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>
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<br>
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o---------------------------------------o
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<p>[[Image:Diff Log Dyn Sys -- Figure 48-a -- Remainder of J.gif|center]]</p>
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| |
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<p><center><font size="+1">'''Figure 48-a. Remainder of ''J'' (Areal)'''</font></center></p>
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| 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)
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</pre>
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<pre>
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<br>
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o-----------------------------o
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<p>[[Image:Diff Log Dyn Sys -- Figure 48-b -- Remainder of J.gif|center]]</p>
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| |
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<p><center><font size="+1">'''Figure 48-b. Remainder of ''J'' (Bundle)'''</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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| 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)
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</pre>
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<pre>
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<br>
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o---------------------------------------------------------------------o
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<p>[[Image:Diff Log Dyn Sys -- Figure 48-c -- Remainder of J.gif|center]]</p>
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| |
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<p><center><font size="+1">'''Figure 48-c. Remainder of ''J'' (Compact)'''</font></center></p>
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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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| / / \ \ |
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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)
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</pre>
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<pre>
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<br>
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o-----------------------------------------------------------o
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<p>[[Image:Diff Log Dyn Sys -- Figure 48-d -- Remainder of J.gif|center]]</p>
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| |
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<p><center><font size="+1">'''Figure 48-d. Remainder of ''J'' (Digraph)'''</font></center></p>
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| u v |
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| @ |
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| ^ |
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| | |
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| | |
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| | |
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| | |
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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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| u (v) @<----------|---------->@ (u) v |
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| du | dv |
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| | |
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| | |
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| | |
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| | |
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| | |
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| | |
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| | |
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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)
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</pre>
=====Summary of Conjunction=====
=====Summary of Conjunction=====