{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Variation of parameters\n", "\n", "**For second-order linear equations**" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "t = var('t')\n", "palette = [(215/255, 0/255, 132/255), (255/255, 1/255, 73/255), (255/255, 121/255, 1/255), (255/255, 210/255, 0/255)]\n", "cool_palette = [(0/255, 150/255, 173/255), (0/255, 200/255, 146/255)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Shock absorber rebound\n", "\n", "### Homogeneous equation describing a shock absorber\n", "\n", "A car seat is mounted on a shock absorber: a spring with lots of friction. You want to know $x(t)$, the position of the seat relative to the car at time $t$. When the car is moving steadily, the seat is described by the homogeneous equation\n", "\n", "$$x''(t) + 3x'(t) + 2x(t).$$\n", "\n", "The solutions are weighted sums of $\\lambda_1(t) = e^{-t}$ and $\\lambda_2(t) = e^{-2t}$. Whatever position and speed it starts with, the seat quickly approaches its equilibrium position, $0$.\n", "\n", "### Inhomogeneous equation describing a quick stop\n", "\n", "Suddenly, the car stops, with acceleration $-\\frac{2}{e^t + e^{-t}}$, graphed as the light solid line below. Now the seat is described by the inhomogeneous equation\n", "\n", "$$x''(t) + 3x'(t) + 2x(t) = \\frac{2}{e^t + e^{-t}}.$$\n", "\n", "Let's find a solution using variation of parameters recipe described in the book. (In Section 7.9, we'll learn why the recipe works.) Instead of working with $y$ and $y'$ directly, we'll work with the rescaled unknowns $X_1$ and $X_2$ defined by the equations\n", "\n", "\\begin{align*}\n", "x & = \\lambda_1 X_1 + \\lambda_2 X_2 \\\\\n", "x' & = \\lambda_1' X_1 + \\lambda_2' X_2.\n", "\\end{align*}\n", "\n", "Set $W = Wr[\\lambda_1, \\lambda_2]$. The parallelogram area formula tells us that $W = \\lambda_1 \\lambda_2' - \\lambda_1' \\lambda_2$, so $W(t) = -e^{-3t}$. Now we can use the book's formulas for $X_1'$ and $X_2'$:\n", "\n", "\\begin{align*}\n", "X_1'(t) & = -\\frac{\\lambda_2(t)}{W(t)}\\,\\frac{2}{e^t + e^{-t}} \\\\\n", "X_2'(t) & = \\hphantom{-}\\frac{\\lambda_1(t)}{W(t)}\\,\\frac{2}{e^t + e^{-t}}.\n", "\\end{align*}\n", "\n", "Plugging in our formulas for $\\lambda_1$, $\\lambda_2$, and $W$, we get\n", "\n", "\\begin{align*}\n", "X_1'(t) & = \\hphantom{-}\\frac{2e^{t}}{e^t + e^{-t}} \\\\\n", "X_2'(t) & = -\\frac{2e^{2t}}{e^t + e^{-t}}.\n", "\\end{align*}\n", "\n", "Choosing the antiderivatives\n", "\n", "\\begin{align*}\n", "X_1(t) & = \\ln(1 + e^{2t}) \\\\\n", "X_2(t) & = 2[\\arctan(e^t) - e^t],\n", "\\end{align*}\n", "\n", "we get the solution\n", "\n", "$$x(t) = e^{-t} \\ln(1 + e^{2t}) + 2e^{-2t}[\\arctan(e^t) - e^t],$$\n", "\n", "graphed as the dark solid line below.\n", "\n", "The acceleration of the passenger is the acceleration of the car plus the relative acceleration of the seat:\n", "\n", "$$-\\frac{2}{e^t + e^{-t}} + x''(t).$$\n", "\n", "It's graphed as the light dashed line below. The shock absorber was meant to reduce the acceleration of the passenger, compared to the acceleration of the car. Did it? If not, what went wrong?" ] }, { "cell_type": "code", "execution_count": 172, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 172, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X1 = log(1 + exp(2*t))\n", "X2 = 2*(arctan(exp(t)) - exp(t))\n", "car_accel = -1/cosh(t)\n", "seat_accel = diff(exp(-t)*X1 + exp(-2*t)*X2, t, t)\n", "seat_labels = ['$t$', '$x(t)$']\n", "plot([car_accel, seat_accel, car_accel + seat_accel], (t, -6, 6), ymin = -1.2, ymax = 0.6, thickness = 3, color = [cool_palette[1], cool_palette[0], cool_palette[1]], linestyle = ['solid', 'solid', 'dashed'], axes_labels = seat_labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A quicker stop\n", "\n", "Suppose the car stops faster, with acceleration $-\\left(\\frac{2}{e^t + e^{-t}}\\right)^{20}$. The antiderivatives of $X_1'$ and $X_2'$ get tedious to calculate, but my laptop can can find formulas for them without a fuss. The acceleration of the car, the relative acceleration of the seat, and the acceleration of the passenger are graphed below. Did the shock absorber work as intended this time?" ] }, { "cell_type": "code", "execution_count": 173, "metadata": {}, "outputs": [ { "data": { "image/png": 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HQuqJxS1lc0fQ8uB0GEllRwKEBwBA+ggPAFAk7K0OJS6nJtoGQY/UYcIDAGAECA8AUCS22cY7zKksk8NIbk0YCcIDAGAkCA8AUCSSZ1pKv8tSKoQHAMBIEB4AoEjYuy2NZKalVBjzAAAYCcIDABSJ5JmW0l/jIRVaHgAAI0F4AIAiEI0ntKurx1KWkW5LTNUKABgBwgMAFIE9XQHFbKtBzxnBGg+pHA6EZJqsMg0ASA/hAQCKgH2mpTqfRzU+z5jPG4on1BmJjfk8AICTA+EBAIpANmZa6sO4BwBAuggPAFAEkgdLjz48VHrclm3CAwAgXYQHACgCSeGhavQzLdX7vZZtBk0DANJFeACAIrDD3m1pDC0P40t8lu0jQcIDACA9hAcAKHCBaEwHeoKWsjljGPMwvoSWBwDA6BAeAKDAvdvZk1Q2u6J01OdrsLU8MOYBAJAuwgMAFDj7eIcpZX6VuF2jPl+DbczDEcIDACBNhAcAKHD28Q5jXRyuwd5tifAAAEgT4QEACtx22wJxYxksLUnj/bYB04HwmM4HADh5EB4AoMDZF4gby2BpSarzW1embgtHFEskxnROAMDJgfAAAAVux1HrgOmxtjyM83mTylpDkTGdEwBwchj9iDsAQNYdDUfUHLJ2KxrrmIebrvu0dLBFWnq+tOwCSVJTMJw0CxMAAHaEBwAoYPbB0k7D0IwxTNMqSQ899JBm/vZZS2tDc5BxDwCA4dFtCQAKmH2a1hkVJfI4x/6r2951qYnwAABIA+EBAApYpqdp7TPONmi6mTEPAIA0EB4AoIDZWx7GOli6T71toTi6LQEA0kF4AIAClulpWvvQbQkAMBqEBwAoUKZpJnVbouUBAJBPhAcAKFBNwbA6IzFL2dyq8oyce5yflgcAwMgRHgCgQNlbHbxOh6aU+TNy7qSWhxDhAQAwPMIDABQo+2Dp2RVlchhGRs5NywMAYDQIDwBQoJKmaa0a2+JwA43zWadqbQ9HFY0nMnZ+AMCJifAAAAUqeZrWzIx3kJK7LUlSa5i1HgAAQyM8AECBSpqmtTJzLQ+1Pq/sHaDougQAGA7hAQAKUMI09a59mtYMzbQkSU6HoVpb1yWmawUADIfwAAAF6EB3UCHbGIS5GVogrg+DpgEAI0V4AIACZB8sXeZ2qWGQcQpjYV9lmpYHAMBwCA8AUICSB0uXycjQNK197IOmaXkAAAyH8AAABShpsHSGuyxJ0ji/dcxDS4jZlgAAQyM8AEABsndbmluZ+fBQZ+u21MIq0wCAYRAeAKAAvdPeZdmek4XwYJ9tqZWWBwDAMAgPAFBggrG4dnX2WMoW1GRumtY+dT66LQEARobwAAAFZvvRLpm2slMyuMZDH1oeAAAjRXgAgAKz1dZlaVp5iUrdroxfZ7AxD6Zpjy0AABxHeACAAvO2LTzMz0Krg5TcbSmaMNUVjWXlWgCAEwPhAQAKjL3lYX51dsKDvduSRNclAMDQCA8AUGDs4WFBlsJDmdslj8P6Z4DpWgEAQyE8AEABiSUS2t5hb3moyMq1DMNIan1oCdLyAABIjfAAAAVkZ0ePognroOVsdVuSksc9tIYJDwCA1DI/fQcAYNS2HrW2OjT4vaoZZGzCWKxatUoul0tXX3216komWx6j5QEAMBTCAwAUkC2tHZbtbLQ6rFmzRhUVvV2hfvfUi5bHGPMAABgK3ZYAoID8pa3Tsr2otjKr10vqtsRsSwCAIRAeAKCAbLGHh5rsDJbuU+e3DZgmPAAAhkB4AIACEY7Htf1ot6VsUU12Wx5qvdZVpml5AAAMhfAAAAVia3uX4qZ1pqVTa7I305I0WMsDYx4AAKkRHgCgQGxptXZZmlFeonKPO6vXrPXSbQkAkD7CAwAUiC1t1pmWsj1YWkpueWgNRWTaWj8AAOhDeACAAvGmbZrWhVkeLC1JdT7rmIdIIqHuaCzr1wUAFCfCAwAUANM09VqLNTwszkHLQ+0gC9DRdQkAkArhAQAKwOFASE1B62Dl0+uqsn7dcrdLbodhKWPQNAAgFcIDABSAV5uPWrbL3S7NqizN+nUNw0hqfWC6VgBAKoQHACgAr7VYw8OSuko5DCPF3pllX+uhLRTNyXUBAMWH8AAABeBVW3jIRZelPkktD2FaHgAAgyM8AEABsHdbOiOH4aHGZ11LopUxDwCAFAgPAJBnLcGw9nUHLWWnj8thy4OXMQ8AgPQQHgAgz15qards+5wOza8qz9n1a21rPRAeAACpEB4AIM9ebGyzbJ85rlpuZ+5+PTPmAQCQLsIDAOTZi03W8HBOQ01Or89UrQCAdBEeACCPTNNM6rZ0dkN1TutgDw9thAcAQAqEBwDIox0d3WoPW9dVOLs+xy0P9gHTdFsCAKRAeACAPHqx0drqMKHEpyll/pzWocbW8tAZiSkaT+S0DgCA4kB4AIA82ni4xbJ9dkO1jBytLN3H3m1JktpofQAADILwAAB59KwtPFwwoS7ndajxJocHBk0DAAZDeACAPDkSCGnb0W5L2Xsn5j48eJwOlbtdljLCAwBgMIQHAMgTe5elcrdLi2sr81IX1noAAKSD8AAAebLhkDU8nD+hVi5Hfn4tM10rACAdhAcAyJN1B5st28vzMN6hDwvFAQDSQXgAgDzY3x3Q2+1dlrILJ47LybVXrVqllStXavXq1f1l9kHTdFsCAAzGNfwuAIBMe3p/k2W72uvWsvrcrCy9Zs0aVVRUWMpoeQAApIOWBwDIg6f2N1q2PzC5Xk5Hbtd3GChplWnCAwBgEIQHAMixWCKhZw5YWx4untKQp9r0ouUBAJAOwgMA5Nizh1rUHo5aylZMqc9TbXoRHgAA6SA8AECOPbz7kGX7jLoqTSkryVNteiVN1cqAaQDAIAgPAJBDpmnqkd2HLWVXzZyYp9ocN1jLg2maeaoNAKBQER4AIIdebGzXgZ6gpeyqGfkPD/apWiOJhHpi8TzVBgBQqAgPAJBDv9i+z7I9t7JMC6rL81Sb4+wtDxLjHgAAyQgPAJAjkXhCa949YCm7Zu4UGUb+pmjtU+lxy2mrR2sonKfaAAAKFeEBAHLkib2HkwYif2ru1DzVxsowjORVpml5AADYEB4AIEd+9Jddlu3zxtdqZkVpnmqTjOlaAQDDITwAQA683dap/zvYbCn73ILp+alMCknhgelaAQA2hAcAyIG733zXsl3n8+jjsybnqTaDS1rrgZYHADhhvfDCC9qwYcOIjyM8AECW7e8O6Gfb9lrKrp8/XT6XM081GlyN123ZptsSAJy4rrzySt1zzz0jPo7wAABZ9pU//0XRxPEF17xOh25aNCuPNRpcrc9r2abbEgCcmLZu3arGxkade+65Iz7WlYX6AACOWXewOWl61uvnT9fEUn+eapQaA6aLQzSe0Lbuo9rS3a6dgU6VxUoUCxtqDUUUjMUVjMcVjCX6/92kbm0rO6CEaWrgmuEOQzIMySFDS3tmqsrwy+t0DPhyqtTlVKXHrU5nQB2OoGo9Po1z+1Tv9Wm8t0QTfX5N8pXK6yysVjQAQ3vuueckScuXLx/xsYQHAMiSaDyhmza+YSmr9rr1T0vn56lGQyM8FJaOcFSvtbXr583vaEugVXtjnTqqoKLOqLXfwJ4qqW2IWbvKwlJtz5DXemZ7kxQZ4i3BhE5pQpeU4jSOoFtTDkxXrdejWp9Hdb7e//d+eVXr9ajZ0aVqr0fT/WWaVVquCV6/HA46QAD5sHHjRlVWVmrx4sUjPpbwAABZcudr2/RWe6el7F/OOlV1fm+KI/KrlnUe8iZhmtrS2qFNR9r058Y2bTrSqp2dPZIjIS05LBmS3CkOdpopHjhmmId7KzDMQoXOxNCHJ6S9XQHt7Qqk3mnBEckXH3CQ5Eg45U445TXdmhtt0OnOCcfCh7c/fPQFkRqvR1Vet1wEDmBU1qxZo7vuukuS9Oqrr6q2tlZnnXWWJOlHP/qRzj777LTOQ3gAgCz43a6D+sfNWy1lS+oq9bkFM/JUo+HR8pBbjcGgHt13UM8fOKon9zeqKTjIit4JhxR2St548mN9hnljn5Zhw8MwCSSWxht6l62eDinhiCusuMKK6OWmVr3cPMSq5iURaV6zjLhD7oRLXtOlUsOjcodHVU6v6lw+XeqfqSklZar1elTn96jW61GNz0PgACStWrVKq1at0v79+zV16lR9+ctf1u233z7i8xAeACDDXm5q17X/97KlzJD0owuWyOkY5k1aHtnDw9FIVPGEWdB1LjbReFw/2r1NPzy0RTudLVKnV9pTM/RBIdfg4cGUHDGn6n1+LZxcr3E+j0pcTvn7vpy9/w87onrHbJLL4ZDDMGRIMk1TMVOKJ0xFzIROP3OCYgkpnEgoHE8oHI8rHE+oOxpTZySmNz0RtUbiihlxxR2J3haRgS+L+HBvzs2xBxBX7zVNV0KRY/91KaAj/XWQ/vh896B1qfK4VevzKFrXqVBJQOWGV5VOr2pcXtW6fKp1+1Tv9muWv0JLy+tV5XWryuMuuBnRgExYt26dJOm9733vqI4nPABABj2866Cu/b+XFYhZ3+z923sW6dzxtXmqVXpqbN2WJKk9HCnYblbFZGNzo/7fzpf1XGS/Yt6o1PctrQr1vhFPDP7G2WkYqolVyBWJaoa7UqeV1OnMyjqdUVmjU8ur5HXm5894PJFQUzikA6EeHQwFFJqQUMkpXrWGI2oJRtQajqg1dPyrKRzU9rhTCWfcGjosJ00jPAzFlBQf/ORHI1EdjUSlmg7JE1RT3wMJSZFjX5K0xyftOv5z6nU6VO11q8rj6Q8U71TuU4nTpUqHR1Uun2pdXtW4fap1e1Xr9mpRSa0m+8tU7napwuNiMDkKzvr161VaWqqlS5eO6vis/9ZZvXq1rr766mxfBnnAc3vi4rkduZ5oTN9+dZu+/eq2pMc+c8o03bp4dh5qNTL2lgept+sS4WF0TNPUd3f8Rf965GUd9XT3vmm2fysdplQV7B/wPKO8ROdNqNW5DbV6z/gaLaiukMeZfpebXP3sOh0OTfCXaIK/RMtGcFwikdDhcFC7erq0J9it/aEeHQoH1BgJaMqcakXDDrUcCxwtofCx/0d6w/hw4SHmUOpkcsxw57CFj3A8oSOBsI4EjnWnMkxpXMuA/Y99DexttbNG6jg+m5rbYajc7Va5x6UKt0vxspAaK1rkk0slDrdKDbfKnG6VOz2qdHpU6fLogyXTVeJyqsTtVInLqVKXS8888lutWnW1Stwu+RwOuUbwukBhy/Xf3PXr1+u8886TyzW6GEB4wKjx3J64eG7TdzQc0S+279e/vPKOGgfps37RpHG6Z/npMozC7/rjc/W+URnYasJaD6PzYmObbn7+Tb0QOijN6h5y3+kNbv3dgsW6dGqDZlWWjem6hf6z63A4NMlfqkn+Ul0wguNCsbh29XTpL91t2h/q0YFQj45EgmqKBtQWC+toIqxYzNSE+mq1BMNqDUfUGYkln2jY8DDMG/J0xpfYxo9EE6bawhG19f0sGT1SXdcg1z72FTD0X881Jj9+7z36Uriy99+zW6SysIyEQw7TkMN0yCWnXHLILacmRau1MD5BpW6X/C6nvA6HfK7e6Xd9TocMh/RG4pD8Tpf8DpdKnS6VOF0qdbpV6nSp3OnWbF+lajy+pGMZP5J5ufy53b9/v3bv3q3rr79+1Oeg2xIAjEBzMKw3Wjv0RkuH1h1q1tP7Gy0LwA306XlTdd/y00f0yXG+1fo8CnQH+7cZND0yB7oDuuPFt/TL7fuPlfikHrdUGrXs54259QH/dH1z9pk6o2Jc7itaZHwupxZUVmlBZVXax0TiCbWFI/1hojUU0R+6dmt/pEstsaCOxsPqNqMKmTGFjZhiRkyOuEvRoU6aTngYawAZbvC61Nti5ZBMR+JY5ogrOqDmbUcT2nJgiEH27ri06EjqxyVpW53Uk9zq6DAkn9Mp1XUrVN8hwzRkyJCj7//HvrxxtxZ3zJTbacjtcMjtMORxOPr/7XY49Jb7kAJGRC7DIbdhyG04ex83HPIaTk13Vmm+u/bYMQ45DUNOhyHXsf/HFNdb0Ra5DIc8x87hOnZ833lmeytV5vT0Hms73mkYCptxRc24vA6HPA6nPA5H/5fbcJw5vIeqAAAgAElEQVRw0wkPNt7h+9//vm6++ea0P+TKWnj4+y2v6XAgqD+3N+n8Fx9LuV+FvGpQef+2/U9wQqZ2qlVS6sbIiapQqeGROeDgXU+v1cwVH5QkdSqkJqX+5MeQoVkaui/yIXUqMMSvlDJ5NV5lluva72OX2o4XDPJeY7zKVarj3Qbs99t7H4NPst389AbVr7hQMzX0wLvDw9xHubyql+2TrwF1TcjU7mP38XZ7o85/4fdJ55igcpUouftDny6F1TzM8zHDTH0fu59eK/+KcxRQ8puavqqWy6tx9vsYICFTe9We8nFJalCZ5T52P71WMwY8t10KqyXVpOfqff6mD3EfMqQjZpeCxhCvK9Or7rWbNOOD1tdU330mZGqfMcx9mMfvY7C3uN0Kq8Ww3sfb7Y264M+PS5IcpqGpqh5yusdGpb4P89h9jFPqeegTMrXfaFfT2g2q/+B7Lcf2qTfL5R8wV6X956NbYbUavdNEmoPU1ZA01awe9Pp7nlmr2SsuVou6FVRU8UTvQNJ4QjITUjCSUEc4po4eU+0dw8976TCku96zSDefNnvIX8aF+Clxrc+j/VkID9m4V9M01RGPqCUWVCgRVygRU8iMK3zs32Ezrg2/+b3O/avLZar3ddG3TJqp3n8nlx0vH4lwLKEnt7fpye2tisRNafNGadkFkgzpUIU0p1WKG5oUr9LFtZN1bu04GYah10PNej3UnLHvyb5wlx5oejtj50vHi797Qmd/5PKcXnPE13VJKpPOLauRhvo7OVeKJUwFo3EFIgkFonH1RBP9263RkDb/4Tm5LjpbIcUUUVxRI664Eoo7EjIdiZTjLvoNN3A83fAwlnMYabzATWPA63jAqU31tk6aMcmVOqD0hCNad2iY1/a8pqRgrYSkp1+RVpwpHSyTDlamPt4TkxYO0koz0DvjpEDq9yRq6JImHZtSu++6A4Wccm4dL4dhyGGod9KBYwssGuotC0xrUtzbex/933nT6P93SUeFyo9Wyug7Vn2LNPbu03ioUVesfVaPf3DkC7aN1ObNm+V0OrVsWW+Hw127dmnPnj0jah3PWnj4wes7Feh2SLGgWrQ39Y6tJdLewf+gSzo+x/VQ3q2VOn3Wsv99XBvrFvX+u6ZHmn409fFxQ8+9MeRnDdKsFqlyiCnk+u5j4HUHst/HYM/RYPcx0FD3sfYpbf/AdD33xjB/6NO9j1Qs9xHQ88ae5H3Gch+SFDe0caj7+O3j0nsmZPA+UrDfx28f13P1A57bsd6HlN7zYb/uQKP9+Rho0PsI6DnH7t5/xg3pjSHqKGXudfXMk9p2ydTB98nA60pvpqjj7x7X8w2Ljt+HfXxjX+5p80sdQwf0BXMd+sSMKVo5sX7YX8YFGR6ytNbDWO41lIjp5Z4mvdbTrNcCzXor0KbD0R41RYMKm0N8uipJv3hA/7E4y43s7T7pQKUUHXCdl587/qYr4pQ6PVJZRAc97Xqgq10PDNJrJSMCLfrM7v/L0slT+NXP9ePTh/jZPFGua0jySPrTeumyuan3W9DU++Y9YfT+3kk4ev8fd/SWGQmpa8DPmSFJZu//DVOKOiVv9Pg5Eo7eN/IDjTU8DHe81HvNga9ju+ECSDoBPFU1+97ED3eOtEJQGvWwX9cmbkrx/k8UBjmhI97bmpPicl3xiLq6hvhdGkno+eaW1I9nUE1NjaqqquTxeNTZ2ak77rhD991334jOkdZvVNM01dU1st90ZjAgBR1SLC71BFPvGDCk4BCD8RyJoY+XpEBACtqaAeNxKXhssZpAcOhzxI3j+6bSE5RcQ7w56ruPgdcdaLT3YXl8iPuIH/s+Z+o+Uhl4H/EUz+1Y7kMa/vnou26m7iPlOWz3YX9uc/W6SvWakrL3uhr43Gby5yOVvvtI9ZqSsvu66vseD3cfPRr0HC6HoRVTGnTDwpm69sjj+sc92/WPe/5Ps7xVurhyqq6snqmzy8cnHReLxdTZ2ZlUni191xrqmhXxqOUeD7e1ZaSOI73XuJnQM0f36bftO/WHo3vVlRhliBnqNTVWcfV+onnEIfUMnLLn2HUj3VJDt1TX3bsidJaqYa1TFu+3kK5ZbNd1yLoqeCqmet+Z2T8IMSWV9kgzd/UGgx5J3ep9g28ax5vNJEmGFOuWykPHA0jfPom+Y0ypJXo8sPT//9i/HabUExj6709wmN+5QdfwfzsCgd4WDLu+73GPSwqmWh1Rkhkd/rkIBqXgINfofzww9Pua0Bjuo89w9xGPywwGRvW7try8fEStBl/60pe0adMmrVq1Sm63W9/61rdUXT3Eh3uDMExz+MbZzs5OVVYO0WwEAAAAIKc6OjpUUVGR02umFR5G0/Kw5Ik/qLE7qnBNpxL+1J8YOQM+edpT9003lVBoUlvKxyXJ01IuZzh1f7ZYSVjR6iFmuzAN+Q8N3RUhXNuphC911yZXwGu5D/s31TRMhSYOfR/e1nI5Q0PfR6R6iOfBNFRyaOixG+HaTsV9QzwfQZ+8bUM8H4ap4MTWwR88Fny9rRX5v4+AT96hXldD3ccxludjkFAfKwkrUjX066rk8NCvq1BtpxLe1K8rZ8Ar79Hh7iMTr6sh7iMxyH3Yvh+hmqF/PtK6jwlp3McwP+fhqtSvK8M0VHJ48NeVKVMJSeGaTpm+qPp/go3+g3s/iYs6ez/F88WGnREylW9Pfo9uGL94dAePUWdnp6ZMmaL9+/en/GPzrZe36q7Xd/Rvf3j6RP38A6ObC3ykGiM9+ts9G/RM575RHe+VU16HU16HSz7DKY/DKdexPsW9Qzl79fVV7iuXjn3wagzYZ8Bjdrtbw2rzdlg/SW4skw5XqLwyockzEiopGdUtAMiSvne7pnns38f+HzMTSpimEubxcVGm2dtI08djuo4fI/X/ieg9p6GgIr2NOn3XGjBuyjQlT8Ipt+k6frys5zIlzSuv0G+Wvn/E9zXSlodMSKvbkmEYI041u65eNaoKAUAhME1TgURMzbGgGqMBHYkEtC3UrtcCzXq9p0XvhFIPVHfKUHyQnq9uw6Grpy1WhTe3nxLZVVRUpPydPrG2RvIff+fb6XTn5FOttwKtumznU9oX75JK/UmPG5IW+mt1euk4LSmp0yxfpRrcJWpwl6je5Zff4cr6H9BIIq5zX3pMbXUHJNnqOM3Uf53+Hn123syimJYXAEaLqVoBYBCGYRyb89yt6YO82X83dFQ/aXpLDzZvVXPM2kc2LlOlDpeuqZ2nJ47u0cFo72xWnx136qDnKiT2heJysc7Ds50H9aHtj6sznnythf5afbb+VH20ZpYmesa2BsJYtEfCWvjS/+iQO3lQflm4RH9YcLkuqEse1wIAJxrCAwCMwmxflb4z9Tx9a/I5+nnLO7pl70Z1J4533epJxPTb9p1ad8pVWtd1UN8/8rq+Nik33X/GIik8hIaZaWuMdoU6dOX2J5KCw3h3if558jn6m3Hz5TTyO8/60XBEC5/7nQ6VJQeHxYmJeu49K1XmHmIwJACcQAgPADAGHodT19efquXlE7Xq3af0WuD4vOatsZCu2fm0Xjj1Y7qhYVHe3wSno9ZrnRUrm4vE9cSjumrHE2qPWwPKOWXj9ejcy1Xvzv/AgY5wVCsef16HWt3SXJfkPzajSkK6rmSxHlic/XnZAaCQFP5fMgAoAnP91Xr+1I/qoorJlvItwVbdsm9jUQQHKbnlIRRPKBgbZi2FUfr87nV6M2CduOCKqun60/yrCiI4dEaiuuSJ57W5qb13jv5366SwU4ob+t649xEcAJyUsv7XbOvWrVq5cqUqKytVXl6uc845R/v2jW4mDRSmz3/+8zIMQ3fffXe+q4Ixikajuv3227Vo0SKVlpZq4sSJ+uu//msdOnQo31UrCn6HS4/OvVyL/NZZnX7c9JZe7D6Sp1qNTI0vuftNNrouPXV0r37Vus1StsBfo1/Pvlh+R/4bxXuiMV36xPN6oXHALGBRp8YdnKj/nX6Fbp29MH+VG+DOO+/UsmXLVF5ervr6el155ZXatm3b8Aei6Nx5550yDEM333xzvquCDDh48KA+9alPqba2ViUlJVqyZIleeeWVfFcrLVkNDzt37tT555+vU045RevXr9cbb7yhr3/96/L58rASJbLikUce0YsvvqiJEyfmuyrIgEAgoFdffVVf//rX9eqrr+p3v/udtm/frpUrV+a7akWjzOnR/865VGUO65vwL+15VokUM2PHzITuOvyq7m3ckosqDqnK40maoDTTXZdiZkK37nvOUlbh9OjhOZep3Jl6Ot5ciSdMffKZzdp0xDp98PgSrzZe8n59dOL0/FRsEBs2bNANN9ygF154QWvXrlUsFtOKFSvU09OT76ohgzZv3qwf//jHOu200/JdFWRAe3u7zjvvPLndbv3xj3/U22+/re9973uqqqrKd9XSktWPd772ta/psssu03e/+93+spkzZ2bzksihgwcP6sYbb9RTTz2lyy+/PN/VQQZUVlZq7dq1lrL//M//1FlnnaV9+/Zp6tSpeapZcZnnr9Y/Tj5Lt+17vr/sxZ5G/bp1mz5Vd4pl35e6j+hzu9fpjUCLSh1ufahqhiZ78zerkNNhqNrrUduAWZYyHR5+0vSW3g5a35j/+9TzNdc/slVOs+XLf96ix/YctpQ1+L1at3K55lWX56lWg3vyySct2w8++KDq6+v1yiuvaPlyulWdCLq7u3XNNdfoJz/5if75n/8539VBBnznO9/RlClT9OCDD/aXTZ8+PX8VGqGstTwkEgk98cQTmjt3ri6++GLV19fr7LPP1iOPPJKtSyKHEomErr32Wt1222069dRT810dZFFHR4cMwyiaT0QKxRcbFmuOz/o9+9r+FxQzjy89tDvUoXPf+o3eCLRIknoSUX3j4Is5redgsjldayAe1T8esN7jkpI6/c24+Rm7xlh8f8t23f3mu5ayaq9bf1p5gU4psOAwmI6ODklSTc3QC1SieNxwww26/PLL9YEPfCDfVUGGPPbYY1q6dKk+9rGPqb6+Xqeffrp+8pOf5LtaactaeGhqalJ3d7f+9V//VZdccomefvppXXXVVfrIRz6iDRs2ZOuyyJHvfOc7crlc+uIXv5jvqiCLQqGQvvrVr+qTn/xkThYKO5F4HE59b+r5lrJ9kS493Lazf3uGr1LX2d40P9i8VTtCyVOC5lLydK2ZCw8/b3knaV2M70+7oCAGlP/r9jd1a8daqez4GA+3w9Ajl7xHC2oK//VvmqZuvfVWnX/++Vq4sDDGZGBs1qxZo1dffVV33nlnvquCDNq1a5fuvfdezZkzR0899ZS+8IUv6Itf/KJ+/vOf57tqacnYb+tf/epXKisr6//qG7D14Q9/WLfccouWLFmir371q7riiit03333ZeqyyAH7c7thwwb94Ac/0M9+9jNWUi1y9ud248aN/Y9Fo1GtWrVKiURC99xzTx5rWbyuqJqus0sbLGU/OPKGZftbk8+xDBCOy9Q3D7yUk/qlkq3wkDBNff/I65ayiyun6kLbDFX58GzLYf1980bJnZDmtEi1vWMGfnrhmVo+sS7PtUvPjTfeqDfffFOrV6/Od1WQAfv379eXvvQl/fKXv2Ss6AkmkUjojDPO0Le//W2dfvrp+vznP6/Pfvazuvfee/NdtbRkLDysXLlSr7/+ev/XkiVL5HK5tGDBAst+8+fPZ7alImN/bjdt2qSmpiZNnTpVLpdLLpdLe/fu1d/93d8VVZ89JD+3S5f2LmIWjUb18Y9/XLt379batWtpdRglwzB084QllrLnuw/rlZ6m/u3xnlLd1GAdBLmmbYcOR/I34LXWaw0PbRnqtvRUx15tt7WqfHnC6Rk591j0RKO6bOsTMl3HupQZkqYd1aoza3XtvOIY53PTTTfpscce07p16zR5cv7DGMbulVdeUVNTk84888z+v7UbNmzQf/zHf8jlcikez84Uysi+CRMmFPX744wNmC4vL1d5ubU/6LJly5KmjNu+fbumTZuWqcsiB+zP7ec+9zl96EMfsuxz8cUX69prr9V1112X6+phDAb7ue0LDjt27NC6detUW1ub4mik46+qZ2mSu1QHo8fDwA+PvKkHZx3vv/yVCWfoPxvfVDDRuwBZzEzov5r+on+afHbO6ytJNVlqefhZ81bL9iJ/rd5fMSUj5x6LD778R/V4rF2pJkar9MtzL8hTjdJnmqZuuukmPfzww1q/fr1mzJiR7yohQ97//vdryxbrDGzXXXedTjnlFN1+++1yOp15qhnG6rzzzivq98dZnW3ptttu0yc+8QktX75c73vf+/Tkk0/q97//vdavX5/NyyLLamtrk95Qut1ujR8/XvPmzctTrZAJsVhMH/3oR/Xqq6/q8ccfVzwe15EjvesT1NTUyOPJ/zSaxcbtcOpvGxbpawde6C/7XftO3Zd4n7yO3j/+tW6/rqmdq/ub3+7f56fNb+v/TTpLjjx0DcxGt6X2WEiPtu+2lH2hYWHeuz5+b8db+rOx11Lmjrj10tKPyOnI/ziM4dxwww369a9/rUcffVTl5eX9P6+VlZXy+/15rh3Gory8PGnsSmlpqWpraxnTUuRuueUWnXvuufr2t7+tj3/843rppZf04x//WD/+8Y/zXbW0ZPU341VXXaX77rtP3/3ud7Vo0SLdf//9+u1vf6vzzz9/+IMB5NyBAwf02GOP6cCBA1qyZIkmTJjQ/7Vp06Z8V69ofXrcfMvaCZ3xiJ7qsL5hvWn8YklSvcuvr09aphdO/VhegoOU3G0pE+Hhf9veVdg83s3CbTi0qnbumM87FvsD3br9yLOyPDmm9MD0D2iSvzRv9RqJe++9Vx0dHbrwwgstP68PPfRQvqsGIIVly5bp4Ycf1urVq7Vw4UJ961vf0t13361rrrkm31VLi2GaKVYtAgBkzPK3f6uNXcdX6r6mdp5+OXuFZZ8/Ht2jiyqm9LdIZFpnZ6cqKyvV0dEx5DiW/3n3gD6x9vig7bmVZdr2yRUp90/HRVsf1rrOA/3bH6mepd/OvWxM5xyrs557TJvd1hB3hXuufn/GxXmqEQAUvsJvkwWAE8AnauZYth9t39U/xqHPpVXTsxYcRiLT6zy0xUJ6tvOgpeyauvy2OvzpQJM2b4lKh8qlYx+hVUVL9bslzKUPAEMhPABADvxVzSw5BvSP6U5E9eTRvUMckT/28NAejigxhkbqPxzdo7iOH+8znLq4Mn8DA3uiMV2//lVJhnSkQto2To6gR4/Nv0zuAghvAFDICA8AkAPjPaV6b8UkS9kfju7JT2WGYQ8PCVPqiERHfT77QOkPVk5VqdM96vON1T+89LZ2dwWOFwQ8+kHt+3VB7fi81QkAigXhAQByZGWVdRrNpzv2qxCHndV4k2fVGu2g6WgirqdsLSwfrs7fdKKvNR/VD95811J2wYRa/e3CWXmqEQAUF8IDAOTIikrrgmP7Il1Ji6YVghKXU16n9c/DaMPDiz2N6kpYWy2uyFN4ME1Tt2x6UwPjms/p0P0XnpG3ma0AoNgQHgAgR+b7qzXJbZ0C9OmO4VcUHct4g9EwDCNjaz0807Hfsr24pE4N7pJR120sfrfrkDYcarGUfe3MUzS3qjzFEQAAO8IDAOSIYRhaUWVtfUgVHlqiQf2i+R1d/e6TmvTaA+qOZ2aV53Rlaq0He3j4QJ5WlA5GY7rtz9bVeqeVl+jvFs9JcQQAYDBZXWEaAGC1onKqHmze2r+9vvOg4mZCTuP4ZzmBeFSTX3vQsqjaMx37dWVN7vrlZ6LlIZSIaXNPo6Xs/ZWTx1Sv0Vr1xjrtrjsgRcqlcO9g7X97z0L5XcyuBAAjQcsDAOTQheXWGZe6E1H9JdBqKStxunVe+QRL2RM5npkpea2H8IjP8WpPsyJmon/bkHRu2YTUB2TJ/kCPfh/eLlUHpQVN0tR2LZtYoY/OnDT8wQAAC8IDAOTQeE+pZnqtqzs/3304ab/Lq6Zbtv9vwOrMuZCJlodNtvta6K9Vpcs7pnqNxrVb1sl0HQsxhqS6gD53+hQZDJIGgBEjPABAjtlbFTZ1HUna5wOV1rEBu8Od2h3qyMj1V61apZUrV2r16tUp97FP19oWHvk6D5u6rOHh3PLctzps6+rQhvgeS9mEaJWunzov53UBgBMBYx4AIMfOLZugX7Rs69+2f0Iv9X5KX+fyqSUW6i9b13lQM3yVY77+mjVrVFFRMeQ+Y215ME1Tm7qtoejcstwvwnbtW+sk54DZqkzpntkX5LweAHCioOUBAHLM3vKwO9ypw5EeS5nDMHRhhXVw8bocdl1KDg8jG/OwO9ypxmjAUpbrloetnUe1OWH9ns2I1enK8dNzWg8AOJEQHgAgxxb4a1ThtL45//MgrQ8X2cLDnzoP5GxF6rFO1WpvTRnn8muWd+ytJiPxubeeS2p1uH/ehTmtAwCcaAgPAJBjTsOhs0obLGWv9jQn7fe+ikmqcfl0RdV0fXvye/Tr2RcrV8vF1fqsA5tHHB5s4zjOLR+f0wHKHeGoXui0ThM7K16ni8blftwFAJxIGPMAAHlweuk4PdN5fAG11wMtSfvM81Wr+Yzr5cjDrED2bks9sbhCsbh8aa6L8FrAGobOyfF4hx+/vVuxXdVSSanU0C1VBfX92efltA4AcCKi5QEA8uD0knGW7dcGaXkwDCMvwUGS6mzhQZJa0hz3kDBNbbGtXbHEdr/ZFI7HdfeWd3s3Ah5pd40u71yiDzVMHfpAAMCwCA8AkAdLSuss24eiPWqyDTDOpxqfRw5bbmkOptd1aWe4Qz0J69Sui0vqUuydeb/esV+HekKWsn9ccmrOrg8AJzLCAwDkwVxflfwOa8/R13uSuy7li8MwVOu1jntoTrPl4Q3bfYxz+TXeXZKxug0lYZr6t9d3WMounFinZfU1Obk+AJzoCA8AkAdOw6HT/LWWstcDyV2X8mmc39p1qTmYXnh4M2gND4tL6nI2WPqZA03a2t5lKfvKkrk5uTYAnAwIDwCQJ6eX2sY9FFx4sLU8pNltyd7ykMsuSz/6yy7L9qnVFbpkakOKvQEAI0V4AIA8sQ8iLqRuS5I0zjfKbkuB/ISHvV0BPb7Xur7EjYtm5nSKWAA40REeACBPTrcNmt4WaldPPDrovqFETC92H9EPj7yhm/c+m4vqjarb0tFYWHsj1m5Dp5XUptg7s/6/t55XorZbciQkSeVul66ZMyUn1waAkwXrPABAniz018qQ+hd+M9UbIM4orbfs927oqOa/+SvFzER/2d9PXKr6LA9CHk3LwxZbq4PbcGi+P/uDlQOxqJ6K7ZCmxqVJnVKbX1dWLlC5x531awPAyYSWBwDIkxKnW9O9FZayd4LtSfvN8FbIY1h/Xb/c05TVukmjG/Ng77I0318tjyO9heXG4h/eeVUJd7x3w2lK4wL60GzGOgBAphEeACCP5vurLdtbBwkPTsOhM2yDq1/uzkd4GL7l4a1gm2U7V+Md/rt1q2W7POrXxybMzMm1AeBkQngAgDw6xWcND++EksODJC0ttX6KnouZmcbZVplOp9vS9tBRy/Z8X/a7LG1qaVKb1zrO4prqU7J+XQA4GREeACCPTrG1PAzWbUlK/gR/S6A1a3XqY295aA9HFY0nUuzdyx4e5vqrMl4vu6/vfFkaOKFS3NC/zFma9esCwMmI8AAAeWRvedgearcMjO6zyDZj0a5wh7rj6a27MFr28CBJreHU1+yJR3Ug0m0pm+vLbniIxRN6NrzPUrbAqFeNx5fV6wLAyYrwAAB5ZJ+JKGImtCfcmbTfAn+NHAM+XjeVPL4g02q9nqSyocY97LC1OhiSZmc5PPxw9zuKea3T23558uKsXhMATmaEBwDIozq3X7Uu66fkg3Vd8jtcmuOrlCRN8ZTpsqppljCRDW6nQ9Ve61SnQ4UHe5elqZ5y+R3ZnRH82V1Hpb1VUndv0PFGPfqbyXOzek0AOJmxzgMA5Nkpvmo93318ZeStwXZdUT0jab9H5l6u8e5SVbmSuxNlyzifV+3h45/sN4dSd1vaZhvsne0uS52RqP64p0mKl0qtpZI3qs+dMYMVpQEgi2h5AIA8Sxo0nWLGpVP8NTkNDtLIpmvdHsztYOlHdh9SaMAAblfUo/83jy5LAJBNhAcAyLPktR6yO5ZhJMb5bdO1jqDb0jzbYPBM+/WO/ZbtS6Y0qG6QQd4AgMwhPABAntnfZNsHHufTOJ+t5SHFWg+maea021JjIKRnDljXuvjknClZux4AoBfhAQDybNaxgdB9WmIhdcayOw1rupK7LQ1er+ZYUB22qWOzGR7+d+dBxU2zf7vE5dTK6ROydj0AQC/CAwDk2QxvRdK8SbvCHXmpi126LQ/2Lktew6mp3vKs1cveZenKGRNV6mYOEADINsIDAOSZz+HSJE+ZpWxngYSH+jQHTG+zTS8721cpp5GdPzF7uwL6c6N1XMgn50zOyrUAAFaEBwAoALO81q5LO0PDh4dwIp70pj0dq1at0sqVK7V69eph900eMD14tyX7OI05Weyy9M0dr0lzm6X6bskTU43XoxWTG7J2PQDAcbTxAkABmOWr1Iaug/3bqVoe9oW79JV9z2tLsFXbgu1yGQ51L/uCXCP4lH/NmjWqqKhIa1/7mIfWcFjxhCmnw9rRak+4y7I92zaOI5Me69gllUV6vyZ3aFy0QW4nn4UBQC7w2xYACsAsr/XNfKqWB7/DpYfadujtYJviMhU249pre+OeSeNLrKtfJ8zBxz3sCXdatqd70gsnI7Wrs0stHuv35n01DJQGgFwhPABAAbDPuLTT9ma8T53Lp2qntTXAPkVqJo3zeWVrZNCRQChpvz0Ra4CZnqXB0nftektymZay22awMBwA5ArhAQAKgH3Mw75wlyKJeNJ+hmFonm1RudGMe0iX02EkzbhkDw+BeFSN0YClbLo3Oy0PD7fvtGzXxZn/ESYAACAASURBVMs005+dawEAkhEeAKAAzLS1PCRk6kCke9B959kGI2/L8qJy9q5LRwLWbkt7I8ndpqZloeXhcE9QR9zWe72ickbGrwMASI3wAAAFoNrpVbnDbSlLNZbBviJ1NlseJGmCLTwctrU82Mc7jHP5Vea0ztKUCffsekdyJyxlt05blPHrAABSIzwAQAEwDEPTbF199kQGH/cwz5/rloehuy3ZZ1rK1niH/2mxdlkqi3u1qKw2K9cCAAyO8AAABcL+pjvdlofD0R51xgZffyETkrstDd3ykI3xDj3RmPbuNqQ9VVK7X4obOr+EheEAINdY5wEACoR9nID9TXmf2b4qfaF+oeb5qjXPX6V5vmqVOd2D7psJw415yEV4eHp/o8JhQwqXSm2lchjSvddekPHrAACGRngAgAJhf9OdquXB63Dq3hnvy0WVJA0/5mG3LTzMyEJ4eGzPYcv2hRPHaXppdrpHAQBSo9sSABSIaR5by8Mgsxjlw/DdlrI75iGeMPX43iOWspXTWRgOAPKB8AAABcLe8nAg0q2YmUixd+7YB0x3RWPqicYkST3xqJpjQcvjme629GJTm1pC1jEdHyY8AEBeEB4AoEDYxzzEzIQORXryVJvj7C0PktQY7B33MFjXKnsLylg9ta/Rsn1qdYWmV5Rm9BoAgPQQHgCgQIxz+eV3WIei7U0xaDqXyt0ulbiclrLDPb1dl+zTyda7/CrJ8ODtpw80WbYvnlqf0fMDANJHeACAAmEYhqZ4yixlB6P5b3kwDCPluIf9Yesq2JleWbo9HNFLTW2WsounNGT0GgCA9BEeAKCATLKFhwOR7hR75lbSQnHBY+HBNqh7Soa7LD28b78Sc5ukiR1SWVhel6ELJtRl9BoAgPQxVSsAFJBJbmtf/oNDjHnYH+7SX4Kt2hY8qm2hdl1aNU0rq2dmpV726Vr7Wh7s4WayLfyM1S8PvyuVRnu/xnfLTLjkcRoZvQYAIH2EBwAoIPY33weHaHm4bd/zeqhtR/92icOVtfBg77bUN+Yhm+HBNE29FDwiDWj0mOmqktOg0RwA8oXfwABQQCZ5rC0PQ3VbmuWrtGzvDHdkpU7SIGs9HJttKZvh4e22TvX4rS0vK2umZ+z8AICRIzwAQAFJbnlI3W1ppm09hV2h7M3MNN5vG/MQCMk0TR2w1W+yJ3NTqP5y327JG7eUfWr8nIydHwAwcoQHACgg9gHTh6I9SpjmoPvaWx52hTtlpth3rCaUJo956IhH1JOIWsoz2fLwaOtuy3ZJwq2FJbUZOz8AYOQIDwBQQOzdlmJmQk3RwKD7zvRaw0NPIqom22rPmWLvttQYDGvfIAvETcxQeAjF4toWb7WULfWPl2EwWBoA8onwAAAFpMFdIqesb5BTrfUwyVMqj23w8K5QdsY9jPdbw0MsYertrqOWsnqXX16HdTG50dpwqFmJsrCl7OP1szJybgDA6BEeAKCAOA2HJtgHTYcHHzTtNByabhv3kK1B0/V+r+yf+W/ttF4rk12WnjrQKO2rlJpLpWDvxIBX1E7L2PkBAKPDVK0AUGAme8ossxgdjA4x45K3UnvCnZrhrdAsX6VqXb6U+46F2+lQQ4lXRwLHWwN2dFm7LWUyPKzd3ywdLen9kvTlM2Zqmi0oAQByj/AAAAVmJAvFrZ59scqdHjlyMBZgalmJJTzs7QpI/uOPZyo8HOwO6i9t1pmjrpo2JSPnBgCMDd2WAKDA2GdcGmqth0qXNyfBQZKmlPkt24d7rGMSMhUenj7QaNmu9Lh1Vn11Rs4NABgbwgMAFJiRrDI9GqtWrdLKlSu1evXqER03tazEst0W/P/bu9cguc76zuO/09eZ6ekezX00kqyRbVm+SZbAIF/wQjbGl5hoA9jLiAoLmw1buxBqqWSLShVbW8ouRQGVEHbLtUWSqmzMYkuBrLkEL1gmgKHs4DjYMr5btm5jSXMfzX36evbFSKM5z+nuOX3T9Gl9P1Uq+zx9TvfzaqZ/83/+z1ObbVofHxp1XN+5uVuhAL+uAKAesGwJAOpMKadMl+PQoUNKJErvHzArD3OLOcd1NcJDNmfrCSM83L2lt+L3BQBUB3/KAYA6U8op05eSWXnIppy/QszQU47nxqc0mUw5xu4iPABA3SA8AECdMXse5nJpzWRSBe6+dMzKg1JBadWB1uYWs+Uwlyzt2NCqrfGWAncDAC41wgMA1Jl8f8Gv9tKlclzh+hJvSenlXyOxQFjxYKTiz/je6SFp8zlpw6IUyrJkCQDqDOEBAOpMUyDkOq+h2FkPqy3lMhpLL9ZiWuppjiocMHZ2Si+fKL0xXHl1YDqZ1q+SI1LPvHTlpLRrWD+LvVrx+wIAqoeGaQCoQ5siMU1kllaui/U9fHfyLf358BEdS87odGpOv7VhQD/Y8dtVn1PAsrSltUXHZlbNJRWUYumqLFn6yelR2THn9q9Xt3AwHADUEyoPAFCHzKbpYsuWZrIp/Xz2jN5OzcmWdGxpumbzcvc9LP8NqhqVh8eHRiUjPLyvbVPF7wsAqB7CAwDUoU1h7+HhyqY2x/Wx5Ixytl3g7sqYOy4pdX7ZUoWVB9u29f/OnJaaso7x2+MbK3pfAEB1ER4AoA6ZTdPD6cLLlq6MOpf2JO2szha5vxKuysNKz0Nl4eHo9JyGbGfFpMkKaVdLV0XvCwCoLsIDANShPuPL+HBqoeC9G8MxNVlBx9hbNVq6dEW+7VpV+bKl5SVLzu1ob23tVcji1xQA1BN+KgNAHeozvoyfTRcOD5ZlaZtRfTiRnKnJvLbUaNnS4aERqdUZHm6P91f0ngCA6iM8AEAd6os4v6QPp+dlF+ljGHCFh9mazMtVecgEpVxly5ZS2Zx+enpMmo1KcxEptzx+W7yvgpkCAGqBrVoBoA6ZX8ZTdk7nskm1G+c/XGBWHo7XqPKQ97TnZKiiZUtPDU9oPpOVziaks5IsWz+4/2bdQbM0ANQdwgMA1KHePF/Gh9MLBcPDb23Yqo5QkwaicQ1EE9rR1F6TecUjYXU0hTW5lF4ZC6XC6igwLy8eHxpxXL+zq133dW0t+/0AALVDeACAOhQNBNUejGoqe/Hcg7OpeV3X3JH3/vvat+m+9m2XZG69rRFHeGhNt8iyrCJPFGeGh7u39Jb9XgCA2qLnAQDqlNk0PVykafpSaos5f3VEUpGy32tkYUlHxp07QxEeAKB+ER4AoE6ZOxjVS3hoMlYo5ZLB/Dd6cHho1HEdD4d0a2/+6goAYP0RHgCgTtVr5SFgnAK9tFi9JUv/clO3wkF+NQFAveInNADUKXd4qM2p0aVKRZKO67mlnBYz2QJ3F5azbT3xtrPycNeWnormBgCoLcIDANQp85Tps0VOmb6UZkOLrrFjM6UHmxfGpzW6mJRak1IkI8mm3wEA6hzhAQDq1EbXQXH1ER4m7EUp5Kw0HJ2eK/l9lpcs2dJVE9KNIwrsGtF/Gv6pXl+cqtJMAQDVxlatAFCnSl22NJtN6ZXFSR1PzuhEckYhK6D/vPEdVZ2TbdsaTS8sd03PXWyUPnqu9PDw2MlhqSkjBZdPzs6Fsnrs3An95bbfqNp8AQDVRXgAgDplLlsazywpncsqHMi/u9ET06f04aM/XLm+IhKveniYzqaUsnNSNCPNRVfG3yix8jC5lNLTIxNSe8oxvjnSqv5Ia1XmCgCoPpYtAUCdMisPkjSSdvcbXDAQTTiu307NKZ0rvZG5mJELS6eiGcf4S5MzJb3P40MjytmSYmnH+N4YPQ8AUM8IDwBQpzpDTQpZzh/To5nCfQ9meMjJ1tup0pcTFTN6ITy0OL/0vzgxrZxte36fx04On38fZ+XhXa2EBwCoZ4QHAKhTlmWpO9TsGBstUnloD0YVD4QdY8eTpVUE1rJS+Wh2hof5TFZvTXvbcSmbs/WjoRHJsl3v864YW7UCQD0jPABAHesJm+GhcOXBsixX9eFEcraq81mpfIRzrh2XXpiY9vQez4xOamIpJTWlXb+F3kF4AIC6RngAgDrWY1YeMoUrD5K0zQwPKXflYXBwUPv27dPBgwdLns/I6vBiVA1emDjn6T1WlixFslLu4vjV0TZtCEXzPwQAqAvstgQAdazbVXkoHh7MysPxJXd4OHTokBKJhGvcC8fnN6el2aaVyxfGvVUevnv8zPL/TDdLR/r1id2bdMdVCdny3jMBAFgfhAcAqGM9xo5LxZYtSdJANC5J2hCMaiAa1xXnr6uleOVh7fDw2tSsXplavZTK0ie3bddtPZ1VmiEAoJYIDwBQx8xlS2NrLFv6d9036N92X1+z5T+OyoOx49KpuUVNLqXU0RQp+Pz/PXbacb2xpUm39HZUdY4AgNqh5wEA6pi7Ybp4eEiEIjXtG3BUHpoyCgctx+u/HJks+vyjx844rj+4rV8ByypwNwCg3hAeAKCOuZctFQ8PteZo2Lak6zqcp0E/NTxR8NnXp2b13LizqfrDV/ZXdX4AgNoiPABAHXOf87Agu4TD2KppKZfRTNZ5qNvevnbH9c/PjBd8/v+8ccpx3dMc1b/o76reBAEANUd4AIA6Zi5bWrKzmsulC9xdW/mqHr/Z7zyX4R9HJjWddM8vZ9v65tEhx9hHt29RKMCvIQDwE35qA0AdM8ODJI2t09KlEWOnp7AV0H2bNyqyKgBkbVv/cHrU9eyTZ8Z1cvbC87YkW//mmitqOFsAQC0QHgCgjsUCYTUHnBvjrVffg7lNbE+oWa2RsGvp0Y9Ojbie/Z8vvnnxoiWt4E0j+uPxn+nzQ/+o700eq8l8AQDVR3gAgDpmWVaeU6aLn/VgWsplqjKXESO0XGjmvmdLr2P8+yfOKp29eHT0W9Nz+t7xsxdvaEkrG8zq8MyQvnjmn/XHQ09XZX4AgNojPABAnSv1lOlXFib1wNEf6uaX/lZdv/orXXXkG1WZhxlaes/P6wNb+xzjI4tJPXZqeOX6T48cdZwdHW51hpl3xLqrMj8AQO0RHgCgzrnPeiheecgop7+bfFO/mh/VRGZJZ9LzSuayFc+jUOVhR3tctxoHvf3Fy8clSb+emNZfvnrc8Vpnu/Nch90thAcA8AvCAwDUuZ6Q86yHscxS0fu3RuKusVOp2YrnYYaW3lVnUHzy+gHHaz8aGtG33nxb//5nzym3quwQDVo6F3C+z00tbNcKAH5BeACAOldq5aEtFFV70HnK9InkTMXzMHdbWj2vf33VZnVEI47XP/LEP+mZ0SnH2O/v3qIl21kFuSlGeAAAvyA8AECdc4eHtXdbGogmHNfHqxAezM/tXVURiYVD+vItNxSfU7xFewecJ1JvDMccFQwAQH0jPABAnXOdMu1ht6WBqHPpUq0rD5L0e9cN6P2bnYfGXdDZFNF377lFryxNOsZ3s2QJAHwltPYtAID11GP8Zd5L5WGbUXk4kays5yFr5zRu9FqYFYOAZenRe27Rf3jyeT286jTpGzsSevjOd2lXZ5uaFq/TVU1tOrIwphcWxnVbfGNF8wIAXFqEBwCoc+Zf+MfSi8rZtgKWVeCJ6i9bmsgsKefYcDX/6det4ZC+eee79NldV+vk7IK2JVq0u2vDylx3NLdrR3N7RXMBAKwfwgMA1Dlzt6WsbJ3LJtURair4zM2xHv1+9/UaiCa0LZrQNU0bpFzB29c0lqfaYS6ncnx+T7tu7iEkAECjITwAQJ0zD4mTlndcKhYebo1v1K3GkqCZmfKrD2MZZ3jYEIwqHAiW/X4AAH+iYRoA6lw0EFQi6NwG1UvfQzWNp539Dl1FggsAoHERHgCgDti2rQMHDqi/v1/Nzc163/vep5dffnnl9R5zx6X0og4cOCDLshz/+vr6ajI/s/KQrxoCAGh8hAcAqANf+cpX9NWvflUPPvignn32WfX19en973+/ZmeXd0ly7bh0frvWG264QWfPnl359+KLL9ZkfmbPQ7F+BwBA4yI8AMA6s21bX/va1/T5z39eH/rQh3TjjTfqoYce0sLCgh555BFJ+XdckqRQKKS+vr6Vf93d3TWZ47hReeii8gAAlyXCAwCss+PHj2t4eFh33XXXylg0GtV73/tePf3005IKnzJ99OhR9ff3a9u2bRocHNSxY8dqMkfXsqUSex5eX5zSf337l3p08k0dW5pWzrbXfggAUHfYbQkA1tnw8LAkqbe31zHe29urkydPSsp3yvSiPrB3r77xjW/ommuu0cjIiL7whS/otttu08svv6zOzs6qztFsmC615+Hns6f1308/u3L9zliP/vnGj1RlbgCAS4fKAwBcYg8//LBaW1tX/qXTaUmSZRz6Ztv2ypj7lOkF3Xvvvfrwhz+snTt36s4779Rjjz0mSXrooYckLZ8KfTI5oydnTuuhsVf1tbPPlz1ns/LQVWLPw5H5ccf11dG2sucCAFg/VB4A4BLbt2+f9u7du3KdTCYlLVcgNm68eDbD6OjoSjWi0LKl1WKxmHbu3KmjR49Kkl5bnNKNLz5y8Yb55We2b98uy7K0adMmbdq0SZK0f/9+7d+/v+CcXQ3TJVYeXlhwhoebWrpKeh4AUB8IDwBwicXjccXj8ZVr27bV19enJ554Qnv27JEkpVIpPfnkk/ryl78sKc9WrRl3eEgmk3r11Vd1xx13SJIGoom8n3/06FElEvlfy8e2bXfDdAk9DznbdoWH3THCAwD4EcuWAGCdWZalz372s/riF7+o73znO3rppZf0iU98Qi0tLfroRz8q6fyypT94UPr2zyVJk5kl/eEf/ZGefPJJHT9+XM8884zuv/9+zczM6OMf/7gkKRYMV2VL1dlsWik75xgr5X2PJac1l0s7xna31GZXKABAbVF5AIA68LnPfU6Li4v61Kc+pampKe3du1eHDx9eqVB0h5ult8elc3MrzxwbOqn9+/drfHxc3d3duuWWW/TLX/5SW7duXblnIBp39SuUyqw6rMzHI7PfoSfUrD6jhwMA4A+EBwCoA5Zl6cCBAzpw4EDe1ztDTbK+e0CrNzj9b3/zde1ao3dgIJrQs/OjFc3NDB9RK6hYIOz5+SMLY47rm1q6XM3hAAB/YNkSAPhAyAqo0+gzGE0vrPlcob6HUuRrli7ly//GcEzvjvWqObD896rdMZYsAYBfUXkAAJ/oCjVrPHPxvIXV/1/IQDS+5j1rMT+nlGZpSfp03y59um+XsnZOR5fOrYQIAID/UHkAAJ8w+wzMikA+21ZVHnpDsbI+11V5KLMJO2gFdG1zh7ZWoRoCAFgf/PkHAHzC/NLupRH6PfF+vbbrd3VFNK703ILa9Aclf67ZMF3qGQ8AgMZBeAAAn+gKO5cLjafXXrYUD0a0ozkiSUqvcW8hlZ4uDQBoHCxbAgCfKKfyUA2Vni4NAGgchAcA8Ilyeh6qwWyYrsbBcwAAfyI8AIBPmF/a8x3eVgtmSDGXTwEALh+EBwDwCbPX4FJVHszlUV4rD+cySQ0lZ2Xb9to3AwB8gYZpAPAJc9nSRGZJOdtWoIanNadyWc1kU44xrw3T35l6S7937B/UEWrS7pYu3d12hT7X/85aTBMAcIkQHgDAJ8y/+Gdl61w2qY4SD20rpRKQb2mU14bpI/PjkqTJzJJ+MvO22oNRz58LAKhPLFsCAJ/I12vgZenSuUxSnznxpB44+kNJUv9zf61Zo5pQiNksbUnqCHkLAUcWxhzXu2Pdnp4DANQvwgMA+ERTIKTWQNgx5mW71mggqAdHfq3D0yclSQt2WieTs54+0wwnHaEmBa21f3XYtq0jC+OOsd0tXZ4+EwBQvwgPAOAj5WzX2hwIqS/c4hg7npzx9HnlNkufSM64eiV2t1B5AAC/IzwAgI90Gf0NXrdr3RZNOK5PeAwP42Vu02pWHTpCTdoUiXl6FgBQvwgPAOAj5R4UN1BmeCi38uDqd2jpklXDXaEAAJcG4QEAfMT88j5mNDQXMhCNO669LlsaTxunS3vcaenFhQnHNf0OANAY2KoVAHzEPGPBXFZUiLvy4LFh2qg8eD3j4W+vvkevLU3pyPy4jiyM6Z4NWz09BwCob4QHAPAR17Iljz0PA5Eyly2ly1u2FA4EtbOlSztbuvQxXevpGQBA/SM8AICPuJYteaw8XNO8QXe3bdXjkr6w+RZd29Uv27bX7EMwz3nwumwJANCYCA8A4CPmbkfml/tCBqIJfWv7vWqT9Jm+3UokEms+I+VbtlTaadYAgMZCwzQA+Ii7Ydpb5aEctm27eiqoPADA5Y3wAAA+Yn55X8xlNJ9N1+SzzmWTysp2jHltmAYANCbCAwD4SL6GZa8HxV0wODioffv26eDBg0Xvy9dPQeUBAC5v9DwAgI8kghGFrYDSdm5lbCy9qK1Rbz0MknTo0CFPPQ9mP0UsEFZzgF8bAHA547cAAPiIZVnqCjXrbHp+ZaxWfQ9m5cFLs/ShiTf0v8de1e6WLu2JdevdsV5d2dRWk/kBAC49wgMA+Ex3uMkZHjxu11oqM5R4WbL0i5kzOjx9SoenT0mSHui4Wt/afm9N5gcAuPQIDwDgM65Tpj1u13rBW0vndDo7odeXpvTJ7huVCEXy3mf2Ung5IO75hTHH9Z6W7pLmBgCob4QHAPCZcg+Ky57vk3jHS4ek2PJ73N7ar1vifXnvdy1bChdftpS1c3phYdwxtidGeACARsJuSwDgM+byIa89D0HL/SP/taWpgve7Tpdeo/Lw5tK0FnIZxxjhAQAaC+EBAHzGbFwudavW1V5fLBwe3A3TxcODuWRpYzim3nBL2XMDANQfwgMA+Iyr8pAuredhtWKVh1Ibpp+fd4aH3S1dZc8LAFCfCA8A4DOunocKKg+vFak8lLpsyQwPLFkCgMZDwzQA+Ixrt6UKtmp9MzmtdC6rcCDoeq3Uhun/2LtTN7R06tm5ET23MMZOSwDQgAgPAOAz5vKhqWyyYABYS8bO6VhyRjua2x3ji7mM5nNp5+euUXn4YMdV+mDHVSvvm7PtkucDAKhvLFsCAJ/J13swUcJZD13B5ecjVkA3NHdoOpt03ZOvmtHl4ZC4C0JWQJEywgwAoL5ReQAAn+kIRl1j45kl9UVinp5/5Oq7ta2zRwPRhEJ5tm+V3H0UQVnakOdzAQCXF8IDAPhMOBBUezCqqVUVA68HxUnS3nifEk2JoveMGzs4dYaaFLCs0iYKAGg4LFsCAB8q96A4r0rdphUAcHkgPACAD7m2a61gx6V8zPdbq1kaAHB5IDwAgA+Z26ZWcsp0PlQeAAD50PMAAD5UzYPi8iml8vDo5JtK5nJ6V2uProq2yaI3AgAaFuEBAHzI1fNQ5WVLZiWjWOXhy2ee0z/Nj0iS2oNRPTjwXn20a0dV5wMAqA8sWwIAH3KdMl3COQ8m27Y1m005xsxKRlco/+nSqVxWLyyMr1xPZZMscQKABkblAQB8qNKG6V8vjOsbY6/p+YUxHVkY167mTv30+g8VfL9CgeClxQkl7axj7OZYT0lzAQD4B+EBAHyo0q1aTyRn9GfDz69cH1kYl23bK/0KY0Ylo1DPw1OzZx3X25s2qL1AlQIA4H8sWwIAHzKXEY1nlmTbtufnd7d0O67PZZM6mZqVJGXsnCbN8FCg8mCGh9ta+zzPAQDgP4QHAPAh88t8xs5p2uhbKGZLpFUdRgA5Mj8mSZrI0z9RqPLw9JwzPNwe3+h5DgAA/yE8AIAP5fsyX8rSJcuytLulyzF25Hzj83ie/onOPEuRhpKzGkrNOcZub+33PAcAgP8QHgDAh1qCYTUHnG1r+b70F+MOD8uVBzOEbAhGFQ4EXc/PZFO6q+0KxQNhScvbtF7b3F7SHAAA/kLDNAD4VHeoWafO9ylIpTdNm30Pz88vVx687rR0Q0unHr/2Xylr5/TSwoSGUnMKcEAcADQ0wgMA+FR32AgPHisPg4ODCoVCuv1DH5Cuuzh+KjWrycySK4QUO11akoJWQDfFunVTrLvofQAA/yM8AIBPmTsuea08HDp0SIlEQulcVj9+/e+1s6VTu1u6tDvWrUQwkqfywNarAIBlhAcA8CmzIjCeLu2U6XAgqCeu+x3XuHlatXmaNQDg8kXDNAD4VKUHxRXiqjwQHgAA5xEeAMCnzC/1Xnse1uLqeSjQMA0AuPwQHgDAp7rC5inTVB4AALVFeAAAn3JVHvKcDF2OtSoPT82e0eFzp5TKZavyeQAA/6BhGgB8ytXzUIVlS7Zt52mYdlY4vnTmV/rBuROKB8K6Z8NWfaZ3l+5IbKr4swEA9Y/KAwD4lLkL0nwurcVcpqL3nM6mlLFzjrHVIWU+m9aPp4ckSbO5tL49+aaGUnMVfSYAwD+oPACAT+VrZB5PL2pLNF7yey3mMvrJ9JC+OfG6+3NWhZTD06e0ZF9crhSUpXs3bC358wAA/kR4AACf2hCMKihLWdkrY2OZ8sLD7S//nZ5fGHONtwRCagmGV64PTrzheP2OeL/aQxwiBwCXC5YtAYBPBSxLncYX91IPirvgN9s25x1fXXWYyaT091PHHa9/pHN7WZ8HAPAnwgMA+Fi1Dor77Q3b1nz/gxNvOJYshayAHui4uqzPAwD4E+EBAHysWgfF3R7fqM2RVtf4hZ2WbNvW/xg+4njt3rat6uQAOQC4rBAeAMDHuqpUeQhaAX2sa4drvD0YlSTZkv5k817d1rpx5bVP9+4s67MAAP5FeAAAHzMrD5WcMv3xrutcY6fOb8MasCw90LldT91wv5654QH9Yd9u3dV2RdmfBQDwJ3ZbAgAf6w47G6YrOShuR3O7ukNNjpOqb451u+57d2uf3t3aV/bnAAD8i8oDAPiYeVBcucuWLkgEI47rm1t7K3o/AEBjITwAgI+5dluqoPIgLZ8wvVpvuKWi9wMANBbCAwD4WI9ReRitIDxk7JwmMs5zIggPAIDVCA8A4GN94ZjjeiqbVDKXLXB3cePpxVVnVS8zwwkA4PJGeAAAH+vNc87CaHqhrPcaMZ6zH0NSbgAACXlJREFU5N4KFgBweSM8AICPtYeaFLacP8rNEODViLHkqSvUrJDFrwkAwEX8VgAAHwtYlmtp0XCZ4WE043yOfgcAgInwAAA+Z37JL7/y4HyuhyVLAAAD4QEAfK4v4gwP5VYezGVLVB4AACbCAwD4XK0qD4QHAICJ8AAAPtcXrk7lwdylKd9OTgCAyxvhAQB8rtTKw+DgoPbt26eDBw8azzmXLfWEqDwAAJxC6z0BAEBlzMrDWuHh0KFDSiQSrnH3siUqDwAAJyoPAOBzZuWhnGVLOdvWaIaGaQBAcYQHAPA5s/IwnU1pKZcp6T3OZZPK2DnHGOEBAGAiPACAz+X7kl/qjkv57u9m2RIAwEB4AACf2xCMKmI5f5xXGh7aghE1BWiLAwA4ER4AwOcsy6q474EzHgAAXhAeAKABlLrjkmmU06UBAB4QHgCgAbjPelgscGd+ZtjoCdHvAABwIzwAQANwL1uaL+l5li0BALwgPABAA3AvWyqt8nCW8AAA8IDwAAANoNLKw5mU8/5NkVjFcwIANB7CAwA0gEorD2fSZnhorXhOAIDGQ3gAgAbgqjykvFce0rmsRo1lS/1UHgAAeRAeAKABmJWH2Vxai7mMp2dH0ouyjbH+MOEBAOBGeACABtCX58u+2cdQyOn0nOM6bAXUGWqqyrwAAI2F8AAADSARiqg1EHaMnU7NFbjbyQwZ/eGYLMuq2twAAI2D8AAADWKz0eT8dpnhgWZpAEAhhAcAaBBlhwdjpyWapQEAhRAeAKBBVKvyQLM0AKAQwgMANAjzYLfTXhumjZBB5QEAUAjhAQAaRNWWLVF5AAAUQHgAgAZRvYZpwgMAID/CAwA0CDM8DKcXlLFzRZ9ZzGU0lU06xli2BAAohPAAAA3C3GI1J1vDqYWiz5zN0xfRH2arVgBAfoQHAGgQXaEmRSznj/W1li6dSs06rlsDYcWD4QJ3AwAud4QHAGgQlmWV3PdwMukMD1ujcU6XBgAURHgAgAZSang4kZxxXA9EE1WfEwCgcYTWewIAgOox+x7yhYfBwUGFQiHt379fJ/d2O17bGonXdH4AAH8jPABAAzErD6fT7vBw6NAhJRLLFYa/evU7jteoPAAAimHZEgA0EDM8nDB6GkwnjWVLW6NUHgAAhREeAKCBXGlUDo4tTRe8N2vndMpY1kR4AAAUQ3gAgAZyZbTNcT2aWdRcNpX33rMp9yFyLFsCABRDeACABrKtyf3l/7ixNOmCEynneJMVVE+ouSbzAgA0BsIDADSQ5kBI/eGYY+ytAkuXOOMBAFAqwgMANJirmpxLl44VqDy4m6VZsgQAKI7wAAANxmyaLlR5MHdiGqBZGgCwBsIDADQYd+Uhf3gweyE4IA4AsBbCAwA0GHPHpbcKLFt6Y+mc49oMHQAAmAgPANBgzGVLJ5Izyhpbsi5k0zqVci5b2tHUXvO5AQD8jfAAAA3GrCCk7ZzeNg6DO2pUHSRpe9OGms4LAOB/hAcAaDDdoWa1BsKOMTMsvG5cb4m0KhZ0PgMAgInwAAANxrIsXdvsXIL064UJx7XZ78CSJQCAF4QHAGhAN7V0Oa5/vTDuuH5tccpxvaOZJUsAgLURHgCgAe0ywsMLRngwr69v7qj5nAAA/kd4AIAGZFYeXlmcVDqXlSQt5TJ6dXHS8fqelu5LNjcAgH8RHgCgAe1q6XRcp+yc3jx/0vQrC5PKyl55zZK007gfAIB8CA8A0IDaQ03aEml1jL24OOH47wXbmzaoNRi5ZHMDAPgX4QEAGpTZ9/Di+R2Xnp8fc4zvNu4DAKAQwgMANCizj+GZuWFJ0i9mzzjGb471XrI5AQD8jfAAAD716KOP6u6771ZXV5csy9KRI0ccr78nvtFx/av5UUnSm0nnGQ+/kdhU24kCABoG4QEAfGp+fl633367vvSlL+V9/bb4RgVkrVxnlHPd0xaMaE+MnZYAAN6E1nsCAIDyfOxjH5MknThxIu/r8WBEt7b26am5swXf4454v4IWf0cCAHjDbwwAaGC/03Fl8dfbi78OAMBqhAcAaGAf6diu4KqlS6u1BsL6SOf2SzwjAICfER4AwAcefvhhtba2rvz7xS9+4em5LdG47u+4Ou9rv9u1g/MdAAAloecBAHxg37592rt378r1pk3ed0j60yveox/PDGlCi8sD/+VvFA1HdCy+SfsCfy5J2r9/v/bv31/VOQMAGg/hAQB8IB6PKx6Pl/Xs5mirnr7+fn3mlcM6LOm+B/9E/+uGe3RFtLz3AwBcvggPAOBTk5OTOnXqlM6cWT707fXXX5ck9fX1qa+vz3HvNc3t+vb2e9Um6ZGr71aC4AAAKAM9DwDgU9///ve1Z88e3XfffZKkwcFB7dmzR1//+tfXeWYAgEZl2bZtr/ckAAC1NzMzo7a2Nk1PTyuRSKz3dAAAPkTlAQAAAIAnhAcAAAAAnhAeAAAAAHhCeAAAAADgCeEBAAAAgCeEBwAAAACeEB4AAAAAeEJ4AAAAAOAJ4QEAAACAJ4QHAAAAAJ4QHgAAAAB4QngAAAAA4AnhAQAAAIAnhAcAAAAAnhAeAAAAAHhCeAAAAADgCeEBAAAAgCeEBwAAAACeEB4AAAAAeEJ4AAAAAOAJ4QEAAACAJ4QHAAAAAJ4QHgAAAAB4QngAgMvM4OCg9u3bp4MHD673VAAAPmPZtm2v9yQAALU3MzOjtrY2TU9PK5FIrPd0AAA+ROUBAAAAgCeEBwAAAACeEB4AAAAAeEJ4AAAAAOAJ4QEAAACAJ4QHAAAAAJ4QHgAAAAB4QngAAAAA4AnhAQAAAIAnhAcAAAAAnhAeAAAAAHhCeAAAAADgCeEBAAAAgCeEBwAAAACeEB4AAAAAeEJ4AAAAAOAJ4QEAAACAJ4QHAAAAAJ4QHgAAAAB4QngAAAAA4AnhAQAAAIAnhAcAAAAAnhAeAAAAAHhCeAAAAADgCeEBAAAAgCeEBwAAAACeEB4A4DIzODioffv26eDBg+s9FQCAz1i2bdvrPQkAQO3NzMyora1N09PTSiQS6z0dAIAPUXkAAAAA4AnhAQAAAIAnhAcAAAAAnhAeAAAAAHhCeAAAAADgCeEBAAAAgCeEBwAAAACeEB4AAAAAeEJ4AAAAAOAJJ0wDwGXCtm3Nzs4qHo/Lsqz1ng4AwIcIDwAAAAA8YdkSAAAAAE8IDwAAAAA8ITwAAAAA8ITwAAAAAMATwgMAAAAATwgPAAAAADwhPAAAAADw5P8DtQhB2VZa0j8AAAAASUVORK5CYII=\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 173, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X1_fast = integrate(exp(t)/cosh(t)^20, t)\n", "X2_fast = integrate(-exp(2*t)/cosh(t)^20, t)\n", "car_accel_fast = -1/cosh(t)^20\n", "seat_accel_fast = diff(exp(-t)*X1_fast + exp(-2*t)*X2_fast, t, t)\n", "plot([car_accel_fast, seat_accel_fast, car_accel_fast + seat_accel_fast], (t, -6, 6), ymin = -1.2, ymax = 0.6, thickness = 3, color = [cool_palette[1], cool_palette[0], cool_palette[1]], linestyle = ['solid', 'solid', 'dashed'], axes_labels = seat_labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Investment in a company\n", "\n", "This example is based on the paper \"Adjustment Costs in the Theory of Investment of the Firm,\" by J.P. Gould.\n", "\n", "Let's say you're considering a long-term investment in a manufacturing company, which makes items at a constant cost and sells them at a constant price. Your discount rate at time $t$ is $\\frac{1}{1+t}$, and the depreciation rate is $\\tfrac{1}{10}$. If you use an investment strategy that maximizes the present value of the company's future profits, the company's capital stock $k(t)$ turns out to be described by the equation\n", "\n", "$$k''(t) - \\frac{1}{1+t} k'(t) - \\left(\\frac{1}{1+t} + \\frac{1}{10}\\right)\\frac{1}{10} k(t) = -A.$$\n", "\n", "The constant $A$ depends on the company's costs and revenues, and on the cost of adjusting the size of the company.\n", "\n", "One of the paper's reviewers came up with a clever, economically inspired trick for solving the homogeneous version of the equation. I used it to find the solutions\n", "\n", "\\begin{align*}\n", "\\lambda_1(t) & = \\left[\\tfrac{1}{10}(1+t) - \\tfrac{1}{2}\\right]e^{t/10} \\\\\n", "\\lambda_2(t) & = e^{-t/10}.\n", "\\end{align*}\n", "\n", "Let's take these as given, without worrying about where they came from.\n", "\n", "The Wronskian $W = Wr[\\lambda_1, \\lambda_2]$ has the formula\n", "\n", "$$W(t) = -\\tfrac{1}{50}(1+t).$$\n", "\n", "Now we can use the recipe from the book to find the rescaled unknowns $K_1$ and $K_2$ defined by the equations\n", "\n", "\\begin{align*}\n", "k & = \\lambda_1 K_1 + \\lambda_2 K_2 \\\\\n", "k' & = \\lambda_1' K_1 + \\lambda_2' K_2.\n", "\\end{align*}\n", "\n", "According to the recipe,\n", "\n", "\\begin{align*}\n", "K_1' & = -\\tfrac{A}{200}\\,\\frac{e^{-t/10}}{1+t} \\\\\n", "K_2' & = -\\tfrac{A}{100}\\left[\\tfrac{1}{10}(1+t) - \\tfrac{1}{2}\\right] \\frac{e^{t/10}}{1+t}.\n", "\\end{align*}\n", "\n", "You can write the antiderivatives of these functions in terms of the \"exponential integral\" function $\\operatorname{Ei}(u)$, whose derivative is $\\tfrac{e^{u}}{u}$. Choosing the antiderivatives\n", "\n", "\\begin{align*}\n", "K_1 & = -\\tfrac{A}{200} e^{1/10} \\operatorname{Ei}\\left[-\\tfrac{1}{10}(1+t)\\right] \\\\\n", "K_2 & = -\\tfrac{A}{200} \\left(e^{-1/10} \\tfrac{1}{2} \\operatorname{Ei}\\left[\\tfrac{1}{10}(1+t)\\right] - e^{t/10}\\right),\n", "\\end{align*}\n", "\n", "we get the solution\n", "\n", "$$k = -\\tfrac{A}{200}\\left( \\left[\\tfrac{1+t}{10} - \\tfrac{1}{2}\\right]e^{(1+t)/10} \\operatorname{Ei}\\left[-\\tfrac{1+t}{10}\\right] + e^{-(1+t)/10} \\tfrac{1}{2} \\operatorname{Ei}\\left[\\tfrac{1+t}{10}\\right] - 1 \\right).$$" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 4 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = 1\n", "b = 1/10\n", "L1 = (b*(1+t) - 1/2)*exp(b*t)\n", "L2 = exp(-b*t)\n", "K1 = -A/(2*b^2) * exp(b) * Ei(-b*(1+t))\n", "K2 = -A/(2*b^2) * exp(-b) * ((1/2)*Ei(b*(1+t)) - exp(b*(1+t)))\n", "k = L1*K1 + L2*K2\n", "k_base = k - k.subs(t==0)*L2\n", "L_base = L1 - (b - 1/2)*L2\n", "k_solutions = [plot(k_base + (m/400)*L_base, (t, 0, 80), thickness = 3, color = palette[m]) for m in range(4)]\n", "invest_labels = ['$t$', '$k(t)$']\n", "show(sum(reversed(k_solutions)), axes_labels = invest_labels)" ] } ], "metadata": { "kernelspec": { "display_name": "SageMath 8.1", "language": "", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15rc1" } }, "nbformat": 4, "nbformat_minor": 2 }