{
"cells": [
{
"cell_type": "markdown",
"id": "2e7ab381",
"metadata": {},
"source": [
"# Separation of Variables"
]
},
{
"cell_type": "markdown",
"id": "b2cad84f",
"metadata": {},
"source": [
"In the corresponding lecture on the method of the separation of variables, we considered\n",
"\n",
"$$\n",
" \\frac{\\partial u}{\\partial t} = \\frac{\\partial^2 u}{\\partial x^2}, \\quad x \\in [0,1],\n",
"$$\n",
"\n",
"with initial condition\n",
"\n",
"$$\n",
" u(x, 0) = 1\n",
"$$ \n",
"\n",
"and boundary conditions\n",
"\n",
"$$\n",
" u(0, t) = 0 \\quad \\mbox{and} \\quad u(1, t) = 0.\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "dc3fd282",
"metadata": {},
"source": [
"The method of separation of variables produced the solution\n",
"\n",
"$$\n",
" U(x, t) = \\sum_{k=0}^\\infty \\frac{4}{(2k + 1)\\pi} \\left( e^{-(2k+1)\\pi^2 t} \\sin((2k+1)\\pi x) \\right).\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "ff9918d7",
"metadata": {},
"source": [
"The purpose of this notebook is to explore the convergence of this solution."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "ac6fdfe3",
"metadata": {},
"outputs": [],
"source": [
"using Plots"
]
},
{
"cell_type": "markdown",
"id": "8d1f7725",
"metadata": {},
"source": [
"## 0. A Sine Profile"
]
},
{
"cell_type": "markdown",
"id": "f88c210b",
"metadata": {},
"source": [
"Why are sine functions good in this model?"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "e64d54ac",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f(x) = sin(pi*x)\n",
"plot(0.0:0.01:1.0, f, label=\"sin(pi*x)\")"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "0c9a3145",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"figsineprofile.png\")"
]
},
{
"cell_type": "markdown",
"id": "1efa84b2",
"metadata": {},
"source": [
"## 1. The Fourier series approximation for one."
]
},
{
"cell_type": "markdown",
"id": "299234f2",
"metadata": {},
"source": [
"At $t=0$, we compute the Fourier approximation of one, for $x \\in [0,1]$."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "70629d24",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"U10 (generic function with 1 method)"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"U10(x) = (4/pi)*sum([sin((2*k+1)*pi*x)/(2*k+1) for k=0:10])"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "926d4b57",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(0:0.0001:1, U10, xlabel=\"x\", label=\"10 terms\", ylims=[-0.03,1.3], legend=(0.5,0.5))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "f04334ae",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"fig10terms.png\")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "3780068d",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"U20 (generic function with 1 method)"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"U20(x) = (4/pi)*sum([sin((2*k+1)*pi*x)/(2*k+1) for k=0:20])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "db17f5ea",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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dpFZvUgVOtOg06/WTUm++HD1P7vWTsiCjmhXSZoVe/4W1XarUWRIcPU+esUU9UVTNp0PaFT5tg1r3e7nJQjluofLifrV6k3fIjN78lcUtlCevVyevV+MWym/9yqrX033LJd5hmfLPA+q5Ev7DWd7qB/mdw9U5UZfKaFCSMj+D/V9HaV6i1LeBMGm9+q8DXsdohdE9G9U9ufzoVOP3g6W5idKRqcbUi+zhbV4f6oV9apGNLx9usI/yEohmdREfbC1O26Ao3pyrT4+xuiZyerAYRfp0gDRrHyvTfAsvO8s6RgkdXM2LPa25uC2H5WqL0JsuscGNRdHNI7NpuKBwruXLsbsleR0i/JgREtdm5cqVixcvfuihh/7whz+43GHHjh0xMTHnz5+XZXnChAnPPvusu0MtWLDg3nvv1fh/OefFxcWVN14oZXELZc9/WOc729XyKg6uMB7ucbfLZTxqrk1hVZcz28yi59osiuvflsq83lxbZqmGA3F+qojFzLMVWF38SmW8+wp5yWlVy3E454evsJh5tjPFLv7vQ1uUmVvcFNfpn6pqaWnp7suswXzbgTznQ312TG25RM6zaCwR55yvzWIN5ts2ZN9wqO05rNF8m/a3ZvfNCbXRfNvKc9f/6nwJG5Ikj1snm6v4gNyAcT5rr9J0kbzinKoyzjkvtvHZB9WG822rMzVdNYfCcj5+ndJ9hZycxRTGFcZTLrCeK+QxyfIVV9fUgwN5rOUS+d6NyqF8VlRcnFPG3/xFjZln+/CId2eJcz4nTW0w3/bhEdX+aT9xlT2yVWm6SN592bt3l21mfVbKY5Pl41ev/eHxq2xMstxvpZxT5l2RPk5XGy+44fSeKWa3r5KnpCpWTR/MazJLWcsl8uyDasV3kmvhfVfKT2zXcu9e9+g2ZdRaufzGs2uW+e2r5Bf3Kaqqms1mLcdZm8USFsn5lS63yviINfJrh7RevitW3mC+Lb3Q9ZuYlqq89avWQ92+Sl5+1u3OD25WPtD2oXp4q/K/dE97jk6WK96P7oxcK6/N8nRx/rJLeTfNxXFcRoTfSWsgtJs1a5a7QPjYY489/fTT9tebN2+OiYlxd5AaCYTHClnbH6p4znVaJqcVVHEXpBey1lUdp/OP8t7cqu+m9w+rnuPK0zuVl/drur//sEWZfdDtJ2lDNmu1RLZp+NCqjPddKX9xzPWuJTbeaon88/mqD6Sq6vkCc8Iitzu/sE9JTJJlbbfkvjwWM8+209XzN62ANZxvS/Z4e1T05XE1YZF88qrz/rLKH9ysJCZpjYUK4w9uVgaucvHk2nmZNV5gm3tK6+Mm28w6LZOf3qk4XSBZ5X/ZpbRfKmdp+zLEOV+dyRrMty07c+1AjhvhTDHr8qP81A5F1XYklfFHtyk9Vrj41z+fVxvMt2n5DNhlFLHmi+XXDzn/Z8b5KwfUVkvk8yVa3927aWqrJfLZSl/RylU+LVUZm6zpE845z7fydkvl9w67emLaeK+f5H8d0BpUP0pXu/wol9hc/CrPwpsuklecVbQEwitW3mShvOmi61ORVcpi5tmOuYltTp7bo/xxm9vyHy1kDefbSjV8yI9cYXELPd2hyVms30pNd0vzxfJRj4V/cZ+i5Zy3XyofueLpOC/vV/7t6jHoi0BYY22Ep0+fbt++vf11+/bt8/LyiouL3eWgNputsALufXcqz11G7eLDKbOqERSH8t1WdjtorB1dcobd7XHE4WPtxG9O8iprRc6X8qRM9nRHt4caGiu0rENfaqjT//IEM4r0SDvXhwo30jeDpCd3sCpneedET+wx3NNCGJ/g+lCv9pCCJXpxf9VTB1ws45PXq18NlPq56qDUOVr48Q7Dg1uUw1eqPuHLz7FXDrINY6TWdZ0PZRDp20FSfJgwdYNSZZUdJ3pkm5pt5smjDPUqjWrq10DYMMbwj31snob2mItlPHG1em8r8cN+kvHGU2UQ6b2+0sNtxcFJmqpbV5xjM7cqq0YYpjR3PufNI4St4w1HCrmWxcLsLUyni/nmsYbKfRPGJ4irRxoe3aZqmUTpbAkfukb9exfxha7OFWMC0b+6i091EIeuUS+WVf3uvjzOPj7KNo2VnDpuEJFJpIVDJIMoaOkjXa7S5PXKhAShcg81IoowUtIIw9xTXEuf7d25/LVD6vLhksueB/WDaclQ6fEdLLusyiPRX/eok5sJ7oYONwkT/tlNempn1TfLBTP/5gT7V3fJ3Q7tI4XBjTU17315gs1sIxjcP5+GxQqnS/j5qj6ZZ0u4VeXtPK472L2+cKigyhJRlpnHu+qr7xBuFEr8Nd1ojQ2ov3r1aljYtabP8PBwIiosLKxTp07lPTMyMn7++efU1FT7j6IoLliwYMCAAe6OXFrqotNLbrEYIhhKSjzVajc2GU/m2wZFevrA7blk6BBOJSWeKtr7RYqfn5KeauGpuvpCmXCqyNQr3FJS4nafpgaKCzH9eLJ8TJynD+4bBwwPNiep3FrivuPASx2EadtMU2JtoZLbD8oVm/DyftPKwbZS951iuobRmFjjM9uUj3t7endfnhKzS8V5/cs9vLtPewoDU0w96lpHx7p9d+UqTdpkerglGxKtuDvUbaH0VldxbDLfONzWMNhtyXfliY/vNC4fZGsocHeH+qAb3b/TdF+q8mVf2V2TBhH97YDhRJH402BZtXCXR2oi0U+DhPGbTaxcvjPB7bvLsQhjN5keaKH+qYXbd/dYM2KyYfAqtnqoLT7U7btbmSX+7aBx2SBb+2Cr41AVbwSB6IcBwl3bjPdvkD/pLbsbDa1yenyPMbdcWDzAxq1U4mqapLZBtGygMGWryWaVPXwyL5QJozea/q+tcm+c6u7dPdyUissMw5LYmqG2+kGe3t2/DpnWDi2vy9xeuy960sQtpr9ut83u4vbe5ER/3G2sZxReaGdzd5wQogX9hYlbTE0MttuiPN0sd6WaPughx5DV3aE6hNBjLaWZ2ylpaImHj1NqjrQp27B7lK3E/X33QDx9dTzo+3Szh48TEb24z/iHFjxcdVskInq6lXDP9qAH480m90HOotD8U0FbR3gqEhGNjTXOP64809bTw3D1GWlgjFjq8pP0mzbBwsG8oJIST18ZCm2CQTAJ1hIPRzKqUqFFrHwclxHBg9DQUEly+2XiGq/yRw9Vo6NHj/7www/tr7Ozs4nIXR1CjVSNrjynjl9XRfb9+iF11t4q9hm2uop6as55kY1HfOe28c/u3TT1ka1V1wZ8f1Idneyp/iHXwqPn2i5paGuZvtF1vYHDH7cpz+ysukglNt58sbzGfTNYeiGLmWf75VLVNUK7LrMG822nitweasZm5a4NmtpsXjuk9lghF7uqpOKcH77CGs63rbtQ9ZHKZJ6YJD+2ze0/fXa30nOFXGVbMuc8rYA1XmBblOH6nGeWsjY/yG/8oqk674MjarPFLmp07eadUhvNtx3Kd/5t5RvBLPM71sh3b1DKXf3bcpXftUEZvkYu01DjtT+PNaxQDevkbDFrsVh+31X1Y2Uv7Ve6LnfbZpyUyRrMt/1SVZsF57zAytu7qfN0/KM+KzW9ux/OqM0Wu23CVBgfsUZ+fk/VN4tNUW9fWf6m+6tcWM4TFsmp2VW/u+05LH6h62pYuyNXWIP5tkINn8yRa+VvTni6NN+eUMd6fOzYpVxgfaqqHb1no+L5f3HOGeeR39s8dxo4mM+6/FjF/5p/Sr1vk4uLclNXjXbo0OHAgQP21wcOHGjRokVoaGhNHbyyUo9jJ+yahtP5qr46/FLAu1ZVNVrHSJ2jhe05nr5MLTvLplaqwqrsrhbigXye4b6P5Yfp6l0txEYhVR6J3ugpfpTuthpqTy5flcln96jqexBRuJG+HSQ9ul112WfMrNDdG9T/9BJbRVRdR9G3gfBqD2l8ilrgKpf990GWXsi/HaRpLqcXu4q9Y4Sx65TK3cYOX+Ej16of9JNGuBnJVFGIgX4eYTh2lc/YrJbfWDUgM3psu7o1h6eMNniYvd2hc7SQMtrw3F72VqUhoXvz+ICf1Sfai//ooumGeqaj+M9u4qAkZf2NI2oURi8fUF/azzaMNVT5sSSiUAOtGmGQGQ1fozh9Ei6W8eFrFIXRzyMMWua76lFfSB5l+L/d7N1KnTZ35fLbk9RnO4t/dlX9WNmrPaQx8cLgJBdjVRedZg9vVVaNMHSJrvrdRQfRutHSh+nsw3QXadN/fmVLz/BV2t7dtObiH1qLE1KUUlcVH3/epRLRG72qvlkkgb7qp7x/RN3pZgTtkzvUCQnCsNiq392AhsLQWOHf7ici/tse9YUuUqSGT+asLtLbaZ66SX9yjD3Roep3N6SxcKbYU+0o47Qhm1WeltmJQHRbtPCrx9aN86W8aaVacSfhRnJ5vXxBayDMzMxMTU09d+7cxYsXU1NTMzIyiCg/Pz8xMTE3N5eIHnnkkRUrViQnJ2dkZMyePfuPf/yjD0tNVCJTRNWBUPBc5X3BzA0iaYk6I+LElGy3lRhZZn6qmA/V8OkPlujhNuJHrm5sIiqy0WfH2POuBvpU1ixCeLy9+NfdLg5VrtKj29V3+4hanu9ENLix8FAb4e6Niu3GgzFOM7aovWKEh1prne7vsXbixKbCyLVKxbDKiWYfYgtPs6SRhlDNlfH/6y91jhZuX3XDpMBLzrA71irv9xXvbqH1oxthpORRBqtKfX9WNl3inIgTbbnE+/+s5Fpo4xhDlPvZDp10ihJ2TZB+zmSDk5TVWfyyhQ7m82d2qRNSlI/6a40TdjPbiIuHGh7Zpt6zUU2+wA/k8+9Osh4/KXvz+J6JBpd93F0KlmjpMGl4nNh1ufLKQXXnZb7zMn/loNp1uTI8Tlw6TAqu+gF4Tdd6ws7x0rKzLDFJWZPFL1voQD5/eqd653rlswHSkx28eHev95Se7CD2/Vn59BizD6PMLOWPbFNf2s9Sxxg8DNt1Eh8mbB4rfXKU/Wnn9aE+pTL9cbu6MINtHCvFBGst0svdxa71hNHrbpiQhRM9v1fdfpn/MEzrZJvxYfTNIMNdG1009H6Yzo4W8rd7az3jc/pI8zPY/nwXz6gV51hmKWk854mNhSgTLTvr+qmy8zK/aqPRTap+ewaRJjYVf3S/9tyhAl4/WPA85sGuaz3hlwKPgbCEmnqcVoaIwo1Cqb/GEWqtGl22bNkdFXz55Zec8/z8/BEjRuTm5tr3Wb58ee/evdu1a/ePf/xDlt2mvTVSNfpumvrX3VVUZWSVstgFnrLvpEw2cq2mjlK7L7PO7hP59w6rD2uoF7Wzj7Ko3DuRc/6vA8pD2sYz2JXJvM0PcuXqrL/sUu5c7033c85VxievVyavVxw1wOUqf3CzMnS1bFWuDZ/QfrR/HVDiF8rfnVSzStm2S2x0stz7J1lLfW9lXx5XY+bZxiTLj25Tuvwo3/ajvK/S+A2NFmSonZbJdb+3RX5v67BU/v6kxk6XzhTGvzupDk6SY+bZOi6TZ+1Vcr0ZOlJRiY2/d1gdulrusUKemqqsOu+pRJ5rhE5cZc/sVPqslPuslJ/ZqZxwU+9aJYXxb0+og1bJMfNsnZbJ/9ireDUwpqJfCtj4dUrot7ZG82315tqe26MUua8J9OBqOX9ws9Jwvu3+Tcr9m5QG820ztyjuqs09YJw/v0dpukied0rNKmVbLrHha2SXXYXdcQyf+OCI2mqJfLpCl9evT6hxC110gvVs8Wm17Q/OFaS5Fh63UN52yYtDrc1iHZfJLhsAJqYoH3sc7VBRygXW133t6KsHq37q2n19Qn3AVa2mw5/dDI2oaPdl1vsnF4Wp/eETNaJGAuG/D6pVDkVQGQ/+xlPb3muHVC0NA/ZDxcyznXPTNbzPSjlFQ3uVwx+3Kf+o1HiZU8bruxnw58HeXNZgvu3XCi0uXx1XWy6RXY5B9Myq8Ps2Ke2Xyh+lqx+nq51/lO9cr9iHH3gbCDnnWy+xcevkxgtsPVbI7x9WNXaFd6nExpedUT8/pm65xKoZuyoosKRR/mQAACAASURBVHLtD76bii/ufz+wKPxCaQ1cuNPF7JsT6rcnVG/vEScbL7IxyXLjBbaeK+SP0lWNY37sKo4j/PSoGjPP9sI+Ze4pdUqq0uaH6wMrvfLYNmXcuusjFy0KH5wkv7jPuy+ynPPbV8nfVmq9O5jPYhdoaka1k1XeYL7NXTjvu1JT8yfnfH8eu81jE+CkFOVH94Ma7Y5cYR2W+ikQBuoyTKUyrx9cRYYuChQfLpwv5W0rda+3+7WAT2qmqUJEFGhsgvjzef50R+f9M4r5+RI+xJtVll7qJnZbofyxvdi0Qu/h5/aoM9uIzauqN3fSK0b4uL80Yq3yek+pe31hQQZbepavHy15WNzEnSCJ5idK6y7wH88xxuk/vaSx8dVfAGVgI2Fgo5r5dIUbqfIQgmqrxpmB3yNYIg9rzmnXIkJo4eXd4dKQxsKQxjXwyXy8vTgsVvj6JEvO4omNhbmDJe3V/hX9r790z0b1jjXK7B4S4/TifrVVHUFL676T9/pIk9arE5uKjqp+TvS3PepL3UQtzah2BpGmNhcXnuYvdHU+1TkWOlHEXa7SU1nHKCGjmNsYuevLeraEN4+o4qYON5K3U19VW6BOum1WKFzD1W0eTmdcj2YkIvr1CtfSaG93ZzNhuauxVvNOsXtaOq/U7FmTMOHZztLMrdfXZlpyhu3K5S+7HzDkwdTm4qoRhlWZ/MHNqlWlfRMNbdwEfi1GNhG+uF36auDvioIAetC6rvBmL2nBEOlPHcTqRUEiMoq0dJh0TwvxH/vUF/erD7UR5yZKHoZnuNMrRpjWQnh0+/XBl58eZcU2eszNMGJ3Hmgluhwyu+IcGxMvehikUVGwRM0jPC1XcLaEV/mlP8zgvzbCQA2EpXLVvUaJqEUd4YyboTOlMmWb3SaLlY2IEw9fcZ5DT+X07Un+UBuvT+Nzt4lBEt29UT16lX9xnD2zS112hxRW3XupV4zw03Dp8BTD//pLDTT0/QGAm4co0JMdxF0TDLsmGB5rV40geM1bvaRcC39ws3rsKv8onb16SF00VPJqxV0isi/FU7mT/KLT7B7NPdTIY3+ZPCsZRKqyQywywqqZFdISNlrWEdzNB324kLeP9DTVgpMgiaY2F787dcPRVmWy+HC6TXNa6SAJtPwOQ/NwmrReXX6ObRyjqUM5AIA7QRKtHWWoF0wT16vrLrAt4wytKq2Eo8Xj7cSPj92QFJ4q4ieL+EgNXU8dutZzO4LidDGvvERPZcESKZy8mqC82gI1EJbKPMz9YoQOrepQhpuq0V8KeLf63n1KHm8vfn7shln23/rVxeqDGgVLNKePdHKaIXmUoWMUoiAA/F5hBvpvX+nkNEPSyOo3kTzUVkzNZhVTiI+OspltRKM3j7qu0W4zwgxtgZCIwgx+SgoDNRBqzAhb1xFOuckIDxXwrl4mYV3rCR2j6PPfZvZbdpZZFLqzWaCeQwCAyuoY6f86Sv/Yd+1Bl1nKF2awZzp514PBXjXq8uGbUcxbu5h804Uwg2BW/NFMGKgPcbO2NsKWdYTzpa7nuT6Yz7t7mRES0bt9pdkH1QP5PL2QP71T/WRAdZq1AQBuZs92Fo8U8o/SWYlM929W/3abpGXikYrqB1Mdk3DGVR5ysog0ZqthRjL7ZXKZgA2E2jLCYIkahQiVp3qyMTp2lVejba9DpPDlQGlUsjIoSXmvr9S/IcIgANxqQgyUNFL6+gSLmS/fFi1onO7KSfd6wgFX8+Ycv1rF+hUOYQYq9UvVaKCOI9QYCImoQyQdL+JOK/UcvsJb1hGq1+N5YlNxXILIOXk1ZAIAIIC0iBB+udNQrlJQdUZ1ERH1jBEO5PO7WtywkXE6Vay1u36YARmhR2aZhxo0ncoOUUJ6ofPG/fm8l/f1og6SgCgIALe+akdBIuoVI+zLc84Iz5Xy6CChypmi7cIMVFb1uo01IFAf52UKhWk7lZ2ihCOVxnXuyeV9XC0MCwAANaJXfeFAPndaXvnIFd45SusRwoyC2S9j6gMyENoYcXI7eY+T21z14t2Vy/siEAIA+ExUEMWGOechv17xYuB1KIZPeFCmuYGQiDpECWdLeFmFs5lnpZwyjqF7AAA+NaChsOPGSWoO5nsxgBvjCD3R3kBIRCaROkUJhyokhdtyWP+GgrczDwEAgFcGNRK23hgI9+Xznt4EwjIEQne0NxDa9W0gVFxResNFPjQ2IN84AEAAGRIrbLzI2G9P3/OlXGVVT7ftEIpeox6YFQr1pi/ToEbC5kvXB9WvzfJu0jwAAKiG+DAhJljY/9towi2X+KDGXgSdUINQhpll3PE2IxwaK+64zC0KEdEvBVwg6oQGQgAA35vYVFjx2wJ2ay/wEXFePHtDMXzCgzKFvBoLHxVEvWKEpCxGRN+dYve2QhQEAPCH6S3FBRlcYWRWaN0FNj7Bi6DjtzbCgJxZpkzxorOM3WPtxHfSWO8YYf4p9sudAfmuAQACTudooXVd+vokK7bRsFjRqwVT/dZGGJAhwduMkIimNBO/O8k6LFNe6yk1CUNGCADgJx/2k4atUUSBto3z7sEdiozQA287yxCRKNCqEYY8KzXEAu4AAH7UMUo4dZdRIE1LBlUUahAsqj9W5g3IQGhRvc4IiUgUEAUBAGqBxslFnfgtIwzIzjJm2bteowAAEHBCEAg9sKg8+HfMiQ4AADc/zCzjiUUhb3uNAgBAYEHVqCdm73uNAgBAYAmRBIuKmWXcqMbwCQAACCxoI/TEolII2ggBAG5poQayIBC6Y0FGCABwq5MEMohk9f10owEZCMsUHoLOMgAAt7oQCYHQDVSNAgDogX9WYgrMQIiqUQAAHQjxSzNhQAZC9BoFANCDEMkfHUcDMhBaVMLMMgAAt7xQA1nQRuiSBZ1lAAB0AFWjblkUdJYBALj1hUjICN0oq9YyTAAAEFiCJcGCXqOVKYyIyBh4BQcAAO+gjdA1DCIEANAJ/0w3GoCBUKEQ1IsCAOgAZpZxzaLyYAldRgEAbn3+6TXqRW5VVFS0devWsLCwQYMGGQwu/tBqte7YscNsNnfr1i0+Pr7mCnnjf0HVKACAPvin16jWQHjq1KlBgwb17t378uXLkiRt2LAhODi44g5ZWVm3335727ZtGzVqNHPmzLfffnvmzJk+KDCVoWoUAEAfgg1Cie2m6TX6+uuv33XXXStXrty+fbvNZlu0aJHTDt98802HDh1SUlLmzp37v//97/XXX6/pol6DQYQAADpxc40j/Omnn6ZPn05EBoNh6tSpK1eudNohIiLCw481yKoiIwQA0AX/9BrVFFJKS0uLiooczX7x8fFLly512ufxxx8/dOjQyJEjGzVqdOzYsa+//trD0TIyMj777DP7j5IkTZgwoX79+u72V1VVVa9/JTDLFCzyilvA1xhjTlcB/A+XoNbhRvA/k8AtClU8595eAlEUBaGK/pWaAqEsy0QkSddqJI1Go81mc9rn+PHju3btmjFjRuPGjY8ePbpmzZoePXq4PFpxcXFBQcG+ffscW7p16+Yhg7TZbOXl5Y4fSyyCSZQqbgFfY4yVl5e77CEFfuN0I4D/2W8Ex5MQ/MDABLNNKi+/nhV6eyMEBwfXTCCMjIwMDg7Oz89v1KgREeXm5jZu3Nhpn1dfffXee+/95z//SURDhgxp27btn/70p6ioqMpHi42N7dOnj4eU0YmqqqGhoY4fmYGFmXhoqEnjn8PvxxgTBKHiVQD/c7oRwP8YY6Io4ir4U2QYk+mGB74vbgRNbYSCIAwYMGDDhg32Hzdu3Dhw4ED7a0dqqKqqKF47miRJqqpWGYSrB51lAAB0IlgSrKrPe41qrex6/vnn7777bkmSsrOzt27d+vHHHxNRXl5egwYNTp061apVqz/84Q8zZ84MDw9v2LDhxx9/PGnSpMjISF+UGJ1lAAB04ubqNTpixIiff/45IyNDFMW9e/fa60jDw8Pfeecdez+XO++8Mzk5+cqVK/v373/88cd/+OEHH5UYc40CAOjETTezzMCBAx01onYhISHPPvus48e+ffv27du3xormhkXB8vQAALoQjLlGXSpXeTCWpwcA0AGsUO8aqkYBAHQiSERG6AqqRgEAdCLE4I9eo4EXCK0qAiEAgC6gjdA1DJ8AANAJeyD0dUoYkIEQGSEAgB6IAhlFKvdxUhiIgRAr1AMA6IUfakcDLxBasDAvAIBuBEvICCtB1SgAgH4ES4JF8W0rIQIhAADcvIIlKme+/RcBGQiDEAgBAPQhWPL55DIBGQiREQIA6ESIAZ1lKrGqPAS9RgEA9AG9Rl0oR9UoAIBuIBC6gOETAAD6EeT7ReoDLBAyTgonU4CVGgAAqinEQFZ0lqkIXUYBAHQFVaPOrFiMEABATxAInaGnDACArgQhEDrBjNsAALqCuUadoY0QAEBXUDXqDNPKAADoCoZPOENnGQAAXQny/cK8ATY0HZ1lwD8WLFiwcuXK2i7FDRRFMRgC5oZt2LDhRx99VNulgFtBiIEsCIQVoWoU/CMlJaVhw4aDBg2q7YIEJM759OnTEQihRgT5vrNMgAXCcpUHodco+EWvXr2mTZtW26UISIyx6dOn13Yp4BYRgs4yTpARAgDoisn3bYQBFgjRRggAoCshBvQavREyQgAAXfFDG2GABUKLgkAIAKAjQSKVM9/+iwALhDaGqlEAAB0JMZAFyzBVhKpRAABdwfAJZ+UqDzFg+AToUVlZ2cqVK7dv3242m/v06TNz5sygoCD7r9LS0j777DOLxXL33XePGjXK6Q9LSkqysrI6dOjg9yID1IAgEcMnboSMEHRrx44dX3/9dYcOHYYOHfrVV185BuqdP39+0KBBCQkJiYmJ999//9q1a53+8MCBAxjVB4Er2ICM8EYYPgG6NWzYsOHDh9tf9+7du2PHjqWlpeHh4Z999tnYsWNnzZpFRMXFxe+8887o0aMdf6Wq6ubNm4uKipYuXUpEU6dOFQThwoULq1evNpvNo0aNsmeKWVlZZ8+ebdiw4YoVKxITEznnDRs2TE9PT0tLS0xMHDBgwN69e9evX9+lS5dx48bZj3zw4MENGzbIstyhQ4cJEyaIYoB9q4ZAESQK5QzDJypARgi6VTHS5OTkhIWFhYSEENHu3bsTExPt2wcPHrx79+6Kf8U5v3TpUnl5+ZkzZ86cOUNEu3btuv322y9evKgoypgxY9avX2/fOGPGjMcee0xVVavV+t57702aNGnNmjWMsbFjx7700ktz5swxmUx/+tOfvv/+eyLaunXrpEmTJEmKiIhYvny51Wr112kA3QmSyOrjzjIBlhFiPUKoLUmZfO4pH3firiBIom8HSQZX31TLysqeeeaZl19+WZIkIsrJyalXr579V/Xr1y8rKysqKqpbt659i8FgmD59+u7du//+97/btzz77LNvvfXW3XffTUQdOnT497//bU80i4qKkpKSIiIiiOjjjz/u3bv3p59+SkSXL19OTk7et2+fIAjR0dHLli2bMWPGzp07R4wY8de//tXX5wEgWPL58IkAC4TlKgUFWBILt4hu9cii+q+jVh2j4DIKlpeXT548uVu3bo4gFBwcbLPZHL8VBCE4ONjdYVVVPXjw4Ny5c3/88UciMpvNx44ds/+qY8eO9iho16NHD/uL2NjYbt26CYJARHFxcbm5uUQ0efLkYcOG3XbbbePGjXvggQfat2//u98xgGsmiWRGjJPos/sv0AIhQ9Uo1I64MGFa81rusWyz2aZOnRoZGfnNN984akqbNGmSmZlpf52ZmRkTE+PoTVqZKIoGg+Gvf/1r8+bN7VvsEY6InMKnPd20q7z8U9u2bc+ePbtjx47ly5f37t17z5496JUKPiIQGUWy+fLhH2DpFVafAN1SVfXBBx80GAzz58+vGKWmTJmyePFie1I4b968qVOnOv1h3bp1r169an8tCMIdd9yRkpLS4jfR0dHVKExRUZHRaExMTPzwww+7dOmSnp5e3bcFULVgHy9AEWAZITrLgG6tXLlyyZIl8fHx7dq1s29JSUlp2bLl9OnT582b171793r16l24cGHz5s1Of9i5c+cmTZq0b98+LCxs7969H3300bRp0/r06dOqVaszZ860bt167ty53hbmP//5T3JycpcuXS5evGixWEaMGPH73yCAO0ES2W6SQLhu3bpVq1bVrVv38ccfj4+Pr7yDoigLFizYs2dPeHj4tGnTevXqVXPlvAbDJ0C3Ro4cefr06Ypb7LdhUFBQamrqwYMHLRZLr169KteLGgyGHTt2FBQUFBUViaIYHx+/c+fOU6dOZWdnx8fHt27dmojGjh07cOBAx5/873//s3dJJaInn3xSUa512hs0aNDy5cuJ6M0333z44YezsrKioqK6dOmCsRPgU8GSfQEKX1UHag2ES5cufeqpp1599dVjx4717dv36NGjjm5pdoyxiRMnFhYW3nPPPeXl5QcPHvRFIERGCLoVFhbWokULl78SBMHRt8WdevXqOTqXiqLYtm3btm3bVjx4WFiY48eGDRs6XkdGRjpeh4aGhoaG2l+3bt3aHkQBfM0kks2XHUe1BsI333xzzpw5M2bMIKLDhw/PnTv36aefrrjDggULMjIyjhw5YjQaa76Yv7GpZEIgBADQk2DJt/Nua6rQKCsrO3jw4LBhw+w/Dh06dPv27U77pKSk3HPPPatWrXrttddSUlJquJi/sWL4BACAzvh6KKGmjDAnJ4eI6tevb/+xQYMGly5dctrn7Nmz27ZtGzJkSOfOnZ988sl777139uzZLo+WnZ29bdu2KVOm2H+UJOm5557r2LGju/9usVgcfeQsipHbLGVlWkoNNYYxZrFYHP3s9UBVfTy5oQ6U3XI3KmMMc+jUCoNgKDLLZaGcbowIWgQHB1fZhq0pEJpMJiJyNJjbbLbKI3YNBkPLli2//fZbIrr99tsHDhz40ksv2f/QSWRkZEJCwl133eXY0rRpUw8jn2w2m+O3MmcRIR72BZ9gjDHGdHXe0fvj97v1PjCMMc75rfe+bn4hBsYlk/3EV4wIWmj5Bq8pEDZs2NBgMGRlZdnnj7hw4UJsbKzTPk2aNHFMS9G2bVubzZaXlxcXF1f5aGFhYU2bNrXP8KSFJEmO+G9VWZjJq28DUAMEQah4FfRAV+mvj9x6Hxgd3gg3iWADl7koSQLdGBFqiqavvUajcezYsYsXLyYiq9W6YsWKSZMmEVFZWdnq1atlWSaiKVOm7Nq1y16htHXr1vr16zdu3Lhmy0oYPgEAoD++XoBCa69R+8y8R44cOX36dLNmzexLsWRnZ48bNy4vL69+/foTJkz4+uuve/Xq1bFjx3Xr1n366ac1XrnEOKmcjKiyAt8TRfHtt9+eN29ebRfkOs55oOSpnHPULUMN8vUi9VoDYZcuXU6cOLF9+/aoqKj+/fvbP+VNmzZNS0uLiooiIkmSVq1atWfPnoKCgnfeeafiOKSagnQQ/Gb27NknTpyo7VLcoKyszDGG7+b3n//8p7aLALeOmyUQElFUVNT48eMrbjGZTJ07d3b8KAhC3759a6xolZQzjJ0AP4mPj3c5fVItKikpqbg6BIB++Hqu0UAKLMgIAQB0yNcZYWAFQiw9AQCgO0GibwfUB1YgREYIAKA7yAivw/xqAAA6FCQJ5aoPh08EUmDB8vQAADqEjPA6LD0BAKBD6DV6HapGAQB0yNfrEQZSYLExdJYBANAdZITXYfgEAIAOmSSyIRDaYfgEAIAOYRzhdWgjBADQIQyfuA5thAAAOoThE9dZUTUKAKA/CITX2RAIAQD0B22E12EZJgAAHUJGeB1mlgEA0CEEwuswjhAAQIcws8x1qBoFANAhZITXodcoAIAOYRzhdeg1CgCgQ8gIr8MUawAAOoThE9fZGJkCqbwAAFADTBLJjHxXNxpIgcWqYoV6AADdEYgMAsk+SwoDKRDaGDeJGD4BAKA7Pm0mDKRAiDZCAAB98ulQwkAKhGgjBADQpyBJsCq+aiUMpMBiVSjYUNuFAAAAvzNJyAiJCBkhAIBeBaON0A5thAAA+oQ2wmuQEQIA6FOwRFZkhERkVTkyQgAAHTJJZEMgpGtzjWIcIQCA7ph8OctaIAVCLMMEAKBPQcgI7cqxQj0AgC4FiUI50/04Qk6kcjIGTHkBAKDGYIo1Ins6KBJaCAEAdAjDJ4gwdgIAQMeQERJhND0AgI4hEBIR2VRuwtgJAABdMokIhBg7AQCgY0GYdJtQNQoAoGM3RWcZs9n8+OOPt27desCAAZs2bfKw51NPPTV16tSaKNsNEAgBAHTLJAk21VfjCLWu7/ePf/zj3LlzGzZs2LFjx+TJkzMyMurXr195t7lz527evDkvL69GC0mEXqMAADpmEulq7bYRWq3W77///o033khISJg+fXrv3r3nz59febecnJy33nrr9ddfr+lCEmFaGQAAHQuSanuu0czMTLPZ3LVrV/uPPXr0SE9Pr7zbU0899corr0RFRdVkAX9jQ2cZAAC98ulco5qqRvPz88PDw0XxWiCKjIw8evSo0z5LliwpLy+fNm3ali1bPB/t1KlTy5YtW7NmzbUSGAzz588fMGCAu/3NZrMgCEWlokRSaalVS4GhZjHGrFYr576qoAct7DdCbZdC1+w3AmM+S0zAA1kqLRdLSy3e3gihoaGO4OWOpkAYGRlpNps55/Z/X1xcXK9evYo7FBcX/+1vf1uwYMGZM2cuXbqkquqZM2fi4+ONRmPlo7Vq1WrChAlffPFFxeN7eGOc8/DwcDGIhRp5eHiQlgJDzWKMSZIUFhZW2wXRNfuNUNul0DXGmMFgCA0Nre2C6FFEKOMiDw8P8sWNoCkQxsfHi6KYkZHRunVrIjp+/LijmtSuoKDAZDI99NBDRGS1WouKioYPH56amtq8efPKRxMEwWQyeVuDakMbIQCAXgXV+nqEERERkydPfueddxhjhw8fTklJuf/++4no3Llzf/7zn4moefPmp3+zcOHC6Ojo06dPu4yC1YYB9QAAunVTrFD/7rvvHj16tH79+kOGDHn//fftQS4/P/+HH35w2tNgMERGRtZwMZERAgDoWJAklNf6OMK4uLht27aVlZWFhIQ42vN69ux58eJFpz0HDBhw8uTJmiwjEWFAPQCAjvl0ZhmtgdCuFluJMaAeAEC3sPoEETJCAAAduynmGq11yAgBAHQLGSERkY1xk4jRxAAAeoSMkAi9RgEAdAwZIRGRVaVgBEIAAF0yiYKN+Wr4RMAEQrQRAgDoFjJCIlSNAgDoGNoIiZARAgDoGDJCIowjBADQMaNIKicfNRIGTCBERggAoGcm0VdJYcDElnIV4wgBAPTLKJLsm2bCgAmENobOMgAA+uW7ZsKACYTlGEcIAKBjvhtKGDCBEG2EAAB6howQvUYBAHTN6LOhhAETCGVGxoApLAAA1LBgZITICAEA9Mx3k8sETCBEGyEAgJ6ZkBFiHCEAgJ6ZMI5QxjhCAAAdQ69RsqoUFDCFBQCAGoZxhMgIAQB0zSSRTc8ZocJIEEhCEyEAgF7pvdcouowCAOic3tsIy1UEQgAAXTOJVK7zjBCj6QEA9CxI522EMuNGDCIEANAxvbcRYn41AACd03sgRGcZAACd0/vwCWSEAAA6p/cB9cgIAQB0DsMnkBECAOia3tsIsSovAIDOISNERggAoGtGnS/DhHGEAAA6p/uMkGENJgAAXTPqvI3QpmINJgAAXQvSeSBERggAoHMmSbCpeh5HiIwQAEDfTKLO2wjRaxQAQN9ulnGEhYWFZ8+eZcxtWfLy8rKyslS1hqO2zMmITqMAADp2U/QafeWVV1q2bDlmzJj27dufPn3a6beHDx9u165du3btBg8e3LRp0/Xr19dgKZERAgDonEmq7XGEaWlpH3zwwS+//HLs2LEJEyY899xzTjsEBwd/+eWXBQUFZ86cmTVr1n333cd5jbVqYhwhAIDO1X7V6KJFi8aNG5eQkEBETzzxxKpVq0pKSiru0Lp164EDB9pfjxkzJj8/32w211Qp0VkGAEDnfFc1atC437lz59q2bWt/3bx5cyK6cOFC+/btXe48d+7c22+/PTw83OVvVVW9cuXKgQMHHFs6d+5sMpk8/PdyRvUDo1sPAAD4hO+mWNMaCEtLS0NCQuyvBUEIDg52yggdVq9e/cknn2zbts3doc6fP79nz55HH33UsWXOnDl9+vRxt7/ZbDZbjdzES0t982UAqsIYs1qtNVjXDdVgNpsFAQ0Etcl+I3joLQg+pVgFq2r09kYIDQ0VxSoSKa2BsEGDBlevXrW/ttlsZrO5YcOGlXdLTU2dOXPmqlWrHOljZS1atBg9evSCBQs0/mvOOZOMESFCeDiywtrBGJMkKSwsrLYLomucc3e1LOAfjDGDwRAaGlrbBdEp2Ugyk8PCwmr8RtAaWrp27bpnzx776z179sTExMTFxTnts3379vvuu++HH37wkN5Vj03FwrwAALoWJNV2Z5n777//119//eCDD/bs2fO3v/3t8ccfNxgMRPTEE098+OGHRHT48OFRo0ZNnTo1Nzd36dKlS5cudVd3Wg02huETAAC65ruZZbRWjUZFRaWmpr7xxhtLly6dOHHi888/b9/epk0be2pos9nuu+8+RVFSU1Ptvxo0aFBERESNlNLGkBECAOiaQSQi8sVso1oDIRF169Zt6dKlThv/8pe/2F/06NHj888/r7Fy3QjDJwAAwCSRzQdJYWDkWTbGTRhQDwCgbyaRZF7zsSAwAiGmWAMAAB9NLhMYgdDGyBgYJQUAAF/x0ZKEgRFebMgIAQB0T9dVo+g1CgAAeq8aRSAEANA5ffcaxfAJAADdCxLJhqpRAADQLZNvVmIKjPCCcYQAAGDyzUpMARIIUTUKAKB7JpFsTK9Vo+WMggKjpAAA4CsmCRkhAADoWJAklOtzQL39XUtowskj7wAAEOxJREFUIgQA0Df9DqhHOggAAOSzJQkDIBDKXMDYCQAA0G8bIQYRAgAA6XmKNZvKTWghBADQPf22EaJqFAAASM8zy5SrqBoFAAA9V40yLEYIAABkFAWl5ocRBkYgRNUoAABQkG6XYbIxjCMEAAAdV43KGD4BAAD2jFCfk26jahQAAIjIqOuMEFWjAAC6p982wnIVq/ICAAAZBd0OqEdGCAAA19oIa/6wARAIbVzAqrwAAGAUBZs+1yO0qWQMgGICAIBv6TsjRNUoAIDu6XjSbYwjBAAAoiBdT7qNjBAAQPf0O44QC/MCAADZq0b1ObOMwsmIcYQAALpn0m9nGaxHCAAAep50G6tPAAAAEQVJeq0alTGgHgAA7APqmV4H1CMjBAAA/U66jV6jAABAuh5Qz7EeIQAA6HmKNVSNAgAAkUAkCqTUdCw0aN81MzMzOTm5Tp0648ePDwsLq7xDWVnZzz//XFxcPHLkyKZNm9ZUEW0M6xECAAARkUng5YwMNZrEaT3Y/v37u3TpcujQoblz5/br16+srMxpB4vF0r9//+++++6XX37p1q3b3r17a6qI5Sph0m0AACAio0hybWWEr7322l/+8peXX36ZMTZgwICFCxc+8sgjFXdYvHix0Whcs2aNKIrx8fGvvvrqqlWraqSIaCMEAAA7X8y7rSnCcM6Tk5MnTZpERKIoTpw4cc2aNU77rFmzZuLEiaIoEtGkSZPWrVvHWM1EbbQRAgCAnVEU5JoeSqgpIywoKCgvL4+NjbX/GBsbe/HiRad9Ll68OGrUKMcOsizn5uY2atSo8tEKCwvT09PfeOMNx5bp06c3adLE3X8vV7nIFFnWUlLwCcaYLMsyrkGtwiWodbgRbgZGgZfZFNmkdX+DwSAIVfQy0RQI7bmd41iCIFTO9hhjFXdw/FVliqLYbLbCwkLHFqvV6iF9/GPL8pbhwTWUXkJ1sN/UdkF0DZeg1uFGuBk827a8gSmoZi+CpkBYv359o9F4+fLlevXqEdHly5cd2aFDbGzs5cuX7a9zcnIkSWrYsKHLo8XExHTr1m3OnDkai3h/K1tEeJDGncEX7Dd/UBCuQm2y2Wy4BLWLMcY5x1WoXTNa2yLCavgSaGojFEVxyJAhjnbBNWvWDBs2jIhUVc3KylJVlYiGDRu2du1a+w5r165NTEyUpJpp2du0aZPVaq2RQ0H15Ofn12A3YKieTZs2lZeX13YpdC03N3f//v21XQq927Bhg81mq9ljau01+sILL0ycOLGkpOTMmTPnzp178MEHiSgnJychIeH8+fMJCQn333//e++9d99997Vu3fqDDz5Yvnx5TRXxn//8Z0JCQteuXWvqgOCt7du3f//990OGDKntgujarFmzWrZs2bFjx9ouiH5t2bJl2bJlgwYNqu2C6Npzzz3XoUOHNm3a1OAxtY5LGDx48Pbt200mU58+ffbt21e3bl0iio6Onj9/fv369YmoTp06e/fu7d+/v9Fo3Lp1Kx6atxLOa366d4CAgxvhVuXFzDKdOnXq1KlTxS0hISH33Xef48fo6OinnnqqxooGAADgexipDgAAuib4P9l/++23//vf/2pv6ti9e3enTp3Cw8N9WirwIC8v7+LFi126dKntgujarl27brvtNpfT/IJ/XL58OTc3t3PnzrVdEF3buXNn165dQ0NDNe4/efLkJ5980vM+XlSN1pQZM2bExsa6HGvv0vnz5+Pj4+1z1kCtKC8vLygoqDxmBvzp3LlzCQkJuBFqkcViKSoq0v7sAl84d+5c06ZNqxwj79C8efMq96mFjBAAAODmgW+XAACgawiEAACgawiEAACgawiEAACga7XQa9SJqqqpqak5OTmDBw9u1qyZy33S0tIOHDjQtm3b/v37OzZaLJbk5OSysrIRI0bExMT4qbi3qNzc3PXr14eFhY0aNSo4OLjyDocOHTpy5EhkZOSQIUMcQ1n2799/9epV++vw8PC+ffv6r8S3HEVRUlNTL1++PGTIkISEhMo7bNmyxbEAUKNGjRyzW5SVlSUnJ1ut1hEjRtineYJqy8nJSU1NjYiIGDVqVOXJtdPT0y9duuT40Wg0Dh48mIj27dtXVFRk3xgREdGnTx+/FfjWYzab09LSgoKCunfv7nIHVVU3bNhw6dKlQYMGVewRmp2dvWHDhujo6JEjRxqNRq/+aS33GuWcjx07Njc3t1u3bitWrFi0aNHw4cOd9vn0009nz549adKk9evXT5482b5sRWlpaf/+/Rs0aNC4ceN169Zt3bq1Xbt2tfEObgXp6emJiYmjR4/Ozs6+cuXK9u3bnQarPfLII9u2bevdu/elS5eOHDmyefNm+9keNGhQcXGx/VtIs2bNvvzyy9p5A4GPMTZq1KirV6/edtttK1asWLZsWeVJCqOjozt06BASEkJEQ4YMeeGFF4iouLi4X79+TZo0qV+/fmpq6vbt21u3bl0Lb+CWkJaWNnTo0LFjx2ZmZpaUlGzbts1+th3efvvt9evX219nZGRERESkpaURUb9+/axWq/1bSKtWrT799FP/F/7W8N///vfvf/97eHh49+7dHae6Is75+PHjL1261L179xUrVixcuHDEiBFEtGfPnjFjxkycOPHkyZOCIGzcuNG7WMhr1fr16+Pj481mM+f8iy++6NOnj9MOFoulXr1627dv55xfuHAhJCQkKyuLc/7xxx8PGDBAVVXO+bPPPvvAAw/4vey3junTpz///POcc1VV+/fv//nnnzvtcPr0afsCNJzze++9d+bMmfbXAwcO/Omnn/xZ1FvVmjVrmjVrVlZWxn/7bFfeJyoqKiMjw2njf//738TERPvVeeaZZxyXBqph6tSpL774IudcUZRevXp9/fXXHnbu37//u+++a3/dt2/f1atX+6OIt7qcnJySkpKPPvrojjvucLnDxo0bmzRpUlpayjn/6quvevXqZd8+atSoN954g3Nus9k6deq0ZMkSr/5vLbcRJiUljRkzxj5HwNSpU/fs2ZObm1txh127dplMpgEDBhBRXFxcz5497Ys9JSUlTZkyxT64eOrUqUlJSbVR/FuE/WQSkSiKkydPrnwyW7Ro4Ri+GhsbW3ENlBMnTqxbty4zM9Nvpb0lJSUljRs3zp5/TJ06dceOHRVXrnY4cODAhg0b8vLyKv7hlClT7FcHN8LvwTlfvXq1/UaQJMnljeBw4sSJffv23XvvvY4tx48fT0lJycrK8kdZb10NGzb0PIlYUlLS6NGj7VVWU6ZM2bdvX05Ojs1mS0lJsV87o9E4ceJEb2+EWg6E2dnZcXFx9tdRUVEhISHZ2dnudiCiuLg4+w4Vt8fFxRUWFprNZn+V+pZSUlJSUlLSpEkT+4+OM+zShQsXvvvuu4cfftj+Y2hoaEpKyvvvv9+xY8dZs2b5o7i3qIqf5wYNGphMpspXoV69et99992rr77aokWLb775pvIfxsXF5eXlYc3C6iksLLRYLBpvhK+++mr8+PGOKWbCwsLWrl377rvvdujQ4aWXXvJHcfWq4gc+MjIyLCwsOzs7JyeHMabx2rlUy51lVFWtOGWUwWBQFMVph4pT6RgMBvs6wBX/0L4CsH07eMt+3hwnWZIkp0vgUFhYOGHChCeeeCIxMdG+ZfXq1faTf/LkyR49ekyYMKFibybQzulGEEWx8lU4fvy4/WyvW7du4sSJ48ePj4mJcboROOeMMb8V+1ai/UZQFGX+/Plff/21Y8u6devsl+bYsWM9e/acMGFC7969fV9kPXIZMrRfO3dqOSNs3Lixoy60rKyspKTEaULLijsQUU5OTuPGjZ22X758OTw8vE6dOv4q9S0lMjIyJCTEUdt2+fJll3OKFhcXjx49evDgwbNnz3ZstN/8RNSmTZsePXocOnTIDwW+JVX8PBcVFVmt1spXwXG2R44cGRYWduzYMap0I9irVfxV6ltKvXr1jEZjlTcCESUlJUmSNHLkSMcWx6Vp3759165df/nlF1+XVrcqfuAtFktxcbFj5mot186dWg6EiYmJ69evt3+HTUlJadOmjf0NlJSUlJWVEVHv3r3z8vJOnDhh37h79257OpKYmLhu3Tr7QVJSUhw5ClTD4MGDK59MznlBQYH90pjN5gkTJnTu3Pm9995zeYTS0tITJ0647PQPWvx/e/cWyu4fxwH8oWgO2QjLKYWU2BJJS5ZzbpyVkMONRw7ZnSgKDU1WblwoGm25UJpphdnFJKwh5cKFIYdYCLNdbDb1/C+eWvr379/f76+e2fN+XW3ffdc+39a3977P4Tt6IlAURRCETqdLT0+Pjo4mCMJutzscjr91vrq6slqtCQkJBCbCz/H39xeLxf8+EWgLCwttbW2e8PvKZrOZzWZMhB/3+vpKL/IKCgr0ej39dWxvb6ekpMTHxwcFBeXm5up0Orrz1tbWtyfCH1/e8yNcLpdAIKivr5fL5TExMUtLS3R7RUXFwMAA/bi/vz8jI2NmZkYsFtfV1dGNj4+PfD6/p6dHKpVyudzd3V1mBuATDAYDl8sdHx/v7u6OiYl5fn6mKIr+2WU2mymKamtrCwkJ6ejoIEmSJEmZTEZR1M3NTUlJycjIyPj4uFAozM/Pd7vdDI/k13I6nWlpaQ0NDdPT03w+f3l5mW4vLy8fHh6mKGpzc7O+vn5iYmJoaCg+Pp4kSbrDw8NDVFRUX1/f2NgYl8s9ODhgbAy/n16v5/F4ExMTnZ2dcXFxLy8vFEU9PDwQBHF9fU33sVgsAQEB9LygXVxclJaWjo6OSqXS9PT0wsLCz89PZgbw+x0dHZEkmZeXFxcXR5Lk/Pw83e7n57e3t0dRlNvtFgqFdXV1crk8NjZWoVDQHdbX1yMiImQyWXt7e1JSkt1u/9bnMv/vE+/v74uLi09PTyUlJZ57p3Q6XXh4eE5ODkEQFEWtrq4eHR2lpqa2tLR47g65v79XKpUOh6OmpiYzM5OxAfiEk5MTtVodEhLS0tJCL8qdTqdSqWxoaAgLC9vY2Ph6ORyfz6+qqnK5XGq1+uzsjCCIjIyM2traf/yNDP+R1WpVKBQvLy9lZWVisZhu3NzcjIqKys7Ofnt7W1tbu7y85HA4ubm5X2+3vbu7U6lUHx8ftbW1QqGQofJ9xPHxsUajCQ0NbW1tpQ+4ORwOlUrV2NhIX814cXFxeHjY2NjoecvHx4daraaPVAuFwurqakyEP3Z1daXX6z1PU1JSioqKCIKYn5+vrKykD5PYbDaFQvH09FRcXEy/SjMajVqtlsfjtbe3f3dnCeaDEAAAgEHYaxQAAFgNQQgAAKyGIAQAAFZDEAIAAKshCAEAgNUQhAAAwGoIQgAAYDUEIQAAsBqCEAAAWA1BCAAArIYgBPBeFoslOTm5ubnZ02I0GiMjI2UyGYNVAfgY7DUK4NW0Wm1lZeXs7GxXV5fVas3KyoqOjt7d3fXsPg8A/xOCEMDbSSSSubm5/f19qVRqMBhOTk4SExOZLgrAdyAIAbydy+XKy8s7Pz+32+0ajaaiooLpigB8Cs4RAni7wMBAkiRtNltOTg5SEODHIQgBvN3t7e3AwIBAIDCZTAsLC0yXA+BrEIQAXu3z87OpqSk0NNRgMJAk2dvbe3p6ynRRAD4F5wgBvNrg4KBcLt/Z2RGJRE6nUyQSud1uk8kUHBzMdGkAPgIrQgDvtbW1NTU1NTk5KRKJCILgcDgrKyu3t7cSiYTp0gB8B1aEAADAalgRAgAAqyEIAQCA1RCEAADAaghCAABgNQQhAACwGoIQAABYDUEIAACs9hcqRiAXuwVI8QAAAABJRU5ErkJggg==",
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\")
"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(0:0.0001:1, U20, xlabel=\"x\", label=\"20 terms\", ylims=[-0.03,1.3], legend=(0.5,0.5))"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "2339ba65",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"fig20terms.png\")"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "eed903fd",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"U40 (generic function with 1 method)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"U40(x) = (4/pi)*sum([sin((2*k+1)*pi*x)/(2*k+1) for k=0:40])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "52523384",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(0:0.0001:1, U40, xlabel=\"x\", label=\"40 terms\", ylims=[-0.03,1.3], legend=(0.5,0.5))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "128da9f6",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"fig40terms.png\")"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "906475e9",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"U80 (generic function with 1 method)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"U80(x) = (4/pi)*sum([sin((2*k+1)*pi*x)/(2*k+1) for k=0:80])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "84f9e8bd",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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zadQVCCtvvcy1UbQ/EVFcgKfr9byVWgRTpIVEwXUxdayEdwwXiKhLhCsQasdtlwihd4ywq3J/b87hDzQS2oUJBsHVXHCkiAcYqUO4MKaZsLwylsxNZxPbGH7XzjD7nOtjLLvIukUK/9fFIAi0/TInIonRF8fU//QW/9JBdLce/PuY+kgzw5KB4tSjqnZkZpbzb06yI4+aJEbu+z1e2ctebG94rbP4p12qu2ILMvjWh4yv7nXFKoXR2M3qxDaGC1b+aeX2vzzBNufwfrGGR5NVLcjl2Wn4BqVPjPDiTtU9dOgvu9X9BXxnLnt5j2v7+wv46E2KxOi+Nap2ZlEYjdkm7i/gv92uLq680pxzjj27TV14nj22SdVOBoUOSlihrLzIe61Q3M/GenO/+tfd6rPb1I8rK3a0mHdfpkxNZf1XK9oHVxg9mqy+ulftsUzZUnkhsuQ8u2eFMnaz+mLl9UShg3qtUJ5PUbsuU9wn0PcPs36rlW7LFPfZIa2Yt1+sPLxeHbFB0QKAzGj8FnXQWrXtImV/ged4br1Q7rFM+cdB1wcvdFDiKqXXSqXXCsUdJ/55lLVZJLeYLy+t3OOpxbztIqXTEuXprap2rpQYPbNV7bBEbrNIcR/2yy+yZvPllgvlaamuFfPtlLhK6bBY6b9acc+a8eER1mKBHD9PTqo8rRwu4m0WKa0Xyr9PUbXI6lTpqa1ql9XmuxZ7RngtPs/i58lN58lfHHdt/7KN7l2ptFskP5CkuAPY2wfVlgvkpvNl90XMvgLeaoHSfrH84k7XZZNdodHJaqclSofFivt6cfY51ny+3HKh7G4Ryarg3ZYpdy9XBiYpWgrCiV7dq3ZYLLdcKLs7Gnbk8tYL5d4rledTXD+McpkGr1WGrVc7LFHOVm7/65Os2zKlxzLlP5X1P1fGOy5Rxm9R+69WtADPOP1mu/rEZrXzEk/912bxHsuUZ7apE7a5tn9Fot4rlXcPq12Werb/3mH29Fb1ic2eH15qMb9nhTL9DOu7WrFW/vBGbFB+PM0eWq+sqfz+Z51jv9muLshgT2xy/fBy7dR3lXqpgj+wjp0pE7RiL+xUk7PZrHPM/fvZepn/PkWJ8qNBa1Wt/g6VHt6gtg2lz4+z+ZX504dH2LES3ilcGLfZtf0zpfwvu9VPE8S3D6qHKy/Nn9uu/qmDoWcDYfI+1/ZnnGWlEu0baXxtr6r9fkqc9O4hdcfDxubBwreVQXTKYfZyJ/G7vuLbh1xBemM2VxktGChql5tEpHL67hR7q5vhpY4G94qzzrIJbYTRzQ2nrrguUFKLOefUPUoY1UxYmekqtiGbPxgnDIwzbL/MtA+wK48nxghElFCZ/+XYOOcUFyh0ihCOVV49nCnlrUMEImoRLGhX55cqeFygQEQx/pRrc+3KYBOJAgWbqFwmbU33YBnv9REa62pDV65cCQwM1F4HBQURUUlJSUhIyNUlz507t3LlyuTkZO1Pg8EwZ86cxMTE6225vLyciGTV4rA5rCI3C5aiMkeMwK/YTUaFWa1qkGC8XEZWq5J5RYwwGqxWexgJWeVmq9WqMMqx+YXxcquVWgSZj+ZWJESxo/mmXlHMalXbBoh78wzWpvKuAkP7EKOjwtrGQidKLPlXyv1FvjXH8vsWktXK+zUwrcmQ4lqrK9KN98eQ1Wq/P8rw0kHTG21tuXbhZIm5Z7DdZCB/g2XLhYqekWzGKdPYZsxqtY9vavz+hNI9SF6eZWgdbGwslo9rLHRPMr99l91f5N+dtKy7X4o18D4NzN+k2f/QWvnosPGp5hSoOCbfJb55yDisgfN4qbAr1/JVd4fRQF+kWdZnVNzbgL262/x2R6WdH/tdS+Nru9Qf75W/PytGmcVnmtj7hgv3J5tHxjoNgvDuQfO6+6U2IXzLJdPUQ/Kf2yp/3G0a25T/rpkjSjT8ZivfPti5q1Bcc9G4d6jEOCWsMz8Q7UyIYk9uNk/rJo9qwhTJOHGrOrO39EGaKHL6oaeUdsXw6HZTaz/JqdJfd5tXD5BaB/PhW83/2Cu90l55fLtpeBx/t7MyM0N8ZD1PfkBKyjHMTzduHSQ5VH5/sl9jk717BBuxyfJRV/nRePbH/aaxyeqM3tIbh002ibYMlHcXGsZu4sv7S1ck4YXdpmX9pJbB9NAW0+u7pL+2Ux/dZhoQzd7trPzntHHwGrZqgLTwojgzXdw5WCqV6aEtFiY5OoaxR7ZZPugijWzMfr/P/Oh69Zte8iuHTOUyPzxU3pxneHi9aX4fOdtGrxwyLe8vNw7gI7aayx3Scy3V8TvNg2LV9QOUfx0zDljNZidK8y+Iq7PFfUOkPDuN3m4usCrNA/mE3aZ/dpUfimO/2W0etV75Vzd58mGTQHR6uLQm2zA4yTS9t3y+XHg31bisnxztx0ZutVy2qk80VZ/dZR7ZRE3qr7yTarxvFfsxQZqZIW7PF/cPlbIqhLHb+JQuSqw//W6P8ePu8uBG/OmdxtEblHc6y68dMgabhNRBJeuLQwauMf18r3SiVJh2wrTyPme4mUZuNeeUqcPj1Gd3m8c2Vdfdp7x5xDhgtfpDgvz9OeO+QuHQMPmcVXhyC/+oqxxmEf6w1/jfnnK/aD5+p2lssvL3jvJfDpgaWPjZEfK8C+L9a0yzE6WDRcJnp0zr73cGGOnhLeaCcnVIQ/XJnebnWqmT2iivHzYNWqP+dK/8+Sljaolw9CH5xBVh/Bb+1T2KxcCf22P6MUG+J4o/tt307Gb57c7KxN2m5kF88TB5Zob4QJJxRX9pW77hkxPGrQ9IBoGGbDYrkjKoIRu+xfxSe+XZlurLB00j1qlzEuX30oznSoVdg6SjVwxPbuHz+8iM04SdpgV95A6hbNR2819SpL93Uh/fYUqIZB91U6ani8PWGdffL23MNfx8yrh5kCQzPjDZL1a0JzTgI5LN/+wij2nK/nrANC5ZnZ0o/e2IUVWEpf3kQ8WGsdv4hvulCoVe3m1Oul9qGcSHbTFP2Sf9uZ0yfrv5yWbszY5KpyDDU9vFzYOsa3MM23JMKQ9KNoUS11v6hDs6hvFnt5q/7Kk8EKvmlZv+vEP5T0/53VRj6yDDq22k+6MMY1NM94ZJxU76/Jg5ZbCzoT8NzDJ/lyaNb6b+KcX0UjveN8zxZgfxzztZ0gApKduQbzP9Jt5ulYXuSebft7DHB/B3Dlp+TJCbGtnDcaaPDip/76RMO2Yc2lCINThebWd4MsX0VGNnvoOSMi0fdZGCjdwimJeflR6IVf+Tav5tS7Xcan+2ufj1MTEhRErOFRv6iU1Ee3gD4a+7zZlF9jAzX5hhWdhXclTwIQ1N808rz7dWlpw1PtiQrFZ7/0jDSwdMf2tnK3AImeXmtn52UaaG/pZdWRVdw9mOHPOoxorVyjqFGHflCI/Gynsuix3DRKvVGm8STpaYy6xWgehsqV8jY4XVyhv7m08WONv5sfMlxiiRrFYlmAzZVtFqtV0qF0KNZqvVSkRmgyX/SnmAyG2SRXU6rFZOzFxW7ig3lV8vWFxTQECAKIq/UIjfjMmTJz/77LPX/NfQoUO/+OIL7XV2djYRVVRUXLPknDlzxo8fX/s3LSsr45y3mC+fK2Wc8x7L5P0FjHPef7W8JYdxzqceVV/do3DOp6WqL+9ROOdlEg+aLnHOL1hZk7mytp2ntyg/nVY5571WyDtzGed8Xz7rulTmnH+apv5xp6IVS1ghb81h2RUsapbEtAqfUx/ZoHDO+66S12YxzrnCeMxsKaOMfXlcfXqLa8V3D6l/2qVctvHwmVK5zDnneTYePlMqcfKBa+S551R3Nf55RP32pDpsnati+/JZ/Dz59BUWOVPKrmDuanx3Un0gSf7imGvFOefUbkvlj46qvVbIWqFymTedJ089qkbPltKKXSu+fVC5b7U8YLX81gFXxdLLWPRsaeI2pf0i2eZ6Tz52szJwjRw7W9qU7VpxSw6LmS3ds1z+7XbXig6F37tCTlghN5svpxe69ub3p9SGc6TY2ZL7E+VU8JYL5FYL5BEbFMW1Mf7aXiV2ttRojnyssmL7C1jsbCl8pvRxqmtFp8pHbVRCZ0j9VsmlkmvFRRlq+Ewpera0Oce1Yp6N91oh+/0kvbTbvXn+4RE14Gep61L5otW17GgRa71QDp0hzT7r2r6k8ue2K6YfpfGbFfcHX3WRxc6W2i6UDxS4Vsy38yFr5bAZ0j+PqJWb55+mqTGzpQfXyrk215K0YtZjmdxivrzyoqf+k3Yq0bOlSTsVZ+WqqzNZ64VyrxWeD55v5yM2KI3nyv897tn+Z2lq47ny6GSlyOFaklrEeq2Q2y+SN1xi7u9/0k4lbq786h5FVl0HwsqLapuFcr9V8ukrrmK5Nj58vRI/T/7upGf7U4+qcXPlJzYpJU7XkoMFrMcy+a5FsvuLtSv8ue1KzGzp9b2eHbcwQ202X05cKZ8tdS3KKmf3r5Hj5srfn3Jtn3H+jwNKg1nS6GTlSuX2d+ay1gvl5vM927dKfEyy4v+z9Nfdnu3/cEoNmS51XSqfqaz/2VLWeYkc+LP0ZeX3ozD+4k7F/KM0KEl2b39tFouaJTWYJa2v/H6KHLz3Stn/Z2niNs/23z+shs2Qms6TT5S4Fh0qZA3nSBEzpX8d8ey4oevkuLly16VyceX3/9NpNWa2FD1bWnLeVSyznMXPkzssloetk7Xtq6o6bqOj61I5erZ0sPL3szaLxc6WeiyT/7zLdeCUSbzNQvmxZKXxXM/v5/W9St9VcqclsvtjHixgMbOlv+5WOi+RJdX1wXssk986oDSbL2+s/Jgfp6oD18iT9ykjN7i2f8HKomZJOy6zBrMk924alCR/fUJ9caeinQw55zPOqPevkc+WsgazXGekUolHzJRyKvijG5VvKn8tYzcrXx5Xd1xmHRa7DpJVF1m/VTLnvOdyOTnbdcbTzk7zzqnuajyfonyWpnLOY2dL2mG4/TLrtULmnP/ziOquRuO58gUrK5d5wM+Syjjn/NU9ykdHVc75xG2K9qPak8fuWS5zzvflsx7LXNWImS1p316L+XJ6GeOc371M3l/AtAOhbtVZIHzllVcmTJigvV65cmWLFi2ut5FfFwibzpMvWBnnPHGlvOOyKyJq57IfTqkTtymc89f2Ku7feugMqcTJt+SwvqtcX+v7h9XJ+xTGech0STs72BUe8LNkV/jYzcqMM64VX9+rvHtInXVWHZ3s2pEFdh42Q7pgZWEzJLtrGX9xp/LuIbXncjkp0/VDvGhlUbOk57YrL6RUFuL8ue1K/9Vyi/muHzrn/PQV1mCWVPVA0or5/SRNPeo5kaUWsZjZ0kPrZNmzjL+0W7lnuecMwjk/VMgeXi8vyvAUUhh/75D67iHVEzQ4P1jA/n5AuVTuWeRU+TcnVe2brLq1hRnVVrTJfPkFNa9CLS8vdy9MK2YnS6qtaJX4njymVlvGT19h7vDmLpZz1dXRpXJWfT1eLnOHUrOYVaq5xH5VmTubN47/29nV+9epcqdabQnj3B3J3PLtNYuVy9x9ieleMa2Y1Sh2tpSdL6tWrNjBt+Yw9zGoqqq1vCIpk6VXL7Yvny3OqPbzv2zjn6apGVWKKYx/cUz9+XS1t1yTyX63Q3FfzHHOz5exURuVr054iskqf3ab0m+VXPXY+eak6v+zpMUhTVoxi5olNZ8vuy+tJJV3WiLHz5OnpXqKvbJH6bdKbjRHLq+8NNySw9oslB9eL7u35lR5g1mSdsno/uxPblG+OqGO36x8WxlBF6SrD6+XT11hTee5tlUu88CfJafKxyQrcyovlB9cK6/JZIcKWeclrmL/Pa5qJ8nBSfK6LKZ9am0j67LY4CRXsZYLXFdjjebI2rmr1wp5T55PA+HFixc3btw4duzYwYMHb9y48ezZs5zzgoKC/v375+Xlcc5PnjwZEhKydu3as2fP3n333R999NH1NvXrAmHjuXJWOeOcP5DkulZqs1A+dYVxzpddcF2kTNiquH9nHRfLR4vYz6fVZ9JJDQUAACAASURBVLa6jqel59URG5SMMk+OyDm/e5mcksuazPVc/yZns57L5THJyo9VfrIPrZO7LpW1cKs5fYWFTJe6L5Or/vw/TlUTVniuATnnV5z8jX1KalG1wya1iB0qrHlYVo1StxtVrRYIwSf0FghvQ6qqXq+h63ZQ7ODlcrUlBXaelFntQrNC5n/br+zNr3a2+eNOZeg6ueqVxz+PqKYfpaoRdP0l1nahHDFTKrB73i50hvT2QeX3Ozxrdl8m78xljee6GvA456/sUf51RJ19Vh272VVsTSYbslbmnLdfJB8vYVqt/H+WOOdzz3mKdVkiHy5knPOImVKhg3POe6+Ud+Z6JRDWto9w//7933zzjfb6o48+euKJJ1q1aiUIgsViEQSBiNq1azd9+vS33367rKxs1KhRL7/88k014/4ilXNREKjK7RPllYNlIixCsZMRUZ6dR/u7hv80DaKL5TzdylsEuzq3O0UIR4vY4SLeNVJwb3ZAI+GTNCYaqFWIa+F9DYUSJ12wsh/6mtzFPk0Q/3mUTbnbM7aoTaiQNtoYZhEMno3RK50Mr3SqNv4o1Ez/6lmzebpThFBjiUCkdRoDAPw64ZaaS6L8aGiTaieWACO9f3fNM9J/etdc8kYXw/B44a5wz7qD44THWghtQg1Rfp63G9bE8MERlvKwJ4480Ej4OI2JArWsPKN2ixRWZvIiJ3Wq3FqLYEq3Eie6WM7jAwWtVqJAZTIVOiiy8lMEm113UDhU8vfyqNHaBsLRo0ePHj26xsLIyMj169e7/xw1atSoUaPqrGrVVRk1KthVTiSUyzzIJBBRlJ9rrHm+g2L8XeWbBwsZZXS2lEY0dS1pGSKUy3xhBk+I9uzdZ1obui9T3unu+R2IAm15SLQrFGr2vHubUOHnfjV/K/FBCF0AcAcSiDqE1zy/TelR8xz4XR/x5U6Gu6M8JZ9tY+i6VHmrm6dkQrTwxn6WY6O3u7mShObBQlY5v1TBg0wUVJluxPoL+XZe5OTuQBtkdN2W4/RMseat+wjrbNSot6mMRAMRkb9IDpU4UYVCQUYioiiL65GEuTaKrQyErUOF06X81BX+emfXty8QDW1imHOO/a2r51N3DBcujTM18K/2Xo2RnAEA/JIgE1WNgkTUPkzIqn5GbRkihJroWLHrFgsisojUJEhIyuJtQj3rxgZQro0KHNQ+TKjcuFCucKcqaJNrkpYR3ua3T3ibJyM0kkMhm0J+ouvbifSjUokkRoUOHu3v+hI7RwizzrJzZbxqdv/RPYbh8UKNlsno6lEQAAB+tavPqHMGiCUS+VeJNp0jhJlnWecqp+JYfyHXzvPt1D/WtSTIROUy2SvbRale3FDvbe5A6C+STaFy2ZNTiwJFWuh4CY+wkKnyA90dJaSV8C6Rgl+VbL5RgPB4i3rzkQEA7gBdI4UBDaulH31jBPdt+JpGAZRdQfl2HlOZzGizrNkVcp/DRQMxvTeNVgbCACPZVbJWdhBqGgYI+wp41fEmQSb6srfYNhSNnAAAt5cJbQy5dj66mSct0SaIzrFRowDXEm1yGYfK/Y2u07jvB8v4nCcjNAp2hVtlIdgzqJMaBwopubxp9dErz7VF8gcAcNsJM9M/qw+njw+ivQWUbfPkM0EmoUziNkWo0jRaT55H6D1XN41WDYQtQmhjNmt1jQndAADgdtcqREjJZaEmCqjMzrRRozbFswR9hJ5RowFGsqlkrdJHSEQdwoQ8O3W+6v48AAC4/bUPE4qd1LHKOTzETNZbFQjrR9Mo4yQIpH1DgUayKZ6HEWoeihcSooUHG9ebuA4AAG4BRprYxtA31nNWDzZRWY1AaND37RPudlEiCjBShUxlEoVUyQgbBQi7R9SPzwIAAFf7pk+1XsNgk2CVmU3hgSavD5apHylU1UAYaBIqFF4mU4j5husAAEC9FWKiMokqFArAfYQaxsk9pWeQkSoUsso8xIQeQQCAO1OImcrkmreM6zoQVs0ItekGSiVkhAAAd6xQM5VKvFzx3CCAQOgJhFoP6hWJwhAIAQDuUKFmoVSqNneKQfDWzDL1IxBWbRoNNglWiV9xIhACANyxAo2kMCp0eMZFIiP0ZIShZiqVqUTi4Rb0EQIA3LHCLXTeyt1PxEMgrHb7BON0qcLz/EYAALjzRFiEc2UUVnmqR9MoNwie/C/CQhesvIE/MkIAgDtWtD9dsPJIC+4jJKLqGSERxfgLgkAN/K6/AgAA1HOx/oLKPQ84NGCKNUOVQNg4kK5IgoiEEADgztU0iASixoGejFDXzyOskRH2iTGEm73zfQAAwO2hT6ywKUcIxKTbGvejJzRvdKkfLboAAPCrDY83DI/3nO11P1imvlQUAAC8A4NlCD2CAAB6JgjE9PyE+hpNowAAoDeiIOi6aVTl9aSiAADgHbrvI+TICAEAdA19hOgjBADQNb0Hwho31AMAgN7ovWkUGSEAgM4hI0RGCACga8gIkRECAOia7jPC+lJRAADwDr1nhGgaBQDQOb1nhGgaBQDQOWSEyAgBAHQNgRCBEABA19A0ykUBkRAAQL+QERLiIACAnuk9I2QYLAMAoG8GIua1LdcDGDUKAKBzaBrFYBkAAF3zXiA01r5oaWnp9u3bAwMD+/XrZzReY0WHw7Fz586Kiopu3bo1adKk7iqJQAgAoHfe6yOsbSA8e/Zsv3797rnnnry8PFEUN23a5OfnV7VAVlZWnz592rZtGxsbO3HixKlTp06cOLGuaommUQAAnfN90+gHH3zw+OOPr1ixIiUlRZKkefPm1Sjw008/3XXXXRs2bJg5c+Z///vfDz74oA5ryYkQBwEA9EwUBJV7JRLWNhAuX7583LhxRGQ0GseMGbNixYoaBYKDg2/w5/8IGSEAgM4JAnknDtauabS8vLy0tNTd7dekSZNFixbVKPP8888fPnz4wQcfjI2NPXny5I8//niDrZ07d+6bb77R/hRFccSIEVFRUdcrr6qqrDKBSFXV2tQW6hxjTFVVfP++hV3gczgQfIyRyvnN7gKDwSD80n3otQqEsiwTkSiK2p8mk0mSpBplTp06tXv37gkTJjRs2PDEiRNJSUk9evS45tbKysqKior279/vXtKtW7cbZJCSJEmyQkxwOvH78w3GmNPpvOYIKbhlJElyOp2+roWuaQeC+0wItxhTDbIi3OyB4OfnVzeBMCwszM/Pr7CwMDY2lojy8/MbNmxYo8yUKVPGjx//97//nYgGDBjQtm3bP/7xj+Hh4VdvrVGjRr169bpByliDqqpGk9ls4gEBllquAnWLMSYIQkBAgK8romuqqmIX+BZjzGAwYC/4ir+FC6Lq7+9f57ugVn2EgiAkJiZu2rRJ+3Pz5s19+/bVXrtTQ1VVDQbX1kRRVFX1F4Nw7aGPEABA53x/H+Hrr7/+xBNPiKKYnZ29ffv2L7/8kogKCgqio6PPnj3bqlWrZ599duLEiUFBQTExMV9++eUjjzwSFhZWV7XkmGsUAEDffD/X6ODBg1euXHnu3DmDwbBv3z6tjTQoKOjjjz/Wxrk8+uij69atKy4uPnDgwPPPP79w4cI6rCUyQgAAnfN9RkhEffv2dbeIavz9/V955RX3nwkJCQkJCXVWtSowswwAgM75/oZ632L1paIAAOAdeg+EaBoFANA53/cR+haaRgEAdE7vGSFGjQIA6JzeM0I0jQIA6JxA5J04WE8CIZpGAQB0Tu9Noxg1CgCgc7oPhJyjjxAAQM/0Hgg5JwMiIQCAjhmImNe2XA+gaRQAQOd0P2qUkVg/agoAAF6h96ZRZIQAADqn+0CI2ycAAPQNgRCBEABA1/QeCDGzDACAzul+1CgyQgAAfTMIAuNeSQkRCAEAoB7Qe9MoRo0CAOic7gMhMkIAAH1DIEQgBADQNQyWQSAEANA1ZIQIhAAAuqb7QFhfKgoAAN7hvUBo9MpW6xoyQrjF5syZs2LFCl/XohpFUYzG+nHAElFYWNhXX31VjyoMtz/v9RHWj58pAiHcYhs2bIiJienXr5+vK1JfPfvss9OmTQsNDfV1ReDOgYwQgRButZ49ez722GO+rkV99bvf/c7XVYA7DfoI60lFAQDAO3QfCDkJyAgBAHRM74GQo2kUAEDftCDgjVBYPwIhmkYBAEA0kOqFkaP1I75gsAwAAAi6zggRCAEAdM9L3YS4fQKg3iguLv76669PnToVExPz3HPPtW/fXlt++vTpL7/8srS09JFHHhk1alSNtWw2W3p6eqdOnW55fQHqmJcCYX3JCLkBw0ZB9wYNGpSamjpu3LiQkJCEhITMzEwiKigoSExMDAsLe/DBBydNmjRv3rwaa505c+bhhx/2RX0B6piBiHshFtSTjLC+RGwArykoKDh06NDatWujo6OHDRu2ZMmSnTt3xsfH//TTT7169XrvvfeISFXVadOmjRs3ruqKmzdvttlsixYtIqIRI0ZYLJa8vLyVK1eWlpYOGjSoS5cuRJSXl5eWltayZcvFixfffffdwcHBQUFBmZmZ+/fvT0hIGDhw4NGjR9esWdO2bdvRo0drmz1+/Pi6descDkebNm1GjhxpNptv+VcCuqPzjBBNo6B3ERERrVu33rhxIxGdOXMmJyenR48eRLRnz57+/ftrZfr373/kyBGHw1F1xezsbEVRMjIyMjIyGGOpqakJCQkZGRmCIIwePXrJkiVEdPTo0WefffaZZ55xOp1Op/Pbb78dM2bM/PnzBUF4/PHH33rrrX/84x9ms/nNN9/8/PPPiejw4cODBw9mjIWGhq5bt66kpORWfx2gS+gj9HUlQN9WZ/KZZ7005e81WET6uZ9orHKlKoriwoULBw8ePGnSJJvN9s0337Rp04aIcnNzIyMjtTJRUVGc89zc3GbNmrlXfPrppxcvXvzGG29of06ePPmNN954/vnniSghIeEPf/iDluQVFxcfPny4QYMGRLRkyZK2bdv+9NNPRGSz2RYsWHDq1ClRFJs3b/7ZZ5/95S9/2bdv37333vvaa6/dki8DwAWB0NeVAH3rFkl29db9CkNMgrF6e01paemIESPee++9cePGpaWljRkzpm3btomJif7+/pIkaWWcTicRBQQE3GDLBw4ckGV58+bNRCRJ0pkzZxhjRNSyZUstCmq0dJOI4uLiunTpIoqi9rqgoICIhg0bNnXq1Pbt2w8fPnz8+PFdu3atu48OcF1eegAFAiFArcQFCo819+WvcNeuXZxzLZPr06fPkCFDli1blpiYGBcXp42aIaLMzEw/P7+oqKgbbMdsNr/44ota1yARffrpp4IgEJGfn1/VYlrk07ifpiQIAueciJo0aXLmzJk9e/YsXbq0X79+Gzdu7NWrV519VIDrEATi+u0jrC8VBfAaLRvLzs4mIlVV09LS4uLiiEjr57PZbEQ0a9asUaNGGQzVDpfQ0NCysjJVVbU/Bw0atG7duubNm7do0aJFixaRkZHCzQ/DKy0tFUUxMTHxk08+6devX2pqah18QoBfgqZRX1cCwKc6d+78+9//vkePHr179z558mR4eLj2qKPhw4dPnz69W7dujRs3PnPmzKZNm2qs2KxZs169erVv3z4kJCQ5OXnq1KmPP/549+7d77rrrszMzIiIiF/xCOKvv/561qxZ3bt3Lyoqunjx4siRI+vmQwLckJeaRl0NHbWxfv36VatWhYaGPv/8802aNLm6gKIoc+bM2bt3b1BQ0GOPPdazZ89rbmfu3Llr1qyZM2dOLd/XarUO3er/0T1iYgyCoW8wxux2e2BgoK8rcutMmDBh4MCBzzzzjK8rUlNWVlZ6enp0dHT79u2rZnJHjx4tLS3t2bOnv7//NVcsKSkpKSlp2rSpKIqc8/T09MzMzEaNGrVr146I7HZ7cXGxlmISUUFBgclkCgsLI6KysjKHwxEdHU1ETqczPz9fO/zPnz9/4cKF4ODgbt26VW1H1YSFhV28ePEOezAvY8zhcNy4Cxa8Km6usuUBe5vo4LrdbG0zwkWLFk2aNGnKlCknT55MSEg4ceJEjZ84Y2zkyJElJSVjx451Op2HDh26XiD8FZARAmiaNGlyzctQd5/f9YSHh4eHh2uvBUFo1apVq1at3P/19/d3R0EiqjpqJiQkJCQkRHttsVjc7968efPmzZv/qg8B8Cv5uGn0X//617Rp0yZMmEBEaWlpM2fO/NOf/lS1wJw5c86dO3fs2DGTyVTntUQfIQAAGATiVPdZUa3ii81mO3To0MCBA7U/77///pSUlBplNmzYMHbs2FWrVr3//vsbNmyo21oiIwQAAF9mhLm5uUTkHpMdHR19+fLlGmXOnz+/Y8eOAQMGdOrU6cUXXxw/frw259PVsrOzd+zY4Z6oSRTF1157rUOHDtd7d7vdrqgWySnbbN55ODH8Eq2P8FeMLay/3GMs4Vez2+3eaB/yIa2P0Ne10DdusjscNttNNBH6+fnVGEd9tVoFQm0WQUVRtD8lSapxyxERGY3Gli1b/vzzz0TUp0+fvn37vvXWW9ecfjAsLCw+Pv7xxx93L2natKnFYrneu0uSRIJgMZuvXwS8izHGGLvBPrrz/OKRA7/IbDbfYb8Zxhjn/A77UPWLaOCi0XRTu6A2V/C1CoQxMTFGozErK0t77MulS5caNWpUo0zjxo2Dg10jedq2bStJUkFBQdXud7fAwMCmTZs+8cQTtXlrIhJFkZNgFA2iqKOM5LYiCIIoilePDLyD6Sr99ZI77zejwwPhdmMQFMFQ97ugVpe9JpPpoYcemj9/PhE5HI5ly5Y98sgjRGSz2dasWSPLMhGNHj169+7dWoPS9u3bo6KiGjZsWFe1RB8hAAD4eIq1d999d9CgQceOHUtPT2/WrJn2eLPs7OyHH364oKAgKipqxIgRP/74Y8+ePTt06LB+/fqvv/66DhuXEAjhFjMYDFOnTp01a5avK+LBOa9HeWpFRQWal6HO+fj2iS5dupw+fTolJSU8PLx3797aT7xp06apqanazUmiKK5atWrv3r1FRUUff/xxTExMHdYSgRBusffee+/06dO+rkU1NputHt3K/e6777r7SgDqiu+nWAsPDx8+fHjVJWazuVOnTu4/BUFISEios6pVgfsI4Ra73n3rPmS1WhFaQOd0/WBezqn+tAkBAIBXeKmPsH4EQmSEAACg64wQfYQAACD4cIo1n0MgBAAAA5E3JhhDIAQAgPpB102jnLyQDAMAQL0iCqTqNhAiIwQAAEGgWj9L/iYgEAIAQP2g66ZRxrkBNxICAOib3u8jRBgEANA5XTeNcjSNAgDonr4zQgRCAADd03UfIW6fAAAAg55nllE54en0AAA6J2BmGQAA0DM0jQIAgK7pOhAiIwQAAARCX1cCAAB8SiCBe6GXEIEQAADqB11nhOgjBAAAXQdC3D4BAAC6DoRoGgUAAP1OsYZ2UQAAID1Puo10EAAASM9No5wTnkUIAAAGIu6FeFAPAiGrF7UEAAAv029GiKZRAAAgPQdCNI0CAADpOhAKQj2oJQAAeJl+H8OEplEAACA9Z4QIhAAAQHoOhLihHgAACE2jAACgc/rNCBEIAQCAEAgBAEDn9DuzDPoIAQCAMOk2AADonJ6bRrkBU8sAAOgenkcIAAC6pt+mUU4CmkYBAEC/GSH6CAEAgHzeR1hRUfH888+3bt06MTFxy5YtNyg5adKkMWPG1EXdXNA0CgAA5LWmUWMty/3f//3fhQsXNm3atHPnzlGjRp07dy4qKurqYjNnzty6dWtBQUEdVhGBEAAAyLdNow6HY8aMGR9++GF8fPy4cePuueee2bNnX10sNzf3o48++uCDD+q2iiojsR604AIAgHf5smk0MzOzoqKia9eu2p89evQ4fvz41cUmTZr0zjvvhIeH12UFiVi96MkEAAAv82XTaGFhYVBQkMHgikdhYWEnTpyoUWbBggVOp/Oxxx7btm3bjbd29uzZxYsXJyUluWpgNM6ePTsxMfF65W02O+fm8vLy2lQVvIEx5nA4uDd+gFBrFRUVAm6o9SntQGDMG41zUCuKJKqKXF6u1n6VgIAAd/C6nloFwrCwsIqKCs65dhyWlZVFRkZWLVBWVvbqq6/OmTMnIyPj8uXLqqpmZGQ0adLEZDJdvbVWrVqNGDHiu+++q7r9GxzhFn8yGgxBQUG1qSp4A2NMFMXAwEBfV0TXOOc4CnyLMWY0GgMCAnxdEf2yWFRJoKAg/7rdbK0CYZMmTQwGw7lz51q3bk1Ep06dcjeTaoqKisxm829+8xsicjgcpaWlgwYNSk5Obt68+dVbEwTBbDbXvgUVt08AAAARGQTBZzfUBwcHjxo16uOPP2aMpaWlbdiw4amnniKiCxcu/PWvfyWi5s2bp1eaO3duREREenr6NaPgr4BACAAA5PMH837yyScnTpyIiooaMGDAZ599pgW5wsLChQsX1ihpNBrDwsLqsIoIhAAAQF4bNVrb+wjj4uJ27Nhhs9n8/f3d/Xl33313Tk5OjZKJiYlnzpypwyriPkIAACCfB0KNT3qJMdcoAACQz5tGfQhNowAAQD6fa9SH0DQKAACk50CIjBAAAEjPj2FCRggAAKTnB/MiIwQAANJzRohACAAApOc+QjSNAgAAaYHQCwGhHgRCZIQAAEBeS4oQCAEAoH5A0ygAAOiangMhplgDAABMsQYAAPqm54wQTaMAAKDjQIiMEAAASM9No8gIAQCAiAwCqV6YWqYeBELGuUFAKAQA0DsvhYJ6EQjRNAoAADqeaxRNowAAQBgsAwAAOieQV5pH60Eg5Nxb7cIAAFCP6DgjrBe1BAAAL8ODeQEAQNd0PFgGTaMAAKDnplEuCPWglgAA4GVoGgUAAF3Tb9MoAiEAABCRQRCYF1LCehAIcUM9AAAQmkYBAEDn0DQKAAC6pt+MEE2jAABAur59AvcRAgAAkYGI63OuUZWTiEAIAKB7aBoFAABd02/TKAbLAAAA6XnUKAnoIgQAAB03jSIjBAAA0nNGiEAIAACk5z5CDJYBAADSc9Mo7iMEAAAiEgVS9RkIWb2oJQAAeJlA5IU4eJMhpqSk5Pz584xdt7eyoKAgKytLVdX/uWIe6CMEAAC6HZpG33nnnZYtWw4bNqx9+/bp6ek1/puWltauXbt27dr179+/adOmGzdurKsqIhACAAD5fNRoamrq559/fuTIkZMnT44YMeK1116rUcDPz+/7778vKirKyMiYPHnyk08+yesocGOwDAAAEJFBIO6FgFDbQDhv3ryHH344Pj6eiF544YVVq1ZZrdaqBVq3bt23b1/t9bBhwwoLCysqKuqkisgIAQCAvNY0aqxluQsXLrRt21Z73bx5cyK6dOlS+/btr1l45syZffr0CQoKuuZ/VVUtLi4+ePCge0mnTp3MZvP13hqjRgEAgLzWNFrbQFheXu7v76+9FgTBz8+vRkbotmbNmq+++mrHjh3X29TFixf37t37u9/9zr1k2rRpvXr1ul55p8xETuXldTkAB24KY8zhcNRVWzf8OhUVFZht0Le0A+EGowXB2+x2QVXF8vLy2q8SEBBgMPxC22dtA2F0dPSVK1e015IkVVRUxMTEXF0sOTl54sSJq1atcqePV2vRosXQoUPnzJlTy7c2Gu1mizkoSKxleahzjDFRFAMDA31dEV3jnF+vlQVuDcaY0WgMCAjwdUX0K0jhJMh1fiDUto+wa9eue/fu1V7v3bu3QYMGcXFxNcqkpKQ8+eSTCxcuvEF692sIJGC4DACA7vn4PsKnnnrq6NGjn3/++d69e1999dXnn3/eaDQS0QsvvPDFF18QUVpa2pAhQ8aMGZOfn79o0aJFixZdr+30ZmGwDAAAkNfmGq1t02h4eHhycvKHH364aNGikSNHvv7669ryNm3aaKmhJElPPvmkoijJycnav/r16xccHPy/VxGBEAAAyOeDZYioW7duixYtqrHwpZde0l706NHj22+/rbN6VYH7CAEAgG6HmWV8BRkhAAAQHsMEAAA6d1tMuu0TyAgBAIB0nRFiZhkAANB1RlgvagkAAF4mCsR8OOm2D6FpFAAASM+jRjFYBgAAiEgggXuhcbQeBEJkhAAAQLoeLEMCAiEAAOh3sAyaRgEAgPScEaJpFAAASM+DZRAIAQCAvDbpdj0IhGgaBQAAQtMoAADoHJpGAQBA19A0CgAAuoamUQAA0DWByBsPYagHgRBPnwAAANJ1RlgvagkAAF6m30CIjBAAAEjXU6wJQj2oJQAAeJl+M0IMlgEAANJzIETTKAAAaLzROloPAiEGywAAgMYbk8vUgxCDjBAAADTeaB2tB4EQfYQAAKDRadMoplgDAAANMkIAANA1gXQaCLmAnBAAAIi88SCmehAIOSEjBAAAIjSNAgCAzmGwDAAA6BoyQgAA0DXdZoQCAiEAAJBuM0I0jQIAgEanGSGaRgEAQKPTjBCBEAAANHqddBtNowAAQEREokCqDgMhMkIAANAIJPC67iVEIAQAgHoDTaMAAKBrBiJW19s01r5oZmbmunXrQkJChg8fHhgYeHUBm822cuXKsrKyBx98sGnTpnVVRWSEAABQifssIzxw4ECXLl0OHz48c+bMe++912az1Shgt9t79+49ffr0I0eOdOvWbd++fXVVRWSEAACg8cbtE7XNCN9///2XXnrpH//4B2MsMTFx7ty5v/3tb6sWmD9/vslkSkpKMhgMTZo0mTJlyqpVq+qkisgIAQBA47Mb6jnn69ate+SRR4jIYDCMHDkyKSmpRpmkpKSRI0caDAYieuSRR9avX89Y3TTkIiMEAACNzzLCoqIip9PZqFEj7c9GjRrl5OTUKJOTkzNkyBB3AVmW8/PzY2Njr95aSUnJ8ePHP/zwQ/eScePGNW7c+HrvzjgxVZHl2tQUvIIxJsuyjH3gU9gFPocD4bbAuazcREQwGo2C8AvJVK0CoZbbubcl74Lt4gAADlRJREFUCMLV2R5jrGoB91pXUxRFkqSSkhL3EofDcYP08YWWjmaBfnWUXsKvwSr5uiK6hl3gczgQbgcvt3XGWix1uxNqFQijoqJMJlNeXl5kZCQR5eXlubNDt0aNGuXl5Wmvc3NzRVGMiYm55tYaNGjQrVu3adOm1bKKT7WSgoMstSwM3qAd/BYL9oIvSZKEXeBbjDHOOfaCb01oLQUH1vEuqFUfocFgGDBggLtfMCkpaeDAgUSkqmpWVpaqqkQ0cODAtWvXagXWrl173333iaJYJ1XcsmWLw+Gok03Br1NYWFiHw4Dh19myZYvT6fR1LXQtPz//wIEDvq6F3m3atEmSpLrdZm1Hjb755psjR460Wq0ZGRkXLlx45plniCg3Nzc+Pv7ixYvx8fFPPfXUp59++uSTT7Zu3frzzz9funRpXVXx73//e3x8fNeuXetqg3CzUlJSZsyYMWDAAF9XRNcmT57csmXLDh06+Loi+rVt27bFixf369fP1xXRtddee+2uu+5q06ZNHW6ztvcR9u/fPyUlxWw29+rVa//+/aGhoUQUERExe/bsqKgoIgoJCdm3b1/v3r1NJtP27dtx0ryT1P39qwD1EA6EO9VNzCzTsWPHjh07Vl3i7+//5JNPuv+MiIiYNGlSnVUNAADA++rBXKMAAADeI9z6ZH/q1Kn//ve/a9/VsWfPno4dOwYFBXm1VnADBQUFOTk5Xbp08XVFdG337t2dO3e+5jS/cGvk5eXl5+d36tTJ1xXRtV27dnXt2jUgIKCW5UeNGvXiiy/euMxNNI3WlQkTJjRq1Oia99pf08WLF5s0aaLNWQM+4XQ6i4qKrr5nBm6lCxcuxMfH40DwIbvdXlpaWvtzF3jDhQsXmjZt+ov3yLs1b978F8v4ICMEAAC4feDqEgAAdA2BEAAAdA2BEAAAdA2BEAAAdM0Ho0ZrUFU1OTk5Nze3f//+zZo1u2aZ1NTUgwcPtm3btnfv3u6Fdrt93bp1Nptt8ODBDRo0uEXVvUPl5+dv3LgxMDBwyJAhfn5+Vxc4fPjwsWPHwsLCBgwY4L6V5cCBA1euXNFeBwUFJSQk3Loa33EURUlOTs7LyxswYEB8fPzVBbZt2+Z+AFBsbKx7dgubzbZu3TqHwzF48GBtmif41XJzc5OTk4ODg4cMGXL15NrHjx+/fPmy+0+TydS/f38i2r9/f2lpqbYwODi4V69et6zCd56KiorU1FSLxdK9e/drFlBVddOmTZcvX+7Xr1/VEaHZ2dmbNm2KiIh48MEHTSbTTb2pj0eNcs4feuih/Pz8bt26LVu2bN68eYMGDapR5uuvv37vvfceeeSRjRs3jho1SntsRXl5ee/evaOjoxs2bLh+/frt27e3a9fOF5/gTnD8+PH77rtv6NCh2dnZxcXFKSkpNW5W++1vf7tjx4577rnn8uXLx44d27p1q/Zt9+vXr6ysTLsKadas2ffff++bD1D/McaGDBly5cqVzp07L1u2bPHixVdPUhgREXHXXXf5+/sT0YABA958800iKisru/feexs3bhwVFZWcnJySktK6dWsffIA7Qmpq6v333//QQw9lZmZardYdO3Zo37bb1KlTN27cqL0+d+5ccHBwamoqEd17770Oh0O7CmnVqtXXX3996yt/Z/j3v//9xhtvBAUFde/e3f1VV8U5Hz58+OXLl7t3775s2bK5c+cOHjyYiPbu3Tts2LCRI0eeOXNGEITNmzffXCzkPrVx48YmTZpUVFRwzr/77rtevXrVKGC32yMjI1NSUjjnly5d8vf3z8rK4px/+eWXiYmJqqpyzl955ZWnn376ltf9zjFu3LjXX3+dc66qau/evb/99tsaBdLT07UH0HDOx48fP3HiRO113759ly9ffiureqdKSkpq1qyZzWbjlb/tq8uEh4efO3euxsJ///vf9913n7Z3/vznP7t3DfwKY8aM+dvf/sY5VxSlZ8+eP/744w0K9+7d+5NPPtFeJyQkrFmz5lZU8U6Xm5trtVr/85//PPDAA9cssHnz5saNG5eXl3POf/jhh549e2rLhwwZ8uGHH3LOJUnq2LHjggULbup9fdxHuHr16mHDhmlzBIwZM2bv3r35+flVC+zevdtsNicmJhJRXFzc3XffrT3safXq1aNHj9ZuLh4zZszq1at9Uf07hPZlEpHBYBg1atTVX2aLFi3ct682atSo6jNQTp8+vX79+szMzFtW2zvS6tWrH374YS3/GDNmzM6dO6s+udrt4MGDmzZtKigoqLri6NGjtb2DA+F/wTlfs2aNdiCIonjNA8Ht9OnT+/fvHz9+vHvJqVOnNmzYkJWVdSvqeueKiYm58SRiq1evHjp0qNZkNXr06P379+fm5kqStGHDBm3fmUymkSNH3uyB4ONAmJ2dHRcXp70ODw/39/fPzs6+XgEiiouL0wpUXR4XF1dSUlJRUXGran1HsVqtVqu1cePG2p/ub/iaLl26NH369Oeee077MyAgYMOGDZ999lmHDh0mT558K6p7h6r6e46OjjabzVfvhcjIyOnTp0+ZMqVFixY//fTT1SvGxcUVFBTgmYW/TklJid1ur+WB8MMPPwwfPtw9xUxgYODatWs/+eSTu+6666233roV1dWrqj/4sLCwwMDA7Ozs3Nxcxlgt9901+XiwjKqqVaeMMhqNiqLUKFB1Kh2j0ag9B7jqitoTgLXlcLO07839JYuiWGMXuJWUlIwYMeKFF1647777tCVr1qzRvvwzZ8706NFjxIgRVUczQe3VOBAMBsPVe+HUqVPat71+/fqRI0cOHz68QYMGNQ4Ezjlj7JZV+05S+wNBUZTZs/+/vfsLaaqN4wD+VBjahlt/dCyNoGQguiGZypDmKsu6cJUKYmF604lS8i4MCkqmsWjRTReBY4WjiyCWMcgdd7GQapix6CIxTcpIm7Ka55Sbm3DeiwcOUva+1mudtfP9XOnjcf7Onj18z/Ps7NHlcDjEFq/XS7tmeHh4586dFoultLT095csR0tGxvL77kcknhFqtVpxLXRubo7n+W82tFx8ACHk48ePWq32m/ZQKKRUKjMzM/9U1SlFrVZnZGSIq22hUGjJPUU5jjt48GBFRUVHR4fYSAc/IUSn0xUXFweDwT9QcEpa/HqenZ2NxWLf94L4bFdVVSkUiuHhYfLdQKDLKn+q6pSycePGtLS0/xwIhBCPx7NmzZqqqiqxReya/Pz8oqKiFy9e/O5qZWvxCz4ajXIcJ+5cvZy++xGJg9BsNvf399NrWJZldTodPQGe5+fm5gghpaWlMzMzIyMjtDEQCNDpiNls9nq99EFYlhXnKPALKioqvn8yBUEIh8O0a75+/WqxWPR6/bVr15Z8hC9fvoyMjCx50z8sBx0IgiAQQliWLSgoyM7OJoTwPB+NRr85eHx8PBKJbNmyhWAgrJzVq1ebTKZ/HwiUw+FoamoSw28xjuNGR0cxEFbcp0+f6CTPbDb7fD7aHf39/Xl5ebm5uRkZGWVlZSzL0oO9Xu9PD4Rfvr1nRcTjcb1eX1dXZ7fbtVrt7du3aXt1dXV7ezv9+uzZs4WFhdevXzeZTLW1tbQxFAppNJqWlhar1apSqQYGBqQ5gZTg9/tVKlVnZ+fp06e1Wu3MzIwgCPSya3R0VBCEpqYmhUJx4sQJhmEYhrHZbIIgvHv3rrKy8uLFi52dnQaDYdeuXYlEQuIz+WvFYrH8/Pz6+vqrV69qNJo7d+7Q9gMHDly4cEEQhL6+vrq6uq6urvPnz+fm5jIMQw+YnJzMyso6c+ZMR0eHSqV6+vSpZOfw9/P5fGq1uqur6+TJkzk5OeFwWBCEyclJQsjbt2/pMVNTU2lpaXRcUGNjY/v27bt06ZLVai0oKNi9e/fCwoI0J/D3GxoaYhimvLw8JyeHYZju7m7avmrVqsePHwuCkEgkDAZDbW2t3W7fvHmz0+mkBzx48GDDhg02m625uXnbtm08z//U35X+v0/Mzs7eunVrenq6srJS/OwUy7Lr168vKSkhhAiCcO/evaGhIZ1O19jYKH465MOHDz09PdFo9MiRI0VFRZKdQEoIBoNut1uhUDQ2NtJJeSwW6+npqa+vz8zMfPjw4eLb4TQazaFDh+LxuNvtfvXqFSGksLCwpqZmyWtkWKZIJOJ0OsPh8P79+00mE23s6+vLysoqLi7+/Pnz/fv337x5k56eXlZWtvjjtu/fv3e5XPPz8zU1NQaDQaLyU8Tz5897e3uVSuXx48fpgls0GnW5XA0NDfRuxrGxsWfPnjU0NIi/Mj8/73a76Uq1wWA4fPgwBsIvGx8f9/l84rd5eXl79uwhhHR3d1ssFrpMwnGc0+mcnp7eu3cv/SkVCAQ8Ho9arW5ubv7ZnSWkD0IAAAAJYa9RAACQNQQhAADIGoIQAABkDUEIAACyhiAEAABZQxACAICsIQgBAEDWEIQAACBrCEIAAJA1BCEAAMgaghAgeU1NTW3fvv3YsWNiSyAQ2LRpk81mk7AqgBSDvUYBkprH47FYLDdu3Dh16lQkEtmxY0d2dvbAwIC4+zwA/E8IQoBk19bWdvPmzSdPnlitVr/fHwwGt27dKnVRAKkDQQiQ7OLxeHl5+evXr3me7+3tra6ulroigJSC9wgBkt3atWsZhuE4rqSkBCkIsOIQhADJbmJior29Xa/XDw4OOhwOqcsBSDUIQoCktrCwcPToUaVS6ff7GYZpbW19+fKl1EUBpBS8RwiQ1M6dO2e32x89emQ0GmOxmNFoTCQSg4OD69atk7o0gBSBGSFA8vJ6vVeuXLl8+bLRaCSEpKen3717d2Jioq2tTerSAFIHZoQAACBrmBECAICsIQgBAEDWEIQAACBrCEIAAJA1BCEAAMgaghAAAGQNQQgAALL2Dxe9j3qwnSmfAAAAAElFTkSuQmCC",
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\")
"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(0:0.0001:1, U80, xlabel=\"x\", label=\"80 terms\", ylims=[-0.03,1.3], legend=(0.5,0.5))"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "5e21d062",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"fig80terms.png\")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "f4d71e42",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"U160 (generic function with 1 method)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"U160(x) = (4/pi)*sum([sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "f6e43cea",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(0:0.0001:1, U160, xlabel=\"x\", label=\"160 terms\", ylims=[-0.03,1.3], legend=(0.5,0.5))"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "7b1fd822",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"fig160terms.png\")"
]
},
{
"cell_type": "markdown",
"id": "7ce1d01f",
"metadata": {},
"source": [
"## 2. plotting for t"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "43be25b2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"U160t9 (generic function with 1 method)"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"U160t1(x) = (4/pi)*sum([exp(-(2*k+1)^2*pi^2*(0.0001))*sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])\n",
"U160t2(x) = (4/pi)*sum([exp(-(2*k+1)^2*pi^2*(0.001))*sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])\n",
"U160t3(x) = (4/pi)*sum([exp(-(2*k+1)^2*pi^2*(0.01))*sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])\n",
"U160t4(x) = (4/pi)*sum([exp(-(2*k+1)^2*pi^2*(0.05))*sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])\n",
"U160t5(x) = (4/pi)*sum([exp(-(2*k+1)^2*pi^2*(0.1))*sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])\n",
"U160t6(x) = (4/pi)*sum([exp(-(2*k+1)^2*pi^2*(0.2))*sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])\n",
"U160t7(x) = (4/pi)*sum([exp(-(2*k+1)^2*pi^2*(0.3))*sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])\n",
"U160t8(x) = (4/pi)*sum([exp(-(2*k+1)^2*pi^2*(0.4))*sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])\n",
"U160t9(x) = (4/pi)*sum([exp(-(2*k+1)^2*pi^2*(0.5))*sin((2*k+1)*pi*x)/(2*k+1) for k=0:160])"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "ca66f3fc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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\")
"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(0:0.0001:1, U160t1, xlabel=\"x\", label=\"t = 0.0001\", ylims=[-0.03,1.1], legend=:outertopright)\n",
"plot!(0:0.0001:1, U160t2, xlabel=\"x\", label=\"t = 0.001\")\n",
"plot!(0:0.0001:1, U160t3, xlabel=\"x\", label=\"t = 0.01\")\n",
"plot!(0:0.0001:1, U160t4, xlabel=\"x\", label=\"t = 0.05\")\n",
"plot!(0:0.0001:1, U160t5, xlabel=\"x\", label=\"t = 0.1\")\n",
"plot!(0:0.0001:1, U160t6, xlabel=\"x\", label=\"t = 0.2\")\n",
"plot!(0:0.0001:1, U160t7, xlabel=\"x\", label=\"t = 0.3\")\n",
"plot!(0:0.0001:1, U160t8, xlabel=\"x\", label=\"t = 0.4\")\n",
"plot!(0:0.0001:1, U160t9, xlabel=\"x\", label=\"t = 0.5\")"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "fd73357d",
"metadata": {},
"outputs": [],
"source": [
"# savefig(\"figheatevolution.png\")"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 1.12",
"language": "julia",
"name": "julia-1.12"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.12.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}