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

Revision as of 13:58, 3 October 2017

980 bytes removed ,  13:58, 3 October 2017
try fixing problem with MathJax's improper handling of "~" in <math> environs
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{{DISPLAYTITLE:Differential Logic and Dynamic Systems 2.0}}
 
{{DISPLAYTITLE:Differential Logic and Dynamic Systems 2.0}}
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* '''Note.''' The MathJax parser is not rendering this page properly.<br>Until it can be fixed please see the [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 InterSciWiki version].
  −
   
'''Author: [[User:Jon Awbrey|Jon Awbrey]]'''
 
'''Author: [[User:Jon Awbrey|Jon Awbrey]]'''
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===Reality at the Threshold of Logic===
 
===Reality at the Threshold of Logic===
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  −
'''Problem Flag''' (check formatting, MathJax handling of tildes, or underlines?)
      
{| width="100%" cellpadding="0" cellspacing="0"
 
{| width="100%" cellpadding="0" cellspacing="0"
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& = & ~~ 0 ~~ \,\cdot\, ~ \texttt{(} \mathrm{d}u \texttt{)} \texttt{(} \mathrm{d}v \texttt{)}
 
& = & ~~ 0 ~~ \,\cdot\, ~ \texttt{(} \mathrm{d}u \texttt{)} \texttt{(} \mathrm{d}v \texttt{)}
 
& + & ~~ u ~  \,\cdot\, ~~ \texttt{(} \mathrm{d}u \texttt{)} \mathrm{d}v
 
& + & ~~ u ~  \,\cdot\, ~~ \texttt{(} \mathrm{d}u \texttt{)} \mathrm{d}v
−
& + & [[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]]) v ~~ \,\cdot\, \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{)}
+
& + & ~ ~ v ~~ \,\cdot\, \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{)}
 
& + & \texttt{((} u \texttt{,} v \texttt{))} \cdot \mathrm{d}u ~ \mathrm{d}v
 
& + & \texttt{((} u \texttt{,} v \texttt{))} \cdot \mathrm{d}u ~ \mathrm{d}v
 
\end{array}\!</math>
 
\end{array}\!</math>
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<math>\begin{array}{*{9}{l}}
 
<math>\begin{array}{*{9}{l}}
 
\mathrm{r}J ~
 
\mathrm{r}J ~
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& = & u \!\cdot\! v \cdot ~ \mathrm{d}u \cdot \mathrm{d}v 21:00, 28 August 2015 (UTC)~
+
& = & u \!\cdot\! v \cdot ~ \mathrm{d}u \cdot \mathrm{d}v ~ ~ ~ ~ ~
 
& + & u \texttt{(} v \texttt{)} \cdot \, \mathrm{d}u \cdot \mathrm{d}v \,
 
& + & u \texttt{(} v \texttt{)} \cdot \, \mathrm{d}u \cdot \mathrm{d}v \,
 
& + & \texttt{(} u \texttt{)} v \cdot \, \mathrm{d}u \cdot \mathrm{d}v \,
 
& + & \texttt{(} u \texttt{)} v \cdot \, \mathrm{d}u \cdot \mathrm{d}v \,
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\texttt{(} x \texttt{)~} y \texttt{~}
 
\texttt{(} x \texttt{)~} y \texttt{~}
 
\\[2pt]
 
\\[2pt]
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\texttt{(} x \texttt{)[[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]])}
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\texttt{(} x \texttt{)~ ~}
 
\\[2pt]
 
\\[2pt]
 
\texttt{~} x \texttt{~(} y \texttt{)}
 
\texttt{~} x \texttt{~(} y \texttt{)}
 
\\[2pt]
 
\\[2pt]
−
\texttt{[[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]])(} y \texttt{)}
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\texttt{~ ~(} y \texttt{)}
 
\\[2pt]
 
\\[2pt]
 
\texttt{(} x \texttt{,~} y \texttt{)}
 
\texttt{(} x \texttt{,~} y \texttt{)}
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\texttt{((} x \texttt{,~} y \texttt{))}
 
\texttt{((} x \texttt{,~} y \texttt{))}
 
\\[2pt]
 
\\[2pt]
−
\texttt{21:00, 28 August 2015 (UTC)} y \texttt{~~}
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\texttt{~ ~ ~ ~} y \texttt{~~}
 
\\[2pt]
 
\\[2pt]
 
\texttt{~(} x \texttt{~(} y \texttt{))}
 
\texttt{~(} x \texttt{~(} y \texttt{))}
 
\\[2pt]
 
\\[2pt]
−
\texttt{~~} x \texttt{21:00, 28 August 2015 (UTC)}
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\texttt{~~} x \texttt{~ ~ ~ ~}
 
\\[2pt]
 
\\[2pt]
 
\texttt{((} x \texttt{)~} y \texttt{)~}
 
\texttt{((} x \texttt{)~} y \texttt{)~}
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\texttt{(} x \texttt{)~} y \texttt{~}
 
\texttt{(} x \texttt{)~} y \texttt{~}
 
\\
 
\\
−
\texttt{(} x \texttt{)[[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]])}
+
\texttt{(} x \texttt{)~ ~}
 
\\
 
\\
 
\texttt{~} x \texttt{~(} y \texttt{)}
 
\texttt{~} x \texttt{~(} y \texttt{)}
 
\\
 
\\
−
\texttt{[[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]])(} y \texttt{)}
+
\texttt{~ ~(} y \texttt{)}
 
\\
 
\\
 
\texttt{(} x \texttt{,~} y \texttt{)}
 
\texttt{(} x \texttt{,~} y \texttt{)}
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\texttt{((} x \texttt{,~} y \texttt{))}
 
\texttt{((} x \texttt{,~} y \texttt{))}
 
\\
 
\\
−
\texttt{21:00, 28 August 2015 (UTC)} y \texttt{~~}
+
\texttt{~ ~ ~ ~} y \texttt{~~}
 
\\
 
\\
 
\texttt{~(} x \texttt{~(} y \texttt{))}
 
\texttt{~(} x \texttt{~(} y \texttt{))}
 
\\
 
\\
−
\texttt{~~} x \texttt{21:00, 28 August 2015 (UTC)}
+
\texttt{~~} x \texttt{~ ~ ~ ~}
 
\\
 
\\
 
\texttt{((} x \texttt{)~} y \texttt{)~}
 
\texttt{((} x \texttt{)~} y \texttt{)~}
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=====Computation of D''f''<sub>8</sub>=====
 
=====Computation of D''f''<sub>8</sub>=====
−
  −
'''Problem Flag''' (check formatting, probably MathJax handling of tildes)
      
<br>
 
<br>
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\\[20pt]
 
\\[20pt]
 
\mathrm{D}f_{8}
 
\mathrm{D}f_{8}
−
& = & [[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]]) 0 ~~ \cdot ~ \texttt{(} \mathrm{d}u \texttt{)} \texttt{(} \mathrm{d}v \texttt{)}
+
& = & ~ ~ 0 ~~ \cdot ~ \texttt{(} \mathrm{d}u \texttt{)} \texttt{(} \mathrm{d}v \texttt{)}
−
& + & [[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]]) u ~~ \cdot ~ \texttt{(} \mathrm{d}u \texttt{)} \mathrm{d}v
+
& + & ~ ~ u ~~ \cdot ~ \texttt{(} \mathrm{d}u \texttt{)} \mathrm{d}v
−
& + & [[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]]) 21:00, 28 August 2015 (UTC) v ~~ \cdot ~ \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{)}
+
& + & ~ ~ ~ v ~~ \cdot ~ \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{)}
 
& + & \texttt{((} u \texttt{,} v \texttt{))} \cdot \mathrm{d}u ~ \mathrm{d}v
 
& + & \texttt{((} u \texttt{,} v \texttt{))} \cdot \mathrm{d}u ~ \mathrm{d}v
 
\end{array}\!</math>
 
\end{array}\!</math>
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|-
 
|-
 
| valign=top | [Whi]
 
| valign=top | [Whi]
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| Whitman, Walt, ''Leaves of Grass'', Vintage Books / The Library of America, New York, NY, 1992.  Originally published in numerous editions, 1855&ndash;1892.
+
| Whitman, Walt, ''Leaves of Grass'', Vintage Books / The Library of America, New York, NY, 1992.  Originally published in numerous editions, 1855–1892.
 
|-
 
|-
 
| valign=top | [Wil]
 
| valign=top | [Wil]
Jon Awbrey
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