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      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
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      <p bold="true">Concluded from collaboration</p>
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      <p bold="true">Identify each component</p>
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      <description active="true" position="Right" lang="eng">
        <p>?</p>
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        <e type="operand">ratio.Am.b_V</e>
        <e type="operand">70</e>
        <e type="operand">10</e>
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        <e type="operand">107</e>
        <e type="operand">10</e>
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        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
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    <math>
      <description active="true" position="Right" lang="eng">
        <p>?</p>
      </description>
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        <e type="operand">ρ.a</e>
        <e type="operand">7850</e>
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        <e type="operand">α.c</e>
        <e type="operand">25</e>
        <e type="operator" args="2">:</e>
        <e type="operand">σ</e>
        <e type="operand">5.67</e>
        <e type="operand">10</e>
        <e type="operand">8</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">/</e>
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        <e type="operand">3</e>
        <e type="operand">1</e>
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    <math>
      <description active="true" position="Right" lang="eng">
        <p>?</p>
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        <e type="operand">Φ</e>
        <e type="operand">1.0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">ε.m</e>
        <e type="operand">0.7</e>
        <e type="operator" args="2">:</e>
        <e type="operand">ε.f</e>
        <e type="operand">1.0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">sys</e>
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    <math>
      <input>
        <e type="operand">k.sh</e>
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      <result action="numeric">
        <e type="operand">0.5888</e>
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  <region id="7" left="18" top="225" width="222" height="32" color="#000000" bgColor="#ffff80" fontSize="10">
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      <description active="false" position="Right" lang="eng">
        <p />
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        <e type="operand">t</e>
        <e type="function" args="1">θ.g</e>
        <e type="operand">20</e>
        <e type="operand">345</e>
        <e type="operand">8</e>
        <e type="operand">t</e>
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        <e type="operand">1</e>
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        <e type="operand">C.a</e>
        <e type="operand">425</e>
        <e type="operand">7.73</e>
        <e type="operand">10</e>
        <e type="operand">1</e>
        <e type="operator" args="2">^</e>
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        <e type="operator" args="2">*</e>
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        <e type="operand">1.69</e>
        <e type="operand">10</e>
        <e type="operand">3</e>
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        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">-</e>
        <e type="operand">2.22</e>
        <e type="operand">10</e>
        <e type="operand">6</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">/</e>
        <e type="operand">θ.a</e>
        <e type="operand">3</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">666</e>
        <e type="operand">13002</e>
        <e type="operand">738</e>
        <e type="operand">θ.a</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">+</e>
        <e type="operand">545</e>
        <e type="operand">17820</e>
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        <e type="operand">731</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">+</e>
        <e type="operand">650</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">mat</e>
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      <p bold="true">system segments specifications</p>
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        <e type="operand">24.36475</e>
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        <e type="operand">120</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">mat</e>
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    <math>
      <input>
        <e type="operand">init</e>
        <e type="operand">20</e>
        <e type="operand">600</e>
        <e type="operand">735</e>
        <e type="operand">900</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">mat</e>
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    </math>
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    <math>
      <input>
        <e type="operand">pts</e>
        <e type="operand">200</e>
        <e type="operand">100</e>
        <e type="operand">100</e>
        <e type="operand">2000</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">mat</e>
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    <math>
      <input>
        <e type="operand">t0</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">time</e>
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    <math optimize="2">
      <description active="true" position="Top" lang="eng">
        <p>collect the piecewise DE ... export vector algo style  d(t,θ.a)</p>
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        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">C.a</e>
        <e type="function" preserve="true" args="1">length</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">d</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">k.sh</e>
        <e type="operand">C.a</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">ρ.a</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="operand">ratio.Am_V</e>
        <e type="operator" args="2">*</e>
        <e type="operand">α.c</e>
        <e type="operand">t</e>
        <e type="function" args="1">θ.g</e>
        <e type="operand">θ.a</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operand">Φ</e>
        <e type="operand">ε.m</e>
        <e type="operator" args="2">*</e>
        <e type="operand">ε.f</e>
        <e type="operator" args="2">*</e>
        <e type="operand">σ</e>
        <e type="operator" args="2">*</e>
        <e type="operand">t</e>
        <e type="function" args="1">θ.g</e>
        <e type="bracket">(</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operand">θ.a</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">-</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
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    <math>
      <description active="true" position="Right" lang="eng">
        <p>solving vector</p>
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        <e type="operand">t</e>
        <e type="operand">θ.a</e>
        <e type="function" args="2">d</e>
        <e type="operand">d</e>
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    <math optimize="2" evaluate="false">
      <description active="true" position="Top" lang="eng">
        <p>collect the piecewise DE solutions from incremented "for loop"</p>
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        <e type="operand">s</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
        <e type="bracket">(</e>
        <e type="operand" style="string">auto-incrementing counter, accumulates sols in Res[s]</e>
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        <e type="operand">i</e>
        <e type="operand">2</e>
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        <e type="operand">Res</e>
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        <e type="operand">init</e>
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        <e type="operand">pts</e>
        <e type="operand">s</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">t</e>
        <e type="operand">θ.a</e>
        <e type="function" args="2">d</e>
        <e type="operand">s</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="5">dn_GearsBDF</e>
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        <e type="operand">s</e>
        <e type="operand">s</e>
        <e type="operand">1</e>
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        <e type="operand">2</e>
        <e type="operand">1</e>
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        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
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    <text lang="eng">
      <p>native</p>
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    <area single="true" collapsed="true" />
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    <math optimize="2">
      <description active="true" position="Top" lang="eng">
        <p>collect the piecewise DE solutions from incremented "for loop"</p>
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        <e type="operand">s</e>
        <e type="operand">1</e>
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        <e type="operand" style="string">auto-incrementing counter, accumulates sols in Res[s]</e>
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        <e type="operand">i</e>
        <e type="operand">2</e>
        <e type="operand">join</e>
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        <e type="operand">1</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="3">mat</e>
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        <e type="operand">init</e>
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        <e type="function" preserve="true" args="2">el</e>
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        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">join</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">pts</e>
        <e type="operand">s</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">t</e>
        <e type="operand">θ.a</e>
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        <e type="operand">s</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" preserve="true" args="5">dn_GearsBDF</e>
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        <e type="operand">s</e>
        <e type="operand">s</e>
        <e type="operand">1</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="function" preserve="true" args="3">for</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
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    <text lang="eng">
      <p>vectorized</p>
    </text>
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    <text lang="eng">
      <p> ◄ seemingly ...slightly faster. </p>
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    <math decimalPlaces="1">
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        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">time</e>
        <e type="operand">t0</e>
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      <result action="numeric">
        <e type="operand">1.9</e>
        <e type="operand" style="unit">s</e>
        <e type="operator" args="2">*</e>
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    <math>
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        <e type="operand">jct</e>
        <e type="operand">54.7</e>
        <e type="operand">900</e>
        <e type="operand" style="string">+</e>
        <e type="operand">30</e>
        <e type="operand" style="string">black</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
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    <math>
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        <e type="operand">ODE</e>
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        <e type="operand">Res</e>
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        <e type="operand">Res</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">Res</e>
        <e type="operand">4</e>
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        <e type="function" preserve="true" args="1">rows</e>
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      <result action="numeric">
        <e type="operand">2404</e>
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        <e type="operand">vy</e>
        <e type="operand">ODE</e>
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        <e type="function" preserve="true" args="2">col</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
        <e type="operand">x</e>
        <e type="function" args="1">sol</e>
        <e type="operand">vx</e>
        <e type="operand">vy</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="3">ainterp</e>
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        <e type="operand">track</e>
        <e type="operand">120</e>
        <e type="operand">256</e>
        <e type="operand">64</e>
        <e type="operand">256</e>
        <e type="operand">u</e>
        <e type="operand">u</e>
        <e type="function" args="1">sol</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
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        <e type="operand">Res</e>
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        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">Res</e>
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        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">Res</e>
        <e type="operand">3</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand" style="string" />
        <e type="operand" style="string" />
        <e type="operand">Res</e>
        <e type="operand">4</e>
        <e type="function" preserve="true" args="2">el</e>
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        <e type="operand">track</e>
        <e type="operand">8</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="10">sys</e>
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      <input>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="1">time</e>
        <e type="operand">t0</e>
        <e type="operator" args="2">-</e>
      </input>
      <result action="numeric">
        <e type="operand">4.7</e>
        <e type="operand" style="unit">s</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
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    <math>
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        <e type="operand">u</e>
        <e type="function" args="1">sol</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">100</e>
        <e type="operand">1015.0271</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
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      </result>
    </math>
  </region>
  <region id="33" top="1359" color="#ff0000" bgColor="#ebebeb">
    <area collapsed="true">
      <title lang="eng">
        <p>     DEcimate optional     </p>
      </title>
    </area>
    <region id="34" left="18" top="1386" width="379" height="177" border="true" color="#000000" bgColor="#ffffe1" fontSize="10">
      <math optimize="2" exponentialThreshold="3">
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          <e type="operand">n</e>
          <e type="function" args="2">Decimate</e>
          <e type="operand" style="string">collect every 'n' pairs</e>
          <e type="operand">range</e>
          <e type="operand">1</e>
          <e type="operand">data</e>
          <e type="function" preserve="true" args="1">rows</e>
          <e type="operand">n</e>
          <e type="function" preserve="true" args="3">range</e>
          <e type="operator" args="2">:</e>
          <e type="operand">k</e>
          <e type="operand">1</e>
          <e type="operator" args="2">:</e>
          <e type="operand">i</e>
          <e type="operand">range</e>
          <e type="operand">u</e>
          <e type="operand">k</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">data</e>
          <e type="operand">i</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="3">el</e>
          <e type="operator" args="2">:</e>
          <e type="operand">v</e>
          <e type="operand">k</e>
          <e type="function" preserve="true" args="2">el</e>
          <e type="operand">data</e>
          <e type="operand">i</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="3">el</e>
          <e type="operator" args="2">:</e>
          <e type="operand">k</e>
          <e type="operand">k</e>
          <e type="operand">1</e>
          <e type="operator" args="2">+</e>
          <e type="operator" args="2">:</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="5">line</e>
          <e type="function" preserve="true" args="3">for</e>
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          <e type="operand">3</e>
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          <e type="function" preserve="true" args="5">line</e>
          <e type="operand">3</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="5">line</e>
          <e type="operator" args="2">:</e>
        </input>
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      <math optimize="2">
        <input>
          <e type="operand">New</e>
          <e type="operand">ODE</e>
          <e type="operand">5</e>
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          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
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      <math>
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          <e type="operand">New</e>
          <e type="function" preserve="true" args="1">rows</e>
        </input>
        <result action="numeric">
          <e type="operand">601</e>
        </result>
      </math>
    </region>
    <region id="37" top="1575" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
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  </region>
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    </math>
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    <math>
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        <e type="function" preserve="true" args="4">mat</e>
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      <result action="numeric">
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        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
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