{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Conformal completion of Minkowski spacetime\n", "\n", "This Jupyter/SageMath notebook is relative to the lectures\n", "[Geometry and physics of black holes](https://relativite.obspm.fr/blackholes/).\n", " \n", "It makes use of SageMath differential geometry tools developed through the \n", "[SageManifolds](http://sagemanifolds.obspm.fr) project." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*NB:* a version of SageMath at least equal to 9.4 is required to run this notebook: " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'SageMath version 10.3, Release Date: 2024-03-19'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "version()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set up the notebook to display mathematical objects using LaTeX formatting:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%display latex" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spherical coordinates on Minkowski spacetime\n", "\n", "We declare the spacetime manifold $M$:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "M = Manifold(4, 'M', structure='Lorentzian')\n", "print(M)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and the spherical coordinates $(t,r,\\theta,\\phi)$ as a chart on $M$:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(M,(t, r, {\\theta}, {\\phi})\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(M,(t, r, {\\theta}, {\\phi})\\right)$" ], "text/plain": [ "Chart (M, (t, r, th, ph))" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS. = M.chart(r't r:(0,+oo) th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "XS" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( 0 , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)\$$" ], "text/latex": [ "$\\displaystyle t :\\ \\left( -\\infty, +\\infty \\right) ;\\quad r :\\ \\left( 0 , +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$" ], "text/plain": [ "t: (-oo, +oo); r: (0, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In term of these coordinates, we set up Minkowski metric as" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle g = -\\mathrm{d} t\\otimes \\mathrm{d} t+\\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle g = -\\mathrm{d} t\\otimes \\mathrm{d} t+\\mathrm{d} r\\otimes \\mathrm{d} r + r^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + r^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "g = -dt⊗dt + dr⊗dr + r^2 dth⊗dth + r^2*sin(th)^2 dph⊗dph" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g = M.metric()\n", "g[0,0] = -1\n", "g[1,1] = 1\n", "g[2,2] = r^2\n", "g[3,3] = r^2*sin(th)^2\n", "g.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Null coordinates\n", "\n", "Let us introduce the null coordinates $u=t-r$ (retarded time) and $v=t+r$ (advanced time):" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(M,(u, v, {\\theta}, {\\phi})\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(M,(u, v, {\\theta}, {\\phi})\\right)$" ], "text/plain": [ "Chart (M, (u, v, th, ph))" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN. = M.chart(r'u v th:(0,pi):\\theta ph:(0,2*pi):\\phi',\n", " coord_restrictions=lambda u,v,th,ph: v-u>0)\n", "XN" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle u :\\ \\left( -\\infty, +\\infty \\right) ;\\quad v :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)\$$" ], "text/latex": [ "$\\displaystyle u :\\ \\left( -\\infty, +\\infty \\right) ;\\quad v :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$" ], "text/plain": [ "u: (-oo, +oo); v: (-oo, +oo); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN.coord_range()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} u & = & -r + t \\\\ v & = & r + t \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} u & = & -r + t \\\\ v & = & r + t \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "u = -r + t\n", "v = r + t\n", "th = th\n", "ph = ph" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XN = XS.transition_map(XN, [t-r, t+r, th, ph])\n", "XS_to_XN.display()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & \\frac{1}{2} \\, u + \\frac{1}{2} \\, v \\\\ r & = & -\\frac{1}{2} \\, u + \\frac{1}{2} \\, v \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & \\frac{1}{2} \\, u + \\frac{1}{2} \\, v \\\\ r & = & -\\frac{1}{2} \\, u + \\frac{1}{2} \\, v \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "t = 1/2*u + 1/2*v\n", "r = -1/2*u + 1/2*v\n", "th = th\n", "ph = ph" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XN.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In terms of the null coordinates $(u,v,\\theta,\\phi)$, the Minkowski metric writes" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle g = -\\frac{1}{2} \\mathrm{d} u\\otimes \\mathrm{d} v -\\frac{1}{2} \\mathrm{d} v\\otimes \\mathrm{d} u + \\left( \\frac{1}{4} \\, u^{2} - \\frac{1}{2} \\, u v + \\frac{1}{4} \\, v^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{1}{4} \\, u^{2} \\sin\\left({\\theta}\\right)^{2} - \\frac{1}{2} \\, u v \\sin\\left({\\theta}\\right)^{2} + \\frac{1}{4} \\, v^{2} \\sin\\left({\\theta}\\right)^{2} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle g = -\\frac{1}{2} \\mathrm{d} u\\otimes \\mathrm{d} v -\\frac{1}{2} \\mathrm{d} v\\otimes \\mathrm{d} u + \\left( \\frac{1}{4} \\, u^{2} - \\frac{1}{2} \\, u v + \\frac{1}{4} \\, v^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{1}{4} \\, u^{2} \\sin\\left({\\theta}\\right)^{2} - \\frac{1}{2} \\, u v \\sin\\left({\\theta}\\right)^{2} + \\frac{1}{4} \\, v^{2} \\sin\\left({\\theta}\\right)^{2} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "g = -1/2 du⊗dv - 1/2 dv⊗du + (1/4*u^2 - 1/2*u*v + 1/4*v^2) dth⊗dth + (1/4*u^2*sin(th)^2 - 1/2*u*v*sin(th)^2 + 1/4*v^2*sin(th)^2) dph⊗dph" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(XN)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a better display, let us factor the metric components:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle g = -\\frac{1}{2} \\mathrm{d} u\\otimes \\mathrm{d} v -\\frac{1}{2} \\mathrm{d} v\\otimes \\mathrm{d} u + \\frac{1}{4} \\, {\\left(u - v\\right)}^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{1}{4} \\, {\\left(u - v\\right)}^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle g = -\\frac{1}{2} \\mathrm{d} u\\otimes \\mathrm{d} v -\\frac{1}{2} \\mathrm{d} v\\otimes \\mathrm{d} u + \\frac{1}{4} \\, {\\left(u - v\\right)}^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{1}{4} \\, {\\left(u - v\\right)}^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "g = -1/2 du⊗dv - 1/2 dv⊗du + 1/4*(u - v)^2 dth⊗dth + 1/4*(u - v)^2*sin(th)^2 dph⊗dph" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.apply_map(factor, frame=XN.frame(), chart=XN,\n", " keep_other_components=True)\n", "g.display(XN)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us plot the coordinate grid $(u,v)$ in terms of the coordinates $(t,r)$:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 33 graphics primitives" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "graph = XN.plot(XS, ambient_coords=(r,t), fixed_coords={th: pi/2, ph: pi}, \n", " number_values=17, plot_points=200, color='green', \n", " style={u: '--', v: '-'}, thickness=1.5)\n", "graph" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 33 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph, xmin=0, xmax=4, ymin=0, ymax=4, aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "graph.save(\"glo_null_coord.pdf\", xmin=0, xmax=4, ymin=0, ymax=4, \n", " aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Compactified null coordinates\n", "\n", "Instead of $(u,v)$, which span $\\mathbb{R}$, let consider the coordinates $U = \\mathrm{atan}\\, u$ and $V = \\mathrm{atan}\\, v$, which span $\\left(-\\frac{\\pi}{2}, \\frac{\\pi}{2}\\right)$:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = plot(atan(u), (u,-6, 6), thickness=2, axes_labels=[r'$u$', r'$U$']) \\\n", " + line([(-6,-pi/2), (6,-pi/2)], linestyle='--') \\\n", " + line([(-6,pi/2), (6,pi/2)], linestyle='--')\n", "show(graph, aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "graph.save('glo_atan.pdf', aspect_ratio=1)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(M,(U, V, {\\theta}, {\\phi})\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(M,(U, V, {\\theta}, {\\phi})\\right)$" ], "text/plain": [ "Chart (M, (U, V, th, ph))" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XNC. = M.chart(r'U:(-pi/2,pi/2) V:(-pi/2,pi/2) th:(0,pi):\\theta ph:(0,2*pi):\\phi',\n", " coord_restrictions=lambda U,V,th,ph: V-U>0)\n", "XNC" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle U :\\ \\left( -\\frac{1}{2} \\, \\pi , \\frac{1}{2} \\, \\pi \\right) ;\\quad V :\\ \\left( -\\frac{1}{2} \\, \\pi , \\frac{1}{2} \\, \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)\$$" ], "text/latex": [ "$\\displaystyle U :\\ \\left( -\\frac{1}{2} \\, \\pi , \\frac{1}{2} \\, \\pi \\right) ;\\quad V :\\ \\left( -\\frac{1}{2} \\, \\pi , \\frac{1}{2} \\, \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$" ], "text/plain": [ "U: (-1/2*pi, 1/2*pi); V: (-1/2*pi, 1/2*pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XNC.coord_range()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} U & = & \\arctan\\left(u\\right) \\\\ V & = & \\arctan\\left(v\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} U & = & \\arctan\\left(u\\right) \\\\ V & = & \\arctan\\left(v\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "U = arctan(u)\n", "V = arctan(v)\n", "th = th\n", "ph = ph" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN_to_XNC = XN.transition_map(XNC, [atan(u), atan(v), th, ph])\n", "XN_to_XNC.display()" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} u & = & \\frac{\\sin\\left(U\\right)}{\\cos\\left(U\\right)} \\\\ v & = & \\frac{\\sin\\left(V\\right)}{\\cos\\left(V\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} u & = & \\frac{\\sin\\left(U\\right)}{\\cos\\left(U\\right)} \\\\ v & = & \\frac{\\sin\\left(V\\right)}{\\cos\\left(V\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "u = sin(U)/cos(U)\n", "v = sin(V)/cos(V)\n", "th = th\n", "ph = ph" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XN_to_XNC.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expressed in terms of the coordinates $(U,V,\\theta,\\phi)$, the metric tensor is" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle g = -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} U\\otimes \\mathrm{d} V -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} V\\otimes \\mathrm{d} U + \\left( \\frac{\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\left(\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle g = -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} U\\otimes \\mathrm{d} V -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} V\\otimes \\mathrm{d} U + \\left( \\frac{\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\left(\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "g = -1/2/(cos(U)^2*cos(V)^2) dU⊗dV - 1/2/(cos(U)^2*cos(V)^2) dV⊗dU + 1/4*(cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2)/(cos(U)^2*cos(V)^2) dth⊗dth + 1/4*(cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2)*sin(th)^2/(cos(U)^2*cos(V)^2) dph⊗dph" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.display(XNC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, for a better display, we may factor the metric components:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle g = -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} U\\otimes \\mathrm{d} V -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} V\\otimes \\mathrm{d} U + \\frac{{\\left(\\cos\\left(V\\right) \\sin\\left(U\\right) - \\cos\\left(U\\right) \\sin\\left(V\\right)\\right)}^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\left(\\cos\\left(V\\right) \\sin\\left(U\\right) - \\cos\\left(U\\right) \\sin\\left(V\\right)\\right)}^{2} \\sin\\left({\\theta}\\right)^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle g = -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} U\\otimes \\mathrm{d} V -\\frac{1}{2 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} V\\otimes \\mathrm{d} U + \\frac{{\\left(\\cos\\left(V\\right) \\sin\\left(U\\right) - \\cos\\left(U\\right) \\sin\\left(V\\right)\\right)}^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\left(\\cos\\left(V\\right) \\sin\\left(U\\right) - \\cos\\left(U\\right) \\sin\\left(V\\right)\\right)}^{2} \\sin\\left({\\theta}\\right)^{2}}{4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "g = -1/2/(cos(U)^2*cos(V)^2) dU⊗dV - 1/2/(cos(U)^2*cos(V)^2) dV⊗dU + 1/4*(cos(V)*sin(U) - cos(U)*sin(V))^2/(cos(U)^2*cos(V)^2) dth⊗dth + 1/4*(cos(V)*sin(U) - cos(U)*sin(V))^2*sin(th)^2/(cos(U)^2*cos(V)^2) dph⊗dph" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g.apply_map(factor, frame=XNC.frame(), chart=XNC,\n", " keep_other_components=True)\n", "g.display(XNC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us call $\\Omega^{-2}$ the common factor: " ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{u^{2} + 1} \\sqrt{v^{2} + 1}} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\end{array}\$$" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{u^{2} + 1} \\sqrt{v^{2} + 1}} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\end{array}$" ], "text/plain": [ "Omega: M → ℝ\n", " (u, v, th, ph) ↦ 2/(sqrt(u^2 + 1)*sqrt(v^2 + 1))\n", " (U, V, th, ph) ↦ 2*cos(U)*cos(V)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega = M.scalar_field({XNC: 2*cos(U)*cos(V)}, name='Omega', \n", " latex_name=r'\\Omega')\n", "Omega.display()" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}} \\end{array}\$$" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}} \\end{array}$" ], "text/plain": [ "Omega: M → ℝ\n", " (t, r, th, ph) ↦ 2/(sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1))" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.display(XS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conformal metric\n", "\n", "We introduce the metric $\\tilde g = \\Omega^2 g$:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\tilde{g} = -2 \\mathrm{d} U\\otimes \\mathrm{d} V -2 \\mathrm{d} V\\otimes \\mathrm{d} U + \\left( \\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + {\\left(\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle \\tilde{g} = -2 \\mathrm{d} U\\otimes \\mathrm{d} V -2 \\mathrm{d} V\\otimes \\mathrm{d} U + \\left( \\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + {\\left(\\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}\\right)} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "gt = -2 dU⊗dV - 2 dV⊗dU + (cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2) dth⊗dth + (cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2)*sin(th)^2 dph⊗dph" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt = M.lorentzian_metric('gt', latex_name=r'\\tilde{g}')\n", "gt.set(Omega^2*g)\n", "gt.display(XNC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly the metric components ${\\tilde g}_{\\theta\\theta}$ and ${\\tilde g}_{\\phi\\phi}$ can be simplified further. Let us do it by hand, by extracting the symbolic expression via expr():" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}\$$" ], "text/latex": [ "$\\displaystyle \\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}$" ], "text/plain": [ "cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g22 = gt[XNC.frame(), 2, 2, XNC].expr()\n", "g22" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\sin\\left(-U + V\\right)^{2}\$$" ], "text/latex": [ "$\\displaystyle \\sin\\left(-U + V\\right)^{2}$" ], "text/plain": [ "sin(-U + V)^2" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g22_simpl = g22.factor().reduce_trig()\n", "g22_simpl" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}\$$" ], "text/latex": [ "$\\displaystyle \\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}$" ], "text/plain": [ "cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g33st = gt[XNC.frame(), 3, 3, XNC].expr() / sin(th)^2\n", "g33st" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}\$$" ], "text/latex": [ "$\\displaystyle \\cos\\left(V\\right)^{2} \\sin\\left(U\\right)^{2} - 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\sin\\left(U\\right) \\sin\\left(V\\right) + \\cos\\left(U\\right)^{2} \\sin\\left(V\\right)^{2}$" ], "text/plain": [ "cos(V)^2*sin(U)^2 - 2*cos(U)*cos(V)*sin(U)*sin(V) + cos(U)^2*sin(V)^2" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g33st.expand_trig()" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\sin\\left(-U + V\\right)^{2} \\sin\\left({\\theta}\\right)^{2}\$$" ], "text/latex": [ "$\\displaystyle \\sin\\left(-U + V\\right)^{2} \\sin\\left({\\theta}\\right)^{2}$" ], "text/plain": [ "sin(-U + V)^2*sin(th)^2" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g33_simpl = g33st.factor().reduce_trig() * sin(th)^2\n", "g33_simpl" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "gt.add_comp(XNC.frame())[2,2, XNC] = g22_simpl\n", "gt.add_comp(XNC.frame())[3,3, XNC] = g33_simpl" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence the final form of the conformal metric in terms of the compactified null coordinates:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\tilde{g} = -2 \\mathrm{d} U\\otimes \\mathrm{d} V -2 \\mathrm{d} V\\otimes \\mathrm{d} U + \\sin\\left(-U + V\\right)^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin\\left(-U + V\\right)^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle \\tilde{g} = -2 \\mathrm{d} U\\otimes \\mathrm{d} V -2 \\mathrm{d} V\\otimes \\mathrm{d} U + \\sin\\left(-U + V\\right)^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin\\left(-U + V\\right)^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "gt = -2 dU⊗dV - 2 dV⊗dU + sin(-U + V)^2 dth⊗dth + sin(-U + V)^2*sin(th)^2 dph⊗dph" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display(XNC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In terms of the non-compactified null coordinates $(u,v,\\theta,\\phi)$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\tilde{g} = \\left( -\\frac{2}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} u\\otimes \\mathrm{d} v + \\left( -\\frac{2}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} v\\otimes \\mathrm{d} u + \\left( \\frac{u^{2} - 2 \\, u v + v^{2}}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{u^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, u v \\sin\\left({\\theta}\\right)^{2} + v^{2} \\sin\\left({\\theta}\\right)^{2}}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle \\tilde{g} = \\left( -\\frac{2}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} u\\otimes \\mathrm{d} v + \\left( -\\frac{2}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} v\\otimes \\mathrm{d} u + \\left( \\frac{u^{2} - 2 \\, u v + v^{2}}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{u^{2} \\sin\\left({\\theta}\\right)^{2} - 2 \\, u v \\sin\\left({\\theta}\\right)^{2} + v^{2} \\sin\\left({\\theta}\\right)^{2}}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "gt = -2/((u^2 + 1)*v^2 + u^2 + 1) du⊗dv - 2/((u^2 + 1)*v^2 + u^2 + 1) dv⊗du + (u^2 - 2*u*v + v^2)/((u^2 + 1)*v^2 + u^2 + 1) dth⊗dth + (u^2*sin(th)^2 - 2*u*v*sin(th)^2 + v^2*sin(th)^2)/((u^2 + 1)*v^2 + u^2 + 1) dph⊗dph" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display(XN)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\tilde{g} = -\\frac{2}{{\\left(u^{2} + 1\\right)} {\\left(v^{2} + 1\\right)}} \\mathrm{d} u\\otimes \\mathrm{d} v -\\frac{2}{{\\left(u^{2} + 1\\right)} {\\left(v^{2} + 1\\right)}} \\mathrm{d} v\\otimes \\mathrm{d} u + \\frac{{\\left(u - v\\right)}^{2}}{{\\left(u^{2} + 1\\right)} {\\left(v^{2} + 1\\right)}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\left(u - v\\right)}^{2} \\sin\\left({\\theta}\\right)^{2}}{{\\left(u^{2} + 1\\right)} {\\left(v^{2} + 1\\right)}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle \\tilde{g} = -\\frac{2}{{\\left(u^{2} + 1\\right)} {\\left(v^{2} + 1\\right)}} \\mathrm{d} u\\otimes \\mathrm{d} v -\\frac{2}{{\\left(u^{2} + 1\\right)} {\\left(v^{2} + 1\\right)}} \\mathrm{d} v\\otimes \\mathrm{d} u + \\frac{{\\left(u - v\\right)}^{2}}{{\\left(u^{2} + 1\\right)} {\\left(v^{2} + 1\\right)}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{{\\left(u - v\\right)}^{2} \\sin\\left({\\theta}\\right)^{2}}{{\\left(u^{2} + 1\\right)} {\\left(v^{2} + 1\\right)}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "gt = -2/((u^2 + 1)*(v^2 + 1)) du⊗dv - 2/((u^2 + 1)*(v^2 + 1)) dv⊗du + (u - v)^2/((u^2 + 1)*(v^2 + 1)) dth⊗dth + (u - v)^2*sin(th)^2/((u^2 + 1)*(v^2 + 1)) dph⊗dph" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.apply_map(factor, frame=XN.frame(), chart=XN,\n", " keep_other_components=True)\n", "gt.display(XN)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "and in terms of the default coordinates $(t,r,\\theta,\\phi)$:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\tilde{g} = \\left( -\\frac{4}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( \\frac{4}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( \\frac{4 \\, r^{2}}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{4 \\, r^{2} \\sin\\left({\\theta}\\right)^{2}}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle \\tilde{g} = \\left( -\\frac{4}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} t\\otimes \\mathrm{d} t + \\left( \\frac{4}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} r\\otimes \\mathrm{d} r + \\left( \\frac{4 \\, r^{2}}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\left( \\frac{4 \\, r^{2} \\sin\\left({\\theta}\\right)^{2}}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\right) \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "gt = -4/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1) dt⊗dt + 4/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1) dr⊗dr + 4*r^2/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1) dth⊗dth + 4*r^2*sin(th)^2/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1) dph⊗dph" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display()" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\tilde{g} = -\\frac{4}{{\\left(r^{2} + 2 \\, r t + t^{2} + 1\\right)} {\\left(r^{2} - 2 \\, r t + t^{2} + 1\\right)}} \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{4}{{\\left(r^{2} + 2 \\, r t + t^{2} + 1\\right)} {\\left(r^{2} - 2 \\, r t + t^{2} + 1\\right)}} \\mathrm{d} r\\otimes \\mathrm{d} r + \\frac{4 \\, r^{2}}{{\\left(r^{2} + 2 \\, r t + t^{2} + 1\\right)} {\\left(r^{2} - 2 \\, r t + t^{2} + 1\\right)}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{4 \\, r^{2} \\sin\\left({\\theta}\\right)^{2}}{{\\left(r^{2} + 2 \\, r t + t^{2} + 1\\right)} {\\left(r^{2} - 2 \\, r t + t^{2} + 1\\right)}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle \\tilde{g} = -\\frac{4}{{\\left(r^{2} + 2 \\, r t + t^{2} + 1\\right)} {\\left(r^{2} - 2 \\, r t + t^{2} + 1\\right)}} \\mathrm{d} t\\otimes \\mathrm{d} t + \\frac{4}{{\\left(r^{2} + 2 \\, r t + t^{2} + 1\\right)} {\\left(r^{2} - 2 \\, r t + t^{2} + 1\\right)}} \\mathrm{d} r\\otimes \\mathrm{d} r + \\frac{4 \\, r^{2}}{{\\left(r^{2} + 2 \\, r t + t^{2} + 1\\right)} {\\left(r^{2} - 2 \\, r t + t^{2} + 1\\right)}} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\frac{4 \\, r^{2} \\sin\\left({\\theta}\\right)^{2}}{{\\left(r^{2} + 2 \\, r t + t^{2} + 1\\right)} {\\left(r^{2} - 2 \\, r t + t^{2} + 1\\right)}} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "gt = -4/((r^2 + 2*r*t + t^2 + 1)*(r^2 - 2*r*t + t^2 + 1)) dt⊗dt + 4/((r^2 + 2*r*t + t^2 + 1)*(r^2 - 2*r*t + t^2 + 1)) dr⊗dr + 4*r^2/((r^2 + 2*r*t + t^2 + 1)*(r^2 - 2*r*t + t^2 + 1)) dth⊗dth + 4*r^2*sin(th)^2/((r^2 + 2*r*t + t^2 + 1)*(r^2 - 2*r*t + t^2 + 1)) dph⊗dph" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.apply_map(factor, keep_other_components=True)\n", "gt.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Einstein cylinder coordinates\n", "\n", "Let us introduce some coordinates $(\\tau,\\chi)$ such that the null coordinates $(U,V)$ are\n", "respectively half the retarded time $\\tau -\\chi$ and half the advanced time $\\tau+\\chi$:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(M,({\\tau}, {\\chi}, {\\theta}, {\\phi})\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(M,({\\tau}, {\\chi}, {\\theta}, {\\phi})\\right)$" ], "text/plain": [ "Chart (M, (tau, ch, th, ph))" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC. = M.chart(r'tau:(-pi,pi):\\tau ch:(0,pi):\\chi th:(0,pi):\\theta ph:(0,2*pi):\\phi',\n", " coord_restrictions=lambda tau,ch,th,ph: [tauch-pi])\n", "XC" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle {\\tau} :\\ \\left( -\\pi , \\pi \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)\$$" ], "text/latex": [ "$\\displaystyle {\\tau} :\\ \\left( -\\pi , \\pi \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$" ], "text/plain": [ "tau: (-pi, pi); ch: (0, pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC.coord_range()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} U & = & -\\frac{1}{2} \\, {\\chi} + \\frac{1}{2} \\, {\\tau} \\\\ V & = & \\frac{1}{2} \\, {\\chi} + \\frac{1}{2} \\, {\\tau} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} U & = & -\\frac{1}{2} \\, {\\chi} + \\frac{1}{2} \\, {\\tau} \\\\ V & = & \\frac{1}{2} \\, {\\chi} + \\frac{1}{2} \\, {\\tau} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "U = -1/2*ch + 1/2*tau\n", "V = 1/2*ch + 1/2*tau\n", "th = th\n", "ph = ph" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XNC = XC.transition_map(XNC, [(tau-ch)/2, (tau+ch)/2, th, ph])\n", "XC_to_XNC.display()" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} {\\tau} & = & U + V \\\\ {\\chi} & = & -U + V \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} {\\tau} & = & U + V \\\\ {\\chi} & = & -U + V \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "tau = U + V\n", "ch = -U + V\n", "th = th\n", "ph = ph" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XNC.inverse().display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The conformal metric takes then the form of the standard metric on the Einstein cylinder\n", "$\\mathbb{R}\\times\\mathbb{S}^3$:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\tilde{g} = -\\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau}+\\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\sin\\left({\\chi}\\right)^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}\$$" ], "text/latex": [ "$\\displaystyle \\tilde{g} = -\\mathrm{d} {\\tau}\\otimes \\mathrm{d} {\\tau}+\\mathrm{d} {\\chi}\\otimes \\mathrm{d} {\\chi} + \\sin\\left({\\chi}\\right)^{2} \\mathrm{d} {\\theta}\\otimes \\mathrm{d} {\\theta} + \\sin\\left({\\chi}\\right)^{2} \\sin\\left({\\theta}\\right)^{2} \\mathrm{d} {\\phi}\\otimes \\mathrm{d} {\\phi}$" ], "text/plain": [ "gt = -dtau⊗dtau + dch⊗dch + sin(ch)^2 dth⊗dth + sin(ch)^2*sin(th)^2 dph⊗dph" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gt.display(XC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The square of the conformal factor expressed in all the coordinates introduced so far:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\begin{array}{llcl} {\\Omega}^{ 2 } : & M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{4}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{4}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2} \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 4 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{4} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{4} - 8 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} + 4 \\, \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{4} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{4} \\end{array}\$$" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} {\\Omega}^{ 2 } : & M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{4}{r^{4} + t^{4} - 2 \\, {\\left(r^{2} - 1\\right)} t^{2} + 2 \\, r^{2} + 1} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{4}{{\\left(u^{2} + 1\\right)} v^{2} + u^{2} + 1} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 4 \\, \\cos\\left(U\\right)^{2} \\cos\\left(V\\right)^{2} \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 4 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{4} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{4} - 8 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} + 4 \\, \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{4} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{4} \\end{array}$" ], "text/plain": [ "Omega^2: M → ℝ\n", " (t, r, th, ph) ↦ 4/(r^4 + t^4 - 2*(r^2 - 1)*t^2 + 2*r^2 + 1)\n", " (u, v, th, ph) ↦ 4/((u^2 + 1)*v^2 + u^2 + 1)\n", " (U, V, th, ph) ↦ 4*cos(U)^2*cos(V)^2\n", " (tau, ch, th, ph) ↦ 4*cos(1/2*ch)^4*cos(1/2*tau)^4 - 8*cos(1/2*ch)^2*cos(1/2*tau)^2*sin(1/2*ch)^2*sin(1/2*tau)^2 + 4*sin(1/2*ch)^4*sin(1/2*tau)^4" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(Omega^2).display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The transition map $(t,r,\\theta,\\phi) \\mapsto (\\tau,\\chi,\\theta,\\phi)$ is obtained by combining the various transition maps obtained so far:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} {\\tau} & = & \\arctan\\left(r + t\\right) + \\arctan\\left(-r + t\\right) \\\\ {\\chi} & = & \\arctan\\left(r + t\\right) - \\arctan\\left(-r + t\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} {\\tau} & = & \\arctan\\left(r + t\\right) + \\arctan\\left(-r + t\\right) \\\\ {\\chi} & = & \\arctan\\left(r + t\\right) - \\arctan\\left(-r + t\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "tau = arctan(r + t) + arctan(-r + t)\n", "ch = arctan(r + t) - arctan(-r + t)\n", "th = th\n", "ph = ph" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XC = M.coord_change(XNC, XC) * M.coord_change(XN, XNC) * M.coord_change(XS, XN)\n", "XS_to_XC.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The inverse transitin map:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & \\frac{\\cos\\left(\\frac{1}{2} \\, {\\tau}\\right) \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)}{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}} \\\\ r & = & \\frac{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right) \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)}{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & \\frac{\\cos\\left(\\frac{1}{2} \\, {\\tau}\\right) \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)}{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}} \\\\ r & = & \\frac{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right) \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)}{\\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "t = cos(1/2*tau)*sin(1/2*tau)/(cos(1/2*ch)^2*cos(1/2*tau)^2 - sin(1/2*ch)^2*sin(1/2*tau)^2)\n", "r = cos(1/2*ch)*sin(1/2*ch)/(cos(1/2*ch)^2*cos(1/2*tau)^2 - sin(1/2*ch)^2*sin(1/2*tau)^2)\n", "th = th\n", "ph = ph" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XS = M.coord_change(XN, XS) * M.coord_change(XNC, XN) * M.coord_change(XC, XNC)\n", "XC_to_XS.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expressions for $t$ and $r$ can be simplified via reduce_trig:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Check of the inverse coordinate transformation:\n", " t == t *passed*\n", " r == r *passed*\n", " th == th *passed*\n", " ph == ph *passed*\n", " tau == arctan((sin(ch) + sin(tau))/(cos(ch) + cos(tau))) + arctan(-(sin(ch) - sin(tau))/(cos(ch) + cos(tau))) **failed**\n", " ch == arctan((sin(ch) + sin(tau))/(cos(ch) + cos(tau))) - arctan(-(sin(ch) - sin(tau))/(cos(ch) + cos(tau))) **failed**\n", " th == th *passed*\n", " ph == ph *passed*\n", "NB: a failed report can reflect a mere lack of simplification.\n" ] } ], "source": [ "t_c = XC_to_XS(tau,ch,th,ph)[0]\n", "r_c = XC_to_XS(tau,ch,th,ph)[1]\n", "\n", "XS_to_XC.set_inverse(t_c.reduce_trig(), r_c.reduce_trig(), th, ph)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & \\frac{\\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)} \\\\ r & = & \\frac{\\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & \\frac{\\sin\\left({\\tau}\\right)}{\\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)} \\\\ r & = & \\frac{\\sin\\left({\\chi}\\right)}{\\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "t = sin(tau)/(cos(ch) + cos(tau))\n", "r = sin(ch)/(cos(ch) + cos(tau))\n", "th = th\n", "ph = ph" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC_to_XS = XS_to_XC.inverse()\n", "XC_to_XS.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conformal Penrose diagram\n", "\n", "Let us draw the coordinate grid $(t,r)$ in terms of the coordinates $(\\tau,\\chi)$:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 112 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphXS = XS.plot(XC, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " max_range=30, number_values=51, plot_points=250, \n", " color={t: 'red', r: 'grey'})\n", "graph_i0 = circle((pi,0), 0.05, fill=True, color='grey') + \\\n", " text(r\"$i^0$\", (3.3, 0.2), fontsize=18, color='grey') \n", "graph_ip = circle((0,pi), 0.05, fill=True, color='red') + \\\n", " text(r\"$i^+$\", (0.25, 3.3), fontsize=18, color='red')\n", "graph_im = circle((0,-pi), 0.05, fill=True, color='red') + \\\n", " text(r\"$i^-$\", (0.25, -3.3), fontsize=18, color='red')\n", "graph_Ip = line([(0,pi), (pi,0)], color='green', thickness=2) + \\\n", " text(r\"$\\mathscr{I}^+$\", (1.8, 1.8), fontsize=18, color='green')\n", "graph_Im = line([(0,-pi), (pi,0)], color='green', thickness=2) + \\\n", " text(r\"$\\mathscr{I}^-$\", (1.8, -1.8), fontsize=18, color='green')\n", "graph = graphXS + graph_i0 + graph_ip + graph_im + graph_Ip + graph_Im\n", "show(graph, figsize=8)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "graph.save('glo_conf_diag_Mink.pdf', figsize=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some blow-up near $i^0$:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "image/png": 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q1AnXoCAiHB1BkshTKtFUqUg3MkIjLw8UClHaCqCgxJVJSgpTJk5Ev1GjSrgLMjJVlypl8b0OFHv30vuzz2gVHMyB6Gj8fv0VfH1ppKXF4IAAblhbs330aNzOn6f3uXNcbNmSBGNjeh47xpVmzagdEYEC0M7LQ6WpiUFaGmptbRSSVGram2JiwrKVK8m4fv3vHLKMzH8OWfgqyscfozhzBu85c2h78SJH4uI4/fPPSHv30sDIiDcuXOCWtTVbR47ENSCAvqdPE+jmRoyZGb19fbnatCk1oqLQUKvRystDraGBQVoaqueI3/IVK8i4efPvHbeMzH8IWfgqyvvvw7RpKK5do/OcOXQ8c4YTSUkcmz8fads26ltbM+zMGe5aWrJ5+HAaBQfT/+RJgps25b6VFX2OHOFa48ZUv38fLZUKTZUKSUMDg/T0ssUPhPgtXy6Ln4zMa0IWvgqSMGsWTJoEEybAw4e0mz2bbseOce7xYw798APSxo3UdXBgxIkT3DM3Z+OwYbjcvMmA48e52qQJkba29C0QP7voaJR5eUVVXPTLEr+CJdgUY2NZ/GRkXhOy8FWQ1StWEDt3LgwbBsOHQ2YmrWfOpNfBg1xMT2fvd9+hXr0ax4YNGenrS7SpKevfeIO6YWEM8vXlesOGhFWrRr/Dh7nZoAG2sbHo5OQAoODF4rds+XIybt/+ewYvI/Mf4S8RviVLluDg4ICuri5ubm6cOXPmmW1jYmIYMWIE9erVQ0NDg+nTp5fZbvv27TRo0AAdHR0aNGjAzp07K+nqS2J6/z5r1qzhwTffQO/eMGgQ6Ojg/n//R//duwnOzGTX11+jXrGCWi1bMvrgQRKMjVk3eDCODx4w+MgRbrq4EFqzJv0PH+amiwvWCQnoZmUhITI6nid+qcbGLPvjD1n8ZGRegUoXvs2bNzN9+nRmz55NUFAQXl5e9OjRg6ioqDLb5+TkYGVlxezZs3F1dS2zjZ+fH0OHDmX06NFcuXKF0aNHM2TIEPz9/StzKACMCQnBOjKStRs2EPH999ChA/TtC7a2uH74IYO2beN6bi7b5s5FtXQp1bt0YcyePTwyNGTNgAHUjI9nyMGDhNarxw0HBwYcOsTtevWwTEpCPzMTdcEm5foZGai0tdFQq8sWv2XLyAgNrfTxysj8F6n0OL5WrVrRvHlzli5dWnTMxcWF/v37M2/evOee26FDB5o2bcqvv/5a4vjQoUNJTU3l4MGDRce6d++OmZkZPj4+L7ymV4njIzmZvE6d2NyiBZE1a/JGv37Ue/ddCA6GEycgMJDbP/3E1uHDcZAkhnz7Ldqffkr81q2sHTAAvexsxuzbR6yREZt79cIhIgLX27fZ2aMHjmFhpJiakm5ggJZKhUpTk0wDA7Ryc1FraDyJ8yvY08M4LY3JU6diWLduxcYgI1PFqVSLLzc3l8DAQLp161bieLdu3Th//vxL9+vn51eqT29v72f2mZOTQ2pqaonHS2NujvbBgww7dQrniAg279rF1R9+gPr1oVs38PSk3rRpDF+3jkgNDTZ++im5P/yA9ahRjN+yhRwdHVb36YN1djYj9uwh0sGBIBcXBu7fT4SjI0apqRilp5OnpYWmSoVeRgb5SmXZlp+REct//530u3dffjwyMlWQShW+xMREVCoVNjY2JY7b2NgQGxv70v3GxsZWqM958+ZhYmJS9KhRo8ZLvzdpaWBnh9aRIww+cgTXiAh2HjpEwPffQ7Vq0KUL9O6N08SJjPrzT6K1tFj/0Udkf/stFlOmMN7HB7WWFqt69sRMkhi1fTsPatQgoEkTBu/bR1StWuhnZmKSmkqutjZaheL3rGmvkRHLli6VxU9GpgL8Jc4NRcHUrBBJkkodq8w+Z86cSUpKStHj/v37L//G/ftDdjbUro3GkSP03bsXj8hIDpw6xZnvvkMyNhbiN2YMtUaNYszy5STo6LD2/ffJ/OYbzN5/n3EbNqCpULDK2xsDXV1Gb9lCrJ0d59zcGLxvHw+rVUOZk4PZ48fkamujnZ+PXlbWM8UvzciIZb//TnpY2MuPS0amClGpwmdpaYmmpmYpSyw+Pr6UxVYRbG1tK9Snjo4OxsbGJR4vzfnzIowlPx8aNEBx6BDdtm+nQ2Qkxy9exPfbb5FUKujaFd5/n2qDBjF2yRJS9PVZM20a6V9/jcknnzBu7Vp0gdVdu6I0NWWMjw+J1tacatWKwXv2EGdnh1Z+PuaPHpGjVKKdm4vu88TP0JA/li6VxU9GphxUqvAplUrc3Nzw9fUtcdzX1xdPT8+X7rd169al+jxy5Mgr9Vlutm2Dfftg8mSRWeHujmLvXtpv2kT3hw/xu3aNvd9+i/rRI+jRA774Ats+fRi3aBFZhoasnjKF1G++wWjOHMauXImhWs3qzp1R2Noydv16UszMON62LYN37ybB2hqFJGGRnEy2ri46ubnoZmeTr6VVUvwKSC8Qv7Tw8Mq/DzIy/2Iqfao7Y8YMVqxYwZ9//snNmzf54IMPiIqKYurUqYCYho4ZM6bEOcHBwQQHB5Oenk5CQgLBwcHcuHGj6PX333+fI0eO8P3333Pr1i2+//57jh49+syYv9dKr16wdi2sWQMffSQsrvbtYds2Wq1aRf+EBILDw9nx9deoIiOhTx/4+WesunRh3MKF5Bsbs2r8eB798AMGc+cy9o8/MFOpWNuhA/k1azJuzRoyjI050qEDg3btItnCArWGBlaJiWTp6qKTk1Na/AqrOSPEb5ksfjIyz+UvKUu1ZMkSfvjhB2JiYmjUqBG//PIL7dq1A2DcuHFERkZy8uTJJxdVxlpdrVq1iIyMLHq+bds25syZQ3h4OE5OTnzzzTcMHDiwXNfzKuEsISEhNG7cGJYuhWnT4JtvYNYs8aKPD4wcya0ZM9hmaoqDmRlDZs9Gu3Vr2L4dRo8m5cwZ1s6YQd7jx4zZtg3Ld94he9YsNr79NnFKJSPOncPw+nXWjh+PVnY23X192dm3L0ZpaWjn5hJvbY1BZiZZurrk6OiglZ9fZqiLU0QEo378EaytKzQ+GZmqgFyPr4LC98UXX+Dt7Y2Hhwd89RX873+wfLnI3wX44w+YOpXwzz9nk1KJnZ4ewz//HF1vb1i9GgYNIi0oiHUffkjmo0eM3rMHmwkTyJ01C5/33uOhUsmwCxcwCwpi7YQJkJ9Pr0OH2NW3L3qZmehmZxP3tPjl5aHW1BTiV+yPRp/Dh2m+Zw9YWb3Guycj8+9HztWtIJ4tWnD48GGOHj2KNHs2vP02vPkm7NolGrz5Jnz3HY5ffMEYbW3ic3NZM2cOGYcPw7vvwrZtGDk7M+6XXzCysGBNv35Eb9iAcu5cRvz6K7Xy8tjo6UliixaMW7ECDU1N9vbsSb/du8nW0yNLTw/buDjSDQzQz8pCmZuLqiDmr2jaW8Beb28u9esHCQl/z82SkfmHIgtfBem6YAHdOnfm3Llz7N6zB9XPP4t83WHD4PRp0eiTT+DTT6n+f//HOBMT0jU1WfXpp6Ts2AGffQZ796Jvb8/YBQuwsLJiTY8e3Nu7F+05cxj688/Uyc1lU6tWRLdpw7jly1FKEnv69KHvnj3kKZWkGxpiHxNDqpERhhkZaOfnk/8M8dvv7U3AgAGQlPQ33TEZmX8e8lS3oqEtSiUMHUrIRx+xa88enJycGNynD8oBA+DSJSF+TZoI8Zk2DZYtI3n9etbFx6NOTWXMggVYvPMOvPMOtG9PblYWm6ZP535CAkPPn6dOy5aofviBnR9+yA09PQYGB+Nw7BhrJ00iXamk/65d7O/dG9RqTFNSuF+9OqYpKaQZGpKvpYVWfj6qp6e9CgU9jh6l5a5dYGHx2u+njMy/jSpl8b2OzYZYtw7Wr6fxxo2MGDGCyMhI1m7eTOaGDeDkBN27Q0SEEJ3Fi2HIEMzHjWO8szNKc3NWvfsusX/8Ifrx9UWpUDBi8WIcbW3xadOGGyEhaL73HgPnz6dJVhbbmzXjjrc3Y5ctwyQ7m50DB9Jz/340FAoemZlRKyqKR6amGKeloalSlW35SRIHu3TBf8AASE5+PTdTRuZfjGzxvUww84IFMH06/PIL0UOGsGHDBvT19Rnl7Y1J9+5is6CzZ4VHNTdXVG85d47MI0fYcO0aSQ8fMuLPP6n5+efQqRO0bYvKwoJdb73F9dhY+t64QVMLC6Rly9j30UdcNjCg1/XrNNq7l/UTJ5JoZMSAHTvw7d6dHC0tbOLjCXdwwCI5mcempqgVCjQLihw8bfl5nziBx86dYGb2Wu+pjMy/CVn4XjaL45NP4IcfwMeHpK5dWb9+PSqVilHt22Pdu7fI2z1xAoyMICMDOneG8HByTpzAJyCAh5GRDN24kTrffAMNG0L79qgdHdk/YQKXY2PpHhZGK4UCacMGDn3wARcNDfG+dYtmO3eyccIEYs3M6L99Oye6diVDV5dqMTHccXLCMjGRR2ZmqBUKtFQq8jU1kZ4Sv24nT9J6xw5Z/GSqLLLwvazwqdUwbhxs2gSHDpHesiXr168nJSWFYe7u1Bo4EFq2hP37xbpgUhJ4eUFGBnmnT7Pt3DnuhoYycMcOGv7wg7AOO3ZEat4c3+HD8YuJodODB7RNSYFduzj2zjucMzGh0507tNqyhU3jx/PAyor+O3ZwqmNH0gwMqPHwIaF16mCVmEiSuTmAmP6WIX5dT53Cc8cOMDV9LfdURubfhCx8r5K3m5cnqjD7+cHp02TXr8/mzZt58OABg+rXp/7IkTBgAGzYIKa/9+9DmzZgZITq5El2nzrFtWvX6H3oEM1//lmsyXXrhtSxI6f79eNkdDSeiYl0uXcPfH05NWUKp8zNaRceTpuNG9k6bhyRNjb037mTs+3a8djEhNr37nGrXj2s4uNJKnBkPEv8Op85Q9tt22Txk6lyVCnnxmtHW1vk7jo7Q48e6MbEMHLkSJydndly/TqBixbBli1iPVCSoEYNOHIE4uLQ7NuXAd2749asGXt79OD8Z5+BsTHs3InC15f2x47hbWvLeUtL9tepA23b0mHFCjonJHDa0ZGTo0YxZM0aHKOj2TlwIJ5nz2L+6BERtWvjcusWCTY2WCYlgUKBSlMTLZVKbGpUzOFxzMuLs2+8ASkpf+ttlJH5q5GF71UxMoIDB8DAAHr2RCstjUGDBuHu7s6+hw858cMPSL/9Bt9+K9rXrw8HD0JICIo33qBn9+60bdEC33btOD57NpKTk5g+b9uGR0AAfS0tuWxkxC43N9RubrRdv57uMTH41a7NkdGjeWP9eupFRbFrwABa+vtjnZDAXUdHGly/TryNDZYJCUgKBWoNDSF+xfJ6kSSOtW3LmSFDZPGTqVLIwldRjh4tfczaWohffDwMHIhGXh49evSgc+fOnE5PZ8/cuagKU9sAWrQQmR7Hj6MYP57O3bvTxcODM25u7P/sM9QtW8KqVbByJc0iIhhkZsY1pZIt7dqRX68erbZto09UFJdq1GDfuHEM2LyZhmFh7O7XD9fLl7GPiyO0bl0aXbtGvK0tVgkJRfm8mvn5pcTvuKcnp4YOhVepTC0j8y9CFr6KMngwlLW3rbMz7N4t6vVNmoQCaNu2LQMGDOCqhgY+n35KznvvPUlt69JFrP1t2gTTp9OmWzf6tmnD5bp12T53Lvndu8PChTB/Pg2zshhmaEgY4NO9O7k1atD8wAEGhoVx1c6OHePG0WfXLlxv3WJf3740vHqVGg8fcrNePRpfvVokfqqCdT7NMiy/k61bc1IWP5kqgix8FaV6deHQSEws/VrbtqJc1fr1MHcuAE2aNGHkyJE8MDJizfvvkz5pknCGgBDRpUvht9/g669p1qULQ9q25batLRu/+oqc0aPhiy9g1izqGhszUqnkQV4e6/v3J9vCgsanTzPk5k1CrazYMnYsPQ4exC0khAO9e1Pv5k0c7t3jposLTa5cId7WFusC8QOeiF8hksQpDw+ODx8ui5/Mf54qJXyvJXNj3z6x78aAAVCwEXgJhg2DefPgyy9FNRbA0dGR8ePHk25lxcpJk0gcMwYKt4Z8880nVV6WLqV+166M8vQk2tCQtd98Q8a778L778O0adSuW5cxkkRCVhZrhgwhQ1+f+pcvMzwkhHtmZmwcO5Yux4/T6vJlDvXsiUNYGI4REVxv2BDX4GDibWywjo8nX1sbKBC/4sVMJYkzLVtybMQISE9/+XskI/MPRw5neZlwFj8/6NgRhg4V4vZ0/UBJEoK2ahUcOiSCl4GUlBQ2rF1LWkwMw48fp+bu3WBjI9pPny4sv82b4Y03iNm1iw3nzqGrrc3oDz/EZMYM2LgRdu0i7vBh1unooGtiwpi1azHW1iaqRg02Nm+OZUYGI3x8OO/uzrlWreh47Bix9vbcdnamSUgIwU2bYh0bS7ytLdo5OUgKBfmamiLcphCFgjaBgXTZuBEMDV/6PsvI/FORha+CwpeYmIilpaUoOjpiRMlCpMXJzxfVl8+fh3PnoFEjALKzs9m8Zg33HzxgYHAwDXx8hLio1TBqlChYeuQItG9P0oYNrA8IQG1szKi33sJq6lTw9YVDh0hasYJ1lpZgbs6Y1asxNzIi2tSU9a1aYZydzcht2wh0ceFU27Z4nTpFsoUFNxo0wPXKFYKbNSuX+HlevkyXDRtQyOIn8x+jSk11XwcrVqwgLCxMbDj0+ecwe7aI5XsaLS0Rw+fgIMrVx8QAoKury8iJE3GpVYutbm74v/eeEEkNDWEhenlBv34QEoLFyJFMqF8f3cREVv3xBw9++QU8PKBvXyzefZfxYWFoJSSwatw44lNTsc/MZNypU2QolawZMoTmd+/S6cQJzrRvj0lKCo1DQrji6krToCAx7Y2NJU9HBw21Gi2VqkQ5KySJ882b4zt6NJI87ZX5jyFbfBW0+DZs2EBYWBje3t60bNECxciRwlN7+rQIU3maBw+EWNnYwKlTRVNHSZI4umIF56OjaZ2WRtcffkChoSEcC+3bi9AYPz+oWZOs777D584dYmvWZOjAgThNmABRUeDrS/r06axv0IBUGxtGrl1LterVSU5JYW2nTiiA0fv2EWphweFu3XAPCCBfS4vgpk1pGhxMsKsr1gkJxNvYoMzKQq2pSb6WVsmpu0KBx5UrdFu3DoWBwcvfdBmZfxCy8FVQ+NRqNb6+vly4cIGmTZvSq3NntLp2hchIuHhRZGc8zZUrwuPbvr0QSS2topf8Fy7kUHIyDTU06D9rFlpaWsI69PQEPT1R5cXcnLwPP2RrbCxhzs4M6NaNRhMmQGYmHDhA1tixbGzZkng7O0asWUOt+vVJiYhgnbc3OVpajDl0iCilkn29e+N69SpaeXkEurvTNCiIYFdXrBISSLCxQScri3xNTVRliF+rkBC816yRxU/mP4EsfC+Zq3vlyhX27t2Lra0tQzt1wqhTJ5HzevZs2Q6BQ4dEGMybb8KiRSWE5eaXX7IjN5dqhoYMff999PT0hNfX01Nkevj6go4OqjFj2JOdzdXGjenZujUtJk8GfX3Yto3cQYPY1KED9+3tGbJhA3WbNSM9MJB1vXqRrqvLqKNHScjNZdeAAbjcuoVBWhoBrVrhGhxMSOPGmCclkWhtLcRPS0uEvTwlfi2uXaPHmjUo9PVf6p7JyPxTkIXvFYoUPHz4kM2bNyNJEkPd3anep4/w4G7fXtJRUMiyZUL45s+HGTOeHJckot55h02GhhhaWDDyzTcxMTEBf3/hPfb2FuuIKhVS374c0dbmgrs77Rs1ov1bb6FwcICVK8nv2ZNtPXtyx86OAVu30sjDg6zDh9kwYACJhoaMPHGC9MeP2fbGGzhFRGAZF4dfmzY0vnqVGw0aYJacLMQvM5N8be0yxc/9xg16rloli5/MvxpZ+F6lOguQnp7Oli1biI6Ople1ajSbMEHE8H32WdknzJwJ338PO3cKJ0Yh+fkkDh3Khlq1UNnYMGLsWGxtbUXcYP/+YgPzJUsgIwOpUyfOWlhw3MODFrVr0+Pdd1G0bg3ffYeqa1f2DBrEVXt7eu7bR4vWrcnZuBGf4cOJNjZm2LlzqB8+ZPOwYdR48IDq9+5xpn17Gly/zu169TB79IhEKyt0MzPJ09YW097iKBS43bxJrz//lMVP5l+LLHyvKHwAKpWKAwcOcPnyZVoA3l99heauXWJq+zRqNQwZIqa+586Bq+uT19LTSe/enY1Nm5Jkb8/QYcNwdHSEP/+EiRNFoPOcOWLXtDZtCHR0ZL+nJw0tLen/4YdoDhgA77yD1K0bh0eNwt/Ojo7Hj+PVogX5y5axZcwYIszMeMPPD527d/EZORKbhATq3LrFic6dqXfzJmF16mDy+DFJBeKXq62NunDNr/CrolDQ/PZteq9ciUJP75Xvn4zMX02VEr7FixezePFiVCoVoaGhr034Crl06RIHDx6kRkoKb6xfj8GpU1CvXumGGRkibCUpSThEbGyevBYXR27btmzt0oVwe3v69u2Lq6srfP21sCJXroQJE4QzxdOTG82bs8PDg1q6ugyZMwedKVOgd2+k3r05PWUKJ62saHXhAt6urqh+/ZUdkyZx29ycAZcuYXr1KhtGj8bs8WMaXr3K0W7dqHv7NpEODhinppJkaYluRga5SmWZ4tc0NJS+K1ei0NV9bfdQRuavoEoJXyGvZPHduiUcDs/g3r17bN2yBa2EBIaeOYPd4cOizt7T3L8vwl+cnOD4cdDRefLajRuo2rZl//DhBFlb0759e9q3a4fi7bdFhZe9e6FHD7h6Fby8iOzShU0tWmCuUjFi3jwMZ84Ugjt0KAHTp3PAyIgmISH0dXZG8cMP7J46latWVvS5fBn7ixdZN3YshpmZNAsI4Ii3N45hYdyvWROD9HQemZsLy09HB3Xhml8x8XO9e5d+K1agKH79MjL/cGThq6jwNW4snA7PWd9KSUlh85o1JMTH0/fhQxqvXFm2s8PfX4S4lJX6dvQoUvfunJ0+neNGRjRp0oQ+PXuiNWQIHDsGZ85As2YiNtDbm7ihQ1nfpAna6emMXLgQi3nzxHtOnsy1OXPYqalJnbt3GWxvj9ZPP3Hgrbe4ZG2N99Wr1Dl9mrXjxqGdl0crPz8Ode9OrXv3iLGzQz8zk0empuhlZZGto4NUuOZXTPyahIfTf/lyFEplxe6ljMzfhJy5UVHCwsSeuM/BxMSE8W+9RQMbG3bUro3vV1+hLl4MoJBWrcT63dq18OOPJV/r0gXF0qV4zZ/PID09rl+/zrqNG8lcuRJcXEQ2SFSUEM6NG7FZt46JDx+iYWHBn++8w8OvvgJzc/j+exp9/TXDdXWJcHRk/aNH5EyfTs8lS/CMi+Nwkybc6NiRcatWoVYoON+2LT0PHeJ+jRpYx8WRrauLaUoKWXp66ObkoMjPF9enUBRZf1cdHNg5ZQpSbu5ruskyMpWLLHwVZelSkVpWUHnlWWhra9P/nXfoqlDgp1az8ddfycrKKt1wxAiR6/vpp7BnT8nXJk+Gjz+m0aefMtbRkcTERFb6+JC8YYOYGvfqJSonDxwIixZh+ssvTMjJwbxmTdZMmMDd2bPFdPqTT6gzcyajLS2Jt7ZmTW4uGdOm0WXpUjrGxHCiYUMud+3KuHXr0MrL41S7dvQ4fJgYe3vMkpPJUSoxSUkhW1cX3ZwcNArFD4qs1JDatdkxdSpSXt4r3mAZmcpHnuq+jHNj4kRRpODixaLiA89ErSZs7Fi2V6uGjqUlQ0aOxM7OrlQbBg8Wgcrnz4vpdPHX3ngDDh0i+dAhNl65QmZmJsM8PKjZrx+4uYnqz0qlEM/vvyfPx4dtKhV3Q0Ppc+QITZcuFaEwf/5J3B9/sP7OHZS5uYxOScH0zz+5MGkSh6tXx/3uXdodPMiGoUNJMzSk04kTHOnSBfOkJNKMjdFQqUg3NEQ3O5scXV2x5ldIwdeo4YMHDFq6FEVB6SsZmX8isvC9jPBlZor829xcuHTpxaWb0tJ43LEjW9q0IcHKit59+ghPbXHS00Va2+PHQlCtrUu+X/v2EB1N1unTbDl7lvv379PP2ZnGo0eLggmrVgnxGTMGtm5Fffgw+5OTuRwSQmd/f9r89huKmTNhzx4erVjBuqAg8rW0GPXgAdZbtnB51Cj21axJw6govA8cYFO/fiRaWtL16FGOduqEcUoKWfr6qBUKsvT00MnJeab4NYiOZvCSJSiejgGUkfmHIAvfy4az3L4N7u7Qt6+ouPx0Tb6nCQ0lr3VrDowYQbClJe7u7nTv3h3N4sIRFSWmpnXrCgdGcU9pTIxYE7SwQHXyJPtOniQ4OJgO5ua0e+89FHPnimoxubnC43v5MtLZs5yKiOBUYCAtQkPp/v33aEyYABcukL56NetPnCDV2JgRoaFU37ePGwMGsL1OHZxiYuh74ADbvL2JtrOj27FjnGjXDv2CoOY8bW2ydXTQzckhS1cXqQzxc4mJYfCiRWjIlp/MPxBZ+F4ljm/zZlFx+Y8/YMqUF7ffvx+pTx8uf/45BzU1sbOz44033ih5DX5+0KGDqM23YkVJQQ0JEfvytm+PtHMnZ86f58SJE7gqFPT58ks0V66EsWPFup+Xl/jXz49LwcEc8PfHJT6eAZ99hlbfvhAdTfbvv7Nx3z5ibWwYGhKC0/HjhHXqxOaGDbFLTmbw/v3sbt+ee7Vr0+3YMU57eqKVl4eGJJGpp0eetjbKvDyydXXFnr2FFHyl6sfF8cZvv6EhW34y/zBk4XvVAOZp04Rn1s9PhJe8iC+/hLlzebhjB1siIlCpVAwePJjatWs/abN6NYwfD7//LnJ7i3PokHBqfPQRfP89ISEh7N69mxoZGQxZtAi9XbtEvvCDB9C6NVhawqlT3Dp1iu3+/lTLzmbYtGnodu0K2trk/fQTW7dsIczBgYFBQTT08+N+06ZsdHfHND2doQcPctjdnVBnZ7odP875li1RqNVo5+eTZmiIqmDbypxC8ZOkErF+/a9dw3XLlrLDeWRk/iZk4XtV4cvOFlZYejoEBT03vg8Alaoo+DjDz49tp09z7949unbtioeHB4pCC68wWPn0abGeWJxffhFFDtatg1GjiIqKYtOmTegnJTFi82bMDx8WAczXrol1w5YtYf9+onbswCcoCGMtLUYOHoxx165Qty6qGTPYvWkTIY0a0TswELegIOJq1WJ9mzYoc3MZcfgwpxo04FqjRnQ9eZKApk3J19JCLzOTx6amAGhIEtk6OkLgiomfbnY2k65cweLAgRcvB8jI/EVUKeGrtJS127eFtTdxotg340XEx0PTplC/PurDhzl28iTnz5+nYcOG9O3bF6VSKdbqOnYUqWmXL5dMa5Mkkbbm4yOEsWVLkpOT2bBuHdmxsQw9dYqae/eChQWcOCGqu4wZA8uXk7B8Oetv3QITE0Z5eWHVpw906YLUuzcHd+4koFUrOl26RNvbt3msp8e6Ll3IVygYefgw/g4OBLm50fn0aa40aECWjg5GaWkkWlqiqVIBkFOG+Onk5DAxJASrvXtl8ZP5R1ClhK+Q112kABA19t59V+yX0bXri9ufPCmmpJ99BnPncuPGDXbv3o2JiQlvvPEGVlZWEB0twlWcncVG5sUdBTk5T4Tx0iWwtycrK4vNa9bwIDqa3qGhNF27VoS5rF0r1v7mzYNPPyX1q6/YEBNDqp0dw52dqTlyJEyahFS9OqeOHuVUx460Dgqia1QU6amprO/dmzQdHUYePUqItTX+Hh54+fkR6uhIipERFsnJxNrYoJ2Xh1pDg9ziTpkCoVPm5DDx5k2sd+yQxU/mb0cWvtclfGq1sKxu3hROCDOzF5/z1VfCE+vrC507k5CQwJYtW0hJSaF37940adJEFDbt2FFMfX/9teT5sbHCC2xnJ1LX9PRQqVTs//NPgqKj8UxNpfMPP6ChqSne58svi3Zxy546lU15eTx0cGCAuTkN3nlH7OGbkMDFgAAO9uhBk+vX6RsfT+6dO2wcOJB4IyOGHj/OPX19TrdvT8vAQB7Y2ZFobo5NfDwP7e3RyclBpaUlxK9w0/KCLA/tnBwmhoZis3WrLH4yfyuy8L3G6iw8eCCCj3v0EFtBvgiVCrp3F0IZHAy2tuTm5rJ//36uXr1K8+bN6d69O9p//CGsyfXrYeTIkn0EBop1vMGDhWWnUCBJEhcWLcI3MRFnbW0GfPwxOkrlk13cTpyAFi3I79uXXSYmXK9fH2+FAo/PPxfFUn19uXb3Ljv79cMhLIwhjx7BuXNsHj6ce+bmDD59msf5+Rzu1o2mISEkmZoSa22NfUwM92rWfBL2oqMj/iDAE/HLzWV8WBh2Pj6y+Mn8bcjC9zqFD4TgjRwJmzaJ4gMvIi5OrPe5uAjLT1MTSZIICgri4MGDWFhY8MbgwVh8+CFs3Sq8x08HPxdudfnDD/Dxx0WH78yZwza1GlMTE4a/+SamenrQpYuoMOPvD1ZWSO3bc7R2bc67utIyIwPvX35BY+tWWLCAiMRENg0ejOXDh4zIyEBn5052jhnDTRsb+p0/j/ToEXt69aJ+aCjZurpEVatGjfv3iaxdG4P0dHJ1dclTKkuJn1ZeHuMjI7Fft04WP5m/BVn4XrfwSZKI7fP1FZZctWovPufECSFIBet9hcTGxrJ161bS09Pp2707DSdOFJkdly6JAgTFmTULvvtOVGzu2VMcU6uJHzUKHxsb8mxsGDpyJDX09UWYi4aGENGsLPDw4FLz5hxo3hznx48ZtGIF2jt3wocfEiNJbBgwAJ3kZEZlZWGyahX7xo8nqHp1vC9exOThQ7b36UOtqCg01WruOjhQOzKSCCcnDFNSyNbTI78M8dPMy2PcgwdUf0HOs4xMZfCXBFctWbIEBwcHdHV1cXNz48yZM89tf+rUKdzc3NDV1cXR0ZHff/+9xOurV69GoVCUemRnZ1fmMMqHQiHyYnV1hZe3PH9XOnYUgvfllyJjowBbW1umTJlC3bp12bZnDwc++YT89HThqHi636+/FvF9I0eKCjIAGhpYL1/O5AsXsLh3jzWrV3PlwQPYv19UcR44UMT5HTiA+4kTDLtxg3BLS9ZMmkTGuHGwaBF2qalM3L8fTE1ZaWpK3JQp9FmxAs+ICA63bElc7doM37mT+9Wrk62jg0toKBEODjiGhZFuYoJ+VhaaeXlP4vgK1v1U2tqsrlGDe5MmvZbbLiNTESpd+DZv3sz06dOZPXs2QUFBeHl50aNHD6KiospsHxERQc+ePfHy8iIoKIhZs2bx3nvvsX379hLtjI2NiYmJKfHQ/adUArawEJWSDx8W1VzKw6xZwss7cqQQpQJ0dHQYNGgQPXv25PKdO6z6+GMenT0rYvmKo6Eh4vosLGDQIJHfC2BggP6WLYzZtYvGDx6wa9cujt67h7Rzpyh9/+670LAh7NyJ844djIuOJsXOjhXDhpH49tuwfj1mkZFMOHkSEy0tVpuaEvHWW3Rds4bOoaGcataM0Pr1Gb1zJwmWliSZmeF67RrhTk44hIWRamKCYUbGE/ErdHhIEiotLdba2xM5depruvEyMuWj0qe6rVq1onnz5iwtJgAuLi7079+fefPmlWr/ySefsGfPHm7evFl0bOrUqVy5cgU/Pz9AWHzTp0/n8ePHL3VNlTrVLc5bb8GaNcJx4ez84vaxsaLaS7t2wgnx1PpXdHQ0W7duJfvRI/pt3Ur9P/8U+bvFuXpVBDwPHizeu7CPs2eROnXiwvvvc8TQkHr16jEwPR3l5MmwYAG8917R3h6Pf/6ZjRoapMXGMuzyZWrNmgU9e5LbqRNb69Yl3NCQAbGxNFq+nEuDBrG/USOa3L6NR3AwG3v1QpmTg+O9e1xyc6N2RASRDg6YPH5MmqEhak1NFGo1UmE9P4UCDZWKkcnJOC5a9Hruu4zMC6hUiy83N5fAwEC6detW4ni3bt04f/58mef4+fmVau/t7c2lS5fIK1brLT09nVq1alG9enV69+5NUFDQM68jJyeH1NTUEo+/hJ9+Emt8o0dD8Rp2z8LWVnhVd+4UHtqnsLe3580336R2vXpsHjKEwz/9hCoxsWSjJk1Exse6dSLlrZC2bVH89hutf/qJ4RYWREREsDIvj0cffggffCCs0wkT4KOPMP3oIyY4OmJbvTrrWrbk2po1sHUrykOHGJaWRuO4OLZXq8aFCRNw37OHQZcuca1uXU60aMHo/ftRa2oSWqcOHhcuEOngQM3ISFJMTTFKTy8SPUWh5adWo9bUZL2FBXenT3+1+y0jU04qVfgSExNRqVTYFM86AGxsbIiNjS3znNjY2DLb5+fnk1jwI69fvz6rV69mz549+Pj4oKurS5s2bbhz506Zfc6bNw8TE5OiR40aNV7D6MqBgYEQoEuXSk9Nn8XAgSLL4t134d69Ui/r6uoyZNgwvFu04KKLC6t/+IGUpy3fkSPF+e+/DxcuPDn+5pswdSrOM2Ywyc2N/Px8lllZETZkiPBA37olHCQ9e6I7ciSj2rWjoZUV22vV4uy5c0hLl6K5YgX97O1pc+sWh2vWxHfUKBqePs2IM2eIrFGDvV5eDPP1RSc3l6uNG9P27FmiatWielQUKSYmGKeloZAkJEBR6PBQq5E0NNhoYkJoMa+0jExl8Zc4NxRPTdkkSSp17EXtix/38PBg1KhRuLq64uXlxZYtW3B2dua3Z6SLzZw5k5SUlKLH/fv3X3os8fHxFTvBw0OUqp87V5SdKg8LF4oA6HHjnnhDi6FQKPDo2ZPx9eqRlpfH7wsXllgaAIS12aKFmPLGxT05vmABtGqF1ZgxTOrZk+rVq7PBxYXznToh9ekjKrps3Ai1a6PZrx/9hw2jnVLJMaWS/Y8fo541C8XcuXRp3x7v8+c5X6sWu954g9q3bjHW15dkc3O2derEwJMnMU1JIcDdHa8zZ3hYvTr20dGkGBtjnJb2ZJpbXPwUCjbp63N79uyK3WMZmQpSqcJnaWmJpqZmKesuPj6+lFVXiK2tbZnttbS0sLCwKPMcDQ0NWrRo8UyLT0dHB2Nj4xKPl+X333/n0KFDFfMgf/UVmJgIC6w8mJiICi0nT5bO1ihG9ZEjeVOScLh5ky1btrB3794nywFKpYj7y88X4TUFubQolbBtGyiV6I0YwfCBA/H09MTX1ZWd7u7kDRsGenpiJ7eMDBSDBtHxgw/om5JCUGoqG62tyR4xAj74AI9Roxi0bx/XqlfHp08frFJSmLBrF/k6Omz09qaHnx92cXH4tW6N1+nTxNnYYBMXR6qREcZpaUWlrIrET5KQFAo2a2lx44svyn9/ZWQqSKUKn1KpxM3NDV9f3xLHfX198fT0LPOc1q1bl2p/5MgR3N3d0X5GUUtJkggODi5d0r0S6NSpE5cvX2bRokUEBwdTLt+QsbEQsF27hKCUh44dxdrbrFlw/fozm+l9/z1vhIbS28+Pq1evsmzZsid/OOztRYra6dNCfAuxsRHOk+BgND76iC5dujBo0CBuNmjAKkdHUmbOhFq1xFrjxYswbRrNvv+eUTdv8jA2lpXNm/PIyws+/JBGb7/NqI0buW9ry+ouXVCamDBxwwb0VSo29OxJ28uXcbp3j7NeXniePUuyhQWWSUlk6ulhmJaGWksLhSSVEr+tksS1b74p372Skakgle7V3bx5M6NHj+b333+ndevWLFu2jOXLl3P9+nVq1arFzJkzefjwIWsLFvMjIiJo1KgRb775JpMnT8bPz4+pU6fi4+PDoEGDAPjiiy/w8PCgbt26pKamsnDhQtatW8e5c+do2bLlC6/pVb26qampHDlyhOvXr2NnZ4e3tze1atV6/kmSJFLZbt0SQmZg8OI3ys4WRQqUSpFp8aztG+/ehaZNSRg1iu1Nm5KYmEjXrl1p2bKlWB748kuRh3vsmChyWsgff8DUqUXlrWJjY9m8fDm5aWm84exM7UmTRJrc6NEiK2TKFJK8vdnYpg1ZlpYM27ePmklJ8PbbxH7zDRunTEEjPZ0RV69ifPEim0eP5oGZGQMOHeJ2nTpcrV8fz3PnuOzmhn5GBumGhmjn55NhaIhmXh6SQoFaQ6OEN3uggQGN5XU/mdfMX5K5sWTJEn744QdiYmJo1KgRv/zyC+3atQNg3LhxREZGcvLkyaL2p06d4oMPPuD69evY29vzySefMLVYrNcHH3zAjh07iI2NxcTEhGbNmjF37lxat25drut5JeFLSAArKwCioqI4fPgw0dHRuLi40LVrV8yeV5zg7l0RrvLBB6JSSnkIChL19P7v/+B5FtDy5TBlCvk7d+Kro8PFixepW7cu/fr1w0BXV1SMuXULrlwpun4kSawjbt0qhLVxYzIzMtj21VfcUyrxbtqUFgMGoJgzR1zvrl3QpAmZ7dqxdcAA7lta0ufwYVw1NcHLi9TffmPj9Ok8zs1laGgoNXbvZuf48dy0t6enry8JtrZcdHXF/eJFbjZogFZeHrlKJQog08AArdxc1BoapcTvHSsrLN5+u3z3S0amHMgpaxUVvk8/FZ7PAiRJIiQkhGPHjpGRkUHLli1p167ds4Opv/xSTDuDg0XgcHn46ithsV2+LMJVykKSxP4fFy/CtWuEPnrE7t270dDQoH///jjp6YmcYHd3kdZWmEmRmSlS2LKyhPfZ2Bh1RgZHpk3D39GRpvXr02vAALSGDxchL+fPQ1YWqk6d2DdlCsGmprQ9d45OlpYolEpytm1jy4wZRAJ9792j8bp1HBoxgoC6dWl/+jQaWlqc8PSk0dWr3K9ZE1WByKk0NcnS1y9T/JzCwhjWuTNa48aV737JyLwAWfgqKnyGhhAR8cRqKiAvL4/z589z7tw5tLW16dChA25ubmg8XXI9J0eIl62tcF6UJ0k/N1cUOjUyEsLzrDLuTwVAp6Wns2vXLsLDw/H09KRTXh6avXqJzcs/+ujJeXfviil1ly7C8aFQwP37XBkxgr2dOmFbowZDevfGuGdPSE4WFWGOH0caMgS/uXPxBVxu3GBAnTpoX7yIKjCQfZMnE6yvT4cHD/BasYKz/fpxolkz3AMCsElJ4UCnTtS5c4dkCwsy9fTE3h06OuTo6KCVn19K/GpHRDCye3chwDIyr4gsfBUVPiMjURuvmNVXnLS0NI4fP05wcDBWVlZ069aNOnXqlGx07JgQmdWrRd5teTh7VmwgtGSJyAh5Fjt2iJS1gr4lSeL8+fMcP34ca2trBoaHY/XzzyJdrfh66K5dMGCAKKhaOK08cYLo0aPZPGkS+QYGDPLywrF3b2E17t8P334L//sft9asYUdEBFYPHzKsRQuMfvsNKSWFM716ccLGhqaxsfRetYornp7s8/Ki/q1bNAwLY2ePHlR7+JAcpZLHpqYYZGaSZmhIvpYWmipVKfGrcf8+o3v1QnvgwPLdMxmZZyALX0WFb9YsEWcXGSkS/J9BTEwMhw8f5t69e9SpU4euXbtiXXyv3JEjRbXm27dLV1p5FlOmCC/trVui+OizGDtWeGRDQoR3FpHutnPnTh49ekSXq1dpFRyMIiiopJPlvfeEw8PfX0yLAebNI+Prr9nx9ddEpKXRsUYN2k6cKNb95s4VcYJHjxJz6BA+Bw5AdjbDW7XC7t13wcGBKzVrsqdePWo/esQQHx8ia9dmW48eVHvwgDYBAWzv0weTx4/Ryc0l2s4Os0ePeGxqilpDAw21GpWGhgh7KRA/++hoxvTti07v3uW7ZzIyZVClhO+17LmRmAi1a4vMiBc4KCRJ4tatW/j6+vL48WNcXV3p0KEDJiYmYlpap46wrr7/vnzvnZws6vZ17Cjq/T2LlBQxna5TR5SsLxCNvLw8jh49ysWLF3GIjKSfoSEmxYO+s7PFel9mppjOGhqKAOp+/VCfP8+pFSs4ffUqzgoF/efNQ2/rVrHRuYcHqFSk7d/PpkWLSDAwYED9+rhMmgT9+xMRE8Pmtm0xzchgxIEDPFar8RkyBOPHj+l29Ci7+vVDKzcXi+RkwhwdsUpIIMnCoijERaWpWWL7Suv4eMb374/uU6mNMjLlpUoJXyGvXKRg5kwxJYyIeK7VV4hKpSIwMJDTp0+TnZ1Ny5Yt8fLyQm/ePLHedvdu+er2wZNCpwcOiPCYZ+HrC926wapVwnNbjPDwcHZv2EBOZiY9GjakyciRT7Jlbt8W632DB4vpMsCjR9C8OVhYELpmDTv37UMvJYUh27Zhe/CgEMcWLcDLi7yFC9n1+efccHKinYkJHWbMQPHxx8Tv3s3Gfv1Qq9WMOHMGzYgINowZg1qtps/evRzu0YMspZKa9+9zy8UF67g44q2s0C4Ic8nX0iqxHmqRlMSEgQPR79ixfPdNRqYYsvC9jPAVWn3vvSfWucpJbm4ufn5+nD9/HoVCQVt3d1qNGoV2//4lCwo8D0kSe3vcuSPiAZ+3neWYMWIt7uZNKD7NBrIzMzn48cdctbbGxcmJ3gMHol/YV+HmRAXxfYCwAD094a23ePT552zx8SExJoaeV67QbNMmsedHr17w2WdIPXpwduZMjrdvTz1JYsD336Pz5Zek/fgjPuPGkaStzaArV7A7fVo8NzKi7+7dnPfyIsHcHJfbt7napAlWcXEkWFujzMlBpaGB6inxM338mIkDB2JYEBolI1NeZOF72fS1Tz+FxYvFWt8zUumeRUZGBqdPn+bSpUsYSBLt9+6l2fr1aNSrV74OwsKE9/bDD0UB0meRkCCmxt27i0Dkp3n4kBv9+7Ove3c0TU3p06cPzoXls0aNElkmISFQs6Y4tnChSLvbs4f8Hj04sH49Qffu0Sw1lR7z5qE9f75YA925E9LTCf3qK7aPGIFJdjbD1q3D/L33yP3sM3a89x6h+vp0vXuX5tu2sX3kSO7WqEGPAwe47eJCZK1aNL52jeCmTbGMjyfR2hqdzEzytbRQaWs/ET9Jwjg1lYmDB2P8jEwgGZmykIXvZYUvIQEcHIQQvGRq1aNHjzjh60vIzZtY5OTQadQoXFxcnlvAoYg5c2D+fGH5Va/+7HaF1tuhQ8JSfBofH9KmTGHP3LncTU/H1dUVb29v9HJyxMZJdeuKdcLCIqL9+omQmuBgqF6doCVLOBAdjYWeHm+8+SYWb70l3svfH9asIXHVKjbNmEFGWhqDjh+njqcn0i+/cHT6dM6bmND8/n26b9zI4R49CGzShDZnzpBiasq1Ro1oGhzMlSZNMHv0iGRLS3QzM8nV1kZdPHVRkjDMyGDikCGYtmhR4c9ApmoiC9+rFCL95BMRXvISVl9xYpYs4ZifH2F16mBjY0PHjh1xdnZ+vgCmpgrnRc+eT9biykKSRNZGWBhcu1Y6VU6SYMAAJH9/rmzfzqHTp9HW1qZXr17Uj44WVaF//llkm4CY5jdtCk5OcPw4aGoS+/77bJMkUq2t6dWtG64TJoh+/fxg2DCyg4LYPmcOYfHxdLl7l9ZZWSgOHyZ45Ej22tpSMymJN3bsIMjZmaOdOtE4JAS9jAwuenjQ4Pp17tSti0F6Oo/NzNDNyiJPqRTT3mJj0MvKYsqoUZg2bvyyH4NMFUIWvlcRvoQEsdY3ffpLW32AqKDSsCH3mjblRI8e3Lt3D3t7ezp27IiTk9OzBXDpUuEVDgoqvfNace7eFdbb+++XHX/48KGYEg8bRtr8+ezbt4/Q0FAaNmxIj/PnMViyRKzxFWaanDolPMvffCMcPTk55LZty/6GDbnq4EDT2rXp8f77KAcNEs6b5s1RW1tz/M03OffgAY2zs+nj64t2fDz3mjZlc4MG6OXmMsLXlxhg14AB1Hj4EMc7dzjeqROOYWHE2NujnZsr8nvz8shTKlFraj7Zt1eS6HHkCC23b39+qM8/nICAAOLi4jA2NiYuLo42bdpgb2//d1/Wfw5Z+F619PyHH4qS7TExYoOhl2XrVhgyBOnkSSJq1ODEiRM8ePCAGjVq0LFjRxwcHEqfk5cnBK1GDRET+DwLce5cEX5z8yY4OpZ+felSmDYNTp5EateOa9eucfDgQRRAj+PHaZiYiOLCBSi0tD79VFiCFy8KC/DmTXBzI/jNNzlgZYUJMHjBAmzmz4f69aFNG5g0iWtOTuxOTsZKV5ehq1ZhYmFBcm4uPh07kq6ryxt+fmhGRLBpxAiMMjJo4e/P4W7dsImLKypdn6NUoqVSka2j82QKXjD27seP02r79nJ52/9pBAcH4+/vz+TJk9HQ0ODhw4esX7+ed955B4PyFLWQKTey8L2q8N2+LX7YPj6i7t3LolaLTAoDAzh1CkmSuHv3LidPniQ6OpratWvToUOH0lVgdu+G/v3h4EHhxHgWGRlQr56I09u6tez3b9cO4uNFIQM9PdLT0zl48CA3btyg/s2b9GreHMP/+z/RPidHXK9KJXJ8dXWFZ/qtt0jYvJltSUkkx8bS3deX5n/+ieLkSZFxsn49sSdPssnIiDwzMwatW4ejmxvZR4+ybehQwi0s6Hn1KrXPnmXDqFHka2vT8eRJjnbsiG5WlihooK+PBKBQkKOrW2rryk5+fnht2SLKgf2L+O2332jRogUeHh5Fx37//XcaN25MmzZt/sYr++8hC9/r+HF4eYkf/lN1BCtMYbpZYKCIm0MEQd++fZuTJ08SFxdHzZo1adeuHY6OjmIKLEkiiPjRI+Fw0NR8dv/r1okQl1OnhMg9zc2bYso8Zw78739Fh2/cuMGBzZtR5eTg3akTrl27ivcOCRHpa+++Kyo+Fzo//PzIu3yZw4GBBF65QsP79+nz44/ovPeeGOOZM2ROm8aOJk0Iq1aNjseP4+XujvTrrxyaPJkAOztahobS5tgxNvftS7y1NV1PnuSCmxu52toYpqeTaGmJTnY2+UoluTo6pcSvbVAQnTZsQPEvsZSSk5P57bffGD16NI7FLPIdO3aQnp7OmDFj/sar++9RpYTvtWRulMWqVWIP3fBwseb3sqhUwmnQvr3YIa0YkiQRGhrKmTNnePjwIfb29rRr1044QQICxG5r69eL4OZnoVYXZVkQEFB2sYP/+z8RnH3r1pMwFiAzIYFDH35IiJMTtWvXplevXlhaWoo6fZ9+Kjy9Hh5i3bNxYzH9PXCA64cPs/f0afS0tBgwejQ1Bw4U7799O+p27Tg9YACnqlWjblgYA6ys0PvlFwLGjuVQzZrUiouj37Fj+DZrxvVGjWh74QLhNWsSb2mJXUwM92vWxCg1layCTcsVBVWmJYUCNDRocfs2Pf78E8U/ZdvR53D37l02bNjApEmTqFYsmL1wvXXGjBl/49X996hSwlfIa7f40tPFgvqHH4q1tFdh/nzhMIiKEhVcnkKSJMLDwzlz5gz37t3D2toaLy8vGnz8MRoPHojtJZ+31nf+vFhv+/NPGD++9OupqWIrzA4dSqfFHTlC2LRp7B8/nlRJom3btrT18EDLy0ukuV2+DDo6IpylRw9Rdfr993m0ZAk7AwN5ULMmbRs0oP2ECWiOGCGm6D17cvebb9iRkYFOTg5vxMRgv3s3ke3asbVxY7Tz8hhy5gyhhoac6tCBhjdukKtUcsfREYfISCIcHTFOSSHdwAC1hobYvY0n4tckKop+S5ei8awirn8hkiSxZcsWHj58yIQJEzA1NS16LSQkhB07dvDWW2+VyOk+cuQIAQEBzJb3IXmt/CWbDf3nMTQU63urVj3Z2+JlmThRVFp+RiaHQqHAycmJcePGMW7cOIyMjNi+fTtLOnYkWFMT1b59z+/f0xPeeEMIdG5u6deNjYXnt7BkfXG6dcOpRQveWrIETzc3zpw5w9Lly4n47jsIDX2Su9y9u/Agf/op3L2L2VtvMS4hgQ7+/py7dYs/Z84kcft2sU740UfUmTuXKU2bop+ZyZ916hDYoQO17t5lyq5d6KtUrPL2xkJDg0F793K7bl0ydXVxDQkhwtERh/BwUo2NMczIEPdHkorED7WaqzVqsOWDD5Be9XN5DeTk5BAWFoZCoUD5lBAXli97uoyZWq1GXcaGUzKvhmzxva4FcD8/ISpHjoi4uVfhnXeEAyIqSlhQL+Dhw4ecOXOG27dvY5qVReuBA2natGmpH1cR16+L6ejvv4uKL0+jVgsnSG6uWG8s/mN88EA4c6ZMIWHmTPbt20dUVBRN1Gq6LViAgZ+fCI3JyBDZJU5OYu0zNhYaNiS6b192uLuTkpBAt1OncF+9GsXQoZCYSP5333F4zRoutWiB67Vr9EpJgXPn2DdqFFft7Wl95Qoud+6wxdsbDZWKBrduccHDg+pRUcTY2aGXnU26kVHJMvaATm4uU27exHznzvLVP6xEcnJy0NTURKt4HCJiy4W1a9cybdo0rIrVetyzZw+3b9/mY7n8/mtFtvheFx4e4ge/cuWr9/Xuu8K7+rwKLMWoVq0aw4YNY6qLC9Xv3uXQwYP8+uuvHD9+nPT09NInNGwIQ4aIOLyyrD4NDbEPcHBwaQ9w9erC+bFwIVbx8YwbN46+fftyR1+fRdOmcfGbb1CrVMI7vXSpqD24fr1YCli8GPs1a5hiZUXTJk040LEjPr/+SvqKFZCYiNb27fSqX58Bu3dzvVEjVtSpw6NBg+i/bBnet25xoXFjTrq7M+rgQfSzs7ncrBltTp8mztYWs8ePydPSQj8jA5W2NhpqdVF1lxwdHZbXr0/c5MkV/CBePzo6OqVED8C8oDTZ059Xdnb2M3cXlHl5ZIvvdYY8FOaqRke/UiYHIBL+o6PFull5rRRJgiZNeOzkxIWpU7l8+TJqtZomTZrQunXrEpbEC62+wmu4e1e0Lf5jLUxnc3AQ5egR+cfH1qwhKD4ea11degwbRu3atYWz5fBh4SyxsBBVX06fhuvXCT1+nD2BgUhGRvS2t8dl8mSxXLBkCfEqFdt69uSRJNE9Npbm69YR2aoVW9u0QScri4HHjnHe1ZVbderQ4uJFbrm4iBp+KhW5SiW5SiWaKpWo51fg6dbOy2O0JFGjAoUl/koWL15My5YtaVEs9W7BggVF5cxkXh+y8L1O4YuPF+Wlfv5ZWG2vwpEjIrfWz09Yk+VlwwZRYCAkhCwnJwIDA/H39yc9PR1nZ2c8PT2pWbOmCEcZNkz0f+dO2Tu4BQWJsJqVK2HChJKvFYbeHD0q0toKiB45koMmJjywsaFhw4Z0bd4cE3d36NNHeKrj44XF2aEDbN1KxnvvsS8piVvOzjRMS6PHxo0YbNsGPXqQ17Mnh3V0CHRwoEF0NH2OHyc7O5vNgwaRYGREj6NHSTEz40yrVtS9fZt0IyPirawwTk0l1di4aK0vX0urKNBZU6ViuIkJTsVL7/9D8PPz49q1a0yaNAmFQsHdu3fZsWMH06ZNw9DQ8O++vP8UsvC97iDXAQOEpebv/2r9qFRiWjl8uBDS8pKbK84bOVJMV4H8/HyuXbvG+fPnSUhIwM7OjpYtW9JIQwMtV9fnh8EMGQIXLghxLL7eKEliHVClEtkbhVZpZCRSvXpcnTWLo4aGZGdn46Wvj+f//R9ahw4JkSysKXj4MLRujdSwIde8vDjYpAmKR4/o8eABDb29UYwZAwsXcmP1avb27IlORgaDwsOx27+fQ8OHE+jkRJMrV6hz/z77unXDOCUFs0ePuOPsjFV8PAlWViLWT0urREkrhVrN4OrVafAXTX0DAgK4cuUKWVlZeHl50bSwuvVTSJLEqVOnSElJwdTUlNjYWNq1a/eX7Bdd1ZCF73UL38qVMHkyJCXB87aaLA/vvAN79ogiCM/aYKgsPvpIFC54+LCEWBVmg1y8eJG7d++ir69Ps9u3cb97F9Ni23uW4MYNYaGVUdCUU6eE5bZli/AUF/Lxx7B0KTk3bnD69m0uXLiAcXo6Xa9exWXvXhSamiLXNyZGBEH7+kLv3qSvWsXB1FRuPHpEfV1del6+jNHx4zB3Lo9nz2bHO+/wQFOTDg8f0nbtWq55eLCvXTtMHz2i84kT+HbpQrqBAc537hDSuLGo52djI6q6KJWoi03XnW/dYuikSWgUs1Yrg7CwMG7fvk3Pnj05cuQI/v7+fPrpp2gXrzAj85cjC9/rFr7ISLH2tWOHsP5ehdOnRTDz+fPCuiovhWK1datYUyuDpKQkAgICCA4IIDc/n3p2drTo1g0HB4fSRRH69BHVpkNCSq83ensLj21w8JPXHj0S3twhQ+D330lMTOTI5s3cSUykuo4OXYYPp1Zamghy/vZbETQ9YoSY3t+8yY0vvuCAvj4qU1O6HzxIEwsLFFpaqE+d4uTgwZyxsaFWUhL9jxwhLzWVLcOGkaKvT/eCen6hzs40uHGDUGdnjNLSSDE2RpmbS7aublFBAxQK6ty9y5APPkDbza3897aCbNiwgaFDh6KlpcXGjRsJCwtj5syZZTo4ZP46qpTwVVrmxtM4OYkA3kWLXq2fl53ughBKU1ORw/sccrOyuNq/PwHu7sQrlVhaWtKiRQtcXV3RKbQWCy27svKBC8V5zx4hkIX8+KNw9Ny9W7ThUcSYMfiamBBjaUm9evXoHBCA1R9/CMeHUinCZAYNgh9+ILNJEw4NGUKIsTFOd+/S09MT888/hxYtiExKYlf79mRpauJ99y4Nd+9m/6BBhNSrh1tgIPrp6Zxp355aEREkW1iQp6WFpFAgaWiQq6ODQqUSAc4KBfYxMYz6+GP0nt4J7zWQkJBAcHAwXbt2JTMzk59//hknJyeGy1tk/u1UKeErpFItPhBe0jNnRO7rq/Luu2Lrx3v3KjbdXbFCXMe9e6J6y/P48UekOXO45+9PwJ073Lx5E21tbRo1akTz5s2xt7ND4eEhgpuPHi19vpeXqBTj5/fE6svIEOl7AweKndsAbt8W63lff81xPT1SUlJodu0aHQwNMfrzT1Hh+YMPhFMlKAjGjSN061YOBAWRrqGBl5UVbWbMQGvOHHK++45Db71FsKkpzrGx9N63j1BbWw52747F48c0DwzkRPv26GZloZ+ZSaytLfqZmWTr6qLS1ERDrUZdIH5mqalM++wztMq7210FkCQJhUKBn58fR44cYciQIbi4uLz295GpGLLwVYbwbdkCQ4eKYN/ybiL0LF52upuWBjY2IkOjsKLKs0hMFHF2CxbAtGmkpqYSGBhIcHAwqamp2NjY0EylosnHH6N39aoogFqcAwdE6Mu5cyKIu5AffoDZs0UOc6H4Tp0KW7aQHxpKwJ07nPb1RZWTg0fTprT29kavRQuRI3z4sLAy4+PJ3b2b09On49eqFWa5ufQ8cgTHJk1gyxZu9+jBXkdH1AoFvS9fxvLqVbYPGkSSuTltLl7kjoMDcVZW1Lx/n0gHB4xSU0kzMkKjIJNDraGBhiQx/OxZ6hw+DJW09rZ06VLS09OZMWMGms8rJCHzlyALX2UIX0KC2NxnzRpRDeVVeJXpbt++YqvJU6de3LZnTyGWZ84UHVKr1YSFhREUFMTt27dR5ObiolDQfPx4ateu/WQtUK0WJa9athThNIWkpYlrnzr1yRaaMTGiHuDs2TBnDlkpKZwbP56LjRujoadHKzMzPKZPR2/bNiGArq7w22+QnU38jz+y///+j6i0NBplZtJt+3aMHBzIuHmT/f36cdPamoYREXQ5cwY/Z2cuenjgFB6OcWoqQU2bUu3BA2JtbNDNzibDyAit3NyirSsVkkSvyEjcVq9+7dkdDx8+ZMWKFbRq1YruzysdJvOXIQtfZdVsa9pU/GifqrLyUowfL2rkXb5csfP++ENUaE5IeLGHuXBvjnv3SlRlKSQ9PZ2rc+dyOT+fJDMzTE1NadKkCY0bNxZVWn7+WeTm3r8vLM1CPv5YTLvv3xc5zSAKnm7bJhxB+vrw+++kf/wx55Yt41J4OJrZ2XjcvYvHn3+i+9ZbYm3x1i0R+lKzJle6dME3MZF8AwO8jh7Fo0EDNJct49rQoRysXRsJ6HbpEgbx8ezx9kZSKGgeGEhAy5Yoc3IAyNbVFet8FIvzAzplZ+P1gv2SK8revXu5fPkyU6dOxcbGhqtXryJJEq7Pq5otU6nIKWuVRefOIl3rdfxd8fQUVVfKSj97Hj17CovxyJEXt+3fX9QU3LKlzJcNDQ3xHDGCtxcsYLyLCw4ODvj7+7N48WKWL1+Of7NmZBgZCQEtzrvvioovGzc+OfbRRyLcZ9068XzCBAzNzfHeu5f333+fprVqcbZOHRbMn8/pgQPJzsoSO9rNm4fC15emjRvzzsGDNI2O5kTnziw2MuJGv340unyZt9eswTk5mT1eXlxwd2fY4cNUi4vjbLt2ON29i0FmJumGhpimpJCvVKKVn49GsaIGtxITySpnqmB5CQ0NxdraGpuCPwjXrl2jXnl31JOpFGSLr7IsvsJ1r1u3xDTwVbh2TaSIHT8u4t8qgqureDwtSGUxcKAITTl/vuzXJUmMpUMHWLaM/Px8QkNDuXr1Knfu3EFSqagTF0fjadOoV6/ekyIJvXsLq7N4UHe/fsLiKwyDWbBACGKBxZjWsSNnnZwIdHBAMz8ft8BAPP74A+M33oDsbPjsMxgwgMQlS/A9e5ZQZ2dqRkXhnZWFvY8Pd7282NeyJRm6urQ/cwYdSeJo27Yoc3Ko8fAhN+vXxyw5mRQTE5R5eWTr6YFajQIwSUlh5LBhWFYkY+Y5/PLLL1SvXp033niDixcvkp+fj6e8Hebfiix8lSV8KSkinGTDBhGj9iqo1WKq+n//J9bGKsLs2bBsGcTFvdgrXDg1Tk5+dtn2//s/MX2Pji5R7TkzM5MbGzdy1c+P+zVroq2tTd26dWnQoAF1b9xAOWSIiANs1EiccPiwCI0pdNo8fgz29iIEZs4csadv376kHz3KhdRULl28SJ6uLk1sbPD87DOs1q0Tewrn5oKbG2Hnz3Okd2/ilUoa379Ph5AQDIODOdG/P/7162ORlITX6dNcdXUlrE4dnO7eJd7KimxdXbTz8sjR1UWloYGGWo2koUHdyEiGL1wIJiYVu99lEB4ezsGDB1EqldSuXZsuXbqUbwtRmUpDFr7K3JfBykrswPY6ikh27y6EZv/+ip3n6wvdupXP8rx7V+yj+3RMXnEKC5mePSv+LU5ODlhb82jGDK537syNGzeIiYlBS0uLOrdu0cDBAefZs0V8oFotwl169xZbdAJMmiSm5eHhYqzOziJPed06csaM4VJSEhc6dSI9PZ16iYl4eHlRa+hQFJs3w4QJqCdM4HJAAKe6dCFDQ4NmsbG0P3SIzLw8DvXtyz07O+qFhlL93j3OenmhlZeHRXIyUbVqYfL4MSmmpmjl5pKvqQkaGnQIC6PdmjUoKhJGJPOvQBa+yhS+Vq2EhfM6SlV9+aWoaJyYWLF4vqQkseNYeSxPSRJZJ/37i/cqC7VaeKynTRPX9DRvvCHCePz8ALFp+s2bN7mxdy8PdXXR1NTEycmJ+vXrU3fzZgyXLxfTa21tUfvP3R327RPLBPPmifeIiRHT4mbNyN+6lZDHj/ELCiLB2hqr1FRaxsXRxNYW5Z9/wtix5K1aRUDfvpytVo1cLS3co6Joe+gQkVZW+Hp7k6Gvj3twMMkmJtypWxfr2FhSTExQa2gU1fBTaWuDJDFaqcRx1qzy32+ZfwXyn7LKxNFRbOT9OvD0FKlgoaEVO8/CQlhW5fEIKxTCKXPixLPbaGhA27Ylwl5K0KOHWMtLTATAzMwMT09PJrVuzfRffqGLqytZWVns2bOH+Xp6LB80iFMbNhATE4PUrJmwOHfuFH2NHSsCo318hJfczQ2tDRtoNm4cb+3cyZhHj7Cws+OAkxM/m5pyqFUrkmxs0M7JwdPIiPd/+QWvuDiCq1Vj4aRJPGjUiNG7d+Pp58elpk2JtrPDLSCAHB0d8rS1MU1JQaWtjXZennh/SeJgdDQxzxqrzL+WKmXx/WUpa4XMni08l1FRr95XdLQIht67V0wPK8LgwcLye56gFfL778ITm5FRdqkqEHUH58wR65hPt3nwQAQrb9sm0s8KSUsDc3MRkzd1KpmZmdy5c4c78+dz19GRHIUCIyMj6iYnU/foUWofP46uvr4Q0txc4SFfsECEx8TEiGtYsgQiI0lp1oxLw4ZxWUuLTC0tamZn0zQggIZ5eShzcsi6fp0LgwZx0c6OXG1tGt++TZO7dwlxdORKgwYYp6RgGxfH3Tp10MnORq2hQa5SiaRQoCFJNAsNpdf69ZUW3Czz11OlhK+Qv2yqW1ipJSurXCXkn4tKJcJNFi4U+9NWhHnzxD4ajx69eJp87pyw6K5cgSZNym5z8aKYxl+4IP59mpo1Ra2/H34oebxtW5EhUryq86RJqAICiNq1i9DQUEKvXiU5MxMFUK16dRySknBctozqAQFo5eWJDZhWrBAWsIuL2Ff4+HHYupX8Vau4+dFHBI8cSXhWFtpAw+BgmurqUvPsWXKTk7ns7Y1f3bqkGRhQ79Yt6t2+ze169bhdvz7miYno5OQQU60a+hkZZOrpiWKm2tq0Bzp8/nkFbrpMZXLr1i1++eUXrl+/DsCvv/6Ku7t7qXaSJPH2228zZ84c7O3ti47LJSIqE0dHsW52755YqH8VNDWFxfcy1mPjxiKWLibmxSl0hV7Xq1efLXyNGolp8fXrZQufh4cQxadp00ZMW4vTrh2aK1fiYGyMg7c33l268MjRkYiJEwk3MeFSQgJnRo9Ge9Eiajk6UnvIEGqdOYPd2LFo1q0rLOAxY2DBArT09GicmEjj6Gge+/tzpUULgh0dCTYxwdTWloYpKTS4fp0We/cS0qIF51u1Yk/9+lgmJeHh70+ctTURDg4YpaSgpVKRaWCAdnY2Km1twu7fp9G1a1gW3h+Zv5XDhw8zf/588vLyqFOnDn379iUiIuJJYY0C5syZQ69evUqIHshrfJVL4cbQ4eGvp7+aNUWcW0UpFLuYmBe3NTER7xMS8uw2+vqi4sqtW2W/3ry5EM6nJxPNm4vrT0h4cqwwni0wUPyrqYlZ3bo0v3yZwYMH8/EnnzBl3z7ap6ejVqs5Vb8+K2vX5rvvvmP10KEcT0jgro0N2fb2wiPcvz8cOIBpt260X7+e91JSGHv4MI7x8VyuVo3lvXqx5P33SapdmwH79jF69Wqs4uLwb9GCB9WqUf/GDSySk3lkZoZeRkZRFedYGxtCly598f2T+Ut4//33MTQ0xMzMjClTphATE8O2bdtKtFm8eDFOTk706tWr1PmyxVeZVK8u9qp4XcJXo8bLCV9hBd/o6PK1r11brNU9DxeXZ1efqVtXrP8lJoqQnkIKU7SuXXsSiO3oKFLZrlwRYTcAbm5FmR4KhQK72rWxu3iRNt9/j+rQIWInTiTq99+JunuXQGdnzvj4wOTJ2GRkYF+/PvYBAdg3aIB1Whpa9epR+88/qV2vHj3XriXSyIjrbdtyuVYtztWvj1FaGnXu3aPX8eM8MjQkpEEDUo2NMX78GP2sLOKtrFCoVGio1Ry1sKDJ7dsYvoasi9jYWAICAoiIiECtVmNpaYm7uzvOzs6ltpiUeT5Tpkzhhx9+YO3atYwsqCS+c+dOHj9+zNtvv13mObLwVSaamiIo9+HD19NfjRpFYSIVwspKXEt5LD4QubZxcc9vU7v2szM86tYV/965U1L4HBzEFDk8/InwaWiI+MLi3mo3N7E+mJgoQnGaNoWffhJ7Zri6Ui06mmoqFa2HDEGqXp1kHx+iIiO5f/Uq0bVqEdyzJ9Lt22jMmoVNdjb2vXtjZ2WFtSRR3d4ep0uX6BUczL3Gjbnj4sKd6tUJatQIDZWKmlFROIaHk2FgwL2aNVFraWGckkKOtjaSpibnN2ygW1lhPOVEkiQOHjxIQEAAGhoaRXvmpqamEhYWho2NDaNGjZL32KgADg4OdO3alaNHj5KYmEhoaCinTp3i12eFZPEXTXWXLFmCg4MDurq6uBVsRP08Tp06hZubG7q6ujg6OvJ7GZtrb9++nQYNGqCjo0ODBg3YWRgC8U9DS0vEvr0Oqld/ORHV1BRiVl6LrzzCZ2VVcspanMKp9dN96OiIPwSRkSWP165d8ljt2uLfwrE2aCAyOxIShHPD3FysL1arhsLEBIuoKJq5utJ3506m9unDzD//ZGJ+Pt63b2Pz+DH369Rhv74+f06axHdt2/JLhw5sGjmSu40aYZOczIDt25n8++94Hz6MVn4+N1xcuFO3LioNDazi4tDJySG/wKN7Mz0d1StsTn7s2DECAgIASmwUXuhjTEhIYN26deTn57/0e1RFBg8ejEqlYv78+Sxfvpz58+c/t32lW3ybN29m+vTpLFmyhDZt2vDHH3/Qo0cPbty4Qc0yqoBERETQs2dPJk+ezPr16zl37lzRJsuDCsIj/Pz8GDp0KF999RUDBgxg586dDBkyhLNnz9KqrMX2/wpKJbzsD+J5QvU05RE+S0thkRWUcS+Bqak4lpRU9nnJySWP2dkJ67AQa2vxb3x8yeeJieL/1aqJoGcQ65FRUU/K/IeFoV2rFtXv3aO6np5wslhakq9Wk3jnDvGdOhF/5w4JDg7cMjfHr27donVG3awszJOTqXPnDtq5ueQplaSamJBgZSUCmoFcTU0Sb97E5iWcHBkZGfi9wGJXq9XEx8dz48YNmjzLuSRTij59+qChocHmzZu5fv36C2seVrrw/fzzz0ycOJFJkyYBwu18+PBhli5dyrwyyv/8/vvv1KxZs8hMdXFx4dKlS/z0009Fwvfrr7/StWtXZs6cCcDMmTOLTFufp72GMgJNzfJXijEwEIUAnoepqYivy84GPb3S72ViIsJnnsbMrPRxU9OSxwqnx4XCZ2kp/i0IisbC4omo2toKkS5sk5wsrMqYGDFFPncOmjVD6/RpbPX1sU1IEDGBbdpAVha5ISEkWlryyNaWZCsrHhkZ8cjYmGRTU1KNjUuIujInBxQKkq5efSnhCw4OpjzRYwqFgosXL8rCVwG0tLQwMTEhISGhXGuklSp8ubm5BAYG8umnn5Y43q1bN84/Y33Iz8+PboWL3AV4e3uzcuVK8vLy0NbWxs/Pjw8++KBUm2fN6XNycsgpqMMGYj3lZZAkiTvFLZPyYGIiBKKiGRdlkZoqLJ6X6cvAQEy5y3NuRoYQkue1TUkRluGdOyK+8GmsrUXQ8tN9GBqKmMTixyVJeIoLj0mS6Ds2VhxLShLPw8OfTHWzs8VrhoZiXLGxos39+0KIHz0S16VQCEtZR0eIroaGaGdgIN7H3BzUarQzMrDJzsZGpRJWdVYW+QoFGQYGZBgYkGlgQIa+PhkGBqRYW5OUlFThndIelnOZQpIk4uPjX/p7+m/EyMjopQs3ZGVl8fbbbzNy5EgWLVrEsWPH6Nmz53PPqdQA5ujoaKpVq8a5c+dKlOH59ttvWbNmDbdv3y51jrOzM+PGjWNWsfzI8+fP06ZNG6Kjo7Gzs0OpVLJ69WpGFMs93bhxI+PHjy8hcIXMnTuXL774otTxigYwFwY+y8i8DP369aNJkyblKj2fnZ3Nd9999xdc1T+Dl00mUKlUTJw4kf/7v/9DoVDQoEEDRo8ezdoXlGH7S7y6Tyt54QYsFWn/9PGK9Dlz5kxmzJhR9Dw1NZUaL9qApwyMjIxKiHVGRgY9evTg4MGDGBgYlH3SsGHCg/nmm4wePZp1hcU3n8Mz2+3ZI1K1CkrJV6g/HR0RgvLhh2W2KTGWffvEPrqHDj2zz98HDGBqUpKo/lJWVkqPHjBmDKMPHCh5je+8Iyyuzz57cmz5cuJ9fLA+frzwYsT5c+dCp05iDW/UKFi0iNE//sg6CwsxPZ47F957T1inM2aIwqtffAHHjpGfmcnmS5cYZm+Ppru72HIzP1+Ezxw/Dg0aoFKpSI2L47GJCWlmZqSamJBmYECagQEZT3lVdbKz0VSpUCsUtGnQgGaDBz/T4mvRokWRA6M4wcHBnChH2qBCocDZ2ZmUlBTgyff1/v37LxSHZ713Zbcrb9tnjcXIyKhc7/E0H374IRMmTKBBgwYANG7cmG3btrFw4UJMTU2feV6lCp+lpSWamprEFi5EFxAfH19UjfZpbG1ty2yvpaWFhYXFc9s8q08dHZ1SEd0vQ+EXspDU1FTi4uJwcnJ69heyMJ/V2Zm0tLQS5z+LZ7YzNhbrXgWvVai/7GyRa/qM9iXGolaLNLvn9G2ZlIRzaqrICnma/PyiDYZKXWNsrAhfKX4sMxN1YuKTdg8finW7GjVEu6Qk8bxePdFferrY8MjZWbStU0eIb1ycyCpZs4bc2rWpFxdHXQcHNB4+JNnOjvjISBLMzUnw8iK+enWSjI2LqrHoZmVh9ugR1ZKTMYiJIV9Li3RDQxKtrEi2sABdXTRzczHKyKBZ585F38Wy0NTULPP70KpVK86cOfNCj60kSXh6epbqw9jY+IXC96z3rux2FW1bnrG8iG+//ZY2bdrQrl27omNjx47lo48+YsOGDc+M4YNKDmdRKpW4ubnh6+tb4rivr+8zK9C2bt26VPsjR47g7u5e9Bf2WW3+6VVtn/dBlKtdVlaJogAV6i8u7ol39EXExZXcN6MMujVt+sSh8DSFXlsLi9LXGB9f+ryHD9FzcnryvDDg28Gh1PO3p00ToS+1a4u1vbAwYcVFRAAgVatGUnw81+rUQdWtG2vbt+f7Zs1Y3KgRW3v3xt/MjHRTU2rduUP3K1cYd/Qo7/7yC4O3bqXmvXvE2tpy0cODy+7uJBRsTGRa4HjJ09LCUKXCtPC6nsGzPhcdHR26dOny3HMVCgWOjo7ULYyFrCCv/B17yXYVbfuqrF69Gn19fd54440Sx8ePH4+xsTELFiwgNzeX2NhYVq1aVer8Sp/qzpgxg9GjR+Pu7k7r1q1ZtmwZUVFRTJ06FRDT0IcPHxbNyadOncqiRYuYMWMGkydPxs/Pj5UrV5bw1r7//vu0a9eO77//nn79+rF7926OHj3K2bNnK3s4FSc3V8Ty8Rq+bPfvl9gjt9z9vfmmqLjyVL7iMymH8LnXqvXE61rWdQLY2/N2v35Pjmdmir6fFo6ICGp5eT15fueOcEoUpvyFhQnRNjTk7QEDxFicnODePbLVah7Y2xMVGMj9iROJ2biRnNGjATBxccFWqaTd8ePYtW6N9dKlGLi6osjPJ/36dW43a4ZfvXqEt29PnrY2xqmpONy7R+2oKOKsrHhQowZphoYYpaWhmZeHSlMTZxubF67RPe9zadWqFWq1mqNHjyJJUtEyTmEws7OzMwMHDnzp7I2qIHwhISGEhoby7bfflnrN3NycnTt38uGHH9K7d2+qVavGV199VapdpQvf0KFDSUpK4ssvvyQmJoZGjRpx4MABatWqBUBMTAxRxRLvHRwcOHDgAB988AGLFy/G3t6ehQsXFoWyAHh6erJp0ybmzJnDZ599hpOTE5s3b/7LY/h0dHT4/PPPnz2Nzs0VQcNlxCu+FE8JX7mJixMezOcIX4mxxMU9EZ1nER7+JND4aQo9309bLYW1CYv3nZ8Pt2/DhAlPjoWGinEWeouDg8X6JJB65gxRjRoRlZtL1ObNxH36Kdy+jUFeHjX09Wmjr4/9okVYfP01psOHkzdvHtrnzkGNGmQ4OBCoVnPdw4N7Bds81njwAK8LFzBJS+NuzZpcc3FBraGBTWwsFgkJJFlZkVGwfqupUuE2efLz70s5aN26NU2aNOHy5cvcv38flUqFhYUFzZs3x9bWtlT7F37P/kW8jrE0btyYxmUtsRTQqVMngoKCntuHXJaqMstSFZZyP3pUFPh8VTw9xbrW6tUVOy8gQOx5e/kyNGv24vZ2dqIMfBl/KYuoXl0UCv3mm9KvffmlqLv3dMD0unWiksrjx0/2srh+XazLnTghNjECsYG6uTns3ElmRgaRXboQ3q0b4RYWPCqYdlpYWFAjKoqa165Rc+VKzOvWRTFnjsgfDgmBrl1hzRpyOnfmRmoqIba2RFarBpKEw4MHNIyPx+nqVcIsLQlo0YJYOzvMkpOpfv8+sba2JNjYYPz4MVn6+uRraqIhSXTOyqL1Tz+9+P7J/OORc3Urk8K1qRdZT+UlKurlBLSw4EB5prqJicIB8Zy/qKSmCqdCgRVWikuXyhbYwEDhiCgeEnTunAh4dnMDID8tjajYWMJ79iR82TJiYmKge3csdHWpU6cODgsXUtPWFoP//U/c1549hXhmZAjv+XffIb39NveOHyd41Chu6OqSp6WFQ0QEva5dwyU0FCk8HH9PT34fMYJsHR3qhofj4O/P7Tp1CHF1xSouDoP0dFKNjdHJyUHS1sYxLAzXwk3RZf71yMJXmRRumvMy09Onyc8X2QgvM22+ckVkO5THuVFYjup5WQPBweLfsrIXJEmUnp8ypfRrZ86IWn3FOXWKtNatCQ0N5c6dO4TfuUPeiBEYSBKOlpa0TE7GYf58TCIihCAfPiyqOwcECCfHoEHCknRyIu3uXS67unJFX59H3btjplbT9uRJXI2MMLlzh8fx8Zzs2ZOgfv1QqNU0DwzEOj6ei61accfJieoFSy4JNjYYpqWBhgYqLS00VCrqNGuGfnnXSGX+8cjCV5mEh4u6dVqv4TZHRwsv5suI6OXLwqIqT2R8SIgIDalT59ltzpwRoTVlWYVhYcLp8bTAJSVBUBC89x6SJBETE0PorVuEmpgQ06ULiv37qVGjBu0zM6mzezfW166J3c1atgQvL5GhsWOHWPfr3l2UvrexQXJzI2raNAJGj+ZmaCia7drRMDGRfgEB1ExNRWFhQaK/PzsGDeJagZe2rb8/1RITOePmhn/r1lR7+BDHsDDCnZwwffQIrdxccpRKkCRUGhq4RUbSsowAeJl/L1VK+IrvufGXEB7++qa5V6+Kf1+mFlxgoFiPKw8XLoi6ec8T67NnxXpjWd7NQ4dEvGCx2CoA9ZEjRNWsyQ19fW798gtpaWnoaGlRNz4ejy5dqNO9O/o6OmLtcMgQkVoWHi4suxkzhCW5cqXYiFyhIHfDBkImTCBg0SLihg/HQleXbjt20LR/f3TmzYMpU3js48Optm250q4dRmlpeAcEUCc8nJNNmnCyTRtsYmNxCwggpHFjNCQJs+RkHpmbo5uVRbaODigU1IqKwmv27IrtbCfzj6dKCd/bb7/N22+//delnoWHQ4sWr6cvPz+Rp/osT+qziI0V1mLBGtpzkSSR1TB+/LPb5OWJdbmn8q+LOHhQ7K1hZIRarebevXvcuHGDm9evkzF+PEb37+Pi4oKLiws1fvoJzQsXYMsWISy+vuJ6R40Sfa1ZI3Jqe/eGkychNJT0RYvwX7qUSxMmkK2nh3NkJF3z83FUqVBER8OdO6TVqMHpzEwuv/ceepmZeF+7huv58wTUrcsfgwahzMuj/blz3HJyItDdnWoPHxJtZyeqLavVqDQ1i6zjDm3aYPwaCo/K/LOQ/4wVsHTpUpo0aVIUUd66dWsOHjz43HOeWzdQkiAsjJCMjNdTN/D8eWFllWO6WnwsbxRYnCfT0l44liENG0JcHKNXry5VA3H16tUoFAq6KpWQlkbT2bNRKBRkF6/ikpaG+uRJwr292bt3L/Pnz2ft2rXcCQ2lSVAQE7W1+eCDD+jRowe1q1VDc/NmsddvoTW1bp3wWru7i83Jf/+da25uNPH0ZPPQoazv3ZsfzpzB/9Ejmqam8l6dOgxfsQKnPn1QbNxI9oQJ+D58yK+jRnHN1hanY8cYs2IFpteusWz4cE526EDzq1dpcuUKp1u3Jl9TE+vYWB5Wq4ZhejpZurpoqtXka2qiqVIx4MEDar2G8JWyPpfyfMdiYmIYMWIE9erVQ0NDg+nTp5dqU/i5PP3IflF1nVekomPZsWMHXbt2xcrKqqj94cOHS7X7q+psysJXQPXq1fnuu++4dOkSly5dolOnTvTr169oF6enKawb6OXlRVBQELNmzeK9995j+/btokFiIqSm8rWPD6NHj+bKlSuMHj2aIUOG4O/vX7GLy8sTO5u1bl3hsSwbMoQUIyO6TZ78wrEMt7JCrVTS6bPPSo6lAGNjY3aNG4eqenUORUcTExODbkGsXWxsLEdWruTXqVNZl51NREQEzZo1Y/LkybxvZka3AweoPnz4k3zqbdvEPSqcgsfFCctv/Hgh7ps2QXw8YYMGMXXECG6/9RYP3d2xjo/ng/nzqevhgdnXX4O3N+qdO7nk5cVvKhUBLVrQ/NIlRu3YQe+rVzncqxebRozALCmJAdu3E16zJv6tWlHv9m1SjY1JNzJCmZtLjq4uaGigViiQFArqPnxIk8WLK/Y5VeBzKc93LCcnBysrK2bPno1rYdn+MjA2NiYmJqbEQ7esijmvkYqO5fTp03Tt2pUDBw4QGBhIx44d6dOnT4l4u8I6m6/8eykHchzfc+L4zM3N+fHHH5k4cWKp1z755BP27NnDzWL7TkydOpUrV66IYpPbt8PgwYxp3561J08WtenevTtmZmYVqxsYGCisoHPnnmzOU17q1oVOnTDfuvXFY6lZU3iPjx0rORaEZfHB++/zyMhI7NP766+kpKRw7do1rl69Snx8PPp5eTSMjaXJ3LlUq1btici1by/W/Y4eFc8lSezOZmIiprcgnBULFoiQHRMTojt14mTTptwxM8MsNxfPgABct25F29OTY6GhaI0eTftVqwhbvJgj164Rb2ODa3AwnZRKjHbs4FLHjvi6u6OTm0s3X19iq1XDr0ULrBMS0EtPJ9LJCcuEBBKtrJ6s6WlogFpN9ehohs2ahcELUtNeB8/7jhWnQ4cONG3atFTptdWrVzN9+nQeP35ceRdZTso7lkIaNmzI0KFD+d///geIZIfU1NQSluNL/V7KQZVa4ysvKpWKrVu3kpGRQetnWFkvrBt47BgRWlo0K56yxfPrBj6T8+dFjm7z5hU7LzQU7t7ldP/+LxzLgLZtRUWW334rPZaCHOlm6enkZWUx9dIlTD/8EGNjY7S0tKhfvz6dmzbFqX17NBcsEA6KQm7ehNOnizYPKhpPQADs3y+ep6XB4sUwZQox2dmcXLWK0I4dsdDTY6CrKw179UJj4ULUO3bAjRt8p6nJujNn8Jkxg9CEBGpoaTHp2DGqpaeTEBvLtmnTuG9uTtPAQFxCQjjesyeJ5uY0v3yZ0Lp1eWxsjGlyMsnm5mjn5JCnpVW0hOAYHs6ISZPQrGTRK893rLykp6dTq1YtVCoVTZs25auvvqJZeQLVXxMvMxa1Wk1aWhrm5uZFxypaZ/NVkIWvGCEhIbRu3Zrs7GwMDQ3ZuXNnUbmbp4mNjS1VDcbGxob8/HwSExOxO3YMX7W6zDZPV5Z5IefOCedEBaYvISEhrHd35wtg2LJlLxxLOzMz8WTw4FJjsbW1xc7OjsnjxzPfxoaaSiXp6ens37+f1atXi37nzhXiXKxGIgC//CIyQYqlHPLrr8I7XZA2xooVxOrrc6pRI24tW4Z5WhoDYmJotG4dGgMGkGttTd2PPuJCVhZn9fR4a/x4VpibY6itzeDNm2ng5YX6/HlODR3Kmd69MXn8mDF79/JAS4utI0di9ugR7hcvctHDA8vERHKVSnJ0dZEAFIqiCi2o1TRs1gzN9u3LfZ8rSkW+Y+Whfv36rF69msaNG5OamsqCBQto06YNV65ceelCB+XlVcYyf/58MjIyGDJkSNGxZ/2mKvx7KQey8BWjXr16BAcH8/jxY7Zv387YsWM5derUMz/MZ9UN1IyJgdBQTmhq0reCtQhLkZsrgnYrmABer149Pnd3J0eSGNu+/QvH0uDqVZHmVVD2XZIkdHV1uX79Onv27CE2NhYjU1Na6urS7J13MDExoXnz5vz+++8snD8fli2D0aNLZmUkJMDatfC//z2pKnPnjojHW7QINDRIuneP45cvc2PKFMzS0uhvaUnjL79Ew99feJj37EFjwwaCT50i8fRpbg8ciKSpSfO0NLpt2IB2y5Yk7NnDrunTiTEwoM3Vq7iHhHCgZUtC69XD9fJl0o2N8ff0pGZkJFG1amGUlkaasTGaeXnka2oiKRRo5eWhu3UrzV9HpewXfC4V+Y69CA8PDzyKxUy2adOG5s2b89tvv7Fw4cLXddll8rJj8fHxYe7cuezevRvrp4LqK1q782WRha8YSqWSOgWBu+7u7gQEBLBgwQL++OOPUm2fVzfQvGDB9oaNDS0rUDewTI4dE7mtxf4ylmssKSkoL16EX39l3ttvP3csTczMqHnxIsydiyRJPHjwgEuXLvHhhx/i5+eHs7MznbKycPrqKzSiokQJd0ThyTt37ghHRUxMaXH+5RcRD/jmm0+OzZkD1aqRMWQIpw4cIPDiRQytrOjbti1NWrRAs3FjEavXtKlIe2vblsx69Ti6Zw83hg3DISmJ5tu3o9LSQgu4oKfHsYkTMUlJYaK/P1mJiSwfMABJQ4P2vr4EtWxJnrY21R48IKp2bQzS0sjQ1we1GklDA0mhQDs/n27HjjEoO5uyy7S+PiryHXsZNDQ0nnwulczLjGXz5s1MnDiRrVu3lirRVdE6m6+CLHzPQZKkMkvZg6iwsXfv3hLHCusGap06Bc2aUb9uXXx9fUusW1S4buDWrSLE43m5s2Wxfr1Ytxo69IVjeUtTk8dKJRHOzgQsX05MTAz5+fmEh4ezbNkyDPX1xRaPffsW5ftKkkRwcDBNGjWCb78V09biKWyJiWK98J13RLocQEAAuTt3cuHHHzm3bBkKoNPJk7T09ES7c2eYPVt4d3/8ERYvRn3jBgGbNnF81y60a9dmgLY2jRctYm2tWvR79Ii1b75JpL4+rUJD6Xj2LKednTk/bBhOkZHUjIzkVKdOWMXHo6GjQ7y1NbqZmeQplai1tFCo1agVClAosElJ4QtTUzz/AmfG0zzvc3nZ/oKDg59bvaSyeNFYfHx8mDBhAj4+PvTq1avU64V1Nl/p91JOqpTwPS9zY9asWfTo0YMaBVWDN23axMmTJzlUUH693HUDN24U5dBHjuT9AQNerW5gbi7s3CnEowLm/qyZM5m9eTN07Up4TAybfvnlmWN5HBeHytKShdOnoz58GHt7eywtLfnggw/w8fERG1vv2QO3b3PhzTexDg8nNTWVhQsXEhwczIahQ0W1mCVLSl7Ezz8L721BqXu1SkXwL79wYsYMMlNTadmyJV5btqB/44boPzRUCN6sWaCpSeJPP7Fn5kzu37iBW1AQrp06UW3WLC66uuIkSSwZORL9zEy89+2j/u3bbBw6lPv29nQ6dYoEExNOdOiA861bRDg4oJedjVqhQFOhIFdbGyQJqeB+1rtzh2hnZw798Uel13Os6HcMRLl6EA6MhIQEgoODUSqVRdPJL774Ag8PD+rWrVvic1n8mkNxXnUsPj4+jBkzhgULFuDh4VFk2enp6RUlE/yldTalKkhKSooESCkpKUXHJkyYINWqVUtSKpWSlZWV1LlzZ+nIkSNFr48dO1Zq3759iX5OnjwpNWvWTFIqlVLt2rWlpUuXStKNG5IEknTwoCRJkrR161apXr16kra2tlS/fn1p+/bt5b/QAwdEX1euVGh8X/XpI0kg9dLSeuZY+vfvL/n4+Ehz586VvvvkE2nNzz9Lbdq0KTmWQry8pHA7O6lmzZpF96dbt27S+XPnJKllS0ny8ip5AQ8eSJKeniTNnClJkiSFhYVJi7//Xpo7d660beFCKTk5WZL8/SVJoZCkRYskSa2WpK5dJcnBQVKlpUlnx4+Xvp4zR1r4009SqIODtN7AQDqrUEi3dHSkZcOHS3PnzpV2jhwpZTVoIIU5OEjff/yxNP/DD6XrLi7SH1OmSF/Pni1tGTRImjt3rrRo2rSiMX4xZ440d+7cosfuHj2kWpqaFf9cXpKX+Y4BpR61atUqen369OmlP5fz5/9xY2nfvn2ZYxk7dmyJfl/p91IB5Di+112Pb9EikVv66JFIt3oVxo8XqWo3b1bI4uPNN0XqWEREiXzavLw8goOD8ff3JykpCRsbG1r6+tI4IwPtZ20s5OcnYgd37HiyaXchO3fCwIGl6w1OmAB79/I4MJAjFy5w8+ZNaiQm0j0iAvu9e0WsoLu7WP/z9xfT+REjiN+8md3h4URnZ9PaxoaOW7agHRYGEyfycPlyto8fT4ZKRe+7d2l08CCnPT052bo1jhERuF+8yL6+fdHOzcU6Pp47zs5YxcWRYGODTnY2+ZqaqIqFrTS5coX+33yD4lmltWT+08jC97qFr2tX8cMux25azyU3V5R/f+ed5xcEfZqMDBE+Mn26KAiKmCYFBAQQEBBAdnY2Li4utGrVihr376No21ZMNfv0Kbu/Ll1E/uyVKyWLEuTnizW9mjXhyJEnx69cIa9FC859/TXn8vLQ09Oja3Y2jf73PxQXL4pYxO++E06OixfBzg5V48acGzqU07a2mCUm0i8tjerOzjBrFtKCBZzfsoXjnTtjFx3NoPh4lL6+7Bw1ijA7O9qfPIlSpeJop07UfPCAPE1N4mxsME5JIdXEBIVaLS63mOhp5eUxum1bavboUZFPROY/RJVa46t0IiOF9VPG5iYVZs8e4c0tcE6Um9WrhfhNmEBCQgJ+fn5cvXoVDY3/b++8w6q8sj38HnoVRJogYhd7L4gFG3YQC2LBqFFjoiaZJDeJqZpmksnMJCaZdDUqdsUuoqCgFFERUAQ7TaqUQ+/f/WMLiqKC0ZlJ2O/znOe555z9fZxzcv3N2nut9Vsa9O7dmwEDBtC0umZv8WLo0gXqOGgGhHj7+4to734nlvXrhWX8PYXJSlUVsR99hN+rr1JQVoajoyNDbG3R6dVLCHHv3sKVetUq+NvfoFcvMmfMwGfGDNKsrBgUH4/zsWNorVsHY8ZQ8PLL7ImO5vqoUQyKjmbEjRuk5eayftkyKhSFmdu3c7FHDy44ONAzMpIbrVpRrq2NflERxQYGNed6lRoaNaKnV1zMvL59sZKi16iREd/TjPg+/FAc6qemCv+4P8LgwWIreE+722MpL0dp356EESMIHT2aK1euYGRkxIABA+jTpw/6+vp311ZvYbdvh/smVQEiMeHkdLdP+N6tdl6eKEB2doY7rUSZmZkcWruW+JISOjRtypg5czBr2hTGjBGJi5gYMDAQEeSNGygXLnBm3TqOpqdjamSEu0qFzYoVsH8/vP461+3t8enXD8rKcI+Pp+3Ro0T27MmBwYOxTktjfGAgB0eOJKNZM/qfPs3Zfv0wLCigyNAQzYoKioyM0CwvR6kuUFapMMrPZ76DA2ZP0XhA8udERnxPi8pKEel5ev5x0Tt7VnRr7N5d70sUReHy2rWcdHEhxdYWi5wc3Nzc6Nq1K1p1eeutWiWivXs7Ku7lwAEhjn5+D54vfvyxmBf8xReUl5cTFBRESEgIptnZzMrLo/2HH4p1mzaJXtxDh8R5588/Q0AA+fv3s2/bNq5lZ9OvqIjRkyejPWgQvPYaypYtBNnZccLRkbbXrzNZWxv9Xbs4PGsW4e3a0ev8eXrfuMG2SZNQgL5nzxLi5IRNSgppVlYYFBdTYGyMRkWFMBy405VhmpPDfGtrmkjRkyAjvqcX8fn5iegmJKTeLioPxctLmH1eu1a32ec9VFVVcenSJU6ePElGRgb2eXk4LVlCu3btHl7x/rhor6xM1A22aCG27vfeJzZW2NKvXMl1T08OHjxIXl4eg3NzGfzrr2jFxICtrajj69RJRHhbtkBcHPTuTezixey3sUEzNxfXgADa79ghfjddXYoWLMDn9GmutW+Pc2AgQ5s2pejIEXYsWECSqSljAwMxLC1lz8iRmN++jUVGBtE9e9Lqxg3i27TBOC+PfENDYc2kKDV1evqFhSwtK8Pwm2/+wH8UyV8JGfE9LdauFf/Q77dcbyipqbBtm0gAPEL0KisruXDhAqdOnSIrK4u2xsaMX7sWe2/vB8c63ouiwPvvPzra+/ZbIbo7d9YWPUWBl1+moGNHjrRvz8VNm2jVqhWz2rXDfMIEYTRwZ5IZy5eLBMjXX0NZGaVz5+I7bRqRTZviUFTEpDVrMDh4EFasgMREbv3wAzvOn6esTRtmHz5Mu5ISUpKT2bZ0KZVVVXgdPkxS06YcGjECh9hYKrS1udC9ey3RKzQwqHFYqRY9VCq6l5Vh8Awa3SV/XqTwPQ2yskRpx2efNazspC5++EHMvHiItU9FRQWRkZEEBweTm5tLx44dcZ88Gdvp00WGdfDgR9//4EGRsNi7t2479bQ0sQ1+8cUHukUUb2/O5eZyzNMTzYQEJk+eTPd27VD17Cn+7p0h8WzaJPz0tm4FKyuS3nmH3YMGUWRujmvbtvScPRvVqlUQFyfu+fXX+F69inVlJdNPnsQkPp7o7t3ZP2AAlpmZTA0NJbB9e6K7dWPg6dMktGxJlpkZtsnJJNxpQyvR06NKS0u0ot0jesOSk3H++ec//t9F8pdCCt/TwNtbDALy8vpj9ykpgR9/hHnzajf7I2rwzp07R0hICPn5+XTt2hVPT0/Rx3jkiJiVUW3z9DDKykQnxahRDy9feecd4Z13pxSmmttXrrDv5EmSJk6kZ7dujB49GgMDA3G/pCRxJlg9J2PpUpg7F8XDg+ANGwjQ1sbWzAyvGTMwGzZMjIEcM4by4cM58NZbROfm0vfCBcbo6qIREoLfrFmEtmpFj7g4hp89y66hQ0mxsWF0QABnevemXEsL05wc0po3R6+4mHIdHcp1dMR/A6gRvTFXrjBw40YpepIHaFTC90yGDVUPwZk0qX7jGx/Fli3C0eTll2teKi8v5+zZswQHB1NUVESPHj1wcnLC3NxcLKishP/7PxFxPa5E49//rnsLW01IiChT+e47MdAbcYYYGhrKcT8/TAwMeM7NjVY9e4r1J04II4IvvxRZ3ooKMS/D3JyCzz9nz/r1XE9MZHBSEs7//jea7u5izXffkeXpyfYlS8jR02PKrl10GzKE0l9/ZcfSpVw1NmbMmTO0iYtj/cSJlOvoMNbfH/+hQzEoKkJLUcgzMUGjspIqDQ3Kqp1fqiM9RcE1KopeO3bIIUGSOpHJjT+a3Kh2Rz5w4OH1cPWhvFwYAXTuDHv3UlFRQUREBCdPnqSwsJCePXsyZMiQuzV41axbJzolwsKEq/HDyMoSIyNnzBBR5f2Uloo6OyMjIYCammRkZLB3715SU1IYGBLC8Jkz0Z43T6zPyxNJDnt7YR+lqSk8+T75hJt79rD78mWUnBzc9++n7YEDYvv7zjtw6BBXvb3Z1bIlRgYGeKxZg+XkyeTu2sWWhQvJ1dRkWlgYOsnJbJ0yBePCQvpGROA3YgRW6emomzRBQ1Eo0tdHu6LirnNyNVVVTDl9mm7794vIVSKpAyl8f1T4Fi4U7WEJCX9sfu7PP8OSJVRGRBBZWUlQUBD5+fl0796doUOH1nKqraGwUDi3DBkiztMexfLlwhvv6tW6I9OPPhJlKufOUdmlC8HBwQQGBmJmYoLb+vW0sLAQoyOrI8X584W9fnS0mPwWEkLV0KEEvv8+QUBrlQr3v/8d461bhSiOH4/y3nsEA/4aGnTQ1WXK3/+OrpMTyTdusNXNDe3iYmYGB5NeUsJeNzfsUlJodfMmJ4YNo8316yTb2mJQXEyuiQl6paWUaWuLc71qKiuZERSEw5Ej4pxUInkIjWqr+9SJjxcjED///I+JXlERVR99xIUXXiAwKIicnBy6dOmCs7Pz3S1tXfzrX2Jr/Nlnj77/2bNim/vll3WL3qVL8Mkn8NZbpFpYsO/XX0lPT8fJyYlha9eidfOm6CSpFr0dO8SWeO1aIXpqNXmLFrFr6VKSVCqGt2zJ4IUL0VixAhwcoG9fyidMYK+pKTH5+QytqsL5l19Q2dpyobKSvVOmYJORgcepU0SameE/YQLdL11Cu6iIE8OG0SkmhssdO2KqVpPdrBm6xcWUa2ndFT1h5cDU48el6EnqhYz4/kjEt3gx7NkjzACe0JBAURTiPv+cgJQUbpub4+DggLOz8+PNF9PTxdZ18WL4xz8evq6i4u5s3zNnHhToqioYMoSK7GyCvvmG4NOnsbCwwNXVFZugIJg5UyRvqi3l4+OFSaiLiyi7Aa7Om4dP8+ZoNWvG1OHDsR8/Xgwl37ULBg8mV0ODbV5eZGVnMzk9nc43bqBERXFi8mSCWrakx7VrjA8M5EjPnkT06cPg0FAyTU250rEj3aKjudC9O2bZ2WSZm6NbXCwMB7S1a87zAMxyc3n+nXcw+KPnrJJGgYz4npSEBHG+tnr1E4teQkICx3x9SS4ro62xMe6LFmFzx+jzsaxcKUTs3Xcfve7rr8V2NCys7qh0zRrSr19n9xtvcPv0aYYOHcrgwYPRTEsTJS0eHkL8QJxDzpwJpqbw889UKQonVq/mZJs2tG/ShMnz52MwfryIuLy9YfFi4svK2DF3LjqpqTx/9ixWrVpRHhrKniVLuGRqysgLF+gXGMjOceO43qoV43x9ueTgwC1bW7pHRxPVsyfNbt8mq1kzdEpKqKp2WYEa0bPIymLBO++gJ0VPUk+k8D0pn30mLNhffLHBl6anp+Pv78/Vq1dpXlWF1/bttAkIEK4q9eHsWXEm+NVXNdnXOrl5U/QPv/zy3ajvHqpiYgjZs4fjS5ZgbmjIojlzsLa2FlHg/Pmgry/qCqu3uB98IKLGkycp1NZm17ffEl9WxsiqKpxefRXV3/4mPltQEMrvv3Pmxg2OzJyJfXo60/bswWDOHPLXrGHrK6+QqamJR0QELU6dYr2nJ9mmprj7+HByyBDymjShw+XLRPXsKUZANmuGdnk5ioZGrYloANbp6cx75x106/vbSSRI4XsyqqO9Tz9tULSXm5vLiRMniIqKomnTpkwbNYrOLi6oXn65/qJXUSH89rp1E5ZVD0NR4KWXwNy8TlurnIwM9vz0E4nOzgwaMIDho0ff7en96ivRY+vnd1dYjxyBL76Azz4j2c6OHT/8QEVmJnOuX6fNtm2i/e2bb+C776jIy+PQqVOcnzCBAYWFuPz4IxoffkjGN9/g/fLLKCUlzI+KQvPcOX5dsABFUZiycye+48ZRqamJXVISl7p0oVlmJtlmZmjeKT+quK+TpcWtW3itWIGOnV39fjuJ5A5S+J6E1atFgfFLL9VreVFRESdPnuTMmTPo6ekxfvx4evfujeYrr4jpY2++Wf+//d13cP686Ld9VLnGli0iC3vgQC3TBEVROH/+PEf27cNAU5N5gwZhf+984LAwsX1++23hLQhiyPfs2ShjxnBm+HCOrFuHTVYW0319aXLypPDqmz8fZs+mYNAgtv/4Iyk9e+Kmo0PPlSvhvfe4uWED2xYvFkYGFy+SlZjItoULMVWrGXH0KHvd3dEvLsZEreZ627aYZWWhNjUFQKUoNdPQqqM9+4QE5rz9Nlpt2tT/t5NI7iCTGw1NbiQmiqTCJ588VrAqKioIDw8nKCgIRVEYNGgQjo6O6OjoiLKSLl1EGcnbb9fvbycliTq/554TAvgwUlOFSejo0bXKXAoKCti/fz9XrlyhV0QEY/r0QffOFHtA+P/17Cmiz6AgIaxlZTB0KGWZmRz45BMuXLlC/6IiXNasQTMwEOzsoH9/aN6c9F9/ZcvGjVRqajKjfXtaLFoES5YQFRPDPmdnWicnM/3cOa5VVeEzeTL2iYn0PX0anylTMM/KQlEUsszNa+ylyrW00KyqorLaZeWO6LW7dg3PN99Es3v3+v1uEsl9NCrhu7dz48qVK08mfC++KDofbt58qP2UoijExsZy7NgxcnNz6du3L8OGDcOwelusKMKR5OrVuz519cHdXVi1x8Y+0NJ2zx8XhdSRkXDhQs2Es7i4ODEVTlFwPXyYjsXFwgHm3kTB9OnCjSUyUpSpACxfzu0dO9j+f/9Hbmkprk2b0vWll0QR9HPPCU++pCSubtvGziNHaJqTw8xhwzB57jkUFxeCdHU50bkzva5eZcLJk5yzs+PwqFF0u3iRttevs2/SJFomJZFvaEiRoSHaZWWU6ulRqquLZkVFLT89AIe4OKa/+SYavXvX7zeTSOqgUW11ly5dytKlS2sivifit9/EmdlDRC8lJQU/Pz8SEhJo164dM2fOxOLOkO4atm0TZ2gHDtRf9PbsEY8dOx4uegA//SQKqg8dgmbNKC8v58iRI5w7d46OHTsyydcXw7NnISKidpb3xx9F+cmOHXdFb+tW4o4dw+ell2iip8eiAQOwcHERgrdokejHjYoifMMGjhw7RocbN5ji5obOyy9T2a0bB5o3J9LamuGxsQz28+PEoEGc7NePgSEhNCkqYs/kyXS8fJlUKysUDQ00Kisp19GhVE/vARNRgC4XLzJFip7kKdCoIr5q/tBW19xc1LLdJ3x5eXkEBAQQFRWFhYUFLi4uNcOWa6FWi6LeQYOE0NSH/Hyxxe3RQzgUP6zp/upVsVWdOxd++IH09HR27dpFTk4OY8aMoc+FC6gWLBDtY7Nn370uPFz0+i5aJKylACUyksA33yTQyYlODg64OTmhO2SIKGUJDoY1a6h89118//lPzubm4hgczKhp09D49ltKS0rYPnky8fr6uF25Qtc9ezjg7s55BwdG+flRYmLCqQED6BEVxdW2bdEpL6dEV1e0ot1xUFbgruipVPQ4fx63N99E9QxmrEoaH1L4Gip8n39e60yurKyMkJAQQkJC0NbWZvjw4fTu3RuNhzXHv/yy6HiIjRXnY/Vh+XJxTUzM3WjsfioqhHhlZaGcP8+ZS5fw8/OjWbNmTJs2DYvbt0VP8YwZ4l7V3L4tenRtbCAwEHR1KU1Nxee997hsZ8fwIUMY4uSEatQoYXAQHg7nz1Pi6cmOt94iXqViwr599B47FiIiyLtwAe9581BXVjIjIYEWO3eyc+5crtnYMGnfPhLatyeya1f6nT7Nhe7dMSwsJN/ICO2KCgqNjNCoqEAFd+dkqFT0OXuWCW+8gWrYsPr9XhLJY2hUW92nwp0SEkVRiI6Oxt/fn6KiIgYMGMCQIUPQ09N7+LXnzomI6ssv6y96R4+KRMaaNQ8XPRCCfOYMRcePs/dOAqN///6MHj0arfJyMf7R3l6YjFZTWSkiv+JiscXV1SUrPZ2tX39NvpUVM0eOpMPgwcIm6+xZIYy5uWQvXcqWV1+lQEeHORs30rprV8jOJi06ms0LF6KRl8eCpCSMDx1i4+LFpJmY4LFrF+f79OFqq1Y4nTxJ+IABmObkkG1mhl5JCYXGxmhUVoJKReU9fnqqykqcliyRoid5qsiI7wla1lJSUjh06BC3bt2iU6dOjBo1qm4TgXuprBTuzGVlQkTq4xySkyPq9Tp1EnV0D4siz54FR0duvP02PqamVFVV4ebmRocOHcT7L74oemvDw2ubi37wgchO+/nBqFFcvXqVXd7eGGVl4enigvmkSaJ27+23xTS1UaNImDiRbSNHom9uzqzffqOZoSFMnMj1DRvYPns2zdLSmJmURFVwMJuef54iLS2m7dtH0ODBJFtb4xgSQoiTExaZmaRbWmJYVESBoSEqRUEFtZyTVRUVzO3alVYNnTQnkTwGGfE1kP379xMREYGVlRXz5s3D3t6+fhf+9NPdIUL1tUtaulQ4sKxb93DRU6up9PTkuKcnwVpatLawwN3dHWNjY/H+9u0icfHjj7VF79AhkaT55BOUkSMJPnUKf39/Oly5gnufPuhNmiSSKStWCKv6yZOJ8vJi35gxtLS2xuO339AvKIAXXiBq7Vr2zZlD2xs3mHbjBrnXruG9ZAmqsjJm7t3L4REjyDI1ZWBoKKeGDKF5aiopzZtjXFBA/j0F4PeL3rxOnWgpRU/yDHimLo05OTl4eXlhYmKCiYkJXl5e5ObmPvIaRVFYuXIlNjY26Ovr4+zsTExMTK01zs7OYqDMPQ9PT89n+E3uEhMTw9ixY1m8eHH9RS8tTQjIokUiqVEftm0TRcjffy+G/tSFopD90kusHT2a0PbtGTVqFF5eXndFLzZWePXNmCHMDKq5elWYDkycSNnrr7Nz5078/f0ZGhyMp4YGeq+9JoqkZ8+GqVNR3n+fgDfeYE+3bvSws2POrl3o37iB8u67nNq5kz3u7vS4dAnPyEjS0tNZt2AB+nl5eBw+zD4XF3KNjelz5gynhg7F5tYtUmxtMc7Pp8DQUIicotSyi9coL2dBx460rDZGkEieMs90qztu3DiSk5P5+eefAVi8eDGtWrUS9WQP4YsvvuDTTz9l/fr1dOjQgU8++YSgoCAuX75c8w/a2dmZDh068NE99uj6+vr1LlH5I1vdwsLCu/V49WX2bLGdvHz50b211dy6JaKzUaOEAD4kixvzr3+xLzMTQ2Njps6di62t7d038/JEYbGWlujGqM5C5+WJLXdVFTl+fmw9eJCc7GzcDx2iU0WFcFVWq0Vvr5UVlcePs+/zz4nW0WFU8+YMCgxEtWsXyrff4rt/P+F9+jA0KgrniAiumJmxc8IEbJOTGRMayvbx46kCOl26xGlHR+wSE0lq2ZImajUFhoZUaWoK0YMa0dMsL2dBu3bYVBueSiTPgGe21Y2NjcXX15ewsDAG3HEG/uWXX3B0dOTy5ct07NjxgWsUReHrr7/m3XffZcqUKQD8/vvvWFlZsXnzZl544YWatQYGBqKhvh6UlpZSWlpa8zwvL++Jv1eDRe/AAXE+tn59/URPUcSgIT292gYB91BRUYHf5s2cycuji6Iw6bXX0L3Xg05RRKSXkiK219WiV1UlrOFv3eLGvn3s3LoVPV1dFvr7Y5mYKM4AAdzcoKqK4u3b2b5mDUkaGkwzNqbLjRuwZQsV33zDnqAgYnr3ZsL58/QNCSGic2cODBuGQ1wcTjExbJ40Cd2SEtrevMlpR0daxseT2KoVTdRqigwMag8GAiF6ZWU836oVzaXoSZ4xz2yrGxoaiomJSY3oAQwcOBATExNCQkLqvObmzZukpaXhck/vqK6uLsOGDXvgGm9vb8zNzenSpQtvvPEG+fn5D/0sq1evrtlum5iYYPefamrPzBQiNnGiqK2rDz/8IBIZv/1W03VxLzk5Oaz79Vcirl1jfFQUUz/4oLbogTAZ2LVLmKRWJzhAWFkdOED411+zKTAQm+bNWXT6NJZhYWLqmrW1EMwLF8jdsoW127eTnpfH3LIyuujqwhdfULJqFd6XLhHXujUeUVH0PX6cUwMGsH/4cPpERjLg0iU2TZyIYX4+Nrduca5fvxrRM87Lo8jAgAptbSHC94ieVmkpi+zsaC4Hfkv+AzyziC8tLQ3LOvzRLC0tSUtLe+g1wAMmnFZWViQkJNQ8nz17Nq1bt8ba2pqLFy+yYsUKoqKiOHr0aJ33XbFiBa+99lrN87y8vGcvfooiXFQqK+GXX+o36evKFXjjDTGmsY7BQXFxcezduxe9vDwWbNuGzeHDwjrqXgICRBb27bdFi1s1u3dT+emn+K5axdnERAYMGIDL6dNobNkiWvB69xZ9w1u3kvL772wODkYnPZ3nb9+mmbs7TJ9O/vLleOfkoDY1xevSJVoePszRyZMJ6dSJocHB2N2+jberK9ZpaRgVFnKxW7daoleipydET1FqiZ52SQkLbWywrB5PKZE8YxosfCtXrmTVqlWPXHPmzBkAVHX8Y1cUpc7X7+X+9++/ZtE9UUHXrl1p3749ffv2JSIigt51tDPp6uo+GBU9azZsELN2d+4UkdTjKCkRSYgWLUTEdg+VlZUcO3aMsLAwHPT1cfvnP9Fbu/bBweHJyeDpKcY33mtFdeECxYsWseP110kAJk6cSJ8bN0QE+NFHYrD4xo3w4YdcWbWKnYmJWN66xcy4OAw/+ADGjydr5kw2GRpSWV7O/Ph4zPfs4cCcOUS0bs2Y48cxKSlh64QJtIqPB+Byhw7YJSWR1LIlRvn5lOjqihGQ1UfKd9yTdUpKWGRujvny5U/8U0skDaXBwrds2bLHZlBbtWpFdHQ06enpD7yXmZn5UFv16jO7tLQ0mt/jT5eRkfFIK/bevXujra3N1atX6xS+/zgJCaJDw8tLiEp9eO01kYUNC6vl8adWq9m5cycpKSmM6dKFAV5eqLy87roiV1NSAtOmibPBLVvu9uFmZpLl5cWW+fMpatYMrxkzaJWWJrbenp7w3nvCmGDBAs68/DKHgY43bzIlJATtdetgwgSSR45kS9u2GGRnM0+txnDHDnYtXEislRVufn6gUrFjzBgc4uIoNDQkxcYG2+Rkklu0QL+oiDIdHcrv/R+eO6KnW1LCIlNTmr3++h/7vSWSBtJg4TM3N3/0AJw7ODo6olarCQ8Pp3///gCcPn0atVrNoIeUdFRvX48ePUqvXr0A0RIWGBjIF1988dC/FRMTQ3l5eS2x/K9R7V5sYlK7S+JRbNsmzvZ+/FH02t7h6tWr+Pj4oKOjw/wpU2gxcaKwslqzpvb1iiLKVaKihJ1UtSlCaSk3nn+eHePGYWRlxcK5czFTq8HVVWxt162D6GiUKVM4tmABIWZmDIiPx+XgQTT27oVZs7jasyc7+vbFOimJmeXlaG7bxtYXXyTe1BSPI0fINTTkyNCh9IiKIsPCgmwzM6zS0rjVogW6JSVUaGndnXtbvcVVFPSKi1lkZIRZfS25JJKnyDMvZ0lJSeGnn34CqKl9u7ecxcHBgdWrV+N+5zzqiy++YPXq1axbt4727dvz2WefceLEiZpyluvXr+Pt7c348eMxNzfn0qVLvP766+jr63PmzBk073PprYunOl7yfv71LxG9+fvDiBGPX3/1KvTpI6ykNm8GlYqqqioCAgIIDg6mffv2TJ40CYOpU0Vt3blz0LJl7Xv84x/ibPDeoUCKwpnlyzncrBltLCyYtnAhesXFoo6wvFxElkVFVAwezJ6xY4mxtWVMaioDN2wQmeg33yTSyIh9zs50uHyZqZqaVOzaxeYlS8jQ12eGnx8JFhYEDRxIv7NniW/ZkgIjI0xzcsi0tETrjqVUqY6OKL6+R/T0CwtZZGBA08ccmUgkz4pn2rnh7e3Nyy+/XJOldXV15bv7DDQvX76MWq2uef7mm29SXFzMSy+9RE5ODgMGDMDPz6+mhk9HRwd/f3+++eYbCgoKsLOzY8KECXz44Yf1Er1nSkyMKFR+9dX6iV5JiRjmY20tOjtUKvLz89m1axeJiYmMGjWKQYMGoXr3XSGkfn4Pit7hw8IQ9e23a0SvqqoK308/5YyFBQOaNsXlpZfQqKgQW+H0dCF6mpoUubmxdeJEUm1s8MjPp9PPP8O2bSiffkpw06b4Dx5M73PnmKCvT6GvL5uWLiVfUxOvQ4e4YG9PeO/eOIWGEtehA6W6upjk5nLbwgKNysraogc1omdQUMBiLS1MpOhJ/ovIXt2nFfGVlYnC4JISEZXdn22ti5deEk4pYWHQsyc3b95k586daGpqMm3aNFq2bAm7d4tzwi+/hP/7v9rXx8XBgAEwdKhoL9PUpLi4mJ3ff098Xh7jNTTos3Ll3drATZvEeV7//uS6ueHt4EBR8+bMBFqsWAHffIMSGIhfSQlh/fszNCgIZ2NjcsPD2ThnDhWVlcz28yPEwYHoLl0YfvIk57t1o0pTE93iYmEVf6fntlRbWwwSr0ZRMMrPZ5Gi0OSf/3w6v7lE8oTIXt2nxUcfCcfj06frJ3rbt9ec6yk9ehASHIy/vz+tWrVi6tSpolA6NlaYfk6fLray95KbKwqNbW3FFldTk+zsbDavXUvR7dvMycyk9a+/irWrV4vzvI0bYfBg0ufNw7tbNzQtLVlgZkazRYvgnXeouniRfYpCVP/+jD9yhH6GhmRcvMjGuXPRKSpirr8//j16cKVdO1wCAgjr1w+Nqiq0S0vJMzGhSqVCq6pKRHr3iV6TvDwWlpdjXN9zT4nkGSIjvqcR8YWGCi+8VatElvRxXLsmkgsTJlC6bh179+0jNjaWwYMHM3z4cOHlV91ypqkpxPRe49PKSnEmGB4uHu3akZSUxNbNm9FPS2NWVBRmBw8KAd68WbTMrVwJH35I/JtvslVTk6ampszu0AGj6dNhwQLKzc3ZdfMmVx0cmHzwIN20tUnOz8d74kRMcnOZcfw4B/v1I97eHpfjxwlydES3tBRFpaJET48ybW20Kyoo1dFBuU/0TNRqFhYWYnSndVEi+W/TqITvqczcuJ/cXCFilpa1Z1g8jJISkWAoKCDzyBG2HzpEXl4ekydPplOnTmJNVRVMmQLHj4s5tvd2X4CI/r7+WnR4jBzJxYsX2bNnDy3S05lx+DD6p06Jc8Pjx8Vsj5kzYf16Yr76Cp+8POz19PAYPBjdceNg7FhKBg1ia0wMt+ztmXHgAO0qK7mhp8fWkSOxTktj6qlT+Dg6kmJjw+jjxzk+ZAiGhYWUaWtToa1Nia4uOmVllOrqPiB6prm5LMzNxXD9+j/2O0skT5FGJXzVPLWIT1GEQJ04IWZYtG79+GtefBHWrePS7t3sjYrCxMQEDw+P2iVCn34qIse9e0Xpyb2sWyfaytasQVm2jFOnThEQEED327eZtGkTWoGB0L272HYPHizOAA8c4PS6dfimptKtshK36dPRHDYMevSgcPZsNp07R66VFbMOH8YuN5dYOzt2OTnROiGBSSEhbHd25raFBaOOH+eYszMmubkUGRiASkWhgQG6paWU6eiI/tt7fxuVimnJyXT55Zcn/40lkmeAPOP7I3z9tUgq7N1bP9H77Teqfv4Z/y++IOTMGTp37oybm5sYN1nNnj1C9D744EHRCwgQ9XovvEDliy9yYN8+IiMjcc7PZ+gPP6A6dEiIXnKyaHlr0wZlxw78vb0JTkvDMTub0a++imrIELC3J3fhQjaGh1NmYcG8o0exSk3lfM+e7O/dm87XruESHs7mUaPIa9KEUSdO4DdiBOa3b6Nu0gTNqiryDQ3RLymh9F7Ru6czw/H2bTrfKWWSSP6XkBHfk0Z8YWEwZAi88soDLWYPW184bhy7XnyReD09Ro0ahaOjY+32vKgocHKCsWNF8uNe89G4OHB0hP79Kdm5k+0+PiQmJuKqoUH3d98VpgYLFghLqcGDIS+PyuBg9h87RlRCAi7XruG4erWwoK+oIPOzz9h45gxa2tp4hYbSNCaGkOHDOdqlC31iYhh8/jybxo6lVE+PYcHBHBkxAqv0dLLMzNApKyPPxAT94mIhepqaNeUqAKhUDMrIYPR339WvR1ki+Q8jhe9JhC8rC3r1En21gYGPd1ROTeXWuHFsHzeOCjMzpk+fTqv752ekpwsPPHNzOHmyVtsamZmiVEZfn5xDh9i8fz+FhYXMMDfH/vnnRYT48ceipGbsWDh/nrLAQLafOcPNhATcz5yh6y+/iG15QgLJ337L5ogIjCsqmHPpEkYnTxIwZQqn2rRhcGQkvaKi2OjqiqKpyaCwMI6MHIltcjLpVlYYFBeT27Qp+kVFDxU9p/R0Rn3/vRQ9yf8scqvbUKqqRJ9rUZFoNXuc6JWVEfHKKxxydaV58+ZMnz37QbEtKRFOKuXlsG9fbdErKYHJk6GggOStW9mybRt6eno836MHzVxdhb/eRx+Jz7VgAQQHU3jwIJuDg7l96xaz/fxos2WLeC8ujus//si26Gisi4qYmZaGnr8/vnPnEt6iBaPPnqXDpUusd3dHu7KS/qdP4ztqFC0TErh1xzU5p1kz0X+rrV2n6A1OTWXkQ3wEJZL/FaTwNZQvvxTzKg4ffuyktMrKSnzfe4+zXbrQp0ULxj73HFr3Z32r7asiIkT0eK/NfLWhaEQEl7ZuxcfPDxsbG2b06YOBs7PIDv/2mxCZd94Bb2+yN21iU0wM5enpzN+5E+tdu0REGBjIpR9+YFdcHG3S0/EoKUFz1y72vfACkZaWTDx9mhZxcaybNg3D4mJ6RkfjO2oUbW7cIKFlS0zVarLMzWtEr7KOM72hKSkM//FHKXqS/3mk8DWU994TIjN27COXFRYWsmPNGpL09Jhoakqf55+ve+Hf/y4srLy9RQb2XlauRNmyhZB//5tjkZF069YNV0dHtJycRLnK7t2goyNMCz7/nJQvv8Q7JQW97GwW/P47TXftEl6A27Zxbs0aDiQm0u36ddzuOLjseuklYs3McD99mmZXrrDew4OmeXl0io3l6IgRtLtyhRtt2tA0J4csCwv0qkXv/tZAlYphyck4//yzFD3JnwJ5xtfQMz5nZ9H29Yh6vdTUVLZu2EDl7dt4lJbS8n43lWr27RPb2HfeEWMe72XjRirnzePQypVEVFUxdOhQnPv3RzVyJMTHi+RKq1awdSvMmsW1N99ke5MmWObnM+vf/8Zg+3Y4exblvfcI/uIL/IuL6RcZybjmzan45Rd2LFvGDSMjpoaHY3D9Ops9PLC6fZs2168TOHQoHeLiuNq+PWbZ2WRZWKBbXEyFlpYQvXvFTaXCOTGRYb/+KkVP8qdBCl9DhS81FR5hf3XhwgX27d2LZWoqM+LiaHL4sIjKHlwotqqjRwuz0nszuEFBlI4fz45ly7hpaMikSZPo2bWrSE74+4stcd++QoDHjydq4UL2NW9O25ISpn31FTobNoBajfLCCxz98ENCVSqGBQczrGNHyn/+mS3LlpGsr49nWBhKUhLbpk+nRWoqtklJBDs50SkmhjgHB5plZXHb0hLd4mIqtbSoqEP0hsfHM3TtWil6kj8VUviekklBVVUV/v7+hISE0P3WLSb6+qIdHl63+3JGhmhHa9pUdHvcm8y4coX8UaPY7OFBjrk5M2bMoHWrVqJ+b/162L9fbLMjImDYMEKmT+eovT09VSomrlqF5nffgZUVVR4e7H/jDSL19Rnr58eAfv0o/uknNi9bRoa2NrOCgynOzGTn1Km0SUzELCOD0wMH0uXCBS516UKz27fvip6mJhVaWg+I3ogbNxiyfr0UPcmfjkZ1xndvy9rTpLi4mF27dnHjxg1c1GoG/v47qqCgukWvtFREbiUlD2Zw09PJnDEDb09PFCsr5s+ZI5ynV66EX38Vwjd2LFy7hjJuHP7u7gTb2+NkYMDIN99E9fHH0K4dFW5u7HzlFa7o6eHu40P34cMp/OUXNi1fjlqlYm5gINn5+fhMn06na9fQy8vj9MCBdI2K4mL37lhkZpJpaYlOSclDRW/U9es4/f67FD3JnxIZ8f3BiC8jI4Nt27ZRXFzMND092rzyyt1i4vtRFGFHv3OnaHMbOPDuewUFJEyZwta+fWlibc3sefPEZ/vpJzF86LPPhNdfWhpVgwdzwNGR8+3a4WJpiePSpcLqfto0SidNYuv8+SQ3acL0zZvpMGECeevXs3HxYoqrqph78iTJ5eXsnzSJ7rGxqMrKiOrRg25RUVzo0eOu6JWWUqVS1Sl6Lteu4bhhgxQ9yZ+WRhXxPW3i4uLw8fHB1NSURd260dTVVXjs1SV6AB9+KLK327bVFr2KCmKWLMFnwADsrK2Z8fzz6OnpiVa4l16CZcuE0WheHhUTJrBr8GAut2nD5DZt6LFggXBf8fKiaMIEvBcsIMvYmDnr1mHv5kaOtzcbXniBqrIy5gcFcVVbmyOurvSJiqJYU5PY7t3pHhVFdM+eWKSnk2llhfYd15WK+xM4KhUuV67guHGjFD3JnxoZ8T1BxKcoCoGBgQQGBtKpUycmd+mCzpAhwkL+0KG6i5qrzQW++EI4Jt+9GaGvvYafqSndzM1xW7JEOEmHhIj2sokTRea2okJEc3Z2JLdqxbQePeg4c6aYqLZ6NfmTJrFx6lQKmzRhzo8/0tzdncz9+9k4Zw7aRUXMDQoiytiY4yNHMvDcOXIMDLjaoQPdLlwgqlr0LC3RLisDlYoKTU0x7PueMZBj4uIY6O1dOxEjkfwJkcLXQOErKytjz549xMbGMnz4cIZ06YLK0VH45oWGgqnpgxcdOyZMA55/XpiP3hETRVE48vHHnFYUnExMGPnKK6J3NzZW9Ox26yasp7S1KfTywrtJE7Lt7Jjp5IT9lCli8NAvv5Dr7s6GCROoaNKEud9+i7mrK2lBQWycPh2jvDxmBwVxxtKSU0OGMDQ0lJRmzbjZpg1dL168K3oWFmhVVKCCOkVvXEwM/bdulaIn+Usgha+BwvfTTz+RnZ3NlClT6Ni6tfC7q3Zebtv2wQuq7aEGDRIZ2Tvbx4qKCnz+9S9iCwoYp6lJvw8+EOtv3RJrmzQRPbsmJuQuX85GDQ3KrKyYPW4c1pMmiZ7e7du5PWsWG0aORMvYmLn//Cem48eTFB3NZldXzLKzmRUYSJC9PeEDBzIyKIh4GxsS7O3pfOkS0T161IieZmUlKkWhsg7RG3/hAv3uN02QSP7EyDO+BlJcXMyCBQuwsrSEhQshOFjU1tUleikpwim5dWvhtnJH9IqLi9n6ww+kqNV45OXh8M03Yn1urogMq6pES5ypKRnvv89GPT20TU1Z4OFB0/HjhbPy1q2kLlzIptGjMTQ2xuvvf8d4xAhuXrnCFjc3mmdkMPPECY46OBDRpw9jAgK43Lo1t2xt6RQbWyN6ty0s0Lojeg9EesCE6Gj67tghRU/yl0IKXwNZtGiRmIfx97+LQUG//y7sqe6noECcz1VVwcGDcGdKXG5uLt6//UZhRgZz4+Ox8/YWQlNtVJCUJGr7WrQg6auv2FxejkmTJsxZsACjiRPFfY8cIenVV/EeMoRmRkbM/vvfMRg0iCuZmWwfO5ZWqalMDwjgcI8eRHfvzoQjR7jg4ECatTUdLl/mQvfuWKSnk2VujkZlJUjRkzQypPA1EENDQ2EW+tZbotVs7twHF1VUgKenmK1x6pQYCIRoZdu8cSNa6ek8f+4czQ4eFFFgZaUYDRkWJkZIdunC1R9/ZHtuLjY6Osxcvhy9yZPh5k3w8+PGypVs7dcPGyMjZn75Jbq9ehFTUcHu4cPpkJjI5IAADgwYQEznzkz09eV8t25kWljQ9to1Yrp1wyIjgyxzczERTVGo1NB4QPQmRkbSZ9eu2kODJJK/CFL4GkpEhCgfmTpVeODdj6KImjpfXxHpde8OwLVr19ixfTvm6enMPHYMo4AAUbysKKJOb98+8PGBIUOIXr+evSkptK+oYOoHH6A9c6aYvXH4MHFr1rCzSxdaGxnh8dVXaHfsyHkjI/b36kXXmzeZ5O/P7mHDuNKuHW4HDhDepw/ZZma0vnGD2C5dMM/IINvMDAANRaFKQwNFQ6OW6LlGRNDLx0eKnuQvS6MSvqfSueHqCp07iy1uXVvAf/5TZG5//lkkPoDIyEj27dtHu8xMpu3YgU5QEFhZifXvvnu3K2PSJE57e+ObkEBPtZpJX36JxgsviBKZ3buJ3ryZPW3a0MnAgClff42mrS2nW7bEt3Nn+ly5whh/f3aMHs2N1q2ZvG8fIQMHojYxoWViInGdOmGemUmOmRmKSoVGVRVVKhVV94me29mz9Lwzo1ci+asis7oNreOzsxMjHesyKti5U8zAXbECPvsMRVEICgrixIkT9L59mwlr16Lh73+3ePlf/4LXXoOvvkJ57TWOb9nCyatXcUxOZvSaNajefx/+8Q/YtImz585xsEkTeurrM+nf/0bDwICT/foR0LYtjrGxOPv7s23CBBLt7HDbu5eTgwdTaGiITUoK19q1wywrC7WpKZUaGmhWVlKlofGA6E0OD6fHvn2PnxQnkfzJkf8f3lD2769b9EJDRTuapyd88glVVVUcPHiQiIgIhqvVDPnhB1T79t0VvQ0bhOi99RZVf/sbhzZv5ty1a4yKjcXpl19E5PiPf8A33xB86RLHTEzor6PD2F9/BQ0N/AcN4lTLlgyLicHR35/N7u6kWFnhvns3x4cPp0RPj+apqUL0srNRm5pSoamJVkVFnaLnHhZG9wMHpOhJGgUy4nsa7ixXroiCYwcHOHqUck1Ndu7cybVr15hUVkbPTz4RQuflJdYfOCB8+ObNo/LHH9mzZQsx164x6exZem3YABs3wt/+hvLRRxwHTlZVMURDg+Hbt0NWFkdcXTndvDmjo6PpHRDAZg8P0s3Nmezjw7FRoyjX1sYyI4ObrVtjmpNDfpMmlGtpPVT0poSE0O3gwcfb6EskfxGk8P1R4UtLE9PP9PTg1CmKDQzYvHkz6enpeOjq0u6NN8QUttdfF+tPnRIefGPHUr55Mzu2beP6jRtMPXGCzps3i6TIokUob72Fr6kp4aWljKqowMnPD+X6dQ7OmME5S0vGR0fTNSCATTNnkm1igpuPD0fGjkXR0KBpdjZJdnaYqNXkGxs/XPQUhanBwXQ9fFiKnqRRIfc1f4S8PFFwXFYGJ06g1tJi09q1FBUV8Vzz5tg+/zy88cZd0YuOFrV9AwdSun49W7y9SUlIYOahQ7TbskV0aixeTNXSpey3sCAyP58JhYX0PXOGqrg49s2dS1SzZrhGR9MhIIANs2ejNjJi8u7dHB4/HpWiYJqTQ3KLFjTJy6PAyIhybW20ysvrFL1pp07RxddXip6k0SGF70mp9tW7eRNOniRDXx/vtWtRqVQs6NiRZtOmia3tF1+I9TduiCxvmzYUbtmC95YtZN+6hdeOHdht3iz6c728qJw7l91t2xKbm4t7Vhbdr16l8tw5fJ5/nksmJky5cIHWx47x+3PPUaSvj9vu3RycNAntigoMCwq4ZWuLUUEBhYaGlOnoPFT0pgcF0flOH7BE0tiQwvckVFXBvHkiQvPzI8nUlM3r1mFiYsLsLl0wHjcOXFxEmYqGhtgOu7iAkRF5O3awcedOitPSmLdxI9abNok5vR4elE+ZwvaePbmZlYXHrVs4ZGZSceoUu5Ys4YqhIdMvXMDW35/1CxZQpqWFq48P+9zc0C8pQbekhDRrawwLCynW1xei95Dt7fQTJ+h89GjdlvgSSSNACl9DURSxdd22DbZv57K1NTs3bMDW1hbPvn3RGz5cuKps3y6iKbVauCYXFZF9+DAb9u+H27eZ/+uvNKu2bXdzo9TFhc2DBpGamcmsa9doU1FBeUAA2196iZt6esy4cAHL48dZ//zzVKlUTNy7l72TJ2NYVIRWWRmZFhboFxVRoqtLqZ6eiPTur9NTFGYEBOBw7JgUPUmjRgpfQ/nHP+Drr+Hbbznfti37t23DwcGBKQMHojV0KFhYiKytgQEUF4ObGyQkkL5/PxuPHkVPrcbr++8x+fln4bAyciRFgwfjPWIEWenpeF28iJ2xMWX797N1+XKStLWZFR2N6cmTrF+4EI3KSsYfOMAed3eM8/PRqKoiu1kzdEtKKNPVpVRf/6Gi5+nvT0d/f9DV/a/+hBLJf5tGJXxPpXPj//4P5Z13ONWjBwH79tGnTx/GDxqEhrOz6Lk9cgSaNYPycvDwgPBwknbsYHNwMKZFRcz55z8x/PZb6NQJhg0jv1cvNo4ZQ2FaGvPOncPa1pbS7dvZ/MorpGloMCcqCsPQUNYvXIhOaSkuvr74TJlCU7WaSiDX1BTtsjIqtLUp0ddH8yGiN/PoUToEBEjRk0iQ5SwNLmdR5s/H18OD8PBwnJ2dGdqvH6oxY+DSJVGq0qmTEMA7szWub9zItuvXaV5RwczPPkPv88+FVdXQoeS2bs0Gd3cqMzLwCg3FvHNnijdtwvuVV7gNzImORufsWTbMm4dBUREj/PzwmToV86wsyrS0KDQyQuNOF0axoeGDkZ5KBVVVzPLzo/3x46LkRiKRNK6I72mwa9w4Lp05w4QJE+jbs6cwKzh3DgIChOgpipiRsW0bsT//zK6rV2mtoYHHJ5+g/e67IhM8eDBZLVqwwc0NzbQ05gcGYjpwIIXr1rHp1VdRV1byXHQ0REayfsECmqjVOPv7s3vaNKwyMynW0aHYwABVVRXKHdHTLC+nUqW6azigUkFlJbOPHKFdYKAUPYnkHqTwNZC4K1eYPn06nRwcxKzbgweFs0p1K9q778KPPxK5Zg37bt2is4EB7m+/jebLL8OiRTBsGBnm5mycOhW9tDS8/P1pMmoUBb/8woZXXqGovJx5UVGUx8Swaf58zLKzGRwYyK7p07FJTaXQwIBifX0AVEDhHdGrqkP05hw+TNugICl6Esl9SOFrIF5eXtjb2ws/vl9/FS4t48eLN7/4AlavJmz1ao5kZ9PbzIwJr72Gxrx5wrvP2ZlUAwM2TptGk7Q0vI4cwdDNjbwffmDDyy9TVlLCvMhIiq5exXvePCwzMnAMCWH31Km0SEkhz8iIUl1d4aMHFBoZoVlR8aDoKQodExJoGxgo3JolEkktpPA1EHt7eyFwX34psrvVRqQ//YTy9tsEfvABgaWlDLK1ZdTSpaimTBFrXVxIVqnY5OFBs7Q05hw8iP6sWeR+9x2/L1uGUlzMvIgI8hIS2Dx3LjYpKfQ9c4bdU6Zgn5RETpMmlOnoUKVSoaEoNaKnwAOiZ5mVxZRvvhGZZYlE8gBS+BrKzz+LGbcffACvvCJe27oV5cUXOfLWW5zW0GBEu3YMXrwY1ciR8OOP4OpKfEkJWzw9sU5LY9aePeguXEjWmjVsWLoUzfx85p07x+20NLbOmUPLxER6REbi4+5Om/h4bjdtSoW2NpWammhWVdUSvar7Re/2bZ7/6CN06pr2JpFIAHimwxRycnLw8vLCxMQEExMTvLy8yM3NfeQ1u3fvZsyYMZibm6NSqYiMjHxgTWlpKcuXL8fc3BxDQ0NcXV1JTk5+Nl/ifpYsgeXLYeVK8fzgQarmzmXfa69xWl+f8d27M2TZMlR9+ojh4TNmcC0nB+8ZM2iRns7sHTvQXbKEzO+/Z/2LL6KjVjP/9GnSMzPZMmsWrW/epHt0NHsmT6bd9etkmplRqaVFhaYmmpWVd0Xv/uztvaJ3x2FZIpHUzTMVvlmzZhEZGYmvry++vr5ERkbiVW3N9BAKCwtxcnLi888/f+iaV199FR8fH7Zu3cqpU6coKChg4sSJf6w+r77Mni22uCoVBAZSMWMGO5cuJapJE9wdHem3ZImYuObjA/PnE5eWxlYPD1qnpzNz82Z0Xn2VtO+/Z/3ixRjm5DAvLIyk/Hy2eXrS/upVOsXGstfVlY5XrpBmaYmioUGZtjZalZUUGhujUR3pVQtetehlZkrRk0jqyTOr44uNjaVz586EhYUxYMAAAMLCwnB0dCQuLo6OHTs+8vr4+Hhat27N+fPn6dmzZ83rarUaCwsLNm7cyIwZMwBISUnBzs6OQ4cOMeaO3fu9lJaWUlpaWvM8Ly8POzu7J7OlKi8XrWjnzlHm4sI2Ly8SzM2ZPmwYHWfNEtPUjh+H117j4sWL7J4yhU6ZmUzZuBHNd97h1nffsWnePJrevo1XWBjXKivxcXeny6VLtEpI4MD48XSOjSXZxgZUKkp1dNCuqKDgjuihUtUteh9/LEVPIqknzyziCw0NxcTEpEb0AAYOHIiJiQkhISFPfN9z585RXl6Oi4tLzWs2NjZ07dr1ofddvXp1zXbbxMQEOzu7J/77aGvDpUsUu7qy0cuLZEtL5owdS8d580RXxNGj8N57RMbGsnvKFLrdvs3UdevQfPddEn/6iQ3z5mGekcHcU6e4rKHB7ilT6B4dTcukJA5MmEC3mBiSbG1RQb1Ez0pGehJJg3lmwpeWloalpeUDr1taWpKWlvaH7qujo0PTpk1rvW5lZfXQ+65YsQK1Wl3zSEpKeuK/z82bFLi68ruHB1nNmzPX1ZVWc+eKSPDYMfjqK85ERbHXzY1eWVlM/uUXND78kJtr17Jpzhyap6czJyiIGH199rq60jsiAuvMTA6NG0eP6GhutmyJRlUVxXp6aJeXP1r0MjJYsGoVOs2aPfn3kUgaIQ0WvpUrV6JSqR75OHv2LACqe+zNq1EUpc7X/yiPuq+uri5NmjSp9XhS8tzcWO/qSqGNDfOmTsXWywuys4XorV1LSHg4hyZMYEB2NhN/+AHVqlVc27CBzR4etExJYXZAANFNm3JgwgT6hYdjplZzZPRoekVGcq11a7QqKynW10envJyCJk3EwO86RM86I4MFH32Ejrn5E38XiaSx0uBylmXLluHp6fnINa1atSI6Opr09PQH3svMzMSqerTiE2BtbU1ZWRk5OTm1or6MjAwGDRr0xPetL+tGj0Zp3pz5Hh6YzZgBiYkQGIji4yMmqrm4MEStZvh336H69FPitm5lx9SptEtKYnpAAGft7DgyahQDQkMxLC3l2IgR9I6IIK5DB3TLyigwNES3tPSu6PFgIsP6TqSnLUVPInkiGix85ubmmNfjH5yjoyNqtZrw8HD69+8PwOnTp1Gr1X9IoPr06YO2tjZHjx7Fw8MDgNTUVC5evMiXX375xPetLxo2NsydMwcTT09hTBAQgBIYiP+xYwQPH86I/HyGfP01fPIJMbt3s9vVFYfERKYcO8bpdu046uzMoFOn0FEUApyd6Xv2LDGdOqFXUkKBkVGN6KkeInrN09OZv2oV2hYWz/y7SiR/VZ5ZAXOnTp0YO3YsixYt4qeffgJg8eLFTJw4sVZG18HBgdWrV+Pu7g5AdnY2iYmJpKSkAHD58mVARHrW1taYmJjw/PPP8/rrr9OsWTPMzMx444036NatG6NGjXpWX6eG+fPmYTRnjpit6+eHcuECvgcPEj54MGOKixn4j3/AqlVEHTrE3vHj6XbzJm5HjxLcuTMBQ4YwJCgIlYYGJ4YMoe+ZM1zq3Bn9khLyjYzQKy0l/47oqXiE6NVxdiqRSOrPM63j8/b2plu3bri4uODi4kL37t3ZuHFjrTWXL19GrVbXPN+3bx+9evViwoQJAHh6etKrVy9+/PHHmjX/+te/mDx5Mh4eHjg5OWFgYMD+/fvR1NR8ll8HAKPFi0W5yr59VKWksN/Hh/D+/ZlYUcHAL76ADz7g3IkT7Bk1ip7Xr+Pm68vJbt0IGDKEYcePg5YWQYMH0+/MGWK6dEG/uJg8Y2MhesbGDxe9tDTmr1wpRU8ieQpIP76GJjq0tWH3bipVKvb+/jsXu3RhsoYG3T/8EFasIPzsWQ47OdHv6lXG+voS2L8/QQMGMNzfn3JDQ04NHEj/06eJ7t4dw4IC1CYmIuIzNkalKKgU5QHRs0lLY96qVWj/gbNRiURyF9mr21A2baLCwIBdv/3GlS5dmKanR+cVK+C11wiNjsbPyYmBV64w2teXgEGDCO7bl5FHj1JsYkJI//4MCAsjqkcPjAoKyDE1xaC4uEb0kKInkfxHkMLXQMqbN2f7b79xs317Zhgb0+GNN2DZMoKvX+dYv344Xb7MCF9fjg0bRmjPnrj4+pJnbk5Y374MCA0lslcvjPPyyGnaVIiekVGN6Cl1id5HH8ntrUTylHmmZ3z/a3z//fd07tyZfv36PfE9Nv/+Own29sxq1kyI3uLFBKWlcaxXL4bGxTHi0CGOjBhBaM+ejD10iFxLS8L69mVgSAjne/emiVpNtpnZXdGDukUvNVVEelL0JJKnjjzja+AZ3+r332e2rS0tly5FmTuXEyUlBDk44Bwby9DDhzk0dixnO3dmwv79ZNjZcaZnTxyDgznXty+mubncbtYMw6Ii8o2MAFA9TPQ++khubyWSZ4Tc6jaQufb22C5ZguLhgX9FBcEODoy8dAmnQ4fYP2kS5zt0YNK+faTY23Oue3cGnTrFmf79aZqdzW1z88eKnm1qKs9J0ZNIniky4mtoVldHB2XiRPyaNCGsdWtcYmIYcOgQ+ydPJrJdO9z27iWxbVvOd+3KoOBgzvTvj1l2NhkWFhgVFJBvbAyIeRlKdYvdHdFrkZLC3I8/lqInkTxjZMTXQBQXFw43bcqZli0ZFxND34MH2Tt1Khdat2ayjw/xHTsS2bkzg06dInzgQMxv3ybd0vJB0au+4T2i99zHH6MlRU8ieeZI4WsgB21sOGdry8SLF+l18CA+Hh7E2Nvjvns317p04ULHjjgFB3P6caJ3z/ZWip5E8p+lUWV1nwbnbGxwvXiRngcPstPTk0stWzJ11y6udu3KhY4dGRQcTNjAgZhnZpJmZYVRYSEF1Wd6PET0PvpIip5E8h9ERnwNxP3SJTofOMCO2bO5amPDtJ07ienZk0vt2wvRc3TEMj2d1ObNMS4ooMDQEEVDQyQyoLbo3bolIj1r6//215JIGhUyudHA5EaFnh7b587lhpUV03fuJLpPH+LatMExJITQQYOwTksjpR6iZ3frFnOl6Ekk/xVkxNdAtj33HPEWFnjs2MH5fv240rr1XdFLTSXFxubxopecLEVPIvkvIs/4Gki8hQUeO3cS0b8/V1u1qhG95qmppNja3hU9TU3RkQG1RK9lteg1b/7f/ioSSaOlUQnf02hZ89yxgzMDB3LN3p6BoaGEODnRPCWFW7a2GOfn3xW9qipxwX2i5yVFTyL5ryPP+Bp4xuc9fz7xtrYMOH2akEGDsL11i2Q7O4zz8ig0MKBKS0uI3n3FyVL0JJL/HRpVxPc0iLe1ZUBYmBC95OR6iZ59UpIUPYnkfwgpfA2kf1gYwYMHC9Fr2bJeojfnk0+k6Ekk/0NI4WsgIYMHY5eYWH/Rk5GeRPI/hxS+BmKXmEiSvT1GeXkU6es/XvRsbP67H1gikTyArONrINWiV6yvT6W2dt2il5iI1yefoClFTyL5n0QKXwN5nOi1SkxkjhQ9ieR/Gil8DeSRopeQIEVPIvkTIM/4GkiltjaqR4mere1/9wNKJJLH0qiE72l0bqiqqh5wTm4tRU8i+VMhOzca2Lmx6sMPa7WhtY6PZ/ann0rRk0j+RDSqiO+pUB3tSdGTSP60SOF7QqToSSR/XmRW9wloEx/PLCl6EsmfFhnxNZA28fHMkokMieRPjUxuNDC5UZmcjGaLFs/ok0kkkv8EMuJrIFL0JJI/P1L4JBJJo0MKn0QiaXQ0KuF7Gp0bEonkz49MbjQwuSGRSP78NKqITyKRSEAKn0QiaYRI4ZNIJI0OKXwSiaTRIYVPIpE0Op6p8OXk5ODl5YWJiQkmJiZ4eXmRm5v7yGt2797NmDFjMDc3R6VSERkZ+cAaZ2dnVCpVrYenp+ez+RISieQvxzMVvlmzZhEZGYmvry++vr5ERkbi5eX1yGsKCwtxcnLi888/f+S6RYsWkZqaWvP46aefnuZHl0gkf2GemS1VbGwsvr6+hIWFMWDAAAB++eUXHB0duXz5Mh07dqzzumphjI+Pf+T9DQwMsLa2rtdnKS0tpbS0tOZ5Xl5eva6TSCR/TZ5ZxBcaGoqJiUmN6AEMHDgQExMTQkJC/vD9vb29MTc3p0uXLrzxxhvk5+c/dO3q1atrttsmJibY2dn94b8vkUj+vDyziC8tLQ1LS8sHXre0tCQtLe0P3Xv27Nm0bt0aa2trLl68yIoVK4iKiuLo0aN1rl+xYgWvvfZazfO8vDwpfhJJI6bBwrdy5UpWrVr1yDVnzpwBQFU9n+IeFEWp8/WGsGjRopr/u2vXrrRv356+ffsSERFB7969H1ivq6uLrq7uH/qbEonkr0ODhW/ZsmWPzaC2atWK6Oho0tPTH3gvMzMTKyurhv7ZR9K7d2+0tbW5evVqncInkUgk99Jg4TM3N8fc3Pyx6xwdHVGr1YSHh9O/f38ATp8+jVqtZtCgQQ3/pI8gJiaG8vJymjdv/lTvK5FI/po8s+RGp06dGDt2LIsWLSIsLIywsDAWLVrExIkTa2V0HRwc8PHxqXmenZ1NZGQkly5dAuDy5ctERkbWnAtev36djz76iLNnzxIfH8+hQ4eYPn06vXr1wsnJ6Vl9HYlE8ldCeYZkZWUps2fPVoyNjRVjY2Nl9uzZSk5OTq01gLJu3bqa5+vWrVOABx4ffvihoiiKkpiYqAwdOlQxMzNTdHR0lLZt2yovv/yykpWVVe/PpVarFUBRq9VP4VtKJJI/G9KPT/rxSSSNDtmrK5FIGh1S+CQSSaNDCp9EIml0NCrhk8OGJBIJyGFDMrkhkTRCGlXEJ5FIJCCFTyKRNEKk8EkkkkaHFD6JRNLokMInkUgaHVL4JBJJo0MKn0QiaXRI4ZNIJI2ORiV8snNDIpGA7NyQnRsSSSOkUUV8EolEAlL4JBJJI0QKn0QiaXRI4ZNIJI0OKXwSiaTRIYVPIpE0OqTwSSSSRocUPolE0uhoVMInOzckEgnIzg3ZuSGRNEIaVcQnkUgkIIVPIpE0QqTwSSSSRocUPolE0uiQwieRSBodUvgkEkmjQwqfRCJpdEjhk0gkjY5GJXyyc0MikYDs3JCdGxJJI6RRRXwSiUQCUvgkEkkjRAqfRCJpdEjhk0gkjQ4pfBKJpNHxTIUvJycHLy8vTExMMDExwcvLi9zc3IeuLy8v56233qJbt24YGhpiY2PD3LlzSUlJqbWutLSU5cuXY25ujqGhIa6uriQnJz/LryKRSP5CPFPhmzVrFpGRkfj6+uLr60tkZCReXl4PXV9UVERERATvv/8+ERER7N69mytXruDq6lpr3auvvoqPjw9bt27l1KlTFBQUMHHiRCorK5/l15FIJH8VlGfEpUuXFEAJCwureS00NFQBlLi4uHrfJzw8XAGUhIQERVEUJTc3V9HW1la2bt1as+bWrVuKhoaG4uvrW697qtVqBVDUanW9P4dEIvnr8MwivtDQUExMTBgwYEDNawMHDsTExISQkJB630etVqNSqTA1NQXg3LlzlJeX4+LiUrPGxsaGrl27PvS+paWl5OXl1XpIJJLGyzMTvrS0NCwtLR943dLSkrS0tHrdo6SkhLfffptZs2bVdFikpaWho6ND06ZNa621srJ66H1Xr15dc85oYmKCnZ1dA7+NRCL5K9Fg4Vu5ciUqleqRj7NnzwKgUqkeuF5RlDpfv5/y8nI8PT2pqqri3//+92PXP+q+K1asQK1W1zySkpIeez+JRPLXRauhFyxbtgxPT89HrmnVqhXR0dGkp6c/8F5mZiZWVlaPvL68vBwPDw9u3rxJQEBArX5aa2trysrKyMnJqRX1ZWRkMGjQoDrvp6uri66u7iP/pkQiaTw0WPjMzc0xNzd/7DpHR0fUajXh4eH0798fgNOnT6NWqx8qUHBX9K5evcrx48dp1qxZrff79OmDtrY2R48excPDA4DU1FQuXrzIl19+2dCvI5FIGiHP1J1l3LhxpKSk8NNPPwGwePFi7O3t2b9/f80aBwcHVq9ejbu7OxUVFUydOpWIiAgOHDhQKzI0MzNDR0cHgBdffJEDBw6wfv16zMzMeOONN8jKyuLcuXNoamo+9nNJdxaJpJHzLFPGWVlZyuzZsxVjY2PF2NhYmT17tpKTk1NrDaCsW7dOURRFuXnzpgLU+Th+/HjNNcXFxcqyZcsUMzMzRV9fX5k4caKSmJhY788ly1kkksaN9OOTEZ9E0uiQvboSiaTRIYVPIpE0OhrlVldRFPLz8zE2Nq5XTaFEIvlr0SiFTyKRNG7kVlcikTQ6pPBJJJJGhxQ+iUTS6JDCJ5FIGh1S+CQSSaNDCp9EIml0SOGTSCSNjv8HHAzPaYPvENsAAAAASUVORK5CYII=", "text/plain": [ "Graphics object consisting of 84 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = XS.plot(XC, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " max_range=100, number_values=41, plot_points=200, \n", " color={t: 'red', r: 'grey'})\n", "graph += circle((pi,0), 0.005, fill=True, color='grey') + \\\n", " text(r\"$i^0$\", (pi, 0.02), fontsize=18, color='grey') \n", "show(graph, xmin=3., xmax=3.2, ymin=-0.2, ymax=0.2, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To produce a more satisfactory figure, let us use some logarithmic radial coordinate:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(M,(t, {\\rho}, {\\theta}, {\\phi})\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(M,(t, {\\rho}, {\\theta}, {\\phi})\\right)$" ], "text/plain": [ "Chart (M, (t, rh, th, ph))" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XL. = M.chart(r't rh:\\rho th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "XL" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & t \\\\ {\\rho} & = & \\log\\left(r\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & t \\\\ {\\rho} & = & \\log\\left(r\\right) \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "t = t\n", "rh = log(r)\n", "th = th\n", "ph = ph" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XL = XS.transition_map(XL, [t, ln(r), th, ph])\n", "XS_to_XL.display()" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & t \\\\ r & = & e^{{\\rho}} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.\$$" ], "text/latex": [ "$\\displaystyle \\left\\{\\begin{array}{lcl} t & = & t \\\\ r & = & e^{{\\rho}} \\\\ {\\theta} & = & {\\theta} \\\\ {\\phi} & = & {\\phi} \\end{array}\\right.$" ], "text/plain": [ "t = t\n", "r = e^rh\n", "th = th\n", "ph = ph" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS_to_XL.inverse().display()" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "XL_to_XC = M.coord_change(XS, XC) * M.coord_change(XL, XS)\n", "XC_to_XL = M.coord_change(XS, XL) * M.coord_change(XC, XS)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 40 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = XL.plot(XC, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " ranges={t: (-20, 20), rh: (-2, 10)}, number_values=19, \n", " color={t: 'red', rh: 'grey'})\n", "graph += circle((pi,0), 0.005, fill=True, color='grey') + \\\n", " text(r\"$i^0$\", (pi, 0.02), fontsize=18, color='grey') \n", "show(graph, xmin=3., xmax=3.2, ymin=-0.2, ymax=0.2, aspect_ratio=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Null radial geodesics in the conformal diagram\n", "\n", "To get a view of the null radial geodesics in the conformal diagram, it suffices to plot the chart $(u,v,\\theta,\\phi)$ in terms of the chart $(\\tau,\\chi,\\theta,\\phi)$. \n", "The following plot shows \n", "- the null geodesics defined by $(u,\\theta,\\phi) = (u_0, \\pi/2,\\pi)$ for 17 values of $u_0$ evenly spaced in $[-8,8]$ (dashed lines) \n", "- the null geodesics defined by $(v,\\theta,\\phi) = (v_0, \\pi/2,\\pi)$ for 17 values of $v_0$ evenly spaced in $[-8,8]$ (solid lines)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 42 graphics primitives" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graphXN = XN.plot(XC, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " number_values=17, plot_points=150, color='green', \n", " style={u: '--', v: '-'}, thickness=1.5)\n", "graph = graphXN + graph_i0 + graph_ip + graph_im + graph_Ip + graph_Im\n", "show(graph, figsize=8)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "graph.save('glo_conf_Mink_null.pdf', figsize=8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conformal factor\n", "\n", "The conformal factor expressed in various coordinate systems:" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{u^{2} + 1} \\sqrt{v^{2} + 1}} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - 2 \\, \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} \\\\ & \\left(t, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{t^{2} + 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1} \\sqrt{t^{2} - 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1}} \\end{array}\$$" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{u^{2} + 1} \\sqrt{v^{2} + 1}} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - 2 \\, \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} \\\\ & \\left(t, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{t^{2} + 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1} \\sqrt{t^{2} - 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1}} \\end{array}$" ], "text/plain": [ "Omega: M → ℝ\n", " (t, r, th, ph) ↦ 2/(sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1))\n", " (u, v, th, ph) ↦ 2/(sqrt(u^2 + 1)*sqrt(v^2 + 1))\n", " (U, V, th, ph) ↦ 2*cos(U)*cos(V)\n", " (tau, ch, th, ph) ↦ 2*cos(1/2*ch)^2*cos(1/2*tau)^2 - 2*sin(1/2*ch)^2*sin(1/2*tau)^2\n", " (t, rh, th, ph) ↦ 2/(sqrt(t^2 + 2*t*e^rh + e^(2*rh) + 1)*sqrt(t^2 - 2*t*e^rh + e^(2*rh) + 1))" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The expression in terms of $(\\tau,\\chi,\\theta,\\phi)$ can be simplified:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle 2 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - 2 \\, \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}\$$" ], "text/latex": [ "$\\displaystyle 2 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2} - 2 \\, \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right)^{2} \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right)^{2}$" ], "text/plain": [ "2*cos(1/2*ch)^2*cos(1/2*tau)^2 - 2*sin(1/2*ch)^2*sin(1/2*tau)^2" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega_XC = Omega.expr(XC)\n", "Omega_XC" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)\$$" ], "text/latex": [ "$\\displaystyle \\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right)$" ], "text/plain": [ "cos(ch) + cos(tau)" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega_XC.trig_reduce() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hence we set" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{u^{2} + 1} \\sqrt{v^{2} + 1}} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right) \\\\ & \\left(t, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{t^{2} + 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1} \\sqrt{t^{2} - 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1}} \\end{array}\$$" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} \\Omega:& M & \\longrightarrow & \\mathbb{R} \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}} \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{u^{2} + 1} \\sqrt{v^{2} + 1}} \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & 2 \\, \\cos\\left(U\\right) \\cos\\left(V\\right) \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\cos\\left({\\chi}\\right) + \\cos\\left({\\tau}\\right) \\\\ & \\left(t, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\frac{2}{\\sqrt{t^{2} + 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1} \\sqrt{t^{2} - 2 \\, t e^{{\\rho}} + e^{\\left(2 \\, {\\rho}\\right)} + 1}} \\end{array}$" ], "text/plain": [ "Omega: M → ℝ\n", " (t, r, th, ph) ↦ 2/(sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1))\n", " (u, v, th, ph) ↦ 2/(sqrt(u^2 + 1)*sqrt(v^2 + 1))\n", " (U, V, th, ph) ↦ 2*cos(U)*cos(V)\n", " (tau, ch, th, ph) ↦ cos(ch) + cos(tau)\n", " (t, rh, th, ph) ↦ 2/(sqrt(t^2 + 2*t*e^rh + e^(2*rh) + 1)*sqrt(t^2 - 2*t*e^rh + e^(2*rh) + 1))" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Omega.add_expr(Omega_XC.trig_reduce(), XC)\n", "Omega.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A plot of $\\Omega$ in terms of the coordinates $(\\tau,\\chi)$:" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n" ], "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "graph = plot3d(Omega.expr(XC), (tau,-pi,pi), (ch,0,pi)) \\\n", " + plot3d(0, (tau,-pi,pi), (ch,0,pi), color='yellow', opacity=0.7)\n", "show(graph, aspect_ratio=1, axes_labels=['tau', 'chi', 'Omega'])" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics3d Object" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(graph, aspect_ratio=1, viewer='tachyon')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Differential of the conformal factor\n", "\n", "The 1-form $\\mathrm{d}\\Omega$ is:" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1-form dOmega on the 4-dimensional Lorentzian manifold M\n" ] } ], "source": [ "dOmega = Omega.differential()\n", "print(dOmega)" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\mathrm{d}\\Omega = \\left( -\\frac{4 \\, {\\left(t^{3} - {\\left(r^{2} - 1\\right)} t\\right)} \\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}}{r^{8} + t^{8} - 4 \\, {\\left(r^{2} - 1\\right)} t^{6} + 4 \\, r^{6} + 2 \\, {\\left(3 \\, r^{4} - 2 \\, r^{2} + 3\\right)} t^{4} + 6 \\, r^{4} - 4 \\, {\\left(r^{6} + r^{4} - r^{2} - 1\\right)} t^{2} + 4 \\, r^{2} + 1} \\right) \\mathrm{d} t + \\left( -\\frac{4 \\, {\\left(r^{3} - r t^{2} + r\\right)} \\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}}{r^{8} + t^{8} - 4 \\, {\\left(r^{2} - 1\\right)} t^{6} + 4 \\, r^{6} + 2 \\, {\\left(3 \\, r^{4} - 2 \\, r^{2} + 3\\right)} t^{4} + 6 \\, r^{4} - 4 \\, {\\left(r^{6} + r^{4} - r^{2} - 1\\right)} t^{2} + 4 \\, r^{2} + 1} \\right) \\mathrm{d} r\$$" ], "text/latex": [ "$\\displaystyle \\mathrm{d}\\Omega = \\left( -\\frac{4 \\, {\\left(t^{3} - {\\left(r^{2} - 1\\right)} t\\right)} \\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}}{r^{8} + t^{8} - 4 \\, {\\left(r^{2} - 1\\right)} t^{6} + 4 \\, r^{6} + 2 \\, {\\left(3 \\, r^{4} - 2 \\, r^{2} + 3\\right)} t^{4} + 6 \\, r^{4} - 4 \\, {\\left(r^{6} + r^{4} - r^{2} - 1\\right)} t^{2} + 4 \\, r^{2} + 1} \\right) \\mathrm{d} t + \\left( -\\frac{4 \\, {\\left(r^{3} - r t^{2} + r\\right)} \\sqrt{r^{2} + 2 \\, r t + t^{2} + 1} \\sqrt{r^{2} - 2 \\, r t + t^{2} + 1}}{r^{8} + t^{8} - 4 \\, {\\left(r^{2} - 1\\right)} t^{6} + 4 \\, r^{6} + 2 \\, {\\left(3 \\, r^{4} - 2 \\, r^{2} + 3\\right)} t^{4} + 6 \\, r^{4} - 4 \\, {\\left(r^{6} + r^{4} - r^{2} - 1\\right)} t^{2} + 4 \\, r^{2} + 1} \\right) \\mathrm{d} r$" ], "text/plain": [ "dOmega = -4*(t^3 - (r^2 - 1)*t)*sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1)/(r^8 + t^8 - 4*(r^2 - 1)*t^6 + 4*r^6 + 2*(3*r^4 - 2*r^2 + 3)*t^4 + 6*r^4 - 4*(r^6 + r^4 - r^2 - 1)*t^2 + 4*r^2 + 1) dt - 4*(r^3 - r*t^2 + r)*sqrt(r^2 + 2*r*t + t^2 + 1)*sqrt(r^2 - 2*r*t + t^2 + 1)/(r^8 + t^8 - 4*(r^2 - 1)*t^6 + 4*r^6 + 2*(3*r^4 - 2*r^2 + 3)*t^4 + 6*r^4 - 4*(r^6 + r^4 - r^2 - 1)*t^2 + 4*r^2 + 1) dr" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega.display()" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\mathrm{d}\\Omega = -2 \\, \\cos\\left(V\\right) \\sin\\left(U\\right) \\mathrm{d} U -2 \\, \\cos\\left(U\\right) \\sin\\left(V\\right) \\mathrm{d} V\$$" ], "text/latex": [ "$\\displaystyle \\mathrm{d}\\Omega = -2 \\, \\cos\\left(V\\right) \\sin\\left(U\\right) \\mathrm{d} U -2 \\, \\cos\\left(U\\right) \\sin\\left(V\\right) \\mathrm{d} V$" ], "text/plain": [ "dOmega = -2*cos(V)*sin(U) dU - 2*cos(U)*sin(V) dV" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega.display(XNC)" ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "M.set_default_chart(XNC)\n", "M.set_default_frame(XNC.frame())" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\mathrm{d}\\Omega = -2 \\, \\cos\\left(V\\right) \\sin\\left(U\\right) \\mathrm{d} U -2 \\, \\cos\\left(U\\right) \\sin\\left(V\\right) \\mathrm{d} V\$$" ], "text/latex": [ "$\\displaystyle \\mathrm{d}\\Omega = -2 \\, \\cos\\left(V\\right) \\sin\\left(U\\right) \\mathrm{d} U -2 \\, \\cos\\left(U\\right) \\sin\\left(V\\right) \\mathrm{d} V$" ], "text/plain": [ "dOmega = -2*cos(V)*sin(U) dU - 2*cos(U)*sin(V) dV" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega.display()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle -2 \\, \\cos\\left(V\\right) \\sin\\left(U\\right) \\mathrm{d} U -2 \\, \\cos\\left(U\\right) \\sin\\left(V\\right) \\mathrm{d} V\$$" ], "text/latex": [ "$\\displaystyle -2 \\, \\cos\\left(V\\right) \\sin\\left(U\\right) \\mathrm{d} U -2 \\, \\cos\\left(U\\right) \\sin\\left(V\\right) \\mathrm{d} V$" ], "text/plain": [ "-2*cos(V)*sin(U) dU - 2*cos(U)*sin(V) dV" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega1 = M.one_form()\n", "dOmega1[0] = -2*cos(V)*sin(U)\n", "dOmega1[1] = -2*cos(U)*sin(V)\n", "dOmega1.display()" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle -2 \\, \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right) \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right) \\mathrm{d} {\\tau} -2 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right) \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right) \\mathrm{d} {\\chi}\$$" ], "text/latex": [ "$\\displaystyle -2 \\, \\cos\\left(\\frac{1}{2} \\, {\\tau}\\right) \\sin\\left(\\frac{1}{2} \\, {\\tau}\\right) \\mathrm{d} {\\tau} -2 \\, \\cos\\left(\\frac{1}{2} \\, {\\chi}\\right) \\sin\\left(\\frac{1}{2} \\, {\\chi}\\right) \\mathrm{d} {\\chi}$" ], "text/plain": [ "-2*cos(1/2*tau)*sin(1/2*tau) dtau - 2*cos(1/2*ch)*sin(1/2*ch) dch" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dOmega1.display(XC.frame(), XC)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Einstein static universe" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4-dimensional differentiable manifold E\n" ] } ], "source": [ "E = Manifold(4, 'E')\n", "print(E)" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(E,({\\tau}, {\\chi}, {\\theta}, {\\phi})\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(E,({\\tau}, {\\chi}, {\\theta}, {\\phi})\\right)$" ], "text/plain": [ "Chart (E, (tau, ch, th, ph))" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XE. = E.chart(r'tau:\\tau ch:(0,pi):\\chi th:(0,pi):\\theta ph:(0,2*pi):\\phi')\n", "XE" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle {\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)\$$" ], "text/latex": [ "$\\displaystyle {\\tau} :\\ \\left( -\\infty, +\\infty \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$" ], "text/plain": [ "tau: (-oo, +oo); ch: (0, pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XE.coord_range()" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle {\\tau} :\\ \\left( -\\pi , \\pi \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)\$$" ], "text/latex": [ "$\\displaystyle {\\tau} :\\ \\left( -\\pi , \\pi \\right) ;\\quad {\\chi} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\theta} :\\ \\left( 0 , \\pi \\right) ;\\quad {\\phi} :\\ \\left( 0 , 2 \\, \\pi \\right)$" ], "text/plain": [ "tau: (-pi, pi); ch: (0, pi); th: (0, pi); ph: (0, 2*pi)" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XC.coord_range()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Embedding of $M$ in $E$" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Differentiable map Phi from the 4-dimensional Lorentzian manifold M to the 4-dimensional differentiable manifold E\n" ] }, { "data": { "text/html": [ "\$$\\displaystyle \\begin{array}{llcl} \\Phi:& M & \\longrightarrow & E \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arctan\\left(r + t\\right) + \\arctan\\left(-r + t\\right), \\arctan\\left(r + t\\right) - \\arctan\\left(-r + t\\right), {\\theta}, {\\phi}\\right) \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arctan\\left(u\\right) + \\arctan\\left(v\\right), -\\arctan\\left(u\\right) + \\arctan\\left(v\\right), {\\theta}, {\\phi}\\right) \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(U + V, -U + V, {\\theta}, {\\phi}\\right) \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) \\\\ & \\left(t, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arctan\\left(t + e^{{\\rho}}\\right) + \\arctan\\left(t - e^{{\\rho}}\\right), \\arctan\\left(t + e^{{\\rho}}\\right) - \\arctan\\left(t - e^{{\\rho}}\\right), {\\theta}, {\\phi}\\right) \\end{array}\$$" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} \\Phi:& M & \\longrightarrow & E \\\\ & \\left(t, r, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arctan\\left(r + t\\right) + \\arctan\\left(-r + t\\right), \\arctan\\left(r + t\\right) - \\arctan\\left(-r + t\\right), {\\theta}, {\\phi}\\right) \\\\ & \\left(u, v, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arctan\\left(u\\right) + \\arctan\\left(v\\right), -\\arctan\\left(u\\right) + \\arctan\\left(v\\right), {\\theta}, {\\phi}\\right) \\\\ & \\left(U, V, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(U + V, -U + V, {\\theta}, {\\phi}\\right) \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) \\\\ & \\left(t, {\\rho}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) = \\left(\\arctan\\left(t + e^{{\\rho}}\\right) + \\arctan\\left(t - e^{{\\rho}}\\right), \\arctan\\left(t + e^{{\\rho}}\\right) - \\arctan\\left(t - e^{{\\rho}}\\right), {\\theta}, {\\phi}\\right) \\end{array}$" ], "text/plain": [ "Phi: M → E\n", " (t, r, th, ph) ↦ (tau, ch, th, ph) = (arctan(r + t) + arctan(-r + t), arctan(r + t) - arctan(-r + t), th, ph)\n", " (u, v, th, ph) ↦ (tau, ch, th, ph) = (arctan(u) + arctan(v), -arctan(u) + arctan(v), th, ph)\n", " (U, V, th, ph) ↦ (tau, ch, th, ph) = (U + V, -U + V, th, ph)\n", " (tau, ch, th, ph) ↦ (tau, ch, th, ph) = (tau, ch, th, ph)\n", " (t, rh, th, ph) ↦ (tau, ch, th, ph) = (arctan(t + e^rh) + arctan(t - e^rh), arctan(t + e^rh) - arctan(t - e^rh), th, ph)" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Phi = M.diff_map(E, {(XC, XE): [tau, ch, th, ph]},\n", " name='Phi', latex_name=r'\\Phi')\n", "print(Phi)\n", "Phi.display()" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Graphics object consisting of 18 graphics primitives" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "XS.plot(XE, mapping=Phi, ambient_coords=(ch, tau), fixed_coords={th: pi/2, ph: pi}, \n", " plot_points=200, color={t: 'red', r: 'grey'})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Embedding of $E$ in $\\mathbb{R}^5$" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5-dimensional differentiable manifold R^5\n" ] } ], "source": [ "R5 = Manifold(5, 'R^5', latex_name=r'\\mathbb{R}^5')\n", "print(R5)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\$$\\displaystyle \\left(\\mathbb{R}^5,({\\tau}, W, X, Y, Z)\\right)\$$" ], "text/latex": [ "$\\displaystyle \\left(\\mathbb{R}^5,({\\tau}, W, X, Y, Z)\\right)$" ], "text/plain": [ "Chart (R^5, (tau, W, X, Y, Z))" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X5. = R5.chart(r'tau:\\tau W X Y Z')\n", "X5" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Differentiable map Psi from the 4-dimensional differentiable manifold E to the 5-dimensional differentiable manifold R^5\n" ] }, { "data": { "text/html": [ "\$$\\displaystyle \\begin{array}{llcl} \\Psi:& E & \\longrightarrow & \\mathbb{R}^5 \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, W, X, Y, Z\\right) = \\left({\\tau}, \\cos\\left({\\chi}\\right), \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)\\right) \\end{array}\$$" ], "text/latex": [ "$\\displaystyle \\begin{array}{llcl} \\Psi:& E & \\longrightarrow & \\mathbb{R}^5 \\\\ & \\left({\\tau}, {\\chi}, {\\theta}, {\\phi}\\right) & \\longmapsto & \\left({\\tau}, W, X, Y, Z\\right) = \\left({\\tau}, \\cos\\left({\\chi}\\right), \\cos\\left({\\phi}\\right) \\sin\\left({\\chi}\\right) \\sin\\left({\\theta}\\right), \\sin\\left({\\chi}\\right) \\sin\\left({\\phi}\\right) \\sin\\left({\\theta}\\right), \\cos\\left({\\theta}\\right) \\sin\\left({\\chi}\\right)\\right) \\end{array}$" ], "text/plain": [ "Psi: E → R^5\n", " (tau, ch, th, ph) ↦ (tau, W, X, Y, Z) = (tau, cos(ch), cos(ph)*sin(ch)*sin(th), sin(ch)*sin(ph)*sin(th), cos(th)*sin(ch))" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Psi = E.diff_map(R5, {(XE, X5): [tau,\n", " cos(ch),\n", " sin(ch)*sin(th)*cos(ph), \n", " sin(ch)*sin(th)*sin(ph), \n", " sin(ch)*cos(th)]},\n", " name='Psi', latex_name=r'\\Psi')\n", "print(Psi)\n", "Psi.display()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Einstein cylinder:" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "