Line 1: |
Line 1: |
| {{DISPLAYTITLE:Differential Logic and Dynamic Systems 2.0}} | | {{DISPLAYTITLE:Differential Logic and Dynamic Systems 2.0}} |
− | * '''Note.''' The MathJax parser is not rendering this page properly.<br>Until it can be fixed please see the [http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0 InterSciWiki version].
| |
− |
| |
| '''Author: [[User:Jon Awbrey|Jon Awbrey]]''' | | '''Author: [[User:Jon Awbrey|Jon Awbrey]]''' |
| | | |
Line 619: |
Line 617: |
| | | |
| ===Reality at the Threshold of Logic=== | | ===Reality at the Threshold of Logic=== |
− |
| |
− | '''Problem Flag''' (check formatting, MathJax handling of tildes, or underlines?)
| |
| | | |
| {| width="100%" cellpadding="0" cellspacing="0" | | {| width="100%" cellpadding="0" cellspacing="0" |
Line 4,866: |
Line 4,862: |
| & = & ~~ 0 ~~ \,\cdot\, ~ \texttt{(} \mathrm{d}u \texttt{)} \texttt{(} \mathrm{d}v \texttt{)} | | & = & ~~ 0 ~~ \,\cdot\, ~ \texttt{(} \mathrm{d}u \texttt{)} \texttt{(} \mathrm{d}v \texttt{)} |
| & + & ~~ u ~ \,\cdot\, ~~ \texttt{(} \mathrm{d}u \texttt{)} \mathrm{d}v | | & + & ~~ u ~ \,\cdot\, ~~ \texttt{(} \mathrm{d}u \texttt{)} \mathrm{d}v |
− | & + & [[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]]) v ~~ \,\cdot\, \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{)} | + | & + & ~ ~ v ~~ \,\cdot\, \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{)} |
| & + & \texttt{((} u \texttt{,} v \texttt{))} \cdot \mathrm{d}u ~ \mathrm{d}v | | & + & \texttt{((} u \texttt{,} v \texttt{))} \cdot \mathrm{d}u ~ \mathrm{d}v |
| \end{array}\!</math> | | \end{array}\!</math> |
Line 5,069: |
Line 5,065: |
| <math>\begin{array}{*{9}{l}} | | <math>\begin{array}{*{9}{l}} |
| \mathrm{r}J ~ | | \mathrm{r}J ~ |
− | & = & u \!\cdot\! v \cdot ~ \mathrm{d}u \cdot \mathrm{d}v 21:00, 28 August 2015 (UTC)~ | + | & = & u \!\cdot\! v \cdot ~ \mathrm{d}u \cdot \mathrm{d}v ~ ~ ~ ~ ~ |
| & + & u \texttt{(} v \texttt{)} \cdot \, \mathrm{d}u \cdot \mathrm{d}v \, | | & + & u \texttt{(} v \texttt{)} \cdot \, \mathrm{d}u \cdot \mathrm{d}v \, |
| & + & \texttt{(} u \texttt{)} v \cdot \, \mathrm{d}u \cdot \mathrm{d}v \, | | & + & \texttt{(} u \texttt{)} v \cdot \, \mathrm{d}u \cdot \mathrm{d}v \, |
Line 6,571: |
Line 6,567: |
| \texttt{(} x \texttt{)~} y \texttt{~} | | \texttt{(} x \texttt{)~} y \texttt{~} |
| \\[2pt] | | \\[2pt] |
− | \texttt{(} x \texttt{)[[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]])} | + | \texttt{(} x \texttt{)~ ~} |
| \\[2pt] | | \\[2pt] |
| \texttt{~} x \texttt{~(} y \texttt{)} | | \texttt{~} x \texttt{~(} y \texttt{)} |
| \\[2pt] | | \\[2pt] |
− | \texttt{[[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]])(} y \texttt{)} | + | \texttt{~ ~(} y \texttt{)} |
| \\[2pt] | | \\[2pt] |
| \texttt{(} x \texttt{,~} y \texttt{)} | | \texttt{(} x \texttt{,~} y \texttt{)} |
Line 6,660: |
Line 6,656: |
| \texttt{((} x \texttt{,~} y \texttt{))} | | \texttt{((} x \texttt{,~} y \texttt{))} |
| \\[2pt] | | \\[2pt] |
− | \texttt{21:00, 28 August 2015 (UTC)} y \texttt{~~} | + | \texttt{~ ~ ~ ~} y \texttt{~~} |
| \\[2pt] | | \\[2pt] |
| \texttt{~(} x \texttt{~(} y \texttt{))} | | \texttt{~(} x \texttt{~(} y \texttt{))} |
| \\[2pt] | | \\[2pt] |
− | \texttt{~~} x \texttt{21:00, 28 August 2015 (UTC)} | + | \texttt{~~} x \texttt{~ ~ ~ ~} |
| \\[2pt] | | \\[2pt] |
| \texttt{((} x \texttt{)~} y \texttt{)~} | | \texttt{((} x \texttt{)~} y \texttt{)~} |
Line 7,692: |
Line 7,688: |
| \texttt{(} x \texttt{)~} y \texttt{~} | | \texttt{(} x \texttt{)~} y \texttt{~} |
| \\ | | \\ |
− | \texttt{(} x \texttt{)[[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]])} | + | \texttt{(} x \texttt{)~ ~} |
| \\ | | \\ |
| \texttt{~} x \texttt{~(} y \texttt{)} | | \texttt{~} x \texttt{~(} y \texttt{)} |
| \\ | | \\ |
− | \texttt{[[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]])(} y \texttt{)} | + | \texttt{~ ~(} y \texttt{)} |
| \\ | | \\ |
| \texttt{(} x \texttt{,~} y \texttt{)} | | \texttt{(} x \texttt{,~} y \texttt{)} |
Line 7,757: |
Line 7,753: |
| \texttt{((} x \texttt{,~} y \texttt{))} | | \texttt{((} x \texttt{,~} y \texttt{))} |
| \\ | | \\ |
− | \texttt{21:00, 28 August 2015 (UTC)} y \texttt{~~} | + | \texttt{~ ~ ~ ~} y \texttt{~~} |
| \\ | | \\ |
| \texttt{~(} x \texttt{~(} y \texttt{))} | | \texttt{~(} x \texttt{~(} y \texttt{))} |
| \\ | | \\ |
− | \texttt{~~} x \texttt{21:00, 28 August 2015 (UTC)} | + | \texttt{~~} x \texttt{~ ~ ~ ~} |
| \\ | | \\ |
| \texttt{((} x \texttt{)~} y \texttt{)~} | | \texttt{((} x \texttt{)~} y \texttt{)~} |
Line 10,428: |
Line 10,424: |
| | | |
| =====Computation of D''f''<sub>8</sub>===== | | =====Computation of D''f''<sub>8</sub>===== |
− |
| |
− | '''Problem Flag''' (check formatting, probably MathJax handling of tildes)
| |
| | | |
| <br> | | <br> |
Line 10,527: |
Line 10,521: |
| \\[20pt] | | \\[20pt] |
| \mathrm{D}f_{8} | | \mathrm{D}f_{8} |
− | & = & [[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]]) 0 ~~ \cdot ~ \texttt{(} \mathrm{d}u \texttt{)} \texttt{(} \mathrm{d}v \texttt{)} | + | & = & ~ ~ 0 ~~ \cdot ~ \texttt{(} \mathrm{d}u \texttt{)} \texttt{(} \mathrm{d}v \texttt{)} |
− | & + & [[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]]) u ~~ \cdot ~ \texttt{(} \mathrm{d}u \texttt{)} \mathrm{d}v | + | & + & ~ ~ u ~~ \cdot ~ \texttt{(} \mathrm{d}u \texttt{)} \mathrm{d}v |
− | & + & [[User:Jon Awbrey|Jon Awbrey]] ([[User talk:Jon Awbrey|talk]]) 21:00, 28 August 2015 (UTC) v ~~ \cdot ~ \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{)} | + | & + & ~ ~ ~ v ~~ \cdot ~ \mathrm{d}u \texttt{(} \mathrm{d}v \texttt{)} |
| & + & \texttt{((} u \texttt{,} v \texttt{))} \cdot \mathrm{d}u ~ \mathrm{d}v | | & + & \texttt{((} u \texttt{,} v \texttt{))} \cdot \mathrm{d}u ~ \mathrm{d}v |
| \end{array}\!</math> | | \end{array}\!</math> |
Line 11,709: |
Line 11,703: |
| |- | | |- |
| | valign=top | [Whi] | | | valign=top | [Whi] |
− | | Whitman, Walt, ''Leaves of Grass'', Vintage Books / The Library of America, New York, NY, 1992. Originally published in numerous editions, 1855–1892. | + | | Whitman, Walt, ''Leaves of Grass'', Vintage Books / The Library of America, New York, NY, 1992. Originally published in numerous editions, 1855–1892. |
| |- | | |- |
| | valign=top | [Wil] | | | valign=top | [Wil] |