{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%html\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Poincaré kujutus ja lõige" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Mõisted\n", "\n", "Kui $n$-mõõtmelise dünaamilise süsteemi faasiruumil $Q$ on selline $(n - 1)$-mõõtmeline alamhulk $S \\subset Q$, et igale algtingimusele $\\underline{x}_0 \\in S$ vastav trajektoor $t \\mapsto \\underline{x}(t)$, kus $\\underline{x}(0) = \\underline{x}_0$, läbib hulka $S$ uuesti ajahetkel $T > 0$, niiet $\\underline{x}(T) \\in S$, ja dünaamikast $f$ määratud tuletis\n", "\n", "$$\\dot{\\underline{x}}(0) = \\left.\\frac{d}{dt}\\underline{x}(t)\\right|_{t = 0} = f(\\underline{x}_0)$$\n", "\n", "aja järgi on $S$ suhtes transversaalne (mitte paralleelne), siis nimetatakse alamhulka $S$ **Poincaré lõikeks**.\n", "\n", "Tingimusest, et $\\dot{\\underline{x}}(0)$ ja $S$ on transversaalsed, järeldub et punkti $\\underline{x}_0 \\in S$ läbiv trajektoor ei ole $S$ suhtes paralleelne. Seega võib valida aega $T$ nii, et $\\underline{x}(0) \\in S$, $\\underline{x}(T) \\in S$ ja $\\underline{x}(t) \\notin S$ kui $0 < t < T$. Kui $T$ on sellisena valitud, siis nimetatakse funktsiooni\n", "\n", "$$\\begin{array}{rcrcl}\n", "P & : & S & \\to & S\\\\\n", "&& \\underline{x}_0 & \\mapsto & \\underline{x}(T)\n", "\\end{array}$$\n", "\n", "**esimese tagasituleku kujutuseks** või **Poincaré kujutuseks**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Üleminek diskreetsetele süsteemidele\n", "\n", "Kujutus $P: S \\to S$ määrab **diskreetse dünaamilise süsteemi** dünaamikat. Süsteemi faasiruum on $S$, ja trajektoor, mis vastab algtingimusele $\\underline{x}_0 \\in S$, on jada $(\\underline{x}_n, n \\in \\mathbb{N})$, mis rahuldab $\\underline{x}_{n + 1} = P(\\underline{x}_n)$. Pidev süsteem ja Poincaré lõike abil tuletatud diskreetne süsteem on tihedalt omavahel seotud:\n", "\n", "* Kui diskreetsel süsteemil on püsipunkt $\\underline{x}_* \\in S$, mis rahuldab $P(\\underline{x}_*) = \\underline{x}_*$, siis on pideva süsteemi trajektoor, mis vastab algtingimusele $\\underline{x}_0 = \\underline{x}_*$, perioodiline. Trajektoori periood on aeg $T$ mis mõõdub kuni trajektoor taas lõikab hulka $S$.\n", "* Kui diskreetse süsteemi trajektoor on perioodiline, see tähendab et on olemas $N \\in \\mathbb{N}$ nii, et kehtib $\\underline{x}_N = \\underline{x}_0$, siis on pideva süsteemi trajektoor, mis vastab algtingimusele $\\underline{x}_0$, samuti perioodiline.\n", "* Kui diskreetse süsteemi trajektoor ei ole perioodiline, siis pideva süsteemi trajektoor ka ei ole perioodiline.\n", "\n", "Selleks et uurida pideva süsteemi trajektoore, nende perioodilisust ja stabiilsust, on tihti kasulik uurida hoopis diskreetset süsteemi. Sellepärast tegeleme järgnevates loengutes diskreetsete süsteemidega." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Interaktiivne näide: hõõrdejõuga mittelineaarne pendel ja erinevad Poincaré lõiked" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Järgnevalt on selgitatud, kuidas on võimalik leida Poincaré lõiget $S$ ja konstrueerida Poincaré kujutust $P$. Selleks kasutame SciPy, NumPy ja PyPlot." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "from scipy.integrate import odeint\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Süsteemi definitsioon\n", "\n", "Süsteem, mida me uurime, on hõõrdejõuga füüsikaline pendel, mille tagasitõmmejõud on mittelineaarne. Pendli asukoht $x \\in S^1$ on punkt ringjoonel, kiirus $v \\in \\mathbb{R}$ on reaalarv. Faasiruum on seega $Q = S^1 \\times \\mathbb{R}$. Pendli liikumist kirjeldab võrrandite süsteem:\n", "\n", "* $\\dot{x} = v,$\n", "* $\\dot{v} = -\\frac{hv + k\\sin x}{m},$\n", "\n", "kus $m$ on pendli mass, $k$ on vedru parameeter ja $h$ on hõõrdetegur. Järgnev Pythoni funktsioon kirjeldab süsteemi dünaamikat:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def pendel(y, t, h, k, m):\n", " x, v = y\n", " dydt = [v, -(h * v + k * np.sin(x)) / m]\n", " return dydt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Konstandid, mida me kasutame, on näiteks sellised:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "h = 0.5\n", "k = 0.5\n", "m = 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Faasiportree\n", "\n", "Järgmisena joonistame faasiportreet. Seda saab teha PyPlot funktsioonidega `streamplot` ja `quiver`. Paneme tähele, et $x \\in S^1$, ja vastav koordinaat asub näiteks vahemikus $(-\\pi, \\pi]$. Tulemus on selline:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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JFXTuwMWLHEjm68u736kT1ZDuGCamEvNHH9kjgGLF2HO1bp37ukgtFhqUAQPo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hAAAg\nAElEQVQHtiVBRgqtW8MUcPKk9LimTWFzvXrV+hiViqhr18xSb+PGWCyuXZOfT8uWkPikFqFmzbAv\nWyI9GjdGcpkSNGsGEle6uHbsCFOKrb72bt1w3cPC8Pu2bdKLqhz0elhjDh6En0RpzsDXX0ND69NH\netzly3gWu3ZVtl+DATkPAwbIj710CSbAFi2U7VsJtmzB8y1n0rMFf/2FHI533yWaPt1++81XsDWF\nN799KI+VYTh8GE0zatRg3rs3+/sTBDTg6NdPepxajZrts2ZJj9uzB65Y0zamajXq8Xz/vfx8xHIG\nUuUSLl5km0vxiin5SqouinVYbGkes2QJ6hdduaJ8GxGhocwTJuCYvr4mfY5twNmzqFRZvTquoVJE\nRuLefPON/NjevW3rKSB2scrUmcoCpk9HCQR7NRoXa0B99ZV99icIeH7btkURvhfVVyGn8ErW3lF8\ngnmM9JnRfeq990AyP/2U/f398AP2JVej5IMP0ElL6sVMSkIziYxVCN97D8Wn5PD8OapUrl9vfYxW\ni1rwS5fK7890XgULMn/2mbLxbdqARJVCo8Hi2bp11gutnT+PxVelQonr0aNRM+jy5czXXBBQ+Oyn\nn3BtiVA2WgnBZsTly/J9vS9dwjE2bFC2T0FAsTMlNYCePUP3s08/VbZvJRg3DhVhbelXbg2xsSB6\nIrwD+Z3wmR2kn+9InxkVDD/4AHdg1qzsVXRMTES9drlqiNeusaJKhF26oMiUKdatY1kJXkS7dpCo\npDBkCOrL21LcbPRoVMFUso2osZw6pXz/YscmqQVLCe7cQZXSOnWwGBOhcFf58ignXaKEsXyziwsk\n5N9+s63mvy3QalE4rWFD5YQnFsVTonVMmYKqlXIVRJXi1CksOD/+aJ/9hYZCw1FSgTO/wEH6+ZD0\nmUH0S5fiLkyZkj3VeNkytBC8fFl6XIsW6Awkhc2b0TzEtIZ8cjK6E82cKT8XsYerqYkoI8Ra7dZK\nCN+7l1kqFVvjHTokPweDAefQu7f8WFN8/DGkdCVtApUgMRGlr9esgSQ8bx6qXP78M8o320OSlYIg\nQJNwdVVuTktNRaXPLl3kF9jgYGZvb9uas0jhyRNoo/7+9jMVMdsm3YeE2PfYOQEH6edT0hexbRtU\n2R49sl7CVaNBgww/P+kHfM8elNc9fdr6mMREzGfSJPP/f/QRWiDKNapITUUddqmuWIIAc8abb1r+\n/quvQFSmC48ggMjfflv6+CJ++YW5cmXmCxeUjWdG/f2mTXGed+8q3y6vYt48vOVS3dRMIQjMgwej\ngYmcqSklBWWX27VjjovL/lxTUtAQvVw5+daHOYHgYDQYsoe2l9NwkH4+J31mSLyenpBwstqP9dw5\n+T6rBgNzkwZabtFC2qQ0fz5e/IgIhtFWEDgoCE9MQIDMRJ4/5+lj47lECekFYvVqzPfhfUOmtzwx\nEcQ7apT5Nps2YdG6dE5eFNNqQUp169rmWH3+HItLxYqQPPMjUlOxaPv7M3/5pfLt/vc/3OPt26XH\nCQJMdAUKwDGfXcTHo4F8hw62LdLZhSBAsBgxApqyszOeSXs5kHMKDtJ/CUifGdJ34cLMrzdKluxu\nlQmHDqWz2pQpIGupZuPXZ2/mtnRMsrViTAwapzRvziycPQcHhCCwvz/MQ5I+iMRETmriz7M/TJSU\nAJOSYAueNYuZe/XK1MpINFmZ9pXVamEr/7XsHDY8lWh9lIZr13AeP/Q/ChuVQoTeSeby5XEse9mq\nXxRu34b93s0NTn6l/qI1a8AISghvwQKM3bo1e3NlRret+vXx7Ms1gskKUlPhZP/xR+b338diVbYs\nnj3R52L6UakgLKxbBzNfbjfVsQQH6edl0jcY8PQoiTVk2OQ/91rMM0pv4NBQhcfYs4e5UydmnY6T\nkmDSaN9e4mW/c4dTnL349QqhkpK4jw+ekN499ZzsUoh5504+cgQvyp49MnOqUUNRP8Qvv4SfIfXN\ngehabTLplBS0AXz3XfNtjh1jnkZf89Na7RUZa5ctY25PRzi2jkRH7Iy4c4fjuw7kssU13KePAgd2\nfDzzihXSjYFNodcjPjQpSdl4ZrCXxCoaFYXew5Ur4/JfviRg9ZaBWg1hoXhx5vlTYyUXCb0efo8S\nJdIivGJjlc+fM4+/ehXO+XLlEGqbCXFxtrGuRsP65zF8+jSEiXfegbNcdJo3bIi+x599hv67GxaH\n88x3w9jX10j4RDBPtmqF33188GiuWcMceuiWfduDZREO0s/LpM/MHB5uk9Hz7qVEblw2nCtWlJbY\n06HVmhm/Dx3CnbXap1YQ+O6+u+zkxLxypfXdduhgfBFq+6r53l2BBQEOvsqVZfwPwcGKCDYyEr1v\nP+z3xKJX87vvsMjcumX+/7G9w7lKsXhFnGMwMHdsb+CWJUNsk9qDg/nuXTh2CxdWEP1x+7ZysVoQ\n4OFVassTBPR/vHYt01ePHzNPngzzYIECMO8lJjImLBOjee8eegm7ujJvmXKOhdFjrJ5DYiJ8MOJz\nI0REwiajdKFTq7GD8HDW65FbUKwYNEeLAo5eD8Hh5k3ZXcfHwzf2bfvd3OG1QCbCvidPhrZz7pwV\nE9+TJ+le++Bg5g8/xHWcNQumyePHMYUWLYxawXuvK2wynINwkH5eJ/0s4PFjSGuNG0MashUjRoCo\nTB2hGTF3LkjCmsOye3c2U3u9vbF+3bkDkrBXxMbatdj/0aOZv1Or8cKNGGHORaGhsO1/+KGyY4SG\nIvoogzKhCHFxiL8nwvHkHNk5DYMBdvSvvgLn1q6Nc/vf/7CIKsW2bbinvr7osysVSqTTweRRsCCa\ntzMzVAtbpPDkZGa9nu/dQz4EEYIDbLC6WURcHHJLiOC/mTULptKshsBqNJZPKy6Oedcu+5i0sgsH\n6b+EpM8M3+Ybb0DVtKWJODPs0D17QkW1RlJJSXjhW7SwbCXp1Mmc9AcMMEpLM2fCd6DQaiUJgwEk\nUL26ZaFRzPLNGLe9eDFs/kqvze7dWEinTbOd+AUBWoerK6J7HjywbXtbodMh2e7MGQjs330HMhs/\nHhIsESTS7t1hbUhIsP0Yu3czDx2qfNvff7eoaCiGTgcLWIEC0J6OH8/6vjIiICDn70legoP0X1LS\nZ4YJtEULSFgnTti27enTIKkJE6yP+e8/qK0LFmT+rmdP2EF79cKTYmoKSkqCHdbWOHhruHEDx5o/\n3/L3Eydikbl+3fg/jYZ50CAkeSk123z3Hc4lq9mjFy7AtPXaa7aVebAVYikJ8ePqimiisWOZZ8+G\nX0OpVSW3YTAg96NaNWRKT5pkmyvDXnPYuhW5ES8DHKT/EpM+M7Tu9u0hIf3zj23brlqFu/zLL9bH\nzJ4Nws2YkBQZCXMOM9LiCxZEpIWIbduw7/37bZuTNcycCTXdkrkpJQWRNHXrmvsSQkLgE3jjDeUJ\nOGJCnLUFRg6xscx9+yLP4K23mIOCsrYfKaSkIIz32jVYUbKTsZ1bEAQsjHXr4nr37Gm/pDdbcPo0\n8leIECX0MsBB+i856TODBLp3Rxje7t22bTt6NLazlmyj0SCqQSqePSYGJQQmTDASkCDA2evrax+p\nMzmZuVIlELglkrt2DYvCBx+Y///IEZh5pk5Vfiwx5HDx4qzNVRCw6FWsCE1p+PBXy7wgBYMBdv8m\nTXCNO3a0rbheVqDR4PpfvgyNeMcO5jFjUE+JyOiELVUK42wtiJfX4CD9V4D0mfFg9+sHgtuyRfl2\najVzy5aITRYl94y4fh0Lg5Rzdu9ePDGm1TaDgmDjlqv7oxT79kHr+P13y9+L5pmMFUpXrmSbCoox\nGxORli/P+nzVasypZEmYYCZNsn6NX3Y8fYrFtEoVBCC0bGnZOZ8dxMdDeFm/nnnGDJgXq1fHO9G4\nMWeKuZf6FCnCXK8eggTWrkXwRH6Bg/RfEdJnhglj2DA8sEpT65lhlilVCg5Ta47dX3/FEyG1oEya\nhMXB9HJ+9RXb1cwzbRpMWZbqCAkCylUUKwaSMf3/yJHQBM6eVXYcQUCpCCKE9WUHSUnMixbB1u/p\nCVNVbpQSeNHQ67FQ9+kD4vXwQF7FyZPZN0lptfChrFyJ0hCi5iB+KlRA+PBHH8GMeegQnPq3b+N5\nj4iAaefttzE3Ijwf//wD4WDRIkRjNW9u1ARq1cL+9u178X4HW+Ag/XxA+vPmwZFkD9uswQAphwhS\nplKIjt1PPrE8D0FAMos1wmWGZOvnB+epGGJuMMD05OOjTFrSaiFdW1t8UlIgtVWsaDkEMTIS3w0b\nZm5WEjWa0qXNfQ9SEASYhZo2xTXNbtndmBj4SIoXx8L01lvMO3fmH6erEggC8ibmz0flUNFW/v33\ntudqmSIiAj6ATz6Bw7dAAezbzQ3BDJMnQ9AJDLS9UF1oKKKfRo60/H10NMx1o0YZz8nPD5rEjh15\n7/45SD+Pk75eD8cfEUIo7VFbRCQrIkgsSrF5M6Qaa7bslBQ87BUrstVSEMHBSGE3jXmPisLL0rKl\nfE7W5ctYfMaNsz7m8WNkfbZrZ3l/Z89Cauvf3zwe++lTmLEGDVKeDydWO3V2RpiqTSUwrCAqCslH\nogPxtddgYz5xIm+m9cshJQWa3MSJiF4SbfWjRsHckhVhJjQU4aZjxqDWUfHi2G/Zsrivy5bBF/Ci\nCVfsdfDDD0aTUZEiiJw6fTpvONUdpJ/HSV/EoUPGSIbhw5VLo9YgCEgnF0MQFT2MMTHptmxr5qFH\njyCl1q/PnPCv5eIjYuSOaROYM2eYmzkH8pyJ8qn/Yp2XTQseWM0oOnEC9n0zx21SUjoL7NqFBWzs\nWPNzv3EDJNukiW11c44eBfFUqJCWrGQn3LwJ6b9iRZxzxYrQKk6ezNsOxfv3kRvRo4dR6q5UCcS/\nb5/tFWHj42FCHD7cuHAQIbls3DgIJFLJhLmFoCBoCaIG0KZNbs/IQfr5hvSZYT5YtQqk6ukJFTk9\nIzExMVPRMUno9cxLlvBPMx4wEdRfWeL/7DMWFizk0e+q2cXFegjo7t14OjxctLy+2hesuZY59XzC\nBEjbpqagn//3iB9Ref5vzr5M4zNi/Hjmgi4pnFypFt54C5P/6Sc2DznV6xH7l+bJFf0QGR3Jly7B\n3NSwvoETP1+msJ4FNIze9e+zu5vA69Yp2kQxDAYsZGPHovqlqeli6lRUtsyuIJAViJUmd+7EdezR\nAyay5s2x6LZvjzo1QUHZk3KfPcMi3agR7OY7d9qWQZzbMBggGEgVKnxRcJB+XiX9iAiIdKtWZeoo\nEhuLwlWurgh73L+f8UYNHYqYxU2blL1he/Ywu7hwUIv3uBDF8ejRMunnT58ye3iwULUqf/B6IHt7\nW4+dhrotMBFzSXrGSwacM5NMU1OZu3Y1z6wUBOazpXozE3Hce5MlbRkaDaSmb7w+5fSUXwvi45gx\nIMczZ9L+8dtvGP/mm8xxcbx4MaebBUxJ8/p1mIjeq3CYBWdnXNuoKImLkzavvw7ys0LV+Av6lD8e\n8Vy+7MK5c7jPGzcqUy2io1l75Sbf3HyFVy+O5cGDjVqAqAkMHQo/0Nq1iNe/fp059pmahTgb6m4L\nQro3UqvFgnbuHOzmP/4Igu/UCXkO6c7R4incrRs0xwMHFJjIbFRVEiJsVA/Uats6mmg0yux6ej0c\nE9euKWsHxwzv7xdfQMXMqTZnCuEg/bxK+swwSpYsCV3eAu7dQ6lXIsTTJzxNRBzZmjXK9i8I8KJO\nm8br14McJ0+WeU8+/JC5Rw9OSjBw06aI6rFUTuHDD41VB8WPtVBKUyTsPMSPPKrxh69fkE3xj4hg\nblImjEPdq7DmN8uF+jUaRB11756WuKXTwdhq4swQzQ8qFXO3bnC+aTR4r8uUYd7vPYATh0k4ETJi\n3jwOr9qKvb0E7t5dgbln5UrcZyU2j+RkLBIFCpgRTlgYaqpNnYpolZIlcU5elMiLaTqryY17uB/i\n6tXh63jzTUTNmH769mXu11vHqxr8yI8K1eFFZVaml20w/bi4wEnZpw+0zePfX+eUHv1ZmDBR2fWJ\niUGYVefOysbHxTF//jnqYCgpXhQRYSz9qaTWR3IyVioPD5CyEuzbB1ue0iJSGg0Ek759lY3PQWSH\n9FUMYnxpoVKp/Ijo4sWLF8nPzy93JvHkCVG5cla/ZiZas4Zo2jSi4sWJNi17Rq+/VUr5/iMiiEqW\nJCKi3buJBgwg6taNaOtWIg8PC+OfPyfy8SFycqLISKLXXydydiY6fZqoWDHjsC1biIYMMf49eDDR\nhg1Erq4y82Gmm8ef0+t9SlCLFkR790pvc/EiUd9WkdRuYAnasIFIpco8JiaGqFUroqQkohMniCp7\nRRKVKJH+/d69RL164XcnJyJBIOrYkejwYaKQEKIBbSMp3q04HT2moooVZeZPhB1ERdH1iBI0dCjR\njRtEH35I9MUXRN7eVraRuc+ZEBxM5OsrOUSrJQoPx67jL9ylh0nFKCS2KEVFEUVFWd/OxaChFgWu\nkt7Dm5zq1qbSpYlKlyYqUwY/ixXDdSIiPIA3bxI9eoQHpmNH+blfv0507x6RTkc0cKDlm2aK8HCi\n27fxs39/Ijc3+WPExhKdP0/UogVR4cLy44mI7t/HDTJ5NiSRlIRPKYXvm8FAFBmJi5iLuHTpEjVu\n3JiIqDEzX7JpY1tXifz2odyW9G1ASAjMHSoVhJystk7cvx8CT8eOykLb7t1Dm7rOnc0r/d6/b5QK\ny5aFUGRLJ6nDh2G+eu89eUvVpk2Q5qWSvMLCkP1bqVLm0NDkZBxLlGRVKnOt5OFDJA117owy9rZA\nq0W0k9jcXLaXgAMO5DAc5p2XhPSZYSpctgwO0ho15PuUWsPx46iV06KFoj4afOkSIl7atDEmpQgC\nLChnzyK8rnx5WJ5sicUWze9KNOhFizB26VLrYx4/Bun7+mZ2eopVQcVEm2++Mf8+LAwhpZ6eWSuP\ne/8+fBhEyIzODaerAw4wO0j/pSJ9EUFBCDls1Yp54cKsxXafP2/MRJw2DfkBUvs5cwb11Tt1suyf\nCwpCvLK/v23+uy+/xBx+/VV+7KxZGLt6tfUx9++jwmfNmuZZr+vXY+E6fhwZsUSZE9GSk2EvJ8IY\nW/1xgoCM5ZIlsaiuWpX3EnccePnhIP2XkPSZYVaYOxemiq5dsxbe9tFHbObAK14ccdbWSPv4cZiG\nunSxTGanT+P7fv2UE6YgwEnt4sJ88KD82EmTcM6bN1sfd/cuHND16pkH5JjO6dtvcc4jRphn2orJ\nWE5OuK5KNKGMiImBo7tIESxAP/2U+81VXkWo1TlT5TSvw0H6Lynpizh4EGRdtqzVICCrMBiMmY7i\nx9tbOrLw77+NY1esyLzY7N4NwpwyRXnctk6H6JtChczr9lib8/Dh0FKkKorevIlze+st6+kNmzZh\nsenZM3OHpoMHQdq+vlb6syrA7duIvlKp4PNYvdpB/i8Cjx4h4U0MN33Vity9MqRPRLOJ6DQRJRNR\njMJt8j3pM8N+7O8PIly0yDZzz6xZRjMPEStKOmrY0DhelIhNKyauWwcJd/p05cSfmIjaPj4+8i0g\ndTpoE+7ucAhbw82biGuvUsV628eDB9FaceHCzN8FByNL2ttbQQ9cCdy8idIPKhXm8/PPtoWX53UI\nAgILnj8H4QYFwXx45AgiJH/7DWULFi0CGX/wAfJQBg7Egtu+PZK96tVD3aZSpRBaW7iw9U+7dvAj\n1a+P3/v2RaSupyeus+i7IcpfSV72wCsTsqlSqeYSURwRlSeikcxcVME2uR+yaSfo9UTz5hEtXEjU\npQvRb78hxFMOt24R1a5N5OJCVLkyIs727UMIpDWcPUvUsqX5/8QQSBErVhBNnkw0ezbRl1/KR+0R\nIQqvUyeix4+Jjh0jqlvX+litlqh3b8z366+JOnSwPO7hQ6KuXYmioxG62bx55jFBQUTVqlkOHU1K\nIpo5k2jVKoSlrlxJVKSI/LlYwo0bRJ9/TvTHH7i+/foRDR9OVFT2Sc1biIkh8vMjSkkhSk7Gz4wo\nXRoRmCJcXIgKFSIqWBA/69XDvfPyIvL0NH7Ev318iFJTrc/BzQ3RxbGxmE9MDMKKExMzjy1QgKhW\nrcyfatUwr5cNr1zIJhENp1dM0jfF33+jjEOvXiZZqjKYPRu5KPHxkJoKFJAuhWwwsFlST+HClqNV\nvv6aFUfniIiOhiZRooS8PTY5GRKeu7t0zk1UFPPrr+O8/vpL+VxECAKk1cKFkcyV3bZ6V69CC3J1\nxdyHDrVPueEXhdRU5DotWICKqGvWIOH4zz+hOZ06hdDX4GBI2ampL+7cwsKMzngi+JiWLUPxt9df\nh8lOLHFRvDiS0L77Dqa4/HL95fDKmHfSJ/2Kkz4zc+hjgVu3xoMtFemSjri49AL0qanI5nRxkaid\nr9Px6I7BLNYtV6lgZ7fkvF24EE/Snn7rFRtXnz9nHlPpIDcoHsa3M5f1MYNajaqLvk4hvPEX66Ey\nKSnIMHVySrsmWXjDQ0MRy0+E8g9ZaThuiogIxPhXrYp91qkDP0lWnMcOmOPkSZjm/PzM/y8I8PEc\nPoyqCW3bGnM4ypWDY3/TJtvKXOU1OEj/ZSD9W7eU1wBhZr5/n/WjxvI3ff5lIoFHjZIJoxTLNbz/\nPvPt26zTodmFSmVeKdMUNz/+lcd4b+S4737jLb9p2ckJNnlLNefnzWNuS8dY65rWQURBDZqoc8Ec\n71SYV3tN5pDT0ouFXs889e0wvkU1+J9u31hNFtDrUQiOiPnrj0JZGD0GhmclTpCUFOYTJ1jQaHnV\nKvgBKlUyry2UVRgMqLLarx8W2wIFEEa7e3fWk/AcwGOtJIosMRGa7dSp8CsQ4R60a4fnP78twvma\n9IloEREJEh8DEVXPsI3NpO/v78+9evUy+2yWignMLv7+G10+Fi+GXUVOAk5KgshSsyaeTCW1fdN6\nBMaVqs69XPZzs2YyTUzu3IFqoFIxBwSwwYCQztatUX8lk2CsVhtF1K+/5q1b4RB+++3MxC8IMAfs\nojc5XUxWQLRJE9G66oxbG757STp9WBCYf2+zmomYS6ue8sr/RVgsyyImldWrx7y6+S+YT5UqKOso\nhyVLYOMZMIAjvt7AbVvrWaWCMzzTOmYwwL41bhw6iPz7r7xqcPUqPz94kX+acocH+T9lD0phLy8s\nBhs3Kkh8szWxwNYED1u1o6yMt3UbW89B7ho9e8ZR+87yX4tv8nsdH3Exp2h2d4cj/sABC5vHxyPO\n+eOPkQxy8WL2u+3YgM2bN2fiLn9//3xN+j5EVF3m45Jhm/wh6f/0k7FimRIj8ZMniMskQp1dOQgC\nwmo8PPjxlG+4QgXYMI8dk9hm7lyk+r79NrPBwIIAFZgI8fGZ3q8//8QxGjdmjo3lP/6ApDpgQObo\nFEFg/mbMLT5cuC/H+FS1Hk5jivh4VrftzE+9fbnPa8dkSyQIOj2XcXqKUgtpFUCrVQNhZsQffzB7\neQp8sFA/Nrh7IEtMDoIA4zARc7durNcaeO1aJGIVLYoIFbP3XauF+kOEAXI9Eh8+hOE5zSD9cONJ\nXrgQnbuIYIbo3BmPzuPHDMN5x46wSxQogJOSwpMnOM+BAyFAyPWBVKtR7/mLL3Cc2bPTvxo6FPNq\n3RoJez17YnH6sM8jXtfqZ75RewAH1hzCM2fisVq4ELb1779H9NK2bcw7dwh86tc7HDJjNcd2G8zq\nBs04KlzLarUE9588iay6rl0RCiVXFvvmTSSWlC+PayTXKFmnw4TTwn+S336Ply6F6Y0IZaU/+QS7\nTcfTp8YB7drlunMgX0v6WfnkG9JnhvGwWzeePeQBL1qkQJW/dAkvoNIuHuHh8OYeO8aRkSjT7OyM\nl87ic5maCs9bhkL6q1fjHRg4MENSliDAm3rsWLoItGsXnGfjx2c2KQkC89xZGm5C53nBzARl70Zy\nMkedC+YedR5w4cLyuQi7fokyyzsgghBmCTdvMjevFs0dPU/zibkSsZ+m0Grx1pvEcIaHo9WeSgU7\nslkYqcEAaX/CBGWSuE4HtahOHbNYw8eP4XAU72GtWsghmPhOLF/vPp31hYuwcMlKH0tTXLkCM56H\nh+XV0BRqNRb2AQMwfsqU9K8WL0ZS3bvv4rno3Zu5+xta/qz2dv7HZxCnuHjzGc8OXKUKZBUfH4S+\nivbz1q2ZiQRuSJd4CX3MoVSWH1IFdiVNun+jVCnmBg2w0A0bhvu4dLGej330J0c3aM/6wkVYe++h\nxanHxMD5Pngw85nDSViwChVSXrvk+HFMPC0ZRBDw2k2ahPW7YUOUJdm2LW2hj4pCkSolAlkO45Uh\nfUKoZgMi+oyI4tN+b0BEXhLb5LpN3xCXwB9+aCxctnatjHaYDSlCpzOWPRg+3LZyCTt2INKkY0d5\nK8XBg9JF3cRm6VOnKj8dMbLIwyO9R4pFaDQot2AaWSTVcSkhAY5gcexffyloWm5l0hcuGAX1Pn0Q\nvZI+3lavb2io1a+iosAtkyYZbdAV6QFXLKfnoUMRTXP9uvRzlPzoOe/fGC2bE5GO+Hj4lpQiJcVq\npp3BYIzrf/AAc/3vlIHPfn+Bd+4EWf/8M3xB48cjwa5VKyxyBQvifL28mGvRTXZxMnC1atA0Ro5E\np63Gjc1zT1auTDvw48e2ZcdFRWXO2mOshTt2GJvdlCuHSKbn97Pp2bcTXiXSX5dm48/48ZfYJtdJ\nX0RwMKwqRHhwd+/OOS1x40aQZ7NmthUGO34cwlLjxvLEKBZ1a97cst/2++853byv1BSdmgoydXa2\n3s6RGSUQiOAGKVMGH6new4JgJE/xU6pU1gqnCQJKRJQrBxfJF1/Yp6+uFKKj8bxMmwaTi6gJeHjg\nXo0ciQJzs2ZBQu/SBXMjgv8+vyElBXENR4/C1DV5MpK5TBu+mH5Gjcq5frqmipO7O5S63A79fGVI\nPyufvET6IgIDISGLKvDp0zlznAsXQEylSyuP52fGQ16qFKSudEnWCgIDodbXqfycPNQAACAASURB\nVGOZPNetY8moH0vQ6UBiRIgRt4THj2GJiI+HubVZM5hzpapn6vVYHEzJwskpg+3WBiQloUdxzZqQ\nSqdPf3FhgAkJWHSXL0fpaj8/89LS4kelQsji3r2IU38ZisMFBiK+wLTBj7u78WerVrDO7d5t36ic\nqChosLNm2W+fWYWD9PMZ6TNDUjh4EHbDJk1QvyUn6oeEh8Mc4eamrPyCiJAQ9EotW1bevRAUhMWl\nShXLUafbtsG09dZbyiUkQcCLS6Ss7ERKijFhZ+5c68dZv96cFFu3tqjd24TISBBBwYJYeCZMQIkC\ntRrzSkpS1tcgu9DpcK2KFjUnRFMziFgjqH17zFlsyXjgADoHxsTkvhSrBGo1Fn2R6NVqCDnLl8M9\nIS7uZcviXFesQPmIlwUO0s+HpC/CYAARFSsGe/P339u//aZaDfWUCCGaSiXuiAiYEry85IOPHj6E\nZlC6tOXiZXv3Ku8AaYoffzRGC8mRsyAY/RmjR1smWq3WSAgNG4IwqldHz4DsIjoakr8liZsoc33/\nnEJsLJyu4nEvXADhHT0KO/rMmfBxDBkCjS5jS8wCBXAvhw+HOfKjj7CYrFuHWPdLl6BdvcCoRas4\netRyC09BgACyahVMXeI98fODOe769fyxuFmDg/TzMemLiIoCURHBRitln84KBAELir8/TEtK+ncz\nQ0rt2RPSolw9/GfPEInRtSvS9O2FHTtQZKtp0/SkYtnxtWuDzC05MbduNTqgb93Cfp2cmOfMsU+F\nzGvXsIBnJP1Dh7K/b6UQBEi3HTrIn5NWi0Xhv//gPP72W0TRfPwxpOTatS3b0uvWRSmN+vVBrCNG\nYEFZsQLX+MQJ9D7IC4Xn4uLghxk4EBFGRFjYFi5U1oI3r8FB+i8B6Ys4cwbEqVLBTGBLlyolOHoU\nL7Cvr/I65DodnLFE6G0tJSHFxsKG7O6evaqVGXHxIiT0cuWYLyuIWrxzB9fR3R3hqFJz1umQnObi\nwtyoUdbLLJvi4UOYe0ylaD8/mFKya07KLajV8KVcuIAIqN9+w3WbMAH1kVq0QAazaF8Xa+CoVDCz\ntGwJzeGTTyCA7NmDZ/BF+xnUauRLfvghghZUKixaO3bkjQVKCRyk/xKRPjNI6NtvIZGUKwfpy56q\naEgIpLSCBaVDI02R0XQipdqr1cYyw+mhdHbAkyfQgry8pIuviUhNRaQFEcjGtP+vJQQGIiKmfXuY\nabJbHmHvXiPhf/45fCQqFcJNJ0/GwvQyQhCw+AcFwW/188/offzuuwjJrVLFaG4pVAhaZLVqKCA4\nfTo0yv/+ezGlEZKScLwWLTCfkiXh68jr0r+D9F8y0hfx5IkxNNGsUYitNojLlzPVZ0hIQNE1lQoh\nfmaLyp07MKZbMIqvXw+J+P33Tb6OjkZijEmoj8GA8EIivMhmjlidDq2r5EKDTHH4MHNSEicnI8xS\npULFBKuLock1CgjAAufrC3u0FFJSQPhubsyVKytfFK1h0SJIweI879+HpOvjg2szYgQk5uwWdstv\nMBjwfP/7LzSxKVMQklm5srl21L49QngXLsQjEBeXc3O6ehV5EaJprn9/RABlpVVpTsNB+vmZ9AUB\neuWlS1afrm3b4Oj18QGBCQFbwSQBAcYu5lKIjYXe3b07si/TdFiDAYmhRAipNJNshw3D0z9tWiax\n559/oK43bIgXl5mRSqpS4Q01MegvX45/Dx6cQY3ftw9f9OwJY7ecKnPkCETk8ePZEHiJZ89G1NPg\nwVYuwe7dWNU2bmROSOB792C6cXe3QuTXrsFmkca+d+4wv/EGrk3v3tLJX1lBairIfuhQHMPDAySz\nc6dtCXUvI5KTETYcEIDns0MHY8IWEUJk330XFSauXbM/KScnQ7gR742vLx7vFxGBpRQO0s9LpK/V\nQrTt1QvS75Yt8naFu3eNrD54sMWsqMhIRLCIUn/yu2PxR/nyymLRjh0DyXp7400xwZYtIJ2hQ01I\nPCoKXjoXF3jkMuDaNRy6bNk0G7vBAKMtUaasqm3bQLbt22dQ2YcN4/SQIiX2K1F1aNGCOSmJt26F\nqad2bSuJpFOncrrOHhzMqalQ3S12WTIYcIFdXBDj+tdfLAiYe5kyiGhZsMBk4Xr2DCw9eDDE0H37\npM8hJQU2qX//hd3j+fN0tnr0CFpLo0acbvIYMQKmkbwQIZMXYDDgsq1fDx9CkyYwEdWpg3pTQ4ag\n5I5s2PPp07iwly4hI1pmhb229hxfLdmJ16hG83SPlfztsIt5IvTTQfp5ifSZ8aaOGIHLW7GissJj\n588jRKVUKbCwFQIRpf7SRdUcVbUpC3Xq4C1Q4h2cPh1G7iZNMomuFy8ifrt0aZPwxT/+gIhTpQrI\nKgOePjXa2PfuZWQ5rVkDUSxDqM+JE6ivUrOmSSx/dDQ8gc2bw+grJ7Kp1Qi/6NABufsaDQcFYZ/e\n3rg2ZtBqUTylTh1ke8mJaqmpMDo7O+M6pXnRExKw3jg7Y3fpmdRiuBIRNBY5r/uRI8aGxeXLW1x9\nbt9Oq4lXzcDj6Qd+7Fmdn3lX4YRS1Tj+vEzjgb//Zp4xA+faq5d5f0tLePAA3tTly2FHlKvTk5gI\nL+6mTbCBLV0qPT4+HnNYuxYC0JQp0quYRgOz4pQpUD379TPvep8BqSkC3/p4LUcWrcGhblX4HlXl\nenSV69fHo37okAVOj45GeJmoNsidMzPz6dNsKIS6H/Pdv+R6tXS5Hu7pIP28RvrMnF63eN48eAeV\nFGU/cADexJ494cm1AlHqr/faYx75jppTpn+GF10OGg3YatcuxG5meHLFRC53d5NChYKAcJZGjSyS\nWlISzB9OTojIYGZIsW3aZIqXvHULmZQ+PibKg9h89e23JTq6ZDgHnQ7xhP/7HzODlAcNwtM8eXKG\nCIzwcExy4UIcQw5xcbCxLF4MjcLkGl2/juxXImR9njzJxqD4efNgB5Azzj9+jEWuUyesslZCqMTi\nX7+M+o+D3WvxMyrBj6kcT6+7n5cswfqaiXh0OhBsmTJYocqVA4laQ0wMFl0xHrNMGbCl1PgvvzQu\nXD4+0HaswWCA6VJUYby9ER8rZZKMigLpu7lBCKpWDRdeChcuMNevz4ZixTmpaDle0XYHlyqFQ7Zs\nCYVy/36T58JgMFabbdhQWdu3K1eYhwxh7ZDhHNe+t/z4HIaD9PMi6TPjrdRq8TLaoqeL28lg506E\nxZUpw3z4bxvtAFYywNRqI7F9/LHJMImMMb3emB05eXLaUCtSe1QUhGlX1wwZwoKQrbrpgoBIIdE6\nk26mMoWtthIL90DMpBZ5rGdP5msX08YpjT1Uq1GzIiVF2Tmr1Ryx4QCv/k7D/bolc4ECOHalSrB5\nb9uWwSKYnAx7UXKyspjfhASMv3BBWR2JlBQUxNm6VbJoXDoEAeav1auVjWeGH2ntWizCSq6rVotj\naLXMSUksCODpuXOhCYpr1NixkL8MhrRjiFVklUBr433OQThIP6+S/gtAaKixjs/UqfZxAgoCNH4n\nJ2jCSnMFfvgBRc3kXBgajbFk/YwZ9nXE/fcf/AxdumStV65SGAxQTMQaMMOGwVryIpCSAsl14kSj\nG4UICuX48eDi/NwK0N4QBPidZsyAtVVUaqZMyeTeyjdwkP4rTPrMIKBly6AR16tnvwf54EEEzFSv\nzrJ9bEUoTW4RBMxZDPhREoSkFBER2CcRSDAnk6G0WlhQSpbE9Z8+/cWRv4iwMGSbjhmDe2Ua5TJ7\nNtwrQUF5M/Rw9GgsXB99BPP63bs5Wx5BECAYfPABrHFubrDi/fZb/oqacpD+K076Iq5eRdKVuztc\nAvZ4ye/ehT+tUCFoz/bGnj0w9b79tn3JUhCgeXh4gPxy+vYnJcG85OMDc/qwYfKm6JzC06fQQsaO\nhWtFjHsvXBhhqHPmwPGe0+WglUBsgiJ25SSCoNGpExas/fuVlwyxFVotIpjF0NxixaAN5PXELGYH\n6TtI3wSpqbCrV6+ODFB7qPnx8QgGUangD7W3JHb9OqQuH58MHansgKAg2N9dXVEW197F7DIiKQm1\nZ8qXx9vVq1fOlc5Wirg4XNcvv8R8SpQwEmyPHvDFLlwIzS43F4LoaMzhiy+QYlGqFKRwlQr3cOpU\nmOzkzIdZwe3beG8KFzamj+zfnze1I2YH6TtI3wL++Qcvd8mSeJGyC4MBEiIRoibtaY5hxgvfuTP8\nCF9/bd+FRaOBBCfWln8RcdZaLWLKa9XCNWvTBtJ1XiARQYA0u2ULpOm2baHJiQtB+fIwj82fjyjQ\nsLDcqUgpCND+1q2D5lSuHObn7Iz+CTNmIP3Enn7VpCSUjRBLnteogUqd2S3JYW84SN9B+hbx7BmI\nlAip//aoICk2RidCKPuuXfbrA6DXo0ojEUIw7b2wHDsGQnvjDQSSvAgCNhhwjZo3R5Ssry98GTll\nssgqDAb0Hw8IwLPSqRMiw8SG7cWL41n65BMsFrdu5bzWlBGCgDmuWQOTUMmSuK4FC0IQ2bw5c9BB\nbCxs+LY2yhEEaGhvvQVhoVgxRALJttl8QXCQvoP0rcJgQDSeiwukI0tNTmzF/PmcLhWaSodydW2U\nYvt2JHzVq2dbeR4liI019hZo1w4k8iIgksiQIXAeenigXv25c3m3rrsoaf/5JwjvzTeRWiDec09P\nlEOYMIH5l18QIWMPwcKW+V2+jOexcWNO1wLE51GsbySWgc4qgoNRk8fTE/6yiRNz/545SD+fkv7M\nmTbae9Vq2ypOCUJ6SMS5c0isLVgQEpFV/Porun1YrFVgRJcupqQvsIebQVnVSNF4KlMf+cYN5OVU\nLBTD16auUx43qtUqKs94+DCuh4cHbP0vstxBRAQKsVWqhOvn5weTgr01m5xCVBSSi5cuxa2sVcvo\nLHZzg1lkzBiYRQIDX9xC8PixsRKs6UelQoJ8dhEdDd/HtGnZ31d24SD9vEL6qamKRYD4eOa29aJ5\nOi3mee2O8cNbCoyGgoAYxE6dUB5BiXH64kWIJ02bcupXy3nEgKT0RtoWQxnVapQWcHVF2q8V8j91\nyvzF2koDWN+osbLYTlFVaNhQ0nMbG4vT/YS+Yp2zGxv69EUNBDlMnYpCP8uXS4ZiJCUxT50i8HDV\nBp5ZcTNfO6iwQ7qdYvv0ekREiSWXW7dGYtyRI3nD9m8LEhPxTKxcCYKtVw9Sd9u2xrDIjz6CwBES\nkrOSckoKcldMq3U6OUFT2bFDoQ/AYMgTSVjW4CD9vEL6T57AY9e2LfTB7dslhxsMzIc+2sM6cmY1\nufHRFjM5Pk7mbdBowA5EELeViKirVmF806YsxCfw+vUoIFanjpWGIUFB0GWrVkVaoxWI9t6+PTQc\nrKrKz11K8rMf/pCfj16P6+TujtoNEgxgMDAv+crAe6kHMxHHj/tEnjF0OmMcnr+/rKh58VA033Wv\ny0zET8o04eR7MuR/7BguXo8e8CbKtTm7eROi/N69sIFZMAw/eICa+2LoYrlysJ/nVtinPZCSgjpO\nK1bArFWlipGEixdHhMyKFSjrZG9+1WhQiJYIz/qKJak8v9Iv3I+2c9eCp3jOOyF87pRW+lFatgzV\n/AYOREhRTjSxziIcpJ9XSJ8ZMW+igXHgQIQ+yCB17e+c6l6I76l8eXTBLbzqJ0GayyMiIMm2bo2w\nBjlzhiDAhrF4MXTxwEC+eRO8VaAA7LGZHv79+2F78vW12lH9wgVEf+j1zPc2neN2FUL4gnNzvj/g\nE/nF6NEjFK/p0QPFtWRsG+f2R/GXhZfwXtc+HN6yr7wnNCYG16hjR9wHmVhEzYMwjilSmSNdS/Mv\n3h/wjrUx0oRw7pyxNdRXX0mHdwgCbCFOThg/YYJVUV4QmM/vjeCLVfvzM1VJfkAVeU+RYbxsid56\nBYOUFNiLJkyACjd2rHQNIIMBIV2//QbWnTdPPknixg1ss3EjNKjz5+XHBwSgXMPChekaWmQk1r45\nc7Aui2tzDbf7HFBuGp9vPI6fdh3B2kUyxdyio/HclCyJNNsBAzI9czodLklaiSbmq1dZU7YSMxGH\n/b+9646Pouy6d9JIIXSUIiWhF5GOooB0wQ+UagEbNgRERfRVUcAKCIqKgiiioKCiFEGkSZUmSkcJ\noSaBBFIJ6dndOd8fZye7SbamsBsz5/fb15fN7uyzszPnueXce31vwo0Sh1697I6OIObPp8tQrZpV\npz3PQyd9byJ9gHH3iRPp64aH0691JpjfvRtxe87iYL17sEO64/nexxz3aEtL4807dy7NQ1enfezf\nTx3anDnISFfzkpqjRtnhiStX2NXyiSechjWSk4HB/bPxuTyNc416Q73iOC8AgN/h3Xc5aNVJaCgx\nEbh7oIpx8iniqzaBYVvhls/5kJbGm3TBAv4OzuY3njmDC39E4ZuWs3BWwvB+0y9w9IiDm/z4cTa/\nef55Hv+jjxybrJs28bcaPJgVY3Pm2M/RmEwwvP8hjP4VEB9cH3/63oaX/T/EwPZxmDXLRgI6Kcky\nZDkkhIL8efPsh7ciIy3T0/38KIf59FP7syLPnLF0tROhGT13rv2J8hkZDOMFByOv89n06dQSW5Vt\nG42MQH74IfD8nYfxt29nQATRchN+vXEM1o3+Afs2X7NtQ6gqSTkoiJnbzp2p97XZeMmMhASgZ0+o\ngwYj88YG2NzwCdyiHEXlymzLYFM48N133BzvuYcGXWn293AROul7G+kDFosgK4s3nxt+euS8jZja\nZSNEaMg7LbCKjAS+/db1tV29mi+s8t135ImmTe3kV41Gvt4FH9xkYtfdUfItpjxx2fW885YtLpXN\nmky8r9v5HMFLLda5PtxEE3y7iO3LLmFWzdnwUVSMH+/AsdB+59hYmpTOzpHm+UVFccMoMNGsEI4d\nA86cQereEzg6ZBpe7fZHXsO1m2+mquboUSsDdM8eFgjs2UOSXbbM8fG3bqVnsGULXz9jhuPX799P\n72zLFlrwEyY4fv3Fi5Qpbd7MEunRox0aD6ZcI2KmLMCPL+zDjFvX4Jd649FETqFKFe45S5bYiI6d\nPMlHRATDMM4q/HJz6XJkZwPffYeEud/if/+jMa8o3C83by5g1Gv/OHiQm7uHoZO+N5J+MWEyMexS\nvTqrBD/7rHR10dog8Z49mQIorhe7fj3X3bhxoQ7LJYI9e2h4Va7sRI1UDOTk0BgPDeXvMH9+0VU+\nixfbN4rdRXo6nZZRoyyj/Zo1o6W6eXMR4uPu/tiqWrT3FAFGI8/b1KmWHJIIFUJTpzLKVFJJ78xM\nNvbURiR06+adhVmATvr/SdLXkJho8do7dHAeSi0OsrLYiEorjipuufvp04zaBAVZ9ecvQSQns2eP\nCBOFrqo63UVcHBUpXbsyr7dmjXscZjJRJy7CYqJly0pOxpiTw6rZV15hd1Hr6M6CBSU/5tHTuHKF\nqYj772dKpXt3Jr1feIFFWCWxAagq5z1MnEjLv2ZNRqoczHO57tBJ/z9M+hr27qUFoij0qEuL4AC2\n5nV1kLgzZGRYhog99VTpdDJctoxtBOrVo7CmtPDXX5Y21rfdZnOYmF0YjcwDau+vXZtEUpIVnqpK\nr2rmTJKhVqjUogW15Rs3lm7H0esNg4HkPGEC8oam1KtHxe7+/SWTcz19mrLhwECmJyZM8I6GbDrp\nlyHSX7my6B0fDQbmk/r2JWmsWlWya7OGNkhcUViFuXYtw9BFuZFUlYrFChXorZRG6+ELF6iUVRRK\nHUtTYr1li0Wg5efHqtT332eod8EC597Y8ePcAIOCqGF/5JGSIylrpKRQNTxmDKuPteKpnj1ZxLR/\n/39nBq/RyOEo48dT0CPC63bmTPu5aXcQH8/8SfXq9PY8LeIpN6QvIg1EZJGInBORTBE5LSLTRcTf\nwXu8hvRVlWP2ROieFrXFQEwM3XcRtj0uLflwVhbykobao2JF9mBxNm7WFg4eBMLC6JZv3Fjy6zUa\nqUr192cYpTRyCRpMJsb4ras+NUVm166uHSMpievVZIutW1MQUxqdLrWplx9/zGsnNJSfWakScyOO\npiqWNRiN9PieeYbVzlpY7Ysvih+yzMhwv49PaaA8kX5/EflKRHqLSEMR+T8RuSwi7zt4j9eQPkDL\n6ssvObnHz4/uYlHaH6sqZdA1a7L/uE2tfQkgKYkWujXx165d9DBNcjKtMRGOY3R16Io7OHSIsm1/\nfxY8lcZnaNi1K3/lp4jzeeEFYTRyPPLw4VyzVgy9YUPpJe8NBoYM336bHlKPHqXzOZ5GTg69nbvu\n4u8UHMxw465dnrfWi4NyQ/o2v4DIZBE54+DvXkX6GjIy6HpWqcLE27Rpzmdq20JiIsMLIowXF7mh\nmgN2eeMNixUrQlm6alLdlzWYP0ObmuXnRwusNJKN2dlURPr6MhdSmj//9OkkFEWxdCAdNqxo+ZCE\nBFr7WuK3Xj2GYlzqa1QMlLW2D0VBdDQ3ubAwntumTRmOc6FVk9ehvJP+OyJywMHfvZL0NSQlccRe\nhQrUXS9YYId/o6Ic+v0bN7IwsX59koYx9gqv8MOHXTNpcnIY/H333UI7R3IyNyYRS3hq6FAg68Up\nNJt+/901k3TRIkqRtm8HTCbs3881V6nCTo6FsGMHtaqxsc6PDTDuVSAzeugQSd/Xl9XDpRHrNxhY\nFyTCGrlFiyztFAYMKNoQFVVl0e9TT1naY7dvzxoFZ9L+kkZpekrOEBfHHEpJrsFkArZtY58jLUE7\nbpzrI0G9AeWW9EWksYhcFZExDl5zfUg/Otq9rNj27WT7NWuAhARER/OfIiSpQtW4aWkUJ3fuTLfA\nRhVVWhq1yyLs0HD5va/4j/BwxpSc4cIFS2uBSZPymX9ffkkCMpmYQK5SBWjaIBvpzTtY2M2Z5W8y\nWZIRbdsCcXFITrb0SHnuuQKkbDJxmoeicLdx9htmZvJ1HTqwzt/cEycnh0oZf38qWfL08ikplLUs\nXMhArTNzNzeXG4uNTfTSJUoJtT8ZDFQVtWrF7zZiRNGHqGRmMkQxdKgl1NatG+PwTpqhFhvaht+7\nNz2OPXuu7yagtY2qUoV1CT//XLR8kj1cvkxPTZsmNnAgsHVlCtQk7zb/yzzpi8gMEVEdPEwi0rTA\ne+qaE7kLnRy7vYige/fuGDRoUL7H8pKs6tm1i7KBdu1cH5CqjaJSFFbVgNZdly4WosgX+rh0yTI+\nyEHmbccO8nxQEHD0jmeg+vuzzN6V8thff2XQvnlzhzKU8+e5/zT1O4uU6uFQGzVyrSo4OZk9hRs3\npkuiqlBVFi0HBPCYkZFWr09N5VoqVuSLnHkt8fGWzl6zZ+f70/Hj3Dfr1+cGk5oKugJahdOoUc5Z\n+cMPuTHecQeF3I4yg6oK05JvcfyhWZjXdTlulz/QKTwR8+Y5IK60NIde09WrrHm46y56L76+3IwX\nLiyZ0ZgFkZzMHMXdd1uSvyEh7PU3axYvkdJUAKkqf6KpU1nzIQJUC0jD4IEGLFrkouQ1IoKG0pdf\n0iW2YdJnZ7OQuW1bIECysTl0KNKq1IWx712MRXowAbB8+fJC3NW9e/cyT/rVRaSpk4ef1evriMgp\nEfnahWNfv/DOwYMcsePvz6vUmZheVUkcrVszwPjzzyQKE63G2rXpfk6daqWvPnKE77n9dpKUHVMv\nLY0JU3/Jwcut1yPxtQ/4Gdu2Of8e//zDu7l5c2oR7RBhTg4N5QZyHi8/FIvcbr0Y7nHWGP6ff3hu\nRo6kaWW+c//+m9ZsxYq8AfPus4gIZh1HjmSsw1FvFYAl+RMmUJs4fHg+eZPBwP0yJITn94cfAHXP\nXgbPmzblF3K2OS5axI26Th0u1BHrZWbmVZCZ/Pzx5p3b4OvLfWbSJBua7/37GXQODqb43EG/oPh4\nYPkb/2JH+GP4VkbjG3kYsxovxAcfONCSX77MHWLePLL5Z5853ugyMuiNfv89jF8uxrn/LcAHb6Wj\nXz8usVIl7oGDB1MZdOKoEeoPP/K4c+cyceUsHrViBa/lhx5igsqBsXH2LPDtpEOICmqKdAlGYkAt\nvNfyWyxe7ORnW7HCIkV76im77oqqsv5i2D0G/FaTybKYm7rg6jonfZ6uM8q8pe/WgmnhnxKR70RE\nceH11zem/++/NMXefpsW7bRpjsnfZOKVHBFBc+rOO/NCN9eusdIyIICclNfkz2SyaAbDw2lh27FE\ntm5l3DwkBPjh9eNQ27Vj+aIr8pvUVPZK6dvXYVx9wwb2LalXx4jzj7/NTcwVvaSqUnbUqFGep3Pt\nGnXrWlVwvlOnqoyZhIeTrR3BZLIcPyyMRG11jqKjucGI8Oud23KG5+Tdd/n6hQsd5yl+/JFrfuwx\nbo6OyF9VGV8aMIBzDW7tgaX3rkSNKgb4+DC8tXOn1fJSUrhZVa5Mt8RZ3uTYMeS2oTYxJqQZZvq+\nhs6yH23bmDB9eoHePADXrSUdmjblxn7kiH3y37mT4nQRxkFmzAAOHEBOphF79/Kr3Xknr1MR4JYa\nF7G/3jBABGpAADP/GzbYrwzTflcttNi7N5sVOsrwX7uGrGGjkBMYissV6mOpjMbd/hsxYogBq1bZ\nyd389RdN+Uce4W/81lsO3aMzkSasvnUm+vpvx06fHjh1Uy/ErfAO8i83pG+28E+LyGbz/79Rezh4\nj+cSuVevWsjf1Wzexo0kzUWL8p46fZpNLkXo1ufT98fE0Mx69lm7h7x2jT21WrQABvbJQer4V6nR\nc9VlXbqUY6wcyItiYhhn9vEBvh6zC2qTJq4Lmk+eZFhszZq8p374wcJ5uwreZzExHCQza5Zrx4+L\no5cwZkyhP61fz/s/IIAqpcxMMIz2yCMsa3XlHJ05Q/Jv0cKxBEvbwfbvB0aNgqlRY3w/PQItW/IS\nMTc/pfOmqrwWsrJo7Q8ZwoXaayaWm8tr7cQJZH04H7Ft78KVkIZ4JnAxOnTgeXzmGX7fzEzwf6ZM\noTX+/vs8nw0aMMBt7/izZtGDmj2bF+JNN9E6NyMjg/vJ//7HMNogWYtF8F6r2gAAIABJREFU/mPx\nUq2l+LPpaGTUrA/Dnb3tn6O4ODZxO3iQ7m3btnzYu460c5STg4SvfkFEmxG4GNAQA+VXVK7MsZiF\npJnabxAfzw2+USOnGtv4eC5nUOh27JAe2NNotMflnuWJ9B8xx/etH6qImBy8x/PqnatX3ZM35uba\n9A7WruV9GRjI+zvPmlFVl3RnmzezP0vlysCPC1Pcu3BdyAcYDHRsFAW4u1sqLl104wOysgp5Hxcu\nMHTu40NCzmdIm0zujY4E7LbKzMgg//n7kwPWrzcThbtVUu5WycXFAbm5MJmY13/gAW4+/v7co7Zs\nKWB8JyW5py9MTUX2mRhs3syIoCZVDAriAJPPPwdioqw+ICPD+dBg6x8hJ8dhuWtyMrB2jQljx/Kz\nFTGhnd8x9Oiu5nG708T2hQvu9Y5IScGpPQl4/XU6hF26MH30/vt24v8Gg8u/W1oaQ1gznvP8MJVy\nQ/pFeXgF6Zcg0tNpSfn50TJ0JURvjeRkhk9FGEEojerP7dsZ7q5Rg7NYigOjkRucry/b+udL8pYw\nIiJosGshH09MrUpMpPHdogXyhFfvvec8jeEKVJXRx9mz6ehpvXmGDmXrim3bSnee7enT7NA9aBDz\nNtr3e/hhqpOKWy1bEKpKUcPo0VQ9+fvTYZoyhY73L78wt/vee3nRxTIDnfTLEelrOHGC4RQRXtTu\nGpkrVjAOX6uW6/NX3EF8PHO0/v600otLJvv2MYoVHMxURmm516pKMmjShB7G00+XbFM0d9axezej\nTOHhJOi+fZkuKkoRny0kJzOM9sQTFslixYpsy7BgQen0SNKQk0NCfu891qeI8Frp25fh/JL+7KQk\n9kbSxG8FH4MHl+znlTZ00i/DpK+qRa+GVFXOBbnxRvYaX7zYPTKMjSUxi/DGLyky0WAyMR/q78/C\nouIWv6SlAWPHIs8Stzs+sASQk0OLu0oVKlRmzfLcnOyrV5ni0ZqmBQWxlfRvv5WcXNJkYrjl3XcZ\nUtO8gObNGebfsKF0+8qfP0+y79uX14vWi2jqVOZfS2qTN5ks7biL0zrD09BJvwyT/po1JMTitARO\nSGA+TYT5OHdaMagqG1HdeSctyqJUjzrDoUMMRQUHFxLRFAkbNzJ8VLly/oKo0kBiInPkvr6MS69c\n6dmWBVFRFM9Yi2kmTy65XvIaUlKoIB4zxhJqCgykYvbDD5lbLa3znppKT/Shh6i6FeG5f/nlwhuA\nqtJ4OXbMvfW8/LKF8LXeSX36cCMtCy0pdNIvw6T/55+WEv7BgylkKSo2bGCiNyiI9STuNOs6c4Y9\n4n182K6gpGO76emWYTDDhxe/34l1bmLo0NKvTP33X8ai69XjJr1hg2cbdmlFS5MmWby1evVKdpiI\n9Wf98w+vqX79LFXBN91ED/GXX0pvvoPBQMHS008zRyTCzw8J4UYQGGghb3d6HZlMTJyLsDRj+XIq\njjTv5vPPvXv2gE76ZZj0AUvHzIYNaVGOG1d0EktLY7WpojDk41J74dRUQFVhMLDU3s+PxPbvv3Ze\nn5Tk3h2RlZUXG/npJ4ZM6tWzIcUsAn7+mWTQsSOPXdrYscPSf6hbN+CPP0r/M51B6yU/bpyll3xp\nbQAAf/oNGyi/b9WK4S9fX56Pd98l+aoqr8U9e5i8ffJJqqKKA20DqFLFQvTaIzDQ/c6vOTncyDQx\ng6ry9xw6lPdP27ZUo5WG2KG40Em/jJO+huxsKisqV2bJ+4wZ5jjqtm3uBbDXr8elByfjoYa7UMHX\ngNmzncSjz54Fbr0VePVV4OBB/HVARbNmvJE++cQGaWRn0+8eOZJM62wDMJkYhB49GlizBjGRmeje\nnQMppk2zURxpMlGyM2eOS3Kdy5eB2YN2or5cwJAhrvdnKypUlQTWti3y2g4Vd8JYScHWBtCvH0NU\n27aVTsuE8+eZ+L3nHosqx/qhhU8mTSq5z5w3r/Dn3HpryXXNPHuWuYzgYD6efda7Rk/qpO9J0s/I\nYIzG1S5QRiOzU2PHMiB9+nShOEFiIq31ypVprW/++F+oVavS73z2WecbgKqyMkUEqZXqonu142jZ\n0slEp02bLP2T165FRoal7/2AATYkg9HRFn97xgzn3zslhYJps9zImGvCxx/Tq+jQwUZYKzmZEhpt\nAU7Or3rmLLIq34Azvk3wZcA4/DjznOPwyx9/sLnR7Nk0R52ZidHRlExZ7VAmEwtzmzblMl1tuXS9\noG0A06ZZ5udWq0aJ5OrVpRO+yMkBvv++8AwGEVr7Jdki2nqIzeTJLGj39WWtw/DhwLp1RWgOd/w4\n2d188SQk8PxVq8Zjjx7N/IGnoZO+J0kfoNnh48Mg49NPO5d5ZGezY5UIg/B2/MfISEu89rmOf8AU\nUIFXnyvi/Jwc+tt16iBpyOPo3vYqfHyo8bfLb9pw1ZYt81pRbtjAQp5q1WyET7ZuZcl8eLhrGdUT\nJxg3atKE0hiTCQcOkDSDgtiuJd8hIiK4sYSH04RzFqc4cABqcDAy/Cuhv2xwntT+9luLGeqsrUNO\nDj0bf39qDOfNy/uTwcBuD/fey0MNGQIc3m7u4Pnqq5QwbdzomIFyc/l94+NLxRxXVSZBp0yxJIGD\ngrjmZctKPidiMFjaaYjw9tA2giZNaPVv2+YmKRsMtA6uXMk7RwsX0sLXrum4OIZsbrkFEFHxYZuv\nsafDs0ia8gFjgc4MposXmbkODWWSyxy/S09nYVb9+gxp6RW5Xvy4buGdJUt4ZdevT3mDMzMqI4OS\nmREjqE3LKwMtjHXrWCk6wudnLB68GoZOt9KsdCYgj4+n3GP2bKiNG+OHR35DQAAdhn37bLxeVelm\nHDjAK3vqVCA3F4mJHAoiQisxXyHstWuMp9x1F0nRTtVrHhISaPWPHs1qq6gopKezRYBm1OerOTh8\nmN/jvvv4emcC7vXrgZ9+QlLrblgbPBLhQbH44AMHPPrFF6xUatSI39eRR2E0MnPp729pG2H1m+Xk\nkPw1h+ahHlFIDzeL0Dt2dE44S5damoI1buw4mKyq1Oj260cFwMiRzttebN3KfjNvv42EF97F8qd3\noGtX7vOKwjGPM2daKXNOnOBmO38+d+R16xwfPzaWSaG33wbeeQfq/AWYPFmF1j4kI4NV5U89RfVV\niKRhfsBzOFb3LlzsdC9yn3jGuS50xQpLDKl+fYexvCNHgFdeNuGjAPYsNyh+OPDaahgNLnRqbd+e\nu9SQITyQGbm5xRhUVILQSd8bSB9go/lz52jGhIU5J/+0NFr9R4/SYu7b167vqPUCCw4Gat9gxL6H\n50MNCyNpuZKpO3kSuO02JN/7GHq2S4GPD11iu/dYRgb7rHTqBEREQFXZUyw0lM5JoSSs1h+5cWP7\n/WEK4scfacV/9x2gqli/nnHo6tXtDH3/+WeS8/z5zr+zyYTMz75CQqUwzG74KTq2M2rt9QsjKYm/\nxRtv8PiLF9uXPmnNwQ4fJiG0b1+I/A0GqkFatwZCJRX7qg3A2VFvsB/R/fdbNfS3gePH6fo0a8Zz\nOW2a441uxQo2KvPzI7MuXmw/qG0ysUJJ21hGjgTWrMHls+l5nkpwMPIqZZ9/TsXJFxZC1Xoq9+tH\nzaqjgo59+2hViNBw+PRT/PBpQiFBgaqyLmD2O9lYUvNFQARJUhVb6o/BlskbkXzFgQsQEWHpTBse\nTvfFQfuI9HRg18NfYmPV+/GrDMQ//m2w7t5FiDvnYIO5epWypNWrucEPHZqP/D0NnfS9hfStERdH\n8g8PZyjDmQWjqiyNbdWKppCd7n/R0bxXRYCJI+OQPOAByklcCSYbjcCcOVAbN8aKx35DhQq04Pfu\ndfCejRtJPuZe9ufO8eMUhR1AC0k7T5zgTTJpkmtyiosXSSZmLyE+ngnB8HBqxAu110lIIHH27Omg\nf7AV4uMRP/ARHAvujPZyEOPGOZEXRkfTC2nXjpaxMzggf5OJT3XpYIC/5OC+4UbsemEVTN26Mybx\n/fe24xvXrnHzv3yZyezWrfl9v/3WthERE8ONcO9eSmrCwugyff217Q0gMpLncPVq9p2oX58xvC+/\nRNb5OKxfz5STlgcY1SMGB2vfjd1jv0XW6Ce46/fty3hHvu5/ZmRlUQj/xRecGdGmDc/n9OkWaU8B\nXFr6O34esx6vNv0ZP8hIREk9/Fb3cfw6cROuXLRxjjIySMIJCdzIbrmF4czFi+17a5mZOHAAeHVY\nBD73HYfz0gAbOr2OQ79esv16DarqdeSvk743kr6Gy5cZ27WqesrKcqChz82lxu277xwedts23ku+\nvsDC4ZuR/eZM19cUEQG8+CL+/UfN0+a//LIDjk5KYscu881kNLJ83s+PoYFCPbeysyn2d9UPVlV+\nZ7OHoKr8+pUqUQu+aZON96xcyViKizD+vh17B7yF0FAWNDnoRk0cOMCYk6vB28OHGXKzQTiqyuZp\nffogT9/+zXOHkHP/w66VKasq1zN2rGs9M0wm9nB47jnKr+wdU4PRyOvzf//LJ7HRrPGZM4GOHVT4\niBE+PkC320345tm/cWX8m1CHD3e8bg1ayW3//k5Lvy9eBD7/IB3TW6/AbxVHoL3PYfTrR0/Tbn8e\nbbETJtAjdILkZGDhzGTMqPY+Jskc3HEHed1hbYtG/i++6PT4pQ2d9L2Z9G1g6lQa9Hn98YuInByS\nb2AgddlWnYldhsFA8U1AABN8f//t+nsPHmRIIDCQRl9J68GjoixE+fTTJdMm4uJFi6fUs2fxiuGK\ngqNH2R4/IIAFRhMn2jaWvRGXLtF4HzzYEiEKD2cIf+vW0hmjGB/PQqnu3ZFXmDVsGHndXV2+LRiN\nDCVqtReNGzN94c2FWYBO+mWO9A8csJSX33578Qt8zp6lN69V9RZFT3z8OL1XX1/3GqRlZpK4tDL2\nku6Ho6qWSVcNGxavXYU1Nm3iDR4ayghESfcdcoa4OJ7n6tUZKhs+nMTpaVWIq8jMRF4Y6NZb+ftX\nrswq1+XLS6dCNyaG0a72nBeDSpUoK966tWQMjv37qavw8aFaberU0hlBWRLQSb+MkT7Am3vTJhKt\nCEOqxdH/qiollXXqMBn38cfuK/9yc4E332TYpm1b90KXmzebFRkh3IDOnXOvDYQznD1rsfYmTiwZ\nqzIri+cpKIjdRr/++vr3XcnMpPWsqaOaN2eIurTaGpQGtJYQ06dbCNnPj2Krjz5yLfXiLiIi+HlD\nhvDzGjbktVsSBVTnzjEy1rs3PYtnnimd71Ac6KRfBklfg8nEfF6jRrT4Hn64eBduaiov2M6duaEU\n5WsfOkQp+m23UTHk6uaRlETy1LTZfn50/wcPdn2IliOYTMyJjxxZshZxVJSl82LHjgyHX2+oKvM0\nI0bwvAUFsb7OnXCbtyA6mt7ZgAEMYzVrxjyrzdGNxYTWgnrMGBocisIc8/ffFz/8k5xMBWqNGvSA\nH3zQxbYm1wE66Zdh0teQk8NYYqdOvHhfe614IYe//uKN5utLaaa7McqsLNYV+fhw+pCrbZFzczlw\nvGA1pqsqTldQWiGQ3btZHSzCTSAqqnQ+xxliYxknr1ePa+nUiYlnZ/PmvRFax8wHHmA4RoQGzuTJ\nzB2XpGeVlkbxjjZnokoVhmiKWyWdkUGdQYMGPO6wYZ4Pw+mk/x8gfQ1paYwxBwbSav7qKzfCJNow\ncDNyc5mkDQykxb1li433nDnj8Aret49y6MBAuuqmI8ec7ka//mpN+CpaNDW4vul4uK+tyUTiqFWL\n1vbOnZ5bi8HAZP9ddzG0FRrK2rC9ez1POkVBdjYrvJ96yjK0pVYtGhfbt5dsOPDUKR5Xm0HQvTvL\nQooTFszNparM1dHMpQmd9MsK6btxVUdFAY8Nv4bH5Cvc0zwC27e5cJcbjZTcjR/PLJuZaSMjLRf/\nI4+w6DYPq1YxIPrsszTHbdwVGRmWZO0Dnc/AcENtNjr58kub9fuqykEcIkCVSkbsl87YWHEozkxd\nUuDDbSA2lqbUW28xtuFsE8jI4M7oaoN3k8mljeXaNbr2pTk4xB2cO8c6Lc3abN6c5OPuxDRvgdFI\nAcPkybz8RFiYN348C/9Kau/PzSXZa/mg2rV5Hi85keZ7O3TS9xTpnzjBbGxsrGuEExvLQOeoUSx2\n+vtvp+879faPMImCi1IHPzV9DacjnGwc6emWGEXXrnmspaocYFKlCm+AH36w+ui330aegNyBXGHb\nNpLO/wVugUnxgRocbDfI+ddfvMF27QLOrT6CDJ8QQATfD/vJuTLo0CHGuEQYCHaGtWsZx6pViyzi\nKAmhqjxmv36Uz6xf7zyOtnUrYxHuDmIvBZhM3JsffJBJRl9f9vlfu9Zzk72KC1WlcuaFFyzjDOvU\noaGxe3fJeQDHjlFtFBLC8zZ8OH9WVQV3h1WreD2XgROpk76nSD83l9WbItTeLV3q/D0xMayYFKGf\n64JJY/pkHoy+/jju3xaPNtuLKVOcxOgvXWL2rG1b9ti1qmiJi2PSS4SVr7Gx4FV///2s5rz5Zoft\nOFNT2S3xrepz8UP4qzA0CLdb6ZSv/uenVTh6y2iclkaYedMnOH7Uyfdeu5bFDOHhtOSdbaqLFzMD\n2qoVW0s6gqpamv3Uret86nhcHKtiNSG3syDx3r08uePGAe+/73wcWXQ0zd5TpyjbcTF2k5zMhGnH\njrSWq1ZlPUNJWsrXGyYTT9fEiTQaQkPZoG3GhIs4v3QXk0vJyc7P0dWrPBkPPcTA/jff5HmxV6+y\nTuyWW5hn6NSJ3oBh+y5+oJ8fs8ElPam9BKGTvqdIH+BV+swzNKGbNaPuz4aleemSVSLu/HlqNO+/\nn3esK+LzlSuR+fseXKrVDl/7jEHbuvH4+WcH1/6lS7zI332Xd02BSs6ffmJctUoV82zdLLN1s28f\nifO11xxaPL+uU1HnRiNaVLqIS23ugjpkiPMGcNnZOLI1EesqPYiDlXrg85fPOrbiLl2yhHt693Ze\n4btyJV2Mzp3pTTmKfZhMlMdMnsxNeOZMx3KPpCQet2ZNxsqcbSzbtlmmfUye7FiDaTDwNVoi5OGH\nHZNacjLjdO3bs1nc+PH450guXnvNEv5p0IA/4b//giqBmTMZwps8mR6Oo8Z4Wkn0m2+y+m/2bIdz\nDTZtAjZP2oCsMeNorr/yivMJOYcPc+2dO/O3Xby40EtMJh7mqaeAapWNeEtezztHWf/nQjY1JYXH\nFqEBdPhwoa/522+Ulmqyz+WT/4ZarTpdjTFjvKO7mg3opO9J0gd49WzdygtkzBib5D90KEl27lwz\nt2iEun8/A+CDBrlWHmowIH7qJ4gLDsNT8jn69zE6f1tEBD/jwQfzxeATEy2zdfv1s5KKZmay1LxN\nG4eawcREbeSciheb/IJdNw6D+vNKp18hKwtYNnwVzkg43m/4GSL+dcEsXbWKsg9X5kAajSzjDAtz\nXLBgMnFjTE5mLqRJE5KdPTP52jXOTtixg9V1zsj/5El6glOmkIUnTnRMIj/+yAqnrl1pfn7xhf3Q\nU24uM5WKwo1ozBhg61aYco3YtYtGbtWq/G3btwc+n30NafeZXbwqVagWOHLEPnFaJ3J8ffMG7Nh6\n/aRJgCIqHlW+Qbovm7Nl3nM/u3I6CpVcukTG9fGhWuCNN+zKxLKyWIX7Xpc1uCqVsEu64XSl9vhr\nzHxkxjkIu+Xm8tzMm8cNplcvGkAFfuODB3l7+PoCt1b6B7MmRCNl7te8l72Q/HXS9zTpF4QN8j9/\nnk/5+DCi8PnnVjlTVaWV2rw5QwLOLGYAiItDzJ2jcbhCZ3Tx/QsvveQkNG0yMRZg1dVSw/r1jKWG\nhFCalnc/7N7N3gyvv+6wRHfFCuQZqQFKDpqGxuL/+uU4rez9c30C1lW8H9t8emHR6+edx25TUihf\n6dwZR7896txBio/nSW/XrlBXOYOBG1a+0QRnz7IIoFMn55Y8gNOLdiCuZU+oPRyQv7bhZGSwTXGL\nFrQA/vjDJoEeXHoCV5NNzBc99xyboT35JENutgh682b+7aef2BMjLIwb9qFDyM5SsXo1N3Ztluyr\nzVdh7+AZSH13Hi3tZs0cEjq2bOHnf/opCbNxY7L87t35iDM2ll9v9O3nMF95BoPlF2yoORqpVerh\n2r2cmGbTkzIaKQuLjaVF1LEjc1Jz59r11JL3n8Lnn+TgvrYRWHrjZET5NMC+Fo/i9FI7siZV5edo\nov6hQ3ldL1hQKE4aFcWvV7EiHd6nx+QibubXXkf+Oul7G+lrsCZ/s8V86hTJRlHIv0uWWBmuOTm0\nTMPCyKQuIHvzDly+8Wa86fcW7rqL975Drzc6mqGlAmLj1FRah926kQvy+sFkZNBlb9vWYa/55cst\nxK9JNYMCTU5zpBkZwOK7f8YZCcdzrX931CHXgq1bcalyczwuX+Lxx10Yj7dnD4n/lVfynoqLs7QP\nGDq0QMXlvn20tocPd3gytfz3Q/V34LJG/s6+sMlEC7hnT24uVo13DAYa7SEhDGkcOQKzW7SMXkXb\nts4rx5KSOFmke3eylnnyTWoqU04DBwJ+vip8fBj5+G5OHNJnz+d6tOE2ttasISGBOZa772Y85Lnn\nCp2jpEQV33zDorzQgGy82Gwd1lV7GKmV6yFt0APOY+UREYzDN23K2LqD0NKpU8CUydl4svKP2Cx9\nEBl0M9ZN2ua8xuXMGXoyDRpQhVYAKSnc5268kYbaA8NzcWH617yXS3LuYxGhk763kr6Gs2cLMdOx\nY8z1idDoyNd8LSXFvcqg3Fxc3B6Zl1MeMMCJQaKqdt3orVu55wQFmXX52v3uwpy7++6zTFwUASaM\nc112sfeXeLRtkIygIDtzeQvAlJaB796LQqVKvDHzqZFswWAo9J210HXdulTCvPaa1b6mqi71xfjz\nT0vfo2FhB/Hjj24kUQ8dKqQJvXiR4qI6dZAnwPruO3OUJDLSedLZGlFRNkuhExPJc7178/eqUYOb\nwfK5l3F1k4Ne/wWRmup0iltaGu2X4cOBSoE56Cub0L6dihkzXGg0p8l6XFBN5eayAeaYnmfRQIlC\nSAhTNn/+6eS6SEkxJz5sIyuLDoGmvRjYNxd/fXXU43USOul7O+k7wIEDeeNscfvtTnrbu4BffmEl\nZ2Agc7iuNk6zRloac34irMZ1ZTojwJyAvz/fV60a//v4464rHdPT2Rm3Rw96HK7MU710iZa6CI3P\nolTRpqcznBwYSMXIkiXuq1/27WMRlQgN7BUriqegyc1lDFvLQ9aowfbXJd2R8/Jl5lC16VnWs1ic\nDUFzF+npTFsMH27p0tmuHSvRS3LoeHQ0yzwaNOD3at+e36c4NRfaYJw2bRh90kn/+pL4LyISJSJZ\nIhIrIktFpLaD13s16WvYvFmb68nIiwOP1inS0oCXXmJSqkULl8LTNrFzp2UyXXAwb56RI0k+9hpQ\nvfEGE4hRUbQmQ0O5CdmsBraD7duZsw0MpOLRld4/q1fTYg8JoYdSFG33hQuWtssPPli087Z3L5Pi\nikLC/vbb4jeHO3mSUZROnbi2Xr0Y8SmJ1sLWiI1lvrPgBvD1185r6txFerrFA9D6Nd1+OzeAkprX\nazRSnaN5YtWrM8JXnPYaquodnTfLG+k/JyKdRaSeiNwqIntEZLeD15cJ0gd4kS5ZwqSqnx+t7eLc\nAEePMjwgwvxnUY516pRloLWIZY74woW2X6+q+XNjFy5YJHFjxzoeQWuNjAyGTn18SHau9E9JTWVF\nZ7du3KAcTSV0BE2co3U/LTQkxgXs30/PQ5NPzptX/B7t6emMy2vVpVWrktDGjaPQ5623+P8feaT4\nxBQby5h2d/OQLz8/bmZfful4dG9RcO0aN8cBA2io+Ppys1m6tORaXp8+zTKUSpV4TQ0ZQg/W0xZ7\nUVGuSL/QFxAZJCJGEfG18/cyQ/oaMjPZM6dSJT4+/bToVp3JxBv1rrto6SxZ4v6Fbq3OEaH01B1X\n2WSiBRccTIGJK1MINezbR2/F35+xblfCVfv2MWygKEyIFiVMYTIxTxAeTpIYM6ZoswKOHqXX4OPD\nJO0777iQeHYBkZG0Wq1/Fx8fS07FQZjabcTF8fe7804e39eXsxMWLiw5q1xDfDxFZlobD63b6IYN\nJVOZm5bG47dsyeMPGsS6raKEQT2Jckv6IlJNRH4QkZ0OXlPmSF9DQgLd+htuoFBi5UoHhJ2W5pDN\nr1zRNPW8Yc8dvsqEgguBZ1UFut5mgogKRVHzYv0OiUVVqZqxag155oylB9DYsTasODtuQHY2VaO+\nviSDP/90umQYDEwIV6rEePjixUWLsWuCqho1GG565ZWidWM4e5Y1fBUqWAa3uJOTtYekJIpcNA9M\nk+GvXVs6k6wuX2ZiU5PX+/hQErpggWtKY3cQFUUxUatWyGvN8PLL+XPTGRncAPfsca97glZao4V+\n6tZlKNELOm24hHJH+iIyU0TSRUQ1h3eqOnitd5B+QoJ7Jvaff3JM0N9/4+QJIwYO5K/Vs6eddjfx\n8fTFH32UzcTt+OC//cZwQ0AA0KPaMeysOhhnhr2MjB/WOlzfoUOAr48Jryvv4Gq7HphR8wOEBmRj\n5kwHMfc//iDD9e9PBk5MhMlEzyUkhBL0fLH+LVuo0375ZTaYKXAXHz7MImZFodou/Y9DvFMPHLC7\niLg4FueKAH06p+LY30Uz6VJTWWMVFEQr8f33ixauiYvjxtG/P0MmDz7osOuFS0hOppLQ15ffU+tf\nU6MGz5MLLZ6KhPh4WvtPPsnP1mSgJe0BqCoLrSdMsAgERPKHHUVosRcFJ07wtvH3p5Hw0kslsyGX\nJso86YvIDDOB23uYRKSp1euriUhjEektIrtE5FcHxy550ldVpvJ/+olZNlcyjbt2MVYwaBB9fGdl\ntKpKM1+EVZqbNmH9et7cPj60lAvdWKdOWe6Kd96xe+i0NEtc2PoRWlHFokX2l3TpEqC++x4gAmOX\n2/DmhPi8mLvduPeSJRYmio7Oe/rcOUvc/MknrSysr7+23NE2THobkTZoAAAgAElEQVSDgUW5wcE8\nZOTwV82LD3U4JHjbNqBDszRs9++D87W6IOupiazydcSG6emMa/z2G2M7qopLl5is9vOjVPSjj4oW\nektN5XvDw5GXxPzpJ/ennWm4eJGWcIUKPJdHjrBGS0uStmzJzba0ZgQkJDCv0KdP/hDQF1+U7AaQ\nnc38lLVnoz3Ony/iQc+eBT77DPErd2HaxGRUqsQN4KmnSmb4T2ngv0D61UWkqZOHn5331jVvDF3s\n/L29iKB79+4YNGhQvsfy5cuLftavXGGxjAiDta5ozrZvp6no60vtmjPzy2RiGf+NNzKucfgwcnPp\n8lauzMe8eQXc+N27mXFr2ZImi4PJG3Rt1Xw3zsrZTioOVZVa0AULgPBwRL7zI1o0V9G4MfcZm6Q1\nZQrv/vBw/tf8vU0mHqZiRRL4hg3m10+bRpM+PJybq43zdP68Zf1bwp6EseaNLLN3YDbn5ACL5l7D\nfp/bABFEdrwfhiQnhUJ791p66Nx5Z573cfYsrUOtwnr+fCAn08iTcOutdC/eeMNpRtW4YTP2v7Ia\nY9vuQ325gCb1szFnjoNWPQ6umejowpJfg4Hn9YEHGJIT4Yb/+eclr8jRoHkAWh1Az57MKX3zDXA1\nRXXf7di2jRv03r384bOycOgQN35r8m/alM5xysb93EUHDaLhtHGj88/45JO8A2W//AbmzOHbRZj0\nLa43VhwsX768EHd17969bJN+cR4iUt9M+t3t/L30wjspKZTHtGzJzOHq1c4v6N9/JxkMGABTt+7O\nr6bcXJbIb97M4Ob48UBSEuLjWUHbvTs/Pl9LgrQ0mp9vvME74bffbB768mVLB2MRoHZAIq7Va8Eq\nJVfM1wsXgL59YRw8BB+9EgcfH6pmCoWftHNy+TI1kT175hOcmw+Djh3ZaywxQeVmdeEC5TP9+9us\nNlNVJltr1TSiR8hfWPPCDqi33OJUqnQ5MhXbmo3FVJmOmIAwnJr4qeMA+JEjTKy0bs1MtFXjrlOn\nyO+KwrDZokWAcc5cPlGlCp9w1sitb19ABKqiYHav9fD356jKp5+2cS737eM6GjbkNffDD/aPDfA8\njx4NPPggch59EvseXYD+/UnG/v4ktu+/t7INkpJoLDz7LMNsc+Y4dj+ys3mdjRwJPPYYJVdWO9aV\nKxQSaJ5lhQAVC2/5DBlV68DUuAmlVs5aG1y9yutAu1B//hkAo4daiOeVV7ixBQTw8dLAE8i6sT7y\nikVccQO++Ya/c3g4MGkScqLi8NVXLFQW4Sb2++/eofgp85a+y4ulVHO8iNxiJvteIrJbRE6JiL+d\n95RuTD89nRftkSOsEnKF/E0mJCYC99X4HZdqd0Du0Ptc6+mRk8OOh2FhtJiNRhw+bJFlPvCAjeEQ\n//xDL+G++2z2MtEMnMBAEk2gZGJ9q5dgaN7KeUtggN/zq6+AsDCcnb4UrVqq8Pdng0a7PLp6daHm\naSYTD1O5Mu+7FSvMp1Cb+N6oETtF2jhoUhJ5vkUL4I5bDYh++ROeo08/ddhs7cABYGD7OCyQpxEd\n2gKX5zvIlJ86RfJes4Y7WwHy/+cfzrcV4R616emVMHzwMeNwYWHs2WDPtNa6bN5yC9CiBbL6/B+W\nPfgrbqptzAv9LFtmleKIj+eHVKhAgnr1VcfzLM+coRckwuqiefMQf/wyPvnEYv2HhJBEAdBl0DLu\njRrRnXTUsTQ7m2SvZZEnT7bZyycmhj95x45AF9mHaKUeMvwrIaV5FxjnzXcsazKZuLm0bs1H//7A\n6tXY8KsRAwZYNADx8bxFmjQBbpQ4rG48GTtGfgZj0+bcmJwZWceOMVkzd24e+RsvxmHFCotj36uX\n54m/PJF+axHZKiIJIpIpImdF5FOvKs5ykfxTUhhzDQww4ZnQb5FcswkMzz7vms996RLNy06dgP37\nYTIxFF6zJsm7SRN+9L59VDYkJ5q4SYSF0e+2krEYDFyu1hJ/0SISb7+qB5DS4Baoz050TVx/8SJw\n990wDrgbsyZehK8vOaxAN1sLkpNpGd56a76EwKVL5FMR/jdvE7t6lfKXtm3tCvB37SIf+PgArz5+\nBTmjx/D1eWxWGForhu41/8Van8GIadAV6ZudbHaqapf8jx5lwZGiAHXrqJg7F0g/H89dsGFDCunt\nNRi6cMEyIX3kSKiNG+P4A+9g+O2xeVHEV14xG60mExeekMCdu2NHnssFC2yTZ24u37x3LzeJxo0Z\nBvz6a5w7fBVvv11ATWU0Uje8aBHDc02bku0WLrQv1N+wgWb955+zrLpFC+psbZRWnz4NfPBaIp6p\n/ysGNjiBT4JeQkKlMCT2HgF13a/2N2vtHO3axSx4eDjDgQUyr9ppfPopFb6+QJVQIxb932pkdrid\n3sUvv7g2lc2K/NXYOGzYYL9G5Xqi3JB+UR4eU++4SP5RUeS+ICUL71adjWs1w2Ca9b5r4ZVdu0hq\nY8YAV64gJYUfVzDBJUKjF3FxjJXfcYfDDFVsLJfuLzlY1vxN5IY3ZXjJGVSVFTVhYbjwxiK0uVmF\nnx8NNLtyus2bSShvvpknltaM+xtu4Aa0aJHV6du7l9bq+PE2G3fl5jIiUbEiUyEbpu+H2rEjN0kH\nM/LS0piq6FdhB/7264zTbYch9x8nZdEOyP/ff1kk5etLK7p6dWDyCwa8MuAwJldfjBcbr8H5n+23\nrQbA3+vdd4HGjZHabzg+HfI7KoeaULEi+zatWlXA8Tl+3DJ/cMQIthC2R56qSqvg2WcZlxo6lCe9\nYAGGduJVlTKgl16i9a+V6jqaExATwx+jQwc+5syxWexw+DANoJtqGdBfNuDX0PuQXKUhrj4+ye5k\ntjzEx1NK1awZf4ONGwuReXQ097nq1bkZT75jHy53Gw61RQtuks6KTgqQvzfMqNRJ3xtJX8PRo+yr\n4KQi6cQJ3sjVJBFLakzCifHzXXMhDQa63y++mPdU//75CV9RCni1GzYw3OPkA1aupHHXJeQ4om6+\nG+o1F8tp4+KAESOQcywC06YxstCypQN9fVoatYW//JLv6aQkJktFqAXPM5BzczncY84cu0uIibGE\nW3r1MOLS9C+4UThBTAzw2KMqRsqP2BIyGD+tUJ3r+1WVa+/evVDxwfnzbENhXUDl68vk+crWU10r\nNTYa2f960CBkLV2BZcss0ZobbwT+97/8bTuy0w2IXrIN/9w1Cerb9lVceTAYKJcdM4Yn3BlUlZvv\nc8/xO7tyoZ46xY29TRu7YnijkTbAQw8BdYJT8KQsxLHQrlg//YDzIVYmE988dCgVYzaQmUkDok0b\nnrt+jc/iZL+JyP3f687XD1jIf9Qo115fitBJ35tJ303s2UPv87bbKHk7csT9Y8TH00LWiMbfn+qS\nolQ0alEYrUagKA2/jhyhoefjw73JXX37pk10TorSRG7TJoa7AgIYBXB1At7Ro5YGaiIk7rZtGV8f\nOtR9GaI2olJ7hIS4xvfO1jhxomVYipabsf6c338v3md4CunpjF7dey+v36AgJvl37ix+PF1V2Wpj\n5Eh6hDfcQNFVSTeYK03opP8fIn3AYjg2a0Yr/fHHzbNs3YAmjw8NtUzH6tyZRVZFwebNjBoEBbk2\nvKogDAbmYStUYDjZ3WZm6emWJnKtXMwxa8jOZlVtUBAtY3eqc7UOntYPPz+HkSKbyMlhCkYroKpU\nif8dNIjnojhElpWFvOI960dAQOlWmD7wAH/TkuyQaQsxMdzsGzXi92rcmP8uiQKq06eZKgoM5Eb8\n/POlV8tQktBJ/z9G+hpycxm5qV6dF+Rbb7luJWu1XatX89+7d3PmuY8Pny/KzOe0NL5XUbiBFMVS\njYigtSzCm83dhlqHD1u6TY4d6zikXBDR0UxpiPAY+/a59r6JE/PrwVu0KNoApZgYWuU1a5KMFy+2\ntBjo2JHSyaIWZwFU5lrPMxDhMLYZM0q+wjQzk+EzzbPo2pXXaml2oFRVWvoPP8wN3MeHg1pWrSre\neQMoLdU6xPr6UuXqLJ3gSeik/x8lfQ0pKczPBQSwEKgo/d4BbiKzZ7OopW5d5iCLYmHu3Uviq1AB\nmDXL/WZVJhMFJyEhFBS5UjtjDaOR769YkRWnrtS5WWPXLkvC+6GHnFvtmZkWrXaFCgwH+Plx03GX\nTE+dyk8mqsrv36cP8iz/mTOLXjileXgiDD8/+CCJ2ceHuZ7vvy9eX/mCuHaNYZi77+Y58fHhd/nq\nK/c2ZHeRmkpB2oMP8rvWqcPwXVGa4lkjLY1eYf36VIINGOBQ/OUx6KT/Hyd9DWfP0rpq356WYZ6l\nev68W7tA3NoD+GDIH/AVAwYNcsGdPX2aSg0r1UJ2NjcQPz/eHPmStMnJVII4aSd5/jxL3f0kF8/e\nG+12y96YGMZ8u3cnobkzg8BoJGnUqMHN5+OPHZPh338ztjx3Lr2t999nx4vAQAo6SqLVwKFDrDeo\nUIHHHTPGgeTVAebNY1hK2wivXqWSUvOw+vVjyHDHjuINeimIxETKGe+8k5txYCCrWX/+ueR7/1vj\n0CFeRyEhtNLvvZe5nOIOsVmxwuKJdetG/YOn9fkadNL3ZtLPzqY0x9UguKoyaP7WW7wrbTDRH39Y\nLNWHHwYS1uxmH4ORI8lkzhIAmZlQu3ZFTnBlrAscjjsD92HuXCdLfOEFfmD79jStzbBO0k6aZBV+\nmj2bT3btSr2onbtFVVkIOSNwOk77NsWpPuOgrlrtmCVUlcecNg3YuhXrf8rIayI3daod8o6IsBlL\n0uolatVisnbpUvtkUXAPS02lDD00lCG4N94omV7z8fEUJ2mN0+64g6e8JLpmRkYyHt6wIY9dvz7l\njCXZihmgB/Thh7w2tBzGY48xsVwSLZJtITWVrZJat0a+urLiJGhNJnrEmlqqXTsX5lBfB+ikfz1J\nPymJd/eiRTRvXSlcmjuXsYgePVjo4oouWDPLGja0ySRGI60qzVId3DISf0onnA1qheQdR53fWAkJ\nQKNGUH18sKLbJ/AREzp0YCGlTRiNDKD6+tIctcoQGgy0fAMDKWXetg28K8aO5XcYPNipKXw5TsXW\n8CcAEZyq1BFR/zg5r1lZllmCdeog40wspkyhNR4WRol6PkREMKbVsiVliQW+aGQklbXajf3nF0fY\n//iHH7hpO2DcxERgztuZqBhsQkgIQ3ElEds2GGgl9+jBddWtS5VJScTnTSYaD089ZWkt1KEDL9WS\nlqGfPMlbRkvE1qlDmenhwyVMniYTDRpzV+/Ro3nugoLY0sLmxrZiBZMe69ZZCr9sQFW5YfXqxU3Y\n09BJ/3qSPkCy17pZ9u/vmh/5wQd8fbNmrklXUlKoEWzfnoFFO2X2yckWPXrBx8OjnGS3Tp1ikHf0\naFy7uSvubXIiz2K3uZelpzMzPGsWJRQFulqeOmXpsfLkk0BKgoHVmZ9+SiZeutTxXW4wIKbnQ/gg\ndBoilSZY+/gax5vXtWs0wdq35wZw4gQiIizx8XvuKaAsOXmSJr2PDwPnNryJPXtY2CoCfNp6AVQt\ngztzpsNTieRk5NzZD/HVmmGj70C84jcbzz+n2s8XpKezzeZXXzGof+yYw+TI0UNGvPPsZVQOzoWv\nL7/bb7+VjNWclcWaDE0eefPNvKy//db1SWeuQL2Whr82J2PiBFNeLcnNN9MptOmcZmYyebNoEb/s\n0aPO40Qff0wXqVs3YMwYJBy9hLfesnQb7d+fh8q7ZXNzLb23/fxcGlJdkuekqNBJ/3qTPkDpSsOG\n3Pp79CjQ8cwOZs8m4Xft6tocvitXeIWtWsWq1cmT7cpuJkwoTPrTanzqWiUtAGzcCLVJU+zu9QZq\nV81Cp06sB7KLyEgGb0eMyGcaap0z69blDa2phxATQ6bq29ex9MVoRGoq8OaoU9ju3wd7agzCifUX\n7L8+KYkb5K+/Mrs8cSLUpGT8+CMtyptuonWcxxX//ssA9wsvcONasqQQc2oVweHhwChlGeKqtUBu\n4+b0EOy1UAAYyjNPqomt1Q6jglchKMCIcePsyBqPH+dmKMLf11li4KuvoAYFITuoMk4GtkUtiUXD\nhgzX2LTOv/+e11r//gz9ObsH/vgD2XcPQWSnB7G61tMYKL8iOJhf6ddfbTg7kZHM4PbqxR1j3jzH\nx8/MZIzHxwdqzZqI7v0IRg43okIF7sO1atHLGj2al1ZYGFCvVi6uNGJXVDRo4JpWduVKup2hoYy/\nJSQgJ4ebmBZuataMoaBr18CLduxYFsc0bMjQqpdPU9FJ3xOkD1ikAjt3ukf+qko2bNXK9Tl8mZls\n2hUezqRqAe/CYGCvG2vJ3twxx2DschvvWld89vR04MUXkdOkFSZ13AkRShzthipUlQQaFkb9oZUV\nHx1taYw4fLj541WV8YpGjVyaeL5vr4rJNy3HGQnHum6zkJ7iJKidnU0vxNxj6FqKEe+9RwMuLMxG\n+/xz5yj/aNvWZpYuO9tcgNkjBhUDDfhh4DcwNHFC/iYTWfivv5Az9D4k1GyOScEL0K9bJh591Eb3\ni8REVr2NHk3CefRRx03BDh0CwsOh1q6N9Ca3YFnnj3BTYAL8/HgpbdxYYA/bsoXFCT4+lAatWOHY\nWt6zh4F+EWR2749V9/+Ids0zIcJQ4rhxFBDknaq4OEuYTZsu4yz+tGgRs9X16wN33420pauwcF6O\nTW81OBjIuJTCSrkHHuAPOWoULXJHXuPevdy533mH7zH3PFJVypeHD2ekskMHRlyvXFa57uRkJoa8\nnPx10vcU6ReEu+RvMIc/tE6Jrlxgmti8S5dCfQ2OHLEU/wwZwsRmeEMTjk74wtJ10pV4wN9/Q23f\nHpF3PomwqimoWrUQp+eH1qynd+98Vryq0tisWRP5j5GSwmBy+/aUxThATg7w4dQULPAdh3/822DP\nzF3O1x8bywx3+/bAH3/g5ElLdW2fPjaI9++/ufZevWyu5+pVxqRDQoCqoQb8MvQbdm10ZvkDwLlz\nyHn6WVyt1hCzQ99EdUnAoEEknjzk5vJDcnKYQ+jWjYUEX39tO/+TnExSO30amDIFxobhiGw7HO92\n2wAfMaJ+ffJWXjfhuDj+9tu3c2eoX595mZ07bYcmk5IYdN+xA3jiCaj16yNx8KNYOGILWrcwwteX\nl+wbb5ijjkbzHIHISBJl8+Y80UuW2I+FHDzI32n7dupmGzSA4fnJ6NPlWr6aiMqVuY9cvmTk987N\npeHQqxfdgi+/dDgzAgA3uS+/5KY0bFhew77z5+nwhYTQMRg71qriPDmZQgEvJX+d9L2F9DW4S/7p\n6bywGjakaenKsM+dO3nRP/poPiv+k094D6kqY+z9+vFXHtUvHteGPkIycUK0ALghzZ4NY8NG+KT7\nTxBR0auXE45buZJWfIEe7ImJlqrgPn2s9oWdO+ntTJrk9MY9exaY0OUA/pIO2NrwMcQdd0Ems28f\nv+8DD0CNjsG6dVyery8LrvKpcTTBfNu2tCjPnSt0uCtXWLEZEADUqmHAxge+gamZi+SfmAjDm+/g\nWs0wLK86DuFyBl27Omj2eOwYWahBA4b1nITE8NtvUIcPR1bdcKxr9zpuDjkLReH5Xr68gHGfkcHd\neOBAhrhef91mJ8w8aEH/IUOgNmyIqBGTMH3wQVQKVW0ngFWVxDp+PDeYUaNsuCAFcPUq8PnnyO54\nO3qG/gXFPNynd286BX5+jCCtXWt1af37r6Vh3PPPO/4OAE/0L79wU7XqtJmURCe6Zk06RPkiYV5K\n/jrpexvpa7Amf1c0cVeu8EZp6mJXS6ORAXStZbINqCrv13r1zBMI399BTdvzz7smnTh7FujbF1du\nHYyWDdIRGGhW59hDSgqzuJ06FSoA2LCB92dwsFUbhexsmqVNmzqdeK6qwA/fGfBa6Mc4p4Th3Aer\nnK/fZKKLER4OfPQRsrOZk61YkeGKQjxhMjHh3LgxNyMb5ygqioayry/Q8CYDkj78htbto486z/Jl\nZcH0+Re4Vq8ltlcfhpskGi1aOJAVpqYyVt6qFRP6zoT78fHA3Lkwtm6D2OZ34vlWmyFCT2vZMhuv\nv3yZCeX27ZkUX7rU8fGTk2k19+gBU8tWODZqBobcqyIggIT5f/9X4JTl5DDhP2wYiXPSJKdl2Ol/\nnkCXWhfQyO88TA89gpQjFzBvnqWffe3aBXoKpaXRY27ThjkjJ9cRAG5Kw4bR+l+5EgCdqvnzLSMs\nR4wo8L018p892/nxSxk66Xsr6WvYtcu9Zi2RkbT0XEVSUoF4QWFozkRqKngjutOJS1WBTZuQnqbi\n7bddbAWxa5fN0ERaGiMBhZyZEyfyzdB1hORk4MPJl2D4241udFevck1mxMZyr7ErvMrKsjtxTENE\nBOPBqgqanysdDGEpCLMAfP+mq3j1VRderzWId2bNWr/+wAFgzx6cOsVojVMu/OcfShddRVRU3k6i\n7QXTpjl4fXIy1UouhBgNBiA1IYehnCtX8p4/dIh2kc3EuKpSh+pMIGGN06cL3TsGA+sivvjCzndw\nt4S8FFAc0ldAYvzPQlGU9iJy8ODBg9K+fXtPL0eHDh06io1Dhw5Jhw4dREQ6ADjkznt9SmdJOnTo\n0KHDG6GTvg4dOnSUI+ikr0OHDh3lCDrp69ChQ0c5gk76OnTo0FGOoJO+Dh06dJQj6KSvQ4cOHeUI\nOunr0KFDRzmCTvo6dOjQUY6gk74OHTp0lCPopK9Dhw4d5Qg66evQoUNHOUKZJX1FUQIURTmiKIqq\nKEobT6+nqPj+++89vQSb8NZ1iehrKyq8dW3eui4R715bUVFmSV9E3heRi8L2omUW3npReeu6RPS1\nFRXeujZvXZeId6+tqCiTpK8oygAR6Ssik0VE8fBydOjQoaPMwM/TC3AXiqLcKCJfiMhgEcny8HJ0\n6NCho0yhLFr6X4vIfACHPb0QHTp06Chr8ApLX1GUGSLyPwcvgYi0EJG7RKSiiMzS3urC4QNFRE6e\nPFmcJZYaUlNT5dAhtwbfXBd467pE9LUVFd66Nm9dl4j3rs2KzwLdfa9XjEtUFKW6iFR38rLzIrJC\nRP6vwPO+ImIUkWUAHrNx7AdFZFlJrFOHDh06vAyjACx35w1eQfquQlGUm0SkktVTdURkk4gME5ED\nAGJtvKe6iPQXkQsikn0dlqlDhw4dpY1AEWkoIpsAJLnzxjJF+gWhKEoDoQfQFsAxT69Hhw4dOrwd\nZTGRWxBld9fSoUOHjuuMMm3p69ChQ4cO9/BfsPR16NChQ4eL0Elfhw4dOsoRyiXpe2OzNkVRflEU\nJUpRlCxFUWIVRVmqKEptL1hXA0VRFimKck5RlExFUU4rijJdURR/L1jba4qi7FEUJUNRlGQPr2W8\noijnzb/ffkVROnlyPRoURemmKMpaRVEuma/3wZ5ek4iIoiivKopyQFGUa4qiXFEUZbWiKE09vS4R\nEUVRxiqKclRRlFTzY6+iKHd5el0FoSjKK+bf9EN33lcuSV+8s1nbNhEZISJNRWSoiDQSkZ88uiKi\nubAI7kkRaSkiL4jIWBF515OLMsNfWLuxwJOLUBTlPhH5QESmiUg7ETkqIpsURanhyXWZESIiR0Rk\nnHjX9d5NROaJSBcR6SP8LTcrihLk0VURMcJi0fYi0kF4b/6iKEoLj67KCmaj4inhteYeAJSrh4gM\nEJF/hGSmikgbT6/JzjoHCYvOfD29FhtrmywiZzy9Dqv1PCIiyR78/P0i8rHVvxWhUfGyp89NgXWq\nIjLY0+uws7Ya5vXd4em12Flfkog85ul1mNdSUUROiUgvEdkuIh+68/5yZelbNWsbLV7crE1RlGoi\nMkpE9gAweXo9NlBFRDwaTvEWmMNcHURkq/YceGf+LiK3eWpdZRBVhJ6IV11XiqL4KIpyv4gEi8g+\nT6/HjM9EZB2AbUV5c7kiffHyZm2KosxUFCVdRBJFpJ6I3OvhJRWCoiiNRWSCiHzu6bV4CWoIW4Fc\nKfD8FRGpdf2XU/agKIoiIh+JyG4A/3p6PSIiiqK0VhQlTURyRGS+iAwBEOHhZYl5A2orIq8W9Rhl\nnvQVRZlhTmbYe5gURWmqKMpEcb9Z23VZm9Vb3hf+oH1FxCQi33rR2kRRlLoiskFEfgSw2FvWpaPM\nY74wX3S/pxdihQgRuUVEOgtzRksVRWnuyQWZ29B8JOy3YyjyccwxojKL0mzWdp3Wdg6A0cZ76woT\nSrcB+NPTa1MUpY4wfri3NM5VUddlfs8jIjIXQLXSWpc9mMM7mSIyDMBaq+e/EZHKAIZc7zXZg6Io\nqojca71OT0NRlE+F+atuAKI9vR57UBRlizCP9YwH13CPiKwSGoSa0eorDIuZRKQCXCB0r2itXByA\nzYacNhxSFOVZEZli9ZTWrG2kiBzw5NrswNf83woltJx8cGdt5g1om4j8JSJjSmM9RVmXNwCAQVGU\ngyLSW0TWiuSFK3qLyCeeXJu3w0z494hID28mfDN8pJTuRTfwu4jcXOC5b0TkpIjMdIXwRf4DpO8q\nAFy0/reiKBnC3fIcbHTnvJ5QFKWziHQSkd0ikiIijUXkLRE5LR5OHpkt/B1Cb+llEbmBnCYCoGAc\n+7pCUZR6IlJNRBqIiK+iKLeY/3QGQMZ1XMqHIvKNmfwPCGWtwcIb0qNQFCVEeD1plmG4+TwlA4jx\n4Lrmi8gDwgl4GWaRhYhIKgCPdsNVFOU9YRgzWkRChaKKHiLSz5PrMl/T+XIeZh5LAuDywJByQ/p2\n4C2xrUyhNn+6UFcdJ7zo3i1O7K6E0FdEws0PjSQU4bnztfem64S3RORhq39r0y56isiu67UIACvM\nmvy3RORGoS6+P4CE67UGB+goDMvB/PjA/PwSKWWvzQnGCtezo8Dzj4nI0uu+mvy4QXh+aotIqogc\nE5F+RVXLlDLc5rAyH9PXoUOHDh2uo8yrd3To0KFDh+vQSV+HDh06yhF00tehQ4eOcgSd9HXo0KGj\nHEEnfR06dOgoR9BJX4cOHTrKEXTS16FDh45yBJ30dejQoeKhghEAAAF4SURBVKMcQSd9HTp06ChH\n0Elfhw4dOsoRdNLXoUOHjnIEnfR16CgGFEWpoShKnKIor1g911VRlBxFUXp6cm06dNiC3nBNh45i\nQlGUASKyRjgTN1LYZXM1gJc8ujAdOmxAJ30dOkoAiqLME7ah/ltEWotIJy9oi61DRyHopK9DRwlA\nUZRAETkhIjeJSHtvGfCtQ0dB6DF9HTpKBo2FIzh9RCTMw2vRocMudEtfh45iwjwc/YCIHBaRU8Jx\nia0BJHp0YTp02IBO+jp0FBOKoswWjrtsIxx9uUNErgEY5Ml16dBhC3p4R4eOYkBRlB4iMlFERgPI\nAK2oh0XkDkVRnvbs6nToKAzd0tehQ4eOcgTd0tehQ4eOcgSd9HXo0KGjHEEnfR06dOgoR9BJX4cO\nHTrKEXTS16FDh45yBJ30dejQoaMcQSd9HTp06ChH0Elfhw4dOsoRdNLXoUOHjnIEnfR16NChoxxB\nJ30dOnToKEfQSV+HDh06yhH+H8VFvNZmg0aAAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_aspect('equal', 'box')\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('v')\n", "\n", "X = np.linspace(-np.pi, np.pi, 101)\n", "Y = np.linspace(-3.5, 3.5, 101)\n", "XX, YY = np.meshgrid(X, Y)\n", "DX, DY = pendel([XX, YY], 0, h, k, m)\n", "ax.streamplot(XX, YY, DX, DY, color='b')\n", "\n", "X = np.linspace(-np.pi, np.pi, 21)\n", "Y = np.linspace(-3.5, 3.5, 21)\n", "XX, YY = np.meshgrid(X, Y)\n", "DX, DY = pendel([XX, YY], 0, h, k, m)\n", "ax.quiver(XX, YY, DX, DY, color='r')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Faasiportree näitab, et on kolm trajektooritüüpi:\n", "\n", "* Tasakaalupunktid $(0, 0)$ ja $(\\pi, 0)$ on püsipunktid. Nendele algtingimustele vastavad trajektoorid koosnevad ainult ühest punktist. Alumine püsipunkt $(0, 0)$ on atraktor, ülemine püsipunkt $(\\pi, 0)$ on sadul.\n", "* Teised trajektoorid on üldjuhul sarnased: Pendel ületab tippu $x = \\pm\\pi$ nii kaua kui energiast piisab, ja siis võngub püsipunkti $(0, 0)$ lähenedes.\n", "* Erijuht on kaks trajektoori, mis lähenevad sadulale $(\\pi, 0)$ kas vasakult või paremalt.\n", "\n", "Ehijuhi trajektoore on mõistlik ka joonistada, pildil on nad punased:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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GffFg8KVLSETw8BACICBA2mtq2J7h0iV0K21oQOfaiAicxuhoBPblHA9QSN8I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\n9sqjRhH9+9/WnVNfI309EXU26acYY/dcir5K+hw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jjAUGMjZhAjzXPIW54xg4kDE/P8bG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\nnBNxxx0RL7zQ+9cQEbFgQX6+t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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Kõige lihtsam on neid trajektoore leida, kui me sadulast tagasi integreerime.\n", "def rpendel(y, t, h, k, m):\n", " return [-dy for dy in pendel(y, t, h, k, m)]\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_aspect(0.5)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('v')\n", "\n", "# Joonistame kõigepealt süsteemi voolu.\n", "X = np.linspace(-np.pi, np.pi, 101)\n", "Y = np.linspace(-7, 7, 201)\n", "XX, YY = np.meshgrid(X, Y)\n", "DX, DY = pendel([XX, YY], 0, h, k, m)\n", "ax.streamplot(XX, YY, DX, DY, color='b')\n", "\n", "# Nüüd integreerime liikumisvõrrandeid.\n", "t = np.linspace(0, 16, 1000)\n", "ysolm = odeint(rpendel, [np.pi - 0.00001, 0], t, args = (h, k, m))\n", "ysolp = odeint(rpendel, [np.pi + 0.00001, 0], t, args = (h, k, m))\n", "\n", "# Pendli asukoha lükkame vahemikku [-pi, pi].\n", "xsolm = np.mod(ysolm[:, 0] + np.pi, 2 * np.pi) - np.pi\n", "xsolp = np.mod(ysolp[:, 0] + np.pi, 2 * np.pi) - np.pi\n", "\n", "# Jooonistamiseks lõikame trajektoori ka tükkideks, sest meil on lõigatud faasiruum.\n", "cutm = np.argwhere(np.fabs(xsolm[1:] - xsolm[:-1]) > np.pi) + 1\n", "cutp = np.argwhere(np.fabs(xsolp[1:] - xsolp[:-1]) > np.pi) + 1\n", "\n", "ycutm = np.split(ysolm, cutm[:, 0])\n", "ycutp = np.split(ysolp, cutp[:, 0])\n", "ycut = ycutm + ycutp\n", "\n", "# Lõpuks joonistame.\n", "for yy in ycut:\n", " xx = np.mod(yy[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vv = yy[:, 1]\n", " ax.plot(xx, vv, 'r')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poincaré lõiked\n", "\n", "Poincaré lõike mõiste nõuab, et trajektooritel, mis vastavad algtingimusele $\\underline{x}(0) = \\underline{x}_0 \\in S$, on transversaalne puutevektor $\\dot{\\underline{x}}(0)$. Seega püsipunktid ei saa kuuluda hulka $S$.\n", "\n", "Eelnevast järeldub, et meil on mitu võimalust valida Poincaré lõiget. Seda saame teha, kui me vaatame süsteemi trajektoore. Selleks on kasulik defineerida sellist funktsiooni, mis joonistab trajektoori ja Poincaré lõiget, ja selle abil uurida erinevaid trajektoore ja algtingimusi. Trajektoor, mida me uurime, on roheline, ja valitud Poincaré lõige on pruun." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def tplot(y0, pl):\n", " fig = plt.figure()\n", " ax = fig.add_subplot(111)\n", " ax.set_aspect(0.5)\n", " ax.set_xlabel('x')\n", " ax.set_ylabel('v')\n", "\n", " ax.streamplot(XX, YY, DX, DY, color='b')\n", "\n", " for po in np.array(pl):\n", " ax.plot(po[:, 0], po[:, 1], '#804000')\n", "\n", " for yy in ycut:\n", " xx = np.mod(yy[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vv = yy[:, 1]\n", " ax.plot(xx, vv, 'r')\n", "\n", " t = np.linspace(0, 20, 1000)\n", " sol = odeint(pendel, y0, t, args = (h, k, m))\n", " xsol = np.mod(sol[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " cut = np.argwhere(np.fabs(xsol[1:] - xsol[:-1]) > np.pi) + 1\n", " cuts = np.split(sol, cut[:, 0])\n", "\n", " for yy in cuts:\n", " xx = np.mod(yy[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vv = yy[:, 1]\n", " ax.plot(xx, vv, '#008000')\n", "\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1. $x = 0, 0 < |v| < v_1$\n", "\n", "Kui me valime algtingimust $(0, v)$ nii, et $0 < |v| < v_1$, kus $v_1$ on see kiirus, et pendel jõuab täpselt sadulani $(\\pi, 0)$, siis pendel võngub tagasi, ületab alumist punkti $x = 0$ teises suunas väiksema kiirusega, ja siis veel kord vahetab suunda ja ületab punkti $x = 0$ jälle algses suunas veel väiksema kiirusega $v'$:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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fuVI6Vwxj+CweDL56FYkIHh5CAAQESPudGrZnuHoV3UobGtC5NiICpzEqCoF9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FA/6OhRpquOHWNKol8/kktQEA2Bj0/bOdhSmC09nSstDchKK8XwygxMRjoiXNMxsiodY2rS0a2u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\nGO6XXUlIR2hPJKGeKxFJE5FvQbP5rvDbn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, 2], [])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1a.\n", "\n", "$$S^{v+}_1 = \\{(0, v), 0 < v < v_1\\}$$\n", "\n", "Trajektoor, mis alustab sellest hulgast $S^{v+}_1$, jõuab hulka $S^{v+}_1$ tagasi, kui pendel on kaks korda oma suunda vahetanud ja liigub jälle algses suunas läbi punkti $x = 0$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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iGMNn8WDw1atIRHB3FwLA31/a79SwPcPVq+hW2tiIzrXh4TiNkZEI7Ms5HqCQ\nvhHIhfT37hXpdtaq8quuFimYvMipshKvrVsnik19fKD5yKEasbUVxH/pErTsjAzctIyB4wwnK/r4\nWH4Q+gsvEL37btdDwKdPhzDmdVtmazPd3AzHNR81VVgIaR8SIhrd9zAgzF0xCQnQhtVquGK4AAgN\nla55X00NLI+EBBxKVRXiEDEx+OyYGIkb8RGEYFYWjv34ccTMNBooQevXi2xbySq/ewmF9I1ALqQf\nEQEzl3dg5EVZISHSBdgeBp7Nwouxjh9HimVjI153chJCwM8PGplU5fmmoKEB+zQsJpswAZbNtGli\nmJafH/Yv5Z7feAOtE0JDRTHYxInYH8/WzM6GMNLp4Nbg2Zpmm5d844ZorHPyJCTlnDlCAPSwx3FX\nrpjAQLiCVq/GW0k141mnw3fJBVBODizSxYuFMSPlxC4OtRrxnOPHkZn2+eeI88yeDQHOq3PNOTO4\nN1BI3wjkQvo8q4UXZZ06hd+JoJQ98ggu8KAg61a86vXIBzcszDp/HgR6+jRSG729cQN6eyNQLIfS\n9NJSYb3wUY+NjSI+EBoKF1FAAM63JVtLNDRAgzx6FGSSn4/nnZ1B/lFRUADMYlmp1bACuP+mqAjB\nkPBwUVE1f/5D38bQFXPwIFxCej2+89Wr4Q9ftky665QPkP/mG7hi6uuhHHEBEB0tbbEfR309rnte\napGXB8Geni79ZxuDQvpGIBfS7wp37og2Ljdu4KIiQpWj4aDuJUus2wOcN0HLzoYwyM7Gxd/aipve\n2RmxhRdftN4eO0OnQ1o8FwIVFSAvvR4porztdEAABJol00YrKkAifBh6cTHc81Onijm4/v5m6CjK\nGIo8eGOdU6fgz1i8WAiA4OAefVBVFVwwBw/isaEB2aVPPolzGBUlXTYMj0NwYyYvD0J7+XIIy5Ur\nLWMFEOE8lJfD529NKKRvBHIm/c6oqoJGyGe0Zmbigre3x6DqGTMESVnb397eLgRBdjbcAGbJWpEQ\njY2wBtLTRfvpmhoILu6+4sLWkj7c4mJ85/HxEAQ1NfjOly8X2ZpmiQc0NuIDeCS1rAzSLiYGqvvK\nlT1yore3i/0mJSHGPHy4aJW8erW07o+SEgie8+cRiG1ogNYfHY1DiI4eWDn5XUEhfSPoT6TfGWo1\nNOszZ6C1JiQIknJxEZpqQIA8umH2N/DWBunpCA7Hx4uagmnTQP7c2vLwkLCXvwF0OpAZz9RMSwPJ\n+vkhFsQLxnvPAAAgAElEQVTHIPZ5TrJejw+Kj8fiszgDAoT/xsWlR5Lm2jXxNqdP4xiWLsVbrF0r\nrRbO++TzwrSsLDzv4YHDiIiAQmKtdF+poJC+EfRn0u8Mbq2npQltlQ98WrECNxbvNe/nJ33mw0BE\nTY2ofuYFPq2tCGA6O4vCLD8/yxT3NDXBK5OdjaDi1avIsgoMFOn6S5eagVRLS+ECOngQ6juvqOIC\nICysR1V+dXUg3/h4uK4aGhDziYvD26xYIW0MqLIS2z98GId07Bi+p7AwMTy9h7JM1lBI3wgGEul3\nhYYGuCxycxG/O3cObiIiuCj8/MSQlCVLrNe+ub+Cz1LJyREp8rW10Pp9fJB9FRoKi8AScYHiYqHV\nHj8uxiA+8gj2ER1thjGIra0IOhw8CPa+cwemBXcDrVrVoygqH1weH4+3KiiA3Fi+XLiBpOwVpdcj\naJ6UBKspJQX1KzNmQADExMASkEONiqlQSN8IBjrpdwbPEuIBzIwMEJaXF352d+84lNzVVZ6ViIyB\nyJydRdfOmTOtr6Hp9XAB8QD86dNwjU+YACEbFiba6PfZBfMQ8DGIhw+jVcTu3dD4AwNFu4U+F4gx\nBuY8eJDowAGYPjY2kHJr10IILFrUo7cqLBTZQKdO4VwuWyZiAQEB0l6LajWInwsBOzscjpubSKMN\nC5P+ezMHFNI3ArmQfkMDgnPWIC2NBvet4VDyy5dx040YgRsvJgZal5eX9SpdDdHYiMBwVpZo2DZl\nSsd0UW9vE5ucSQDDPv5HjkBBLikRbfSXL7fc1KW7d5HdkpgIYmtuRibYqlXCv93nPZSWgrkPHIDv\nRK1G8yQuAAIDe8TcDQ04V/v2Yb8VFbBQVq4Uc3MlmYBmgLIyZMzxLKrbt3Hd+/iIVNqAAHnGAxTS\nNwK5kH5UFMxbw4Zd1vQtNjUhjsfz8ZubcR8ToY7Hw0OQq5cXlDlrCYJ790S6KN9vZSU0Mnv7juMd\nvb2tm9lk2Eafz1MpLUV8ZeFCQSb+/tI2wmtrg1bL0/UnT4alx10rcXFw2fcJLS1gywMH4MPhJs+q\nVRACMTE9Upv1enyv8fGiMMvGBoIyLg55+W5u0t4r/HvjlbknTsByu3ABRg2fgePtLQ/LWCF9I5AL\n6fPCnNOncYFrtSAC7hMOC4PrxZoXVF0dBAFPw8zKghZLBKJqaUGDKi8vPDo7WyajpTMYg5uZC4CM\nDPzc0IDXnZwgAEJDEeT08OiorX30EbqQ7t6Nm1jqvfIMoYQEkElNDYKLoaFCCEg5AYsI32NiIog1\nORn+dldX0fmyz64VztwHDsB/k5+Pi2P5cmEF9HDYb0kJ9pqRgeB1SwtSQLnLKjJS+i6sej2SJLgA\nOHUK1qe9PdFjjxF98IG0n/8wKKRvBHIhfUM0N4MEuE/47FkQ6I0b0AB5mqCfn/XbHnBBcPUq9pqT\nAxJjDES6ZAkEQEAASMTNzTrBYj7wnbdm4MPTq6qgUXt4iNYMH3wA4hs2DFPHtm617D5zc0Ub/ZQU\n4SG5csUyll9jI9w/XLOuqACRTpsm0vX7HJS+eVMIgORkaDm9yONsbRUjIxMScI8MG4YC41WrsFcp\nB7dzaLVQhE6cgCz7yU+k/byHQSF9I5Aj6XdGWxuIKjVVrJoa3BNLl0IAhIfjPpk92/rBzMZGVEXm\n5OBGyMmB1ZKcDG3RxQVxgmXLIBCWLrVOcMyw0yjvNtq5IyYRms39/e89VkTNvsf0dLiwLCl8OLiC\nfuoU0Wef4XwNGQLLc80arB50bTCO+npRzpuYiPQnLmHWrIHE6WH+6/XrwmVVUQEBOn++aM+wfPng\nGJmokL4R9AfS7wy9Hpo1zxVPTUUALjcX+eKGLQS8vKTrgmgKWlpgDufkwDLIyYE/lA94iY2F1eLp\nKQSCNRrNnT2L89YVPD3FKMqAAOv2QLIWbt0SKZYnTgg30Pbtoj6hT24orRYXNc8GunEDF3BkJCyA\n1at73NWtqQmKBm/PUFwMKyA0VNQwDISc/K6gkL4R9EfS7wrl5UJbTU+HG6OlBVoZrz6cPx++bCcn\neVTntrcjeH3+PDIjkpIguHgXz5kzhRDgzdscHKS9SRMT4cceOhQEFh4OHrK3h9sqLQ3aJBECd5Mm\niZGJ1u6BZGk0NiIWdeAA/OzHjyOnffVqWEcmKOhdg885PHgQKzUVGo+Xl7ACetjVjRcu8m7TycnI\nRmtuFq0sIiMt06TNElBI3wgGCul3hlYLzZr3kKmoEENSxo4V2Sx8SdUS11To9XCxcGuAP86dCzfD\n5Mkdg8WennjNXIKA9wxatKj72ENlJc7puXMgj8xMpL3a28MKCA5GAN7Xt+9WllYLUo2IsH4/JWPQ\n6XCt7d+Pdf06jn3FCqGg97nIqboajN25qxtvDhcV1WPfjVoNAZ6QgFTay5dxDfn4CCFglqZ2VsKg\nJX2VSvXfRPR7InqLMfZKN38zIEm/K9TViWwW3ma4vByvrVkD7d8wz91affw7g2fj5OaKGEFODvzc\nRCBDPoSE79+SIx9bW3Fez5xB4DU1FXzEXWvh4fCBBwSY7k/OzITw4C00OCH5+sojNbA7XL0KYXXg\nAM5HcDAE2Lp1EAJ9nr7Fu7odPAjmvnYNmQPLlwshYELO6d27sDSPHMFjTQ1iTbNmQZZERfUvV9Cg\nJH2VSuVDRF8SUT0RnVRI/0EwhoudT5tKThbzaIkQuOQk6ucH90VnQXDnDu6v118n2rzZsvsvKxMp\npPfuwTVz6xZeGzdOWAR8mLqlBIFOJ6pyk5MRBK2qAkn7+kIA8AE5PXF/3LwpqkSPHcP3M2YM3BEx\nMRACfc6plxCVlVDM9+7FMbS0wMW4di2EgFkqbXmLaN7Vrb0dKW98zmJQUI8LH3hTu/R09OtPTYUl\nN22aqMyNirL+oBRjGHSkr1KpRhNRNhG9QERvENF5uZP+n/4EjdGSzbq6AmNIZTTsjZ+dDa3n9Glc\n6DzrxtMTcbZX7p/ZF18kevNN61YoVlV13HtWFgTT9OkIGhsOU/fxsUzFrl6P2MWpU0IIVFTgfIaE\nmPZeOh2OiXfZrK9HQHzhQgTDY2MhUOTaQ0mtRgB4/34o6WVl8KM/84ywZPpcFdzQIFpEJybiQ+zt\n4WviJ8nBocdv19IipmUdOwYrkzGQ/4IFeAwPl49lTDQ4Sf/fRFTJGPuJSqU6Sf2A9F94gejLLzs2\n6+KVuUFB1u33odeD3HNzhWslJwcu1s6YM4fov/+b6Pnn5REsJhKpe2fPijYT3K01Y4ao1PX3x3mX\n+lzz+OT8+X2vuq2vB4nyDJW7d+FSWr4c3LZyJYhJjtDr8V1wF9CpU1AYeKLOmjVmEMq88CEhASfo\n3Dk8t2SJyOMMDDTpi6ipgfDOy8M9e/Uqnl+yBLGXmBi8tTUxqEhfpVI9TkQ/IyJvxlh7fyF9ou6b\nddnYED36KDQJ3sPd2qYldw3FxECL7Qzes8fDQ6RgurrKQwPlezfsNXTvHo6DzyLgc3T9/fF7f8jK\n4SMMuQA4cwYuLb1etFYIDpa2vUNfUFgI7X//fsRGdDoI43XrsMzSaqG6GibS4cNYFRWwAjhbx8SY\nXHhQUoJ2Grw6d+FCuOOsiUFD+iqVaiYRZRFRFGPs4v3n+g3pdwZv1sUrXY8cEcVDs2YJARAUZL0W\nDdOni5YqcXHQmuvrYa3k5UHJunIFylR6OgJ4Hh5YvAWCHMxiXvvA017PnUOnAL0e7gZvb1EFHRgo\nfbMvc6CxEdfO/v1QdO/dgxUTHQ0hEBuLJnVyRE0NBNf+/XicMAGEzzM1w8LM4EbU63GR8jzO9HRE\nmxcswEmKiYHfxgTTjzHUB1i7Un4wkf46ItpLRDoi4jqBLRGx+8/ZsU4HxEk/NDSUxnaqLd+yZQtt\n2bJF8n2bgvJypJrxytzsbMSswsPxOtdO/fwsMxIuPR03n4dH9+6clhZooOfPC0GQl4ccaSLRv3zG\nDCEQFiywvnuouRnn9+xZpL8ePSrcQnxIfWAgHo2V+ms0oi2FtcAYzjtvrZCRgefXroVLa+1a6ZuW\n9RZtbXD98HT9W7cgiGNisO9Vq8w0EKihAar60aPQsIqKoEn5+eECXbECJ0tmeZy7du2iXbt2dXiu\nvr6eTp8+TTQISH8UEc3p9PQOIiogoj8yxh5wRMhZ0+8JWltFd0nep4e3Gp4zRwiAgABo1nKoziUS\n+fi5uVg1NfDt8jTMUaPgIzW0CtzdrRfgJhKzCLjQTUtDEJUxaKJRUbB0QkLgzuLc8NJLaGGQkIDv\nQg6oqIBye/48Gsw1NaHeYe1arJAQebqBGMM55wIgIwOCau1anNvVq+FGNIvwKiyEnyYpCcKgrg4q\nfFiYSOORqaQcNJp+V+jP7p3egPuruYvi7FmRfZOVhWvUMIPF3V1eiktlpbAGuEVQUIDsO140xeME\nXCBY0z1UX4/znJkJv25aGjJURo2CoA0NJXrnHZDssGFEu3YRbdxovf12hbY2BCZ5/zM+CCs2Fntd\nscIM07YkQlkZhNeBA2JGwOzZIoaxfLmZFB2dDjdSUhKc9zyPc8oUfEhEBB7NMqG+7xjspH+CiHJl\nTfp37hC9+y4YIjDQ7A7B9nZoR4aBy0uXcB3b2UEgxMbCMvD0ROBSToKgtRWEn5MDQcDdRNw95OAg\nAq48lXTWLOsNpMnJgdWVkiJa7hpi40aiDz+UJ5EyhnPLC6tGjwa/hYURrV+PgKq1kwi6Q2srzjdP\n1y8uBuFHRWHfK1aYsWmeWi3yOE+ehEal0yGnMzLSTB/Sewxq0n8YZEH6J0+iCXdlJdJEPD1FBU9w\nsCT19y0tIFDec76hAVoe9z27uwsC9fTE73LIvOEwTCM9fx5uoUOHcAqJkPvN+/bwY3B0tHyc4JNP\niJ5+Gj+rVDi/RNhHaKiYnOXrK88JTHfvgvz374eHQ6vFuVy/Hkum3g1iDBZiQgIE8OHD2LurKxQc\nE+u1Ho6GBkj58HBZtPFUSN8IZEH6RJSXy2h6w1WaUnAKV+mpU8gFU6ng3DaMGkrU3rGp6cGWyJcv\nQ4EJD0e2G3epcD+7nBpUMQby5/16+LpzBxrrkCGieRtf8+ZJS1r/+79Er74KtxTvx1NdDaF17hy+\n5ro60acmOBia6dKl1g9kd0ZdncioSUyEBbN+PTIcN2yAO4untra3E73xBrpvurpad99E2PuxY9j3\noUOiXisqCkIgJsY6rbOlgkL6RiAX0vf3BwksWHC/KCuEUcS8YppZdJpUKafhLOZVINOnCwEQGAgm\nkyjqplbDNVRQgPhAbi5SGVta8PqsWRAAISEIBC5dCo1aTnntVVXYd2amCHrfvo3Xxo8XrRr8/fFo\nQrHmQ8EY3A7d+ZV1OgjalBQkjJw6hXM7aRK8BDxpRG6ExOMAyclEO3aARKdMgRtlwwZo1WvXwkhN\nTsZ1IRfwTCZez1BYiOQHZ2eRqRkWZt2kgb5CIX0jkAvpl5XhxudFWTwrZOZMCIHoaCLvuVW0uDad\nbM+lQQhkZIBRhg9HVJY3e/fzM0NLw+6h0wnXCl+2tjCliXCzuLnBQFm6FI/u7vLyYVdUdJyre/Wq\nkKkODtDI/fxEta6l8q750JRjxxAzzMqCVeDkJIaXy20QiF4PheCbb7AKCxET0mphRY0aBQ8mOEh+\nqK3F+eaZmnfuQIcKCRG9jdzd5Wd5GYNC+kYgF9LvjNpaxIm4EGhuRq64vT000sBAomBfDfmPyKXR\neWkij5DnPM6aBcbiPZS9vCTvL1BRASsgPx/aa34+3EMaDQi0tFQIgCVLsBYulE+3yHv3YG3xDqSZ\nmXB58Srd5GQz5YObgNpakRW0d68YBBISIgaBmC1F0QzggeDAQFiJHCoVLJcvvpCXS7AzGEMxIRcA\nyclQYoYMgcDlmZpz51p7p8ahkL4RyJX0O6O5GVpfWppYNTW4mdzdYUo7zmcUNOs2OdZkkk1WhvBn\ncOZavFgIAR8fqOESRw/b26FBX7mCrXChUFKC1+3sYFYHBcG/zgXC1KnWJzKdDvs+dw5E9tZb1t2T\n4SCQw4chDFpbYZnExMASiIqSQzVo91q9rS1cJxs2IB4wc6Zl92YqWlthxRw5gkSdrCx8D46OQgDw\nYTpygkL6RtBfSL8z9HoxySktDSR65AguyDFj4JLw8yPy9dJR0KSrNLk4QzTTz8sDGw8dCjWRN8dZ\ntgyCwAKsUVMDFxYXAs3NCBDyWMGkScIa4ILA1VU+xWVygFoNl+DhwziHx4/jKw0LgwBYvRrkZGk0\nNiIldepU6BkLFyKQXlaG7/ibb7BXrZZoyxZcchs3woUld9TWQvvnHTevXkWdiIODyMQKDTXD4Pg+\nQiF9I+ivpN8VGhqgiXD3xLlzojqXD0nx8iLyWdJGPnb5NLEwA6ku58/Dd6TRQJVdsKDj5HILDazV\n61H5bigMLlxA/GDuXJTfOzmJOAF/tFZOfl9w8iROd0976vcERUWIqyQkiPdftAjkv2qVvJqt1daK\nzsf79kGAubmB/DdswHfbH77Tu3fhVT10CCmtd+7AiOZtLqwFhfSNYCCRflfgQ1IuX4aGkp0thqQ4\nOEAIeHkR+XtqyMOugCbfPU+q3PuCwHBgrYODyNV0d8dycrJIFVdzM/bP4wQ8ZsCPY9w4sS2+RVdX\neea9czz6KNHXX+P0BQQIV4Gvr3lOaVOTaCkfHw/BUlMD8l+7FmmK1mzXbYiWFlip33yDWpG6Orj6\nNm4keuQRnBM5ZYN1Bz6LoqrK+u02FNI3goFO+p3B+8fw4Sh8ubqiFe+UKQa5+Ev05DOxiObVnyfb\n3PsDa/PzhfkwbBjsdzc3MC5/nD1bcjWNt5vgAqC4GK6Oa9fw2pAhiBUY1hV4eMinOyYvHjp+HCs5\nGS0dRo+Ge2DdOgRDzRGk5S3l+fzavDwIluXL8Tlr1sinylajwbn45hsUhanV2CtPBY2IkLcwlwsU\n0jeCwUb6XYExjOQz7HmTmytGD44YAa1rxIj7lbpzqslddZHG3r4At9CF+48NDfgHe/sHBYGbm0Wi\nXc3N2I7hceTng0xsbdHJs/NgdTm0F9ZqEQDlQqChASEYBweROx4VZZ7Ml1u3RJXtqVP47JgYuH82\nboSwlINrRaeDi9IwFXTMGFgrGzbAWrF20FquUEjfCORC+k89BbMwNBR+Xi8v6/e/qakRgqC8HGls\nly6BQIlAoDzY6rmMkdvYO+TUdpGGXTUQBgUF4h+mTXtQGLi4SJ50rtPBAuhcqVtfj9dnzgT5Bwdj\nWz4+1s/G4EHaI0ewLl0CEfv4gKBjY/FzX9NdeZVtZibRBx/ALbRwofCt+/jIQwAwhkuKC4DcXGj8\na9ageG3NGtQsKgAU0jcCuZD+22/D95qeDm115Ej4ekNCrD831xBaLdIGuW+dB1vnzEE9gY0NXP1u\nbvd53VlLy0ZfpzkNF8i2wMAqKCzEnaxSoY6fCwEuECSOF3D/q6EQyM9HhgkRAseG2a2entbVKktK\nRO54UhLO982byNOPi8NjX62A1lZYGXv3whKoqoJAXL8evvXgYPnUVBQXQ1jt3g3hqNfjHuFN4RYv\nloewshYU0jcCuZA+R3s7NFLepTElBZkO/v4g3IAAsSRqwdMr1Ncj2HrxYsdVUYHXvbxwbK6uUO6X\nODbT0mEFNKvuAtlcNhAGneMFXBBwYSBhqg4XBDyzNTMTwqClBR8ZE4OP9/fH+V+0yDpVmjod9peY\niEDt+fPYh78/BEBcHKyvvpwmrRYxnm++gRCYNw9G24YNRJs2IR5gbUuUo6oK52H/fgjFlhboDHw2\nQGCgfISVpaCQvhHIjfQ7Q68HmaanQwCkpyOFkQjmLBcAQUEIVHbOY794kei114j+/GeQlKVRWQnX\nRGGhaOl86RIEGRFMdF4zNncukcesalpqe5FmVF8gm0sGbiKeRTR2bEergC8JOpESgfwuXwbJZmUh\nPe/SJQiI8ePFgJqAAPxsjYyYe/cgABITYQU0NUHznzcPWm94uAh+Xr5M9KMfEf3jHz3Pi2cMwf6v\nvkLGUVERjp1bAFFR8gmuqtWwVvbvx2Vz7hyC96tWwQUUE2P9HHpLQCF9I5A76XeFigpUCaanY2Vm\nQns+f174pPnas4fod7+DMNixg2jzZmvvHiRSXi4EwKVLCFwePizSMIcPhzBwdSVydWHkNfk2ubEL\nNK3qAtlcvIA7+soVsDIR/BCGsQJ3d0QkJWCj+noIAX7+z57FvhcvxnkOCRFLwhZIXaKtTRRs7dkD\nF5C9PYTAunV47b33UHaRkmK6IsDbLHz9NYTAtWsQdM89J3pEyaUFt16P7yk+Hqmg+fnQ+Hnx2po1\n1ileswQU0jeC/kj6nWFsSIqNDS5+js2boeVZO1DZFRiDd+fSJWikhkLBzg7CbuRICDhXV6IlizXk\nO+4aOWsv0ISSC6TiwoCnHdnaIirJR23xcVtmPng+VD0tTbjkiorwmpOTEABhYbBmOrtdeE79unXm\n9Vzx0YL798NHn5UlXrOxgcZ75gzOZ2/f/9IlCIC8PBRZjRkDl8rmzRAAcrEAiHBZJCRAAJw4AUt5\n+HBYAbGxEFpy2m9foJC+EQwE0u8KLS3Q/GNjH5zcRATu48W2y5bBByzX9DfeJ//SJXh7DB/59Kwx\nY2DZODkReS5oIN9Rl8ip7QKNvJ4v5i42NeGPZ87s2HrCw8PsAZKSEhAq75x68SK0yvb2jtP1Zs4k\n+v3v4YJ78km0L5DKVx4fD+22M9auJfrLX/reBuHSJWj/X30FoT1mDATZ5s3IsJEToTY1IV113z4E\nhEtKkEQWGYl7hk+S669QSN8IBirpE4HsuY95+HBom1OmgESHDxfdF9rboYXevSv63PBHufXGN4Re\nj774Fy8iyJibK7JEuddn9mwcy1J3PYU53CA3bS5NKz1PNnn3q455pHn8eGEReHoibceM805ra0H+\nycnQMvPz8byTE1xb5eX4qKgoBE5HjzbLx3bAX/9K9OMf42dbW2T7VFTA5aHVwjP2yCNI13R379uh\ncwGweze+j6gopPg+9hh+lks7CCJhER06hLhIaiqs5OXLcUlER8MKkEP2XE+hkL4RDGTSZ4zo44+h\nsQQHd+1r1WiglRUUiC6YFy6AhIjgo3Z1hQY0adJ9H7urvPvdaDRwt/Bj4amljY0g2JEjIdA8ljIK\nnFdKPsNyaX79eRp28b4g4L6ZceM65m36+potGbyqCgLgyBFo94YYOZLo9deJXnnFvNpxbS0Cm46O\nCPLyjBbeBmHvXrg+Ghsh+6KjoaX3tQ/OpUvIAvr0U3wv48YhC+ixx2DxyCULiINP2crJIdq5E8rQ\nsGFIloiOhtWybJm8++srpG8EciH9vXtx8QcFyaNVQEWFIMwLF2AN7N0rumCOHg1fMPevu7khKDh7\ntnwtg+pqeHl4W6HcXAg7Hvvgue6Bi2soZEQWOdVm0LC8TDAll4IzZwoBwCet9KG4jLtcOsdeiED+\n4eGiInfRIukFLW+DsHs3iLqmBgbP5s3oF9QXAcA16t27ib78ElloEyfCstiyBZao3FIrGYOgOnoU\nmVEnT8KlOGkSBJefnzz76yukbwRyIf3ISJj9RCBQXpQVEmLe8X19AXen8CCr4ePSpQhkDh+O2Kmz\nM7JZ+OPChfJsi9zaimPgrqH0dAiGtjYQsbMzkbcXo/AFdynYLpPmVmbQkOz7+ZuNjZBwHh6Q1nyZ\n8IXl5GCGrquraH7n6AhhlJQEDTwlBWQcGgohGxcHDVlqd0N7O67Jr76SRgDk5kIAfPUVTiVjcC9t\n3oxjlaPyoNEgW+voUQSGP/8c98X8+XBbyaW/vkL6RiAX0ueN0Hj2B28eRgRTfNMmPPr7w98qJ42I\nC4MrV8QqKMAjd5m7uMBKWLQIa/Fi8fOMGfJyFbW3QxBkZYmRivn5EFxXr8K0D/DTU/TMy+TbnkoT\nr6aSKjVVuIXmzu0oBFxd+8RgLS3Qvg8fRvZJURGEa0SEKMaSOuhoKAB43cjixUSPP47VlxoQvR7C\nb/durFu3kOq6aRMEQHCwfF0phv31jx/HNa+0VpY55EL6XaG8XGSA3LgBrU+rhYbHB3nzJde+IzU1\nIMriYmjQfIpWYaEIto4ejeM5edK6ezUGjQaaaUYGNL2zZ3EMRAiO+/kRbfAvJT9dGi2sOENDzqXC\nj6TVwokdFibSdlxde81i3N0QHw8BcOaMCMI+/jj8zd7e0pKkRgOf9xdfIPulsRHGzuOPw0/fF1cH\nYzjHX34JAXP3Lq7t7duRZRQQIF8BQIQsoIoKKAbWhEL6RiBn0u+MlhZoRJx00tPFSNzVqxET4C4C\nLy+LzD3pNdrbIQiuXAGJqdVEv/iFtXdlGiorOwqBmhp8P8OGwd2/3K+FVk3KoKX1p2hE+kli6emk\n0miITZpEqvBwMWqpD41i6uvhajh6FPn4lZWwnNatQ8VseLi0mTKtrch6+eILBIHVapBzRAQEwLRp\nvX9vPnD94EGif/8bNRwODrAAHn1U/gLAmlBI3wj6E+l3hbt3cWNcuoSUwOxs0T1y1izRRtjPDwqm\n3FwpAwlaLeIChi46norp7k60eXkazUwOojivZ2jSlQJIDK0WzLh8OaK10dG9Ntu0WsRV9u2DD/7m\nTaTsxsVBAEjdiripCQSdmkr0/vsIkEdEEG3diqBnXzpl6PU4tt27UQxmKAA2b4a1qwgAAYX0jaC/\nk35n8KZhnYekuLjgppkwQbRD5svVtX/lIPcXMAYXEHfRVRblkBd50XvZ2TRtgSetDG6i9ZNTaWnt\nSbJLOY4vijF8KStXQggEBfUqb5Nnyuzbh1VcDKEQFQWiXLNG2j5BNTVoA7FrF3zeQ4dC+Gzdise+\nBPX1eggW3guIkz1vBhccLM8gsCWhkL4RDDTS7wp8SIphznpeHlok8+7GGzdCM+NpmDzrRhEG5kPp\ntRx6/zteNH1NNqXmedLx4/AB29rCHbQtppIi9UnkVHSEbJKOwEwYNUpYAStXIn2mF7h5EyT81VfI\nQMGO6cMAACAASURBVLWzw1tu2gR3jJRNyEpKoKF//jmC4lFR0NKfeAKH1pekBO4C2r0bx3f3LmIs\nGzYgEyg8XH51AJaAQvpGMBhIvzu0tCATIz8fN2ZKCn4vKcHrKhWCci4u8J9OnYoMloUL8bPiJjIN\nnPSffy+bpi/0JMYQoD9xAquoCKQ4dizRikg9Pe6aT5GawzTu3BERsXV2hpq+di18Gr1QaW/fFgIg\nPR0+f/6WGzZI6wK6dg19gN5/H0rH1KkIAD/xBALQfbmmeIO1PXuwioth2T7+OFxbUVHyaQYnNQYV\n6atUqp8R0QYiWkxEaiJKI6JXGWPXuvl7WZB+QwNuNjkQaX09Aqy8UvfyZRDD/v2igGjMGCEAFi6E\nVTB/PnLM5VBcJkd0Jv3O0OkQCD58GOvsWZxvFxeitcsb6Ympx8i58CDZJsYjYjtpkmgXGR3dq94N\nd+6g6C4rCxWzw4fj7bZsAVFKRZKM4TM//xxB4LIytKTYupXo6adR5NfX9z9/Hu6fa9cgBEaNwjGt\nX48ma+PHm+dY5IjBRvqJRLSLiLKIaAgR/YGI3IjImTGm7uLvZUH6kZEg1+Bg0ZVxyRJ5+Sbb2uCj\nvnbtwTV7Nrp7EuFmcnSEJ8LRUawFCxCzHKwBt4eRfmfU1iL3mwuBUaMQwIyN0dFTLhkUVn+ARiQd\nEFI5MhKq+vr1vUrdunULqZK7diE9dexYUS3bVzeMMeh0sHQ+/xzk/NlnXTeG6wsKCkR8IyMDxxIe\njlO1dq18BsObC4OK9DtDpVJNIqIKIgpljJ3p4nVZkH5SEi78M2dwUWo00PwDAyEIwsKQ+ytFIy5z\noL4eAuHGjQcfS0rgJrp5E5rjvHmwCrhlwH+eN29gxxBMJX1DMAY33MGDcI9kZkJ4BgcTbQ8spLWq\ngzQlfT9SuIjAaI8+CiHQi6b+BQXQwD//HN9hWBgqcLdvRzaYVBapWg0fvJTFhyUlsFr37UNtiK8v\nUk9Xr8by8ur/islgJ/0FRHSViNwZY5e7eF0WpG+I1laYvjztLzUVpJifD1Pfz0+0fnFzk1d1bldQ\nq+Gv7m61tgqLZvJkIQQMhcH8+chklJPlYyr6QvoPvFcpCrQOHEChVGsrXBchiypo2+h9NPPc16Q6\ncQL+odBQRGw3bkTOrgngU7MOHcIchvJyhBW2b4cfvq9uGGuDN1fbuxfHWFcHGckrnVeskG/LcWMY\ntKSvUqlURHSQiOwZY2Hd/I3sSL8zdDoxso+vCxfw/IgR0ExiYnADenjgpuwvGQt6PYikO4HAi8+I\n4PO1tX3QbeToCEtCTv3au8LtK+fokxf8zUL6hmhpEcVZ+/aBuBwdiZ6Mq6btY/bT3KyvSHXsGC6Y\noCAktj/2GNJcTIBWC4t05058TmsrLIAnn0SmjDVGRZoTWi0C2/HxWJcv4z7avh3KVkwM0pvlEHd7\nGAYz6f+LiGKIKIgxVtrN38ie9LtCczMCVVwI1NbixieCe9fVFQKAL3f3rgNX+fm4aX/7W5i2coNa\nDbdQURGyMa5fh9uosBDPaTT4Oz64XKtFYNnJSTzOnSsPIbj+k5WUWnCE1i57jNZ5bqWwOWE0drh5\ncyU1Grgs9uxBgVZVFfrybIurpacnHaB52V+R6sgRqPDR0VDX1683uVNoQwO045078XmRkdCQn3oK\n/v/+7h4hwvWWkAAFa+dOXIvTp+O08RbLcq16H5Skr1Kp3iGiNUQUwhi7beTvPIkoOzQ0lMZ2Slbe\nsmULbdmyRdqNmhENDSBx3jY4NxcDRtraEBguLBQ5+Dwf//RpojfewP8/8wzR3/7Wf8xZvR7+WR4/\nuHsXN+i1a3iutRV/N2QIXETR0YgZODuL1dP89JoaCM2+aHk7T75Nb3/xI6pa6EC3mkrIVmVLPg4+\nFDUviqLmR5H/TH+yG2I+c0Wrxfe7Zw9cGEVFCFg+u76Knhr9FU0/8Rl8hyNHwvf/xBNgMhP9hXfu\nIP3zvfdEUP9b38IaKDNoW1sRbztyBMoVH4Lj6YnQiY8PjChrpITu2rWLdu3a1eG5+vp6Oo34zuAg\n/fuEv46IwhhjRQ/5236p6fcUWi162/DJUjwF8/p1WPuGUKkQKA4Kwgi/BQv6jwDoDL0eQuD6dRDR\n9esQisePw3LgmDFDCEEvLxyzu3tHV8Xt2yCvTZsw8KS37fMNffrqyePoeNFxOlZ8jI4XHadqdTWN\nGDKCQueEUrRjNK1euJoWTlzYp3NgCK0W8aHPP0caY10dArMvrCymx/S7aFz8p7g4Jk+G62fbNgSN\nTJByjCHNdMcOBIEbGhBO+Pa3ce7667XUFUpL4eo6ehTW1JEjIPygIBhO3/++dfc3qDR9lUr1TyLa\nQkRricgwN7+eMdbaxd8PaNLvDhoNtOHHH4d23B2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1lLH/+i9IruHDEbG+dcssn8cYzsMn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9Kl7DiaMsU6vDepFCl3zJJiaIsW8bMPCWE0Nm6c5TMuBgMH2uREamoqcCK1FiEDTqL2cDq8lHRM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\nYSQRJvqGYRhJxP8Dl7f0/ejTQ00AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, 2], [[(0, 0), (0, 2.5)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1b.\n", "\n", "$$S^{v-}_1 = \\{(0, v), -v_1 < v < 0\\}$$\n", "\n", "Siin kehtib täpselt sama kui eelmise valiku puhul, lihtsalt et algne kiirus on negatiivne:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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4MPjCBSQieHoKARAUJO93atqe4cIFdCttakLn2qgonMaYGAT2lRwPUEnfDJRC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QE0BF5ebedgS2G29HSOtDQgO60UIyozMAXpCHNKx6iqdIytTUeP+jIAYBnplMk3S3dasYss1Ur1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\naN9e34VEx0Q/Afn0U+Dxx4EHH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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, -2], [[(0, 0), (0, -2.5)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 1c.\n", "\n", "$$S^{v\\pm}_1 = \\{(0, v), 0 < |v| < v_1\\}$$\n", "\n", "Trajektoor, mis algab sellest hulgast $S^{v\\pm}_1$, jõuab hulka $S^{v\\pm}_1$ tagasi, kui pendel on ükskord oma suunda vahetanud ja liigub vastassuunas läbi punkti $x = 0$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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iGMNn8WDw1atIRHB3FwLA31/a79SwPcPVq+hW2tiIzrXh4TiNkZEI7Ms5HqCQ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\nQkRricgwN7+eMdbaxd8PaNLvDhoNtOHHH4d23B2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1lLH/+i9IruHDEbG+dcssn8cYzsMn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bfdxmGp5GxlJbuO167lOWo05K2VK5k8mzDBMvuxBN55hyGxlBTOzoYOVQ1AaKjlE9YNodUyJJKS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\n+AXJTbVsY6IfAocOqfC52bnbt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, 2], [[(0, -2.5), (0, 2.5)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. $x = 0, v_n < |v| < v_{n + 1}$\n", "\n", "Lisaks kiirustele $v_1$ ja $-v_1$ viivad sadulani ka algtingimused $(0, v_n)$, kus $n \\in \\mathbb{N}$, ja pendel ületab tippu $x = \\pi$ veel $n - 1$ korda enne kui ta läheneb sadulale. Teistele algtingimustele kujul $(0, v)$ vastavad sellised trajektoorid:\n", "\n", "* Kui $0 < |v| < v_1$, siis pendel lihtsalt võngub - seda me juba uurisime.\n", "* Kui $v_n < |v| < v_{n + 1}$, siis pendel ületab tippu $n$ korda samas suunas, enne kui ta jääb võnkuma.\n", "\n", "Teine trajektoori tüüp on siis selline:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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U9zs1Hc9w9SqnlXZ0cHJtZCRPY0wME/vWnA/QSH8IWAvpHzggy+0s1eXX1CRL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\nvVvkhRcad2DDhok8+aTIhg0iZWWtO0ZxM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, 5], [])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2a.\n", "\n", "$$S^{v+}_n = \\{(0, v), 0 < v < v_n\\} \\setminus \\{(0, v_1), \\ldots, (0, v_{n - 1})\\}$$\n", "\n", "Trajektoor, mis algab sellest hulgast $S^{v+}_n$ kiirusega $v$, mis rahuldab $v_k < v < v_{k + 1}$, kus $k < n$, jõuab hulka $S^{v+}_n$ tagasi, kui pendel on ükskord tippu ületanud ja liigub väiksema kiirusega edasi algses suunas läbi punkti $x = 0$. Kui algne kiirus $v$ rahuldab hoopis $0 < v < v_1$, kehtib sama kui seletatud punkti 1a all. Alljärgnev joonis näitab $S^{v+}_2$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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aGqFfZGfToq9fLwX86OgRFZEPnpSp0fCch4bSC09JMZ0Uoyh8L5EMvn6dhQie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\nDME88wwVTS1BRgbw4ovs8g0IoNSzMuPIzWUEZdEiyuW/8QaTnABnQun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mAAAg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\nQDhGPTAJ3RMcDXc82d+7nWiL6ENEOvQDQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, 5], [[(0, 0), (0, 5.55)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2a'.\n", "\n", "$$S^{v+}_{\\infty} = \\bigcup_{n = 1}^{\\infty}S^{v+}_n = \\{(0, v), v > 0\\} \\setminus \\{(0, v_n), n \\in \\mathbb{N}\\}$$\n", "\n", "Poincaré lõikeks sobib ka terve positiivne poolsirge, millest on eemaldatud need punktid, kust trajektoor läheneb sadulale." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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WYVi1TD+b6aZk3rjB61Ol4rlISKAgcHRkX6jf/Q74h38A/uzP5vc8iKyk8nLg4495zyxb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\nFkGE/w8WU9pnc5rS5wAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, 7], [[(0, 0), (0, 8)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2b.\n", "\n", "$$S^{v-}_n = \\{(0, v), -v_n < v < 0\\} \\setminus \\{(0, -v_1), \\ldots, (0, -v_{n - 1})\\}$$\n", "\n", "Siin kehtib kvalitatiivselt sama kui hulga $S^{v+}_n$ puhul, lihtsalt et algne kiirus on negatiivne. Alljärgnev joonis näitab $S^{v-}_2$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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vXUIigpubEAB+fvJ+p8btGS5dQrfShgZ0rg0Lw2mMiEBgX8nxAJX0TUAppL9r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\neOQR5uPvvht45x0KzIoVVj6+W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LYTuP9+kXffFfnuO9ePUVND8XUehY0YIXLFFfx3+/Z0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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, -5], [[(0, 0), (0, -5.55)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2b'.\n", "\n", "$$S^{v-}_{\\infty} = \\bigcup_{n = 1}^{\\infty}S^{v-}_n = \\{(0, v), v < 0\\} \\setminus \\{(0, -v_n), n \\in \\mathbb{N}\\}$$\n", "\n", "Poincaré lõikeks sobib ka terve negatiivne poolsirge, millest on eemaldatud need punktid, kust trajektoor läheneb sadulale." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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Xg69cgRDB1VUYAD8/ab9Tw/EMV65gWmlTEybXhoXhNEZGorAv53qAQvpGIBfS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\n9lVWMgcQE8PkYkoKY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Eyya0VbG1NGt22zrs+JE/zdqlV0mGJj+XCnNhpG9HvBXUT/kUfY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\nKf5r13JQGzUKqG+uR3ZZNlKOpCD1aCoOn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O4BMAfAuy61iNwKQAH4KoD5AL4Btr/4iSuN\nascHwD8A/LcrjVBKfRbAfwL4AYAlYCPANKXUeFfa1c5IALsBfA3udb/HAHgFQBiAleC13GiTmu1K\nToAFo0EAgsHv5odKqQCXWmVDu1PxCHiv9Q0R8agHgNUAPgHFrA3AIlfb1IOddwBoAeDlalu6se1b\nAIpdbYeNPf8EoMqFx88D8LLN/xXoVDzt6nPTyc42MNvN5bZ0Y9v4dvuiXW1LD/adB/Cwq+1ot2UU\ngE8BrACQAeBXfXm9R3n6SqmJAF4H8AUwz98tUUrdCBaU5YhIq6vt6YZxAFwaTnEX2sNcwWAaMQBA\n+M3cDCDCVXYNQsaBMxG3uq+UUkOUUp8Du/nmutqedn4L4GMRSe/Piz1K9AG8CeBVEdnlakO6Qyn1\nM6VUDYBzAKYDuMvFJnVBKeUP4AkAv3O1LW7CeHCPh869nyoBTLr25gw+lFIKwEsAtonIAVfbAwBK\nqQVKqcsAGsGeX3eLyCEXm4X2ASgQwHf7+x6DXvSVUi+0L2b09GhVSs1TSj0FTot+rl/qLrbZvOQX\n4AVNANAK4M9uZBuUUlMBpAD4u4i84S52GQY9r4LrRZ9ztSE2HAKwGEAouGb0P0qpW11pkFJqGjg4\nPigizf1+n/YY0aDFzoZtx8AFv9s7Pe8Fxs3fFpGHXWRbiYi0dPPaqeCCUoSI5LvaNqXUFDB+uN0Z\n56q/drW/5p8A/FpEbnSWXT3RHt6pA3CviHxk8/yfAIwVkbuvtU09oZRqA3CXrZ2uRin1X+D6VYyI\nlLnanp5QSm0C17Eed6ENdwJ4D3QItdPqBYbFWgEMEzsE3eUN1waK2N+w7UkA37d5agrYrOh+AAWu\ntK0HvNp/DnOQOR3oi23tA1A62Priy86wpz92uQMi0qyUKgQQD+Aj4Eq4Ih7Ab1xpm7vTLvh3Aljm\nzoLfzhA46bvYBzYDWNjpuT+BPcl+Zo/gA9eB6NuLiJTb/l8pVQuOliUicso1Vl2xJRRACIBtAC6A\n20I+D+AIXLx41O7hZ4KzpacBTKCmAdLzHgbXBKXUdAA3ApgJwEsptbj9V8Vi0377GvArAH9qF/8C\nMK11BPiFdClKqZHg/aQ9w9nt56lKRE640K5XATwAYB2A2vYkCwCoFhGXdsNVSv0UDGOWARgNJlUs\nA5DoSrva7+kOax7tOnZeROzeMMRjRL8H3CW2VQfm5j8H5lVXgDfdTwYSu3MQCQBmtz+0SCjw3Hn1\n9KJrxPMAHrL5v97tYjmArGtlhIj8oz0n/3kAE8G8+FUicvZa2dALS8GwnLQ//rP9+bfg5FnbVXgM\ntCez0/MPA/ifa25NRyaA52cygGoAewEk9jdbxsn0WcMGfUzfYDAYDPYz6LN3DAaDwWA/RvQNBoPB\ngzCibzAYDB6EEX2DwWDwIIzoGwwGgwdhRN9gMBg8CCP6BoPB4EEY0TcYDAYPwoi+wWAweBBG9A0G\ng8GDMKJvMBgMHoQRfYNhACilxiulKpRSz9g8F6mUalRKLXelbQZDd5iGawbDAFFKrQbwAbgn7mGw\ny+b7IvJtlxpmMHSDEX2DwQEopV4B21DvBLAAQIgbtMU2GLpgRN9gcABKqeEA9gOYBiDIXTb4Nhg6\nY2L6BoNj8Ae34BwCwM/FthgMPWI8fYNhgLRvjl4AYBeAT8HtEheIyDmXGmYwdIMRfYNhgCilXgS3\nu1wEbn2ZCeCSiNzhSrsMhu4w4R2DYQAopZYBeArAF0SkVuhFPQQgWin1qGutMxi6Yjx9g8Fg8CCM\np28wGAwehBF9g8Fg8CCM6BsMBoMHYUTfYDAYPAgj+gaDweBBGNE3GAwGD8KIvsFgMHgQRvQNBoPB\ngzCibzAYDB6EEX2DwWDwIIzoGwwGgwdhRN9gMBg8iP8HkUNECSNyDf8AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, -7], [[(0, 0), (0, -8)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2c.\n", "\n", "$$S^{v\\pm}_n = \\{(0, v), 0 < |v| < v_n\\} \\setminus \\{(0, \\pm v_1), \\ldots, (0, \\pm v_{n - 1})\\}$$\n", "\n", "Trajektoor, mis algab sellest hulgast $S^{v\\pm}_n$ kiirusega $v$, mis rahuldab $v_k < v < v_{k + 1}$, kus $k < n$, jõuab hulka $S^{v\\pm}_n$ tagasi, kui pendel on ükskord tippu ületanud ja liigub väiksema kiirusega edasi algses suunas läbi punkti $x = 0$. Kui algne kiirus $v$ rahuldab hoopis $0 < |v| < v_1$, kehtib sama kui seletatud punkti 1c all. Alljärgnev joonis näitab $S^{v\\pm}_2$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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aGqFfZGfToq9fLwX86OgRFZEPnpSp0fCch4bSC09JMZ0Uoyh8L5EMvn6dhQie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\nAaR3tVrGy7itYX6f0zcYDAZD5/H76h2DwWAwdB4j+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, 5], [[(0, -5.55), (0, 5.55)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2c'.\n", "\n", "$$S^{v\\pm}_{\\infty} = \\bigcup_{n = 1}^{\\infty}S^{v\\pm}_n = \\{(0, v), v \\neq 0\\} \\setminus \\{(0, \\pm v_n), n \\in \\mathbb{N}\\}$$\n", "\n", "Poincaré lõikeks sobib ka terve sirge $x = 0$, millest on eemaldatud need punktid, kust trajektoor läheneb sadulale." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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WYVi1TD+b6aZk3rjB61Ol4rlISKAgcHRkX6jf/Q74h38A/uzP5vc8iKyk8nLg4495zyxb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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([0, 7], [[(0, -8), (0, 8)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3. $0 < |x| < \\pi, v = 0$\n", "\n", "Kui me valime algtingimust $(x, 0)$ nii, et pendel on paigalolekus, aga ei asu püsipunktis, siis ta hakkab võnkuma, ületab alumist punkti $x = 0$, vahetab suunda, ületab punkti $x = 0$ vastassuunas jne:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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xfBYPBl++jEQEFxchAHx8pP1O9dszXL6MbqX19ehcGxKC0xgejsC+nOMBCukb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\naT1XfLTgvn3w0WdmitesrKDxnjmD89n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Rj71uHVwAd+9CKFy7Bi3ZygpaDR8gRYSgqp0d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\nMNM3DMPwEf8P+4zknDqB4esAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([3, 0], [])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3a.\n", "\n", "$$S^{x+} = \\{(x, 0), 0 < x < \\pi\\}$$\n", "\n", "Trajektoor, mis algab sellest hulgast $S^{x+}$, jõuab sinna tagasi, kui pendel on võnkunud ühes suunas $v < 0$ ja tagasi teises suunas $v > 0$, kuni ta on jälle paigalolekus ja vahetab teist korda liikumissuunda." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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xfBYPBl++jEQEFxchAHx8pP1O9dszXL6MbqX19ehcGxKC0xgejsC+nOMBCukb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\naT1XfLTgvn3w0WdmitesrKDxnjmD89n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Rj71uHVwAd+9CKFy7Bi3ZygpaDR8gRYSgqp0d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\nI8HF0QsAfArgS+hyiX1I7vRUmGE0gJm+Y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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([3, 0], [[(0, 0), (np.pi, 0)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3b.\n", "\n", "$$S^{x-} = \\{(x, 0), -\\pi < x < 0\\}$$\n", "\n", "Trajektoor, mis algab sellest hulgast $S^{x-}$, jõuab sinna tagasi, kui pendel on võnkunud ühes suunas $v > 0$ ja tagasi teises suunas $v < 0$, kuni ta on jälle paigalolekus ja vahetab teist korda liikumissuunda." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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Mn8WDwRcuIBHBy0sIgKAgab9T0/YMFy6gW2lTEzrXRkXhNMbEILAv53iAQvpm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\n904voHt3Ff8JE7SBFslYwObNO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BE5Dvo8OS3Dzv7rVERyu4d2ZQG4DMBEACX+IAsAKCbp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\nDcMwEggTfcMwjATCRN8wDCOB+H90IOueqXjl0QAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([-3, 0], [[(0, 0), (-np.pi, 0)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3c.\n", "\n", "$$S^{x\\pm} = \\{(x, 0), 0 < |x| < \\pi\\}$$\n", "\n", "Veel üks võimalus on valida hulka $S^{x\\pm}$ nii, et pendel on paigalolekus, ja asub kas vasakul või paremal pool. Trajektoor, mis algab sellest hulgast, jõuab sinna tagasi pärast esimest võnkumist, kui ta on jälle paigalolekus, kuid siis teisel pool tasakaalupunktist." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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xfBYPBl++jEQEFxchAHx8pP1O9dszXL6MbqX19ehcGxKC0xgejsC+nOMBCukb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\naT1XfLTgvn3w0WdmitesrKDxnjmD89n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Rj71uHVwAd+9CKFy7Bi3ZygpaDR8gRYSgqp0d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\nxIEDahMaIcgO0rE/d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wF8DuBr6HKJ3Unu9tQww6gFE33DiBEReRi63GVP6NKX\nHwPYR3K8l3YZRm2Ye8cwYkBEhgG4AcAkkiXUVtRlAIaIyFRvrTOMmlhL3zAMw0dYS98wDMNHmOgb\nhmH4CBN9wzAMH2GibxiG4SNM9A3DMHyEib5hGIaPMNE3DMPwESb6hmEYPsJE3zAMw0eY6BuGYfgI\nE33DMAwfYaJvGIbhI/4fzGMoBHNYHsYAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tplot([3, 0], [[(-np.pi, 0), (np.pi, 0)]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poincaré kujutus\n", "\n", "Lõpuks konstrueerime Poincaré kujutusi erinevate Poincaré lõigete valiku puhul. Täpsemalt uurime valikuid $S^{v+}_{\\infty}$, $S^{v\\pm}_{\\infty}$, $S^{x+}$ ja $S^{x\\pm}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $S^{v+}_{\\infty}$\n", "\n", "Kõigepealt uurime Poincaré lõiget\n", "\n", "$$S^{v+}_{\\infty} = \\{(0, v), v > 0\\} \\setminus \\{(0, v_n), n \\in \\mathbb{N}\\},$$\n", "\n", "ja konstrueerime Poincaré kujutust. Poincaré kujutuse $P$ kvalitativset käitumist saame leida, kui me vaatame erinevaid trajektoore. Sõltuvalt algtingimusest $(0, v)$ leiame:\n", "\n", "* Kui $0 < v < v_1$, siis pendel jõuab tagasi hulka $S^{v+}_{\\infty}$ siis, kui ta on edasi ja tagasi võnkunud, ja liigub taas algses suunas, kuid väiksemal kiirusel $P(v)$, mis rahuldab $0 < P(v) < v$.\n", "* Kui $v_1 < v < v_2$, siis pendel ületab tippu ja jõuab tagasi hulka $S^{v+}_{\\infty}$ kiirusega $P(v)$, mis on tipu ületamiseks liiga väike, ehk $0 < P(v) < v_1$.\n", "* Kui $v_n < v < v_{n + 1}$ ja $n > 1$, siis pendel ületab tippu ja jõuab tagasi hulka $S^{v+}_{\\infty}$ kiirusega $P(v)$, millega ta saab tippu veel $n - 1$ korda ületada, ehk $v_{n - 1} < P(v) < v_n$.\n", "\n", "Täpsemalt saame uurida Poincaré kujutust järgneva funktsiooni abil." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "def poinca(v0):\n", " y0 = [0, v0]\n", "\n", " # Eeldame, et trajektoor jõuab tagasi samasse hulka 20s jooksul, ja integreerime.\n", " t = np.linspace(0, 20, 1000)\n", " sol = odeint(pendel, y0, t, args = (h, k, m))\n", " \n", " # Jagame lahendust x ja v väärtusteks.\n", " xsol = np.mod(sol[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vsol = sol[:, 1]\n", " \n", " # Otsime, millal:\n", " # 1. Asukoha x absoluutväärtus on minimaalne (pendel ületab alumist punkti).\n", " # 2. Kiiruse v märk on sama kui algsel hetkel.\n", " xabs = np.fabs(xsol)\n", " xmin = np.r_[True, xabs[1:] < xabs[:-1]] & np.r_[xabs[:-1] < xabs[1:], True] & (vsol * v0 > 0)\n", " xzero = np.argwhere(xmin)\n", " first = xzero[1, 0]\n", " t0 = t[first]\n", "\n", " # Arvutame veel kord sobitatud ajasammuga, et tulemus oleks täpsem.\n", " t = np.linspace(0, 1.5 * t0, 1000)\n", " sol = odeint(pendel, y0, t, args = (h, k, m))\n", " xsol = np.mod(sol[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vsol = sol[:, 1]\n", " xabs = np.fabs(xsol)\n", " xmin = np.r_[True, xabs[1:] < xabs[:-1]] & np.r_[xabs[:-1] < xabs[1:], True] & (vsol * v0 > 0)\n", " xzero = np.argwhere(xmin)\n", " first = xzero[1, 0]\n", "\n", " # Tulemus on tagasituleku aeg T(v) ja Poincaré kujutus P(v).\n", " return [t[first], vsol[first]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Selle funktsiooni abil võime nüüd $T(v)$ ja $P(v)$ arvutada." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true }, "outputs": [], "source": [ "vv = np.linspace(0.01, 10, 500)\n", "res = np.array([poinca(v) for v in vv])\n", "tt = res[:, 0]\n", "pp = res[:, 1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Joonistame kõigepealt $T(v)$. Joonis näitab, et kiiruse $v = v_1$ ümbruses tagasitulekuaeg hajub, $T(v) \\to \\infty$. See on sellepärast, et sadula $(\\pi, 0)$ ümbruses liigub pendel aeglaselt, ja võnkumine võtab kauem aega." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_xlabel('v')\n", "ax.set_ylabel('T(v)')\n", "ax.plot(vv, tt)\n", "ax.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Järgmisena joonistame $P(v)$. Paneme tähele, et kehtib $0 < P(v) < v$, kuna pendel aeglustub, ja Poincaré lõige on valitud sellisena, et liikussuund on alati positiivne. Joonis näitab, et $P(v)$ ei ole pidev kiiruse $v = v_1$ ümbruses. Aga tuletame meelde, et vastav algtingimus $(0, v_1) \\notin S^{v+}_{\\infty}$. Seega on Poincaré kujutus siiski pidev oma lähtehulgas $S^{v+}_{\\infty}$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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FVatg2jS4807YdtumP6Yyj54yj54yT7ZYnM6Q+GvXrl3oEmJp6VK4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\niIiINMn/A50NKEnxi8TbAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_xlabel('v')\n", "ax.set_ylabel('P(v)')\n", "ax.plot(vv, pp)\n", "ax.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $S^{v\\pm}_{\\infty}$\n", "\n", "Järgmisena uurime Poincaré lõiget\n", "\n", "$$S^{v\\pm}_{\\infty} = \\{(0, v), v \\neq 0\\} \\setminus \\{(0, \\pm v_n), n \\in \\mathbb{N}\\},$$\n", "\n", "ja konstrueerime Poincaré kujutust. Poincaré kujutuse $P$ kvalitativset käitumist saame leida, kui me vaatame erinevaid trajektoore. Sõltuvalt algtingimusest $(0, v)$ leiame:\n", "\n", "* Kui $0 < |v| < v_1$, siis pendel jõuab tagasi hulka $S^{v\\pm}_{\\infty}$ siis, kui ta on oma liikumissuunda vahetanud, ja ületab punkti $x = 0$ kiirusel $P(v)$, mis rahuldab $0 < |P(v)| < v$ ja $\\mathrm{sgn} P(v) = -\\mathrm{sgn} v$.\n", "* Kui $v_1 < |v| < v_2$, siis pendel ületab tippu ja jõuab tagasi hulka $S^{v+}_{\\infty}$ kiirusega $P(v)$, mis on tipu ületamiseks liiga väike, ehk $0 < |P(v)| < v_1$, aga suund jääb samaks, $\\mathrm{sgn} P(v) = -\\mathrm{sgn} v$.\n", "* Kui $v_n < |v| < v_{n + 1}$ ja $n > 1$, siis pendel ületab tippu ja jõuab tagasi hulka $S^{v+}_{\\infty}$ kiirusega $P(v)$, millega ta saab tippu veel $n - 1$ korda ületada, ehk $v_{n - 1} < |P(v)| < v_n$, ja suund jääb samaks, $\\mathrm{sgn} P(v) = -\\mathrm{sgn} v$.\n", "\n", "Täpsemalt saame uurida Poincaré kujutust järgneva funktsiooni abil." ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def poincb(v0):\n", " y0 = [0, v0]\n", "\n", " # Eeldame, et trajektoor jõuab tagasi samasse hulka 20s jooksul, ja integreerime.\n", " t = np.linspace(0, 20, 1000)\n", " sol = odeint(pendel, y0, t, args = (h, k, m))\n", " \n", " # Jagame lahendust x ja v väärtusteks.\n", " xsol = np.mod(sol[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vsol = sol[:, 1]\n", " \n", " # Otsime, millal asukoha x absoluutväärtus on minimaalne (pendel ületab alumist punkti).\n", " xabs = np.fabs(xsol)\n", " xmin = np.r_[True, xabs[1:] < xabs[:-1]] & np.r_[xabs[:-1] < xabs[1:], True]\n", " xzero = np.argwhere(xmin)\n", " first = xzero[1, 0]\n", " t0 = t[first]\n", "\n", " # Arvutame veel kord sobitatud ajasammuga, et tulemus oleks täpsem.\n", " t = np.linspace(0, 1.5 * t0, 1000)\n", " sol = odeint(pendel, y0, t, args = (h, k, m))\n", " xsol = np.mod(sol[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vsol = sol[:, 1]\n", " xabs = np.fabs(xsol)\n", " xmin = np.r_[True, xabs[1:] < xabs[:-1]] & np.r_[xabs[:-1] < xabs[1:], True]\n", " xzero = np.argwhere(xmin)\n", " first = xzero[1, 0]\n", "\n", " # Tulemus on tagasituleku aeg T(v) ja Poincaré kujutus P(v).\n", " return [t[first], vsol[first]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Selle funktsiooni abil võime nüüd $T(v)$ ja $P(v)$ arvutada." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "vv = np.linspace(0.01, 10, 500)\n", "vv = np.concatenate((np.flipud(-vv), vv), 0)\n", "res = np.array([poincb(v) for v in vv])\n", "tt = res[:, 0]\n", "pp = res[:, 1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Joonistame kõigepealt $T(v)$. Joonis näitab, et kiiruse $v = \\pm v_1$ ümbruses tagasitulekuaeg hajub, $T(v) \\to \\infty$. See on sellepärast, et sadula $(\\pi, 0)$ ümbruses liigub pendel aeglaselt, ja võnkumine võtab kauem aega." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "image/png": 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+z/fo4U+ZLFpUuppEktbmoOGc65TQaROAq4BbgQVmthaYC1zjnNNJwQwZO3Zs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\n4brrfICKQxz9fP55OOMMPzr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_xlabel('v')\n", "ax.set_ylabel('T(v)')\n", "ax.plot(vv, tt)\n", "ax.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Järgmisena joonistame $P(v)$. Paneme tähele, et kehtib $0 < |P(v)| < |v|$, kuna pendel aeglustub, ja vahetab suunda täpselt siis kui $0 < v < v_1$. Joonis näitab, et $P(v)$ ei ole pidev kiiruse $v = \\pm v_1$ ümbruses. Aga tuletame veel kord meelde, et vastavad algtingimused $(0, \\pm v_1) \\notin S^{v\\pm}_{\\infty}$. Seega on Poincaré kujutus siiski pidev oma lähtehulgas $S^{v\\pm}_{\\infty}$." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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wzjlw662+SVm5DkYo+XTlKulfo9I2rb3CsTtQbWYPAI8As1ZeVTCzdev/vC9w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\nISIiIhmnhkNEREQyTg2HiIiIZNz/B1WLz/71jZfzAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_xlabel('v')\n", "ax.set_ylabel('P(v)')\n", "ax.plot(vv, pp)\n", "ax.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $S^{x+}$\n", "\n", "Uurime nüüd Poincaré lõiget\n", "\n", "$$S^{x+} = \\{(x, 0), 0 < x < \\pi\\},$$\n", "\n", "ja konstrueerime Poincaré kujutust. Poincaré kujutuse $P$ kvalitativne käitumine on tegelikult lihtne:\n", "\n", "* Kui $0 < x < \\pi$, siis pendel jõuab tagasi hulka $S^{x+}$ siis, kui ta on edasi ja tagasi võnkunud, ja vahetab suunda teist korda. Tema asukoht on siis $P(x)$, ja rahuldab $0 < P(x) < x$.\n", "\n", "Täpsemalt saame uurida Poincaré kujutust järgneva funktsiooni abil." ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "def poincc(x0):\n", " y0 = [x0, 0]\n", "\n", " # Eeldame, et trajektoor jõuab tagasi samasse hulka 20s jooksul, ja integreerime.\n", " t = np.linspace(0, 20, 1000)\n", " sol = odeint(pendel, y0, t, args = (h, k, m))\n", " \n", " # Jagame lahendust x ja v väärtusteks.\n", " xsol = np.mod(sol[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vsol = sol[:, 1]\n", " \n", " # Otsime, millal:\n", " # 1. Kiiruse v absoluutväärtus on minimaalne (pendel vahetab suunda).\n", " # 2. Asukoha x märk on sama kui algsel hetkel.\n", " vabs = np.fabs(vsol)\n", " vmin = np.r_[True, vabs[1:] < vabs[:-1]] & np.r_[vabs[:-1] < vabs[1:], True] & (xsol * x0 > 0)\n", " vzero = np.argwhere(vmin)\n", " first = vzero[1, 0]\n", " t0 = t[first]\n", "\n", " # Arvutame veel kord sobitatud ajasammuga, et tulemus oleks täpsem.\n", " t = np.linspace(0, 1.5 * t0, 1000)\n", " sol = odeint(pendel, y0, t, args = (h, k, m))\n", " xsol = np.mod(sol[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vsol = sol[:, 1]\n", " vabs = np.fabs(vsol)\n", " vmin = np.r_[True, vabs[1:] < vabs[:-1]] & np.r_[vabs[:-1] < vabs[1:], True] & (xsol * x0 > 0)\n", " vzero = np.argwhere(vmin)\n", " first = vzero[1, 0]\n", "\n", " # Tulemus on tagasituleku aeg T(x) ja Poincaré kujutus P(x).\n", " return [t[first], xsol[first]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Selle funktsiooni abil võime nüüd $T(x)$ ja $P(x)$ arvutada." ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": true }, "outputs": [], "source": [ "xx = np.linspace(0.01, np.pi - 0.01, 500)\n", "res = np.array([poincc(x) for x in xx])\n", "tt = res[:, 0]\n", "pp = res[:, 1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Joonistame kõigepealt $T(x)$. Joonis näitab, et tipu $x = \\pi$ ümbruses tagasitulekuaeg hajub, $T(x) \\to \\infty$. See on sellepärast, et sadula $(\\pi, 0)$ ümbruses liigub pendel aeglaselt, ja võnkumine võtab kauem aega." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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IKAunHFyhcli/Hk47DX7xC/jlL+Hyy9M3sqHXRHw0aVRERGK3ciVMnAg33ww3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\n7x//Rll6TTjl4JRDRFnEJxU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('T(x)')\n", "ax.plot(xx, tt)\n", "ax.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Järgmisena joonistame $P(x)$. Paneme tähele, et kehtib $0 < P(x) < x$, kuna pendel kaotab energiat, ja Poincaré lõige on valitud sellisena, et pendli asukoht $x$ on alati positiivne." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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H+OiKDpLTiBEjku5CKowYMYJPP4U+fcJYlGeegW98I+leJUP7RKAcIsoiUA7x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\nbEm79FJ4+WV4/vniKFCAsv+Fq6McIso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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('P(x)')\n", "ax.plot(xx, pp)\n", "ax.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $S^{x\\pm}$\n", "\n", "Lõpuks uurime Poincaré lõiget\n", "\n", "$$S^{x\\pm} = \\{(x, 0), 0 < |x| < \\pi\\},$$\n", "\n", "ja konstrueerime Poincaré kujutust. Poincaré kujutuse $P$ kvalitativne käitumine on ka sel juhul lihtne:\n", "\n", "* Kui $0 < |x| < \\pi$, siis pendel jõuab tagasi hulka $S^{x\\pm}$ siis, kui ta on teisele poole võnkunud, ja vahetab suunda esimest korda. Tema asukoht on siis $P(x)$, ja rahuldab $0 < |P(x)| < |x|$ ja $\\mathrm{sgn} P(x) = -\\mathrm{sgn} x$.\n", "\n", "Täpsemalt saame uurida Poincaré kujutust järgneva funktsiooni abil." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "def poincd(x0):\n", " y0 = [x0, 0]\n", "\n", " # Eeldame, et trajektoor jõuab tagasi samasse hulka 20s jooksul, ja integreerime.\n", " t = np.linspace(0, 20, 1000)\n", " sol = odeint(pendel, y0, t, args = (h, k, m))\n", " \n", " # Jagame lahendust x ja v väärtusteks.\n", " xsol = np.mod(sol[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vsol = sol[:, 1]\n", " \n", " # Otsime, millal kiiruse v absoluutväärtus on minimaalne (pendel vahetab suunda).\n", " vabs = np.fabs(vsol)\n", " vmin = np.r_[True, vabs[1:] < vabs[:-1]] & np.r_[vabs[:-1] < vabs[1:], True]\n", " vzero = np.argwhere(vmin)\n", " first = vzero[1, 0]\n", " t0 = t[first]\n", "\n", " # Arvutame veel kord sobitatud ajasammuga, et tulemus oleks täpsem.\n", " t = np.linspace(0, 1.5 * t0, 1000)\n", " sol = odeint(pendel, y0, t, args = (h, k, m))\n", " xsol = np.mod(sol[:, 0] + np.pi, 2 * np.pi) - np.pi\n", " vsol = sol[:, 1]\n", " vabs = np.fabs(vsol)\n", " vmin = np.r_[True, vabs[1:] < vabs[:-1]] & np.r_[vabs[:-1] < vabs[1:], True]\n", " vzero = np.argwhere(vmin)\n", " first = vzero[1, 0]\n", "\n", " # Tulemus on tagasituleku aeg T(x) ja Poincaré kujutus P(x).\n", " return [t[first], xsol[first]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Selle funktsiooni abil võime nüüd $T(x)$ ja $P(x)$ arvutada." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": true }, "outputs": [], "source": [ "xx = np.linspace(0.01, np.pi - 0.01, 500)\n", "xx = np.concatenate((np.flipud(-xx), xx), 0)\n", "res = np.array([poincd(x) for x in xx])\n", "tt = res[:, 0]\n", "pp = res[:, 1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Joonistame kõigepealt $T(x)$. Joonis näitab, et tipu $x = \\pm\\pi$ ümbruses tagasitulekuaeg hajub, $T(x) \\to \\infty$. See on sellepärast, et sadula $(\\pm\\pi, 0)$ ümbruses liigub pendel aeglaselt, ja võnkumine võtab kauem aega." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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aiggNHw4vv+z3rBARkbZ58EEYNAj69g1dSfqoqUi5ioqKBseOPho6d45vtKKx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\nU6Y4t3FjvFnrU864ZCXnSSe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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('T(x)')\n", "ax.plot(xx, tt)\n", "ax.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Järgmisena joonistame $P(x)$. Paneme tähele, et kehtib $0 < |P(x)| < |x|$ ja $\\mathrm{sgn} P(x) = -\\mathrm{sgn} x$, kuna pendel kaotab energiat, ja Poincaré lõige on valitud sellisena, et pendli asukoht $x$ vahetab märki igal võnkumisel." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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wipkNNbMuwE1AG/zZEsxshpldXuv11wCHmNloM9vJzCbgB8teV+A6RaQAmjWD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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('P(x)')\n", "ax.plot(xx, pp)\n", "ax.grid()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 1 }