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Directory talk:Jon Awbrey/Papers/Differential Logic and Dynamic Systems 2.0 (view source)
Revision as of 20:58, 13 July 2008
, 20:58, 13 July 2008→The Extended Universe of Discourse: add material to work on
===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]</math>
<math>[\mathbb{D}^n]</math>
|}<br>
|}<br>
====Table 9====
<font face="courier new">
{| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:left; width:96%"
|+ '''Table 9. Higher Order Differential Features'''
| width=50% |
{| cellpadding="4"
| <font face="lucida calligraphy">A</font>
| =
| d<sup>0</sup><font face="lucida calligraphy">A</font>
| =
| {''a''<sub>1</sub>,
| …,
| ''a''<sub>''n''</sub>}
|-
| d<font face="lucida calligraphy">A</font>
| =
| d<sup>1</sup><font face="lucida calligraphy">A</font>
| =
| {d''a''<sub>1</sub>,
| …,
| d''a''<sub>''n''</sub>}
|-
|
|
| d<sup>''k''</sup><font face="lucida calligraphy">A</font>
| =
| {d<sup>''k''</sup>''a''<sub>''1''</sub>,
| …,
| d<sup>''k''</sup>''a''<sub>''n''</sub>}
|-
| d<sup>*</sup><font face="lucida calligraphy">A</font>
| =
| {d<sup>0</sup><font face="lucida calligraphy">A</font>,
| …,
| d<sup>''k''</sup><font face="lucida calligraphy">A</font>,
| …}
|}
| width=50% |
{| cellpadding="4"
| E<sup>0</sup><font face="lucida calligraphy">A</font>
| =
| d<sup>0</sup><font face="lucida calligraphy">A</font>
|-
| E<sup>1</sup><font face="lucida calligraphy">A</font>
| =
| d<sup>0</sup><font face="lucida calligraphy">A</font> ∪ d<sup>1</sup><font face="lucida calligraphy">A</font>
|-
| E<sup>''k''</sup><font face="lucida calligraphy">A</font>
| =
| d<sup>0</sup><font face="lucida calligraphy">A</font> ∪ … ∪ d<sup>''k''</sup><font face="lucida calligraphy">A</font>
|-
| E<sup>∞</sup><font face="lucida calligraphy">A</font>
| =
| ∪ d<sup>*</sup><font face="lucida calligraphy">A</font>
|}
|}
</font><br>
<font face="courier new">
{| align="center" border="1" cellpadding="4" cellspacing="0" style="text-align:left; width:96%"
|+ '''Table 9. Higher Order Differential Features'''
| width=50% |
{| cellpadding="4"
| <font face="lucida calligraphy">A</font>
| =
| d<sup>0</sup><font face="lucida calligraphy">A</font>
| =
| {''a''<sub>1</sub>,
| …,
| ''a''<sub>''n''</sub>}
|-
| d<font face="lucida calligraphy">A</font>
| =
| d<sup>1</sup><font face="lucida calligraphy">A</font>
| =
| {d''a''<sub>1</sub>,
| …,
| d''a''<sub>''n''</sub>}
|-
|
|
| d<sup>''k''</sup><font face="lucida calligraphy">A</font>
| =
| {d<sup>''k''</sup>''a''<sub>''1''</sub>,
| …,
| d<sup>''k''</sup>''a''<sub>''n''</sub>}
|-
| d<sup>*</sup><font face="lucida calligraphy">A</font>
| =
| {d<sup>0</sup><font face="lucida calligraphy">A</font>,
| …,
| d<sup>''k''</sup><font face="lucida calligraphy">A</font>,
| …}
|}
| width=50% |
{| cellpadding="4"
| E<sup>0</sup><font face="lucida calligraphy">A</font>
| =
| d<sup>0</sup><font face="lucida calligraphy">A</font>
|-
| E<sup>1</sup><font face="lucida calligraphy">A</font>
| =
| d<sup>0</sup><font face="lucida calligraphy">A</font> ∪ d<sup>1</sup><font face="lucida calligraphy">A</font>
|-
| E<sup>''k''</sup><font face="lucida calligraphy">A</font>
| =
| d<sup>0</sup><font face="lucida calligraphy">A</font> ∪ … ∪ d<sup>''k''</sup><font face="lucida calligraphy">A</font>
|-
| E<sup>∞</sup><font face="lucida calligraphy">A</font>
| =
| ∪ d<sup>*</sup><font face="lucida calligraphy">A</font>
|}
|}
</font><br>