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Directory:Jon Awbrey/Papers/Differential Logic and Dynamic Systems (view source)
Revision as of 14:25, 19 June 2007
, 14:25, 19 June 2007→Transformations of Type '''B'''<sup>2</sup> → '''B'''<sup>2</sup>: wiki table
In their application to the present example, namely, the logical transformation ''F'' = ‹''f'', ''g''› = ‹((''u'')(''v'')), ((''u'', ''v''))›, the operators E and D respectively produce the enlarged map E''F'' = ‹E''f'', E''g''› and the difference map D''F'' = ‹D''f'', D''g''›, whose components can be given as follows, if the reader, in lieu of a special font for the logical parentheses, can forgive a syntactically bilingual formulation:
In their application to the present example, namely, the logical transformation ''F'' = ‹''f'', ''g''› = ‹((''u'')(''v'')), ((''u'', ''v''))›, the operators E and D respectively produce the enlarged map E''F'' = ‹E''f'', E''g''› and the difference map D''F'' = ‹D''f'', D''g''›, whose components can be given as follows, if the reader, in lieu of a special font for the logical parentheses, can forgive a syntactically bilingual formulation:
<pre>
<br><font face="courier new">
{| align="center" border="1" cellpadding="12" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:left; width:96%"
| |
|
| Ef = ((u + du)(v + dv)) |
{| align="left" border="0" cellpadding="12" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:left; width:100%"
| |
| width="8%" | E''f''
| Eg = ((u + du, v + dv)) |
| width="4%" | =
| |
| width="88%" | ((''u'' + d''u'')(''v'' + d''v''))
|-
</pre>
| width="8%" | E''g''
| width="4%" | =
| width="88%" | ((''u'' + d''u'', ''v'' + d''v''))
|}
|}
</font><br>
<pre>
<pre>