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diff --git a/appeal.tex b/appeal.tex new file mode 100644 index 0000000..6af3109 --- /dev/null +++ b/appeal.tex @@ -0,0 +1,77 @@ +\documentclass[a4paper]{letter} + +\usepackage[utf8]{inputenc} % why not type "Bézout" with unicode? +\usepackage[T1]{fontenc} % vector fonts plz +\usepackage{newtxtext,newtxmath} % Times for PR +\usepackage[ + colorlinks=true, + urlcolor=purple, + linkcolor=black, + citecolor=black, + filecolor=black +]{hyperref} % ref and cite links with pretty colors +\usepackage{xcolor} +\usepackage[style=phys]{biblatex} + +\addbibresource{bezout.bib} + +\signature{ + \vspace{-6\medskipamount} + \smallskip + Jaron Kent-Dobias \& Jorge Kurchan +} + +\address{ + Laboratoire de Physique\\ + Ecole Normale Sup\'erieure\\ + 24 rue Lhomond\\ + 75005 Paris +} + +\begin{document} +\begin{letter}{ + Editorial Office\\ + Physical Review Letters\\ + 1 Research Road\\ + Ridge, NY 11961 +} + +\opening{To the editors of Physical Review,} + +We wish to appeal your decision on our manuscript \emph{Complex complex +landscapes}, which received a single referee report. + +We believe that the referee's overall criticisms of our paper are not entirely +justified (and above all, difficult to answer). We have, however, submitted a +revised manuscript clarifying the specific aspects that the referee found trying. + +The referee seems particularly worried that we have cited articles that are not +themselves sufficiently cited, so we thought it may be useful propose a set of +referees that are beyond suspicion of incompetence or uncitedness: + +\begin{tabular}{ll} + G Ben Arous & Courant \\ + M Berry & Bristol\\ + Y Fyodorov & King's College London \\ + Daniel Fisher& Stanford\\ + T Lubensky & U Penn\\ + M Moore & Manchester \\ + E Witten & IAS Princeton +\end{tabular} + +We have also pointed out some very first results of the geometric implications for a +random complex landscape of our calculation, something we plan to expend on in +a future full article. + +Let us conclude by remarking that, although it is probably true that this paper will not +make more than one hundred citations next year, we are confident that it will still +be considered relevant in ten years time. + + +\closing{Sincerely,} + +\vspace{1em} + +\end{letter} + +\end{document} @@ -42,69 +42,100 @@ \maketitle -Spin-glasses have long been considered the paradigm of many variable `complex -landscapes,' a subject that includes neural networks and optimization problems, -most notably constraint satisfaction \cite{Mezard_2009_Information}. The most tractable family of these -are the mean-field spherical $p$-spin models \cite{Crisanti_1992_The} (for a -review see \cite{Castellani_2005_Spin-glass}) defined by the energy +Spin-glasses are the paradigm of many-variable `complex landscapes,' a category +that also includes neural networks and optimization problems like constraint +satisfaction \cite{Mezard_2009_Information}. The most tractable family of +these are the mean-field spherical $p$-spin models \cite{Crisanti_1992_The} +(for a review see \cite{Castellani_2005_Spin-glass}) defined by the energy \begin{equation} \label{eq:bare.hamiltonian} H_0 = \frac1{p!}\sum_{i_1\cdots i_p}^NJ_{i_1\cdots i_p}z_{i_1}\cdots z_{i_p}, \end{equation} where $J$ is a symmetric tensor whose elements are real Gaussian variables and -$z\in\mathbb R^N$ is constrained to the sphere $z^2=N$. This problem has been +$z\in\mathbb R^N$ is constrained to the sphere $z^Tz=N$. This problem has been studied in the algebra \cite{Cartwright_2013_The} and probability literature \cite{Auffinger_2012_Random, Auffinger_2013_Complexity}. It has been attacked from several angles: the replica trick to compute the Boltzmann--Gibbs distribution \cite{Crisanti_1992_The}, a Kac--Rice \cite{Kac_1943_On, Rice_1939_The, Fyodorov_2004_Complexity} procedure (similar to the Fadeev--Popov integral) to compute the number of saddle-points of the energy -function \cite{Crisanti_1995_Thouless-Anderson-Palmer}, and the -gradient-descent---or more generally Langevin---dynamics staring from a -high-energy configuration \cite{Cugliandolo_1993_Analytical}. Thanks to the -simplicity of the energy, all these approaches yield analytic results in the -large-$N$ limit. +function \cite{Crisanti_1995_Thouless-Anderson-Palmer}, and gradient-descent +(or more generally Langevin) dynamics starting from a high-energy configuration +\cite{Cugliandolo_1993_Analytical}. Thanks to the simplicity of the energy, all +these approaches yield analytic results in the large-$N$ limit. In this paper we extend the study to complex variables: we shall take $z\in\mathbb C^N$ and $J$ to be a symmetric tensor whose elements are \emph{complex} normal, with $\overline{|J|^2}=p!/2N^{p-1}$ and $\overline{J^2}=\kappa\overline{|J|^2}$ for complex parameter $|\kappa|<1$. The -constraint remains $z^2=N$. +constraint remains $z^Tz=N$. -The motivations for this paper are of two types. On the practical side, there +The motivations for this paper are of three types. On the practical side, there are indeed situations in which complex variables appear naturally in disordered problems: such is the case in which the variables are \emph{phases}, as in random laser problems \cite{Antenucci_2015_Complex}. Quiver Hamiltonians---used to model black hole horizons in the zero-temperature limit---also have a Hamiltonian very close to ours \cite{Anninos_2016_Disordered}. A second reason is that, as we know from experience, extending a real problem to the complex -plane often uncovers underlying simplicity that is otherwise hidden, sheding +plane often uncovers underlying simplicity that is otherwise hidden, shedding light on the original real problem, e.g., as in the radius of convergence of a series. -Deforming an integral in $N$ real variables to a surface of dimension $N$ in -$2N$-dimensional complex space has turned out to be necessary for correctly -defining and analyzing path integrals with complex action (see +Finally, deforming an integral in $N$ real variables to a surface of dimension +$N$ in $2N$-dimensional complex space has turned out to be necessary for +correctly defining and analyzing path integrals with complex action (see \cite{Witten_2010_A, Witten_2011_Analytic}), and as a useful palliative for the sign problem \cite{Cristoforetti_2012_New, Tanizaki_2017_Gradient, -Scorzato_2016_The}. In order to do this correctly, the features of landscape -of the action in complex space---like the relative position of its -saddles---must be understood. Such landscapes are in general not random: here -we propose to follow the strategy of computer science of understanding the -generic features of random instances, expecting that this sheds light on the -practical, nonrandom problems. +Scorzato_2016_The}. In order to do this correctly, features of the action's +landscape in complex space---such as the relative position of saddles and the +existence of Stokes lines joining them---must be understood. This is typically +done for simple actions with few saddles, or for a target phenomenology with +symmetries that restrict the set of saddles to few candidates. Given the recent +proliferation of `glassiness' in condensed matter and high energy physics, it +is inevitable that someone will want to apply these methods to a system with a +complex landscape, and will find they cannot use approaches that rely on such +assumptions. Their landscape may not be random: here we follow the standard +strategy of computer science by understanding the generic features of random +instances of a simple case, expecting that this sheds light on practical, +nonrandom problems. While in this paper we do not yet address analytic +continuation of integrals, understanding the distribution and spectra of +critical points is an essential first step. Returning to our problem, the spherical constraint is enforced using the method -of Lagrange multipliers: introducing $\epsilon\in\mathbb C$, our energy is +of Lagrange multipliers: introducing $\epsilon\in\mathbb C$, our constrained +energy is \begin{equation} \label{eq:constrained.hamiltonian} H = H_0+\frac p2\epsilon\left(N-\sum_i^Nz_i^2\right). \end{equation} -We choose to constrain our model by $z^2=N$ rather than $|z|^2=N$ in order to -preserve the analyticity of $H$. The nonholomorphic constraint also has a -disturbing lack of critical points nearly everywhere: if $H$ were so -constrained, then $0=\partial^* H=-p\epsilon z$ would only be satisfied for -$\epsilon=0$. - -The critical points are of $H$ given by the solutions to the set of equations +One might balk at the constraint $z^Tz=N$---which could appropriately be called +a \emph{hyperbolic} constraint---by comparison with $z^\dagger z=N$. The reasoning +behind the choice is twofold. + +First, we seek to draw conclusions from our model that are applicable to generic +holomorphic functions without any symmetry. Samples of $H_0$ nearly provide +this, save for a single anomaly: the value of the energy and its gradient at +any point $z$ correlate along the $z$ direction, with $\overline{H_0\partial +H_0}\propto \overline{H_0(\partial H_0)^*}\propto z$. This anomalous direction +should thus be forbidden, and the constraint surface $z^Tz=N$ accomplishes this. + +Second, taking the constraint to be the level set of a holomorphic function +means the resulting configuration space is a \emph{bone fide} complex manifold, +and therefore permits easy generalization of the integration techniques +referenced above. The same cannot be said for the space defined by $z^\dagger +z=N$, which is topologically the $(2N-1)$-sphere and cannot admit a complex +structure. + +Imposing the constraint with a holomorphic function +makes the resulting configuration space a \emph{bone fide} complex manifold, which is, as we mentioned, the +situation we wish to model. The same cannot be said for the space defined by $z^\dagger +z=N$, which is topologically the $(2N-1)$-sphere, does not admit a complex +structure, and thus yields a trivial structure of saddles. +However, we will introduce the bound $r^2\equiv z^\dagger z/N\leq R^2$ +on the `radius' per spin as a device to classify saddles. We shall see that this +`radius' $r$ and its upper bound $R$ are insightful knobs in our present +problem, revealing structure as they are varied. Note that taking $R=1$ reduces +the problem to that of the ordinary $p$-spin. + +The critical points are of $H$ given by the solutions to \begin{equation} \label{eq:polynomial} \frac{p}{p!}\sum_{j_1\cdots j_{p-1}}^NJ_{ij_1\cdots j_{p-1}}z_{j_1}\cdots z_{j_{p-1}} = p\epsilon z_i @@ -114,20 +145,16 @@ equations of degree $p-1$, to which one must add the constraint. In this sense this study also provides a complement to the work on the distribution of zeroes of random polynomials \cite{Bogomolny_1992_Distribution}, which are for $N=1$ and $p\to\infty$. We see from \eqref{eq:polynomial} that at any critical -point, $\epsilon=H/N$, the average energy. - -Since $H$ is holomorphic, any critical point of $\operatorname{Re}H$ is also a -critical point of $\operatorname{Im}H$. The number of critical points of $H$ is -therefore the same as that of $\operatorname{Re}H$. From each saddle -emerge gradient lines of $\operatorname{Re}H$, which are also ones of constant -$\operatorname{Im}H$ and therefore constant phase. +point $\epsilon=H_0/N$, the average energy. -Writing $z=x+iy$, $\operatorname{Re}H$ can be considered a real-valued function -of $2N$ real variables. Its number of saddle-points is given by the usual -Kac--Rice formula: +Since $H$ is holomorphic, any critical point of $\operatorname{Re}H$ is also +one of $\operatorname{Im}H$, and therefore of $H$ itself. Writing $z=x+iy$ for +$x,y\in\mathbb R^N$, $\operatorname{Re}H$ can be considered a real-valued +function of $2N$ real variables. The number of critical points of $H$ is thus given by the +usual Kac--Rice formula applied to $\operatorname{Re}H$: \begin{equation} \label{eq:real.kac-rice} \begin{aligned} - \mathcal N_J&(\kappa,\epsilon) + \mathcal N&(\kappa,\epsilon,R) = \int dx\,dy\,\delta(\partial_x\operatorname{Re}H)\delta(\partial_y\operatorname{Re}H) \\ &\hspace{6pc}\times\left|\det\begin{bmatrix} \partial_x\partial_x\operatorname{Re}H & \partial_x\partial_y\operatorname{Re}H \\ @@ -135,14 +162,21 @@ Kac--Rice formula: \end{bmatrix}\right|. \end{aligned} \end{equation} -The Cauchy--Riemann equations may be used to write this in a manifestly complex -way. With the Wirtinger derivative $\partial=\frac12(\partial_x-i\partial_y)$, -one can write $\partial_x\operatorname{Re}H=\operatorname{Re}\partial H$ and +This expression is to be averaged over $J$ to give the complexity $\Sigma$ as +$N \Sigma= \overline{\log\mathcal N}$, a calculation that involves the replica +trick. Based on the experience from similar problems \cite{Castellani_2005_Spin-glass}, the +\emph{annealed approximation} $N \Sigma \sim \log \overline{ \mathcal N}$ is +expected to be exact wherever the complexity is positive. + +The Cauchy--Riemann equations may be used to write \eqref{eq:real.kac-rice} in +a manifestly complex way. With the Wirtinger derivative +$\partial\equiv\frac12(\partial_x-i\partial_y)$, one can write +$\partial_x\operatorname{Re}H=\operatorname{Re}\partial H$ and $\partial_y\operatorname{Re}H=-\operatorname{Im}\partial H$. Carrying these -transformations through, we have +transformations through, one finds \begin{equation} \label{eq:complex.kac-rice} \begin{aligned} - \mathcal N_J&(\kappa,\epsilon) + \mathcal N&(\kappa,\epsilon,r) = \int dx\,dy\,\delta(\operatorname{Re}\partial H)\delta(\operatorname{Im}\partial H) \\ &\hspace{6pc}\times\left|\det\begin{bmatrix} \operatorname{Re}\partial\partial H & -\operatorname{Im}\partial\partial H \\ @@ -155,8 +189,9 @@ transformations through, we have \end{aligned} \end{equation} This gives three equivalent expressions for the determinant of the Hessian: as -that of a $2N\times 2N$ real matrix, that of an $N\times N$ Hermitian matrix, -i.e. the norm squared of that of an $N\times N$ complex symmetric matrix. +that of a $2N\times 2N$ real symmetric matrix, that of the $N\times N$ Hermitian +matrix $(\partial\partial H)^\dagger\partial\partial H$, or the norm squared of +that of the $N\times N$ complex symmetric matrix $\partial\partial H$. These equivalences belie a deeper connection between the spectra of the corresponding matrices. Each positive eigenvalue of the real matrix has a @@ -167,57 +202,13 @@ Hessian is therefore the same as the distribution of singular values of $\partial\partial H$, or the distribution of square-rooted eigenvalues of $(\partial\partial H)^\dagger\partial\partial H$. -The expression \eqref{eq:complex.kac-rice} is to be averaged over $J$ to give -the complexity $\Sigma$ as $N \Sigma= \overline{\log\mathcal N} = \int dJ \, -\log \mathcal N_J$, a calculation that involves the replica trick. In most the -parameter-space that we shall study here, the \emph{annealed approximation} $N -\Sigma \sim \log \overline{ \mathcal N} = \log\int dJ \, \mathcal N_J$ is -exact. - A useful property of the Gaussian $J$ is that gradient and Hessian at fixed -$\epsilon$ are statistically independent \cite{Bray_2007_Statistics, +energy $\epsilon$ are statistically independent \cite{Bray_2007_Statistics, Fyodorov_2004_Complexity}, so that the $\delta$-functions and the Hessian may -be averaged independently. The $\delta$-functions are converted to exponentials -by the introduction of auxiliary fields $\hat z=\hat x+i\hat y$. The average -of those factors over $J$ can then be performed. A generalized -Hubbard--Stratonovich allows a change of variables from the $4N$ original -and auxiliary fields to eight bilinears defined by $Na=|z|^2$, $N\hat a=|\hat -z|^2$, $N\hat c=\hat z^2$, $Nb=\hat z^*z$, and $Nd=\hat zz$ (and their -conjugates). The result, to leading order in $N$, is -\begin{equation} \label{eq:saddle} - \overline{\mathcal N}(\kappa,\epsilon) - = \int da\,d\hat a\,db\,db^*d\hat c\,d\hat c^*dd\,dd^*e^{Nf(a,\hat a,b,\hat c,d)}, -\end{equation} -where the argument of the exponential is -\begin{widetext} - \begin{equation} - f=2+\frac12\log\det\frac12\begin{bmatrix} - 1 & a & d & b \\ - a & 1 & b^* & d^* \\ - d & b^* & \hat c & \hat a \\ - b & d^* & \hat a & \hat c^* - \end{bmatrix} - +\int d\lambda\,\rho(\lambda)\log|\lambda|^2 - +p\operatorname{Re}\left\{ - \frac18\left[\hat aa^{p-1}+(p-1)|d|^2a^{p-2}+\kappa(\hat c^*+(p-1)b^2)\right]-\epsilon b - \right\}. - \end{equation} - The integral of the distribution $\rho$ of eigenvalues of $\partial\partial - H$ comes from the Hessian and is dependant on $a$ alone. This function has an - extremum in $\hat a$, $b$, $\hat c$, and $d$ at which its value is - \begin{equation} \label{eq:free.energy.a} - f(a)=1+\frac12\log\left(\frac4{p^2}\frac{a^2-1}{a^{2(p-1)}-|\kappa|^2}\right)+\int d\lambda\,\rho(\lambda)\log|\lambda|^2 - -2C_+[\operatorname{Re}(\epsilon e^{-i\theta})]^2-2C_-[\operatorname{Im}(\epsilon e^{-i\theta})]^2, - \end{equation} -\end{widetext} -where $\theta=\frac12\arg\kappa$ and -\begin{equation} - C_{\pm}=\frac{a^p(1+p(a^2-1))\mp a^2|\kappa|}{a^{2p}\pm(p-1)a^p(a^2-1)|\kappa|-a^2|\kappa|^2}. -\end{equation} -This leaves a single parameter, $a$, which dictates the magnitude of $|z|^2$, -or alternatively the magnitude $y^2$ of the imaginary part. The latter vanishes -as $a\to1$, where (as we shall see) one recovers known results for the real -$p$-spin. +be averaged independently. First we shall compute the spectrum of the Hessian, +which can in turn be used to compute the determinant. Then we will treat the +$\delta$-functions and the resulting saddle point equations. The results of +these calculations begin around \eqref{eq:bezout}. The Hessian $\partial\partial H=\partial\partial H_0-p\epsilon I$ is equal to the unconstrained Hessian with a constant added to its diagonal. The eigenvalue @@ -229,28 +220,28 @@ Hessian of the unconstrained Hamiltonian is =\frac{p(p-1)}{p!}\sum_{k_1\cdots k_{p-2}}^NJ_{ijk_1\cdots k_{p-2}}z_{k_1}\cdots z_{k_{p-2}}, \end{equation} which makes its ensemble that of Gaussian complex symmetric matrices, when the -direction along the constraint is neglected. Given its variances -$\overline{|\partial_i\partial_j H_0|^2}=p(p-1)a^{p-2}/2N$ and +anomalous direction normal to the constraint surface is neglected. Given its variances +$\overline{|\partial_i\partial_j H_0|^2}=p(p-1)r^{p-2}/2N$ and $\overline{(\partial_i\partial_j H_0)^2}=p(p-1)\kappa/2N$, $\rho_0(\lambda)$ is constant inside the ellipse \begin{equation} \label{eq:ellipse} - \left(\frac{\operatorname{Re}(\lambda e^{i\theta})}{a^{p-2}+|\kappa|}\right)^2+ - \left(\frac{\operatorname{Im}(\lambda e^{i\theta})}{a^{p-2}-|\kappa|}\right)^2 - <\frac{p(p-1)}{2a^{p-2}} + \left(\frac{\operatorname{Re}(\lambda e^{i\theta})}{r^{p-2}+|\kappa|}\right)^2+ + \left(\frac{\operatorname{Im}(\lambda e^{i\theta})}{r^{p-2}-|\kappa|}\right)^2 + <\frac{p(p-1)}{2r^{p-2}} \end{equation} where $\theta=\frac12\arg\kappa$ \cite{Nguyen_2014_The}. The eigenvalue spectrum of $\partial\partial H$ is therefore constant inside the same ellipse translated so that its center lies at $-p\epsilon$. Examples of these distributions are shown in the insets of Fig.~\ref{fig:spectra}. -The eigenvalue spectrum of the Hessian of the real part is different from the -spectrum $\rho(\lambda)$ of $\partial\partial H$, but rather equivalent to the +The eigenvalue spectrum of the Hessian of the real part is not the +spectrum $\rho(\lambda)$ of $\partial\partial H$, but instead the square-root eigenvalue spectrum of $(\partial\partial H)^\dagger\partial\partial H$; in other words, the singular value spectrum $\rho(\sigma)$ of $\partial\partial H$. When $\kappa=0$ and the elements of $J$ are standard complex normal, this is a complex Wishart distribution. For $\kappa\neq0$ the problem changes, and to our knowledge a closed form is not in the literature. We have worked out an -implicit form for this spectrum using the replica method. +implicit form for the singular value spectrum using the replica method. Introducing replicas to bring the partition function into the numerator of the Green function \cite{Livan_2018_Introduction} gives @@ -263,25 +254,24 @@ Green function \cite{Livan_2018_Introduction} gives \right] \right\}, \end{equation} - with sums taken over repeated Latin indices. The average is then made over + with sums taken over repeated Latin indices. The average is then made over $J$ and Hubbard--Stratonovich is used to change variables to the replica matrices - $N\alpha_{\alpha\beta}=(\zeta^{(\alpha)})^*\cdot\zeta^{(\beta)}$ and - $N\chi_{\alpha\beta}=\zeta^{(\alpha)}\cdot\zeta^{(\beta)}$ and a series of - replica vectors. The replica-symmetric ansatz leaves all off-diagonal - elements and vectors zero, and - $\alpha_{\alpha\beta}=\alpha_0\delta_{\alpha\beta}$, + $N\alpha_{\alpha\beta}=(\zeta^{(\alpha)})^\dagger\zeta^{(\beta)}$ and + $N\chi_{\alpha\beta}=(\zeta^{(\alpha)})^T\zeta^{(\beta)}$, and a series of + replica vectors. The replica-symmetric ansatz leaves all replica vectors + zero, and $\alpha_{\alpha\beta}=\alpha_0\delta_{\alpha\beta}$, $\chi_{\alpha\beta}=\chi_0\delta_{\alpha\beta}$. The result is \begin{equation}\label{eq:green.saddle} \overline G(\sigma)=N\lim_{n\to0}\int d\alpha_0\,d\chi_0\,d\chi_0^*\,\alpha_0 \exp\left\{nN\left[ - 1+\frac{p(p-1)}{16}a^{p-2}\alpha_0^2-\frac{\alpha_0\sigma}2+\frac12\log(\alpha_0^2-|\chi_0|^2) + 1+\frac{p(p-1)}{16}r^{p-2}\alpha_0^2-\frac{\alpha_0\sigma}2+\frac12\log(\alpha_0^2-|\chi_0|^2) +\frac p4\operatorname{Re}\left(\frac{(p-1)}8\kappa^*\chi_0^2-\epsilon^*\chi_0\right) \right]\right\}. \nonumber % He's too long, and we don't cite him (now)! \end{equation} \end{widetext} -\begin{figure}[b] +\begin{figure} \centering \includegraphics{fig/spectra_0.0.pdf} @@ -290,25 +280,27 @@ Green function \cite{Livan_2018_Introduction} gives \includegraphics{fig/spectra_1.5.pdf} \caption{ - Eigenvalue and singular value spectra of the matrix $\partial\partial H$ - for $p=3$, $a=\frac54$, and $\kappa=\frac34e^{-i3\pi/4}$ with (a) - $\epsilon=0$, (b) $\epsilon=-\frac12|\epsilon_{\mathrm{th}}|$, (c) + Eigenvalue and singular value spectra of the Hessian $\partial\partial H$ + of the $3$-spin model with $\kappa=\frac34e^{-i3\pi/4}$. Pictured + distributions are for critical points at `radius' $r=\sqrt{5/4}$ and with + energy per spin (a) $\epsilon=0$, (b) + $\epsilon=-\frac12|\epsilon_{\mathrm{th}}|$, (c) $\epsilon=-|\epsilon_{\mathrm{th}}|$, and (d) - $\epsilon=-\frac32|\epsilon_{\mathrm{th}}|$. The shaded region of each inset - shows the support of the eigenvalue distribution. The solid line on each - plot shows the distribution of singular values, while the overlaid - histogram shows the empirical distribution from $2^{10}\times2^{10}$ complex - normal matrices with the same covariance and diagonal shift as - $\partial\partial H$. + $\epsilon=-\frac32|\epsilon_{\mathrm{th}}|$. The shaded region of each + inset shows the support of the eigenvalue distribution \eqref{eq:ellipse}. + The solid line on each plot shows the distribution of singular values + \eqref{eq:spectral.density}, while the overlaid histogram shows the + empirical distribution from $2^{10}\times2^{10}$ complex normal matrices + with the same covariance and diagonal shift as $\partial\partial H$. } \label{fig:spectra} \end{figure} The argument of the exponential has several saddles. The solutions $\alpha_0$ are the roots of a sixth-order polynomial, and the root with the smallest value -of $\operatorname{Re}\alpha_0$ in all the cases we studied gives the correct -solution. A detailed analysis of the saddle point integration is needed to -understand why this is so. Given such $\alpha_0$, the density of singular -values follows from the jump across the cut, or +of $\operatorname{Re}\alpha_0$ gives the correct solution in all the cases we +studied. A detailed analysis of the saddle point integration is needed to +understand why this is so. Evaluated at such a solution, the density of +singular values follows from the jump across the cut, or \begin{equation} \label{eq:spectral.density} \rho(\sigma)=\frac1{i\pi N}\left( \lim_{\operatorname{Im}\sigma\to0^+}\overline G(\sigma) @@ -318,77 +310,109 @@ values follows from the jump across the cut, or Examples can be seen in Fig.~\ref{fig:spectra} compared with numeric experiments. -The transition from a one-cut to two-cut singular value spectrum naturally -corresponds to the origin leaving the support of the eigenvalue spectrum. -Weyl's theorem requires that the product over the norm of all eigenvalues must -not be greater than the product over all singular values \cite{Weyl_1912_Das}. -Therefore, the absence of zero eigenvalues implies the absence of zero singular -values. The determination of the threshold energy -- the energy at which the -distribution of singular values becomes gapped -- is then reduced to a -geometry problem, and yields +The formation of a gap in the singular value spectrum naturally corresponds to +the origin leaving the support of the eigenvalue spectrum. Weyl's theorem +requires that the product over the norm of all eigenvalues must not be greater +than the product over all singular values \cite{Weyl_1912_Das}. Therefore, the +absence of zero eigenvalues implies the absence of zero singular values. The +determination of the threshold energy---the energy at which the distribution +of singular values becomes gapped---is reduced to the geometry problem of +determining when the boundary of the ellipse defined in \eqref{eq:ellipse} +intersects the origin, and yields \begin{equation} \label{eq:threshold.energy} |\epsilon_{\mathrm{th}}|^2 - =\frac{p-1}{2p}\frac{(1-|\delta|^2)^2a^{p-2}} + =\frac{p-1}{2p}\frac{(1-|\delta|^2)^2r^{p-2}} {1+|\delta|^2-2|\delta|\cos(\arg\kappa+2\arg\epsilon)} \end{equation} -for $\delta=\kappa a^{-(p-2)}$. +for $\delta=\kappa r^{-(p-2)}$. Notice that the threshold depends on both the +energy per spin $\epsilon$ on the `radius' $r$ of the saddle. + +We will now address the $\delta$-functions of \eqref{eq:complex.kac-rice}. +These are converted to exponentials by the introduction of auxiliary fields +$\hat z=\hat x+i\hat y$. The average over $J$ can then be performed. A +generalized Hubbard--Stratonovich allows a change of variables from the $4N$ +original and auxiliary fields to eight bilinears defined by $Nr=z^\dagger z$, +$N\hat r=\hat z^\dagger\hat z$, $Na=\hat z^\dagger z$, $Nb=\hat z^Tz$, and +$N\hat c=\hat z^T\hat z$ (and their conjugates). The result, to leading order +in $N$, is +\begin{equation} \label{eq:saddle} + \overline{\mathcal N}(\kappa,\epsilon,R) + = \int dr\,d\hat r\,da\,da^*db\,db^*d\hat c\,d\hat c^*e^{Nf(r,\hat r,a,b,\hat c)}, +\end{equation} +where the argument of the exponential is +\begin{widetext} + \begin{equation} + f=2+\frac12\log\det\frac12\begin{bmatrix} + 1 & r & b & a \\ + r & 1 & a^* & b^* \\ + b & a^* & \hat c & \hat r \\ + a & b^* & \hat r & \hat c^* + \end{bmatrix} + +\int d\lambda\,d\lambda^*\rho(\lambda)\log|\lambda|^2 + +p\operatorname{Re}\left\{ + \frac18\left[\hat rr^{p-1}+(p-1)|b|^2r^{p-2}+\kappa(\hat c^*+(p-1)a^2)\right]-\epsilon a + \right\}. + \end{equation} + The spectrum $\rho$ is given in \eqref{eq:ellipse} and is dependant on $r$ alone. This function has an + extremum in $\hat r$, $a$, $b$, and $\hat c$ at which its value is + \begin{equation} \label{eq:free.energy.a} + f=1+\frac12\log\left(\frac4{p^2}\frac{r^2-1}{r^{2(p-1)}-|\kappa|^2}\right)+\int d\lambda\,\rho(\lambda)\log|\lambda|^2 + -2C_+[\operatorname{Re}(\epsilon e^{-i\theta})]^2-2C_-[\operatorname{Im}(\epsilon e^{-i\theta})]^2, + \end{equation} +\end{widetext} +where $\theta=\frac12\arg\kappa$ and +\begin{equation} + C_{\pm}=\frac{r^p(1+p(r^2-1))\mp r^2|\kappa|}{r^{2p}\pm(p-1)r^p(r^2-1)|\kappa|-r^2|\kappa|^2}. +\end{equation} +Notice that level sets of $f$ in energy $\epsilon$ also give ellipses, but of +different form from the ellipse in \eqref{eq:ellipse}. -Given $\rho$, the integral in \eqref{eq:free.energy.a} may be preformed for -arbitrary $a$. The resulting expression is maximized for $a=\infty$ for all -values of $\kappa$ and $\epsilon$. Taking this saddle gives +This expression is maximized for $r=R$, its value at the boundary, for +all values of $\kappa$ and $\epsilon$. Evaluating the complexity at this +saddle, in the limit of unbounded spins, gives \begin{equation} \label{eq:bezout} - \log\overline{\mathcal N}(\kappa,\epsilon) + \lim_{R\to\infty}\log\overline{\mathcal N}(\kappa,\epsilon,R) =N\log(p-1). \end{equation} -This is, to this order, precisely the Bézout bound, the maximum number of -solutions that $N$ equations of degree $p-1$ may have -\cite{Bezout_1779_Theorie}. That we saturate this bound is perhaps not -surprising, since the coefficients of our polynomial equations -\eqref{eq:polynomial} are complex and have no symmetries. Reaching Bézout in -\eqref{eq:bezout} is not our main result, but it provides a good check. -Analogous asymptotic scaling has been found for the number of pure Higgs states -in supersymmetric quiver theories \cite{Manschot_2012_From}. - -More insight is gained by looking at the count as a function of $a$, defined by -$\overline{\mathcal N}(\kappa,\epsilon,a)=e^{Nf(a)}$. In the large-$N$ limit, -this is the cumulative number of critical points, or the number of critical -points $z$ for which $|z|^2\leq a$. We likewise define the $a$-dependant -complexity $\Sigma(\kappa,\epsilon,a)=N\log\overline{\mathcal -N}(\kappa,\epsilon,a)$ +This is, to leading order, precisely the Bézout bound, the maximum number of +solutions to $N$ equations of degree $p-1$ \cite{Bezout_1779_Theorie}. That we +saturate this bound is perhaps not surprising, since the coefficients of our +polynomial equations \eqref{eq:polynomial} are complex and have no symmetries. +Reaching Bézout in \eqref{eq:bezout} is not our main result, but it provides a +good check. Analogous asymptotic scaling has been found for the number of pure +Higgs states in supersymmetric quiver theories \cite{Manschot_2012_From}. \begin{figure}[htpb] \centering \includegraphics{fig/complexity.pdf} \caption{ - The complexity of the 3-spin model at $\epsilon=0$ as a function of - $a=|z|^2=1+y^2$ at several values of $\kappa$. The dashed line shows + The complexity of the 3-spin model as a function of the maximum `radius' + $R$ at zero energy and several values of $\kappa$. The dashed line shows $\frac12\log(p-1)$, while the dotted shows $\log(p-1)$. } \label{fig:complexity} \end{figure} -Everything is analytically tractable for $\epsilon=0$, giving +For finite $R$, everything is analytically tractable at $\epsilon=0$: \begin{equation} \label{eq:complexity.zero.energy} - \Sigma(\kappa,0,a) - =\log(p-1)-\frac12\log\left(\frac{1-|\kappa|^2a^{-2(p-1)}}{1-a^{-2}}\right). + \Sigma(\kappa,0,R) + =\log(p-1)-\frac12\log\left(\frac{1-|\kappa|^2R^{-4(p-1)}}{1-R^{-4}}\right). \end{equation} -Notice that the limit of this expression as $a\to\infty$ corresponds with -\eqref{eq:bezout}, as expected. This is plotted as a function of $a$ for -several values of $\kappa$ in Fig.~\ref{fig:complexity}. For any $|\kappa|<1$, -the complexity goes to negative infinity as $a\to1$, i.e., as the spins are -restricted to the reals. This is natural, given that the $y$ contribution to -the volume shrinks to zero as that of an $N$-dimensional sphere $\sum_i y_i^2=N(a-1)$ with volume -$\sim(a-1)^N$. However, when the result is analytically continued to +This is plotted as a function of $R$ for several values of $\kappa$ in +Fig.~\ref{fig:complexity}. For any $|\kappa|<1$, the complexity goes to +negative infinity as $R\to1$, i.e., as the spins are restricted to the reals. +This is natural, since volume of configuration space vanishes in this limit +like $(R^2-1)^N$. However, when the result is analytically continued to $\kappa=1$ (which corresponds to real $J$) something novel occurs: the -complexity has a finite value at $a=1$. Since the $a$-dependence gives a -cumulative count, this implies a $\delta$-function density of critical points -along the line $y=0$. The number of critical points contained within is +complexity has a finite value at $R=1$. This implies a $\delta$-function +density of critical points on the $r=1$ (or $y=0$) boundary. The number of +critical points contained there is \begin{equation} - \lim_{a\to1}\lim_{\kappa\to1}\log\overline{\mathcal N}(\kappa,0,a) + \lim_{R\to1}\lim_{\kappa\to1}\log\overline{\mathcal N}(\kappa,0,R) = \frac12N\log(p-1), \end{equation} half of \eqref{eq:bezout} and corresponding precisely to the number of critical -points of the real $p$-spin model (note the role of conjugation symmetry, -already underlined in \cite{Bogomolny_1992_Distribution}). The full +points of the real $p$-spin model. (Note the role of conjugation symmetry, +already underlined in \cite{Bogomolny_1992_Distribution}.) The full $\epsilon$-dependence of the real $p$-spin is recovered by this limit as $\epsilon$ is varied. @@ -396,23 +420,35 @@ $\epsilon$ is varied. \centering \includegraphics{fig/desert.pdf} \caption{ - The minimum value of $a$ for which the complexity is positive as a function - of (real) energy $\epsilon$ for the 3-spin model at several values of - $\kappa$. + The value of bounding `radius' $R$ for which $\Sigma(\kappa,\epsilon,R)=0$ as a + function of (real) energy per spin $\epsilon$ for the 3-spin model at + several values of $\kappa$. Above each line the complexity is positive and + critical points proliferate, while below it the complexity is negative and + critical points are exponentially suppressed. The dotted black lines show + the location of the ground and highest exited state energies for the real + 3-spin model. } \label{fig:desert} \end{figure} +In the thermodynamic limit, \eqref{eq:complexity.zero.energy} implies that most +critical points are concentrated at infinite radius $r$. For finite $N$ the +average radius of critical points is likewise finite. By differentiating +$\overline{\mathcal N}$ with respect to $R$ and normalizing, one obtains the +distribution of critical points as a function of $r$. This yields an average +radius proportional to $N^{1/4}$. One therefore expects typical critical +points to have a norm that grows modestly with system size. + These qualitative features carry over to nonzero $\epsilon$. In -Fig.~\ref{fig:desert} we show that for $\kappa<1$ there is always a gap of $a$ -close to one for which there are no solutions. When $\kappa=1$---the analytic -continuation to the real computation---the situation is more interesting. In -the range of energies where there are real solutions this gap closes, which is -only possible if the density of solutions diverges at $a=1$. Another -remarkable feature of this limit is that there is still a gap without solutions -around `deep' real energies where there is no real solution. A moment's thought -tells us that this is a necessity: otherwise a small perturbation of the $J$s -could produce an unusually deep solution to the real problem, in a region where -this should not happen. +Fig.~\ref{fig:desert} we show that for $\kappa<1$ there is always a gap in $r$ +close to one in which solutions are exponentially suppressed. When +$\kappa=1$---the analytic continuation to the real computation---the situation +is more interesting. In the range of energies where there are real solutions +this gap closes, which is only possible if the density of solutions diverges at +$r=1$. Outside this range, around `deep' real energies where real solutions are +exponentially suppressed, the gap remains. A moment's thought tells us that +this is necessary: otherwise a small perturbation of the $J$s could produce +an unusually deep solution to the real problem, in a region where this should +not happen. \begin{figure}[t] \centering @@ -425,37 +461,38 @@ this should not happen. \caption{ Energies at which states exist (green shaded region) and threshold energies (black solid line) for the 3-spin model with - $\kappa=\frac34e^{-i3\pi/4}$ and (a) $a=2$, (b) $a=1.325$, (c) $a=1.125$, - and (d) $a=1$. No shaded region is shown in (d) because no states exist at + $\kappa=\frac34e^{-i3\pi/4}$ and (a) $r=\sqrt2$, (b) $r=\sqrt{1.325}$, (c) $r=\sqrt{1.125}$, + and (d) $r=1$. No shaded region is shown in (d) because no states exist at any energy. } \label{fig:eggs} \end{figure} The relationship between the threshold and ground, or extremal, state energies -is richer than in the real case. In Fig.~\ref{fig:eggs} these are shown in the +is richer than in the real case. In Fig.~\ref{fig:eggs} these are shown in the complex-$\epsilon$ plane for several examples. Depending on the parameters, the -threshold might always come at smaller magnitude than the extremal state, or -always come at larger magnitude, or cross as a function of complex argument. -For sufficiently large $a$ the threshold always comes at larger magnitude than -the extremal state. If this were to happen in the real case, it would likely -imply our replica symmetric computation is unstable, since having a ground -state above the threshold implies a ground state Hessian with many negative -eigenvalues, a contradiction. However, this is not an obvious contradiction in -the complex case. The relationship between the threshold, i.e., where the gap -appears, and the dynamics of, e.g., a minimization algorithm or physical -dynamics, are a problem we hope to address in future work. - - This paper provides a first step towards the study of a complex landscape with - complex variables. The next obvious one is to study the topology of the +threshold might have a smaller or larger magnitude than the extremal state, or +cross as a function of complex argument. For sufficiently large $r$ the +threshold is always at a larger magnitude. If this were to happen in the real +case, it would likely imply our replica symmetric computation were unstable, +since having a ground state above the threshold implies a ground state Hessian +with many negative eigenvalues, a contradiction. However, this is not an +contradiction in the complex case, where the energy is not bounded from below. +The relationship between the threshold, i.e., where the gap appears, and the +dynamics of, e.g., a minimization algorithm, deformed integration cycle, or +physical dynamics, are a problem we hope to address in future work. + + This paper provides a first step towards the study of complex landscapes with + complex variables. The next obvious step is to study the topology of the critical points, the sets reached following gradient descent (the Lefschetz thimbles), and ascent (the anti-thimbles) \cite{Witten_2010_A, Witten_2011_Analytic, Cristoforetti_2012_New, Behtash_2017_Toward, Scorzato_2016_The}, which act as constant-phase integrating `contours.' Locating and counting the saddles that are joined by gradient lines---the Stokes points, which play an important role in the theory---is also well within - reach of the present-day spin-glass literature techniques. We anticipate - that the threshold level, where the system develops a mid-spectrum gap, will - play a crucial role as it does in the real case. + reach of the present-day spin-glass literature techniques. We anticipate + that the threshold level, where the system develops a mid-spectrum gap, plays + a crucial role in determining whether these Stokes points proliferate under + some continuous change of parameters. \begin{acknowledgments} We wish to thank Alexander Altland, Satya Majumdar and Gregory Schehr for a useful suggestions. diff --git a/fig/complexity.pdf b/fig/complexity.pdf Binary files differindex b68f2cf..93b16ce 100644 --- a/fig/complexity.pdf +++ b/fig/complexity.pdf diff --git a/fig/desert.pdf b/fig/desert.pdf Binary files differindex e19484a..c0be63f 100644 --- a/fig/desert.pdf +++ b/fig/desert.pdf diff --git a/fig/spectra_0.0.pdf b/fig/spectra_0.0.pdf Binary files differindex ca4ea49..6fb798a 100644 --- a/fig/spectra_0.0.pdf +++ b/fig/spectra_0.0.pdf diff --git a/fig/spectra_0.5.pdf b/fig/spectra_0.5.pdf Binary files differindex 205d964..b4cc9d3 100644 --- a/fig/spectra_0.5.pdf +++ b/fig/spectra_0.5.pdf diff --git a/fig/spectra_1.0.pdf b/fig/spectra_1.0.pdf Binary files 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1)",ExpressionUUID->"f96215bf-f7cc-4f3d-bf51-c090e4d3694f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345880220715*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"5ed95346-9786-4908-be51-33a68772c260"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345880304141*^9}, + CellLabel-> + "(kernel 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3)",ExpressionUUID->"5e6777bc-bde9-49ff-90e9-45716ba74fb6"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458805447693`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"c0fc00a1-71ca-4ffc-9015-0551e3d80ab3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345880628023*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"b91c70b4-51a2-4e87-8d4d-6ba3f8aa4907"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345880633904*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"305b364a-ea7e-457c-b156-9f7266a72085"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458807165403`*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"ba1325fb-a070-4e99-a073-93df7cbe604e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345880725522*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"0049c5a0-5030-4d9a-8063-17d1b5174641"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345880734107*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"740d2588-adc7-4e89-afdc-b13e5f3aa49f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345880808773*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"755df0c4-02d6-4e98-b79b-034d7d5b81f7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345880925797*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"e77b3e92-b908-4c33-ae9c-13c4961fdc07"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345880997251*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"82426e88-df80-427f-bbe8-b2cbeefbf863"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345881072401*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"e551f98f-fc07-4734-98bf-1bfa97a555a7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345881131517*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"a50e93ef-7ab3-4fc0-a66f-56c663627bdb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458811836147`*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"5e0aff12-3391-47a0-8224-409d4f2b4a01"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345881322146*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"47e6227d-6f30-4d70-88f8-be87b3f3534d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345881377212*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"b25d2a81-dfc4-46e1-a578-eb2aee9f1db8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345881429841*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"5bace815-d93c-4c75-98b1-f57224543926"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345881490279*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"e1c87755-55ba-49fa-a995-02b881bd33bb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345881554147*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"5849197f-e06b-4b2f-9ee2-e43e70f3c9b5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458827416973`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"d36f3cdf-c11d-45a3-86e2-a304e4f5e02f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345882796545*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"6fc1b7f4-1ff8-4bf8-9546-431e892fe708"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345882852096*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"e875c28c-e8d6-4be7-bca8-f37d34c6f197"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458829112043`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"db6ed3a1-7899-4c4b-b813-1cf3a5fc4b9b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458875653057`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"5cf4214d-d36b-4127-8e68-22028667e216"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345890948574*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"adfaf162-a248-427f-8c1f-76b94bfa8cc0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458910251904`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"ede8f108-44c1-4281-b17c-ae4288203020"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345891103443*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"c115e6f6-f394-47bd-94ac-0b86c5368aac"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345891156783*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"38c7491b-41ea-4b85-a13f-d9c3af5203c8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345892927318*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"ce20e33e-9282-48b4-8e94-5c32c563f74d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345892984914*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"26fd7ead-4b4f-4e6c-97a7-b875f70ab8ed"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458930646048`*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"fb33003b-08af-4f4b-8e63-a6a4565527c1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345893117043*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"3c3f4fa0-d474-4259-a98c-bb8dd4b0a556"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458938872128`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"91f458bd-cf46-49f4-885e-491288741517"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458940459023`*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"f197abfb-d0ef-4a5a-a16f-7f39b621a6bb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345894091887*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"2f20668b-2dd5-4412-bf60-1bf43d737373"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345894155861*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"a54337a5-f757-4b50-9b98-924be7c7f31c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345894207011*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"deb9a9e3-5fc6-4d13-b777-8bb77563de68"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458948837223`*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"bd6082c0-9929-4575-82be-cc166b86d757"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345895440095*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"2df7e6ab-0734-4cb1-99c2-eceba2126f50"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345895495902*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"3191bba6-cffd-4b12-9072-7b1648acf19f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345895545525*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"bbf075d6-ddc1-42e0-859d-c117e1e7f8d3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345895587934*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"2140fd35-235f-4db6-a262-e9b7bccde7c8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345896886058*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"9fc40d74-c6a9-477e-b319-40a70bb799b6"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458969623957`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"214e21c6-65fe-49e9-839f-bfbb2b1e74f7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458970125837`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"b3123def-790f-432f-b01e-10b8f3ac99b1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634589706489*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"b3e3b02c-410b-4af0-8632-3df0951e86c9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345897478693*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"2fd21520-09b8-441b-8073-917daf5ea165"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345898586136*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"8f696efe-f35a-4171-b3dd-6d47710d7526"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345898640205*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"b9c68675-9c1d-45ab-9579-4152686ab336"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345898690014*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"2ee5e2de-f616-4613-9a80-bd23e36bfacb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345898737012*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"a6969433-8026-47ba-b91b-78c6f1eb2dc8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345899919788*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"3c180826-077a-4673-aab4-180165864380"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263458999635057`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"a259ce9c-d1f7-49df-8494-97875ee00a92"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634590001798*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"5bdf0c70-3e44-4a78-81c2-8f7d33ba7e41"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345900076825*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"3bef3290-ff57-434f-b304-f286aba102ad"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634590013905*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"cef69e9a-a0e1-4356-a0c2-fa3a00eb04d9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345900988443*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"bd43a493-7fc6-4b92-b394-7fc09dc2594c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345901049855*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"a8c57e1a-e9e0-4aef-84e2-280c44b62757"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345901106474*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"ace0176d-5198-4238-b6c9-fbbcee135c7a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345901155546*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"72c7dae1-9694-4e3b-bb24-6afcdae6e348"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459020288258`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"b8974682-160d-4e9f-b397-c343c3262758"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345903295794*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"c1b444b8-57dd-4504-9cf0-a541c586d68c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459071972637`*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"bd063fdc-d35b-49c4-86b1-a0a56d48d6cb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345907236268*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"b8c9ccfb-f4ac-44dd-8aa5-f3abd27c01fe"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345907271278*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"4a7be221-5e78-455f-9b70-b3c6e835d889"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345907313057*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"906ae12a-2aeb-4477-83df-e51ac66ad482"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459085898037`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"6b8e1eee-f3ef-47c7-88c8-a601ce528dfb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459096589212`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"b3b61c1e-c68a-4214-9665-99ad0e50ec5c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345912312202*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"39ab8912-52ed-446f-bd2d-f5bc058aa52b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345912340567*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"a396ce33-611e-4267-a45b-a8f024c300af"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459123783484`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"6aa5a106-2e0c-44cf-b763-e6cdf80b8d37"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634591240659*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"3461d81e-0ae4-4c04-b79c-123dba86a11c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634591287328*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"1a0bcc5f-fd30-4cbf-b1f9-de44f1c72bb0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345913791287*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"a007b3be-9ded-42dc-8560-b745e80f624f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345913843272*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"bcf30ede-a537-49da-b4a8-abd76e27fcbf"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345913890732*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"c828bfd3-4da1-4d66-8279-2341d7de1cc7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345913936466*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"5b4a88c5-d13c-4a05-a961-6b4964f06b4d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459139906683`*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"65c5eb77-ec4f-48d7-95f9-783ca0b7a25d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345914037673*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"851d24e4-b6e4-43c4-8152-4d76241bc688"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345914088592*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"bcb50763-5465-49a9-8fcf-28e8b4f3a818"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459141489983`*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"465c0f5a-2fd3-4204-9950-73711cfbc5ac"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459142083273`*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"4d162071-34ff-4019-97b7-94f08d661cd9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345914253827*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"663c64d6-af75-41bc-a0d6-e080a00ee4ef"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345914309342*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"1fab5968-ee10-4c76-a2ea-c8eabad9802b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345914365662*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"84c7069d-041e-45e8-93ee-e702ade749aa"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634591456052*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"22f90fcb-3744-4d9c-bfba-deebf5770785"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345914636858*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"89add76f-d787-4f88-8730-4add7d066eb1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345914703702*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"9b09d79b-a73c-49c9-9a64-5a89765b21fa"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345914758502*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"eecaf081-1c46-400a-a081-b3a7666f6ba7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634591502713*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"031f241f-60ca-46e0-9902-11b146f74cbf"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345915131041*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"3cbae34b-789c-4862-8f1a-21faa8689ed3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345915219438*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"c45cab54-658a-4a7a-b6a6-4e95858366d8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634591527219*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"3534b758-18b8-46c8-ae94-8367bead2ce6"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459153242083`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"df7dae07-d146-495b-a1ad-ad9c770a44a7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345915390407*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"374cd1ce-f80e-4374-915d-2e013a2e6510"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345915443779*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"798b4b38-56a1-4a0c-9ddf-601ba8e53b16"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345915511551*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"2910d53c-29ee-4240-91f7-03e7e78130f3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459155626507`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"9ed7da4a-9073-48e5-b77e-a68195b26923"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459156151533`*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"ccbc15eb-f5ac-491a-a236-7ccc22a20751"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345915621108*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"1555ab20-83eb-4559-b6a1-e6bd248b0da5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345915662613*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"00b4c406-8a32-4c30-9c5a-89a6c2b401b3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459157140217`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"40f10f3e-7d39-4b7d-b1b8-413d9e59a387"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345915827693*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"2cd8bc44-855d-46b0-984e-7aa298be6006"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459159108353`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"9bdb1641-9b20-483a-8195-43709b435ed5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345915959009*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"ad76bdb3-55a2-4f6f-84bf-432840ba7a89"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459166791687`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"248eacd0-e2fc-432f-b62b-e01735f200f7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345920373268*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"44090342-05de-4aab-927d-d0777d913084"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345923204002*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"457a5ce9-40d3-441f-a8d8-bb989cd67141"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345923257399*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"eb8bb6c7-5361-4d7a-9370-4c5b5384fef1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459233095503`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"9380dae2-5d36-47c7-b566-2aed9d342dc2"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459233580523`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"b14f919c-1811-4c58-8fe3-a84d554947f1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345923810235*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"b30b165a-684e-45eb-926b-49a405f8ed11"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345923903273*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"d8d9e562-182e-4183-871d-32fcfa727224"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345923962323*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"35aa5d0b-ec02-45d7-8dec-14ab12d505ec"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345924003993*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"a2339664-f192-43a1-9338-220157fd5373"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345925520639*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"bb1164e2-a5b0-4198-b12e-42fa61c20581"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345925577709*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"a20b4610-421c-4784-9497-d670353aeb70"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459256368427`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"ea708535-4351-45b0-8ee2-4f1606bdf4b1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345925680443*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"00c9ecaa-7041-41a3-9687-e6fd0a931704"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459293631067`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"2c615eba-b45f-41ce-83ac-24ae52222310"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345929448983*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"6d8e8cfd-e2a9-416a-a62f-4a9c4adf1fc8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345929528796*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"9572e8a9-e919-4f7f-9b04-6c9ac32ae106"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345929586235*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"9fedf00c-b1a9-4738-8748-74e0cd371535"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345929728773*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"f37b5f45-d49b-4506-b07a-f17218c094eb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634593035001*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"0b7af16b-9fd1-49d9-8e81-548086a90bba"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459304298763`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"0f4f7b5e-6c73-495b-a136-4798046c47b2"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634593052252*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"70dfd261-ce3e-4efa-af73-30f567f28804"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345930593463*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"e6966dbe-374f-4255-904a-5464338dc520"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345931543901*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"abca962b-716a-44b0-b96d-692463bf3bc9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345931606257*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"c9f8db85-d86a-4953-ad59-82cf8e63e7c5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345931664029*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"6830b319-55cb-49d8-80bd-01d6edf6627b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345931719219*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"d230a909-9394-466a-ad1e-af9ff5728236"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345935603109*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"ab190145-b087-4b53-a36c-24f9cd30e4d1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345935679743*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"580cb3bc-89b6-4f9a-b44c-e3488d17f53b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345935690572*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"3d72b13e-c348-4080-a7a1-21b8e784a6d9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345935751278*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"2126164d-fa84-46cc-b08f-c8984675ec2f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459358196383`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"ce4b5120-4327-400b-8e2c-dbc931416fc7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345937847211*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"3f38d658-68cd-43d9-8d06-003545b08f57"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345937920569*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"212f5576-f78a-4339-b37b-ff413cdba6af"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345937992244*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"3d6e6e22-d61c-446c-b79c-39d0d8cb28a0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345938058167*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"e52a78a5-d8d7-4f2b-9dab-00d809d46fca"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345939109874*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"cc873a64-8dfe-44d4-86d1-51226f57cf63"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345940895029*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"70b7cda6-1df4-454d-a972-a6a139828a79"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345940941058*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"44d8d221-e202-40fb-a16b-e2dc73c9074f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459409929447`*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"1a63e52f-442a-4cf9-aa45-077690a03020"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459410455427`*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"de7807dc-2082-4adc-94bf-20069b07d345"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459433207397`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"9989ecc8-babd-434e-aea9-b2d8ae45b51e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345943326366*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"48f4c901-a994-46d4-b441-26e4311b8fe5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345943397252*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"fa228080-3792-46cb-9ebc-070d7de9dc07"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345943455556*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"103c53a4-92a2-499a-be59-5c1452dfe218"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459435197067`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"f802d54c-c860-4f12-967a-f472d49db87a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459435873013`*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"7c578ad3-29f3-43d7-a1ad-94a9c820dc7a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345943669643*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"e33ef7c1-ba04-4114-8476-91e863faa877"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345943742074*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"e578fc52-a5da-47d5-8703-e7ca06908209"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459438087893`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"a63db450-e79c-4848-a16d-d5145e9def2f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634594387201*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"ff547d16-4e3f-492c-a37c-f5444c14aaa9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459439359217`*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"7b7d185d-95fd-4cd1-bdd7-ae12ef77b978"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345944014896*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"8b9c4fb0-4eb7-4d1a-aff2-d8c75ee05a92"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345944091227*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"a6121b36-0f1c-4e2b-89ab-714e62a629c9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345944153822*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"6849bd49-f782-4337-8c4c-b95ddd4fb61f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345944213292*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"69b45c83-3055-4dd5-9505-8e0d650adf96"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345944278246*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"e7464d65-5829-4ce9-a7d4-5497a667e6e0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345944349566*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"deb367ad-9e96-42c9-ab52-1295becbcc77"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345944418672*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"def304b3-8d3c-4774-8f5c-f2e30c3e31a2"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459444889097`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"6076b058-3c40-4485-b2d0-64680741d4a9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345944553425*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"7615c5d8-6a70-4e7d-bc41-37ee9bdad8fe"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459446342077`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"3864b58c-65e7-43a3-9b0d-31de3c78cc6b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634594470448*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"d88a79f9-cf97-49ca-badf-52fdc2e135da"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345944770266*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"ceefb892-55f1-4fd6-bfac-3bf1c012cae2"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459448500757`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"855a771e-db96-4155-8e2e-917497ee6769"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345945373769*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"74979533-00ec-4420-9f01-d8f4e4919cd5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459454446087`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"35e0f592-d253-42b6-8cd9-b4d83357c396"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459455041113`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"81ba5f42-b0ca-4379-825b-9180bb1d9d8f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459455818377`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"082b4593-3455-4ffb-93c5-c3cdd33c544a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "bddir"}], "MessageName"], " ", ":", + " ", "\<\"The search direction \\!\\(\\*RowBox[{\\\"{\\\", \ +\\\"5.2220915145539229651`20.*^-15\\\", \\\"}\\\"}]\\) is not a descent \ +direction for the merit function. The step will be taken without the line \ +search.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345946295125*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"893436cb-9a63-42dc-a787-6213fb608882"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345952157078*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"4947542e-f25b-49a2-8a13-81de2d4a507d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345952236478*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"a43f3a0b-ab5f-4f34-ab5b-bd57de1d13c3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345952305726*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"3dba5024-dc04-4d6e-a65d-507cf3cdad28"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345952366354*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"05f72cb6-e11a-4277-8d8a-54cbd5614507"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345952423294*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"7d44bb60-bd68-45a2-bc8c-65b295192230"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459524808826`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"c0cec7f2-6f5d-425d-9406-089375c93241"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345952559156*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"5077cf52-4cc7-4c45-bd2e-734cb49dd969"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634595263699*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"d7baa5d2-a469-4c5b-9c54-0eea6571f919"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459538881693`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"c8d362d7-c462-4391-8a6b-d56dd921b07d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459539661694`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"7aaa464b-dcea-41f9-92c7-3f0f8d3bbc92"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345954036077*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"9d337a05-cfda-417e-a2f1-22ef594210d1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345954101797*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"9b07c716-6e96-477e-979e-de518c44fd41"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345957042115*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"437e294d-3922-4948-884f-a469667b9c05"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345957106147*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"d7a50c78-a75e-4754-ae1c-5a25b30b743e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345957162573*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"7f66f3f6-42f5-4c81-9f26-2fbd67c328e8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345957228156*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"22277cce-bcff-4bc2-bcfe-4bf980cfd802"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345959949389*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"98f19bc9-bc5f-4c2d-996c-46091fd379a3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634596003832*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"6df65c42-265d-4a1f-962f-50bbcd3248c9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459601036167`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"d92abf87-8cd3-46d2-a711-ed59426b7d7c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459601787863`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"6b3bba6d-af29-4235-870e-7dfbef2ecd43"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634596024721*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"13e30252-a9ef-4694-8f0f-4019250da29c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345960327958*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"3dfeaef7-339d-4eb3-9b11-d3dda3c930f0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345960377021*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"00bc0b46-d78f-4cab-b77f-32e9b2f19f2e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459604397717`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"c6ce2613-627c-4849-b1b2-550c82f53249"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "nlnum"}], "MessageName"], " ", ":", + " ", "\<\"The function value \\!\\(\\*RowBox[{\\\"{\\\", \\\"Indeterminate\ +\\\", \\\"}\\\"}]\\) is not a list of numbers with dimensions \ +\\!\\(\\*RowBox[{\\\"{\\\", \\\"1\\\", \\\"}\\\"}]\\) at \ +\\!\\(\\*RowBox[{\\\"{\\\", \\\"loga\\\", \\\"}\\\"}]\\) = \ +\\!\\(\\*RowBox[{\\\"{\\\", RowBox[{\\\"-\\\", \\\"38.12164785733958`\\\"}], \ +\\\"}\\\"}]\\).\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345960507634*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"9379d9c0-e903-478f-accc-b481d7fee271"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459653966303`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"5222bf17-0e90-430d-821a-dbf4a284d4fb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345965462831*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"0f22eee2-6947-4691-a2eb-95cc12c12b68"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459655344877`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"9cdca55e-5822-47ba-a959-d8fd078a1ea0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345965601069*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"56fe29e1-9a43-4b53-b24f-07068dcefa89"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459656681843`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"9adcdc53-3669-49d8-8705-6a24f41ab51f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345966264514*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"ba9370ee-c5ca-4c51-9e97-d276eebee7f7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345967860849*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"47b83af7-dab2-41ee-9dde-1af1fbbf8882"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459679463577`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"51e5618e-093b-4346-9f84-d5d526064fe4"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459680231256`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"596a90f5-2538-4be4-a533-4e4a62c611fb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345968098921*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"182cdc57-f0ac-4977-8d8e-ea02b1ae83a2"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345969002721*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"d70070a5-2c1d-4670-8292-67916c02f8b6"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345969071035*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"801533e9-9558-415a-8db4-5349b89b50ae"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345969134262*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"d807abe5-bb14-4c6f-870a-b1aeb48347e0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345969198677*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"69f9f278-6645-48a2-829c-19fe4ebfc578"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459701388073`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"4d6d8271-b66a-4ed7-bbfc-7e9e7a15564c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345970209096*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"44b091e5-0e8c-4c03-99d3-e8fb14fb987b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345970276791*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"135cd65a-fb66-4d62-affb-6df93d3a45ff"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634597034975*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"4702768e-9a7c-46ab-b2a5-bb93126935a7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345970439312*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"f49879dd-a092-4e0e-a7d6-a2a028fc3b03"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345983018442*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"7ee37be0-db19-4eae-9e1d-5d254ffb28fa"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345985346136*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"3f693613-47ef-4e2f-a685-74475e674919"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345985416479*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"75ae9353-f245-4ef0-8ffc-1518f7ed223c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345985484437*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"73e9c7b0-675f-4557-9d80-300f51d02ae5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459855653152`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"cc11b446-57f9-4495-ae5c-9a8def358e36"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459858273153`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"f826c32b-795f-4ba3-9362-1c3a7afb62c8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345985893723*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"c0378200-dc93-4828-86b2-e48745b35f59"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345985973804*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"d65fa205-8216-4dea-a13d-e3cac2082912"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345986034309*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"471b4661-3240-44ac-8449-619a85c6c2bb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345987997908*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"fda59fcd-3cdd-40c4-967c-8a2d4f2eb5a9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459880898333`*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"fa153bb3-6a9b-45cc-be7b-40865a7d8674"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459881702833`*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"4d630a65-bdbc-443f-a578-9779ffcec9e1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345988247558*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"a461856c-ceb8-4364-9969-200ae74f75c4"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345989521221*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"aabda5dc-d9ad-43fa-8e34-d8287399df15"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345989596356*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"d7fd4ed2-57ae-40ec-ba71-941d6fe5a55a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459896635036`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"9bfc0ae6-4529-410f-aece-1d1e0a9371d1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345989750352*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"4e66aedc-297f-44fd-978a-6dda40646c69"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459905766973`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"0a59f16b-4c98-4c7a-970f-2c2a110c6171"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345991756518*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"a2951630-a78b-411e-92b1-0b1b0f2459b2"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345991823653*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"25672ae0-345b-4a7e-9773-631ec0d35d1d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634599188336*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"1e7f37c7-6d18-4a5d-afc2-e05139b4ef78"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345993075211*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"5482ce83-48e9-4edb-bef4-ec77f7825b8e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345997205296*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"25220d62-efc4-45b5-addf-54675c7cd245"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345997273622*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"e5e2aebd-7377-4996-8fb0-92069ef6b284"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345997333962*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"ce177ce7-32e1-4d94-a4f0-7ed702cac54d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345997402977*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"f6985399-d23a-4a6c-bcc8-f4b453d96c9b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459976212063`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"20ba3386-66db-4cba-b343-dbc490c78ee1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345997695841*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"32cafcb9-3dc9-4842-bfea-003100a10307"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345997755548*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"7789d30a-e590-471a-b4b0-bae9faf5adc3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345997809948*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"bad98833-2a19-4419-ad20-2fa5d0a5987d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345998643755*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"878546f2-b2de-48c1-970a-61e03c5b5db1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345998722122*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"7dd9bc04-3cbb-46d4-85c2-c92efbf5b6c9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345998785953*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"f7bb5154-f8a7-4bc4-873f-1536c90c7a52"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345998884313*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"fa8dee13-01fe-42f3-a75c-795db9a89f53"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345999484551*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"d672d830-3500-4fae-a77b-eabf0c0cd32a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345999559577*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"4ed0bac6-abbe-48cb-9913-7772d42c77ca"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826345999632862*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"e98dbab4-f683-4537-a9a6-c9bfffff57b9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263459996886253`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"9a321f4f-47b6-4728-9f43-7023c29d89c5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "nlnum"}], "MessageName"], " ", ":", + " ", "\<\"The function value \\!\\(\\*RowBox[{\\\"{\\\", \\\"Indeterminate\ +\\\", \\\"}\\\"}]\\) is not a list of numbers with dimensions \ +\\!\\(\\*RowBox[{\\\"{\\\", \\\"1\\\", \\\"}\\\"}]\\) at \ +\\!\\(\\*RowBox[{\\\"{\\\", \\\"loga\\\", \\\"}\\\"}]\\) = \ +\\!\\(\\*RowBox[{\\\"{\\\", RowBox[{\\\"-\\\", \\\"44.955469689020774`\\\"}], \ +\\\"}\\\"}]\\).\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346001442999*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"b15ab9f4-88cf-4e17-96df-005c555d529a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346002789283*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"7ef5d1cc-fb20-4658-a4c3-30451be31dcc"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "nlnum"}], "MessageName"], " ", ":", + " ", "\<\"The function value \\!\\(\\*RowBox[{\\\"{\\\", \\\"Indeterminate\ +\\\", \\\"}\\\"}]\\) is not a list of numbers with dimensions \ +\\!\\(\\*RowBox[{\\\"{\\\", \\\"1\\\", \\\"}\\\"}]\\) at \ +\\!\\(\\*RowBox[{\\\"{\\\", \\\"loga\\\", \\\"}\\\"}]\\) = \ +\\!\\(\\*RowBox[{\\\"{\\\", RowBox[{\\\"-\\\", \\\"44.75885863329767`\\\"}], \ +\\\"}\\\"}]\\).\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263460028664703`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"8a289038-693f-40bc-9d93-5968bfa844f7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346002941616*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"423edbc8-4a77-46f7-b154-6e4c51687dec"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346003005175*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"4330450d-8323-4693-9c54-6da559330158"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634600307001*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"80b7a4e2-8c9f-4043-9c7b-cd60ab4766cd"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346004907888*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"669e39d6-a49b-4cd7-a24a-2781114d4c2d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346004979617*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"7767ce43-e555-4a47-8f63-edb5204ab341"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346005050479*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"49e28d51-08f7-4e88-9b30-ebb7100b5f31"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346005121667*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"8bbb7e47-060d-497b-a5f5-a7b4cd6ef8f3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346006745409*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"a96e94bc-238d-44d5-b57b-e683e4650676"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634600707195*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"93cdf34b-3b95-4ec8-bedb-4d03687ad245"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346007140594*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"f6174739-672c-4437-b3ce-9a1194bd6b0f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346007192149*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"466b0b20-37a9-429e-bacf-9186051a6780"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263460072692003`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"d1d95e1f-a32c-4a96-a627-4bc6d5ec6af1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346007328657*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"8eff9354-ff20-4a6c-aac1-2d07b07dbe7b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. 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RGBColor[0.368417, 0.506779, 0.709798], + AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, + ImageSize -> {20, 10}, PlotRangePadding -> None, + ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #}, { + GraphicsBox[{{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.880722, 0.611041, 0.142051], + AbsoluteThickness[1.6]], { + LineBox[{{0, 10}, {20, 10}}]}}, { + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.880722, 0.611041, 0.142051], + AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, + ImageSize -> {20, 10}, PlotRangePadding -> None, + ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #2}, { + GraphicsBox[{{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.560181, 0.691569, 0.194885], + AbsoluteThickness[1.6]], { + LineBox[{{0, 10}, {20, 10}}]}}, { + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.560181, 0.691569, 0.194885], + AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, + ImageSize -> {20, 10}, PlotRangePadding -> None, + ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #3}, { + GraphicsBox[{{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.922526, 0.385626, 0.209179], + AbsoluteThickness[1.6]], { + LineBox[{{0, 10}, {20, 10}}]}}, { + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.922526, 0.385626, 0.209179], + AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, + ImageSize -> {20, 10}, PlotRangePadding -> None, + ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #4}, { + GraphicsBox[{{ + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.528488, 0.470624, 0.701351], + AbsoluteThickness[1.6]], { + LineBox[{{0, 10}, {20, 10}}]}}, { + Directive[ + EdgeForm[ + Directive[ + Opacity[0.3], + GrayLevel[0]]], + PointSize[0.5], + RGBColor[0.528488, 0.470624, 0.701351], + AbsoluteThickness[1.6]], {}}}, AspectRatio -> Full, + ImageSize -> {20, 10}, PlotRangePadding -> None, + ImagePadding -> Automatic, + BaselinePosition -> (Scaled[0.1] -> Baseline)], #5}}, + GridBoxAlignment -> { + "Columns" -> {Center, Left}, "Rows" -> {{Baseline}}}, + AutoDelete -> False, + GridBoxDividers -> { + "Columns" -> {{False}}, "Rows" -> {{False}}}, + GridBoxItemSize -> { + "Columns" -> {{All}}, "Rows" -> {{All}}}, + GridBoxSpacings -> { + "Columns" -> {{0.5}}, "Rows" -> {{0.8}}}], "Grid"]}}, + GridBoxAlignment -> { + "Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> + False, GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{0}}}], + "Grid"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}}, + AutoDelete -> False, + GridBoxItemSize -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, + GridBoxSpacings -> { + "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"], + Alignment -> Left, AppearanceElements -> None, + ImageMargins -> {{5, 5}, {5, 5}}, ImageSizeAction -> + "ResizeToFit"], LineIndent -> 0, StripOnInput -> False], { + FontFamily -> "Times", + GrayLevel[0], FontSize -> 10}, Background -> Automatic, + StripOnInput -> False], TraditionalForm]& ), + InterpretationFunction :> (RowBox[{"LineLegend", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.004583333333333334`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.368417, 0.506779, 0.709798], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.24561133333333335`, 0.3378526666666667, + 0.4731986666666667], FrameTicks -> None, PlotRangePadding -> + None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.368417`", ",", "0.506779`", ",", "0.709798`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.368417, 0.506779, 0.709798]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.368417, 0.506779, 0.709798], Editable -> False, + Selectable -> False], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.004583333333333334`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.880722, 0.611041, 0.142051], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.587148, 0.40736066666666665`, 0.09470066666666668], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.880722`", ",", "0.611041`", ",", "0.142051`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.880722, 0.611041, 0.142051]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.880722, 0.611041, 0.142051], Editable -> False, + Selectable -> False], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.004583333333333334`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.560181, 0.691569, 0.194885], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.37345400000000006`, 0.461046, 0.12992333333333334`], + FrameTicks -> None, PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.560181`", ",", "0.691569`", ",", "0.194885`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.560181, 0.691569, 0.194885]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.560181, 0.691569, 0.194885], Editable -> False, + Selectable -> False], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.004583333333333334`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.922526, 0.385626, 0.209179], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.6150173333333333, 0.25708400000000003`, + 0.13945266666666667`], FrameTicks -> None, + PlotRangePadding -> None, ImageSize -> + Dynamic[{ + Automatic, + 1.35 (CurrentValue["FontCapHeight"]/AbsoluteCurrentValue[ + Magnification])}]], + StyleBox[ + RowBox[{"RGBColor", "[", + RowBox[{"0.922526`", ",", "0.385626`", ",", "0.209179`"}], + "]"}], NumberMarks -> False]], Appearance -> None, + BaseStyle -> {}, BaselinePosition -> Baseline, + DefaultBaseStyle -> {}, ButtonFunction :> + With[{Typeset`box$ = EvaluationBox[]}, + If[ + Not[ + AbsoluteCurrentValue["Deployed"]], + SelectionMove[Typeset`box$, All, Expression]; + FrontEnd`Private`$ColorSelectorInitialAlpha = 1; + FrontEnd`Private`$ColorSelectorInitialColor = + RGBColor[0.922526, 0.385626, 0.209179]; + FrontEnd`Private`$ColorSelectorUseMakeBoxes = True; + MathLink`CallFrontEnd[ + FrontEnd`AttachCell[Typeset`box$, + FrontEndResource["RGBColorValueSelector"], { + 0, {Left, Bottom}}, {Left, Top}, + "ClosingActions" -> { + "SelectionDeparture", "ParentChanged", + "EvaluatorQuit"}]]]], BaseStyle -> Inherited, Evaluator -> + Automatic, Method -> "Preemptive"], + RGBColor[0.922526, 0.385626, 0.209179], Editable -> False, + Selectable -> False], ",", + RowBox[{"AbsoluteThickness", "[", "1.6`", "]"}]}], "]"}], + ",", + RowBox[{"Directive", "[", + RowBox[{ + RowBox[{"PointSize", "[", "0.004583333333333334`", "]"}], + ",", + InterpretationBox[ + ButtonBox[ + TooltipBox[ + GraphicsBox[{{ + GrayLevel[0], + RectangleBox[{0, 0}]}, { + GrayLevel[0], + RectangleBox[{1, -1}]}, { + RGBColor[0.528488, 0.470624, 0.701351], + RectangleBox[{0, -1}, {2, 1}]}}, DefaultBaseStyle -> + "ColorSwatchGraphics", AspectRatio -> 1, Frame -> True, + FrameStyle -> + RGBColor[ + 0.3523253333333333, 0.3137493333333333, + 0.46756733333333333`], FrameTicks -> None, + 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suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462195171824`*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"80ee130d-62b6-4cf4-b992-30b1b1ecf81a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462196188507`*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"f4be69ab-ce64-4959-bf30-69254bb33c00"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462196829023`*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"75351899-f36e-4137-9657-8ab989540a22"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346219689659*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"9652fe48-7001-4939-ad94-07facfd22a84"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634621974325*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"981034e4-7681-467b-83b1-2cd4aeb3c3cb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346219834752*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"cd607010-5273-4d75-9ef0-6fd155a6d136"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346219840817*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"509d84b0-e48e-47f5-885b-f5eb3c190772"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346219891622*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"b23ee381-5407-43d0-8ef0-ed7984916eb1"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346219943609*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"f38ea902-c711-4b5a-a15c-3451051e36ef"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462199510612`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"bdacfe71-2fa4-40b7-b4af-a0db7040e7fe"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346220011609*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"876bc206-5401-466b-8019-b09db82faa35"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346220069949*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"d542ecd4-cfb6-4a55-87d5-2b0a6a50cfb7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346220076706*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"343e0c3f-e59f-448e-8669-2f96d55c7ce4"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634622014285*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"8433f9e9-4a22-4aa6-ad9d-7aabe210d6b5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462202034473`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"abd245ff-de69-4926-b42b-274c908268d8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346221427822*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"4890ee92-ba63-408a-9cbc-668fcfe128da"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346221519158*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"a2982e41-2475-47b2-9d5a-09c6527de8fd"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462216207952`*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"620956e6-bba9-43b5-9ef7-d6b70206bd1c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346221679591*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"beedfccd-1461-414b-9ff6-31207af634e5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346222998115*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"72ba1f05-5d62-42f7-a8e6-e324bcf528e6"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346223091227*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"232786d3-54c0-4039-894e-4ca208f0a1bd"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462231679087`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"d24a0eef-896c-4776-a2e0-92395282410a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462232165813`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"d75cbf0a-096f-48ba-b579-13f10e55881f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462260656652`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"835c03d7-5210-433c-88b1-64cb18a44f89"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346226153957*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"0f605e73-35aa-4f16-ad2c-f9c54085f982"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462262426147`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"21088a7b-e00c-4729-8e40-b8ef7130229a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346226300832*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"62175a58-88f1-4a3f-ab5b-ffb9bbe5634d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462390599623`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"2bc4ad06-359c-45b5-a42d-b94a103249f2"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462391368647`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"f07c87cc-63d6-4c9f-a373-9c60501fc4cc"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462392260036`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"03414564-ba76-4a8e-a511-f14e8da80d0f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346239277419*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"67743ee9-355e-4a48-98fb-c27464321727"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346240828051*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"9f32ad43-69dd-42d7-9062-7faa84e7fa16"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462416539993`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"fba37843-44df-479b-9805-97119fd6b6eb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346241778982*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"6ad7d88e-234a-4946-ba01-d17c0ab33ffa"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462419154367`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"bc697720-8293-4ca5-a2a2-7b3791c7b601"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346241973834*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"85ce6d73-328c-4275-be85-68c8f3bf9bb8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346242797592*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"5bd0ad8c-a4d5-4fbb-9718-c799b14dc474"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462428622417`*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"b320ee52-17dc-4f5d-896b-f27d5e6d4766"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346242939196*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"9f107287-310c-452c-9882-f5a57ef71845"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346242996772*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"69c3bff9-7c2f-4cb5-a109-3966349dd51e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346243351636*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"cdd720b2-0c1f-4f03-beba-335cdec2f2b0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346243357645*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"03b4c995-62cf-4a62-8945-3af041112e31"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346243430614*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"8ccc0b58-38eb-49e4-bd87-07b9af2e9c3d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462434741*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"f4e77fb0-1fe5-4d72-a0af-97a37da3626a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462435295753`*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"34591764-52b4-48a5-8645-10a8ad784120"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346243589264*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"aa30a471-7c76-4bcc-b5fc-d1d0c9e1a978"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346243646282*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"89333cee-2e48-4a52-a449-e0aaca5242d4"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346243658958*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"66f1068c-a833-4aef-980d-3ceaae39a065"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462453522053`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"b34d51ef-06e5-41dc-8ca4-12f61b7e5098"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346245453431*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"844c744e-9d36-43d0-a765-509ce1334a19"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462455559177`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"37745f8d-1368-40da-a283-c5654d012653"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462456092243`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"413ecbbd-3bf3-4a49-a043-c28f9a6ce05c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634624595829*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"f8c5d63a-65d3-49f6-8275-d3edafcdb5b4"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346246047266*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"ba4a6c36-a665-4f44-b0e9-f108b024dd21"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346246124354*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"3d245659-15cd-494a-b93d-0e250515038e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462461778927`*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"55b01a4a-526e-4dee-afb1-acdef5ad8623"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634626250105*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"92fc6cae-4539-45e6-b9e9-5fc6501ccaf6"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346262636405*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"99b32fc2-0af8-4535-aedd-ad6945b8b14e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346262760317*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"2c03c84e-d0ee-4d26-aa37-92fd157dea79"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634626282524*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"e1f8db48-1fac-43c2-b569-4c23c1d83070"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346262937182*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"22afd2ad-368c-452c-a2e3-679822ff7b67"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346263027087*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"fd014501-cbd5-4806-bf4e-c4aa7ee5c89a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634626311662*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"4fa5574f-0933-4ff9-a354-390a263a7d57"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346263178738*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"8c72094e-a44e-42f1-86cb-479d317c1521"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346263874704*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"2429caa1-b89d-408d-8722-1347cc2ca0e0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346263963396*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"8a80d050-440d-453d-9ac5-39065eb20e07"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346264052081*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"33420c5c-fb58-49e8-bbc1-ea51f18052cb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346264110228*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"cc36f5ce-0bc6-4c30-8f5c-d0d9490e15c2"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346265551619*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"d0f57b16-18cf-4ebe-92a7-ae7fe53b473c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462656281013`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"a36c6104-2bab-4692-b123-57b1f7a29864"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346265693221*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"db58bc6e-8734-4008-b418-f0800b71f2a5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346265756185*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"b9ec8ed6-951b-40d2-891a-1a0edea41400"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346267705971*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"d04439b0-834c-4777-8694-daacf0384dc9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346267795516*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"49ff2cda-63b5-433c-a45b-dfc084797aa5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346267885088*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"20ece0ff-b680-4b8e-aa46-7bd031c1a581"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346267948987*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"4b4e0c3b-2728-4c23-9356-77918a85af75"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346268236375*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"573e06fd-64b6-401a-8f14-dc6ea2161ee9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462683497047`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"9f393dc5-7ab4-4ca2-a556-16a1a135b80f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346268462531*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"f37c8654-4e16-4d83-8b20-825738070f5e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462685198307`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"9b757907-2f6c-4b70-945b-90b98353dcba"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346276969636*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"26215cac-66da-46e3-baf8-3ebb2c233cdd"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346277059145*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"8cff57ee-0689-456d-953d-c8b644f7b55d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462771592417`*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"75504a94-b04c-4687-9a54-8d0d7e942fa9"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346277219673*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"2c2f9b40-cff4-466a-90bb-bb028b700cab"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462779776*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"151ca284-6fef-4a5b-b004-13cae03db70d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346278090392*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"88392e11-a889-4c8c-8827-36df3d136f14"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462782034283`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"9e1a60b0-8d2b-4cd8-9557-83c72fd01f7b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462782632437`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"94a0caa8-8c15-452a-aca2-523927259284"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346278665595*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"2b009632-06f2-4cd1-85eb-dcfd846529d3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346278741955*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"b7d63cf7-899b-4705-a6f8-2ed4c9e1dccb"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346278830048*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"ae74e38e-34ca-4ea8-b3d0-64463e9ea543"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346278889526*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"e07331c0-d9d8-4efc-87fa-773bfa32206b"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634628169268*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"51881a3a-11a8-4da8-9aab-139b6ce1de41"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346281783012*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"df52b9e3-02a9-431b-ae1a-4b3c8f8c0e14"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346281873452*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"f0a130c4-0be4-49fa-9d43-bd4fef9b62c6"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346281933276*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"71a2e57c-d561-4346-a09d-5e6748f07015"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346285384368*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"e7d417ab-10ee-41b1-890b-003e65711483"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346287706871*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"a58a29ca-5a92-4ebd-8e17-3eb7d90f0295"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462878610353`*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"16dc3bff-9ba9-4770-9a23-9c47ef31beed"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346287976068*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"7d049eb3-934a-4a9f-abc6-7c3fff947a88"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346288066132*^9}, + CellLabel-> + "(kernel 8)",ExpressionUUID->"a5f59212-926b-41d7-952f-5be92e72c3fd"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346290234393*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"64b9f3fc-1001-44e3-909a-e942e20ed60c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462903254757`*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"b3d84f7e-e5aa-4cb2-96ff-70e521eae5f0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346290476891*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"25fdd85b-d420-4a9e-b6e4-92600eb3e102"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346290529747*^9}, + CellLabel-> + "(kernel 2)",ExpressionUUID->"6a048741-e183-4f33-be5b-62fd874d9532"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346291583024*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"9f7dfda9-4d4f-4d89-890c-05b6136e5ce7"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346296723514*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"2591ee59-e039-43d4-94c2-9bbf7e1983f5"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346296843848*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"813d2439-d853-460a-bd23-22c55cf606a0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346297023819*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"920914cf-5242-425b-8bb8-26db61579372"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.82634629713972*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"b846d998-9b8d-45cf-b304-39e145e8565f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346299442038*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"db7a3fe7-c773-4018-84e2-c252faf8ec5c"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346299542137*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"0b9988c0-dd26-475a-99d7-5f1180ebfd33"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346299619012*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"5e7fc3e6-0b74-4eb5-8710-40d23238f77a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263462996801023`*^9}, + CellLabel-> + "(kernel 7)",ExpressionUUID->"2170c169-52ad-462b-8111-6a40c2e73458"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346302296797*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"10ae9c01-3616-4775-8b9a-71eb8697d61e"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346302671054*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"cef04bdb-c148-422f-91fc-169c55b7e6d0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346302739051*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"b7d34f17-30b9-4b36-8d60-80bc8b566855"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346302800519*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"09e5c6c6-1b8a-4f18-afd9-545211f47575"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346302869577*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"165d59c9-0020-4548-a5a8-97f41e81efd6"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346302932252*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"dbd8007a-b4a1-4dc1-86c2-983132832545"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346302993598*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"e06d4a20-04c2-4550-8e25-5e71fd058e77"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263463030637903`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"7ca3f9b5-fdd7-4d51-a9fd-fc7cdddd7771"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346303129848*^9}, + CellLabel-> + "(kernel 5)",ExpressionUUID->"1cfb3636-c68d-46e8-bb42-3dfda46bf0e0"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346304817165*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"cf27f023-6b2d-4721-ab59-f0e1900cab65"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346304931551*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"3b21c9fb-3922-4176-8c81-1af33f7f65bd"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346305009302*^9}, + CellLabel-> + "(kernel 4)",ExpressionUUID->"78b2f907-049c-40ce-b8f5-9807a93dc5e8"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346305062724*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"99faa3aa-7e1a-4534-adb0-d75cefd5858a"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"General", "::", "stop"}], "MessageName"], " ", ":", + " ", "\<\"Further output of \\!\\(\\*StyleBox[RowBox[{\\\"NIntegrate\\\", \ +\\\"::\\\", \\\"slwcon\\\"}], \\\"MessageName\\\"]\\) will be suppressed \ +during this calculation.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346305111319*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"98429721-d514-4d59-b633-9a20a6a22ed3"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"FindRoot", "::", "lstol"}], "MessageName"], " ", ":", + " ", "\<\"The line search decreased the step size to within tolerance \ +specified by AccuracyGoal and PrecisionGoal but was unable to find a \ +sufficient decrease in the merit function. You may need more than \ +\\!\\(\\*RowBox[{\\\"20.`\\\"}]\\) digits of working precision to meet these \ +tolerances.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346311073678*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"8a209287-e3cf-42bf-8313-43aed9699d68"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346322950252*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"99d6f1d1-cc56-4f86-ba9b-fd045c7411aa"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263463230014133`*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"725544e9-c72d-4aa4-915e-86b141a99074"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346323057399*^9}, + CellLabel-> + "(kernel 3)",ExpressionUUID->"dc4141be-8bcf-469f-ae75-42aa5d45b598"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346323110897*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"d45f9432-fcdc-453d-a600-f95937fcc56f"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.8263463231640387`*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"ebd281f4-51af-4e86-9fca-89a1e2f24561"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ 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too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346323297261*^9}, + CellLabel-> + "(kernel 1)",ExpressionUUID->"7cdf5f1c-c68d-4dc0-a952-43520d22bb26"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", "MSG", + ShowCellLabel->True, + CellChangeTimes->{3.826346323349619*^9}, + CellLabel-> + "(kernel 6)",ExpressionUUID->"30c8081e-8f43-498e-83d5-286810e32c8d"], + +Cell[BoxData[ + RowBox[{ + StyleBox[ + RowBox[{"NIntegrate", "::", "slwcon"}], "MessageName"], " ", ":", + " ", "\<\"Numerical integration converging too slowly; suspect one of the \ +following: singularity, value of the integration is 0, highly oscillatory \ +integrand, or WorkingPrecision too small.\"\>"}]], "Message", 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a/referee_respose.txt b/referee_respose.txt new file mode 100644 index 0000000..3b204c6 --- /dev/null +++ b/referee_respose.txt @@ -0,0 +1,158 @@ +---------------------------------------------------------------------- +Response to Referee A -- LZ16835/Kent-Dobias +---------------------------------------------------------------------- + +Referee A wrote: +> The authors consider the mean-field p-spin spherical model with +> *complex* variables and study the number of saddle points of the +> energy and the eigenvalue distribution of their Hessian matrix. The +> main result of the rather technical computation is that in a +> particular limit (concretely kappa->1) the known results for the real +> p-spin spherical model are reproduced, the (expected) Bézout bound for +> the number of solutions of the saddle point equations is reached and +> that the relationships between the “threshold” and extremal state +> energies is richer in the complex case than in the real case. +> +> I must admit that I was not able to grasp any far-reaching +> consequences of the computational tour de force only hinted at in the +> manuscript, and I fear that a nonexpert reader would also not be able +> to do so. Two arguments are pushed forward by the authors to justify +> the dissemination of their results to the broader readership of PRL: +> One is that there are indeed situations in which complex variables +> appear naturally in disordered system. The first example the authors +> mention is a Hamiltonian that could be relevant for with random Laser +> problems and was analyzed 2015 in PRA, which has up to now 30 +> citations according to Google Scholar, and the second example is a +> Hamiltonian from sting theory that was analyzed in 2016 in JHEP, which +> has up to now 31 citations. I do not feel that these two examples +> prove that the enumeration of saddle points if the p-spin model is +> important or of broad interest. +> +> The second argument of the authors is that extending a real problem to +> the complex plane often uncovers underlying simplicity that is +> otherwise hidden, shedding light on the original real problem. Here I +> come back to what I already mentioned above: I do not see any +> simplicity emerging from the present calculation and I also do not see +> the original problem in a new light. Therefore, I do not think that +> one of the four PRL criteria is actually fulfilled and I recommend to +> transfer the manuscript to PRE. + +We disagree with the referee's assessment here, as we have also explained in +our letter to the editors. Something in particular that goes unaddressed is +another motivation (which in the referee's defense we did not enumerate clearly +in our draft): that understanding the distribution of complex critical points +is necessary in the treatment of a large class of integrals involved both in +the definition of quantum mechanics with a complex action and in ameliorating +the sign problem in, e.g., lattice QCD. + +If the criteria for publication is to be "first past the post" of cited +citations, one might examine our citations of that literature: + + - Analytic continuation of Chern-Simons theory, E Witten (2011): 444 citations + + - New approach to the sign problem in quantum field theories: High density + QCD on a Lefschetz thimble, M Cristoforetti et al (2012): 285 citations + +Both works are concerned with the location and relative positions of critical +points of complex theories. In the resubmitted manuscript we have better +emphasized this motivation. + +Referee A wrote: +> Although the first part of the manuscript is well written and well +> understandable (at least for me) from page 2 on it becomes very +> technical and unreadable for a non-expert. If the reader skips to the +> results and tries to understand the figures she/he is left with the +> ubiquitous parameter a, whose physical meaning is hidden deep in the +> saddle point calculation (“dictates the magnitude of |z|^2” – well, +> with respect to the solutions of (3): is “a” the average value of the +> modulus squared of the solution z’s or not?). Similar with epsilon: +> apparently it is the average energy of the saddle point solution – why +> not writing so also in the figure captions? The paper would profit a +> lot from a careful rewriting of at least the result section and to +> provide figure captions with the physical meaning of the quantities +> and parameters shown. + +We thank the referee for their helpful suggestions with regards to the +readability of our manuscript. In the resubmitted version, much has been +rewritten for clarity. We would like to highlight several of the most +substantive changes: + + - The ubiquitous parameter 'a' was replaced by the more descriptive 'r^2', as + it is a sort of radius, along with a new parameter 'R^2' which bounds it. + Descriptions in English of these were added to the figure captions. + + - The technical portion of the paper was reordered to connect better with the + sections preceding and following it. + + - The location of the results is now indicated before the beginning of the + technical portion for readers interested in skipping ahead. + +Referee A wrote: +> A couple of minor, technical, quibbles: +> +> 1) If there is any real world application of a p-spin model with +> complex variables it will NOT have a spherical constraint. I would +> suggest to discuss the consequences of this constraint, which is +> introduced for computational simplicity. +> +> 2) After eq. (2): ”We choose to constrain our model by z^2=N.“ Then it +> is not a spherical constraint any more – does it have any physical +> relevance? + +We have added a more detailed discussion of the constraint to address these +confusions, emphasizing its purpose. The new paragraphs are: + +> One might balk at the constraint $z^Tz=N$---which could appropriately be +> called a \emph{hyperbolic} constraint---by comparison with $z^\dagger z=N$. +> The reasoning behind the choice is twofold. +> +> First, we seek draw conclusions from our model that are applicable to generic +> holomorphic functions without any symmetry. Samples of $H_0$ nearly provide +> this, save for a single anomaly: the value of the energy and its gradient at +> any point $z$ correlate along the $z$ direction, with $\overline{H_0\partial +> H_0}\propto \overline{H_0(\partial H_0)^*}\propto z$. This anomalous +> direction should thus be forbidden, and the constraint surface $z^Tz=N$ +> accomplishes this. +> +> Second, taking the constraint to be the level set of a holomorphic function +> means the resulting configuration space is a \emph{bone fide} complex +> manifold, and therefore permits easy generalization of the integration +> techniques referenced above. The same cannot be said for the space defined by +> $z^\dagger z=N$, which is topologically the $(2N-1)$-sphere and cannot admit +> a complex structure. +> +> Imposing the constraint with a holomorphic function makes the resulting +> configuration space a \emph{bone fide} complex manifold, which is, as we +> mentioned, the situation we wish to model. The same cannot be said for the +> space defined by $z^\dagger z=N$, which is topologically the $(2N-1)$-sphere, +> does not admit a complex structure, and thus yields a trivial structure of +> saddles. However, we will introduce the bound $r^2\equiv z^\dagger z/N\leq +> R^2$ on the `radius' per spin as a device to classify saddles. We shall see +> that this `radius' $r$ and its upper bound $R$ are insightful knobs in our +> present problem, revealing structure as they are varied. Note that taking +> $R=1$ reduces the problem to that of the ordinary $p$-spin. + +Referee A wrote: +> 3) On p.2: “…a, which dictates the magnitude of |z|^2, or +> alternatively the magnitude y^2 of the imaginary part. The last part +> is hard to understand, should be explained. + +We thank the referee for pointing out this confusing statement, which was +unnecessary and removed. + +> 4) On p.2: “In most the parameter space we shall study her, the +> annealed approximation is exact.” I think it is necessary to provide +> some evidence her, because the annealed approximation is usually a +> pretty severe approximation. + +We have nuanced the statement in question and added a citation to a review +article which outlines the reasoning for analogous models. The amended sentence +reads: + +> Based on the experience from similar problems \cite{Castellani_2005_Spin-glass}, +> the \emph{annealed approximation} $N\Sigma\sim\log\overline{\mathcal N}$ is +> expected to be exact wherever the complexity is positive. + +Sincerely, +Jaron Kent-Dobias & Jorge Kurchan + diff --git a/referee_respose_2.txt b/referee_respose_2.txt new file mode 100644 index 0000000..4ddc8e3 --- /dev/null +++ b/referee_respose_2.txt @@ -0,0 +1,21 @@ +The latest reviews had nothing to say about the scientific content of our +paper, only about its relevance to Physical Review Letters. For resubmission to +Physical Review Research, we have therefore changed nothing except to expand on +our reasoning regarding the relevance of this work to the broader physics +community, and indeed across disciplines. The end of the fourth paragraph now +reads: + +> [...] In order to do this correctly, features of the action's landscape in +> complex space---such as the relative position of saddles and the existence of +> Stokes lines joining them---must be understood. This is typically done for +> simple actions with few saddles, or for a target phenomenology with +> symmetries that restrict the set of saddles to few candidates. Given the +> recent proliferation of `glassiness' in condensed matter and high energy +> physics, it is inevitable that someone will want to apply these methods to a +> system with a complex landscape, and will find they cannot use approaches +> that rely on such assumptions. Their landscape may not be random: here we +> follow the standard strategy of computer science by understanding the generic +> features of random instances of a simple case, expecting that this sheds +> light on practical, nonrandom problems. While in this paper we do not yet +> address analytic continuation of integrals, understanding the distribution +> and spectra of critical points is an essential first step. |