof analyticity. X X\CLAIM {Conjecture}(analdom) XFor a fixed $\lambda \in (-3/4, 1/4)$, $\omega$ irrational, $\theta \in \real$, Xthe function X$\epsilon\to u_\epsilon (\theta)$ is defined in a domain $D$ Xindependent of $\theta$. This domain agrees with the Xdomain of analyticity of $\epsilon \mapsto \hat u_{\epsilon}^k$. X XTo justify \clm(analdom) we see that if, Xfor a fixed $\theta$, the function $\epsilon\to u_\epsilon (\theta)$ Xcan be defined in a certain domain $D(\theta)$, \equ(Lindstedt) shows Xthat $\epsilon\to u_\epsilon (\theta +\omega)$ can be defined in a Xdomain that is at least as big. Therefore $D(\theta) \subset D(\theta +\omega)$. XIn our case, however, we expect that $D(\theta) = D(\theta +\omega)$ since Xthe only way that the domain of analyticity $D(\theta +\omega)$ could Xactually be bigger than $D(\theta)$ is by using that the function X$u\to u^2+\lambda$ is not invertible and can transform certain Xsingularities into analytic functions. Such behavior seems unlikely, Xespecially in view of our numerical computations. X XNotice that the argument for \clm(analdom) uses heavily Xthat $\omega$ is irrational and, if X$\omega$ were rational, the domain does depend on X$\theta$. (See section 9 for a discussion of analyticity domains in the Xcase that the frequency is rational.) XAlso, if the system we consider is not \equ(logistic) but Xhad special Xsymmetries that force all the coefficients in the expansion to Xhave odd parity, the function $u_\epsilon(\theta)$ Xvanishes identically at certain values of $\theta$, Xhence is trivially entire in $\epsilon$ for those values. X XOur computations are also evidence that the analyticity domain of Xall the observables mentioned in X\clm(analdom) are the same, so that it is a reasonable conjecture that Xthey agree with the domain of analyticity of $\epsilon \mapsto u_\epsilon$. X X\SECTION Pad\'e Approximations X XWe recall that a Pad\'e approximant $[M/N]$ to an analytic function Xis a rational function with numerator $P$ of degree $M$ and denominator $Q$ Xof degree $N$ whose Taylor expansion up to order $M+N$ agrees with that Xof $S$. X XWe can assume without loss of generality that $D(0)=1$. XIf we impose this normalization, under mild non-degeneracy conditions, Xthe Pad\'e approximant of order $[M/N]$ exists and is unique. X XWe refer to \cite{B}, \cite{BGM}, \cite{M}, \cite{Gi} Xfor a survey of mathematical results about Pad\'e approximants and Xtheir applications in problems of theoretical physics. XThey have indeed been widely used in almost all fields in Physics Xin which perturbative expansions and their breakdown play a role. X XIf the Taylor expansions of $S(\epsilon)$ and of $P(\epsilon)/D(\epsilon)$ Xare to match up to order $\epsilon^{N+M+1}$ we can write X$S(\epsilon) D(\epsilon) = P(\epsilon) +O(\epsilon^{N+M+1})$ which, Xtogether with the normalization $D(0)=1$, leads to the equations X$$\eqalign{ XP_i & = S_i + \sum_{j=1}^{\min (N,i)} S_{i-j} D_j\qquad 0\le i\le M\cr X0 & = S_i + \sum_{j=1}^{\min (N,i)} S_{i-j} D_j\qquad M< i\le M+N\cr} X\EQ(match)$$ X XNotice that the second set the equations involves only the $D$'s Xand that once we know the $D$'s, by substitution in the first set Xof equations, it is possible to compute the $P$'s. X XThere are other computationally more efficient methods to compute XPad\'e approximants based on recursions (see e.g., \cite{BGM} vol. 1, pg.66). XNevertheless, the algorithm sketched above has the advantage that, by Xusing careful standard numerical analysis routines we can obtain condition Xnumbers that give a measure of the reliability of the calculations. We Xwill give more details in the section devoted to numerical implementations. X XThe standard method to compute the domain of analyticity of $S(\epsilon)$ Xbased on Pad\'e approximants consists in computing $D$ and $P$ as before. XOne then expects that the boundary Xof the domain of analyticity for $S$ will be approximated by Xthe poles of $P/D$. That is, the zeros of $D$ which are not zeros of $P$ X(or at least zeros of a smaller order). XThis is expressed in the following quote (\cite{Gi}, pg. 310): X X{\sl ``Tous les theor\`emes de convergence des approximants de Pad\'e, Xainsi que les resultats num\'eriques indiquent que ces Xapproximants ont une tendence visible \'a reproduire les propriet\'es Xd' analycit\'e d' une fonction.''} X X\SECTION \vbox{ X\vbox{A new method to compute domains of analyticity from }\breakline X\vbox{Pad\'e approximants.}} X XThe usual method of computing domains of analyticity of functions Xis just to compute the zeros of the denominator of the XPad\'e approximation. XUnfortunately, the calculation of zeros of a polynomial frequently Xhas large condition numbers (see \cite{Wi} for some examples, X\cite{He} for a discussion of algorithms). This is particularly Xunfortunate since the calculation of Pad\'e approximants out of the Xcoefficients in the expansion is also very ill conditioned. X XThe previous remarks are especially true for the zeros which Xare not close to the origin. The elementary example -- which we learned Xfrom G. Baker -- X$$S(\epsilon ) = {1\over \epsilon -a_1} + {1\over \epsilon -a_2} X= \sum_{n=0} \epsilon^n X\left( \left( { 1\over a_1}\right)^{n+1} + \left( { 1\over a_2}\right)^{n+1} X\right)$$ Xshows that the information about the outermost pole is hidden in the Xhigh precision part of the coefficients of the expansion. For many of the Xperturbation expansions in classical mechanics, whose terms alternate widely Xin sizes, this seems particularly dangerous. X XSince the number of zeros of the denominator is roughly half the degree Xof $S(\epsilon)$ (in practice considerably less since sometimes the zeros Xof the numerator are also zeros of the denominator) it is clear that it is Xnot very easy to obtain a very detailed picture of the boundary since the Xcondition number for the computation of zeros worsens very fast with the Xnumber of zeros. X XIn the expansions in celestial mechanics such as the Lindstedt method, we Xcan take advantage of the presumed fact that Xwhen the frequency is irrational the domain of analyticity Xshould be independent of $\theta$, to do several calculations and obtain Xsignificantly more points in the boundary. Such enhancement is not Xavailable for most of the situations to which Pad\'e approximants are Xapplied. X XWe state the following conjecture: X X\CLAIM {Conjecture}(Padeapprox) XLet $f$ be one of the Xfucntions appearing in the XLindstedt-Poincar\'e Xexpansions. Then, $f$ Xis analytic in a topological disc ${\cal D} \subset \complex$ Xwith a natural boundary for $f$ and the Xsequence of $[N/N]$ Pad\'e approximants converges to X$f$ in measure, as $N \to \infty$, on any compact subset of ${\cal D}$. X XThe method we propose is based on \clm(Padeapprox). XIf, according to \clm(Padeapprox), $\frac{P_N(z)}{D_N(z)}$ converges as X$N \to \infty$, $\left|\frac{P_N(z)}{D_N(z)} - \frac{P_M(z)}{D_M(z)}\right|$ Xshould converge to Xzero as $N,M\to\infty$. XHence, a reasonable approximation to the boundary of convergence of the Xdiagonal Pad\'e series --- and hence, according to \clm(Padeapprox), Xto the domain of analyticity of the function --- could Xbe the level curve X$$\left| {P_N(z) \over D_N(z)} - {P_M(z) \over D_M(z)}\right| X= \delta$$ Xfor a reasonably small $\delta$ and sufficiently large $N,M$, Xand $z$ not in the neighborhood of a spurious pole of the $[M/M]$, $[N/N]$ Xapproximants. X XUnfortunately, the practical Ximplementation of the criterion Xcannot take the limit as $N,M$ tend to infinity Xbut rather just take some reasonably high value. XThen, the criterion involves a free parameter X$\delta$ as a function of the degree of the Xapproximation and the results could depend on its choice. XIn the examples we have considered, we have found that any Xchoice between $10^{-5}$ and $10^{-1}$ leads to results not more uncertain Xthan those obtained by finding the zeros of $D_M$. X XThe dependence on the parameter $\delta$ can be further reduced Xby plotting the level surface X$$ X\left| {P_{N_1}(z) \over D_{N_1}(z)} X- {P_{N_2}(z) \over D_{N_2}(z)} \right| + \cdots + X\left| {P_{N_{j-1}} (z) \over D_{N_{j-1}} (z)} X- {P_{N_j}(z) \over D_{N_j}(z)}\right| = \delta X$$ Xwhich, according to \clm(Padeapprox), will also provide an approximation to the Xdomain of analyticity. X X XUnfortunately, little is known about the Xcovergence of Pad\'e approximants in the case that the Xfunction has natural boundaries. XFor a class of functions Xwith natural boundaries -- but which remain Xquasianalytic accross the boundary -- X(see \cite{Gi}, pg. 306--309) \cite{GN} have shown that Xthe $[(N+J)/N]$ Pad\'e approximants converge in measure to the Xfunction as $N \to \infty$, in any closed, bounded region of the Xcomplex plane. Specifically: X X\CLAIM Theorem (Nuttal) XFor the function $f(z) = \sum_{n=1}^{\infty} X\frac{A_n}{(1-z\alpha_n)}$, where the $\alpha_n$ lie densely on the Xunit circle and $|A_n| < Ce^{-n^{1+\gamma}}, \gamma > 0$, the sequence Xof $[(N+J)/N]$ Pad\'e approximants to $f(z)$ converges in measure to $f$ Xas $N \to \infty$ in any closed, bounded region of the complex plane. X X XThe method of proof, as remarked in \cite{GN} can Xbe extended to other cases and that the condition X$|\alpha_n| = 1$ can be modified to X$|\alpha_n | < a$. They also discuss how Xslightly faster rates of growth in the coefficients, Xcould lead to divergence. X XResults such as this one make it reasonable to Xbe hopeful that convergence of the Pad\'e approximants is Xa reasonably general phenomenon and, hence, lend Xindirect support to \clm(Padeapprox) X XOur numerical results, also support X\clm(Padeapprox) XOn the other had we note that, in contrast with the X\clm(Nuttal), we to observe that the XPad\'e approximants of our Xfunctions seem to diverge outside of the Xdomain analyticity of the function. X XIt is not clear to us what could be a reasonably general Xcondition that implies convergence of Xthe Pad\'e approximants for the cases we are interested in. X X\SECTION Newton Method X XFor a fixed $\epsilon_0$, it is possible to solve equation X\equ(Lindstedt) using a Newton method. X XWe see that if $u_{\epsilon_0}$ fails to satisfy \equ(Lindstedt) by a small Xamount $R_{\epsilon_0} (\theta)$ i.e., X$$u_{\epsilon_0} (\theta +\omega) - u_{\epsilon_0} (\theta)^2 - \lambda - X\epsilon_0 \cos 2\pi \theta = R_{\epsilon_0}(\theta) X\EQ(error)$$ Xwe can try to improve the solution by setting it to X$u_{\epsilon_0}(\theta) + \Delta_{\epsilon_0} (\theta)$, Xwhere $\Delta_{\epsilon_0} (\theta)$ will be conveniently chosen. X XIf $\Delta_{\epsilon_0}(\theta)$ satisfies X$$\Delta_{\epsilon_0} (\theta +\omega) - 2u_{\epsilon_0} (\theta) X\Delta_{\epsilon_0} (\theta) = R_{\epsilon_0} (\theta) X\EQ(Newton)$$ Xthen, $u_{\epsilon_0}(\theta) +\Delta_{\epsilon_0} (\theta)$ Xwill satisfy \equ(Lindstedt) up to error terms which are much Xsmaller than $R_{\epsilon_0}(\theta)$. X XWe will postpone for the moment a discussion of the numerical Xdiscretizations used to solve \equ(Newton). X XThis method, as it is well known from even finite dimensional examples, Xhas the shortcoming that it Xonly converges when sufficiently good guesses are taken as starting points. X XIn our case one could perform a Xcontinuation method starting from very small values of $\epsilon$. That is, Xwhen one exact solution is found, we take it as an approximate solution Xfor the equation with a slightly bigger parameter. We note that the Xsolution when X$\epsilon = 0$ is known exactly. XWe could also take for some values of $\epsilon$ the sum of the Xseries \equ(recursion) as an initial guess. This would provide us with Xan independent verification that the series is converging to solutions of the Xequation. X XWe emphasize that the validity of the solution of the Newton method Xis independent of the method used to obtain the initial guess since, Xin the process of running the Newton method one checks that the equation Xis indeed satisfied. X XFor practical calculations in concrete problems the Newton method seems Xto have advantages over the method of expansion in powers of $\epsilon$. XFor example, notice that the expansions in powers of $\epsilon$ can only Xconverge on a disk of radius equal to the distance from the origin to the Xclosest singularity. If the shape of the analyticity domain is very Xdifferent from a disk, this implies that there will be several Xvalues of $\epsilon$ for which the invariant circles exist and for which Xthe $\epsilon$ expansion does not converge. For a continuation method, it Xis quite possible to obtain the solution in all the connected domain where Xthe solution exists. XNotice also that the method of expansion in powers requires the storage Xof many functions. The Newton method requires only the storage of one. XOn the other hand, one should also mention that if one requires solutions Xfor many values of the parameter, the $\epsilon$ expansion method could Xbe faster and gives more global information. X X\SECTION Multipoint Pad\'e Approximation X XThe multipoint Pad\'e approximation is an interesting compromise Xbetween rational interpolation and the Pad\'e approximation (which we Xcould consider as a degenerate case of interpolation in which all Xthe interpolation points are infinitesimally close). X XWe recall, see e.g. \cite{BGM} vol.2, pg.5, that given a set of points X$\{z_i\}_{i=1,k}$ in the complex plane and a function $S(z)$ with XTaylor expansions of order $\ell_i$ around those points, we define Xthe $[N/M]$ multipoint Pad\'e (or rational) approximant as: X$${P(z)\over D(z)}\ ,\quad \degree P=N\ ,\quad \degree D=M\ ,\quad XD(0)=1$$ Xsuch that $M+N+1 = \sum_{i=1}^k (\ell_i +1)$ and X$${d^s\over dz^s} \bigl( P(z) - D(z) S(z)\bigr) \big|_{z=z_i} =0 X\ ,\qquad s \le \ell_i\ ,\ i= 1,k.$$ XSetting X$$\eqalign{ X&P(z) = \sum_{j=0}^N P_j z^j\cr X&D(z) = \sum_{j=0}^M D_j z^j\ ,\quad D(0) = D_0 = 1\cr X&S(z) = \sum_{j=0}^{\ell_i} S_{i;j} (z-z_i)^j\ , i=1,k X}$$ Xwe require X$$\displaylines{ X\hfill \sum_{j=s}^N P_j {j!\over (j-s)!} \, z_i^{j-s} X= \left[ \sum_{n=0}^s {s\choose n} S^{(s-n)} D^{(n)} \right] (z_i)\hfill\cr}$$ Xwhere X$$S^{(s)} (z_i) \equiv {d^s \over dz^s} S(z)\big|_{z=z_i}.$$ XSince X$$\displaylines{\hfill XD^{(n)} (z_i) = \sum_{m=n}^M {m!\over (m-n)!} \, D_m z_i^{m-n}\ ,\qquad 0\le n\le M\hfill \cr X\hfill S^{(s-n)} (z_i) = (s-n)! \, S_{i;s-n}\ , \qquad 0\le s-n < M+N+1 \hfill \cr}$$ Xor X$$\sum_{j=s}^N P_j {j!\over (j-s)!} \, z_i^{j-s} X= s! \sum_{n=0}^s \sum_{m=n}^M {m\choose n} S_{i;s-n} D_m z_i^{m-n}$$ Xwhere, to simplify the notation, we extend the usual combinatorial Xnumbers by: X$${m\choose n} = X\cases{ X\displaystyle {m!\over n!(m-n)!}\ , &$m\ge n$\cr X0\ ,&$m1 \hfill \ \cr} X\EQ(recursionnewton)$$ X XIf we assume that we know $\Delta^1,\ldots,\Delta^{n-1}$ then $\Delta^n$ Xcan be found by solving an equation of the form X$$\Delta^n (\theta + \omega) - 2u_{\epsilon_i}(\theta) \Delta^n(\theta) = XR^n(\theta) \EQ(deltarecursion)$$ XTo solve \equ(deltarecursion) we prove the following lemma : X\CLAIM{Lemma}(deltabound) XIf $u_{\epsilon_i}(\theta)$ is an analytic function satisfying X\vskip1pt X\item{(i)} $\|2u_{\epsilon_i}\|_{\delta} \le A$ X\vskip1pt X\item{(ii)} For some $m \in \natural, 0<\gamma<1, \quad \| 2u_{\epsilon_i}(\theta) \cdots 2u_{\epsilon_i}(\theta+m\omega)\|_{\delta}\le\gamma$ X\vskip1pt Xthen, X\vskip1pt X Given any $R^n$ analytic in X$\{\theta \big| |\Im(\theta)| \le \delta\}$, Xwe can find a unique $\Delta^n$ solving X\equ(deltarecursion). Moreover, X\vskip1pt X$\| \Delta^n\|_{\delta} \le K \|R^n\|_{\delta}$, where $K$ Xcan be taken to be $K = A^m/(1 - \gamma^{1/m})$. X X X\PROOF XApplying \equ(deltarecursion) repeatedly we have X$$\eqalign{\Delta^n (\theta + \omega) & = \sum_{k=0}^N \left(\prod_{j=1}^k X\bigl(2u_{\epsilon_i}(\theta-j\omega)\bigr)\right) R^n(\theta -k\omega)\cr X&\qquad + \prod_{k=0}^N \Bigl( 2u_{\epsilon_i}\bigl(\theta - k\omega\bigr) X\Bigr) \Delta^n \bigl( \theta -N\omega\bigr).} X\EQ(iterated)$$ X XIf there is a bounded solution, then the last term in X\equ(iterated) should tend to zero, so that the only Xsolution of \equ(deltarecursion) should be: X$$ \Delta^n (\theta) = \sum_{k=0}^{\infty} \left(\prod_{j=1}^k( 2u_{\epsilon_i}(\theta X-j\omega))\right)R^n(\theta-k\omega). X\EQ(deltaR)$$ XConsidering blocks of length m we can bound the products appearing in X\equ(deltaR) by: X$$ \bigl\|\prod_{j=1}^k(2u_{\epsilon_i}(\theta-j\omega))\bigr\|_{\delta} X\le A^m \gamma^{[k/m]} = A^m [\gamma^{1/m}]^k$$ Xso that X$$\| \Delta \|_\delta \le \| R\|_\delta \frac{A^m}{1-\gamma^{1/m}} = K \|R\|_{\delta}.$$ X XThe above estimates show also that the series \equ(deltaR) converge absolutely, Xso that it is possible to rearrange terms and show that Xindeed it solves \equ(deltarecursion). X\QED XNow we can show convergence for the series \equ(recursionnewton). X X\CLAIM{Lemma}(deltaconv) XIf $ | \hat \epsilon | < \frac12 K ^{-2} e^{-2\pi \delta} $ (where $K$ as in X\clm(deltabound)) the series obtained by summing the $\Delta^n$'s computed Xfrom \equ(recursionnewton) converges uniformly on X$\{\theta \big| \ |\Im \theta | < \delta \}$. X X\PROOF XWe notice that $R^1(\theta) = \cos 2\pi \theta$ so that X$$\| \Delta^1 \|_{\delta} \le K\|R^1\|_{\delta} \le \frac12 K e^{2 \pi \delta}$$ XFrom \equ(recursionnewton) we have that for $n>1$ X$$ \|\Delta^n \|_{\delta} \le K\|R^n\|_{\delta} \le K \sum_{m=1}^{n-1} X\| \Delta^{n-m}\|_{\delta} \| \Delta^m\|_{\delta} X\EQ(deltabound)$$ XThis recursion is the same Xas \equ(estimates) and to obtain the Xestimates claimed, it suffices to use the same argument that Xwe used in \clm(convergence) X\QED X\REMARK X\clm(deltaconv), together with \clm(convergence) show that the mapping X$\epsilon \to u_\epsilon$ is analytic in $|\epsilon| \le \frac12 K^{-2}$ Xwhen we give the $u_\epsilon$ the topology induced by $\Norm_\delta$. XThis is much stronger than saying that for a fixed $\theta$ the series X$\sum_{n=0}^\infty u^n (\theta) \epsilon^n$ or $\sum_{n=1}^\infty \Delta^n(\theta) \hat \epsilon^n $ converge. X X\REMARK XNotice that the equations appearing in the recursion for $n>1$ are very Xsimilar to the equations we encountered in the study of the Newton method X(this is not a coincidence since the procedure we carried out is just a very Xexplicit form of the implicit function theorem --- the equation X\equ(Newton) is just inverting the derivative, which also plays a role Xin the implicit function theorem). X XAgain, once we have computed the expansions, in terms of X$\epsilon$, of the function by evaluating at Xdifferent values of $\theta$ we obtain several Xnumerators and denominators and several possible candidates for the domain Xof convergence. They should agree. X X X XWe point out that the hypotheses of \clm(deltabound) Xon the existence of a uniformly contractive analytic Xinvariant circle, for this model, are implied by the X\`a priori much weaker conditions that there exists Xa continuous invariant circle with negative Lyapunov Xexponent. Hence, the boundary of the domain of analyticity Xis given by the boundary of the domain of Xexistence of continuous circles with negative XLyapunov exponent. X X XWe recall -- see e.g. \cite{W} Thm 6.20 -- that rotations by an Xirrational number are uniquely ergodic. That is, they admit Xonly one invariant measure. Hence, it makes sense to speak of Xthe Lyapunov exponent of the invariant circle without specifying Xexplicitly the measure. X X\CLAIM Lemma(Lyap) XLet $u$ be a continuous function solving \equ(Lindstedt) Xwith $\omega$ irrational. XIf $\int \ln | 2 u( \theta) | d \theta < 0$, Xthen, we can find an $m$ such that X$$\bigl|2u(\theta) \cdot 2u(\theta + \omega) \cdots X2 u( \theta + Xm \omega)\bigr| \le \gamma < 1.$$ X X\PROOF XDenote by $\phi(\theta)$ a continuous function X$\phi(\theta) \ge \ln | 2 u(\theta) |$, X$ \int \phi(\theta) d \theta = \gamma_1 < 0$. X(Such function can be obtained Xby setting $\phi( \theta) = \ln( \max( |2 u(\theta)| , \rho))$ Xfor sufficiently small $\rho > 0$.) XWe recall that (see e.g \cite{W} Thm 6.19) that for Xa uniquely ergodic map, the Birkhoff sums of a continuous Xfunction converge uniformly. XIn our case, they should converge uniformly to $\gamma_1$. XHence, we can find $m$ such that X$\phi(\theta) + \phi(\theta + \omega) + \cdots X + \phi(\theta + m \omega) \le \ln \gamma < 0.$ X Since $\phi(\theta) \ge \ln( | 2 u(\theta)|)$, Xthe lemma is established. X\QED X\CLAIM{Lemma}(analyticu) XLet $u$ be a continuous map solving \equ(Lindstedt) and Xsuch that, for some $m \in \natural, 0< \gamma < 1$, X$ | 2 u( \theta) \cdot 2 u(\theta + \omega) \cdots 2 u(\theta + m \omega) | \le \gamma < 1$, for $\theta \in \torus^1.$ XThen $u$ is analytic. X XNotice that, even if \clm(Lyap) requires that $\omega$ is irrational, X\clm(analyticu) works even for rational $\omega$. X X\PROOF XConsider the graph transform operator X$$ X\Gamma[u](\theta) = X u(\theta - \omega)^2+ \lambda + \epsilon\cos 2 \pi (\theta-\omega). X\EQ(graphtransform) X$$ XIt is equivalent that $u$ is a fixed point of X$\Gamma$ and that it satisfies \equ(Lindstedt). X XWe will show that, under the hypotheses Xof \clm(analyticu), we can find a Xball in $C^0$ and in $C^{\omega,\delta}$, for $\delta$ Xsufficiently small, with non-empty Xintersection, on which $\Gamma^{m+1}$ is a contraction with the Xcorresponding norms and that the $C^0$ ball contains the Xgiven fixed point $u$. Then, if we take a point belonging to Xthe intersection of the two balls, by the uniqueness part Xof the contraction mapping theorem, by iterating it, it Xhas to converge to $u$. On the other hand, by the contraction Xon $C^{\omega,\delta}$, it converges to an analytic fixed point. X XTo prove the claim, we observe that Xthe derivative of $\Gamma^{m+1}$ at the fixed point $u$ Xcan be computed both in X$C^0$ and in $C^{\omega, \delta}$ as: X$$ XD\Gamma^{m+1}(u)[\eta](\theta) = 2 u( \theta - \omega) X\cdot 2 u( \theta - 2 \omega)\cdots 2 u(\theta - (m+1) \omega) X\eta( \theta - (m+1) \omega) X\EQ(derivativeformula) X$$ XWe note that for other functions in place of the logistic, Xthe derivative of $\Gamma^{m+1}$ Xis still obtained by a multiplication operator and a shift. X XDenote by $K_\alpha$ the heat kernel and Xobserve that $ \| u - K_\alpha u\|_{C^0}$ converges uniformly to $0$ Xas $\alpha \to 0$. Also X$\|K_\alpha u\|_{\delta} \to_{\scriptstyle \delta \to 0} X\|K_\alpha u\|_{C^0} \to_{\scriptstyle \alpha \to 0} \|u\|_{C^0}$ Xwhere the convergence, Xdue to the periodicity of u, is uniform in $\alpha, \delta$. X XUsing the previous observations Xby choosing $\alpha$,$\delta$ sufficiently small, Xwe can get that X$\| \Gamma^{m+1} [K_\alpha u ] - K_\alpha u\|_\delta$ Xis arbitrarily small and X$\| D \Gamma^{m+1}( K_\alpha u) \|_\delta$ Xis as close to $\gamma$ as desired, Xin particular less than $1$. X XMoreover $D^2 \Gamma^{m+1}(u) ( \eta_1 ,\eta_2) = \sum_{i,j} \left(\prod_{i' \ne i \atop i' \ne j} 2u(\theta - {i'}\omega)\right) \eta_1( \theta - i \omega) \eta_2( \theta - j \omega).$ X Hence if we pick a neighborhood of Xradius $\rho$ in the $C^{\omega,\delta}$ space, Xwe can bound the size of the second derivative uniformly in X$\alpha, \delta$ as they become arbitrarily small. X XHence for all $\alpha$, $\delta$ sufficiently small, Xit is possible to get a $C^{\omega,\delta}$ ball around $K_\alpha u$ Xso that $\Gamma^{m+1}$ is a contraction on it. XWe can also arrange that $K_\alpha u$ is Xin the $C^0$ ball around $u$ for which $\Gamma^{m+1}$ is Xa $C^0$ contraction. X\QED X X\SECTION Non-perturbative methods X XIf the invariant curve is contractive, it can be approximated numerically Xby iterating the map \equ(logistic) forward. XBy changing $\epsilon$ in small steps X we can compute the invariant curve for Xall the domain in which it is Xcontractive. Because of \clm(deltaconv), X\clm(convergence), which guarantee analyticity Xin $\epsilon$ for contractive invariant circles, Xif we succeed in finding parameter values along a path that goes Xthrough the origin, for which the orbits Xsettle onto an invariant curve Xwe can ensure that these points belong to the domain of analyticity of Xthe invariant curve. X XOn the other hand, if we find real values of $\epsilon$ Xfor which some orbits escape to infinity X-- by the quadratic behavior of the map it suffices to check that X$r$ is larger than a certain number -- Xwe are sure that there are no invariant circles separating the Xbeginning of the orbit and infinity. X XWhen $\epsilon$ is complex, the existence of orbits escaping to infinity Xdoes not preclude the existence of an invariant circle in X$\torus^1 \times \complex$. Nevertheless, the fact that the basin of attraction Xof the invariant circle shrinks to nothing is indication of a sudden change in Xbehavior. If it was just that the invariant circle lost stability, Xthis could be discovered by iterating backwards. For all the values of the Xparameters we are reporting after breakdown, we found no evidence of Xinvariant circles. X XSo, if we increment $\epsilon$ along a path, and find values Xfor which the orbit settles in an invariant circle and Xvery nearby values for which all orbits seem to escape, Xwe conclude that these values belong to the boundary of the Xdomain of analyticity. By taking several paths of a Xfamily, e.g radii, we can obtain a reasonable estimate of the boundary. XSince the boundary can bend back with respect to a family of paths, Xwe should use several families to obtain a better approximation. X XOne side effect of this Xalgorithm is that it allows to compute the invariant curves just Xbefore breakdown. For real values of $\epsilon$ the invariant curve Xremains smooth until breakdown. At breakdown it undergoes a saddle node Xbifurcation of invariant circles and disappears (the theory of this phenomenon Xis worked out in \cite{AKL1}). For complex values of $\epsilon$ the invariant Xcurve disappears by becoming very oscillating at small scales. XThis phenomenon requires further study but we will Xnot concern with it here. X XWe emphasize that just finding the values of $\epsilon$ Xfor which there are points that do not escape Xwhich are close to other for which escape takes place, Xdoes not Xprovide X always with a reliable approximation for the Xdomain of analyticity of the invariant circle. XOne has to check that the invariant set in which the Xorbit settles is an invariant circle. XIndeed, for some values of $\lambda$, the invariant circles Xexperience period doubling bifurcations. These periodic circles are Xbarriers for the escape but nevertheless are not direct continuations Xof the original invariant circle. X XIn the practical implementation, we have just checked visually Xfor some of the values that indeed the attracting set was a circle. XFor the values of $\lambda$ we report, the evidence that the Xsets remain one dimensional up to extremely close to breakdown Xis very clear. XEven if we have not been able to obtain a mathematical Xargument that shows that there are no other bifurcations of the circle Xfor the values of $\lambda$ that we have considered, the numerical Xresults show that these bifurcations, if they happen, Xcan only occupy a very small region in the parameters space. X X\def\omegab{{\bar \omega}} X\def\deltab{{\bar \delta}} X\SECTION Behavior at rational frequencies X XIn this section we study the analyticity domains for the case that the Xfrequency is rational. A motivation for this is that it is possible to show X-- see Theorem 9.1 below for a precise statement -- that the analyticity Xdomains at irrational $\omega$ are approximated by those at rational Xfrequencies $p/q$ when $p/q \approx \omega$. Nevertheless, when the frequency Xis rational, many of the analytical problems become algebraic and we can Xperform a detailed analysis. In particular, we can discuss in detail what is Xthe nature of the singularities when the perturbation expansions break down. X XWe also point out that, when $\omega$ is rational, several of the domains Xthat we conjectured to agree for $\omega$ irrational, differ. Nevertheless, Xwe observe in our numerical experiments that Xas the rational numbers approach their irrational Xlimiting values these domains seem to approach each other. This may serve Xas additional support for these conjectures. X XWe start by discussing some justification for the Xapproximation of the analyticity domains for circles with Xfrequency $\omega$ by those of Xapproximate frequencies. X X\CLAIM{Theorem}(Greenanal) XIf, for fixed $\epsilon$, $\lambda$, and $\omega$ irrational there exists an Xanalytic $u_{ \omega}(\theta)$ that satisfies \equ(Lindstedt) and X\item {$(i)$} X$\|2 u_\omega(\theta -\omega)2 u_\omega(\theta - 2 \omega) \cdots 2u_\omega( \theta - m \omega)\|_\delta \le \gamma < 1$ X\vskip1pt Xthen, X\vskip1pt Xfor $\omegab$ in a neighborhood of $\omega$, there exists an analytic X$u_{\omegab}(\theta)$ satisfying \equ(Lindstedt). X X\PROOF XWe will use a version of the Xcontractive mapping theorem similar to those we used in Xsections 6 and 7. XWe introduce the operator $\Gamma_\omega$ Xas in \equ(graphtransform). Since the dependence in $\omega$ Xwill play an important role, we make it explicit in the notation. X XSince $u_{\omega}$ satisfies X$\Gamma_\omega[ u_\omega] - u_\omega = 0$ Xwe see that we also have for $\deltab \le \delta$, X$$\|\Gamma_\omegab[ u_\omega] - u_\omega \|_\deltab \le 2 \| u_\omega\|_\deltab \| u_\omega'\|_\deltab| \omega - \omegab| \le K |\omega - \omegab|$$ Xwhere $K$ depends on $u_\omega$, $\delta$, $\deltab$ Xbut not on $|\omega - \omegab|$. X XFrom that, it is very easy to show that X$\Gamma_\omegab^m$ has a fixed point. XUsing condition $(i)$, it is Xpossible to show that $D \Gamma^m_\omegab [u_\omega]$, Xwhich can be expressed as multiplication by Xshifted versions of $u_\omega$, is Xa contraction in $\| \quad\|_\deltab$ Xwith a factor as close as desired to $\gamma$, if Xwe assume that $\omega - \omegab$ is small enough. XWe can also bound the $D^2 \Gamma^m_\omegab$ in a neighborhood Xof $u_\omega$. X XThe argument to prove that $\Gamma_\omegab$ has a fixed point Xis only slightly more complicated. XWe observe that, proceeding as in \clm(deltabound), Xgiven $R \in C^{\omega,\deltab}$ Xwe can solve the equation Xfor $\eta$, $D \Gamma_\omegab[ u_\omega] \eta = R$ Xand we have $\| \eta\|_\deltab \le K \|R\|_\deltab$ Xwhere $K$ can be chosen uniformly for $|\omega - \omegab|$ Xsufficiently small. XIf we consider the auxiliary operator X$\Phi(v) = -\left( D\Gamma_\omegab(u_\omega) - {\rm Id} \right)^{-1} \left( \Gamma_\omegab(v) - v \right) + v,$ Xwe Xsee that $\Phi$ is a contraction Xin $\|\quad\|_\deltab$ of Xa factor $1/2$ in a neighborhood Xof $u_\omega$ that can be chosen uniformly as X$|\omega - \omegab| $ is small. XSince $\| \Phi(u_\omega) - u_\omega\|_\deltab$ Xcan be made as small as desired by choosing X$\omega - \omegab$ to be small, we conclude that X$\Phi$ has a fixed point for all $\omegab$ Xin a neighborhood of $\omega$. But a fixed point Xof $\Phi$ is a fixed point of X$\Gamma_\omegab$. X\QED X\REMARK X\clm(Greenanal) is an analog of the justification Xof Greene's criterion for the approximation of Xinvariant curves by periodic orbits for the case of Hamiltonian systems, Xin the spirit of \cite{FL2}, in the case of Xhyperbolic circles. (See also \cite{McK2}.) X XThe main consequence of X\clm(Greenanal) is that Xall the non-perturbative methods X based on the Xcontinuation of attractive invariant circles Xwill provide a reasonable approximation Xto the domain of parameters for which there is an attractive Xinvariant circle. According to X\clm(deltaconv) for the values of $\lambda$ Xwe considered, Xthis agrees with the domain of analyticity. X XNow, we start to discuss the perturbative methods. XWe first observe that Xthe Lindstedt series for the case of rational frequencies do not exhibit Xsmall denominators, as can be easily established from \equ(Kdefined), and Xthe calculation of the XPad\'e approximants goes through. X X XTo study the nature of the boundary Xof the domain of analyticity Xfor the invariant circles for $\omega = p/q$ it is more convenient to Xinvestigate the behavior of the $q^{th}$ iterate of \equ(logistic). We have: X$$ F^q_{\lambda,\epsilon,\omega}(r, \theta) =(P_{\lambda, \epsilon, \theta}(r), \theta) X\EQ(iterate)$$ Xwhere $P_{\lambda,\epsilon,\theta}$ is a polynomial in $r$ Xof degree $2^q$, with Xonly even orders of $r$. XHence, $\theta$ enters only as a parameter in the Xdynamics of the $q^{\rm th}$ iterate of the map. X XPeriodic orbits of period $q$ are solutions of: X$$r=P_{\lambda,\epsilon,\theta}(r). X\EQ(fixedpoint)$$ X XSince \equ(fixedpoint) is a polynomial equation in $r$ Xof degree $2^q$, in general, Xit has $2^q$ Xdistinct solutions. The only way for the solution to a polynomial equation Xto lose analyticity on its dependence to the coefficients is if two or more Xsolutions coincide (there we may get a branch point). XIf we fix $\lambda$, $\theta$ and choose one solution for $\epsilon = 0$ and Xthen vary $\epsilon$ over the complex Xplane and follow that solution, the possible Xbranch points for the solution in terms Xof $\epsilon$, are the values of $\epsilon$ Xsuch that our solution is a root of \equ(fixedpoint) Xof multiplicity at least two. XOf course, there could be values of the parameter for Xwhich the root becomes double but which do not cause Xa loss of analyticity of the branches of the solutions. XThis, nevertheless, can only happen in degenerate situations X(e.g transcritical saddle node). In practice, once we have Xobtained a finite number of candidates, it is easy to verify that the Xnon-degeneracy conditions that imply that there is a branch point Xtake place. X X\REMARK XNotice that the position of the branch points depends on $\theta$, and that Xalthough generically there are branch points, there can be values of $\theta$ Xsuch that some branch points disappear. For example for $\omega = 1/1$ the Xposition of the branch point is determined by X $\lambda + \epsilon \cos(2 \pi \theta) = 1/4$, Xand for $\theta = 1/4$ the branch point is at $\infty$. X X XNotice that one important consequence Xof the previous discussion is that in the Xcase that $\omega$ is rational, the only possible Xways of breaking analyticity is branch points and that, Xtypically, we expect that these branch points are of Xorder $2$. This has important consequences for the Xbehavior of Pad\'e approximants. XAccording to a long standing conjecture, Pad\'e approximants of functions Xwith branch points tend to arrange their poles and zeros along lines Xthat are uniquely determined from the position of the poles ( see X\cite{BGM} vol.1, pg. 51, \cite{Gi} pg. 288, \cite{N}). XThe results we obtained Xfrom the Pad\'e approximants are remarkably close to the behavior Xoutlined above, since the poles and zeros of the Pad\'e approximants lie Xalong lines that emanate from the branch point and go radially to Xinfinity (forming a Mittag-Leffler star, see \cite{BGM} vol.1, pg. 50). XWe have also noticed that the poles (and the Xzeros) of the Pad\'e approximant tend to accumulate to the branch point. XAs the denominator increases the Xnumber of the branch points gets bigger and for large values of the denominator Xthe branch points tend to accumulate to Xthe natural boundary investigated in previous sections. X XSimilar behavior for the poles of the Pad\'e approximants for the Lindstedt Xseries, for invariant circles of the standard map Xwith complex $\omega$ with rational real part, Xwas reported in \cite{BM}. XThe poles (the zeros were not investigated in \cite{BM}) lied Xalong lines that emanate from points that tend to the origin as X$\Im \omega \to 0$, and go radially to infinity. It can be argued that the Xresemblance is due to the absence of small denominators for complex frequencies. XIt can also be argued that the effect of the imaginary part of the frequency Xis very similar to introducing dissipation in the system. XBased on this analogy, we conjecture X\CLAIM Conjecture(BM) XThe behavior observed in X\cite{BM} corresponds to branch points in the complex domain. XIn particular, the zeros of the numerator of the Pad\'e approximant Xshould also be in the same line in which the poles were found. X XSince this paper is mainly concerned with the rotating logistic Xmap, we will not discuss the standard map any further. X XTo compute the position of the branch points for the case of the rational Xfrequencies we fixed $\lambda$, $\theta$. XWe observe that the polynomial in $r$ given by X$P_{\epsilon, \lambda, \theta}(r) - r$ Xis a polynomial whose coefficients are Xpolynomials in $\epsilon$. XWe recall that the discriminant of a polynomial X$P(x)$ of degree $N$ is defined as disc($P(x)$) $= \prod_{i>j} (x_i - x_j)^2$ Xwhere $x_i$ are the roots. Hence, a polynomial has double Xroots if and only if the discriminant is zero. The importance of this remark is Xthat the discriminant of a polynomial is an algebraic function of the Xcoefficients. In particular, if the coefficients are polynomials in Xanother variable, the discriminant will be a Xpolynomial in the auxiliary variable. Reasonably efficient algorithms Xexist to compute discriminants of polynomials. XIn particular, the resultant algorithm X-- see e.g \cite{Kn} vol. 2 -- works in the case when the Xcoefficients are polynomials. X XNotice that to Xcompute analyticity Xdomains we are only interested in the Xcollisions of a particular root with the others, however the discriminant Xwill vanish whenever any two roots collide. XSo that finding all the values of $\epsilon$ for Xwhich the discriminant vanishes will provide us Xwith a discrete subset that includes, but which could be bigger than, Xthe set of branch points of the periodic solution that we are tracing. XUnfortunately, it is not so easy to decide whether a place where Xthe discriminant vanishes corresponds to a branch point of Xthe root we are tracing. This requires a global continuation method Xand one should follow all the Riemann sheets, since the roots Xchange identity by going into different sheets. XThis is a question that merits a more detailed study, Xbut we have not pursued it in this paper. We just observe that, Xin the cases that we studied, many of the values of X$\epsilon$ where the Xdiscriminant vanishes are indeed at the tip of Xthe accumulation of zeros and poles of the XPad\'e approximations. X XThe study of the domain of no escape becomes more Xcomplicated in the case of rational frequencies than what it was for Xirrational frequencies. XThe case $\omega = 1/1$ is relatively simple, X$P_{\lambda, \epsilon, \theta}(r) = r^2 + \lambda + \epsilon \cos (2\pi\theta)$ X and for any $\theta$ such that $\cos(2\pi\theta)\not= 0$ we get Xa distorted quadratic family $F_q = z^2 + \epsilon$. There exist only two Xfixed points, with only one of them attractive for some domain in the X$\epsilon$ plane. The domain of existence of the attractive fixed point Xis the main cardioid of the Mandelbrot set and can be computed by : X$$ z_0 = F_q(z_0),\quad | F'_q (z)|_{z=z_0} < 1$$ Xor X$$ |1 \pm \sqrt{1-4\epsilon}| < 1. X\EQ(stablefixed)$$ XThe cusp of the cardioid is located at the branch point of the domain of Xanalyticity of the roots and corresponds to a collision of the Xattractive and repelling fixed points. X XFor $\omega = p/q, \quad q>1$ the situation is no longer simple. XTo understand the full dynamics of the problem one has to consider Xiterations of polynomial maps of degree $2^q$ in the Xcomplex domain (for an overview see \cite{Bl1}). XSuch maps have $2^q$ fixed points, and although our solution follows one of Xthem, that is attractive for some domain in the parameter space, it can Xundergo a bifurcation and either disappear Xor become unstable. On the same time other stable fixed points, to which Xforward iteration of the map will converge, may still exist. XThe behavior of the map under forward iteration, is characterized Xby the behavior of the critical points of the map ($r_{cr}$ such that, X$P_{\lambda,\epsilon,\theta}'(r_{cr}) = 0$) under forward iteration. XIf an attractive periodic point exists, then at least one critical Xpoint belongs to its' basin of attraction (see \cite{Br}). XOne can recover the behavior of all the Xcritical points at a fixed $\theta$ by looking at the behavior of the Xcritical point at zero of X$P_{\lambda, \epsilon, \theta + n \frac{p}{q}}(r), \quad n=0,\ldots, q-1$, Xsince : X$$\eqalign{P_{\lambda, \epsilon, \theta}'(r) &= \left( X\underbrace{F_{\lambda, \epsilon, p/q}\circ \cdots X\circ F_{\lambda, \epsilon, p/q}}_{q \quad \rm times}(r, \theta)\right)' \hfill \cr X&= \underbrace{F_{\lambda, \epsilon, p/q}' \circ \cdots X\circ F_{\lambda, \epsilon, p/q}}_{q\quad \rm times}(r, \theta) X\underbrace{F_{\lambda, \epsilon, p/q}' \circ \cdots X\circ F_{\lambda, \epsilon, p/q}}_{q-1\quad \rm times}(r, \theta) \cdots XF_{\lambda, \epsilon, p/q}'(r, \theta).}$$ XThis feature is characteristic of our problem. X XDepending on the initial conditions and the numerical Ximplementation, the domain of no escape for a particular choice will Xbe a subset of the domain where at least one critical point remains bounded. XCaution should be taken at the interpretation of these results, since, as Xwas pointed out, the solution we are following may have changed stability Xas we varied $\epsilon$ in the complex plane and the forward iteration Xmay have followed a different solution (not necessarily a fixed point Xeither). Studies for Xcubic polynomials have been performed in \cite{BH},\cite{Bl2},\cite{Mil}. X XThe cusps of the domain of existence of at least one attractive fixed point Xcorrespond to saddle-node bifurcations between attractive and Xrepelling fixed points. The branch points in the domain of analyticity of Xthe root we follow form a subset of the set of points where Xthe cusps occur. X XTo interpret the dependence on $\theta$ we note that Xdifferent $\theta$ corresponds to a different slice of the parameter space. XFor the cases $\omega = 1/1$ and $\omega = 1/2$, the behavior for different X$\theta$'s can be recovered from the behavior for $\theta=0$ after Xthe scaling transformation $\epsilon \to \epsilon\cos(2\pi\theta)$. For Xother $\omega$'s such a simple scaling no longer exists. X X\SECTION Numerical Implementation X XWe have written a package in {\tt C} to manipulate one-dimensional XFourier series. This package has the feature that the arithmetic Xis done through function calls so that by changing a definitions file, Xwe can switch the arithmetic from single to extended precision. X XThe use of extended precision is a convenient way of handling Xthe severe numerical instabilities of the recursion, the Pad\'e approximation Xand the search for zeros. XWe have used the arithmetic library of the public domain program X{\tt PARI/GP}. X XTo increase the accuracy of the computation of the terms of the Lindstedt Xexpansion, we used a technique also used in \cite{FL1}. XWe considered the expansion in powers not of $\epsilon$ but of X$\epsilon/\rho$ where $\rho$ is chosen so as to make the series Xhave radius of convergence~1. XThe value of $\rho$ is determined from a preliminary run of the program. X XFrom this series expansion, we solved \equ(match) using Gaussian Xelimination verifying that the condition was always much smaller Xthan the accuracy of the previous results. The actual algorithm Xwas a translation into {\tt C} of the well known X{\tt DECOMP} and {\tt SOLVE} from \cite{FMM}. X XTo find the zeros of the denominator we used the routines ``{\tt xzroot}'', X``{\tt zroot}'' from ``Numerical Recipes'' translated to Xuse the {\tt PARI/GP} arithmetic and then checked if the answer Xwas indeed correct by evaluating the Xpolynomial and requiring that Xthe result was smaller than a tolerance. We eliminated zeros of the denominator Xthat are also zeros of the numerator. For some values of $N, M, \theta$ Xwe encountered spurious poles, that disappeared as $N, M, \theta$ Xchanged, but we did not Xeliminate them from the figures. X XTo implement the Newton method we discretized \equ(Newton) by Xtruncating the Fourier series representation of the function X$$u_{\epsilon_0} (\theta) = \sum_{k=-n}^n \hat u_{\epsilon_0,k} Xe^{2\pi ik\theta}\ ,\quad X\Delta(\theta) = \sum_{\ell=-n}^n \hat\Delta_\ell e^{2\pi i\ell\theta}\ ,\quad XR(\theta) =\sum_{m=-n}^n \hat R_m e^{2\pi im\theta}$$ Xwhere $n$ is a large number ($n\sim 100$). X XEquation \equ(Newton) reduces to X$$\mathop{{M}}_\approx \cdot \mathop{{\Delta}}_\sim X= - \mathop{{R}}_\sim$$ Xwhere X$$\displaylines{\hfill X\mathop{{\Delta}}_\sim X= (\hat\Delta_{-n},\ldots,\hat\Delta_n)^T\quad ,\quad X\mathop{{R}}_\sim = (\hat R_{-n},\ldots, \hat R_n)^T \hfill\cr X\hfill M_{k\ell} = \cases{ X2u_{\epsilon_0,k-\ell} - \delta_{k\ell} e^{2\pi i\omega k} X&,\quad $|k-\ell| \le n$\cr X0&,$\quad |k-\ell| >n$\cr}\hfill \cr}$$ XWe verified that the Xprocedure was converging in a quadratic fashion Xfor the cases that we studied. XThis gives us confidence that the Ximplementation was correct and that Xsources of error that make the truncated derivative Xdifferent from the derivative of the Xtruncation are small. XWhen $R(\theta)$ stopped decreasing we stopped the procedure. X XAs for the multipoint Pad\'e method we considered sequences of points Xwhich were distributed according to a sequence of powers of a fixed Xcomplex number. We used roots of unity, which leads to points evenly Xdistributed in a circle or a number of modulus slightly smaller than one, Xwhich leads to a spiral converging to the origin. XAgain the equations for the interpolation equations were solved by XGaussian elimination so as to have an estimate of the condition. XWe observed that, for the same number of points, distributing the points Xon a spiral seemed to lead to smaller condition numbers than distributing Xthem on a circle. X XNotice that the equations \equ(logistic) are invariant under the Xchange $\epsilon\to -\epsilon$, $\theta\to \theta+\pi$, Xtherefore the final domains of analyticity should be invariant Xunder the change $\epsilon\to-\epsilon$. XSince the coefficients of the series at zero are real, Xthe domains of analyticity should be invariant also under Xthe change $\epsilon\to \epsilon^*$. XSince the numerical methods we used were not built Xtaking into account such symmetries, the accuracy with Xwhich they are reflected in the final result Xcan give an estimate of the accuracy of the whole procedure. X XFor the non-perturbative methods we considered paths which Xwere radial, horizontal and vertical and found no discrepancies Xexcept in the places where the boundary shadows some of the Xpoints in the boundary. X XSome symbolic manipulation packages such as X{\tt MAXIMA} and {\tt MAPLE} implement Xthe resultant algorithm, for the calculation of the discriminant, Xin such a way that it is possible to compute with polynomial coefficients. XWe indeed implemented such calculations. XNevertheless, we found it more efficient to Xcompute the discriminant by evaluating the discriminant Xfor a discrete set of values of $\epsilon$ and then, Xusing the knowledge that the discriminant is a Xpolynomial in $\epsilon$ whose degree Xwe know, interpolate. XTo find the interpolating polynomial we adapted the routine ``{\tt toeplz}'' Xfrom \cite{FPTV} to Xbe able to use {\tt PARI/GP}. XWe found the results to agree with those obtained using the Xsymbolic algebra packages. X X\SECTION References X X X\ref\no{AKL1}\by{R.A. Adomaitis, I.G. Kevrekidis, R. de la Llave}\paper{Predicting the complexity of disconnected basins of attraction for a noninvertible system}. Preprint\endref X\ref\no{AKL2}\by{R.A. Adomaitis, I.G. Kevrekidis, R. de la Llave}\paper{Global bifurcations for the rotating logistic map. Some rigorous and numerical results}. Preprint\endref X\ref\no{B}\by{G.Baker}\book{Essentials of Pad\'e approximants}\publisher{Academic Press}\yr{1975}\endref X\ref\no{BC}\by{A. Berretti, L. Chierchia}\paper{On the complex analytic structure of the golden invariant curve for the standard map}\jour{Nonlinearity}\vol{3}\pages{39--44}\yr{1990}\endref X\ref\no{BCCF}\by{A. Berretti, A. Celletti, L. Chierchia, C. Falcolini}\paper{Natural boundaries for area preserving twist maps}\jour{Preprint}\endref X\ref\no{BH}\by{B. Branner, J. H. Hubbard}\paper{The iteration of cubic polynomials. Part I: The global topology of parameter space}\jour{Acta Mathematica}\vol{160}\pages{143--206}\yr{1988}\endref X\ref\no{Bl1}\by{P. Blanchard}\paper{Complex analytic dynamics on the Riemann sphere}\jour{Bull. Am. Math. Soc.}\vol{11}\pages{85--141}\yr{1984}\endref X\ref\no{Bl2}\by{P. Blanchard}\paper{Disconnected Julia sets}\inbook{Chaotic Dynamics and Fractals, M. F. Barnsley, S. G. Demko ed.}\publisher{Academic Press}\yr{1986}\endref X\ref\no{BGM}\by{G. Baker, M. Graves--Morris}\book{Pad\'e Approximants}\publisher{Addison Wesley}\yr{1981}\endref X%\ref\no{BGW}\by{G. Baker, J. L. Gammel, J. G. Wills}\paper{An investigation of the applicability of the Pad\'e approximant method}\jour{Jour. Math. Anal. App.}\vol{2}\pages{405--418}\yr{1961}\endref X\ref\no{BM}\by{A. Berretti, S. Marmi}\paper{Standard map at complex rotation numbers : Creation of natural boundaries}\jour{Phys. Rev. Lett.}\vol{68}\pages{1443--1446}\yr{1992}\endref X\ref\no{Bo}\by{J.-B. Bost}\paper{Tores invariants des syst\`emes dynamiques hamiltoniens}\jour{ Seminaire Bourbaki no. 639, Ast\'erisque}\vol{133--134} \pages{113}\yr{1986}\endref X\ref\no{Br}\by{H. Brolin}\paper{Invariant sets under iterations of rational functions}\jour{Arkiv for Matematik}\vol{6}\pages{103--144}\yr{1965}\endref X\ref\no{CE}\by{P. Collet, J.-P. Eckmann}\book{Iterated maps of the interval as dynamical systems}\publisher{Birkhauser, Boston}\yr{1980}\endref X\ref\no{CI}\by{A. Cenciner, G. Ioos}\paper{Bifurcations de tores invariants}\jour{Arch. Rational Mech. Anal.}\vol{69}\pages{109--198}\yr{1979}\endref X\ref\no{Fe}\by{N. Fenichel}\paper{Persistence and smoothness of invariant manifolds for flows}\jour{Int. Math. Jour.}\vol{21}\pages{193--226}\yr{1971}\endref X\ref\no{FL1}\by{C. Falcolini, R. de la Llave}\paper{Numerical Calculation of domains of analyticity for perturbation theories in the presence of small divisors}\jour{Jour. Stat. Phys.} \vol{67}\pages{645--666}\yr{1992}\endref X\ref\no{FL2}\by{C. Falcolini, R. de la Llave}\paper{A rigorous partial justification of Greene's criterion}\jour{Jour. Stat. Phys.} \vol{67}\pages{609--643}\yr{1992}\endref X\ref\no{FMM}\by{G.E. Forsythe, M.A. Malcolm, C. E. Moler}\book{Computer methods for mathematical computations}\publisher{Prentice Hall, Englewood Cliffs}\yr{1977}\endref X\ref\no{FPTV}\by{W.H. Press, B.P. Flannery, S. Teukolski, W. T. Vetterling}\book{Numerical Recipes}\publisher{Cambridge Univ. Press, Cambridge}\yr{1986}\endref X\ref\no{G}\by{J. Guckenheimer}\paper{Sensitive dependence on initial conditions for one dimensional maps}\jour{Comm. Math. Phys.}\vol{70}\pages{133--160}\yr{1979}\endref X\ref\no{Gi}\by{J. Gilewicz}\book{Approximants de Pad\'e}\publisher{Springer--Verlag}\yr{1978}\endref X%\ref\no{GN}\by{J. L. Gammel, J. Nuttall}\paper{Convergence of Pad\'e approximants to quasi-analytic functions beyond natural boundaries}\jour{Jour. Math. Anal. App.}\vol{43}\pages{694--696}\yr{1973}\endref X\ref\no{He}\by{P. Henrici}\book{Applied and computational complex analysis I} \publisher{J. Wiley, New York}\yr{1974}\endref X\ref\no{Ka}\by{K. Kaneko}\book{Collapse of tori and genesis of chaos in dissipative systems}\publisher{Book Scientific, Singapore}\yr{1986}\endref X\ref\no{Kn}\by{D.E. Knuth}\book{The art of computer programming, vol. II 2$^{nd}$ edition}\publisher{Addison Wesley}\yr{1981}\endref X\ref\no{M}\by{J.C. Mason}\paper{Some applications and drawbacks of Pad\'e approximants}\inbook{Approximation theory and applications} \pages{207} \publisher{Academic Press, New York}\yr{1981}\endref X\ref\no{McK1}\by{R.S. McKay}\paper{Renormalization in area preserving maps}\jour{Princeton thesis}\yr{1982}\endref X\ref\no{McK2}\by{R.S. McKay}\paper{On Greene's residue criterion}\jour{Nonlinearity}\vol{5}\pages{161--187}\yr{1992}\endref X\ref\no{N} \by{J.N. Nutall} \paper{The convergence of Pad\'e approximants to functions with branch points} \inbook{Pad\'e and rational approximation, E.B.~Saff, R.H.~Varga (eds.)} \pages{101--109} \publisher{Academic Press, New York} \yr{1977} \endref X\ref\no{Po}\by{H. Poincar\'e}\book{Les m\'ethodes nouvelles de la m\'ecanique c\'eleste}\publisher{Gauthier Villars}\yr{1899}\endref X%\ref\no{Pom}\by{Ch. Pommerenke}\paper{Pad\'e approximants and convergence in capacity}\jour{J. Math. Anal. Appl.}\vol{41}\pages{775--780}\yr{1973}\endref X\ref\no{R} \by{D. Rand} \paper{Universality for the breakdown of dissipative golden invariant tori} \inbook{ Proceedings of the 1986 I.A.M.P. meeting} \pages{537--547} \publisher{World Scientific, Singapore} \yr{1987} \endref X\ref\no{RA}\by{R. H. Rand, D. Armbruster}\book{Perturbation methods, bifurcation theory and computer algebra}\publisher{Springer--Verlag, New York}\yr{1987}\endref X\ref\no{SB}\by{J. Stoer, R. Burlisch}\book{Introduction to numerical analysis}\publisher{Springer--Verlag, N.Y.}\yr{1980}\endref X\ref\no{Si}\by{D. Singer}\paper{Stable orbits and bifurcations of maps of the interval}\jour{SIAM Jour. App. Math.}\vol{35}\pages{260}\yr{1978}\endref X\ref\no{W}\by{P. Walters}\book{An introduction to ergodic theory}\publisher{Springer--Verlag, N.Y.}\yr{1982}\endref X\ref\no{Wi}\by{H. Wilkinson} \paper{The perfidious polynomial}\inbook{Studies in numerical analysis, H. Golub ed.}\publisher{M.A.A., Washington}\yr{1985}\endref X\ref\no{Ze1}\by{E. Zehnder}\paper{Generalized implicit function theorems with applications to some small divisor problems I}\jour{Comm. Pure and Appl. Math.}\vol{28}\pages{91--140}\yr{1975}\endref X\ref\no{Ze2}\by{E. Zehnder}\paper{Generalized implicit function theorems with applications to some small divisor problems II}\jour{Comm. Pure and Appl. Math.}\vol{29}\pages{49--111}\yr{1976}\endref X\SECTION Captions X XFigure 1. XThe boundary of no escape (Set 1), X computed by iterating the map forward and using a continuation method until Xescape occurs (three families of paths (radial, vertical, horizontal) Xare used and the results are superimposed) with Xthe poles of the Pad\'e approximants $[50/50]$ for several angles (Set 2) Xand with the poles of the Pad\'e approximants for several Fourier coefficients Xof the $\epsilon$ expansion (Set 3) for X$\lambda = 0.2$. X XFigure 2. XThe boundary of no escape (Set 1) Xwith Xthe poles of the Pad\'e approximants $[50/50]$ for several angles (Set 2) Xfor $\lambda = 0.1$. X XFigure 3. Boundaries where the Pad\'e approximants $[24/24]$ and $[20/20]$ Xfor $\lambda = 0.2, \theta = 0.72$ Xdiffer more than $\delta$, superimposed with the boundary of no escape under Xforward iteration (Set 0). For Set 2 $\delta = 3 \times 10^{-5}$, Xfor Set 3 $\delta = 3 \times 10^{-4}$, for Set 4 $\delta = 2 \times 10^{-3}$, Xfor Set 5 $\delta = 2 \times 10^{-2}$. X XFigure 4. The poles of the multi-point Pad\'e approximant $[90/90]$ for X$\lambda = 0.2 $ and several angles Xsuperimposed with the boundary of no escape under forward iteration (Set 1). XExpansion Xin $\epsilon$ around 21 points with order of the expansion around zero 20 Xand around the other points 7. Set 2 : Expansion around $z_k = 0.1 Xe^{2 \pi i k /20} , k= 1,\ldots , 20$. Set 3 : Expansion around X$z_k = ( 0.19 e^{2 \pi i/20})^k , k=1, \ldots ,20$. X XFigure 5. Invariant curve close to breakdown. An example Xof a saddle node bifurcation. X$\lambda = 0.2$, $\epsilon= 0.589$. X XFigure 6. Invariant curve close to breakdown. XAn example of an Xinvariant curve becoming discontinuous. XReal part of the invariant circle for X$\lambda = 0.2$, $\epsilon = 0.22 + 0.677i$. X XFigure 7. Invariant curve close to breakdown. XAn example of an Xinvariant curve becoming discontinuous. XImaginary part of the invariant circle for X$\lambda = 0.2$, $\epsilon = 0.22 + 0.677i$. X X XFigure 8. Branch points (Set 2) and branch cuts (Set 3) Xfor rational frequency superimposed Xwith the domain of existence of an Xattractive fixed point (Set 1). The zeros and the Xpoles of the $[40/40]$ Pad\'e approximant seem to converge to the Xbranch cut on a straight line. X$\omega = 1/2$, $\lambda=0.2$, $\theta= 0$. X XFigure 9. As in figure 6 with $\omega = 2/3$, $\lambda=0.2$, $\theta= 0$. 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X1828 1988 D X1881 1966 D X1925 1943 D X1962 1918 D X1974 1886 D X1933 1833 D X1854 1764 D X1855 1723 D X1849 1678 D X1838 1629 D X1890 1608 D X1935 1585 D X1984 1564 D X2037 1547 D X2087 1529 D X2126 1505 D X2180 1491 D X2248 1486 D X2288 1465 D X2305 1429 D X2310 1383 D X2359 1368 D X2405 1352 D X2446 1331 D X2478 1304 D X2519 1284 D X2558 1263 D X2606 1250 D X2654 1238 D X2708 1232 D X2758 1225 D X2809 1218 D X2859 1212 D X2909 1208 D X2955 1198 D X3005 1195 D X3051 1186 D X3100 1185 D X3148 1181 D X3195 1178 D X3242 1176 D X3287 1171 D X3331 1165 D X3376 1161 D X3419 1153 D X3462 1145 D X3503 1131 D X3544 1118 D X3584 1098 D X3626 1080 D X3668 1062 D X3712 1051 D X3754 1021 D X3799 998 D X3844 973 D X3890 942 D X3940 947 D X3988 921 D X4037 944 D X4087 942 D X4133 970 D X4179 995 D X4222 1028 D X4265 1051 D X4309 1062 D X4351 1080 D X4393 1098 D X4433 1118 D X4474 1131 D X4515 1145 D X4558 1153 D X4601 1161 D X4645 1168 D X4690 1171 D X4737 1173 D X4782 1178 D X4829 1181 D X4877 1185 D X4924 1189 D X4974 1192 D X5020 1201 D X5070 1205 D X5118 1212 D X5168 1218 D X5219 1225 D X5269 1232 D X5323 1238 D X5371 1250 D X5419 1263 D X5461 1282 D X5494 1309 D X5531 1331 D X5578 1347 D X5618 1368 D X5667 1383 D X5672 1429 D X5686 1467 D X5736 1482 D X5797 1491 D X5851 1505 D X5894 1527 D X5940 1547 D X5993 1564 D X6042 1585 D X6095 1604 D X6131 1632 D X6128 1678 D X6122 1723 D X6123 1764 D X6044 1833 D X6012 1883 D X6015 1918 D X6048 1944 D X6096 1966 D X6145 1989 D X6184 2015 D X6209 2045 D X6243 2074 D X6267 2106 D X6281 2139 D X6303 2172 D X6414 2189 D X6161 2265 D X6189 2294 D X6183 2329 D X6223 2358 D X6243 2389 D X6077 2435 D X6040 2469 D X6006 2501 D X5966 2532 D X5874 2562 D X5744 2590 D X5747 2590 D X5866 2611 D X5926 2632 D X6015 2653 D X6015 2674 D X6015 2695 D X6045 2716 D X6075 2737 D X6105 2758 D X6254 2779 D X6254 2800 D X6254 2821 D X6224 2842 D X6164 2863 D X6194 2884 D X6194 2905 D X6164 2926 D X6403 2947 D X6403 2968 D X6433 2989 D X6313 3010 D X6313 3031 D X6283 3052 D X6283 3073 D X6283 3094 D X6254 3115 D X6224 3136 D X6194 3157 D X6194 3178 D X6134 3199 D X6105 3220 D X6075 3241 D X6015 3262 D X6015 3283 D X6015 3304 D X6045 3325 D X6045 3346 D X6075 3367 D X6105 3388 D X6134 3409 D X6134 3430 D X6134 3451 D X6134 3472 D X6134 3493 D X6134 3514 D X6134 3535 D X6134 3556 D X6075 3577 D X6045 3598 D X5985 3619 D X5956 3640 D X5896 3660 D X5836 3681 D X5717 3702 D X5687 3723 D X5687 3744 D X5687 3765 D X5687 3786 D X5628 3807 D X5568 3828 D X5538 3849 D X5509 3870 D X5479 3891 D X5449 3912 D X5360 3933 D X5211 3954 D X5061 3975 D X4853 3996 D X4614 4017 D X4525 4038 D X4465 4059 D X4406 4080 D X4376 4101 D X4287 4122 D X4257 4143 D X4227 4164 D X4197 4185 D X4138 4206 D X4108 4227 D X4048 4248 D X4018 4269 D X2230 2590 D X2111 2611 D X2051 2632 D X1962 2653 D X1962 2674 D X1932 2695 D X1932 2716 D X1902 2737 D X1872 2758 D X1843 2779 D X1723 2800 D X1723 2821 D X1753 2842 D X1813 2863 D X1783 2884 D X1813 2905 D X1813 2926 D X1574 2947 D X1544 2968 D X1544 2989 D X1664 3010 D X1664 3031 D X1694 3052 D X1694 3073 D X1694 3094 D X1723 3115 D X1753 3136 D X1783 3157 D X1783 3178 D X1843 3199 D X1872 3220 D X1932 3241 D X1962 3262 D X1962 3283 D X1962 3304 D X1932 3325 D X1932 3346 D X1902 3367 D X1872 3388 D X1843 3409 D X1843 3430 D X1843 3451 D X1843 3472 D X1843 3493 D X1843 3514 D X1813 3535 D X1843 3556 D X1872 3577 D X1932 3598 D X1992 3619 D X2051 3640 D X2081 3660 D X2141 3681 D X2260 3702 D X2260 3723 D X2290 3744 D X2290 3765 D X2290 3786 D X2349 3807 D X2379 3828 D X2439 3849 D X2468 3870 D X2498 3891 D X2528 3912 D X2617 3933 D X2766 3954 D X2916 3975 D X3124 3996 D X3363 4017 D X3452 4038 D X3512 4059 D X3571 4080 D X3601 4101 D X3690 4122 D X3720 4143 D X3750 4164 D X3780 4185 D X3839 4206 D X3869 4227 D X3929 4248 D X3959 4269 D X2230 2590 D X2111 2569 D X2051 2548 D X1962 2527 D X1962 2506 D X1932 2485 D X1932 2464 D X1902 2443 D X1872 2422 D X1843 2401 D X1723 2380 D X1723 2359 D X1753 2338 D X1813 2317 D X1783 2296 D X1813 2275 D X1813 2254 D X1574 2233 D X1544 2212 D X1544 2191 D X1664 2170 D X1664 2149 D X1694 2128 D X1694 2107 D X1694 2086 D X1723 2065 D X1753 2044 D X1783 2023 D X1783 2002 D X1843 1981 D X1872 1960 D X1932 1939 D X1962 1918 D X1962 1897 D X1962 1876 D X1932 1855 D X1932 1834 D X1902 1813 D X1872 1792 D X1843 1771 D X1843 1750 D X1843 1729 D X1843 1708 D X1843 1687 D X1843 1666 D X1813 1645 D X1843 1624 D X1872 1603 D X1932 1582 D X1992 1561 D X2051 1541 D X2081 1520 D X2141 1499 D X2260 1478 D X2260 1457 D X2290 1436 D X2290 1415 D X2290 1394 D X2349 1373 D X2379 1352 D X2439 1331 D X2468 1310 D X2498 1289 D X2528 1268 D X2617 1247 D X2766 1226 D X2916 1205 D X3124 1184 D X3363 1163 D X3452 1142 D X3512 1121 D X3571 1100 D X3601 1079 D X3690 1058 D X3720 1037 D X3750 1016 D X3780 995 D X3839 974 D X3869 953 D X3929 932 D X3959 911 D X5747 2590 D X5866 2569 D X5926 2548 D X6015 2527 D X6015 2506 D X6015 2485 D X6045 2464 D X6075 2443 D X6105 2422 D X6254 2401 D X6254 2380 D X6254 2359 D X6224 2338 D X6164 2317 D X6194 2296 D X6194 2275 D X6164 2254 D X6403 2233 D X6403 2212 D X6433 2191 D X6313 2170 D X6313 2149 D X6283 2128 D X6283 2107 D X6283 2086 D X6254 2065 D X6224 2044 D X6194 2023 D X6194 2002 D X6134 1981 D X6105 1960 D X6075 1939 D X6015 1918 D X6015 1897 D X6015 1876 D X6045 1855 D X6045 1834 D X6075 1813 D X6105 1792 D X6134 1771 D X6134 1750 D X6134 1729 D X6134 1708 D X6134 1687 D X6134 1666 D X6134 1645 D X6134 1624 D X6075 1603 D X6045 1582 D X5985 1561 D X5956 1541 D X5896 1520 D X5836 1499 D X5717 1478 D X5687 1457 D X5687 1436 D X5687 1415 D X5687 1394 D X5628 1373 D X5568 1352 D X5538 1331 D X5509 1310 D X5479 1289 D X5449 1268 D X5360 1247 D X5211 1226 D X5061 1205 D X4853 1184 D X4614 1163 D X4525 1142 D X4465 1121 D X4406 1100 D X4376 1079 D X4287 1058 D X4257 1037 D X4227 1016 D X4197 995 D X4138 974 D X4108 953 D X4048 932 D X4018 911 D XLT0 X6486 4346 M X(Set 2) Rshow X6654 4346 C2 X3687 4134 C2 X3687 4134 C2 X3687 1046 C2 X3567 1135 C2 X3567 1135 C2 X3567 4045 C2 X3567 4045 C2 X4690 4060 C2 X4690 4060 C2 X4923 1200 C2 X4923 1200 C2 X5122 998 C2 X5122 998 C2 X5122 4182 C2 X5122 4182 C2 X2796 3983 C2 X2771 987 C2 X2771 987 C2 X2771 987 C2 X2771 4193 C2 X2771 4193 C2 X5669 1293 C2 X5669 1293 C2 X5669 3887 C2 X5669 3887 C2 X2283 1502 C2 X2283 3678 C2 X2110 2590 C2 X5882 1842 C2 X6007 1300 C2 X6007 3880 C2 X1957 2590 C2 X1900 3262 C2 X1900 1918 C2 X1900 1918 C2 X6168 3369 C2 X6168 3369 C2 X6168 1811 C2 X6168 1811 C2 X1807 1402 C2 X1807 3778 C2 X6193 2590 C2 X6193 2590 C2 X1728 2196 C2 X1728 2984 C2 X1728 2984 C2 X6258 2175 C2 X6258 3005 C2 X4170 4062 C2 X4170 1118 C2 X3638 1044 C2 X3638 4136 C2 X4506 4060 C2 X4506 1120 C2 X3419 1196 C2 X3419 3984 C2 X3287 1093 C2 X3287 4087 C2 X4722 1156 C2 X4722 4024 C2 X5004 4027 C2 X5004 1153 C2 X2967 1039 C2 X2967 4141 C2 X2810 3960 C2 X2810 1220 C2 X5473 1208 C2 X5473 3972 C2 X5721 1560 C2 X5721 3620 C2 X5739 1362 C2 X5739 3818 C2 X2233 657 C2 X2233 4523 C2 X2212 3407 C2 X2212 1773 C2 X2142 1439 C2 X2142 3741 C2 X5870 2590 C2 X2094 2590 C2 X6003 2590 C2 X1931 2590 C2 X1905 2857 C2 X1905 2323 C2 X6080 1857 C2 X6080 3323 C2 X1887 3278 C2 X1887 1902 C2 X6153 3030 C2 X6153 2150 C2 X6680 2590 C2 X3718 4144 C2 X3718 1036 C2 X4303 4232 C2 X4303 948 C2 X4430 1102 C2 X4430 4078 C2 X3518 4019 C2 X3518 1161 C2 X3364 4116 C2 X3364 1064 C2 X4641 4035 C2 X4641 1145 C2 X3182 1112 C2 X3182 4068 C2 X4878 4009 C2 X4878 1171 C2 X2911 1178 C2 X2911 4002 C2 X5301 1120 C2 X5301 4060 C2 X5534 3626 C2 X5534 1554 C2 X2358 1426 C2 X2358 3754 C2 X5869 2590 C2 X5949 3730 C2 X5949 1450 C2 X6024 2590 C2 X1935 2590 C2 X1925 1902 C2 X1925 3278 C2 X1924 3789 C2 X1924 1391 C2 X6087 3020 C2 X6087 2160 C2 X6243 1915 C2 X6243 3265 C2 X1722 2893 C2 X1722 2287 C2 X1397 3155 C2 X1397 2025 C2 X6584 1567 C2 X6584 3613 C2 X4031 4253 C2 X4031 927 C2 X3703 1103 C2 X3703 4077 C2 X4399 4134 C2 X4399 1046 C2 X3437 4135 C2 X3437 1045 C2 X4602 4066 C2 X4602 1114 C2 X3247 4063 C2 X3247 1117 C2 X4778 4024 C2 X4778 1156 C2 X4808 4377 C2 X4808 803 C2 X3027 1135 C2 X3027 4045 C2 X5138 3979 C2 X5138 1201 C2 X2499 1263 C2 X2499 3917 C2 X5623 1436 C2 X5623 3744 C2 X2123 1311 C2 X2123 3869 C2 X5870 2590 C2 X1958 2590 C2 X1956 1848 C2 X1956 3332 C2 X6034 2590 C2 X1904 2997 C2 X1904 2183 C2 X6086 1923 C2 X6086 3257 C2 X6147 2300 C2 X6147 2880 C2 X1606 2590 C2 X1575 1979 C2 X1575 3201 C2 X6545 3534 C2 X6545 1646 C2 X6927 2590 C2 X4241 4230 C2 X4241 950 C2 X3598 1157 C2 X4412 4114 C2 X4412 1066 C2 X3423 1114 C2 X3423 4066 C2 X3423 4066 C2 X4593 1183 C2 X4659 1137 C2 X4659 4043 C2 X4659 4043 C2 X3159 1166 C2 X3159 4014 C2 X5001 1165 C2 X5001 4015 C2 X2839 1134 C2 X2839 4046 C2 X5540 1276 C2 X5540 3904 C2 X2424 4021 C2 X2424 1159 C2 X2303 3759 C2 X2303 1421 C2 X5693 3742 C2 X5693 1438 C2 X5962 2590 C2 X6023 1526 C2 X6023 3654 C2 X1949 1904 C2 X1949 3276 C2 X6101 1919 C2 X6101 3261 C2 X1853 2267 C2 X1853 2913 C2 X1793 2590 C2 X1714 3427 C2 X1714 1753 C2 X6299 2273 C2 X6299 2907 C2 X6420 2590 C2 XLT0 X6486 4206 M X(Set 3) Rshow X6654 4206 T2 X3889 844 T2 X4088 4336 T2 X4476 602 T2 X3501 4578 T2 X3172 4133 T2 X4805 1047 T2 X5806 2590 T2 X2171 2590 T2 X5980 1274 T2 X1997 3906 T2 X1985 1381 T2 X5992 3799 T2 X1916 2593 T2 X6061 2587 T2 X4240 4226 T2 X3737 954 T2 X3722 4221 T2 X4255 959 T2 X3603 943 T2 X4374 4237 T2 X3576 4224 T2 X4401 956 T2 X4561 4147 T2 X3416 1033 T2 X3381 4174 T2 X4596 1006 T2 X4982 4291 T2 X2995 889 T2 X2632 4328 T2 X5345 852 T2 X5685 1255 T2 X2292 3925 T2 X5726 4002 T2 X2251 1178 T2 X2251 3752 T2 X5726 1428 T2 X5737 3726 T2 X2240 1454 T2 X5964 3988 T2 X2013 1192 T2 X1878 3289 T2 X6099 1891 T2 X1868 2576 T2 X6109 2604 T2 X6109 3295 T2 X1868 1885 T2 X6458 2736 T2 X1519 2444 T2 X1349 1900 T2 X6628 3280 T2 X6716 1549 T2 X1261 3631 T2 X3881 879 T2 X4096 4301 T2 X4604 829 T2 X3373 4351 T2 X3159 822 T2 X4818 4358 T2 X5815 573 T2 X2162 4607 T2 X5817 2594 T2 X2160 2586 T2 X2109 1422 T2 X5868 3758 T2 X5870 1314 T2 X2107 3866 T2 X1971 1832 T2 X6006 3348 T2 X1794 2550 T2 X6183 2630 T2 X6189 1864 T2 X1788 3316 T2 X4084 4221 T2 X3893 959 T2 X3434 4214 T2 X4543 966 T2 X2933 724 T2 X5044 4456 T2 X2931 4270 T2 X5046 910 T2 X2323 3933 T2 X5654 1247 T2 X5869 3702 T2 X2108 1478 T2 X6025 2627 T2 X1952 2553 T2 X6149 2967 T2 X1828 2213 T2 X6155 1892 T2 X1822 3288 T2 X3737 850 T2 X4240 4330 T2 X4462 974 T2 X3515 4206 T2 X3031 4174 T2 X4946 1006 T2 X5501 1236 T2 X2476 3944 T2 X2397 1485 T2 X5580 3695 T2 X2278 1600 T2 X5699 3580 T2 X5877 2765 T2 X2100 2415 T2 X1973 2649 T2 X6004 2531 T2 X1896 3303 T2 X6081 1877 T2 X3815 970 T2 X4162 4210 T2 X4287 1002 T2 X3690 4178 T2 X3605 1016 T2 X4372 4164 T2 X3471 1028 T2 X4506 4152 T2 X3433 4174 T2 X4544 1006 T2 X3424 4201 T2 X4553 979 T2 X2988 4279 T2 X4989 901 T2 X5127 4381 T2 X2850 799 T2 X5312 1019 T2 X2665 4161 T2 X5520 3965 T2 X2457 1215 T2 X5606 1283 T2 X2371 3897 T2 X2266 1449 T2 X5711 3731 T2 X5754 1432 T2 X2223 3748 T2 X2115 1469 T2 X5862 3711 T2 X5872 4494 T2 X2105 686 T2 X1952 2705 T2 X6025 2475 T2 X1906 3283 T2 X6071 1897 T2 X1849 1824 T2 X6128 3356 T2 X1810 2240 T2 X6167 2940 T2 X6223 2544 T2 X1754 2636 T2 X1737 3325 T2 X6240 1855 T2 X6547 2084 T2 X1430 3096 T2 Xstroke Xgrestore Xend Xshowpage END_OF_FILE if test 20399 -ne `wc -c <'figure1.ps'`; then echo shar: \"'figure1.ps'\" unpacked with wrong size! fi # end of 'figure1.ps' fi if test -f 'figure2.ps' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'figure2.ps'\" else echo shar: Extracting \"'figure2.ps'\" \(19614 characters\) sed "s/^X//" >'figure2.ps' <<'END_OF_FILE' X%!PS-Adobe-2.0 X%%Creator: gnuplot X%%DocumentFonts: Courier X%%BoundingBox: 50 50 554 770 X%%Pages: (atend) X%%EndComments X/gnudict 40 dict def Xgnudict begin X/Color false def X/gnulinewidth 5.000 def X/vshift -46 def X/dl {10 mul} def X/hpt 15.5 def X/vpt 15.5 def X/vpt2 vpt 2 mul def X/hpt2 hpt 2 mul def X/vpt4 vpt 4 mul def X/hpt4 hpt 4 mul def X/Lshow { currentpoint stroke moveto X 0 vshift rmoveto show } def X/Rshow { currentpoint stroke moveto X dup stringwidth pop neg vshift rmoveto show } def X/Cshow { currentpoint stroke moveto X dup stringwidth pop -2 div vshift rmoveto show } def X/DL { Color {setrgbcolor [] 0 setdash pop} X {pop pop pop 0 setdash} ifelse } def X/BL { stroke gnulinewidth 2 mul setlinewidth } def X/AL { stroke gnulinewidth 2 div setlinewidth } def X/PL { stroke gnulinewidth setlinewidth } def X/LTb { BL [] 0 0 0 DL } def X/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def X/LT0 { PL [] 0 1 0 DL } def X/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def X/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def X/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def X/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def X/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def X/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def X/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def X/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def X/M {moveto} def X/L {lineto} def X/P { stroke [] 0 setdash X currentlinewidth 2 div sub moveto X 0 currentlinewidth rlineto stroke } def X/D { stroke [] 0 setdash 2 copy vpt add moveto X hpt neg vpt neg rlineto hpt vpt neg rlineto X hpt vpt rlineto hpt neg vpt rlineto closepath stroke X P } def X/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add moveto X 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto X hpt2 neg 0 rlineto closepath stroke X P } def X/C { stroke [] 0 setdash exch hpt sub exch vpt add moveto X hpt2 vpt2 neg rlineto currentpoint stroke moveto X hpt2 neg 0 rmoveto hpt2 vpt2 rlineto stroke } def X/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add moveto X hpt neg vpt -1.62 mul rlineto X hpt 2 mul 0 rlineto X hpt neg vpt 1.62 mul rlineto closepath stroke X P } def X/D2 { stroke [] 0 setdash 2 copy vpt2 add moveto X hpt2 neg vpt2 neg rlineto hpt2 vpt2 neg rlineto X hpt2 vpt2 rlineto hpt2 neg vpt2 rlineto closepath stroke X P } def X/A2 { stroke [] 0 setdash vpt2 sub moveto 0 vpt4 rlineto X currentpoint stroke moveto X hpt2 neg vpt2 neg rmoveto hpt4 0 rlineto stroke X } def X/B2 { stroke [] 0 setdash 2 copy exch hpt2 sub exch vpt2 add moveto X 0 vpt4 neg rlineto hpt4 0 rlineto 0 vpt4 rlineto X hpt4 neg 0 rlineto closepath stroke X P } def X/C2 { stroke [] 0 setdash exch hpt2 sub exch vpt2 add moveto X hpt4 vpt4 neg rlineto currentpoint stroke moveto X hpt4 neg 0 rmoveto hpt4 vpt4 rlineto stroke } def X/T2 { stroke [] 0 setdash 2 copy vpt2 1.12 mul add moveto X hpt2 neg vpt2 -1.62 mul rlineto X hpt2 2 mul 0 rlineto X hpt2 neg vpt2 1.62 mul rlineto closepath stroke X P } def Xend X%%EndProlog X%%Page: 1 1 Xgnudict begin Xgsave X50 50 translate X0.100 0.100 scale X90 rotate X0 -5040 translate X0 setgray X/Courier findfont 140 scalefont setfont Xnewpath XLTa X1008 2590 M X6969 2590 L X3989 491 M X3989 4689 L XLTb X1008 491 M X1071 491 L X6969 491 M X6906 491 L X924 491 M X(-1) Rshow X1008 911 M X1071 911 L X6969 911 M X6906 911 L X924 911 M X(-0.8) Rshow X1008 1331 M X1071 1331 L X6969 1331 M X6906 1331 L X924 1331 M X(-0.6) Rshow X1008 1750 M X1071 1750 L X6969 1750 M X6906 1750 L X924 1750 M X(-0.4) Rshow X1008 2170 M X1071 2170 L X6969 2170 M X6906 2170 L X924 2170 M X(-0.2) Rshow X1008 2590 M X1071 2590 L X6969 2590 M X6906 2590 L X924 2590 M X(0) Rshow X1008 3010 M X1071 3010 L X6969 3010 M X6906 3010 L X924 3010 M X(0.2) Rshow X1008 3430 M X1071 3430 L X6969 3430 M X6906 3430 L X924 3430 M X(0.4) Rshow X1008 3849 M X1071 3849 L X6969 3849 M X6906 3849 L X924 3849 M X(0.6) Rshow X1008 4269 M X1071 4269 L X6969 4269 M X6906 4269 L X924 4269 M X(0.8) Rshow X1008 4689 M X1071 4689 L X6969 4689 M X6906 4689 L X924 4689 M X(1) Rshow X1008 491 M X1008 554 L X1008 4689 M X1008 4626 L X1008 351 M X(-1) Cshow X1604 491 M X1604 554 L X1604 4689 M X1604 4626 L X1604 351 M X(-0.8) Cshow X2200 491 M X2200 554 L X2200 4689 M X2200 4626 L X2200 351 M X(-0.6) Cshow X2796 491 M X2796 554 L X2796 4689 M X2796 4626 L X2796 351 M X(-0.4) Cshow X3392 491 M X3392 554 L X3392 4689 M X3392 4626 L X3392 351 M X(-0.2) Cshow X3989 491 M X3989 554 L X3989 4689 M X3989 4626 L X3989 351 M X(0) Cshow X4585 491 M X4585 554 L X4585 4689 M X4585 4626 L X4585 351 M X(0.2) Cshow X5181 491 M X5181 554 L X5181 4689 M X5181 4626 L X5181 351 M X(0.4) Cshow X5777 491 M X5777 554 L X5777 4689 M X5777 4626 L X5777 351 M X(0.6) Cshow X6373 491 M X6373 554 L X6373 4689 M X6373 4626 L X6373 351 M X(0.8) Cshow X6969 491 M X6969 554 L X6969 4689 M X6969 4626 L X6969 351 M X(1) Cshow XLTb X1008 491 M X6969 491 L X6969 4689 L X1008 4689 L X1008 491 L X140 2590 M Xcurrentpoint gsave translate 90 rotate 0 0 moveto X(Im epsilon) Cshow Xgrestore X3988 211 M X(Real epsilon) Cshow X4088 1 M X(Figure 2) Cshow XLT0 XLT0 X6486 4486 M X(Set 1) Rshow X6654 4486 D X3989 4080 D X4018 4059 D X4048 4038 D X4078 4038 D X4108 4038 D X4138 4017 D X4167 3996 D X4197 3996 D X4227 3996 D X4257 3954 D X4287 3933 D X4316 3933 D X4346 3933 D X4376 3912 D X4406 3891 D X4436 3870 D X4465 3870 D X4495 3849 D X4525 3828 D X4555 3828 D X4585 3807 D X4614 3807 D X4644 3807 D X4674 3786 D X4704 3786 D X4734 3786 D X4763 3786 D X4793 3786 D X4823 3765 D X4853 3765 D X4883 3765 D X4912 3765 D X4942 3744 D X4972 3744 D X5002 3744 D X5032 3723 D X5061 3723 D X5091 3723 D X5121 3702 D X5151 3702 D X5181 3702 D X5211 3681 D X5240 3681 D X5270 3681 D X5300 3660 D X5330 3660 D X5360 3660 D X5389 3640 D X5419 3640 D X5449 3640 D X5479 3619 D X5509 3619 D X5538 3598 D X5568 3577 D X5598 3577 D X5628 3577 D X5658 3556 D X5687 3556 D X5717 3556 D X5747 3535 D X5777 3535 D X5807 3514 D X5836 3451 D X5866 3451 D X5896 3430 D X5926 3409 D X5956 3367 D X5985 3346 D X6015 3325 D X6045 3325 D X6075 3304 D X6105 3304 D X6134 3304 D X6164 3283 D X6194 3262 D X6224 3241 D X6254 3220 D X6283 3199 D X6313 3178 D X6343 2947 D X6373 2926 D X6403 2905 D X6433 2905 D X6462 2884 D X6492 2884 D X6522 2863 D X6552 2863 D X6582 2863 D X6611 2842 D X6641 2821 D X6671 2716 D X6701 2716 D X6731 2716 D X6760 2695 D X6790 2632 D X6820 2632 D X6850 2611 D X6880 2611 D X3989 4080 D X3959 4059 D X3929 4059 D X3899 4059 D X3869 4038 D X3839 4017 D X3810 3996 D X3780 3996 D X3750 3996 D X3720 3954 D X3690 3933 D X3661 3933 D X3631 3933 D X3601 3912 D X3571 3891 D X3541 3870 D X3512 3870 D X3482 3849 D X3452 3828 D X3422 3828 D X3392 3807 D X3363 3807 D X3333 3807 D X3303 3807 D X3273 3786 D X3243 3786 D X3214 3786 D X3184 3786 D X3154 3765 D X3124 3765 D X3094 3765 D X3065 3765 D X3035 3765 D X3005 3744 D X2975 3744 D X2945 3744 D X2916 3723 D X2886 3723 D X2856 3702 D X2826 3702 D X2796 3702 D X2766 3681 D X2737 3681 D X2707 3681 D X2677 3681 D X2647 3660 D X2617 3660 D X2588 3640 D X2558 3640 D X2528 3640 D X2498 3619 D X2468 3598 D X2439 3598 D X2409 3577 D X2379 3577 D X2349 3577 D X2319 3556 D X2290 3556 D X2260 3556 D X2230 3535 D X2200 3535 D X2170 3514 D X2141 3451 D X2111 3451 D X2081 3430 D X2051 3409 D X2021 3367 D X1992 3346 D X1962 3325 D X1932 3325 D X1902 3304 D X1872 3304 D X1843 3304 D X1813 3283 D X1783 3262 D X1753 3220 D X1723 3220 D X1694 3199 D X1664 3199 D X1634 2947 D X1604 2926 D X1574 2905 D X1544 2905 D X1515 2884 D X1485 2884 D X1455 2884 D X1425 2863 D X1395 2842 D X1366 2842 D X1336 2821 D X1306 2716 D X1276 2716 D X1246 2716 D X1217 2695 D X1187 2632 D X1157 2632 D X1127 2611 D X1097 2611 D X3989 1100 D X3959 1121 D X3929 1121 D X3899 1121 D X3869 1142 D X3839 1163 D X3810 1184 D X3780 1184 D X3750 1184 D X3720 1226 D X3690 1247 D X3661 1247 D X3631 1247 D X3601 1268 D X3571 1289 D X3541 1310 D X3512 1310 D X3482 1331 D X3452 1352 D X3422 1352 D X3392 1373 D X3363 1373 D X3333 1373 D X3303 1373 D X3273 1394 D X3243 1394 D X3214 1394 D X3184 1394 D X3154 1415 D X3124 1415 D X3094 1415 D X3065 1415 D X3035 1415 D X3005 1436 D X2975 1436 D X2945 1436 D X2916 1457 D X2886 1457 D X2856 1478 D X2826 1478 D X2796 1478 D X2766 1499 D X2737 1499 D X2707 1499 D X2677 1499 D X2647 1520 D X2617 1520 D X2588 1541 D X2558 1541 D X2528 1541 D X2498 1561 D X2468 1582 D X2439 1582 D X2409 1603 D X2379 1603 D X2349 1603 D X2319 1624 D X2290 1624 D X2260 1624 D X2230 1645 D X2200 1645 D X2170 1666 D X2141 1729 D X2111 1729 D X2081 1750 D X2051 1771 D X2021 1813 D X1992 1834 D X1962 1855 D X1932 1855 D X1902 1876 D X1872 1876 D X1843 1876 D X1813 1897 D X1783 1918 D X1753 1960 D X1723 1960 D X1694 1981 D X1664 1981 D X1634 2233 D X1604 2254 D X1574 2275 D X1544 2275 D X1515 2296 D X1485 2296 D X1455 2296 D X1425 2317 D X1395 2338 D X1366 2338 D X1336 2359 D X1306 2464 D X1276 2464 D X1246 2464 D X1217 2485 D X1187 2548 D X1157 2548 D X1127 2569 D X1097 2569 D X3989 1100 D X4018 1121 D X4048 1142 D X4078 1142 D X4108 1142 D X4138 1163 D X4167 1184 D X4197 1184 D X4227 1184 D X4257 1226 D X4287 1247 D X4316 1247 D X4346 1247 D X4376 1268 D X4406 1289 D X4436 1310 D X4465 1310 D X4495 1331 D X4525 1352 D X4555 1352 D X4585 1373 D X4614 1373 D X4644 1373 D X4674 1394 D X4704 1394 D X4734 1394 D X4763 1394 D X4793 1394 D X4823 1415 D X4853 1415 D X4883 1415 D X4912 1415 D X4942 1436 D X4972 1436 D X5002 1436 D X5032 1457 D X5061 1457 D X5091 1457 D X5121 1478 D X5151 1478 D X5181 1478 D X5211 1499 D X5240 1499 D X5270 1499 D X5300 1520 D X5330 1520 D X5360 1520 D X5389 1541 D X5419 1541 D X5449 1541 D X5479 1561 D X5509 1561 D X5538 1582 D X5568 1603 D X5598 1603 D X5628 1603 D X5658 1624 D X5687 1624 D X5717 1624 D X5747 1645 D X5777 1645 D X5807 1666 D X5836 1729 D X5866 1729 D X5896 1750 D X5926 1771 D X5956 1813 D X5985 1834 D X6015 1855 D X6045 1855 D X6075 1876 D X6105 1876 D X6134 1876 D X6164 1897 D X6194 1918 D X6224 1939 D X6254 1960 D X6283 1981 D X6313 2002 D X6343 2233 D X6373 2254 D X6403 2275 D X6433 2275 D X6462 2296 D X6492 2296 D X6522 2317 D X6552 2317 D X6582 2317 D X6611 2338 D X6641 2359 D X6671 2464 D X6701 2464 D X6731 2464 D X6760 2485 D X6790 2548 D X6820 2548 D X6850 2569 D X6880 2569 D X6876 2590 D X6796 2631 D X6771 2672 D X6680 2709 D X6666 2748 D X6670 2788 D X6622 2824 D X6545 2856 D X6454 2884 D X6381 2911 D X6339 2942 D X6324 2976 D X6321 3012 D X6325 3050 D X6334 3089 D X6336 3127 D X6337 3166 D X6280 3190 D X6231 3215 D X6199 3245 D X6163 3272 D X6112 3294 D X6041 3307 D X5990 3327 D X5956 3352 D X5936 3382 D X5916 3412 D X5880 3435 D X5823 3448 D X5836 3494 D X5793 3513 D X5750 3532 D X5700 3545 D X5650 3558 D X5600 3569 D X5556 3584 D X5513 3598 D X5472 3613 D X5429 3626 D X5388 3640 D X5350 3655 D X5306 3665 D X5259 3672 D X5215 3680 D X5177 3692 D X5133 3699 D X5094 3710 D X5055 3721 D X5017 3731 D X4975 3737 D X4939 3749 D X4897 3754 D X4858 3761 D X4819 3768 D X4778 3771 D X4740 3779 D X4701 3784 D X4664 3791 D X4626 3798 D X4589 3804 D X4554 3816 D X4520 3830 D X4486 3844 D X4452 3861 D X4419 3883 D X4385 3905 D X4348 3917 D X4309 3926 D X4273 3946 D X4237 3973 D X4196 3983 D X4156 3992 D X4117 4030 D X4075 4042 D X4032 4049 D X3988 4063 D X3945 4049 D X3902 4042 D X3860 4030 D X3821 3995 D X3781 3979 D X3740 3976 D X3705 3943 D X3666 3932 D X3629 3917 D X3592 3902 D X3558 3883 D X3525 3861 D X3491 3844 D X3457 3830 D X3423 3816 D X3387 3807 D X3351 3798 D X3315 3788 D X3276 3784 D X3237 3779 D X3199 3771 D X3158 3768 D X3117 3764 D X3078 3757 D X3036 3752 D X2999 3740 D X2960 3731 D X2922 3721 D X2883 3710 D X2844 3699 D X2803 3690 D X2759 3682 D X2715 3674 D X2671 3665 D X2627 3655 D X2589 3640 D X2548 3626 D X2505 3613 D X2464 3598 D X2421 3584 D X2377 3569 D X2320 3562 D X2277 3545 D X2223 3534 D X2184 3513 D X2141 3494 D X2154 3448 D X2101 3434 D X2064 3411 D X2041 3382 D X2021 3352 D X1987 3327 D X1932 3309 D X1869 3292 D X1814 3272 D X1778 3245 D X1746 3215 D X1697 3190 D X1640 3166 D X1641 3127 D X1643 3089 D X1647 3050 D X1652 3012 D X1644 2977 D X1638 2942 D X1596 2911 D X1523 2884 D X1427 2856 D X1360 2824 D X1298 2789 D X1311 2748 D X1297 2709 D X1211 2672 D X1186 2631 D X1101 2590 D X1186 2549 D X1211 2508 D X1297 2471 D X1311 2432 D X1298 2391 D X1360 2356 D X1427 2324 D X1523 2296 D X1596 2269 D X1638 2238 D X1644 2203 D X1652 2168 D X1647 2130 D X1643 2091 D X1641 2053 D X1640 2014 D X1697 1990 D X1746 1965 D X1778 1935 D X1814 1908 D X1869 1888 D X1932 1871 D X1987 1853 D X2021 1828 D X2041 1798 D X2064 1769 D X2101 1746 D X2154 1732 D X2141 1686 D X2184 1667 D X2223 1646 D X2277 1635 D X2320 1618 D X2377 1611 D X2421 1596 D X2464 1582 D X2505 1567 D X2548 1554 D X2589 1540 D X2627 1525 D X2671 1515 D X2715 1506 D X2759 1498 D X2803 1490 D X2844 1481 D X2883 1470 D X2922 1459 D X2960 1449 D X2999 1440 D X3036 1428 D X3078 1423 D X3117 1416 D X3158 1412 D X3199 1409 D X3237 1401 D X3276 1396 D X3315 1392 D X3351 1382 D X3387 1373 D X3423 1364 D X3457 1350 D X3491 1336 D X3525 1319 D X3558 1297 D X3592 1278 D X3629 1263 D X3666 1248 D X3705 1237 D X3740 1204 D X3781 1201 D X3821 1185 D X3860 1150 D X3902 1138 D X3945 1131 D X3988 1117 D X4032 1131 D X4075 1138 D X4117 1150 D X4156 1188 D X4196 1197 D X4237 1207 D X4273 1234 D X4309 1254 D X4348 1263 D X4385 1275 D X4419 1297 D X4452 1319 D X4486 1336 D X4520 1350 D X4554 1364 D X4589 1376 D X4626 1382 D X4664 1389 D X4701 1396 D X4740 1401 D X4778 1409 D X4819 1412 D X4858 1419 D X4897 1426 D X4939 1431 D X4975 1443 D X5017 1449 D X5055 1459 D X5094 1470 D X5133 1481 D X5177 1488 D X5215 1500 D X5259 1508 D X5306 1515 D X5350 1525 D X5388 1540 D X5429 1554 D X5472 1567 D X5513 1582 D X5556 1596 D X5600 1611 D X5650 1622 D X5700 1635 D X5750 1648 D X5793 1667 D X5836 1686 D X5823 1732 D X5880 1745 D X5916 1768 D X5936 1798 D X5956 1828 D X5990 1853 D X6041 1873 D X6112 1886 D X6163 1908 D X6199 1935 D X6231 1965 D X6280 1990 D X6337 2014 D X6336 2053 D X6334 2091 D X6325 2130 D X6321 2168 D X6324 2204 D X6339 2238 D X6381 2269 D X6454 2296 D X6545 2324 D X6622 2356 D X6670 2392 D X6666 2432 D X6680 2471 D X6771 2508 D X6796 2549 D X6876 2590 D X6880 2590 D X6850 2611 D X6790 2632 D X6790 2653 D X6790 2674 D X6760 2695 D X6671 2716 D X6671 2737 D X6671 2758 D X6671 2779 D X6671 2800 D X6641 2821 D X6582 2842 D X6552 2863 D X6462 2884 D X6403 2905 D X6373 2926 D X6343 2947 D X6343 2968 D X6343 2989 D X6343 3010 D X6343 3031 D X6343 3052 D X6343 3073 D X6343 3094 D X6343 3115 D X6343 3136 D X6343 3157 D X6313 3178 D X6283 3199 D X6254 3220 D X6224 3241 D X6194 3262 D X6164 3283 D X6075 3304 D X6015 3325 D X5985 3346 D X5956 3367 D X5956 3388 D X5926 3409 D X5896 3430 D X5836 3451 D X5836 3472 D X5866 3493 D X5807 3514 D X5777 3535 D X5687 3556 D X5568 3577 D X5538 3598 D X5479 3619 D X5389 3640 D X5330 3660 D X5211 3681 D X5121 3702 D X5061 3723 D X4942 3744 D X4853 3765 D X4674 3786 D X4585 3807 D X4525 3828 D X4495 3849 D X4436 3870 D X4406 3891 D X4376 3912 D X4287 3933 D X4257 3954 D X4257 3975 D X4167 3996 D X4138 4017 D X4048 4038 D X4018 4059 D X1097 2590 D X1127 2611 D X1187 2632 D X1187 2653 D X1187 2674 D X1217 2695 D X1306 2716 D X1306 2737 D X1306 2758 D X1306 2779 D X1276 2800 D X1336 2821 D X1395 2842 D X1455 2863 D X1515 2884 D X1574 2905 D X1604 2926 D X1634 2947 D X1634 2968 D X1634 2989 D X1634 3010 D X1634 3031 D X1634 3052 D X1634 3073 D X1634 3094 D X1634 3115 D X1634 3136 D X1634 3157 D X1664 3178 D X1694 3199 D X1723 3220 D X1753 3241 D X1783 3262 D X1813 3283 D X1902 3304 D X1962 3325 D X1992 3346 D X2021 3367 D X2021 3388 D X2051 3409 D X2081 3430 D X2141 3451 D X2141 3472 D X2141 3493 D X2170 3514 D X2230 3535 D X2319 3556 D X2379 3577 D X2439 3598 D X2498 3619 D X2588 3640 D X2647 3660 D X2766 3681 D X2856 3702 D X2916 3723 D X3035 3744 D X3154 3765 D X3273 3786 D X3392 3807 D X3452 3828 D X3482 3849 D X3541 3870 D X3571 3891 D X3601 3912 D X3690 3933 D X3720 3954 D X3720 3975 D X3810 3996 D X3839 4017 D X3929 4038 D X3959 4059 D X1097 2590 D X1127 2569 D X1187 2548 D X1187 2527 D X1187 2506 D X1217 2485 D X1306 2464 D X1306 2443 D X1306 2422 D X1306 2401 D X1276 2380 D X1336 2359 D X1395 2338 D X1455 2317 D X1515 2296 D X1574 2275 D X1604 2254 D X1634 2233 D X1634 2212 D X1634 2191 D X1634 2170 D X1634 2149 D X1634 2128 D X1634 2107 D X1634 2086 D X1634 2065 D X1634 2044 D X1634 2023 D X1664 2002 D X1694 1981 D X1723 1960 D X1753 1939 D X1783 1918 D X1813 1897 D X1902 1876 D X1962 1855 D X1992 1834 D X2021 1813 D X2021 1792 D X2051 1771 D X2081 1750 D X2141 1729 D X2141 1708 D X2141 1687 D X2170 1666 D X2230 1645 D X2319 1624 D X2379 1603 D X2439 1582 D X2498 1561 D X2588 1541 D X2647 1520 D X2766 1499 D X2856 1478 D X2916 1457 D X3035 1436 D X3154 1415 D X3273 1394 D X3392 1373 D X3452 1352 D X3482 1331 D X3541 1310 D X3571 1289 D X3601 1268 D X3690 1247 D X3720 1226 D X3720 1205 D X3810 1184 D X3839 1163 D X3929 1142 D X3959 1121 D X6880 2590 D X6850 2569 D X6790 2548 D X6790 2527 D X6790 2506 D X6760 2485 D X6671 2464 D X6671 2443 D X6671 2422 D X6671 2401 D X6671 2380 D X6641 2359 D X6582 2338 D X6552 2317 D X6462 2296 D X6403 2275 D X6373 2254 D X6343 2233 D X6343 2212 D X6343 2191 D X6343 2170 D X6343 2149 D X6343 2128 D X6343 2107 D X6343 2086 D X6343 2065 D X6343 2044 D X6343 2023 D X6313 2002 D X6283 1981 D X6254 1960 D X6224 1939 D X6194 1918 D X6164 1897 D X6075 1876 D X6015 1855 D X5985 1834 D X5956 1813 D X5956 1792 D X5926 1771 D X5896 1750 D X5836 1729 D X5836 1708 D X5866 1687 D X5807 1666 D X5777 1645 D X5687 1624 D X5568 1603 D X5538 1582 D X5479 1561 D X5389 1541 D X5330 1520 D X5211 1499 D X5121 1478 D X5061 1457 D X4942 1436 D X4853 1415 D X4674 1394 D X4585 1373 D X4525 1352 D X4495 1331 D X4436 1310 D X4406 1289 D X4376 1268 D X4287 1247 D X4257 1226 D X4257 1205 D X4167 1184 D X4138 1163 D X4048 1142 D X4018 1121 D XLT0 X6486 4346 M X(Set 2) Rshow X6654 4346 C2 X3819 1229 C2 X3819 3951 C2 X4272 3977 C2 X4272 1203 C2 X4453 3862 C2 X4453 1318 C2 X3507 4174 C2 X3507 1006 C2 X3464 1322 C2 X3464 3858 C2 X4573 1350 C2 X4573 3830 C2 X3298 1364 C2 X3298 3816 C2 X4816 1349 C2 X4816 3831 C2 X3070 3777 C2 X3070 1403 C2 X5086 1456 C2 X5086 3724 C2 X2780 3684 C2 X2780 1496 C2 X2745 1387 C2 X2745 3793 C2 X5394 3750 C2 X5394 1430 C2 X5468 1634 C2 X5468 3546 C2 X2310 3526 C2 X2310 1654 C2 X5929 3714 C2 X5929 1466 C2 X2007 3388 C2 X2007 1792 C2 X6076 1765 C2 X6076 3415 C2 X6317 2196 C2 X6317 2984 C2 X1581 3007 C2 X1581 2173 C2 X1541 2590 C2 X6437 2590 C2 X6456 3101 C2 X6456 2079 C2 X1439 3715 C2 X1439 1465 C2 X3776 3933 C2 X3776 1247 C2 X4245 1245 C2 X4245 3935 C2 X3554 1025 C2 X3554 4155 C2 X4468 1329 C2 X4468 3851 C2 X3435 1313 C2 X3435 3867 C2 X4593 3817 C2 X4593 1363 C2 X3279 3801 C2 X3279 1379 C2 X4842 3803 C2 X4842 1377 C2 X2985 1389 C2 X2985 3791 C2 X5148 1490 C2 X5148 3690 C2 X2726 3729 C2 X2726 1451 C2 X2604 1644 C2 X2604 3536 C2 X5386 3831 C2 X5386 1349 C2 X5491 3778 C2 X5491 1402 C2 X2347 1492 C2 X2347 3688 C2 X2270 2590 C2 X5792 1774 C2 X5792 3406 C2 X5795 1875 C2 X5795 3305 C2 X2094 3411 C2 X2094 1769 C2 X6413 2175 C2 X6413 3005 C2 X1562 2141 C2 X1562 3039 C2 X1155 2590 C2 X4078 1416 C2 X4078 3764 C2 X3817 1092 C2 X3817 4088 C2 X3796 4398 C2 X3796 782 C2 X4423 1238 C2 X4423 3942 C2 X3483 3891 C2 X3483 1289 C2 X4534 1348 C2 X4534 3832 C2 X3348 1361 C2 X3348 3819 C2 X4745 1364 C2 X4745 3816 C2 X3109 3840 C2 X3109 1340 C2 X5051 3753 C2 X5051 1427 C2 X2848 1471 C2 X2848 3709 C2 X5212 1614 C2 X5212 3566 C2 X2715 3794 C2 X2715 1386 C2 X5263 1465 C2 X5263 3715 C2 X2331 1634 C2 X2331 3546 C2 X5698 2590 C2 X2270 3173 C2 X2270 2007 C2 X5713 1662 C2 X5713 3518 C2 X1923 3421 C2 X1923 1759 C2 X6078 1814 C2 X6078 3366 C2 X6159 4027 C2 X6159 1153 C2 X1703 2440 C2 X1703 2740 C2 X6405 2189 C2 X6405 2991 C2 X3934 4092 C2 X3934 1088 C2 X4274 3878 C2 X4274 1302 C2 X3580 3920 C2 X3580 1260 C2 X4499 1298 C2 X4499 3882 C2 X3423 3835 C2 X3423 1345 C2 X4677 3843 C2 X4677 1337 C2 X3244 3840 C2 X3244 1340 C2 X4889 3763 C2 X4889 1417 C2 X4940 1350 C2 X4940 3830 C2 X2911 3740 C2 X2911 1440 C2 X2903 1465 C2 X2903 3715 C2 X5210 3707 C2 X5210 1473 C2 X2488 1504 C2 X2488 3676 C2 X2446 3419 C2 X2446 1761 C2 X5642 1610 C2 X5642 3570 C2 X5723 1793 C2 X5723 3387 C2 X6094 1757 C2 X6094 3423 C2 X1830 1482 C2 X1830 3698 C2 X1707 1969 C2 X1707 3211 C2 X6397 2212 C2 X6397 2968 C2 X1412 2234 C2 X1412 2946 C2 X4128 1119 C2 X4128 4061 C2 X3671 1248 C2 X3671 3932 C2 X4471 1271 C2 X4471 3909 C2 X3478 1338 C2 X3478 3842 C2 X4627 1346 C2 X4627 3834 C2 X3328 1349 C2 X3328 3831 C2 X4757 3783 C2 X4757 1397 C2 X3035 1407 C2 X3035 3773 C2 X5135 3747 C2 X5135 1433 C2 X2761 3772 C2 X2761 1408 C2 X2606 3517 C2 X2606 1663 C2 X2475 3700 C2 X2475 1480 C2 X5565 1545 C2 X5565 3635 C2 X5746 3545 C2 X5746 1635 C2 X2099 1805 C2 X2099 3375 C2 X5909 3311 C2 X5909 1869 C2 X1765 3258 C2 X1765 1922 C2 X6312 2590 C2 X6316 4616 C2 X6316 564 C2 X6395 2197 C2 X6395 2983 C2 X1434 2182 C2 X1434 2998 C2 Xstroke Xgrestore Xend Xshowpage X%%Trailer X%%Pages: 1 X%%Trailer X%%Pages: 1 END_OF_FILE if test 19614 -ne `wc -c <'figure2.ps'`; then echo shar: \"'figure2.ps'\" unpacked with wrong size! fi # end of 'figure2.ps' fi if test -f 'figure3.ps' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'figure3.ps'\" else echo shar: Extracting \"'figure3.ps'\" \(31303 characters\) sed "s/^X//" >'figure3.ps' <<'END_OF_FILE' X%!PS-Adobe-2.0 X%%Creator: gnuplot X%%DocumentFonts: Courier X%%BoundingBox: 50 50 554 770 X%%Pages: (atend) X%%EndComments X/gnudict 40 dict def Xgnudict begin X/Color false def X/gnulinewidth 5.000 def X/vshift -46 def X/dl {10 mul} def X/hpt 15.5 def X/vpt 15.5 def X/vpt2 vpt 2 mul def X/hpt2 hpt 2 mul def X/vpt4 vpt 4 mul def X/hpt4 hpt 4 mul def X/Lshow { currentpoint stroke moveto X 0 vshift rmoveto show } def X/Rshow { currentpoint stroke moveto X dup stringwidth pop neg vshift rmoveto show } def X/Cshow { currentpoint stroke moveto X dup stringwidth pop -2 div vshift rmoveto show } def X/DL { Color {setrgbcolor [] 0 setdash pop} X {pop pop pop 0 setdash} ifelse } def X/BL { stroke gnulinewidth 2 mul setlinewidth } def X/AL { stroke gnulinewidth 2 div setlinewidth } def X/PL { stroke gnulinewidth setlinewidth } def X/LTb { BL [] 0 0 0 DL } def X/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def X/LT0 { PL [] 0 1 0 DL } def X/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def X/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def X/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def X/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def X/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def X/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def X/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def X/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def X/M {moveto} def X/L {lineto} def X/P { stroke [] 0 setdash X currentlinewidth 2 div sub moveto X 0 currentlinewidth rlineto stroke } def X/D { stroke [] 0 setdash 2 copy vpt add moveto X hpt neg vpt neg rlineto hpt vpt neg rlineto X hpt vpt rlineto hpt neg vpt rlineto closepath stroke X P } def X/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add moveto X 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto X hpt2 neg 0 rlineto closepath stroke X P } def X/C { stroke [] 0 setdash exch hpt sub exch vpt add moveto X hpt2 vpt2 neg rlineto currentpoint stroke moveto X hpt2 neg 0 rmoveto hpt2 vpt2 rlineto stroke } def X/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add moveto X hpt neg vpt -1.62 mul rlineto X hpt 2 mul 0 rlineto X hpt neg vpt 1.62 mul rlineto closepath stroke X P } def X/D2 { stroke [] 0 setdash 2 copy vpt2 add moveto X hpt2 neg vpt2 neg rlineto hpt2 vpt2 neg rlineto X hpt2 vpt2 rlineto hpt2 neg vpt2 rlineto closepath stroke X P } def X/A2 { stroke [] 0 setdash vpt2 sub moveto 0 vpt4 rlineto X currentpoint stroke moveto X hpt2 neg vpt2 neg rmoveto hpt4 0 rlineto stroke X } def X/B2 { stroke [] 0 setdash 2 copy exch hpt2 sub exch vpt2 add moveto X 0 vpt4 neg rlineto hpt4 0 rlineto 0 vpt4 rlineto X hpt4 neg 0 rlineto closepath stroke X P } def X/C2 { stroke [] 0 setdash exch hpt2 sub exch vpt2 add moveto X hpt4 vpt4 neg rlineto currentpoint stroke moveto X hpt4 neg 0 rmoveto hpt4 vpt4 rlineto stroke } def X/T2 { stroke [] 0 setdash 2 copy vpt2 1.12 mul add moveto X hpt2 neg vpt2 -1.62 mul rlineto X hpt2 2 mul 0 rlineto X hpt2 neg vpt2 1.62 mul rlineto closepath stroke X P } def Xend X%%EndProlog X%%Page: 1 1 Xgnudict begin Xgsave X50 50 translate X0.100 0.100 scale X90 rotate X0 -5040 translate X0 setgray X/Courier findfont 140 scalefont setfont Xnewpath XLTa X1008 2590 M X6969 2590 L X3989 491 M X3989 4689 L XLTb X1008 491 M X1071 491 L X6969 491 M X6906 491 L X924 491 M X(-1) Rshow X1008 911 M X1071 911 L X6969 911 M X6906 911 L X924 911 M X(-0.8) Rshow X1008 1331 M X1071 1331 L X6969 1331 M X6906 1331 L X924 1331 M X(-0.6) Rshow X1008 1750 M X1071 1750 L X6969 1750 M X6906 1750 L X924 1750 M X(-0.4) Rshow X1008 2170 M X1071 2170 L X6969 2170 M X6906 2170 L X924 2170 M X(-0.2) Rshow X1008 2590 M X1071 2590 L X6969 2590 M X6906 2590 L X924 2590 M X(0) Rshow X1008 3010 M X1071 3010 L X6969 3010 M X6906 3010 L X924 3010 M X(0.2) Rshow X1008 3430 M X1071 3430 L X6969 3430 M X6906 3430 L X924 3430 M X(0.4) Rshow X1008 3849 M X1071 3849 L X6969 3849 M X6906 3849 L X924 3849 M X(0.6) Rshow X1008 4269 M X1071 4269 L X6969 4269 M X6906 4269 L X924 4269 M X(0.8) Rshow X1008 4689 M X1071 4689 L X6969 4689 M X6906 4689 L X924 4689 M X(1) Rshow X1008 491 M X1008 554 L X1008 4689 M X1008 4626 L X1008 351 M X(-1) Cshow X1604 491 M X1604 554 L X1604 4689 M X1604 4626 L X1604 351 M X(-0.8) Cshow X2200 491 M X2200 554 L X2200 4689 M X2200 4626 L X2200 351 M X(-0.6) Cshow X2796 491 M X2796 554 L X2796 4689 M X2796 4626 L X2796 351 M X(-0.4) Cshow X3392 491 M X3392 554 L X3392 4689 M X3392 4626 L X3392 351 M X(-0.2) Cshow X3989 491 M X3989 554 L X3989 4689 M X3989 4626 L X3989 351 M X(0) Cshow X4585 491 M X4585 554 L X4585 4689 M X4585 4626 L X4585 351 M X(0.2) Cshow X5181 491 M X5181 554 L X5181 4689 M X5181 4626 L X5181 351 M X(0.4) Cshow X5777 491 M X5777 554 L X5777 4689 M X5777 4626 L X5777 351 M X(0.6) Cshow X6373 491 M X6373 554 L X6373 4689 M X6373 4626 L X6373 351 M X(0.8) Cshow X6969 491 M X6969 554 L X6969 4689 M X6969 4626 L X6969 351 M X(1) Cshow XLTb X1008 491 M X6969 491 L X6969 4689 L X1008 4689 L X1008 491 L X140 2590 M Xcurrentpoint gsave translate 90 rotate 0 0 moveto X(Im epsilon) Cshow Xgrestore X3988 211 M X(Real epsilon) Cshow X4088 1 M X(Figure 3) Cshow XLT0 XLT0 X6486 4486 M X(Set 1) Rshow X6654 4486 D X3989 4269 D X4018 4269 D X4048 4248 D X4078 4248 D X4108 4227 D X4138 4206 D X4167 4206 D X4197 4185 D X4227 4164 D X4257 4143 D X4287 4122 D X4316 4122 D X4346 4101 D X4376 4101 D X4406 4080 D X4436 4080 D X4465 4059 D X4495 4059 D X4525 4038 D X4555 4038 D X4585 4038 D X4614 4017 D X4644 4017 D X4674 4017 D X4704 4017 D X4734 4017 D X4763 4017 D X4793 4017 D X4823 4017 D X4853 3996 D X4883 3996 D X4912 3996 D X4942 3996 D X4972 3996 D X5002 3996 D X5032 3996 D X5061 3975 D X5091 3975 D X5121 3975 D X5151 3975 D X5181 3975 D X5211 3954 D X5240 3954 D X5270 3954 D X5300 3954 D X5330 3954 D X5360 3933 D X5389 3933 D X5419 3933 D X5449 3912 D X5479 3891 D X5509 3870 D X5538 3849 D X5568 3849 D X5598 3828 D X5628 3807 D X5658 3807 D X5687 3723 D X5717 3702 D X5747 3702 D X5777 3702 D X5807 3702 D X5836 3681 D X5866 2611 D X3989 4269 D X3959 4269 D X3929 4248 D X3899 4248 D X3869 4227 D X3839 4227 D X3810 4206 D X3780 4185 D X3750 4164 D X3720 4143 D X3690 4122 D X3661 4122 D X3631 4122 D X3601 4101 D X3571 4080 D X3541 4080 D X3512 4059 D X3482 4059 D X3452 4038 D X3422 4038 D X3392 4038 D X3363 4017 D X3333 4017 D X3303 4017 D X3273 4017 D X3243 4017 D X3214 4017 D X3184 4017 D X3154 4017 D X3124 3996 D X3094 3996 D X3065 3996 D X3035 3996 D X3005 3996 D X2975 3996 D X2945 3996 D X2916 3975 D X2886 3975 D X2856 3975 D X2826 3975 D X2796 3975 D X2766 3975 D X2737 3954 D X2707 3954 D X2677 3954 D X2647 3954 D X2617 3933 D X2588 3933 D X2558 3933 D X2528 3912 D X2498 3891 D X2468 3870 D X2439 3849 D X2409 3849 D X2379 3828 D X2349 3807 D X2319 3807 D X2290 3723 D X2260 3702 D X2230 3702 D X2200 3702 D X2170 3702 D X2141 3681 D X2111 2611 D X3989 911 D X3959 911 D X3929 932 D X3899 932 D X3869 953 D X3839 953 D X3810 974 D X3780 995 D X3750 1016 D X3720 1037 D X3690 1058 D X3661 1058 D X3631 1058 D X3601 1079 D X3571 1100 D X3541 1100 D X3512 1121 D X3482 1121 D X3452 1142 D X3422 1142 D X3392 1142 D X3363 1163 D X3333 1163 D X3303 1163 D X3273 1163 D X3243 1163 D X3214 1163 D X3184 1163 D X3154 1163 D X3124 1184 D X3094 1184 D X3065 1184 D X3035 1184 D X3005 1184 D X2975 1184 D X2945 1184 D X2916 1205 D X2886 1205 D X2856 1205 D X2826 1205 D X2796 1205 D X2766 1205 D X2737 1226 D X2707 1226 D X2677 1226 D X2647 1226 D X2617 1247 D X2588 1247 D X2558 1247 D X2528 1268 D X2498 1289 D X2468 1310 D X2439 1331 D X2409 1331 D X2379 1352 D X2349 1373 D X2319 1373 D X2290 1457 D X2260 1478 D X2230 1478 D X2200 1478 D X2170 1478 D X2141 1499 D X2111 2569 D X3989 911 D X4018 911 D X4048 932 D X4078 932 D X4108 953 D X4138 974 D X4167 974 D X4197 995 D X4227 1016 D X4257 1037 D X4287 1058 D X4316 1058 D X4346 1079 D X4376 1079 D X4406 1100 D X4436 1100 D X4465 1121 D X4495 1121 D X4525 1142 D X4555 1142 D X4585 1142 D X4614 1163 D X4644 1163 D X4674 1163 D X4704 1163 D X4734 1163 D X4763 1163 D X4793 1163 D X4823 1163 D X4853 1184 D X4883 1184 D X4912 1184 D X4942 1184 D X4972 1184 D X5002 1184 D X5032 1184 D X5061 1205 D X5091 1205 D X5121 1205 D X5151 1205 D X5181 1205 D X5211 1226 D X5240 1226 D X5270 1226 D X5300 1226 D X5330 1226 D X5360 1247 D X5389 1247 D X5419 1247 D X5449 1268 D X5479 1289 D X5509 1310 D X5538 1331 D X5568 1331 D X5598 1352 D X5628 1373 D X5658 1373 D X5687 1457 D X5717 1478 D X5747 1478 D X5777 1478 D X5807 1478 D X5836 1499 D X5866 2569 D X5744 2590 D X5874 2618 D X5966 2648 D X6006 2679 D X6040 2711 D X6077 2745 D X6243 2791 D X6223 2822 D X6183 2851 D X6189 2886 D X6161 2915 D X6414 2991 D X6303 3008 D X6281 3041 D X6267 3074 D X6243 3106 D X6209 3135 D X6184 3165 D X6145 3191 D X6096 3214 D X6048 3236 D X6015 3262 D X6012 3297 D X6044 3347 D X6123 3416 D X6122 3457 D X6128 3502 D X6131 3548 D X6095 3576 D X6042 3595 D X5993 3616 D X5940 3633 D X5894 3653 D X5851 3675 D X5797 3689 D X5736 3698 D X5686 3713 D X5672 3751 D X5667 3797 D X5618 3812 D X5578 3833 D X5531 3849 D X5494 3871 D X5461 3898 D X5419 3917 D X5371 3930 D X5323 3942 D X5269 3948 D X5219 3955 D X5168 3962 D X5118 3968 D X5070 3975 D X5020 3979 D X4974 3988 D X4924 3991 D X4877 3995 D X4829 3999 D X4782 4002 D X4737 4007 D X4690 4009 D X4645 4012 D X4601 4019 D X4558 4027 D X4515 4035 D X4474 4049 D X4433 4062 D X4393 4082 D X4351 4100 D X4309 4118 D X4265 4129 D X4222 4152 D X4179 4185 D X4133 4210 D X4087 4238 D X4037 4236 D X3988 4259 D X3940 4233 D X3890 4238 D X3844 4207 D X3799 4182 D X3754 4159 D X3712 4129 D X3668 4118 D X3626 4100 D X3584 4082 D X3544 4062 D X3503 4049 D X3462 4035 D X3419 4027 D X3376 4019 D X3331 4015 D X3287 4009 D X3242 4004 D X3195 4002 D X3148 3999 D X3100 3995 D X3051 3994 D X3005 3985 D X2955 3982 D X2909 3972 D X2859 3968 D X2809 3962 D X2758 3955 D X2708 3948 D X2654 3942 D X2606 3930 D X2558 3917 D X2519 3896 D X2478 3876 D X2446 3849 D X2405 3828 D X2359 3812 D X2310 3797 D X2305 3751 D X2288 3715 D X2248 3694 D X2180 3689 D X2126 3675 D X2087 3651 D X2037 3633 D X1984 3616 D X1935 3595 D X1890 3572 D X1838 3551 D X1849 3502 D X1855 3457 D X1854 3416 D X1933 3347 D X1974 3294 D X1962 3262 D X1925 3237 D X1881 3214 D X1828 3192 D X1789 3166 D X1768 3135 D X1730 3107 D X1701 3076 D X1696 3041 D X1674 3008 D X1563 2991 D X1816 2915 D X1784 2886 D X1821 2848 D X1754 2822 D X1729 2791 D X1895 2745 D X1942 2711 D X1971 2679 D X2034 2648 D X2075 2618 D X2233 2590 D X2075 2562 D X2034 2532 D X1971 2501 D X1942 2469 D X1895 2435 D X1729 2389 D X1754 2358 D X1821 2332 D X1784 2294 D X1816 2265 D X1563 2189 D X1674 2172 D X1696 2139 D X1701 2104 D X1730 2073 D X1768 2045 D X1789 2014 D X1828 1988 D X1881 1966 D X1925 1943 D X1962 1918 D X1974 1886 D X1933 1833 D X1854 1764 D X1855 1723 D X1849 1678 D X1838 1629 D X1890 1608 D X1935 1585 D X1984 1564 D X2037 1547 D X2087 1529 D X2126 1505 D X2180 1491 D X2248 1486 D X2288 1465 D X2305 1429 D X2310 1383 D X2359 1368 D X2405 1352 D X2446 1331 D X2478 1304 D X2519 1284 D X2558 1263 D X2606 1250 D X2654 1238 D X2708 1232 D X2758 1225 D X2809 1218 D X2859 1212 D X2909 1208 D X2955 1198 D X3005 1195 D X3051 1186 D X3100 1185 D X3148 1181 D X3195 1178 D X3242 1176 D X3287 1171 D X3331 1165 D X3376 1161 D X3419 1153 D X3462 1145 D X3503 1131 D X3544 1118 D X3584 1098 D X3626 1080 D X3668 1062 D X3712 1051 D X3754 1021 D X3799 998 D X3844 973 D X3890 942 D X3940 947 D X3988 921 D X4037 944 D X4087 942 D X4133 970 D X4179 995 D X4222 1028 D X4265 1051 D X4309 1062 D X4351 1080 D X4393 1098 D X4433 1118 D X4474 1131 D X4515 1145 D X4558 1153 D X4601 1161 D X4645 1168 D X4690 1171 D X4737 1173 D X4782 1178 D X4829 1181 D X4877 1185 D X4924 1189 D X4974 1192 D X5020 1201 D X5070 1205 D X5118 1212 D X5168 1218 D X5219 1225 D X5269 1232 D X5323 1238 D X5371 1250 D X5419 1263 D X5461 1282 D X5494 1309 D X5531 1331 D X5578 1347 D X5618 1368 D X5667 1383 D X5672 1429 D X5686 1467 D X5736 1482 D X5797 1491 D X5851 1505 D X5894 1527 D X5940 1547 D X5993 1564 D X6042 1585 D X6095 1604 D X6131 1632 D X6128 1678 D X6122 1723 D X6123 1764 D X6044 1833 D X6012 1883 D X6015 1918 D X6048 1944 D X6096 1966 D X6145 1989 D X6184 2015 D X6209 2045 D X6243 2074 D X6267 2106 D X6281 2139 D X6303 2172 D X6414 2189 D X6161 2265 D X6189 2294 D X6183 2329 D X6223 2358 D X6243 2389 D X6077 2435 D X6040 2469 D X6006 2501 D X5966 2532 D X5874 2562 D X5744 2590 D X5747 2590 D X5866 2611 D X5926 2632 D X6015 2653 D X6015 2674 D X6015 2695 D X6045 2716 D X6075 2737 D X6105 2758 D X6254 2779 D X6254 2800 D X6254 2821 D X6224 2842 D X6164 2863 D X6194 2884 D X6194 2905 D X6164 2926 D X6403 2947 D X6403 2968 D X6433 2989 D X6313 3010 D X6313 3031 D X6283 3052 D X6283 3073 D X6283 3094 D X6254 3115 D X6224 3136 D X6194 3157 D X6194 3178 D X6134 3199 D X6105 3220 D X6075 3241 D X6015 3262 D X6015 3283 D X6015 3304 D X6045 3325 D X6045 3346 D X6075 3367 D X6105 3388 D X6134 3409 D X6134 3430 D X6134 3451 D X6134 3472 D X6134 3493 D X6134 3514 D X6134 3535 D X6134 3556 D X6075 3577 D X6045 3598 D X5985 3619 D X5956 3640 D X5896 3660 D X5836 3681 D X5717 3702 D X5687 3723 D X5687 3744 D X5687 3765 D X5687 3786 D X5628 3807 D X5568 3828 D X5538 3849 D X5509 3870 D X5479 3891 D X5449 3912 D X5360 3933 D X5211 3954 D X5061 3975 D X4853 3996 D X4614 4017 D X4525 4038 D X4465 4059 D X4406 4080 D X4376 4101 D X4287 4122 D X4257 4143 D X4227 4164 D X4197 4185 D X4138 4206 D X4108 4227 D X4048 4248 D X4018 4269 D X2230 2590 D X2111 2611 D X2051 2632 D X1962 2653 D X1962 2674 D X1932 2695 D X1932 2716 D X1902 2737 D X1872 2758 D X1843 2779 D X1723 2800 D X1723 2821 D X1753 2842 D X1813 2863 D X1783 2884 D X1813 2905 D X1813 2926 D X1574 2947 D X1544 2968 D X1544 2989 D X1664 3010 D X1664 3031 D X1694 3052 D X1694 3073 D X1694 3094 D X1723 3115 D X1753 3136 D X1783 3157 D X1783 3178 D X1843 3199 D X1872 3220 D X1932 3241 D X1962 3262 D X1962 3283 D X1962 3304 D X1932 3325 D X1932 3346 D X1902 3367 D X1872 3388 D X1843 3409 D X1843 3430 D X1843 3451 D X1843 3472 D X1843 3493 D X1843 3514 D X1813 3535 D X1843 3556 D X1872 3577 D X1932 3598 D X1992 3619 D X2051 3640 D X2081 3660 D X2141 3681 D X2260 3702 D X2260 3723 D X2290 3744 D X2290 3765 D X2290 3786 D X2349 3807 D X2379 3828 D X2439 3849 D X2468 3870 D X2498 3891 D X2528 3912 D X2617 3933 D X2766 3954 D X2916 3975 D X3124 3996 D X3363 4017 D X3452 4038 D X3512 4059 D X3571 4080 D X3601 4101 D X3690 4122 D X3720 4143 D X3750 4164 D X3780 4185 D X3839 4206 D X3869 4227 D X3929 4248 D X3959 4269 D X2230 2590 D X2111 2569 D X2051 2548 D X1962 2527 D X1962 2506 D X1932 2485 D X1932 2464 D X1902 2443 D X1872 2422 D X1843 2401 D X1723 2380 D X1723 2359 D X1753 2338 D X1813 2317 D X1783 2296 D X1813 2275 D X1813 2254 D X1574 2233 D X1544 2212 D X1544 2191 D X1664 2170 D X1664 2149 D X1694 2128 D X1694 2107 D X1694 2086 D X1723 2065 D X1753 2044 D X1783 2023 D X1783 2002 D X1843 1981 D X1872 1960 D X1932 1939 D X1962 1918 D X1962 1897 D X1962 1876 D X1932 1855 D X1932 1834 D X1902 1813 D X1872 1792 D X1843 1771 D X1843 1750 D X1843 1729 D X1843 1708 D X1843 1687 D X1843 1666 D X1813 1645 D X1843 1624 D X1872 1603 D X1932 1582 D X1992 1561 D X2051 1541 D X2081 1520 D X2141 1499 D X2260 1478 D X2260 1457 D X2290 1436 D X2290 1415 D X2290 1394 D X2349 1373 D X2379 1352 D X2439 1331 D X2468 1310 D X2498 1289 D X2528 1268 D X2617 1247 D X2766 1226 D X2916 1205 D X3124 1184 D X3363 1163 D X3452 1142 D X3512 1121 D X3571 1100 D X3601 1079 D X3690 1058 D X3720 1037 D X3750 1016 D X3780 995 D X3839 974 D X3869 953 D X3929 932 D X3959 911 D X5747 2590 D X5866 2569 D X5926 2548 D X6015 2527 D X6015 2506 D X6015 2485 D X6045 2464 D X6075 2443 D X6105 2422 D X6254 2401 D X6254 2380 D X6254 2359 D X6224 2338 D X6164 2317 D X6194 2296 D X6194 2275 D X6164 2254 D X6403 2233 D X6403 2212 D X6433 2191 D X6313 2170 D X6313 2149 D X6283 2128 D X6283 2107 D X6283 2086 D X6254 2065 D X6224 2044 D X6194 2023 D X6194 2002 D X6134 1981 D X6105 1960 D X6075 1939 D X6015 1918 D X6015 1897 D X6015 1876 D X6045 1855 D X6045 1834 D X6075 1813 D X6105 1792 D X6134 1771 D X6134 1750 D X6134 1729 D X6134 1708 D X6134 1687 D X6134 1666 D X6134 1645 D X6134 1624 D X6075 1603 D X6045 1582 D X5985 1561 D X5956 1541 D X5896 1520 D X5836 1499 D X5717 1478 D X5687 1457 D X5687 1436 D X5687 1415 D X5687 1394 D X5628 1373 D X5568 1352 D X5538 1331 D X5509 1310 D X5479 1289 D X5449 1268 D X5360 1247 D X5211 1226 D X5061 1205 D X4853 1184 D X4614 1163 D X4525 1142 D X4465 1121 D X4406 1100 D X4376 1079 D X4287 1058 D X4257 1037 D X4227 1016 D X4197 995 D X4138 974 D X4108 953 D X4048 932 D X4018 911 D XLT2 X6486 4346 M X(Set 2) Rshow X6654 4346 C2 X5644 2590 C2 X5640 2614 C2 X5639 2639 C2 X5643 2663 C2 X5652 2688 C2 X5654 2713 C2 X5654 2738 C2 X5664 2764 C2 X5661 2789 C2 X5662 2815 C2 X5664 2841 C2 X5654 2865 C2 X5659 2892 C2 X5640 2915 C2 X5641 2941 C2 X5619 2963 C2 X5608 2987 C2 X5601 3012 C2 X5595 3038 C2 X5587 3063 C2 X5588 3092 C2 X5599 3124 C2 X5586 3148 C2 X5591 3180 C2 X5576 3205 C2 X5578 3236 C2 X5560 3260 C2 X5559 3292 C2 X5534 3313 C2 X5536 3347 C2 X5504 3365 C2 X5494 3395 C2 X5468 3416 C2 X5449 3441 C2 X5430 3466 C2 X5400 3485 C2 X5393 3519 C2 X5350 3529 C2 X5336 3559 C2 X5307 3579 C2 X5278 3598 C2 X5247 3617 C2 X5203 3624 C2 X5185 3653 C2 X5137 3656 C2 X5121 3688 C2 X5068 3684 C2 X5038 3702 C2 X4997 3709 C2 X4964 3724 C2 X4924 3731 C2 X4890 3745 C2 X4850 3751 C2 X4816 3764 C2 X4776 3768 C2 X4744 3785 C2 X4701 3784 C2 X4668 3798 C2 X4628 3801 C2 X4591 3809 C2 X4554 3817 C2 X4516 3821 C2 X4481 3833 C2 X4441 3831 C2 X4406 3844 C2 X4366 3842 C2 X4329 3849 C2 X4292 3852 C2 X4254 3854 C2 X4217 3864 C2 X4178 3859 C2 X4141 3868 C2 X4103 3866 C2 X4065 3869 C2 X4027 3871 C2 X3988 3870 C2 X3950 3875 C2 X3912 3868 C2 X3874 3877 C2 X3837 3864 C2 X3798 3869 C2 X3761 3859 C2 X3723 3856 C2 X3686 3851 C2 X3649 3844 C2 X3610 3844 C2 X3575 3831 C2 X3536 3830 C2 X3501 3819 C2 X3464 3813 C2 X3425 3811 C2 X3391 3799 C2 X3351 3797 C2 X3316 3785 C2 X3278 3780 C2 X3240 3774 C2 X3206 3762 C2 X3163 3761 C2 X3132 3744 C2 X3088 3744 C2 X3059 3724 C2 X3016 3721 C2 X2988 3700 C2 X2945 3697 C2 X2918 3674 C2 X2874 3670 C2 X2851 3645 C2 X2811 3636 C2 X2788 3612 C2 X2751 3600 C2 X2729 3575 C2 X2696 3559 C2 X2674 3535 C2 X2643 3518 C2 X2623 3493 C2 X2592 3475 C2 X2573 3450 C2 X2541 3433 C2 X2526 3406 C2 X2490 3391 C2 X2481 3361 C2 X2449 3344 C2 X2438 3316 C2 X2409 3296 C2 X2398 3268 C2 X2371 3248 C2 X2360 3220 C2 X2337 3198 C2 X2328 3171 C2 X2307 3147 C2 X2300 3119 C2 X2281 3095 C2 X2277 3067 C2 X2260 3043 C2 X2259 3014 C2 X2247 2989 C2 X2248 2960 C2 X2241 2934 C2 X2244 2905 C2 X2247 2878 C2 X2246 2851 C2 X2259 2822 C2 X2256 2796 C2 X2269 2769 C2 X2281 2742 C2 X2289 2716 C2 X2295 2690 C2 X2300 2665 C2 X2308 2640 C2 X2312 2615 C2 X2312 2590 C2 X2312 2565 C2 X2308 2540 C2 X2300 2515 C2 X2295 2490 C2 X2289 2464 C2 X2281 2438 C2 X2269 2411 C2 X2256 2384 C2 X2259 2358 C2 X2246 2329 C2 X2247 2302 C2 X2244 2275 C2 X2241 2246 C2 X2248 2220 C2 X2247 2191 C2 X2259 2166 C2 X2260 2137 C2 X2277 2113 C2 X2281 2085 C2 X2300 2061 C2 X2307 2033 C2 X2328 2009 C2 X2337 1982 C2 X2360 1960 C2 X2371 1932 C2 X2398 1912 C2 X2409 1884 C2 X2438 1864 C2 X2449 1836 C2 X2481 1819 C2 X2490 1789 C2 X2526 1774 C2 X2541 1747 C2 X2573 1730 C2 X2592 1705 C2 X2623 1687 C2 X2643 1662 C2 X2674 1645 C2 X2696 1621 C2 X2729 1605 C2 X2751 1580 C2 X2788 1568 C2 X2811 1544 C2 X2851 1535 C2 X2874 1510 C2 X2918 1506 C2 X2945 1483 C2 X2988 1480 C2 X3016 1459 C2 X3059 1456 C2 X3088 1436 C2 X3132 1436 C2 X3163 1419 C2 X3206 1418 C2 X3240 1406 C2 X3278 1400 C2 X3316 1395 C2 X3351 1383 C2 X3391 1381 C2 X3425 1369 C2 X3464 1367 C2 X3501 1361 C2 X3536 1350 C2 X3575 1349 C2 X3610 1336 C2 X3649 1336 C2 X3686 1329 C2 X3723 1324 C2 X3761 1321 C2 X3798 1311 C2 X3837 1316 C2 X3874 1303 C2 X3912 1312 C2 X3950 1305 C2 X3988 1310 C2 X4027 1309 C2 X4065 1311 C2 X4103 1314 C2 X4141 1312 C2 X4178 1321 C2 X4217 1316 C2 X4254 1326 C2 X4292 1328 C2 X4329 1331 C2 X4366 1338 C2 X4406 1336 C2 X4441 1349 C2 X4481 1347 C2 X4516 1359 C2 X4554 1363 C2 X4591 1371 C2 X4628 1379 C2 X4668 1382 C2 X4701 1396 C2 X4744 1395 C2 X4776 1412 C2 X4816 1416 C2 X4850 1429 C2 X4890 1435 C2 X4924 1449 C2 X4964 1456 C2 X4997 1471 C2 X5038 1478 C2 X5068 1496 C2 X5121 1492 C2 X5137 1524 C2 X5185 1527 C2 X5203 1556 C2 X5247 1563 C2 X5278 1582 C2 X5307 1601 C2 X5336 1621 C2 X5350 1651 C2 X5393 1661 C2 X5400 1695 C2 X5430 1714 C2 X5449 1739 C2 X5468 1764 C2 X5494 1785 C2 X5504 1815 C2 X5536 1833 C2 X5534 1867 C2 X5559 1888 C2 X5560 1920 C2 X5578 1944 C2 X5576 1975 C2 X5591 2000 C2 X5586 2032 C2 X5599 2056 C2 X5588 2088 C2 X5587 2117 C2 X5595 2142 C2 X5601 2168 C2 X5608 2193 C2 X5619 2217 C2 X5641 2239 C2 X5640 2265 C2 X5659 2288 C2 X5654 2315 C2 X5664 2339 C2 X5662 2365 C2 X5661 2391 C2 X5664 2416 C2 X5654 2442 C2 X5654 2467 C2 X5652 2492 C2 X5643 2517 C2 X5639 2541 C2 X5640 2566 C2 X5644 2590 C2 XLT2 X6486 4206 M X(Set 3) Rshow X6654 4206 B2 X5704 2641 B2 X5709 2666 B2 X5718 2692 B2 X5732 2719 B2 X5747 2746 B2 X5745 2773 B2 X5764 2801 B2 X5755 2827 B2 X5767 2856 B2 X5753 2881 B2 X5764 2911 B2 X5738 2934 B2 X5734 2961 B2 X5703 2982 B2 X5682 3005 B2 X5651 3025 B2 X5650 3053 B2 X5680 3091 B2 X5700 3127 B2 X5704 3159 B2 X5714 3193 B2 X5698 3219 B2 X5700 3253 B2 X5682 3278 B2 X5689 3315 B2 X5660 3337 B2 X5657 3371 B2 X5635 3396 B2 X5617 3423 B2 X5607 3455 B2 X5576 3476 B2 X5567 3510 B2 X5532 3528 B2 X5508 3554 B2 X5487 3581 B2 X5451 3599 B2 X5431 3628 B2 X5392 3643 B2 X5361 3663 B2 X5335 3688 B2 X5291 3699 B2 X5263 3723 B2 X5219 3732 B2 X5184 3749 B2 X5147 3764 B2 X5103 3772 B2 X5071 3791 B2 X5022 3792 B2 X4990 3812 B2 X4941 3810 B2 X4904 3823 B2 X4860 3826 B2 X4820 3835 B2 X4781 3844 B2 X4740 3848 B2 X4705 3865 B2 X4661 3864 B2 X4625 3876 B2 X4584 3880 B2 X4545 3889 B2 X4507 3897 B2 X4468 3904 B2 X4429 3912 B2 X4389 3917 B2 X4350 3923 B2 X4310 3928 B2 X4267 3919 B2 X4230 3936 B2 X4188 3925 B2 X4150 3942 B2 X4109 3944 B2 X4069 3946 B2 X4029 3946 B2 X3988 3947 B2 X3948 3949 B2 X3908 3946 B2 X3867 3949 B2 X3827 3942 B2 X3787 3942 B2 X3747 3936 B2 X3707 3932 B2 X3667 3928 B2 X3631 3910 B2 X3588 3917 B2 X3555 3893 B2 X3515 3890 B2 X3477 3880 B2 X3439 3872 B2 X3393 3880 B2 X3355 3871 B2 X3317 3862 B2 X3279 3853 B2 X3242 3841 B2 X3197 3842 B2 X3162 3827 B2 X3119 3823 B2 X3081 3813 B2 X3040 3805 B2 X3001 3794 B2 X2961 3785 B2 X2923 3772 B2 X2883 3762 B2 X2849 3745 B2 X2806 3737 B2 X2776 3715 B2 X2729 3709 B2 X2709 3679 B2 X2671 3665 B2 X2646 3640 B2 X2616 3619 B2 X2590 3596 B2 X2566 3571 B2 X2541 3547 B2 X2516 3524 B2 X2494 3499 B2 X2463 3479 B2 X2444 3452 B2 X2407 3435 B2 X2394 3406 B2 X2358 3388 B2 X2346 3359 B2 X2312 3339 B2 X2303 3309 B2 X2272 3288 B2 X2265 3257 B2 X2236 3235 B2 X2229 3205 B2 X2200 3183 B2 X2197 3152 B2 X2167 3129 B2 X2171 3097 B2 X2143 3073 B2 X2149 3041 B2 X2133 3015 B2 X2137 2984 B2 X2131 2955 B2 X2122 2927 B2 X2137 2896 B2 X2147 2866 B2 X2148 2837 B2 X2170 2807 B2 X2175 2779 B2 X2193 2750 B2 X2215 2721 B2 X2232 2694 B2 X2248 2667 B2 X2262 2641 B2 X2270 2615 B2 X2268 2590 B2 X2270 2565 B2 X2262 2539 B2 X2248 2513 B2 X2232 2486 B2 X2215 2459 B2 X2193 2430 B2 X2175 2401 B2 X2170 2373 B2 X2148 2343 B2 X2147 2314 B2 X2137 2284 B2 X2122 2253 B2 X2131 2225 B2 X2137 2196 B2 X2133 2165 B2 X2149 2139 B2 X2143 2107 B2 X2171 2083 B2 X2167 2051 B2 X2197 2028 B2 X2200 1997 B2 X2229 1975 B2 X2236 1945 B2 X2265 1923 B2 X2272 1892 B2 X2303 1871 B2 X2312 1841 B2 X2346 1821 B2 X2358 1792 B2 X2394 1774 B2 X2407 1745 B2 X2444 1728 B2 X2463 1701 B2 X2494 1681 B2 X2516 1656 B2 X2541 1633 B2 X2566 1609 B2 X2590 1584 B2 X2616 1561 B2 X2646 1540 B2 X2671 1515 B2 X2709 1501 B2 X2729 1471 B2 X2776 1465 B2 X2806 1443 B2 X2849 1435 B2 X2883 1418 B2 X2923 1408 B2 X2961 1395 B2 X3001 1386 B2 X3040 1375 B2 X3081 1367 B2 X3119 1357 B2 X3162 1353 B2 X3197 1338 B2 X3242 1339 B2 X3279 1327 B2 X3317 1318 B2 X3355 1309 B2 X3393 1300 B2 X3439 1308 B2 X3477 1300 B2 X3515 1290 B2 X3555 1287 B2 X3588 1263 B2 X3631 1270 B2 X3667 1252 B2 X3707 1248 B2 X3747 1244 B2 X3787 1238 B2 X3827 1238 B2 X3867 1231 B2 X3908 1234 B2 X3948 1231 B2 X3988 1233 B2 X4029 1234 B2 X4069 1234 B2 X4109 1236 B2 X4150 1238 B2 X4188 1255 B2 X4230 1244 B2 X4267 1261 B2 X4310 1252 B2 X4350 1257 B2 X4389 1263 B2 X4429 1268 B2 X4468 1276 B2 X4507 1283 B2 X4545 1291 B2 X4584 1300 B2 X4625 1304 B2 X4661 1316 B2 X4705 1315 B2 X4740 1332 B2 X4781 1336 B2 X4820 1345 B2 X4860 1354 B2 X4904 1357 B2 X4941 1370 B2 X4990 1368 B2 X5022 1388 B2 X5071 1389 B2 X5103 1408 B2 X5147 1416 B2 X5184 1431 B2 X5219 1448 B2 X5263 1457 B2 X5291 1481 B2 X5335 1492 B2 X5361 1517 B2 X5392 1537 B2 X5431 1552 B2 X5451 1581 B2 X5487 1599 B2 X5508 1626 B2 X5532 1652 B2 X5567 1670 B2 X5576 1704 B2 X5607 1725 B2 X5617 1757 B2 X5635 1784 B2 X5657 1809 B2 X5660 1843 B2 X5689 1865 B2 X5682 1902 B2 X5700 1927 B2 X5698 1961 B2 X5714 1987 B2 X5704 2021 B2 X5700 2053 B2 X5680 2089 B2 X5650 2127 B2 X5651 2155 B2 X5682 2175 B2 X5703 2198 B2 X5734 2219 B2 X5738 2246 B2 X5764 2269 B2 X5753 2299 B2 X5767 2324 B2 X5755 2353 B2 X5764 2379 B2 X5745 2407 B2 X5747 2434 B2 X5732 2461 B2 X5718 2488 B2 X5709 2514 B2 X5704 2539 B2 X5701 2565 B2 X5701 2590 B2 XLT2 X6486 4066 M X(Set 4) Rshow X6654 4066 C2 X5761 2642 C2 X5782 2669 C2 X5809 2698 C2 X5844 2727 C2 X5843 2755 C2 X5872 2786 C2 X5869 2814 C2 X5898 2847 C2 X5882 2873 C2 X5890 2904 C2 X5892 2934 C2 X5875 2961 C2 X5884 2993 C2 X5873 3021 C2 X5857 3048 C2 X5866 3082 C2 X5861 3112 C2 X5849 3141 C2 X5871 3180 C2 X5846 3205 C2 X5844 3239 C2 X5841 3272 C2 X5826 3301 C2 X5834 3340 C2 X5804 3365 C2 X5800 3400 C2 X5784 3430 C2 X5763 3459 C2 X5765 3499 C2 X5727 3519 C2 X5708 3550 C2 X5692 3582 C2 X5653 3602 C2 X5636 3635 C2 X5604 3659 C2 X5567 3678 C2 X5549 3712 C2 X5505 3727 C2 X5469 3748 C2 X5448 3781 C2 X5394 3787 C2 X5359 3808 C2 X5324 3829 C2 X5272 3834 C2 X5237 3855 C2 X5188 3861 C2 X5141 3869 C2 X5100 3883 C2 X5046 3880 C2 X5005 3892 C2 X4954 3890 C2 X4908 3894 C2 X4866 3904 C2 X4819 3904 C2 X4779 3914 C2 X4738 3924 C2 X4695 3928 C2 X4659 3946 C2 X4615 3948 C2 X4575 3958 C2 X4534 3965 C2 X4491 3969 C2 X4451 3978 C2 X4407 3975 C2 X4367 3987 C2 X4322 3979 C2 X4281 3983 C2 X4240 3993 C2 X4197 3990 C2 X4156 3998 C2 X4115 4007 C2 X4073 4007 C2 X4031 4024 C2 X3988 4017 C2 X3946 4031 C2 X3903 4019 C2 X3860 4031 C2 X3819 4016 C2 X3775 4021 C2 X3735 4004 C2 X3692 4005 C2 X3653 3986 C2 X3611 3982 C2 X3573 3966 C2 X3534 3954 C2 X3492 3951 C2 X3454 3938 C2 X3415 3929 C2 X3372 3926 C2 X3328 3926 C2 X3288 3916 C2 X3243 3916 C2 X3201 3910 C2 X3158 3903 C2 X3109 3906 C2 X3072 3891 C2 X3021 3894 C2 X2985 3875 C2 X2933 3878 C2 X2898 3859 C2 X2844 3860 C2 X2811 3838 C2 X2762 3833 C2 X2726 3814 C2 X2686 3798 C2 X2638 3790 C2 X2613 3761 C2 X2574 3744 C2 X2540 3723 C2 X2521 3691 C2 X2484 3672 C2 X2474 3634 C2 X2451 3607 C2 X2442 3571 C2 X2417 3545 C2 X2389 3522 C2 X2364 3497 C2 X2323 3480 C2 X2299 3455 C2 X2259 3436 C2 X2244 3406 C2 X2206 3387 C2 X2202 3352 C2 X2166 3331 C2 X2161 3297 C2 X2129 3275 C2 X2123 3242 C2 X2090 3219 C2 X2084 3187 C2 X2047 3165 C2 X2048 3131 C2 X2022 3105 C2 X2016 3074 C2 X2007 3043 C2 X1983 3016 C2 X1999 2981 C2 X1989 2951 C2 X2000 2919 C2 X2011 2886 C2 X2012 2856 C2 X2044 2822 C2 X2064 2790 C2 X2077 2760 C2 X2118 2728 C2 X2150 2699 C2 X2180 2670 C2 X2207 2643 C2 X2230 2616 C2 X2234 2590 C2 X2230 2564 C2 X2207 2537 C2 X2180 2510 C2 X2150 2481 C2 X2118 2452 C2 X2077 2420 C2 X2064 2390 C2 X2044 2358 C2 X2012 2324 C2 X2011 2294 C2 X2000 2261 C2 X1989 2229 C2 X1999 2199 C2 X1983 2164 C2 X2007 2137 C2 X2016 2106 C2 X2022 2075 C2 X2048 2049 C2 X2047 2015 C2 X2084 1993 C2 X2090 1961 C2 X2123 1938 C2 X2129 1905 C2 X2161 1883 C2 X2166 1849 C2 X2202 1828 C2 X2206 1793 C2 X2244 1774 C2 X2259 1744 C2 X2299 1725 C2 X2323 1700 C2 X2364 1683 C2 X2389 1658 C2 X2417 1635 C2 X2442 1609 C2 X2451 1573 C2 X2474 1546 C2 X2484 1508 C2 X2521 1489 C2 X2540 1457 C2 X2574 1436 C2 X2613 1419 C2 X2638 1390 C2 X2686 1382 C2 X2726 1366 C2 X2762 1347 C2 X2811 1342 C2 X2844 1320 C2 X2898 1321 C2 X2933 1302 C2 X2985 1305 C2 X3021 1286 C2 X3072 1289 C2 X3109 1274 C2 X3158 1277 C2 X3201 1270 C2 X3243 1264 C2 X3288 1264 C2 X3328 1254 C2 X3372 1254 C2 X3415 1251 C2 X3454 1242 C2 X3492 1229 C2 X3534 1226 C2 X3573 1214 C2 X3611 1198 C2 X3653 1194 C2 X3692 1175 C2 X3735 1176 C2 X3775 1159 C2 X3819 1164 C2 X3860 1149 C2 X3903 1161 C2 X3946 1149 C2 X3988 1163 C2 X4031 1156 C2 X4073 1173 C2 X4115 1173 C2 X4156 1182 C2 X4197 1190 C2 X4240 1187 C2 X4281 1197 C2 X4322 1201 C2 X4367 1193 C2 X4407 1205 C2 X4451 1202 C2 X4491 1211 C2 X4534 1215 C2 X4575 1222 C2 X4615 1232 C2 X4659 1234 C2 X4695 1252 C2 X4738 1256 C2 X4779 1266 C2 X4819 1276 C2 X4866 1276 C2 X4908 1286 C2 X4954 1290 C2 X5005 1288 C2 X5046 1300 C2 X5100 1297 C2 X5141 1311 C2 X5188 1319 C2 X5237 1325 C2 X5272 1346 C2 X5324 1351 C2 X5359 1372 C2 X5394 1393 C2 X5448 1399 C2 X5469 1432 C2 X5505 1453 C2 X5549 1468 C2 X5567 1502 C2 X5604 1521 C2 X5636 1545 C2 X5653 1578 C2 X5692 1598 C2 X5708 1630 C2 X5727 1661 C2 X5765 1681 C2 X5763 1721 C2 X5784 1750 C2 X5800 1780 C2 X5804 1815 C2 X5834 1840 C2 X5826 1879 C2 X5841 1908 C2 X5844 1941 C2 X5846 1975 C2 X5871 2000 C2 X5849 2039 C2 X5861 2068 C2 X5866 2098 C2 X5857 2132 C2 X5873 2159 C2 X5884 2187 C2 X5875 2219 C2 X5892 2246 C2 X5890 2276 C2 X5882 2307 C2 X5898 2333 C2 X5869 2366 C2 X5872 2394 C2 X5843 2425 C2 X5844 2453 C2 X5809 2482 C2 X5782 2511 C2 X5761 2538 C2 X5747 2564 C2 X5747 2590 C2 XLT2 X6486 3926 M X(Set 5) Rshow X6654 3926 B2 X5873 2646 B2 X5911 2675 B2 X5943 2706 B2 X5999 2739 B2 X6004 2769 B2 X6040 2803 B2 X6052 2836 B2 X6051 2867 B2 X6073 2902 B2 X6076 2935 B2 X6060 2965 B2 X6061 2997 B2 X6067 3032 B2 X6038 3059 B2 X6035 3092 B2 X6030 3125 B2 X6012 3154 B2 X6028 3194 B2 X6003 3222 B2 X6008 3259 B2 X5998 3292 B2 X5987 3326 B2 X5993 3366 B2 X5968 3395 B2 X5971 3436 B2 X5952 3467 B2 X5933 3500 B2 X5943 3547 B2 X5905 3571 B2 X5885 3604 B2 X5887 3650 B2 X5837 3667 B2 X5805 3694 B2 X5790 3732 B2 X5745 3751 B2 X5704 3773 B2 X5685 3810 B2 X5635 3825 B2 X5597 3848 B2 X5578 3887 B2 X5522 3895 B2 X5480 3915 B2 X5452 3948 B2 X5400 3958 B2 X5346 3966 B2 X5304 3984 B2 X5260 4001 B2 X5190 3987 B2 X5141 3995 B2 X5075 3981 B2 X5022 3982 B2 X4959 3967 B2 X4905 3962 B2 X4858 3966 B2 X4816 3977 B2 X4771 3981 B2 X4729 3991 B2 X4691 4011 B2 X4650 4023 B2 X4609 4038 B2 X4566 4046 B2 X4524 4058 B2 X4475 4052 B2 X4431 4058 B2 X4383 4048 B2 X4337 4042 B2 X4293 4044 B2 X4251 4052 B2 X4207 4056 B2 X4164 4063 B2 X4122 4080 B2 X4078 4091 B2 X4033 4101 B2 X3988 4112 B2 X3943 4120 B2 X3898 4119 B2 X3850 4136 B2 X3807 4116 B2 X3761 4112 B2 X3717 4105 B2 X3675 4084 B2 X3631 4077 B2 X3593 4051 B2 X3553 4031 B2 X3512 4021 B2 X3474 4002 B2 X3433 3990 B2 X3391 3983 B2 X3347 3981 B2 X3300 3983 B2 X3248 3993 B2 X3206 3983 B2 X3155 3986 B2 X3109 3982 B2 X3063 3976 B2 X3011 3976 B2 X2969 3964 B2 X2911 3971 B2 X2872 3952 B2 X2811 3960 B2 X2771 3941 B2 X2711 3944 B2 X2667 3929 B2 X2620 3917 B2 X2550 3924 B2 X2520 3894 B2 X2481 3873 B2 X2429 3862 B2 X2375 3852 B2 X2359 3812 B2 X2334 3780 B2 X2300 3755 B2 X2260 3733 B2 X2234 3703 B2 X2364 3578 B2 X2338 3552 B2 X2227 3573 B2 X2182 3556 B2 X2137 3538 B2 X2107 3511 B2 X2111 3469 B2 X2091 3438 B2 X2083 3403 B2 X2072 3369 B2 X2061 3336 B2 X2031 3311 B2 X2017 3279 B2 X1985 3254 B2 X1958 3227 B2 X1926 3201 B2 X1906 3171 B2 X1856 3149 B2 X1854 3114 B2 X1833 3083 B2 X1788 3058 B2 X1795 3021 B2 X1799 2986 B2 X1792 2953 B2 X1774 2922 B2 X1817 2882 B2 X1846 2845 B2 X1852 2812 B2 X1924 2774 B2 X1962 2740 B2 X2002 2707 B2 X2056 2676 B2 X2121 2645 B2 X2186 2617 B2 X2209 2590 B2 X2186 2563 B2 X2121 2535 B2 X2056 2504 B2 X2002 2473 B2 X1962 2440 B2 X1924 2406 B2 X1852 2368 B2 X1846 2335 B2 X1817 2298 B2 X1774 2258 B2 X1792 2227 B2 X1799 2194 B2 X1795 2159 B2 X1788 2122 B2 X1833 2097 B2 X1854 2066 B2 X1856 2031 B2 X1906 2009 B2 X1926 1979 B2 X1958 1953 B2 X1985 1926 B2 X2017 1901 B2 X2031 1869 B2 X2061 1844 B2 X2072 1811 B2 X2083 1777 B2 X2091 1742 B2 X2111 1711 B2 X2107 1669 B2 X2137 1642 B2 X2182 1624 B2 X2227 1607 B2 X2338 1628 B2 X2364 1602 B2 X2234 1477 B2 X2260 1447 B2 X2300 1425 B2 X2334 1400 B2 X2359 1368 B2 X2375 1328 B2 X2429 1318 B2 X2481 1307 B2 X2520 1286 B2 X2550 1256 B2 X2620 1263 B2 X2667 1251 B2 X2711 1236 B2 X2771 1239 B2 X2811 1220 B2 X2872 1228 B2 X2911 1209 B2 X2969 1216 B2 X3011 1204 B2 X3063 1204 B2 X3109 1198 B2 X3155 1194 B2 X3206 1197 B2 X3248 1187 B2 X3300 1197 B2 X3347 1199 B2 X3391 1197 B2 X3433 1190 B2 X3474 1178 B2 X3512 1159 B2 X3553 1149 B2 X3593 1129 B2 X3631 1103 B2 X3675 1096 B2 X3717 1075 B2 X3761 1068 B2 X3807 1064 B2 X3850 1044 B2 X3898 1061 B2 X3943 1060 B2 X3988 1068 B2 X4033 1079 B2 X4078 1089 B2 X4122 1100 B2 X4164 1117 B2 X4207 1124 B2 X4251 1128 B2 X4293 1136 B2 X4337 1138 B2 X4383 1132 B2 X4431 1122 B2 X4475 1128 B2 X4524 1122 B2 X4566 1134 B2 X4609 1142 B2 X4650 1157 B2 X4691 1169 B2 X4729 1189 B2 X4771 1199 B2 X4816 1203 B2 X4858 1214 B2 X4905 1218 B2 X4959 1213 B2 X5022 1198 B2 X5075 1199 B2 X5141 1185 B2 X5190 1193 B2 X5260 1179 B2 X5304 1196 B2 X5346 1214 B2 X5400 1222 B2 X5452 1232 B2 X5480 1265 B2 X5522 1285 B2 X5578 1293 B2 X5597 1332 B2 X5635 1355 B2 X5685 1370 B2 X5704 1407 B2 X5745 1429 B2 X5790 1448 B2 X5805 1486 B2 X5837 1513 B2 X5887 1530 B2 X5885 1576 B2 X5905 1609 B2 X5943 1633 B2 X5933 1680 B2 X5952 1713 B2 X5971 1744 B2 X5968 1785 B2 X5993 1814 B2 X5987 1854 B2 X5998 1888 B2 X6008 1921 B2 X6003 1958 B2 X6028 1986 B2 X6012 2026 B2 X6030 2055 B2 X6035 2088 B2 X6038 2121 B2 X6067 2148 B2 X6061 2183 B2 X6060 2215 B2 X6076 2245 B2 X6073 2278 B2 X6051 2313 B2 X6052 2344 B2 X6040 2377 B2 X6004 2411 B2 X5999 2441 B2 X5943 2474 B2 X5911 2505 B2 X5873 2534 B2 X5796 2563 B2 X5778 2590 B2 Xstroke Xgrestore Xend Xshowpage X%%Trailer X%%Pages: 1 END_OF_FILE if test 31303 -ne `wc -c <'figure3.ps'`; then echo shar: \"'figure3.ps'\" unpacked with wrong size! fi # end of 'figure3.ps' fi if test -f 'figure4.ps' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'figure4.ps'\" else echo shar: Extracting \"'figure4.ps'\" \(20654 characters\) sed "s/^X//" >'figure4.ps' <<'END_OF_FILE' X%!PS-Adobe-2.0 X%%Creator: gnuplot X%%DocumentFonts: Courier X%%B2oundingBox: 50 50 554 770 X%%Pages: (atend) X%%EndComments X/gnudict 40 dict def Xgnudict begin X/Color false def X/gnulinewidth 5.000 def X/vshift -46 def X/dl {10 mul} def X/hpt 15.5 def X/vpt 15.5 def X/vpt2 vpt 2 mul def X/hpt2 hpt 2 mul def X/vpt4 vpt 4 mul def X/hpt4 hpt 4 mul def X/Lshow { currentpoint stroke moveto X 0 vshift rmoveto show } def X/Rshow { currentpoint stroke moveto X dup stringwidth pop neg vshift rmoveto show } def X/Cshow { currentpoint stroke moveto X dup stringwidth pop -2 div vshift rmoveto show } def X/DL { Color {setrgbcolor [] 0 setdash pop} X {pop pop pop 0 setdash} ifelse } def X/B2L { stroke gnulinewidth 2 mul setlinewidth } def X/AL { stroke gnulinewidth 2 div setlinewidth } def X/PL { stroke gnulinewidth setlinewidth } def X/LTb { B2L [] 0 0 0 DL } def X/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def X/LT0 { PL [] 0 1 0 DL } def X/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def X/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def X/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def X/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def X/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def X/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def X/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def X/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def X/M {moveto} def X/L {lineto} def X/P { stroke [] 0 setdash X currentlinewidth 2 div sub moveto X 0 currentlinewidth rlineto stroke } def X/D { stroke [] 0 setdash 2 copy vpt add moveto X hpt neg vpt neg rlineto hpt vpt neg rlineto X hpt vpt rlineto hpt neg vpt rlineto closepath stroke X P } def X/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add moveto X 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto X hpt2 neg 0 rlineto closepath stroke X P } def X/C { stroke [] 0 setdash exch hpt sub exch vpt add moveto X hpt2 vpt2 neg rlineto currentpoint stroke moveto X hpt2 neg 0 rmoveto hpt2 vpt2 rlineto stroke } def X/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add moveto X hpt neg vpt -1.62 mul rlineto X hpt 2 mul 0 rlineto X hpt neg vpt 1.62 mul rlineto closepath stroke X P } def X/D2 { stroke [] 0 setdash 2 copy vpt2 add moveto X hpt2 neg vpt2 neg rlineto hpt2 vpt2 neg rlineto X hpt2 vpt2 rlineto hpt2 neg vpt2 rlineto closepath stroke X P } def X/A2 { stroke [] 0 setdash vpt2 sub moveto 0 vpt4 rlineto X currentpoint stroke moveto X hpt2 neg vpt2 neg rmoveto hpt4 0 rlineto stroke X } def X/B2 { stroke [] 0 setdash 2 copy exch hpt2 sub exch vpt2 add moveto X 0 vpt4 neg rlineto hpt4 0 rlineto 0 vpt4 rlineto X hpt4 neg 0 rlineto closepath stroke X P } def X/C2 { stroke [] 0 setdash exch hpt2 sub exch vpt2 add moveto X hpt4 vpt4 neg rlineto currentpoint stroke moveto X hpt4 neg 0 rmoveto hpt4 vpt4 rlineto stroke } def X/T2 { stroke [] 0 setdash 2 copy vpt2 1.12 mul add moveto X hpt2 neg vpt2 -1.62 mul rlineto X hpt2 2 mul 0 rlineto X hpt2 neg vpt2 1.62 mul rlineto closepath stroke X P } def Xend X%%EndProlog X%%Page: 1 1 Xgnudict begin Xgsave X50 50 translate X0.100 0.100 scale X90 rotate X0 -5040 translate X0 setgray X/Courier findfont 140 scalefont setfont Xnewpath XLTa X1008 2590 M X6969 2590 L X3989 491 M X3989 4689 L XLTb X1008 491 M X1071 491 L X6969 491 M X6906 491 L X924 491 M X(-1) Rshow X1008 911 M X1071 911 L X6969 911 M X6906 911 L X924 911 M X(-0.8) Rshow X1008 1331 M X1071 1331 L X6969 1331 M X6906 1331 L X924 1331 M X(-0.6) Rshow X1008 1750 M X1071 1750 L X6969 1750 M X6906 1750 L X924 1750 M X(-0.4) Rshow X1008 2170 M X1071 2170 L X6969 2170 M X6906 2170 L X924 2170 M X(-0.2) Rshow X1008 2590 M X1071 2590 L X6969 2590 M X6906 2590 L X924 2590 M X(0) Rshow X1008 3010 M X1071 3010 L X6969 3010 M X6906 3010 L X924 3010 M X(0.2) Rshow X1008 3430 M X1071 3430 L X6969 3430 M X6906 3430 L X924 3430 M X(0.4) Rshow X1008 3849 M X1071 3849 L X6969 3849 M X6906 3849 L X924 3849 M X(0.6) Rshow X1008 4269 M X1071 4269 L X6969 4269 M X6906 4269 L X924 4269 M X(0.8) Rshow X1008 4689 M X1071 4689 L X6969 4689 M X6906 4689 L X924 4689 M X(1) Rshow X1008 491 M X1008 554 L X1008 4689 M X1008 4626 L X1008 351 M X(-1) Cshow X1604 491 M X1604 554 L X1604 4689 M X1604 4626 L X1604 351 M X(-0.8) Cshow X2200 491 M X2200 554 L X2200 4689 M X2200 4626 L X2200 351 M X(-0.6) Cshow X2796 491 M X2796 554 L X2796 4689 M X2796 4626 L X2796 351 M X(-0.4) Cshow X3392 491 M X3392 554 L X3392 4689 M X3392 4626 L X3392 351 M X(-0.2) Cshow X3989 491 M X3989 554 L X3989 4689 M X3989 4626 L X3989 351 M X(0) Cshow X4585 491 M X4585 554 L X4585 4689 M X4585 4626 L X4585 351 M X(0.2) Cshow X5181 491 M X5181 554 L X5181 4689 M X5181 4626 L X5181 351 M X(0.4) Cshow X5777 491 M X5777 554 L X5777 4689 M X5777 4626 L X5777 351 M X(0.6) Cshow X6373 491 M X6373 554 L X6373 4689 M X6373 4626 L X6373 351 M X(0.8) Cshow X6969 491 M X6969 554 L X6969 4689 M X6969 4626 L X6969 351 M X(1) Cshow XLTb X1008 491 M X6969 491 L X6969 4689 L X1008 4689 L X1008 491 L X140 2590 M Xcurrentpoint gsave translate 90 rotate 0 0 moveto X(Im epsilon) Cshow Xgrestore X3988 211 M X(Real epsilon) Cshow X4088 1 M X(Figure 4) Cshow XLT0 XLT0 X6486 4486 M X(Set 1) Rshow X6654 4486 D X3989 4269 D X4018 4269 D X4048 4248 D X4078 4248 D X4108 4227 D X4138 4206 D X4167 4206 D X4197 4185 D X4227 4164 D X4257 4143 D X4287 4122 D X4316 4122 D X4346 4101 D X4376 4101 D X4406 4080 D X4436 4080 D X4465 4059 D X4495 4059 D X4525 4038 D X4555 4038 D X4585 4038 D X4614 4017 D X4644 4017 D X4674 4017 D X4704 4017 D X4734 4017 D X4763 4017 D X4793 4017 D X4823 4017 D X4853 3996 D X4883 3996 D X4912 3996 D X4942 3996 D X4972 3996 D X5002 3996 D X5032 3996 D X5061 3975 D X5091 3975 D X5121 3975 D X5151 3975 D X5181 3975 D X5211 3954 D X5240 3954 D X5270 3954 D X5300 3954 D X5330 3954 D X5360 3933 D X5389 3933 D X5419 3933 D X5449 3912 D X5479 3891 D X5509 3870 D X5538 3849 D X5568 3849 D X5598 3828 D X5628 3807 D X5658 3807 D X5687 3723 D X5717 3702 D X5747 3702 D X5777 3702 D X5807 3702 D X5836 3681 D X5866 2611 D X3989 4269 D X3959 4269 D X3929 4248 D X3899 4248 D X3869 4227 D X3839 4227 D X3810 4206 D X3780 4185 D X3750 4164 D X3720 4143 D X3690 4122 D X3661 4122 D X3631 4122 D X3601 4101 D X3571 4080 D X3541 4080 D X3512 4059 D X3482 4059 D X3452 4038 D X3422 4038 D X3392 4038 D X3363 4017 D X3333 4017 D X3303 4017 D X3273 4017 D X3243 4017 D X3214 4017 D X3184 4017 D X3154 4017 D X3124 3996 D X3094 3996 D X3065 3996 D X3035 3996 D X3005 3996 D X2975 3996 D X2945 3996 D X2916 3975 D X2886 3975 D X2856 3975 D X2826 3975 D X2796 3975 D X2766 3975 D X2737 3954 D X2707 3954 D X2677 3954 D X2647 3954 D X2617 3933 D X2588 3933 D X2558 3933 D X2528 3912 D X2498 3891 D X2468 3870 D X2439 3849 D X2409 3849 D X2379 3828 D X2349 3807 D X2319 3807 D X2290 3723 D X2260 3702 D X2230 3702 D X2200 3702 D X2170 3702 D X2141 3681 D X2111 2611 D X3989 911 D X3959 911 D X3929 932 D X3899 932 D X3869 953 D X3839 953 D X3810 974 D X3780 995 D X3750 1016 D X3720 1037 D X3690 1058 D X3661 1058 D X3631 1058 D X3601 1079 D X3571 1100 D X3541 1100 D X3512 1121 D X3482 1121 D X3452 1142 D X3422 1142 D X3392 1142 D X3363 1163 D X3333 1163 D X3303 1163 D X3273 1163 D X3243 1163 D X3214 1163 D X3184 1163 D X3154 1163 D X3124 1184 D X3094 1184 D X3065 1184 D X3035 1184 D X3005 1184 D X2975 1184 D X2945 1184 D X2916 1205 D X2886 1205 D X2856 1205 D X2826 1205 D X2796 1205 D X2766 1205 D X2737 1226 D X2707 1226 D X2677 1226 D X2647 1226 D X2617 1247 D X2588 1247 D X2558 1247 D X2528 1268 D X2498 1289 D X2468 1310 D X2439 1331 D X2409 1331 D X2379 1352 D X2349 1373 D X2319 1373 D X2290 1457 D X2260 1478 D X2230 1478 D X2200 1478 D X2170 1478 D X2141 1499 D X2111 2569 D X3989 911 D X4018 911 D X4048 932 D X4078 932 D X4108 953 D X4138 974 D X4167 974 D X4197 995 D X4227 1016 D X4257 1037 D X4287 1058 D X4316 1058 D X4346 1079 D X4376 1079 D X4406 1100 D X4436 1100 D X4465 1121 D X4495 1121 D X4525 1142 D X4555 1142 D X4585 1142 D X4614 1163 D X4644 1163 D X4674 1163 D X4704 1163 D X4734 1163 D X4763 1163 D X4793 1163 D X4823 1163 D X4853 1184 D X4883 1184 D X4912 1184 D X4942 1184 D X4972 1184 D X5002 1184 D X5032 1184 D X5061 1205 D X5091 1205 D X5121 1205 D X5151 1205 D X5181 1205 D X5211 1226 D X5240 1226 D X5270 1226 D X5300 1226 D X5330 1226 D X5360 1247 D X5389 1247 D X5419 1247 D X5449 1268 D X5479 1289 D X5509 1310 D X5538 1331 D X5568 1331 D X5598 1352 D X5628 1373 D X5658 1373 D X5687 1457 D X5717 1478 D X5747 1478 D X5777 1478 D X5807 1478 D X5836 1499 D X5866 2569 D X5744 2590 D X5874 2618 D X5966 2648 D X6006 2679 D X6040 2711 D X6077 2745 D X6243 2791 D X6223 2822 D X6183 2851 D X6189 2886 D X6161 2915 D X6414 2991 D X6303 3008 D X6281 3041 D X6267 3074 D X6243 3106 D X6209 3135 D X6184 3165 D X6145 3191 D X6096 3214 D X6048 3236 D X6015 3262 D X6012 3297 D X6044 3347 D X6123 3416 D X6122 3457 D X6128 3502 D X6131 3548 D X6095 3576 D X6042 3595 D X5993 3616 D X5940 3633 D X5894 3653 D X5851 3675 D X5797 3689 D X5736 3698 D X5686 3713 D X5672 3751 D X5667 3797 D X5618 3812 D X5578 3833 D X5531 3849 D X5494 3871 D X5461 3898 D X5419 3917 D X5371 3930 D X5323 3942 D X5269 3948 D X5219 3955 D X5168 3962 D X5118 3968 D X5070 3975 D X5020 3979 D X4974 3988 D X4924 3991 D X4877 3995 D X4829 3999 D X4782 4002 D X4737 4007 D X4690 4009 D X4645 4012 D X4601 4019 D X4558 4027 D X4515 4035 D X4474 4049 D X4433 4062 D X4393 4082 D X4351 4100 D X4309 4118 D X4265 4129 D X4222 4152 D X4179 4185 D X4133 4210 D X4087 4238 D X4037 4236 D X3988 4259 D X3940 4233 D X3890 4238 D X3844 4207 D X3799 4182 D X3754 4159 D X3712 4129 D X3668 4118 D X3626 4100 D X3584 4082 D X3544 4062 D X3503 4049 D X3462 4035 D X3419 4027 D X3376 4019 D X3331 4015 D X3287 4009 D X3242 4004 D X3195 4002 D X3148 3999 D X3100 3995 D X3051 3994 D X3005 3985 D X2955 3982 D X2909 3972 D X2859 3968 D X2809 3962 D X2758 3955 D X2708 3948 D X2654 3942 D X2606 3930 D X2558 3917 D X2519 3896 D X2478 3876 D X2446 3849 D X2405 3828 D X2359 3812 D X2310 3797 D X2305 3751 D X2288 3715 D X2248 3694 D X2180 3689 D X2126 3675 D X2087 3651 D X2037 3633 D X1984 3616 D X1935 3595 D X1890 3572 D X1838 3551 D X1849 3502 D X1855 3457 D X1854 3416 D X1933 3347 D X1974 3294 D X1962 3262 D X1925 3237 D X1881 3214 D X1828 3192 D X1789 3166 D X1768 3135 D X1730 3107 D X1701 3076 D X1696 3041 D X1674 3008 D X1563 2991 D X1816 2915 D X1784 2886 D X1821 2848 D X1754 2822 D X1729 2791 D X1895 2745 D X1942 2711 D X1971 2679 D X2034 2648 D X2075 2618 D X2233 2590 D X2075 2562 D X2034 2532 D X1971 2501 D X1942 2469 D X1895 2435 D X1729 2389 D X1754 2358 D X1821 2332 D X1784 2294 D X1816 2265 D X1563 2189 D X1674 2172 D X1696 2139 D X1701 2104 D X1730 2073 D X1768 2045 D X1789 2014 D X1828 1988 D X1881 1966 D X1925 1943 D X1962 1918 D X1974 1886 D X1933 1833 D X1854 1764 D X1855 1723 D X1849 1678 D X1838 1629 D X1890 1608 D X1935 1585 D X1984 1564 D X2037 1547 D X2087 1529 D X2126 1505 D X2180 1491 D X2248 1486 D X2288 1465 D X2305 1429 D X2310 1383 D X2359 1368 D X2405 1352 D X2446 1331 D X2478 1304 D X2519 1284 D X2558 1263 D X2606 1250 D X2654 1238 D X2708 1232 D X2758 1225 D X2809 1218 D X2859 1212 D X2909 1208 D X2955 1198 D X3005 1195 D X3051 1186 D X3100 1185 D X3148 1181 D X3195 1178 D X3242 1176 D X3287 1171 D X3331 1165 D X3376 1161 D X3419 1153 D X3462 1145 D X3503 1131 D X3544 1118 D X3584 1098 D X3626 1080 D X3668 1062 D X3712 1051 D X3754 1021 D X3799 998 D X3844 973 D X3890 942 D X3940 947 D X3988 921 D X4037 944 D X4087 942 D X4133 970 D X4179 995 D X4222 1028 D X4265 1051 D X4309 1062 D X4351 1080 D X4393 1098 D X4433 1118 D X4474 1131 D X4515 1145 D X4558 1153 D X4601 1161 D X4645 1168 D X4690 1171 D X4737 1173 D X4782 1178 D X4829 1181 D X4877 1185 D X4924 1189 D X4974 1192 D X5020 1201 D X5070 1205 D X5118 1212 D X5168 1218 D X5219 1225 D X5269 1232 D X5323 1238 D X5371 1250 D X5419 1263 D X5461 1282 D X5494 1309 D X5531 1331 D X5578 1347 D X5618 1368 D X5667 1383 D X5672 1429 D X5686 1467 D X5736 1482 D X5797 1491 D X5851 1505 D X5894 1527 D X5940 1547 D X5993 1564 D X6042 1585 D X6095 1604 D X6131 1632 D X6128 1678 D X6122 1723 D X6123 1764 D X6044 1833 D X6012 1883 D X6015 1918 D X6048 1944 D X6096 1966 D X6145 1989 D X6184 2015 D X6209 2045 D X6243 2074 D X6267 2106 D X6281 2139 D X6303 2172 D X6414 2189 D X6161 2265 D X6189 2294 D X6183 2329 D X6223 2358 D X6243 2389 D X6077 2435 D X6040 2469 D X6006 2501 D X5966 2532 D X5874 2562 D X5744 2590 D X5747 2590 D X5866 2611 D X5926 2632 D X6015 2653 D X6015 2674 D X6015 2695 D X6045 2716 D X6075 2737 D X6105 2758 D X6254 2779 D X6254 2800 D X6254 2821 D X6224 2842 D X6164 2863 D X6194 2884 D X6194 2905 D X6164 2926 D X6403 2947 D X6403 2968 D X6433 2989 D X6313 3010 D X6313 3031 D X6283 3052 D X6283 3073 D X6283 3094 D X6254 3115 D X6224 3136 D X6194 3157 D X6194 3178 D X6134 3199 D X6105 3220 D X6075 3241 D X6015 3262 D X6015 3283 D X6015 3304 D X6045 3325 D X6045 3346 D X6075 3367 D X6105 3388 D X6134 3409 D X6134 3430 D X6134 3451 D X6134 3472 D X6134 3493 D X6134 3514 D X6134 3535 D X6134 3556 D X6075 3577 D X6045 3598 D X5985 3619 D X5956 3640 D X5896 3660 D X5836 3681 D X5717 3702 D X5687 3723 D X5687 3744 D X5687 3765 D X5687 3786 D X5628 3807 D X5568 3828 D X5538 3849 D X5509 3870 D X5479 3891 D X5449 3912 D X5360 3933 D X5211 3954 D X5061 3975 D X4853 3996 D X4614 4017 D X4525 4038 D X4465 4059 D X4406 4080 D X4376 4101 D X4287 4122 D X4257 4143 D X4227 4164 D X4197 4185 D X4138 4206 D X4108 4227 D X4048 4248 D X4018 4269 D X2230 2590 D X2111 2611 D X2051 2632 D X1962 2653 D X1962 2674 D X1932 2695 D X1932 2716 D X1902 2737 D X1872 2758 D X1843 2779 D X1723 2800 D X1723 2821 D X1753 2842 D X1813 2863 D X1783 2884 D X1813 2905 D X1813 2926 D X1574 2947 D X1544 2968 D X1544 2989 D X1664 3010 D X1664 3031 D X1694 3052 D X1694 3073 D X1694 3094 D X1723 3115 D X1753 3136 D X1783 3157 D X1783 3178 D X1843 3199 D X1872 3220 D X1932 3241 D X1962 3262 D X1962 3283 D X1962 3304 D X1932 3325 D X1932 3346 D X1902 3367 D X1872 3388 D X1843 3409 D X1843 3430 D X1843 3451 D X1843 3472 D X1843 3493 D X1843 3514 D X1813 3535 D X1843 3556 D X1872 3577 D X1932 3598 D X1992 3619 D X2051 3640 D X2081 3660 D X2141 3681 D X2260 3702 D X2260 3723 D X2290 3744 D X2290 3765 D X2290 3786 D X2349 3807 D X2379 3828 D X2439 3849 D X2468 3870 D X2498 3891 D X2528 3912 D X2617 3933 D X2766 3954 D X2916 3975 D X3124 3996 D X3363 4017 D X3452 4038 D X3512 4059 D X3571 4080 D X3601 4101 D X3690 4122 D X3720 4143 D X3750 4164 D X3780 4185 D X3839 4206 D X3869 4227 D X3929 4248 D X3959 4269 D X2230 2590 D X2111 2569 D X2051 2548 D X1962 2527 D X1962 2506 D X1932 2485 D X1932 2464 D X1902 2443 D X1872 2422 D X1843 2401 D X1723 2380 D X1723 2359 D X1753 2338 D X1813 2317 D X1783 2296 D X1813 2275 D X1813 2254 D X1574 2233 D X1544 2212 D X1544 2191 D X1664 2170 D X1664 2149 D X1694 2128 D X1694 2107 D X1694 2086 D X1723 2065 D X1753 2044 D X1783 2023 D X1783 2002 D X1843 1981 D X1872 1960 D X1932 1939 D X1962 1918 D X1962 1897 D X1962 1876 D X1932 1855 D X1932 1834 D X1902 1813 D X1872 1792 D X1843 1771 D X1843 1750 D X1843 1729 D X1843 1708 D X1843 1687 D X1843 1666 D X1813 1645 D X1843 1624 D X1872 1603 D X1932 1582 D X1992 1561 D X2051 1541 D X2081 1520 D X2141 1499 D X2260 1478 D X2260 1457 D X2290 1436 D X2290 1415 D X2290 1394 D X2349 1373 D X2379 1352 D X2439 1331 D X2468 1310 D X2498 1289 D X2528 1268 D X2617 1247 D X2766 1226 D X2916 1205 D X3124 1184 D X3363 1163 D X3452 1142 D X3512 1121 D X3571 1100 D X3601 1079 D X3690 1058 D X3720 1037 D X3750 1016 D X3780 995 D X3839 974 D X3869 953 D X3929 932 D X3959 911 D X5747 2590 D X5866 2569 D X5926 2548 D X6015 2527 D X6015 2506 D X6015 2485 D X6045 2464 D X6075 2443 D X6105 2422 D X6254 2401 D X6254 2380 D X6254 2359 D X6224 2338 D X6164 2317 D X6194 2296 D X6194 2275 D X6164 2254 D X6403 2233 D X6403 2212 D X6433 2191 D X6313 2170 D X6313 2149 D X6283 2128 D X6283 2107 D X6283 2086 D X6254 2065 D X6224 2044 D X6194 2023 D X6194 2002 D X6134 1981 D X6105 1960 D X6075 1939 D X6015 1918 D X6015 1897 D X6015 1876 D X6045 1855 D X6045 1834 D X6075 1813 D X6105 1792 D X6134 1771 D X6134 1750 D X6134 1729 D X6134 1708 D X6134 1687 D X6134 1666 D X6134 1645 D X6134 1624 D X6075 1603 D X6045 1582 D X5985 1561 D X5956 1541 D X5896 1520 D X5836 1499 D X5717 1478 D X5687 1457 D X5687 1436 D X5687 1415 D X5687 1394 D X5628 1373 D X5568 1352 D X5538 1331 D X5509 1310 D X5479 1289 D X5449 1268 D X5360 1247 D X5211 1226 D X5061 1205 D X4853 1184 D X4614 1163 D X4525 1142 D X4465 1121 D X4406 1100 D X4376 1079 D X4287 1058 D X4257 1037 D X4227 1016 D X4197 995 D X4138 974 D X4108 953 D X4048 932 D X4018 911 D XLT0 X6486 4346 M X(Set 2) Rshow X6654 4346 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X3729 2633 B2 X4262 2637 B2 X4263 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4264 2634 B2 X4043 887 B2 X3809 4334 B2 X4268 4310 B2 X3588 878 B2 X4411 940 B2 X3340 4278 B2 X4700 4214 B2 X4803 991 B2 X3127 960 B2 X5055 4079 B2 X2907 4161 B2 X5215 1098 B2 X2724 1108 B2 X5350 3959 B2 X2534 3988 B2 X5578 1276 B2 X2383 1292 B2 X5697 3791 B2 X2208 3777 B2 X5900 1502 B2 X2077 1514 B2 X6011 3564 B2 X1945 3537 B2 X1838 1771 B2 X6157 1751 B2 X1743 3271 B2 X6235 3297 B2 X1670 2049 B2 X6336 2043 B2 X6383 2993 B2 X1592 2983 B2 X1553 2345 B2 X6448 2364 B2 X1522 2665 B2 X6466 2679 B2 X3983 2742 B2 X2897 4110 B2 X2558 3942 B2 X2558 3942 B2 X2558 3942 B2 X2557 3942 B2 X5432 1560 B2 X2513 3725 B2 X5529 2570 B2 X5615 1519 B2 X2284 3758 B2 X2284 3757 B2 X2283 3756 B2 X5755 1524 B2 X2000 3562 B2 X1999 3562 B2 X6046 1593 B2 X6070 3522 B2 X6070 3522 B2 X1745 3300 B2 X6283 2091 B2 X6342 2945 B2 X6342 2945 B2 X6368 2360 B2 X6368 2360 B2 X6368 2360 B2 X6368 2360 B2 X6368 2360 B2 X6368 2360 B2 X6394 2661 B2 X6394 2661 B2 X6394 2661 B2 X6394 2661 B2 X1522 2676 B2 X6767 2049 B2 X3927 2337 B2 X4144 3196 B2 X4160 3119 B2 X4162 3052 B2 X4166 3140 B2 X4168 3113 B2 X4169 3129 B2 X4175 3141 B2 X4185 3105 B2 X4215 3125 B2 X4224 3072 B2 X4225 3117 B2 X4257 3178 B2 X4266 3211 B2 X4274 3092 B2 X4275 2014 B2 X4319 3214 B2 X4384 3123 B2 X3398 3811 B2 X6160 1803 B2 X6292 2085 B2 X6292 2085 B2 X6305 2099 B2 X6337 2955 B2 X6381 2361 B2 X6381 2361 B2 X6381 2361 B2 X6381 2361 B2 X6381 2361 B2 X6381 2361 B2 X6403 2668 B2 X6403 2668 B2 X6403 2668 B2 X6852 2630 B2 X3987 870 B2 X4200 4341 B2 X3715 4330 B2 X4410 896 B2 X3553 893 B2 X4654 4274 B2 X3281 4239 B2 X4837 959 B2 X5072 4159 B2 X2891 4110 B2 X2722 1116 B2 X5259 1093 B2 X2554 3933 B2 X5457 3990 B2 X2390 1305 B2 X2390 1305 B2 X2389 1304 B2 X5628 1287 B2 X2299 3757 B2 X5790 3781 B2 X2103 1508 B2 X5937 1522 B2 X1998 3568 B2 X6068 3523 B2 X6166 1806 B2 X1740 3300 B2 X6247 3227 B2 X6285 2093 B2 X6337 2951 B2 X1635 2046 B2 X6370 2358 B2 X1585 2989 B2 X6402 2664 B2 X1540 2364 B2 X1528 2675 B2 XLT0 X6486 4206 M X(Set 3) Rshow X6654 4206 C2 X3450 875 C2 X4586 4501 C2 X2974 4407 C2 X2830 787 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X2518 1976 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X5702 2402 C2 X1790 3117 C2 X1487 1712 C2 X1358 3370 C2 X1314 1980 C2 X1314 1980 C2 X1314 1980 C2 X6677 2247 C2 X3975 609 C2 X3772 4573 C2 X4215 4563 C2 X4414 649 C2 X3517 615 C2 X3331 4528 C2 X4656 4501 C2 X4794 717 C2 X3091 728 C2 X2892 4382 C2 X2818 2392 C2 X5229 817 C2 X2747 860 C2 X2676 4248 C2 X5309 4252 C2 X5310 4254 C2 X5555 1005 C2 X2364 1002 C2 X5685 4151 C2 X2254 4141 C2 X5828 1174 C2 X2095 1150 C2 X1954 3945 C2 X6031 3946 C2 X6144 1363 C2 X1711 1381 C2 X6319 3675 C2 X6325 2511 C2 X1630 3708 C2 X6412 1638 C2 X1541 1897 C2 X6470 2308 C2 X1490 3186 C2 X6496 3393 C2 X1476 1764 C2 X6566 3123 C2 X6569 1943 C2 X6572 2436 C2 X1378 3361 C2 X6681 2807 C2 X1202 2180 C2 X1145 2893 C2 X1142 2530 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X2597 2504 C2 X3979 693 C2 X4143 4503 C2 X3807 4446 C2 X4337 675 C2 X3548 663 C2 X4540 4473 C2 X3415 4516 C2 X4729 750 C2 X3057 907 C2 X4959 4394 C2 X2930 790 C2 X2875 4412 C2 X5122 835 C2 X2670 4133 C2 X5309 4240 C2 X5484 987 C2 X2407 986 C2 X5614 4111 C2 X2319 4137 C2 X5787 1141 C2 X2137 1283 C2 X5918 3942 C2 X1983 3892 C2 X1940 1397 C2 X6068 1346 C2 X6207 3736 C2 X1695 1584 C2 X1688 2339 C2 X1686 3686 C2 X6304 1547 C2 X1620 2745 C2 X6406 3454 C2 X1554 3296 C2 X1486 3207 C2 X6541 3238 C2 X6549 1825 C2 X1396 1881 C2 X6657 2127 C2 X6702 2363 C2 X1268 2301 C2 X1266 2764 C2 X6716 2969 C2 X6722 2663 C2 X3985 696 C2 X4138 4503 C2 X3805 4451 C2 X4318 684 C2 X3543 667 C2 X4559 4476 C2 X3417 4513 C2 X4735 736 C2 X3059 881 C2 X4968 4384 C2 X2946 819 C2 X2895 4405 C2 X5131 841 C2 X5295 4236 C2 X2632 4146 C2 X5460 987 C2 X2426 978 C2 X5612 4113 C2 X2346 4134 C2 X5776 1134 C2 X2090 1275 C2 X5919 3941 C2 X2005 1385 C2 X1960 3905 C2 X6066 1339 C2 X6206 3732 C2 X1707 2748 C2 X1681 3652 C2 X6312 1548 C2 X1646 1581 C2 X1611 3351 C2 X1603 2330 C2 X6397 3456 C2 X6529 3244 C2 X6550 1824 C2 X1410 3163 C2 X1400 1905 C2 X6663 2129 C2 X1308 2311 C2 X6691 2368 C2 X1270 2758 C2 X6715 2976 C2 X6741 2659 C2 Xstroke Xgrestore Xend Xshowpage X%%Trailer X%%Pages: 1 END_OF_FILE if test 20654 -ne `wc -c <'figure4.ps'`; then echo shar: \"'figure4.ps'\" unpacked with wrong size! fi # end of 'figure4.ps' fi if test -f 'figure5.ps' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'figure5.ps'\" else echo shar: Extracting \"'figure5.ps'\" \(28099 characters\) sed "s/^X//" >'figure5.ps' <<'END_OF_FILE' X%!PS-Adobe-2.0 X%%Creator: gnuplot X%%DocumentFonts: Courier X%%BoundingBox: 50 50 554 770 X%%Pages: (atend) X%%EndComments X/gnudict 40 dict def Xgnudict begin X/Color false def X/gnulinewidth 5.000 def X/vshift -46 def X/dl {10 mul} def X/hpt 31.5 def X/vpt 31.5 def X/vpt2 vpt 2 mul def X/hpt2 hpt 2 mul def X/Lshow { currentpoint stroke moveto X 0 vshift rmoveto show } def X/Rshow { currentpoint stroke moveto X dup stringwidth pop neg vshift rmoveto show } def X/Cshow { currentpoint stroke moveto X dup stringwidth pop -2 div vshift rmoveto show } def X/DL { Color {setrgbcolor [] 0 setdash pop} X {pop pop pop 0 setdash} ifelse } def X/BL { stroke gnulinewidth 2 mul setlinewidth } def X/AL { stroke gnulinewidth 2 div setlinewidth } def X/PL { stroke gnulinewidth setlinewidth } def X/LTb { BL [] 0 0 0 DL } def X/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def X/LT0 { PL [] 0 1 0 DL } def X/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def X/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def X/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def X/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def X/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def X/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def X/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def X/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def X/M {moveto} def X/L {lineto} def X/P { stroke [] 0 setdash X currentlinewidth 2 div sub moveto X 0 currentlinewidth rlineto stroke } def X/D { stroke [] 0 setdash 2 copy vpt add moveto X hpt neg vpt neg rlineto hpt vpt neg rlineto X hpt vpt rlineto hpt neg vpt rlineto closepath stroke X P } def X/A { stroke [] 0 setdash vpt sub moveto 0 vpt2 rlineto X currentpoint stroke moveto X hpt neg vpt neg rmoveto hpt2 0 rlineto stroke X } def X/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add moveto X 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto X hpt2 neg 0 rlineto closepath stroke X P } def X/C { stroke [] 0 setdash exch hpt sub exch vpt add moveto X hpt2 vpt2 neg rlineto currentpoint stroke moveto X hpt2 neg 0 rmoveto hpt2 vpt2 rlineto stroke } def X/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add moveto X hpt neg vpt -1.62 mul rlineto X hpt 2 mul 0 rlineto X hpt neg vpt 1.62 mul rlineto closepath stroke X P } def X/S { 2 copy A C} def Xend X%%EndProlog X%%Page: 1 1 Xgnudict begin Xgsave X50 50 translate X0.100 0.100 scale X90 rotate X0 -5040 translate X0 setgray X/Courier findfont 140 scalefont setfont Xnewpath XLTa X1008 2590 M X6969 2590 L X1008 491 M X1008 4689 L XLTb X1008 491 M X1071 491 L X6969 491 M X6906 491 L X924 491 M X(-1) Rshow X1008 911 M X1071 911 L X6969 911 M X6906 911 L X924 911 M X(-0.8) Rshow X1008 1331 M X1071 1331 L X6969 1331 M X6906 1331 L X924 1331 M X(-0.6) Rshow X1008 1750 M X1071 1750 L X6969 1750 M X6906 1750 L X924 1750 M X(-0.4) Rshow X1008 2170 M X1071 2170 L X6969 2170 M X6906 2170 L X924 2170 M X(-0.2) Rshow X1008 2590 M X1071 2590 L X6969 2590 M X6906 2590 L X924 2590 M X(0) Rshow X1008 3010 M X1071 3010 L X6969 3010 M X6906 3010 L X924 3010 M X(0.2) Rshow X1008 3430 M X1071 3430 L X6969 3430 M X6906 3430 L X924 3430 M X(0.4) Rshow X1008 3849 M X1071 3849 L X6969 3849 M X6906 3849 L X924 3849 M X(0.6) Rshow X1008 4269 M X1071 4269 L X6969 4269 M X6906 4269 L X924 4269 M X(0.8) Rshow X1008 4689 M X1071 4689 L X6969 4689 M X6906 4689 L X924 4689 M X(1) Rshow X1008 491 M X1008 554 L X1008 4689 M X1008 4626 L X1008 351 M X(0) Cshow X2200 491 M X2200 554 L X2200 4689 M X2200 4626 L X2200 351 M X(0.2) Cshow X3392 491 M X3392 554 L X3392 4689 M X3392 4626 L X3392 351 M X(0.4) Cshow X4585 491 M X4585 554 L X4585 4689 M X4585 4626 L X4585 351 M X(0.6) Cshow X5777 491 M X5777 554 L X5777 4689 M X5777 4626 L X5777 351 M X(0.8) Cshow X6969 491 M X6969 554 L X6969 4689 M X6969 4626 L X6969 351 M X(1) Cshow XLTb X1008 491 M X6969 491 L X6969 4689 L X1008 4689 L X1008 491 L X140 2590 M Xcurrentpoint gsave translate 90 rotate 0 0 moveto X(Real epsilon) Cshow Xgrestore X3988 211 M X(theta) Cshow X4088 1 M X(Figure 5) Cshow XLT0 XLT0 X6486 4486 M X() Rshow X6570 4486 M X6822 4486 L X1009 3051 M X1009 3051 L X1012 3050 L X1016 3049 L X1019 3048 L X1021 3048 L X1023 3047 L X1028 3045 L X1031 3045 L X1035 3043 L X1038 3042 L X1039 3042 L X1042 3041 L X1046 3040 L X1049 3039 L X1051 3039 L X1053 3038 L X1058 3037 L X1060 3036 L X1065 3035 L X1068 3034 L X1069 3034 L X1072 3033 L X1076 3032 L X1079 3031 L X1083 3030 L X1086 3030 L X1088 3029 L X1090 3029 L X1095 3028 L X1098 3027 L X1099 3027 L X1102 3026 L X1106 3025 L X1109 3025 L X1113 3024 L X1116 3023 L X1118 3023 L X1120 3023 L X1125 3022 L X1127 3021 L X1129 3021 L X1132 3021 L X1135 3020 L X1136 3020 L X1139 3019 L X1143 3019 L X1146 3018 L X1148 3018 L X1150 3018 L X1155 3017 L X1157 3017 L X1162 3016 L X1164 3016 L X1166 3015 L X1169 3015 L X1173 3015 L X1176 3014 L X1178 3014 L X1180 3014 L X1185 3013 L X1187 3013 L X1192 3013 L X1194 3012 L X1196 3012 L X1199 3012 L X1203 3012 L X1206 3012 L X1210 3011 L X1213 3011 L X1215 3011 L X1217 3011 L X1222 3011 L X1224 3011 L X1226 3010 L X1229 3010 L X1233 3010 L X1236 3010 L X1240 3010 L X1243 3010 L X1245 3010 L X1247 3010 L X1252 3010 L X1254 3010 L X1256 3010 L X1259 3010 L X1261 3010 L X1263 3010 L X1266 3010 L X1270 3010 L X1273 3010 L X1275 3010 L X1277 3010 L X1282 3010 L X1284 3010 L X1289 3011 L X1291 3011 L X1293 3011 L X1296 3011 L X1300 3011 L X1303 3011 L X1304 3011 L X1307 3012 L X1312 3012 L X1314 3012 L X1319 3013 L X1321 3013 L X1323 3013 L X1326 3013 L X1330 3014 L X1333 3014 L X1337 3014 L X1340 3015 L X1342 3015 L X1344 3015 L X1349 3016 L X1351 3016 L X1353 3016 L X1356 3017 L X1360 3017 L X1363 3018 L X1367 3018 L X1370 3019 L X1371 3019 L X1374 3019 L X1379 3020 L X1381 3021 L X1383 3021 L X1386 3021 L X1390 3022 L X1393 3023 L X1397 3024 L X1400 3024 L X1401 3024 L X1404 3025 L X1408 3026 L X1411 3026 L X1416 3027 L X1418 3028 L X1420 3028 L X1423 3029 L X1427 3030 L X1430 3030 L X1431 3031 L X1434 3031 L X1438 3032 L X1441 3033 L X1446 3034 L X1448 3035 L X1450 3035 L X1453 3036 L X1457 3037 L X1460 3038 L X1461 3038 L X1464 3039 L X1467 3040 L X1468 3040 L X1471 3041 L X1475 3042 L X1478 3043 L X1480 3043 L X1483 3044 L X1487 3046 L X1490 3046 L X1494 3048 L X1497 3048 L X1498 3049 L X1501 3050 L X1505 3051 L X1508 3052 L X1510 3053 L X1512 3053 L X1517 3055 L X1520 3056 L X1524 3057 L X1527 3058 L X1528 3059 L X1531 3060 L X1535 3061 L X1538 3062 L X1542 3064 L X1545 3065 L X1547 3065 L X1550 3066 L X1554 3068 L X1557 3069 L X1558 3069 L X1561 3070 L X1565 3072 L X1568 3073 L X1572 3075 L X1575 3076 L X1577 3076 L X1579 3077 L X1584 3079 L X1587 3080 L X1588 3081 L X1591 3082 L X1595 3084 L X1598 3085 L X1602 3087 L X1605 3088 L X1607 3088 L X1609 3090 L X1614 3091 L X1616 3092 L X1621 3094 L X1624 3095 L X1625 3096 L X1628 3097 L X1632 3099 L X1635 3100 L X1637 3101 L X1639 3102 L X1644 3104 L X1646 3105 L X1651 3107 L X1654 3109 L X1655 3109 L X1658 3111 L X1662 3113 L X1665 3114 L X1669 3116 L X1672 3117 L X1674 3118 L X1676 3119 L X1681 3121 L X1683 3122 L X1685 3123 L X1688 3125 L X1692 3127 L X1695 3128 L X1699 3130 L X1702 3131 L X1704 3132 L X1706 3133 L X1711 3136 L X1713 3137 L X1715 3138 L X1718 3139 L X1722 3141 L X1725 3143 L X1729 3145 L X1732 3146 L X1734 3147 L X1736 3148 L X1741 3151 L X1743 3152 L X1748 3154 L X1750 3156 L X1752 3156 L X1755 3158 L X1759 3160 L X1762 3162 L X1764 3162 L X1766 3164 L X1771 3166 L X1773 3168 L X1778 3170 L X1780 3171 L X1782 3172 L X1785 3174 L X1789 3176 L X1792 3177 L X1794 3178 L X1796 3180 L X1799 3181 L X1801 3182 L X1803 3184 L X1808 3186 L X1810 3188 L X1812 3188 L X1815 3190 L X1819 3192 L X1822 3194 L X1826 3196 L X1829 3198 L X1831 3199 L X1833 3200 L X1838 3203 L X1840 3204 L X1842 3205 L X1845 3207 L X1849 3209 L X1852 3211 L X1856 3213 L X1859 3215 L X1860 3216 L X1863 3217 L X1868 3220 L X1870 3221 L X1875 3224 L X1877 3225 L X1879 3226 L X1882 3228 L X1886 3230 L X1889 3232 L X1890 3233 L X1893 3235 L X1898 3237 L X1900 3239 L X1905 3241 L X1907 3243 L X1909 3244 L X1912 3245 L X1916 3248 L X1919 3250 L X1920 3251 L X1923 3252 L X1927 3255 L X1930 3257 L X1935 3259 L X1937 3261 L X1939 3262 L X1942 3263 L X1946 3266 L X1949 3268 L X1953 3270 L X1956 3272 L X1957 3273 L X1960 3275 L X1965 3277 L X1967 3279 L X1969 3280 L X1972 3282 L X1976 3284 L X1979 3286 L X1983 3289 L X1986 3290 L X1987 3291 L X1990 3293 L X1994 3296 L X1997 3297 L X1999 3299 L X2002 3300 L X2004 3302 L X2006 3303 L X2009 3305 L X2013 3307 L X2016 3309 L X2017 3310 L X2020 3312 L X2024 3315 L X2027 3316 L X2031 3319 L X2034 3321 L X2036 3322 L X2039 3324 L X2043 3326 L X2046 3328 L X2047 3329 L X2050 3331 L X2054 3334 L X2057 3335 L X2061 3338 L X2064 3340 L X2066 3341 L X2069 3343 L X2073 3345 L X2076 3347 L X2080 3350 L X2083 3352 L X2084 3353 L X2087 3355 L X2091 3357 L X2094 3359 L X2096 3360 L X2098 3362 L X2103 3365 L X2106 3367 L X2110 3369 L X2113 3371 L X2114 3372 L X2117 3374 L X2121 3377 L X2124 3379 L X2126 3380 L X2128 3381 L X2131 3383 L X2133 3384 L X2135 3386 L X2140 3389 L X2143 3391 L X2144 3392 L X2147 3394 L X2151 3396 L X2154 3398 L X2158 3401 L X2161 3403 L X2163 3404 L X2165 3406 L X2170 3409 L X2173 3410 L X2174 3412 L X2177 3413 L X2181 3416 L X2184 3418 L X2188 3421 L Xcurrentpoint stroke moveto X2191 3423 L X2193 3424 L X2195 3426 L X2200 3428 L X2202 3430 L X2207 3433 L X2210 3435 L X2211 3436 L X2214 3438 L X2218 3441 L X2221 3442 L X2223 3444 L X2225 3445 L X2230 3448 L X2232 3450 L X2237 3453 L X2239 3455 L X2241 3456 L X2244 3458 L X2248 3460 L X2251 3462 L X2253 3463 L X2255 3465 L X2260 3468 L X2262 3470 L X2267 3473 L X2269 3474 L X2271 3476 L X2274 3477 L X2278 3480 L X2281 3482 L X2285 3485 L X2288 3487 L X2290 3488 L X2292 3490 L X2297 3492 L X2299 3494 L X2301 3495 L X2304 3497 L X2308 3500 L X2311 3502 L X2315 3505 L X2318 3506 L X2320 3508 L X2322 3509 L X2327 3512 L X2329 3514 L X2331 3515 L X2334 3517 L X2336 3519 L X2338 3520 L X2341 3521 L X2345 3524 L X2348 3526 L X2350 3527 L X2352 3529 L X2357 3532 L X2359 3533 L X2364 3536 L X2366 3538 L X2368 3539 L X2371 3541 L X2375 3544 L X2378 3545 L X2379 3547 L X2382 3548 L X2387 3551 L X2389 3553 L X2394 3556 L X2396 3557 L X2398 3559 L X2401 3560 L X2405 3563 L X2408 3565 L X2412 3568 L X2415 3569 L X2417 3570 L X2419 3572 L X2424 3575 L X2426 3577 L X2428 3578 L X2431 3579 L X2435 3582 L X2438 3584 L X2442 3587 L X2445 3588 L X2446 3589 L X2449 3591 L X2454 3594 L X2456 3596 L X2458 3597 L X2461 3598 L X2465 3601 L X2468 3603 L X2472 3605 L X2475 3607 L X2476 3608 L X2479 3610 L X2483 3613 L X2486 3614 L X2491 3617 L X2493 3619 L X2495 3620 L X2498 3621 L X2502 3624 L X2505 3626 L X2506 3627 L X2509 3628 L X2513 3631 L X2516 3633 L X2521 3635 L X2523 3637 L X2525 3638 L X2528 3640 L X2532 3642 L X2535 3644 L X2539 3646 L X2542 3648 L X2543 3649 L X2546 3651 L X2550 3653 L X2553 3655 L X2555 3656 L X2558 3658 L X2562 3660 L X2565 3662 L X2569 3664 L X2572 3666 L X2573 3667 L X2576 3668 L X2580 3671 L X2583 3673 L X2585 3674 L X2587 3675 L X2592 3678 L X2595 3679 L X2599 3682 L X2602 3683 L X2603 3684 L X2606 3686 L X2610 3688 L X2613 3690 L X2617 3692 L X2620 3694 L X2622 3695 L X2625 3696 L X2629 3699 L X2632 3701 L X2633 3701 L X2636 3703 L X2640 3705 L X2643 3707 L X2647 3709 L X2650 3711 L X2652 3712 L X2654 3713 L X2659 3716 L X2662 3717 L X2663 3718 L X2666 3720 L X2669 3721 L X2670 3722 L X2673 3724 L X2677 3726 L X2680 3728 L X2682 3728 L X2684 3730 L X2689 3732 L X2692 3734 L X2696 3736 L X2699 3738 L X2700 3738 L X2703 3740 L X2707 3742 L X2710 3744 L X2712 3745 L X2714 3746 L X2719 3748 L X2721 3750 L X2726 3752 L X2729 3754 L X2730 3754 L X2733 3756 L X2737 3758 L X2740 3760 L X2744 3762 L X2747 3763 L X2749 3764 L X2751 3766 L X2756 3768 L X2758 3769 L X2760 3770 L X2763 3771 L X2767 3774 L X2770 3775 L X2774 3777 L X2777 3779 L X2779 3780 L X2781 3781 L X2786 3783 L X2788 3785 L X2790 3785 L X2793 3787 L X2797 3789 L X2800 3790 L X2804 3792 L X2807 3794 L X2809 3795 L X2811 3796 L X2816 3798 L X2818 3800 L X2823 3802 L X2825 3803 L X2827 3804 L X2830 3805 L X2834 3807 L X2837 3809 L X2839 3809 L X2841 3811 L X2846 3813 L X2848 3814 L X2853 3816 L X2855 3818 L X2857 3818 L X2860 3820 L X2864 3822 L X2867 3823 L X2869 3824 L X2871 3825 L X2874 3827 L X2876 3827 L X2878 3829 L X2883 3831 L X2885 3832 L X2887 3833 L X2890 3834 L X2894 3836 L X2897 3837 L X2901 3839 L X2904 3841 L X2906 3841 L X2908 3843 L X2913 3845 L X2915 3846 L X2917 3847 L X2920 3848 L X2924 3850 L X2927 3851 L X2931 3853 L X2934 3855 L X2936 3855 L X2938 3857 L X2943 3859 L X2945 3860 L X2950 3862 L X2952 3863 L X2954 3864 L X2957 3865 L X2961 3867 L X2964 3868 L X2965 3869 L X2968 3870 L X2973 3872 L X2975 3873 L X2980 3875 L X2982 3876 L X2984 3877 L X2987 3878 L X2991 3880 L X2994 3882 L X2995 3882 L X2998 3884 L X3002 3885 L X3005 3887 L X3010 3889 L X3012 3890 L X3014 3891 L X3017 3892 L X3021 3894 L X3024 3895 L X3028 3897 L X3031 3898 L X3032 3899 L X3035 3900 L X3040 3902 L X3042 3903 L X3044 3904 L X3047 3905 L X3051 3907 L X3054 3908 L X3058 3910 L X3061 3911 L X3062 3912 L X3065 3913 L X3069 3915 L X3072 3916 L X3077 3918 L X3079 3919 L X3081 3920 L X3084 3921 L X3088 3923 L X3091 3924 L X3092 3924 L X3095 3926 L X3099 3927 L X3102 3929 L X3106 3930 L X3109 3932 L X3111 3932 L X3114 3933 L X3118 3935 L X3121 3936 L X3122 3937 L X3125 3938 L X3129 3940 L X3132 3941 L X3136 3943 L X3139 3944 L X3141 3945 L X3144 3946 L X3148 3948 L X3151 3949 L X3155 3951 L X3158 3952 L X3159 3953 L X3162 3954 L X3166 3956 L X3169 3957 L X3171 3957 L X3173 3958 L X3178 3960 L X3181 3961 L X3185 3963 L X3188 3964 L X3189 3965 L X3192 3966 L X3196 3968 L X3199 3969 L X3201 3970 L X3203 3971 L X3206 3972 L X3208 3973 L X3210 3974 L X3215 3976 L X3218 3977 L X3219 3977 L X3222 3979 L X3226 3980 L X3229 3981 L X3233 3983 L X3236 3984 L X3238 3985 L X3240 3986 L X3245 3988 L X3248 3989 L X3249 3990 L X3252 3991 L X3256 3993 L X3259 3994 L X3263 3996 L X3266 3997 L X3268 3997 L X3270 3998 L X3275 4000 L X3277 4001 L X3282 4003 L X3285 4004 L X3286 4005 L X3289 4006 L X3293 4008 L X3296 4009 L X3298 4010 L X3300 4011 L X3305 4013 L X3307 4014 L X3312 4015 L X3314 4017 L X3316 4017 L X3319 4018 L X3323 4020 L X3326 4021 L X3328 4022 L X3330 4023 L X3335 4025 L X3337 4026 L X3342 4028 L X3344 4029 L X3346 4030 L X3349 4031 L X3353 4032 L X3356 4034 L X3360 4035 L X3363 4036 L X3365 4037 L X3367 4038 L X3372 4040 L X3374 4041 L X3376 4042 L X3379 4043 L X3383 4045 L Xcurrentpoint stroke moveto X3386 4046 L X3390 4048 L X3393 4049 L X3395 4049 L X3397 4051 L X3402 4052 L X3404 4053 L X3406 4054 L X3409 4055 L X3411 4056 L X3413 4057 L X3416 4058 L X3420 4060 L X3423 4061 L X3425 4062 L X3427 4063 L X3432 4065 L X3434 4066 L X3439 4068 L X3441 4069 L X3443 4069 L X3446 4071 L X3450 4072 L X3453 4074 L X3454 4074 L X3457 4075 L X3462 4077 L X3464 4078 L X3469 4080 L X3471 4081 L X3473 4082 L X3476 4083 L X3480 4085 L X3483 4086 L X3487 4088 L X3490 4089 L X3492 4090 L X3494 4091 L X3499 4093 L X3501 4094 L X3503 4094 L X3506 4095 L X3510 4097 L X3513 4098 L X3517 4100 L X3520 4101 L X3521 4102 L X3524 4103 L X3529 4105 L X3531 4106 L X3533 4107 L X3536 4108 L X3538 4109 L X3540 4110 L X3543 4111 L X3547 4113 L X3550 4114 L X3551 4115 L X3554 4116 L X3558 4117 L X3561 4119 L X3566 4120 L X3568 4122 L X3570 4122 L X3573 4123 L X3577 4125 L X3580 4126 L X3581 4127 L X3584 4128 L X3588 4130 L X3591 4131 L X3596 4133 L X3598 4134 L X3600 4135 L X3603 4136 L X3607 4138 L X3610 4139 L X3614 4141 L X3617 4142 L X3618 4142 L X3621 4143 L X3625 4145 L X3628 4146 L X3630 4147 L X3633 4148 L X3637 4150 L X3640 4151 L X3644 4153 L X3647 4154 L X3648 4155 L X3651 4156 L X3655 4158 L X3658 4159 L X3660 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3093 L X6865 3092 L X6869 3090 L X6872 3089 L X6873 3088 L X6876 3087 L X6880 3085 L X6883 3084 L X6885 3083 L X6888 3082 L X6890 3081 L X6892 3080 L X6895 3079 L X6899 3077 L X6902 3076 L X6903 3076 L X6906 3074 L X6910 3073 L X6913 3072 L X6917 3070 L X6920 3069 L X6922 3068 L X6925 3067 L X6929 3066 L X6932 3065 L X6933 3064 L X6936 3063 L X6940 3061 L X6943 3061 L X6947 3059 L X6950 3058 L X6952 3057 L X6955 3057 L X6959 3055 L Xcurrentpoint stroke moveto X6962 3054 L X6966 3053 L X6969 3052 L Xstroke Xgrestore Xend Xshowpage X%%Trailer X%%Pages: 1 END_OF_FILE if test 28099 -ne `wc -c <'figure5.ps'`; then echo shar: \"'figure5.ps'\" unpacked with wrong size! fi # end of 'figure5.ps' fi if test -f 'figure6.ps' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'figure6.ps'\" else echo shar: Extracting \"'figure6.ps'\" \(28098 characters\) sed "s/^X//" >'figure6.ps' <<'END_OF_FILE' X%!PS-Adobe-2.0 X%%Creator: gnuplot X%%DocumentFonts: Courier X%%BoundingBox: 50 50 554 770 X%%Pages: (atend) X%%EndComments X/gnudict 40 dict def Xgnudict begin X/Color false def X/gnulinewidth 5.000 def X/vshift -46 def X/dl {10 mul} def X/hpt 31.5 def X/vpt 31.5 def X/vpt2 vpt 2 mul def X/hpt2 hpt 2 mul def X/Lshow { currentpoint stroke moveto X 0 vshift rmoveto show } def X/Rshow { currentpoint stroke moveto X dup stringwidth pop neg vshift rmoveto show } def X/Cshow { currentpoint stroke moveto X dup stringwidth pop -2 div vshift rmoveto show } def X/DL { Color {setrgbcolor [] 0 setdash pop} X {pop pop pop 0 setdash} ifelse } def X/BL { stroke gnulinewidth 2 mul setlinewidth } def X/AL { stroke gnulinewidth 2 div setlinewidth } def X/PL { stroke gnulinewidth setlinewidth } def X/LTb { BL [] 0 0 0 DL } def X/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def X/LT0 { PL [] 0 1 0 DL } def X/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def X/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def X/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def X/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def X/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def X/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def X/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def X/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def X/M {moveto} def X/L {lineto} def X/P { stroke [] 0 setdash X currentlinewidth 2 div sub moveto X 0 currentlinewidth rlineto stroke } def X/D { stroke [] 0 setdash 2 copy vpt add moveto X hpt neg vpt neg rlineto hpt vpt neg rlineto X hpt vpt rlineto hpt neg vpt rlineto closepath stroke X P } def X/A { stroke [] 0 setdash vpt sub moveto 0 vpt2 rlineto X currentpoint stroke moveto X hpt neg vpt neg rmoveto hpt2 0 rlineto stroke X } def X/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add moveto X 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto X hpt2 neg 0 rlineto closepath stroke X P } def X/C { stroke [] 0 setdash exch hpt sub exch vpt add moveto X hpt2 vpt2 neg rlineto currentpoint stroke moveto X hpt2 neg 0 rmoveto hpt2 vpt2 rlineto stroke } def X/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add moveto X hpt neg vpt -1.62 mul rlineto X hpt 2 mul 0 rlineto X hpt neg vpt 1.62 mul rlineto closepath stroke X P } def X/S { 2 copy A C} def Xend X%%EndProlog X%%Page: 1 1 Xgnudict begin Xgsave X50 50 translate X0.100 0.100 scale X90 rotate X0 -5040 translate X0 setgray X/Courier findfont 140 scalefont setfont Xnewpath XLTa X1008 2590 M X6969 2590 L X1008 491 M X1008 4689 L XLTb X1008 491 M X1071 491 L X6969 491 M X6906 491 L X924 491 M X(-1) Rshow X1008 911 M X1071 911 L X6969 911 M X6906 911 L X924 911 M X(-0.8) Rshow X1008 1331 M X1071 1331 L X6969 1331 M X6906 1331 L X924 1331 M X(-0.6) Rshow X1008 1750 M X1071 1750 L X6969 1750 M X6906 1750 L X924 1750 M X(-0.4) Rshow X1008 2170 M X1071 2170 L X6969 2170 M X6906 2170 L X924 2170 M X(-0.2) Rshow X1008 2590 M X1071 2590 L X6969 2590 M X6906 2590 L X924 2590 M X(0) Rshow X1008 3010 M X1071 3010 L X6969 3010 M X6906 3010 L X924 3010 M X(0.2) Rshow X1008 3430 M X1071 3430 L X6969 3430 M X6906 3430 L X924 3430 M X(0.4) Rshow X1008 3849 M X1071 3849 L X6969 3849 M X6906 3849 L X924 3849 M X(0.6) Rshow X1008 4269 M X1071 4269 L X6969 4269 M X6906 4269 L X924 4269 M X(0.8) Rshow X1008 4689 M X1071 4689 L X6969 4689 M X6906 4689 L X924 4689 M X(1) Rshow X1008 491 M X1008 554 L X1008 4689 M X1008 4626 L X1008 351 M X(0) Cshow X2200 491 M X2200 554 L X2200 4689 M X2200 4626 L X2200 351 M X(0.2) Cshow X3392 491 M X3392 554 L X3392 4689 M X3392 4626 L X3392 351 M X(0.4) Cshow X4585 491 M X4585 554 L X4585 4689 M X4585 4626 L X4585 351 M X(0.6) Cshow X5777 491 M X5777 554 L X5777 4689 M X5777 4626 L X5777 351 M X(0.8) Cshow X6969 491 M X6969 554 L X6969 4689 M X6969 4626 L X6969 351 M X(1) Cshow XLTb X1008 491 M X6969 491 L X6969 4689 L X1008 4689 L X1008 491 L X140 2590 M Xcurrentpoint gsave translate 90 rotate 0 0 moveto X(Real epsilon) Cshow Xgrestore X3988 211 M X(theta) Cshow X4088 1 M X(Figure 6) Cshow XLT0 XLT0 X6486 4486 M X() Rshow X6570 4486 M X6822 4486 L X1009 3840 M X1009 3840 L X1011 3919 L X1013 3931 L X1016 3947 L X1020 3995 L X1023 4032 L X1027 4103 L X1030 4153 L X1031 4186 L X1034 4243 L X1039 4334 L X1041 4375 L X1043 4397 L X1046 4413 L X1050 4393 L X1053 4353 L X1057 4151 L X1060 3989 L X1061 4078 L X1064 3994 L X1069 3879 L X1071 3815 L X1073 3769 L X1076 3701 L X1080 3606 L X1083 3548 L X1087 3459 L X1090 3420 L X1091 3382 L X1094 3338 L X1098 3257 L X1101 3190 L X1106 3128 L X1108 3360 L X1110 3464 L X1113 3456 L X1117 3430 L X1120 3428 L X1121 3416 L X1124 3385 L X1128 3381 L X1131 3362 L X1135 3266 L X1138 3312 L X1140 3315 L X1143 3296 L X1147 3273 L X1150 3262 L X1154 3249 L X1157 3243 L X1158 3239 L X1161 3235 L X1165 3232 L X1168 3230 L X1170 3229 L X1173 3229 L X1177 3227 L X1180 3225 L X1184 3197 L X1187 3319 L X1188 3259 L X1191 3243 L X1195 3237 L X1198 3234 L X1200 3232 L X1202 3230 L X1207 3222 L X1210 3218 L X1214 3216 L X1217 3204 L X1218 3198 L X1221 3191 L X1225 3173 L X1228 3154 L X1232 3107 L X1235 3079 L X1237 3093 L X1239 3275 L X1244 3237 L X1247 3347 L X1248 3348 L X1251 3311 L X1255 3327 L X1258 3314 L X1262 3216 L X1265 3257 L X1267 3278 L X1269 3269 L X1274 3243 L X1277 3229 L X1278 3221 L X1281 3208 L X1284 3197 L X1285 3190 L X1288 3179 L X1292 3161 L X1295 3155 L X1297 3148 L X1299 3139 L X1304 3125 L X1306 3114 L X1311 3033 L X1314 3052 L X1315 3104 L X1318 3110 L X1322 3106 L X1325 3102 L X1327 3100 L X1329 3093 L X1334 3089 L X1336 3085 L X1341 3073 L X1343 3070 L X1345 3071 L X1348 3066 L X1352 3058 L X1355 3054 L X1359 3048 L X1362 3045 L X1364 3043 L X1366 3042 L X1371 3042 L X1373 3044 L X1375 3045 L X1378 3048 L X1382 3055 L X1385 3059 L X1389 3064 L X1392 3103 L X1394 3083 L X1396 3087 L X1401 3093 L X1403 3097 L X1405 3099 L X1408 3104 L X1412 3109 L X1415 3113 L X1419 3125 L X1422 3122 L X1424 3125 L X1426 3130 L X1431 3136 L X1433 3141 L X1438 3174 L X1440 3369 L X1442 3461 L X1445 3193 L X1449 3168 L X1452 3176 L X1454 3169 L X1456 3168 L X1461 3169 L X1463 3166 L X1468 3131 L X1470 3166 L X1472 3163 L X1475 3157 L X1479 3157 L X1482 3158 L X1483 3159 L X1486 3161 L X1489 3163 L X1491 3164 L X1493 3167 L X1498 3171 L X1500 3173 L X1502 3174 L X1505 3177 L X1509 3180 L X1512 3182 L X1516 3179 L X1519 3216 L X1521 3179 L X1523 3189 L X1528 3186 L X1530 3184 L X1532 3183 L X1535 3182 L X1539 3176 L X1542 3173 L X1546 3176 L X1549 3161 L X1550 3158 L X1553 3154 L X1558 3140 L X1560 3128 L X1565 3102 L X1567 3083 L X1569 3072 L X1572 3072 L X1576 3292 L X1579 3584 L X1580 3704 L X1583 3517 L X1587 3647 L X1590 3741 L X1595 3026 L X1597 3241 L X1599 3262 L X1602 3155 L X1606 3117 L X1609 3107 L X1610 3100 L X1613 3092 L X1616 3085 L X1617 3079 L X1620 3073 L X1625 3064 L X1627 3057 L X1629 3053 L X1632 3047 L X1636 3034 L X1639 3022 L X1643 2951 L X1646 3014 L X1647 3058 L X1650 3056 L X1654 3048 L X1657 3046 L X1659 3042 L X1662 3033 L X1666 3030 L X1669 3023 L X1673 3002 L X1676 3005 L X1677 3006 L X1680 2999 L X1684 2989 L X1687 2984 L X1692 2975 L X1694 2971 L X1696 2968 L X1699 2964 L X1703 2958 L X1706 2955 L X1707 2954 L X1710 2951 L X1714 2948 L X1717 2945 L X1721 2923 L X1724 2989 L X1726 2963 L X1729 2953 L X1733 2949 L X1736 2948 L X1737 2946 L X1740 2945 L X1744 2941 L X1747 2939 L X1751 2937 L X1754 2931 L X1756 2927 L X1758 2923 L X1763 2912 L X1766 2899 L X1770 2859 L X1773 2815 L X1774 2823 L X1777 3079 L X1781 3063 L X1784 3048 L X1786 3037 L X1788 3011 L X1793 3027 L X1796 3014 L X1800 2947 L X1803 2980 L X1804 2992 L X1807 2984 L X1811 2970 L X1814 2963 L X1816 2959 L X1818 2953 L X1821 2948 L X1823 2944 L X1825 2939 L X1830 2931 L X1833 2928 L X1834 2924 L X1837 2920 L X1841 2913 L X1844 2906 L X1848 2850 L X1851 2860 L X1853 2925 L X1855 2921 L X1860 2921 L X1862 2923 L X1864 2923 L X1867 2919 L X1871 2924 L X1874 2923 L X1878 2913 L X1881 2920 L X1883 2925 L X1885 2925 L X1890 2926 L X1892 2928 L X1897 2934 L X1900 2941 L X1901 2945 L X1904 2956 L X1908 2980 L X1911 2997 L X1913 3009 L X1915 3032 L X1920 3073 L X1922 3100 L X1927 3212 L X1929 3140 L X1931 3139 L X1934 3179 L X1938 3209 L X1941 3223 L X1943 3234 L X1945 3250 L X1950 3273 L X1952 3287 L X1957 3310 L X1959 3321 L X1961 3333 L X1964 3347 L X1968 3378 L X1971 3409 L X1975 3514 L X1978 3387 L X1980 3208 L X1982 3261 L X1987 3275 L X1989 3271 L X1991 3277 L X1994 3293 L X1998 3290 L X2001 3298 L X2005 3341 L X2008 3323 L X2010 3318 L X2012 3325 L X2017 3337 L X2019 3343 L X2024 3351 L X2026 3354 L X2028 3356 L X2031 3359 L X2035 3363 L X2038 3364 L X2040 3365 L X2042 3365 L X2047 3366 L X2049 3369 L X2054 3416 L X2056 3265 L X2058 3315 L X2061 3337 L X2065 3340 L X2068 3338 L X2069 3339 L X2072 3339 L X2077 3340 L X2079 3341 L X2084 3343 L X2086 3344 L X2088 3349 L X2091 3353 L X2095 3364 L X2098 3378 L X2102 3423 L X2105 3484 L X2106 3546 L X2109 3661 L X2114 3643 L X2116 3148 L X2118 3121 L X2121 3196 L X2125 3161 L X2128 3170 L X2132 3217 L X2135 3228 L X2136 3192 L X2139 3184 L X2144 3202 L X2146 3212 L X2148 3218 L X2151 3227 L X2153 3233 L X2155 3237 L X2158 3244 L X2162 3257 L X2165 3258 L X2166 3262 L X2169 3267 L X2173 3272 L X2176 3275 L X2181 3292 L X2183 3404 L X2185 3378 L X2188 3320 L Xcurrentpoint stroke moveto X2192 3313 L X2195 3319 L X2196 3317 L X2199 3319 L X2203 3325 L X2206 3326 L X2210 3312 L X2213 3335 L X2215 3335 L X2218 3335 L X2222 3342 L X2225 3347 L X2229 3356 L X2232 3362 L X2233 3365 L X2236 3372 L X2240 3383 L X2243 3389 L X2245 3393 L X2248 3400 L X2252 3410 L X2255 3417 L X2259 3460 L X2262 3394 L X2263 3402 L X2266 3419 L X2270 3425 L X2273 3426 L X2275 3429 L X2277 3431 L X2282 3435 L X2285 3437 L X2289 3444 L X2292 3444 L X2293 3448 L X2296 3453 L X2300 3464 L X2303 3478 L X2307 3542 L X2310 3721 L X2312 3850 L X2314 3386 L X2319 3377 L X2322 3372 L X2323 3372 L X2326 3383 L X2330 3373 L X2333 3375 L X2337 3381 L X2340 3389 L X2342 3378 L X2344 3376 L X2349 3381 L X2352 3384 L X2353 3385 L X2356 3388 L X2359 3390 L X2360 3392 L X2363 3394 L X2367 3398 L X2370 3398 L X2372 3400 L X2374 3401 L X2379 3404 L X2381 3406 L X2386 3438 L X2389 3336 L X2390 3336 L X2393 3377 L X2397 3373 L X2400 3365 L X2402 3363 L X2404 3359 L X2409 3347 L X2411 3342 L X2416 3347 L X2419 3321 L X2420 3321 L X2423 3316 L X2427 3304 L X2430 3299 L X2434 3302 L X2437 3322 L X2439 3344 L X2441 3409 L X2446 3614 L X2448 3772 L X2450 3884 L X2453 4036 L X2457 4106 L X2460 4012 L X2464 2853 L X2467 3395 L X2469 3478 L X2471 3262 L X2476 3071 L X2478 2996 L X2480 2948 L X2483 2893 L X2487 2830 L X2490 2807 L X2494 2803 L X2497 2773 L X2499 2767 L X2501 2769 L X2506 2764 L X2508 2764 L X2513 2901 L X2515 3104 L X2517 3135 L X2520 3011 L X2524 2970 L X2527 2983 L X2529 2968 L X2531 2951 L X2536 2957 L X2538 2946 L X2543 2852 L X2545 2933 L X2547 2932 L X2550 2920 L X2554 2918 L X2557 2921 L X2561 2928 L X2564 2933 L X2566 2937 L X2568 2943 L X2573 2956 L X2575 2961 L X2577 2965 L X2580 2972 L X2584 2982 L X2587 2988 L X2591 3013 L X2594 3026 L X2596 2989 L X2598 3002 L X2603 3004 L X2605 3004 L X2607 3005 L X2610 3007 L X2614 3006 L X2617 3007 L X2621 3015 L X2624 3005 L X2625 3006 L X2628 3006 L X2633 3003 L X2635 3000 L X2640 3004 L X2642 3051 L X2644 3141 L X2647 3282 L X2651 3286 L X2654 3175 L X2655 3147 L X2658 3112 L X2663 3133 L X2665 3111 L X2670 2956 L X2672 3068 L X2674 3074 L X2677 3049 L X2681 3031 L X2684 3025 L X2685 3022 L X2688 3017 L X2691 3014 L X2692 3012 L X2695 3010 L X2700 3008 L X2702 3006 L X2704 3005 L X2707 3004 L X2711 3001 L X2714 2995 L X2718 2916 L X2721 3085 L X2722 3105 L X2725 3060 L X2729 3058 L X2732 3065 L X2734 3064 L X2737 3064 L X2741 3074 L X2744 3075 L X2748 3058 L X2751 3083 L X2752 3088 L X2755 3089 L X2759 3097 L X2762 3104 L X2767 3117 L X2769 3127 L X2771 3134 L X2774 3146 L X2778 3169 L X2781 3182 L X2782 3192 L X2785 3208 L X2789 3233 L X2792 3249 L X2796 3322 L X2799 3249 L X2801 3255 L X2804 3282 L X2808 3298 L X2811 3304 L X2812 3310 L X2815 3318 L X2819 3330 L X2822 3337 L X2826 3350 L X2829 3356 L X2831 3363 L X2833 3372 L X2838 3393 L X2841 3415 L X2845 3513 L X2848 3538 L X2849 3254 L X2852 3295 L X2856 3304 L X2859 3299 L X2861 3303 L X2863 3316 L X2868 3310 L X2871 3316 L X2875 3344 L X2878 3335 L X2879 3329 L X2882 3334 L X2886 3342 L X2889 3347 L X2891 3350 L X2893 3354 L X2896 3357 L X2898 3359 L X2900 3362 L X2905 3367 L X2908 3368 L X2909 3369 L X2912 3370 L X2916 3373 L X2919 3376 L X2923 3430 L X2926 3261 L X2928 3311 L X2930 3341 L X2935 3342 L X2937 3338 L X2939 3338 L X2942 3337 L X2946 3334 L X2949 3334 L X2953 3337 L X2956 3332 L X2958 3336 L X2960 3338 L X2965 3344 L X2967 3353 L X2972 3385 L X2975 3434 L X2976 3486 L X2979 3649 L X2983 4013 L X2986 3476 L X2988 3140 L X2990 3180 L X2995 3164 L X2997 3120 L X3002 3125 L X3004 3175 L X3006 3115 L X3009 3085 L X3013 3106 L X3016 3117 L X3018 3123 L X3020 3133 L X3023 3139 L X3025 3143 L X3027 3149 L X3032 3161 L X3034 3160 L X3036 3163 L X3039 3166 L X3043 3168 L X3046 3166 L X3050 3164 L X3053 3313 L X3055 3315 L X3057 3234 L X3062 3220 L X3064 3227 L X3066 3223 L X3069 3220 L X3073 3225 L X3076 3224 L X3080 3194 L X3083 3225 L X3085 3225 L X3087 3222 L X3092 3225 L X3094 3228 L X3099 3234 L X3101 3239 L X3103 3242 L X3106 3248 L X3110 3259 L X3113 3265 L X3115 3269 L X3117 3276 L X3122 3288 L X3124 3296 L X3129 3327 L X3131 3314 L X3133 3299 L X3136 3315 L X3140 3323 L X3143 3326 L X3144 3329 L X3147 3334 L X3152 3339 L X3154 3343 L X3159 3357 L X3161 3351 L X3163 3355 L X3166 3361 L X3170 3366 L X3173 3371 L X3177 3391 L X3180 3481 L X3181 3723 L X3184 3724 L X3189 3823 L X3191 3482 L X3193 3449 L X3196 3441 L X3200 3452 L X3203 3437 L X3207 3322 L X3210 3430 L X3211 3422 L X3214 3399 L X3219 3396 L X3221 3399 L X3223 3401 L X3226 3405 L X3228 3409 L X3230 3412 L X3233 3417 L X3237 3429 L X3240 3433 L X3241 3437 L X3244 3444 L X3248 3452 L X3251 3452 L X3256 3379 L X3258 3742 L X3260 3701 L X3263 3584 L X3267 3585 L X3270 3607 L X3271 3609 L X3274 3619 L X3278 3648 L X3281 3660 L X3285 3638 L X3288 3709 L X3290 3717 L X3293 3730 L X3297 3768 L X3300 3798 L X3304 3853 L X3307 3890 L X3308 3914 L X3311 3955 L X3315 4020 L X3318 4050 L X3320 4067 L X3323 4086 L X3327 4092 L X3330 4085 L X3334 4102 L X3337 3811 L X3338 3900 L X3341 3879 L X3345 3819 L X3348 3780 L X3350 3752 L X3352 3706 L X3357 3640 L X3360 3595 L X3364 3505 L X3367 3486 L X3368 3450 L X3371 3401 L X3375 3314 L X3378 3232 L X3382 2944 L Xcurrentpoint stroke moveto X3385 2987 L X3387 3148 L X3390 3303 L X3394 3313 L X3397 3295 L X3398 3294 L X3401 3270 L X3405 3257 L X3408 3242 L X3412 3228 L X3415 3187 L X3417 3193 L X3419 3182 L X3424 3151 L X3427 3133 L X3431 3104 L X3434 3088 L X3435 3078 L X3438 3063 L X3442 3041 L X3445 3030 L X3447 3023 L X3449 3013 L X3454 2997 L X3456 2985 L X3461 2905 L X3464 3073 L X3465 3037 L X3468 2995 L X3472 2983 L X3475 2980 L X3477 2976 L X3479 2970 L X3484 2962 L X3486 2956 L X3491 2942 L X3494 2942 L X3495 2934 L X3498 2925 L X3502 2907 L X3505 2888 L X3509 2825 L X3512 2730 L X3514 2631 L X3516 2539 L X3521 2524 L X3523 2864 L X3525 2926 L X3528 2934 L X3532 2921 L X3535 2942 L X3539 3052 L X3542 2937 L X3544 2957 L X3546 2986 L X3551 2979 L X3553 2971 L X3555 2965 L X3558 2956 L X3560 2947 L X3562 2942 L X3565 2933 L X3569 2915 L X3572 2910 L X3574 2905 L X3576 2896 L X3581 2886 L X3583 2883 L X3588 2893 L X3590 2706 L X3592 2729 L X3595 2794 L X3599 2796 L X3602 2784 L X3604 2783 L X3606 2778 L X3611 2764 L X3613 2759 L X3618 2771 L X3620 2738 L X3622 2735 L X3625 2730 L X3629 2716 L X3632 2706 L X3636 2688 L X3639 2677 L X3641 2669 L X3643 2657 L X3648 2636 L X3650 2624 L X3652 2616 L X3655 2604 L X3659 2586 L X3662 2574 L X3666 2512 L X3669 2598 L X3671 2583 L X3673 2560 L X3678 2549 L X3680 2545 L X3682 2541 L X3685 2536 L X3689 2528 L X3692 2523 L X3696 2515 L X3699 2510 L X3700 2504 L X3703 2497 L X3708 2480 L X3710 2461 L X3715 2376 L X3717 2211 L X3719 2858 L X3722 2598 L X3726 2582 L X3729 2590 L X3730 2584 L X3733 2570 L X3738 2577 L X3740 2570 L X3745 2535 L X3747 2551 L X3749 2557 L X3752 2552 L X3756 2543 L X3759 2539 L X3760 2537 L X3763 2533 L X3766 2530 L X3767 2528 L X3770 2526 L X3775 2522 L X3777 2521 L X3779 2520 L X3782 2519 L X3786 2517 L X3789 2514 L X3793 2460 L X3796 2659 L X3797 2585 L X3800 2553 L X3804 2552 L X3807 2556 L X3809 2555 L X3812 2557 L X3816 2559 L X3819 2559 L X3823 2555 L X3826 2560 L X3827 2556 L X3830 2553 L X3834 2546 L X3837 2536 L X3842 2504 L X3844 2464 L X3846 2427 L X3849 2327 L X3853 2019 L X3856 1853 L X3857 1843 L X3860 2191 L X3864 3214 L X3867 3465 L X3871 2723 L X3874 2788 L X3876 2904 L X3879 2864 L X3883 2808 L X3886 2786 L X3887 2774 L X3890 2757 L X3893 2745 L X3894 2737 L X3897 2726 L X3901 2707 L X3904 2705 L X3906 2699 L X3908 2692 L X3913 2684 L X3916 2679 L X3920 2645 L X3923 2546 L X3924 2553 L X3927 2626 L X3931 2636 L X3934 2628 L X3936 2631 L X3938 2629 L X3943 2623 L X3946 2622 L X3950 2640 L X3953 2613 L X3954 2613 L X3957 2613 L X3961 2606 L X3964 2601 L X3968 2592 L X3971 2586 L X3973 2582 L X3975 2576 L X3980 2565 L X3983 2559 L X3984 2555 L X3987 2548 L X3991 2538 L X3994 2531 L X3998 2503 L X4001 2526 L X4003 2532 L X4005 2517 L X4010 2510 L X4012 2507 L X4014 2504 L X4017 2500 L X4021 2495 L X4024 2491 L X4028 2480 L X4031 2482 L X4033 2479 L X4035 2474 L X4040 2467 L X4042 2462 L X4047 2442 L X4050 2388 L X4051 2291 L X4054 2241 L X4058 2202 L X4061 2383 L X4063 2406 L X4065 2415 L X4070 2403 L X4072 2413 L X4077 2490 L X4079 2418 L X4081 2421 L X4084 2436 L X4088 2436 L X4091 2433 L X4093 2432 L X4095 2428 L X4098 2424 L X4100 2422 L X4102 2417 L X4107 2408 L X4109 2405 L X4111 2402 L X4114 2397 L X4118 2391 L X4121 2390 L X4125 2424 L X4128 2261 L X4130 2267 L X4132 2317 L X4137 2315 L X4139 2303 L X4141 2302 L X4144 2296 L X4148 2281 L X4151 2274 L X4155 2284 L X4158 2251 L X4160 2246 L X4162 2240 L X4167 2222 L X4169 2210 L X4174 2186 L X4176 2170 L X4178 2159 L X4181 2141 L X4185 2109 L X4188 2091 L X4190 2078 L X4192 2059 L X4197 2030 L X4199 2013 L X4204 1913 L X4206 2066 L X4208 2034 L X4211 2005 L X4215 1993 L X4218 1991 L X4219 1988 L X4222 1986 L X4227 1981 L X4229 1980 L X4234 1987 L X4236 1977 L X4238 1975 L X4241 1976 L X4245 1969 L X4248 1959 L X4252 1955 L X4255 2388 L X4256 2404 L X4259 2150 L X4264 2114 L X4266 2130 L X4268 2118 L X4271 2108 L X4275 2118 L X4278 2111 L X4282 2037 L X4285 2103 L X4286 2103 L X4289 2093 L X4294 2091 L X4296 2093 L X4301 2097 L X4303 2101 L X4305 2103 L X4308 2108 L X4312 2118 L X4315 2123 L X4316 2127 L X4319 2133 L X4323 2143 L X4326 2148 L X4331 2129 L X4333 2245 L X4335 2181 L X4338 2185 L X4342 2186 L X4345 2187 L X4346 2187 L X4349 2190 L X4353 2187 L X4356 2186 L X4361 2194 L X4363 2178 L X4365 2174 L X4368 2170 L X4372 2152 L X4375 2132 L X4379 2075 L X4382 2013 L X4383 1959 L X4386 1889 L X4390 3281 L X4393 2911 L X4395 2618 L X4398 2480 L X4402 2566 L X4405 2474 L X4409 2176 L X4412 2342 L X4413 2367 L X4416 2314 L X4420 2279 L X4423 2266 L X4425 2258 L X4427 2247 L X4430 2239 L X4432 2233 L X4435 2225 L X4439 2212 L X4442 2208 L X4443 2203 L X4446 2196 L X4450 2185 L X4453 2174 L X4457 2090 L X4460 2081 L X4462 2156 L X4465 2190 L X4469 2191 L X4472 2188 L X4473 2187 L X4476 2180 L X4480 2178 L X4483 2174 L X4487 2167 L X4490 2157 L X4492 2160 L X4494 2156 L X4499 2146 L X4502 2140 L X4506 2129 L X4509 2123 L X4510 2120 L X4513 2114 L X4517 2105 L X4520 2101 L X4522 2098 L X4524 2095 L X4529 2089 L X4531 2085 L X4536 2029 L X4539 2168 L X4540 2130 L X4543 2110 L X4547 2108 L X4550 2109 L X4552 2109 L X4554 2109 L X4559 2108 L X4561 2107 L X4566 2109 L X4569 2103 L X4570 2098 L X4573 2093 L Xcurrentpoint stroke moveto X4577 2075 L X4580 2051 L X4584 1948 L X4587 1732 L X4589 1536 L X4591 2709 L X4596 2814 L X4598 2425 L X4600 2389 L X4603 2342 L X4607 2387 L X4610 2364 L X4614 2233 L X4617 2311 L X4619 2336 L X4621 2319 L X4626 2302 L X4628 2297 L X4630 2292 L X4633 2287 L X4635 2284 L X4637 2282 L X4640 2279 L X4644 2273 L X4647 2275 L X4649 2272 L X4651 2271 L X4656 2267 L X4658 2259 L X4663 2140 L X4665 2192 L X4667 2460 L X4670 2378 L X4674 2395 L X4677 2423 L X4679 2429 L X4681 2435 L X4686 2486 L X4688 2504 L X4693 2470 L X4695 2566 L X4697 2598 L X4700 2622 L X4704 2689 L X4707 2747 L X4711 2870 L X4714 2971 L X4716 3042 L X4718 3177 L X4723 3438 L X4725 3585 L X4727 3680 L X4730 3801 L X4734 3899 L X4737 3899 L X4741 3708 L X4744 3311 L X4746 3481 L X4748 3420 L X4753 3289 L X4755 3214 L X4757 3164 L X4760 3088 L X4764 2988 L X4767 2928 L X4771 2827 L X4774 2799 L X4775 2761 L X4778 2713 L X4783 2631 L X4785 2558 L X4790 2330 L X4792 2382 L X4794 2487 L X4797 2645 L X4801 2653 L X4804 2635 L X4805 2633 L X4808 2608 L X4813 2595 L X4815 2580 L X4820 2555 L X4822 2526 L X4824 2531 L X4827 2519 L X4831 2489 L X4834 2472 L X4838 2445 L X4841 2430 L X4842 2421 L X4845 2408 L X4850 2387 L X4852 2377 L X4854 2370 L X4857 2361 L X4861 2346 L X4864 2335 L X4868 2266 L X4871 2411 L X4872 2377 L X4875 2339 L X4879 2327 L X4882 2323 L X4884 2319 L X4887 2313 L X4891 2303 L X4894 2297 L X4898 2282 L X4901 2279 L X4902 2271 L X4905 2261 L X4909 2241 L X4912 2221 L X4917 2157 L X4919 2064 L X4921 1979 L X4924 2010 L X4928 1968 L X4931 2226 L X4932 2269 L X4935 2270 L X4939 2260 L X4942 2274 L X4946 2355 L X4949 2260 L X4951 2278 L X4954 2300 L X4958 2291 L X4961 2280 L X4962 2274 L X4965 2263 L X4968 2253 L X4969 2247 L X4972 2237 L X4976 2216 L X4979 2210 L X4981 2204 L X4983 2194 L X4988 2180 L X4991 2174 L X4995 2171 L X4998 1989 L X4999 2026 L X5002 2087 L X5006 2086 L X5009 2072 L X5011 2070 L X5013 2063 L X5018 2047 L X5021 2039 L X5025 2046 L X5028 2012 L X5029 2008 L X5032 2001 L X5036 1983 L X5039 1970 L X5043 1948 L X5046 1934 L X5048 1925 L X5050 1910 L X5055 1886 L X5058 1872 L X5059 1864 L X5062 1851 L X5066 1831 L X5069 1819 L X5073 1749 L X5076 1861 L X5078 1836 L X5080 1812 L X5085 1801 L X5088 1797 L X5089 1794 L X5092 1790 L X5096 1782 L X5099 1778 L X5103 1775 L X5106 1766 L X5108 1761 L X5110 1756 L X5115 1740 L X5117 1721 L X5122 1650 L X5125 1713 L X5126 2146 L X5129 1888 L X5133 1858 L X5136 1869 L X5138 1859 L X5140 1844 L X5145 1851 L X5147 1841 L X5152 1782 L X5154 1820 L X5156 1824 L X5159 1814 L X5163 1804 L X5166 1800 L X5168 1798 L X5170 1794 L X5173 1792 L X5175 1791 L X5177 1789 L X5182 1787 L X5184 1787 L X5186 1786 L X5189 1786 L X5193 1786 L X5196 1783 L X5200 1723 L X5203 1939 L X5205 1851 L X5207 1825 L X5212 1821 L X5214 1823 L X5216 1822 L X5219 1823 L X5223 1820 L X5226 1819 L X5230 1816 L X5233 1812 L X5235 1805 L X5237 1800 L X5242 1783 L X5244 1765 L X5249 1712 L X5251 1651 L X5253 1594 L X5256 1452 L X5260 1215 L X5263 1574 L X5265 2028 L X5267 2211 L X5272 2121 L X5274 2744 L X5279 1935 L X5281 2061 L X5283 2172 L X5286 2115 L X5290 2050 L X5293 2025 L X5294 2011 L X5297 1991 L X5300 1976 L X5302 1967 L X5304 1953 L X5309 1930 L X5311 1925 L X5313 1918 L X5316 1909 L X5320 1896 L X5323 1887 L X5327 1825 L X5330 1720 L X5332 1750 L X5334 1838 L X5339 1848 L X5341 1838 L X5343 1840 L X5346 1835 L X5350 1827 L X5353 1824 L X5357 1840 L X5360 1808 L X5361 1808 L X5364 1807 L X5369 1796 L X5371 1788 L X5376 1774 L X5378 1766 L X5380 1760 L X5383 1751 L X5387 1735 L X5390 1727 L X5391 1721 L X5394 1712 L X5398 1697 L X5401 1688 L X5406 1639 L X5408 1702 L X5410 1699 L X5413 1675 L X5417 1664 L X5420 1661 L X5421 1657 L X5424 1651 L X5428 1643 L X5431 1637 L X5436 1623 L X5438 1624 L X5440 1618 L X5443 1610 L X5447 1597 L X5450 1584 L X5454 1535 L X5457 1422 L X5458 1239 L X5461 1361 L X5465 1278 L X5468 1563 L X5470 1590 L X5473 1586 L X5477 1582 L X5480 1590 L X5484 1666 L X5487 1579 L X5488 1593 L X5491 1611 L X5495 1606 L X5498 1599 L X5500 1595 L X5502 1588 L X5505 1580 L X5507 1576 L X5510 1568 L X5514 1552 L X5517 1546 L X5518 1541 L X5521 1532 L X5525 1520 L X5528 1517 L X5532 1548 L X5535 1253 L X5537 1316 L X5540 1409 L X5544 1408 L X5547 1391 L X5548 1389 L X5551 1379 L X5555 1357 L X5558 1346 L X5562 1359 L X5565 1306 L X5567 1301 L X5569 1291 L X5574 1261 L X5577 1239 L X5581 1200 L X5584 1174 L X5585 1158 L X5588 1131 L X5592 1090 L X5595 1071 L X5597 1059 L X5599 1047 L X5604 1039 L X5606 1039 L X5611 983 L X5614 1230 L X5615 1159 L X5618 1160 L X5622 1190 L X5625 1213 L X5627 1228 L X5629 1255 L X5634 1294 L X5636 1321 L X5641 1385 L X5644 1391 L X5645 1413 L X5648 1447 L X5652 1504 L X5655 1558 L X5659 1821 L X5662 2074 L X5664 1885 L X5666 1629 L X5671 1599 L X5673 1621 L X5675 1615 L X5678 1629 L X5682 1643 L X5685 1650 L X5689 1610 L X5692 1690 L X5694 1684 L X5696 1686 L X5701 1709 L X5703 1726 L X5708 1754 L X5710 1770 L X5712 1780 L X5715 1797 L X5719 1824 L X5722 1837 L X5724 1846 L X5726 1860 L X5731 1882 L X5733 1896 L X5738 1972 L X5740 1863 L X5742 1859 L X5745 1905 L X5749 1917 L X5752 1919 L X5754 1923 L X5756 1929 L X5761 1934 L X5763 1938 L X5768 1958 L Xcurrentpoint stroke moveto X5770 1945 L X5772 1950 L X5775 1956 L X5779 1961 L X5782 1965 L X5786 1986 L X5789 2043 L X5791 2131 L X5793 2484 L X5798 2407 L X5800 2463 L X5802 2194 L X5805 2118 L X5809 2176 L X5812 2102 L X5816 1816 L X5819 2036 L X5821 2027 L X5823 1964 L X5828 1949 L X5830 1950 L X5832 1950 L X5835 1952 L X5837 1955 L X5839 1955 L X5842 1959 L X5846 1968 L X5849 1969 L X5850 1970 L X5853 1974 L X5858 1975 L X5860 1969 L X5865 1886 L X5867 2093 L X5869 2140 L X5872 2080 L X5876 2077 L X5879 2088 L X5880 2087 L X5883 2086 L X5888 2100 L X5890 2102 L X5895 2078 L X5897 2110 L X5899 2116 L X5902 2117 L X5906 2125 L X5909 2131 L X5913 2143 L X5916 2151 L X5917 2157 L X5920 2167 L X5925 2187 L X5927 2199 L X5929 2208 L X5932 2222 L X5936 2246 L X5939 2260 L X5943 2296 L X5946 2322 L X5947 2300 L X5950 2320 L X5955 2339 L X5957 2349 L X5959 2357 L X5962 2369 L X5966 2385 L X5969 2396 L X5973 2422 L X5976 2422 L X5977 2430 L X5980 2443 L X5984 2460 L X5987 2472 L X5992 2518 L X5994 2752 L X5996 3382 L X5999 2591 L X6003 2542 L X6006 2564 L X6007 2552 L X6010 2554 L X6014 2565 L X6017 2563 L X6021 2500 L X6024 2576 L X6026 2571 L X6029 2563 L X6033 2571 L X6036 2578 L X6037 2582 L X6040 2591 L X6043 2599 L X6044 2604 L X6047 2612 L X6051 2629 L X6054 2636 L X6056 2642 L X6059 2651 L X6063 2665 L X6066 2672 L X6070 2655 L X6073 2834 L X6074 2706 L X6077 2721 L X6081 2722 L X6084 2724 L X6086 2725 L X6088 2729 L X6093 2724 L X6096 2724 L X6100 2736 L X6103 2712 L X6104 2706 L X6107 2701 L X6111 2678 L X6114 2655 L X6118 2603 L X6121 2567 L X6123 2547 L X6125 2530 L X6130 2649 L X6133 2864 L X6134 3072 L X6137 3467 L X6141 3905 L X6144 3904 L X6148 2852 L X6151 3151 L X6153 3295 L X6155 3178 L X6160 3064 L X6163 3017 L X6164 2986 L X6167 2942 L X6171 2884 L X6174 2847 L X6178 2781 L X6181 2761 L X6183 2734 L X6185 2699 L X6190 2633 L X6192 2570 L X6197 2395 L X6200 2589 L X6201 2684 L X6204 2724 L X6208 2722 L X6211 2718 L X6213 2714 L X6215 2695 L X6220 2694 L X6222 2684 L X6227 2641 L X6229 2649 L X6231 2655 L X6234 2645 L X6238 2628 L X6241 2619 L X6245 2607 L X6248 2602 L X6250 2599 L X6252 2595 L X6257 2592 L X6259 2591 L X6261 2591 L X6264 2591 L X6268 2593 L X6271 2592 L X6275 2556 L X6278 2689 L X6280 2644 L X6282 2626 L X6287 2625 L X6289 2627 L X6291 2627 L X6294 2628 L X6298 2627 L X6301 2627 L X6305 2629 L X6308 2624 L X6310 2620 L X6312 2617 L X6317 2603 L X6319 2587 L X6324 2531 L X6326 2474 L X6328 2477 L X6331 2747 L X6335 2712 L X6338 2799 L X6340 2800 L X6342 2772 L X6347 2794 L X6349 2786 L X6354 2734 L X6356 2750 L X6358 2772 L X6361 2772 L X6365 2758 L X6368 2751 L X6369 2746 L X6372 2739 L X6375 2733 L X6377 2729 L X6379 2724 L X6384 2713 L X6386 2711 L X6388 2707 L X6391 2702 L X6395 2695 L X6398 2689 L X6402 2630 L X6405 2593 L X6407 2668 L X6409 2689 L X6414 2694 L X6416 2693 L X6418 2694 L X6421 2691 L X6425 2693 L X6428 2692 L X6432 2690 L X6435 2686 L X6436 2690 L X6439 2690 L X6444 2687 L X6446 2686 L X6451 2685 L X6453 2686 L X6455 2687 L X6458 2690 L X6462 2700 L X6465 2708 L X6466 2714 L X6469 2727 L X6473 2750 L X6476 2766 L X6481 2802 L X6483 2846 L X6485 2824 L X6488 2843 L X6492 2867 L X6495 2880 L X6496 2890 L X6499 2906 L X6503 2928 L X6506 2943 L X6511 2974 L X6513 2980 L X6515 2991 L X6518 3009 L X6522 3038 L X6525 3065 L X6529 3188 L X6532 3426 L X6533 3217 L X6536 3078 L X6540 3067 L X6543 3078 L X6545 3076 L X6548 3087 L X6552 3094 L X6555 3099 L X6559 3086 L X6562 3125 L X6563 3121 L X6566 3123 L X6570 3137 L X6573 3146 L X6575 3152 L X6577 3162 L X6580 3172 L X6582 3177 L X6585 3187 L X6589 3203 L X6592 3210 L X6593 3216 L X6596 3224 L X6600 3237 L X6603 3246 L X6607 3292 L X6610 3214 L X6612 3218 L X6615 3250 L X6619 3256 L X6622 3257 L X6623 3259 L X6626 3262 L X6630 3264 L X6633 3266 L X6637 3278 L X6640 3268 L X6642 3271 L X6644 3274 L X6649 3274 L X6652 3274 L X6656 3279 L X6659 3297 L X6660 3326 L X6663 3471 L X6667 4175 L X6670 3594 L X6672 3381 L X6674 3357 L X6679 3385 L X6681 3332 L X6686 3156 L X6689 3299 L X6690 3282 L X6693 3235 L X6697 3229 L X6700 3231 L X6702 3231 L X6704 3234 L X6707 3236 L X6709 3236 L X6711 3238 L X6716 3244 L X6719 3244 L X6720 3244 L X6723 3246 L X6727 3245 L X6730 3240 L X6734 3189 L X6737 3309 L X6739 3349 L X6741 3310 L X6746 3305 L X6748 3311 L X6750 3310 L X6753 3307 L X6757 3314 L X6760 3313 L X6764 3293 L X6767 3313 L X6769 3316 L X6771 3314 L X6776 3315 L X6778 3317 L X6783 3321 L X6786 3324 L X6787 3326 L X6790 3330 L X6794 3338 L X6797 3343 L X6799 3346 L X6801 3353 L X6806 3363 L X6808 3369 L X6813 3372 L X6815 3424 L X6817 3399 L X6820 3405 L X6824 3413 L X6827 3419 L X6829 3422 L X6831 3428 L X6836 3435 L X6838 3440 L X6843 3455 L X6845 3450 L X6847 3453 L X6850 3457 L X6854 3458 L X6857 3455 L X6861 3434 L X6864 3434 L X6866 3628 L X6868 3905 L X6873 4016 L X6875 3660 L X6877 3629 L X6880 3613 L X6884 3635 L X6887 3620 L X6891 3511 L X6894 3607 L X6896 3609 L X6898 3590 L X6903 3586 L X6905 3589 L X6907 3590 L X6910 3593 L X6912 3597 L X6914 3599 L X6917 3603 L X6921 3613 L X6924 3617 L X6926 3620 L X6928 3627 L X6933 3634 L X6935 3634 L X6940 3552 L X6942 3866 L X6944 3881 L X6947 3767 L X6951 3774 L X6954 3798 L X6955 3801 L Xcurrentpoint stroke moveto X6958 3812 L X6963 3848 L X6965 3863 L Xstroke Xgrestore Xend Xshowpage X%%Trailer X%%Pages: 1 END_OF_FILE if test 28098 -ne `wc -c <'figure6.ps'`; then echo shar: \"'figure6.ps'\" unpacked with wrong size! fi # end of 'figure6.ps' fi if test -f 'figure7.ps' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'figure7.ps'\" else echo shar: Extracting \"'figure7.ps'\" \(28016 characters\) sed "s/^X//" >'figure7.ps' <<'END_OF_FILE' X%!PS-Adobe-2.0 X%%Creator: gnuplot X%%DocumentFonts: Courier X%%BoundingBox: 50 50 554 770 X%%Pages: (atend) X%%EndComments X/gnudict 40 dict def Xgnudict begin X/Color false def X/gnulinewidth 5.000 def X/vshift -46 def X/dl {10 mul} def X/hpt 31.5 def X/vpt 31.5 def X/vpt2 vpt 2 mul def X/hpt2 hpt 2 mul def X/Lshow { currentpoint stroke moveto X 0 vshift rmoveto show } def X/Rshow { currentpoint stroke moveto X dup stringwidth pop neg vshift rmoveto show } def X/Cshow { currentpoint stroke moveto X dup stringwidth pop -2 div vshift rmoveto show } def X/DL { Color {setrgbcolor [] 0 setdash pop} X {pop pop pop 0 setdash} ifelse } def X/BL { stroke gnulinewidth 2 mul setlinewidth } def X/AL { stroke gnulinewidth 2 div setlinewidth } def X/PL { stroke gnulinewidth setlinewidth } def X/LTb { BL [] 0 0 0 DL } def X/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def X/LT0 { PL [] 0 1 0 DL } def X/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def X/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def X/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def X/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def X/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def X/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def X/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def X/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def X/M {moveto} def X/L {lineto} def X/P { stroke [] 0 setdash X currentlinewidth 2 div sub moveto X 0 currentlinewidth rlineto stroke } def X/D { stroke [] 0 setdash 2 copy vpt add moveto X hpt neg vpt neg rlineto hpt vpt neg rlineto X hpt vpt rlineto hpt neg vpt rlineto closepath stroke X P } def X/A { stroke [] 0 setdash vpt sub moveto 0 vpt2 rlineto X currentpoint stroke moveto X hpt neg vpt neg rmoveto hpt2 0 rlineto stroke X } def X/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add moveto X 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto X hpt2 neg 0 rlineto closepath stroke X P } def X/C { stroke [] 0 setdash exch hpt sub exch vpt add moveto X hpt2 vpt2 neg rlineto currentpoint stroke moveto X hpt2 neg 0 rmoveto hpt2 vpt2 rlineto stroke } def X/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add moveto X hpt neg vpt -1.62 mul rlineto X hpt 2 mul 0 rlineto X hpt neg vpt 1.62 mul rlineto closepath stroke X P } def X/S { 2 copy A C} def Xend X%%EndProlog X%%Page: 1 1 Xgnudict begin Xgsave X50 50 translate X0.100 0.100 scale X90 rotate X0 -5040 translate X0 setgray X/Courier findfont 140 scalefont setfont Xnewpath XLTa X1008 2590 M X6969 2590 L X1008 491 M X1008 4689 L XLTb X1008 491 M X1071 491 L X6969 491 M X6906 491 L X924 491 M X(-1) Rshow X1008 911 M X1071 911 L X6969 911 M X6906 911 L X924 911 M X(-0.8) Rshow X1008 1331 M X1071 1331 L X6969 1331 M X6906 1331 L X924 1331 M X(-0.6) Rshow X1008 1750 M X1071 1750 L X6969 1750 M X6906 1750 L X924 1750 M X(-0.4) Rshow X1008 2170 M X1071 2170 L X6969 2170 M X6906 2170 L X924 2170 M X(-0.2) Rshow X1008 2590 M X1071 2590 L X6969 2590 M X6906 2590 L X924 2590 M X(0) Rshow X1008 3010 M X1071 3010 L X6969 3010 M X6906 3010 L X924 3010 M X(0.2) Rshow X1008 3430 M X1071 3430 L X6969 3430 M X6906 3430 L X924 3430 M X(0.4) Rshow X1008 3849 M X1071 3849 L X6969 3849 M X6906 3849 L X924 3849 M X(0.6) Rshow X1008 4269 M X1071 4269 L X6969 4269 M X6906 4269 L X924 4269 M X(0.8) Rshow X1008 4689 M X1071 4689 L X6969 4689 M X6906 4689 L X924 4689 M X(1) Rshow X1008 491 M X1008 554 L X1008 4689 M X1008 4626 L X1008 351 M X(0) Cshow X2200 491 M X2200 554 L X2200 4689 M X2200 4626 L X2200 351 M X(0.2) Cshow X3392 491 M X3392 554 L X3392 4689 M X3392 4626 L X3392 351 M X(0.4) Cshow X4585 491 M X4585 554 L X4585 4689 M X4585 4626 L X4585 351 M X(0.6) Cshow X5777 491 M X5777 554 L X5777 4689 M X5777 4626 L X5777 351 M X(0.8) Cshow X6969 491 M X6969 554 L X6969 4689 M X6969 4626 L X6969 351 M X(1) Cshow XLTb X1008 491 M X6969 491 L X6969 4689 L X1008 4689 L X1008 491 L X140 2590 M Xcurrentpoint gsave translate 90 rotate 0 0 moveto X(Im epsilon) Cshow Xgrestore X3988 211 M X(theta) Cshow X4088 1 M X(Figure 7) Cshow XLT0 XLT0 X6486 4486 M X() Rshow X6570 4486 M X6822 4486 L X1009 1276 M X1009 1276 L X1011 1276 L X1013 1288 L X1016 1291 L X1020 1294 L X1023 1301 L X1027 1320 L X1030 1343 L X1031 1361 L X1034 1402 L X1039 1506 L X1041 1586 L X1043 1647 L X1046 1756 L X1050 1946 L X1053 2068 L X1057 2646 L X1060 1993 L X1061 2082 L X1064 2212 L X1069 2262 L X1071 2269 L X1073 2273 L X1076 2268 L X1080 2256 L X1083 2239 L X1087 2174 L X1090 2182 L X1091 2162 L X1094 2124 L X1098 2064 L X1101 2003 L X1106 1722 L X1108 1616 L X1110 1642 L X1113 1847 L X1117 1889 L X1120 1865 L X1121 1876 L X1124 1874 L X1128 1858 L X1131 1857 L X1135 1919 L X1138 1831 L X1140 1834 L X1143 1835 L X1147 1815 L X1150 1801 L X1154 1776 L X1157 1762 L X1158 1753 L X1161 1739 L X1165 1716 L X1168 1706 L X1170 1698 L X1173 1687 L X1177 1670 L X1180 1659 L X1184 1601 L X1187 1675 L X1188 1682 L X1191 1650 L X1195 1641 L X1198 1638 L X1200 1634 L X1202 1629 L X1207 1623 L X1210 1618 L X1214 1604 L X1217 1608 L X1218 1603 L X1221 1596 L X1225 1586 L X1228 1575 L X1232 1534 L X1235 1458 L X1237 1375 L X1239 1315 L X1244 1299 L X1247 1459 L X1248 1498 L X1251 1525 L X1255 1503 L X1258 1526 L X1262 1678 L X1265 1549 L X1267 1553 L X1269 1581 L X1274 1588 L X1277 1585 L X1278 1584 L X1281 1581 L X1284 1576 L X1285 1574 L X1288 1569 L X1292 1558 L X1295 1555 L X1297 1551 L X1299 1545 L X1304 1538 L X1306 1538 L X1311 1572 L X1314 1392 L X1315 1402 L X1318 1455 L X1322 1454 L X1325 1443 L X1327 1442 L X1329 1438 L X1334 1424 L X1336 1419 L X1341 1430 L X1343 1400 L X1345 1396 L X1348 1392 L X1352 1378 L X1355 1369 L X1359 1351 L X1362 1340 L X1364 1333 L X1366 1320 L X1371 1300 L X1373 1288 L X1375 1280 L X1378 1268 L X1382 1250 L X1385 1239 L X1389 1184 L X1392 1255 L X1394 1242 L X1396 1222 L X1401 1211 L X1403 1206 L X1405 1202 L X1408 1197 L X1412 1189 L X1415 1184 L X1419 1176 L X1422 1171 L X1424 1165 L X1426 1159 L X1431 1145 L X1433 1129 L X1438 1065 L X1440 1022 L X1442 1286 L X1445 1230 L X1449 1217 L X1452 1222 L X1454 1217 L X1456 1205 L X1461 1209 L X1463 1203 L X1468 1172 L X1470 1185 L X1472 1189 L X1475 1184 L X1479 1176 L X1482 1172 L X1483 1169 L X1486 1166 L X1489 1163 L X1491 1161 L X1493 1158 L X1498 1154 L X1500 1153 L X1502 1152 L X1505 1150 L X1509 1147 L X1512 1144 L X1516 1102 L X1519 1245 L X1521 1194 L X1523 1170 L X1528 1168 L X1530 1170 L X1532 1169 L X1535 1169 L X1539 1169 L X1542 1169 L X1546 1165 L X1549 1167 L X1550 1163 L X1553 1160 L X1558 1153 L X1560 1143 L X1565 1114 L X1567 1077 L X1569 1041 L X1572 947 L X1576 730 L X1579 800 L X1580 1007 L X1583 1271 L X1587 1111 L X1590 1545 L X1595 1303 L X1597 1315 L X1599 1397 L X1602 1402 L X1606 1361 L X1609 1344 L X1610 1334 L X1613 1320 L X1616 1310 L X1617 1304 L X1620 1295 L X1625 1279 L X1627 1277 L X1629 1272 L X1632 1266 L X1636 1259 L X1639 1256 L X1643 1227 L X1646 1131 L X1647 1139 L X1650 1204 L X1654 1213 L X1657 1205 L X1659 1208 L X1662 1207 L X1666 1200 L X1669 1199 L X1673 1217 L X1676 1191 L X1677 1191 L X1680 1191 L X1684 1185 L X1687 1180 L X1692 1171 L X1694 1165 L X1696 1162 L X1699 1155 L X1703 1144 L X1706 1138 L X1707 1134 L X1710 1127 L X1714 1117 L X1717 1110 L X1721 1080 L X1724 1107 L X1726 1111 L X1729 1096 L X1733 1089 L X1736 1086 L X1737 1083 L X1740 1079 L X1744 1073 L X1747 1069 L X1751 1059 L X1754 1060 L X1756 1056 L X1758 1051 L X1763 1044 L X1766 1037 L X1770 1010 L X1773 943 L X1774 829 L X1777 849 L X1781 803 L X1784 983 L X1786 1003 L X1788 1007 L X1793 999 L X1796 1007 L X1800 1074 L X1803 1007 L X1804 1012 L X1807 1026 L X1811 1025 L X1814 1021 L X1816 1019 L X1818 1015 L X1821 1011 L X1823 1008 L X1825 1004 L X1830 993 L X1833 990 L X1834 987 L X1837 981 L X1841 974 L X1844 972 L X1848 1001 L X1851 815 L X1853 842 L X1855 898 L X1860 897 L X1862 885 L X1864 883 L X1867 877 L X1871 862 L X1874 855 L X1878 864 L X1881 830 L X1883 826 L X1885 819 L X1890 800 L X1892 786 L X1897 762 L X1900 745 L X1901 735 L X1904 717 L X1908 688 L X1911 674 L X1913 664 L X1915 652 L X1920 637 L X1922 629 L X1927 567 L X1929 721 L X1931 682 L X1934 670 L X1938 676 L X1941 683 L X1943 687 L X1945 697 L X1950 709 L X1952 719 L X1957 745 L X1959 743 L X1961 750 L X1964 764 L X1968 783 L X1971 799 L X1975 905 L X1978 1143 L X1980 1094 L X1982 902 L X1987 877 L X1989 892 L X1991 885 L X1994 887 L X1998 896 L X2001 896 L X2005 852 L X2008 908 L X2010 906 L X2012 903 L X2017 912 L X2019 919 L X2024 932 L X2026 940 L X2028 945 L X2031 953 L X2035 968 L X2038 975 L X2040 980 L X2042 988 L X2047 1001 L X2049 1008 L X2054 1033 L X2056 1032 L X2058 1007 L X2061 1026 L X2065 1031 L X2068 1033 L X2069 1035 L X2072 1038 L X2077 1039 L X2079 1041 L X2084 1052 L X2086 1042 L X2088 1043 L X2091 1044 L X2095 1040 L X2098 1035 L X2102 1025 L X2105 1028 L X2106 1050 L X2109 1224 L X2114 1178 L X2116 1551 L X2118 1319 L X2121 1225 L X2125 1285 L X2128 1221 L X2132 998 L X2135 1144 L X2136 1153 L X2139 1110 L X2144 1091 L X2146 1087 L X2148 1084 L X2151 1081 L X2153 1079 L X2155 1077 L X2158 1076 L X2162 1075 L X2165 1074 L X2166 1073 L X2169 1072 L X2173 1069 L X2176 1064 L X2181 998 L X2183 1083 L X2185 1129 L X2188 1116 L Xcurrentpoint stroke moveto X2192 1116 L X2195 1120 L X2196 1120 L X2199 1117 L X2203 1123 L X2206 1123 L X2210 1111 L X2213 1122 L X2215 1125 L X2218 1125 L X2222 1126 L X2225 1127 L X2229 1129 L X2232 1131 L X2233 1132 L X2236 1136 L X2240 1142 L X2243 1147 L X2245 1150 L X2248 1156 L X2252 1166 L X2255 1172 L X2259 1171 L X2262 1229 L X2263 1208 L X2266 1212 L X2270 1221 L X2273 1227 L X2275 1231 L X2277 1238 L X2282 1246 L X2285 1252 L X2289 1267 L X2292 1266 L X2293 1269 L X2296 1275 L X2300 1279 L X2303 1279 L X2307 1269 L X2310 1313 L X2312 1804 L X2314 1439 L X2319 1399 L X2322 1420 L X2323 1409 L X2326 1403 L X2330 1417 L X2333 1413 L X2337 1352 L X2340 1412 L X2342 1414 L X2344 1407 L X2349 1409 L X2352 1412 L X2353 1414 L X2356 1419 L X2359 1423 L X2360 1426 L X2363 1431 L X2367 1441 L X2370 1447 L X2372 1450 L X2374 1457 L X2379 1466 L X2381 1469 L X2386 1429 L X2389 1688 L X2390 1549 L X2393 1532 L X2397 1535 L X2400 1541 L X2402 1543 L X2404 1548 L X2409 1550 L X2411 1552 L X2416 1559 L X2419 1551 L X2420 1545 L X2423 1542 L X2427 1525 L X2430 1505 L X2434 1452 L X2437 1406 L X2439 1373 L X2441 1317 L X2446 1267 L X2448 1304 L X2450 1367 L X2453 1548 L X2457 1977 L X2460 2265 L X2464 3195 L X2467 2025 L X2469 2191 L X2471 2323 L X2476 2282 L X2478 2229 L X2480 2191 L X2483 2123 L X2487 2033 L X2490 1973 L X2494 1868 L X2497 1846 L X2499 1809 L X2501 1761 L X2506 1680 L X2508 1608 L X2513 1406 L X2515 1511 L X2517 1590 L X2520 1696 L X2524 1710 L X2527 1698 L X2529 1699 L X2531 1682 L X2536 1676 L X2538 1667 L X2543 1648 L X2545 1629 L X2547 1635 L X2550 1627 L X2554 1607 L X2557 1595 L X2561 1578 L X2564 1569 L X2566 1564 L X2568 1557 L X2573 1548 L X2575 1544 L X2577 1541 L X2580 1538 L X2584 1533 L X2587 1529 L X2591 1483 L X2594 1610 L X2596 1576 L X2598 1552 L X2603 1548 L X2605 1549 L X2607 1547 L X2610 1547 L X2614 1544 L X2617 1542 L X2621 1539 L X2624 1536 L X2625 1531 L X2628 1526 L X2633 1513 L X2635 1497 L X2640 1441 L X2642 1372 L X2644 1337 L X2647 1503 L X2651 1465 L X2654 1619 L X2655 1636 L X2658 1623 L X2663 1633 L X2665 1636 L X2670 1649 L X2672 1615 L X2674 1635 L X2677 1646 L X2681 1637 L X2684 1630 L X2685 1625 L X2688 1618 L X2691 1612 L X2692 1608 L X2695 1602 L X2700 1589 L X2702 1586 L X2704 1582 L X2707 1576 L X2711 1568 L X2714 1563 L X2718 1529 L X2721 1430 L X2722 1490 L X2725 1530 L X2729 1534 L X2732 1529 L X2734 1529 L X2737 1525 L X2741 1521 L X2744 1518 L X2748 1521 L X2751 1504 L X2752 1506 L X2755 1504 L X2759 1495 L X2762 1490 L X2767 1480 L X2769 1476 L X2771 1473 L X2774 1468 L X2778 1464 L X2781 1464 L X2782 1464 L X2785 1466 L X2789 1472 L X2792 1476 L X2796 1462 L X2799 1550 L X2801 1524 L X2804 1525 L X2808 1536 L X2811 1544 L X2812 1549 L X2815 1558 L X2819 1570 L X2822 1579 L X2826 1600 L X2829 1600 L X2831 1605 L X2833 1615 L X2838 1628 L X2841 1637 L X2845 1683 L X2848 1977 L X2849 1993 L X2852 1749 L X2856 1726 L X2859 1741 L X2861 1735 L X2863 1736 L X2868 1747 L X2871 1748 L X2875 1704 L X2878 1758 L X2879 1758 L X2882 1755 L X2886 1762 L X2889 1769 L X2891 1773 L X2893 1780 L X2896 1788 L X2898 1792 L X2900 1800 L X2905 1815 L X2908 1822 L X2909 1828 L X2912 1837 L X2916 1850 L X2919 1857 L X2923 1859 L X2926 1923 L X2928 1878 L X2930 1893 L X2935 1898 L X2937 1901 L X2939 1904 L X2942 1908 L X2946 1910 L X2949 1913 L X2953 1925 L X2956 1913 L X2958 1912 L X2960 1913 L X2965 1904 L X2967 1893 L X2972 1861 L X2975 1831 L X2976 1810 L X2979 1800 L X2983 2357 L X2986 2777 L X2988 2545 L X2990 2275 L X2995 2428 L X2997 2288 L X3002 1904 L X3004 2113 L X3006 2143 L X3009 2071 L X3013 2036 L X3016 2027 L X3018 2021 L X3020 2014 L X3023 2010 L X3025 2006 L X3027 2002 L X3032 1998 L X3034 1996 L X3036 1993 L X3039 1990 L X3043 1984 L X3046 1976 L X3050 1893 L X3053 1935 L X3055 1999 L X3057 2021 L X3062 2025 L X3064 2026 L X3066 2027 L X3069 2022 L X3073 2026 L X3076 2025 L X3080 2018 L X3083 2017 L X3085 2022 L X3087 2021 L X3092 2017 L X3094 2014 L X3099 2010 L X3101 2009 L X3103 2008 L X3106 2006 L X3110 2005 L X3113 2006 L X3115 2006 L X3117 2007 L X3122 2009 L X3124 2009 L X3129 1974 L X3131 2086 L X3133 2055 L X3136 2043 L X3140 2045 L X3143 2049 L X3144 2050 L X3147 2054 L X3152 2057 L X3154 2059 L X3159 2064 L X3161 2062 L X3163 2060 L X3166 2059 L X3170 2050 L X3173 2035 L X3177 1969 L X3180 1855 L X3181 1799 L X3184 2367 L X3189 2359 L X3191 2310 L X3193 2296 L X3196 2263 L X3200 2299 L X3203 2287 L X3207 2211 L X3210 2252 L X3211 2277 L X3214 2273 L X3219 2263 L X3221 2260 L X3223 2257 L X3226 2254 L X3228 2252 L X3230 2251 L X3233 2249 L X3237 2245 L X3240 2246 L X3241 2245 L X3244 2244 L X3248 2241 L X3251 2237 L X3256 2168 L X3258 2115 L X3260 2270 L X3263 2278 L X3267 2292 L X3270 2301 L X3271 2305 L X3274 2305 L X3278 2325 L X3281 2331 L X3285 2325 L X3288 2343 L X3290 2358 L X3293 2366 L X3297 2380 L X3300 2393 L X3304 2422 L X3307 2447 L X3308 2465 L X3311 2502 L X3315 2586 L X3318 2645 L X3320 2689 L X3323 2767 L X3327 2901 L X3330 2990 L X3334 3390 L X3337 3022 L X3338 3064 L X3341 3180 L X3345 3255 L X3348 3285 L X3350 3307 L X3352 3334 L X3357 3374 L X3360 3393 L X3364 3403 L X3367 3432 L X3368 3444 L X3371 3450 L X3375 3472 L X3378 3489 L X3382 3400 L Xcurrentpoint stroke moveto X3385 3039 L X3387 2961 L X3390 3184 L X3394 3242 L X3397 3227 L X3398 3247 L X3401 3271 L X3405 3266 L X3408 3283 L X3412 3406 L X3415 3311 L X3417 3312 L X3419 3331 L X3424 3342 L X3427 3344 L X3431 3344 L X3434 3343 L X3435 3342 L X3438 3339 L X3442 3331 L X3445 3329 L X3447 3327 L X3449 3322 L X3454 3317 L X3456 3315 L X3461 3317 L X3464 3229 L X3465 3299 L X3468 3297 L X3472 3302 L X3475 3305 L X3477 3307 L X3479 3308 L X3484 3317 L X3486 3321 L X3491 3318 L X3494 3337 L X3495 3341 L X3498 3347 L X3502 3367 L X3505 3385 L X3509 3426 L X3512 3441 L X3514 3413 L X3516 3136 L X3521 3208 L X3523 3062 L X3525 3098 L X3528 3176 L X3532 3140 L X3535 3179 L X3539 3393 L X3542 3272 L X3544 3250 L X3546 3281 L X3551 3318 L X3553 3334 L X3555 3344 L X3558 3358 L X3560 3369 L X3562 3377 L X3565 3388 L X3569 3405 L X3572 3412 L X3574 3418 L X3576 3427 L X3581 3442 L X3583 3455 L X3588 3553 L X3590 3490 L X3592 3431 L X3595 3438 L X3599 3444 L X3602 3446 L X3604 3449 L X3606 3457 L X3611 3460 L X3613 3465 L X3618 3482 L X3620 3481 L X3622 3479 L X3625 3485 L X3629 3493 L X3632 3497 L X3636 3503 L X3639 3505 L X3641 3507 L X3643 3508 L X3648 3507 L X3650 3506 L X3652 3504 L X3655 3501 L X3659 3494 L X3662 3490 L X3666 3488 L X3669 3439 L X3671 3463 L X3673 3459 L X3678 3453 L X3680 3449 L X3682 3447 L X3685 3442 L X3689 3437 L X3692 3432 L X3696 3419 L X3699 3424 L X3700 3421 L X3703 3416 L X3708 3411 L X3710 3408 L X3715 3384 L X3717 3156 L X3719 2825 L X3722 3330 L X3726 3364 L X3729 3354 L X3730 3364 L X3733 3367 L X3738 3365 L X3740 3370 L X3745 3419 L X3747 3372 L X3749 3376 L X3752 3385 L X3756 3386 L X3759 3385 L X3760 3384 L X3763 3382 L X3766 3380 L X3767 3379 L X3770 3377 L X3775 3371 L X3777 3370 L X3779 3368 L X3782 3365 L X3786 3361 L X3789 3360 L X3793 3371 L X3796 3312 L X3797 3361 L X3800 3349 L X3804 3353 L X3807 3356 L X3809 3358 L X3812 3359 L X3816 3368 L X3819 3372 L X3823 3369 L X3826 3389 L X3827 3393 L X3830 3399 L X3834 3417 L X3837 3433 L X3842 3469 L X3844 3496 L X3846 3515 L X3849 3537 L X3853 3423 L X3856 3135 L X3857 2836 L X3860 2356 L X3864 2472 L X3867 3027 L X3871 3562 L X3874 3308 L X3876 3319 L X3879 3447 L X3883 3476 L X3886 3483 L X3887 3489 L X3890 3495 L X3893 3501 L X3894 3507 L X3897 3513 L X3901 3520 L X3904 3528 L X3906 3532 L X3908 3538 L X3913 3551 L X3916 3565 L X3920 3635 L X3923 3569 L X3924 3522 L X3927 3524 L X3931 3533 L X3934 3535 L X3936 3540 L X3938 3550 L X3943 3553 L X3946 3560 L X3950 3583 L X3953 3579 L X3954 3579 L X3957 3585 L X3961 3596 L X3964 3602 L X3968 3611 L X3971 3615 L X3973 3618 L X3975 3623 L X3980 3628 L X3983 3631 L X3984 3633 L X3987 3636 L X3991 3639 L X3994 3643 L X3998 3667 L X4001 3598 L X4003 3625 L X4005 3636 L X4010 3640 L X4012 3642 L X4014 3643 L X4017 3645 L X4021 3649 L X4024 3652 L X4028 3654 L X4031 3661 L X4033 3664 L X4035 3668 L X4040 3680 L X4042 3693 L X4047 3732 L X4050 3780 L X4051 3793 L X4054 3561 L X4058 3592 L X4061 3554 L X4063 3561 L X4065 3587 L X4070 3573 L X4072 3584 L X4077 3642 L X4079 3618 L X4081 3605 L X4084 3611 L X4088 3625 L X4091 3632 L X4093 3636 L X4095 3643 L X4098 3649 L X4100 3652 L X4102 3658 L X4107 3668 L X4109 3671 L X4111 3674 L X4114 3679 L X4118 3687 L X4121 3693 L X4125 3740 L X4128 3765 L X4130 3704 L X4132 3694 L X4137 3694 L X4139 3695 L X4141 3696 L X4144 3700 L X4148 3700 L X4151 3702 L X4155 3709 L X4158 3711 L X4160 3708 L X4162 3710 L X4167 3714 L X4169 3716 L X4174 3718 L X4176 3718 L X4178 3717 L X4181 3714 L X4185 3705 L X4188 3697 L X4190 3690 L X4192 3677 L X4197 3652 L X4199 3634 L X4204 3579 L X4206 3562 L X4208 3581 L X4211 3554 L X4215 3528 L X4218 3513 L X4219 3502 L X4222 3485 L X4227 3460 L X4229 3443 L X4234 3409 L X4236 3402 L X4238 3387 L X4241 3367 L X4245 3330 L X4248 3292 L X4252 3117 L X4255 3015 L X4256 3332 L X4259 3362 L X4264 3364 L X4266 3359 L X4268 3357 L X4271 3341 L X4275 3339 L X4278 3331 L X4282 3320 L X4285 3299 L X4286 3306 L X4289 3301 L X4294 3284 L X4296 3274 L X4301 3257 L X4303 3248 L X4305 3242 L X4308 3233 L X4312 3219 L X4315 3213 L X4316 3208 L X4319 3201 L X4323 3191 L X4326 3183 L X4331 3107 L X4333 3289 L X4335 3247 L X4338 3207 L X4342 3201 L X4345 3202 L X4346 3200 L X4349 3198 L X4353 3197 L X4356 3195 L X4361 3184 L X4363 3192 L X4365 3186 L X4368 3181 L X4372 3172 L X4375 3162 L X4379 3125 L X4382 3064 L X4383 2989 L X4386 2691 L X4390 2414 L X4393 3423 L X4395 3396 L X4398 3298 L X4402 3340 L X4405 3334 L X4409 3372 L X4412 3281 L X4413 3325 L X4416 3353 L X4420 3341 L X4423 3332 L X4425 3326 L X4427 3318 L X4430 3311 L X4432 3308 L X4435 3301 L X4439 3288 L X4442 3287 L X4443 3284 L X4446 3279 L X4450 3275 L X4453 3277 L X4457 3304 L X4460 3122 L X4462 3105 L X4465 3189 L X4469 3199 L X4472 3189 L X4473 3192 L X4476 3192 L X4480 3182 L X4483 3182 L X4487 3209 L X4490 3175 L X4492 3172 L X4494 3173 L X4499 3167 L X4502 3161 L X4506 3151 L X4509 3144 L X4510 3139 L X4513 3130 L X4517 3113 L X4520 3104 L X4522 3097 L X4524 3085 L X4529 3066 L X4531 3054 L X4536 3016 L X4539 3017 L X4540 3035 L X4543 3013 L X4547 2998 L X4550 2991 L X4552 2985 L X4554 2976 L X4559 2964 L X4561 2955 L X4566 2931 L X4569 2936 L X4570 2928 L X4573 2918 L Xcurrentpoint stroke moveto X4577 2905 L X4580 2897 L X4584 2870 L X4587 2748 L X4589 2231 L X4591 2524 L X4596 2351 L X4598 2795 L X4600 2825 L X4603 2817 L X4607 2814 L X4610 2822 L X4614 2927 L X4617 2806 L X4619 2824 L X4621 2847 L X4626 2841 L X4628 2832 L X4630 2827 L X4633 2817 L X4635 2808 L X4637 2802 L X4640 2791 L X4644 2767 L X4647 2759 L X4649 2752 L X4651 2738 L X4656 2720 L X4658 2715 L X4663 2786 L X4665 2136 L X4667 2337 L X4670 2529 L X4674 2531 L X4677 2501 L X4679 2498 L X4681 2479 L X4686 2443 L X4688 2425 L X4693 2447 L X4695 2347 L X4697 2348 L X4700 2330 L X4704 2277 L X4707 2240 L X4711 2181 L X4714 2154 L X4716 2142 L X4718 2140 L X4723 2210 L X4725 2303 L X4727 2387 L X4730 2562 L X4734 2904 L X4737 3132 L X4741 4093 L X4744 3214 L X4746 3288 L X4748 3503 L X4753 3605 L X4755 3633 L X4757 3652 L X4760 3666 L X4764 3684 L X4767 3686 L X4771 3662 L X4774 3683 L X4775 3682 L X4778 3673 L X4783 3670 L X4785 3669 L X4790 3559 L X4792 3289 L X4794 3213 L X4797 3389 L X4801 3440 L X4804 3422 L X4805 3439 L X4808 3458 L X4813 3448 L X4815 3460 L X4820 3566 L X4822 3476 L X4824 3475 L X4827 3489 L X4831 3492 L X4834 3490 L X4838 3484 L X4841 3479 L X4842 3476 L X4845 3469 L X4850 3457 L X4852 3452 L X4854 3447 L X4857 3440 L X4861 3430 L X4864 3425 L X4868 3415 L X4871 3350 L X4872 3406 L X4875 3400 L X4879 3399 L X4882 3398 L X4884 3398 L X4887 3396 L X4891 3398 L X4894 3398 L X4898 3390 L X4901 3403 L X4902 3405 L X4905 3406 L X4909 3417 L X4912 3427 L X4917 3451 L X4919 3444 L X4921 3388 L X4924 3137 L X4928 3172 L X4931 3151 L X4932 3177 L X4935 3233 L X4939 3200 L X4942 3229 L X4946 3417 L X4949 3298 L X4951 3278 L X4954 3305 L X4958 3332 L X4961 3343 L X4962 3349 L X4965 3359 L X4968 3365 L X4969 3370 L X4972 3377 L X4976 3386 L X4979 3389 L X4981 3393 L X4983 3398 L X4988 3407 L X4991 3416 L X4995 3510 L X4998 3411 L X4999 3356 L X5002 3374 L X5006 3375 L X5009 3373 L X5011 3374 L X5013 3378 L X5018 3374 L X5021 3375 L X5025 3390 L X5028 3380 L X5029 3376 L X5032 3377 L X5036 3378 L X5039 3377 L X5043 3375 L X5046 3372 L X5048 3369 L X5050 3364 L X5055 3352 L X5058 3344 L X5059 3338 L X5062 3328 L X5066 3309 L X5069 3297 L X5073 3263 L X5076 3244 L X5078 3262 L X5080 3246 L X5085 3230 L X5088 3221 L X5089 3215 L X5092 3205 L X5096 3191 L X5099 3181 L X5103 3160 L X5106 3159 L X5108 3151 L X5110 3139 L X5115 3121 L X5117 3103 L X5122 3020 L X5125 2703 L X5126 2782 L X5129 3082 L X5133 3104 L X5136 3094 L X5138 3099 L X5140 3093 L X5145 3090 L X5147 3089 L X5152 3117 L X5154 3074 L X5156 3080 L X5159 3083 L X5163 3076 L X5166 3070 L X5168 3066 L X5170 3059 L X5173 3053 L X5175 3049 L X5177 3043 L X5182 3031 L X5184 3026 L X5186 3022 L X5189 3016 L X5193 3006 L X5196 3000 L X5200 2977 L X5203 3008 L X5205 3025 L X5207 2996 L X5212 2995 L X5214 2998 L X5216 2997 L X5219 2996 L X5223 3001 L X5226 3002 L X5230 2993 L X5233 3012 L X5235 3012 L X5237 3015 L X5242 3025 L X5244 3035 L X5249 3054 L X5251 3061 L X5253 3059 L X5256 3013 L X5260 2520 L X5263 2066 L X5265 2080 L X5267 2593 L X5272 2265 L X5274 2606 L X5279 3213 L X5281 2954 L X5283 2981 L X5286 3103 L X5290 3121 L X5293 3122 L X5294 3124 L X5297 3125 L X5300 3126 L X5302 3128 L X5304 3130 L X5309 3129 L X5311 3134 L X5313 3137 L X5316 3139 L X5320 3148 L X5323 3160 L X5327 3235 L X5330 3112 L X5332 3054 L X5334 3082 L X5339 3093 L X5341 3090 L X5343 3094 L X5346 3103 L X5350 3101 L X5353 3106 L X5357 3137 L X5360 3120 L X5361 3118 L X5364 3123 L X5369 3130 L X5371 3133 L X5376 3137 L X5378 3139 L X5380 3140 L X5383 3140 L X5387 3139 L X5390 3139 L X5391 3138 L X5394 3136 L X5398 3132 L X5401 3131 L X5406 3149 L X5408 3061 L X5410 3098 L X5413 3104 L X5417 3103 L X5420 3101 L X5421 3100 L X5424 3098 L X5428 3097 L X5431 3096 L X5436 3090 L X5438 3097 L X5440 3099 L X5443 3101 L X5447 3110 L X5450 3124 L X5454 3171 L X5457 3221 L X5458 3181 L X5461 2758 L X5465 2759 L X5468 2860 L X5470 2884 L X5473 2922 L X5477 2890 L X5480 2909 L X5484 3029 L X5487 2953 L X5488 2934 L X5491 2950 L X5495 2965 L X5498 2971 L X5500 2974 L X5502 2979 L X5505 2982 L X5507 2985 L X5510 2988 L X5514 2992 L X5517 2993 L X5518 2995 L X5521 2996 L X5525 3001 L X5528 3007 L X5532 3096 L X5535 3029 L X5537 2925 L X5540 2948 L X5544 2941 L X5547 2932 L X5548 2930 L X5551 2930 L X5555 2913 L X5558 2909 L X5562 2923 L X5565 2897 L X5567 2886 L X5569 2881 L X5574 2868 L X5577 2856 L X5581 2832 L X5584 2812 L X5585 2798 L X5588 2771 L X5592 2712 L X5595 2672 L X5597 2643 L X5599 2593 L X5604 2506 L X5606 2448 L X5611 2197 L X5614 2412 L X5615 2392 L X5618 2309 L X5622 2252 L X5625 2227 L X5627 2207 L X5629 2181 L X5634 2143 L X5636 2120 L X5641 2093 L X5644 2068 L X5645 2050 L X5648 2031 L X5652 1987 L X5655 1942 L X5659 1851 L X5662 2232 L X5664 2448 L X5666 2246 L X5671 2202 L X5673 2214 L X5675 2198 L X5678 2170 L X5682 2176 L X5685 2159 L X5689 2052 L X5692 2118 L X5694 2123 L X5696 2105 L X5701 2086 L X5703 2079 L X5708 2070 L X5710 2066 L X5712 2064 L X5715 2062 L X5719 2063 L X5722 2062 L X5724 2063 L X5726 2064 L X5731 2066 L X5733 2064 L X5738 2006 L X5740 2226 L X5742 2131 L X5745 2109 L X5749 2102 L X5752 2103 L X5754 2101 L X5756 2100 L X5761 2093 L X5763 2090 L X5768 2089 L Xcurrentpoint stroke moveto X5770 2075 L X5772 2067 L X5775 2058 L X5779 2033 L X5782 2005 L X5786 1924 L X5789 1832 L X5791 1757 L X5793 1763 L X5798 1734 L X5800 2594 L X5802 2502 L X5805 2353 L X5809 2425 L X5812 2374 L X5816 2173 L X5819 2242 L X5821 2295 L X5823 2277 L X5828 2235 L X5830 2214 L X5832 2202 L X5835 2184 L X5837 2169 L X5839 2160 L X5842 2146 L X5846 2121 L X5849 2114 L X5850 2106 L X5853 2095 L X5858 2078 L X5860 2067 L X5865 1992 L X5867 1884 L X5869 1953 L X5872 2022 L X5876 2026 L X5879 2016 L X5880 2016 L X5883 2007 L X5888 1998 L X5890 1992 L X5895 1998 L X5897 1969 L X5899 1969 L X5902 1964 L X5906 1949 L X5909 1939 L X5913 1922 L X5916 1911 L X5917 1905 L X5920 1894 L X5925 1877 L X5927 1869 L X5929 1863 L X5932 1854 L X5936 1842 L X5939 1834 L X5943 1768 L X5946 1898 L X5947 1869 L X5950 1845 L X5955 1838 L X5957 1838 L X5959 1836 L X5962 1834 L X5966 1830 L X5969 1827 L X5973 1825 L X5976 1820 L X5977 1814 L X5980 1809 L X5984 1792 L X5987 1771 L X5992 1675 L X5994 1494 L X5996 1924 L X5999 1990 L X6003 1964 L X6006 1981 L X6007 1971 L X6010 1950 L X6014 1966 L X6017 1956 L X6021 1897 L X6024 1929 L X6026 1941 L X6029 1933 L X6033 1923 L X6036 1918 L X6037 1916 L X6040 1912 L X6043 1909 L X6044 1907 L X6047 1904 L X6051 1901 L X6054 1901 L X6056 1899 L X6059 1899 L X6063 1897 L X6066 1893 L X6070 1820 L X6073 2113 L X6074 2011 L X6077 1954 L X6081 1954 L X6084 1963 L X6086 1963 L X6088 1966 L X6093 1974 L X6096 1976 L X6100 1970 L X6103 1985 L X6104 1980 L X6107 1978 L X6111 1971 L X6114 1959 L X6118 1914 L X6121 1856 L X6123 1804 L X6125 1682 L X6130 1378 L X6133 1217 L X6134 1154 L X6137 1223 L X6141 1767 L X6144 2207 L X6148 2792 L X6151 2203 L X6153 2296 L X6155 2459 L X6160 2482 L X6163 2480 L X6164 2481 L X6167 2478 L X6171 2479 L X6174 2475 L X6178 2450 L X6181 2462 L X6183 2458 L X6185 2444 L X6190 2428 L X6192 2412 L X6197 2217 L X6200 2036 L X6201 2042 L X6204 2199 L X6208 2233 L X6211 2213 L X6213 2223 L X6215 2229 L X6220 2214 L X6222 2217 L X6227 2288 L X6229 2206 L X6231 2206 L X6234 2210 L X6238 2199 L X6241 2188 L X6245 2170 L X6248 2158 L X6250 2150 L X6252 2138 L X6257 2116 L X6259 2105 L X6261 2097 L X6264 2085 L X6268 2067 L X6271 2056 L X6275 2005 L X6278 2040 L X6280 2059 L X6282 2033 L X6287 2023 L X6289 2019 L X6291 2015 L X6294 2009 L X6298 2002 L X6301 1997 L X6305 1980 L X6308 1986 L X6310 1981 L X6312 1974 L X6317 1966 L X6319 1958 L X6324 1925 L X6326 1840 L X6328 1715 L X6331 1651 L X6335 1616 L X6338 1817 L X6340 1850 L X6342 1871 L X6347 1850 L X6349 1868 L X6354 2007 L X6356 1887 L X6358 1888 L X6361 1911 L X6365 1917 L X6368 1916 L X6369 1915 L X6372 1912 L X6375 1908 L X6377 1907 L X6379 1902 L X6384 1892 L X6386 1889 L X6388 1886 L X6391 1880 L X6395 1874 L X6398 1874 L X6402 1934 L X6405 1713 L X6407 1717 L X6409 1779 L X6414 1776 L X6416 1763 L X6418 1761 L X6421 1756 L X6425 1738 L X6428 1731 L X6432 1744 L X6435 1706 L X6436 1700 L X6439 1693 L X6444 1675 L X6446 1661 L X6451 1636 L X6453 1619 L X6455 1608 L X6458 1589 L X6462 1556 L X6465 1537 L X6466 1525 L X6469 1505 L X6473 1476 L X6476 1457 L X6481 1364 L X6483 1494 L X6485 1469 L X6488 1438 L X6492 1423 L X6495 1418 L X6496 1414 L X6499 1408 L X6503 1399 L X6506 1394 L X6511 1391 L X6513 1382 L X6515 1376 L X6518 1372 L X6522 1356 L X6525 1339 L X6529 1284 L X6532 1525 L X6533 1698 L X6536 1507 L X6540 1478 L X6543 1489 L X6545 1479 L X6548 1466 L X6552 1472 L X6555 1464 L X6559 1404 L X6562 1446 L X6563 1449 L X6566 1439 L X6570 1431 L X6573 1429 L X6575 1427 L X6577 1426 L X6580 1425 L X6582 1424 L X6585 1424 L X6589 1426 L X6592 1427 L X6593 1428 L X6596 1430 L X6600 1432 L X6603 1432 L X6607 1389 L X6610 1544 L X6612 1479 L X6615 1466 L X6619 1463 L X6622 1465 L X6623 1464 L X6626 1464 L X6630 1461 L X6633 1460 L X6637 1461 L X6640 1452 L X6642 1447 L X6644 1442 L X6649 1426 L X6652 1409 L X6656 1357 L X6659 1296 L X6660 1237 L X6663 1104 L X6667 1579 L X6670 2049 L X6672 1865 L X6674 1708 L X6679 1791 L X6681 1724 L X6686 1520 L X6689 1601 L X6690 1642 L X6693 1616 L X6697 1584 L X6700 1570 L X6702 1561 L X6704 1549 L X6707 1540 L X6709 1534 L X6711 1525 L X6716 1510 L X6719 1506 L X6720 1501 L X6723 1494 L X6727 1484 L X6730 1477 L X6734 1428 L X6737 1354 L X6739 1395 L X6741 1451 L X6746 1456 L X6748 1449 L X6750 1450 L X6753 1445 L X6757 1439 L X6760 1436 L X6764 1442 L X6767 1422 L X6769 1422 L X6771 1420 L X6776 1411 L X6778 1405 L X6783 1394 L X6786 1387 L X6787 1382 L X6790 1375 L X6794 1363 L X6797 1357 L X6799 1352 L X6801 1346 L X6806 1335 L X6808 1328 L X6813 1281 L X6815 1363 L X6817 1347 L X6820 1327 L X6824 1320 L X6827 1318 L X6829 1315 L X6831 1312 L X6836 1307 L X6838 1303 L X6843 1295 L X6845 1293 L X6847 1287 L X6850 1281 L X6854 1266 L X6857 1249 L X6861 1183 L X6864 1031 L X6866 799 L X6868 1409 L X6873 1373 L X6875 1403 L X6877 1399 L X6880 1372 L X6884 1393 L X6887 1385 L X6891 1360 L X6894 1351 L X6896 1371 L X6898 1372 L X6903 1361 L X6905 1354 L X6907 1350 L X6910 1343 L X6912 1338 L X6914 1334 L X6917 1328 L X6921 1316 L X6924 1313 L X6926 1309 L X6928 1303 L X6933 1293 L X6935 1287 L X6940 1255 L X6942 1049 L X6944 1229 L X6947 1269 L X6951 1278 L X6954 1278 L X6955 1279 L Xcurrentpoint stroke moveto X6958 1274 L X6963 1282 L X6965 1282 L Xstroke Xgrestore Xend Xshowpage X%%Trailer X%%Pages: 1 END_OF_FILE if test 28016 -ne `wc -c <'figure7.ps'`; then echo shar: \"'figure7.ps'\" unpacked with wrong size! fi # end of 'figure7.ps' fi if test -f 'figure8.ps' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'figure8.ps'\" else echo shar: Extracting \"'figure8.ps'\" \(14714 characters\) sed "s/^X//" >'figure8.ps' <<'END_OF_FILE' X%!PS-Adobe-2.0 X%%Creator: gnuplot X%%DocumentFonts: Courier X%%BoundingBox: 50 50 554 770 X%%Pages: (atend) X%%EndComments X/gnudict 40 dict def Xgnudict begin X/Color false def X/gnulinewidth 5.000 def X/vshift -46 def X/dl {10 mul} def X/hpt 15.5 def X/vpt 15.5 def X/vpt2 vpt 2 mul def X/hpt2 hpt 2 mul def X/vpt4 vpt 4 mul def X/hpt4 hpt 4 mul def X/vpt8 vpt 8 mul def X/hpt8 hpt 8 mul def X/Lshow { currentpoint stroke moveto X 0 vshift rmoveto show } def X/Rshow { currentpoint stroke moveto X dup stringwidth pop neg vshift rmoveto show } def X/Cshow { currentpoint stroke moveto X dup stringwidth pop -2 div vshift rmoveto show } def X/DL { Color {setrgbcolor [] 0 setdash pop} X {pop pop pop 0 setdash} ifelse } def X/BL { stroke gnulinewidth 2 mul setlinewidth } def X/AL { stroke gnulinewidth 2 div setlinewidth } def X/PL { stroke gnulinewidth setlinewidth } def X/LTb { BL [] 0 0 0 DL } def X/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def X/LT0 { PL [] 0 1 0 DL } def X/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def X/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def X/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def X/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def X/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def X/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def X/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def X/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def X/M {moveto} def X/L {lineto} def X/P { stroke [] 0 setdash X currentlinewidth 2 div sub moveto X 0 currentlinewidth rlineto stroke } def X/D { stroke [] 0 setdash 2 copy vpt add moveto X hpt neg vpt neg rlineto hpt vpt neg rlineto X hpt vpt rlineto hpt neg vpt rlineto closepath stroke X P } def X/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add moveto X 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto X hpt2 neg 0 rlineto closepath stroke X P } def X/C { stroke [] 0 setdash exch hpt sub exch vpt add moveto X hpt2 vpt2 neg rlineto currentpoint stroke moveto X hpt2 neg 0 rmoveto hpt2 vpt2 rlineto stroke } def X/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add moveto X hpt neg vpt -1.62 mul rlineto X hpt 2 mul 0 rlineto X hpt neg vpt 1.62 mul rlineto closepath stroke X P } def X/D2 { stroke [] 0 setdash 2 copy vpt2 add moveto X hpt2 neg vpt2 neg rlineto hpt2 vpt2 neg rlineto X hpt2 vpt2 rlineto hpt2 neg vpt2 rlineto closepath stroke X P } def X/B2 { stroke [] 0 setdash 2 copy exch hpt4 sub exch vpt4 add moveto X 0 vpt8 neg rlineto hpt8 0 rlineto 0 vpt8 rlineto X hpt8 neg 0 rlineto closepath stroke X P } def X/C2 { stroke [] 0 setdash exch hpt2 sub exch vpt2 add moveto X hpt4 vpt4 neg rlineto currentpoint stroke moveto X hpt4 neg 0 rmoveto hpt4 vpt4 rlineto stroke } def Xend X%%EndProlog X%%Page: 1 1 Xgnudict begin Xgsave X50 50 translate X0.100 0.100 scale X90 rotate X0 -5040 translate X0 setgray X/Courier findfont 140 scalefont setfont Xnewpath XLTa X1008 2590 M X6969 2590 L X3989 491 M X3989 4689 L XLTb X1008 491 M X1071 491 L X6969 491 M X6906 491 L X924 491 M X(-1) Rshow X1008 911 M X1071 911 L X6969 911 M X6906 911 L X924 911 M X(-0.8) Rshow X1008 1331 M X1071 1331 L X6969 1331 M X6906 1331 L X924 1331 M X(-0.6) Rshow X1008 1750 M X1071 1750 L X6969 1750 M X6906 1750 L X924 1750 M X(-0.4) Rshow X1008 2170 M X1071 2170 L X6969 2170 M X6906 2170 L X924 2170 M X(-0.2) Rshow X1008 2590 M X1071 2590 L X6969 2590 M X6906 2590 L X924 2590 M X(0) Rshow X1008 3010 M X1071 3010 L X6969 3010 M X6906 3010 L X924 3010 M X(0.2) Rshow X1008 3430 M X1071 3430 L X6969 3430 M X6906 3430 L X924 3430 M X(0.4) Rshow X1008 3849 M X1071 3849 L X6969 3849 M X6906 3849 L X924 3849 M X(0.6) Rshow X1008 4269 M X1071 4269 L X6969 4269 M X6906 4269 L X924 4269 M X(0.8) Rshow X1008 4689 M X1071 4689 L X6969 4689 M X6906 4689 L X924 4689 M X(1) Rshow X1008 491 M X1008 554 L X1008 4689 M X1008 4626 L X1008 351 M X(-1) Cshow X1604 491 M X1604 554 L X1604 4689 M X1604 4626 L X1604 351 M X(-0.8) Cshow X2200 491 M X2200 554 L X2200 4689 M X2200 4626 L X2200 351 M X(-0.6) Cshow X2796 491 M X2796 554 L X2796 4689 M X2796 4626 L X2796 351 M X(-0.4) Cshow X3392 491 M X3392 554 L X3392 4689 M X3392 4626 L X3392 351 M X(-0.2) Cshow X3989 491 M X3989 554 L X3989 4689 M X3989 4626 L X3989 351 M X(0) Cshow X4585 491 M X4585 554 L X4585 4689 M X4585 4626 L X4585 351 M X(0.2) Cshow X5181 491 M X5181 554 L X5181 4689 M X5181 4626 L X5181 351 M X(0.4) Cshow X5777 491 M X5777 554 L X5777 4689 M X5777 4626 L X5777 351 M X(0.6) Cshow X6373 491 M X6373 554 L X6373 4689 M X6373 4626 L X6373 351 M X(0.8) Cshow X6969 491 M X6969 554 L X6969 4689 M X6969 4626 L X6969 351 M X(1) Cshow XLTb X1008 491 M X6969 491 L X6969 4689 L X1008 4689 L X1008 491 L X140 2590 M Xcurrentpoint gsave translate 90 rotate 0 0 moveto X(Im epsilon) Cshow Xgrestore X3988 211 M X(Real epsilon) Cshow X4088 1 M X(Figure 8) Cshow XLT0 XLT0 X6486 4486 M X(Set 1) Rshow X6654 4486 T X1917 1729 T X1917 1981 T X1917 3209 T X1917 3461 T X1932 1666 T X1932 2044 T X1932 3146 T X1932 3524 T X1947 1624 T X1947 2086 T X1947 3104 T X1947 3566 T X1962 1593 T X1962 2118 T X1962 3073 T X1962 3598 T X1977 1561 T X1977 2149 T X1977 3041 T X1977 3629 T X1992 1541 T X1992 2170 T X1992 3020 T X1992 3650 T X2006 1509 T X2006 2202 T X2006 2989 T X2006 3681 T X2021 1488 T X2021 2223 T X2021 2968 T X2021 3702 T X2036 1467 T X2036 2244 T X2036 2947 T X2036 3723 T X2051 1446 T X2051 2265 T X2051 2926 T X2051 3744 T X2066 1436 T X2066 2286 T X2066 2905 T X2066 3755 T X2081 1415 T X2081 2296 T X2081 2894 T X2081 3776 T X2096 1404 T X2096 2317 T X2096 2873 T X2096 3786 T X2111 1383 T X2111 2328 T X2111 2863 T X2111 3807 T X2126 1373 T X2126 2349 T X2126 2842 T X2126 3818 T X2141 1352 T X2141 2359 T X2141 2831 T X2141 3839 T X2155 1341 T X2155 2370 T X2155 2821 T X2155 3849 T X2170 1331 T X2170 2391 T X2170 2800 T X2170 3860 T X2185 1320 T X2185 2401 T X2185 2789 T X2185 3870 T X2200 1310 T X2200 2412 T X2200 2779 T X2200 3881 T X2215 1289 T X2215 2422 T X2215 2768 T X2215 3902 T X2230 1278 T X2230 2433 T X2230 2758 T X2230 3912 T X2245 1268 T X2245 2443 T X2245 2747 T X2245 3923 T X2260 1257 T X2260 2454 T X2260 2737 T X2260 3933 T X2275 1247 T X2275 2464 T X2275 2726 T X2275 3944 T X2290 1247 T X2290 2475 T X2290 2716 T X2290 3944 T X2305 1236 T X2305 2485 T X2305 2705 T X2305 3954 T X2319 1226 T X2319 2496 T X2319 2695 T X2319 3965 T X2334 1215 T X2334 2496 T X2334 2695 T X2334 3975 T X2349 1205 T X2349 2506 T X2349 2684 T X2349 3986 T X2364 1205 T X2364 2517 T X2364 2674 T X2364 3986 T X2379 1194 T X2379 2527 T X2379 2663 T X2379 3996 T X2394 1184 T X2394 2527 T X2394 2663 T X2394 4007 T X2409 1173 T X2409 2538 T X2409 2653 T X2409 4017 T X2424 1173 T X2424 2538 T X2424 2653 T X2424 4017 T X2439 1163 T X2439 2548 T X2439 2642 T X2439 4028 T X2454 1152 T X2454 2559 T X2454 2632 T X2454 4038 T X2468 1152 T X2468 2559 T X2468 2632 T X2468 4038 T X2483 1142 T X2483 2569 T X2483 2621 T X2483 4049 T X2498 1142 T X2498 2569 T X2498 2621 T X2498 4049 T X2513 1131 T X2513 2580 T X2513 2611 T X2513 4059 T X2528 1131 T X2528 2580 T X2528 2611 T X2528 4059 T X2543 1121 T X2543 2580 T X2543 2611 T X2543 4070 T X2558 1121 T X2558 2590 T X2558 2600 T X2558 4070 T X2573 1110 T X2573 2590 T X2573 2600 T X2573 4080 T X2588 1110 T X2588 2590 T X2588 2600 T X2588 4080 T X2603 1100 T X2603 2590 T X2603 2600 T X2603 4091 T X2617 1100 T X2617 2590 T X2617 2600 T X2617 4091 T X2632 1100 T X2632 4091 T X2647 1089 T X2647 4101 T X2662 1089 T X2662 4101 T X2677 1089 T X2677 4101 T X2692 1079 T X2692 4112 T X2707 1079 T X2707 4112 T X2722 1079 T X2722 4112 T X2737 1068 T X2737 4122 T X2752 1068 T X2752 4122 T X2766 1068 T X2766 4122 T X2781 1068 T X2781 4122 T X2796 1068 T X2796 4122 T X2811 1058 T X2811 4133 T X2826 1058 T X2826 4133 T X2841 1058 T X2841 4133 T X2856 1058 T X2856 4133 T X2871 1058 T X2871 4133 T X2886 1058 T X2886 4133 T X2901 1047 T X2901 4143 T X2916 1047 T X2916 4143 T X2930 1047 T X2930 4143 T X2945 1047 T X2945 4143 T X2960 1047 T X2960 4143 T X2975 1047 T X2975 4143 T X2990 1047 T X2990 4143 T X3005 1047 T X3005 4143 T X3020 1047 T X3020 4143 T X3035 1047 T X3035 4143 T X3050 1047 T X3050 4143 T X3065 1047 T X3065 4143 T X3079 1047 T X3079 4143 T X3094 1047 T X3094 4143 T X3109 1047 T X3109 4143 T X3124 1058 T X3124 4133 T X3139 1058 T X3139 4133 T X3154 1058 T X3154 4133 T X3169 1058 T X3169 4133 T X3184 1058 T X3184 4133 T X3199 1058 T X3199 4133 T X3214 1058 T X3214 4133 T X3228 1068 T X3228 4122 T X3243 1068 T X3243 4122 T X3258 1068 T X3258 4122 T X3273 1068 T X3273 4122 T X3288 1079 T X3288 4112 T X3303 1079 T X3303 4112 T X3318 1079 T X3318 4112 T X3333 1089 T X3333 4101 T X3348 1089 T X3348 4101 T X3363 1089 T X3363 4101 T X3377 1100 T X3377 4091 T X3392 1100 T X3392 4091 T X3407 1100 T X3407 4091 T X3422 1110 T X3422 4080 T X3437 1110 T X3437 4080 T X3452 1121 T X3452 4070 T X3467 1121 T X3467 4070 T X3482 1131 T X3482 4059 T X3497 1131 T X3497 4059 T X3512 1142 T X3512 4049 T X3527 1152 T X3527 4038 T X3541 1152 T X3541 4038 T X3556 1163 T X3556 4028 T X3571 1163 T X3571 4028 T X3586 1173 T X3586 4017 T X3601 1184 T X3601 4007 T X3616 1184 T X3616 4007 T X3631 1194 T X3631 3996 T X3646 1205 T X3646 3986 T X3661 1215 T X3661 3975 T X3676 1226 T X3676 3965 T X3690 1236 T X3690 3954 T X3705 1247 T X3705 3944 T X3720 1257 T X3720 3933 T X3735 1268 T X3735 3923 T X3750 1278 T X3750 3912 T X3765 1289 T X3765 3902 T X3780 1299 T X3780 3891 T X3795 1310 T X3795 3881 T X3810 1320 T X3810 3870 T X3825 1341 T X3825 3849 T X3839 1352 T X3839 3839 T X3854 1373 T X3854 3818 T X3869 1383 T X3869 3807 T X3884 1404 T X3884 3786 T X3899 1425 T X3899 3765 T X3914 1446 T X3914 3744 T X3929 1467 T X3929 3723 T X3944 1499 T X3944 3692 T X3959 1530 T X3959 3660 T X3974 1572 T X3974 3619 T X3989 1645 T X3989 3545 T X4003 1572 T X4003 3619 T X4018 1530 T X4018 3660 T X4033 1499 T X4033 3692 T X4048 1467 T X4048 3723 T X4063 1446 T X4063 3744 T X4078 1425 T X4078 3765 T X4093 1404 T X4093 3786 T X4108 1383 T X4108 3807 T X4123 1373 T X4123 3818 T X4138 1352 T X4138 3839 T X4152 1341 T X4152 3849 T X4167 1320 T X4167 3870 T X4182 1310 T X4182 3881 T X4197 1299 T X4197 3891 T X4212 1289 T X4212 3902 T X4227 1278 T X4227 3912 T X4242 1268 T X4242 3923 T X4257 1257 T X4257 3933 T X4272 1247 T X4272 3944 T X4287 1236 T X4287 3954 T X4301 1226 T X4301 3965 T X4316 1215 T X4316 3975 T X4331 1205 T X4331 3986 T X4346 1194 T X4346 3996 T X4361 1184 T X4361 4007 T X4376 1184 T X4376 4007 T X4391 1173 T X4391 4017 T X4406 1163 T X4406 4028 T X4421 1163 T X4421 4028 T X4436 1152 T X4436 4038 T X4450 1152 T X4450 4038 T X4465 1142 T X4465 4049 T X4480 1131 T X4480 4059 T X4495 1131 T X4495 4059 T X4510 1121 T X4510 4070 T X4525 1121 T X4525 4070 T X4540 1110 T X4540 4080 T X4555 1110 T X4555 4080 T X4570 1100 T X4570 4091 T X4585 1100 T X4585 4091 T X4600 1100 T X4600 4091 T X4614 1089 T X4614 4101 T X4629 1089 T X4629 4101 T X4644 1089 T X4644 4101 T X4659 1079 T X4659 4112 T X4674 1079 T X4674 4112 T X4689 1079 T X4689 4112 T X4704 1068 T X4704 4122 T X4719 1068 T X4719 4122 T X4734 1068 T X4734 4122 T X4749 1068 T X4749 4122 T X4763 1058 T X4763 4133 T X4778 1058 T X4778 4133 T X4793 1058 T X4793 4133 T X4808 1058 T X4808 4133 T X4823 1058 T X4823 4133 T X4838 1058 T X4838 4133 T X4853 1058 T X4853 4133 T X4868 1047 T X4868 4143 T X4883 1047 T X4883 4143 T X4898 1047 T X4898 4143 T X4912 1047 T X4912 4143 T X4927 1047 T X4927 4143 T X4942 1047 T X4942 4143 T X4957 1047 T X4957 4143 T X4972 1047 T X4972 4143 T X4987 1047 T X4987 4143 T X5002 1047 T X5002 4143 T X5017 1047 T X5017 4143 T X5032 1047 T X5032 4143 T X5047 1047 T X5047 4143 T X5061 1047 T X5061 4143 T X5076 1047 T X5076 4143 T X5091 1058 T X5091 4133 T X5106 1058 T X5106 4133 T X5121 1058 T X5121 4133 T X5136 1058 T X5136 4133 T X5151 1058 T X5151 4133 T X5166 1058 T X5166 4133 T X5181 1068 T X5181 4122 T X5196 1068 T X5196 4122 T X5211 1068 T X5211 4122 T X5225 1068 T X5225 4122 T X5240 1068 T X5240 4122 T X5255 1079 T X5255 4112 T X5270 1079 T X5270 4112 T X5285 1079 T X5285 4112 T X5300 1089 T X5300 4101 T X5315 1089 T X5315 4101 T X5330 1089 T X5330 4101 T X5345 1100 T X5345 4091 T X5360 1100 T X5360 2590 T X5360 2600 T X5360 4091 T X5374 1100 T X5374 2590 T X5374 2600 T X5374 4091 T X5389 1110 T X5389 2590 T X5389 2600 T X5389 4080 T X5404 1110 T X5404 2590 T X5404 2600 T X5404 4080 T X5419 1121 T X5419 2590 T X5419 2600 T X5419 4070 T X5434 1121 T X5434 2580 T X5434 2611 T X5434 4070 T X5449 1131 T X5449 2580 T X5449 2611 T X5449 4059 T X5464 1131 T X5464 2580 T X5464 2611 T X5464 4059 T X5479 1142 T X5479 2569 T X5479 2621 T X5479 4049 T X5494 1142 T X5494 2569 T X5494 2621 T X5494 4049 T X5509 1152 T X5509 2559 T X5509 2632 T X5509 4038 T X5523 1152 T X5523 2559 T X5523 2632 T X5523 4038 T X5538 1163 T X5538 2548 T X5538 2642 T X5538 4028 T X5553 1173 T X5553 2538 T X5553 2653 T X5553 4017 T X5568 1173 T X5568 2538 T X5568 2653 T X5568 4017 T X5583 1184 T X5583 2527 T X5583 2663 T X5583 4007 T X5598 1194 T X5598 2527 T X5598 2663 T X5598 3996 T X5613 1205 T X5613 2517 T X5613 2674 T X5613 3986 T X5628 1205 T X5628 2506 T X5628 2684 T X5628 3986 T X5643 1215 T X5643 2496 T X5643 2695 T X5643 3975 T X5658 1226 T X5658 2496 T X5658 2695 T X5658 3965 T X5672 1236 T X5672 2485 T X5672 2705 T X5672 3954 T X5687 1247 T X5687 2475 T X5687 2716 T X5687 3944 T X5702 1247 T X5702 2464 T X5702 2726 T X5702 3944 T X5717 1257 T X5717 2454 T X5717 2737 T X5717 3933 T X5732 1268 T X5732 2443 T X5732 2747 T X5732 3923 T X5747 1278 T X5747 2433 T X5747 2758 T X5747 3912 T X5762 1289 T X5762 2422 T X5762 2768 T X5762 3902 T X5777 1310 T X5777 2412 T X5777 2779 T X5777 3881 T X5792 1320 T X5792 2401 T X5792 2789 T X5792 3870 T X5807 1331 T X5807 2391 T X5807 2800 T X5807 3860 T X5822 1341 T X5822 2370 T X5822 2821 T X5822 3849 T X5836 1352 T X5836 2359 T X5836 2831 T X5836 3839 T X5851 1373 T X5851 2349 T X5851 2842 T X5851 3818 T X5866 1383 T X5866 2328 T X5866 2863 T X5866 3807 T X5881 1404 T X5881 2317 T X5881 2873 T X5881 3786 T X5896 1415 T X5896 2296 T X5896 2894 T X5896 3776 T X5911 1436 T X5911 2286 T X5911 2905 T X5911 3755 T X5926 1446 T X5926 2265 T X5926 2926 T X5926 3744 T X5941 1467 T X5941 2244 T X5941 2947 T X5941 3723 T X5956 1488 T X5956 2223 T X5956 2968 T X5956 3702 T X5971 1509 T X5971 2202 T X5971 2989 T X5971 3681 T X5985 1541 T X5985 2170 T X5985 3020 T X5985 3650 T X6000 1561 T X6000 2149 T X6000 3041 T X6000 3629 T X6015 1593 T X6015 2118 T X6015 3073 T X6015 3598 T X6030 1624 T X6030 2086 T X6030 3104 T X6030 3566 T X6045 1666 T X6045 2044 T X6045 3146 T X6045 3524 T X6060 1729 T X6060 1981 T X6060 3209 T X6060 3461 T XLT0 X6486 4346 M X(Set 2) Rshow X6654 4346 B2 X3988 3539 B2 X3988 1641 B2 X2624 2590 B2 X5353 2590 B2 XLT0 X6486 4206 M X(Set 3) Rshow X6654 4206 C2 X3989 3545 C2 X3989 1619 C2 X3989 3561 C2 X3989 1590 C2 X3989 3590 C2 X3989 3635 C2 X3989 3699 C2 X3989 1481 C2 X3989 1481 C2 X3990 3793 C2 X3990 1387 C2 X3991 3932 C2 X3991 1248 C2 X3994 4155 C2 X3994 1025 C2 X4004 607 C2 X4004 4573 C2 X5361 2590 C2 X2616 2590 C2 X5385 2590 C2 X2591 2590 C2 X2591 2590 C2 X5428 2590 C2 X5428 2590 C2 X2477 2590 C2 X5590 2590 C2 X2376 2590 C2 X5731 2590 C2 X2226 2590 C2 X5946 2590 C2 X1996 2590 C2 X6302 2590 C2 X1600 2590 C2 X3989 3545 C2 X3990 1618 C2 X3995 1539 C2 X3995 3641 C2 X4001 3958 C2 X4009 3813 C2 X4020 1373 C2 X4025 3971 C2 X4025 1209 C2 X4025 3971 C2 X4025 3971 C2 X4025 3971 C2 X4058 941 C2 X4058 4239 C2 X3906 3985 C2 X3795 4010 C2 X2616 2590 C2 X2371 2590 C2 X5766 2590 C2 X1980 2590 C2 X6296 2337 C2 X6394 2635 C2 X1566 2590 C2 X1566 2590 C2 X6434 3562 C2 X6464 2590 C2 X6464 2590 C2 X6464 2590 C2 X1471 1385 C2 X1433 3545 C2 X6548 1489 C2 X1065 1493 C2 Xstroke Xgrestore Xend Xshowpage X%%Trailer X%%Pages: 1 END_OF_FILE if test 14714 -ne `wc -c <'figure8.ps'`; then echo shar: \"'figure8.ps'\" unpacked with wrong size! fi # end of 'figure8.ps' fi if test -f 'figure9.ps' -a "${1}" != "-c" ; then echo shar: Will not clobber existing file \"'figure9.ps'\" else echo shar: Extracting \"'figure9.ps'\" \(15975 characters\) sed "s/^X//" >'figure9.ps' <<'END_OF_FILE' X%!PS-Adobe-2.0 X%%Creator: gnuplot X%%DocumentFonts: Courier X%%BoundingBox: 50 50 554 770 X%%Pages: (atend) X%%EndComments X/gnudict 40 dict def Xgnudict begin X/Color false def X/gnulinewidth 5.000 def X/vshift -46 def X/dl {10 mul} def X/hpt 15.5 def X/vpt 15.5 def X/vpt2 vpt 2 mul def X/hpt2 hpt 2 mul def X/vpt4 vpt 4 mul def X/hpt4 hpt 4 mul def X/vpt8 vpt 8 mul def X/hpt8 hpt 8 mul def X/Lshow { currentpoint stroke moveto X 0 vshift rmoveto show } def X/Rshow { currentpoint stroke moveto X dup stringwidth pop neg vshift rmoveto show } def X/Cshow { currentpoint stroke moveto X dup stringwidth pop -2 div vshift rmoveto show } def X/DL { Color {setrgbcolor [] 0 setdash pop} X {pop pop pop 0 setdash} ifelse } def X/BL { stroke gnulinewidth 2 mul setlinewidth } def X/AL { stroke gnulinewidth 2 div setlinewidth } def X/PL { stroke gnulinewidth setlinewidth } def X/LTb { BL [] 0 0 0 DL } def X/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def X/LT0 { PL [] 0 1 0 DL } def X/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def X/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def X/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def X/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def X/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def X/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def X/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def X/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def X/M {moveto} def X/L {lineto} def X/P { stroke [] 0 setdash X currentlinewidth 2 div sub moveto X 0 currentlinewidth rlineto stroke } def X/D { stroke [] 0 setdash 2 copy vpt add moveto X hpt neg vpt neg rlineto hpt vpt neg rlineto X hpt vpt rlineto hpt neg vpt rlineto closepath stroke X P } def X/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add moveto X 0 vpt2 neg rlineto hpt2 0 rlineto 0 vpt2 rlineto X hpt2 neg 0 rlineto closepath stroke X P } def X/C { stroke [] 0 setdash exch hpt sub exch vpt add moveto X hpt2 vpt2 neg rlineto currentpoint stroke moveto X hpt2 neg 0 rmoveto hpt2 vpt2 rlineto stroke } def X/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add moveto X hpt neg vpt -1.62 mul rlineto X hpt 2 mul 0 rlineto X hpt neg vpt 1.62 mul rlineto closepath stroke X P } def X/D2 { stroke [] 0 setdash 2 copy vpt2 add moveto X hpt2 neg vpt2 neg rlineto hpt2 vpt2 neg rlineto X hpt2 vpt2 rlineto hpt2 neg vpt2 rlineto closepath stroke X P } def X/B2 { stroke [] 0 setdash 2 copy exch hpt4 sub exch vpt4 add moveto X 0 vpt8 neg rlineto hpt8 0 rlineto 0 vpt8 rlineto X hpt8 neg 0 rlineto closepath stroke X P } def X/C2 { stroke [] 0 setdash exch hpt2 sub exch vpt2 add moveto X hpt4 vpt4 neg rlineto currentpoint stroke moveto X hpt4 neg 0 rmoveto hpt4 vpt4 rlineto stroke } def Xend X%%EndProlog X%%Page: 1 1 Xgnudict begin Xgsave X50 50 translate X0.100 0.100 scale X90 rotate X0 -5040 translate X0 setgray X/Courier findfont 140 scalefont setfont Xnewpath XLTa X1008 2590 M X6969 2590 L X3989 491 M X3989 4689 L XLTb X1008 975 M X1071 975 L X6969 975 M X6906 975 L X924 975 M X(-1) Rshow X1008 1783 M X1071 1783 L X6969 1783 M X6906 1783 L X924 1783 M X(-0.5) Rshow X1008 2590 M X1071 2590 L X6969 2590 M X6906 2590 L X924 2590 M X(0) Rshow X1008 3397 M X1071 3397 L X6969 3397 M X6906 3397 L X924 3397 M X(0.5) Rshow X1008 4205 M X1071 4205 L X6969 4205 M X6906 4205 L X924 4205 M X(1) Rshow X1696 491 M X1696 554 L X1696 4689 M X1696 4626 L X1696 351 M X(-1) Cshow X2842 491 M X2842 554 L X2842 4689 M X2842 4626 L X2842 351 M X(-0.5) Cshow X3989 491 M X3989 554 L X3989 4689 M X3989 4626 L X3989 351 M X(0) Cshow X5135 491 M X5135 554 L X5135 4689 M X5135 4626 L X5135 351 M X(0.5) Cshow X6281 491 M X6281 554 L X6281 4689 M X6281 4626 L X6281 351 M X(1) Cshow XLTb X1008 491 M X6969 491 L X6969 4689 L X1008 4689 L X1008 491 L X140 2590 M Xcurrentpoint gsave translate 90 rotate 0 0 moveto X(Im epsilon) Cshow Xgrestore X3988 211 M X(Real epsilon) Cshow X4088 1 M X(Figure 9) Cshow XLT0 XLT0 X6486 4486 M X(Set 1) Rshow X6654 4486 T X2200 2065 T X2200 2170 T X2200 3018 T X2200 3123 T X2212 2009 T X2212 2227 T X2212 2961 T X2212 3179 T X2223 1976 T X2223 2259 T X2223 2929 T X2223 3212 T X2235 1944 T X2235 2283 T X2235 2905 T X2235 3244 T X2246 1928 T X2246 2307 T X2246 2881 T X2246 3260 T X2258 1904 T X2258 2332 T X2258 2856 T X2258 3284 T X2269 1888 T X2269 2348 T X2269 2840 T X2269 3300 T X2280 1871 T X2280 2364 T X2280 2824 T X2280 3317 T X2292 1855 T X2292 2380 T X2292 2808 T X2292 3333 T X2303 1839 T X2303 2396 T X2303 2792 T X2303 3349 T X2315 1823 T X2315 2404 T X2315 2784 T X2315 3365 T X2326 1815 T X2326 2420 T X2326 2768 T X2326 3373 T X2338 1799 T X2338 2429 T X2338 2760 T X2338 3389 T X2349 1791 T X2349 2445 T X2349 2743 T X2349 3397 T X2361 1783 T X2361 2453 T X2361 2735 T X2361 3405 T X2372 1767 T X2372 2461 T X2372 2727 T X2372 3422 T X2384 1758 T X2384 2469 T X2384 2719 T X2384 3430 T X2395 1750 T X2395 2485 T X2395 2703 T X2395 3438 T X2407 1742 T X2407 2493 T X2407 2695 T X2407 3446 T X2418 1734 T X2418 2501 T X2418 2687 T X2418 3454 T X2429 1726 T X2429 2509 T X2429 2679 T X2429 3462 T X2441 1718 T X2441 2509 T X2441 2679 T X2441 3470 T X2452 1710 T X2452 2517 T X2452 2671 T X2452 3478 T X2464 1702 T X2464 2525 T X2464 2663 T X2464 3486 T X2475 1694 T X2475 2533 T X2475 2655 T X2475 3494 T X2487 1694 T X2487 2542 T X2487 2647 T X2487 3494 T X2498 1686 T X2498 2542 T X2498 2647 T X2498 3502 T X2510 1678 T X2510 2550 T X2510 2638 T X2510 3510 T X2521 1670 T X2521 2558 T X2521 2630 T X2521 3518 T X2533 1670 T X2533 2558 T X2533 2630 T X2533 3518 T X2544 1662 T X2544 2566 T X2544 2622 T X2544 3526 T X2556 1654 T X2556 2566 T X2556 2622 T X2556 3535 T X2567 1654 T X2567 2574 T X2567 2614 T X2567 3535 T X2578 1645 T X2578 2574 T X2578 2614 T X2578 3543 T X2590 1645 T X2590 2582 T X2590 2606 T X2590 3543 T X2601 1637 T X2601 2582 T X2601 2606 T X2601 3551 T X2613 1637 T X2613 2590 T X2613 2598 T X2613 3551 T X2624 1629 T X2624 2590 T X2624 2598 T X2624 3559 T X2636 1629 T X2636 2590 T X2636 2598 T X2636 3559 T X2647 1621 T X2647 2590 T X2647 2598 T X2647 3567 T X2659 1621 T X2659 2590 T X2659 2598 T X2659 3567 T X2670 1613 T X2670 3575 T X2682 1613 T X2682 3575 T X2693 1613 T X2693 3575 T X2705 1605 T X2705 3583 T X2716 1605 T X2716 3583 T X2728 1605 T X2728 3583 T X2739 1597 T X2739 3591 T X2750 1597 T X2750 3591 T X2762 1597 T X2762 3591 T X2773 1589 T X2773 3599 T X2785 1589 T X2785 3599 T X2796 1589 T X2796 3599 T X2808 1589 T X2808 3599 T X2819 1589 T X2819 3599 T X2831 1581 T X2831 3607 T X2842 1581 T X2842 3607 T X2854 1581 T X2854 3607 T X2865 1581 T X2865 3607 T X2877 1581 T X2877 3607 T X2888 1581 T X2888 3607 T X2899 1581 T X2899 3607 T X2911 1581 T X2911 3607 T X2922 1581 T X2922 3607 T X2934 1581 T X2934 3607 T X2945 1242 T X2945 1290 T X2945 1581 T X2945 3607 T X2945 3898 T X2945 3946 T X2957 1210 T X2957 1323 T X2957 1581 T X2957 3607 T X2957 3866 T X2957 3979 T X2968 1193 T X2968 1347 T X2968 1581 T X2968 3607 T X2968 3841 T X2968 3995 T X2980 1177 T X2980 1363 T X2980 1581 T X2980 3607 T X2980 3825 T X2980 4011 T X2991 1169 T X2991 1379 T X2991 1581 T X2991 3607 T X2991 3809 T X2991 4019 T X3003 1153 T X3003 1387 T X3003 1581 T X3003 3607 T X3003 3801 T X3003 4035 T X3014 1145 T X3014 1395 T X3014 1581 T X3014 3607 T X3014 3793 T X3014 4043 T X3026 1145 T X3026 1411 T X3026 1581 T X3026 3607 T X3026 3777 T X3026 4043 T X3037 1137 T X3037 1419 T X3037 1581 T X3037 3607 T X3037 3769 T X3037 4051 T X3048 1129 T X3048 1427 T X3048 1581 T X3048 3607 T X3048 3761 T X3048 4059 T X3060 1129 T X3060 1436 T X3060 1581 T X3060 3607 T X3060 3753 T X3060 4059 T X3071 1121 T X3071 1444 T X3071 1589 T X3071 3599 T X3071 3744 T X3071 4067 T X3083 1121 T X3083 1452 T X3083 1589 T X3083 3599 T X3083 3736 T X3083 4067 T X3094 1121 T X3094 1452 T X3094 1589 T X3094 3599 T X3094 3736 T X3094 4067 T X3106 1121 T X3106 1460 T X3106 1589 T X3106 3599 T X3106 3728 T X3106 4067 T X3117 1121 T X3117 1468 T X3117 1589 T X3117 3599 T X3117 3720 T X3117 4067 T X3129 1113 T X3129 1476 T X3129 1597 T X3129 3591 T X3129 3712 T X3129 4075 T X3140 1121 T X3140 1484 T X3140 1597 T X3140 3591 T X3140 3704 T X3140 4067 T X3152 1121 T X3152 1484 T X3152 1597 T X3152 3591 T X3152 3704 T X3152 4067 T X3163 1121 T X3163 1492 T X3163 1605 T X3163 3583 T X3163 3696 T X3163 4067 T X3175 1121 T X3175 1500 T X3175 1605 T X3175 3583 T X3175 3688 T X3175 4067 T X3186 1121 T X3186 1508 T X3186 1605 T X3186 3583 T X3186 3680 T X3186 4067 T X3198 1129 T X3198 1508 T X3198 1613 T X3198 3575 T X3198 3680 T X3198 4059 T X3209 1137 T X3209 1516 T X3209 1613 T X3209 3575 T X3209 3672 T X3209 4051 T X3220 1137 T X3220 1524 T X3220 1613 T X3220 3575 T X3220 3664 T X3220 4051 T X3232 1145 T X3232 1532 T X3232 1621 T X3232 3567 T X3232 3656 T X3232 4043 T X3243 1161 T X3243 1541 T X3243 1621 T X3243 3567 T X3243 3648 T X3243 4027 T X3255 1177 T X3255 1193 T X3255 1201 T X3255 1549 T X3255 1629 T X3255 3559 T X3255 3639 T X3255 3987 T X3255 3995 T X3255 4011 T X3266 1193 T X3266 1557 T X3266 1629 T X3266 3559 T X3266 3631 T X3266 3995 T X3278 1193 T X3278 1565 T X3278 1637 T X3278 3551 T X3278 3623 T X3278 3995 T X3289 1185 T X3289 1573 T X3289 1637 T X3289 3551 T X3289 3615 T X3289 4003 T X3301 1185 T X3301 1581 T X3301 1645 T X3301 3543 T X3301 3607 T X3301 4003 T X3312 1185 T X3312 1589 T X3312 1645 T X3312 3543 T X3312 3599 T X3312 4003 T X3324 1185 T X3324 1597 T X3324 1654 T X3324 3535 T X3324 3591 T X3324 4003 T X3335 1177 T X3335 1613 T X3335 1662 T X3335 3526 T X3335 3575 T X3335 4011 T X3347 1177 T X3347 1621 T X3347 1662 T X3347 3526 T X3347 3567 T X3347 4011 T X3358 1177 T X3358 1637 T X3358 1670 T X3358 3518 T X3358 3551 T X3358 4011 T X3369 1177 T X3369 1645 T X3369 1678 T X3369 3510 T X3369 3543 T X3369 4011 T X3381 1177 T X3381 1662 T X3381 1686 T X3381 3502 T X3381 3526 T X3381 4011 T X3392 1177 T X3392 1670 T X3392 1694 T X3392 3494 T X3392 3518 T X3392 4011 T X3404 1177 T X3404 1686 T X3404 1694 T X3404 3494 T X3404 3502 T X3404 4011 T X3415 1177 T X3415 1694 T X3415 1702 T X3415 3486 T X3415 3494 T X3415 4011 T X3427 1177 T X3427 4011 T X3438 1177 T X3438 4011 T X3450 1177 T X3450 4011 T X3461 1177 T X3461 4011 T X3473 1177 T X3473 4011 T X3484 1177 T X3484 4011 T X3496 1177 T X3496 4011 T X3507 1169 T X3507 4019 T X3518 1169 T X3518 4019 T X3530 1169 T X3530 4019 T X3541 1169 T X3541 4019 T X3553 1169 T X3553 4019 T X3564 1169 T X3564 4019 T X3576 1169 T X3576 4019 T X3587 1161 T X3587 4027 T X3599 1161 T X3599 4027 T X3610 1161 T X3610 4027 T X3622 1161 T X3622 4027 T X3633 1161 T X3633 4027 T X3645 1153 T X3645 4035 T X3656 1153 T X3656 4035 T X3668 1153 T X3668 4035 T X3679 1153 T X3679 4035 T X3690 1153 T X3690 4035 T X3702 1145 T X3702 4043 T X3713 1145 T X3713 4043 T X3725 1145 T X3725 4043 T X3736 1145 T X3736 4043 T X3748 1137 T X3748 4051 T X3759 1137 T X3759 4051 T X3771 1137 T X3771 4051 T X3782 1137 T X3782 4051 T X3794 1137 T X3794 4051 T X3805 1129 T X3805 4059 T X3817 1129 T X3817 4059 T X3828 1129 T X3828 4059 T X3839 1129 T X3839 4059 T X3851 1129 T X3851 4059 T X3862 1121 T X3862 4067 T X3874 1121 T X3874 4067 T X3885 1121 T X3885 4067 T X3897 1121 T X3897 4067 T X3908 1121 T X3908 4067 T X3920 1121 T X3920 4067 T X3931 1113 T X3931 4075 T X3943 1113 T X3943 4075 T X3954 1113 T X3954 4075 T X3966 1113 T X3966 4075 T X3977 1113 T X3977 4075 T X3988 1113 T X3988 4075 T X4000 1113 T X4000 4075 T X4011 1113 T X4011 4075 T X4023 1113 T X4023 4075 T X4034 1105 T X4034 4084 T X4046 1105 T X4046 4084 T X4057 1105 T X4057 4084 T X4069 1105 T X4069 4084 T X4080 1105 T X4080 4084 T X4092 1105 T X4092 4084 T X4103 1105 T X4103 4084 T X4115 1105 T X4115 4084 T X4126 1105 T X4126 4084 T X4138 1105 T X4138 4084 T X4149 1105 T X4149 4084 T X4160 1105 T X4160 4084 T X4172 1105 T X4172 4084 T X4183 1105 T X4183 4084 T X4195 1105 T X4195 4084 T X4206 1113 T X4206 4075 T X4218 1113 T X4218 4075 T X4229 1113 T X4229 4075 T X4241 1113 T X4241 4075 T X4252 1113 T X4252 4075 T X4264 1113 T X4264 4075 T X4275 1113 T X4275 4075 T X4287 1113 T X4287 4075 T X4298 1113 T X4298 4075 T X4309 1121 T X4309 4067 T X4321 1121 T X4321 4067 T X4332 1121 T X4332 4067 T X4344 1121 T X4344 4067 T X4355 1121 T X4355 4067 T X4367 1129 T X4367 4059 T X4378 1129 T X4378 4059 T X4390 1129 T X4390 4059 T X4401 1137 T X4401 4051 T X4413 1137 T X4413 4051 T X4424 1137 T X4424 4051 T X4436 1137 T X4436 4051 T X4447 1145 T X4447 4043 T X4459 1145 T X4459 4043 T X4470 1145 T X4470 4043 T X4481 1153 T X4481 4035 T X4493 1153 T X4493 4035 T X4504 1161 T X4504 4027 T X4516 1161 T X4516 4027 T X4527 1161 T X4527 4027 T X4539 1169 T X4539 4019 T X4550 1169 T X4550 4019 T X4562 1177 T X4562 4011 T X4573 1177 T X4573 4011 T X4585 1185 T X4585 4003 T X4596 1185 T X4596 4003 T X4608 1193 T X4608 3995 T X4619 1201 T X4619 3987 T X4630 1201 T X4630 3987 T X4642 1210 T X4642 3979 T X4653 1218 T X4653 3970 T X4665 1218 T X4665 3970 T X4676 1226 T X4676 3962 T X4688 1234 T X4688 3954 T X4699 1234 T X4699 3954 T X4711 1242 T X4711 3946 T X4722 1250 T X4722 3938 T X4734 1258 T X4734 3930 T X4745 1266 T X4745 3922 T X4757 1274 T X4757 3914 T X4768 1274 T X4768 3914 T X4779 1282 T X4779 3906 T X4791 1290 T X4791 3898 T X4802 1306 T X4802 3882 T X4814 1314 T X4814 3874 T X4825 1323 T X4825 3866 T X4837 1331 T X4837 3857 T X4848 1339 T X4848 3849 T X4860 1355 T X4860 3833 T X4871 1363 T X4871 3825 T X4883 1379 T X4883 3809 T X4894 1387 T X4894 3801 T X4906 1403 T X4906 3785 T X4917 1419 T X4917 3769 T X4929 1436 T X4929 3753 T X4940 1452 T X4940 1791 T X4940 1799 T X4940 3389 T X4940 3397 T X4940 3736 T X4951 1468 T X4951 1775 T X4951 1791 T X4951 3397 T X4951 3413 T X4951 3720 T X4963 1492 T X4963 1758 T X4963 1791 T X4963 3397 T X4963 3430 T X4963 3696 T X4974 1524 T X4974 1734 T X4974 1783 T X4974 3405 T X4974 3454 T X4974 3664 T X4986 1557 T X4986 1702 T X4986 1783 T X4986 3405 T X4986 3486 T X4986 3631 T X4997 1783 T X4997 3405 T X5009 1775 T X5009 3413 T X5020 1775 T X5020 3413 T X5032 1775 T X5032 3413 T X5043 1775 T X5043 3413 T X5055 1767 T X5055 3422 T X5066 1767 T X5066 3422 T X5078 1767 T X5078 3422 T X5089 1767 T X5089 3422 T X5100 1767 T X5100 3422 T X5112 1767 T X5112 3422 T X5123 1767 T X5123 3422 T X5135 1767 T X5135 3422 T X5146 1767 T X5146 3422 T X5158 1767 T X5158 3422 T X5169 1767 T X5169 3422 T X5181 1767 T X5181 3422 T X5192 1767 T X5192 3422 T X5204 1775 T X5204 2590 T X5204 2598 T X5204 3413 T X5215 1775 T X5215 2590 T X5215 2598 T X5215 3413 T X5227 1775 T X5227 2590 T X5227 2598 T X5227 3413 T X5238 1775 T X5238 2590 T X5238 2598 T X5238 3413 T X5249 1775 T X5249 2590 T X5249 2598 T X5249 3413 T X5261 1783 T X5261 2582 T X5261 2606 T X5261 3405 T X5272 1783 T X5272 2582 T X5272 2606 T X5272 3405 T X5284 1783 T X5284 2574 T X5284 2614 T X5284 3405 T X5295 1791 T X5295 2574 T X5295 2614 T X5295 3397 T X5307 1791 T X5307 2566 T X5307 2622 T X5307 3397 T X5318 1799 T X5318 2566 T X5318 2622 T X5318 3389 T X5330 1799 T X5330 2558 T X5330 2630 T X5330 3389 T X5341 1807 T X5341 2558 T X5341 2630 T X5341 3381 T X5353 1807 T X5353 2550 T X5353 2638 T X5353 3381 T X5364 1815 T X5364 2542 T X5364 2647 T X5364 3373 T X5376 1815 T X5376 2542 T X5376 2647 T X5376 3373 T X5387 1823 T X5387 2533 T X5387 2655 T X5387 3365 T X5399 1831 T X5399 2525 T X5399 2663 T X5399 3357 T X5410 1831 T X5410 2517 T X5410 2671 T X5410 3357 T X5421 1839 T X5421 2509 T X5421 2679 T X5421 3349 T X5433 1847 T X5433 2501 T X5433 2687 T X5433 3341 T X5444 1855 T X5444 2493 T X5444 2695 T X5444 3333 T X5456 1863 T X5456 2485 T X5456 2703 T X5456 3325 T X5467 1871 T X5467 2477 T X5467 2711 T X5467 3317 T X5479 1880 T X5479 2469 T X5479 2719 T X5479 3309 T X5490 1888 T X5490 2461 T X5490 2727 T X5490 3300 T X5502 1896 T X5502 2453 T X5502 2735 T X5502 3292 T X5513 1904 T X5513 2437 T X5513 2751 T X5513 3284 T X5525 1920 T X5525 2429 T X5525 2760 T X5525 3268 T X5536 1928 T X5536 2412 T X5536 2776 T X5536 3260 T X5548 1944 T X5548 2404 T X5548 2784 T X5548 3244 T X5559 1952 T X5559 2388 T X5559 2800 T X5559 3236 T X5570 1968 T X5570 2372 T X5570 2816 T X5570 3220 T X5582 1985 T X5582 2356 T X5582 2832 T X5582 3204 T X5593 2009 T X5593 2332 T X5593 2856 T X5593 3179 T X5605 2025 T X5605 2307 T X5605 2881 T X5605 3163 T X5616 2057 T X5616 2283 T X5616 2905 T X5616 3131 T X5628 2089 T X5628 2243 T X5628 2945 T X5628 3099 T XLT0 X6486 4346 M X(Set 2) Rshow X6654 4346 B2 X3444 1722 B2 X3444 3458 B2 X3252 1197 B2 X3252 3983 B2 X4922 3376 B2 X4922 1804 B2 X5201 2590 B2 X2662 2590 B2 XLT0 X6486 4206 M X(Set 3) Rshow X6654 4206 C2 X3430 1694 C2 X3382 1591 C2 X3382 3589 C2 X3297 3875 C2 X3297 1305 C2 X4839 1097 C2 X4839 4083 C2 X4968 3412 C2 X4968 1768 C2 X5163 1596 C2 X5163 3584 C2 X5222 2590 C2 X5307 2590 C2 X2620 2590 C2 X2468 2590 C2 X5528 2590 C2 X2047 2590 C2 X6502 2590 C2 X3443 3864 C2 X3443 1316 C2 X3434 3488 C2 X3434 1692 C2 X3410 3601 C2 X3410 1579 C2 X4884 4205 C2 X4885 975 C2 X4990 1762 C2 X4990 3418 C2 X5038 2086 C2 X5038 3094 C2 X5226 2590 C2 X5328 2590 C2 X2618 2590 C2 X5376 3744 C2 X5376 1436 C2 X2460 2590 C2 X5645 2590 C2 X2006 2590 C2 Xstroke Xgrestore Xend Xshowpage X%%Trailer X%%Pages: 1 END_OF_FILE if test 15975 -ne `wc -c <'figure9.ps'`; then echo shar: \"'figure9.ps'\" unpacked with wrong size! fi # end of 'figure9.ps' fi echo shar: End of shell archive. exit 0