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<title>Linalg</title>
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<!-- * Created with wxMaxima version 19.07.0 * -->
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<p>Please enable JavaScript in order to get a 2d display of the equations embedded in this web page.</p>
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<p hidden="hidden">\( \DeclareMathOperator{\abs}{abs}
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<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
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|
|
|
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|
|
|
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|
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|
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|
|
|
</mrow>
|
|
|
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|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
</mfrac>
|
|
|
</mtd>
|
|
|
<mtd>
|
|
|
<mfrac>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<mo>+</mo>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
</mtd>
|
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|
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|
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|
|
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|
|
|
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|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
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|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
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|
|
|
</msub>
|
|
|
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|
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|
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|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
</mfrac>
|
|
|
</mtd>
|
|
|
</mtr>
|
|
|
<mtr>
|
|
|
<mtd>
|
|
|
<mfrac>
|
|
|
<mrow>
|
|
|
<mrow>
|
|
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<mi>Nl</mi>
|
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|
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|
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|
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<mo>+</mo>
|
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|
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|
</mrow>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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</mtd>
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|
|
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|
|
|
<msub>
|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
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|
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|
|
|
</mrow>
|
|
|
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|
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|
</mrow>
|
|
|
</mrow>
|
|
|
</mfrac>
|
|
|
</mtd>
|
|
|
<mtd>
|
|
|
<mfrac>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
</mfrac>
|
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|
</mtd>
|
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|
</mtr>
|
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|
<mtr>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
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|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
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|
|
|
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|
|
|
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|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
<mrow>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mrow>
|
|
|
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|
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|
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|
|
|
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|
|
|
<mi>g</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<mo>δ</mo>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
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|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
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|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
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|
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|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
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|
|
|
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|
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|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
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|
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|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
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|
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|
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|
</msub>
|
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|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
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|
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|
</mrow>
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|
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|
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|
<mrow>
|
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|
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|
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<mi>l</mi>
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|
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</msub>
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|
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|
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|
|
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|
|
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|
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<mi>Nsl</mi>
|
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|
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|
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|
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|
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<mo>+</mo>
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<mi>M</mi>
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|
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<mi>g</mi>
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|
|
<mi>Nl</mi>
|
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|
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|
</msub>
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|
|
<mo>+</mo>
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|
<mn>1</mn>
|
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|
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|
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|
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|
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|
</mrow>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
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|
</mrow>
|
|
|
<mo></mo>
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|
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<mi>l</mi>
|
|
|
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|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
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|
|
|
<mi>l</mi>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
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|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
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|
|
|
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|
|
|
<mo>(</mo>
|
|
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|
|
|
<msub>
|
|
|
<mi>l</mi>
|
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|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
<mi>Nl</mi>
|
|
|
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|
|
|
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|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
<mi>NSl</mi>
|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
<mi>Nsl</mi>
|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
<mi>l</mi>
|
|
|
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|
|
|
</msub>
|
|
|
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|
|
|
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|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
</mfrac>
|
|
|
</mtd>
|
|
|
<mtd>
|
|
|
<mfrac>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
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|
|
|
<mi>−</mi>
|
|
|
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|
|
|
<mi>l</mi>
|
|
|
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|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
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|
|
|
<mi>l</mi>
|
|
|
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|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mi>−</mi>
|
|
|
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|
|
|
<mi>Nsl</mi>
|
|
|
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|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
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|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
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|
|
|
<mi>l</mi>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
<mrow>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>g</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<mo>δ</mo>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
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|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>l</mi>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo>+</mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>NSl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>g</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<mo>δ</mo>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>l</mi>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>NSl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
</mfrac>
|
|
|
</mtd>
|
|
|
</mtr>
|
|
|
</mtable>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mtd>
|
|
|
</mlabeledtr>
|
|
|
</mtable>
|
|
|
</math>
|
|
|
<!-- Code cell -->
|
|
|
<table>
|
|
|
<tr>
|
|
|
<td>
|
|
|
<span class="prompt">(%i3)
|
|
|
</span>
|
|
|
</td>
|
|
|
<td>
|
|
|
<span class="input">
|
|
|
<span class="code_variable">b</span>
|
|
|
<span class="code_operator">:</span>
|
|
|
<span class="code_function">matrix</span>(
|
|
|
<br/> [
|
|
|
<span class="code_variable">b1</span>],
|
|
|
<br/> [
|
|
|
<span class="code_variable">b2</span>],
|
|
|
<br/> [
|
|
|
<span class="code_variable">b3</span>]
|
|
|
<br/>)
|
|
|
<span class="code_endofline">;</span>
|
|
|
</span>
|
|
|
</td>
|
|
|
</tr>
|
|
|
</table>
|
|
|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
|
|
|
<mtable>
|
|
|
<mlabeledtr columnalign="left">
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<mtd>
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<mtext>(b)</mtext>
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</mtd>
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<mtd>
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<mrow>
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<mo>(</mo>
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<mrow>
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<mtable>
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<mtr>
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<mtd>
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<mi>b1</mi>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mi>b2</mi>
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</mtd>
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</mtr>
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<mtr>
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<mtd>
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<mi>b3</mi>
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</mtd>
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</mtr>
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</mtable>
|
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</mrow>
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<mo>)</mo>
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</mrow>
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</mtd>
|
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</mlabeledtr>
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</mtable>
|
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</math>
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<!-- Code cell -->
|
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<table>
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<tr>
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<td>
|
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<span class="prompt">(%i8)
|
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</span>
|
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</td>
|
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<td>
|
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|
<span class="input">
|
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|
<span class="code_variable">x</span>
|
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|
<span class="code_operator">:</span>
|
|
|
<span class="code_function">invert</span>(
|
|
|
<span class="code_variable">A</span>).
|
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|
<span class="code_variable">b</span>
|
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|
<span class="code_endofline">;</span>
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|
</span>
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</td>
|
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</tr>
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</table>
|
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|
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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<mtable>
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<mlabeledtr columnalign="left">
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<mtd>
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<mtext>(x)</mtext>
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</mtd>
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<mtd>
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<mrow>
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<mo>(</mo>
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<mrow>
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<mtable>
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<mtr>
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<mtd>
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<mrow>
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<mfrac>
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<mrow>
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<mi>b2</mi>
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<mo></mo>
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<mrow>
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<mo>(</mo>
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<mrow>
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<mi>−</mi>
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<mrow>
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<mo>(</mo>
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<mrow>
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<msub>
|
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<mi>g</mi>
|
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<mi>D</mi>
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</msub>
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<mi>−</mi>
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<mo>δ</mo>
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<mo>+</mo>
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<mi>M</mi>
|
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<mo></mo>
|
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<msub>
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<mi>Nl</mi>
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<mi>D</mi>
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</msub>
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<mo>+</mo>
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<mn>1</mn>
|
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</mrow>
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<mo>)</mo>
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</mrow>
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<mo></mo>
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<mrow>
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<mo>(</mo>
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<mrow>
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<mi>−</mi>
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<msub>
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<mi>l</mi>
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<mi>s</mi>
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</msub>
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<mo></mo>
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<mi>s</mi>
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<mi>−</mi>
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<mi>l</mi>
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<mi>−</mi>
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<msub>
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<mi>Nsl</mi>
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<mi>S</mi>
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</msub>
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<mo>+</mo>
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<mn>1</mn>
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</mrow>
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<mo>)</mo>
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</mrow>
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<mi>−</mi>
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<mi>M</mi>
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<mo></mo>
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<msub>
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<mi>NSl</mi>
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<mi>D</mi>
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</msub>
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<mo></mo>
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<mrow>
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<mo>(</mo>
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<mrow>
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<msub>
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<mi>l</mi>
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<mi>s</mi>
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</msub>
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|
<mo>+</mo>
|
|
|
<msub>
|
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|
<mi>Nl</mi>
|
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|
<mi>S</mi>
|
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|
</msub>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
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|
</mrow>
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</mrow>
|
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|
<mo>)</mo>
|
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|
</mrow>
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|
</mrow>
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|
<mrow>
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<mrow>
|
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<mo>(</mo>
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<mrow>
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<mrow>
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<mo>(</mo>
|
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|
<mrow>
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<msub>
|
|
|
<mi>g</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<mo>δ</mo>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>l</mi>
|
|
|
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|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo>+</mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>M</mi>
|
|
|
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|
|
|
<msub>
|
|
|
<mi>NSl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>g</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<mo>δ</mo>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
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|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>l</mi>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>NSl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
</mfrac>
|
|
|
<mo>+</mo>
|
|
|
<mfrac>
|
|
|
<mrow>
|
|
|
<mi>b3</mi>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>l</mi>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
<mrow>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>g</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<mo>δ</mo>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>l</mi>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo>+</mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>NSl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>g</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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</mtd>
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|
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|
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|
<mi>M</mi>
|
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<mo></mo>
|
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|
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<mi>Nl</mi>
|
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|
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|
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|
</msub>
|
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<mo>+</mo>
|
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|
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|
</mrow>
|
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|
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</mrow>
|
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|
</mrow>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
<mo></mo>
|
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|
<mrow>
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|
<mo>(</mo>
|
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|
<mrow>
|
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<msub>
|
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<mi>g</mi>
|
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|
<mi>D</mi>
|
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|
</msub>
|
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|
<mi>−</mi>
|
|
|
<mo>δ</mo>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>D</mi>
|
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|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
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|
<mo>)</mo>
|
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|
</mrow>
|
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|
</mrow>
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|
<mo>)</mo>
|
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|
</mrow>
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|
<mo></mo>
|
|
|
<mrow>
|
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|
<mo>(</mo>
|
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|
<mrow>
|
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|
<mi>−</mi>
|
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|
<msub>
|
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|
<mi>l</mi>
|
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|
<mi>s</mi>
|
|
|
</msub>
|
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|
<mo></mo>
|
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|
<mi>s</mi>
|
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|
<mi>−</mi>
|
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|
<mi>l</mi>
|
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|
<mo>+</mo>
|
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|
<mn>1</mn>
|
|
|
</mrow>
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|
<mo>)</mo>
|
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|
</mrow>
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<mo>+</mo>
|
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<mi>M</mi>
|
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|
<mo></mo>
|
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|
<mrow>
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|
<mo>(</mo>
|
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<mrow>
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<msub>
|
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|
<mi>l</mi>
|
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|
<mi>s</mi>
|
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|
</msub>
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|
<mo>+</mo>
|
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|
<msub>
|
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|
<mi>Nl</mi>
|
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|
<mi>S</mi>
|
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|
</msub>
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</mrow>
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|
<mo>)</mo>
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</mrow>
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|
<mo></mo>
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|
<mrow>
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|
<mo>(</mo>
|
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|
<mrow>
|
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|
<msub>
|
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|
<mi>NSl</mi>
|
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|
<mi>D</mi>
|
|
|
</msub>
|
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|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
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|
<mo></mo>
|
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|
<mi>s</mi>
|
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|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
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|
<mo>)</mo>
|
|
|
</mrow>
|
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|
</mrow>
|
|
|
</mfrac>
|
|
|
<mo>+</mo>
|
|
|
<mfrac>
|
|
|
<mrow>
|
|
|
<mi>b1</mi>
|
|
|
<mo></mo>
|
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|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>NSl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
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|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
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|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
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|
<mrow>
|
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|
<mrow>
|
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|
<mo>(</mo>
|
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|
<mrow>
|
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|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
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|
|
|
<msub>
|
|
|
<mi>g</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<mo>δ</mo>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>l</mi>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo>+</mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>NSl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>g</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mi>−</mi>
|
|
|
<mo>δ</mo>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<mi>l</mi>
|
|
|
<mo>+</mo>
|
|
|
<mn>1</mn>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo>+</mo>
|
|
|
<mi>M</mi>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>s</mi>
|
|
|
</msub>
|
|
|
<mo>+</mo>
|
|
|
<msub>
|
|
|
<mi>Nl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
<mo></mo>
|
|
|
<mrow>
|
|
|
<mo>(</mo>
|
|
|
<mrow>
|
|
|
<msub>
|
|
|
<mi>NSl</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
<mi>−</mi>
|
|
|
<msub>
|
|
|
<mi>Nsl</mi>
|
|
|
<mi>S</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<msub>
|
|
|
<mi>l</mi>
|
|
|
<mi>D</mi>
|
|
|
</msub>
|
|
|
<mo></mo>
|
|
|
<mi>s</mi>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mrow>
|
|
|
</mfrac>
|
|
|
</mrow>
|
|
|
</mtd>
|
|
|
</mtr>
|
|
|
</mtable>
|
|
|
</mrow>
|
|
|
<mo>)</mo>
|
|
|
</mrow>
|
|
|
</mtd>
|
|
|
</mlabeledtr>
|
|
|
</mtable>
|
|
|
</math>
|
|
|
<hr/>
|
|
|
<p>
|
|
|
<small> Created with
|
|
|
<a href="https://wxMaxima-developers.github.io/wxmaxima/">wxMaxima</a>.</small>
|
|
|
</p>
|
|
|
</body>
|
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|
</html>
|