{ "metadata": { "name": "", "signature": "sha256:fba091bb7fda43bdea908832df43e46dad908a7876b21a3ed7c3110c92aa13a3" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "
A Conjeture About Trigonometric Polynomials
" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "
Grupo de AnĂ¡lisis Funcional no Lineal
\n", "
Bogot\u00e1 D.C. 2014
" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Conjeture Formulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $\\Omega =(0,\\pi)\\times (0,2\\pi)$ and let $\\psi:\\Omega\\to \\mathbb{R}$ defined by $$\\psi(x,t)=\\sum_{k^2-j^2=-\\lambda_0}a_{kj}\\sin(kx)\\sin(jt)+b_{kj}\\sin(kx)\\cos(jt),$$ where $\\lambda_0\\in \\mathbb Z\\setminus\\{0\\}$ fixed and $\\int_\\Omega \\psi^2 = 1$. Let $\\alpha,\\beta>0$ and $E_0=\\{(x,t)\\in\\Omega\\,:\\,|\\psi(x,t)|<\\epsilon^\\beta\\}$. Then, if $0<\\alpha<\\beta<1$, there are $M,\\epsilon_0>0$ such that if $\\epsilon\\in(0,\\epsilon_0)$ then $\\mu(E_0)\\beta$ there is no such $M$. Obviously this conjeture can be extended in a more general setting, but this is the case we are interested in." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Experimental Approach" ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Libraies" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Instruction for inline graphics\n", "%matplotlib inline\n", "#Plotting library\n", "import matplotlib.pyplot as plt\n", "import matplotlib.patches as mpatches\n", "#Basic mathematical functions library\n", "import numpy as np\n", "#Numerical analysis library integration funcitons\n", "from scipy.integrate import quad\n", "from scipy.integrate import dblquad" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 104 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "$\\psi$ function definition and testing conditions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are going to define a trigonometric polinomial correspondign to $-\\lambda_0=15$. The posible values for the couples $k,j$ are $(4,1)$ and $(8,7)$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def psi(x,t):\n", " return 0.434777248914389*np.sin(4*x)*np.sin(t)-0.1*np.sin(4*x)*np.cos(t)+0.05*np.sin(8*x)*np.sin(7*t)-(1/30)*np.sin(8*x)*np.cos(7*t);" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 21 }, { "cell_type": "code", "collapsed": false, "input": [ "dblquad(lambda x, t: (psi(x,t))**2,0,2*np.pi, lambda x: 0, lambda x: np.pi)[0]" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 22, "text": [ "1.0000000000000007" ] } ], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's clear thath the chosen $\\psi$ satisface the conditions of the conjeture." ] }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Defining the area function, the estimate function and the steps of the iterations" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def area(eps,beta,N):\n", " A = 0;\n", " Dx = np.pi/N;\n", " Dy = 2*np.pi/(2*N);\n", " for i in range(0,N):\n", " for j in range(0,2*N):\n", " if (np.abs(psi(i*Dx,j*Dy)) < eps**(beta)):\n", " A = A + Dx*Dy;\n", " return A;" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 54 }, { "cell_type": "code", "collapsed": false, "input": [ "#This is the steps of the area calculation (the N)\n", "\n", "max_area_steps = 300;\n", "\n", "#This is the max plot steps\n", "\n", "max_plot_steps = 50;\n", "\n", "#Defining the $\\epsilon_0$\n", "\n", "epsilon_not = 0.01\n", "\n", "x = np.linspace(0,epsilon_not,max_plot_steps);\n", "\n", "#y is the vector of the areas of E_0\n", "\n", "def area_vector(beta):\n", " y = np.linspace(0,epsilon_not,max_plot_steps);\n", " for i in range(0,max_plot_steps):\n", " y[i] = area(x[i],beta,max_area_steps);\n", " return y;\n", "\n", "#z is the vector of the estimators $M\\epsilon^\\alpha$\n", "\n", "def estimator(alpha,M):\n", " z = np.linspace(0,epsilon_not,max_plot_steps);\n", " for i in range(0,max_plot_steps):\n", " z[i] = M*x[i]**(alpha);\n", " return z;" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 182 }, { "cell_type": "heading", "level": 4, "metadata": {}, "source": [ "Graphing the situation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the next code we are going to graph for different values of $\\alpha$, $\\beta$ and $M$ the curves $\\mu(E_0)$ and $\\epsilon^\\alpha$ depending on $\\epsilon$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.rc('text', usetex=True)\n", "plt.rc('font', family='serif')\n", "fig, (ax1,ax2,ax3) = plt.subplots(1, 3, sharey=False, figsize=(20,5))\n", "\n", "alpha1 = 0.2\n", "beta1 = 0.5\n", "M1 = 300\n", "alpha2 = 0.001\n", "beta2 = 1\n", "M2 = 1\n", "alpha3 = 0.3 \n", "beta3 = 0.7\n", "M3 = 20\n", "\n", "ax1.plot(x,area_vector(beta1),label=\"$\\\\mu(E_0)$\");\n", "ax1.plot(x,estimator(alpha1,M1), label=\"$M\\\\epsilon^\\\\alpha$\");\n", "ax1.set_title(\"$\\\\alpha=$\" + str(alpha1) + \", $\\\\beta=$\" + str(beta1) + \" y $M=$\" + str(M1), fontsize = 25)\n", "ax1.set_xlabel(\"$\\\\epsilon$\",fontsize = 20)\n", "ax1.legend()\n", "ax2.plot(x,area_vector(beta2),label=\"$\\\\mu(E_0)$\");\n", "ax2.plot(x,estimator(alpha2,M2), label=\"$M\\\\epsilon^\\\\alpha$\");\n", "ax2.set_title(\"$\\\\alpha=$\" + str(alpha2) + \", $\\\\beta=$\" + str(beta2) + \" y $M=$\" + str(M2), fontsize = 25)\n", "ax2.set_xlabel(\"$\\\\epsilon$\",fontsize = 20)\n", "ax2.legend()\n", "ax3.plot(x,area_vector(beta3),label=\"$\\\\mu(E_0)$\");\n", "ax3.plot(x,estimator(alpha3,M3), label=\"$M\\\\epsilon^\\\\alpha$\");\n", "ax3.set_title(\"$\\\\alpha=$\" + str(alpha3) + \", $\\\\beta=$\" + str(beta3) + \" y $M=$\" + str(M3), fontsize = 25)\n", "ax3.set_xlabel(\"$\\\\epsilon$\",fontsize = 20)\n", "ax3.legend()\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { 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UlS+UJ8RVlL/Kplwjvqw/jpfJFt+jdtqz1PaLy1SmB1FZojCXiUsp/D2o+uGIh0RgDg/s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\nC9OmWRySVDhyWiCqrKpkmxI7iCRJ6dlBJElqjHza5r6qKmyqsPfesHw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"text": [ "" ] } ], "prompt_number": 186 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the preciding graphics the estimate $M\\epsilon^\\alpha$ is above the graph of $\\mu(E_0)$ for small enough $\\epsilon$. You can change the values of $\\alpha$, $\\beta$ and $M$ to test the conjeture." ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "The case $\\alpha>\\beta$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the case $\\alpha>\\beta$ there is no $M$ such that $\\mu(E_0)\\leq M\\alpha^\\beta$. In the next code we graph the situation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plt.rc('text', usetex=True)\n", "plt.rc('font', family='serif')\n", "fig, (ax1,ax2,ax3) = plt.subplots(1, 3, sharey=False, figsize=(20,5))\n", "\n", "alpha1 = 0.7\n", "beta1 = 0.4\n", "M1 = 1\n", "alpha2 = 0.7\n", "beta2 = 0.4\n", "M2 = 50\n", "alpha3 = 0.7 \n", "beta3 = 0.4\n", "M3 = 1000\n", "\n", "ax1.plot(x,area_vector(beta1),label=\"$\\\\mu(E_0)$\");\n", "ax1.plot(x,estimator(alpha1,M1), label=\"$M\\\\epsilon^\\\\alpha$\");\n", "ax1.set_title(\"$\\\\alpha=$\" + str(alpha1) + \", $\\\\beta=$\" + str(beta1) + \" y $M=$\" + str(M1), fontsize = 25)\n", "ax1.set_xlabel(\"$\\\\epsilon$\",fontsize = 20)\n", "ax1.legend()\n", "ax2.plot(x,area_vector(beta2),label=\"$\\\\mu(E_0)$\");\n", "ax2.plot(x,estimator(alpha2,M2), label=\"$M\\\\epsilon^\\\\alpha$\");\n", "ax2.set_title(\"$\\\\alpha=$\" + str(alpha2) + \", $\\\\beta=$\" + str(beta2) + \" y $M=$\" + str(M2), fontsize = 25)\n", "ax2.set_xlabel(\"$\\\\epsilon$\",fontsize = 20)\n", "ax2.legend()\n", "ax3.plot(x,area_vector(beta3),label=\"$\\\\mu(E_0)$\");\n", "ax3.plot(x,estimator(alpha3,M3), label=\"$M\\\\epsilon^\\\\alpha$\");\n", "ax3.set_title(\"$\\\\alpha=$\" + str(alpha3) + \", $\\\\beta=$\" + str(beta3) + \" y $M=$\" + str(M3), fontsize = 25)\n", "ax3.set_xlabel(\"$\\\\epsilon$\",fontsize = 20)\n", "ax3.legend()\n", "plt.show()\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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hMtZsWMN9J97H4XsdvtljcnKaJk80bWlJUtZo2bIlK1asiDqMlNW8eQvuu285s2fD7Nkw\ndy7svHPUUUlS8pgnata8eQvuvLM8T7z1Fuy9d9RRSVJymCNqd0KLE1i+fHnCtm/PIEkNkpOTg9/z\n6uXk5NCtW4x27eDQQ8OlZcumq+RnAPOElOHMEzXLycnhzDPL80TbtrDjjuaJCswTUgYzR9Suun3U\nVHnCYpCkBrEBr1miG+8MYJ6QMpx5ombmiVqZJ6QMZo6oXaLzhBNIS5IkSZIkZRGLQZIkSZIkSVnE\nYpCkrLNkyRImT568yW1Lly6lc+fO9OjRg9GjRzN69GgGDhxIu3btqtzG6NGjkxGqJCkC5glJUk0y\nIU+4mpikrDN69Gj69u27yW2tWrUiJyeH66+/njZt2pTd3rp16yq3kZ+fz+jRo+nWrVtCY5UkJZ95\nQpJUk0zIE/YMkpRVJk2axKGHHlrlfUuWLClruOOV/o4dO1b52FatWjFz5szEBClJiox5QpJUk0zJ\nExaDJGWkHj16lF0//fTTy66PGjWKDh06bPb4OXPmkJeXx+jRo+nRowerVq0CoHnz5tW+xk477cTS\npUubMGpJUrKYJyRJNcn0POEwMUkZJ94Qx9WlgZ00aRI9evSgW7du5Obmlo3tXbVqFbFYjCFDhpCX\nl0deXh5t27YFIC8vjyVLltCqVavE/CGSpIQwT0iSapINecKeQZISIienaS4NMWnSJLp06QKEhrxz\n585l9y1fvrza53Tq1AkIXTmbN2/O0qVLWb58OUOGDOGiiy6iW7duDBo0qOw5ubm5rFy5smFBSlKW\nM09Ikmpinkgsi0GSEiIWa5pLQ4wcObJsHO/IkSPp1KkTc+fOBaBly5ZVPmfWrFnsu+++m9w2atSo\nsrG8O+64IxDGAcetXLmS3NzchgUpSVnOPCFJqol5IrEsBknKKCtXrmTJkiU89dRTzJ07l5122okl\nS5aUNbK5ubll43chdNu89tpr2WmnncqWgBwyZAhdunTZZGK41atXb/ZaM2fOpH379on/oyRJTcY8\nIUmqSbbkCecMkpRRJk2axPXXX0/v3r0BysbjxvXs2ZNJkyaVLeHYvHlzBgwYwIABAzZ5XGFhYdn1\n9u3b8/XXX7PjjjtuVrmPV/glSenBPCFJqkm25AmLQZIyyqxZs7j44ourvb9t27bMmjWrXtvs06cP\ngwcPJjc3l+uvvx4IS0WeccYZjYpVkpR85glJUk2yJU80cDqlWsViDR2cJykt5OTkkM7f88mTJ9Ox\nY8cGPXfVqlXMmjWrxudXt39ywix2iWp704l5Qspw5gnzRCOZJ6QMlu45AtI/T1gMktQgmdCAJ5IH\n+bUyT0gZzjxRM/NErcwTUgYzR9Qu0XnCCaQlSZIkSZKyiMUgSfX24YdRRyBJSmXvvht1BJIkqSZO\nIC2pVsXF8OabMG4cPP88fPJJ1BFJklLJ+vUwfXp5nvj++6gjkiRJNbFnkKQqLV8OTzwB55wDu+0G\nF10UikL33QeffRZ1dJKkqH32GfzrX9CtG+y6K/z5z9C8ecgdH30UdXSSJKkmTiAtCYC1a2HGDJgy\nBSZNgrfegoICOOkkOOEE+PGPN328k77VzIlBa2WekNLMt9/Cq69CURFMnAiLF0OXLnDiiSFP7Lrr\npo83T9TMPFEr84SUwcwRtXM1MUkJsW5dGPo1ZUo4sJ85E372s1AA6tABjj0Wttmm+ufbgNfMg/xa\nmSekFPfdd/DaayFHTJkSThLk58Ovfx3yxFFHQbNm1T/fPFEz80StzBNSBjNH1M5ikKQm89lnMHZs\nuLz8Mvz0p6H48+tfw9FHw4471n1bNuA18yC/VuYJKQV98EGY82fs2FAIOuSQkCMKCuDII2G77eq+\nLfNEzcwTtTJPSBnMHFE7l5aX1GCxGMybB3//Oxx2GBx4YOja3707LF0aegMNHBi6+NenEJQOli5d\nykUXXUSXLl02u2/JkiW0aNGCoUOH1riNIUOGMHnyZIYMGcKqVasSFaokRaa4GF5/Ha6/Hg46KOSK\n2bOhT5+wWMD06SGHdOxYv0JQOjBPJFV3oCPwYIXbBpT+LEx+OJJUu0zPExaDpAwTi4UD+WuugVat\nQuFn+XLo3x+++AJGjAiTQu+0U9SRJlarVq3o0aMHS5Ys2ey+OXPmcNhhh9G7d+9qnz948GBat25N\nx44dmT17NrNmzUpkuJKUNCUlMG0aXHYZ7LlnKPwADB4Mn34KjzwSJoXeYYdIw0w480TSdCy9TAby\ngDaltxcC7wOLI4pLkmqU6XnCpeWlDBCLwYIFodAzYkS4rWdPeO65cKY3J0s7m8diMXJzcze5be7c\nuaxYsYLTTz+9xufOmTOHPvH/kIC8vLyExChJyRCLhUUCRoyAp56Cli1Dnpg2DfbfP+roomOeSIrJ\npReAlsC80uuFwOhIIpKkOsrkPOGcQVKaisVg/nx4+ulwYL9mDfToEQ7u8/MTXwCqbZxvzs1NE0Ds\npoa1JUuXLqVly5YUFhYyYMAAWrVqtcltt99+O/vuu2/Z4ydNmsTcuXPJy8ujW7duzJ07l1mzZpGX\nl8ecOXPIzc2lsLDuPdmdC6JW5gkpwUpK4I03Qp4YNQq23TbkiJ49w7DhRDNP1CzL8kRzoA+whPIC\nUGHp7/nAwCqeY56QMlhd5gwyTyQ2T9gzSEojJSXhzO7o0eHgPicHunaFhx+Gww9PrR5ADW10m8qS\nJUto1aoVeXl5ZddXrlxJq1atmDNnziYN95IlS7j99tuZMGFC2W1t27albdu2AHTs2DHZ4UtSg2zY\nAFOnhhzxzDNhSHDXrqnZU9Q8kVVWEQo+E4A5wFJgSOl9nSkfRiZJZcwTiWUxSEpxa9aEZX3Hjg0H\n9i1bhrkcnnkGDj44tQ7sU1Hr1q1ZsmQJLVu2pG3btixZsoT8/PxNHjNq1CgOPfRQRo8eTV5eXlmj\nLUnpYPVqmDQprAL2/POQlxcKQEVF8JOfRB1d6jNPJFw+EAPmEgpB3YGVwHJCL6GvCXMJbVYM6tev\nX9n1goICCgoKEh6sJFUWdZ4oKiqiqKioybYXZzFISkHLlsG4ceEydSq0aQMnnQRTpoTl4FV3eXl5\nDBo0iM6dOwOh+2b8elxOTg6dOnVKyYq9JFUWi8F775XniTffhKOOCnni5pvhxz+OOsL0Yp5IuI6E\nIhBALvAmoadQfCbVnYCJVT2xYjFIkqISdZ6oXAy/+eabm2S7FoOkFLBiRVi+95VX4MUX4fPP4fjj\nw6pfjz0GLVpEHWH6WLVqFddeey05OTl07NiRdu3aMXfuXPbdd18mTZrE7bffvtlkb3379mXgwPLp\nCjzYl5RqPv88TPb8yivwwguh1+hJJ8Ef/hCWff/hD6OOMH2YJ5JuMNCD0PtnBfB06e3dSn9+Rfmk\n0pIUuWzJE04gLUXg00/DQf3UqeGydCkccQT86lfQuTMcdhhsuWXUUdasLpO+ZbMsmxi0IcwTUg0+\n/LA8R0ydCl98Ab/8ZcgTxx0HhxyS+sOEzRM1M0/UyjwhZTBzRO0SnScsBklJsnIlPPFEmOx50SI4\n+mg45phwadsWmjWLOsL6sQGvmQf5tTJPSJV8/nnoDfrII/DVV6HwE88Tv/hF6p8kqMw8UTPzRK3M\nE1IGM0fUzmKQlMZKSmDy5FAAGj8eunSBCy4IvX/S7aC+MhvwmnmQXyvzhERY/WvcuJAnXnklTPzc\nq1c4YZDqPX9qY56omXmiVuYJKYOZI2rn0vJSGlq0CP7973B2d+edw4H9PfeEJX4lSZo/Hx59FIYP\nDwsD9OoVrjv3jyRJSgaLQVITWb4cRowIXfwXL4YzzwxL/B5ySNSRSZJSwSefwOOPhzyxcmVYJGD6\ndNh//6gjkyRJ2cZhYlIjrF8fhn899hhMmhRWAPvd78JwsHSbA6i+7NpZM7v/18o8oazw3XcwZkzI\nEzNmwGmnhTxxzDGwxRZRR5dY5omamSdqZZ6QMpg5onYOE5NSzMaNMGVK6AU0Zgz87GfhwP6hhyA3\nN+roJElRW7cOXnwx5Inx4+HII+G88+Dpp2G77aKOTpIkyWKQVCfFxWEp+BEjYPRo2Gcf6NkT5syB\nH/846uii0aJFi3hVWlVo0aJF1CFISqL160MP0REj4Lnn4OCDQ564807Ybbeoo4uGeaJm5glJ2cwc\nUbtE5wmHiUnViMVg1qwwoefIkbDrruHAvkcPaN066uiUruz+X8Y8obRXUgJTp4Z5gJ5+Gn7yk5An\nTj8d9tgj6uiUrswTZcwTUpYoLinmnjfv4R9T/8GVR15J36P60mzLDJ9zoxEcJiYlyPvvhwLQ44+H\ngtDZZ8PLL8MBB0QdmSQparFYWAns8cfhiSfCKpFnnQWzZ4deo5Ikqe4WfL6A3s/3ZtuttuW1C1/j\nJzv9JOqQsobFIAn46qtQABo+HJYtgzPOgGHDoH17sPeiJOmjj8Ik0MOHh0mhzzorzAv0859HHZkk\nSeln7ca13DL1Fh6c/SC3driVC/MvZIucDF9ZIcVYDFLWisWgqAgGDw4H9CefDP/4B3ToAFv5zZCk\nrLdxI7zwQsgTr70WhgkPHgxHHeWJAkmSGmr6sukUPl/IATsfwPyL57PHDo6tjoJzBinrfPEFPPpo\nOKDfdlvo0wfOOceVwJQczgVRxjyhlLVsWVgh8qGHwiIBffqEQpArgSkZzBNlzBNShlm9bjV/nvRn\nxrw7hntOuIeuB3aNOqS0FPWcQd2AlUAeMKSxQUiJtn596P3z2GNhtZfTTgvXDz/cs7tSgpgnlFa+\n/z6sAvbvf8OMGWG+uBdegIMOijoySZLS37j3xnHJuEvo0roLCy9ZSIttXVExag0pBrUFlgBzK/w+\nt/qHS9GIxUK3/uHD4amn4MADw8H90KHQvHnU0UkZzTyhtFBcHBYIGDYsFIKOOCLkiVGj7AUkSVJT\n+PK7L/nTS3/ijf+9wcOnPkzHvI5Rh6RSDe0ZNADoQjjjO7npwpEa77//LZ8Meptt4NxzYeZM2Hff\nqCOTsop5QikpFoM5c0KOeOIJ2HvvUAAaMAB+9KOoo5MkKTPEYjGeWPgEV750JeccfA4LLlnAds08\n05JKGlIMmgssBZYDhU0bjtQwH38MTz4Zlvr99FM480wYPRratHEYmBQB84RSzuLFIUcMHw4bNoQC\nUFER/PSnUUcmSVJm+WjVR1wy7hKWrVrG82c+T/s920cdkqrQkGJQLrCIcIA/BJhDOOiXkmrVqlDw\nGT4c5s4N8wDdfjsUFMCWW0YdnZTVzBNKCV98ASNGhDyxdGmYBPqRR5wvTpKkRCiJlTB49mBunHIj\nlx92OU/3fJqtt9w66rBUjYYUgwqBQcBqwuSg3YGBlR/Ur1+/susFBQUUFBQ0KECpso8/hltuCQf3\nHTvCpZfCSSeFIWFSqikqKqKoqCjqMJLNPKFIvfce9OsH48fDySeH6506wVYNHRwvJVCW5glJGWbR\n8kX0fq43azauoei8In6+68+jDkm1aMh5sb5selAfP/NbkUtBqsl9/jn07x9WeundG/r2hZ13jjoq\nqX6yZMlg84Qi8cEH8Le/wfPPwxVXwOWXww47RB2VVD9ZkifqwjwhpYHikmLueuMubpt+G9f/6nr+\nePgf2XILh2kkUpRLyw8kHOgvAVriksFKsOXLYeBAGDwYzjkH3n7bST6lFGeeUFLFe4yOHAm//z28\n/z7k5kYdlSRJme3tL97mgucuYLtm2/FG7zfYr+V+UYekemhoh+nNuvtLTW35cvjnP+Hee6FbN5g3\nL6z6IiktmCeUcJ98Ek4WPPooFBaG1STtMSpJUmJtKN5A/+n9+eeb/+Qfv/4HhYcWskXOFlGHpXpy\n9LxSzqefwp13wkMPwSmnwIwZ0Lp11FFJklLF4sVhwYCnnoLf/S70GN1996ijkiQp8839dC69nu3F\nHjvswZw+c9i7uWfr05XlO6WMJUvgkkvg5z+HtWvDCmEPP2whSJIULFgAZ50VVgPbdVd491246y4L\nQZIkJdq6jeu44eUbOG7YcVxxxBWMO2uchaA0Z88gRW7hwjAx9IsvwkUXhW7+u+4adVSSpFTxxhtw\n660wc2aYGPrBB2HHHaOOSpKk7PDmx29ywbMXsF/L/Zh/8Xx238GzMJnAYpAiM28e/P3v8Oqr8Mc/\nwn33QfMdCM6pAAAgAElEQVTmUUclSUoVU6eG1cEWLYJrroERI2DbbaOOSpKk7LBmwxpuKrqJf8//\nN3cffzc9ft4jvpKVMoDFICXdzJmhCDRrVlge/t//hu23jzoqSVIqiMXg5ZdDEejjj+H66+Hcc6FZ\ns6gjkyQpe7z+0ev0erYXB+92MAsuWcAu2+8SdUhqYhaDlDSvvRaKQAsXwrXXeoZXklQuFgvDhf/+\n97Ca5F/+AmeeCVt5pCJlgu7ACuB04OLS27oBK4E8YEhEcUmqZM2GNdw45UaGLxjOPSfcQ/efdY86\nJCWIh1hKuDlzwpndd9+FP/8ZxoyBH/wg6qgkSaliypSQJ775Bm68Ebp3hy23jDoqSU2kY+nlEuBa\noC0QH2cymVAMagvMjSQ6SWVeXfYqFzx3Afm757PgkgXsvN3OUYekBLIYpIR5771wUD9tGtxwA/Tu\nDVtvHXVUkqRUMXt2KAItXhyGhZ1xBmzhOqdSpplcegFoSSj6DABeKr1tCdAJi0FSZL7f8D03vHwD\nTy58kntPvJeuB3aNOiQlgYdcanL/+x/06QO//CW0aQPvvw+XXmohSJIUvPsu9OgBp5wCv/0tvPNO\nWDLeQpCUsZoDfYHbKvy+vML9OyU9IkkATF82nUMePITPvv2MBZcssBCURTzsUpP56qswIfQhh0DL\nluXDwpwcWpIE8NFH4WTB0UdDfn7oQXrJJZ4skLLAKmAgcBHQqvQ2lySSIrRmwxqueukqejzVg4Gd\nB/J4t8fZaTvrstnEYWJqtOXL4f/+Dx58MJzpXbAA9tgj6qgkSani44/httvgiSdCMei996BFi6ij\nkpQk+UCMMAxsDmEy6ZWEIWMALYCvq3piv379yq4XFBRQUFCQwDCl7PH6R69z/rPnk797Pm9d8pZz\nA6W4oqIiioqKmny7iarIx2KxWII2rVSxciXceSfcdx907RpWftlnn6ijklJbTk4OeDYUzBNZ4bPP\noH9/+Pe/4cILQ+/RXXeNOioptWVgnuhLKAJNBh4EJgBLgXaEVcT6AhOBeZWeZ56QmtiaDWv465S/\nMmzBMO478T6HhKWppsoTDhNTva1eDf/4B+y/PyxbBm++CYMHWwiSJAVffAFXXw0/+xnk5IQ5gQYO\ntBAkZanBhBXDCgnLyz9N+WTRHQm9hCoXgiQ1sRn/m0H+4HyWrV7GWxe/ZSFIDhNT3X3/Pdx7L/y/\n/wfHHQevvgo/+UnUUUmSUsWKFSFHPPggnHlmGDa8555RRyUpYqsIPYAqi982uYr7JDWRdRvXcfMr\nN/Ovuf/inhPu4fSfnx51SEoRFoNUq3XrYMgQuPXWsEJYUVE42ytJEsA338Ddd8Ndd4XVwebOhR//\nOOqoJEnKbnM/nct5Y86jdcvWzL94Prv9cLeoQ1IKsRikam3cCI8+Cn/7G/ziFzB2bFj9RZIkgDVr\n4IEH4PbboWNHeP31MIRYkiRFZ0PxBm6ddiv3zbyPO467g7MPOjs+z4xUxmKQNhOLwZgxcO21oXv/\nE0/AUUdFHZUkKVWUlMDDD8NNN0H79jBxIhx0UNRRSZKkhV8s5Lwx57Hr9rsy96K57Lmj47VVNYtB\n2sSiRXD55WFi6Pvug06dwuSfkiRBGAJ2ySUhNzzzTCgGSZKkaBWXFPN/r/8fA18byG0db+PCthfa\nG0g1shgkIHT1HzAgTBB97bXwpz9Bs2ZRRyVJShWrVsGNN8KIEWEOuV69YAvXJJUkKXKLli/ivDHn\nsfWWWzOzcCb75u4bdUhKAx7GifHjw5xACxeGM759+1oIkiQFsRgMGwYHHhgWFHjnHbjwQgtBkiRF\nLRaLcf/M+zli6BH0+FkPJv9usoUg1Zk9g7LY4sWh8LNgAdx/f1guXpKkuPnz4Y9/hNWrw5Cwww+P\nOiJJkgTw0aqPuPC5C1m1bhXTL5jOATsfEHVISjOe18tCX3wBf/hDOKg/9NBQDLIQJEmK++ADOPfc\nkBt69ICZMy0ESZKUCmKxGI/Nf4xDBx/Ksfscy6sXvGohSA1iz6As8u23cMcdcPfdcM458J//wC67\nRB2VJClVfPVVmA/o0Ufhssvg/fdhhx2ijkqSJAF8+d2XXDzuYt77+j1eOucl2u7eNuqQlMbsGZQF\nNmyABx6An/wE3n03nOG9+24LQZKk4PvvQxHogAPCvEBvvw0332whSJKkVDH2vbEc8uAh5OXmMbNw\npoUgNZo9gzJYLAbjxsGVV8I++8DYsZCfH3VUkqRUUVISJoe+/no46ih4/XXYf/+oo5IkSXHfrPuG\nK1+6kslLJ/Nk9yc5Zp9jog5JGcJiUIb6z3/giivCvA933w0nnBB1RJKkVDJjRpg/LhaDp56CI4+M\nOiJJklTRtA+ncd6Y8+jQqgPzL57PDj+wy66ajsPEMsyKFWHll2OOgeOPD5NDWwiSJMV9/DH87nfQ\ntStceim88YaFIEmSUsm6jeu4duK19BzVk7uPv5uhpwy1EKQmZzEoQ2zcGOYFis/38M478Kc/QbNm\nUUcmSUoFa9eGeYEOPhj22gv++1847zzYwiMBSZJSxsIvFnL40MN5b/l7zL94Pif/9OSoQ1KGcphY\nBpg/Hy64IEz0OWECHHJI1BFJklLJK69A797wi1+ERQTy8qKOSJIkVVQSK+GuN+7itum3cXun2zm/\nzfnk5OREHZYymMWgNLZ+PdxyS+gRNGAAnH8+2F5IkuK++Qauuw7GjIH774dTT406IkmSVNmyVcs4\nf8z5rC9ez4zeM8hr4VkbJZ6dw9PU7NnQrh3MmQNz50KvXhaCJEnlJk6Egw6CNWtg4UILQZIkpZpY\nLMbwt4bTbnA7Oud15pXzX7EQpKSxZ1CaWbsWbr4Z/vUvuOMOOOssi0CSpHKrVsHVV4dhw4MGhcUE\nJElSalmxZgWXjr+U+Z/N58VzXiR/9/yoQ1KWsWdQGpkxA9q2hUWL4K234OyzLQRJksq98EKYF2ir\nrcJqkhaCJElKPVOWTqHNoDbsvO3OzO4z20KQImHPoDSwfj387W8wdCjccw+cfnrUEUmSUsk338BV\nV4XeQI8+Ch06RB2RJEmqbN3Gddw45UaGLxjO0JOHcsL+J0QdkrKYxaAUt2AB/O53sPfeMG8e/OhH\nUUckSUolU6eGBQR+/evQa3THHaOOSJIkVfb2F29z9tNns2/uvsy7aB67bL9L1CEpyzlMLEUVF0P/\n/uHs7h/+AM8+ayFIklRu7drQG+iMM+Duu+GhhywESZKUamKxGPfMuIeCRwu47LDLeKbnMxaClBLs\nGZSC3n8fzjsPttkGZs2CffaJOiJJUiqZNSv0Gv35z0NvoJ13jjoiSZJU2efffs75z57P8jXLee2C\n19h/p/2jDkkqY8+gFBKLweDBcNRR4UzvpEkWgiRJ5YqL4ZZb4MQT4YYbYORIC0GSJKWice+No82g\nNhy6+6FM7zXdQpBSjj2DUsSXX0JhISxbFuZ/OPDAqCOSJKWSDz6Ac8+FrbeGOXNgr72ijkiSJFW2\nZsMa+k7sy9j3xjKi+wiO2eeYqEOSqmTPoBTw0kvQpg389KfwxhsWgiRJmxo+HA47DE49FSZOtBAk\nSVIqmv/ZfNoNacfXa75m3sXzLAQppdkzKEJr18K118Izz8CwYWElGEmS4lauhEsvDatJvvQStG0b\ndUSS1CCFpT9bA9eVXh8AXFt635AogpKaSkmshH/O+Ce3TLuFO7rcwTkHn0NOTk7UYUk1smdQRBYs\ngPbt4dNPw0G+hSBJUkXTpoVeoy1ahAmjLQRJSlMdgUmEgk9e6e8QikDvA4sjiktqEp9/+zknPX4S\nTy58khm9Z3DuIedaCFJasBiUZCUl8H//F5aMv+oqGDECWraMOipJUqpYtw6uuw569IB774X77oPt\ntos6KklqsDygU+n1JUCr0uuFwP7Ay1EEJTWFFxe9SNtBbTl090OZ1msaeS3yog5JqjOHiSXRsmVh\nyfgNG+DNN6FVq9qfI0nKHm+/DWefHVaSnD8fdt016ogkqdEqDgHLB54svd6S0EsoHxiY7KCkxli3\ncR3XTbqO0f8ZzRPdnuDYfY+NOiSp3uwZlASxWJj8s107OO44eOUVC0GSpHIlJXDXXVBQAJddBmPG\nWAiSlHHygdnAvNLfhwCTgZ0oHzompbz/fPkfDh96OMtWL2PexfMsBClt2TMowZYvD5N/vvWWk39K\nkjb3v//B+efD99+HFSVbt446IklKiI7An0uvFwLLgdHA14ShZJMrP6Ffv35l1wsKCigoKEh0jFK1\nYrEYQ+cM5c+T/8ytHW+lML/QuYGUFEVFRRQVFTX5dhP16Y3FYrEEbTp9TJ8OZ54J3brBbbfBtttG\nHZGkqJUeNHjkYJ4A4NlnobAQ/vjHsLrkVp6ikbJehuaJPsDg0uvxXkCzgFVAf8LQsXmVnmOeUMpY\nuXYlfZ7vw7tfv8uT3Z7kwF0OjDokZbGmyhMNHSaWD3SjfJlIVfLEE9C1KwwaFLr+WwiSlGXMEzWI\nxeDOO+H3v4exY+Evf7EQJCljdSIUfBYRegPFCL2AOhHyxFdsXgiSUsZrH71G20Ft2XX7XZnRe4aF\nIGWMhlaTRgI9gL6EpSLnVro/ayv5sRj07w8PPBAO8A8+OOqIJKWSDD3jWxXzRDWKi+FPf4IpU2D8\nePjxj6OOSFIqyaI8UZuszRNKDcUlxfSf3p9/vvlPBv1mEL894LdRhyQBTZcnGnIesjsws/S6M/9X\nsGEDXHIJzJkT5n3YY4+oI5KkSJgnqvHtt2H48Nq18Oqr0Lx51BFJkqTKPvnmE855+hyKY8XMKpzF\n3s33jjokqck1ZJhYO8Ks/20JZ3wFrF4NJ50En34KU6daCJKU1cwTVfj0Uzj22LBK2PjxFoIkSUpF\nL7z/AvmD8jl2n2N5+XcvWwhSxmronEFfUd7lv1sTxZK2PvoIjj4a9tsvTAb6wx9GHZEkRc48UcHC\nhXDkkWEuuaFDoVmzqCOSJEkVrS9eT98Jfekztg8jTx/JTQU3seUWW0YdlpQwDRkm9jWwtPT6SqA9\nYVnITWTLUpBvvhkO7q+4Aq68ElxdUFJFiVoKMsWZJyp44QU477ywmMBZZ0UdjaRUk6V5QkopS1cs\n5YzRZ7DLdrsw96K57LzdzlGHJCVcQ0oXrQjzQQwkdP9fDDxd6TFZMeHbI49A377hLO+pp0YdjaR0\nkCUTg5onCAsKDBgA99wDI0fCL38ZdUSS0kGW5Im6yPg8odQw6p1RXDruUq47+jquOOKK+HdQSllR\nTiC9lHCmtxvQkiycHHTDBrj66nC295VX4Gc/izoiSUopWZ8nvvsOLrgAli4NPUj33DPqiCRJUkVr\nNqzhypeuZMKSCYw7axzt92wfdUhSUiWq7JmxlfyvvoIePeAHP4AnnoDc3KgjkpROPONbJmPzxAcf\nwG9/C23awIMPwjbbRB2RpHRiniiTsXlC0Xv3q3fpMaoHB+x8AIN/M5jm27iqg9JHU+WJhk4gnZXm\nzYP27eGww2DsWAtBkqRNvfwyHHEE9OoFDz9sIUiSpFQz/K3hHP3w0Vza7lKe7PakhSBlrYYME8tK\nI0fC738P994LPXtGHY0kKdXccw/ccgs8/jh06BB1NJIkqaI1G9bwhxf+wNRlU5l07iQO+dEhUYck\nRcpiUB3ccQfceSdMmABt20YdjSQplZSUhMUEXnwRXn8dWrWKOiJJklTRf7/6Lz2e6sEvdv0Fswpn\nscMPdog6JClyFoNqUFIC11wD48fDq6/Cj38cdUSSpFSyfj2cfz589BFMmwYtW0YdkSRJquix+Y9x\n5YQrubXDrfTO7+1qYVIpi0HVWL++fCWY6dM9wJckbeqbb6BrV9h++9BzdNtto45IkiTFxYeFTVs2\njcm/m8zBux0cdUhSSnEC6Sp88w385jfh56RJFoIkSZv6/HMoKIC8PBg1ykKQJEmp5L2v3+OIh47g\nuw3fMbNwpoUgqQoWgyr5/HP49a/DnA+jR3uAL0na1KJFcNRRcOqpYen4rexjK0lSynjq7ac4+l9h\ntbDhXYc7P5BUDQ9hK1iyBLp0gXPOgZtuAoeTSpIqmj0bTj4Z+vWDPn2ijkaSJMWt27iOqydczfhF\n43nxnBfJ3z0/6pCklGYxqNTSpaFH0LXXwqWXRh2NJCnVzJkDJ54YegOddlrU0UiSpLgPVn5Aj6d6\nsNeOezG7z2xyt8mNOiQp5TlMDPjwQ+jQwUKQJKlq8+eHQtCgQRaCJElKJWPfG8vhQw/nrIPOYnSP\n0RaCpDrK+p5B//tfKARdcYWFIEnS5hYuhOOPh3vvhd/+NupoJEkSwMaSjfx1yl8Z9tYwxvQcw5F7\nHxl1SFJayepi0CefhKFhl14Kf/hD1NFIklLNO++EueTuvBO6d486GkmSBPD5t59z5ugz2XKLLZnd\nZza7bL9L1CFJaSdrh4l99lnoEdS7N1x1VdTRSJJSzbvvQufOcPvtcMYZUUcjSZIApi+bzqGDD+WX\ne/+SF89+0UKQ1EBZ2TPoiy9CIeicc8I8QZIkVbRoEXTqBLfcEnKFJEmKViwW447X7+D2127nkVMf\n4YT9T4g6JCmtZV0xaMWKcIB/+ulwww1RRyNJSjUffggdO8JNN8H550cdjSRJWr1uNRc8ewEfrvqQ\nN3u/yT65+0QdkpT2smqY2MaN0KNH6BXUr1/U0UiSUs2338Ipp8Af/xiGEUuSpGi98+U7HDbkMHbe\nbmem95puIUhqIjkJ2m4sFoslaNMNd/nloev/2LGw5ZZRRyMpG+Xk5EDi2t50knJ5oqQEunWDnXeG\nwYMhx3dJUgTME2VSLk8o+Ua+PZLfj/89AzsP5Pw250cdjpQSmipPZM0wsQcfhEmT4I03LARJkjZ3\n443w9dcwYoSFIEmSorSheAPXTbqOZ/77DBPOmUDb3dtGHZKUcbKiGDRlSpj74dVXoXnzqKORJKWa\nxx+HJ56AGTNg662jjkaSpOz12bef0XNUT7Zvtj2z+syi5bYtow5JykgZP2fQokVw5pnhIH+//aKO\nRpKUambMgD/9CZ57DnZxdVpJSoTC0kv/Crd1AzqW3i4B8NpHr9FucDt+ve+vGXvWWAtBUgJldM+g\nVavCRKD9+oVJoyVJquh//4OuXeGhh+AXv4g6GknKSB2BScBSYGTp78tL75sM5AFtgbmRRKeUEIvF\neGDWA/Qr6sfDpz7MST85KeqQpIyXscWg4uLQI6hDB7j44qijkSSlmu+/h1NPDSuHnXxy1NFIUsbK\nK70MAZaUXu8MTCy9fwnQCYtBWWvtxrVcMu4SZn0yi9cufI39WjqcQ0qGjB0mdu21sH493Hln1JFI\nklJNLAa9eoXeQH37Rh2NJGW0IaUXgHxgFpALfF3hMTslOyilhmWrlnH0v47m+w3f8/qFr1sIkpIo\nI3sGPfccjB4Ns2dDs2ZRRyNJSjX33w+LF8P06a4cJklJkg/MprwHUK2tb79+/cquFxQUUFBQkIi4\nFJGXl77M2U+fzVVHXsVVR14VXy5bUiVFRUUUFRU1+XYT9Y2LxWKxBG26Zh9/DIceCk8/DUcdFUkI\nklSt0gMdj3YizBPz50OnTvDaa7D//pGEIEnVyuA80RcYWHq9P2GY2GSgO9Cqwn1xkeUJJVYsFuPO\nN+7k9ldvZ3jX4XTM6xh1SFJaaao8kVE9g4qL4eyz4fLLLQRJkjb33Xdwxhlwxx0WgiQpifpQXuzp\nCIwA2hGKQa0onz9IGe77Dd9T+Hwh//nyP8zoPYN9cveJOiQpa2XUnEG33QZbbAHXXRd1JJKkVPSn\nP0H79nDuuVFHIklZoxOhJ9AiwipiMcqHinUEVgLzoglNyfThyg85+l9HAzD9gukWgqSIZcwwsVdf\nhW7dwjxBe+6Z1JeWpDrL4O7/9ZX0PDFyJPzlLzBnDuywQ1JfWpLqzDxRxmFiGeSVD17hjNFncPWR\nV3PlkVc6P5DUCA4Tq2DFijA8bMgQC0GSpM198AFcdhmMH28hSJKkZInFYtw/837+NvVvDDttGJ1b\nd446JEml0r5nUCwGp58eikB3352Ul5SkBvOMb5mk5YkNG+DYY0Pv0auuSspLSlKDmSfK2DMoza3b\nuI5Lx13Km5+8yZieY2jdsnXUIUkZwZ5BpYYOhUWLYNiwqCORJKWim2+GHXeEK66IOhJJkrLDp998\nSteRXdljhz14/cLX+eHWP4w6JEmVpHXPoHfeCWd7p02DAw5I+MtJUqN5xrdMUvLElClhGPHcubDb\nbgl/OUlqNPNEGXsGpalZn8zitBGnUZhfyA3H3MAWORm1ZpEUuazvGRSLwcUXw9//biFIkrS59euh\nT5/Qg9RCkCRJiffkwie5/IXLGfSbQXQ9sGvU4UiqQdoWg557DlauhMLCqCORJKWiQYNgv/3gxBOj\njkSSpMxWEivhxpdv5PGFjzPp3Ekc8qNDog5JUi3ScpjYhg1w0EFw111w/PEJexlJanJ2/y+T0Dyx\nahX85CcwaVLIF5KULswTZRwmlia+WfcN5zxzDivXrmTU6aPYZftdog5JymhNlSfScgDn0KGw995w\n3HFRRyJJSkX9+8NvfmMhSJKkRFqyYglHPnQkP9r+R0w8d6KFICmNpF3PoG++CWd7X3gB2rRJyEtI\nUsJ4xrdMwvLERx+F/PDWW7Dnngl5CUlKGPNEGXsGpbipH06l56ie/OVXf+H37X8f/+xKSrCsnUD6\n9tuhSxcLQZKkqt1wA1x6qYUgSZIS5eG5D3Pd5OsYdtowOrfuHHU4khogrYpBH38M998P8+ZFHYkk\nKRXNmwcTJsB770UdiSRJmae4pJjrJl3HmHfH8Mr5r3DAzi7rLKWrtCoG/fWvYZngvfeOOhJJUqqJ\nxaBv35Ardtgh6mgkScos36z7hrOePovv1n/HjN4zaLlty6hDktQIaVMMWrAAxo2Dd9+NOhJJUip6\n6aUwX1Dv3lFHIklSZvlg5Qec/MTJHLnXkdx34n0027JZ1CFJaqS0WU3smmvgL3+B5s2jjkSSlGqK\ni0OvoAEDoJnHp5IkNZnXP3qdox46it5tezPoN4MsBEkZIi16Bk2aBIsWwUUXRR2JJCkVPfootGgB\np5wSdSSSJGWOEQtHcPkLl/PIbx/hxP1PjDocSU0o5ZeWLymBQw8Nq8N069Ykm5SkyLhkcJkmyxPf\nfQc//Sk8/TQcdliTbFKSImOeKOPS8hGKxWLcMu0WhswZwvNnPs/Bux0cdUiSSmXN0vLPPgtbbw1d\nu0YdiSQpFQ0dCkccYSFIkqSmsG7jOvqM7cPbX7zNGxe+we477B51SJISIOWLQYMHw2WXQY7nRyRJ\nlcRiIU/cf3/UkUiSlP6+/v5ruo7syk7b7sQr57/C9ltvH3VIkhKksRNI922SKKrx4Yfw5pvQvXsi\nX0WSlEAJzROvvw4bN8IxxyTyVSRJynzvf/0+Rz50JIfveTijeoyyECRluMYUgzoBnZsqkKr8619w\n1lmw7baJfBVJUoIkPE8MGRKWkrf3qCRJDffqslf51cO/4uqjrub2zrezRU7aLDotqYEaM0wsoTO6\nFReHYtC4cYl8FUlSAiU0T6xaBWPGhOXkJUlSwzz19lP8fvzveey0xzhuv+OiDkdSkjS05NsWmNyU\ngVT24ouwxx5wsBPXS1I6SnieePxx6NQJdt01ka8iSVJmisViDHx1IFdOuJKJ5060ECRlmYb2DGrZ\npFFUYcgQKCxM9KtIkhIkKXmif/9Ev4okSZlnY8lG/vDCH5i+bDqvX/g6e+24V9QhSUqyhhSD6nS2\nt1+/fmXXCwoKKCgoqPMLfPopvPIKDBvWgOgkKYUUFRVRVFQUdRjJlvA8MXs2rFgRegZJUjrL0jyh\nCH23/jvOGH0G6zauY1qvaTTfpnnUIUmKQEOm3OxW+nMnoA9QCMyt9JhYLNbwqSJuvRWWLg1nfSUp\nk+SEmY4zfbrjhOeJiy+GvfaCG25o8CYkKSVlSZ6oi0blCVXts28/4zeP/4aDdzuYQb8ZRLMtm0Ud\nkqR6aqo80ZA5g0aXXmJAc5p4gtCSEhg61CFikpTGEponvv0WRo6EXr2acquSpASrPN1//HeP+pPk\n3a/e5aiHjuKUn57CQ6c8ZCFIynKNWTNwCLA/MK+JYgHg5Zdhhx2gffum3KokKQIJyRMjR8LRR8Oe\nezblViVJCdSH8l6jcYXA+8Di5IeTfd743xsc+8ix3HjMjfz12L/GexZIymKNKQYlRHziaNsnSVJV\nXGBAktLOYGBJpdsKCScMXk5+ONnluXef45QnTuHhUx+mV1u71UoKUqoY9OWX8NJLcPbZUUciSUpF\nCxfCRx/BCSdEHYkkqZFaAh2BvlEHkskGzx7MRWMvYtxZ4zhhf5OnpHINXVo+If79bzjlFGjRIupI\nJEmpaMiQMFfQVimVvSRJDRBfKqYzoShU6yqUqrtYLEa/on4MXzCcab2msV/L/aIOSVKKSZnD6Vgs\nHOS7gpgkqSpr18Lw4TBrVtSRSJIaqRBYTlhs4GsgjyqKQf369Su7XlBQQEFBQXKiS3MbSzZy8diL\nmf/5fF694FV2++FuUYckqRGKioooKipq8u0mamaeei8FOW0a9OkD77zjfEGSMpdLBpepd54YPjz0\nIH3ppQRFJEkpIIPzxASgS+n1jsAsYBXQH3iSzRcbcGn5BlizYQ09R/VkffF6RvUYxQ+3/mHUIUlq\nYlEuLZ8QQ4ZA794WgiRJVXPiaElKW92BdkDv0t8nA50IK4x9RROvOpmtVq5dSZdhXdjhBzvw3JnP\nWQiSVKOU6Bm0Zg3sthssXgy77JKgiCQpBWTwGd/6qleeWLYM8vPhk09g660TGJUkRcw8UcaeQfXw\n6Tefcvzw4ynYp4A7j7+TLXJS5py/pCaWUT2DpkyBNm0sBEmSqjZ+fFhBzEKQJEmbWrR8EUc/fDQ9\nf96Tu46/y0KQpDpJiZZi3Dg48cSoo5AkpSrzhCRJm5v76VyOefgYrv3ltVz/q+vjPQYkqVaRDxOL\nxeq+6aAAACAASURBVCAvD557Dg46KEHRSFKKsPt/mTrnibVrYddd4YMPoGXLxAYlSVEzT5RxmFgt\nij4oosdTPXjgpAfo9rNuUYcjKUmaKk9EvrT8f/4DxcXwi19EHYkkKRUVFcHBB1sIkiQp7rl3n6P3\nc715svuTdGjVIepwJKWhyItB48eHrv/2aJQkVWX8eDjppKijkCQpNTy+4HGufOlKxp01jvZ7to86\nHElpKvI5g8aN8yBfklS1WMw8IUlS3IOzHuSaidcw+XeTLQRJapRIewatWgWzZkEHezZKkqrw3nuw\nfr1zykmSNGD6AAbNHsTUXlPJa5EXdTiS0lykxaCJE+GXv4Ttt48yCklSqoqvIuZQYklStorFYvzl\n5b8w5r9jmNZrGnvuuGfUIUnKAJEOE7PrvySpJi4pL0nKZiWxEi4bfxkTFk9gaq+pFoIkNZnIlpYv\nKYE99oBXX4XWrRMUhSSlGJcMLlNrnli9GvbcEz79FH74wyRFJUkRM0+Uyfql5TeWbOTC5y7kg5Uf\n8PyZz7PjD3aMOiRJKSDtl5afMwdycy0ESZKqNmkSHHWUhSBJUvbZULyBc545h5VrV/LC2S+wXbPt\nog5JUoaJrBjkUsGSpJqMH+8QMUlS9lm3cR09R/WkOFbMs2c8yzZbbRN1SJIyUGRzBjkPhCSpOrGY\nJw0kSdlnzYY1nDbiNLbcYktG9xhtIUhSwkRSDPriC3j3XfjVr6J4dUlSqps3LwwP22+/qCORJCk5\nvlv/HSc/cTK52+QyovsItt5y66hDkpTBIikGvfgidOwIW9u+SZKq4GqTkqRs8s26bzhh+Ans3Xxv\nHjvtMbbaIrLZPCRliUiKQQ4RkyTVxDwhScoWK9eupMuwLhy484E8dMpDbLnFllGHJCkLJH1p+Y0b\nYZdd4O23w9LykpRNXDK4TLV54quvwkqTX3wBP/hBkqOSpIiZJ8pkxdLyK9eu5Lhhx3HYHofxzxP+\nGX//JalaTZUnkt4z6LXXoFUrC0GSpKq9+CJ06GAhSJKU2eKFoMP3PNxCkKSkS3oxyNVhJEk1cUl5\nSVKmW7V2VVkh6O7j77YQJCnpkl4MclJQSVJ1Nm6El16yGCRJylyr1q6iy7AuHLbHYRaCJEUmqcWg\nZcvgs8+gfftkvqokKV3MmAF77w177hl1JJIkNb14Iaj9Hu0dGiYpUkktBo0fD8cfD1s6Qb4kqQr2\nHpUkZar40LD2e7TnnhPusRAkKVJJLQZNmwYdOybzFSVJ6cQ8IUnKRKvXrea4Ycdx6O6HWgiSlBKS\nWgz67DPYa69kvqIkKZ2YJyRJmea79d/xm8d/Q5sfteHeE++1ECQpJSS1GPTFF7Drrsl8RUlSOjFP\nSJIyydqNa/ntiN/SqkUr7j/pfgtBklKGxSBJUkpYuxbWrIHmzaOORJKkxltfvJ7uI7vTctuWPHTK\nQ2yRk/SFnCWpWklrkUpK4OuvYaedkvWKkqR08uWXsMsu4ElTScpIAyr93g3oCBRGEEvCbSzZyNlP\nn82WW2zJsNOGsdUWW0UdkiRtImnFoOXLw9neZs2S9YqSpHTy5Zf2HpWkDNWHUPyJyy/9Obn0Z9vk\nhpNYJbESej3bi9XrVjOi+wiabek/QJJST9KKQQ4RkyTVxDwhSRlrMLCkwu89gBWl15cAnZIeUYLE\nYjEuHnsxy1Yt45mez7DNVttEHZIkVSlp/RU9yJck1cQ8IUlZIxdYXuH3jJhIIhaLceVLV/LW528x\n8dyJbNdsu6hDkqRqWQySJKUE84QkZZWMmyHulmm38PIHL1N0XhE7/GCHqMORpBpZDJIkpQTzhCRl\njZVAy9LrLYCvq3pQv379yq4XFBRQUFCQ6Lga7IGZD/DwvIeZ3ms6LbZtEXU4kjJIUVERRUVFTb7d\npBaDdtklWa8mSUo3X3wBBxwQdRSSpCQYAbQjTCDdCphY1YMqFoNS2ci3R/KPaf9g6vlT2X2H3aMO\nR1IaKS6GlSthxYqw6Nby5eH6ihWwejV8+y18801B6SX8Djc3yWsnrRj05Zdw0EHJejVJUrpxNTFJ\nyljdCcWf3sBQYG7p7x0JvYTmRRda40xYPIHLxl/GxHMn0rpl66jDkZRkGzaEos2q/9/evUdXVd75\nH/8kXBMCuROCQMiVcCdcFJQqHRTxglotqL2odQRnWqcu2jr2N501w1pljW11zVg7jmPpuDpOreKl\nttUyWkkFHZA7CCSQEBISgZB7AgkJhHP274/n3AK5c072OTnv11p7Pc/Z+1y+Zyc735PvefazmzoW\ndNxFnfp6U+w5e7bzpblZGjNGSkiQ4uPNkpAgxcWZ9aNHS0lJpnUvH3zgn9g5TQwAEBTIEwAwaL3t\nWnxtcLX5ClE7T+7U13/3db17/7uaPW623eEA6AOHw1vEuXzpqnDT2XLxohQb6y3ouIs67v64cdKU\nKd77dLZEDtg13juiGAQACArkCQBAqCisKdTdb9ytX9/9ay2etNjucICw1Nra+SlWl4/KaWoyrW+/\npUWKiTEjcGJjr1zchZrUVG9/9GjvNncbFSVFhOh0+BSDAAC2syzmlgMAhIaKpgot/81yPbfsOd2R\nc4fd4QAh6/x5qa5Oqq01bV2dGW1z7tyVrW9Bp6HBtJIp5viOxvE91Sonx2x3L7Gx3v7o0faNyAkW\nTCANALBdc7NJyKNG2R0JAABda2ht0PLfLNfahWv1jVnfsDscwHaWZT7H+RZp3H13gae+vmPfXfxx\nOs18OImJpk1IMAWb0aPNqJvx480pVu6ROfHx3mJOfLw0cqTd7z60DUgx6OJF8wsSz1UWAQCdYPQo\nACDYXbh0QV/Z+BXdmnmr1i5aa3c4gN9ZlhmBU13tXWpqOo7c8e3X15v7R0V1HIHjLtokJppl5kxv\nPyHBWwCKjg7dU6wGgwEpBtXWmh94uA/DAgB0jiuJAQCCmdNy6lt/+JYSoxP13LLn7A4H6JXW1itH\n5riLO76t7xIVZT6TJSd726QkM0pn1ixvUcc9kicuTho6YOcbwZ8G5MfGN74AgO6QJwAAwewf//KP\nOtF4QvkP5WtI5BC7w0GYcThMoaayUjpzxix1dd55dC5v3QUgh8NbvHGPyklONktmpnTddd5ij3s9\np16Fj/4Wg1a72kxJP+zpznzIB4CwQ54AAAwKL+95WW8Xvq3tf71dUcOi7A4Hg4TDYYo21dVSVZUp\n8FRVXdmvrDT3c1+mPDVVSkkxBZzYWCk72zsxsvtKWO7Cz6hRnIaFrvWnGLRU0mZJZZLedN3O7+4B\nfMgHgLBCngAADAp/Kv6T1m1dp0+/9amSopPsDgdBrqXFFHDcBR7f/uXz8DQ0mAJOcrIp8qSkeJfc\nXG8/NdV8RuJULPhbf36lMlzLBkmlrn6PH/K5khgAhI1+5YlJkwYgMgAAemnP6T165A+P6L0H31NW\nQpbd4cAmTqcZmeMu7rhH65w+fWV76ZK3iDN2rLeflSXdcINZ556HJzGRAg/s1Z9fvw0+/bmS3ujp\nAUwMCgBhpV95Yv78wAUEAKGg3dFudwhwqWiq0N1v3K0NKzZo4YSFdocDP7Ms89nj1KkrR/Bc3q+t\nNZc19y3yjB9vlrw806ammnbMGE7LQui4mlrkXEl7JR3obOO6des8/c8/X6J7711yFS8FAKFpy5Yt\n2rJli91h2KXXeeLo0SV6+OElAxIUANjl7IWzqmiqUHljuWmbyrV7224V7ytWU1uTWi622B0iJLVc\nbNFdr9+l7y38nu7JvcfucNAPlmVOw6qokE6ckMrKOi4nTkgjRkgTJnQ8PWvsWHMZdN9RPcnJ0vDh\ndr8jwP+upm75lKRnu9hmWZblubFihbR6tXTXXVfxagAwCESYr4vC5TujXueJ2bOl//5vac6cAYkL\nAPzOaTlV3VKt8sZylTeVdyj4lDeZ/kXHRaXFpmlS7CSlxaYpLc7bnxQ7SeNHj9fwocOl8MkT3emQ\nJwaK03Jq1VurNHrEaL1y1yvuvI0g43CY07LKyzsuFRVmKS83p2BNmiSlpUnp6VcuY8bY/S6A/vHX\n/xP9HRm0Rt4P+EwMCgC4HHkCwKDS7mjXybMnPYUe37aiqUJfnP1Co4eP7lDgyUrI0tKMpZ5iT0JU\nAsWFIPfjrT/W6XOn9fG9H/OzspFlmc8GpaVmJE9pqbdfXm5O70pMNIWeyZNNO2eOGXwwaZJZYmPt\nfhdAcOvPX7ibZa4OUy8pQdJXJf3lsvt0qOSnp0v5+VJGRn/DBIDBIUxGBvUpTzidZqh2SwvDsAHY\np7W9tUOB50TjiQ63q5qrNC5mnNLi0syoHtfIHt8RPtHDoq86jjDJE70x4COD3il8R9/78/e087Gd\nGhczbkBfOxw1NXlP2fJt3cWfqCjz/6N7cY/oSUuTJk6URo60+x0A9vBXnghUounwx3vUKOnMGWn0\n6AC9GgCECD7ke3jyRF2ducpGQ4PNEQEY1M5dOOct8jR6iz3utrGt0Xv6VmyaJsdN7lDsmTBmgoZG\nBv7SP+QJjwEtBh04c0C3/M8t+vM3/qy81LwBe93B7MIFU+Bxj+jxLfSUlUnt7d4Cz+TJHdv0dEb2\nAF2x+zSxXmtpMd/6xsQE+pUAAKGIK04C8IemtqYOBZ7L+63trZ4Cz+RY085NnetZNy5mnCIjIu1+\nG7BBVXOV7n7jbv3H7f9BIaiPLMucslVUZJbiYm//9Gkzgsd3np4FC7z9xESuvAXYKeDFIPeHfA50\nAEBnmC8IQG+4iz0dliZvv93Rrslxk01xJzZN6fHpWjRhkWddUnQSc8DgChcuXdC9b96rR2Y/opXT\nV9odTlC6eNGM5Dl+3Cylpd5+WZmZiHnKFO9y882mTU83kzgDCE4BPzz5kA8A6A55AoBkTuM60XhC\nZY1lngKPb7/d0a70+HRT3HGN7Fk8abGn2MPkzOiP72z6jlJjUvXPS/7Z7lBs5XCYIk9xsXTsmFlK\nSkx7+rS5BHtWlpm7JzNTuukm71w+nAEChCaKQQAAW5EngPBwvv28yhvLPQWesoYynWhytY0n1Hqp\n1VPYSY8zRZ/rJ17vuU2xB/72yv5X9NnJz7TzsZ1hc4rgpUumyFNY6F0KCkwRKCXFjOjJzpZycqQ7\n7jD9yZOlYcPsjhyAv1EMAgDYijwBDA7tjnZ9cfYLlTWUqayxzNu6+o1tjWa+Hp9iz/zx8z0FoLGj\nxlLswYA5cOaAnt78tD555BPFDB98Q1ucTjN58+HD3sVd9LnmGmn6dGnaNOm226Tvf1/KzTUX/QEQ\nPgakGJScHOhXAQCEqupq84EUQHCzLEtnms+otKG002JPZXOlUmNSlR6f7in23JZ1m+d26ujUsBl9\ngeDW1NaklW+t1AvLX9DU5Kl2h3PVamqkQ4fMcvCgaQsLzQTN06dLM2ZIy5dLP/iBKfpER9sdMYBg\nMCATSKemBvpVAAChiquJAcHj3IVzKmssU2lDqSn6NJSptLHUcypXzPAYZcRneAo8iyYs0tdmfk0Z\n8RmaOGaihg3hXBIEN8uy9OgfH9WyjGV6cOaDdofTJ+fPmyLP4cPe4s+hQ1JrqzRzpjRrlrla16OP\nmgIQl2YH0J0BGRk0e3agXwUAEKo4TQwYOA6nQyfPnlRpQ6mONxz3jPJxF39aLrYoIz7DFHzi0pWV\nkKVbMm9RRnyGJsdNHpSn0yC8PL/jeVU0Vei39/7W7lC61dAg7dol7dwpHThgij4nT5q5fGbONMuT\nT5oC0IQJXLkZQN8xZxAAwFbkCcC/mtqaPMUdz9Jo2i+avlDyqOQOBZ87s+9Ueny6MuIzlDIqhXl7\nMGht/2K7frLtJ9r52E6NGDrC7nA82tvNaJ8dO0zxZ8cO6dQpad486brrpPvvl9avN5M5M5EzAH+h\nGAQAsBV5Augbp+XUqbOndLzhuI7XH+8wyqe0oVRtl9qUEZ+hzIRMZcRlaMbYGbpryl3KTMhUWmxa\nUP0TDAyUmpYaPfD2A/qvu/5Lk+Mm2xbHpUvSkSPSnj1m2bvXjPqZPFlauFC6/npp7Voz18/QgP+n\nBiCcBeqrH8uyLElmtvodO6SJEwP0SgAQQlzfuPO1uytPtLdLUVHSxYtSJPPKAh5tl9pMkcen2OMu\n/pxoPKGEqART7InPUGZ8pjLjMz0FoOToZEb3hDDyhIfn/4mr5XA6dNtrt2le6jw9c/MzfnnO3jp9\nWtq+XfrsM7N8/rn5v2j+fLPMmyfl5UkxnIEJoJf8lScCWgyyLGnECOnsWWnkyAC9EgCEED7ke1iW\nZamyUpozR6qqsjscYOA1tTXpeMNxldSX6Hi9q3UVfWpaajQpdpIyEzI9xR538ScjPkPRw7gc0GAV\nRnnip5KelrRa0oZOtvutGLT+k/XaXLpZmx/arKGRgRtu43CYYs///Z8p/GzfLjU3S4sWmRE/Cxea\n4g8TOwO4GiFRDGpslNLSpKamAL0KAISYMPqQ3xPLsiwdPCh9/etmiDww2FiWpdrztSqpL/EUenz7\nbZfaPEUed8EnKyFLmQmZmjBmQkD/aUXwCqM8US+pTtLjkv7SyXa/FIP2nt6r2167Tfse36cJYyZc\n9fP5cjrNXD8ff2yWrVvNVZS/9CVvASg7m8mdAfiXv/JEQD9lMA8EAKA75AmEOsuydKb5jKfIU1Jf\nopIGb39IxBBlJ2Z7Cj3LMpfp2wu+rcz4TI0dNZbTuRDOVkt6J5Av0Nreqm+++009v/x5vxWCKiul\n99+XPvzQFH/i4qQvf9lM8vzSS6YYBAChgGIQAMA25AmEAnfB51j9MZXUl+hY3TFPv6S+RFHDopSd\nkK2shCxlJ2Trnin3eEb4JEQl2B0+EKwSJC2VNFfSs4F4gX/I/wfNTJmpB2c82O/nsCxz6td775nl\n2DHp1lulFSukf/s35kUFELooBgEAbEOeQLCwLEvVLdU6Vn/MU+xx90vqSxQ9LFrZidmeos/KaSuV\nlZClrIQsxY5kAhCgH9zzBN0iUxTK9+eTf1z2sd4sfFMH/+Zgn0fgORxm3p+33pL++EdzOfcVK6Rn\nnjGngA0f7s9IAcAeAS8GJScH8hUAAKGMPIGB1tDaoOK6Yk+hp7i+2FP8GRY5zFPwyU7I1n1T7/MU\nfyj4AH61WmbOoHdk5g3KUCfFoHXr1nn6S5Ys0ZIlS3r15E1tTXrkD4/oVyt+pcToxF49xrKkXbuk\nN96Q3nzT5KZVq6QPPpCmTmXeHwD22bJli7Zs2eL35w3oBNI//rF04YK0fn2AXgUAQkwYTQzaE8uy\nLD32mHTttdKaNXaHg8HkfPt5ldSXqLiu2FP4cfcvXLqg7MR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"text": [ "" ] } ], "prompt_number": 184 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Aparently the third graphic above satisfice inequality $\\mu(E_0)" ] } ], "prompt_number": 189 }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }