Class_Work/ME_2016/HW1.ipynb
2024-09-18 16:35:33 -04:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "d9b87334-514c-41fa-aab5-ecef29c4c94d",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sympy import *"
]
},
{
"cell_type": "markdown",
"id": "6b45c0a5-2069-4b11-b208-e2fa3dcc1820",
"metadata": {},
"source": [
"**Dane Sabo**\n",
"\n",
"*September 18th, 2024*"
]
},
{
"cell_type": "markdown",
"id": "0f1d7205-998f-4cbc-b3b3-df3afda5804c",
"metadata": {},
"source": [
"# Instructions\n",
"\n",
"Please do a written solution for problems 1 and 2. We will review them on Monday, Sept 16 in class prior to the assignment being due.\n",
"\n",
"Please upload a Jupyter Notebook for problems 3 and 4.\n",
"\n",
"Problems 1 and 2 are worth 10 points each, problems 3 and 4 are worth 15 points each.\n",
"\n",
"# Written Problems\n",
"**I assumed for both of these written problems that $t>0$.**\n",
"\n",
"## Problem 1\n",
"Please find the general solution of \n",
"$$\n",
"\\bf{\\dot{X}} = \n",
"\\begin{bmatrix} \n",
"-1 & 5 & 2\\\\ \n",
"4 & -1 & -2\\\\\n",
"0 & 0 & 6\n",
"\\end{bmatrix}\n",
"\\bf{X}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "fc73f387-de90-4c25-b24c-ec91ea774ce8",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}\\frac{d}{d t} x_{1}{\\left(t \\right)}\\\\\\frac{d}{d t} x_{2}{\\left(t \\right)}\\\\\\frac{d}{d t} x_{3}{\\left(t \\right)}\\end{matrix}\\right] = \\left[\\begin{matrix}- x_{1}{\\left(t \\right)} + 5 x_{2}{\\left(t \\right)} + 2 x_{3}{\\left(t \\right)}\\\\4 x_{1}{\\left(t \\right)} - x_{2}{\\left(t \\right)} - 2 x_{3}{\\left(t \\right)}\\\\6 x_{3}{\\left(t \\right)}\\end{matrix}\\right]$"
],
"text/plain": [
"Eq(Matrix([\n",
"[Derivative(x1(t), t)],\n",
"[Derivative(x2(t), t)],\n",
"[Derivative(x3(t), t)]]), Matrix([\n",
"[-x1(t) + 5*x2(t) + 2*x3(t)],\n",
"[ 4*x1(t) - x2(t) - 2*x3(t)],\n",
"[ 6*x3(t)]]))"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"t = symbols('t', positive=True)\n",
"s = symbols('s')\n",
"\n",
"x = Matrix([Function('x1')(t), Function('x2')(t), Function('x3')(t)])\n",
"x_dot = x.diff(t) \n",
"A = Matrix([[-1, 5, 2],[4, -1, -2], [0, 0, 6]])\n",
"\n",
"eq = Eq(x_dot,A*x)\n",
"eq"
]
},
{
"cell_type": "markdown",
"id": "9203ea18-e9e6-424b-bb2e-c12ef880f40b",
"metadata": {},
"source": [
"First we have to find the fundamental matrix $\\bf{\\Psi}(t) = e^{\\bf{A}t}$:\n",
"$$e^{\\bf{A}t} = \\mathcal{L}^{-1} \\{ (sI-\\bf{A})^{-1} \\} $$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "bcfcdd55-34a5-4fb5-a91c-f1b540cef71f",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)} & \\frac{\\sqrt{5} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{2} & \\frac{4 e^{6 t}}{29} + \\frac{3 \\sqrt{5} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{29} - \\frac{4 e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)}}{29}\\\\\\frac{2 \\sqrt{5} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{5} & e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)} & - \\frac{6 e^{6 t}}{29} - \\frac{8 \\sqrt{5} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{145} + \\frac{6 e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)}}{29}\\\\0 & 0 & e^{6 t}\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[ exp(-t)*cosh(2*sqrt(5)*t), sqrt(5)*exp(-t)*sinh(2*sqrt(5)*t)/2, 4*exp(6*t)/29 + 3*sqrt(5)*exp(-t)*sinh(2*sqrt(5)*t)/29 - 4*exp(-t)*cosh(2*sqrt(5)*t)/29],\n",
"[2*sqrt(5)*exp(-t)*sinh(2*sqrt(5)*t)/5, exp(-t)*cosh(2*sqrt(5)*t), -6*exp(6*t)/29 - 8*sqrt(5)*exp(-t)*sinh(2*sqrt(5)*t)/145 + 6*exp(-t)*cosh(2*sqrt(5)*t)/29],\n",
"[ 0, 0, exp(6*t)]])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"psi_t = ((s*eye(3) - A).inv()).applyfunc(lambda i: inverse_laplace_transform(i,s,t))\n",
"psi_t"
]
},
{
"cell_type": "markdown",
"id": "36a38aad-7fee-4d94-924c-75afc0cffd1e",
"metadata": {},
"source": [
"Now that we have our fundamental matrix, we know the following is true for an autonomous system:\n",
"$$ {\\bf{x}}(t) = {\\bf{\\Psi}}(t) {\\bf{C}}$$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "26b31bac-00b4-429e-aabc-26757b8f4702",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}c_{1} e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)} + \\frac{\\sqrt{5} c_{2} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{2} + c_{3} \\left(\\frac{4 e^{6 t}}{29} + \\frac{3 \\sqrt{5} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{29} - \\frac{4 e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)}}{29}\\right)\\\\\\frac{2 \\sqrt{5} c_{1} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{5} + c_{2} e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)} + c_{3} \\left(- \\frac{6 e^{6 t}}{29} - \\frac{8 \\sqrt{5} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{145} + \\frac{6 e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)}}{29}\\right)\\\\c_{3} e^{6 t}\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[ c1*exp(-t)*cosh(2*sqrt(5)*t) + sqrt(5)*c2*exp(-t)*sinh(2*sqrt(5)*t)/2 + c3*(4*exp(6*t)/29 + 3*sqrt(5)*exp(-t)*sinh(2*sqrt(5)*t)/29 - 4*exp(-t)*cosh(2*sqrt(5)*t)/29)],\n",
"[2*sqrt(5)*c1*exp(-t)*sinh(2*sqrt(5)*t)/5 + c2*exp(-t)*cosh(2*sqrt(5)*t) + c3*(-6*exp(6*t)/29 - 8*sqrt(5)*exp(-t)*sinh(2*sqrt(5)*t)/145 + 6*exp(-t)*cosh(2*sqrt(5)*t)/29)],\n",
"[ c3*exp(6*t)]])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = Matrix([symbols('c1:4')])\n",
"psi_t*c.transpose()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "f75fc677-968c-4076-b4d8-06634896a70f",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}x_{1}{\\left(t \\right)}\\\\x_{2}{\\left(t \\right)}\\\\x_{3}{\\left(t \\right)}\\end{matrix}\\right] = \\left[\\begin{matrix}c_{1} e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)} + \\frac{\\sqrt{5} c_{2} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{2} + c_{3} \\left(\\frac{4 e^{6 t}}{29} + \\frac{3 \\sqrt{5} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{29} - \\frac{4 e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)}}{29}\\right)\\\\\\frac{2 \\sqrt{5} c_{1} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{5} + c_{2} e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)} + c_{3} \\left(- \\frac{6 e^{6 t}}{29} - \\frac{8 \\sqrt{5} e^{- t} \\sinh{\\left(2 \\sqrt{5} t \\right)}}{145} + \\frac{6 e^{- t} \\cosh{\\left(2 \\sqrt{5} t \\right)}}{29}\\right)\\\\c_{3} e^{6 t}\\end{matrix}\\right]$"
],
"text/plain": [
"Eq(Matrix([\n",
"[x1(t)],\n",
"[x2(t)],\n",
"[x3(t)]]), Matrix([\n",
"[ c1*exp(-t)*cosh(2*sqrt(5)*t) + sqrt(5)*c2*exp(-t)*sinh(2*sqrt(5)*t)/2 + c3*(4*exp(6*t)/29 + 3*sqrt(5)*exp(-t)*sinh(2*sqrt(5)*t)/29 - 4*exp(-t)*cosh(2*sqrt(5)*t)/29)],\n",
"[2*sqrt(5)*c1*exp(-t)*sinh(2*sqrt(5)*t)/5 + c2*exp(-t)*cosh(2*sqrt(5)*t) + c3*(-6*exp(6*t)/29 - 8*sqrt(5)*exp(-t)*sinh(2*sqrt(5)*t)/145 + 6*exp(-t)*cosh(2*sqrt(5)*t)/29)],\n",
"[ c3*exp(6*t)]]))"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq2 = Eq(x,psi_t*c.transpose())\n",
"eq2"
]
},
{
"cell_type": "markdown",
"id": "14643f79-07ea-4d87-b81e-39244b1a3fa7",
"metadata": {},
"source": [
"## Problem 2\n",
"Please find the general solution of \n",
"$$\n",
"\\bf{\\dot{X}} = \n",
"\\begin{bmatrix} \n",
"-6 & 5 \\\\ \n",
"-5 & 4 \\\\\n",
"\\end{bmatrix}\n",
"\\bf{X}\n",
"$$\n",
"\n",
"Following the same process as problem 1:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "390b5ac8-c156-4606-8d69-1b86b80fcefd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"⎡d ⎤ \n",
"⎢──(x₁(t))⎥ \n",
"⎢dt ⎥ ⎡-6⋅x₁(t) + 5⋅x₂(t)⎤\n",
"⎢ ⎥ = ⎢ ⎥\n",
"⎢d ⎥ ⎣-5⋅x₁(t) + 4⋅x₂(t)⎦\n",
"⎢──(x₂(t))⎥ \n",
"⎣dt ⎦ \n"
]
}
],
"source": [
"t = symbols('t', positive=True)\n",
"s = symbols('s')\n",
"\n",
"x = Matrix([Function('x1')(t), Function('x2')(t)])\n",
"x_dot = x.diff(t) \n",
"A = Matrix([[-6, 5],[-5, 4]])\n",
"\n",
"eq = Eq(x_dot,A*x)\n",
"eq"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "d1cb0d2f-0618-4ef5-b0fe-d7d47dc7f3d6",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}- 5 t e^{- t} + e^{- t} & 5 t e^{- t}\\\\- 5 t e^{- t} & 5 t e^{- t} + e^{- t}\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[-5*t*exp(-t) + exp(-t), 5*t*exp(-t)],\n",
"[ -5*t*exp(-t), 5*t*exp(-t) + exp(-t)]])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"psi_t = ((s*eye(2) - A).inv()).applyfunc(lambda i: inverse_laplace_transform(i,s,t))\n",
"psi_t"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "1f829f42-f36b-41af-80f7-71885cfe9193",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}c_{1} \\left(- 5 t e^{- t} + e^{- t}\\right) + 5 c_{2} t e^{- t}\\\\- 5 c_{1} t e^{- t} + c_{2} \\left(5 t e^{- t} + e^{- t}\\right)\\end{matrix}\\right]$"
],
"text/plain": [
"Matrix([\n",
"[c1*(-5*t*exp(-t) + exp(-t)) + 5*c2*t*exp(-t)],\n",
"[-5*c1*t*exp(-t) + c2*(5*t*exp(-t) + exp(-t))]])"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c = Matrix([symbols('c1:3')])\n",
"psi_t*c.transpose()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "4bde70fb-c015-4a0b-b4e4-dadd5b88333d",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\left[\\begin{matrix}x_{1}{\\left(t \\right)}\\\\x_{2}{\\left(t \\right)}\\end{matrix}\\right] = \\left[\\begin{matrix}c_{1} \\left(- 5 t e^{- t} + e^{- t}\\right) + 5 c_{2} t e^{- t}\\\\- 5 c_{1} t e^{- t} + c_{2} \\left(5 t e^{- t} + e^{- t}\\right)\\end{matrix}\\right]$"
],
"text/plain": [
"Eq(Matrix([\n",
"[x1(t)],\n",
"[x2(t)]]), Matrix([\n",
"[c1*(-5*t*exp(-t) + exp(-t)) + 5*c2*t*exp(-t)],\n",
"[-5*c1*t*exp(-t) + c2*(5*t*exp(-t) + exp(-t))]]))"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"eq2 = Eq(x,psi_t*c.transpose())\n",
"eq2"
]
},
{
"cell_type": "markdown",
"id": "4c0f6f7a-d495-4f06-8d7c-a81f0f9ac2fc",
"metadata": {},
"source": [
"# Python Problems\n",
"## Problem 3\n",
"The Archimedes Spiral can be plotted by taking all the positive whole numbers (e.g.j = 0, 1, 2, 3, 4, 5, ...) and putting them into the format $n = (j,j)$ , and plotting them in polar coordinates where the first term, $n_1$, is the radius, and the second term, $n_2$, is the angle in radians.\n",
"### Part A\n",
"You need to plot the first 1000 terms in a scatter plot. In addition, we would like to only look at the top right quadrant! What you're going for is shown in Figure 1."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "5e4b28fb-f18f-44ae-887e-9088446f2e5d",
"metadata": {},
"outputs": [],
"source": [
"archimedes_nos = np.array(range(1000))"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "7bcd76ea-9df5-40a5-a19b-382afcecee98",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Archimedes Spiral, 1st Quadrant')"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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3lf6NHz8ely5dwmeffVbteho1aoSePXviL3/5C06ePOnynixXl48++ijKysoqdScB9rmQHI1aamoqQkJCsGDBApeyO+4Aq7jO/Px8fPXVV5Xeu3DhAkpLSwGg0q3SVqsVnTp1AgC343wcdu7c6fZxJCdOnMC+ffvcdpu8++67zv8XQuDdd99FSEiIx3c7ATczBhXr0N228IerV6/i2rVrLq+1atUK9evXd9mOdevWrfVMyN27d0daWhqys7OxcuXKSu+/+OKLOHjwIJ577jnnJJQtWrRAUFCQcwyYw8KFC13+ru32CwoKQnp6OlasWOFy/Ozfv9/tvlWVoKAgWCwWl8zU8ePHsWLFilqvoyLHXFKcWZq8xYwQSe2zzz7DpUuX3M6fAtgbiUaNGiEnJwe/+93vql3X/Pnzcffdd+PXv/41Ro0ahaSkJBw/fhz/93//hx07duhQes/06tULo0ePxpw5c7Bjxw6kpaUhJCQEhw4dwscff4x33nkHv/3tb9GoUSP813/9F+bMmYP7778f/fv3x/bt2/Hll186bx92mDJlCj777DPcf//9GD58OLp06YIrV65g9+7d+Mc//oHjx48jNjYW/+///T+cP38effr0QWJiIk6cOIEFCxagc+fOaNu2bZVlzsvLw4wZM/DAAw+ge/fuznmC/vKXv+D69euVnhcWHh6O3NxcZGRkoFu3bvjyyy/xf//3f/jDH/7gVddfZGSkcxxOSUkJmjZtin/96184duxYrT7vmKogOzu7xlmeP//8c+zcuROAfUbtXbt2Obv9HnjgAXTq1AkHDx5E37598eijj6Jdu3YIDg7Gp59+iqKiIgwZMsS5ri5duiArKwuvvPIKkpOTERcXhz59+lT53R988AH69OmDBx98EI8//jjuueceXL9+HZ988gnWrl2LJ554As8884xz+aioKDzyyCNYsGABLBYLWrVqhZUrVzrHhHmz/WbOnInc3Fzcc889GDt2LEpLS7FgwQK0b9/e2TVXkwEDBuDtt9/Gfffdh8cffxxnzpzBe++9h+Tk5Fqvo6IuXboAsAeEQ4YMQUhICAYOHOjXyTbJ4AJ2vxpRLQwcOFCEh4eLK1euVLnM8OHDRUhIiDh79qzz9uCqbl/es2ePGDRokIiOjhbh4eHi1ltvFdOmTXO+77hNu/yt3EK4v/W6qtvnt27d6vLZqtaZkZEh6tatW6mMixcvFl26dBERERGifv36omPHjuK5554TP/74o3OZsrIyMXPmTNG4cWMREREh7r33XrFnz55KZRJCiEuXLompU6eK5ORkERoaKmJjY8Vdd90l3nrrLXHjxg0hhBD/+Mc/RFpamoiLixOhoaGiefPmYvTo0eL06dNut6PD0aNHxfTp00X37t1FXFycCA4OFo0aNRIDBgwQq1evdvt7jxw5ItLS0kSdOnVEfHy8mDFjhigrK3NZFlXcPl9xGwohREFBgbNOo6KixCOPPCJ+/PHHSutwV4cLFiwQAERubm61v9NRfgBu/zluRz979qwYN26caNOmjahbt66IiooS3bp1E3//+99d1lVYWCgGDBgg6tevLwDU6lb6S5cuiZkzZ4r27duL8PBw53eX33/L++mnn8TgwYNFnTp1RIMGDcTo0aPFnj17Kt0+X9vtJ4QQ69atE126dBGhoaHilltuEYsWLXLWTXkAxLhx49yWa8mSJaJ169YiLCxMtGnTRmRnZ3u0Dnf7+OzZs0XTpk2F1WrlrfTkMYsQkvQLEJGpDR8+HP/4xz9w+fLlQBfF6dFHH8Xx48exZcuWQBfFY6dOncJdd92F0tJS5Ofnu73DiohqxjFCRKQkIQTWrl2r6V1t/tS0aVPk5ubi2rVr+M1vfsNbyom8xDFCRKQki8VSacyM0bRt21bzZ6oRqYYZISIiIlKWx4HQ+vXrMXDgQDRp0gQWi6XSbY9CCEyfPh2NGzdGREQEUlNTK809cf78eQwdOhSRkZGIjo5GZmZmpXEDjgdkhoeHo1mzZpg7d67nv46IpLF06VKpxgcREQFeBEJXrlzBbbfd5nZyOwCYO3cu5s+fj0WLFmHz5s2oW7cu0tPTXebWGDp0KPbu3Yu8vDysXLkS69evx6hRo5zvFxcXIy0tDS1atMC2bdvw5ptv4uWXX8bixYu9+IlERERE7vl015jFYsGnn36Khx56CIA9G9SkSRM8++yz+K//+i8A9mfVxMfHY+nSpRgyZAj279+Pdu3aYevWrejatSsAIDc3F/3790dBQQGaNGmCrKwsvPjiiygsLERoaCgA4IUXXsCKFSvw/fff+/iTiYiIiOw0HSx97NgxFBYWukznHxUVhW7duiE/Px9DhgxBfn4+oqOjnUEQYJ8p12q1YvPmzRg0aBDy8/PRs2dPZxAEAOnp6XjjjTfw888/V3qwJGCf/bb8zK02mw3nz59HTEwMp2AnIiIyCCEELl26hCZNmsBq1X8os6aBkOMJy/Hx8S6vx8fHO98rLCys9ITk4OBgNGzY0GWZik8udqyzsLDQbSA0Z84czJw5U5sfQkRERAH1ww8/IDExUffvMc3t81OnTsXkyZOdf1+8eBHNmzfHwYMH0bBhQ4/WdeoUcPSoBbfcItC0qdYlVU9JSQnWrFmD3r17IyQkJNDFURrrQh6sC7mwPuRx/vx5/OpXv0L9+vX98n2aBkIJCQkAgKKiIjRu3Nj5elFRETp37uxcpuLcHaWlpTh//rzz8wkJCSgqKnJZxvG3Y5mKwsLCXJ5m7NCwYUPExMTU+jcsWQKMGgXYbIDVCixeDGRm1vrj5EZJSQnq1KmDmJgYnmACjHUhD9aFXFgf8vHXsBZNO9+SkpKQkJCAVatWOV8rLi7G5s2bkZKSAgBISUnBhQsXsG3bNucyq1evhs1mQ7du3ZzLrF+/HiUlJc5l8vLycOutt7rtFtNKQcHNIAiw/3f0aPvrREREZD4eB0KXL1/Gjh07nE/rPnbsGHbs2IGTJ0/CYrFg0qRJeOWVV/DZZ59h9+7dGDZsGJo0aeK8s6xt27a47777MHLkSGzZsgX//ve/MX78eAwZMgRNmjQBADz++OMIDQ1FZmYm9u7di7/97W945513XLq+9HDo0M0gyKGsDDh8WNevJSIiogDxuGvs22+/Re/evZ1/O4KTjIwMLF26FM899xyuXLmCUaNG4cKFC7j77ruRm5uL8PBw52dycnIwfvx49O3bF1arFYMHD8b8+fOd70dFReFf//oXxo0bhy5duiA2NhbTp093mWtID61b27vDygdDQUFAcrKuX0tEREQB4nEgdO+996K6qYcsFgtmzZqFWbNmVblMw4YNsWzZsmq/p1OnTvjmm288LZ5PEhPtY4JGj7ZngoKCgPfft79ORERE5mOau8a0kpkJpKfbu8OSkxkEERERmRkDITcSExkAERERqYBPnyciIiJlMRAiIiIiZTEQIiIiImUxECIiIiJlMRAiIiIiZTEQIo8VFABr1vDRI0REZHwMhMgjS5YALVoAffrY/7tkSaBLRERE5D0GQlRrfCgtERGZDQMhqjU+lPYmdg8SEZkDAyEvqNoIOh5KW56KD6Vl9yARkXkwEPKQyo2g46G0QUH2v1V8KC27B4mIzIWBkAfYCNofSnv8uD0jdvy4/W+VsHuQiMhc+NBVD1TXCKqUFVH5obSO7sHy+4GK3YNERGbBjJAHOEaG2D1IRGQuDIQ8wEaQAHYPEhGZCbvGPJSZCaSn27vDkpMZBKlK5e5BIiIzYSDkBTaCRERE5sCuMSIiIlIWAyEiIiJSFgMhIiIiUhYDISIiIlIWAyEiIiJSFgMh8pmqD6ElIiLjYyBEPlH5IbRERGR8DITIa3wILRERGR0DIQ2p1kWk+pPYVatvIiIzYiCkERW7iFR+CK2K9U1EZEYMhDSgaheRqg+hVbW+iYjMiM8a00B1XURmDwpUfAityvVNRGQ2DIQ04OgiKt84qtJFBKj3EFrV65uIyEzYNaYBVbuIVMX6JiIyD2aENKJiF5HKWN9ERObAQEhDqnURqY71TURkfOwaIyIiImUxECIiIiJlMRAiIo9xVm0iMgsGQkTkEc6qTURmwkCIiGqNs2oTkdkwECKiWlP9QbtEZD4MhEhTHDtibio/aJeIzImBEGmGY0fMj7NqE5HZMBAiTXDsiDoyM4Hjx+2Zv+PH7X8TERkVZ5b2g4IC+9iK1q3Ne+Vc3diR+PjAlIn0w1m1icgsmBHSmSrdRaqOHeGYKCIiY2MgpCOVuotUHDuiSpBLRGRmDIR0pNqtxiqNHVEpyCUiMjOOEdKRo7uofDBk9u4iVcaOVBfkqvD7iYjMghkhHanYXaQKVcdEERGZDQMhnanUXaQSBrlERObArjE/UKW7SDWZmUB6ur07LDmZdUxEZEQMhIh8wCCXiMjY2DVGREREymIgRES1xgkkichsGAgRUa1wAkkiMiMGQkRUI04gSURmxUCIiGqk2izpRKQOBkKkC44lMRdOIElEZsVAiDRXcSxJdrYl0EUiH3ECSSIyKwZCpCl3Y0nGjg3C2bPhgS0Y+YyzpBORGXFCxQAqKLCPvWjd2jxX1u7Hklhw+nTdwBSINMUJJInIbJgRChCz3orsfiyJQOPGVwJTIB1xHBQRkfFpHgiVlZVh2rRpSEpKQkREBFq1aoXZs2dDCOFcRgiB6dOno3HjxoiIiEBqaioOHTrksp7z589j6NChiIyMRHR0NDIzM3H58mWtixsQZr4V2d1YkoULyxAbey2wBdOYWQNZIiLVaB4IvfHGG8jKysK7776L/fv344033sDcuXOxYMEC5zJz587F/PnzsWjRImzevBl169ZFeno6rl272VgOHToUe/fuRV5eHlauXIn169dj1KhRWhc3IMx+K3LFsSQjRoiaPmIoZg5kiYhUo/kYoY0bN+LBBx/EgAEDAAAtW7bERx99hC1btgCwZ4PmzZuHl156CQ8++CAA4IMPPkB8fDxWrFiBIUOGYP/+/cjNzcXWrVvRtWtXAMCCBQvQv39/vPXWW2jSpInWxfYrR/dR+WDIbLcilx9LUlIS2LJorbpAluNniIiMRfNA6K677sLixYtx8OBB/OpXv8LOnTuxYcMGvP322wCAY8eOobCwEKmpqc7PREVFoVu3bsjPz8eQIUOQn5+P6OhoZxAEAKmpqbBardi8eTMGDRpU6XuvX7+O69evO/8uLi4GAJSUlKBEspY4Ph7IyrJg7NgglJVZEBQksHBhGeLjhemCBgDO7S9bPXirZUvAag2GzXZzWoCgIIEWLUqlrz+z1YWRsS7kwvqQh7/rQPNA6IUXXkBxcTHatGmDoKAglJWV4dVXX8XQoUMBAIWFhQCA+Ph4l8/Fx8c73yssLERcXJxrQYOD0bBhQ+cyFc2ZMwczZ86s9PqaNWtQp04dn3+X1uLjgfffD8fp03XRuPEVxMZewxdfBLpU+srLywt0ETQzZkxzZGXdBpvNCqvVhqee2oldu05i165Al6x2zFQXRse6kAvrI/CuXr3q1+/TPBD6+9//jpycHCxbtgzt27fHjh07MGnSJDRp0gQZGRlaf53T1KlTMXnyZOffxcXFaNasGXr37o2YmBjdvpdqVlJSgry8PPTr1w8hISGBLo4m+vcHnn22DEeO2NCqlUBiYgcAHQJdrBqZsS6MinUhF9aHPM6dO+fX79M8EJoyZQpeeOEFDBkyBADQsWNHnDhxAnPmzEFGRgYSEhIAAEVFRWjcuLHzc0VFRejcuTMAICEhAWfOnHFZb2lpKc6fP+/8fEVhYWEICwur9HpISAh3akmYrS6Skuz/jMhsdWFkrAu5sD4Cz9/bX/O7xq5evQprhYlkgoKCYPvP6NKkpCQkJCRg1apVzveLi4uxefNmpKSkAABSUlJw4cIFbNu2zbnM6tWrYbPZ0K1bN62LTERERIrSPCM0cOBAvPrqq2jevDnat2+P7du34+2338aTTz4JALBYLJg0aRJeeeUVtG7dGklJSZg2bRqaNGmChx56CADQtm1b3HfffRg5ciQWLVqEkpISjB8/HkOGDDH8HWNEZAxmnPmdiCrTPBBasGABpk2bhrFjx+LMmTNo0qQJRo8ejenTpzuXee6553DlyhWMGjUKFy5cwN13343c3FyEh998HlVOTg7Gjx+Pvn37wmq1YvDgwZg/f77WxSWiGqgYECxZcnOuKKvVPkkon61GZE6aB0L169fHvHnzMG/evCqXsVgsmDVrFmbNmlXlMg0bNsSyZcu0Lh4ReUDFgKCqCTPT09UJBIlUwmeNEZFbqs6gbfaZ34nIFQMh0lVBAbB2rQVnz4bXvDBJRdWAwP2Dg8018zsR3cRAiHTjeDBpWlowRo5MQ3a2peYPkTRUDQjcPTj4/ffZLUZkVgyEJFJQYH9QqRm6Hip2qwhhf6SIGX6bKlQOCCo+ONjs46KIVKb5YGnyjtkGpbrvVrHwwaQGk5lpHyR8+LA9E6RS3ZV/cDARmRczQhIw46BU990qwjTdKmbK3tUkMRG4914GBURkTgyEJGDGQakVu1WsVhsWLiwzRWPqGPvUp4/9v0uWBLpERETkLQZCEjDroFTHOIu8vFIsXpyHESNEoIvkMzNm74iIVMZASAJmHpSamAj06iUQG3st0EXRhBmzd0REKuNgaUmoPCjVSBzZu/LBkBmyd0REqmJGSCIclCo/M2fviIhUxIwQkYeYvSMiMg8GQkRe4BwzRETmwK4xIlKaSnNCEVFlDISISFmcE4qIGAgRkQtVMiScE4qIAAZCRFSOShkSzglFRAADISL6D9UyJGad0Z2IPMNAiHRXUADs3h1r2gbVLFTLkHBOKCICGAiRzpYsAZKTgzFtWg8kJwebuqvF6FTMkDieh7dmjf2/mZmBLpH/qTImjKgqDIQkZvQT1M2uFgsA+3/N3NVidKpmSFSe0V2lMWFEVWEgJCkznKBU62oxA2ZI1KHamDCiqjAQkpBZTlBm7GoxepauNlTOkKiEFypEdgyEJGSWE9TNrhYBwP5fI3e1mCFLR+RgxgsVIm8wEJKQmU5QmZnAoUOlmD17Aw4dKjVsV4tZsnREDqqOCSOqiIGQhMx2gkpMBDp2PGfY8gPmydIRlccxYUR8+ry0MjOB9HR7Q5ucbNwgyCwcWbrywZBRs3RE5SUm8vxCajN9RuibbyyG7b7goFV5mC1LR0REdqYPhAYNCubAVtIEuxGIiMzH9IEQwIGtpB1m6YiIzEWJQAjgwFYi1akwBxQReU6ZQIgDW4kqUyU44BxQRFQVJQIhDmwlqkyV4IBzQBFRdUwfCK1YUcqBrUQVqBQccA4oIqqO6QOhu+8WzAQRVXD4sEWZ4MBMM7UTkfZMHwhR4BUUALt3x5oy22BUyclCmeCAc0ARUXUYCJGuliwBkpODMW1aDyQnB5t2HIrRqBYcqDoHlCqD4Yl8wUDIIIx4Qrs5DsUCwP5fs45DMSLVggPV5oBSZTA8ka8YCBmAUU9oHKQqP9WCA1WoNBieyFcMhCRn5BOamQapGjEjR+riRQhR7TEQkpyRT2g3x6EIAPb/GnEcilEzcqQuM12EEOmNgZDkjH5Cy8wEDh0qxezZG3DoUKnhxqEYOSNH6lJtMDyRLxgISc4MJ7TERKBjx3OGKrODkTNypDbVBsMTeSs40AUIhIICewPXurUxAorMTCA93d74Jicbo8xm4cjIlQ+GjJSRI7UlJvJ8QVQT5TJCRh3vwbt7AsMMGTkiIqqaUoEQx3uQN9jFQERkXkp1jVU33oNX+FQddjHIz2hd3kQkB6UyQka/A4uI3DNqlzcRBZ5SgRDHe5DKCgqAtWstOHs2PNBF0RS7vInIF0p1jQG8A4vUtGSJI1gIhsWShrKyMowaFehSaYNd3kTkC6UyQg68A4tUUjFjIoQFY8cGmSZjwi5vIvKFkoEQkUrcZ0wsppkUUsUubz77jkg7DIRIV2Ydl2Ik7jMmwlQZE5WmOODAcCJtMRAi3ThO2GlpwRg5Mg3Z2ZZAF0lJFTMmVqsNCxeWmS5jokKXNweGE2mPgZDBGCUlbvZxKUbjyJjk5ZVi8eI8jBghAl0k8gKffUekPQZCBmKklLjZx6UYUWIi0KuXQGzstUAXhbzEgeFE2mMgZBBGS4kbfVyKUTJvpBYVB4YT6Y2BkEEYLSVu5HEpRsq8kXpUGhhO5A/KTahoVI4MS/lgSPaUuGPyyu+/L8WJE6swbFifQBepRlVl3tLTedVN8uCz74i0w4yQQRg1JW60cSlGy7wREZFvmBH6DyM8uZqPB9GfETNvRETkPWaEYKwxISrMlRJIRs28ERGRd5QPhIx2Nxbpj4NR5cQ7+YhID7oEQqdOncITTzyBmJgYREREoGPHjvj222+d7wshMH36dDRu3BgRERFITU3FoUOHXNZx/vx5DB06FJGRkYiOjkZmZiYuX76seVk5JoTcYeZNLkbK2hKRsWgeCP3888/o0aMHQkJC8OWXX2Lfvn344x//iAYNGjiXmTt3LubPn49FixZh8+bNqFu3LtLT03Ht2s0BtUOHDsXevXuRl5eHlStXYv369Rg1apTWxeUEZWQqZsyaMGtLgDn3bZKD5oHQG2+8gWbNmiE7Oxt33nknkpKSkJaWhlatWgGwZ4PmzZuHl156CQ8++CA6deqEDz74AD/++CNWrFgBANi/fz9yc3Px5z//Gd26dcPdd9+NBQsWYPny5fjxxx81LS/HhJBZmDVrwqwtmXXfJjloftfYZ599hvT0dDzyyCNYt24dmjZtirFjx2LkyJEAgGPHjqGwsBCpqanOz0RFRaFbt27Iz8/HkCFDkJ+fj+joaHTt2tW5TGpqKqxWKzZv3oxBgwZV+t7r16/j+vXrzr+Li4sBACUlJSgpKam2zMOG2Q+wI0csaNVKIDERqOEj5AHH9q+pHsh79qxJMGw2+4Nt7VkTgT59Sl2CeiPWRcuWgNV687cB9lnKW7QoNfRxasS6CITa7tu+Yn3Iw991oHkgdPToUWRlZWHy5Mn4wx/+gK1bt+Lpp59GaGgoMjIyUFhYCACIj493+Vx8fLzzvcLCQsTFxbkWNDgYDRs2dC5T0Zw5czBz5sxKr69ZswZ16tSpdfl37bL/I+3l5eUFugimtXt3LGy2Hi6vlZVZkJOzGR07nqu0vNHqYsyY5sjKug02mxVWqw1PPbUTu3adNMWxWr4uzp4Nx+nT9dC48WXDzL2lN0/3bV8Z7dgwo6tXr/r1+zQPhGw2G7p27YrXXnsNAHD77bdjz549WLRoETIyMrT+OqepU6di8uTJzr+Li4vRrFkz9O7dGzExMbp9L9WspKQEeXl56NevH0JCQgJdHFPq1AmYMUNUypoMHdqtUkbIiHXRvz/w7LNlOHLE9p+sbQcAHQJdLJ9UrIvsbAvGjAmCzWaB1SqQlVWGESNEoIsZcLXdt31l1GPDjM6d0z7ArY7mgVDjxo3Rrl07l9fatm2Lf/7znwCAhIQEAEBRUREaN27sXKaoqAidO3d2LnPmzBmXdZSWluL8+fPOz1cUFhaGsLCwSq+HhIRwpw4QxySVLVva/2Zd6CcpyT7WbfRo+/gZ+1g3C5KS3G9vI9ZFUpL9n9mEhISgqCgEY8aUHxBuwdixwejfn+MVPd23fWXEY8Ns/L39NR8s3aNHDxw4cMDltYMHD6JFixYAgKSkJCQkJGDVqlXO94uLi7F582akpKQAAFJSUnDhwgVs27bNuczq1aths9nQrVs3rYtsOEa4e6L84Mbk5GDk5TUPdJFMj/MfGRcHhFeP+zbpSfNA6JlnnsGmTZvw2muv4fDhw1i2bBkWL16McePGAQAsFgsmTZqEV155BZ999hl2796NYcOGoUmTJnjooYcA2DNI9913H0aOHIktW7bg3//+N8aPH48hQ4agSZMmWhfZUIxw90Tl250tyMq6TerAzSw4/5ExcRqPmnHfJr1oHgjdcccd+PTTT/HRRx+hQ4cOmD17NubNm4ehQ4c6l3nuuecwYcIEjBo1CnfccQcuX76M3NxchIeHO5fJyclBmzZt0LdvX/Tv3x933303Fi9erHVxDcUo86m4u7q12aw4csTi/gMSMEKWjcyL03gQBY4uD129//77cf/991f5vsViwaxZszBr1qwql2nYsCGWLVumR/EMq7r0uUwnTHcPLrVa7YNcZbRkyc0A02q1N0hMvZO/8aHKRIGh/LPGjMQo6fPKV7cCY8bslPLEbpQsG6mB3T9E/sdAyECMlD4vP7jx0KFS9Ot3MtBFcouDVImI1KZL15gZOG79bt1arkDDSOnzxEQ4Z+mWdeI7d914MmbZiIhIH8wIuSH7nVlMn2vHSFk2IiLSHgOhCjhmRD2coyTweNceEQUKA6EKOGZETcyyBY7sGVjSB4NfkgUDoQqMcmcWqctMDQgzsGpi8EsyYSBUAceMkMzM1oAwA6seBr8kGwZCbnDMCMnIjA2IChlYM2XwtMDgl2TDQKgKHDNCsjFjA2L2DKzZMnhaUCH4JWNhIERkEGZtQMyagTVjBk8LZg9+yXgYCBEZhJkbEDNmYM2YwdOKWYNfMibOLE2ak3VWbjMw0sziquOs5dVzzDxPFGjMCBmUrAMwOSZCf2bMnpiRmTN4RGbCQMiAZA02OCaCyBW7gIjkx0DIYGQONqoaE3HkiCUwBaqCrNk0Midm8IjkxkDIYGQegFnVXU2tWonAFMgNWbNpREQUGAyEDEbmW6hlHxMhczaNiIgCg4GQwcgebMg8JkLmbBoREQUGb5+vBdluB5f9FmpZb4vl7cz+J9uxQ/pgPZORMSNUA1nHlHAApudkz6aZjazHDmmL9UxGx0CoGhxTYj4yd92ZCY8dNbCeyQwYCFWDY0rMyQjZNKPf4s9jRw2sZzIDBkLVkPkOLTIvM3Q1mP3YMXqgqhWz1zOpgYFQNTimhPzNLF0NZj52zBCoasXM9awlBs5yYyBUA44pIX8yU1eDGY8dswSqWjJjPWuJgbP8ePt8Lch6OziZj9lu8TfbsVNdoGqm3+kps9WzVqoKnNPTub1kwowQkUTY1SA3jokhT5gpw2tmDIRIE+wD1w67GuTFQJU8wcDZGBgIkc/YB649I9ziryoGqlRbDJyNgWOEDEqWKe3ZB04q4pgYqi3ZH4lEzAgZkkwZGJn7wNldR0QyYIZXbgyEDEa223dl7QOXKVgkIiJ5MRAyGNkyMDL2gcsWLBIZCTOppBoGQgYjYwZGtsGjsgWLZsTG0pyYSSUVMRDyUKAbABkzMI5yydIHLmOwaCZsLM2JmVRSFQMhD8jSAMiWgZGNrMGiGbCxNC9mUklVvH2+lmS7TZy371aPt6zqw6yPmJBlOopAMtvjXbTGfcS8mBGqJV4tGY9M3XUVBbqL1Vtm7HaUJdMbaMykVo37iLkxEKolMzYAFBhGPqmarbFkV58rdrtXxn3E/BgI1ZLZGgAKDDOcVM3UWDLTW5nMmdRA4D5ifhwj5AGOOyFfmWWMjVnGqHFcDNWE+4j5MSPkIV4tkS/YxSoXZnqpJtxHzI8ZISI/cpxUR4+2Z4J4Ug08ZnqpJtxHzI2BEJGf8aQqH7N09ZF+uI+YFwMh8grn1PANT6pERHLgGCEDCvQcNEa+/ZuIiKg8BkIGE+ggRMbbvwMdGBLJiMcFUe0wEDIQGYIQ2ebUCHRgSCQjHhdEtcdAyEBkCEJkuv1bhsDQTJhBMAceF0SeYSBkIDIEITLNqSFDYGgWzCCYB48LIs8wEPJSIK6eZQlCZHnEggyBoRmYLYOgemaLx0XVVN83yD0GQl4I5NWzLEGIDDNsyxIYGp2ZMgjMbPG4qAr3DaoKAyEPyXD1LEMQIgtZAsPyjHbVaZYMggzHpixkPC4CifsGVYeBkIfMdPVsFjIFhka86jRLBoHHpiuZjotA475B1WEg5CGzXD2T9ox81WmGDAKPTaoK9w2qDgMhD5nl6pm0Z/SrTqNnEHhsUlW4b1B1+KwxL/ChmeSO46qzfDDEq07/4rFJVeG+QVVhIOQlPjSTKnJcdY4ebc8E8aozMHhsUlW4b5A7DISINMSrTiIiY2EgRKQxXnWSlgoK7OPPWrfmfkWkBw6Wplox2tw4RGZgxOkYiIyGgRDVSIaTMQMxUo2Rp2MgMhLdA6HXX38dFosFkyZNcr527do1jBs3DjExMahXrx4GDx6MoqIil8+dPHkSAwYMQJ06dRAXF4cpU6agtLRU7+JKLRDBgAwnYxkCMaNiAGlcRp+OQS/cp0lrugZCW7duxfvvv49OnTq5vP7MM8/g888/x8cff4x169bhxx9/xMMPP+x8v6ysDAMGDMCNGzewceNG/PWvf8XSpUsxffp0PYsrtUAFA4E+GcsQiBkVA0hj4ySAlXGfJj3oNlj68uXLGDp0KP77v/8br7zyivP1ixcvYsmSJVi2bBn69OkDAMjOzkbbtm2xadMmdO/eHf/617+wb98+fP3114iPj0fnzp0xe/ZsPP/883j55ZcRGhpa6fuuX7+O69evO/8uLi4GAJSUlKCkpESvn+kX9mAgGDabBYAjGBDo06dU98GTLVsCVuvN7waAoCCBFi1KUdvN6tj+3tTD/v0W2Gyuu2lZGfD996WIjxcer08VVe0zPXvas6pGOSYKCoDDhy1IThamGyhc03ERHw9kZVkwdmwQysosCAoSWLiwDPHxotbHnpnofR705TxF2vJ3HegWCI0bNw4DBgxAamqqSyC0bds2lJSUIDU11flamzZt0Lx5c+Tn56N79+7Iz89Hx44dER8f71wmPT0dY8aMwd69e3H77bdX+r45c+Zg5syZlV5fs2YN6tSpo/Gv86/du2Nhs/Vwea2szIKcnM3o2PGc7t8/ZkxzZGXdBpvNCqvVhqee2oldu05i1y7P1pOXl+fxd589Gw6LJQ1C3AzErFYbTpxYhS++uObx+lRR1T7zt79tQ8eO3tWFv+XlNcfChZ0hhAUWi8DYsTvQr9/JQBdLc9XVRXw88P774Th9ui4aN76C2Nhr+OILPxZOIv46Dxrh2DC7q1ev+vX7dAmEli9fju+++w5bt26t9F5hYSFCQ0MRHR3t8np8fDwKCwudy5QPghzvO95zZ+rUqZg8ebLz7+LiYjRr1gy9e/dGTEyMLz8n4Dp1AmbMEJWyMkOHdvPLVXL//sCzz5bhyBEbWrUSSEzsAKBDrT9fUlKCvLw89OvXDyEhIR5/f1lZWYWrYhuGDevj8XpUUtU+87vfdcG+ff/yui78paAAePjhYGcALIQFixZ1xrPPdjBNZsjX40I1ep8HWR/yOHdO/wv88jQPhH744QdMnDgReXl5CA8P13r1VQoLC0NYWFil10NCQnTbqf01v0dSkrsZiy1ISvLfwZqUZP/nC2/rYtQoezBmn6TQgsTEwEx/ZaT5XKraZ1q2DMa+ffoeF1o4ftzd2DQLTpwI8Xk/lI3sdSELf50HWR+B5+/tr/lg6W3btuHMmTP49a9/jeDgYAQHB2PdunWYP38+goODER8fjxs3buDChQsunysqKkJCQgIAICEhodJdZI6/HcsEmr8H7Znh6eC+CPQDQY04SNPI+wwHCpM7Rt6nSV6aB0J9+/bF7t27sWPHDue/rl27YujQoc7/DwkJwapVq5yfOXDgAE6ePImUlBQAQEpKCnbv3o0zZ844l8nLy0NkZCTatWundZE9Fqg7mQIdDKjKyHeuGXWf4dPCqSpG3adJXpr3MdSvXx8dOriOH6lbty5iYmKcr2dmZmLy5Mlo2LAhIiMjMWHCBKSkpKB79+4AgLS0NLRr1w6///3vMXfuXBQWFuKll17CuHHj3HZ/+Vt1t5Tz4DQf1ndg8LltROQPARls8ac//QlWqxWDBw/G9evXkZ6ejoULFzrfDwoKwsqVKzFmzBikpKSgbt26yMjIwKxZswJR3EocafvyjSPT9ubF+g4cPreNiPTml0Bo7dq1Ln+Hh4fjvffew3vvvVflZ1q0aIEvJL1P1JG2dx20xxO2WbG+yVdGGmhPpBo+fd5LTNurhfVN3lqy5OYYM6vVHlRzkC+RPBgI+YBpe7WwvslTVQ20T0+3T5ZIpAVmHH3Dp88TEekk0M/qkxEfmqotI07tIRvTB0IffmipeSFywROVvFg3xsL5kFyx0daWkaf2kInpA6HJk4O4U3ggUCcqNvA1M3Ijomr9cj6km9hoa48ZR22YPhCy2SyG3yn81YgE6kRl5AbeX4zciKhev5wN2Y6NtvaYcdSG6QMhq1UYeqfwZyMSiBOVkRt4fzJqI8L6teNsyGy09cCMozZMHwi9/XaZYXcKfzcigThRGbWB9zejNiKsX3Jgo60PZhx9Z/pA6IknRKCL4DV/NyKBOFHJ0MAbYfyKURsRGeqX5MFGWx/MOPrG9IGQkQWiEfH3iSrQDbyRxq8YsREJdP2SfNhok2w4oaIP9J7EKlCPdvD3xIGBmrW5usnuZD1JG3FSR87KTUQyYyDkJX9Nm69KIxKIBp5PlfcfIwZwFXH2XiJzYteYF/w9iJmpZH1w/ArVlpG6UInIMwyEvMA7YcyB41eoNjgFAOnJCDdrmB0DIS8wk2AeRhyATP7FC5+b2Ghri5lGOTAQ8gIzCebCrkeqDi987Nhoa4uZRnkwEPISMwlEauCFDxttPTDTKA/eNeYDM9wJQ4FjxLuQjFhmLahy92ZVeIel9hyZxvLbVcVMowxMnxE6dYp92iQfI3YzGLHMWlK5C5Xdg9pjplEepg+EOncOVvbEXRN/Dnw8ezYca9daGJDCmN0MRiwzaYeNtj44xEIOpg+EhLAA4Im7In9e3WdnWzByZBrS0oIZkMKYYwOMWGbSFhttfaicaZSF6QOh8oxy4tY7U+PPq/uCAmDMmCAGpOUYsZvBiGUm7bHRJjNSKhAywonbH5kaf17d27/L4pfvMgojdjMYscxERLVh+rvGrFYBm80YJ25/PQTUn3cr2L9LuARD/ghIZb+7yYh3IRmxzOXJvk8QUWCYPiO0fXupYfq0/ZWp8efVfWIikJVVBqvVpvt3ORjl7iYjdjMYscyAcfYJIvI/02eEmjYFOnUKdClqx5+ZGn9e3Y8YIRAUlIcWLfqiTZtgXb/LX1k1Mg7uE3bMiGmL29M8TJ8RMhJ/j8Pw59V9bOw19OoldP8u3t1EFXGfYEZMa9ye5sJAyEt63dnFW1R9w7ubqCLV9wnOAaUtbk/zYSDkBb2vBow6DkMGvLuJKlJ9n2BGTFvcnubDQMhDvBqQH7Nq1VNxlm+V9wnVM2Ja4/Y0HwZCHuLVgDH4O6vmz8eV+ELlWb5VzbSqnhHTGren+TAQ8hCvBqgiowyc5Czf6lI5I6YHbk9zYSDkIV4NUHlG6irlLN9qUzUjphduT/Mw/TxCejD6DLukneq6SmXbLwI1yzcRkcyYEfKSUa4G/DF2xSjjY/RgpK7SQMzyTUQkO2UCIRUba3+MXTHK+Bi9GK2rdMQIgcWL85CXV2qosQ0qHr+kD+5LVJESgZCKjbU/xq4YaXyMnow2cNJfs3xrRcXjtyI23trgvkTumD4QOnVK/sZaj5OcP27z9+dUArI3BEbpKjUaBttsvLXCfYmqYvpA6OhRi9Tz/uh1kvPH2BV/jY9hQ6Au1eftYuOtHdX3Jaqa6QOhW24R0g5m1fMk54+xK/74DjYEajPSYHQ9sPHWjur7ElXN9IFQ06byDmbV+yTnj7Eren8HGwK1GW0wutbYeGtH9X2JqqbEPEKyzvvjOMmVb+i1PsklJur/e/X8Dn9sIyMqKLAHia1by7M/60XW49cfHI336NH2CwA23r5ReV+iqpk+I+Qg42BWXqHUjNuoMhXHTMl4/PqL0e5KlJ3K+xK5p0RGSGtaXo3zCqVm/txGsmdaqhozlZ4uZ3lJG/7I7BKpSpmMkFb0uBrnFUrN/LGNjJBp4ZgpIpKN7NOb1ISBkAd4B5N5GaVuOXiWiGRihAvImjAQ8gCvxs3LKHVr1DFTRr9i9Jaqv1sP3JbyMcoFZE0YCHmAV+PmZaS6NdrgWTNcMXpD1d+tB25LORnlArImDIQ8YNSrcaqZ0erWKOPKzHLF6ClVf7ceuC3lZaQLyOowEPKQ0a7GfaFaKlqluvUXs1wxekrV360Hbkt5Ge0Csiq8fd4Lst3Kqsct30uW3LwKs1rtO7sKgYFsdWt0qk6Iqerv1gO3pdzMMAWMUhkhM2Y49Og790cq2ox1QZWZ5YrRU6r+bj1wW8rPKF31VVEmEDLjYDu9Aha9U9FmrAuqmqpdjqr+bj1wW5KelOgak202Xq26sqoLWHxZr56paNnqIlBkn8Faa6p2Oar6u/XAbUl6USIjJNNgOy2zIXqN2NczFS1TXQQKM2JEFGgcnnCTEoGQLLf4ad2VpWfAolcqWpa6CBTeCkwqYWMrJ16MuVIiEJJlsJ0e2RA9+871GADnr7qQ9QRstIyYrNtRb6r+bi2xsZUTL8YqUyIQAuQYbKdnV5aRRuzrXRcyn4CNlBGTeTvqSdXfrSU2tvIy2sWYPygTCAGBDxhkyUzJQK+6kP0EbJR9QPbtqBdVf7fW2NjKy0gXY/6iVCDkKy3S5TJkpszMCCdgI+wDRtiOelD1d2uNja28jHIx5k8MhGpJy3R5oDNTZmaUE7Ds+4BRtqPWVP3dWmNjKzcjXIz5EwOhWmC63Dh4AtaGqttR1d+tBza2cpP9YsyflJhQ0Vd6TVxI+jDDs29koOp2VPV364GTIJIRaJ4RmjNnDu644w7Ur18fcXFxeOihh3DgwAGXZa5du4Zx48YhJiYG9erVw+DBg1FUVOSyzMmTJzFgwADUqVMHcXFxmDJlCkpLS7Uubq2YKV2uym3BvNrRhqrbUdXfTaQizQOhdevWYdy4cdi0aRPy8vJQUlKCtLQ0XLlyxbnMM888g88//xwff/wx1q1bhx9//BEPP/yw8/2ysjIMGDAAN27cwMaNG/HXv/4VS5cuxfTp07Uubq2YJV2u123BqgRX5an4m4kosHje0YfmXWO5ubkufy9duhRxcXHYtm0bevbsiYsXL2LJkiVYtmwZ+vTpAwDIzs5G27ZtsWnTJnTv3h3/+te/sG/fPnz99deIj49H586dMXv2bDz//PN4+eWXERoaWul7r1+/juvXrzv/Li4uBgCUlJSgpKTE5981bJg9gDhyxIJWrQQSEwENVlsrBQXA4cMWJCcLr4Mv+zinYNhsFgCOcU4CffqU+hTQZWdbMGZMEGw2C6xWgaysMowYIVyWcWx/LepBBrX5zbIyW10Ymax1ocX5xohkrQ8HI593POXvOtB9jNDFixcBAA0bNgQAbNu2DSUlJUhNTXUu06ZNGzRv3hz5+fno3r078vPz0bFjR8THxzuXSU9Px5gxY7B3717cfvvtlb5nzpw5mDlzZqXX16xZgzp16mj6m3btsv/zh7y85li4sDOEsMBiERg7dgf69Tvp8Xp2746FzdbD5bWyMgtycjajY8dzXpXt7NlwPPVUGoRwBFcWjBljRVBQHmJjr7n5LXlefY9MPP3NgXT2bDhOn66Hxo0vVyqbGeqioup+r8xkqgutzjdGJlN9OBjpvKOFq1ev+vX7dA2EbDYbJk2ahB49eqBDhw4AgMLCQoSGhiI6Otpl2fj4eBQWFjqXKR8EOd53vOfO1KlTMXnyZOffxcXFaNasGXr37o2YmBjn60a62ikoAB5+ONi58wthwaJFnfHssx08LnunTsCMGcKZEQKAoCCBoUO7eb0d1q61OMvmYLNZ0aJFX/TqdfNKpaSkBHl5eejXrx9CQkK8+zJJ1PY3B1pVV49mqovyjHi1LFtdaHm+MSLZ6qM8o5x3tHLunHcX597SNRAaN24c9uzZgw0bNuj5NQCAsLAwhIWFVXo9JCTEuVMvWXLzNnir1T7uR+ZbOo8fd3e3mgUnToQgKcmzdSUl2X/v6NH2O97s45wsSEry/oBv29a+HcuXMSgIaNMmGO7OI+XrojYKCux37LVuLc94LE9/cyAUFABjxpSf7sGCsWOD0b8/4Li+8LQuZFbd75Vlv6mOLHWh5fnGyGSpj/KMcN7Rkr+3v27zCI0fPx4rV67EmjVrkFjubJSQkIAbN27gwoULLssXFRUhISHBuUzFu8gcfzuW8VQg5gLydWCb1neraT2vh56DyGV93pMRBs6rNjuyar9XL2a6O9ZsjHDeMTLNAyEhBMaPH49PP/0Uq1evRlKFS4kuXbogJCQEq1atcr524MABnDx5EikpKQCAlJQU7N69G2fOnHEuk5eXh8jISLRr186rcvn7ZKlFQ67Hzq/1bcF6TJom+wSWsk8Up1qDptrv1QsbW7nJft4xMs27xsaNG4dly5bhf//3f1G/fn3nmJ6oqChEREQgKioKmZmZmDx5Mho2bIjIyEhMmDABKSkp6N69OwAgLS0N7dq1w+9//3vMnTsXhYWFeOmllzBu3Di33V+14ThZVkwt6nGyrKohT0/3/KRihMndtJ40zQgTWMo8UZyjQXPtBoVf73T0p+p+L3nGCOcblcl83jEyzQOhrKwsAMC9997r8np2djaGDx8OAPjTn/4Eq9WKwYMH4/r160hPT8fChQudywYFBWHlypUYM2YMUlJSULduXWRkZGDWrFlel8ufJ0utG3LVdn5/Bq1mpVqDptrv1ZNq5xsizQMhIWoewR4eHo733nsP7733XpXLtGjRAl988YWWRfPbyZINuW94ha8N1Ro01X5veTLeWECsF6NQ7qGr/pg6n33tvmN/uDo4W65vZL2xQHWsF+NQLhDyFzbkvtMraGXDKw82Fr6R/cYCVbFejIWBUA18aTT54Eb5GKHhVSVQY2PhO04dICfWi7EwEKqGERpNQNuG08yNsBEaXqPsc1pgY+E7Th0gJ9aLsTAQqoIRGk1A24bT7I2w7A2vUfY5rbCx8B3HI8qJ9WIsDISqIHujCWjbcOrVCBcU2J+Tc/ZsuG8r0oDsDa8R9jktsbHQBscjyon1Yhy6P33eqPx1C7wvt1dqOV+RHpMY3ny2WzAsljSUlZVh1Cjv1qUF2W/LV3HaBc7/ow2Vpw6QGevFGJgRqoI/rlZ97YrSMsOhdbakYoZJCAvGjg0KeDePzFdpqmZIVLypQKZMKd109mw41q61BPw8Rf7FQKgaejaaWnRFadlwat0Iu88wWaTo5pG54ZU5UCNtOC6A0tKCMXJkGrKzLYEuEgHIzrZg5Mg0pKUFm3KMJFXNImozFbQBFRcXIyoqCmfPnkVMTEygi1PJmjX2TJC71ys8naRGBQXadS1ota6CAvvJ3rWbR+D4cYuUAYgqSkpK8MUXX6B///4ICQnxah2cLdd7PC7kZK8XAZvtZlAaFGS/GGG9+N+5c+cQGxuLixcvIjIyUvfvUy4jJMvt4Vp2RWmZ4dBqXRUzTFarDQsXlvGkYnBmv7NQbzJnSlVmrxfXzJyZb1QgV0oFQnqdxL0JrlQYD+Lo5snLK8XixXkYMcL35KMsgWxFspZLS6rd3q8H9xdAwtQD4o3AXi+u5yez36hANykTCOl1EvcluFJhPEhiItCrl0Bs7DWf1yVrNkLWcmlNtdv79cBMqZwSE4GsrDJYrfYd3IwXplQ1ZW6f1+P28KqCq/T02q+Tt1fWjhbbWqVy6UHF2/v14Jgy4PvvS3HixCoMG+ZmsCD53YgRAkFBeWjRoi/atAk23fFLVVMmI6THZHq8QvYfWbe1rOXSgwrduf6iZaaUtBMbew29egnu04pRJhDS4yQu80zFZhuzIuu2lrVcelGhO9cdsx1PZsF6IS0oEwgB2p/EZb1C1nLMiiwnGlm3tazl0pPM8zDpQZUxYEbDeiGtKBUIAdqfxPW4QvYl+NByULhsJxpZsxGylqs8WQJao+GdcnJivZCWlAuEauLtrfBaBVe+Bh9ajVmR9UQjazZC1nIBrvtUcnIw8vKaB7pIhqHSGDAjYb2QlhgIlRPoDIgWwYdWY1ZUONGokCWpvE9ZkJV1m6l/s5ZUGwNmFKwX0hIDof+QIQOiRfCh1ZgVrU80sj3MMNBBr7+426dsNiuOHOHzrWpDxTFgRsB6IS0xEPoPrTMg3mQbtAo+tBizouWJRraHGcoQ9PqLu33KarWhVStTPmJQF0YYA6Yi1gtphYHQf2iZAfE226D10+R9HbOixYmmoAAYMyYIQtgzEDIEHSp0+zlU3qcExozZaforZ627PWUeA6Yy1gtpgYHQf2gVhPiabZDtKsfXE42MDzNUbXxB+X3q0KFS9Ot3MtBF0pUq3Z5Go8KYPDImBkLlaBGEaDXOxyxXOTI+zNAI4wuY0fCOSt2eRsLglGTGQKgCXxsM1bINNZH1YYayZd7KY6PhPZW6PY2Cwal6jJb9UyoQ8nWiwtp81gjZBn8bMUJg8eI85OWVShV0yJglYaPhG16IyIfBqVqMeCGnTCDkS+V4+llZsg0yReVaPcxQpt+kBzYavuGFiHwYnKrDqBdySgRCvlSOt5/VItvgS6NvxKi8Jmb8TRWx0fCdLBciZMfgVB1GvZBTIhDypXICVbG+NPpGjcqrY8bf5I6KjYYeWT4Zuz1VxuBUDUa9kFMiEPKlcrSoWE9P9L42+loGb7J0RRn1SsMbKjUaKmT5jIp3LpKnjHohp0Qg5Evl+Fqx3pzofW30tYrKZWqkZL/SYKPhOVWyfEYk07FPxmLECzklAiHAt8rx9rPenuh9bfS1iMpla6RkvtJgo+EdlbJ8RiLbsU/GY7QLOWUCIcC3yvHms96e6LVo9H2NymVspGS80mCj4T3Zs3yqkvHYJ/3IMvwhkJQKhNzRcyfw5USv1YNTvQ38ZG2kZLvSYKPhPZmzfCqT9dgn7TGbbad0IOTNTuBJ4OTriT6Qjb6WjVRBAbB7d6wprzhUbDS0vHiQMcunOgaoamA2+ybTB0Iffmhx+7o3O4E3gZORT/RalH3JEiA5ORjTpvVAcnKw6a44VGs09LiClC3LZ0RaZ7aNfN6i2mE2+ybTB0KTJwe5PTl4uhP4Ej0b+UTvS9lvbjN7MGqzWaS54mBWw3O8gpSTXt0bRj5vUc1UzGZXxfSBkM1mcRvceLoT+Dt69sdz0fQm6xUHsxrekbU+VcbglLylWja7OqYPhKxW4Ta48XQn8DZ69iYo8edz0fQk4xUHGw7vyVifqmNwSr5QJZtdE9MHQm+/XVZlcOPJTuBN9OztYGx/PxdNLze3mQBg/2+grzhUazi0zA7yClI+DE7VwsfR6MP0gdATT4hq3/dkJ/AkcPI2KJHhuWhaj585dKgUs2dvwKFDpQG/4lCp4dAjO8grSLkwOFWHTNl+szF9IATUrmGvbeNf28DJ26Ak0M9F02v8TMeO57w+OTOr4Tk9s4O8gvQN7/AiT8mW7Tcb0wdCH35oqbFh96Txr+1JzNugJJDPRZPxYGNWwztVBeJHjrifToL8o/z+nJwcjLy85pqsl8GpuanWpe9vpg+EnnkmqNqG3ZPG35NG2ZegJBDPRQPkO9iY1fBeVYF4q1bVdxWTfirvzxZkZd3Gq3qqkUpd+oFg+kBICNcr4IoNe20bf28aZV+CEn8/Fw2Q72CTLTDTG7sAzc3d/myzWZmloxrxeNaX6QMhi8X1Crhiw17bxt+XB6jWNigJ9Pw/sh1ssgVmemIXoPm525+tVhuzdFQrPJ71Y/pA6E9/Kqu2Ya9t4+9Jo+zvuYO05OvBxqyG59gFKCetL0wq788CY8bsZN2YFG91Nw7TB0JPPCFqbNhr0/jXtlH299xBjs9rfcL25mBjVsM7qnUBGoFeFybl9+dDh0rRr99JbVZMUpHlwpZqx/SBEHCzYQeqDxhEDRnqmhrlQMwdJMsBp1JWQ+vAU6UuQCPQ++5J2fZn0paMd99S9ZQIhIDqAwZP7war6iTm77mDZDrgVMlq6DXPkgpdgEahyr5M+uD+YzymD4ROnao+YKhNMCHr3EEyHXAqZDX0DDxV6AI0ChX2ZdIP9x/jMX0g1LlzMN55p+qAoaZgQua5g3w94Diw2TN6B57sMvEe92WSBfcf4wkOdAH0JoQFb79tDxjKN2LlA4aq3qsqA5CeXvVOnZlpf//wYfs6PNn5ExM9X37xYnuZyso8O+CWLLn526xW+3p8zUL48tv1UlBgD2Bat/a9PI7As6r9iAJDlX2Z9OE4R7Rsqd06uf8Yi+kzQoD9BDl5svsIvbrovaYMQFVXodVd2cvwnCFVBjZrPZ6HV3ryUWVfJn3o9cgTgPuPkSgRCAUFARMnVh0wVBVMVNf15E0jq9cdXp4ecDKNLdKLXg0kx/LIRYV9mfTBR56Qg+kDIatVuGR/HAFDxcyMu2CiqgwA4HkjK9NcQbIO5tPyN+rZQPJKz3uceoBkwUeekIPpA6Ht20uRmel6Aq4qM+PuJO0uA+BNIyvTXEEydvFo/RvZQMqHUw+QTPjIE3ISJnXx4kUBQHz66Tnx5ptCWK1CAEJYLPZ/9ukT7f+CgoTLMlarEH/+c9Xr/uGHm8uWX8cPP2j7GV8+Vxs//CDEmjXarKs6N27cECtWrBA3btyoshx6/MY//9m+Hsf6qqtTVdRUF3rRcz92rN8f+7KWAlUXRvbDD0KsXq1dPbueI2xi3LjvWB8SOHv2rAAgLl686JfvM31GaNCgYEyZcjMb4zgNl1dWBjz/fNXzDFXMEtV0FerNZ6oiYxeP1t0bev1GjufxjVG6KgF2V6pA70f48JEn6jJ9IFQbFW+JBuwn6XfeqfrAq6qRre5gDcRcQVrT42Sk529kA+kddlWSTHh3IOlJyUDIYrl5Ug4KAl5/3V1fMfD229UfeBUPoNocrJ4edL6MgdA6c6PXyYjjPOSiRz2zjskXvDuQ9CR1IPTee++hZcuWCA8PR7du3bBlyxZN1uvoHhs9Gli2DHjsscon6cmT/TcguqaAxZtMkh6ZGz1PRuzG8h67KsnsmFEkPUkbCP3tb3/D5MmTMWPGDHz33Xe47bbbkJ6ejjNnzmiyfiHsV6S/+509UABcT9ITJ7o/8OrWrbrR8eZgrW3A4kkmSa/Mjd4nI6aoPceuSpKR1sE5M4qkJ2kDobfffhsjR47EiBEj0K5dOyxatAh16tTBX/7yF82/yxEoADdP0u4OvCeeALp3r7rR8fRg1Stg0euKnicj37CrklSg18SxzCiSXqR81tiNGzewbds2TJ061fma1WpFamoq8vPz3X7m+vXruH79uvPvixcv/uf/imv1nWVlwNKlZXjgARuaNrW/9tBDwB13AMeOWVCnjkB6ejCEsE+2ZbMBo0YJ3HFHqXP5ip9JShJo2hQ4d879d377rQU2m2sVlJUB27aVIiLC+7ksYmIAi+VmWQH7xJING5ZWWZba8uT3OZSUlODq1as4d+4cQkJCfCuAQX34oQXPPBMEISywWAT+9KcyPPGEb/OVeLP/1LYuvKln8owZj4tTp4CRI2s+T3orIgLo2NH+/1rvj2asD6M6f/48AEBUvMVbL365Sd9Dp06dEgDExo0bXV6fMmWKuPPOO91+ZsaMGQIA//Ef//Ef//Ef/5ng35EjR/wRcggpM0LemDp1KiZPnuz8+8KFC2jRogVOnjyJqKioAJaMiouL0axZM/zwww+IjIwMdHGUxrqQB+tCLqwPeVy8eBHNmzdHw4YN/fJ9UgZCsbGxCAoKQlFRkcvrRUVFSEhIcPuZsLAwhIWFVXo9KiqKO7UkIiMjWReSYF3Ig3UhF9aHPKwV79rQ63v88i0eCg0NRZcuXbBq1SrnazabDatWrUJKSkoAS0ZERERmImVGCAAmT56MjIwMdO3aFXfeeSfmzZuHK1euYMSIEYEuGhEREZmEtIHQ7373O/z000+YPn06CgsL0blzZ+Tm5iI+Pr5Wnw8LC8OMGTPcdpeRf7Eu5MG6kAfrQi6sD3n4uy4sQvjr/jQiIiIiuUg5RoiIiIjIHxgIERERkbIYCBEREZGyGAgRERGRshgIERERkbJMGQi99957aNmyJcLDw9GtWzds2bIl0EUynTlz5uCOO+5A/fr1ERcXh4ceeggHDhxwWebatWsYN24cYmJiUK9ePQwePLjSbOEnT57EgAEDUKdOHcTFxWHKlCkoLS31508xnddffx0WiwWTJk1yvsa68J9Tp07hiSeeQExMDCIiItCxY0d8++23zveFEJg+fToaN26MiIgIpKam4tChQy7rOH/+PIYOHYrIyEhER0cjMzMTly9f9vdPMbSysjJMmzYNSUlJiIiIQKtWrTB79myXB3myLvSzfv16DBw4EE2aNIHFYsGKFStc3tdq2+/atQv33HMPwsPD0axZM8ydO9fzwvrliWZ+tHz5chEaGir+8pe/iL1794qRI0eK6OhoUVRUFOiimUp6errIzs4We/bsETt27BD9+/cXzZs3F5cvX3Yu89RTT4lmzZqJVatWiW+//VZ0795d3HXXXc73S0tLRYcOHURqaqrYvn27+OKLL0RsbKyYOnVqIH6SKWzZskW0bNlSdOrUSUycONH5OuvCP86fPy9atGghhg8fLjZv3iyOHj0qvvrqK3H48GHnMq+//rqIiooSK1asEDt37hQPPPCASEpKEr/88otzmfvuu0/cdtttYtOmTeKbb74RycnJ4rHHHgvETzKsV199VcTExIiVK1eKY8eOiY8//ljUq1dPvPPOO85lWBf6+eKLL8SLL74oPvnkEwFAfPrppy7va7HtL168KOLj48XQoUPFnj17xEcffSQiIiLE+++/71FZTRcI3XnnnWLcuHHOv8vKykSTJk3EnDlzAlgq8ztz5owAINatWyeEEOLChQsiJCREfPzxx85l9u/fLwCI/Px8IYT9QLFaraKwsNC5TFZWloiMjBTXr1/37w8wgUuXLonWrVuLvLw80atXL2cgxLrwn+eff17cfffdVb5vs9lEQkKCePPNN52vXbhwQYSFhYmPPvpICCHEvn37BACxdetW5zJffvmlsFgs4tSpU/oV3mQGDBggnnzySZfXHn74YTF06FAhBOvCnyoGQlpt+4ULF4oGDRq4nKOef/55ceutt3pUPlN1jd24cQPbtm1Damqq8zWr1YrU1FTk5+cHsGTmd/HiRQBwPi1427ZtKCkpcamLNm3aoHnz5s66yM/PR8eOHV1mC09PT0dxcTH27t3rx9Kbw7hx4zBgwACXbQ6wLvzps88+Q9euXfHII48gLi4Ot99+O/77v//b+f6xY8dQWFjoUhdRUVHo1q2bS11ER0eja9euzmVSU1NhtVqxefNm//0Yg7vrrruwatUqHDx4EACwc+dObNiwAb/5zW8AsC4CSattn5+fj549eyI0NNS5THp6Og4cOICff/651uWR9hEb3jh79izKysoqPYYjPj4e33//fYBKZX42mw2TJk1Cjx490KFDBwBAYWEhQkNDER0d7bJsfHw8CgsLncu4qyvHe1R7y5cvx3fffYetW7dWeo914T9Hjx5FVlYWJk+ejD/84Q/YunUrnn76aYSGhiIjI8O5Ld1t6/J1ERcX5/J+cHAwGjZsyLrwwAsvvIDi4mK0adMGQUFBKCsrw6uvvoqhQ4cCAOsigLTa9oWFhUhKSqq0Dsd7DRo0qFV5TBUIUWCMGzcOe/bswYYNGwJdFCX98MMPmDhxIvLy8hAeHh7o4ijNZrOha9eueO211wAAt99+O/bs2YNFixYhIyMjwKVTy9///nfk5ORg2bJlaN++PXbs2IFJkyahSZMmrAtyYaqusdjYWAQFBVW6G6aoqAgJCQkBKpW5jR8/HitXrsSaNWuQmJjofD0hIQE3btzAhQsXXJYvXxcJCQlu68rxHtXOtm3bcObMGfz6179GcHAwgoODsW7dOsyfPx/BwcGIj49nXfhJ48aN0a5dO5fX2rZti5MnTwK4uS2rO0clJCTgzJkzLu+Xlpbi/PnzrAsPTJkyBS+88AKGDBmCjh074ve//z2eeeYZzJkzBwDrIpC02vZanbdMFQiFhoaiS5cuWLVqlfM1m82GVatWISUlJYAlMx8hBMaPH49PP/0Uq1evrpSe7NKlC0JCQlzq4sCBAzh58qSzLlJSUrB7926XnT0vLw+RkZGVGhOqWt++fbF7927s2LHD+a9r164YOnSo8/9ZF/7Ro0ePStNIHDx4EC1atAAAJCUlISEhwaUuiouLsXnzZpe6uHDhArZt2+ZcZvXq1bDZbOjWrZsffoU5XL16FVaraxMXFBQEm80GgHURSFpt+5SUFKxfvx4lJSXOZfLy8nDrrbfWulsMgDlvnw8LCxNLly4V+/btE6NGjRLR0dEud8OQ78aMGSOioqLE2rVrxenTp53/rl696lzmqaeeEs2bNxerV68W3377rUhJSREpKSnO9x23bKelpYkdO3aI3Nxc0ahRI96yrYHyd40Jwbrwly1btojg4GDx6quvikOHDomcnBxRp04d8eGHHzqXef3110V0dLT43//9X7Fr1y7x4IMPur1t+PbbbxebN28WGzZsEK1bt+Yt2x7KyMgQTZs2dd4+/8knn4jY2Fjx3HPPOZdhXejn0qVLYvv27WL79u0CgHj77bfF9u3bxYkTJ4QQ2mz7CxcuiPj4ePH73/9e7NmzRyxfvlzUqVOHt88LIcSCBQtE8+bNRWhoqLjzzjvFpk2bAl0k0wHg9l92drZzmV9++UWMHTtWNGjQQNSpU0cMGjRInD592mU9x48fF7/5zW9ERESEiI2NFc8++6woKSnx868xn4qBEOvCfz7//HPRoUMHERYWJtq0aSMWL17s8r7NZhPTpk0T8fHxIiwsTPTt21ccOHDAZZlz586Jxx57TNSrV09ERkaKESNGiEuXLvnzZxhecXGxmDhxomjevLkIDw8Xt9xyi3jxxRddbrVmXehnzZo1btuIjIwMIYR2237nzp3i7rvvFmFhYaJp06bi9ddf97isFiHKTbNJREREpBBTjREiIiIi8gQDISIiIlIWAyEiIiJSFgMhIiIiUhYDISIiIlIWAyEiIiJSFgMhIiIiUhYDISIiIlIWAyEiIiJSFgMhIiIiUhYDISIiIlLW/wcIv8z8LVfp5wAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = archimedes_nos*np.cos(archimedes_nos)\n",
"y = archimedes_nos*np.sin(archimedes_nos)\n",
"plt.figure()\n",
"plt.plot(x,y,'.b')\n",
"plt.xlim(0,1000)\n",
"plt.ylim(0,1000)\n",
"plt.grid()\n",
"plt.title(\"Archimedes Spiral, 1st Quadrant\")"
]
},
{
"cell_type": "markdown",
"id": "fde7a33e-6eb1-47b0-8867-85792164a17c",
"metadata": {},
"source": [
"### Part B\n",
"You need to plot the first 25 terms, looking at the entire polar plot (all quadrants, and then, put a *smooth* line through it. What you're going for is shown in Figure 2.)\n",
"Hint: [This will be a useful reference](https://matplotlib.org/stable/gallery/pie_and_polar_charts/index.html)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "d03285bf-09a6-4b79-b6e2-aaf35c56f96f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0.5, 1.0, 'Polar Plot of First 25 Archimedes Spiral Terms')"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure()\n",
"plt.polar(archimedes_nos[:25],archimedes_nos[:25],'.b')\n",
"plt.polar(np.linspace(0,25,1000),np.linspace(0,25,1000),'-r')\n",
"\n",
"plt.title(\"Polar Plot of First 25 Archimedes Spiral Terms\")"
]
},
{
"cell_type": "markdown",
"id": "607410b5-74aa-44fd-ad88-4ed702dad2bc",
"metadata": {},
"source": [
"## Problem 4\n",
"Consider the following system:\n",
"$$\n",
"\\bf{\\dot{X}} = \n",
"\\begin{bmatrix} \n",
"1 & 2 & 1\\\\ \n",
"3 & 1+x & 1\\\\\n",
"1 & 0 & 0\n",
"\\end{bmatrix}\n",
"\\bf{X}\n",
"$$\n",
"This linear differential equation systems behavior is governed by its eigenvalues. In particular, the eigenvalues relate to stability and we may wish to see where they cross the 0 line (in terms of their real value). The constant x varies over the interval [5, 5]. Using a Jupyter Notebook (local, or on Google Colab), Python, NumPy, and Matplotlibs PyPlot, you should evaluate the eigenvalues for 50 evenly spaced values of x between 5 and 5, and produce a plot that visualizes the variation in the three eigenvalues as x varies. An example plot is shown in Figure 3 (for a different matrix!)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "4e31260e-2d13-4709-91d9-be043a733cd0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#A cursed line of code.\n",
"import matplotlib.pyplot as plt; import numpy as np; eig = lambda x: np.linalg.eig([[1, 2, 1], [3, 1+x, 1], [1, 0, 0]])[0]; x_vals = np.linspace(-5, 5, 50); [plt.plot(x, eig(x)@[0,0,1], '.b', x, eig(x)@[0,1,0], '.r', x, eig(x)@[1,0,0], '.g') for x in x_vals]; plt.title(\"Eigenvalues of A for Range of X Values\"); plt.xlabel(\"X Values\"); plt.ylabel(\"Eigenvalue-value\"); plt.grid(); plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "f813a4d9-2da4-4e28-a244-f8aa5fc37bf8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Human Readable Code\n",
"#Create Eigenvalue Function\n",
"eig = lambda x: np.linalg.eig([[1, 2, 1],[3, 1+x, 1],[1,0,0]]).eigenvalues\n",
"\n",
"#Allocate memory to x and eigenvalue storage\n",
"x = np.linspace(-5,5,50)\n",
"eigs = np.zeros((3,50))\n",
"\n",
"#Calculate eigenvalues\n",
"for i in range(50):\n",
" eigs[:,i] = eig(x[i])\n",
"\n",
"#Plotting\n",
"plt.figure()\n",
"plt.title(\"Eigenvalues for Range of X Values\")\n",
"plt.plot(x,eigs[0,:],'.r',x,eigs[1,:],'.b',x,eigs[2,:],'.g')\n",
"plt.xlabel(\"X Values\")\n",
"plt.ylabel(\"Eigenvalue-value\")\n",
"plt.grid()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.12.3"
}
},
"nbformat": 4,
"nbformat_minor": 5
}