12,089
edits
Changes
MyWikiBiz, Author Your Legacy — Wednesday September 10, 2025
Jump to navigationJump to searchDirectory:Jon Awbrey/Papers/Differential Analytic Turing Automata (view source)
Revision as of 19:35, 5 March 2009
, 19:35, 5 March 2009→Note 10: markup
{| align="center" cellpadding="8" width="90%"
{| align="center" cellpadding="8" width="90%"
|
|
<math>\begin{array}{ccccc}
<math>\begin{array}{lll}
\operatorname{E}G_1 & = & G_1 (u + du, v + dv)
\operatorname{E}G_1 & = & G_1 (u + du, v + dv)
\\ \\
\\ \\
Second, the ''difference map'' (or the ''chordal transformation'') <math>\operatorname{D}G = (\operatorname{D}G_1, \operatorname{D}G_2) : \operatorname{E}U^\circ \to \operatorname{E}X^\circ</math> is defined in a component-wise fashion as the boolean sum of the initial proposition <math>G_j\!</math> and the ''enlarged'' or ''shifted'' proposition <math>\operatorname{E}G_j,</math> for <math>j = 1, 2,\!</math> in accord with following pair of equations:
Second, the ''difference map'' (or the ''chordal transformation'') <math>\operatorname{D}G = (\operatorname{D}G_1, \operatorname{D}G_2) : \operatorname{E}U^\circ \to \operatorname{E}X^\circ</math> is defined in a component-wise fashion as the boolean sum of the initial proposition <math>G_j\!</math> and the ''enlarged'' or ''shifted'' proposition <math>\operatorname{E}G_j,</math> for <math>j = 1, 2,\!</math> in accord with following pair of equations:
{| align="center" cellpadding="8" width="90%"
|
<math>\begin{array}{lllll}
\operatorname{D}G_1 & = & G_1 (u, v) & + & \operatorname{E}G_1 (u, v, du, dv)
\\ \\
& = & G_1 (u, v) & + & G_1 (u + du, v + dv)
\\ \\
\operatorname{D}G_2 & = & G_2 (u, v) & + & \operatorname{E}G_2 (u, v, du, dv)
\\ \\
& = & G_2 (u, v) & + & G_2 (u + du, v + dv)
\end{array}</math>
|}
<pre>
<pre>
