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Directory talk:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)
Revision as of 01:32, 14 July 2008
, 01:32, 14 July 2008→Table 9: cleanup
===The Extended Universe of Discourse===
===The Extended Universe of Discourse===
====Table 8====
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%"
<math>(\mathbb{D}^n\ +\!\to \mathbb{B})</math><br>
<math>(\mathbb{D}^n\ +\!\to \mathbb{B})</math><br>
<math>[\mathbb{D}^n]</math>
<math>[\mathbb{D}^n]</math>
|}<br>
====Table 9====
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:left; width:96%"
|+ '''Table 9. Higher Order Differential Features'''
|
<p><math>\begin{array}{lllll}
\operatorname{d}^0 \mathcal{A}
& = & \{a_1, \ldots, a_n\}
& = & \mathcal{A} \\
\operatorname{d}^1 \mathcal{A}
& = & \{\operatorname{d}a_1, \ldots, \operatorname{d}a_n\}
& = & \operatorname{d}\mathcal{A} \\
\end{array}</math></p>
<p><math>\begin{array}{lll}
\operatorname{d}^k \mathcal{A}
& = & \{\operatorname{d}^k a_1, \ldots, \operatorname{d}^k a_n\} \\
\operatorname{d}^* \mathcal{A}
& = & \{\operatorname{d}^0 \mathcal{A}, \ldots, \operatorname{d}^k \mathcal{A}, \ldots \} \\
\end{array}</math></p>
|
<p><math>\begin{array}{lll}
\operatorname{E}^0 \mathcal{A}
& = & \operatorname{d}^0 \mathcal{A} \\
\operatorname{E}^1 \mathcal{A}
& = & \operatorname{d}^0 \mathcal{A}\ \cup\ \operatorname{d}^1 \mathcal{A} \\
\operatorname{E}^k \mathcal{A}
& = & \operatorname{d}^0 \mathcal{A}\ \cup\ \ldots\ \cup\ \operatorname{d}^k \mathcal{A} \\
\operatorname{E}^\infty \mathcal{A}
& = & \bigcup\ \operatorname{d}^* \mathcal{A} \\
\end{array}</math></p>
|}<br>
|}<br>