| Line 4,162: |
Line 4,162: |
| | Figures 48-a through 48-d illustrate the proposition r''J'' = d<sup>2</sup>''J'', which forms the remainder map of ''J'' and also, in this instance, the second order differential of ''J''. | | Figures 48-a through 48-d illustrate the proposition r''J'' = d<sup>2</sup>''J'', which forms the remainder map of ''J'' and also, in this instance, the second order differential of ''J''. |
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| − | <pre> | + | <br> |
| − | o---------------------------------------o
| + | <p>[[Image:Diff Log Dyn Sys -- Figure 48-a -- Remainder of J.gif|center]]</p> |
| − | | | | + | <p><center><font size="+1">'''Figure 48-a. Remainder of ''J'' (Areal)'''</font></center></p> |
| − | | o |
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| − | | / \ |
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| − | | / \ |
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| − | | / \ |
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| − | | o o |
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| − | | / \ / \ |
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| − | | / \ / \ |
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| − | | / \ / \ |
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| − | | o o o |
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| − | | / \ /%\ / \ |
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| − | | / \ /%%%\ / \ |
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| − | | / \ /%%%%%\ / \ |
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| − | | o o%%%%%%%o o |
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| − | | / \ /%\%%%%%/%\ / \ |
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| − | | / \ /%%%\%%%/%%%\ / \ |
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| − | | / \ /%%%%%\%/%%%%%\ / \ |
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| − | | o o%%%%%%%o%%%%%%%o o |
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| − | | |\ / \%%%%%/%\%%%%%/ \ /| |
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| − | | | \ / \%%%/%%%\%%%/ \ / | |
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| − | | | \ / \%/%%%%%\%/ \ / | |
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| − | | | o o%%%%%%%o o | |
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| − | | | |\ / \%%%%%/ \ /| | |
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| − | | | | \ / \%%%/ \ / | | |
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| − | | | u | \ / \%/ \ / | v | |
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| − | | o---+---o o o---+---o |
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| − | | | \ / \ / | |
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| − | | | \ / \ / | |
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| − | | | du \ / \ / dv | |
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| − | | o-------o o-------o |
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| − | | \ / |
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| − | | \ / |
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| − | | \ / |
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| − | | o |
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| − | | |
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| − | o---------------------------------------o
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| − | Figure 48-a. Remainder of J (Areal) | |
| − | </pre> | |
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| − | <pre> | + | <br> |
| − | o-----------------------------o
| + | <p>[[Image:Diff Log Dyn Sys -- Figure 48-b -- Remainder of J.gif|center]]</p> |
| − | | |
| + | <p><center><font size="+1">'''Figure 48-b. Remainder of ''J'' (Bundle)'''</font></center></p> |
| − | | o-----o o-----o |
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| − | | / \ / \ |
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| − | | / o \ |
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| − | | / /%\ \ |
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| − | | o o%%%o o |
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| − | @ | du |%%%| dv | |
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| − | /| o o%%%o o |
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| − | / | \ \%/ / |
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| − | / | \ o / |
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| − | / | \ / \ / |
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| − | / | o-----o o-----o |
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| − | / | |
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| − | / o-----------------------------o
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| − | /
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| − | o----------------------------------------/----o o-----------------------------o
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| − | | / | | |
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| − | | @ | | o-----o o-----o |
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| − | | | | / \ / \ |
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| − | | o---------o o---------o | | / o \ |
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| − | | / \ / \ | | / /%\ \ |
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| − | | / o \ | | o o%%%o o |
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| − | | / /`\ @------\-----------@ | du |%%%| dv | |
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| − | | / /```\ \ | | o o%%%o o |
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| − | | / /`````\ \ | | \ \%/ / |
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| − | | / /```````\ \ | | \ o / |
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| − | | o o`````````o o | | \ / \ / |
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| − | | | |````@````| | | | o-----o o-----o |
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| − | | | |`````\```| | | | |
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| − | | | |``````\``| | | o-----------------------------o
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| − | | | u |```````\`| v | |
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| − | | | |````````\| | | o-----------------------------o
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| − | | | |`````````| | | | |
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| − | | | |`````````|\ | | | o-----o o-----o |
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| − | | o o`````````o \ o | | / \ / \ |
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| − | | \ \```````/ \ / | | / o \ |
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| − | | \ \`````/ \ / | | / /%\ \ |
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| − | | \ \```/ \ / | | o o%%%o o |
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| − | | \ @------\-/---------\---------------@ | du |%%%| dv | |
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| − | | \ o \ / | | o o%%%o o |
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| − | | \ / \ / | | \ \%/ / |
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| − | | o---------o o---------o \ | | \ o / |
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| − | | \ | | \ / \ / |
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| − | | \ | | o-----o o-----o |
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| − | | \ | | |
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| − | o----------------------------------------\----o o-----------------------------o
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| − | \
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| − | \ o-----------------------------o
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| − | \ | |
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| − | \ | o-----o o-----o |
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| − | \ | / \ / \ |
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| − | \ | / o \ |
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| − | \ | / /%\ \ |
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| − | \| o o%%%o o |
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| − | @ | du |%%%| dv | |
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| − | | o o%%%o o |
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| − | | \ \%/ / |
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| − | | \ o / |
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| − | | \ / \ / |
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| − | | o-----o o-----o |
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| − | | |
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| − | o-----------------------------o
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| − | Figure 48-b. Remainder of J (Bundle) | |
| − | </pre> | |
| | | | |
| − | <pre> | + | <br> |
| − | o---------------------------------------------------------------------o
| + | <p>[[Image:Diff Log Dyn Sys -- Figure 48-c -- Remainder of J.gif|center]]</p> |
| − | | | | + | <p><center><font size="+1">'''Figure 48-c. Remainder of ''J'' (Compact)'''</font></center></p> |
| − | | |
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| − | | o-------------------o o-------------------o |
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| − | | / \ / \ |
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| − | | / o \ |
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| − | | / / \ \ |
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| − | | / / \ \ |
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| − | | / / \ \ |
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| − | | / / \ \ |
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| − | | / / \ \ |
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| − | | o o o o |
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| − | | | | | | |
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| − | | | | | | |
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| − | | | | du dv | | |
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| − | | | u @<------------------------->@ v | |
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| − | | | | | | |
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| − | | | | | | |
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| − | | | | | | |
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| − | | o o @ o o |
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| − | | \ \ ^ / / |
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| − | | \ \ | / / |
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| − | | \ \ | / / |
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| − | | \ \ | / / |
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| − | | \ \|/ / |
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| − | | \ du | dv / |
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| − | | \ /|\ / |
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| − | | o-------------------o | o-------------------o |
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| − | | | |
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| − | | | |
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| − | | v |
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| − | | @ |
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| − | | |
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| − | o---------------------------------------------------------------------o
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| − | Figure 48-c. Remainder of J (Compact) | |
| − | </pre> | |
| | | | |
| − | <pre> | + | <br> |
| − | o-----------------------------------------------------------o
| + | <p>[[Image:Diff Log Dyn Sys -- Figure 48-d -- Remainder of J.gif|center]]</p> |
| − | | |
| + | <p><center><font size="+1">'''Figure 48-d. Remainder of ''J'' (Digraph)'''</font></center></p> |
| − | | u v |
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| − | | @ |
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| − | | ^ |
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| − | | | |
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| − | | | |
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| − | | du | dv |
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| − | | u (v) @<----------|---------->@ (u) v |
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| − | | du | dv |
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| − | | | |
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| − | | | |
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| − | | v |
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| − | | @ |
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| − | | (u) (v) |
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| − | | |
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| − | o-----------------------------------------------------------o
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| − | Figure 48-d. Remainder of J (Digraph) | |
| − | </pre> | |
| | | | |
| | =====Summary of Conjunction===== | | =====Summary of Conjunction===== |