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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems (view source)
Revision as of 19:13, 10 June 2007
, 19:13, 10 June 2007→Summary of Conjunction: wiki table
To establish a convenient reference point for further discussion, Table 49 summarizes the operator actions that have been computed for the form of conjunction, as exemplified by the proposition ''J''.
To establish a convenient reference point for further discussion, Table 49 summarizes the operator actions that have been computed for the form of conjunction, as exemplified by the proposition ''J''.
<pre>
<font face="courier new">
Table 49. Computation Summary for J
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:96%"
|+ Table 49. Computation Summary for ''J''
| |
|
| !e!J = uv . 1 + u(v) . 0 + (u)v . 0 + (u)(v) . 0 |
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
| |
| <math>\epsilon</math>''J''
| EJ = uv . (du)(dv) + u(v) . (du)dv + (u)v . du(dv) + (u)(v) . du dv |
| = || ''uv'' || <math>\cdot</math> || 1
| |
| + || ''u''(''v'') || <math>\cdot</math> || 0
| DJ = uv . ((du)(dv)) + u(v) . (du)dv + (u)v . du(dv) + (u)(v) . du dv |
| + || (''u'')''v'' || <math>\cdot</math> || 0
| |
| + || (''u'')(''v'') || <math>\cdot</math> || 0
| dJ = uv . (du, dv) + u(v) . dv + (u)v . du + (u)(v) . 0 |
|-
| |
| E''J''
| rJ = uv . du dv + u(v) . du dv + (u)v . du dv + (u)(v) . du dv |
| = || ''uv'' || <math>\cdot</math> || (d''u'')(d''v'')
| |
| + || ''u''(''v'') || <math>\cdot</math> || (d''u'')d''v''
| + || (''u'')''v'' || <math>\cdot</math> || d''u''(d''v'')
</pre>
| + || (''u'')(''v'') || <math>\cdot</math> || d''u'' d''v''
|-
| D''J''
| = || ''uv'' || <math>\cdot</math> || ((d''u'')(d''v''))
| + || ''u''(''v'') || <math>\cdot</math> || (d''u'')d''v''
| + || (''u'')''v'' || <math>\cdot</math> || d''u''(d''v'')
| + || (''u'')(''v'') || <math>\cdot</math> || d''u'' d''v''
|-
| d''J''
| = || ''uv'' || <math>\cdot</math> || (d''u'', d''v'')
| + || ''u''(''v'') || <math>\cdot</math> || d''v''
| + || (''u'')''v'' || <math>\cdot</math> || d''u''
| + || (''u'')(''v'') || <math>\cdot</math> || 0
|-
| r''J''
| = || ''uv'' || <math>\cdot</math> || d''u'' d''v''
| + || ''u''(''v'') || <math>\cdot</math> || d''u'' d''v''
| + || (''u'')''v'' || <math>\cdot</math> || d''u'' d''v''
| + || (''u'')(''v'') || <math>\cdot</math> || d''u'' d''v''
|}
|}
</font><br>
====Analytic Series : Coordinate Method====
====Analytic Series : Coordinate Method====