Notes/gis_obs_angle.svg

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->

<svg
   xmlns:ns0="http://www.iki.fi/pav/software/textext/"
   xmlns:dc="http://purl.org/dc/elements/1.1/"
   xmlns:cc="http://creativecommons.org/ns#"
   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
   xmlns:svg="http://www.w3.org/2000/svg"
   xmlns="http://www.w3.org/2000/svg"
   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
   width="297mm"
   height="210mm"
   viewBox="0 0 297 210"
   version="1.1"
   id="svg8"
   inkscape:version="0.92.3 (2405546, 2018-03-11)"
   sodipodi:docname="gis_obs_angle.svg">
  <sodipodi:namedview
     id="base"
     pagecolor="#ffffff"
     bordercolor="#666666"
     borderopacity="1.0"
     inkscape:pageopacity="0.0"
     inkscape:pageshadow="2"
     inkscape:zoom="1.2622844"
     inkscape:cx="562.64725"
     inkscape:cy="344.93311"
     inkscape:document-units="mm"
     inkscape:current-layer="g1672"
     showgrid="false"
     inkscape:window-width="1853"
     inkscape:window-height="1021"
     inkscape:window-x="67"
     inkscape:window-y="31"
     inkscape:window-maximized="1"
     objecttolerance="1">
    <inkscape:grid
       enabled="false"
       snapvisiblegridlinesonly="false"
       id="grid3853"
       type="xygrid" />
  </sodipodi:namedview>
  <defs
     id="defs2">
    <inkscape:path-effect
       only_selected="false"
       apply_with_weight="true"
       apply_no_weight="true"
       helper_size="0"
       steps="2"
       weight="33.333333"
       is_visible="true"
       id="path-effect1676"
       effect="bspline" />
    <marker
       inkscape:collect="always"
       inkscape:isstock="true"
       style="overflow:visible"
       id="marker5138"
       refX="0"
       refY="0"
       orient="auto"
       inkscape:stockid="Arrow1Mend">
      <path
         transform="matrix(-0.4,0,0,-0.4,-4,0)"
         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1.00000003pt;stroke-opacity:1"
         d="M 0,0 5,-5 -12.5,0 5,5 Z"
         id="path5136"
         inkscape:connector-curvature="0" />
    </marker>
    <marker
       inkscape:isstock="true"
       style="overflow:visible"
       id="marker5138-5"
       refX="0"
       refY="0"
       orient="auto"
       inkscape:stockid="Arrow1Mend">
      <path
         transform="matrix(-0.4,0,0,-0.4,-4,0)"
         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1.00000003pt;stroke-opacity:1"
         d="M 0,0 5,-5 -12.5,0 5,5 Z"
         id="path5136-3"
         inkscape:connector-curvature="0" />
    </marker>
    <marker
       inkscape:stockid="Arrow1Mend"
       orient="auto"
       refY="0"
       refX="0"
       id="marker10973"
       style="overflow:visible"
       inkscape:isstock="true">
      <path
         inkscape:connector-curvature="0"
         id="path10971"
         d="M 0,0 5,-5 -12.5,0 5,5 Z"
         style="fill:#008000;fill-opacity:1;fill-rule:evenodd;stroke:#008000;stroke-width:1.00000003pt;stroke-opacity:1"
         transform="matrix(-0.4,0,0,-0.4,-4,0)" />
    </marker>
    <marker
       inkscape:isstock="true"
       style="overflow:visible"
       id="marker7907-2"
       refX="0"
       refY="0"
       orient="auto"
       inkscape:stockid="Arrow1Mend">
      <path
         transform="matrix(-0.4,0,0,-0.4,-4,0)"
         style="fill:#008000;fill-opacity:1;fill-rule:evenodd;stroke:#008000;stroke-width:1.00000003pt;stroke-opacity:1"
         d="M 0,0 5,-5 -12.5,0 5,5 Z"
         id="path7905-8"
         inkscape:connector-curvature="0" />
    </marker>
  </defs>
  <metadata
     id="metadata5">
    <rdf:RDF>
      <cc:Work
         rdf:about="">
        <dc:format>image/svg+xml</dc:format>
        <dc:type
           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
        <dc:title />
        <cc:license
           rdf:resource="http://creativecommons.org/licenses/by-nc-sa/4.0/" />
      </cc:Work>
      <cc:License
         rdf:about="http://creativecommons.org/licenses/by-nc-sa/4.0/">
        <cc:permits
           rdf:resource="http://creativecommons.org/ns#Reproduction" />
        <cc:permits
           rdf:resource="http://creativecommons.org/ns#Distribution" />
        <cc:requires
           rdf:resource="http://creativecommons.org/ns#Notice" />
        <cc:requires
           rdf:resource="http://creativecommons.org/ns#Attribution" />
        <cc:prohibits
           rdf:resource="http://creativecommons.org/ns#CommercialUse" />
        <cc:permits
           rdf:resource="http://creativecommons.org/ns#DerivativeWorks" />
        <cc:requires
           rdf:resource="http://creativecommons.org/ns#ShareAlike" />
      </cc:License>
    </rdf:RDF>
  </metadata>
  <g
     transform="translate(0,-87)"
     id="layer1"
     inkscape:groupmode="layer"
     inkscape:label="Calque 1">
    <g
       transform="matrix(0.34148157,0,0,0.34148157,-8.7811631,111.19765)"
       id="g1672">
      <circle
         r="27.316223"
         cy="286.85818"
         cx="155.00452"
         id="path819"
         style="fill:#ececec;fill-opacity:1;stroke:#000000;stroke-width:1.17136629;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1" />
      <circle
         r="40.974331"
         cy="287.04501"
         cx="155.48387"
         id="path823"
         style="fill:none;fill-opacity:1;stroke:#66ff00;stroke-width:1.17136629;stroke-miterlimit:4;stroke-dasharray:9.37093033,4.68546516;stroke-dashoffset:0;stroke-opacity:1" />
      <path
         sodipodi:nodetypes="cc"
         inkscape:connector-curvature="0"
         id="path5128"
         d="m 53.165264,287.58268 814.103196,0"
         style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1.46420789;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#marker5138)" />
      <path
         sodipodi:nodetypes="cc"
         inkscape:connector-curvature="0"
         id="path5128-5"
         d="M 155.26608,334.69969 V 179.66954"
         style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1.46420786;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#marker5138-5)" />
      <path
         sodipodi:nodetypes="csc"
         inkscape:connector-curvature="0"
         id="path3834"
         d="m 77.447928,256.29601 c 42.260782,-53.1903 102.737432,-50.27576 190.173542,-43.71805 89.86878,6.74015 271.05194,29.14536 556.67652,73.59205"
         style="fill:none;stroke:#008000;stroke-width:1.75704944;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" />
      <path
         sodipodi:nodetypes="cc"
         inkscape:connector-curvature="0"
         id="path3836"
         d="m 156.14101,288.35977 653.5345,99.35491"
         style="fill:none;stroke:#000000;stroke-width:1.17136629;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;stroke-miterlimit:4;stroke-dasharray:none" />
      <path
         sodipodi:nodetypes="cc"
         inkscape:connector-curvature="0"
         id="path3836-3"
         d="M 824.29799,286.17001 808.85493,387.75106"
         style="fill:none;stroke:#000000;stroke-width:0.87852472;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:3.51409887,3.51409887;stroke-opacity:1;stroke-dashoffset:0" />
      <circle
         r="4.9070621"
         cy="286.92166"
         cx="823.7804"
         id="path3874"
         style="fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.31182578;stroke-miterlimit:4;stroke-dasharray:1.24730297, 1.24730297;stroke-dashoffset:0" />
      <circle
         r="4.9070621"
         cy="255.75757"
         cx="79.039711"
         id="path3874-6"
         style="fill:#008000;fill-opacity:1;stroke:none;stroke-width:0.31182578;stroke-miterlimit:4;stroke-dasharray:1.24730297, 1.24730297000000001;stroke-dashoffset:0" />
      <path
         sodipodi:nodetypes="cc"
         inkscape:connector-curvature="0"
         id="path3891"
         d="m 824.07764,262.30346 v 48.05816"
         style="fill:#784421;stroke:#784421;stroke-width:2.92841573;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1" />
      <g
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
         id="content-2"
         transform="matrix(3.26395,0,0,-3.26395,120.89733,2583.1224)"
         xml:space="preserve"
         stroke-miterlimit="10.433"
         font-style="normal"
         font-variant="normal"
         font-weight="normal"
         font-stretch="normal"
         font-size-adjust="none"
         letter-spacing="normal"
         word-spacing="normal"
         ns0:text="$x$"
         ns0:preamble="/home/eric/BHLectures/Notes/latex_inkscape.ini">
<path
   style="fill:#000000;stroke-width:0"
   inkscape:connector-curvature="0"
   d="m 226.76,710.12 0.01,0.03 0.01,0.03 v 0.03 l 0.01,0.04 0.01,0.04 0.02,0.04 0.01,0.04 0.01,0.05 0.02,0.04 0.02,0.05 0.02,0.05 0.02,0.05 0.02,0.05 0.02,0.05 0.03,0.05 0.03,0.05 0.03,0.05 0.03,0.04 0.03,0.05 0.04,0.04 0.03,0.05 0.04,0.04 0.05,0.04 0.04,0.03 0.05,0.03 0.04,0.03 0.03,0.01 0.03,0.02 0.02,0.01 0.03,0.01 0.03,0.01 h 0.03 l 0.02,0.01 0.03,0.01 h 0.03 0.04 l 0.03,0.01 h 0.03 c 0.05,0 0.29,0 0.5,-0.13 -0.28,-0.05 -0.48,-0.3 -0.48,-0.54 0,-0.16 0.11,-0.35 0.38,-0.35 0.22,0 0.54,0.18 0.54,0.58 0,0.52 -0.59,0.66 -0.93,0.66 -0.58,0 -0.93,-0.53 -1.05,-0.76 -0.25,0.66 -0.78,0.76 -1.07,0.76 -1.04,0 -1.61,-1.29 -1.61,-1.53 0,-0.1 0.1,-0.1 0.12,-0.1 0.08,0 0.11,0.02 0.13,0.11 0.34,1.05 1,1.3 1.34,1.3 0.18,0 0.53,-0.09 0.53,-0.67 0,-0.31 -0.16,-0.97 -0.53,-2.36 -0.16,-0.62 -0.51,-1.04 -0.95,-1.04 -0.06,0 -0.29,0 -0.5,0.13 0.25,0.05 0.47,0.26 0.47,0.54 0,0.27 -0.22,0.35 -0.37,0.35 -0.3,0 -0.55,-0.26 -0.55,-0.58 0,-0.46 0.5,-0.65 0.94,-0.65 0.66,0 1.02,0.69 1.05,0.75 0.11,-0.37 0.47,-0.75 1.07,-0.75 1.03,0 1.6,1.28 1.6,1.53 0,0.1 -0.09,0.1 -0.12,0.1 -0.09,0 -0.11,-0.05 -0.13,-0.11 -0.33,-1.07 -1.01,-1.31 -1.33,-1.31 -0.39,0 -0.55,0.32 -0.55,0.66 0,0.22 0.06,0.44 0.17,0.87 z"
   id="path6892-9" />
</g>      <path
         sodipodi:nodetypes="cc"
         inkscape:connector-curvature="0"
         id="path10963"
         d="m 453.94102,232.72361 24.13316,3.22902"
         style="fill:none;fill-rule:evenodd;stroke:#008000;stroke-width:2.049891;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#marker10973)" />
      <path
         transform="scale(1,-1)"
         d="m 241.38353,-301.92568 a 86.315247,86.315247 0 0 1 1.05171,15.47035"
         sodipodi:open="true"
         sodipodi:end="0.022065544"
         sodipodi:start="6.125364"
         sodipodi:ry="86.315247"
         sodipodi:rx="86.315247"
         sodipodi:cy="-288.35977"
         sodipodi:cx="156.14101"
         sodipodi:type="arc"
         id="path7897-9"
         style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:2.34273258;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1" />
      <path
         transform="scale(-1,1)"
         d="m -730.6699,271.7718 a 86.315239,86.315239 0 0 1 1.05171,15.47035"
         sodipodi:open="true"
         sodipodi:end="0.022065544"
         sodipodi:start="6.125364"
         sodipodi:ry="86.315239"
         sodipodi:rx="86.315239"
         sodipodi:cy="285.33771"
         sodipodi:cx="-815.91241"
         sodipodi:type="arc"
         id="path7897-9-7"
         style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:2.34273258;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1" />
      <path
         sodipodi:nodetypes="ccc"
         inkscape:connector-curvature="0"
         id="path4810"
         d="m 796.01824,385.59543 2.00931,-13.08862 12.95133,1.85019"
         style="fill:none;stroke:#000000;stroke-width:0.77481002px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
      <g
         id="g957"
         transform="translate(3.6828941,8.5934197)">
        <rect
           y="249.47501"
           x="692.93256"
           height="34.373676"
           width="23.324997"
           id="rect951"
           style="fill:#ffffff;fill-opacity:1;stroke:none;stroke-width:1.58219802;stroke-miterlimit:4;stroke-dasharray:6.32879174, 3.16439586;stroke-dashoffset:0;stroke-opacity:1" />
        <g
           id="content"
           transform="matrix(3.26395,0,0,-3.26395,-30.657691,2590.277)"
           xml:space="preserve"
           stroke-miterlimit="10.433"
           font-style="normal"
           font-variant="normal"
           font-weight="normal"
           font-stretch="normal"
           font-size-adjust="none"
           letter-spacing="normal"
           word-spacing="normal"
           ns0:text="$\\hat{b}$"
           ns0:preamble="/home/eric/BHLectures/Notes/latex_inkscape.ini"
           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
<polygon
   style="fill:#000000;stroke-width:0"
   points="226.9,715.3 225.57,716.65 224.24,715.3 224.41,715.12 225.57,716.13 226.72,715.12 "
   id="polygon910" />
<path
   style="fill:#000000;stroke-width:0"
   inkscape:connector-curvature="0"
   d="m 225.82,713.91 v 0 h -0.01 v 0 0 0.01 0 0 0.01 0 0.01 0 0 0.01 0 l -0.01,0.01 v 0 0.01 0 l -0.01,0.01 v 0 l -0.01,0.01 v 0 0 0 l -0.01,0.01 v 0 0 h -0.01 v 0 0.01 h -0.01 v 0 0 h -0.01 v 0 h -0.01 v 0 l -0.01,0.01 v 0 h -0.01 v 0 h -0.01 v 0 h -0.01 v 0 c -0.23,0 -0.96,-0.08 -1.22,-0.1 -0.08,-0.01 -0.19,-0.02 -0.19,-0.2 0,-0.12 0.09,-0.12 0.24,-0.12 0.48,0 0.5,-0.07 0.5,-0.17 0,-0.07 -0.09,-0.4 -0.14,-0.61 l -0.82,-3.24 c -0.12,-0.5 -0.16,-0.66 -0.16,-1 0,-0.95 0.53,-1.56 1.27,-1.56 v 0.21 c -0.34,0 -0.67,0.27 -0.67,1.01 0,0.19 0,0.37 0.16,1 l 0.22,0.92 c 0.06,0.21 0.06,0.23 0.15,0.34 0.49,0.65 0.93,0.8 1.19,0.8 0.36,0 0.63,-0.3 0.63,-0.94 0,-0.58 -0.33,-1.72 -0.51,-2.1 -0.33,-0.67 -0.78,-1.03 -1.17,-1.03 v -0.21 c 1.17,0 2.4,1.48 2.4,2.91 0,0.9 -0.53,1.59 -1.33,1.59 -0.45,0 -0.86,-0.29 -1.16,-0.6 z"
   id="path912" />
</g>      </g>
      <g
         transform="translate(-438.87822,27.007878)"
         id="g957-7">
        <rect
           y="249.47501"
           x="692.93256"
           height="34.373676"
           width="23.324997"
           id="rect951-5"
           style="fill:#ffffff;fill-opacity:1;stroke:none;stroke-width:1.58219802;stroke-miterlimit:4;stroke-dasharray:6.32879174, 3.16439586;stroke-dashoffset:0;stroke-opacity:1" />
        <g
           id="content-3"
           transform="matrix(3.26395,0,0,-3.26395,-30.657691,2590.277)"
           xml:space="preserve"
           stroke-miterlimit="10.433"
           font-style="normal"
           font-variant="normal"
           font-weight="normal"
           font-stretch="normal"
           font-size-adjust="none"
           letter-spacing="normal"
           word-spacing="normal"
           ns0:text="$\\hat{b}$"
           ns0:preamble="/home/eric/BHLectures/Notes/latex_inkscape.ini"
           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
<polygon
   style="fill:#000000;stroke-width:0"
   points="226.72,715.12 226.9,715.3 225.57,716.65 224.24,715.3 224.41,715.12 225.57,716.13 "
   id="polygon910-5" />
<path
   style="fill:#000000;stroke-width:0"
   inkscape:connector-curvature="0"
   d="m 225.82,713.91 v 0 h -0.01 v 0 0 0.01 0 0 0.01 0 0.01 0 0 0.01 0 l -0.01,0.01 v 0 0.01 0 l -0.01,0.01 v 0 l -0.01,0.01 v 0 0 0 l -0.01,0.01 v 0 0 h -0.01 v 0 0.01 h -0.01 v 0 0 h -0.01 v 0 h -0.01 v 0 l -0.01,0.01 v 0 h -0.01 v 0 h -0.01 v 0 h -0.01 v 0 c -0.23,0 -0.96,-0.08 -1.22,-0.1 -0.08,-0.01 -0.19,-0.02 -0.19,-0.2 0,-0.12 0.09,-0.12 0.24,-0.12 0.48,0 0.5,-0.07 0.5,-0.17 0,-0.07 -0.09,-0.4 -0.14,-0.61 l -0.82,-3.24 c -0.12,-0.5 -0.16,-0.66 -0.16,-1 0,-0.95 0.53,-1.56 1.27,-1.56 v 0.21 c -0.34,0 -0.67,0.27 -0.67,1.01 0,0.19 0,0.37 0.16,1 l 0.22,0.92 c 0.06,0.21 0.06,0.23 0.15,0.34 0.49,0.65 0.93,0.8 1.19,0.8 0.36,0 0.63,-0.3 0.63,-0.94 0,-0.58 -0.33,-1.72 -0.51,-2.1 -0.33,-0.67 -0.78,-1.03 -1.17,-1.03 v -0.21 c 1.17,0 2.4,1.48 2.4,2.91 0,0.9 -0.53,1.59 -1.33,1.59 -0.45,0 -0.86,-0.29 -1.16,-0.6 z"
   id="path912-6" />
</g>      </g>
      <g
         id="g1045"
         transform="matrix(3.26395,0,0,-3.26395,-567.74641,2487.7698)"
         xml:space="preserve"
         stroke-miterlimit="10.433"
         font-style="normal"
         font-variant="normal"
         font-weight="normal"
         font-stretch="normal"
         font-size-adjust="none"
         letter-spacing="normal"
         word-spacing="normal"
         ns0:text="$y$"
         ns0:preamble="/home/eric/BHLectures/Notes/latex_inkscape.ini"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
<path
   style="fill:#000000;stroke-width:0"
   inkscape:connector-curvature="0"
   d="m 228.28,710.91 v 0.01 0 0.01 h 0.01 v 0.02 0.01 0.01 l 0.01,0.01 v 0.01 0 0.01 0.01 l 0.01,0.01 v 0.01 0 0.01 0 0.01 0.01 0 l 0.01,0.01 v 0 0.01 0.01 0.01 0.01 0.01 0.01 0 0.01 c 0,0.18 -0.14,0.27 -0.29,0.27 -0.1,0 -0.26,-0.06 -0.35,-0.21 -0.02,-0.05 -0.1,-0.36 -0.14,-0.54 -0.07,-0.26 -0.14,-0.52 -0.2,-0.79 l -0.45,-1.79 c -0.04,-0.15 -0.47,-0.85 -1.13,-0.85 -0.5,0 -0.61,0.44 -0.61,0.81 0,0.46 0.17,1.07 0.51,1.95 0.16,0.4 0.19,0.51 0.19,0.71 0,0.45 -0.31,0.82 -0.81,0.82 -0.95,0 -1.32,-1.44 -1.32,-1.53 0,-0.1 0.1,-0.1 0.12,-0.1 0.1,0 0.11,0.02 0.16,0.18 0.27,0.93 0.67,1.23 1.01,1.23 0.08,0 0.25,0 0.25,-0.32 0,-0.25 -0.1,-0.51 -0.17,-0.7 -0.4,-1.05 -0.58,-1.62 -0.58,-2.08 0,-0.89 0.63,-1.18 1.22,-1.18 0.39,0 0.72,0.16 1,0.44 -0.13,-0.51 -0.25,-1 -0.64,-1.53 -0.27,-0.34 -0.64,-0.62 -1.1,-0.62 -0.14,0 -0.59,0.03 -0.76,0.41 0.16,0 0.29,0 0.43,0.12 0.1,0.09 0.2,0.22 0.2,0.41 0,0.31 -0.27,0.35 -0.37,0.35 -0.23,0 -0.56,-0.16 -0.56,-0.65 0,-0.49 0.44,-0.86 1.06,-0.86 1.02,0 2.05,0.9 2.33,2.02 z"
   id="path1043" />
</g>      <g
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
         ns0:preamble="/home/eric/BHLectures/Notes/latex_inkscape.ini"
         ns0:text="$r_{\\mathscr{O}}$"
         text-anchor="start"
         word-spacing="normal"
         letter-spacing="normal"
         font-size-adjust="none"
         font-stretch="normal"
         font-weight="normal"
         font-variant="normal"
         font-style="normal"
         fill-opacity="1"
         fill-rule="evenodd"
         fill="none"
         stroke-opacity="1"
         stroke-dashoffset="0"
         stroke-dasharray="none"
         stroke-miterlimit="10.433"
         stroke-linejoin="miter"
         stroke-linecap="butt"
         stroke="black"
         xml:space="preserve"
         transform="matrix(3.26395,0,0,-3.26395,-252.24515,2617.2849)"
         id="g1155">
<path
   id="path1151"
   fill="black"
   stroke-width="0"
   d="M224.31,707.71 L224.31,707.7 L224.3,707.68 L224.3,707.67 L224.3,707.65 L224.29,707.62 L224.28,707.59 L224.28,707.56 L224.27,707.52 L224.26,707.49 L224.25,707.46 L224.25,707.45 L224.25,707.43 L224.24,707.42 L224.24,707.4 L224.24,707.39 L224.23,707.38 L224.23,707.36 L224.23,707.35 L224.23,707.34 L224.23,707.33 L224.22,707.32 L224.22,707.31 L224.22,707.3 L224.22,707.3 L224.22,707.29 L224.22,707.28 C224.22,707.1,224.36,707.02,224.51,707.02 C224.63,707.02,224.81,707.09,224.88,707.29 C224.9,707.33,225.24,708.68,225.28,708.86 C225.36,709.19,225.54,709.89,225.6,710.16 C225.64,710.28,225.91,710.75,226.15,710.97 C226.23,711.04,226.52,711.3,226.95,711.3 C227.21,711.3,227.36,711.18,227.37,711.18 C227.07,711.13,226.85,710.89,226.85,710.63 C226.85,710.47,226.96,710.28,227.23,710.28 C227.5,710.28,227.78,710.51,227.78,710.87 C227.78,711.22,227.46,711.52,226.95,711.52 C226.3,711.52,225.87,711.03,225.68,710.75 C225.6,711.2,225.24,711.52,224.77,711.52 C224.31,711.52,224.12,711.13,224.03,710.95 C223.85,710.61,223.72,710.02,223.72,709.99 C223.72,709.89,223.82,709.89,223.84,709.89 C223.94,709.89,223.95,709.9,224.01,710.11 C224.18,710.82,224.38,711.3,224.74,711.3 C224.91,711.3,225.05,711.22,225.05,710.84 C225.05,710.63,225.02,710.52,224.89,710.01 Z " />
<path
   id="path1153"
   fill="black"
   stroke-width="0"
   d="M233.86,710.19 L233.83,710.22 L233.8,710.24 L233.77,710.27 L233.74,710.29 L233.71,710.31 L233.68,710.33 L233.65,710.35 L233.61,710.37 L233.58,710.39 L233.54,710.4 L233.51,710.42 L233.47,710.43 L233.43,710.45 L233.39,710.46 L233.35,710.47 L233.31,710.48 L233.27,710.5 L233.23,710.51 L233.19,710.51 L233.14,710.52 L233.06,710.54 L232.97,710.55 L232.88,710.56 L232.78,710.56 L232.69,710.57 L232.59,710.57 L232.57,710.37 C233.06,710.37,233.46,710.28,233.67,710.06 C233.75,709.98,233.8,709.88,233.8,709.75 C233.8,709.63,233.76,709.49,233.65,709.33 C233.56,709.21,233.44,709.1,233.3,709.02 C233.25,708.98,233.19,708.96,233.14,708.94 C233.04,709.36,232.69,709.62,232.14,709.62 C231.84,709.62,231.49,709.4,231.2,709.17 C230.79,708.85,230.46,708.48,230.21,708.11 C229.78,707.52,229.66,706.96,229.6,706.45 V706.44 C229.6,706.4,229.63,706.36,229.67,706.35 C229.7,706.35,229.74,706.37,229.75,706.4 C229.76,706.4,229.77,706.4,229.78,706.4 C229.79,706.4,229.8,706.4,229.82,706.4 C229.84,706.42,229.86,706.44,229.86,706.47 C229.93,706.96,230.03,707.46,230.42,708.02 C230.68,708.36,230.97,708.72,231.35,709.02 C231.61,709.25,231.9,709.43,232.12,709.43 C232.56,709.43,232.79,709.21,232.83,708.89 C232.51,708.91,232.28,709.01,232.04,709.13 C232.03,709.14,232.02,709.14,232.01,709.14 C231.99,709.14,231.97,709.13,231.95,709.11 L231.93,709.09 L231.92,709.09 L231.9,709.06 C231.9,709.04,231.89,709.04,231.89,709.02 C231.89,709,231.9,708.98,231.92,708.97 C232.15,708.79,232.45,708.71,232.84,708.7 C232.81,708.25,232.54,707.7,232.14,707.14 C231.88,706.79,231.58,706.44,231.18,706.15 C230.86,705.92,230.5,705.76,230.24,705.76 C229.64,705.76,229.33,706.05,229.3,706.51 V706.58 C229.3,707.12,229.66,707.8,230.16,708.5 C230.49,708.97,230.86,709.44,231.37,709.84 C231.78,710.15,232.23,710.37,232.57,710.37 L232.59,710.57 C232.12,710.57,231.53,710.33,230.99,709.99 C230.39,709.6,229.88,709.11,229.52,708.6 C229.07,707.96,228.81,707.32,228.81,706.78 C228.81,706.68,228.82,706.58,228.84,706.48 C228.96,705.9,229.46,705.56,230.22,705.56 C230.58,705.56,231.02,705.74,231.42,706 C231.87,706.29,232.25,706.66,232.52,707.04 C232.93,707.61,233.17,708.18,233.17,708.67 V708.75 C233.26,708.77,233.34,708.81,233.42,708.86 C233.6,708.95,233.76,709.09,233.86,709.23 C234,709.42,234.05,709.59,234.05,709.75 C234.05,709.92,233.98,710.07,233.86,710.19 Z " />
</g>      <g
         id="g1269"
         transform="matrix(3.26395,0,0,-3.26395,91.491637,2662.0935)"
         xml:space="preserve"
         stroke-miterlimit="10.433"
         font-style="normal"
         font-variant="normal"
         font-weight="normal"
         font-stretch="normal"
         font-size-adjust="none"
         letter-spacing="normal"
         word-spacing="normal"
         ns0:text="$b$"
         ns0:preamble="/home/eric/BHLectures/Notes/latex_inkscape.ini"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
<path
   style="fill:#000000;stroke-width:0"
   inkscape:connector-curvature="0"
   d="m 225.82,713.91 v 0 h -0.01 v 0 0 0.01 0 0 0.01 0 0.01 0 0 0.01 0 l -0.01,0.01 v 0 0.01 0 l -0.01,0.01 v 0 l -0.01,0.01 v 0 0 0 l -0.01,0.01 v 0 0 h -0.01 v 0 0.01 h -0.01 v 0 0 h -0.01 v 0 h -0.01 v 0 l -0.01,0.01 v 0 h -0.01 v 0 h -0.01 v 0 h -0.01 v 0 c -0.23,0 -0.96,-0.08 -1.22,-0.1 -0.08,-0.01 -0.19,-0.02 -0.19,-0.2 0,-0.12 0.09,-0.12 0.24,-0.12 0.48,0 0.5,-0.07 0.5,-0.17 0,-0.07 -0.09,-0.4 -0.14,-0.61 l -0.82,-3.24 c -0.12,-0.5 -0.16,-0.66 -0.16,-1 0,-0.95 0.53,-1.56 1.27,-1.56 v 0.21 c -0.34,0 -0.67,0.27 -0.67,1.01 0,0.19 0,0.37 0.16,1 l 0.22,0.92 c 0.06,0.21 0.06,0.23 0.15,0.34 0.49,0.65 0.93,0.8 1.19,0.8 0.36,0 0.63,-0.3 0.63,-0.94 0,-0.58 -0.33,-1.72 -0.51,-2.1 -0.33,-0.67 -0.78,-1.03 -1.17,-1.03 v -0.21 c 1.17,0 2.4,1.48 2.4,2.91 0,0.9 -0.53,1.59 -1.33,1.59 -0.45,0 -0.86,-0.29 -1.16,-0.6 z"
   id="path1267" />
</g>      <g
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
         ns0:preamble="/home/eric/BHLectures/Notes/latex_inkscape.ini"
         ns0:text="$\\mathscr{O}$"
         word-spacing="normal"
         letter-spacing="normal"
         font-size-adjust="none"
         font-stretch="normal"
         font-weight="normal"
         font-variant="normal"
         font-style="normal"
         stroke-miterlimit="10.433"
         xml:space="preserve"
         transform="matrix(3.26395,0,0,-3.26395,83.512037,2562.0415)"
         id="g1387">
<path
   id="path1385"
   d="m 230.55,711.75 0.05,0.03 0.04,0.03 0.04,0.03 0.05,0.03 0.04,0.03 0.04,0.03 0.04,0.04 0.04,0.03 0.04,0.03 0.04,0.04 0.03,0.04 0.04,0.03 0.03,0.04 0.03,0.04 0.03,0.03 0.03,0.04 c 0.2,0.28 0.28,0.55 0.28,0.78 0,0.21 -0.07,0.4 -0.2,0.55 -0.32,0.4 -0.92,0.54 -1.59,0.54 -0.62,0 -1.42,-0.35 -2.13,-0.83 -0.84,-0.56 -1.53,-1.27 -2.04,-1.98 -0.68,-0.98 -1.1,-1.93 -1.1,-2.74 0,-0.08 0.01,-0.18 0.02,-0.27 0.1,-0.79 0.69,-1.29 1.7,-1.29 0.46,0 1.06,0.25 1.59,0.62 0.63,0.43 1.15,0.95 1.53,1.49 0.59,0.85 0.98,1.7 0.98,2.42 v 0.02 l -0.01,0.22 c -0.08,0.58 -0.49,0.98 -1.23,0.98 -0.38,0 -0.86,-0.33 -1.24,-0.64 -0.56,-0.46 -1.01,-0.99 -1.38,-1.51 -0.59,-0.84 -0.84,-1.64 -0.93,-2.36 v -0.04 c 0.01,-0.03 0.04,-0.05 0.07,-0.05 0.01,0 0.03,0 0.04,0.01 l 0.14,0.05 c 0.02,0.01 0.04,0.04 0.05,0.07 0.08,0.68 0.31,1.43 0.87,2.22 0.36,0.5 0.77,1 1.29,1.45 0.36,0.31 0.76,0.58 1.05,0.58 0.59,0 0.85,-0.34 0.86,-0.83 -0.4,0.02 -0.67,0.19 -0.99,0.34 -0.01,0.01 -0.03,0.01 -0.04,0.01 -0.02,0 -0.04,-0.01 -0.06,-0.02 l -0.05,-0.06 c -0.02,-0.02 -0.03,-0.04 -0.03,-0.06 0,-0.03 0.02,-0.06 0.05,-0.07 0.3,-0.17 0.65,-0.34 1.11,-0.35 -0.07,-0.67 -0.5,-1.47 -1.08,-2.28 -0.35,-0.5 -0.76,-1 -1.31,-1.43 -0.42,-0.33 -0.9,-0.57 -1.25,-0.57 -0.77,0 -1.12,0.44 -1.12,1.07 v 0.05 c 0.03,0.82 0.6,1.84 1.32,2.87 0.47,0.66 0.97,1.34 1.69,1.91 0.53,0.44 1.15,0.78 1.58,0.78 0.65,0 1.16,-0.13 1.43,-0.46 0.09,-0.11 0.14,-0.25 0.14,-0.4 0,-0.2 -0.08,-0.43 -0.26,-0.69 -0.12,-0.17 -0.28,-0.34 -0.49,-0.46 -0.08,-0.05 -0.15,-0.09 -0.23,-0.11 l 0.01,-0.22 c 0.12,0.04 0.24,0.1 0.35,0.15 z"
   inkscape:connector-curvature="0"
   style="fill:#000000;stroke-width:0" />
</g>      <g
         id="g1509"
         transform="matrix(3.26395,0,0,-3.26395,-390.39437,2516.066)"
         xml:space="preserve"
         stroke="black"
         stroke-linecap="butt"
         stroke-linejoin="miter"
         stroke-miterlimit="10.433"
         stroke-dasharray="none"
         stroke-dashoffset="0"
         stroke-opacity="1"
         fill="none"
         fill-rule="evenodd"
         fill-opacity="1"
         font-style="normal"
         font-variant="normal"
         font-weight="normal"
         font-stretch="normal"
         font-size-adjust="none"
         letter-spacing="normal"
         word-spacing="normal"
         text-anchor="start"
         ns0:text="$\\mathscr{L}$"
         ns0:preamble="/home/eric/BHLectures/Notes/latex_inkscape.ini"
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:#008000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
<path
   style="fill:#008000"
   d="M231.41,708.52 L231.41,708.52 L231.41,708.52 L231.41,708.53 L231.41,708.53 L231.41,708.54 L231.41,708.54 L231.4,708.55 L231.4,708.55 L231.4,708.55 L231.4,708.56 L231.4,708.56 L231.4,708.56 L231.39,708.57 L231.39,708.57 L231.39,708.57 L231.39,708.57 L231.38,708.58 L231.38,708.58 L231.38,708.58 L231.37,708.58 L231.37,708.58 L231.37,708.59 L231.36,708.59 L231.36,708.59 L231.36,708.59 L231.35,708.59 L231.35,708.59 L231.34,708.59 L231.34,708.59 L231.34,708.59 L231.33,708.59 L231.33,708.59 H231.21 C231.19,708.59,231.16,708.59,231.15,708.57 C230.69,707.93,229.77,707.44,229.13,707.44 C228.46,707.44,227.89,707.57,227.32,707.71 C227.96,708.1,228.53,708.6,228.93,709.16 L229.92,710.55 C231.21,710.74,232.54,711.24,233.27,712.29 C233.57,712.72,233.73,713.15,233.73,713.48 C233.73,713.94,233.45,714.25,232.85,714.25 L232.81,714.02 C233.18,714.02,233.36,713.82,233.36,713.51 C233.36,713.22,233.21,712.83,232.9,712.39 C232.28,711.53,231.21,711.04,230.12,710.83 C231.35,712.53,232.51,714.02,232.81,714.02 H232.81 L232.85,714.25 C231.87,714.25,230.41,712.48,229.11,710.7 C228.96,710.69,228.81,710.68,228.66,710.68 C227.63,710.68,226.91,711.05,226.91,711.71 C226.91,711.97,227.02,712.28,227.28,712.64 C227.76,713.32,228.71,713.86,229.38,713.86 C229.4,713.86,229.43,713.87,229.43,713.89 L229.48,713.95 C229.49,713.96,229.49,713.98,229.49,714 C229.49,714.03,229.48,714.05,229.46,714.06 C229.46,714.07,229.45,714.07,229.43,714.08 C229.34,714.11,229.24,714.12,229.13,714.12 C228.36,714.12,227.3,713.51,226.75,712.74 C226.47,712.34,226.35,711.99,226.35,711.71 C226.35,710.86,227.38,710.46,228.62,710.46 C228.73,710.46,228.84,710.46,228.94,710.47 C228.64,710.05,228.35,709.65,228.08,709.26 C227.71,708.74,227.22,708.25,226.7,707.87 C226.22,707.98,225.73,708.07,225.15,708.07 H225.09 L225.11,707.85 C225.59,707.85,225.99,707.76,226.36,707.63 C225.91,707.35,225.46,707.18,225.07,707.18 H225.07 C224.49,707.18,224.13,707.2,224.13,707.36 C224.13,707.4,224.14,707.44,224.18,707.49 C224.37,707.76,224.77,707.85,225.11,707.85 L225.09,708.07 C224.6,708.07,223.99,708.06,223.66,707.59 C223.59,707.49,223.55,707.4,223.55,707.33 C223.55,706.98,224.35,706.96,224.87,706.96 H225.03 C225.59,706.96,226.23,707.15,226.86,707.45 L226.98,707.4 C227.55,707.17,228.12,706.96,228.9,706.96 C229.71,706.96,230.82,707.66,231.39,708.47 C231.4,708.49,231.41,708.5,231.41,708.52 Z "
   stroke-width="0"
   fill="black"
   id="path1507" />
</g>      <g
         style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:#008000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
         ns0:preamble="/home/eric/BHLectures/Notes/latex_inkscape.ini"
         ns0:text="$S$"
         word-spacing="normal"
         letter-spacing="normal"
         font-size-adjust="none"
         font-stretch="normal"
         font-weight="normal"
         font-variant="normal"
         font-style="normal"
         stroke-miterlimit="10.433"
         xml:space="preserve"
         transform="matrix(3.26395,0,0,-3.26395,-675.16415,2557.7449)"
         id="g1635">
<path
   id="path1633"
   d="m 229.86,714.03 v 0 0.01 0 0 0.01 0 0 0.01 0 0.01 h -0.01 v 0 0.01 0 0.01 h -0.01 v 0 0.01 h -0.01 v 0 l -0.01,0.01 v 0 h -0.01 v 0.01 h -0.01 v 0 0 h -0.01 v 0 0 h -0.01 v 0.01 0 h -0.01 v 0 0 h -0.01 v 0 h -0.01 c -0.05,0 -0.05,-0.01 -0.18,-0.15 l -0.47,-0.57 c -0.26,0.47 -0.78,0.72 -1.43,0.72 -1.27,0 -2.46,-1.14 -2.46,-2.35 0,-0.8 0.53,-1.26 1.03,-1.41 l 1.07,-0.28 c 0.37,-0.08 0.92,-0.23 0.92,-1.05 0,-0.89 -0.82,-1.83 -1.8,-1.83 -0.64,0 -1.74,0.22 -1.74,1.45 0,0.24 0.05,0.48 0.06,0.54 0.01,0.04 0.02,0.05 0.02,0.07 0,0.1 -0.07,0.11 -0.12,0.11 -0.05,0 -0.07,-0.01 -0.1,-0.04 -0.04,-0.04 -0.6,-2.3 -0.6,-2.33 0,-0.06 0.05,-0.1 0.11,-0.1 0.05,0 0.06,0.01 0.18,0.14 l 0.49,0.57 c 0.43,-0.57 1.11,-0.71 1.68,-0.71 1.36,0 2.54,1.32 2.54,2.55 0,0.69 -0.34,1.02 -0.49,1.16 -0.23,0.23 -0.38,0.27 -1.27,0.5 -0.22,0.06 -0.58,0.16 -0.67,0.18 -0.27,0.09 -0.61,0.37 -0.61,0.9 0,0.81 0.8,1.65 1.75,1.65 0.83,0 1.44,-0.43 1.44,-1.54 0,-0.32 -0.04,-0.5 -0.04,-0.56 0,-0.01 0,-0.09 0.12,-0.09 0.1,0 0.11,0.02 0.14,0.19 z"
   style="fill:#008000;stroke-width:0"
   inkscape:connector-curvature="0" />
</g>      <path
         style="fill:none;fill-rule:evenodd;stroke:#803300;stroke-width:2.92841578;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
         d="m 778.25295,260.65398 45.42233,25.78026"
         id="path886"
         inkscape:connector-curvature="0" />
      <path
         style="fill:none;fill-rule:evenodd;stroke:#784421;stroke-width:2.92841578;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1"
         d="M 777.59917,314.34916 823.0215,288.5689"
         id="path886-3"
         inkscape:connector-curvature="0" />
    </g>
  </g>
</svg>