Line 4,058:
Line 4,058:
Figures 46-a through 46-d illustrate the proposition d''J'', rounded out in our usual array of prospects. This proposition of E''U''<sup> •</sup> is what we refer to as the (first order) differential of ''J'', and normally regard as ''the'' differential proposition corresponding to ''J''.
Figures 46-a through 46-d illustrate the proposition d''J'', rounded out in our usual array of prospects. This proposition of E''U''<sup> •</sup> is what we refer to as the (first order) differential of ''J'', and normally regard as ''the'' differential proposition corresponding to ''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 46-a -- Differential of J.gif|center]]</p>
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| |
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<p><center><font size="+1">'''Figure 46-a. Differential 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 46-a. Differential 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 46-b -- Differential of J.gif|center]]</p>
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| |
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<p><center><font size="+1">'''Figure 46-b. Differential 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 46-b. Differential 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 46-c -- Differential of J.gif|center]]</p>
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| |
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<p><center><font size="+1">'''Figure 46-c. Differential 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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| | |/ \| | |
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| | u (du)/ dv du \(dv) 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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| \ v \ du dv / v / |
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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 o-------------------o |
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| |
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| |
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o---------------------------------------------------------------------o
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Figure 46-c. Differential 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 46-d -- Differential of J.gif|center]]</p>
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| |
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<p><center><font size="+1">'''Figure 46-d. Differential 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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| (du) dv / \ du (dv) |
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| / \ |
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| / \ |
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| / \ |
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| / \ |
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| v v |
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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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| |
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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 46-d. Differential of J (Digraph)
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</pre>
=====Remainder of Conjunction=====
=====Remainder of Conjunction=====