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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)

Revision as of 02:36, 9 September 2013

146 bytes removed ,  02:36, 9 September 2013
update
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{| align="center" cellpadding="1" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:70%"
+
{| align="center" cellpadding="6" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:70%"
 
|+ style="height:30px" | <math>\text{Table 50.} ~~ \text{Computation of an Analytic Series in Terms of Coordinates}\!</math>
 
|+ style="height:30px" | <math>\text{Table 50.} ~~ \text{Computation of an Analytic Series in Terms of Coordinates}\!</math>
−
| width="50%" |
+
|- style="height:40px; background:ghostwhite"
−
{| align="center" cellpadding="6" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:100%"
+
| style="width:8%; border-bottom:1px solid black" | <math>u\!</math>
−
|- style="height:35px; background:ghostwhite"
+
| style="width:8%; border-bottom:1px solid black" | <math>v\!</math>
−
| style="width:16%; border-bottom:1px solid black" | <math>u\!</math>
+
| style="width:8%; border-bottom:1px solid black; border-left:1px solid black" | <math>\mathrm{d}u\!</math>
−
| style="width:16%; border-bottom:1px solid black" | <math>v\!</math>
+
| style="width:8%; border-bottom:1px solid black" | <math>\mathrm{d}v\!</math>
−
| style="width:16%; border-bottom:1px solid black; border-left:1px solid black" | <math>\mathrm{d}u\!</math>
+
| style="width:8%; border-bottom:1px solid black; border-left:1px solid black" | <math>u'\!</math>
−
| style="width:16%; border-bottom:1px solid black" | <math>\mathrm{d}v\!</math>
+
| style="width:8%; border-bottom:1px solid black" | <math>v'\!</math>
−
| style="width:16%; border-bottom:1px solid black; border-left:1px solid black" | <math>u'\!</math>
+
| style="width:10%; border-bottom:1px solid black; border-left:4px double black" | <math>\boldsymbol\varepsilon J\!</math>
−
| style="width:16%; border-bottom:1px solid black" | <math>v'\!</math>
+
| style="width:10%; border-bottom:1px solid black" | <math>\mathrm{E}J\!</math>
 +
| style="width:12%; border-bottom:1px solid black; border-left:1px solid black" | <math>\mathrm{D}J\!</math>
 +
| style="width:10%; border-bottom:1px solid black; border-left:1px solid black" | <math>\mathrm{d}J\!</math>
 +
| style="width:10%; border-bottom:1px solid black" | <math>\mathrm{d}^2\!J\!</math>
 
|-
 
|-
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\0\\1\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\1\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\0\\1\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:4px double black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\1\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 +
<math>\begin{matrix}0\\0\\0\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
 
|-
 
|-
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\0\\1\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\1\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\0\\1\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black" |
 +
<math>\begin{matrix}1\\0\\1\\0\end{matrix}\!</math>
 +
| style="vertical-align:top; border-top:1px solid black; border-left:4px double black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}1\\0\\1\\0\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\1\\0\end{matrix}\!</math>
−
|-
  −
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
  −
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
   
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\0\\1\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\1\\0\end{matrix}\!</math>
−
| style="vertical-align:top; border-top:1px solid black" |
  −
<math>\begin{matrix}0\\1\\0\\1\end{matrix}</math>
   
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}1\\1\\0\\0\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\1\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
 
|-
 
|-
 
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
−
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
+
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\0\\1\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\1\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}1\\1\\0\\0\end{matrix}</math>
+
<math>\begin{matrix}1\\1\\0\\0\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}1\\0\\1\\0\end{matrix}</math>
+
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
−
|}
+
| style="vertical-align:top; border-top:1px solid black; border-left:4px double black" | <math>0\!</math>
−
| width="50%" |
  −
{| align="center" cellpadding="6" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:100%"
  −
|- style="height:35px; background:ghostwhite"
  −
| style="width:20%; border-bottom:1px solid black" | <math>\boldsymbol\varepsilon J\!</math>
  −
| style="width:20%; border-bottom:1px solid black" | <math>\mathrm{E}J\!</math>
  −
| style="width:20%; border-bottom:1px solid black; border-left:1px solid black" | <math>\mathrm{D}J\!</math>
  −
| style="width:20%; border-bottom:1px solid black; border-left:1px solid black" | <math>\mathrm{d}J\!</math>
  −
| style="width:20%; border-bottom:1px solid black" | <math>\mathrm{d}^2\!J\!</math>
  −
|-
  −
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
   
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\0\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\1\\0\\0\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\0\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\1\\0\\0\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\0\\0\\0\end{matrix}</math>
+
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\0\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
 
|-
 
|-
−
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
+
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
−
| style="vertical-align:top; border-top:1px solid black" |
+
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
−
<math>\begin{matrix}0\\0\\1\\0\end{matrix}</math>
   
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\0\\1\\0\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\1\\1\end{matrix}\!</math>
−
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
  −
<math>\begin{matrix}0\\0\\1\\1\end{matrix}</math>
   
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\0\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
−
|-
  −
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
  −
| style="vertical-align:top; border-top:1px solid black" |
  −
<math>\begin{matrix}0\\1\\0\\0\end{matrix}</math>
   
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\1\\0\\0\end{matrix}</math>
+
<math>\begin{matrix}1\\1\\0\\0\end{matrix}\!</math>
−
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
  −
<math>\begin{matrix}0\\1\\0\\1\end{matrix}</math>
   
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\0\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}1\\0\\1\\0\end{matrix}\!</math>
−
|-
+
| style="vertical-align:top; border-top:1px solid black; border-left:4px double black" | <math>1\!</math>
−
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
   
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}1\\0\\0\\0\end{matrix}</math>
+
<math>\begin{matrix}1\\0\\0\\0\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
<math>\begin{matrix}0\\1\\1\\1\end{matrix}\!</math>
 
<math>\begin{matrix}0\\1\\1\\1\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
−
<math>\begin{matrix}0\\1\\1\\0\end{matrix}</math>
+
<math>\begin{matrix}0\\1\\1\\0\end{matrix}\!</math>
 
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
−
<math>\begin{matrix}0\\0\\0\\1\end{matrix}</math>
+
<math>\begin{matrix}0\\0\\0\\1\end{matrix}\!</math>
−
|}
   
|}
 
|}
   Line 6,934: Line 6,923:  
|+ style="height:30px" | <math>\text{Table 67.} ~~ \text{Computation of an Analytic Series in Terms of Coordinates}\!</math>
 
|+ style="height:30px" | <math>\text{Table 67.} ~~ \text{Computation of an Analytic Series in Terms of Coordinates}\!</math>
 
|- style="height:40px; background:ghostwhite"
 
|- style="height:40px; background:ghostwhite"
−
| style="border-bottom:1px solid black" | <math>u\!</math>
+
| style="width:6%; border-bottom:1px solid black" | <math>u\!</math>
−
| style="border-bottom:1px solid black" | <math>v\!</math>
+
| style="width:6%; border-bottom:1px solid black" | <math>v\!</math>
−
| style="border-bottom:1px solid black; border-left:1px solid black" | <math>\mathrm{d}u\!</math>
+
| style="width:6%; border-bottom:1px solid black; border-left:1px solid black" | <math>\mathrm{d}u\!</math>
−
| style="border-bottom:1px solid black" | <math>\mathrm{d}v\!</math>
+
| style="width:6%; border-bottom:1px solid black" | <math>\mathrm{d}v\!</math>
−
| style="border-bottom:1px solid black; border-left:1px solid black" | <math>u'\!</math>
+
| style="width:6%; border-bottom:1px solid black; border-left:1px solid black" | <math>u'\!</math>
−
| style="border-bottom:1px solid black" | <math>v'\!</math>
+
| style="width:6%; border-bottom:1px solid black" | <math>v'\!</math>
−
| style="border-bottom:1px solid black; border-left:4px double black" | <math>f\!</math>
+
| style="width:6%; border-bottom:1px solid black; border-left:4px double black" | <math>f\!</math>
−
| style="border-bottom:1px solid black" | <math>g\!</math>
+
| style="width:6%; border-bottom:1px solid black" | <math>g\!</math>
−
| style="border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{E}f}\!</math>
+
| style="width:6%; border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{E}f}\!</math>
−
| style="border-bottom:1px solid black" | <math>{\mathrm{E}g}\!</math>
+
| style="width:6%; border-bottom:1px solid black" | <math>{\mathrm{E}g}\!</math>
−
| style="border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{D}f}\!</math>
+
| style="width:6%; border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{D}f}\!</math>
−
| style="border-bottom:1px solid black" | <math>{\mathrm{D}g}\!</math>
+
| style="width:6%; border-bottom:1px solid black" | <math>{\mathrm{D}g}\!</math>
−
| style="border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{d}f}\!</math>
+
| style="width:6%; border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{d}f}\!</math>
−
| style="border-bottom:1px solid black" | <math>{\mathrm{d}g}\!</math>
+
| style="width:6%; border-bottom:1px solid black" | <math>{\mathrm{d}g}\!</math>
−
| style="border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{d}^2\!f}\!</math>
+
| style="width:6%; border-bottom:1px solid black; border-left:1px solid black" | <math>{\mathrm{d}^2\!f}\!</math>
−
| style="border-bottom:1px solid black" | <math>{\mathrm{d}^2\!g}\!</math>
+
| style="width:6%; border-bottom:1px solid black" | <math>{\mathrm{d}^2\!g}\!</math>
 
|-
 
|-
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
Line 6,961: Line 6,950:  
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
 
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
−
| style="vertical-align:top; border-top:1px solid black; border-left: 4px double black" | <math>0\!</math>
+
| style="vertical-align:top; border-top:1px solid black; border-left:4px double black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
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| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
 
<math>\begin{matrix}1\\0\\1\\0\end{matrix}\!</math>
 
<math>\begin{matrix}1\\0\\1\\0\end{matrix}\!</math>
−
| style="vertical-align:top; border-top:1px solid black; border-left: 4px double black" | <math>1\!</math>
+
| style="vertical-align:top; border-top:1px solid black; border-left:4px double black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
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| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
 
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
 
<math>\begin{matrix}0\\1\\0\\1\end{matrix}\!</math>
−
| style="vertical-align:top; border-top:1px solid black; border-left: 4px double black" | <math>1\!</math>
+
| style="vertical-align:top; border-top:1px solid black; border-left:4px double black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>0\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
Line 7,048: Line 7,037:  
| style="vertical-align:top; border-top:1px solid black" |
 
| style="vertical-align:top; border-top:1px solid black" |
 
<math>\begin{matrix}1\\0\\1\\0\end{matrix}\!</math>
 
<math>\begin{matrix}1\\0\\1\\0\end{matrix}\!</math>
−
| style="vertical-align:top; border-top:1px solid black; border-left: 4px double black" | <math>1\!</math>
+
| style="vertical-align:top; border-top:1px solid black; border-left:4px double black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black" | <math>1\!</math>
 
| style="vertical-align:top; border-top:1px solid black; border-left:1px solid black" |
 
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Jon Awbrey
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