From 9ea7fe6ed01d6fd04c1d392e9c95ee9be83c2676 Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Sat, 8 Aug 2015 18:17:15 -0700 Subject: [PATCH] Fixed explanation of time invarient systems. --- 07-Kalman-Filter-Math.ipynb | 40 +++++++++++++++++-------------------- 1 file changed, 18 insertions(+), 22 deletions(-) diff --git a/07-Kalman-Filter-Math.ipynb b/07-Kalman-Filter-Math.ipynb index aa726da..1b67d07 100644 --- a/07-Kalman-Filter-Math.ipynb +++ b/07-Kalman-Filter-Math.ipynb @@ -28,6 +28,7 @@ "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n", "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n", "@import url('http://fonts.googleapis.com/css?family=Arimo');\n", + "@import url('http://fonts.googleapis.com/css?family=Fira_sans');\n", "\n", " div.cell{\n", " width: 900px;\n", @@ -118,9 +119,9 @@ " white-space: nowrap;\n", " }\n", " div.text_cell_render{\n", - " font-family: 'Arimo',verdana,arial,sans-serif;\n", + " font-family: 'Fira sans', verdana,arial,sans-serif;\n", " line-height: 125%;\n", - " font-size: 120%;\n", + " font-size: 115%;\n", " text-align:justify;\n", " text-justify:inter-word;\n", " }\n", @@ -586,9 +587,9 @@ }, { "data": { - "image/png": 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+ "image/png": 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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -620,9 +621,9 @@ "outputs": [ { "data": { - "image/png": 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tOCK7w6nR/TqrVXiw2dEAADWEUg0ALnA6nRVbkt+TFK3/LPtBXlaL/jLqJpOT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\nAC76/6J/ufuQYyGBAAAAAElFTkSuQmCC\n", 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VU/fYKJ27UKhJCzeZHQ8A8BOUagDwYGMuz1b/47ONunipSH+9t6sk6d1PN+pCQZGZ0QAA\nP0GpBgAPdnNslOKahutUzgVNXZKmm2IaqkOzejqde0H//nqL2fEAAJdRqgHAg1ksFtds9YS5ybI7\nnHrh3pK11W/OS1Zhkd3MeACAyyjVAODhBnRppiaRoTqcmaN5K3epX2JTtWhQWxkn8zTzu+1mxwMA\niFINAB7Pz8+q5+5OlCSNn50ki0UaM7Rk9vr12etktzvMjAcAEKUaACqE+29po7qhVbTj0Ekt2XhQ\n99zcSg3q2LQvI1sLk/aaHQ8AfB6lGgAqgMAAf40alCCpZHa6kr+fa/b6tVlJcjqdZsYDAJ9HqQaA\nCuLRvu1VvUqQ1mw/ouSdGXqod4zCalTW5v0n9G3qIbPjAYBPo1QDQAVRrXKgnhwQL6lktjo4sJJG\n3tVJUslsNQDAPJRqAKhAnr6zo4IC/LUoeZ92pZ/U4/3iVK1yoFalHdb6XRlmxwMAn0WpBoAKJKxG\nZT3Uq50k6Y05ybJVCdJTl2evma0GAPNQqgGgghl9d6L8rBbNWr5DR7Ny9czATgoK8NeXyft1MPOc\n2fEAwCdRqgGggomqW0N339RKxXaH3p6/XmE1KuvhPjGSpGkrDpqcDgB8E6UaACqg5y9vXf6vr7fo\ndO4FjR6cKH8/q77ddkI/ZF8wOR0A+B7DS/XkyZMVFRWl4OBgxcXFKSmJNX4AYLQ2jeqod8doXSgo\n0vsLNqnBddV1b4/WsjucmrHqe7PjAYDPMbRUz507VyNGjNDYsWOVlpamxMRE9erVSxkZ3JEOAEb7\ncbb6vQWbdP5ioZ4f0lkWi/Rl6g/KPJNvcjoA8C2Gluq3335bDz74oIYPH66mTZtq4sSJqlu3rqZM\nmWLkMAAASV3b1FdCywidybuof3+9Rc0b1NYNLeuosNihd+avNzseAPgUw0p1YWGhtmzZop49e15x\nvmfPnkpOTjZqGADAZRaLRWOGdJEkvTV/vQqL7PrTzY0lSZO/SNXZcxfNjAcAPsXfqAudPn1adrtd\nderUueJ8WFiYMjMzr/p/UlNTjRoePoifH0C6rpJTUXWqKD0rT69+9KX6xkWoXs1gHTtzUX+dtFDD\ne0SbHRHwKPztwLWKji799ylP/wCACsxqtWjYjY0kSf/8Zr/+uWyfjp0pmaGeufqQCgrtZsYDAJ9h\n2Ex1rVq15Ofnp6ysrCvOZ2VlqW7dulf9P3FxcUYNDx/y4ywDPz9AibbtYvTRynRlnMxT03o2Pdyj\nsdIyLih133Fty7LoyTv4rAD87YC7cnNzS/2+YTPVAQEBat++vb755psrzn/77bdKTEw0ahgAwM9U\n8vfT6MElv2c/WfG92jcK1ZjLTwZ5c956FdsdZsYDAJ9g6PKPUaNG6ZNPPtFHH32kPXv26JlnnlFm\nZqYee+wxI4cBAPzMw31iVcsWol0ZOXI4pQFdmqlJZKgOZ+Zo3spdZscDAK9naKkePHiw3n33XY0b\nN04xMTFKTk7W4sWLFRkZaeQwAICfCQmqpBF3dZQkfbLioPz8rPrL3SWz1+NnJ8npdJoZDwC8nuE3\nKj7++ONKT09XQUGBUlJS1KVLF6OHAABcxZMDOqhyoL9SDmZr055juu+WNgqvVVU7Dp3Uko0HzY4H\nAF6Np38AgJeoXiVIAxMbSJJem5WkwAB/jbyrk6SS2WoAQNmhVAOAFxnSpaEC/K1amLRXuw+f0qN9\n26t6lSCt3X5UyTszzI4HAF6LUg0AXqRWtSDdHh8hSXp99jpVqxyoJwfEu44BAGWDUg0AXub+GxvJ\nz2rRzO+263Bmjp6+s6OCAvy1KHmfdqWfNDseAHglSjUAeJl6NUM0pHtr2R1OvTk3WWE1KuuhXu0k\nSW/MSTY5HQB4J0o1AHihHzd/+WjxVmWdydfouxPlZ7Vo1vIdOppV+q5gAIA/jlINAF6oZVSY+ndu\nqoLCYv3js42KqltDd9/USsV2h96ev97seADgdSjVAOClXhhask/ApC9SlJtfoOcvz17/6+stOp17\nwcxoAOB1KNUA4KU6tojQTTENlXf+kiZ/kaI2jeqod8doXSgo0vsLNpkdDwC8CqUaALzYj7PV73y6\nQRcKilyz1e8t2KTzFwvNjAYAXoVSDQBerEf76xXXNFynci7o4yVb1bVNfSW0jNCZvIv699dbzI4H\nAF6DUg0AXsxisbhmqyfMTVax3aExQ0qO35q/XoVFdjPjAYDXoFQDgJcb0KWZmtWvpaNZuZq9fKf6\nJjRRiwa1lXEyT7OX7zA7HgB4BUo1AHg5q9Xiem71+NlJkqS/3JMoSXp9zjo5HE7TsgGAt6BUA4AP\nGNqjterXsWnPkdP6Yt1eDeneWpFh1bTnyGl9mbzP7HgAUOFRqgHAB1Ty99PowQmSpNdmJamSv1XP\nDio5Hj97nZxOZqsBwB2UagDwEcN7x6p29RCl7D2u5VvS9XCfWNWsFqwNu3/Q2u1HzY4HABUapRoA\nfERIUCWNGNhJkvTazCRVDg7Q03d2kPTftdYAgGtDqQYAH/LEgHhVDQnQiq3p2rTnmJ4a0EEhQZW0\nZONBbTuYaXY8AKiwKNUA4EOqVwnSkwPiJZWsrQ61heiRPrGSpNdnrzMzGgBUaJRqAPAxIwZ2UlCA\nvxYm7dWu9JMaNShB/n5WzV21S4eOnzU7HgBUSJRqAPAxdWpW0UO92kkqmZ2uX8eme3u0lsPh1Fvz\nkk1OBwAVE6UaAHzQc/d0lp/VolnLd+hwZo7+ck/J5jAfL0lT1pl8k9MBQMVDqQYAH9Twuuoa2r21\n7A6nJsxZpxYNa6tfYlMVFBZr4ucbzY4HABUOpRoAfNTzQ66cnR4ztOR48hepyjt/ycxoAFDhUKoB\nwEe1jApT/84ls9PvfrZBCS0j1a1NA+XkF+jDrzabHQ8AKhRKNQD4sBeGdpEkTVqYopz8Atds9dvz\n1+tSYbGZ0QCgQqFUA4AP69giQjfHROnchUJNXpii2zo0Vpvr6+hEdr6mf7vd7HgAUGFQqgHAx71w\nb8ls9bufbdDFS8WutdZvzFknu91hZjQAqDAMK9UffvihbrrpJlWvXl1Wq1VHjx416tIAgDLUPTZK\n8c3CdSrngj5eslWDb2qphtdV14Efzmhh0l6z4wFAhWBYqb548aJuu+02/e1vfzPqkgCAcmCxWFxr\nqyfMTZbT6dRzdydKksbPXien02lmPACoEAwr1c8884yef/55de7c2ahLAgDKSf/OzdS8QS0dzcrV\nzO926MFe7VTLFqLUfce1ZtsRs+MBgMdjTTUAQFarRWOGlMxWvzYrSQH+fnpyQLwk6c15682MBgAV\ngr+Zg6emppo5PCo4fn6AX3ctn48m1R0Krxms/RnZen3qV+rcOFSB/lZ9tX6/5n+9UlF1qpZBUqB8\n8bcD1yo6OrrU75c6Uz127FhZrdZSv9asWWNoYACAOfz9rPrTzY0lSR99d0C2kAD1jYuQJM1ck25m\nNADweBZnKXegZGdnKzs7u9QLREZGKjg42HWcmpqqDh066PDhw6pfv/4v3p+bm+t6bbPZriUzfNyP\nswxxcXEmJwE8j7ufj8IiuxrdO1E/nMrTZ38brNbXh6npA++rkr+fjswZoetqVjEyLlBu+NsBd/1W\nhy11pjo0NFRNmjQp9eunhRoAULEFVPJzPad63Iw1alyvpgZ0aabCIrveX7DJ5HQA4LkMu1ExMzNT\naWlp2r9/vyRp165dSktL09mzZ40aAgBQDob3jtF1Nato64FMfb3hgEYPLnm83uQvUpR/sdDkdADg\nmQwr1R988IFiY2N13333yWKxqE+fPmrfvr2+/PJLo4YAAJSD4MBKrudUj5u+RgktI5TQMkJnzxVo\n6pKtJqcDAM9kWKl++eWX5XA45HA4ZLfbXf8+8MADRg0BACgn/3N7e9WyhWjjnmP6bvMhV8l+59MN\nKmbrcgD4BZ5TDQD4hcrBAXp2cIIk6ZXpa9Qvsaka16up9BM5+nzNHpPTAYDnoVQDAK7qif7xqlE1\nSGu3H1XSjqMaNaiTJOnNeclsXQ4AP0OpBgBcVbXKgXpmYEdJJbPVw24t2bo8Ze9xrd1+1OR0AOBZ\nKNUAgF/19J0dVTUkQMu3pGvb95murcsnzE02ORkAeBZKNQDgV9WoGqw/39FBkjRu+lo90T9eQQH+\n+mr9fu05csrkdADgOSjVAIBSjRyUoMpBlbR44wFlnMzVsFvbSpLenr/e5GQA4Dko1QCAUtWyhejx\n/iVbO4+bsVajBiXIYpH+8812ZZ7JNzkdAHgGSjUA4Dc9OzhRQQH+Wpi0VwWFxerfma3LAeCnKNUA\ngN90Xc0qeqRPrCTp7zPWavTlZ1hP/iJF59m6HAAo1QCA3+cvQzoroJKf5q/epZrVgl1bl3/M1uUA\nQKkGAPw+EbWr6cHb2snplF6bmaTRg9m6HAB+RKkGAPxuY4Z2kZ/VolnLd6hVVJhr6/IFa9m6HIBv\no1QDAH63htdV1/0928rucOqNOetcW5dPmMvW5QB8G6UaAPCH/PXeLrJaLZq2bJtuiolSaLVgti4H\n4PMo1QCAPyQ6IlT33NRKxXaHJn62ka3LAUCUagDANfjf+7rKYpE+WrJVd3RtztblAHwepRoA8Ie1\naFhbA7u1UGGRXdOWpbF1OQCfR6kGAFyT/72vqyTpn19u1n23tGHrcgA+jVINALgm7Rpfp9sTm+ji\npWJ9mbyPrcsB+DRKNQDgmr14fzdJ0qSFKXrwtnaS2LocgG+iVAMArll8s3q6Nb6RzhcUKWXfMXVq\nUbJ1+dSlaWZHA4ByRakGALjlx9nqiZ9v0sO9YyRJ7366QXa2LgfgQyjVAAC3dG5dXzfFNFTe+Us6\nkpWrqLrV9f3xs/p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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1022,9 +1023,9 @@ "outputs": [ { "data": { - "image/png": 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J386doXPni/vA0io162wAk8nk9gAuWLCAsrIy5s2bR15eHsOGDSM5OZmAgIDm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\n", 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Z6tOnz3keiTRnek6kLvScNK2cLz/hP+89zY9dm25izq+8krAjxYTlleBf6mRn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\njwUFhHLnqKm0iekEoGUpIiIizYSCuYg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LFy9W165dG90/0hGlTtFdJLEEHgAAAMJTk4L09OnTdeutt2rMmDEyTbNJB647Kn38FNM7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\nPp8vWLBATz31lP74xz9q8+b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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -1309,7 +1310,7 @@ "\n", "We derived this equation in that chapter by using techniques that are much easier to understand. The advantage of the Taylor series expansion is that we can use it for any arbitrary set of differential equations which are time invariant. \n", "\n", - "Time invariant? This means equations that do not depend on time. For example, $f(x) = sin(t)t$ is not time invariant; the value will be different at different times due to the multiplication by t. On the other hand $f(x) = sin(t)*3$ is time invariant. $x(t)$ is dependent on time, but that is allowed. This is because to be time invariant it must be true that if $f(t) = x(t)$ then $f(t+\\Delta t) = x(t+\\Delta t)$. This will be true for the second equation, but not the first.\n", + "Time invariant? This means systems that do not depend on time. Suppose the input is $x(t) = \\sin(t)$, and the sytem is $f(x) = t\\times x(t) = t \\sin(t)$. This is not time invariant; the value will be different at different times due to the multiplication by t. On the other hand $f(x) = 3 \\sin(t)$ is time invariant. The input $x(t)$ is dependent on time, but that is allowed. This is because to be time invariant it must be true that if $f(t) = x(t)$ then $f(t+\\Delta t) = x(t+\\Delta t)$. In other words, the output is just time shifted, not altered. This will be true for the second equation, but not the first.\n", "\n", "However, we often use a Taylor expansion even when the equations are not time invariant. The answer will still be reasonably accurate so long as the time step is short and the system is nearly constant over that time step." ] @@ -2005,7 +2006,7 @@ "data": { "image/png": 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IhyAiIiJaSnSCDqXVV/FdwXHcrL8+Yb+vRxC2rn8YSVFbYG8ntUKFNF/ThvATJ04Y/fzn\nP/8ZCoUCOTk5uP/++yc959ixYxgYGEBWVhZkMhliYmJQXl6Od955hyGciIiIaBpDw4PILT+D0/lf\nQNVRP2F/RFAstiY8jOjQBIhF0zY00CI3q55wtVoNnU435Sg4AFy6dAmbNm2CTCYzbNuxYwd+9atf\noba2FiEhnBSeiIiIaLyefjXOF32NC9e+Qnd/l9E+sUiM9as3YmvCwwj2WWmlCsncZhXCX3jhBaxf\nvx4pKSlTHqNUKrFixQqjbb6+voZ9U4XwvLy82ZRCZDV8VsmW8HklW7Icn1d1fxtKG6/gVnMRtDrj\nxXXsJVJE+CYgKiAZLjIFVLc7oLq9/P4ZWZsgALdbZLhW5YJrVS4oqnZB4fvzv+6MQ/hLL72EnJwc\nXLhwASKRaMrjpttHREREtNwJgoDm7jqUNlxBXXvFhP1OUldEB2xAhO86SO24uI6lDQ6LUF7npA/d\n1S4ornZGR4/9nUfN+z4zCuEZGRn4+OOPcfr0aYSGhk57rJ+fH5RKpdE2lUpl2DeVpKSkmZRCZDWj\nIzR8VskW8HklW7JcnletTouiW5fxXf5x1CpvTNgf5B2OrQkPY31EGiQSziJtKW1dAnKKgYvFQE4R\nkFsOaOafsU0y+W/4hRdewCeffILTp09j9erVJi+YkpKCV155BRqNxtAXnp2djcDAQPaDExER0bKj\nGezH5dJvcabgS7SpVRP2x4QmYmvCLkQErWVHwQITBAE364GLRSOhuxgoqzF9nrscSIsDUmOBtFjz\n1DJtCH/uuefwwQcf4PPPP4dCoTCMcMvlcjg7OwMA9u3bh9zcXJw6dQoA8NRTT+H111/Hnj17sH//\nflRUVODNN9/EgQMHzFMxERERkQ3o6m3HucJ/4ELxCfRreo32SSR2SI5Kxz3rH4a/Z7CVKlz6BocE\n5FeMjXJfLAaaO0yftypIH7ZT4/S/R4UAYvHY/yB1dU1z8gxNG8KPHDkCkUiEbdu2GW0/cOAAXn31\nVQD6ly2rqqoM+1xdXZGdnY3nnnsOSUlJ8PDwwMsvv4yMjIz5V0tERES0yDW21uJ0/nHkVZyb8LKl\nk4Mcm+Luw6a4H8LVeerZ5mhuOtQCcq7rR7pzioHvS4EBE60ldhIgMXIscKfFAb4eC/83EtOGcJ1O\nZ/ICmZmZE7atXbsWZ8+enXtVRERERDZEEATcqCvCt/mfo7y2YMJ+b4U/0tc/iA0xWyGz58uW5iAI\nAqoa9KPboyPdJdWmz3OTA6lrR1pL4oDkaMDJwfJtQOz6JyIiIpqjYe0Q8m9cwHf5x9HYWjNhf5h/\nFLYm7EJseDLEYonlC1xChoYFFNwYG+W+UASo2k2fFx4w1s+9MQ6IDjVuLbEWhnAiIiKiWerT9OBi\n8Tc4V/h3dPUaJ0GRSIy4lXdha8LDCPOPslKFtq+zW8Cl6yMj3UX61pJ+zfTn2EmA9avHAndqLODv\nZf3APRmGcCIiIqIZalOrcLbg77hUkg3N0IDRPqmdDHev2YYt6x6Et5u/lSq0TYIgoKZJH7gvXNOP\ndJdU6xfKmY7CBUhZqx/pTosFNsRYp7VkLhjCiYiIiEyoVVbidMFxFFTmQBCM35mTO7lhS/z9SIu7\nD84OcitVaFuGhgVcq9S3lOSMjHQ3tZk+L9R/bIQ7LQ5YE7Y4WkvmgiGciIiIaBI6QYeS6jx8l38c\ntxpKJuz38wjG1oRdSIzcDHu7O1dUpPG6ekZaS0ZC95VSoG9g+nMkEmB9xFjgTosFArxtM3BPhiGc\niIiIaJzBYQ1yy87gdMEXaO5omLB/dXActibsQnTIei6uMwlBEFCrNF4Qp/iW6dYSV2d9a8lo6N4Q\nDbg4Ld1/vgzhRERERAC6+7pwoehrnC/6Gj39xquxiMUSJKzeiK0JDyPIO9xKFS5Ow8MCrt00XhCn\nocX0eSF+xgvirA0HJJKlG7rvxBBOREREy5qqowFn8r/A92WnMaQ1XtnFQeqEtNgd2Bz/ANzlXlaq\ncHFR9wq4fH1slPtyCdDbP/05YjGwLmJs2fe0OCDIZ/kE7skwhBMREdGyIwgCbjWW4rv84yipyoUA\n414Jd7k30tc9iLvX3AtHmZOVqlwcbisFwzSBF4uA4irA1HqOLo4jrSUjo9x3xQBy5+Uduu/EEE5E\nRETLhlanxbWbl/Bd/nHcVlVO2B/ssxJbE3ZhXUQqJMtwcR2tVkDRLeMFceqbTZ8X7DvSWjIyP3fs\nyuXVWjIXDOFERES05A0M9uNyySmcKfgC7d0TG5bXhCVha8IurApcs6xetuzuFXCldGRBnGv61pKe\nGbSWxK0cCdzx+vAd7Lt8/pmZC0M4ERERLVmdPW04V/gPXCw+gf7BPqN9dhJ7bIhOR/r6h+DnEWyl\nCi2rvlnAxaKx+bmv3TTdWuLsCNy9ZmyawLvWAK5sLZk3hnAiIiJachpaanC64DiuVpyHVjdstM/Z\nQY5NcT/ExridcHV2s1KFC0+rFXC9ynhBnNsq0+cFehsviBO3ErCzY+g2N4ZwIiIiWhKGhodQVnsV\n54u+RsXtaxP2e7sF4J71D2FD9D2Q2susUOHC6ukbaS0pGpu1RN07/Tki0UhrSdzYrCUrfLGsWnKs\nhSGciIiIbJYgCKhuKkdu+VkU3LiAPk3PhGPCA6KxNWEX1oYnQywSW6HKhdHQIowtiFMEFN4EtNrp\nz3Fy0LeWjI5y370GULgwcFsDQzgRERHZnOaORuSWn0FexVm0dU3ssRCJxIhfdTe2JuxCqN9qK1Ro\nXlqtgJJq4wVxappMn+fvqX95cnR+7vgIwJ6tJYsCQzgRERHZhO6+LhRUXkBu+VnUKm9MeoyH3BtJ\nUem4e802eCn8LFyh+fT2C/i+dGxBnJzimbWWrA0fG+VOiwVC/dlaslgxhBMREdGiNTiswfWqXOSW\nn0FZbQF0uon9Fo5SJ6xfnYbkqHSEBUTbZMtJU+vYgjg5xUDBDWDYRGuJo0y/CM5oP3fKWsBNzsBt\nKxjCiYiIaFHRCTrcrC9BXvkZFN68hIE7phYEAInYDjGhCUiOSseasCTY20mtUOnc6HQCSmuMF8Sp\nbjR9np/n2II4aXHA+tVsLbFlDOFERES0KDS13UZumb7Pu7OnbdJjwvyjkByVjvURqXB2dLVwhXPT\nNyAgt2xs2fdLJUBnt+nz1oSNjXJvjAPCAthaspQwhBMREZHVdPW2o7ThMm61FKPj4uSTWHsr/JEU\nnY6kyM3wdvO3cIWzp2o3XhAnv8J0a4mDFNgQM7bse8pawN2VgXspYwgnIiIii9IM9qOo6gpyy86g\noq4IgjBxyUZnBzkSVm9CcnQ6QnwjFu0IsE4noLx2bNn3i8XArQbT5/m4j8zLPbLs+/rVgNR+cX5G\nWhgM4URERLTgtDotbtQVIbf8DIpuXsbgsGbCMXYSe8SGb0BS1BbEhCRAIll8MaVfIyCvbGyUO6cY\n6JhBa0l06NiMJWlxwMpAtpYsd4vv6SYiIqIlQRAE1LdUI7f8DPIrzkPd1zHpcb6uIQj3icWue38M\nR5mzhaucXnOH8YI4VyuAoeHpz5FJgQ3RYy9QpqwFPBUM3GSMIZyIiIjMql3dgqsV55BbfgbK9rpJ\nj/HzCEZyVDoSIzej6kYtAFg9gAvCSGvJyCj3xWKgcvLyjXi76cP2aOhOWA3IpAzdND2GcCIiIpq3\nfk0vCm9eQm75GdyqL4EAYcIxcic3JEZuRnJUOoK8wwztGFWotXS5AIABjYC88rFR7pzrQFuX6fOi\nQowXxIkIZmsJzR5DOBEREc2JVjuM0tp85JWfxfWqXAxpByccI7WTIW7V3UiOSsfq4DhIxBIrVKrX\n0iEg5/rYSHdeOTA4NP05UnsgOXps2ffUWMDLjYGb5o8hnIiIiGZMEATUqiqRW3YG+TfOo3dg4luJ\nIpEYkcFxSI5OR1z4XZBJHa1S543bI7OWjMxccmMGrSWeipGwPTLKnRgJOMgYusn8GMKJiIjIpJbO\nJuRVnENe+Vm0dE6+vGOQdziSorYgMXITFM4eFq1PMyjgaoVxP3drp+nzVgcbL4izegVbS8gyTIbw\nc+fO4fe//z3y8/PR2NiIzMxMPPvss1MeX1NTg/Dw8AnbT5w4gR07dsyvWiIiIrKY3n418isvIq/8\nLKqbyic9xt3FC4lRW5ActQX+nissVltbl2AI2xeL9K0lmondMEbs7YCkqJEFceKB1LWAtzsDN1mH\nyRDe29uLuLg4PPvss9i9e/eM/+/w5MmTiI+PN/zs7u4+9yqJiIjIIoaGB1FSnYe8irMoqb4KrW7i\nfHwOUiesW5WC5Oh0rAxcA7FIvKA1CYKAm/UwWoWyfAbvcnq4Gr9AmRTF1hJaPEyG8J07d2Lnzp0A\ngD179sz4wh4eHvDx8ZlzYURERGQZOkGHqsYy5JWfQUFlDvo1vROOEYsliAlJQFLUFqwNT4bUTrZg\n9QwOCcivMF4Qp3nyKcaNrArSt5SMBu/IFYBYzNBNi9OC9YQ/8sgjGBgYQEREBDIyMvDoo48u1K2I\niIhoDlTt9cgtP4u88jNo726Z9JgQv9VIjkrH+og0yJ0UC1JHV68ERdUu+DRX32KSWwYMzKC1JDFy\nrJ87NRbw9WDgJtth9hAul8vx9ttvIy0tDXZ2djh+/DieeOIJZGVl4emnn57yvLy8PHOXQrQg+KyS\nLeHzSnfqH+xFTWsJqlqK0dbTNOkxLg5uCPeORbh3LFwdPYAhoKK00iz3FwSgvlWGa9XOKKpywbVq\nF1Qr15k8z9VpGLGhPYgP70VcWA9iVvTCQTo2F3ldlf4XkSVERETM+xpmD+Genp7IyMgw/JyQkIC2\ntjYcOnRo2hBOREREC2NYO4S69gpUtRSjsaNq0oV0pHYOCPWKQbh3LLzlQWabIWRoWISKekdcq3Yx\nhO72bnuT5wV5DSAurBfx4T2IC+tBmO8AxAvbek5kURaZojA5ORlHjx6d9pikpCRLlEI0Z6MjinxW\nyRbweSWdTovK+uvILT+DazcvQTM0MOEYicQOa8OSkRy1BTGhibCTmA7HpnSoBVy6PrIKZTHwfSnQ\nr5n+HIlYQFRwH7bf7Yy0kX5uP09HAI4AvOZdE5G5dXXNYGlVEywSwgsLCxEQEGCJWxERES1rDS01\nyC0/g6sV59DV2z7pMSsDYpAcnY51q1Lh5OAy53sJgoDqxrFpAi8WASXVps9TuOinBxzt57YbKICD\nVOD/NNKyMqMpCisr9X1gOp0OtbW1KCwshKenJ4KDg7Fv3z7k5ubi1KlTAICsrCxIpVKsW7cOYrEY\nX375JQ4fPoxDhw4t7CchIiJapjp72nC14hxyy8+isbVm0mN83AORHJWOpKjN8HT1ndN9hoYFFFaO\nLYhzoQhQtpk+Lyxg7OXJtDhgTZjxrCV5eRPbY4iWOpMhPDc3F1u3bgWgX0Hqtddew2uvvYY9e/bg\n6NGjUCqVqKoaexNCJBLh4MGDqK2thUQiQWRkJDIzM/HUU08t3KcgIiJaZgYG+3Ht5iXklp9BZV3x\npH3eckcFEiI3ITkqHcE+K2fd593VM9JaMjLK/X0Z0Dexq8WIRAKsjzCenzvAm7OWEN3JZAhPT0+H\nTqebcn9mZqbRz7t378bu3bvnXxkREREZ0eq0KK8tQF75WRRVXcHQ8MR5/OztpIgLvwvJ0emIDI6H\nRDKzzlNBEFCrNF4Q53qVfjaT6bg6AylrR1ahjAM2xADOjgzdRKZYpCeciIiI5kYQBNQ130Ju+Rnk\nV5xHd//EF8JEEGF1cBySorYgflUKHKSOJq87PCzg2s2xwH2xCGhsNV1PiJ9+dDstXv/7mjBAImHo\nJpothnAiIqJFZlg7hKrGMpRU56GkOg/NnY2THhfgFYrkqC1IjNwMNxfPaa+p7h1rLckpBq6UAr39\n09chkQDxq8baStLigEC2lhCZBUM4ERHRItDZ04bSmnyU1lxFxe3CSacUBACFsweSojYjKTIdgd6h\nU17vtlLAhaKRqQKLgOIqYJruUgCA3GmstSQtDrgrBnBxYugmWggM4URERFag1WlR01SB0pqrKK25\nioYpZjUBAJm9A+JXpSA5Kh0RQWshFkuM9g8PCyi6NTbKfbEYqG82XcMKX33YTo3Vj3THrmRrCZGl\nMIQTERFMM62NAAAemElEQVRZSHdfJ8pqC1BacxVltQXo1/ROeaynwhdrQpMQE5qIVUFrILWTjV2n\nV8DlkrFR7sslQI+J1hKxWN9aMn7WkmBfBm4ia2EIJyIiWiA6QYc61S2U1lxFSc1V1KluTjqVIKBf\nvXJV4BrEhCZiTWgivN0CDFMK1qkEXCwWDCPd126abi1xcQTuXjO2IM7dawC5M0M30WLBEE5ERGRG\nfQM9KL9dONJmko+eSWYzGeXm4omY0ETEhCYiMjgOMqkjtFoBxbeAT74Dcor1fd11KtP3DfIxXhAn\nbiVgZ8fQTbRYMYQTERHNgyAIaGytQclIb3d1UwUEYfJharFIjLCA6JHR7gT4e4agt18/U8nnZ/Wh\n+9J1oLtv+nuKRPqQPTrKvTEOWOHHwE1kSxjCiYiIZmlgsB836q6NtJnko6tn6rXb5Y4K/Wh3WCIi\nV8SjQ+2Mi0XAmx/oX6S8dhPQaqe/n7OjfqaS0QVx7l4LuLK1hMimMYQTERGZIAgCmjsaDKPdtxpK\nodUNT3qsCCKs8ItATGgiooIT0dUbjkvXRXj7mP5Fylql6fsFeI28PDky0h2/iq0lREsNQzgREdEk\nBoc0qKwvNszd3aaeujHbSeaC6JD1CAtIRndvAvIrnPHHj4BL1wH11BOgANC3lqwNN14QJ8QPhpcy\niWhpYggnIiIa0dql1L9QWX0VlfXXMaQdnPLYIO9w+LpvRHffBlTWBeC9v4lQUGm6tcRRNjJryUjg\nvnsN4CZn4CZabhjCiYho2RrWDuFWQ6lhJhNVR/2Ux0rtnSB32Ire/lTcVoXjHxdkqJ58NXkj/p7j\nFsSJA9ZFAPZsLSFa9hjCiYhoWenobkVZ7ejy8NemXB5+aFiKoaE0DGg2or45AkU3XdDZYzo8rw03\nXhAnLICtJUQ0EUM4EREtafrl4ctRMtLb3TjF8vC9/W5o6ViL/oGNaGyNRGWdAsPa6cOzgxS4a83Y\nsu8pawF3VwZuIjKNIZyIiJYcU8vDC4II7eogNLVGoUO9Hsq2NVC1u5q8rq/HyII4I6Pc61cDUnuG\nbiKaPYZwIiKyefrl4W+OTCGYj9uqSqP9w8NSqDpWoak1Csq2GDS3x6BvwNHkdWNCxwJ3WhywMpCt\nJURkHgzhRERkk3oHulFeW2gY7R6/PHzfgAJNrVEjv6LR0rkSOt30/8lzkALJ0WP93KmxgAdbS4ho\ngTCEExGRTZhqeXhBADq6g9DUmoym1mg0tUahqyfA5PW83cbC9sY4ICGSrSVEZDkM4UREtGgNDPaj\n4va1kSkEr6Krtx3DWns0t69CU+su/Uh3WxQ0g3KT14oKGQvcaXHAqiC2lhCR9TCEExHRoiEIAlQd\n9YYFc241lqGnzwlNbVFoan0QTa1RaO5YCZ3OftrryKRAUtTYNIGpsYCngoGbiBYPhnAiIrKq0eXh\nS2quoqT6Kqoa7Ed6ubegqe1n6OwONHkNL7exsJ0WByRGAjIpQzcRLV4M4UREZHGjy8NfqyzExeIB\n1DevRFPrOjS1PYEBjcLk+ZErxs1aEgusXsHWEiKyLQzhRES0oARBQEd3C6oay1B4sxpn8gdQXuON\nprZoqNq3m2wtkdrrW0sMs5asBbzdGbiJyLYxhBMRkVlpdVo0ttbgVkMZLpeokFMsQlVDEBpbo9HZ\nvdnk+R6uAtJiRYaR7qQowEHG0E1ESwtDOBERzcvAYD9qlTdQfrsc5wvVyCt3QH3zKjS1bkT/DFpL\nwgOHsTnezjDSHblCBLGYoZuIljaGcCIimpWO7lZUN5Wj6GYVzhZqcL3KA00tkVC174JWJ532XDuJ\nFmvCB3BPggM2xUuQGgv4ekzfjkJEtBQxhBMR0ZR0Oi2a2upwq6EUl0ubcKlYhMr6QDS1RqNDnWby\nfLnTIJKjh7E10QGb4sVIipbAUeZigcqJiBY3hnAiIjLQDA2gVlmJG3XlOFfYhbwyGW6rVkHZdjf6\nBtxNnh/k04+0WBG2JjkgLRaICpFCLJZZoHIiIttiMoSfO3cOv//975Gfn4/GxkZkZmbi2Wefnfac\n4uJiPP/888jNzYWHhwd+9rOf4Ve/+pXZiiYiIvPo6m1HVWM5im/dwtnCQRTfdENjayRU7Q9Cq50+\nPEvEOsSE9SM9QYot6+yRGgv4eTpZqHIiIttmMoT39vYiLi4Ozz77LHbv3m1yHla1Wo3t27cjPT0d\neXl5KCsrw969e+Hs7IyXXnrJbIUTEdHs6AQdVO31uNVQhiulDbhYBFTWBaCpNRrt6hST57s4DiI5\neghbEx2xMV6M5GgxnBzYWkJENBcmQ/jOnTuxc+dOAMCePXtMXvDYsWMYGBhAVlYWZDIZYmJiUF5e\njnfeeYchnIjIgoa1Q7jZUIIbdeU4X9iF70uluK0KQ1NrEvoGdpg8P9C7H6mxwD0JjtgYD8SEsrWE\niMhczN4TfunSJWzatAky2dgX9Y4dO/CrX/0KtbW1CAkJMfctiYgIQHdfF6qbylDVWIZLxWU4U5CM\nxpZIqNrvx7CJ1hKxWIeY0H5sWS/FlvX2SIsF/L3YWkJEtFDMHsKVSiVWrFhhtM3X19ewb6oQnpeX\nZ+5SiBYEn1VaDARBgLq/Dc3ddWhW16NZXYfugXbDfs2gE3JLfwtAPOn5jlINYkI6kbhqCOtW9mLN\nij44ynSG/Q01+l9ElsTvV7IVERER876G2UO4qZ5xIiKaPa1uGG09TWhW16G5ux4t6npohvumPF4m\n7YOn4jbaukIBAN6KbsSF9SBx1SDiw3sR7t8PyeT5nIiILMDsIdzPzw9KpdJom0qlMuybSlJSkrlL\nITKr0REaPqtkCb39alQ1laO6sRxVjWW43XwTw9qhac+RSOywwmcVwgOioeu1h7esH5ER+lUoA71d\nAbhapniiWeL3K9marq6ueV/D7CE8JSUFr7zyCjQajaEvPDs7G4GBgewHJyKahCAIaOlsGunnLkdV\nUxlU7fUmz3NykCPcPwphAdFYGRCNYJ+VsLfTr1iZl5eHYM8+JCXxbyeJiBajGU1RWFlZCQDQ6XSo\nra1FYWEhPD09ERwcjH379iE3NxenTp0CADz11FN4/fXXsWfPHuzfvx8VFRV48803ceDAgQX9IERE\ntmJYO4T6lmpUNepfoqxuLEN3v+lRFW+FP8IDohEWEI3wgCj4uAdCLGJPCRGRLTIZwnNzc7F161YA\n+n7v1157Da+99hr27NmDo0ePQqlUoqqqynC8q6srsrOz8dxzzyEpKQkeHh54+eWXkZGRsXCfgoho\nEesb6EF1Uzmqm/StJbXKSgxpB6c9RyyWINhnJcL9oxAeEIMw/yi4OrtZqGIiIlpoJkN4eno6dDrd\nlPszMzMnbFu7di3Onj07v8qIiGyQIAhoVzejqqkMVQ1lqGoqg7KtDgKEac9zlDkjzD/K0F4S4hsB\nqT3n5CYiWqrM3hNORLScaHVaNIy2lozM0a3u7TB5nqerL8ICorByZJTbzzOYrSVERMsIQzgR0QwN\nDPajsbUWDS1VaGitQUNLNRrbajE0bKK1RCRGkHc4wgKiEB4QjXD/aChcPCxUNRERLUYM4UREdxAE\nAR3drWhorUZjaw3qW6rR2FKDlq6mGZ0vkzoaWkvCR1pLZFLHBa6aiIhsCUM4ES1rw9ohKNvr0NCi\nH9keHeHu0/TM+BruLl6GWUtWBkTD33MFxGLJAlZNRES2jiGciJaN3n41GkZHtkd+V7XXQ6sbntH5\nYpEYvh5BCPQKQ6B3GAK9QhHoHQq5E2ctISKi2WEIJ6IlRyfo0NqpRENr9bgR7mp09rTN+BqOUicE\neIchyDsMAV6hCPIOg59HsGExHCIiovlgCCcim6YZGkBja61hZFvfx12LwaGBGV/D09V33Mh2GAK9\nQ+Eh94FIxNUmiYhoYTCEE5FNEAQBXb3t+lHtcb3bLZ1NJufgHmUnsUeAZwgCvPUj24FeoQjwCoWj\nzHmBqyciIjLGEE5Ei45WOwxVR71R73ZDaw16+9UzvobcUTEyqj06wh0OH/cASPjCJBERLQIM4URk\nVX0DPXf0btegqf02tNqZvSwpEonh4x6AIK8wQw93oFcoXJ3dF7hyIiKiuWMIJyKL0Ak6tHWpjEa2\nG1qq0dHdMuNryKSO+lHtcbOT+Huu4PLuRERkcxjCicjsBoc1aGq9bTzC3VYDzWD/jK/hLvc2BO2g\nkbYSD1cfLu1ORERLAkM4Ec2LurfDaGS7obUazR2NEATdjM6XSOzg77HCaGaSQK8wODm4LHDlRERE\n1sMQTkQzotVp0dzRYAjaoyPc3f1dM76Gs6OrYWR7dO5tX/cgSCT8KiIiouWF/+Ujogn6Nb0Tereb\n2m5jWDs0o/NFEMHbzf+OubfDoHD24NzbREREYAgnWrZG591u7mhES2cjmjsa0NzZCGVbHdrUqhlf\nR2rvgACvEAR6ja0uGeAVApm9wwJWT0REZNsYwomWuL6BHjSPhGx92G5Ec2cjWjqbZrWqJAC4uXiO\nzUwy0rvt5ebHlyWJiIhmiSGcaAkYHNagtVNpGM1uGQnazZ2Ns1rgZpRYLIGfR7BR73agVyicHV0X\noHoiIqLlhyGcyEbodFq0d7eMax9pRHNnA1o6GtHR3TrjpdvHc5Q5w8c9ED5uAfBxD4C3WwB83QPh\n4x4Eezv7BfgUREREBDCEEy0qgiCgu69zpH2kES2dDYb2kdYu5YxXkRzPXiKFt5s/vN0DxoXtQPi4\nB8DZQc4XJYmIiKyAIZzICvo1fUYvQ45vH5nNgjajRCIxPF194OMWMC5sB8LbLQBuck/2bBMRES0y\nDOFEC2RoeAhtauUd7SP6wK3u65jTNV2d3OHtHgDfcaPZPm4B8HD1ZfsIERGRDWEIJ5oHnaBDZ3fr\nuBlHxnq129UtM141cjwHqdMdI9r6Xm1vtwA4ypwW4FMQERGRpTGEE5kgCAJ6+tVoVtdB3d+Gxotl\naBlpI2ntVGJIOzjra0okdvBW+BsC9vhebbmTgn3aRERESxxDONEIzdCAYSR7fPtIc0cD+jW9s76e\nCCK4u3objWaPzkTiLveCWCxZgE9BREREtoAhnJYVrXYYbWqVUX/26AuRXT1tc7qmi6PC0JvtPW66\nPy+FH+ztpGb+BERERLQUMITTkqMZ7Ed7dws6ulvQpm5GS2eTIWy3dSmhm0OfttTeAS5SN7g6eiAy\nfO1Y6HYLgJODywJ8CiIiIlrKGMLJpugEHbr7OtHR3Yp2dTM6ulvR0d2M9u5WdIz83KfpmdO1xWIJ\nvBR+d7SPBMDHLRCuzu64evUqACApKcmcH4mIiIiWoRmF8MOHD+Ott96CUqnEmjVr8Ic//AEbN26c\n9NiamhqEh4dP2H7ixAns2LFjftXSkjc0PDgSrFsMo9kd6paxn3ta57RgzXjuLl6GmUfGz6nt4eoD\nCfu0iYiIyAJMhvCPPvoIL774Io4cOYKNGzfivffew86dO1FaWorg4OApzzt58iTi4+MNP7u7u5un\nYrJZgiCgb6BbP2rd3Ww0mj0auLv7Oud9H4nEDh4u3nB39Ya73BveCj9Dr7a3mz+k9jIzfBoiIiKi\nuTMZwt955x3s3bsXP/3pTwEAf/zjH3HixAkcOXIEv/nNb6Y8z8PDAz4+PuarlBY9rU6Lrp42Q6Bu\nHz+C3d2Cju5WDA4NzPs+Tg5yeMi94S73goerD9zlXnCX+8BD7gV3uTdcnBRcIZKIiIgWtWlD+ODg\nIPLz8/Hv//7vRtt37NiBnJycaS/8yCOPYGBgABEREcjIyMCjjz46/2rJqgYG+0dGrluMRq9H20U6\ne9vntDjNeGKRGG4unnCX60ey9WF77JeH3AsyqaOZPhERERGRdUwbwltbW6HVauHr62u03cfHB0ql\nctJz5HI53n77baSlpcHOzg7Hjx/HE088gaysLDz99NPmq5zMavSFx9HR645JRrPnMlf2nWT2DiOj\n16PB2ssQtD1cveHq7MG+bCIiIlryzD47iqenJzIyMgw/JyQkoK2tDYcOHZo2hOfl5Zm7FBpHqxtG\nr6YLPZou9Gq60KtRj/w++mc1dIJ23vdxtHeBs0wx8ssVLg4KOEsVcHbQ/yyVOExcDbIH6OjpQ0dT\nLYDaedew0Piski3h80q2hM8r2YqIiIh5X2PaEO7l5QWJRAKVSmW0XaVSwd/ff8Y3SU5OxtGjR+dW\nIZkkCAI0w/0TwnXPuJ8HhuY/ii0WSeAsU8BlJGAbhW2ZAk4yV0jEnPWSiIiIyJRpE5NUKkViYiK+\n+eYbo57u7OxsPPbYYzO+SWFhIQICAqY9hnMvT04QBPQP9kLd2wF1byc6e1rvmBtb3y4yOKyZ972c\nHeRT9GHrf5c7KSaOYi8joyM0fFbJFvB5JVvC55VsTVdX17yvYXLY8qWXXsIzzzyDDRs2IDU1FX/6\n05+gVCrx85//HACwb98+5Obm4tSpUwCArKwsSKVSrFu3DmKxGF9++SUOHz6MQ4cOzbvYpWRYO4Tu\nvi59uO7rGPm9E92Gnzuh7m2Huq8Tw9qhed9PLJaMvfAo94KH3OeO2UW8IbN3MMMnIyIiIiJTTIbw\nxx9/HG1tbTh48CCampoQGxuLr776yjBHuFKpRFVVleF4kUiEgwcPora2FhKJBJGRkcjMzMRTTz21\ncJ9ikbhz1Lq7rwNdvR3oNoTqscDdO9Bt1nvLpI5jLziOe9FxdDRb4ewOMV94JCIiIloURIIgCNa6\n+fihfIVCYa0yTLpz1Lq7r1MfrsePWvd1oLu3E0PaQbPfX2bvAFdnD7g6ucHV2X0kXPuMzSzi6g1H\nqfOybhWxBP51KdkSPq9kS/i8kq0xR4Zdtm/RjY5ad/d2GkarLTVqDQAikRhyRwVcnd3h6uQGubM7\nFM7ukDu5GQVuVyc3zotNREREtMQsuRCu1Q5D3dc5xaj1uO0LOWrt5A5XZ3fInd2gcPbQB+uRba7O\n+j+7OLqyPYSIiIhombKJED7ZqLW+BaTdeNS6rxO9/Wqz33901Fru7AaFk/sdo9buYwGbo9ZERERE\nNAOLJoQXV32P7tGRaguPWsud7wzTIyPWI3/mqDURERERmdOiCeH/35e/Mct1Jhu1NvRXc9SaiIiI\niBaBRRPCTZHaO4yE6nGj1qMvMXLUmoiIiIhsyKIJ4dEhCYYR6rFR67GZQjhqTURERERLxaIJ4f+6\n61Vrl0BEREREZBFiaxdARERERLTcMIQTEREREVkYQzgRERERkYUxhBMRERERWRhDOBERERGRhTGE\nExERERFZGEM4EREREZGFMYQTEREREVkYQzgRERERkYUxhBMRERERWRhDOBERERGRhTGEExERERFZ\nGEM4EREREZGFMYQTEREREVkYQzgRERERkYUxhBMRERERWRhDOBERERGRhTGEExERERFZGEM4ERER\nEZGFMYQTEREREVkYQzgRERERkYXNKIQfPnwYYWFhcHR0RFJSEi5cuDDt8cXFxdiyZQucnJwQFBSE\nN954wyzFEhEREREtBSZD+EcffYQXX3wR+/fvR2FhIVJTU7Fz507U1dVNerxarcb27dvh7++PvLw8\nvPvuu3jrrbfwzjvvmL14IiIiIiJbZDKEv/POO9i7dy9++tOfIjIyEn/84x/h7++PI0eOTHr8sWPH\nMDAwgKysLMTExODRRx/FK6+8whBORERERDRi2hA+ODiI/Px87Nixw2j7jh07kJOTM+k5ly5dwqZN\nmyCTyYyOb2xsRG1trRlKJiIiIiKybdOG8NbWVmi1Wvj6+hpt9/HxgVKpnPQcpVI54fjRn6c6h4iI\niIhoObEz9wVFItGczuvq6jJzJUTmFRERAYDPKtkGPq9kS/i80nI07Ui4l5cXJBIJVCqV0XaVSgV/\nf/9Jz/Hz85sw4j16vp+f33xqJSIiIiJaEqYN4VKpFImJifjmm2+MtmdnZyM1NXXSc1JSUnD+/Hlo\nNBqj4wMDAxESEmKGkomIiIiIbJtIEARhugM+/vhjPPPMMzh8+DBSU1Pxpz/9CZmZmSgpKUFwcDD2\n7duH3NxcnDp1CoB+isLIyEikp6dj//79qKiowN69e3HgwAFkZGRY5EMRERERES1mJnvCH3/8cbS1\nteHgwYNoampCbGwsvvrqKwQHBwPQv2xZVVVlON7V1RXZ2dl47rnnkJSUBA8PD7z88ssM4ERERERE\nI0yOhBMRERERkXnNaNl6c/mv//ov3HPPPXBzc4NYLMbt27dndN6nn36KmJgYODg4YM2aNfj8888X\nuFIiQKPR4Be/+AW8vb3h4uKChx9+GA0NDdOe8/7770MsFhv9kkgkGBwctFDVtJwcPnwYYWFhcHR0\nRFJSEi5cuDDt8cXFxdiyZQucnJwQFBSEN954w0KVEs3uea2pqZnwXSoWiye8o0a0EM6dO4eHHnoI\nQUFBEIvFyMrKMnnOXL5fLRrC+/v7cd999+H111+f8TmXLl3Ck08+iWeeeQbXrl3D008/jcceewzf\nf//9AlZKBLz44ov43//9X/z1r3/F+fP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ur1YBC2dYbwpdmgLMSgAUCoZzqTGsExER0ZBYLGacu3QCh05/g9yiLAhh6dEn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\nWSlRVUREREREzsHl1lnX6XRSl0CDFB8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jx65PQ26na+dNRCSn7KvHoBZVAAAHG3e42HrLnEh+7N+JyNDVNVXhUkWOdDzB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\nktUFp7UYTnsy44vhTNwkmwuS1cXPtSaijPI++Qk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DlkrSHzzK3uIBnrYecQf5V05H+vfo7sPKRPyT1oyLiIgIAB9tLmHIPXb2Fp/e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\niFw4hXEREWlVPtpcwuxlZaz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AMYmigNFZgzA6axDuWjIJ9S127DlRjaKDZTh1rjmgvrXyRtExTB1qwg0F/u2N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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -2823,11 +2824,6 @@ "\n", "$$\\mathbf{P}^- = \\mathbf{FPF}^\\mathsf{T}$$" ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [] } ], "metadata": {