{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1616aV4grSYQ"
      },
      "source": [
        "#Présentation expérimentale de la cinétique de décoloration du bleu de bromophénol\n",
        "\n",
        "## Suivi cinétique\n",
        "\n",
        "Le bleu de bromophénol est fortement coloré, alors que le composé ayant réagi avec les ions hydroxyde est incolore. Cette propriété va être mise à profit pour suivre la cinétique de la réaction grâce au spectrophotomètre.\n",
        "\n",
        "La réaction qui a lieu peut être symbolisée par :\n",
        "\t\t\t\t$ BBPH^{-}   +   HO^{–}    \\to  BBP^{2-} + H_2O$\n",
        "\n",
        "On propose d’écrire la loi de vitesse s’écrit selon $v = k [BBPH^{-}]^{\\alpha} \\cdot [HO^{–}]^{\\beta}$\n",
        "\n",
        "## Rappel de la loi de Beer - Lambert\n",
        "\n",
        "La spectrophotométrie est l'étude de l'interaction entre la matière et le rayonnement.\n",
        "Nous profitons donc du fait que le bleu de bromophénol est une molécule colorée et absorbe dans le visible selon la loi de Beer - Lambert.\n",
        "\n",
        "- L'absorbance d'une solution caractérise son aptitude à absorber une radiation de longueur d'onde donnée. Elle se note $A$ et n'a pas d'unité.\n",
        "\n",
        "- Soit $I_0$ l'intensité lumineuse en entrée de la cuve contenant la solution, soit $I_{sortant}$ celle en sortie de cuve, on écrit : $\\mathrm {A = - log_{10} \\dfrac {I_0}{I_{sortant}}}$\n",
        "\n",
        "- Ici, nous n'avons qu'une seule espèce colorée : le bleu de bromophénol : $\\mathrm {A = \\varepsilon_i(\\lambda) \\ell C_i }$\n",
        "  - la concentration $C_i$ est la concentration molaire de l'espèce colorée $i$,\n",
        "  - $\\ell$ est la longueur de la cuve en $cm$ (souvent $\\ell = 1,0 \\ cm$)\n",
        "  - $\\varepsilon_i( \\lambda)$ est le coefficient d'extinction molaire en $mol^{-1}.L.cm^{-1}$ et dépend de la longueur d'onde de travail $\\lambda$\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2drkOqBZ_0Li"
      },
      "source": [
        "# Etude mathématique\n",
        "\n",
        "## Ordre partiel $0$ supposé par rapport au $BBPH^{-}$ renommé B dans la suite\n",
        "\n",
        "- Equation cinétique : $\\mathrm { - \\dfrac {d[\\mathsf {\\text {$B$}}]}{\\mathsf {\\text {$dt$}}} = \\mathsf {\\text {$k$}}^{'}}$ qui donne après intégration entre l'instant initial $t = 0$ et l'instant $t$ : $\\mathrm { [\\mathsf {\\text {$B$}}] = [\\mathsf {\\text {$B$}}]_0 - \\mathsf {\\text {$k^{'}$}}\\mathsf {\\text {$t$}} }$.\n",
        "Comme l'absorbance est proportionnelle à la concentration, on peut tracer également $ A = A_0 - \\varepsilon (\\lambda) \\ell k^{'}t$ ou plus simplement $A = f(t)$\n",
        "\n",
        "## Ordre partiel $1$ supposé par rapport au $BBPH^{-}$\n",
        "\n",
        "- Equation cinétique : $\\mathrm { - \\dfrac {d[\\mathsf {\\text {$B$}}]}{\\mathsf {\\text {$dt$}}} = \\mathsf {\\text {$k$}}^{'}[\\mathsf {\\text {$B$}}]}$ qui donne après intégration entre l'instant initial $t = 0$ et l'instant $t$ : $\\mathrm { ln ( \\dfrac {[\\mathsf {\\text {$B$}}]}{[\\mathsf {\\text {$B$}}]_0}) =  - \\mathsf {\\text {$k^{'}$}}\\mathsf {\\text {$t$}} }$\n",
        "Comme l'absorbance est proportionnelle à la concentration, on peut tracer également $\\mathrm { ln (\\dfrac {[\\mathsf {\\text {$A$}}]}{[\\mathsf {\\text {$A$}}]_0}) =  - \\mathsf {\\text {$k^{'}$}}\\mathsf {\\text {$t$}} }$ ou plus simplement $lnA = f(t)$\n",
        "\n",
        "## Ordre partiel $2$ supposé par rapport au $BBPH^{-}$\n",
        "\n",
        "- Equation cinétique : $\\mathrm { - \\dfrac {d[\\mathsf {\\text {$B$}}]}{\\mathsf {\\text {$dt$}}} = \\mathsf {\\text {$k$}}^{'}[\\mathsf {\\text {$B$}}]^{2}}$ qui donne après intégration entre l'instant initial $t = 0$ et l'instant $t$ : $\\mathrm { ( \\dfrac {1}{[\\mathsf {\\text {$B$}}]}- \\dfrac {1}{[\\mathsf {\\text {$B$}}]_0}) =   \\mathsf {\\text {$k^{'}$}}\\mathsf {\\text {$t$}} }$.\n",
        "\n",
        "Comme l'absorbance est proportionnelle à la concentration, on peut tracer également  simplement $1/A = f(t)$ en faisant attention au coefficient de proportionnalité $\\varepsilon (\\lambda) \\ell $\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m7vX_SUAmFO9"
      },
      "source": [
        "# Suivi cinétique de la solution\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "umf_pxxJePH3"
      },
      "source": [
        "# importation des biliothèques\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from math import *\n",
        "\n",
        "A = np.array([0.815, 0.753, .691, .639, .585, .537, .494, .454, .417, .383, .351, .322, .298, .274, .252, .230, .210, .195, .176, .162, .148, .135, .126, .114, .105, .097 ]) # ordre 0\n",
        "\n",
        "time = np.array([0.17, 0.67, 1.17, 1.67, 2.17, 2.67, 3.17, 3.67, 4.17, 4.67, 5.17, 5.67, 6.17, 6.67, 7.17, 7.67, 8.17, 8.67, 9.17, 9.67, 10.17, 10.67, 11.17, 11.67, 12.17, 12.67]) # temps en min\n",
        "\n",
        "Z1 = np.log(A) # ordre 1\n",
        "\n",
        "Z2 = (1/A) # ordre 2\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Affichage graphique : ordre 0 supposé\n",
        "plt.figure(1)\n",
        "plt.title(r'Tracé de $A$ en fonction du temps ')\n",
        "plt.ylabel(r'$A$')\n",
        "plt.xlabel('temps en min (min)')\n",
        "plt.plot(time, A,'r+', label='points expérimentaux')\n",
        "plt.xlim(0,20)\n",
        "plt.ylim(0,1)\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 475
        },
        "id": "AMIIua2NmF9C",
        "outputId": "7c4e3d17-b544-436f-e9ae-c7ec327bff91"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Affichage graphique ; ordre 1 supposé\n",
        "plt.figure(2)\n",
        "plt.title(r'Tracé de $lnA$ en fonction du temps ')\n",
        "plt.ylabel(r'$lnA$')\n",
        "plt.xlabel('temps en minutes (min)')\n",
        "plt.plot(time, Z1,'r+', label='points expérimentaux')\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 475
        },
        "id": "1bBpO74FmFuE",
        "outputId": "84679155-7be8-4dba-fad8-b41fb2cfcf96"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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fevTRelfbbuPN8TB58mQRFRVVbX0DBw4UnTt3rvb8AwcOiLvvvltER0eLJk2aiFmzZomysjL7fOXl5WLu3Lmie/fuIjo6WkRFRYnu3buLd955x+02UmDRCaGiO/+IiIjq2bx58zB//nycO3eu2ifPSJt4zxARERFpGoshIiIi0jQWQ0RERKRpvGeIiIiINI1nhoiIiEjTWAwRERGRprHTRQ8oioLTp08jOjq6xqNOExERkX8IIVBSUoLExESXnb8CLIY8cvr06ToZ/4eIiIh879SpU2jZsqXL37MY8kB0dDQAa5i1GQfIZDJh9erVGD58OEJDQ+u6eQGP+bjHjOSYjxzzkWM+coGcT3FxMZKTk+3v466wGPKA7dJYo0aNal0MRUZGolGjRgF3IPkC83GPGckxHznmI8d85IIhH3e3uPAGaiIiItI0FkNERESkaSyGfMBgMKBHjx4wGAz+booqMR/3mJEc85FjPnLMR04L+bAHag8UFxcjJiYGly5dqtU9Q0RE3lAUBVevXvV3M4hUJzQ0VFqkefr+zRuofcBsNmPz5s245ZZbEBLCyKtiPu4xI7lgzufq1as4fvw4FEWp9TKEECgvL0d4eDj7SnOC+cipPZ/GjRsjPj7eq7YF118NldLr9ejSpYu0wyctYz7uMSO5YM1HCAGj0QiDwYDk5ORab58QAmazGSEhIap8M/M35iOn1nyEECgtLUVBQQEAICEhodbLYjHkA3q9Hs2bN/d3M1SL+bjHjOSCNR+z2YzS0lIkJiYiMjLS380hUp2IiAgAQEFBAZo3b17r+5qC698olTKZTFixYgVMJpO/m6JKzMc9ZiQXrPlYLBYAQFhYmFfLURQFFy9e9OpSWzBjPnJqz8f2j4I3r38WQz5iNpv93QRVYz7uMSO5YM5HTZcmiNSmLl4fLIaIiIj8aOPGjViyZIm/m6FpLIb8yWgE5s2zficiIrtly5ahcePG/m5Gvfvtt99w77334vrrr3c774kTJ6DT6ZCdnV3/DdMYFkP+ZDQC8+ezGCIiquIPf/gDDh8+XKPnDBo0CHPmzKmfBtWD8vJyTJw4EZmZmejTp4/b+ZOTk2E0GtGlSxcftE5u3rx56NGjh7+bUWf4aTIiIg3QnTkD3euvAw8+CHjxEWRfiYiIsH9SKFiFh4dj586dHs179epVhIWFIT4+vp5bpU08M+RrRiOQlVXxBTg+5lkiIqoH+rNnoXvuOZ/8jRk0aBBmzZqFWbNmISYmBs2aNcMzzzyDygMeFBUV4f7770eTJk0QGRmJkSNH4siRI/bfV71MZjsT8cEHH6BNmzaIiYnBxIkTUVJSAgCYMmUKNm3ahDfffBM6nQ46nQ4nTpxAUVERJk2ahLi4OERERKB9+/ZYunSpy7YrioIFCxagbdu2iIiIQPfu3fHFF18AsPZrM2zYMKSmptq35cKFC2jZsiWeffZZANb7f3Q6HVasWIFu3bqhQYMGuPHGG5GTk+Ownq1bt2LAgAGIiIhAcnIyHnnkEfz+++/237dp0wbPP/887r//fjRq1AgzZsyodpnMtq5Vq1ahZ8+eiIiIwJAhQ1BQUIAffvgBKSkpaNSoEe655x6UlpZ6tI2Vl7tu3Tr06dMHDRs2xPDhw5Gbm2vfN/Pnz8fevXvtWS9btgwA8Pe//x1du3ZFVFQUkpOT8fDDD+Py5cvV9mNlb7zxBtq0aQMAuHLlCjp37owZM2bYf3/s2DFER0fjX//6l8v95jVBbl26dEkAEJcuXarV8xVFEZcuXRKKogiRni4E4PorPb1O2x4IHPIhp5iRXLDmU1ZWJg4cOCDKysq8Wo6iKMK8c6f1b8zu3XXUOtcGDhwoGjZsKGbPni0OHTokPvzwQxEZGSnee+89+zxjxowRKSkpYvPmzSI7O1ukpqaKa6+9Vly9elUIIcTSpUtFTEyMff709HTRsGFDceedd4r9+/eLzZs3i/j4ePHnP/9ZCCHExYsXRb9+/cT06dOF0WgURqNRmM1mMXPmTNGjRw+xa9cucfz4cbFmzRrx7bffVs/HbBaKoogXXnhBdOzYUfz444/i2LFjYunSpSI8PFxs3LhRCCHEf//7X9GkSRPxxhtvCCGEGD9+vOjbt68wmUxCCCE2bNggAIiUlBSxevVqsW/fPnH77beLNm3a2Lft6NGjIioqSrz++uvi8OHD4qeffhI9e/YUU6ZMsbepdevWolGjRuLVV18VR48eFUePHhXHjx8XAMSePXsc1nXjjTeKrVu3iqysLHHttdeKgQMHiuHDh4usrCyxefNmERsbK15++WX7st1to225N9xwg9i4caPIyckRN998s+jfv78QQojS0lLx+OOPi86dO9uzLi0tFUII8frrr4v169eL48ePi3Xr1okOHTqIhx56yGE/du/e3SH/119/XbRu3dr+eM+ePSIsLEx8/fXXwmw2ixtvvFGMGzfO5fEme514+v7NYsgDdVEMXb161fqH+vRp6x+j3buFyMy0/nHKzKyYdvp0Hbde/RzyIaeYkVyw5uN1MfS/vzfKL78IS0aGz/7eDBw4UKSkpDjsjyeffFKkpKQIIYQ4fPiwACB++ukn++8LCwtFRESE+Oyzz4QQzouhyMhIUVxcbJ82d+5cccMNNzisd/bs2Q5tGT16tJg6daq0vYqiCIvFIsrKykRkZKTYtm2bw++nTZsm/vjHP9off/bZZ6JBgwbiqaeeElFRUeLw4cP239kKiU8//dQ+7fz58yIiIkL8+9//ti9vxowZDuvYsmWL0Ov19n3dunVrMXbsWId5XBVDa9eutc+zYMECAUAcO3bMPi0tLU2kpqYKIYS4cuWK222sulxFUcR3330nANjb56yocebzzz8XsbGx9seeFENCCPHKK6+IZs2aiVmzZomEhARRWFjoch11UQzxMpkPmM1mrFy50toPSkIC0KtXxRfg+DgAruXXNYd8yClmJMd8XMjIAHr3hq5PH+jT0qzTpk8Heve2fmVk1Nuqb7zxRof+X/r164cjR47AYrHg4MGDCAkJwQ033GD/fWxsLDp06ICDBw+6XGabNm0QHR1tf5yQkGAfisGVhx56CJ9++il69OiB//f//h+2bdtWbR4hBIqLi3HkyBGUlpbi1ltvRcOGDe1f77//Po4dO2aff/z48Rg3bhxefvllvPrqq2jfvn21Zfbr18/+c9OmTR22be/evVi2bJnDOlJTU6EoCo4fP25/nic3VQNAt27d7D+3aNECkZGRaNeuncM0W05Hjx71aBsrL1cIYR/k1F3ea9euxdChQ5GUlITo6Gjcd999OH/+vMNlOk88/vjjuO666/D222/jX//6F2JjY2v0/JriDdQ+EBISglGjRgXdAJJ1hfm4x4zkmI8LaWnAmDEQQkDs3m0tiDIzK/4RC7B/vkJDQx0e63Q6t70ijxw5EidPnsTKlSuxZs0aDB06FDNnzsSrr77qsJxGjRrZ79lZsWIFkpKSHJYTHh5u/7m0tBS7d++GwWBwuM/JU5cvX0ZaWhoeeeSRar9r1aqV/eeoqCiPllc5F51OJ83Jdv+Ou22svFydToeGDRsCgDTvEydO4Pbbb8dDDz2EF198EU2bNsXWrVsxbdo0XL16FZGRkdDr9Q73jgHOe44uKCjA4cOH7RmPGDFCmoG3+JfDR8rKyhz+owFg/UOUnh5wf5Dqg9N8yAEzkmM+TiQkWL+EgLC9iVU+K12PduzY4fD4559/Rvv27WEwGJCSkgKz2YwdO3agf//+AIDz588jNzcXnTp1qvU6w8LC7EOYVBYXF4fJkydj8uTJGDBgAObOnetQDAHWsx+dOnVCeHg48vLyMHDgQJfrefzxx6HX6/HDDz9g1KhRuO222zBkyJBq22srbIqKinD48GGkpKQAAHr16oUDBw7g2muvrfW21pan21hV1QLGWda7d++Goih47bXX7IMKf/bZZw7zxMXF4cyZMxBC2M8cOus36YEHHkDXrl0xbdo0TJ8+HcOGDbPnVx94mcwHzGYzNmzYUP0UfkKCtdNFjRdDLvMhO2Ykx3zkxP9G9/alvLw8PPbYY8jNzcUnn3yCRYsWYfbs2QCA9u3b44477sD06dOxdetW7N27F/feey+SkpJwxx131Hqdbdq0wY4dO3DixAkUFhZCURQ8++yz+Oabb3D06FH8+uuv+P7776u9qQohUFJSgoYNG+KJJ57Ao48+iuXLl+PYsWPIysrCokWLsHz5cgDWMyr/+te/8NFHH+HWW2/F3LlzMXnyZBQVFTks87nnnsO6deuQk5ODKVOmoFmzZhg7diwA4Mknn8S2bdswa9YsZGdn48iRI/jmm28wa9asWm+7p6Kjo91uY1XOjp82bdrg+PHjyM7ORmFhIcrLy3HttdfCZDJh0aJF+O233/DBBx/g3XffdXjeoEGDcO7cObzyyis4duwYFi9ejB9++MFhnsWLF2P79u1Yvnw5Jk2ahLFjx2LSpEm4evVq3YZRCYshIiINUFq0gHj2WZ/983X//fejrKwMffv2xcyZMzF79myHj0svXboUvXv3xu23345+/fpBCIGVK1dWu8RTE0888QQMBgM6deqEuLg45OXlISwsDE8//TS6deuGW265BQaDAZ9++qnLZTz//PN45plnsGDBAqSkpGDEiBFYsWIF2rZti3PnzmHatGmYN28eev3v7Nr8+fPRokULPPjggw7LefnllzF79mz07t0bZ86cwXfffWcfcLdbt27YtGkTDh8+jAEDBqBnz5549tlnkZiYWOttrwnZNnrqrrvuwogRIzB48GDExcXhk08+Qffu3fH3v/8dCxcuRJcuXfDRRx9hwYIFDs9LSUnBO++8g8WLF6N79+7YuXMnnnjiCfvvDx06hLlz5+Kdd95BcnIyAOCdd95BYWEhnnnmmboJwAmdqHrui6opLi5GTEwMLl26ZL+JrCZMJhNWrlyJUaNGefVCD1bMxz1mJBes+Vy5cgXHjx9H27Zt0aBBg1ovR1EUFBcXo1GjRvbLF/Vp0KBB6NGjB9544416X1ddqMt8Nm7ciMGDB6OoqChohhPx9fFTU7LXiafv3+rbKqo5jnFGRERUayyGggHHOCMiIqo1fpqMiIjq1MaNG/3dBL8ZNGhQtU9ekfqxGPKROu//xGisOBNUeYwzG9tHagME+4dxjxnJMR8iqi3eQO0Bb2+grhfz5lkvjbmSnm6dh4gCVl3dQE0UzHgDdYBQFAUFBQVue0qtkbQ0YPdu61dmpnVaZmbFNFvX+wGgXvIJMsxILtjz8fZ/ViEETCYTL9+4wHzk1J5PXbSLxZAPKIqCnJycuv1DHURjnNVLPkGGGckFaz4GgwEA6qSzubKyMq+XEcyYj5ya87F1COlNtxq8TOYBVV4mqywryzro4u7dPulmn4h8QwiBvLw8mEwmJCYmqrKPFyJ/sfWMXVBQgMaNGyPByUkAT9+/ecehDyiKglOnTiE5Obl+/pgF+Bhn9Z5PEGBGcsGaj06nQ0JCAo4fP46TJ0/WejlCCFgsFhgMBoeR5MmK+cipPZ/GjRsjPj7eq2WwGPIBi8WC7Ozs+vvPzjbGWYCq93yCADOSC+Z8wsLC0L59e68ulZlMJmzevBm33HJLUPXQXVeYj5ya8wkNDbVfTvYGiyEiIpXT6/VefZrMYDDAbDajQYMGqnszUwPmI6eFfILrXygiIiKiGmIxRERERJrGYoiIiIg0jcUQOTIarTdjc9BXIiLSCBZDPqDT6RAXF6fKjyRWYzRah/nwYTEUUPn4CTOSYz5yzEeO+chpIR92uugB1Xe6WJfYgSMREQUJjk2mIhaLBYcOHYLFYvF3U5wzGq1FkO0LcHxcz2eJVJ+PCjAjOeYjx3zkmI+cFvJhP0M+ouZxXZCRYb00Vtn06RU/p6fXe6eOqs5HJZiRHPORYz5yzEcu2PPhZTIPBP1lMqOx4uxPVpa1EMrMrLhMlpAQsEN9EBGRdvEymYpYLBbs2bNHvacYExIcR7wHHB/XcyGk+nxUgBnJMR855iPHfOS0kA+LIR9QFAV5eXlQFMXfTVEl5uMeM5JjPnLMR475yGkhHxZD5CghwXqPEC+LERGRRvAGanKUkFDvN0sTERGpCc8MERERkaaxGCIiIiJNYzFE9YNjnBERUYBgMeQDer0eHTp0gF6vobhrMMaZJvOpIWYkx3zkmI8c85HTQj7sdNEDQd/pYn3gGGdERORn7HRRRcxmM7Zt2waz2ezvptSvWo5xppl8vMCM5JiPHPORYz5yWsiHH633Ab1ej6SkpKA+xQig1mOcaSYfLzAjOeYjx3zkmI+cFvLhZTIP8DKZhzjGGRERqQgvk6mI2WzG+vXrg/oUI4Baj3GmmXy8wIzkmI8c85FjPnJayIfFkA8IIVBSUgKehHOO+bjHjOSYjxzzkWM+clrIJ6CKoQsXLmDSpElo1KgRGjdujGnTpuHy5cvS5wwaNAg6nc7h68EHH/RRizWMY5wREVGACKgbqCdNmgSj0Yg1a9bAZDJh6tSpmDFjBj7++GPp86ZPn47nnnvO/jgyMrK+m0oc44yIiAJEwBRDBw8exI8//ohdu3ahT58+AIBFixZh1KhRePXVV5GYmOjyuZGRkYiPj/dVU4mIiCiABMxlsu3bt6Nx48b2QggAhg0bBr1ejx07dkif+9FHH6FZs2bo0qULnn76aZSWltZ3c4mIiChABMyZoTNnzqB58+YO00JCQtC0aVOcOXPG5fPuuecetG7dGomJidi3bx+efPJJ5Obm4ssvv3T5nPLycpSXl9sfFxcXAwBMJhNMJlO1+fV6PQwGAywWCwDAYDDAbDbbbzazPcf23WAwQK/Xw2w2Q6/XQ6/XO11u5e0ErHf0V/7ZldDQUCiKAkVREBISAkVR7G2rSqfTISQkxKHtFosFiqI4nd+2rZXbXnlbq7Jtq8lkctn2yvlUnse2He7aXnlbPWm7q/3kqu1q2E+25VgsFoft8OV+crWtathPNrZlavn15GxbbXkoiuIyGy29nqruJxtX7dHa68nVfnKWTyC8njzh92LoqaeewsKFC6XzHDx4sNbLnzFjhv3nrl27IiEhAUOHDsWxY8dwzTXXOH3OggULML9q54EAVq9e7fR+o1atWqFnz57Yt28fIiIi0LFjR+zcuRPnzp1zmG/NmjUAgB49eqB169bYvHkzunTpgubNm2P16tUud9rgwYMRERGBlStXYtSoUSgrK8OGDRuczhsSEoLbbrsNhYWFyMnJwZAhQ3Dq1ClkZ2c7nT8uLg79+/fHkSNHUFZWZt+OvLw8p/N36NDBvn1JSUn27SgpKXE6f79+/ezbN2DAAPt2OLNmzRr79m3ZssW+Hdu3b3c6f3R0tH378vPz7duRm5vrdH5P95ON2vZTv379cPz4cVy5csWv+wmA6vZTcnIyIiIiUFRUhPj4eL6e/qfyfurXrx+KiopcnknX2uup8n7q3r07mjdvbv8bXZXWXk9V95Mtd2f5qP319NNPPzmdtyq/d7p47tw5nD9/XjpPu3bt8OGHH+Lxxx9HUVGRfbrZbEaDBg3w+eefY9y4cR6t7/fff0fDhg3x448/IjU11ek8zs4MJScno7Cw0GmnTcH0H5Ja/pO1/4eUnw/x7rtQpk+v9sk0Lf8nq7r9pNL/ZN21nfupetu5n1xvK/eTvO1q3E8XLlxAbGys+06TRYA4cOCAACB++eUX+7RVq1YJnU4n8vPzPV7O1q1bBQCxd+9ej59z6dIlAUBcunSpRm22uXr1qvj+++/F1atXa/X8YCfNZ/duIQDrdw3jMSTHfOSYjxzzkQvkfDx9//b7maGaGDlyJM6ePYt3333X/tH6Pn362D9an5+fj6FDh+L9999H3759cezYMXz88ccYNWoUYmNjsW/fPjz66KNo2bIlNm3a5PF6vR2OQ/yvw6ro6GjodLoaPz/YSfPJygJ69wZ2767o1VqDeAzJMR855iPHfOQCOR9P37/9fs9QTXz00UeYNWsWhg4dCr1ej7vuugtvvfWW/fcmkwm5ubn2T4uFhYVh7dq1eOONN/D7778jOTkZd911F/7617/6vO0RERE+X2cgccin6hhnlb8Dmh3jjMeQHPORYz5yzEcu2PMJqDND/uLtmSGTyWS/uSw0NLQeWhjYquUzbx7g5AZ2u/R0zXXoyGNIjvnIMR855iMXyPkE5Zkh0oi0NGDMGOvPWVnA9OlAZmbFZTINnhUiIqL6w2KI1MfZZbBevTR9zxAREdWfgOmBmoiIiKg+sBgidUtIsN4jxEtjRERUT3iZjNQtIUFzN0sTEZFv8cwQERERaRo/Wu+Buuh00dZVeaB1WOULzMc9ZiTHfOSYjxzzkQvkfDx9/+aZIR8pKyvzdxNUjfm4x4zkmI8c85FjPnLBng+LIR8wm83YsmWLdPA6LWM+7jEjOeYjx3zkmI+cFvLhZTIPeHuZjFTAaAQyMqwdOvKTaUREmsDLZCqiKAoKCgqgKIq/m6JKPsnHaLQO8WEb8yzA8BiSYz5yzEeO+chpIR8WQz5gsViwfft2WCwWfzdFlZiPe8xIjvnIMR855iOnhXzYzxAFL6Ox4kyQbdR723fA+bAfRESkOSyGKHhlZFgvjVU2fXrFz+np7NCRiIhYDFEQS0sDxoyx/pyVZS2EMjMrBnzlWSEiIgKLIQpmzi6D9epVUQwRERGBN1ATERGRxrEY8gGdTofo6OiA68bcV3yST0KC9R6hAL00xmNIjvnIMR855iOnhXzY6aIH2OkiERFR4GGniyqiKApOnjwZ1B1WeYP5uMeM5JiPHPORYz5yWsiHxZAPKIqC/Pz8oD6QvMF83GNGcsxHjvnIMR85LeTDy2Qe4GUyIiKiwMPLZCpisVhw6NChoO7K3BsBlY/RaO2o0cdjnAVURn7AfOSYjxzzkdNCPiyGfEBRFOTm5gb1KUZvBFQ+fhrwNaAy8gPmI8d85JiPnBbyYTFEREREmsYeqInc4YCvRERBjcUQkTsc8JWIKKixGCJyhwO+EhEFNRZDRO5wwFcioqDGG6h9QK/Xo1WrVtDrGbczzMc9ZiTHfOSYjxzzkdNCPux00QPsdJHsjEbrPURpabw8RkSkcux0UUUsFgv27NkT1B1WeSOg8klIsN4s7eNCKKAy8gPmI8d85JiPnBbyYTHkIxEREf5ugqoxH/eYkRzzkWM+csxHLtjz4WUyD/AyGRERUeDhZTIVMZvN2LZtG8xms7+bokrMxz1mJMd85JiPHPOR00I+LIZ8QAiBc+fOgSfhnNNkPjUc8FWTGdUA85FjPnLMR04L+bAYIvIHPw34SkRE1bEYIiIiIk1jD9REvsIBX4mIVInFEJGvcMBXIiJVYjFE5Csc8JWISJVYDPmAwWBAjx49YDAY/N0UVdJMPl4M+KqZjGqJ+cgxHznmI6eFfFgM+YBer0fr1q393QzVYj7uMSM55iPHfOSYj5wW8uGnyXzAbDZj/fr1Qd1hlTc0mU9CgvUeIQ8vjWkyoxpgPnLMR475yGkhHw7H4QFvh+NQFAWFhYVo1qwZ9HrWn1UxH/eYkRzzkWM+csxHLpDz8fT9m8WQBzg2GRERUeDh2GQqYjKZsGLFCphMJn83RZWYj3vMSI75yDEfOeYjp4V8WAz5SDBfa60LzMc9ZiTHfOSYjxzzkQv2fFgMERERkaaxGCIKZEajtddqDvhKRFRrLIaIApnRaB3ig8UQEVGtsRgiIiIiTWMP1ESBxmisOBNkG/Xe9h1wPuwHERG5xH6GPOBtP0NCCJSUlCA6Oho6na4eWhjYmI97DhnNn2+9NOZKerr1PiIN4TEkx3zkmI9cIOfj6fs3zwz5SEREhL+boGrMxz17RmlpwJgx1p+zsoDp04HMzIoBXzV6VojHkBzzkWM+csGeD+8Z8gGz2YyVK1cGfT8NtcV83HPIKCGhYrR7WwFU+bEGiyEeQ3LMR475yGkhH14m80BdXCYzm80ICQkJuFOMvsB83HOZUVYW0Ls3sHt3RWGkQTyG5JiPHPORC+R8OByHypSVlfm7CarGfNxzmlFCgvUeIQ2eDaqKx5Ac85FjPnLBng+LIR8wm83YsGFDUJ9i9Abzcc9lRgkJ1pulNV4M8RiSYz5yzEdOC/mwGCIiIiJNYzFEREREmsZiiIiIiDSNxRARccBXItI0FkNExAFfiUjTWAz5SEgIO/uWYT7uMSM55iPHfOSYj1yw58NOFz3gbaeLRKpUdcBXZ8N6aPwj+0QU2NjpooooioKCggIoiuLvpqgS83GvXjLKyLD2Xt27t7UQAqzfbdMyMupuXfWMx5Ac85FjPnJayIfFkA8oioKcnJygPpC8wXzcq5eM0tKsw3js3m09IwRYv9umpaXV3brqGY8hOeYjx3zktJBPQF0me/HFF7FixQpkZ2cjLCwMFy9edPscIQTS09ORmZmJixcv4qabbsKSJUvQvn17j9fLy2QU9DjGGREFoaC8THb16lWMHz8eDz30kMfPeeWVV/DWW2/h3XffxY4dOxAVFYXU1FRcuXKlHlvqSFEUnDx5Mqiram8wH/eYkRzzkWM+csxHTgv5BFQxNH/+fDz66KPo2rWrR/MLIfDGG2/gr3/9K+644w5069YN77//Pk6fPo2vv/66fhtbicViQXZ2NiwWi8/WGUiYj3v1nlGAD/jKY0iO+cgxHzkt5BPUn5U7fvw4zpw5g2HDhtmnxcTE4IYbbsD27dsxceJEp88rLy9HeXm5/XFxcTEAwGQywWQyVZtfr9fDYDDYDxSDwQCz2QzbFUjbc2zfDQYD9Ho9zGYz9Ho99Hq90+Xa2D7SaDabHX52JTQ0FIqiQFEUhISEQFEUlwexTqdDSEiIQ9stFovL/wBs21q57ZW3tSrbtppMJpdtr5xP5Xls2+Gu7ZW31ZO2u9pPrtquhv1kW47FYnHYjjrbTy1aQD9vnnUf/G8eWdvVtp9sbMvU8uvJ2bba8lAUxWU2Wno9Vd1PNq7a46v9pJbXk6v95CyfQHg9eSKoi6EzZ84AAFq0aOEwvUWLFvbfObNgwQLMnz+/2vTVq1cjMjKy2vRWrVqhZ8+e2LdvHyIiItCxY0fs3LkT586dc5hvzZo1AIAePXqgdevW2Lx5M7p06YLmzZtj9erVLnfa4MGDERERgZUrV2LUqFEoKyvDhg0bnM4bEhKC2267DYWFhcjJycGQIUNw6tQpZGdnO50/Li4O/fv3x5EjR1BWVmbfjry8PKfzd+jQwb59SUlJ9u0oKSlxOn+/fv3s2zdgwAD7djizZs0a+/Zt2bLFvh3bt293On90dLR9+/Lz8+3bkZub63R+T/eTjZr2U7NmzQAAx44dw9WrV/26nwCobj8lJiYCAM6fP4/ExES+nv6n8n6y5bNr1y6n82rp9VR1P3Xp0gVAxd/oqrT2eqq6n2y5O8tH7a+nn376yem8Vfn9BuqnnnoKCxculM5z8OBBdOzY0f542bJlmDNnjtsbqLdt24abbroJp0+fRkKl0/8TJkyATqfDv//9b6fPc3ZmKDk5GYWFhU5vwPLkzNCaNWtw6623IjQ0VNX/IfnrzJAtn4iICPs8av4PyZn6PjO0evVqpKam2o8hNZxxUMt+slgsWLlyJUaMGIHw8HBNv56cbWtZWRnWrFmDESNGQK93fneEll5PVfeToihYuXKl/W+0q23Vyuup6n4qLS11eA9z1XY1vp4uXLiA2NhYtzdQ+/3M0OOPP44pU6ZI52nXrl2tlh0fHw8AOHv2rEMxdPbsWfTo0cPl88LDwxEeHl5temhoqNMXik3l0/XOeuus+vzK88iW62wed/PbDoSqP7tSue0Gg8HhsTOV2+5Jz6SetD00NBQ6nc5hHk/aXnkeT9rubj9Vpbb9ZGu/v/aTs/n9vZ9sfyxty1fDfqr8s5r2U022VQuvJ6Di8qq7v/FaeT1VncfWLlk+gfx6AlRQDMXFxSEuLq5elt22bVvEx8dj3bp19uKnuLgYO3bsqNEn0oiIiCh4BdSnyfLy8pCdnY28vDz73e3Z2dm4fPmyfZ6OHTviq6++AmA9xTZnzhy88MIL+Pbbb7F//37cf//9SExMxNixY33Wbp1Oh7i4OPtZD3LEfNwLmIyMRmDePJ8P+Bow+fgJ85FjPnJayMfv9wzVxJQpU7B8+fJq0zds2IBBgwYBsO60pUuX2i+92TpdfO+993Dx4kXcfPPNeOedd3Ddddd5vF52ukjkIXbeSEQq4un7d0AVQ/7ibTFksVhw5MgRtG/f3u21Ti1iPu4FTEZ+KoYCJh8/YT5yzEcukPPx9P3b7/cMaUVZWZm/m6BqzMc91WZkNFZcFsvKcvwOWDty9EFnjqrNRyWYjxzzkQv2fHhmyAO8TEYkMW8e4KRfLrv0dOs8REQ+FpRjkwUqi8WCPXv2BHVX5t5gPu6pOqO0tIqR7jMzrdMyMyumpaXVexNUnY8KMB855iOnhXxYDPmAoijIy8sL6kHuvMF83FN1RgkJ1vuDbF+A42MfXCJTdT4qwHzkmI+cFvJhMURERESaxmKIiOpOQoL1HiEfnA0iIqor/DQZEdWdhATeLE1EAYdnhoiIiEjTWAwRERGRprEY8gG9Xo8OHTq4HZlXq5iPe8xIjvnIMR855iOnhXzY6aIH2OkiERFR4GGniypiNpuxbds2mM1mfzdFlZiPe5rLyGi03ohtG+bDDc3lU0PMR475yGkhHxZDPqDX65GUlBTUpxi9wXzc01xGRqN1iA8PiyHN5VNDzEeO+chpIR9+tN4H9Ho9Wrdu7e9mqBbzcY8ZyTEfOeYjx3zktJBP8JZ5KmI2m7F+/fqgPsXoDebjniYyMhqto93bvgDHx5KzRJrIxwvMR475yGkhH54Z8gEhBEpKSsB71Z1jPu5pIqOMDOulscqmT6/4OT3dZYeOmsjHC8xHjvnIaSEfFkNEpA5pacCYMdafs7KshVBmZsXgrxzig4jqCYshIlKHhITqBU+vXhXFEBFRPeE9Q0RERKRpLIaISH0SEqz3CPHSGBH5AC+TEZH6JCS4vFmaiKiucTgOD3g7HIeiKCgsLESzZs2CutOq2mI+7jEjOeYjx3zkmI9cIOfj6fs3iyEPcGwyIiKiwMOxyVTEZDJhxYoVMJlM/m6KKjEf95iRnMt8ajjGWbDi8SPHfOS0kA/PDHnA2zNDtg6roqOjodPp6qGFgY35uMeM5Fzmk5UF9O4N7N6t6Y/o8/iRYz5ygZwPzwypTEREhL+boGrMxz1mJMd85JiPHPORC/Z8WAz5gNlsxsqVK4N6XBdvMB/3mJGcQz5ejHEWrHj8yDEfOS3kU2fFUHFxMTZv3oy33nqrrhZJRFRzGRnWS2O9e1eMbTZ9esW0jAz/to+IVKdW/Qzl5eUhOzvb4evkyZMQQiAqKgqPPPJIXbeTiMgzHOOMiGqoRsXQkCFDsHfvXhQVFSEmJgadOnVCly5dkJeXh3/+858YOnQokpOT66utRETucYwzIqqhGl0m27p1Kx588EGcOnUKRUVF+Omnn5CRkQGdToe+ffuyECIiIqKAU6NiaMeOHdiyZQtmzpyJw4cP11ebiIjqBsc4IyIP1KgY6tmzJzZv3owJEyYgNTUVM2fOREFBQX21jYjIO7YxzlgMEZFErTtdLC0txUsvvYSMjAxcuHAB2dnZ6Nq1a123TxXqotNFs9mMkJCQgOuwyheYj3vMSI75yDEfOeYjF8j51Huni5GRkXjhhRewY8cO3H777Rg6dCheffVVlJWV1XaRQY25yDEf95iRHPORYz5yzEcu2PPxup+hdu3a4ZtvvsGHH36IpUuXol27dnXRrqBiNpuxZcuWoO6wyhvMxz1mJMd85JiPHPOR00I+dTo2mdlsxttvv405c+bU1SJVgaPWE2mc0WjtrDEtjfcfEQWQer1MtmvXLgwdOhTdunXDnXfeieeeew7ffvstjEZj0BVCdUFRFBQUFEBRFH83RZWYj3vMSK7e8zEagfnzA3YoDx4/csxHTgv51KoYuu+++2AwGDBjxgy0bdsWmzZtwtSpU9G6dWvExsbWdRsDnsViwfbt22GxWPzdFFViPu4xIznmI8d85JiPnBbyqdVwHKdOncKKFStwzTXXOEw/efIksrOz66JdRET+ZTRWnAmqPOCrjbOerokoINWqGOrXrx/y8/OrFUOtW7dG69at66RhRER+lZFhvTRWmW3gV8DameO8eT5tEhHVj1pdJnv00Ufx3HPP4cKFC3XdHiIidUhLA3bvtn5lZlqnZWZWTEtL82/7iKjO1OrM0OjRo6HT6XDdddfhjjvuQL9+/dCzZ0907doVYWFhdd1GIiLf44CvRJpRq2Lo6NGj2Lt3r/3rpZdewokTJxAaGooOHTpg3759dd1OIiIionrhcTF05513okePHujRowe6d++OcePGYdy4cfbfFxcXY+/evSyEnNDpdIiOjg64bsx9hfm4x4zk6j2fAB/wlcePHPOR00I+Hne6OHfuXGRnZ2Pv3r0oLCxE48aN0b17d3Tv3h09evRAz5490alTJ4SGhtZ3m32OnS4SEREFHk/fv2vVA3V+fj6ys7Mdvn777TeEhIQgJSUl6D5e720xpCgKTp06heTkZOj1Xo+AEnSYj3vMSI75yDEfOeYjF8j5ePr+Xat7hpKSkpCUlITbbrvNPu3y5cv2M0fkSFEU5OfnIykpKeAOJF9gPu4xIznmI8d85JiPnBbyqdOxyYIVL5MREREFnnodm4xqxmKx4NChQ0Hdlbk3mI97zEguYPIxGq0dNfp4jLOAycdPmI+cFvJhMeQDiqIgNzc3qAe58wbzcY8ZyQVMPn4a8DVg8vET5iOnhXxYDBEREZGm1eoGaiIi8hAHfCVSPRZDRET1iQO+EqkeiyEiovqUlgaMGWP9OSvLWghlZlaMccazQkR+x2KIiKg+ccBXItXjDdQ+oNfr0apVq6DtrMpbzMc9ZiTHfOSYjxzzkdNCPux00QPsdJGI6oTRaL2HKC2Nl8eIfICdLqqIxWLBnj17grrDKm8wH/eYkVzA5JOQYL1Z2seFUMDk4yfMR04L+bAY8pGIiAh/N0HVmI97zEiO+cgxHznmIxfs+fAymQd4mYyIiCjw8DKZipjNZmzbtg1ms9nfTVEl5uMeM5JjPnLMR475yGkhHxZDPiCEwLlz58CTcM4xH/eYkRzzkWM+csxHTgv5sBgiIiIiTWMxREQUaIxG66fSbGOeEZFXWAwREQUao9E63hmLIaI6wWKIiIiINI1jkxERBQKjseJMUFaW43fA+RhoROSRgDoz9OKLL6J///6IjIxE48aNPXrOlClToNPpHL5GjBhRvw2twmAwoEePHjAYDD5db6BgPu4xIzlN5JORAfTubf2aPt06bfr0imkZGS6fqol8vMB85LSQT0B1upieno7GjRvjv//9L/75z3/i4sWLbp8zZcoUnD17FkuXLrVPCw8PR5MmTTxeLztdJCK/q3pmaPp0IDMT6NXLOo1nhoiqCcpOF+fPn49HH30UXbt2rdHzwsPDER8fb/+qSSFUF8xmM9avXx/UHVZ5g/m4x4zkNJFPQoK18LF9AY6PJYWQJvLxAvOR00I+mrhnaOPGjWjevDmaNGmCIUOG4IUXXkBsbKzL+cvLy1FeXm5/XFxcDAAwmUwwmUzV5tfr9TAYDPZB7AwGA8xms72DKkVR0LFjR1gsFgghYDAYoNfrYTabodfrodfrnS7XJiTEupvMZrPDz66EhoZCURQoioKQkBAoiuJygD2dToeQkBCHtlssFiiK4nR+27ZWbnvlba3Ktq0mk8ll2yvnYzsNazab7dvhru2Vt9WTtrvaT67arob9JIRAly5dIISw5+Tr/eRqW9Wyn1JSUuzTgv71ZDYjFNbjwuzBtlosFnTp0gWA62y09Hqqup9sx4/tb7SrbdXS66nytlosFof3MFdtV+vryRNBXwyNGDECd955J9q2bYtjx47hz3/+M0aOHInt27e7vP65YMECzJ8/v9r01atXIzIystr0Vq1aoWfPnti3bx8iIiLQsWNH7Ny5E+fOnXO6/B49eqB169bYvHkzunTpgubNm2P16tUud9rgwYMRERGBlStXYtSoUSgrK8OGDRuczhsSEoLbbrsNhYWFyMnJwZAhQ3Dq1ClkZ2c7nT8uLg79+/fHkSNHUFZWZt+OvLw8p/N36NDBvn1JSUn27SgpKXE6f79+/ezbN2DAAPt2uGLbvi1btti3Y/v27U7njY6Otm9ffn6+fTtyc3Odzh8M++nQoUPcT1XY9tPBgwdhMBhUsZ/q+/W0KTcXA556Cvq4uBrtp4KCAr/vJzW9nirvpzNnzmDnzp1O59fi66nyflq7dq1q9lNNX08//fST03mr8vs9Q0899RQWLlwonefgwYPo2LGj/fGyZcswZ84cj+4Zquq3337DNddcg7Vr12Lo0KFO53F2Zig5ORmFhYVOrzm6q7xNJhPWr1+PIUOGIDQ0VNX/IfnjjEPlfGwjI6v1PyR/7SfbaeqhQ4fajyGeGapou8ViwapVq3DrrbciPDxc068nZ9tqe4MaNmwY9Hrnd0do6fVUdT8pioJVq1bZ/0a72latvJ6q7qfS0lKH9zBXbVfj6+nChQuIjY11e8+Q388MPf7445gyZYp0nnbt2tXZ+tq1a4dmzZrh6NGjLouh8PBwhIeHV5seGhrq9IViU/lMk+2gsLFYLNWeX3ke2XKdzeNuftuBUPVnT9puMBjcfmqgcturbqsz7tpuy0en0znM40nbK8/jSdtl+8kZtewns9nssH3+2E+u5vf3frJYLLBYLPbla/315Gx+2xtETbY1mF9PQEXbbW/I7v7Ga+X1VHWe0NBQt/kE8usJUEExFBcXh7i4OJ+t77///S/Onz+PBH7qgoiIiBBgnybLy8tDdnY28vLyYLFYkJ2djezsbFy+fNk+T8eOHfHVV18BAC5fvoy5c+fi559/xokTJ7Bu3TrccccduPbaa5GamuqvzSAiIiIV8fuZoZp49tlnsXz5cvvjnj17AgA2bNiAQYMGAQByc3Nx6dIlANbTafv27cPy5ctx8eJFJCYmYvjw4Xj++eedXgYjIiIi7QmoYmjZsmVYtmyZdJ7KN4VFRERg1apV9dwqIqIAZTRae65OS2OHjaRpAXWZjIiI6pDRCMyfX9GzNZFG+f2j9YHA2+E4hBAoKSlBdHS0/dNSVIH5uMeM5JiPnMt8srKs45rt3l3Rq7UG8fiRC+R8PH3/DqjLZIHM1n8OOcd83GNGcsxHzp5P1THOKn8HNDvGGY8fuWDPh5fJfMBsNmPlypVBPa6LN5iPe8xIjvnIOeSTkVEx0v306dYZpk+vmJaR4d/G+gGPHzkt5MPLZB6oi8tktt45A+0Uoy8wH/eYkRzzkXPI58wZxzND06cDmZkVl8k0eGaIx49cIOfDy2QqU1ZWhujoaH83Q7WYj3vMSI75yNnzcVbs9Oql6XuGAB4/7gR7PrxM5gNmsxkbNmwI6lOM3mA+7jEjOeYjx3zkmI+cFvJhMUREpFUJCUB6uuYuixFVxctkRERalZAAzJvn71YQ+R3PDBEREZGmsRgiIiIiTWMxRERE3jEarZfbOKwHBSgWQz4SEsLbs2SYj3vMSI75yNVrPkEwxhmPH7lgz4edLnrA204XiYiCGsc4I5Xy9P2bZ4Z8QFEUFBQUQFEUfzdFlZiPe8xIjvnI1Us+RqO1CLJ9AY6PA+gsEY8fOS3kw2LIBxRFQU5OTlAfSN5gPu4xIznmI1cv+QTRGGc8fuS0kA8vk3mAl8mIiKowGjnGGakeL5OpiKIoOHnyZFBX1d5gPu4xIznmI1cv+SQkVIxpZiuAKj8OoEKIx4+cFvJhMeQDFosF2dnZsFgs/m6KKjEf95iRHPORYz5yzEdOC/mwGCIiIu9wjDMKcMHdcQAREdU/jnFGAY5nhoiIiEjTWAwRERGRprEYIiIiIk1jMeQDOp0OcXFx0Ol0/m6KKjEf95iRHPORYz5yzEdOC/mw00UPsNNFIiKiwMNOF1XEYrHg0KFDQd1HgzeYj3vMSI75yDEfOeYjp4V8WAz5SFlZmb+boGrMxz1mJMd85AIiH6PR+hF9PwzyGhD5+FGw58PLZB7gZTIiIh/IyrIO8rp7d8UQH0Re4GUyFbFYLNizZ09Qn2L0BvNxjxnJMR855iPHfOS0kA+LIR9QFAV5eXlBPcidN5iPe8xIjvnIqTofo9F6Rsj2BTg+9sElM1XnowJayIfDcRARkf9kZADz5ztOmz694uf0dA71QfWOxRAREflPWhowZoz156wsayGUmVlxzxAHfyUfYDFERET+k5BQveDp1Ys3UJNP8Z4hIiIi0jQWQ0REpA4JCdZ7hHhpjHyMl8l8QK/Xo0OHDtDrWXs6w3zcY0ZyzEcuYPJJSPDLzdIBk4+faCEfdrroAXa6SEREFHjY6aKKmM1mbNu2DWaz2d9NUSXm4x4zkmM+csxHjvnIaSEfFkM+oNfrkZSUFNSnGL3BfNxjRnLMR475yDEfOS3kw8tkHuBlMiKiAGI0WjtzTEvjzdgax8tkKmI2m7F+/fqgPsXoDebjHjOSYz5ymsvHaLT2au3hUB6ay6eGtJAPiyEfEEKgpKQEPAnnHPNxjxnJMR855iPHfOS0kA8/Wk9ERIHPaKw4E1R5wFcbZz1dE/0PiyEiIgp8HPCVvMBiiIiIAh8HfCUvsBgiIqLAxwFfyQu8gZqIiIg0jcWQDxgMBvTr1w8Gg8HfTVEl5uMeM5JjPnKay6eGA75qLp8a0kI+7HTRA+x0kYiIKPCw00UVMZlMWLFiBUwmk7+bokrMxz1mJMd85JiPHPOR00I+PDPkAW/PDNk6rIqOjoZOp6uHFgY25uMeM5JjPnLMR475yAVyPjwzpDIRERH+boKqMR/3mJEc85FjPnLMRy7Y82Ex5ANmsxkrV64M6nFdvMF83GNGcsxHjvnIMR85LeTDYoiIiMgZo9Haa7WHA75S4GIxRERE5IzRaB3ig8VQ0GMxRERERJrG4TiIiIhsjMaKM0G2Ue9t3wHnw35QwGMxREREZJORYb00Vtn06RU/p6db7yOioMJiiIiIyCYtDRgzxvpzVpa1EMrMrBjwlWeFghI7XfRAXXS6aDabERISEnAdVvkC83GPGckxHznmI+cyn6wsoHdvYPfuimJIgwL5+GGniypTVlbm7yaoGvNxjxnJMR855iPHfOSCPR8WQz5gNpuxZcuWoO6wyhvMxz1mJMd85JiPnMt8EhKs9whp/NKYFo4fXibzAEetJyIiCjy8TKYiiqKgoKAAiqL4uymqxHzcY0ZyzEeO+cgxHzkt5MNiyAcsFgu2b98Oi8Xi76aoEvNxjxnJMR855iPHfOS0kA+LISIiItI0FkNERESkaQFTDJ04cQLTpk1D27ZtERERgWuuuQbp6em4evWq9HlXrlzBzJkzERsbi4YNG+Kuu+7C2bNnfdRqIiIiUruAKYYOHToERVGQkZGBX3/9Fa+//jreffdd/PnPf5Y+79FHH8V3332Hzz//HJs2bcLp06dx5513+qjVRESkeUajdQgP25hnpDoBMxzHiBEjMGLECPvjdu3aITc3F0uWLMGrr77q9DmXLl3CP//5T3z88ccYMmQIAGDp0qVISUnBzz//jBtvvNEnbSciIg0zGq3jnY0Zo/k+i9QqYIohZy5duoSmTZu6/P3u3bthMpkwbNgw+7SOHTuiVatW2L59u8tiqLy8HOXl5fbHxcXFAACTyQSTyVRtfr1eD4PBYL/T3mAwwGw2w9aFk9lsRsOGDe0dVhkMBuj1epjNZuj1euj1eqfLtQkJCbEvp/LProSGhkJRFCiKgpCQECiK4vJTADqdDiEhIQ5tt1gsLj9CadvWym2vvK1V2bbVZDK5bHvlfCrPY9sOd22vvK2etN3VfnLVdjXsJ4vFgujoaPs8/thPrrZVDftJp9OhYcOG9nm0/Hpyta3R0dEQQrjMRkuvp6r7yXb8uFq+1/tJCOgAmMxmwMk2q+31VHU/VX0Pc9V2tb6ePBGwxdDRo0exaNEil2eFAODMmTMICwtD48aNHaa3aNECZ86ccfm8BQsWYH7VUYsBrF69GpGRkdWmt2rVCj179sS+ffsQERGBjh07YufOnTh37ly15wNAjx490Lp1a2zevBldunRB8+bNsXr1apc7bfDgwYiIiMDKlSsxatQolJWVYcOGDU7nDQkJwW233YbCwkLk5ORgyJAhOHXqFLKzs53OHxcXh/79++PIkSMoKyuzb0deXp7T+Tt06GDfvqSkJPt2lJSUOJ2/X79+9u0bMGCAfTucWb16tX37tmzZYt+O7du3O50/Ojravn35+fn27cjNzXU6v6f7yUZt+2nIkCE4dOiQ3/cTAFXuJ51Oh4sXL/p9P6nl9QRU308FBQV+309qeT1V3U9Nmza1/42uqlb7yWLBz599hp49e6LBwYMIAZDz/vu4tHUrAOBKkyYo/98/82p8PVXeT+vXr4fZbHaaj9pfTz/99JPTeavyew/UTz31FBYuXCid5+DBg+jYsaP9cX5+PgYOHIhBgwbhH//4h8vnffzxx5g6darDWR4A6Nu3LwYPHuxyvc7ODCUnJ6OwsNBpD5buKm9FUZCfn4+kpCT7vGr9D8kf/8lWzicsLMw+jxr/Q/LXfhJCwGg0IjEx0WE71HDGQQ37CbB+yKJVq1YICQnR9OvJ2bZevXoVZ86cQVJSkstla+n15OzM0MmTJ+2vL1fbWqP99Nxz1ktjLlj++lcozz5bbVvV8Hqqup/Ky8sd3sMqU/vr6cKFC4iNjXXbA7Xfzww9/vjjmDJlinSedu3a2X8+ffo0Bg8ejP79++O9996TPi8+Ph5Xr17FxYsXHc4OnT17FvHx8S6fFx4ejvDw8GrTQ0NDERoa6vJ5tj/KQMUBAlgPjDNnztj/UDubR7ZcZ/O4m992IFT92ZO2GwwGh8fOuNoOV2Rtr5yPbURk2zyetL3yPJ603dV+ckUN+8lsNtv/GNna7+v9JJvf3/up8jFU07Z7Mn8gvZ5ctcd2/NRkW4P19WRja7vZbIbRaERycrJ0G2q0n9LSrPcIAUBWFjB9OpCZCfTqZV13QgIMVbZHLa+nqvMYDAan72HO2l71Z3dtV8PrCVDBmaGayM/Px+DBg9G7d298+OGHbgO5dOkS4uLi8Mknn+Cuu+4CAOTm5qJjx47Se4aq4thkRERUa1lZQO/ewO7d9mKIfCPoxibLz8/HoEGD0KpVK7z66qs4d+4czpw543DvT35+vv16IQDExMRg2rRpeOyxx7Bhwwbs3r0bU6dORb9+/Xz6STKLxYJDhw4FdVfm3mA+7jEjOeYjx3zkmI+cFvIJmGJozZo1OHr0KNatW4eWLVsiISHB/mVjMpmQm5uL0tJS+7TXX38dt99+O+666y7ccsstiI+Px5dffunTtiuKgtzc3KAe5M4bzMc9ZiTHfOSYj1y955OQAKSnB+zH6rVw/Pj9niFPTZkyxe29RW3atKl2U1iDBg2wePFiLF68uB5bR0RE5EJCgrXTRVKtgDkzRERERFQfWAwREREFAg7rUW9YDBEREQUC27AeLIbqHIshIiIi0rSAuYE6kOn1erRq1cptx1JaxXzcY0ZyzEeO+cipOh+jseJMUFaW43fAenN2PX9KTdX51JGA6nTRX9jpIhER+cW8edJhPZCezk+qSQRdp4uBzGKxYM+ePUHdYZU3mI97zEiO+cgxHzlV55OWZu25evdu63AegPW7bVpaWr03QdX51BFeJvORiIgIfzdB1ZiPe8xIjvnIMR851ebj7DJYr14+H9ZDtfnUEV4m8wAvkxERkd9xjLMa42UyFTGbzdi2bRvMZrO/m6JKzMc9ZiTHfOSYj1zA5OOnYT0CJh8v8DKZDwghcO7cuWpDhZAV83GPGckxHznmIxcw+fhpWI+AyccLPDNEREREmsZiiIiIiDSNxRARERFpGoshIiIi0jQWQ0RERKRpLIZ8wGAwoEePHjAYDP5uiioxH/eYkRzzkWM+cprLx2i0firNNuaZG1rIh50ueoCdLhIRUdDQUOeN7HRRRcxmM9avXx/UHVZ5g/m4x4zkmI8c85FjPnJayIedLvqAXq9Hly5doNez9nSG+bjHjOSYjxzzkdNEPkZjxWWxrCzH74DzMdD+Rwv58DKZB3iZjIiIAtq8ecD8+a5/n57ul96t6xsvk6mIyWTCihUrYDKZ/N0UVWI+7jEjOeYjx3zkNJFPWpr1HqHdu4HMTOu0zMyKaWlpLp+qhXx4mcxHgvlaa11gPu4xIznmI8d85II+H2eXwXr18vgG6mDPh2eGiIiISNNYDBEREWlJQoL1HiEXN0xrES+TERERaUlCQlDeLO0NnhkiIiIiTWMxRERERJrGfoY84G0/Q0IIlJSUIDo6Gjqdrh5aGNiYj3vMSI75yDEfOeYjF8j5sJ8hlYmIiPB3E1SN+bjHjOSYjxzzkWM+ck7zqeGAr2rGYsgHzGYzVq5cGfT9NNQW83GPGckxHznmI8d85FzmYzRae7UOgmKIl8k8UBeXycxmM0JCQgLuFKMvMB/3mJEc85FjPnLMR85lPllZQO/e1h6sPey80dc8ff/mR+t9pKysDNHR0f5uhmoxH/eYkRzzkWM+csxHzp6PFwO+qhkvk/mA2WzGhg0beArWBebjHjOSYz5yzEeO+cg55JORYT0b1Ls3MH26dYbp0yumZWT4t7G1xDNDRERE5Jm0NGDMGOvPWVnWQigzs+IyWQCeFQJYDBEREZGnvBzwVa14mYyIiIg0jcUQERER1VwQDfjKy2RERERUc0E04CvPDPlISAjrThnm4x4zkmM+csxHjvnIBXs+7HTRA952ukhERES+x7HJVERRFBQUFEBRFH83RZWYj3vMSI75yDEfOeYjp4V8WAz5gKIoyMnJCeoDyRvMxz1mJMd85JiPHPORq/d8VDDgKy+TeYCXyYiIiOpJPY5xxstkKqIoCk6ePMn/OlxgPu4xIznmI8d85JiPnBbyYTHkAxaLBdnZ2bBYLP5uiioxH/eYkRzzkWM+csxHrl7yMRqtZ4RsX4DjYx9fMgvuz8oRERGR+mRkAPPnO06zDfwKWDtz9GEfRiyGiIiIyLdUNuAriyEiIiLyLZUN+Mp7hoiIiEjTWAwRERGR/6hgwFdeJvMBnU6HuLg46HQ6fzdFlZiPe8xIjvnIMR855iNX7/moYMBXdrroAXa6SEREFHjY6aKKWCwWHDp0iH1YuMB83GNGcsxHjvnIMR85LeTDYshHysrK/N0EVWM+7jEjOeYjx3zkmI9csOfDy2Qe4GUyIiKiwMPLZCpisViwZ8+eoD7F6A3m4x4zkmM+csxHjvnIaSEfFkM+oCgK8vLygnqQO28wH/eYkRzzkWM+csxHTgv5sBgiIiIiTWMxRERERJrGYoiIiIg0jcUQERERaRqH4/CArfeB4uLiWj3fZDKhtLQUxcXFCA0NrcumBQXm4x4zkmM+csxHjvnIBXI+tvdtd70IsRjyQElJCQAgOTnZzy0hIiKimiopKUFMTIzL37PTRQ8oioLTp08jOjq6VgPVFRcXIzk5GadOnWKnjU4wH/eYkRzzkWM+csxHLpDzEUKgpKQEiYmJ0Otd3xnEM0Me0Ov1aNmypdfLadSoUcAdSL7EfNxjRnLMR475yDEfuUDNR3ZGyIY3UBMREZGmsRgiIiIiTWMx5APh4eFIT09HeHi4v5uiSszHPWYkx3zkmI8c85HTQj68gZqIiIg0jWeGiIiISNNYDBEREZGmsRgiIiIiTWMxRERERJrGYsgHFi9ejDZt2qBBgwa44YYbsHPnTn83SRUWLFiA66+/HtHR0WjevDnGjh2L3NxcfzdLtV5++WXodDrMmTPH301Rjfz8fNx7772IjY1FREQEunbtil9++cXfzVIFi8WCZ555Bm3btkVERASuueYaPP/8827HaApmmzdvxujRo5GYmAidToevv/7a4fdCCDz77LNISEhAREQEhg0bhiNHjvinsX4gy8dkMuHJJ59E165dERUVhcTERNx///04ffq0/xpch1gM1bN///vfeOyxx5Ceno6srCx0794dqampKCgo8HfT/G7Tpk2YOXMmfv75Z6xZswYmkwnDhw/H77//7u+mqc6uXbuQkZGBbt26+bspqlFUVISbbroJoaGh+OGHH3DgwAG89tpraNKkib+bpgoLFy7EkiVL8Pbbb+PgwYNYuHAhXnnlFSxatMjfTfOb33//Hd27d8fixYud/v6VV17BW2+9hXfffRc7duxAVFQUUlNTceXKFR+31D9k+ZSWliIrKwvPPPMMsrKy8OWXXyI3NxdjxozxQ0vrgaB61bdvXzFz5kz7Y4vFIhITE8WCBQv82Cp1KigoEADEpk2b/N0UVSkpKRHt27cXa9asEQMHDhSzZ8/2d5NU4cknnxQ333yzv5uhWrfddpt44IEHHKbdeeedYtKkSX5qkboAEF999ZX9saIoIj4+Xvztb3+zT7t48aIIDw8Xn3zyiR9a6F9V83Fm586dAoA4efKkbxpVj3hmqB5dvXoVu3fvxrBhw+zT9Ho9hg0bhu3bt/uxZep06dIlAEDTpk393BJ1mTlzJm677TaH44iAb7/9Fn369MH48ePRvHlz9OzZE5mZmf5ulmr0798f69atw+HDhwEAe/fuxdatWzFy5Eg/t0ydjh8/jjNnzji8zmJiYnDDDTfw77ULly5dgk6nQ+PGjf3dFK9xoNZ6VFhYCIvFghYtWjhMb9GiBQ4dOuSnVqmToiiYM2cObrrpJnTp0sXfzVGNTz/9FFlZWdi1a5e/m6I6v/32G5YsWYLHHnsMf/7zn7Fr1y488sgjCAsLw+TJk/3dPL976qmnUFxcjI4dO8JgMMBiseDFF1/EpEmT/N00VTpz5gwAOP17bfsdVbhy5QqefPJJ/PGPfwzIwVurYjFEqjBz5kzk5ORg69at/m6Kapw6dQqzZ8/GmjVr0KBBA383R3UURUGfPn3w0ksvAQB69uyJnJwcvPvuuyyGAHz22Wf46KOP8PHHH6Nz587Izs7GnDlzkJiYyHzIKyaTCRMmTIAQAkuWLPF3c+oEL5PVo2bNmsFgMODs2bMO08+ePYv4+Hg/tUp9Zs2ahe+//x4bNmxAy5Yt/d0c1di9ezcKCgrQq1cvhISEICQkBJs2bcJbb72FkJAQWCwWfzfRrxISEtCpUyeHaSkpKcjLy/NTi9Rl7ty5eOqppzBx4kR07doV9913Hx599FEsWLDA301TJdvfZP69lrMVQidPnsSaNWuC4qwQwGKoXoWFhaF3795Yt26dfZqiKFi3bh369evnx5apgxACs2bNwldffYX169ejbdu2/m6SqgwdOhT79+9Hdna2/atPnz6YNGkSsrOzYTAY/N1Ev7rpppuqdcVw+PBhtG7d2k8tUpfS0lLo9Y5/4g0GAxRF8VOL1K1t27aIj493+HtdXFyMHTt28O/1/9gKoSNHjmDt2rWIjY31d5PqDC+T1bPHHnsMkydPRp8+fdC3b1+88cYb+P333zF16lR/N83vZs6ciY8//hjffPMNoqOj7dflY2JiEBER4efW+V90dHS1+6eioqIQGxvL+6oAPProo+jfvz9eeuklTJgwATt37sR7772H9957z99NU4XRo0fjxRdfRKtWrdC5c2fs2bMHf//73/HAAw/4u2l+c/nyZRw9etT++Pjx48jOzkbTpk3RqlUrzJkzBy+88ALat2+Ptm3b4plnnkFiYiLGjh3rv0b7kCyfhIQE3H333cjKysL3338Pi8Vi/5vdtGlThIWF+avZdcPfH2fTgkWLFolWrVqJsLAw0bdvX/Hzzz/7u0mqAMDp19KlS/3dNNXiR+sdfffdd6JLly4iPDxcdOzYUbz33nv+bpJqFBcXi9mzZ4tWrVqJBg0aiHbt2om//OUvory83N9N85sNGzY4/ZszefJkIYT14/XPPPOMaNGihQgPDxdDhw4Vubm5/m20D8nyOX78uMu/2Rs2bPB3072mE0LD3ZESERGR5vGeISIiItI0FkNERESkaSyGiIiISNNYDBEREZGmsRgiIiIiTWMxRERERJrGYoiIiIg0jcUQEWneoEGDMGfOHH83o9Zyc3MRHx+PkpISr5bTpk0bvPHGGx7Pf+DAAbRs2RK///67V+sl8jd2ukgUoAYNGoQePXrU6M2LnLtw4QJCQ0MRHR1dZ8tctmwZ5syZg4sXL9bZMl2588470bt3b/zlL3/xajnnzp1DVFQUIiMjPX7O3Xffje7du+OZZ57xat1E/sQzQ0SkeU2bNq3TQsiX8vLy8P3332PKlCleLysuLq5GhRAATJ06FUuWLIHZbPZ6/UT+wmKIKABNmTIFmzZtwptvvgmdTgedTocTJ04AAHJycjBy5Eg0bNgQLVq0wH333YfCwkL7cwcNGoQ//elPmDNnDpo0aYIWLVogMzPTPoBwdHQ0rr32Wvzwww/252zcuBE6nQ4rVqxAt27d0KBBA9x4443Iycmxz3Py5EmMHj0aTZo0QVRUFDp37oyVK1e63Iby8nI88cQTSEpKQlRUFG644QZs3LjR/vtly5ahcePGWLVqFVJSUtCwYUOMGDECRqPR5TJt7Vy1ahV69uyJiIgIDBkyBAUFBfjhhx+QkpKCRo0a4Z577kFpaalDJpUvk7Vp0wYvvfQSHnjgAURHR6NVq1YOA8Da1lP5rE92drZ9P2zcuBFTp07FpUuX7Ptn3rx5Hm13TXP87LPP0L17dyQlJVXL7vvvv0eHDh0QGRmJu+++G6WlpVi+fDnatGmDJk2a4JFHHoHFYnHY7spnGnU6Hf7xj39g3LhxiIyMRPv27fHtt986rP/WW2/FhQsXsGnTJpdtJFI7FkNEAejNN99Ev379MH36dBiNRhiNRiQnJ+PixYsYMmQIevbsiV9++QU//vgjzp49iwkTJjg8f/ny5WjWrBl27tyJP/3pT3jooYcwfvx49O/fH1lZWRg+fDjuu+8+h4IBAObOnYvXXnsNu3btQlxcHEaPHg2TyQQAmDlzJsrLy7F582bs378fCxcuRMOGDV1uw6xZs7B9+3Z8+umn2LdvH8aPH48RI0bgyJEj9nlKS0vx6quv4oMPPsDmzZuRl5eHJ554wm0+8+bNw9tvv41t27bh1KlTmDBhAt544w18/PHHWLFiBVavXo1FixZJl/Haa6+hT58+2LNnDx5++GE89NBDyM3NdbtuAOjfvz/eeOMNNGrUyL5/bO12t901zXHLli3o06dPtemlpaV466238Omnn+LHH3/Exo0bMW7cOKxcuRIrV67EBx98gIyMDHzxxRfSbZk/fz4mTJiAffv2YdSoUZg0aRIuXLhg/31YWBh69OiBLVu2eJQNkSr5d5xYIqotZyPYP//882L48OEO006dOiUA2EffHjhwoLj55pvtvzebzSIqKkrcd9999mlGo1EAENu3bxdCVIxm/emnn9rnOX/+vIiIiBD//ve/hRBCdO3aVcybN8+jtp88eVIYDAaRn5/vMH3o0KHi6aefFkIIsXTpUgFAHD161P77xYsXixYtWrhcrq2da9eutU9bsGCBACCOHTtmn5aWliZSU1Ptj6tm2bp1a3HvvffaHyuKIpo3by6WLFnisJ6ioiL7PHv27BEAxPHjx+3tj4mJqfF21yRHIYTo3r27eO655xymOcsuLS1NREZGipKSEvu01NRUkZaW5rDdr7/+uv0xAPHXv/7V/vjy5csCgPjhhx8c1jdu3DgxZcoUj9tMpDYhfqrBiKge7N27Fxs2bHB6JuHYsWO47rrrAADdunWzTzcYDIiNjUXXrl3t01q0aAEAKCgocFhGv3797D83bdoUHTp0wMGDBwEAjzzyCB566CGsXr0aw4YNw1133eWwnsr2798Pi8Vib49NeXk5YmNj7Y8jIyNxzTXX2B8nJCRUa5MzldfbokULREZGol27dg7Tdu7c6fEydDod4uPjPVq3jCfbXZMcAaCsrAwNGjSoNr1qdi1atECbNm0cjo0WLVq43abK646KikKjRo2qPSciIqLaWUSiQMJiiCiIXL58GaNHj8bChQur/S4hIcH+c2hoqMPvdDqdwzSdTgcAUBTF43X/3//9H1JTU+2XoRYsWIDXXnsNf/rTn5y202AwYPfu3TAYDA6/q/xm7aydwoMPwFbdFmfLcbdtsufo9dY7DCq3xXa5UMaT7a5JjgDQrFkzFBUVedT+us7B5sKFCw6FF1Gg4T1DRAEqLCzM4eZXAOjVqxd+/fVXtGnTBtdee63DV1RUlNfr/Pnnn+0/FxUV4fDhw0hJSbFPS05OxoMPPogvv/wSjz/+ODIzM50up2fPnrBYLCgoKKjWzvj4eK/bWd/i4uIAwOFm7uzsbId5nO0fT7fb0xxtyzxw4EAdbFXt5eTkoGfPnn5tA5E3WAwRBag2bdpgx44dOHHiBAoLC6EoCmbOnIkLFy7gj3/8I3bt2oVjx45h1apVmDp1arU35tp47rnnsG7dOuTk5GDKlClo1qwZxo4dCwCYM2cOVq1ahePHjyMrKwsbNmxwKJQqu+666zBp0iTcf//9+PLLL3H8+HHs3LkTCxYswIoVK7xuZ3279tprkZycjHnz5uHIkSNYsWIFXnvtNYd52rRpg8uXL2PdunUoLCxEaWmpR9tdkxwBIDU1Fdu3b6+T/VsbJ06cQH5+PoYNG+aX9RPVBRZDRAHqiSeegMFgQKdOnRAXF4e8vDwkJibip59+gsViwfDhw9G1a1fMmTMHjRs3tl/a8cbLL7+M2bNno3fv3jhz5gy+++47hIWFAQAsFgtmzpyJlJQUjBgxAtdddx3eeecdl8taunQp7r//fjz++OPo0KEDxo4di127dqFVq1Zet7O+hYaG4pNPPsGhQ4fQrVs3LFy4EC+88ILDPP3798eDDz6IP/zhD4iLi8Mrr7wCwP121zTHkSNHIiQkBGvXrq2/DZb45JNPMHz4cLRu3dov6yeqC+yBmojc2rhxIwYPHoyioiI0btzY382hKhYvXoxvv/0Wq1at8ul6r169ivbt2+Pjjz/GTTfd5NN1E9Ul3kBNRBTg0tLScPHiRZSUlPi0J+28vDz8+c9/ZiFEAY9nhojILZ4ZIqJgxmKIiIiINI03UBMREZGmsRgiIiIiTWMxRERERJrGYoiIiIg0jcUQERERaRqLISIiItI0FkNERESkaSyGiIiISNNYDBEREZGm/X+2cKDwK0CjUgAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Affichage graphique : ordre 2 supposé\n",
        "plt.figure(5)\n",
        "plt.title(r'Tracé de $1/A$ en fonction du temps ')\n",
        "plt.ylabel(r'$1/A$')\n",
        "plt.xlabel('temps en minutes (min)')\n",
        "plt.plot(time, Z2,'r+', label='points expérimentaux')\n",
        "#plt.xlim(0,15)\n",
        "#plt.ylim(0,1)\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 475
        },
        "id": "XbN8vXtZmFbx",
        "outputId": "f8e3f713-198f-4807-94e4-2315bb34e263"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Régression linéaire sur la courbe sélectionnée"
      ],
      "metadata": {
        "id": "iOi7rKQspdvX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "p1 = np.polyfit(time, Z1, 1)                      #Régression linéaire de lnA en fonction de t\n",
        "\n",
        "delta_A =(2/100)*A # demi - étendue du spectrophotomètre donné par le constructeur\n",
        "u_A = delta_A/np.sqrt(3) # incertitude - type par rapport à l'absorbance\n",
        "u_Z1=u_A/A # incertitude - type par rapport au calcul du ln : axe des Y\n",
        "\n",
        "modele1=(\"ln A = \"+ format(p1[0], \"#.3e\")+\"x t +\"+ format(p1[1], \"#.3g\"))   # on fabrique l'équation de la droite de régression\n",
        "plt.plot(time,np.polyval(p1,time),color='green',label=modele1)\n",
        "\n",
        "plt.plot(time, np.polyval(p1,time))\n",
        "plt.errorbar(time, Z1, yerr=u_Z1, fmt='.r')   #On ajoute les barres d'incertitude\n",
        "plt.xlabel('t/min')\n",
        "plt.ylabel('ln A' )\n",
        "plt.title('Évolution de $lnA$ en fonction de t')\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()\n",
        "\n",
        "print(\"kapp =\",-p1[0],'min^-1')                   #Affichage de kapp, l'opposé de la pente de la droite de régression\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 492
        },
        "id": "tulzewUAp_S4",
        "outputId": "692badd1-4e73-4dcd-b18e-3fade97ce616"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "kapp = 0.17119422182738275 min^-1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Pour s'assurer efficacement que la droite de régression passe par les barres d'incertitude, on peut tracer :\n",
        "- les résidus avec les barres d'incertitude ;\n",
        "- les résidus normalisés directement.\n",
        "\n",
        "Notre critère de décision est le dépassement, en valeur absolue, de la valeur 2 pour l'écart normalisé."
      ],
      "metadata": {
        "id": "LeFRvW5upJbn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#Tracé des résidus\n",
        "\n",
        "plt.figure(3)\n",
        "plt.title(\"Résidus\")\n",
        "plt.ylabel('lnA - modèle affine')\n",
        "plt.xlabel('temps en (s)')\n",
        "plt.errorbar(time,Z1-np.polyval(p1,time), yerr = u_Z1, fmt = 'ro',label=\"Résidus\")\n",
        "plt.plot((np.min(time), np.max(time)), (0, 0) )\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "# Tracé des résidus normalisés z\n",
        "plt.figure(4)\n",
        "plt.title('Résidus normalisés')\n",
        "z = (Z1-np.polyval(p1,time))/(u_Z1)\n",
        "plt.plot(time, z,'bo')\n",
        "plt.xlabel('temps en (s)')\n",
        "plt.ylabel('Résidus normalisés de $lnA$' )\n",
        "plt.plot((np.min(time), np.max(time)), (0, 0) )\n",
        "plt.grid(linestyle=\"-.\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "id": "c4uUW7KAn3k6",
        "outputId": "4c3db82e-4f1c-476c-8024-0c7ab29708a5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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Va4Eagns1DgE3xBEsCStXrkw6Ql58zw9WQ1yiDArlYv6orIb45NqNyNeAHwMtBHsWZ4Cm8DFtFBcXJx0hL77nB6shLlEGhXIxf1RWQ3xy3dP4R0CBdwM/EJHnROQ7IrJVRN4eX7ypdf78+aQj5MX3/GA1xCXKoFAu5o/KaohPTnsaqvpD4IfDr0WkBHgZsAa4nmlyJVV5eXnSEfLie36wGuKydWv2OQ249KBQLuaPymqIz6QGYVLVAVV9SlUfUNU7Ch0qKa7eTJMr3/OD1RCXKINCuZg/KqshPs6M3Ccit4jIQRF5VkTuHGf+e0XkZyKyL3y8P4mcxvhq82Y4cgSGhoKvdtWUmYy8R+4rBBEpBu4FbgY6gCdF5CFVPTBq0X9W1Q9OeUBjjDFA9L6nRETeJSIfD19fF3ZcmK/rgWdV9bCqXgC+DmwqwHqNMcYUUNQ9jc8CQ8BrgT8HeoF/BV6VZ44lwPGM1x1AwzjL/ZqIbATagI+o6vHRC4jIFmALwOLFi9m+fXvW/EWLFlFTU0NbWxt1dXXs3LlzZN7Zs2fZvn07GzZsoL29naqqKjo7Ozl+PPttlixZQlVVFe3t7dTW1rJr164xQRsbG2lra6OmpoaOjg5OnDiRNX/p0qVUVlbS0dFBTU0Nu3fvHrOOjRs30traSm1tLe3t7Zw6dSprfnV1NRUVFXR2dlJVVTWSP+NnwY033khLSwt1dXW0tbVx+nT2uFnLly+nvLycrq4uKisrGd0rcElJCY2NjTQ3N7N27VpaW1s5c+ZM1jIrVqwglUrR19dHRUUFzc3NWfNTqRQbNmygqamJdevW0dLSMqZfnZUrV45cYtjd3T3meO6cOXNoaGgYWUdzczM9PT1Zy6xatYrBwUGGhoZIpVLs378/a35ZWRnr168fWcfevXvp6+vLWmb16tWk02mKioooLi7mwIHsnd158+ZRX18/so49e/bQ39+ftUxxcTHHjh1j9uzZDA4OcvDgwaz58+fPZ82aNSPr2L17N+l0OmuZ+vp6urq6KCsrI51Oc+jQoaz5CxYsoK6ujn379lFfX8+uXbsYGBjIWmb9+vV0dnZSUVFBb28vhw8fzpq/cOFCamtraW1tZc2aNezYsQNVzfo9amhooKOjg8rKSrq6ujhy5EjWOib6PA1L4vM0+rMA0T9Pe/bsyZo/1Z8nVaWnpyevz9P58+cpLy+f1OfpUiJ1jS4izapaLyI/VtVXhtNaVHVNzisZf723Abeo6vvD1+8GGjIPRYnIAqBPVdMi8t+Bd6jqaydar3WNbowx0RWsa3TgYnj+QcMVX0Ow55GvE8DSjNdV4bQRqnpGVYf/HfsisK4A75vF1UFPcuV7frAaXOB7frAa4hR1T2Mz8A6gHvgKcBvwsXz7ngrv+2gDXkfQWDwJ/IaqtmYsc62qngyfvw34E1WdsAsT29MwxpjoCranoarbgD8G/hI4Cby1EJ0VquoA8EHgUeBp4F9UtVVE/lxE3hIu9mERaRWRFuDDBMPOFtToY4e+8T0/WA0u8D0/WA1xinzJrao+AzxT6CCq+gjwyKhpH894/lHgo4V+30y5nghyle/5wWpwge/5wWqIU64dFv7BRPNV9W8KE8cYY4zLct3TGO4EZSXB5bUPha9vBX5U6FDGGGPclGuHhZ8EEJGdQL2q9oav72aajA9ujDHm8qJeclsJXMh4fSGcNi2sWrUq6Qh58T0/WA0u8D0/WA1xitpofBX4kYjcHe5l7AHuL3SopAwODiYdIS++5werwQW+54eprSGusddd3Q6Rrp5S1a0i8l3gl8NJ71PVHxc+VjKGhgpxn2JyfM8PVoMLfM8PU1dDnGOvu7odJnPJbTPg5gXEeUqlUklHyIvv+cFqcIHv+WHqapho7PV8Gw1Xt4Mz42m4YHQHd77xPT9YDS7wPT9MXQ1Rxl6PytXtYI2GMcZMUpSx16eLqONpvF1EysPnHxORB0WkPp5oxhjjtq1bg7HWM11q7PXpIuqexp+paq+INAI3AV8CPlf4WMYY474oY69PF1FPhA9fA/YrwH2q+rCI/EWBMyWmrKws6Qh58T0/WA0u8D0/TG0NmzfH00i4uh2ido3+HYKuy18PvBLoB36U7yBMcbGu0WeObduCK1aOHQuOJ2/dOr3/2zMmToUchOnXCbovf72qPg9UAHfkmc8Zrg56kivf88Pkahi+Vv7oUVB98Vr5Qt1kFZXv28H3/GA1xCnqnoYA7wJqVPXPReQ6YJGqOtlpoe1pzAzV1UFDMdqyZTBqSGtjTA7y2tMQkcZwiFeAzwI3ALeHr3uBewuS0gG+NzC+54fJ1RDntfKT4ft28D0/WA1xyuXw1BAvXiHVoKofAM4DqGo3cEVM2aZcX19f0hHy4nt+mFwNrl0r7/t28D0/WA1xumyjoaqPE+xhAFwM9zoUQESuIWhUjCmoKJ3AzcRr5Y1JSk4nwlV1X/j0M8A3gYUishXYBXwqpmxmhop6YnsmXitvTFKi9nK7TUSagNeFkzaFY4YbUzCT6QQurmvljTHZIncjApxQ1XsJLrf91HTqRmT16tVJR8iL7/khqMG1E9tR+b4dfM8PVkOc8ulG5LVMs25E0ul00hHy4nL+XM9RpNNp505sR+XydsiF7/nBaohT1EYjsxuRL6jqw0yjq6eKivzu9NfV/FHOURQVFXl/YtvV7ZAr3/OD1RCnqKlOiMj/Ad4BPCIiqUmsw1nFxcWXX8hhruaf6BzFaMXFxd6f2HZ1O+TK9/xgNcRpst2IvGE6diNy4MCBpCPkxdX8Uc5RDNeweXNwN/fQUPDVlwYD3N0OufI9P1gNcYrUaKjqOVV9UFUPha9Pqur34olmpgsXz1FEuQ/EGPOinBoNEdkVfu0VkZ6MR6+I9MQb0fj+B861cxSudXDoKt9/70w8cr25rzH8Wq6q8zIe5ao6L96IM9t0+APn2jmKKOdYZqrp8Htn4jFtTmIXwrx57rV/Uf7AuZh/WK7nKKaihrjvA3F5O+Ri3rx53jesvm8DcLeGnLpGF5Fegv6mZJzZ6urexnToGr2oKPhPbzSR4A+wic66Ur88+72b2fIehCnjsFT5OA8nG4zJcHHQkygnkacyf1zHu6eihsmeY8m1Zhd/j6Joampy8uKFKHzfBuBwDaoa6QHMB64HNg4/oq5jqh7r1q1T3z3wgGppqWrwf1/wKC0NplumyXvgAdVly1RFgq+Xyz4dao5iptVrsgF79VJtwKVmjLswvB94CugGHiMYI/yHUdYxlY+ojcYTTzwRafmpkusfuKnKv2xZ9h+T4ceyZfmv29VtEKVmV2vI1XD+qA2rS3zfBqrJ1jBRoxGpl1vg94BXAU+o6mtE5KVMo67R+/v7k44wrlx7cJ2q/HGeSHZ1G0Sp2dUacjWc3+eeg33fBuBuDVGvnjqvqucBRCSlQbfoKwsfy7jM9+PdkzETazZmPFEbjQ4RuQr4FvB9Efk2MM51KGY6c+1mvakwE2s2ZjxRuxF5m6o+r6p3A39G0DX6WwsRRERuEZGDIvKsiNw5zvyUiPxzOH+PiFQX4n1NdK7drDcVZmLNxownp/s0Yg8RjDveBtwMdABPArer6oGMZf4H8ApV/R0ReSfwNlV9x0TrjXqfRnd3N/Pnz59MCU7wPT9YDS7wPT9YDfma6D6NSCfCRWQ9cBewLPN7VfUVeSUMLuF9VlUPh+/zdWATkNnN4ybg7vD5N4B/EBHRArZ6vb29Ixvpk//WyoGf+tWtVjqdJpVKJR0jL1ZD8nzPD1YDwKrF8/jErXUFTBSIevXUNoKu0J8CCnlf6BLgeMbrDqDhUsuo6oCIvAAsAH6euZCIbAG2ACxevJjt27dnrWTRokXU1NTQ1tZGXV0dO3fuHJk3MDDA4cOH2bBhA91d3QwOwsWLFzh/PnsErVQqRSqV4vz588yZM4cXXnhhTEFXXnkl/f39zJ49m3Q6PWYUrtmzU8yadQXpdJo5c2bzwgtjG6irrrqKs2fPUlo6h/7+81y4cGHUOmYza9YsLly4QCqV4ty5c1lXXIjAlVdexdmzfZSWzqW/v3/MOubMmUNxcTEDAxeZNesKent7s+aLCFdeeSV9fX2UlZVx9uxZLl68mLVMaekcRIoYHBxk1qxZY9ZRVFTEvHnz6OvrpaysnLNn+7h4cWDUOkoREQYGBiguLqavry9rfnFxEeXlL66jr6+PgYHsdcydOze8NFwRKeLs2bOj1lFMeXn5yDp6e3sZHBwcZx1DgCAiY9ZRUlJCWVlZxjp6GBzM/ijMnp0inU5TVFSEqnJuVH8cs2aVMHfui+vo6elhaNRt1uXl5Vy8eJHi4mJUhzh3rn/UOmYxd+7cke3ywgsvMPr/p2AdFygpmcXg4OCYq3GuuOIK5syZw7lzZ5k7t4wXXnie4cvwh5edN28e6XSaK664gosXL3L+/Plx1jGbc+f6mTt3Ls8//zyjXXnlPPr7z5NKpabs8zT6swDRP089Pdmfyan+PA0MDFBSUjLpz1P/uX6OHTtGeXk5LS0tY3I2NDTQ1NTEunXraG5uHlPvpUQ6PCUiuzTsvLCQROQ24BZVfX/4+t1Ag6p+MGOZ/eEyHeHr58Jlfj7eOiH64amTJ09y7bXXTrKK5PmeH6wGF/ieH6yGfOXdjUiGT4jIF0XkdhH51eFHATKeAJZmvK4Kp427jIiUAFcCZwrw3iMOHjxYyNVNOd/zg9XgAt/zg9UQp6iNxvuAtcAtwK3h480FyPEksEJEakTkCuCdwEOjlnkIeE/4/DaCO9GTP4tvjDEOiXsclKjnNF6lqgW/mS88R/FBgqFki4Evq2qriPw5we3sDxFc3vs1EXkW6CJoWIwxxoSGx0EZPo02PA4KFO7y8KiNxuMisirzUthCUdVHgEdGTft4xvPzwNsL/b7GGDNdTDQOSlKNxg3APhFpB9IE42toAS65dYLv13X7nh+sBhf4nh9mbg1xDzAGEa6eEhEBfplxug1RVSe7EpkOgzAZY0yuCjXAWEGungpPOt+rqkdHP3KP4jZnBz3J0XD+yZwIi/vkWa583wbgfw0u558pA2HB5GqYkj7SLtVn+ngP4CsEJ8MTHysjl8d0GIQpqskMnmMD7hgf2O9pbgoxDgoFHITpGWAAeA74CcGd4T+Jso6pfERtNB5//PFIy7vm8ccfn9QASXEOqhSV79tA1f8aXM0f5ffU1RqiSLKGiRqNqCfC31CwXRwHje6awDfpdHpSJ8Km4uRZrnzfBuB/Da7mj/J76moNUbhaQ9Su0Y8CV/HijX1X6TQ6pzEdTGawIBtgyPjAfk/dEKnREJHfI+i0cGH4eEBEPhRHMDM5kzkRZgMMGR/Y76kbonYj8t8IOgn8uAY33t0A/HbhY5nJmsxgQTbAkPGB/Z66IWovt08RXD01PE74bOBJVX15TPnyEvU+jZ6eHubNmxdjonj5nh+sBhf4nh+shnwVspfbfwT2iMjdIvJJ4Angy/kGdEVXV1fSEfLie36wGlzge36wGuIU6eopVf0bEdkONAIKvE9VfxxHsCSUlZUlHSEvvucHq8EFvucHqyFOUU+Ep4CXAmXAfOBWEfn4xN/lD1cvccuV7/nBanCB7/nBaohT1MNT3yYYq3sAOJvxmBYOHTqUdIS8+J4frAYX+J4frIY4Rb25r0pVb4kliTHGGOdF3dN4XEScvFLKGGNM/KLuaTQC752u42kYY4yZWNRG442xpHDEggULko6QF9/zg9XgAt/zg9UQp0g39/km6s19Q0NDFBVFPWLnDt/zg9XgAt/zg9WQr0Le3Det7du3L+kIefE9P1gNLvA9P1gNcbI9DWOMMVlsTyNHu3btSjpCXnzPD1aDC3zPD1ZDnKLeEf52ESkPn39MRB4Ukfp4ok29gYGBpCPkxff8YDW4wPf8YDXEKeqexp+paq+INAI3AV8CPlf4WMaYmWDbNqiuhqKi4Ou2bUknMpcTtdEYDL/+CnCfqj4MXFHYSMaYmWDbNtiyBY4eDUb7Pno0eG0Nh9uiNhonROT/AO8EHgk7MLTzIsaYyO66C86dy5527lww3bgr6iBMpcAtwFOqekhErgVerqrfiytgPqJePdXX1+dsd8S58D0/WA0umKr8RUXBHsZoIsEIXRYAABV3SURBVDA0lN+6fd8GkGwNhbx66o+A1cDtYZfov00w5Ou00NnZmXSEvPieH6wGF0xV/uuuizY9Ct+3AbhbQ9RGI7M79EGCbkWqC5wpMRUVFUlHyIvv+cFqcMFU5d+6FUpLs6eVlgbT8+X7NgB3a4jUaKjq/854bAVeDSyPJVkCent7k46QF9/zg9XggqnKv3kz3HcfLFsWHJJatix4vXlz/uv2fRuAuzXkexK7FKgqRBAXHD58OOkIefE9P1gNLpjK/Js3w5EjwTmMI0cK02CA/9sA3K0hUi+3IvIUwdjgAMXANcD/LHQoY4wxboraNfqbM54PAJ2q6uZti8YYYwoup0ZDRP5ggnmo6t8ULpIxxhhX5bqnUR5+XQm8CngofH0r8KNCh0rKwoULk46QF9/zg9XgAt/zg9UQp6g39+0EfkVVe8PX5cDDqroxpnx5iXpz38DAACUlUY/YBd0e3HUXHDsWXGO+dWvhTuhFMdn8LrEakud7frAa8lXIm/sqgQsZry+E0yZNRCpE5Psicij8Ov8Syw2KyL7w8dB4y+SrtbU18ve41H/OZPK7xmpInu/5wWqIU9Q9jbuAXwe+GU56K/DPqvqXkw4g8tdAl6reIyJ3AvNV9U/GWa5PVSPdUz8VgzBVVwcNxWjLlgWXEBpjjG8KtqcR3tD3W0B3+HhfPg1GaBPwlfD5VwgaokTs2LEj8vccOxZtOsTXHfRk8rvGakie7/nBaohT5ANmqtoENBUwQ6Wqngyfn+LSh7tmi8hegkt971HVb423kIhsAbYALF68mO3bt2fNX7RoETU1NbS1tVFXV8fOnTtH5vX19bF9+3Y2bNhAe3s7VVVVdHZ2cvz48ax1LFmyhKqqKtrb21m69GUcOyZjcixdqhw48DQ1NTV0dHRw4sQJAH7wg4V8+tMrSaeLgeHDWcrTTz/NTTedzlrHxo0baW1tpba2lvb2dk6dOpU1v7q6moqKCjo7O6mqqqK3tzerXhHhxhtvpKWlhbq6Otra2jh9Ovs9li9fTnl5OV1dXVRWVjJ6z6ykpITGxkaam5tZu3Ytra2tnDlzJmuZFStWkEql6Ovro6Kigubm5qz5qVSKDRs20NTUxLp162hpaaG7uztrmZUrV1JcXEw6naa7u5uWlpas+XPmzKGhoWFkHc3NzfT09GQts2rVKgYHBxkaGiKVSrF///6s+WVlZaxfv35kHXv37qWvry9rmdWrV5NOpykqKqK4uJgDBw5kzZ83bx719fUj69izZw/9/f1ZywwMDHDs2DFmz57N4OAgBw8ezJo/f/581qxZM7KO3bt3k06ns5apr6+nq6uLsrIy0uk0hw4dypq/YMEC6urq2LdvH/X19ezatWvMoD3r16+ns7OTiooKent7x9wstnDhQmpra2ltbWXNmjXs2LEDVR35HAA0NDTQ0dFBZWUlXV1dHBm1+zzR52lYlM9TbW3tuCPWNTY20tbWNubzNGzp0qVUVlbS0dFBTU3NyGfhBz9YyBe/uJzTp1MsXQq/+7vH+chHKnP6PO3Zsydr/lR/ntLpND09PXl9ns6fP095efmkPk+XpKqXfQC7wq+9QE/GoxfoyeH7fwDsH+exCXh+1LLdl1jHkvDrcuAI8JLLve+6des0isceeyzS8qqqDzygWlqqGpzRCB6lpcH08Sxblr3s8GPZsshvPcZk8rvGakie7/lVgxqifjZdk+R2APbqJf6u5rSnoaqN4dfyyy17ie+/6VLzRKRTRK5V1ZNhV+unx1tOVU+EXw+LyHbglcBzk8lTSMNXSeV69dRkDmcZY6KbaLyOJK5unC4KMUb4K/PM8BDwnvD5e4Bvj/O+88MBnxCRq4FfAg6MXi4pUfrPibM7aGPMi+wftHgUYozwz+eZ4R7gZhE5FK7zHgARWS8iXwyXeRmwV0RagMcIzmkUvNFoaGgo9CrHiLM76KnIHzerIXm+54egBt//QXN1OyQ+RriqnlHV16nqClW9SVW7wul7VfX94fPHVfXlqrom/PqlfN7zUjo6OuJYbZY4u4OeivxxsxqS53t+CGqI8x+0qeDqdoh69dTwGOE3A3813cYIr6zM6z7FnG3eHM8x1anKHyerIXm+54eghqjnG13j6naI+gf/14FHgTeo6vNABXBHwVMlpKurK+kIefE9P1gNLvA9P7xYQ1zjdUyF4Rriuq9rsqLe3HdOVR9U1UPh65Oq+r14ok290deg+8b3/GA1uMD3/DB9anCpm6JhUa+eEhF5l4h8PHx9nYhcH080Y4yZ2Sa6bDgpl200RKRRRIrDl58FNgC3h697gXtjymaMMTOai5cN57KnMQR8LnzeoKofAM4DqGo3eV49ZYwxZnwuXjZ82UZDVR8n2MMAuBjudSiAiFxD0KhMC4sWLUo6Ql58zw9Wgwt8zw/TpwYXLxvO6ZyGqu4Ln36GoFv0hSKyFdgFfCqmbFOupqYm6Qh58T0/WA0u8D0/TJ8a4ryva7KiXj21Dfhj4C+BnwK3MY0OT7W1tSUdIS++5werwQW+54fpVYNrlw3nNAiTiMwDPgAsIegr6vvAB4E/BFpUdVOcIScr6iBMQ0NDFBX5e6+i7/nBanCB7/nBashXIQZh+hqwEngKeD9B/0+3AW91tcGYjPHGAvCJ7/nBanCB7/nBaohTrt2ILFfVlwOEnQieBK5T1fOxJTPGGOOcXPc0Lg4/UdVBoMMaDGOMmXly3dNYIyLDYwEKMCd8LYCq6rxY0hljjHFKriP3FV9+KWOMMdNdTldP+Srq1VPpdJpUKhVjonj5nh+sBhf4nh+shnwV4uqpGaG9vT3pCHnxPT9YDS7wPT9YDXGyRiNDVVVV0hHy4nt+sBpc4Ht+sBriZI1Ghs7OzqQj5MX3/GA1uMD3/GA1xMkajQzHjx9POkJefM8PVoMLfM8PVkOcrNEwxhiTM2s0jDHG5MwaDWOMMTmzRiPDkiVLko6QF9/zg9XgAt/zg9UQJ2s0Mrh6iVuufM8PVoMLfM8PVkOcrNHI4OrNNLnyPT9YDS7wPT9YDXGybkQyDAwMUFKSax+O7vE9P1gNLvA9P1gN+bJuRHK0a9eupCPkxff8YDW4wPf84HYN27ZBdTUUFQVft20bfzlXa/C7KTbGGI9s2wZbtsC5c8Hro0eD15D82N+5sj0NY4yZInfd9WKDMezcuWC6L6zRMMaYKXLsWLTpLrJGwxhjpsh110Wb7iK7eiqD71dc+J4frAYX+J4f3K1h9DkNgNJSuO++sec07OopD7S1tSUdIS++5werwQW+5wd3a9i8OWggli0DkeDreA0GuFuD7Wlk6O/vZ86cOTEmipfv+cFqcIHv+cFqyJftaeSoo6Mj6Qh58T0/WA0u8D0/WA1xSrzREJG3i0iriAyJyLgtW7jcLSJyUESeFZE748hy4sSJOFY7ZXzPD1aDC3zPD1ZDnBJvNID9wK8COy+1gIgUA/cCbwRWAbeLyKqpiWeMMWZY4pcXqOrTACIy0WLXA8+q6uFw2a8Dm4ADsQc0xhgzIvFGI0dLgMwBczuAhvEWFJEtwBaAxYsXs3379qz5ixYtoqamhra2Nurq6ti588UdnL6+PrZv386GDRtob2+nqqqKzs7OMWP1LlmyhKqqKtrb26mtrR23j5jGxkba2tqoqamho6NjzK7m0qVLqayspKOjg5qaGnbv3j1mHRs3bqS1tZXa2lra29s5depU1vzq6moqKiro7OykqqpqJH/Gz4Ibb7yRlpYW6urqaGtr4/Tp01nrWL58OeXl5XR1dVFZWcnoCwdKSkpobGykubmZtWvX0traypkzZ7KWWbFiBalUir6+PioqKmhubs6an0ql2LBhA01NTaxbt46Wlha6u7uzllm5ciXFxcVcuHCB7u5uWlpasubPmTOHhoaGkXU0NzfT09OTtcyqVasYHBxkaGiIVCrF/v37s+aXlZWxfv36kXXs3buXvr6+rGVWr15NOp2mqKiI4uJiDhzI/r9k3rx51NfXj6xjz5499Pf3Zy0zMDDAsWPHmD17NoODgxw8eDBr/vz581mzZs3IOnbv3k06nc5apr6+nq6uLsrKykin0xw6dChr/oIFC6irq2Pfvn3U19eza9cuBgYGspZZv349nZ2dVFRU0Nvby+HDh7PmL1y4kNraWlpbW1mzZg07duxAVbN+jxoaGujo6KCyspKuri6OHDmStY6JPk/Dkvg8jf4sQPTP0549e7LmT/Xn6cKFC/T09OT1eTp//jzl5eWT+jxdypRcPSUiPwAWjTPrLlX9drjMduCPVHXM5U4ichtwi6q+P3z9bqBBVT840ftGvXrqueee4yUveUnOy7vG9/xgNbjA9/xgNeQr8aunVPUmVV09zuPbOa7iBLA043VVOK2gKisrgdx7oXTNcH6fWQ3J8z0/WA1xcuFEeC6eBFaISI2IXAG8E3io0G/S0dExcsfm0aOg+mIvlD40HK5eoheF1ZA83/OD1RCnxG/uE5G3AX8PXAM8D+xT1TeIyGLgi6r6pnC5NwF/CxQDX1bVrZdbd9TDU+l0mpUrUxw9OnbesmUw6nCuc9LpNKlUKukYebEakud7frAa8pX44amJqOo3VbVKVVOqWqmqbwin/3S4wQhfP6Kqtar6klwajMnYvXu3171Qjncy3TdWQ/J8zw+Tr8GlQ9OubofEGw3XTIdeKI0x0fl8aHoqWaMxytatQa+TmUpLg+nGmOlrOgyQNBWs0RglSi+Uxpjpw+dD01PJl5v7ptTmzdZIGDPTXHcd414EY4emsyV+9VScol49NTQ0RFGRvztfvucHq8EFvueHydUQZYCkqZDkdnD66imXtLa2Jh0hL77nB6vBBb7nh8nV4NqhaVe3g+1pZPD92m7f84PV4ALf84PVkC/b08hRe3t70hHy4nt+sBpc4Ht+sBriZI1GhtG9XvrG9/xgNbjA9/xgNcTJGg1jjDE5s0bDGGNMzqzRMMYYk7NpffWUiPwMGOd2nUu6Gvh5THGmgu/5wWpwge/5wWrI1zJVvWa8GdO60YhKRPZe6jIzH/ieH6wGF/ieH6yGONnhKWOMMTmzRsMYY0zOrNHIdl/SAfLke36wGlzge36wGmJj5zSMMcbkzPY0jDHG5MwaDWOMMTmzRgMQkVtE5KCIPCsidyadJyoRWSoij4nIARFpFZHfSzrTZIhIsYj8WES+k3SWyRCRq0TkGyLyjIg8LSIbks4UlYh8JPwd2i8i/yQis5POdDki8mUROS0i+zOmVYjI90XkUPh1fpIZJ3KJ/P8r/D36iYh8U0SuSjJjphnfaIhIMXAv8EZgFXC7iKxKNlVkA8Afquoq4AbgAx7WAPB7wNNJh8jD3wH/rqovBdbgWS0isgT4MLBeVVcDxcA7k02Vk/uBW0ZNuxP4D1VdAfxH+NpV9zM2//eB1ar6CqAN+OhUh7qUGd9oANcDz6rqYVW9AHwd2JRwpkhU9aSqNofPewn+WC1JNlU0IlIF/ArwxaSzTIaIXAlsBL4EoKoXVPX5ZFNNSgkwR0RKgFLgpwnnuSxV3Ql0jZq8CfhK+PwrwFunNFQE4+VX1e+p6kD48gmgasqDXYI1GsEf1+MZrzvw7A9uJhGpBl4J7Ek2SWR/C/wxMJR0kEmqAX4G/GN4iO2LIjI36VBRqOoJ4NPAMeAk8IKqfi/ZVJNWqaonw+engMokw+Tpt4DvJh1imDUa04iIlAH/Cvy+qvYknSdXIvJm4LSqNiWdJQ8lQD3wOVV9JXAWtw+JjBEe999E0AAuBuaKyLuSTZU/De4r8PLeAhG5i+Dw87akswyzRgNOAEszXleF07wiIrMIGoxtqvpg0nki+iXgLSJyhODw4GtF5IFkI0XWAXSo6vAe3jcIGhGf3AS0q+rPVPUi8CDwiwlnmqxOEbkWIPx6OuE8kYnIe4E3A5vVoRvqrNGAJ4EVIlIjIlcQnPh7KOFMkYiIEBxLf1pV/ybpPFGp6kdVtUpVqwl+/j9UVa/+w1XVU8BxEVkZTnodcCDBSJNxDLhBRErD36nX4dnJ/AwPAe8Jn78H+HaCWSITkVsIDte+RVXPJZ0n04xvNMKTTR8EHiX4gPyLqrYmmyqyXwLeTfAf+r7w8aakQ81AHwK2ichPgLXApxLOE0m4l/QNoBl4iuDvg5NdWWQSkX8CdgMrRaRDRP4bcA9ws4gcItiDuifJjBO5RP5/AMqB74ef588nGjKDdSNijDEmZzN+T8MYY0zurNEwxhiTM2s0jDHG5MwaDWOMMTmzRsMYY0zOrNEwM1bYK+3/SDpHIYjItRP1DiwiV4jIzrBPKWMmzRoNM5NdBUyLRgP4A+ALl5oZdsb5H8A7piyRmZas0TAz2T3AS8Kbp/4XgIjcISJPhuMYfDKcVh2ObXC/iLSJyDYRuUlE/iscr+H6cLm7ReRrIrI7nP7b4fRrw//y94XjVPzy6CAisk5EdohIk4g8mtEFxnYR+SsR+VH43mO+N/RrwL+H31MXLr8vrGNFuMy3gM0F/PmZGch2Vc1MdifBmAVrAUTk9cAKgu7yBXhIRDYSdK/xC8DbCXocfRL4DaAReAvwp7zY9fYrCMY0mQv8WEQeBm4HHlXVreH4LaWZIcJ+w/4e2KSqPxORdwBbw/cCKFHV68O7/D9BcIdz5vfXAN2qmg4n/Q7wd6q6Lewapzicvh941aR/WsZgjYYxmV4fPn4cvi4jaESOEXTk9xSAiLQSDPCjIvIUUJ2xjm+raj/QLyKPETRATwJfDhuHb6nqvlHvuxJYTdBlBAR/5E9mzB/ugLJp1HsNu5agW/Zhu4G7wjFKHlTVQwCqOigiF0SkPBx3xZjI7PCUMS8S4C9VdW34+AVV/VI4L52x3FDG6yGy//ka3S+PhoPsbCToPfl+EfnNcd63NeN9X66qr8+YP/xeg4z/j14/MDIsq6r+X4I9oH7gERF5bcayKeD8OOswJifWaJiZrJegU7hhjwK/FY5LgogsEZGFEde5SURmi8gC4NXAkyKyDOhU1S8QjEw4usv0g8A1Eo4pLiKzRKQuwnu2kbEHIiLLgcOq+hmC3l1fEU5fAPw87PbcmEmxw1NmxlLVM+HJ7P3Ad1X1DhF5GbA7PEzUB7yL4D/8XP0EeAy4GvifqvpTEXkPcIeIXAzXmbWnoaoXROQ24DPhsLElBCMZ5tTbsqqeFZHnROQXVPVZ4NeBd4fvd4oXe9t9DfBwhFqMGcN6uTWmQETkbqBPVT+dwHu/DVinqh+bYJkHgTtVtW3qkpnpxvY0jJkGVPWb4eGncYVXUX3LGgyTL9vTMMYYkzM7EW6MMSZn1mgYY4zJmTUaxhhjcmaNhjHGmJxZo2GMMSZn/x/lbUt4vAlB/QAAAABJRU5ErkJggg==\n"
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    {
      "cell_type": "markdown",
      "source": [
        "On valide le résultat si, sur le graphe des résidus normalisés, les points représentés sont inférieurs à 2. Cela signifie qu'il y a moins de deux incertitudes types entre le modèle affine et les points expérimentaux.\n",
        "Si ce n'est pas le cas, il est possible que :\n",
        "* le modèle d'ordre choisi ne permette pas de décrire correctement ces résultats expérimentaux et la loi est autre ;\n",
        "* certaines incertitudes aient été sous-estimées ;\n",
        "* une erreur de manipulation ait été commise."
      ],
      "metadata": {
        "id": "lLYPsViKud3c"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YqU_FcdQyGhq"
      },
      "source": [
        "# Méthode de MC pour la régression linéaire\n",
        "# Méthode de Monte Carlo\n",
        "Une autre méthode (appelée Monte-Carlo) consiste à réaliser un grand nombre d'expériences virtuelles, en faisant varier les paramètres qu'on sait ne pas être connus de manière certaine. Pour simuler un résultat de mesure (l’ensemble des valeurs raisonnablement attribuables à une grandeur), on génère un ensemble de valeurs aléatoires. Selon les cas, pour modéliser les grandeurs mal connues, on choisit une distribution de probabilité  ou uniforme :\n",
        "- normale (gaussienne) si on a des raisons de connaître l'écart-type de la distribution ;\n",
        "- uniforme si on ne pense que connaitre l'étendue de la distribution.\n",
        "\n",
        "### Nombres aléatoires\n",
        "\n",
        "On utilise le sous-module `random` de la bibliothèque Numpy :\n",
        "1. dans sa version la plus simple, l' expression  `rd.uniform(x-a, x+a, N)` permet de créer un array de $N$ valeurs tirées aléatoirement entre $x−a$ et $x+a$ et issues d'une distribution uniforme (autrement dit rectangulaire) ; ici `x`et `a` sont des scalaires ;\n",
        "2. l' expression  `X + rd.uniform(-a, +a, N)` permet de rajouter à `X`, un scalaire __ou un `array`__, un array de $N$ valeurs tirées aléatoirement entre $−a$ et $+a$, issues d'une distribution uniforme ; cette expression permet de gérer le cas où on a un ensemble de différentes valeurs mesurées, auxquelles on rajoute des variables aléatoires uniformes ayant toute la même étendue `a` ;\n",
        "3. l' expression  `X + A * rd.uniform(-1, +1, N)`  permet de gérer le cas où on a un ensemble de différentes valeurs mesurées, auxquelles on rajoute des variables aléatoires uniforme de __différentes__ étendues, contenues dans un array `A` ; ainsi peut-on prendre en compte le fait que la « précision » varie en fonction de la valeur de la lecture à l'appareil.\n",
        "\n",
        "4. l'expression `rd.normal(loc=0.0, scale=1.0, size=None)` crée un array de taille `size` qu’on peut préciser (si on ne le précise pas on obtient un scalaire), contenant des valeurs tirées aléatoirement issues d’une distribution gaussienne d’espérance `loc` et d’écart-type `scale`.\n",
        "    - C’est ce qu’on utlise habituellement si on a un processus qu’on peut raisonnablement penser comme Gaussien, par exemple en application du théorème de la limite centrale (un processus additif de nombreuses variables aléatoires).\n",
        "    - On fait souvent **l’hypothèse gaussienne lorsqu’on souhaite modéliser un résultat de mesurage dont on ne connait pas la distribution exacte, mais dont on connait une estimation de l’espérance et de l’écart-type** (la valeur mesurée et l’incertitude-type, en termes métrologiques).\n",
        "    \n",
        "### Détermination de l'incertitude - type des paramètres de la droite de régression\n",
        "\n",
        "* Le résultat d'une mesure est l'ensemble des valeurs raisonnablement attribuables à la grandeur mesurée. On caractérise cet ensemble par la valeur mesurée (parfois une moyenne), et l'écart-type expérimental ; ce dernier est par définition l'incertitude-type associée à la valeur mesurée.\n",
        "\n",
        "* L'idée pour estimer l'incertitude-type associée à la pente de la droite   consiste à simuler *in silico* le résultat de $N$ expériences virtuelles. Pour cela on  ajoute aux observations de la grandeur portée en $Y$ des valeurs aléatoires dont l'écart-type est égal à l'incertitude-type qu'on a évalué lors de l'expérience. On fait la même chose pour la grandeur portée en $X$.\n",
        "\n",
        "* Pour chaque graphe de $Y$ en fonction de $X$, on fait une régression linéaire et on obtient une valeur la pente. L'ensemble des valeurs de la pente  représente l'ensemble de des valeurs raisonnablement attribuables à cette pente, donc le résultat de la mesure.\n",
        "\n",
        "* On la caractérise par :\n",
        "    * sa valeur moyenne, autrement dit la valeur mesurée ;\n",
        "    * son écart-type, autrement dit l'incertitude-type.\n",
        "\n",
        "* Bien entendu, pour chaque graphe on peut récupérer également l'ordonnée à l'origine (oo) dont on peut calculer la moyenne et l'écart-type."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 368
        },
        "id": "3aAIDln7yCuT",
        "outputId": "732b9b0a-3c3b-4e91-a31b-8adf31111cc1"
      },
      "source": [
        "\n",
        "from numpy import random as rd\n",
        "# importation des biliothèques\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from math import *\n",
        "\n",
        "A = np.array([0.815, 0.753, .691, .639, .585, .537, .494, .454, .417, .383, .351, .322, .298, .274, .252, .230, .210, .195, .176, .162, .148, .135, .126, .114, .105, .097 ])\n",
        "\n",
        "time = np.array([0.17, 0.67, 1.17, 1.67, 2.17, 2.67, 3.17, 3.67, 4.17, 4.67, 5.17, 5.67, 6.17, 6.67, 7.17, 7.67, 8.17, 8.67, 9.17, 9.67, 10.17, 10.67, 11.17, 11.67, 12.17, 12.67])\n",
        "\n",
        "#Proposition des valeurs des précisions :\n",
        "p_time = 0.2/(2*60) # demi - étendue du déclenchement et arrêt du chronomètre\n",
        "delta_A=(2/100)*A # demi - étendue de l'absorbance donnée par le constructeur\n",
        "\n",
        "\n",
        "# Paramètres\n",
        "N_sim = 20000     # Nombre d'itérations souhaitées\n",
        "N = len(time)        # Nombre de données de notre expérience\n",
        "p1_sim=np.zeros(N_sim)\n",
        "\n",
        "\n",
        "for i in range(0, N_sim):   # Création d'une boucle for permettant de générer les N_sim expériences virtuelles\n",
        "\n",
        "    time_sim = time + rd.uniform(-p_time, p_time, N)                 # Génère les N valeurs aléatoires de pH selon une loi rectangulaire\n",
        "\n",
        "    A1_sim = A + delta_A*rd.uniform(-1, 1, N)        # Si on connaissait une précision, on génererait les N valeurs aléatoires de A selon une loi rectangulaire\n",
        "\n",
        "    Z1_sim = np.log(A1_sim)\n",
        "\n",
        "    p1_sim [i]= np.polyfit(time_sim, Z1_sim, 1)[0]\n",
        "\n",
        "\n",
        "plt.figure(2)\n",
        "plt.title('Pour 20 000 iterations')\n",
        "plt.hist(-p1_sim, bins='rice', color='brown', label = \"$k'_{1}$\") # tracé d'un histogramme\n",
        "plt.xlabel(r\"$k'_{1}$ \")\n",
        "plt.ylabel('effectif')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "print(\"k'1 = \", format(np.average(-p1_sim), \"#.5g\"), 'min^-1')\n",
        "print(\"u(k'1) = \", format(np.std(-p1_sim, ddof=1), \"#.3g\"), 'min^-1')\n",
        "\n",
        "print(\"k'1 = \", format(np.average(-p1_sim), \"#.4e\"), 'min^-1')\n",
        "print(\"u(k'1) = \", format(np.std(-p1_sim, ddof=1), \"#.3g\"), 'min^-1')\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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HjgYuL/v/eWnF7Nxw5Zi6mDcWShu3ZlsiSyLilIgYWz6nAktq7nMqsBz4WkTcFhEXR8RLgB0bEsODwI5leiKwtGH9/lImSeqwZpPI3wAHAcuovsRfQ9W1VMcYYD/gwszcF3iStQftKa2OHGLdYUXE7IhYEBELli9fXjM0SdL6aCqJZObDmXlsZu6QmTtm5vGZ+XDNffYD/Zl5S5mfR5VUHoqInQHKz4HtLwMmN6w/qZQNjnFOZk7LzGl9fX01Q5MkrY+mkkhE7B4R8yPirjL/6oj4ZJ0dlgc6Lo2IvypF04FfAzcCs0rZLOCGMn0j8O5yldaBwErHQySpOzQ7OP5V4O+AiwAy846IuBL4TM39fgi4IiI2pxpbOYkqoV0TEScD9wMzS93vAIcDi4GneP5FWZKkDms2iWyZmb+IiMayNXV3mpm3A9OGWDR9iLoJfKDuviRJrdNsEnkkIl5JGeyOiBmAXUpShw13CbVP91W7NJtEPgDMAV4VEcuA3wPvbFlUkqSeMNIDGE/NzPOBnTPzTeV+jhdl5hPtCU+S1M1GujprYBD7iwCZ+aQJRJI0YKTurEUR8Vtg4qBHwft6XEnSupNIZh4XETsB3wOOak9IkqReMdKYyPzMnB4R3yuPgJck6TkjdWftHBEHAUdGxFWDF2bmr1oTliSpF4yURD4F/A+q51WdW8oG7jhM4OAWxSVJ6gEjjYnMA+ZFxKeo7g2ZmplnRcTLgZ3aEaAkqXs1+yj4CcCBwHFl/gngSy2JSJLUM5q9Y/2AzNwvIm4DyMzHysMTJXWhoR6H4qNQ1ArNtkRWR8RmPP/srD7g2ZZFJUnqCc22RC4ArgN2iIizgRlArfeJaOPku9SlTVNTSSQzr4iIW6ke1R7AMZm5qKWRSZK6XrMtETLzHuCeFsYiSeoxzY6JSJL0AiYRSVJtJhFJUm0mEUlSbSYRSVJtJhFJUm0mEUlSbSYRSVJtJhFJUm1N37Eugc/I6mXD/e58uq82hC0RSVJtJhFJUm0dSyIRsVlE3BYR3yrzUyPilohYHBFXD7z0KiK2KPOLy/IpnYpZkrS2TrZETgUaHyf/eeC8zNwVeAw4uZSfDDxWys8r9SRJXaAjSSQiJgFvBS4u8wEcDMwrVS4DjinTR5d5yvLppb4kqcM61RL538DHeP4Vu+OBxzNzTZnvByaW6YnAUoCyfGWpv5aImB0RCyJiwfLly1sZuySpaHsSiYgjgIcz89bR3G5mzsnMaZk5ra+vbzQ3LUkaRifuE3kdcFREHA6MA14KnA9sExFjSmtjErCs1F8GTAb6I2IM8DJgRfvDliQN1vaWSGZ+PDMnZeYU4Fjg+5n5TuAHwIxSbRZwQ5m+scxTln8/M7ONIUuShtFN94mcDpwWEYupxjzmlvK5wPhSfhpwRofikyQN0tHHnmTmD4EfluklwAFD1HkaeHtbA5MkNaWbWiKSpB5jEpEk1WYSkSTVZhKRJNXm+0Q0LN8dImkkJhFpEzfUHwu+qErNsjtLklSbSUSSVJtJRJJUm0lEklSbSUSSVJtJRJJUm0lEklSbSUSSVJtJRJJUm0lEklSbjz2Rz8iSVJstEUlSbSYRSVJtJhFJUm0mEUlSbSYRSVJtXp0l6QWGu2LPl1VpMFsikqTaTCKSpNpMIpKk2kwikqTa2j6wHhGTgcuBHYEE5mTm+RGxHXA1MAW4D5iZmY9FRADnA4cDTwEnZuav2h33xsJHnEgaTZ1oiawBPpKZewIHAh+IiD2BM4D5mbkbML/MA7wF2K18ZgMXtj9kSdJQ2p5EMvOBgZZEZj4BLAImAkcDl5VqlwHHlOmjgcuz8nNgm4jYuc1hS5KG0NH7RCJiCrAvcAuwY2Y+UBY9SNXdBVWCWdqwWn8pewBJbTVUd6j3jmzaOjawHhFbAf8CfDgz/9i4LDOTarxkfbY3OyIWRMSC5cuXj2KkkqThdCSJRMRYqgRyRWZeW4ofGuimKj8fLuXLgMkNq08qZWvJzDmZOS0zp/X19bUueEnSc9qeRMrVVnOBRZn5hYZFNwKzyvQs4IaG8ndH5UBgZUO3lySpgzoxJvI64ATgzoi4vZT9PfA54JqIOBm4H5hZln2H6vLexVSX+J7U3nAlScNpexLJzJ8AMczi6UPUT+ADLQ1qI+T9IJLawTvWJUm1mUQkSbX5PhFJG8R3j2zabIlIkmoziUiSajOJSJJqM4lIkmoziUiSajOJSJJqM4lIkmrzPhFJLeG7RzYNtkQkSbWZRCRJtZlEJEm1OSayEfCx75I6xSTSQ0wWkrqN3VmSpNpsiUhqm/VpTXs5cG+wJSJJqs0kIkmqzSQiSarNMZEu5ZVYknqBLRFJUm22RCR1peFa41611V1siUiSarMl0kaOc0gbzhZKd7ElIkmqzZZIC9jikNrPl2B1Rs8kkYh4M3A+sBlwcWZ+rsMhSepydn21Xk8kkYjYDPgScAjQD/wyIm7MzF+3KwZbF5L0Qj2RRIADgMWZuQQgIq4CjgZakkRMGNLGbUP/j9uSeV6vJJGJwNKG+X7gNY0VImI2MLvMroqI3zQs3h54pKURdrdN/fjBc7CpHz+M4jl4Z8RobKYTRjoHr1jfDfZKEhlRZs4B5gy1LCIWZOa0NofUNTb14wfPwaZ+/OA5gNacg165xHcZMLlhflIpkyR1UK8kkV8Cu0XE1IjYHDgWuLHDMUnSJq8nurMyc01EfBD4HtUlvpdk5vqMbA3ZzbUJ2dSPHzwHm/rxg+cAWnAOIjNHe5uSpE1Er3RnSZK6kElEklRbzyWRiHhzRPwmIhZHxBlDLH9DRPwqItZExIxBy14eETdFxKKI+HVETCnlB5d17oqIyyKiq8eK6p6DiPjriLi94fN0RBxTlk2NiFvKNq8uFzB0pRYd/wfL9jIitm/n8dTRonNwRdnmXRFxSUSMbecxrY8WHf/ciFgYEXdExLyI2Kqdx7S+WnEOGupcEBGrmgokM3vmQzWo/jtgF2BzYCGw56A6U4BXA5cDMwYt+yFwSJneCtiSKpEuBXYv5WcBJ3f6WFt1DhrqbAc8CmxZ5q8Bji3TXwHe1+ljbfPx71vWuw/YvtPH2aFzcDgQ5fONTfDfwEsbln0BOKPTx9ruc1DKpgFfB1Y1E0uvtUSee/xJZj4DDDz+5DmZeV9m3gE821geEXsCYzLz5lJvVWY+BYwHnsnMe0vVm4H/2uLj2BC1z8EgM4B/zcynIiKAg4F5ZdllwDHDrtlZo378ZZ3bMvO+FsU82lp1Dr6TBfALqvuxulGrjv+PAOX/w4uBbr7qqCXnIKrnFJ4DfKzZQHotiQz1+JOJTa67O/B4RFwbEbdFxDnlhD0CjImIgbs4Z7D2jY3dZkPOQaNjqf7ahCqRPp6ZazZwm+3QiuPvNS09B6Ub6wTgu7Wia72WHX9EfA14EHgV8MW6AbZBq87BB4EbM/OBZjfQa0lkQ4wBXg98FNifqhl4Yvmr61jgvIj4BfAE8JeORdkGEbEz8B+o7rvZ5Gzqxw8jnoMvAz/KzB+3N6r2Ge74M/MkYAKwCHhHB0Jrm8HnICImAG9nPZNnryWRDXn8ST9we2n+rQGuB/YDyMyfZebrM/MA4EfAvevYTqeNxiNgZgLXZebqMr8C2KbhgoJufqxMK46/17TsHETEmUAfcNoGRdhaLf03kJl/oeoe6uZu7Vacg32BXYHFEXEfsGVELB5pI72WRDbk8Se/pPqi7CvzB1MeJR8RO5SfWwCnUw0sd6vReATMcTQ0YUtr7AdUXXkAs4AbRiHWVhj14+9BLTkHEfEe4DDguMxcVz96p4368Udl14Fp4CjgnlGKtxVa8T3w7czcKTOnZOYU4KnM3HXErXT6KoP1/VBdQXIv1ZUJnyhlZwFHlen9qVodT1L9hX13w7qHAHcAdwKXApuX8nOomq+/AT7c6WNs8TmYQvUXy4sGbXMXqsHUxcD/Abbo9HG2+fhPKeusAf5A9fbMjh9rm8/BmrK928vnU50+znYdP9Uf1P+vfDfcBVxBw9Va3fhpxb+BQdtv6uosH3siSaqt17qzJEldxCQiSarNJCJJqs0kIkmqzSQiSarNJCK1WUS8rdMxSKPFJCK1SERMj4ivDyrbFTi0QyFJo84kIrXOPsBtg8oOBS7oQCxSS3T1y5ekHrcPcGl5nM5FVHfCL83MRZ0NSxo9JhGpdV4NPEz1lNSLM/OfOxyPNOp87InUAuWdHI8A9wPvzcyfDVq+C/AJ4GWZOWOITUg9wTERqTX2oHrS6hqGeD9NVq8kOLntUUmjzCQitcY+wE+pHtH9tYjYscPxSC1hEpFaYx/grsy8l+odNdeULi5po+KYiNQBETEeOJvqHTcXZ+ZnOxySVItJRJJUm91ZkqTaTCKSpNpMIpKk2kwikqTaTCKSpNpMIpKk2kwikqTaTCKSpNpMIpKk2v4/zTo3hWvDBxkAAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "k'1 =  0.17120 min^-1\n",
            "u(k'1) =  0.000604 min^-1\n",
            "k'1 =  1.7120e-01 min^-1\n",
            "u(k'1) =  0.000604 min^-1\n"
          ]
        }
      ]
    }
  ]
}