Módulo 2_ITEM_1_Questão_10_Jessika_.ipynb

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      "cell_type": "markdown",
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        "<a href=\"https://colab.research.google.com/github/jessikamorais/Metodos_Numericos/blob/main/M%C3%B3dulo%202_ITEM_1_Quest%C3%A3o_10_Jessika_.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "metadata": {
        "id": "JXtkarR0rUrX"
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      "source": [
        "**RESOLUÇÃO DO ITEM 1.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_toqeKXb4wnH"
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      "source": [
        "**Resolução do exercício 10_Artigo**: \"*A Collection of 10 Numerical Problems in Chemical Engineering Solved by Various mathematical Software Packages*\".\n",
        "\n",
        "O problema consiste em um tanque agitado com aquecimento que opera de forma contínua e possui um contralador PI.\n",
        "\n",
        "As equações para modelagem do sistema e controle são apresentadas a seguir:\n",
        "\n",
        "____\n",
        "\n",
        "$\\frac{dT}{dt}=\\frac{WC_p(T_i-T) + q}{\\rho VC_{p}}$ ___ Equação A.40  \n",
        "_____\n",
        "\n",
        "$T_o(t) = t(T-\\tau_d)$ ___ Equação A.41\n",
        "\n",
        "____\n",
        "\n",
        "$\\frac{dT_o}{dt} = [T - T_o - (\\frac{\\tau _d}{2})(\\frac{dT}{dt})] \\frac{2}{\\tau _d}$ ___Equação A.42\n",
        "____\n",
        "\n",
        "$\\frac{dT_m}{dt}=\\frac{T_o-T_m}{\\tau_m}$ ___ Equação A.43\n",
        "\n",
        "____\n",
        "\n",
        "$q_{s}=WC_p(T_r - Tis)$ ___ Equação A.45\n",
        "\n",
        "____\n",
        "\n",
        "$\\frac{d}{dT}(errsum)= T_r - T_m $ ___ Equação A.46\n",
        "\n",
        "____\n",
        "\n",
        "$q = Q_s + K_c(T_r - T-m) + \\frac{K_c}{\\tau _I}(errsum)$ ___ Equação A.47\n",
        "\n",
        "____\n",
        "\n",
        "**Item 1**. No primeiro item do exercício é pedido a resolução do problema sem o controle PI ($K_c=0 $) e a modificação da temperatura da corrente de entrada no tanque ($T_i$) modificada para 40°C decorridos 10 minutos do processo.\n",
        "Requisita-se também a verificação da aproximação de Padé (Equação A.42) para o cálculo da tempetura $T_o$.\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
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        "id": "5pDzfZR_ro66"
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      "source": [
        "***Resposta***\n",
        "Na roslução do exercício, primeiramente foram resolvidas utilizando o Método de Runge Kutta de 4ª ordem as equações diferenciais (Equações A.40, A.43 e A.46), com a aproximação de Padé (Equação A.43) para o cálculo de $T_o$ que também é uma equação diferencial.   \n",
        "Em um segundo momento, foram resolvidas as mesmas equações diferenciais (Equações A.40, A.43 e A.46), porém, considerando a Equação A.41 para calcular o valor de $T_o$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1FqdWwVtCeSu"
      },
      "source": [
        "# Importando as bibliotecas necessárias:\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "from scipy.integrate import odeint\n",
        "from pylab import *"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jAaQ9UiAJGUS",
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          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7996161b-c34b-41e0-d6c7-a3b71972114f"
      },
      "source": [
        "#Importando a pasta do github que será utilizada:\n",
        "!git clone https://github.com/jessikamorais/Metodos_Numericos #clonar do Github\n",
        "%cd Metodos_Numericos"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "fatal: destination path 'Metodos_Numericos' already exists and is not an empty directory.\n",
            "/content/Metodos_Numericos\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6ln1rA4oCXkI"
      },
      "source": [
        "#Definindo as variáveis necessárias:\n",
        "\n",
        "termo1 = 4000.0 #ro*V*Cp [kJ/°C]\n",
        "Tis = 60 #Constante de tempo integral [°C]\n",
        "TauD = 1 #Tempo morto, tempo que o sistema demora para atingir a T de Set point[min]\n",
        "Kc = 40 #Ganho proporcional [kJ/min °C] #Condição para o Item 1\n",
        "termo2 = 500 # W*Cp [kJ/min °C] \n",
        "Tr = 80 #[°C] #Temperatura do SetPoint\n",
        "TauM = 5 #[min] #Constante de tempo do termopar\n",
        "TauI = 2 #[min]\n",
        "t_plot = []\n",
        "q_plot = []\n",
        "qlim_plot = []\n",
        "T_plot = []\n",
        "ToPade_plot = []\n",
        "Tm_plot = []\n",
        "ToReal_plot = []\n",
        "TReal_plot = []\n",
        "TmReal_plot = []\n",
        "t_plot2 = []\n",
        "\n",
        "#Tm = #Temperatura lida no termopar [°C]\n",
        "#To = #Temperatura de saída do tanque ou temperatura que entra no termopar\n",
        "#Ti = #Temperatura de entrada\n",
        "#Tis = #Temperatura de projeto de estado estacionário\n",
        "\n",
        "#Condição inicial do sistema (t= 0 min):\n",
        "T0 = Tr\n",
        "To0Pade = Tr\n",
        "Tm0 = Tr\n",
        "derrsum0 = 0.0\n",
        "Ti = 60.0\n",
        "T0Real = Tr\n",
        "ToReal = Tr\n",
        "Tm0Real = Tr\n",
        "derrsum0Real = 0.0"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2wjhmT9n22iq"
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      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SK_bdSHMtAyF"
      },
      "source": [
        "**Etapa 1_ Resolvendo o sistema utilizando a aproximação de Padé:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c0mRUM9JJaY5"
      },
      "source": [
        "def model(Resp, t):\n",
        "\n",
        "# Definindo o valor da temperatura de entrada no tanque (Ti) com relação ao tempo:\n",
        "  if t < 10.0:\n",
        "    Ti = 60.0\n",
        "  elif t >= 10.0:\n",
        "    Ti = 40.0\n",
        "  \n",
        "  # Definindo as equações utilizadas:\n",
        "  T, ToPade, Tm, derrsum = Resp[0], Resp[1], Resp[2], Resp[3]\n",
        "  T, ToPade, Tm, derrsum = Resp\n",
        "  qs = termo2*(Tr-Ti) #Calor necessário para atingir o Set Point\n",
        "  q = qs + Kc*(Tr-Tm) + (Kc/TauI)*derrsum #Calor que entra no tanque\n",
        "  \n",
        "  # Definindo as Equações Diferenciais utilizadas:\n",
        "  dT  = (termo2/(Ti-T)+q)/(termo1)\n",
        "  dToPade = ((T - ToPade) - (TauD/2)*(dT))/(2/TauD) #Calculo para o efeito do tempo morto (aproximação de Padé)\n",
        "  dTm = ((ToPade - Tm)/TauM) #Modelagem do termopar\n",
        "  derrsum = (Tr - Tm) #Nova variável para calcular a integral de q\n",
        "\n",
        "  #Capturando os valores para a construção de gráficos:\n",
        "  t_plot.append(t)\n",
        "  T_plot.append(T)\n",
        "  ToPade_plot.append(ToPade)\n",
        "  Tm_plot.append(Tm)\n",
        " \n",
        "  return [dT, dToPade, dTm, derrsum]"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3rHlOmLfF27n"
      },
      "source": [
        "#Importando a função de Runge Kutta de ordem 4:\n",
        "from rk4_sys import rk4"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tvYW-I5Hdmll"
      },
      "source": [
        "# Resolvendo pelo Método de Runge Kutta de ordem 4:\n",
        "\n",
        "t0 = 0.0\n",
        "x0 = [T0, To0Pade, Tm0, derrsum0] \n",
        "tf = 120.0\n",
        "\n",
        "t, x = rk4( model, t0, tf,x0)\n",
        "\n"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GvklJT5DtLXJ"
      },
      "source": [
        "**Etapa 2_Resolvendo o sistema desconsiderando a aproximação de Padé:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xLRIYrbpR2a8"
      },
      "source": [
        "def modelReal(RespReal, t):\n",
        "\n",
        "# Definindo o valor da temperatura de entrada no tanque (Ti) com relação ao tempo:\n",
        "  if t < 10.0:\n",
        "    Ti = 60.0\n",
        "  elif t >= 10.0:\n",
        "    Ti = 40.0\n",
        "  \n",
        "  # Definindo as equações utilizadas:\n",
        "  TReal, TmReal, derrsumReal= RespReal[0], RespReal[1], RespReal[2]\n",
        "  ToReal = TReal*(t - TauD) #Expressão para o tempo morto\n",
        "  qs = termo2*(Tr-Ti) #Calor necessário para atingir o Set Point\n",
        "  q = qs + Kc*(Tr-TmReal) + (Kc/TauI)*derrsumReal #Calor que entra no tanque\n",
        "  \n",
        "  # Definindo as Equações Diferenciais utilizadas:\n",
        "  dTReal  = (termo2/(Ti-TReal)+q)/(termo1)\n",
        "  dTmReal = ((ToReal - TmReal)/TauM) #Modelagem do termopar\n",
        "  derrsumReal = (Tr - TmReal) #Nova variável para calcular a integral de q\n",
        "\n",
        "\n",
        "  #Capturando os valores para a construção de gráficos:\n",
        "  t_plot2.append(t)\n",
        "  TReal_plot.append(TReal)\n",
        "  TmReal_plot.append(TmReal)\n",
        "  ToReal_plot.append(ToReal)\n",
        "\n",
        "  return [dTReal, dTmReal, derrsumReal]"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "36Yw2uSGScVA"
      },
      "source": [
        "# Resolvendo pelo Método de Runge Kutta de ordem 4:\n",
        "\n",
        "t0 = 0.0\n",
        "x0 = [T0Real, Tm0Real, derrsum0Real] \n",
        "tf = 120.0\n",
        "\n",
        "t, x = rk4( modelReal, t0, tf,x0)\n",
        "\n"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uV0yoLSttX42"
      },
      "source": [
        "**Plotando os gráficos das temperaturas $T$, $To$ e $T_m$ em função do tempo considerando a aproximação de Padé.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "abNlNE2qt-i_",
        "outputId": "831bb4c7-8b90-4c55-8f33-12afbd65d886"
      },
      "source": [
        "# Plotando o gráfico de temperaturas (T, ToReal, Tm) com relação ao tempo:\n",
        "# Os gráficos são plotados consideração a aproximação de Padé para To:\n",
        "\n",
        "figure()\n",
        "plot(t_plot, T_plot,'-r',t_plot, ToPade_plot,'-b',t_plot, Tm_plot,'-y')\n",
        "grid()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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BubnplbrhmofNSl7LBmpx2w1XF3G8BspQ2tZgMBgqicRE+O47cZssVP1pzhzw84N+/WwbSmtNbOx0fHy64+PTufQT7IyJeDUYDIbFiyE9/Zzlenw8/PijlPdzdbVtqDNn1pOSElElVvFglLzBYDCIqaZdu3MS0nz5pVT+K2SmL5HY2Ok4O3tXaGGQkjBK3mAwXNzs2QN//y2avJAD/Ny5ovc7dLBtqOzs0xw/Hoaf3z24uFSNWASj5A0Gw8XNvHng5HSOf+SWLfIo24brQnJz0wgKqhqmGjBK3mAwXMzk5EhF7n79INA668rcueDmBnffbdtQWmtiYj7H27srPj425iGuAIySNxgMFy/h4XD06DlG98xMWLgQbroJ6ta1baikpA2kpGyrUqt4MEreYDBczMydC7VqiTYvwPLlcOJE2Uw1sbEzcHLyws/PxqV/BWGUvMFguDg5c0YKdd911zmFuufMgYAAuP5624bKzj5DXNwi/PzuwsWlph2EPX+MkjcYDBcnX38txVoLLdfj4uCnn8Q33sXGcNHjxxeRm5tS5Uw1YJS8wWC4WJk3D1q3hh49rJq//FL2Y8viGx8TMx0vr074+HQvZyEvHKPkDQbDxce+fbBmzTm+8VqLqaZ7d4mNsoWkpE0kJ/9HUNBIlK2FXyuQsiQoM1RHjh+HFSsgNhYiI+HQIdlROnECMjKIz6nDfxntOOHZiCM0JjEghPQ6QWR61sKjZUN8/D2pUweaN4cWLeTh5lbZkzIYLpD588U3fsgQq+bNm2H7dvjsM9uHiomZgZOTB/7+95azkOWDUfKORmYmrFoFy5bBH3/Arl35XTowiMjAq/jVeSgzM6/nVJY3sSmWYpWZ8uSWmIEHabiRSdpvOSQXGt7dHbp1g0svFdfiyy+3PaeHwVAlyM0VJX/ttdCggVVXnm/8XTZmJMjOTub48YX4+Q3CxcXGwq8VjFHyjoDWsHo1jBkDf/4p77294Yor0EOGssXnchbu6c7i72tw5D85xcMDBg6EkBApZ9mmDTRqBF5eNeB0OvyzGdauJefvfzm5ZicHMhuwj5Zs63ov+2rVY926k2zbdoyvvz5I06a16dkziyZNsvD0bIGLS108PFrg7t64Uv8sBkOR/PknREXB++9bNWdkiG/8wIFQu7ZtQx0/HkZOTnKVSUZWFEbJV2eSkmD2bJg27eyKfehQuOMOki65hrlh7kybBjt3ymq7f394/XW47jpo0qSEcX194frryb22L8lJG0mLW4Hn/mW0yFhKw1oLizxFa7EEFUSpGkAj9uy5Hl/f3tSu3Rc3N/+iTjcYKo65c6FmTdHmBfjxRzh1CoaXofJFbOx0vLzaU7Nmz/KVsRwxSr46kpAAn3wCH38sr3v2lN2iO+/k6ClPHn4Y1twrbsA9esg94I47pB5CaWRnn+HkyZ+Ij1/CqVO/kJubAoBn3bb4et+CV2YQnr/txu3r33E9morLtTeT9uTrfLe9JQsWpLJv3ymaNYtn6NB99Oy5m2PHwomLm0dMzBRA4evbi3r1bsXP725q1Aiw79/JYChMcjIsXQr33is/Zwswdy4EBYkVxxaSkjaTlLSBli0/qZIbrnkYJV+dSEmBCRPgjTfk/c03wyuvQI8eHDsG778suh/Epvj003DJJaUPq7UmMfEPYmKmceLE92idgZtbIAEBQ6ld+xp8fa/Aza1A3bPOwAOJMH48TJqE24IfGfbUUwxdOobVmwN55x0YPrwPjRrBffftZMyYViQnb+HUqZ+Ij/+W/ftHceDAC9StezNBQQ9Tu/bVVfqfxOBALFki/0eF/COPHZMKUM89B87Otg0lEa7u+PuXofBrZVBche/CD2A2UqQ7okDbGKQ49xbLY0CBvpeR0n+7gettuUZoaOh5Vyt36Ar0OTlaz52rdVCQlIzv1k3rrVu11lonJWn98stae3hIkfkRI7Q+cMC262RnJ+uoqHE6PFzp8HD0mjW19Z49T+jExLU6NzfHtkGOHdN65EiRq2FDrb/5Rmut9Z9/at2lizT37q31zp1nT0lJ2aX37n1Wr1lTV4eHozdu7Kbj47/Xubm5tl2zknCU75ijzEPr85hLnz5aBwdrXei7Nn68fFcjI20bJjs7Wa9eXVPv3Dm0bNcvgQv5XICNuhi9WhY/+blAUQWwJmqtO1seywGUUm2Bu4B2lnM+U0rZeH80WPHff9C0qUTlNWwovr0bNqA7dGTRIonleP99uOUWMcvPnAnNmpU8ZFZWIlFR7/HPP005cOBFvLw60Lr1PC69NJrg4E/w9e2FUjZ+Nfz94fPP4a+/xB50660wdChXdD7Dhg3w3HO7iIyELl1g3DgpwODpGULLluO59NKjhITMJCvrFBERN7NpUyiJiX9e6F/MYCiagwfF46wY3/iePeX/yRaOH19MTs4ZAgMftI+s5YjNSl5rvRo4ZePhNwNhWusMrfVBZEXfo5RzDAVJTYXnnxej+pEj8i38+2/o3ZvISOjTB+65R/Jr/PWXeAW0bFnykDk5qRw69Dbr1tXm4MFX8fHpQZcua+nefSsBAUNxdvYoeYCSuPRS2LRJTEkLF0KnTjj/s44bbjjGjh1www3w0kvQu/fZDVpnZ3cCA0fQo8duWreeR1bWSbZs6cOOHXeQlnbo/GUxGIpi/nxR7oV84zdtgh07ypqMbDqenm3w9e1VvjLaASUrfRsPVqop8KPWur3l/RjgPuAMsBF4VmudoJSaDPyjtV5gOW4W8LPWekkRY44ERgL4+/uHhoWFnddEkpOT8fauGpVYLpQaf/1F58mT8YiNJeaGGzjw0ENk+/iQk6NYvLghc+Y0w8MjhwcfPED//rE22BBzgJXALOAE4A+8DQTbRf6aO3bQ5t13cY+LY8eIEZy4+240ivBwPz76qBVKaV56aRe9ep0sdGY68BWwCKkZPxJZL1SNwGxH+Y45yjygDHPJzeWSwYNJCwpi2/jxVl0ffxzM8uUBLF36N97e2TZcdT/wAPAYcPt5SF00F/K59O3bd5PWuluRncXZcYp6AE2xtsn7A87If+G7wGxL+2RgcIHjZgG3lzb+RW+Tz8jQ+vnnda5SYjf844/8rh07tO7eXeyGt94qpnBbSExcp1ev9rXYvnvohITVdhK+EKdPa33TTSLwsGFap6VprbXet0/rrl2l+YUXtM7OPvfUtLRDesuW63R4OHrz5j46NdXGTQY74xDfMe0489C6DHP580/50n3xhVVzWprWtWtrfffdtl9zz57H9R9/1NCZmSdsP8kGqoJNvqgbRJzWOkdrnQvM4KxJJhpoVODQhpY2Q3FERopR8MMPibnxRomvvvJKtIbJk6FrVzEpfvWVOAj4l+JunpV1it27H2Lz5l7k5JymTZtFdO36D7VqXV4x86lZE779loP33SeJoK64Ao4fp0ULWLcOHn4YPvhA9hKSC4XVurs3oWPHFYSEzCQp6T82buxMfPw3FSO3wTGZNw98fOQLV4AffhAvZFtNNTk5qRw79gX169+Oq6uN1UQqmQtS8kqpgvWybgEiLK+XAXcppWoopZohdoF/L+RaDs20adC2rdjev/+evc88A15enDol+5hPPAFXXy12wzvvPKfWsBVaa44dW8C//7YmNnYWDRs+S+/eSfj731XxbopOTkQNGwbffQcREXDZZbB/P+7uMHUqfPqppHS9/HIpzlMQpRSBgSPo3n0bnp6t2bHjNvbufZrc3MyKnYOh+pOSAosXyz+Pl5dV19y5ktng6qttGyo+fgk5OacJCqr6G6552KzklVKLgL+BEKXUUaXUCOADpdR2pdQ2oC/wDIDWegewGNgJrAAe01rnlLv01Z20NBgxAh55RHZQt23Lr1Czbh107ixK8KOPZMXh51fycBkZsURE3MSuXUNwd29OaOhGWrYcX/lV42++GX7/HRITZYN240YAHn9cogz375cfMZGR557q7t6ELl3W0KDBU0RHf8yWLX3IzIyr4AkYqjXffCM/Fwv5xsfGSu6+oUNt942PiZmOh0crfH2vsIOg9qEs3jV3a60DtdauWuuGWutZWushWusOWuuOWuubtNaxBY5/V2vdQmsdorX+2T7iV2MOHhRXk9mz4dVXZSkbGIjWMH9+E3r3llxjf/0FzzwjCfNK4vjxxWzY0J6EhN9o0WIiXbuuw8enc8XMxRZ69pQ7l6cn9O0La9cCkmph7VrJ333FFeIxWhgnJzeCgyfRtu1ikpO3sGnTJSQnR5x7oMFQFPPmSRrV3r2tmr/4QnKV2WqqSUnZwZkz66psSuHiqBpuCxcb06bJl27/fskW+c474OxMaioMHgxz5jTD1xf27JGMjyWRlXWSnTvvZufOQXh4tCQ0dDONGj1NlQxLCAmRu1aDBpLCcvVqQBKkrV59Vv+vW1f06X5+d9C582q0zmDz5ss4eXJFBQpvqJYcPiy/IovwjZ87VyyIrVrZNlRMzAyUcsPfvwzVRKoARslXJFpL3oFHHpF8phs3wo03AuI73qsXLFoEI0YcICFB9i5LIiHhDzZs6EB8/FKaNXuHLl3W4eVlYzRHZREUBOHhkvKyf38JTgGCg2VFHxAgCdQs+v8catbsRteu/+Lh0YKIiBuJi/uy4mQ3VD+++EL+74YOtWresEHMg7ZvuKYRFzef+vVvtU7xUQ0wSr6iyMqCxx6Dp56SDEjx8fnRS7//Liv2gwfFRj148OFSNldzOXToHbZuvRpn55p07fovTZq8ipNTNUlFFBgoyr1pUxgwIN9006iRKPfGjSV4av36ok93d29E585/4uvbm8jIwURHT60w0Q3ViLzlet++8l0rwNy5UhvhzjttGyo+finZ2QlVOqVwcRglXxEkJorWmjoVXnxRdnssy/Tp02Xl6u8vq4sBA0oeKjPzONu29ePQodfx87ub0NCNVcv2biv+/mdX9P/7n2w6W5pXrZLnfv3Ek7QoXFxq0qHDcurW/R979z5KVNR7FSi8oVrw119S5q/Qhmt6uvxivvVWyaptC7GxM/DwaEmtWn3KX047Y5S8vTlwQAx/f/whm6xjx4KTE7m5ou8fekiU/D//iMmiJBIT/2Tjxs6cPr2GkJCZtGnzReV7zlwIfn6wcqX4L193nexRIBadVavkPnjttZIPvyicnT1o124pfn73cPDgqxw69HYFCm+o8sybJy6Tt91m1bxsmay7bM0bn5Kyi9OnVxMY+GC12nDNwyh5e7Jxo3iVxMWJMrN8q9LSJBXwBx+IeX7ZMtFzxZFnntmy5SqcnX3o2nU9gYEjquUX7hwaN4Zff5XMZddeK35tSFGTVatk66JfP4guJpTOycmVNm3m4+8/hEOHRnP48AcVKLyhypKaKpGDd9whVdIKMHeu/IDs29e2oWJjZ6CUKwEB95W7mBWBUfL2YuVKySLm5SWJxa68EhBT/NVXS9Tq+PEwZQq4lGBKtzbP3EVo6Ea8vTtWzBwqijZtJJl3fLyYtSwhsC1bwvLlEpE4YIAUQSkKpZxp3XoOfn53ceDAixw5MqkChTdUSb77Tr4whUw10dHwyy+2+8bn5KRz7Ng86tUbiJtbKYEqVRSj5O3BokWirFq0ELugxUdr925Z2G/eDF9/Dc8+W3L0akHzTKtWM2jTZgEuLiUs+asz3bvLymvrVqnakyOxc507SyGfnTvFhppZTMCrKPr51Kt3G/v3P0NMzOcVKLyhyjF3ruTcvsI6aGnBAvGNH2ajF+SJE9+SnX2yWm645mGUfHkzaZLkAO7VS1xFAiXzw+rVEuyZlCT7jYXMhIXIJSrqXSvzTFDQA45hnimJAQOkpOGyZbJhYeG66yRP/qpV8MAD4jRRFE5OrrRt+yV16tzAnj2PEh//bQUJbqhSHDkCv/0mmrxAFGGes02vXqXvf+URGzsDd/dm1K59lX1krQCMki8vtBbF9MwzcPvtYn6wbN2PHi3WGn9/2WDtWULN38zM48CLHDz4Gn5+gxzTPFMSjz8ujwkTxPXIwrBh8NZb4vb8QQlmdycnN9q1W0zNmj3YufNuEhPXVoDQhipFMb7x//4rhXVs3XBNTd1DYmK4ZcO1+qrK6it5VSInR8wzH3wAjz4KYWHg7o7W8N578Pbb4jHy118S6FociYmr2WXYsfEAACAASURBVLixC7CVVq2m06bNQsc1z5TExIkSKPXoo/nBUgCvvQaDBsHLL0s8QXE4O3vSvv0PuLs3ISLiRlJSdthfZkPVIK/MU58+55RImztXanffcYdtQ8XGzkQpFwICbLwrVFGMkr9QsrIkF8HPP4u5YfJkcHYmKwtGjpS0NHfeKZ6UtWsXPYTWORbvmb44O3sDnxEUVD3dtcoFFxe5UbZsKVrdkqJSKfFC7dJFLGJFJTTLw82tHh07/oKTkzvbtvUjI8Nkur4oyPONLxTKmucbf9ttpUeSA+TmZnDs2Bzq1r2JGjUC7CNrBWGU/IWQni6mmbAwWcX/9BMoRVKSZCuYOVNWn2FhUKNG0UNkZsad4z0DpdTxuxioWVOyB6amyt84IwOQ/DbffScrsptuEs+b4vDwaEqHDj+TnZ1IRMRAcnJSK0h4Q6Uxd26RvvHffw+nT9uexuDEie/JyjpBUFD13XDNwyj58yU1VbTMsmWyen/+eUBctC6/XPZ9Zs4UU01xC/KEhN/ZsKETp0+vswQ3ObD3zPnQtq38065fL+kgLDRqJPo/KkpW9Lm5xQ/h49OZNm0WkpS0iV277s+rVGZwRErwjZ8zR0IybPWNj4n5nBo1mlC79jV2ELRiMUr+fDhzRiJ0Vq0S+8FjjwGwZYtsqu7fL4v6ESOKPl3rHA4efIOtW6/B1bUOXbv+6zjBTeXNbbfJhvbnn8OsWfnNvXpJ0ZEVK2TfoyTq1buJ5s3fJz7+K6Ki3rGzwIZK49tvxX2t0HI9OlrCVgo52xRLaupeEhN/t5hMq2A21zJilHxZOXVKIjP//hu+/DJ/q/6rryR7gdawZg1cf33Rp6el7Wfz5iuIinqLgIBhhIZuwNu7fQVOoBryzjtwzTVyM926Nb955EhxqX/jDUnyVhKNGr2Av/9QDh0aTXz8UjsLbKgU8nzjL7cucZmXN95W33iJcHUhIOD+8pexEjBKvizs2wcdOsiSfelSGDSInBx45RVJU9C1q2Qy6FxEvjCtNTExM9iwoRMpKTto02YhrVvPwdnZ69yDDda4uMDChVCnjmzEWiJilZLU/CEhcPfdEBNT/BBKKUJCplOz5mVERg4hOXlbBQlvqBAOH5Zf1sX4xl9+ucQmlob1hmtg6SdUA8pS/m+2Uuq4UiqiQFsdpdRKpdRey3NtS7tSSn2ilNqnlNqmlOpqD+ErjNOnYcwYiaCIiZFafDfdxNGjssB8/31ZVf7+u+RDL0xGxjEiIm5iz56R1KzZk+7dt+Pvf0+FT6Na4+cn4Yp79ogfvQVvb0kRkZwsij47u/ghnJxq0L79N7i41CYi4layshIrQHBDhTB/fpG+8evXS6S5rRuu8fHfWjZcHyp/GSuJsqzk5wL9CrW9BKzSWgcDqyzvAfojxbuDgZFA9Uz4nZQE774ruajffFPMNGvXknP1dcybJxWNNmwQs/znn0syrYJonUtMzHQ2bGhDQsJvtGw5iU6dfsXdvVGlTKfac9VV4q40b578BrfQtq38/VevhtdfL3kINzd/2rX7moyMKHbtGorWJezaGqoHecv1YnzjPT3L4hv/uSXCtfpvuOZRlhqvq4FThZpvBuZZXs8DBhZon6+Ff4BaSqnq89snJQU+/FAil157TWpD/vcfuSt+ZUlsLzp0kJVBq1aSh6aoCLqUlJ1s2XIle/Y8hLd3Z7p120LDhk9V68i5KsHo0fLb+5FHZIlmYfBgePBBGDeudPu8r+9ltGgxgZMnf+Dw4bF2Fthgd9atE2+HQv+IqanivnzbbSVneT17/G4SE/+o9hGuhVFlcSlTSjUFftRat7e8T9Ra17K8VkCC1rqWUupHYKzWeq2lbxXwotZ6YxFjjkRW+/j7+4eGhYWd10SSk5Px9r6w3OpOGRkELVtG40WLcEtI4FS3bhwcPpwzbdqybl1d5s9vyt69PjRpksLw4Ye4/PL4InbrTyP3u2WAF/AIcD1gu+dMecylqmCPudSIj6fbAw+QUb8+mz77DG35CZWW5sRDD3UjLc2ZmTM34Otbgu0GDbwD/AF8AISWel1H+VwcZR4gcwmdOpX64eH8tXQpuR4e+X2//urP+++3YeLEzXTufNqG0aYCS4HFQB07SVw8F/K59O3bd5PWuuiK0Fprmx9AUyCiwPvEQv0Jlucfgd4F2lcB3UobPzQ0VJ8v4eHh532uTkvT+uOPtQ4I0Bq0vuoqrdes0Tk5Wi9erHXHjtLcvLnW8+ZpnZ197hDZ2ck6KmqsXr26pg4Pd9a7dz+sMzKOV/xcqhh2m8sPP8iH8vzzVs3//ae1q6vWt9yidW5uyUNkZSXp9evb6rVr6+m0tMOlXtJRPhdHmYfWWv+5fLnWPj5aDx9+Tt+VV2rdsmXp3wOttc7OTtNr1tTVERG3l7+QNnIhnwuwURejVy/0N0lcnhnG8nzc0h4NFDQ8N7S0VS0yMuCzzyR8/qmnxP7yxx9k/7KKBYd60769pCTIyBAz8O7d5+ahzspKJCrqXf75pykHDrxErVpX0L37Nlq1moqbW/3Km5uj87//SVmt8ePhzz/zm7t0kY3wb7+FGTNKHsLFxZv27b8hNzedyMh7yM0taeVvqIrUX7OmSN/4PXvkazFiRMnpvPM4ceIbS0phx9lwzeNClfwyIM/7dBjwfYH2oRYvm57Aaa117AVeq/zIzJSduuBg8b1u2hRWrSJr5R/M3n8lbdrAkCGizMPCYMcOUe4Fi3ukpOxk375n+Oefxhw8+Bo+Pj3o3HkNHTr8gJdX20qb2kXF+PHiFzd0qHhAWXjmGdkjf/ppyTpYEp6eIbRqNY3Tp9cSFfWWnQU2lDcBP/8se2e9e1u1z54t/7+2+sbHxHyOu3vzap1SuDjK4kK5CPgbCFFKHVVKjQDGAtcqpfYC11jeAywHDgD7gBnAo+Uq9fmSlSVRk61awcMPS2rIX34h47c1TNtzFcGtFCNGyCbNN99I3M2gQWdX7jk5aRw7Np///uvNhg3tiI6eQt26NxAaupmOHX+iVq3eJV/fUL54e4tbZXS0VdoDJ6ezXhX33FN8oZE8/P3vxd9/GFFR75CQEG5fmQ3lx7591N6yBe6/38o3PitLfnnfcEN+OYcSSUmJ5PTp1QQFjXSoDdc8Sig8Z43W+u5iuq4u4lgNPHa+QpU72dkSTPPWW5IOsls3mDqVpF79mDFTMWG4uL9fcomU4xsw4OxPPK1zOXPmb+LiFnL8+CKysxPx8AimefMPCQgYZkwylc0ll0iqz7fekqxwlsRUQUGymrv5Zul6p5RsBsHBkzlz5m8iIwfTrdtW3NzqVYDwhgti9my0kxOqkKlm+XI4dqz4tCKFOVvDtXqnFC4Ox7ttFSQnR1Z6bduKzc7XF5YtI+a7f3npz/40aqx49lmx2qxcKZkKbrgBQJOcvJ0DB17hn3+as3lzb44dm0udOv3p1CmcHj1207jxc0bBVxVee01u3A89lF8IHCR/3PDhYqNfv77kIVxcvGnb9iuysk6wa9d9JpFZVSc7G+bM4eQll0CDBlZds2bJCn7AgNKHOVvD9ZZqW8O1NBxTyefkiDG9fXsxrnt4oL/5lvWfbWL4NzfStJniww+lrNz69VKX4qqrMklI+I29e59m/fqWbNzYkcOHP8DLqw2tW8/nssviaNv2S2rX7mMSiVU1XF3lZp6aek59wIkTRQcMGwZpaSUP4+PTmRYtxnPq1E8cPfqxnYU2XBCW5XpsIU0eEyPJAYcNs95DK474+CVkZ59yiJTCxWGzuaZakJsrOWXGjJHKz+3aEfP5DyxNH8DMMU5s2yappkeOhKeeOkO9eps4fXoNW7eu4fTpv8nNTcHJyZ1ata6mUaPnqV//Voe9uzscISEwdqzY5ufPz99x8/UVs82114pV56OPSh6mQYPHSUj4jQMHXqBWrT74+BSRiMhQ+cyaBQEBnCpUS3PePFED99uYWywmZgoeHiHUqmVjDuJqiEMo+RPxCST++hvb3x1NRnQssYEd2NX3ObadDiJ28UmcnRdw3XUxjBkTQ5Mm+8jIiCA6+gjR0QAKL68OBATcR50611O79tU4O3tW9pQM58Pjj8PXX4tbzbXXimEeyS/06KNSY33gQLjiiuKHUErRuvVsNmxoz65dQ+jadQPOzu4VNAGDTeQt159/Hl1guZ6bK7r/yittK9SdlLSJM2f+oWXLjx1ywzUPh1Dyf03/iFrXvcvJ6+S9D/vozrd0L3Scs3NNcnKa4ut7BV5e7fH27kjNmpfh6lqrwmU22AEnJ1m2d+wo3lPff5+/gz5uHPzyi2zNbNt2Tk0JK1xd6xISMpvt2wdw8OCrtGw5oWLkN9jGvHlikr3/fiwrNUByF+3fLz/kbSE6egpOTl4EBNjoZ1lNcQgl3/G2ofwxKwmv0D7k4E7jxi60aOGKu7sLSrng7FwTd/fGJq3vxUBwsCSVe/ZZyfd/772AKPW5c2UV//zzMLWUlHl16/YnKOhRjh79iLp1b3BI/+lqSeHlegElP3OmmOcKVf4rkqyskxw/vgh//2G4uPjaUeDKxyGUfNPWwTS9YSB9+vSpbFEMVYGnnpL8w08+CVdfnZ//uXdvGDUKJkwQRXBNKYkGW7T4gISE39i16z66dTP556sEf/5Z5HI9IUE+8hEjpP5vacTGziE3N50GDaqOp7e9cFxDlOHixdlZzDYpKRLRXMDb5p13JBbuwQelu+RhvGjT5gsyMmLYt+8JOwttsIlZs4pcri9YIOlHHnig9CG0ziEm5jN8fS/H27uDnQStOhglb3BMWreWKKhvvpHNWAvu7qInDh0Sb5vSqFmzB02bjiYubgFgomErlbzl+uDBVst1rcX81qOH5C4qjVOnVpCefpAGDR4v/WAHwCh5g+MyahR07y6r+fj4/ObevaXpk08kAK40Gjd+BR+fHsBEMjKqXp69i4aFC4tcrq9ZA5GRstduC9HRU3BzC6RevVvsIGTVwyh5g+Pi4gJz5kjyslGjrLrefx8aNhQbbkZGycM4ObnQps0CIItdu0aYaNjKQGtJKhgaek4R5WnTxIIzaFDpw6Sm7uPUqRUEBo7EycnVTsJWLYySNzg27drBSy+J0faXX/KbfXxEZ0RGijNOaXh6BgMPkZDwC7Gxs+wnr6Fo1q2DiIhzlusJCa4sWSKxb542hLfExExFKWeHjnAtjFHyBsfnlVckIvbhh612W/v3l6wX778vvvOlcxO1al3F/v2jSE+Pspu4hiKYOlWW63db50lcsSKArCzbTDU5OakcOzaHevVuoUaNIDsJWvUwSt7g+Li7SwWRQ4fgjTesuiZOhNq1xWyTXWrNECdCQmYB2phtKpL4eNlwHTpU8pJYyM2FH38M4soroU2b0oeJi1tAdnbCRbPhmodR8oaLg8svl6RFEyfCpk35zXXrwuTJsHGjdJWGh0dTWrSYQGLiKmJiPrejwIZ85syRogCFlusrV0JMjIdNq3itNUePTsLbuwu+vpfbSdCqiVHyhouHcePA31+c5Ass2++4Q3LajB4Ne/eWPkxg4IPUrn0t+/c/R1raQTsKbCA3VzZPrrhCUoYXYNo0qFUrk1tvLX2YU6d+ITU1koYNn7nossgaJW+4eKhVCz79FDZvlmxlFpSSYjE1aoj+z80teRilFCEhs1DKmd27R6B1KScYzp9ff5VCP488YtV89Cj88AMMGBCLm1vpwxw9Ogk3twD8/GxwwXEwykXJK6UOKaW2K6W2KKU2WtrqKKVWKqX2Wp5rl8e1DIYL4tZbpZrI6NGiPCwEBcGHH0rU/OzZpQ/j7t6Ili0nkpgYTkxMKYlwDOfP1Kng50fh5frMmXIzvuGG0ktHp6TsJCHhF4KCHsPJyYY7goNRniv5vlrrzlrrbpb3LwGrtNbBwCrLe4Ohcslbtru4iI23wObpiBGS9+r556V8XGkEBAynTp3+7N//Amlp++0o9EXK4cPw44/ywRRYrmdlyT769ddDUFB6qcMcPToJJyd3goJsjJZyMOxprrkZmGd5PQ8YaMdrGQy207Ch+E2uXCn+8xacnGD6dKkg9eSTpQ8jZhupD7pr13BjtilvZs6Um/BIa5/2pUslpfwTNqQTysw8QVzcF/j7D7lo6/aq8nADU0odBBIADXyutZ6ulErUWtey9CsgIe99oXNHAiMB/P39Q8PCws5LhuTkZLxLShJejTBzqQByc+ny5JN4HjnCv/PmkVXr7FdzwYLGzJrVnHfe2U6vXifz24ufywpgHFK7/nZ7S37BVNnPpAAqK4ued91FcnAw28eOtep7/PEuJCa6Mn/+v6SmljaXBcAsYA7Q1H4ClwMX8rn07dt3UwErijVa6wt+AA0sz37AVuAKILHQMQmljRMaGqrPl/Dw8PM+t6ph5lJBRERo7eqq9eDBVs0ZGVp36KB1gwZanz59tr24ueTm5upt2/6n//zTQ6ek7LajwOVDlf5M8li0SGvQ+qefrJr//VeaP/5Y3pc0l5ycDL1uXaDesuU6OwpaflzI5wJs1MXo1XIx12itoy3Px4FvgR5AnFIqEMDyfLw8rmUwlBsFUx78+mt+s5ub2HxjYiRYtjSUUrRq9TlOTu4Ws02OHYW+SJg8GVq0gH79rJo//VQKwNx3X+lDHD/+FZmZsTRs+Ix9ZKwmXLCSV0p5KaV88l4D1wERwDIgr67WMOD7C72WwVDuFEx5kJqa33zJJWLz/ewz+Ouv0oepUSOI4OBPOXPmL44csSGqylA8mzdLrprHHpONEgtxcfDVVzB8ONSsWfIQWudy+PA4PD3bUafOdXYWuGpTHit5f2CtUmor8C/wk9Z6BTAWuFYptRe4xvLeYKhauLtLsM3Bg+dUG3rnHWjUSHznS8tUCeDndw/16t3CwYOvkZISaR95LwYmT5ZsY8OHWzVPny6Br4/bkJXg5MnlpKbuoHHjFx26SLctXPDstdYHtNadLI92Wut3Le0ntdZXa62DtdbXaK1PXbi4BoMduPJKyVH+0UeyirTg4yNu2jt3SrBsaYjZZirOzt7s2jWM3NxSk+EYCnPypNTmHTJEgtcsZGbKZ9Gvn1T2Ko0jR8ZRo0Zj/PzusqOw1YOL+xZnMOTxwQdQr945KQ8GDJDEh+++C1FRpeeydXPzp1WrqSQlbeDIkQ/sKbFjMns2pKeLqaYAS5dCbKxtrq2nT6/j9Om1NGr07EWTM74kjJI3GEBSUX7yiSQv+/RTq65Jk2Szb/z4kFJTHgD4+d1B/fp3cujQGJKTt9tJYAckJ0c2Qfr0gQ7WtVc//hiCgyUAqjQOHx6Hi0tdAgNH2EfOaoZR8gZDHnfcAf/7H7z2mqQltuDnBxMmQESEL5/bmHgyOHgKLi61LWabLPvI62h895383QsZ3detg/XrZRXvVIrGSknZwcmTP9Cw4RM4O3uVfPBFglHyBkMeeSkPnJwkIVaBQMFhw6Br1wRefBGibSjz6uZWj1atPic5eTOHD79nR6EdBK0leVCLFpIStAAffgh16pyzD1skhw9/gJOT50WXM74kjJI3GArSuLEY4FesgALR10rBqFG7yc4Wc7EtgeL16w/E338wUVHvkJT0nx2FdgD++kuW66NGgbNzfvPu3bBsmfzNvUpZmKenH+b48S8JChqJq2tdOwtcfTBK3mAozGOPQY8e8NRTcOqsU1iDBumMGQPffw/ffGPbUC1bfoKra3127bqP3Fwb/DAvVsaPlwouhaKcPvpIgtMK7cMWyeHDYwFFw4ajSj32YsIoeYOhMM7OEvKakADPPWfVNWoUdOkiZuPExNKHcnWtTUjIDFJStnPo0Ft2Erias2eP3DkffdSqGndcHMybJ6Yyf/+Sh0hPP0Js7EwCA0fg7t7IzgJXL4ySNxiKomNHUfBz5sDvv+c3u7iI/j9+HF580bah6ta9gYCA4Rw+PJYzZzbYSeBqTDHL9SlTxD/+2WdLH0JW8dC48cv2kLBaY5S8wVAco0fLRuBDD0n+YQuhobKinz5diozYQsuWE6lRI4hdu4aRk1N6DvSLhuPHZbk+dKjVcj0lRZT8zTeXHvyUnn6U2NiZBATcj7t7YzsLXP0wSt5gKA4PD0l5sG+f5DgowJtvQrNmkuo83Qad7eLiS0jILFJTIzl06HU7CVwNmTJF/oCjrO3oc+bIdkgha1mRyCpe06SJWcUXhVHyBkNJXH21bAZ+8AFe+89Wf/L0FP2/Z48449hCnTrXERj4EEeOTOD0aRuynjk6SUkSeHbTTdC6dX5zVpbEJVx6KfTqVdog8cTGziAg4D7c3ZvYVdzqilHyBkNpjB8PtWsTMmGCRGVauPZasTKMHQvbbQxsbdHiQ9zdm7Br133k5KSWfoIj89lnsrn96qtWzV98ITFRr71myyCLgFwaN7YhJ/RFilHyBkNp1K0LkyZRMzJSFFMBJkyQPFoPPmil/4vFxcWHkJDZpKXt5cCBi7jscWqq/PGuu07cVS1kZ8N778m+R//+JQ+RlnYQ+IGAgPvx8GhqV3GrM0bJGwy2cPfdnOreXfLPHzmS31yvnuS2Wb/eNvsxQO3afWnQ4Emioz/l5MkVdhK4ijNjBsTHw+vW+xOLFsH+/bLnrVTJQxw6NBpwomnT0faT0wEwSt5gsAWl2PPMM5CbK2mJC4S83nOPFLGYNEn2aG2hefNxeHm1Z9eu+8jMjLeT0FWU9HTJ+nnlldC7d35zTo7sb3fqBDfeWPIQycnbiItbCNxGjRoN7CtvNccoeYPBRtIDA+GFF6RUYAGzjVKSc97XV/Kr2GK2cXZ2p02bL8nOTmT37hF5dZAvDubOldqKhVbxixfLRvbrr5e+ij9w4GVcXHyBu+0mpqNglLzBUBbyNglffRWOHctvbtBAMhWvXSvPtuDt3YEWLcZx8uQPxMTYmN6yupOZKTvVPXvCVVflN+fmyiq+XTu45ZaSh0hMXM2pU8tp3PglwMe+8joAdlfySql+SqndSql9SqmLeKfJ4BC4uEBkpJgcHn7YymwzZIh4A77yiiTWsoUGDZ6gdu3r2b9/FCkpu+wkdBVi9myIijrH6L5okfwaev31ktMJa605cOAl3NyCaNDgiQoQuPpjVyWvlHIGpgD9gbbA3Uqptva8psFgd1q3Fuf477+HhQvzm5US33lPT8m3YovZRiknWreeg7OzF5GR95Cbm2lHwSuZtDR4+21xfu/XL785M1OUe+fOktK/JOLjv+bMmb9p2vRNnJ1Lr9RlsP9Kvgewz1IHNhMIA2628zUNBvvz9NOirJ54QuzLFgICJIhz/Xpxr7eFGjUCCQmZRXLyZnbtsiFpenXls8/kb/Xee1ar+JkzpY76e++VvIrPyUlj//7n8fLqRGCgA/+dyhllzw0fpdTtQD+t9QOW90OAS7TWjxc4ZiQwEsDf3z80rEAO77KQnJyMt7f3hQtdBTBzqZoUnovH0aN0e+ABEjt3Zvv77+crLq1hzJh2/P13XT7/fCPNmtka9PQs8B8wFrikvMXPpzI+E+eUFHrecw9JrVqx7cMP89vT0py4996eNGqUyqRJW0rZcJ0PzAEmAp0Bx/5+lYW+fftu0lp3K7JTa223B3A7MLPA+yHA5OKODw0N1edLeHj4eZ9b1TBzqZoUOZePP9YatJ4926o5Lk7revW0Dg3VOjPTtvGzss7oP/5w0WvX1tPp6UcvXOBiqJTPZMwY+Ttt2GDV/N570rxuXcmnp6Ud0X/+6akjIm63anf475eNABt1MXrV3uaaaKBgcueGljaDwTF4/HHx9376aasgKT8/mDZN6oK/+aZtQ7m4+NCt23ZyctLYufMucnOz7SR0BXPypES33nordDu72Dx1CsaNE5/4yy4reYgDB15C6xyaN/+w5AMN52BvJb8BCFZKNVNKuQF3AcvsfE2DoeJwchKPkZwcSWSWm5vfddtt4jf/3nuwerVtw3l5tSYkZDqnT6/l4EGbkrdUfd58U3IHv/22VfNbb0mOstISvCUmrub48YU0avScSV9wHthVyWuts4HHgV+ASGCx1nqHPa9pMFQ4zZvDxx9LcZFCu62ffCIp6QcPllxctuDvfw+BgSM5cmQcJ0/+ZAeBK5Bdu2TDdeRIaNvWqnnKFMn506FD8afn5mawZ89DuLs3NamEzxO7+8lrrZdrrVtprVtorW1MymowVDPuv1+W7q++KjYaC97e8OWXEBt7jlt9ibRs+THe3p2JjBxCevphOwldATz3nFTgLmSzGjVKmgst7s/h8OFxpKbuIjj4M5ydS6nkbSgSE/FqMJQHSkmpqIAASWaTkpLf1b27mCYWL5YiSLbg7OxO27Zfo3U2O3bcRk5OWuknVTVWroSffpIbn59ffvPPP8tj9GioX7/401NT9xAV9S716w+ibt1SUlIaisUoeYOhvKhTBxYsgL17ZSO2AC+8IPuzjz9uexIzT8+WtGmzgKSkjezZM7J65bfJzpblerNm8NRT+c1ZWdIcHCx/i+LQOpc9ex7G2dmTli0nVYDAjotR8gZDeXLllfDSSxLhs3RpfrOzsxTDcHODQYNsKxkIUK/eTTRt+jZxcQs4evQjOwltB6ZNg4gIyTZZo0Z+86RJYo+fMEH+FsUREzOVxMRwmjf/gBo1AipAYMfFKHmDobx5802x0TzwgIRyWmjUSMw1//1ntbgtlSZNXqVevdvYv/8FTp36xQ4ClzOxsWKiufZa2aewcOgQvPGGFOcuKZVwauoe9u9/njp1+hEY+ID95XVwjJI3GMobV1cIC5Nd1jvusFq233ijLPSnT4f5820bTilF69Zz8fJqx7Zt/UhK2mInwcuJUaMgI0PcZwpEAT/2mHicfvpp8afm5mYTGTkEJyd3QkJmoUrLOWwoFaPkDQZ70Ly5aPFNm86xz7/9NvTpI942ttaGdXHxpn377wHYtKlL1S00snKl3OBeflkM7xaWLIHlyyWdcKNGxZ9++PD7JCX9S6tWAet1dwAAD6tJREFUU6lRI6gCBHZ8jJI3GOzFTTfBiy9KasovvshvdnGR1Lq+vnD55ZCYaNtwHh7N6NJlHU5O7mzffmPVKwSelgaPPirK/cUX85sTEsQ81bVryZutiYmrOXToTfz87sbPb1AFCHxxYJS8wWBP3nlHlu0PPmjlPx8QAF99BadPS4rdAoGyJeLrexlt2iwkKelfdu68B61tyGdcUbz6qrgOTZsG7u75zY8/LuVcZ8yQG1xRZGYeZ+fOu/DwaE6rVtMqSOCLA6PkDQZ7krdsz8iQvC0nT+Z3XXGF2KmjouC1MmQwqF//Vlq2nMTJk9+zd++TVcO1cs0acZ159FGrik9ffy3BYKNHy0q+KLTOITLyXrKzE2jX7mtcXGpWkNAXB0bJGwz2JiBAIqEAbr9dnMUtfPqpRPy//7642NtKw4ZP0rDhs8TEfMbBg69WrqJPTpa8Pc2aScYxC7Gx8Mgj4mj0cgkZCQ4efJ2EhN8IDp6Mt3cn+8t7kWGUvMFQEdxxh2zE/vGH2C8sSlkpmDxZLDoPPAD//GP7kC1afEhg4EgOH36fqKh37CK2TTz/vLiKzpkjeRwQ89P990vg7/z5xZtpjh2bz+HD7xMY+CABAfdXoNAXD8X86Q0GQ7kzZIgUMh07VipWP/kkIB6XS5ZAvXpw6aVi1m7RovThlFK0ajWV3NwMDh0ajZOTO40bP2/nSRRiyRKxwY8aJfYnCx98ACtWiBdl69ZFn5qYuJbdux+kVq2+BAdPMe6SdsKs5A2GiuTdd+Hqq8XdJM+EA9StC1ss7u/XXw9xcbYNJzViZ+HndxcHDrxAVNT7FWe6OXAARoyAHj3E3mThzz9lD3bQIDHXFEVKSiQREQNxd29Cu3ZLcHJyrRiZL0KMkjcYKhInJ/juO3k9aBCsXZvf1akT/P232LL794czZ2wbUilnWreej5/fvRw8+AoHDrxgf0WfmSnyKyV+8ZYcBceOwd13Q8uW4k1T1OI8Le0gW7deg1IudOiwHFfXOvaV9SLHKHmDoaLx9objxyEkBP73P9i2Lb+rZ0+xgGzfDgMH2p7jxsnJlTZt5hMU9BhHjoxn48aO9qsslRe+unGjFExp1gwQN/mBA8Xv/+uvwcfn3FMzMqLZuvUacnPT6dRpJZ6eLe0joyEfo+QNhsqgfn345RdR+P36ienDQv/+socZHi5KM83GLMNKOREc/CkNGjxFSkoEmzf3IivLxkirsvDJJ5KA7ZVXpKQfoveHD4f162HhQujY8dzT0tL2s3lzb7Ky4unYcQXe3iVUCzGUG0bJGwyVRZMmougzMsS9Zv/+/K7Bg0WP/vqrJPSyXdErgoMn0bz5WJKTN/Pffz1JTd1TfjKvWCGbrAMHWlX8GD1agrvGjoVbbjn3tOTk7Wze3Jvs7CQ6dfqdmjW7l59MhhK5ICWvlBqjlIpWSm2xPAYU6HtZKbVPKbVbKXX9hYtqMDgg7drBqlWQmippivecVcgjRsCsWZIOxtPTqg5JqTRu/CKdOq0iO/sUmzb14PjxxaWfVBr//iuuoO3bS5oGJ1EfH30kgb0jRkje/MKcOLGMzZt7Ac506bKGmjW7nXuQwW6Ux0p+ota6s+WxHEAp1RYp2t0O6Ad8ppRyLodrGQyOR+fOYpvJzJQV/c6d+V3Dh0uJ1LzDjh+3fdhatS4nNHQDnp6t2blzELt23U92dvL5ybhjh9iR6teXsk4Wf/jp0+HZZyXGa9o0641WrXM4dOgtIiJuxsOjFV27/o2XV5vzu77hvLGXueZmIExrnaG1PgjsA3rY6VoGQ/WnQwdR9FpDr17ih2jhkUfg228hOlr86PeUwfri7t6ELl3W0KTJaxw7Noe1a32Av8sm2+7dkhu+Rg347TcIkuyQU6ZIJs0BA8QOXzDgKS3tIFu29OXQoTfw9x9Mly5rcHcvIf2kwW6oC3G1UkqNAe4DzgAbgWe11glKqcnAP1rrBZbjZgE/a62XFDHGSGAkgL+/f2hYWNh5yZKcnIy3ZXVR3TFzqZpUxFzcjx2jw0sv4REdzd6nnyb2hhvy+3bu9OGxx0IBGDduGz16nCrj6H8Dr1he1wEmASUrXu+9e+n4wgugFFsnTCClWTO0hvnzmzB3bjMuu+wEo0fvpEaNvAxrmcC3wDxkDfkEcB1gn0An8/0S+vbtu0lrXbQdTGtd4gP4DYgo4nEz4A84I5/mu8BsyzmTgcEFxpgF3F7atUJDQ/X5Eh4eft7nVjXMXKomFTaXU6e0bt9ea9D6sce0zsrK79q7V5qV0vrNN7XOySnb0Dk5GTo8/H4dHo4OD0dv3nyVTkraUvTB4eFa+/pq3aiR1rt3a621TkvT+v77RYZhw86KlpOTqWNj5+u//26hw8PRW7feoNPSoso+9zJivl8CsFEXo1dLNddora/RWrcv4vG91jpOa52jtc4FZnDWJBON9RKhoaXNYDCURu3a4oPeqZPYRK66CmJiAAkySk4W75s33hA7fVTU/9u7/9iqyjOA49+HlvZihRY6YIVWWgv+YKUCYa6TbSE6HHUEcNkY0Igo24iBTfEHlkCMEpZM+dFhAixOC3UBHAPcEDMyQAgbiUhxhPGjSKGEUsBCoEDGGAWf/fG+lStQdksrt+f4fJKb3nPO7b3vw3P7cO97znlO7E/dpk0S8BgPPPApmZnPUVf3AeXlfdm2rS+HD8+mvv6UmzJasMBN0WRkuBO27rqL6mrXuaC01HXNLC2Fixf3U1X1Mps3J1FRMZaEhHbk568lP38NkcgdX86/j2mSZvWuEZEMVT3mFx/FfcIHWA0sFZG5QDegF/BRc17LmK+U5GTX52DJEtemMj8f5s2DMWNISRHKytyBOcXF7mCXp55ynQUSYjy8ISmpCz17ziYrazJHj/6emprXOXjwBQ4efIG2/4nQdfcFkqbfQ/vxr5HQ4SRrlp6npOQs7drV8f77VeTmbqe8/O+cP18BQPv295Od/RKdOhUiYkdmtybNbVD2moj0BRQ4BEwAUNXdIrIc2ANcAiZqq7q6gTEBUVTkGrE/8YT7+L5sGcybh+Tm8uKLMGqUayMwaxa89547T2nw4NifPjm5Ozk5L5Od/RJn353JqbUzODb4Akd+AlABlcMAt6911qwrv1dbm0pq6kAyMn5O584jiUQyWzRs03KaVeRV9bEbbPs1bp7eGNMc994LW7a4Cj59ulseMwZmzKBHjzvYssW1K547Fx5+2E2pPPus65gQ0yf7AweQKVNIXbWK1EiEnCf/we72A1i0aC+bNtXSocNJxo6to7CwM4mJ7UhJySM5ubt9Yg8Iy5IxQZCQAJMnw/797gIdZWXujNmiImTDen45SamogJIS19p9xAjXrvj5591JqlHXKXFUXQ+C0aNdD521a6me+BveePU0eT8rIC8vkfnz+zBw4EMsX/5Txo2bQNeuPyI9vZBIJMsKfIBYP3ljgqRbN3cG0qRJbhJ+6VJ3S08nedAgnikqYtLG/qzalsXit9swZw7MmQORiPLN++rJvf04aVU1bKl+hZr6LiS1/S7Vd07l4wu9OTT/SjmYORMmTHA97k2wWZE3Jojy8938/MKF7lTT9eth5UpYuZJEYCQwMiuL0z3SWXpuKJ+c+TrlW/uyjh4cZTSfH1hXD3e3gQHfgmGPutYEffpcv0WwCSYr8sYEWVqaO8SmuNj1Jd6xw3U1O3cOTpyg4+XLTGxzGLpcgKzL0O8zNp3bxcDBQ1D9vA28CTEr8saERSTiGtIXFNz4cZs20dYuxPSVYXtPjDEmxKzIG2NMiFmRN8aYELMib4wxIWZF3hhjQsyKvDHGhJgVeWOMCTEr8sYYE2LNuvxfSxORE0ATLoHwBV8DTrbgcOLJYmmdwhJLWOIAi6VBD1XtfL0NrarIN4eIlGtj1zgMGIuldQpLLGGJAyyWWNh0jTHGhJgVeWOMCbEwFfk34j2AFmSxtE5hiSUscYDF8n+FZk7eGGPMtcL0Sd4YY8xVrMgbY0yIhaLIi8gQEdknIpUiUhzv8TSFiGSJyEYR2SMiu0Xkab++k4isE5H9/mfHeI81FiKSICL/FJE1fjlHRLb63PxRRAJxLSIRSRORFSJSISJ7ReTbAc7JZP/e2iUiy0QkEpS8iEipiNSKyK6oddfNgziv+5h2ikj/+I38ixqJY5Z/f+0UkXdFJC1q21Qfxz4R+UFzXjvwRV5EEoD5QCHQGxgtIr3jO6omuQQ8p6q9gQJgoh9/MbBBVXsBG/xyEDwN7I1afhUoUdWewGlgfFxG1XTzgLWqeg9wHy6mwOVERLoDvwIGqGoekACMIjh5WQwMuWpdY3koBHr52y+AhbdojLFYzLVxrAPyVDUf+ASYCuD//kcB3/C/s8DXuZsS+CIP3A9UqupBVb0IvAMMj/OYYqaqx1T1Y3//HK6YdMfFUOYfVgaMiM8IYycimcAPgTf9sgAPAiv8Q4ISRyrwPeAtAFW9qKp1BDAnXiLQTkQSgduAYwQkL6q6GTh11erG8jAceFudD4E0Ecm4NSO9sevFoap/U9VLfvFDINPfHw68o6r/VdUqoBJX525KGIp8d6A6avmIXxc4IpIN9AO2Al1V9ZjfdBzoGqdhNcVvgSnAZ345HaiLeiMHJTc5wAlgkZ96elNEUghgTlS1BpgNHMYV9zPAdoKZlwaN5SHIteBJ4K/+fovGEYYiHwoicjuwEnhGVc9Gb1N3nGurPtZVRIYCtaq6Pd5jaQGJQH9goar2A/7NVVMzQcgJgJ+vHo77j6sbkMK10waBFZQ83IiITMNN2y75Mp4/DEW+BsiKWs706wJDRNriCvwSVV3lV3/a8FXT/6yN1/hiNBAYJiKHcFNmD+LmtdP8NAEEJzdHgCOqutUvr8AV/aDlBOD7QJWqnlDVemAVLldBzEuDxvIQuFogIuOAoUCRXjlpqUXjCEOR3wb08kcLJOF2WKyO85hi5uet3wL2qurcqE2rgcf9/ceBv9zqsTWFqk5V1UxVzcbl4ANVLQI2Aj/2D2v1cQCo6nGgWkTu9qseAvYQsJx4h4ECEbnNv9caYglcXqI0lofVwFh/lE0BcCZqWqfVEZEhuOnNYap6PmrTamCUiCSLSA5uR/JHN/1Cqhr4G/AIbu/0AWBavMfTxLF/B/d1cyeww98ewc1nbwD2A+uBTvEeaxNiGgSs8ffv9G/QSuBPQHK8xxdjDH2Bcp+XPwMdg5oT4BWgAtgF/AFIDkpegGW4fQn1uG9Y4xvLAyC4I+0OAP/CHVEU9xhuEEclbu694e/+d1GPn+bj2AcUNue1ra2BMcaEWBima4wxxjTCirwxxoSYFXljjAkxK/LGGBNiVuSNMSbErMgbY0yIWZE3xpgQ+x/GS+uRjX2cfgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UCqfATi4uNfN"
      },
      "source": [
        "**Plotando os gráficos das temperaturas  T ,  To  e  Tm  em função do tempo não considerando a aproximação de Padé.**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 276
        },
        "id": "vXqaYAh1fdDN",
        "outputId": "578cb37a-2ee1-4b72-e4d8-b84dced6f4ff"
      },
      "source": [
        "# Plotando o gráfico de temperaturas (T, ToReal, Tm) com relação ao tempo:\n",
        "# Os gráficos são plotados consideração a aproximação de Padé para To:\n",
        "\n",
        "figure()\n",
        "plot(t_plot2, TReal_plot,'-r',t_plot2, ToReal_plot,'-b',t_plot2, TmReal_plot,'-y')\n",
        "grid()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vs86DOgUuVPf"
      },
      "source": [
        "**Plotando o gráfico de comparação entre $T_o$ calculado pela aproxição de Padé ($T_oPade$) e $T_o$ calculado sem a aproximação ($T_oReal$).**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6JtT_okhD3t8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 290
        },
        "outputId": "58ffde43-779a-4daa-822d-93f534c8f83b"
      },
      "source": [
        "# Plotando o gráfico de comparação entre To calculado pela aproximação de Padé To (ToPade) e To calculado sem a aproximação (ToReal):\n",
        "\n",
        "figure()\n",
        "plot(t_plot, ToPade_plot,'-r')\n",
        "plot(t_plot2, ToReal_plot,'-b')\n",
        "ylabel('Comparação das temperaturas To (°C)')\n",
        "xlabel('Tempo (min)')\n",
        "grid()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}