From c8a239994d29a2d940b2d1722ce66fe8a6978ecd Mon Sep 17 00:00:00 2001
From: Luke Naylor <l.naylor@sms.ed.ac.uk>
Date: Wed, 3 Jul 2024 19:10:12 +0100
Subject: [PATCH] Readjust bound on d from first condition (wall radius)
---
notebooks/other_P_choice.ipynb | 116 +++++++++++++++---------------
tex/bounds-on-semistabilisers.tex | 20 +++---
2 files changed, 67 insertions(+), 69 deletions(-)
diff --git a/notebooks/other_P_choice.ipynb b/notebooks/other_P_choice.ipynb
index 7df3c58..7150920 100644
--- a/notebooks/other_P_choice.ipynb
+++ b/notebooks/other_P_choice.ipynb
@@ -26,7 +26,9 @@
"metadata": {},
"outputs": [],
"source": [
- "var(\"R C D r c d A B\", domain=\"real\")\n",
+ "var(\"R C D r c d\", domain=\"real\")\n",
+ "var(\"A\", latex_name=r\"{\\alpha_0}\", domain=\"real\")\n",
+ "var(\"B\", latex_name=r\"{\\beta_0}\", domain=\"real\")\n",
"P = A, B"
]
},
@@ -45,7 +47,7 @@
"$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = R \\\\ \\mathrm{ch}_{1} = C \\ell^{1} \\\\ \\mathrm{ch}_{2} = D \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Chern_Char object at 0x7fb2f797cf10>"
+ "<pseudowalls.chern_character.Chern_Char object at 0x7fd4b12cb3d0>"
]
},
"execution_count": 3,
@@ -67,13 +69,13 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\text{ Twisted Chern Character for $\\beta={ B }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = R \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^B(v)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^B(v)} \\ell^{2} \\end{array}\\)</html>"
+ "<html>\\(\\displaystyle \\text{ Twisted Chern Character for $\\beta={ {{\\beta_0}} }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = R \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^{\\beta_0}(v)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^{\\beta_0}(v)} \\ell^{2} \\end{array}\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\text{ Twisted Chern Character for $\\beta={ B }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = R \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^B(v)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^B(v)} \\ell^{2} \\end{array}$"
+ "$\\displaystyle \\text{ Twisted Chern Character for $\\beta={ {{\\beta_0}} }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = R \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^{\\beta_0}(v)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^{\\beta_0}(v)} \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7fb2edbeb890>"
+ "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7fd4a72f1e50>"
]
},
"execution_count": 4,
@@ -84,8 +86,8 @@
"source": [
"twisted_v = Twisted_Chern_Char(B,\n",
" R,\n",
- " var(\"twisted_v1\", latex_name = r\"\\mathrm{ch}_1^B(v)\", domain=\"real\"),\n",
- " var(\"twisted_v2\", latex_name = r\"\\mathrm{ch}_2^B(v)\", domain=\"real\"),\n",
+ " var(\"twisted_v1\", latex_name = r\"\\mathrm{ch}_1^{\\beta_0}(v)\", domain=\"real\"),\n",
+ " var(\"twisted_v2\", latex_name = r\"\\mathrm{ch}_2^{\\beta_0}(v)\", domain=\"real\"),\n",
")\n",
"twisted_v"
]
@@ -115,7 +117,7 @@
"$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = r \\\\ \\mathrm{ch}_{1} = c \\ell^{1} \\\\ \\mathrm{ch}_{2} = d \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Chern_Char object at 0x7fb2edc01390>"
+ "<pseudowalls.chern_character.Chern_Char object at 0x7fd4a72f3410>"
]
},
"execution_count": 6,
@@ -137,13 +139,13 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\text{ Twisted Chern Character for $\\beta={ B }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = r \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^B(u)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^B(u)} \\ell^{2} \\end{array}\\)</html>"
+ "<html>\\(\\displaystyle \\text{ Twisted Chern Character for $\\beta={ {{\\beta_0}} }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = r \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^{\\beta_0}(u)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^{\\beta_0}(u)} \\ell^{2} \\end{array}\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\text{ Twisted Chern Character for $\\beta={ B }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = r \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^B(u)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^B(u)} \\ell^{2} \\end{array}$"
+ "$\\displaystyle \\text{ Twisted Chern Character for $\\beta={ {{\\beta_0}} }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = r \\\\ \\mathrm{ch}_{1} = {\\mathrm{ch}_1^{\\beta_0}(u)} \\ell^{1} \\\\ \\mathrm{ch}_{2} = {\\mathrm{ch}_2^{\\beta_0}(u)} \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7fb2edc03850>"
+ "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7fd4a7106010>"
]
},
"execution_count": 7,
@@ -154,8 +156,8 @@
"source": [
"twisted_u = Twisted_Chern_Char(B,\n",
" r,\n",
- " var(\"twisted_u1\", latex_name = r\"\\mathrm{ch}_1^B(u)\", domain=\"real\"),\n",
- " var(\"twisted_u2\", latex_name = r\"\\mathrm{ch}_2^B(u)\", domain=\"real\"),\n",
+ " var(\"twisted_u1\", latex_name = r\"\\mathrm{ch}_1^{\\beta_0}(u)\", domain=\"real\"),\n",
+ " var(\"twisted_u2\", latex_name = r\"\\mathrm{ch}_2^{\\beta_0}(u)\", domain=\"real\"),\n",
")\n",
"twisted_u"
]
@@ -185,10 +187,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle A^{2} = \\frac{2 \\, {\\mathrm{ch}_2^B(v)}}{R}\\)</html>"
+ "<html>\\(\\displaystyle {{\\alpha_0}}^{2} = \\frac{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}{R}\\)</html>"
],
"text/latex": [
- "$\\displaystyle A^{2} = \\frac{2 \\, {\\mathrm{ch}_2^B(v)}}{R}$"
+ "$\\displaystyle {{\\alpha_0}}^{2} = \\frac{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}{R}$"
],
"text/plain": [
"A^2 == 2*twisted_v2/R"
@@ -224,10 +226,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle -\\frac{1}{2} \\, A^{2} r + {\\mathrm{ch}_2^B(u)} > 0\\)</html>"
+ "<html>\\(\\displaystyle -\\frac{1}{2} \\, {{\\alpha_0}}^{2} r + {\\mathrm{ch}_2^{\\beta_0}(u)} > 0\\)</html>"
],
"text/latex": [
- "$\\displaystyle -\\frac{1}{2} \\, A^{2} r + {\\mathrm{ch}_2^B(u)} > 0$"
+ "$\\displaystyle -\\frac{1}{2} \\, {{\\alpha_0}}^{2} r + {\\mathrm{ch}_2^{\\beta_0}(u)} > 0$"
],
"text/plain": [
"-1/2*A^2*r + twisted_u2 > 0"
@@ -239,7 +241,7 @@
}
],
"source": [
- "stability.Tilt(*P).degree(twisted_u) > 0"
+ "( radius_condition_before_sub := stability.Tilt(*P).degree(twisted_u) > 0 )"
]
},
{
@@ -251,10 +253,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle R {\\mathrm{ch}_2^B(u)} - r {\\mathrm{ch}_2^B(v)} > 0\\)</html>"
+ "<html>\\(\\displaystyle R {\\mathrm{ch}_2^{\\beta_0}(u)} - r {\\mathrm{ch}_2^{\\beta_0}(v)} > 0\\)</html>"
],
"text/latex": [
- "$\\displaystyle R {\\mathrm{ch}_2^B(u)} - r {\\mathrm{ch}_2^B(v)} > 0$"
+ "$\\displaystyle R {\\mathrm{ch}_2^{\\beta_0}(u)} - r {\\mathrm{ch}_2^{\\beta_0}(v)} > 0$"
],
"text/plain": [
"R*twisted_u2 - r*twisted_v2 > 0"
@@ -267,7 +269,7 @@
],
"source": [
"radius_condition = expand(\n",
- " (stability.Tilt(*P).degree(twisted_u) / r > 0).expand().subs(\n",
+ " ( radius_condition_before_sub / r ).expand().subs(\n",
" A2_subs\n",
" ) * r * R\n",
")\n",
@@ -283,10 +285,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle d > \\frac{1}{2} \\, B^{2} r + B q + \\frac{r {\\mathrm{ch}_2^B(v)}}{R}\\)</html>"
+ "<html>\\(\\displaystyle d > \\frac{1}{2} \\, {{\\beta_0}}^{2} r + {{\\beta_0}} q + \\frac{r {\\mathrm{ch}_2^{\\beta_0}(v)}}{R}\\)</html>"
],
"text/latex": [
- "$\\displaystyle d > \\frac{1}{2} \\, B^{2} r + B q + \\frac{r {\\mathrm{ch}_2^B(v)}}{R}$"
+ "$\\displaystyle d > \\frac{1}{2} \\, {{\\beta_0}}^{2} r + {{\\beta_0}} q + \\frac{r {\\mathrm{ch}_2^{\\beta_0}(v)}}{R}$"
],
"text/plain": [
"d > 1/2*B^2*r + B*q + r*twisted_v2/R"
@@ -402,7 +404,7 @@
"id": "9d591f22",
"metadata": {},
"source": [
- "### Specialize last 2 conditions to $\\beta=B$"
+ "### Specialize last 2 conditions to $\\beta=\\beta_0$"
]
},
{
@@ -439,10 +441,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\frac{1}{2} \\, B^{2} r\\)</html>"
+ "<html>\\(\\displaystyle \\frac{1}{2} \\, {{\\beta_0}}^{2} r\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\frac{1}{2} \\, B^{2} r$"
+ "$\\displaystyle \\frac{1}{2} \\, {{\\beta_0}}^{2} r$"
],
"text/plain": [
"1/2*B^2*r"
@@ -466,10 +468,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\frac{1}{2} \\, B^{2} r\\)</html>"
+ "<html>\\(\\displaystyle \\frac{1}{2} \\, {{\\beta_0}}^{2} r\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\frac{1}{2} \\, B^{2} r$"
+ "$\\displaystyle \\frac{1}{2} \\, {{\\beta_0}}^{2} r$"
],
"text/plain": [
"1/2*B^2*r"
@@ -507,7 +509,7 @@
"$\\displaystyle \\text{Chern Character:} \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 3 \\\\ \\mathrm{ch}_{1} = 2 \\ell^{1} \\\\ \\mathrm{ch}_{2} = -2 \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Chern_Char object at 0x7fb2edc02d10>"
+ "<pseudowalls.chern_character.Chern_Char object at 0x7fd4a711ff50>"
]
},
"execution_count": 19,
@@ -547,7 +549,7 @@
"$\\displaystyle \\text{ Twisted Chern Character for $\\beta={ -\\frac{67}{99} }$ } \\\\ \\begin{array}{l} \\mathrm{ch}_{0} = 3 \\\\ \\mathrm{ch}_{1} = \\frac{133}{33} \\ell^{1} \\\\ \\mathrm{ch}_{2} = \\frac{265}{6534} \\ell^{2} \\end{array}$"
],
"text/plain": [
- "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7fb2edc25690>"
+ "<pseudowalls.chern_character.Twisted_Chern_Char object at 0x7fd4a710c950>"
]
},
"execution_count": 21,
@@ -682,7 +684,7 @@
"outputs": [
{
"data": {
- "image/png": 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6deuu+rmxsTHTpk1jzZo1FBYW8re//Y1NmzbR0HLPu3fvxtbWFldXV0ANjgkJCVy6dOlGFV8I0RGVpsHpz2D3ZNjoCDvvoPzsl+yvNOe5stuwPVWBW/IRFl7MwLvL7Xxz7zdcev4SR2YfYfmdy7mr511Ym9iSnAxvv60GNwcHtV/cZ5/BbbepX8+dg5MnYdUqmDz51h78cN0UPbZy5UqlT58+Ss+ePRVAKSgoaLVzl5SUKAcPHlRKSkpqt1WUKEnpSY2+SipK6p3L29tbWb58eZ1tAwcOVF555RVFURQlNDRU6dOnj6LVanWfL1iwQOnTp4/u/bX2KS4uVszNzZV9+/bVuc6MGTOUBx98UHeOQYMGNen+G7tecXGxYmJionz11Ve6zyoqKhQPDw9l2bJlTb7vmusEBwfX2ScgIEBZsGCBoiiKUlRUpJiamirffPON7vPc3FzFwsJCeeaZZxRFUZTvvvtO6dWrV5Pu67PPPlN+//13RVEU5c0331ScnZ0b/L557733lM8++0z3vqqqSlm5cqXy0EMPKQcOHFAURVGmTp2qrF+/vknXbUxVVZXy4YcfKtOnT9ed+8KFC0poaGid/bKzs5VRo0Y1+bxarVb5/vvvlf/7v/9TduzYUeezNWvW1Du/k5OTEh0dfc3z1vxsfPXVV8ry5cuV3NzcJpdJCNHOVVcpSlacohxepChbBinKVyjarwyV8//xVD5Z31UZ8qaxwt9R3N5xU/5v4/8pnyd/rpzLO1fvNGfOKMonnyjKffcpiqOjooCiWFoqyp13KsrbbyvK4cOKUl3dBvd3C2hWjd3SpUsJCAjAxsYGFxcX7r77bk6ePNnoMTExMRgYGNR7/fbbb9e83pw5czh+/Hi9JsAb5bec3xiyZkijr99yrl3uhgwbNqxOrVNQUBC///57nRG/je1z/PhxysvLueOOO7C2tta9vvjiC86cOaM7xt/f/7rLdPr0aSorKxkxYoTuMxMTEwIDAzlx4kSz733AgAF13ru7u5OVlQXAmTNnqKioICgoSPe5g4MDvXr10r2fPHlyk75fiouLyc7OxsfHB4BnnnkGS0tL3nrrrXr7Xrx4ERcXF937H374gQceeIDS0lLOnTsHwMSJEyksLGz6jV7F5s2bmTJlCmVlZaSkpACwfft2unTpUmc/JyenOn+X15KTk0NycjKOjo71+s7l5ORgbm5eZ5u5uTn5+fktuwkhRMelyYWUryDu/1C+c4HtIyg98T7Rl7N4NNsMxzNaBp4p4iezQTwyajnHnjxGekQ6G+7ZwKN+j+Jt701ODnz7LcyaBd27qzVxTz4JFy6o88nFxPwx59xP8PzzMHCgDH64UZo1eCI2NpY5c+YQEBBAVVUVL774ImPGjOH48eNYWVk1euzJkyextbXVvXd2dm5ZiW+g3k69SZqVdM19/szQ0LBec1hjfbtaQqvVAhAVFUXnzp3rfGZ2ReeDa/09NMefmz8VRamzran3bWJiUu+8Nffz5+Ovx6effsrMmTN1783NzXn99deZNWsWTz75ZJ3nVlxcjIWFhe796NGj0Wq17Nmzhw0bNgBw2223NTiw4oMPPtAFtIaEhoYyefJk3fvw8HAAdu7cyeeffw6o/+FpqA9kU5qc09PT+fDDD6msrOTpp5/G29u73j52dnb1nm1xcTFOTk719hVC3GIUBfIOQ/oWlPQoyNmPAVrOYM+mwnL+WwC/VmkZ7uVL+JBw5nQPx8/NDyPD2q4rpaXq1CM188kdPqxu79MH7rpLHfAQGgoyocXN16xg9/PPP9d5/89//hMXFxeSkpIICQlp9FgXFxfs9bzR3NLEksHug5t9nLOzMxkZGbr3hYWF9X7xJyQk1Hvfo0ePOn28Gtunb9++mJmZkZqaSmhoaLPL2JCrXc/HxwdTU1P27t3L1KlTATWwHTx4kGeffVa3f1Pu+1p8fHwwMTEhISEBrz8mIsrLy+PUqVPNus/MzEzMzc1xdHSss33q1KksX76cl19+mbVr1+q2Ozk5kZeXp3tvb2/Pl19+SVhYmC7wHT16lEceeaTetZ555pnm3CK2trZ88803hISE6IJ3bGwsb7zxBvn5+XV+LoyNr/4jee7cOVatWoWpqSlz587F3d39qvv27t2bTz/9VPdeo9FQVFTUYAgUQtwCKovUgQ/pUVRf/BEjTRZlmLCr3Jj/FmjZUWaEl5svo3uN5q1u4QzrMgwz49pKg6oqSDhQu1TXvn1QUQHu7mqImzdP7Tf3p3oH0Qaua7qTgoICQG06uxY/Pz/Ky8vp27cvixcvbnTKBo1Gg0aj0b1vjeawG2n06NGsW7eOiRMn0qlTJ1566aV6nfIvXLhAREQEjz/+OMnJyXz44Yf1Rn82to+NjQ3PP/888+bNQ6vVEhwcTGFhIfv27cPa2prp06c3u9xXu56VlRVPPPEE8+fPx8HBAS8vL5YtW0ZpaSkzZsxo1n1fi7W1NTNmzGD+/Pk4Ojri6urKiy++iOEVdfSbNm0iMjKy0ebY1atXM2vWrAZHlS5cuJApU6Ywb948+vXrB0CfPn1ITU2ts9+lS5fqhEtra+s65bgeFy5c0DUR//rrr5iYmODi4sL69et57LHHADU829jYNHj8O++8Q2lpKQsXLqwXXhsSEhJCVlYWFy9epEuXLsTGxhIQECDBTohbhaJA0SlIi6Li4g8Y58RhqFRzptqUTYUVbCmBIrs+hHa7g7+OHM0HXiOxMbOpc/hvv9XWyO3aBYWFYGMDo0bBO++oga5374697mp71OJgpygKERERBAcH635ZNsTd3Z01a9YwZMgQNBoNX375JeHh4cTExFy1lm/p0qW8+uqrLS3aTRcZGcnZs2e56667sLOz47XXXqtXczVt2jTKysoIDAzEyMiIp59+mlmzZjVrn9deew0XFxeWLl3K2bNnsbe3Z/DgwSxatKhF5W7sem+++SZarZaHH36YoqIi/P392bp1K506dWrWfTfF22+/TXFxMZMmTcLGxobnnntO958GUP8D0VhfzlOnTvH666+zZMmSRq+zaNEiNm/eDMCdd97JzJkzee6553SfT5kyhYiICL788kuqqqpaFJav5t5772XBggV8++23AAwZMoSVK1fWqRFMTExk9OjRDR7f2OTFDTE2Nmb9+vW8/vrrDBs2jNjYWL766qsWl18I0Q5Ul8OlGCou/kDVhe+x1GSiUQyILlXYUgInTLrS0/tOwoeE823XsDprrgKkp9cu1xUdDWlpYGKiziH3/PNqkAsIgEYaFoQeMFBa2Mlpzpw5REVFsXfv3nqdwK9l4sSJGBgY6H7J/llDNXaenp4UFBTU6ad3PUpLS3VLSVlaWrbKOa+mKctj6fsSXx3RrFmzWLJkCW5ubm1dFECdzmbSpEkEBga2aTlqfjZOnjxJVlYW06ZNa1KtvBCiDZSkUnlhM4Up/8ImLxFTqjhfCVElkKA4YOo+lpHdxzK622g87TzrHFpYCLGxtbVyx4+r2wcOVEPc7bfDyJHQil23xU3Qotz99NNPs3nzZnbv3t3sUAfqaMyaDuoNMTMzqzMgQIgb4eWXX2blypX84x//aOuiUFhYSHZ29lVD3fLlyxsdMTtq1CjuvffeG1U8IYS+0FZSnbWX7N/XYZS5DefKTAwUOFoGuyosKHAcRU+fvxDe/XaecOxZZ0BWRYU66W9Njdz+/VBdDd7eaoh76SUYPRqumDBAtEPNCnaKovD000+zadMmYmJiWrw80aFDhxrt+C3EzdClSxcmT57Mli1bGD9+fJuVQ1EUli9f3mjAnDdv3k0skRBCnyhll8g49Tkl5/+LR/FRrKjEoAp+LjMi1XoQtl73MMJnAq+4DcLQoLZfsFYLR4/W1sjFxqqjWR0c1AC3apUa6Lp3l35yHUmzgt2cOXP417/+xQ8//ICNjQ2ZmZmAOrVCzUjCyMhI0tLS+OKLLwB1kfWuXbvi6+tLRUUFGzZsYOPGjWzcuLGVb0V/xcTEtMo+ovUNGTKkrYtAbm4uTzzxhF5OASSEaAOKlszUKDJOrsU2dy/dtLm4AQc1Buwx9qTKbSx9ev4fD3gGYWpUdz3w8+dra+SioyErC8zN1SbVl19Wg9ygQaBHi+6IVtasYLd69WpA7Q92pX/+85+6TuAZGRl1RhtWVFTw/PPPk5aWhoWFBb6+vkRFRTWphmTVqlWsWrWqziS+QnQ0MrecECIn/zSnjq2CtC30rDiDm2E15tVwQGtPosM4XH2mE3jbXQSa1u3wdvmyOmK1plbu9Gm19s3fH2bMUIPc8OFquBO3hhYPnriZCgsLsbOza7eDJ4RoT2TwhBA3Xn5ZHodOfkVRyje4Fx3Gz6gEYwM4VW3GOcu+mHlNpn/fWThYudY5rqwM4uJqa+WSktSpSXr2VENceLg6HckVExiIW4wMWhZCCCFusOKKYval7CDt9y+xyd2DP9mMMoEyxYCTZl1Icr0P7z5P0NM1kJ5XHFddDYcO1dbI7d0LGo06wOH229Vlu8LD4Y8pOIWQYHer0vfpVW5m+WpqboUQorWUV5UTfyGeQ79vhIyf6FuZQpi5grkhXDK1Jsc+nMzbHsLttikMMqptJ1UUtTn1yomB8/LUKUfCwuDNN9Ug16+fDHgQDZNgJ25p77//PpMmTbrmftnZ2axfv77RiYLT09Px8PBozeIJIdqJyupKEtMTiTm7jdzUH/AsOspYy2oiTKHKxIBM254Uek3GzGc6rra9cL0ilV26BDt31oa51FR1cMOwYTB3rlozFxgIpqaNFECIP+h1sJPBE9enoqIC01v0X4KwsDDmzp3LPffcc9V9tm3bhrOzM927d7/m+ZydnQkJCWHVqlXMmTOnwX1iYmKIiYnhwQcfbHTJvCslJiby1Vdf4efnR1xcHJGRkS2eRkgIcfNUa6s5nHmYnSk7OXRuC/a5+wg3r+ApS7A1gmJHWypcw9F2/z+M3cfQxaR2ua7iYti9uzbIHT2qbu/XD+65Rw1yISHq8l1CNFfrLIR5g8yZM4fjx4+TmJjY1kVpVNeuXes1GQ4aNIi///3vgBoynnrqKZ566ins7e1xdHRk8eLFXDlupSn7KIrCsmXL6N69OxYWFgwcOJD//ve/9c4RERGBk5MTd9xxR6Plrqqquur1NBoNc+fOxcXFBXNzc4KDg+v9PVzrvmvKNHfuXF544QUcHBxwc3Or8zlASUkJ06ZNw9raGnd393pr6DbX999/j5GREQsXLqSysvKq+61YsYIpU6Y0+byBgYEcOHCgwfVoAaZOncpHH33EhQsXeOyxx/jpp58aPZ9Go+G+++4jMjKS6dOn8+ijj/Loo482uTxCiJtHq2g5eukoK/av4J6v/8K4D+zZstGfO04t4F8GMaxyqmSsR3+sBi6BO5Oxvj8fh7DvMPS6l0ps2LcPlixRA1unTjBhAvznPzBkCGzYoC7ndfQoLF+ufiahTrSUXge7jmT9+vUYGxuzf/9+VqxYwfLly/nss8+atc/ixYv55z//yerVqzl27Bjz5s3joYceIjY2tt454uLi+OSTT1pcphdeeIGNGzeyfv16kpOT8fHxYezYsVy+fLlF925lZcX+/ftZtmwZS5YsYfv27brP58+fz65du9i0aRPbtm0jJiaGpKQk3efr1q2rM3t6Y6qqqkhKSuLbb78lKyvrqs/gl19+oUuXLhg1czKnSZMmsW7duqt+bmxszLRp01izZg2FhYX87W9/Y9OmTTQ0+Hz37t3Y2tri6qqOegsMDCQhIYFLly41q0xCiNanKAqnck/xycFPeOC/D9D7XRfe2DAAp8Pz+Kd2C9tci1noakv/Hg9A0AYM7snC+q5fMOr/EkonP44dN+CDD2DiRHVC4BEj4L33wMkJPvgAfvtNbXL95z/h//4PZM5+0Vr0uin2ZistVX/YGtO7N7RkdhRPT0+WL1+OgYEBvXr14ujRoyxfvpyZM2c2aZ+SkhLee+89du7cSVBQEADdu3dn7969fPLJJ4SGhgLg4+PDsmXLrqtMU6dOZfXq1axbt45x48YB8Omnn7J9+3bWrl3L/Pnzm3XvAwYM4JVXXgGgR48erFy5kujoaO644w6Ki4tZu3YtX3zxha6Gcf369XWWqrOzs6NXr15Nutb69euZPn06jo6OREZGsmTJEqZNm1Zvmpzo6GgCAgJ076urq1m9ejUHDx5kzpw5BAQEcPHiRR566KE6k0eHhoayatWqRvvaARgaGvLAAw9w//33s3nzZh5++GEeffRRwsPDdfucO3euzjQiRkZG2NjYcOzYMV3YE0LcPOfzz7MzZSe7zu1iZ0o0jpp07rI2YJG9Nf09ijEEtPb9MOx8F3hMwMRxKBiq/zm8eFGdfqSmeTUzU+0TN2IEREaqzauDB4Ox/NYVN5hef4vd7D52v/2mVos3JilJ/eFsrmHDhtWpdQoKCuLdd9+lurpaV2vU2D7Hjx+nvLy8XvNqRUUFfn5+uvf+/v7XXabTp09TWVnJiBEjdJ+ZmJgQGBjIiRMnmn7TfxgwYECd9+7u7mRlZQFw5swZKioqdGEVwMHBoU6Qmzx5MpMnT77mdYqLi8nOzsbHxweAZ555htWrV/PWW2/x+uuv19n34sWLdSba3rx5M1OmTGHPnj2kpKQQEBDA9u3b662F7OTk1OiarX+Wk5NDcnIyjo6O9frO5eTkYP6nWUPNzc3Jz89v8vmFEC2XUZTBrnO72JWyi53ndnIp/yx3WMLDzo6s8NBgrwXFyBID93DwmAAe4zC07AxAfj7EbK4NcidPqqNU/fxg2jQ1yI0Y0bKKACGuh14Huzlz5jBnzhzdBMU3Wu/eanC71j5/ZmhoWK+prbG+XS2h1WoBiIqKonPnznU+MzMz0/3ZyqrurOTX48/Nn4qi1NnW1Ps2MTGpd96a+2nN+bE//fTTOjWg5ubmvP7668yaNYsnn3yyznMrLi7WLYMH6GrSdu7cyeeffw6ogyEa6qfYlGbh9PR0PvzwQyorK3n66afx9vaut4+dnV29+y8uLpaVKIS4QXJLc4k5F6OrlTuRcwIfE5jh6sZzbib0cDbGSKkCWydwHw+dx2PgPBKMzNBoID6+NsglJqprsXbvroa4115TJwaWH1/R1vQ62N1slpYtq41zdnYmIyND976wsJCUlJQ6+yQkJNR736NHjzp9vBrbp2/fvpiZmZGamqprdr1eV7uej48Ppqam7N27l6lTpwJqYDt48CDPPvusbv+m3Pe1+Pj4YGJiQkJCAl5/zLCZl5fHqVOnmnWfmZmZmJub4+joWGf71KlTWb58OS+//DJr167VbXdyciIvL0/33tbWlm+++YaQkBBdOI6NjeWNN94gPz8fe3t73b7GjbSlnDt3jlWrVmFqasrcuXNxb6TjTO/evfn000917zUaDUVFRQ2GQCFE8xVqCtl9frcuyB3JPIKJgcJUFw8+dHEg0NUNm4pMMMwD5zDweB48xoOND1otHD4M0V+qQW7PHnXVBycndR65xx5Tv8ogdqFvJNi1gtGjR7Nu3TomTpxIp06deOmll+p1yr9w4QIRERE8/vjjJCcn8+GHH9Yb/dnYPjY2Njz//PPMmzcPrVZLcHAwhYWF7Nu3D2tra6ZPn97scl/telZWVjzxxBPMnz8fBwcHvLy8WLZsGaWlpcyYMaNZ930t1tbWzJgxg/nz5+Po6Iirqysvvvgihoa143o2bdpEZGQkvzXSAXL16tXMmjWrwRGrCxcuZMqUKcybN49+/foB0KdPnzprGtc8j5pm3F9//RUTExNcXFxYv349jz32GKAGXJurDFd75513KC0tZeHChfUCZkNCQkLIysri4sWLdOnShdjYWAICAiTYCdFCpZWlxKXGsTNlJzvP7SQpPYlqpZpAe3ee8fAm3GMQnUt/w7A6HUyMwOMvahOr22gUIyt+/x2iN6h95XbtUtdhtbBQR7IuWaLWzA0YAIYy7FDoMQl2rSAyMpKzZ89y1113YWdnx2uvvVav5mratGmUlZURGBiIkZERTz/9NLNmzWrWPq+99houLi4sXbqUs2fPYm9vz+DBg1m0aFGLyt3Y9d588020Wi0PP/wwRUVF+Pv7s3XrVjpdsQBhU+67Kd5++22Ki4uZNGkSNjY2PPfccxQUFOg+Lygo4OTJk1c9/tSpU7z++ussWbKk0essWrSIzZs3A3DnnXcyc+ZMnnvuOd3n9957LwsWLODbb78FYMiQIaxcuZJHHnlEt09iYiKjR49u8PzXGlDxZ8bGxqxfv57XX3+dYcOGERsby1dffdWscwhxK9NUaUi4mPDHYIedJFxMoFJbibuVM7O8B/BJlzvoU5GCWfFJqMoC8+Fw2ytqrZxdP9IzDNi5Uw1y0dFw4YI6MfDQoTBnjlojN2wYXNHbRQi9Z6C0ZienVnbl4IlTp05RUFBQb3RjS9UsdN6nTx8sb3Dv1qYsj6XvS3x1RLNmzWLJkiW4ubk1+ZjFixczadIkAgMDb2DJ2lbNz8bJkyfJyspi2rRpdUbvCtFWKqorOJB2gF0pu4g5H8O+C/soryqnk3knJnkH8X9OjgQa5GCbl4BBRR6YOYPHODXIuY8hv7QTMTG1Qa5mLNiAAWqICw+XiYFF+9esGrulS5fy3Xff8dtvv2FhYcHw4cN56623rjkVRWxsLBERERw7dgwPDw9eeOEFZs+efc3r3ezBE+LW8vLLL7Ny5Ur+8Y9/NGn/wsJCsrOzrxrqli9f3uiI2VGjRnHvvfe2qKxC3Ioqqys5mH5QHbl6bhdxqXGUVZVhZ2ZHqNdIPh0xm9Fm5bgXJmOQ+xNkKeDgDz2fBo8JlFn6E7fPkOiP1SCXlKQOeOjWTQ1xr7yiDnhwcWnrOxWi9TQr2MXGxurm+KqqquLFF19kzJgxHD9+/KqjMVNSUhg/fjwzZ85kw4YNxMXF8eSTT+Ls7Cy/5ESb6tKlC5MnT2bLli2MHz++0X0VRWH58uWNhsB58+a1dhGFuKVUaatISk8i5lwMu87tYm/qXkoqS7AxtWGk90jeDI1kvI0Z3UtPYJjxM6T/D0xswW0M9HiCKuc7STruRvT/1CAXFwcajRrcRo+GWbNkwIPo+K6rKTY7OxsXFxdiY2MJCQlpcJ8FCxawefPmOvOfzZ49myNHjhAfH9+k69TU2LXXpljR/uXk5KDVanG5Bf5rL02x4map1lZzKPMQu1LUGrk9qXsorijGysSKkd4jCfMKZZxrN3yrzmOU8TNk7QGlCuz6gscEFPfxHM8ZQfROE6KjISYGCgvVptTQ0Nrm1X791DnmhLgVXNfgiZoO7o39ox8fH8+YMWPqbBs7dixr166lsrKy3hxnoE77oNFodO8LCwuvp5hCXDeZW06I61etrebIpSO6Grnd53dTqCnE0sSSEZ4jWBS8iNGeQQwxKsQ4cxukfwIXzoGRBbiOhiEfkMZ4tsV1JfprtVauZoWHoCB4/nl15Kq/PzTwq0WIW0KLg52iKERERBAcHKybQqIhmZmZ9ZZHcnV1paqqipycnAbn+Vq6dCmvvvpqS4smhBBCD2gVLUcvHdX1kdt9fjf55fmYG5szwnME84fPZ1TXUQTYO2OauQPSo2D/EqguB6uu4DGBAusJ7DgaxvZvLIiOhtOn1dq3wYPVFR7CwyE4WFZ4EKJGi4PdU089xS+//MLevXuvuW9DKxg0tL1GZGQkERERuveFhYV4enq2tKhCCCFuAq2i5VjWMV2NXOz5WC6XXcbMyIwgzyDmDZtHWNcwhroPxizvoBrkjs6CguNgYAwuI9H0+gf7L45nc0xvoqMNOHxYPXevXjBmDLz1FoSFgfQOEKJhLQp2Tz/9NJs3b2b37t311tL8Mzc3NzIzM+tsy8rKwtjY+KqTuJqZmdVZJkvftZepSvS9nDezfIqisGzZMv7zn/+wcOFCCgsLOXHiBEuXLq2zskRNP0whRH2KonAi54Ru+pGYczHklOZgamTKsC7DeCrgKUZ1G8WwLsMwr8yH9J8g9UM4sA0qC8HcDa3beE6aLOH7/Xfw02pbEhKgshI8PNTauGefVb9e41eNEOIPzQp2iqLw9NNPs2nTJmJiYuotat6QoKAgfvzxxzrbtm3bhr+/f4P964RoDaWlpSiKctXR2gYGBtja2nLffffx17/+FYDJkydz+PBh/P39AXj//feZNGlSk66XnZ3N+vXrmz1JsRDtiaIonMo9pWtajTkXQ1ZJFsaGxgztPJTZQ2YT1jWMIM8gLI3NITcR0rfAjufhchJggOI4lEz759lxfALfbB1E7G5DSkrA3l6demT5cjXI9eolAx6EaIlmBbs5c+bwr3/9ix9++AEbGxtdTZydnZ1uQfXIyEjS0tL44osvAHUE7MqVK4mIiGDmzJnEx8ezdu1avv7661a+FVGjoqICU1PTti5Gm4mKiuK5555jypQp/P3vf7/qflu3biUyMhKA3NxcNBoNAwYMANT/fDg7O9O9e/cmXdPZ2ZmQkBBWrVrFnDlzrvseaiQmJvLVV1/h5+dHXFwckZGRTfoPlRCtQVEUTl8+rQtxMediyCjOwMjAiIDOAczwm8GorqMY7jkcK1MrqMiDjG2QOBsyfgZNNoppJ4ptxpJY/ixf7RzL5q3O5OSAubnaN+6ll9Qg5+enrvoghLg+zVrxbvXq1RQUFBAWFoa7u7vu9e9//1u3T0ZGRp01OLt168aWLVuIiYlh0KBBvPbaa6xYsaJJc9itWrWKvn37EhAQ0JxitimNRsPcuXNxcXHB3Nyc4OBgEhMTdZ//+OOP2Nvbo9VqATh8+DAGBgbMnz9ft8/jjz/Ogw8+CNQ2GXbv3h0LCwsGDhzIf//73zrXDAsL46mnniIiIgInJyfuuOOOq5avqqqKp556Cnt7exwdHVm8eDFXznhzrfJ37dq1XlPpoEGD6gSosLAw5s6dywsvvICDgwNubm71AlZJSQnTpk3D2toad3f3euvmXo8JEybwwAMPNLpPVVUV+/fvp6ioiB07dhAbG8sPP/ygC8QrVqxgypQpzbpuYGAgBw4caHC92pbQaDTcd999REZGMn36dB599FEeffTRVjm3EA1RFIWzeWdZm7yWh757CM/lnvRc2ZMnop7gTN4Zpg2cxk//9xP5C/OJnxHPG6Nf5w5HN6x+/xC2h8BGZ4ibQmXOEY5pHmPpwT34vJCF7Z1fM2bWQxw/48zjj8POnZCXB9u3w4IF6ihWCXVCtI5mN8Vey7p16+ptCw0NJTk5uTmXAtrnyhMvvPACGzduZP369Xh7e7Ns2TLGjh3L6dOncXBwICQkhKKiIg4dOsSQIUOIjY3FycmJ2NhY3TliYmJ0k90uXryY7777jtWrV9OjRw92797NQw89hLOzM6Ghobpj1q9fzxNPPEFcXFyjf0/r169nxowZ7N+/n4MHDzJr1iy8vb2ZOXNmk8rfVOvXryciIoL9+/cTHx/PI488wogRI3Shc/78+ezatYtNmzbh5ubGokWLSEpKYtCgQbpzrFu3jkcffbRJ33d/drWBOTXi4+MZOXIkt99+e73PfvnlF7p06YJRC37TTJo0iXXr1tVrkv3ggw8oKChg1qxZTV7CbPfu3dja2upGlQcGBpKQkMClS5fqjTQXoiUUReFM3hliz8USez6WmHMxXCi8gKGBIX5ufjzY70FGdRtFsFcwtmZ/zCFaVQKZ0WoTa/oWKL2AYmRFJrcTe+YjPo0az84EtUNcv34wcZJaIxcaCq00DakQohHXNY9dh1NVCoW/Nb6PbW8wbnhcfUlJCatXr2bdunWMGzcOgE8//ZTt27ezdu1a5s+fj52dHYMGDSImJoYhQ4boQtyrr75KUVERJSUlnDp1irCwMEpKSnjvvffYuXMnQUFBAHTv3p29e/fyySef1Al2Pj4+LFu27Jq36OnpyfLlyzEwMKBXr14cPXqU5cuXM3PmzCaVv6kGDBjAK6+8AkCPHj1YuXIl0dHR3HHHHRQXF7N27Vq++OILXdBbv359vYE4dnZ211yubt++fXzzzTf079+fM2fOcNdddxEcHAyofx/r168H4Pvvv2fDhg1YWVlx5MgRVqxYgYODA/n5+djb29c5Z3R0dL1a4urqalavXs3Bgwd1q69cvHiRhx56iJiYGN1+oaGhrFq1ql6we+aZZ7h06RIff/wxJSUlzJgx45r3du7cuTph2sjICBsbG44dOybBTrRITR+52PNqkIs9F0taURqGBoYMchvEX/v+lVFdRzHSeyT25va1BxadhnPrIC0KsmJAW0GpUQ8OZ93DN3sm8NnmEMo0Znh7qyHuX3PVlR7k21SIm0+C3ZUKf4OfhzS+z51J4DC4wY/OnDlDZWUlI0aM0G0zMTEhMDCwzsobYWFhxMTEEBERwZ49e/jHP/7Bxo0b2bt3L/n5+bi6utK7d28SExMpLy+v17RaUVGBn59fnW01Hf6vZdiwYXVqs4KCgnj33Xeprq5ucvmboqavWg13d3eysrIA9TlVVFTowiqok1z/OehMnjyZyZMnX/UaGRkZ3HvvvRw6dEjX3JuUlKQLdvv37+ftt98GYOPGjWzdupV77rmHgQMH8p///Oeq57148SJhYWF1tm3evJkpU6awZ88eUlJSCAgIYPv27fXCqJOT01XXi3V1deWVV16hqKiIzz77jJUrVzJ16tQ6z+FKOTk5mJub19lmbm5Ofn7+VcsuxJVqRq3W1MjFno8lszgTIwMjBrsPZmr/qYR6hxLsFYyd+RWtItUayNyhBrn0LVB0Cq2BKedLQ/npl2V89P14jqX2wMlJDXDvr1ADXffuMuBBiLYmwe5Ktr3V4Hatfa7iavPzKYpSZ1tYWBhr167lyJEjGBoa0rdvX0JDQ4mNjSUvL09XE1fTDy8qKorOnTvXOeefp4O52ujP5mhK+Q0NDes1jVZWVtY7159HPBsYGOju5zpWsatj48aNeHl56Zo2/9yPb8iQ2pDu4ODQ5BVMiouLdYOBaoSHhwOwc+dOPv/8c0BtMm+oP+O1moFtbGyYN28eFRUVfPXVV3z++edMnz5dF0hr2NnZ1XtWxcXFsgqGuKqaeeRqQtzu87t1o1b9PfyZPnA6YV3DGOE5Ahszm7oHl6bpmleVzB0YVBVTrO1MXMoE1u9Yxub94WBsTWgo/O0ZNcj17w+GzeqpLYS40fQ62K1atYpVq1ZRXV19cy5obHnV2rim8PHxwdTUlL179zJ16lRADT0HDx7k2Wef1e1X08/u/fffJzQ0FAMDA0JDQ1m6dCl5eXk888wzAPTt2xczMzNSU1PrNLtej4SEhHrve/TogZGRUZPK7+zsTEZGhu74wsJCUlJSmlUGHx8fTExMSEhIwMvLC4C8vDxOnTrVrPvUarWNhsSW9JEDtdYtLy+vzjZbW1u++eYbQkJCdCE6NjaWN954o15z7pXz4DWmsLCQtLQ0rK2tG1yDtnfv3nz66ae69xqNhqKiIry9vVtwV6IjqlnZIeZcjC7I5ZblYmJoQmDnQB7ze0w3/Yi1qfWfDq6G3AQ1zKVFQf4RtIohv+cN57uERXy9ewK/ZfZn2DADwsNh6xsQGChLdQmh7/Q62LW3wRNWVlY88cQTzJ8/HwcHB7y8vFi2bBmlpaXMmDFDt19NP7sNGzbwwQcfAGrYu++++6isrNQ1A9rY2PD8888zb948tFotwcHBFBYWsm/fPqytrZk+fXqzy3jhwgUiIiJ4/PHHSU5O5sMPP9SNSG1K+UePHs26deuYOHEinTp14qWXXmp2gLK2tmbGjBnMnz8fR0dHXF1defHFFzH803/9N23aRGRkJL/91nC/x8mTJ/Paa6+RmpqqC4jffPPNNUezZmVlsW3bNgwNDUlKSuKtt96qE8b69OlTZ2R3jQsXLuDj4wPAr7/+iomJCS4uLqxfv57HHnsMUIOwjY1NvWOvlJKSwpo1azA0NGT27NlXXVUlJCSErKwsLl68SJcuXYiNjSUgIECC3S3syrVWY8/Hsuf8HvLK83QTAj8Z8CRhXcMY1mUYliYN9AUuz4GMrZAehTZ9K4aVlymudCT6+Di+3r2Q7b+OwbuHA+HhsGwNjBwJrdAYIIS4ifQ62LVHb775JlqtlocffpiioiL8/f3ZunUrnTp1qrPfqFGjSE5O1oW4Tp060bdvX9LT0+usdPDaa6/h4uLC0qVLOXv2LPb29gwePJhFixa1qHzTpk2jrKyMwMBAjIyMePrpp5k1a1aTyx8ZGcnZs2e56667sLOz47XXXmt2jR3A22+/TXFxMZMmTcLGxobnnnuOgoKCOvsUFBRw8uTJq57D09OTjRs3snjxYoKDg9FqtYwfP56ff/6Z//3vf1RWVvK///2PoqIi4uLiuHjxIr179+bcuXPk5+fz1FNPkZCQwI4dO7jzzjt1573zzjuZOXMmzz33XJ3r3XvvvSxYsIBvv/0WUJt6V65cySOPPKLbJzExkdGjRzdY3kOHDrF+/Xrc3Nx44YUX6n1P/JmxsTHr16/n9ddfZ9iwYcTGxvLVV181eozoWKq0VRzKOKQLcntT91KgKcDc2JygLkE8M/QZdYmuLkMxNzavfwJFgbzDkB5F1YUtGOUlYIDC8czBbIyfQ9Th8eQbBhA2yoi/PgerRsFVFgQSQrQTBkprdXi6gWpq7AoKCrBtpfHypaWluuWiLGX16FvW/fffz7Jly+jatWud7bNmzWLJkiVNnpqkxuLFi5k0aRKBgYF1tn/wwQeYm5szffr0egMi9E3Nz8bJkyfJyspi2rRpzZrqRrRcZXUlSRlJxJ6LJeZ8DHGpcRRVFGFpYslwz+GEeocS6h1KYOdAzIyvsuxiZRFkbqcqdQvVF7Zgps2gpMKGnw+PIerweI5kjaN/oDujR6srPcgy3EJ0LFJjJ25ZUVFR3HffffVCHcDLL7/MypUr+cc//tHk8xUWFpKdnV0v1AG6fpNCXKmiuoLEtETdYIe41DhKKkuwMrEi2CuYyOBIQruG4u/hj6nRVVaTURQoPEn1xS0Un4zCumwPRgaV/J7eh6hDU9l7dgKW3iMIHWVK5Bzw8ZGRq0J0ZHod7G764Alxy0hMTMTV1RV/f3+OHz9O375963zepUsXJk+ezJYtWxg/fvw1z6coCsuXL29WEBS3Hk2Vhv1p+3XTj+y7sI+yqjJsTG0Y6T2Sl0NfJtQ7lMHugzExamSUQnU52swYcn+JwiR7C/bGZ6moMCfu+Ciif1tOodU4fId2Z+xCiPCVkatC3EqkKVaaYm858fHxPP7447i4uFBRUcHq1avx9fW9rnPm5OSg1WobHN3a3khTbOsp0hQRfzGe3ed3syd1D/sv7kdTrcHOzI4Q7xC1abVrKIPcBmFs2Pj/s5XiVC4diqL87BbcDaIxMy7jXLY3Px+dwIXq8XTqPYqQUZYMHgxNHJgthOiA5Mdf3HKCgoL45ZdfWvWcMrecAMgtzWVv6l52n9/N7tTdHMo4RLVSjbOlMyO9R/LW7W8R4h3CANcBGBleYzS5tpLMX/eRfXgLncqi6GJzDMcqY+JOB7Ml/1W0buPpP6Ivj842wOwq3e2EELceCXZCCNFCaYVputq43ed3cyz7GABedl6EeIcwc/BMQrxD6OXY65oTVwNkp17izN6fMc6KoqfNNtwsCqDYlQMXx7HL6u+4+93BsHvsCLO+5qmEELcoCXZCCNEEiqJwJu+MWhv3R5g7m3cWgN5OvRnpNZKFwQsZ6TUSb/umzTWYd1nLkV1JlJ2JoovhFvp7JOKoNeDXygD25ERg6TOeQVMGM8lBOskJIZqm2cFu9+7dvP322yQlJZGRkcGmTZu4++67r7p/TEwMo0aNqrf9xIkT9O599eW5QAZPCCHajlbR8mvWr+w5v4fdqWqYyyzOxAADBrkN4q4edxHiHUKwVzCu1k1b7b6kBBJ255N5aBt2JVsI6PITYXZZFDjac7JwLPE8xW0hdzLAy4UB1z6dEELU0+xgV1JSwsCBA3n00Ue59957m3zcyZMn6wx8cHZ2vuYx7W3lCSFE+1VZXUlyRrKuNm5v6l7yyvMwMTQhoHMAjwx8hJHeIxnuORx7c/smnVOjgf0JCr/GHcMgYwu+naII7RGHcddqLhT145LFo2h9x+PefziB1xg8IYQQTdHsf0nGjRvHuHHjmn0hFxeXOutpCiFEWyqrLGN/2n5d02r8xXhKK0uxNLEkqEsQzw57lhDvEAI7Bza8PFcDqqogORl27yql4OROvIyjGNNvCyFdUynvYkmGNpzsritx8xuPp7UXMjewEKK13bT/Ivr5+VFeXk7fvn1ZvHhxg82zNTQaDRqNRve+sLDwZhRRCNGBFZQXEHchTte0mpiWSKW2Entze0Z6jeTvoX8nxDvk2nPIXUGrhWPHYOdOOLb/LPalUYzqtYWn+u7C3FNDXtVtVDrfTXX/8Zi7h9LNSL9XHRFCtH83PNi5u7uzZs0ahgwZgkaj4csvvyQ8PJyYmBhCQkIaPGbp0qW8+uqrN7poQogOLL0onbjUOPam7mVP6h6OXDqCVtHiZu1GiHcIU/tNZaT3SPq59MPQoGmDExQFzpxRg1zsrgrKU/cwvNsW7vKL4pm7TlKtmFBkEYJJr6XgOZ5ONj1lmQchxE11w4Ndr1696NWrl+59UFAQFy5c4J133rlqsIuMjCQiIkL3vrCwEE9Z0FAIcRVaRctvOb+xN3UvcRfUMFczYrV7p+6M9BrJU4FPMdJrJD4OPk2aeqTGxYuwaxdER8OxxHQGOP/EXYOjWDN2O1amxZQbemDsOR68lmLkdjv2JjY36jaFEOKa2qS37rBhw9iwYcNVPzczM8PsJs24WVZWdlOuI0R70R5+JjRVGpIyktibulcX5i6XXcbIwIhBboOY2HMiwV7BjPAcgbuNe7POnZ0NMTFqrVzMrmrsqw8wwS+KBUFb6DPmEAqGVHcahrHnQug8AXP7gVIrJ4TQG20S7A4dOoS7e/P+sW1txsbGGBoacu7cuTYthxD6SFEUqqqq2roYOnlleey7sE8Nchf2kpiWiKZag5WJFUGeQcwNnEuwVzBDuwzF2rR5s/devgyxsWqt3K5dkJZymbEDtjIlJIq3I3/G2iQXrYkDhh53QufnMXAfi7GZ4w26UyGEuD7NDnbFxcWcPn1a9z4lJYXDhw/j4OCAl5cXkZGRpKWl8cUXXwDw/vvv07VrV3x9famoqGDDhg1s3LiRjRs3tt5dtICpqSm+vr7k5ubyv//9Dysrq5tWSyiEvquurqaysrJNrq0oCucLzqs1calx7L2wl1+zfgXAzdqNkV7q0lzBXsEMdBt4zTVW/6ygAPbsUUPczp1w5IjCAK8jPDRqC989EcVtdgkYGmih0yDwmA0e4zF0HArXWgJMCCH0QLOD3cGDB+uMaK3pCzd9+nTWrVtHRkYGqampus8rKip4/vnnSUtLw8LCAl9fX6Kiohg/fvw1r3WjJyg2NTXFzMyMkpISKisrJdgJcYUrR6bfSNXaao5mHdU1q+5N3UtaURoAfZz6EOwVzPzh8wn2Cqabfbdm9Y8DKC6GvXtra+SSksDCpJgpoTtYPiWKgOe3YGWQDsbW4HYHeHwCHuPAsvONuF0hhLihDBRFUdq6ENdSM0FxQUFBnUmOW0NJSQn//ve/ZUoVIRpga2vLAw88gJWVVauds6SihANpB3TNqvEX4imqKNJNBBzsGUywVzDDPYfjaNn8Js+yMti3rzbIHTigzi83vN8pHp+0hdG9o+hsvBsDpQJse4H7eOg8AZyDwUj+cyeEaN9u+WAHari7WbUTQrQnZmZm1x3qLhZeZN+FfbrXocxDVGmrsDe3Z4TnCN0gB38PfyxMLJp9fo0GEhJqg1xCAlRUQGe3cmbfE8sk/y30tt2CqeY0GJqBaxh4TACP8WBz23XdmxBC6BsJdkKIVlNZXcnhzMNqiLuoBrmLhRcBuK3TbQR5BjG8y3BGeo+kr3PfJs8fV+calZCYWBvk4uKgvBw6dYJ77rzA1LAt+LtHYVMajUF1KVh61gY5t9Fg3Hq1j0IIoW8k2AkhWiy7JJv4i/G62riD6QcpqyrDzMiMgM4BBHUJYrjncIK6BOFq7dqia1RVwaFDtYMd9u6FkhKwsYGw0Cqm3hFPWM8tuFZHYVBwFAyMwHmEGuQ8JoCdr0xHIoS4Zeh1sLty8MSpU6ck2AnRhqq11RzPPl6nNu70ZXWEvIeNByM8R+iCnJ+7H6ZGpi26jlYLR47U1sjt3g2FhWBpCSNHwvjwbCb4/Uw3sygMM7dCZT6YOasDHjwmgPsdYNqpFe9cCCHaD70OdjWkxk6Im6+gvID9aft1tXEJFxMoqijCyMAIP3c/XYgb7jkcT1vPZo9WraEoteut7tqlzimXlwfm5jB8OIwapeWu4Yfo5xCF8aUtkHsAUMDBv7aJ1dEfWtCsK4QQHY0EOyEEWkXLqdxT7L+4X1cjdyzrGAoKjhaOur5xwz2H4+/hj5Vpy/upKQqcPFlbIxcTo672YGICQUEwahTcHlpAoNd2TLO3QPpPUJ4JJrbgPlYNcu7jwKJlTbtCCNGRSbAT4haUW5rL/rT97L+4n4S0BA6kHSC/PB8DDOjr3FdXEzfcczg9HHq0uDYO1CB39mxtH7mYGMjIAGNjCAhQg9yoMIUR/U9gkbcF0qIgey8oVWr/uJq+cs7DwdCk9R6CEEJ0QBLshOjgKqorOJJ5hP1p+0m4mMD+tP26vnFOlk4M6zKMoZ2HMrTzUAI6B2Bvbn9d11MUOHdODXAxMWqgu3ABDA1hyJA/gtwoCB5WinVJDKRHQfoWKDkHRhbgOlqdV859HFh3va6yCCHEraZN1optqhu98oQQHU3Nclz7L9aGuOSMZDTVGkwMTfBz92O8z3iGdhnKsC7DWrSSQ/1r1g1yMTGQmqoORB04EP76VzXIhYSAndG52iC3dSdUl4NVN+h8l1oz5xIGxs2fy04IIYRKauyEaMeKNEUkpifqQlzCxQSySrIA6GbfTVcbN6zLMAa5DcLM+PpXVmgsyA0aBGFh6mvkSOhkV6k2q6b/0cRaeAIMjMElpLaJ1baXTEcihBCtRIKdEO1ElbaKY1nHOJB2QO0fl7ZfN8DB1syWwM6BuhAX2DkQFyuXVrlus4JcJ6AsUx3wkB4FmduhshDM3dQg13kCuN2uDoQQQgjR6iTYCaGHtIqW33N/52D6QRLTE0lMT+RQxiHKqsowNDCkv0t/XYgb2mUovZ16t2gVh4Y0O8hpq+Hywdom1stJgAE4DlWDnMd46DRIpiMRQoibQIKdEG1MURRSC1LrhLik9CQKNAWAuhRXQOcAAjzUl5+7H9am1q14/asHOT+/2iAXHPxHkAOoyIP0rWqQy/gJNDnqpMDud/4xHcmdYO7UamUUQgjRNHod7GTlCdERZZVkkZiWqAtxiWmJZJdmA9DZprMuxPl7+OPv4Y+DhUOrXr9FQU5RIP+oGuTSoyBnHyhasB9Y28TqOBQM9Xo8lhBCdHjNDna7d+/m7bffJikpiYyMDDZt2sTdd9/d6DGxsbFERERw7NgxPDw8eOGFF5g9e3aTryk1dqK9yijKIDkjWX1lJpOUnsSFwgsAOFo4EtA5AH93f12Yc7dxb/UyKAqkpNQNchcu1A9yI0eCvf0VB1YWw6WdtU2spRfB2ErtI+cxQV3Cy7JLq5dXCCFEyzX7v9clJSUMHDiQRx99lHvvvfea+6ekpDB+/HhmzpzJhg0biIuL48knn8TZ2blJxwvRHtQ0p14Z4pIzkskszgSgk3knBrsP5gHfB3Qhrqt91+ueaqThsjQe5O677ypBDqDotDp6NX0LZMWAtgJseoDnX/+YjiQEjK5/ZK0QQogb47qaYg0MDK5ZY7dgwQI2b97MiRMndNtmz57NkSNHiI+Pb9J1pMZO6BOtouXM5TP1QtzlsssAuFi5MMR9CIPdB+te3nbeNyTEwXXUyAFUayBrd20Ta9HvYGiqzifnMV592fa4IeUWQgjR+m54h5j4+HjGjBlTZ9vYsWNZu3YtlZWVmJjUXyJIo9Gg0Wh07wsLC290MYVoUGV1JSdzT3I48zBJ6UkkZyZzKOMQRRVFAHjaejLYfTDPDH1GF+Lcrd1vWIgDNcidPg2xsbB7d22QMzRUg9z999f2kasX5EBtUtVNR7IDqkrUJlWP8eD3jrryg0nrDc4QQghx89zwYJeZmYmra93Ful1dXamqqiInJwd39/p9ipYuXcqrr756o4smRB3ZJdkcuXSEXy79ovt6PPs4FdUVgDo6dbD7YBaNXMRg98H4ufnhbOV8w8ul1cKJE7VBbvduda3VJgc5bRXk7q9tYs0/ok494jQcfBergc6+v0wSLIQQHcBNGcL259qLmtbfq9VqREZGEhERoXtfWFiIp6dni6792ObHeCX0FTztWna86Hgqqyv5Lee3OgHuyKUjuv5wFsYW9HPph7+7P38b9DcGug1kgOuA615Dtamqq+GXX+oGudxcMDaGgACYPl1dnmvECLhqz4TyHMj4+Y/pSH5Wpycxc1LXX+27ENzHgFnrjrYVQgjR9m54sHNzcyMzM7POtqysLIyNjXF0dGzwGDMzM8zMWqeD9g8nf2DDLxuYEzCHiKAIOtt2bpXzCv2nKAqZxZkcyz7Gkcwj/JL1C0cyj3A8+ziV2koAvO28GeA6gMf8HmOA6wAGuA7Ax8EHI0Ojm1bOykpITq4Ncnv3QkEBmJnBsGEwZ44a5IYNAyurq94s5B2qXbordz+gQKfB0PMpdRSrgz/cxPsSQghx893wYBcUFMSPP/5YZ9u2bdvw9/dvsH9dazsz9wzL45fzbvy7rDiwgvt97+fZoc8S0Dnghl9b3ByKopBelM7x7OMczz7Osexjuq/55fkAWJpY0s+lH4GdA3ls8GMMdB1If9f+N60W7krl5XDgQG1t3L59UFKihrbhw2H+fDXIBQSAuXkjJ6osVPvIpUWpkwSXZYCxjVob57MWPO4Ei9afPkUIIYT+avao2OLiYk6fPg2An58f7733HqNGjcLBwQEvLy8iIyNJS0vjiy++ANTpTvr168fjjz/OzJkziY+PZ/bs2Xz99ddNnu6kNUbFFpQX8M/D/2TF/hWk5Kcw3HM4cwLmcHfvu7E0sWzROcXNpSgKaUVpamjLOlYnxNWs0mBubE5vp974OvvS17mv7mv3Tt1vai3clUpKICFBrZGLjYX9+0GjUZtRR45UQ1xoKAweDI3+X0dRoPBk7bxy2XtAWwm2fWqX7nIaAUamN+3ehBBC6JdmB7uYmBhGjRpVb/v06dNZt24djzzyCOfOnSMmJkb3WWxsLPPmzdNNULxgwYImTVB8I1aeqNZW8+OpH/lg/wfEnIvB2tSae/vcy8MDHiasa1ib/fIXtUoqSvj98u+cyj1V53Ui5wSFGnWEtIWxBX2c+9QJb32d+9LNvlub/x0WFkJcXG3TamIiVFWBo6Ma4mqC3IABYHStolaVqfPJpW9RX8VnwcgcXEbVhjnrbjfjtoQQQrQDer2kWI0bNY/d2byzbPhlA1/+8iWnL5/GzdqNiT0nMrHnRMK7h0tN3g1UWV1JSn5KvfB2KvcUaUVpuv2cLJ3o6diTno496eXYC19nX3xdfPG2827zAFcjNxf27FFDXGwsHD6sjmR1c1MDXE2Q69NHHcl6TSXna/vKXdoJ1WVg5f3Hag/jwXUUGMv3phBCiPpu6WBXQ1EU9qftZ+Pxjfxw8gd+v/w7FsYWBHsFE+odSmjXUAI8AjAzlhn3m0pRFLJLs0nJSyElP6X26x9/Ppd/jmqlGlD7v9WEt54OPXV/7uHYo9XXSW0NmZm1/eNiY+HXX9XtXl51g5yPTxNnENFWQva+2ibWgmNgYAzOwbXrsNr2kelIhBBCXJMEuwaczDnJj6d+ZNe5XexN3UuhphBzY3OGdRlGiFcI/h7+DHYfjIeNxw2diFafVVZXklGcQVphGmlFaVwouFAvuJVUluj272TeiW6dutHNXn1179SdXk696OXYS6+fo6LA+fNqjVxNrdzJk+pnPj51g5y3dzNOXHZJHfCQvgUytkFlAZi7quuvekwAtzvA1O6G3JMQQoiOS6+D3Y3oY9dcVdoqjmQeIfZ8LLHnY9mburfO0lEDXQfSy7EXvZx66WqavOy8MDRoSpub/lEUhfzyfNKL0kkrStMFN93XP/6cVZKFQu23joWxRZ3gpvvzH1/tzNtHSNFq4dix2iC3Zw+k/dEy3LdvbZALCQEPj2acWNFC7sHapbsuHwQMwDGwdukuh8HqxMFCCCFEC+l1sKuhT2vFKorChcILJGeoS0sdzTrKydyTnL58WrdCgbmxOd523njZeeFm7YaLlQvOls7qVytn3XtnK2csTSxbPQRqFS0lFSUUagopqiiiSFNEUUWR+l5TRF55HjmlOeSU5pBdml3755JscstyqdJW1Tmfk6UTnW0609m2s/r1yj//8dXBwkFva90aU1EBBw/Whri4OMjPVycD9vdXV3MYOVKdDPgq0y42cvJ8tTYuPUpdwkuTDSb24D72jzB3J5i7tP5NCSGEuGVJsGsl1dpqUgtSOZl7klO5pziXf47UglQyizPJLs0mqyRLN6fan1kYW2BhYoGliaXuZWFsgZGhEUYGRhgaGGJoYIiCQmV1JZXayga/VlRXUFRRRHFFcaNlNTMyw9nKGSdLJ5wt1a9//rO7jTudbTrjYePRofoWFhWp88bVBLkDB9R55aysIChIDXEjR8LQoWDZ3PEJiqL2j9NNRxIHSrW6XJfHeLWJ1SkIDG/Kgi9CCCFuQRLsbqKK6gpdzVh2aTbZJdmUVJZQWllKaWUpZZVluj+XVpVSra1Gq2h1LwATIxNMDP94GdX/amtmi42pDTZmNtiY2qjv//RnMyOzdlm71hKXLqkBbu9e9WvNiFVn59rauJEjYdAgtZau2apKIHNn7XQkpalgZAlut/8R5saBlVcr35UQQgjRMAl2osNQFDhzpjbE7dkDv/+uftatW22ICw6GXr2uY5Bp0ZnavnKXYkCrAevbrpiOJFSda04IIYS4yfQ62OnD4Amhv6qr4ejR2hC3dy9kZKiBrX//2hA3ciR0vp4lgqsr1FUe0qIgY4u6+oOhCbiE1jax2vSQ6UiEEEK0Ob0OdjWkxk4AlJaqfeLi4tQQt2+fusqDqam6rmpNkBs+HDp1ut6Lpdc2r2Zuh6pisPCoDXJu4WBi0yr3JYQQQrQW6cUt9FZ6uhrial6HD6tLc9naqgMdXnhBDXMBAWBhcZ0X01ZD7oHagQ95h9SpRxyHgW+kGujsB0qtnBBCCL0mwU7ohepqdQWHmhC3bx+cO6d+1q2bOt3IjBnq1759m7DGalNociFj6x9NrD9DxWUwcwT3O6HP8+q0JGbNneNECCGEaDsS7ESbKCqC/ftrQ1xCgtqsamwMgwfD5MlqiBs+HNzdW+miigL5R9Qgl74FchPUiYM7+UGPJ9QmVsdA0JM1aIUQQojm0utgd+XgCdG+pabWhri4ODhyRJ12pFMnNbwtXKgGOX//Fswf15jKIsiMrm1iLUsHY2t1ya7ANeA+Diybs4SEEEIIob9aNHjio48+4u233yYjIwNfX1/ef/99Ro4c2eC+MTExjBo1qt72EydO0Lt37yZdTwZPtC9VVWpwqwlxcXFw8aL6WY8etTVxI0ZA795g2JoLbygKFJ2qHfiQFQvaSrDtVTsdifNIMDJtxYsKIYQQ+qHZNXb//ve/efbZZ/noo48YMWIEn3zyCePGjeP48eN4eV19ItaTJ0/WCWXOzs4tK7HQOwUFalNqTYjbvx9KStTRqkOGwJQptWHO5UasoFVdDpdia2vlis+AoRm4jgK/d9UwZ3PbDbiwEEIIoV+aXWM3dOhQBg8ezOrVq3Xb+vTpw913383SpUvr7V9TY5eXl4e9vX2LCik1dvpDq4WTJyE+Xg1z8fFw7JhaUebkVFsTN2KEGurMb9Q8vSWp6vqr6VFqU2t1KVh6qrVynSeooc7Y6gZdXAghhNBPzaqxq6ioICkpiYULF9bZPmbMGPbt29fosX5+fpSXl9O3b18WL17cYPNsDY1Gg0aj0b0vLCxsTjFFK8rLU+eOqwly+/dDfr4660e/fuq0I/PmqUGuZ88bOBuItgpy4mtr5fKPgoEROI+A/q+otXJ2vjIdiRBCiFtas4JdTk4O1dXVuLq61tnu6upKZmZmg8e4u7uzZs0ahgwZgkaj4csvvyQ8PJyYmBhCQkIaPGbp0qW8+uqrzSmaaAXV1XD8eG1NXEICnDihfuboCMOGwXPPqWEuIECdT+6GKs/+o1ZuizotSWU+mLuoAx58F4P7GDC1v8GFEEIIIdqPZjXFpqen07lzZ/bt20dQUJBu++uvv86XX37Jb7/91qTzTJw4EQMDAzZv3tzg5w3V2Hl6ekpTbCvLzVXDW02QO3BAnYbE0BAGDFAD3LBh6lcfn5tQGaZo4XJy7TqsuYmAAg4Bao1c5wngMESdOFgIIYQQ9TSrxs7JyQkjI6N6tXNZWVn1avEaM2zYMDZs2HDVz83MzDAzM2tO0cQ1VFWpEwBf2Tfu99/Vz1xc1AC3aJH61d8frK1vUsEqCtQlu9Kj1Nq58ktgYqtODtzjSXWyYIumf28JIYQQt7JmBTtTU1OGDBnC9u3bmTx5sm779u3b+ctf/tLk8xw6dAj3Vpt1VvyZoqjTixw4UPtKTFRHqhobw6BBMHYs/P3vapDr1u0mdk1TFCg8UTtJcPZeUKrU/nHdpv8xHclwMDS5SQUSQgghOo5mT3cSERHBww8/jL+/P0FBQaxZs4bU1FRmz54NQGRkJGlpaXzxxRcAvP/++3Tt2hVfX18qKirYsGEDGzduZOPGja17J7ewvDw1uF0Z4moqVT091f5wr7yiNqkOHtzKEwA3RVUpXNpV28Rach6MLMA1HPxXqGHOyvsmF0oIIYToeJod7B544AFyc3NZsmQJGRkZ9OvXjy1btuDtrf5izsjIIDU1Vbd/RUUFzz//PGlpaVhYWODr60tUVBTjx4+/5rVk5Yn6ysrg8OG6Ia6mSdXeHgID1TVVAwPVQNdmFaPFKWqQS4uCrF3qXHNW3aDzRHVKEpdQMLZoo8IJIYQQHVOLVp642W7Veeyqq9VRqVeGuF9+UfvLmZmptW8BAWqICwy8SQMcrlrYCsiJq21iLTwBBsbgElK74oNtL5mORAghhLiB9Hqt2FuJosD582p4q2lWPXhQ7RdnYAB9+6rhbeZM9Wu/furKDm2qLOOK6Ui2QVURWLirIW7gP8DtdnUghBBCCCFuCqmxawOKAmfPQnIyJCWpr+RkuHxZ/dzLq7YWLjBQrZmzsWnbMgOgrYbLibVNrHnJgAE4DVPDnMcE6DRIauWEEEKINiI1djeYVgtnztQPcfn56udduqhLbz37rBrghgwBN7e2LPGfaC6rtXHpUZDxM2hywLSTOg1J7wh1WhJzp7YupRBCCCHQ82DX3gZPaLXqQIaa8FbztWZFNC8vNbg9/7z6dfBgdQ45vaIo6nJdNUt35exTJw62Hwg+s9SaOcehYKjX3zpCCCHELUmaYltIo1GX3zpyRH0lJ8OhQ+rKDQBdu6rhreY1eDA46WvFVmUxXIr+YzqSLVB6EYytwO2OP5pYx4Fll7YupRBCCCGuQapdmiA7Ww1vhw/XBrkTJ9TRqaCORvXzgxdfVEOcn5+6tqpeK/y9dl65rFjQVoBNT/D8q7p0l/NIMJLVP4QQQoj2RGrsrlBdrTalXhngDh+GjAz1c0tL6N9fXblh4ED11b+/ngxsuJZqDWTtrm1iLfodDE3BJUwNch7jwcanrUsphBBCiOtwy9bY5ebCsWNw9GhtkPv1V3UCYIDOndUA9+ijaoAbNAhuuw2MjNqw0M1VerG2eTVzB1SVqE2qHhPA7x1wHQ0mN2tRWCGEEELcaHod7Fpj8ERBgRrgjh1Tg1vNn2uW3DIxUeeIGzgQpkxRA9yAAXrcH64x2irISahtYs3/BQyMwGk4+C5Wa+bs+sl0JEIIIYSeO3LkCO+88w4pKSksXLiQESNG8Oqrr6LRaMjMzOSVV15h0KBB9Y7r8E2xNRnG0FDtC+frq7769VO/9uypBxP9Xo/yHHUakvQoyNgKFXlg5gTu49Qg5z5GnZ5ECCGEEO3G3/72N9asWcObb77JihUrCAkJ4YMPPuDUqVOMHTuWxx9/nA8//LDecXpdY9caNmxQA1zv3mBu3talaQWKFvIO1y7dlbsfUMBhCPR8Wu0r5+APhu2pzVgIIYQQNc6cOYOHhwfGxsakp6dz+fJlFi1aROfOnYmPj8fa2pqJEyc2eGyHr7HrECoLIWN7bX+58kwwtlFr4zwmqNORWOjTrMZCCCGEaKl9+/ZhYWGBn58fAwYMwMHBgZiYmCYdq9c1du1tguJWoyhQ+NsV05HsAaUKbPtAt4fUWjmnEWDUntuQhRBCCNGQ4cOHA5CTk8Ovv/7Kyy+/3ORjDVtywY8++ohu3bphbm7OkCFD2LNnT6P7x8bGMmTIEMzNzenevTsff/xxk64zZ84cjh8/TmJiYkuK2b5UlUH6T5D4FGy+DaL6wi+LwcgChrwPk87CXcfB721wHSWhTgghhOjgdu3ahaIohIWFNfmYZtfY/fvf/+bZZ5/lo48+YsSIEXzyySeMGzeO48eP4+XlVW//lJQUxo8fz8yZM9mwYQNxcXE8+eSTODs7c++99zb38h1LyfnavnKXdkJ1GVh5/9G8OkENcMYWbV1KIYQQQrSBXbt2YWZmxrBhw5p8TLP72A0dOpTBgwezevVq3bY+ffpw9913s3Tp0nr7L1iwgM2bN3PixAndttmzZ3PkyBHi4+ObdM0O08dOWwnZcbVNrAXHwcAYnINrJwm27SPTkQghhBCCPn364Orq2uT+ddDMGruKigqSkpJYuHBhne1jxoxh3759DR4THx/PmDFj6mwbO3Ysa9eupbKyEhMTk3rHaDQaNBqN7n1hYWFziqmjKApFNYu3tpWyS+rkwBlb1Vq5yiIwd1YHPnRdoNbKmdrV7t/W5RVCCCFEq7OxscGgGRU3mZmZ/PbbbzzwwAPNuk6zgl1OTg7V1dW4urrW2e7q6kpmzYy/DRSsof2rqqrIycnB3d293jFLly7l1VdfbU7RGlRUVISdnd21d7zpsoGv/ngJIYQQoqNrbqvjpUuXcHV15f7772/WdVo0KvbPiVNRlEZTaEP7N7S9RmRkJBEREbr3hYWFeHp6NrucNjY2FBQUNGnfgICAlg/SqMiHzGjI3KZOS6LJpaDcALsek8F9LLiFq7V016HmGVy4cKHVmqOv657b4fnkGV6fG/H8QL/vubXPJ8/w+rWHn+MbcU55hvp1vpY8Q5tmLiw/cODAq1aaNaZZwc7JyQkjI6N6F8rKyqpXK1fDzc2twf2NjY1xdHRs8BgzMzPMzMyaU7QGGRgYNPmBGxkZNf0bXFGg4JjaTy4tCnL2gVIN9v2h/0zwGM+IUbM4emzjdZS+Yba2tq32g9ise+4A56shz/D6tObzA/2/Z3mG+nc+0O+f4xtxTnmG+nc+aP2f5dbQrGBnamrKkCFD2L59O5MnT9Zt3759O3/5y18aPCYoKIgff/yxzrZt27bh7+/fYP+6tjJnzpym72xgAPb91FffBQ3uMvvJp1qpZDdOs+65A5zvRtD3e5ZnqH/nuxH0/Z71/RneiPLJM9S/c+r7M2wtzR4V++9//5uHH36Yjz/+mKCgINasWcOnn37KsWPH8Pb2JjIykrS0NL744gtAne6kX79+PP7448ycOZP4+Hhmz57N119/3eTpTmoGQTS342FH0mFGBrcheYbXR57f9ZNneP3kGV4/eYbXT5+fYbP72D3wwAPk5uayZMkSMjIy6NevH1u2bMHb2xuAjIwMUlNTdft369aNLVu2MG/ePFatWoWHhwcrVqxo1hx2zWlS7ajMzMx45ZVXWqWJ+lYlz/D6yPO7fvIMr588w+snz/D66fMzbBdrxQohhBBCiGtr0ZJiQgghhBBC/0iwE0IIIYToICTYCSGEEEJ0EBLshBBCCCE6CAl2ei4tLY2HHnoIR0dHLC0tGTRoEElJSW1drHajqqqKxYsX061bNywsLOjevTtLlixBq9W2ddH01u7du5k4cSIeHh4YGBjw/fff1/lcURT+/ve/4+HhgYWFBWFhYRw7dqxtCqunGnuGlZWVLFiwgP79+2NlZYWHhwfTpk0jPT297Qqsh671fXilxx9/HAMDA95///2bVr72oCnP8MSJE0yaNAk7OztsbGwYNmxYnZktbnXXeobFxcU89dRTdOnSBQsLC/r06cPq1avbprB/kGCnx/Ly8hgxYgQmJib89NNPHD9+nHfffRd7e/u2Llq78dZbb/Hxxx+zcuVKTpw4wbJly3j77bf58MMP27poequkpISBAweycuXKBj9ftmwZ7733HitXriQxMRE3NzfuuOMOioqKbnJJ9Vdjz7C0tJTk5GReeuklkpOT+e677zh16hSTJk1qg5Lqr2t9H9b4/vvv2b9/Px4eHjepZO3HtZ7hmTNnCA4Opnfv3sTExHDkyBFeeuklzM3Nb3JJ9de1nuG8efP4+eef2bBhAydOnGDevHk8/fTT/PDDDze5pFdQhN5asGCBEhwc3NbFaNcmTJig/O1vf6uz7Z577lEeeuihNipR+wIomzZt0r3XarWKm5ub8uabb+q2lZeXK3Z2dsrHH3/cBiXUf39+hg05cOCAAijnz5+/OYVqZ672DC9evKh07txZ+fXXXxVvb29l+fLlN71s7UVDz/CBBx6QfwuboaFn6OvrqyxZsqTOtsGDByuLFy++iSWrS2rs9NjmzZvx9/fnvvvuw8XFBT8/Pz799NO2Lla7EhwcTHR0NKdOnQLgyJEj7N27l/Hjx7dxydqnlJQUMjMzGTNmjG6bmZkZoaGh7Nu3rw1L1r4VFBRgYGAgtfHNoNVqefjhh5k/fz6+vr5tXZx2R6vVEhUVRc+ePRk7diwuLi4MHTq00SZvUV9wcDCbN28mLS0NRVHYtWsXp06dYuzYsW1WJgl2euzs2bOsXr2aHj16sHXrVmbPns3cuXN1y7WJa1uwYAEPPvggvXv3xsTEBD8/P5599lkefPDBti5au5SZmQmAq6trne2urq66z0TzlJeXs3DhQqZOnXrLr7DTHG+99RbGxsbMnTu3rYvSLmVlZVFcXMybb77JnXfeybZt25g8eTL33HMPsbGxbV28dmPFihX07duXLl26YGpqyp133slHH31EcHBwm5Wp2UuKiZtHq9Xi7+/PG2+8AYCfnx/Hjh1j9erVTJs2rY1L1z78+9//ZsOGDfzrX//C19eXw4cP8+yzz+Lh4cH06dPbunjt1p/XbFYU5ZZdx/l6VFZWMmXKFLRaLR999FFbF6fdSEpK4oMPPiA5OVm+71qoZgDZX/7yF+bNmwfAoEGD2LdvHx9//DGhoaFtWbx2Y8WKFSQkJLB582a8vb3ZvXs3Tz75JO7u7tx+++1tUiYJdnrM3d2dvn371tnWp08fNm7c2EYlan/mz5/PwoULmTJlCgD9+/fn/PnzLF26VIJdC7i5uQFqzZ27u7tue1ZWVr1aPNG4yspK7r//flJSUti5c6fU1jXDnj17yMrKwsvLS7eturqa5557jvfff59z5861XeHaCScnJ4yNjRv8HbN37942KlX7UlZWxqJFi9i0aRMTJkwAYMCAARw+fJh33nmnzYKdNMXqsREjRnDy5Mk6206dOoW3t3cblaj9KS0txdCw7re5kZGRTHfSQt26dcPNzY3t27frtlVUVBAbG8vw4cPbsGTtS02o+/3339mxYweOjo5tXaR25eGHH+aXX37h8OHDupeHhwfz589n69atbV28dsHU1JSAgAD5HXMdKisrqays1LvfMVJjp8fmzZvH8OHDeeONN7j//vs5cOAAa9asYc2aNW1dtHZj4sSJvP7663h5eeHr68uhQ4d47733+Nvf/tbWRdNbxcXFnD59Wvc+JSWFw4cP4+DggJeXF88++yxvvPEGPXr0oEePHrzxxhtYWloyderUNiy1fmnsGXp4ePDXv/6V5ORk/ve//1FdXa3rn+jg4ICpqWlbFVuvXOv78M9h2MTEBDc3N3r16nWzi6q3rvUM58+fzwMPPEBISAijRo3i559/5scffyQmJqbtCq1nrvUMQ0NDmT9/PhYWFnh7exMbG8sXX3zBe++913aFbrPxuKJJfvzxR6Vfv36KmZmZ0rt3b2XNmjVtXaR2pbCwUHnmmWcULy8vxdzcXOnevbvy4osvKhqNpq2Lprd27dqlAPVe06dPVxRFnfLklVdeUdzc3BQzMzMlJCREOXr0aNsWWs809gxTUlIa/AxQdu3a1dZF1xvX+j78M5nupL6mPMO1a9cqPj4+irm5uTJw4EDl+++/b7sC66FrPcOMjAzlkUceUTw8PBRzc3OlV69eyrvvvqtotdo2K7OBoijKTciPQgghhBDiBpM+dkIIIYQQHYQEOyGEEEKIDkKCnRBCCCFEByHBTgghhBCig5BgJ4QQQgjRQUiwE0IIIYToICTYCSGEEEJ0EBLshBBCCCE6CAl2QgghhBAdhAQ7IYQQQogOQoKdEEIIIUQHIcFOCCGEEKKD+H9xgpC5fZYqCQAAAABJRU5ErkJggg==\n",
+ "image/png": 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\n",
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"Graphics object consisting of 3 graphics primitives"
]
@@ -735,10 +737,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\left[\\left(-\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}, 1\\right), \\left(\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}, 1\\right)\\right]\\)</html>"
+ "<html>\\(\\displaystyle \\left[\\left(-\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^{\\beta_0}(v)}}}, 1\\right), \\left(\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^{\\beta_0}(v)}}}, 1\\right)\\right]\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\left[\\left(-\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}, 1\\right), \\left(\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}, 1\\right)\\right]$"
+ "$\\displaystyle \\left[\\left(-\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^{\\beta_0}(v)}}}, 1\\right), \\left(\\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^{\\beta_0}(v)}}}, 1\\right)\\right]$"
],
"text/plain": [
"[(-sqrt(1/2)*q*sqrt(R/twisted_v2), 1), (sqrt(1/2)*q*sqrt(R/twisted_v2), 1)]"
@@ -766,10 +768,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}\\)</html>"
+ "<html>\\(\\displaystyle \\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^{\\beta_0}(v)}}}\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^B(v)}}}$"
+ "$\\displaystyle \\sqrt{\\frac{1}{2}} q \\sqrt{\\frac{R}{{\\mathrm{ch}_2^{\\beta_0}(v)}}}$"
],
"text/plain": [
"sqrt(1/2)*q*sqrt(R/twisted_v2)"
@@ -841,10 +843,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\left[\\left(\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)} + 2 \\, R {\\mathrm{ch}_2^B(v)}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right), \\left(-\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)} - 2 \\, R {\\mathrm{ch}_2^B(v)}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right)\\right]\\)</html>"
+ "<html>\\(\\displaystyle \\left[\\left(\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^{\\beta_0}(v)}} {\\left(q - {\\mathrm{ch}_1^{\\beta_0}(v)}\\right)} + 2 \\, R {\\mathrm{ch}_2^{\\beta_0}(v)}}{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}, 1\\right), \\left(-\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^{\\beta_0}(v)}} {\\left(q - {\\mathrm{ch}_1^{\\beta_0}(v)}\\right)} - 2 \\, R {\\mathrm{ch}_2^{\\beta_0}(v)}}{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}, 1\\right)\\right]\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\left[\\left(\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)} + 2 \\, R {\\mathrm{ch}_2^B(v)}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right), \\left(-\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^B(v)}} {\\left(q - {\\mathrm{ch}_1^B(v)}\\right)} - 2 \\, R {\\mathrm{ch}_2^B(v)}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right)\\right]$"
+ "$\\displaystyle \\left[\\left(\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^{\\beta_0}(v)}} {\\left(q - {\\mathrm{ch}_1^{\\beta_0}(v)}\\right)} + 2 \\, R {\\mathrm{ch}_2^{\\beta_0}(v)}}{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}, 1\\right), \\left(-\\frac{\\sqrt{2} \\sqrt{R {\\mathrm{ch}_2^{\\beta_0}(v)}} {\\left(q - {\\mathrm{ch}_1^{\\beta_0}(v)}\\right)} - 2 \\, R {\\mathrm{ch}_2^{\\beta_0}(v)}}{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}, 1\\right)\\right]$"
],
"text/plain": [
"[(1/2*(sqrt(2)*sqrt(R*twisted_v2)*(q - twisted_v1) + 2*R*twisted_v2)/twisted_v2,\n",
@@ -875,10 +877,10 @@
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle -\\frac{\\sqrt{2} \\sqrt{R} q}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^B(v)}}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + R\\)</html>"
+ "<html>\\(\\displaystyle -\\frac{\\sqrt{2} \\sqrt{R} q}{2 \\, \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}}} + \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^{\\beta_0}(v)}}{2 \\, \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}}} + R\\)</html>"
],
"text/latex": [
- "$\\displaystyle -\\frac{\\sqrt{2} \\sqrt{R} q}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^B(v)}}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + R$"
+ "$\\displaystyle -\\frac{\\sqrt{2} \\sqrt{R} q}{2 \\, \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}}} + \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^{\\beta_0}(v)}}{2 \\, \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}}} + R$"
],
"text/plain": [
"-1/2*sqrt(2)*sqrt(R)*q/sqrt(twisted_v2) + 1/2*sqrt(2)*sqrt(R)*twisted_v1/sqrt(twisted_v2) + R"
@@ -937,23 +939,23 @@
},
{
"cell_type": "code",
- "execution_count": 55,
+ "execution_count": 34,
"id": "0e900943",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} \\min\\left(q, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^B(v)}} - q + {\\mathrm{ch}_1^B(v)}\\right)}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}}\\)</html>"
+ "<html>\\(\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} \\min\\left(q, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}} - q + {\\mathrm{ch}_1^{\\beta_0}(v)}\\right)}{2 \\, \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}}}\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} \\min\\left(q, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^B(v)}} - q + {\\mathrm{ch}_1^B(v)}\\right)}{2 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}}$"
+ "$\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} \\min\\left(q, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}} - q + {\\mathrm{ch}_1^{\\beta_0}(v)}\\right)}{2 \\, \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}}}$"
],
"text/plain": [
"1/2*sqrt(2)*sqrt(R)*min(q, sqrt(2)*sqrt(R)*sqrt(twisted_v2) - q + twisted_v1)/sqrt(twisted_v2)"
]
},
- "execution_count": 55,
+ "execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
@@ -981,23 +983,23 @@
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 35,
"id": "09b81707",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\frac{1}{2} \\, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^B(v)}} + \\frac{1}{2} \\, {\\mathrm{ch}_1^B(v)}\\)</html>"
+ "<html>\\(\\displaystyle \\frac{1}{2} \\, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}} + \\frac{1}{2} \\, {\\mathrm{ch}_1^{\\beta_0}(v)}\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\frac{1}{2} \\, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^B(v)}} + \\frac{1}{2} \\, {\\mathrm{ch}_1^B(v)}$"
+ "$\\displaystyle \\frac{1}{2} \\, \\sqrt{2} \\sqrt{R} \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}} + \\frac{1}{2} \\, {\\mathrm{ch}_1^{\\beta_0}(v)}$"
],
"text/plain": [
"1/2*sqrt(2)*sqrt(R)*sqrt(twisted_v2) + 1/2*twisted_v1"
]
},
- "execution_count": 34,
+ "execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
@@ -1013,23 +1015,23 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 36,
"id": "d9c2f5fc",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^B(v)}}{4 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + \\frac{1}{2} \\, R\\)</html>"
+ "<html>\\(\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^{\\beta_0}(v)}}{4 \\, \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}}} + \\frac{1}{2} \\, R\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^B(v)}}{4 \\, \\sqrt{{\\mathrm{ch}_2^B(v)}}} + \\frac{1}{2} \\, R$"
+ "$\\displaystyle \\frac{\\sqrt{2} \\sqrt{R} {\\mathrm{ch}_1^{\\beta_0}(v)}}{4 \\, \\sqrt{{\\mathrm{ch}_2^{\\beta_0}(v)}}} + \\frac{1}{2} \\, R$"
],
"text/plain": [
"1/4*sqrt(2)*sqrt(R)*twisted_v1/sqrt(twisted_v2) + 1/2*R"
]
},
- "execution_count": 35,
+ "execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
@@ -1053,24 +1055,24 @@
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": 37,
"id": "7b6ac93e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
- "<html>\\(\\displaystyle \\left[\\left(-\\frac{R {\\varepsilon} + \\sqrt{R^{2} {\\varepsilon}^{2} + 2 \\, R q^{2} {\\mathrm{ch}_2^B(v)}}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right), \\left(-\\frac{R {\\varepsilon} - \\sqrt{R^{2} {\\varepsilon}^{2} + 2 \\, R q^{2} {\\mathrm{ch}_2^B(v)}}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right)\\right]\\)</html>"
+ "<html>\\(\\displaystyle \\left[\\left(-\\frac{R {\\varepsilon} + \\sqrt{R^{2} {\\varepsilon}^{2} + 2 \\, R q^{2} {\\mathrm{ch}_2^{\\beta_0}(v)}}}{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}, 1\\right), \\left(-\\frac{R {\\varepsilon} - \\sqrt{R^{2} {\\varepsilon}^{2} + 2 \\, R q^{2} {\\mathrm{ch}_2^{\\beta_0}(v)}}}{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}, 1\\right)\\right]\\)</html>"
],
"text/latex": [
- "$\\displaystyle \\left[\\left(-\\frac{R {\\varepsilon} + \\sqrt{R^{2} {\\varepsilon}^{2} + 2 \\, R q^{2} {\\mathrm{ch}_2^B(v)}}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right), \\left(-\\frac{R {\\varepsilon} - \\sqrt{R^{2} {\\varepsilon}^{2} + 2 \\, R q^{2} {\\mathrm{ch}_2^B(v)}}}{2 \\, {\\mathrm{ch}_2^B(v)}}, 1\\right)\\right]$"
+ "$\\displaystyle \\left[\\left(-\\frac{R {\\varepsilon} + \\sqrt{R^{2} {\\varepsilon}^{2} + 2 \\, R q^{2} {\\mathrm{ch}_2^{\\beta_0}(v)}}}{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}, 1\\right), \\left(-\\frac{R {\\varepsilon} - \\sqrt{R^{2} {\\varepsilon}^{2} + 2 \\, R q^{2} {\\mathrm{ch}_2^{\\beta_0}(v)}}}{2 \\, {\\mathrm{ch}_2^{\\beta_0}(v)}}, 1\\right)\\right]$"
],
"text/plain": [
"[(-1/2*(R*epsilon + sqrt(R^2*epsilon^2 + 2*R*q^2*twisted_v2))/twisted_v2, 1),\n",
" (-1/2*(R*epsilon - sqrt(R^2*epsilon^2 + 2*R*q^2*twisted_v2))/twisted_v2, 1)]"
]
},
- "execution_count": 36,
+ "execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
@@ -1086,7 +1088,7 @@
],
"metadata": {
"kernelspec": {
- "display_name": "SageMath 10.0",
+ "display_name": "SageMath 10.1",
"language": "sage",
"name": "sagemath"
},
@@ -1100,7 +1102,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.11.6"
+ "version": "3.11.7"
}
},
"nbformat": 4,
diff --git a/tex/bounds-on-semistabilisers.tex b/tex/bounds-on-semistabilisers.tex
index b536737..63a5bb0 100644
--- a/tex/bounds-on-semistabilisers.tex
+++ b/tex/bounds-on-semistabilisers.tex
@@ -268,13 +268,8 @@ $\chern^{\beta_0}_0(u)$ in terms of the former).
\subsubsection{Size of pseudo-wall\texorpdfstring{: $\chern_2^P(u)>0$}{}}
\label{subsect-d-bound-radiuscond}
-This condition refers to condition
-\ref{item:radiuscond:lem:num_test_prob1}
-from Lemma \ref{lem:num_test_prob1}
-(or corollary \ref{cor:num_test_prob2}).
-In the case where we are tackling problem \ref{problem:problem-statement-2}
-(with $\beta = \beta_{-}$), this condition, when expressed as a bound on $d$,
-amounts to:
+In the context of Problem \ref{problem:problem-statement-2}, this condition,
+when rearranged to a bound on $d$, amounts to:
\begin{align}
\label{eqn:radius-cond-betamin}
@@ -287,18 +282,19 @@ amounts to:
import other_P_choice as problem1
\end{sagesilent}
-In the case where we are tackling problem \ref{problem:problem-statement-1},
-with some Chern character $v$ with positive rank, and some choice of point
-$P=(A,B) \in \Theta_v^-$.
+In the case where we are tackling Problem \ref{problem:problem-statement-1},
+with
+$P=(\alpha_0,\beta_0) \in \Theta_v^-$.
Then $\sage{problem1.A2_subs}$ follows from $\chern_2^P(v)=0$. Using this substitution into the
-condition $\chern_2^P(u)>0$ yields:
+condition $\chern_2^P(u) = \sage{problem1.radius_condition_before_sub}$ yields:
\begin{equation*}
\sage{problem1.radius_condition}
\end{equation*}
\noindent
-Expressing this as a bound on $d$, then yields:
+Expanding $\chern^{\beta_0}_2(u)$ in terms of $r$, $c$, $d$, and rearranging for
+$d$ then yields:
\begin{equation*}
\sage{problem1.radius_condition_d_bound}
--
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