Changes

13,898 bytes added , 15:00, 25 August 2007

add image stub

Line 1,141: Line 1,141:

Figure 12. The Anchor

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 12 -- The Anchor.gif|center]]

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<center>'''Figure 12. The Anchor'''</center>

===Figure 13. The Tiller===

Line 1,174: Line 1,178:

Figure 13. The Tiller

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 13 -- The Tiller.gif|center]]

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<center>'''Figure 13. The Tiller'''</center>

===Table 14. Differential Propositions===

Line 1,667: Line 1,675:

|}

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===Figure 16. A Couple of Fourth Gear Orbits===

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[[Image:Diff Log Dyn Sys -- Figure 16 -- A Couple of Fourth Gear Orbits.gif|center]]

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<center>'''Figure 16. A Couple of Fourth Gear Orbits'''</center>

===Figure 16-a. A Couple of Fourth Gear Orbits: 1===

Line 2,064: Line 2,078:

Figure 18-a. Extension from 1 to 2 Dimensions: Areal

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 18-a -- Extension from 1 to 2 Dimensions.gif|center]]

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<center>'''Figure 18-a. Extension from 1 to 2 Dimensions: Areal'''</center>

===Figure 18-b. Extension from 1 to 2 Dimensions: Bundle===

Line 2,093: Line 2,111:

Figure 18-b. Extension from 1 to 2 Dimensions: Bundle

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 18-b -- Extension from 1 to 2 Dimensions.gif|center]]

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<center>'''Figure 18-b. Extension from 1 to 2 Dimensions: Bundle'''</center>

===Figure 18-c. Extension from 1 to 2 Dimensions: Compact===

Line 2,124: Line 2,146:

Figure 18-c. Extension from 1 to 2 Dimensions: Compact

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 18-c -- Extension from 1 to 2 Dimensions.gif|center]]

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<center>'''Figure 18-c. Extension from 1 to 2 Dimensions: Compact'''</center>

===Figure 18-d. Extension from 1 to 2 Dimensions: Digraph===

Line 2,143: Line 2,169:

Figure 18-d. Extension from 1 to 2 Dimensions: Digraph

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 18-d -- Extension from 1 to 2 Dimensions.gif|center]]

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<center>'''Figure 18-d. Extension from 1 to 2 Dimensions: Digraph'''</center>

===Figure 19-a. Extension from 2 to 4 Dimensions: Areal===

Line 2,186: Line 2,216:

Figure 19-a. Extension from 2 to 4 Dimensions: Areal

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 19-a -- Extension from 2 to 4 Dimensions.gif|center]]

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<center>'''Figure 19-a. Extension from 2 to 4 Dimensions: Areal'''</center>

===Figure 19-b. Extension from 2 to 4 Dimensions: Bundle===

Line 2,247: Line 2,281:

Figure 19-b. Extension from 2 to 4 Dimensions: Bundle

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 19-b -- Extension from 2 to 4 Dimensions.gif|center]]

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<center>'''Figure 19-b. Extension from 2 to 4 Dimensions: Bundle'''</center>

===Figure 19-c. Extension from 2 to 4 Dimensions: Compact===

Line 2,287: Line 2,325:

Figure 19-c. Extension from 2 to 4 Dimensions: Compact

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 19-c -- Extension from 2 to 4 Dimensions.gif|center]]

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<center>'''Figure 19-c. Extension from 2 to 4 Dimensions: Compact'''</center>

===Figure 19-d. Extension from 2 to 4 Dimensions: Digraph===

Line 2,330: Line 2,372:

Figure 19-d. Extension from 2 to 4 Dimensions: Digraph

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 19-d -- Extension from 2 to 4 Dimensions.gif|center]]

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<center>'''Figure 19-d. Extension from 2 to 4 Dimensions: Digraph'''</center>

===Figure 20-i. Thematization of Conjunction (Stage 1)===

Line 2,360: Line 2,406:

Figure 20-i. Thematization of Conjunction (Stage 1)

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 20-i -- Thematization of Conjunction (Stage 1).gif|center]]

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<center>'''Figure 20-i. Thematization of Conjunction (Stage 1)'''</center>

===Figure 20-ii. Thematization of Conjunction (Stage 2)===

Line 2,407: Line 2,457:

Figure 20-ii. Thematization of Conjunction (Stage 2)

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 20-ii -- Thematization of Conjunction (Stage 2).gif|center]]

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<center>'''Figure 20-ii. Thematization of Conjunction (Stage 2)'''</center>

===Figure 20-iii. Thematization of Conjunction (Stage 3)===

Line 2,450: Line 2,504:

Figure 20-iii. Thematization of Conjunction (Stage 3)

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 20-iii -- Thematization of Conjunction (Stage 3).gif|center]]

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<center>'''Figure 20-iii. Thematization of Conjunction (Stage 3)'''</center>

===Figure 21. Thematization of Disjunction and Equality===

Line 2,516: Line 2,574:

Figure 21. Thematization of Disjunction and Equality

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 21 -- Thematization of Disjunction and Equality.gif|center]]

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<center>'''Figure 21. Thematization of Disjunction and Equality'''</center>

===Table 22. Disjunction ''f'' and Equality ''g''===

Line 3,673: Line 3,735:

Figure 30. Generic Frame of a Logical Transformation

</pre>

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'''Note.''' The following image was corrupted in transit between software platforms.

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[[Image:Diff Log Dyn Sys -- Figure 30 -- Generic Frame of a Logical Transformation.gif|center]]

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<center>'''Figure 30. Generic Frame of a Logical Transformation'''</center>

===Formula Display 3===

Line 3,729: Line 3,797:

Figure 31. Operator Diagram (1)

</pre>

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'''Note.''' The following image was corrupted in transit between software platforms.

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[[Image:Diff Log Dyn Sys -- Figure 31 -- Operator Diagram (1).gif|center]]

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<center>'''Figure 31. Operator Diagram (1)'''</center>

===Figure 32. Operator Diagram (2)===

Line 3,754: Line 3,828:

Figure 32. Operator Diagram (2)

</pre>

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'''Note.''' The following image was corrupted in transit between software platforms.

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[[Image:Diff Log Dyn Sys -- Figure 32 -- Operator Diagram (2).gif|center]]

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<center>'''Figure 32. Operator Diagram (2)'''</center>

===Figure 33-i. Analytic Diagram (1)===

Line 3,774: Line 3,854:

Figure 33-i. Analytic Diagram (1)

</pre>

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'''Note.''' The following image was corrupted in transit between software platforms.

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[[Image:Diff Log Dyn Sys -- Figure 33-i -- Analytic Diagram (1).gif|center]]

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<center>'''Figure 33-i. Analytic Diagram (1)'''</center>

===Figure 33-ii. Analytic Diagram (2)===

Line 3,794: Line 3,880:

Figure 33-ii. Analytic Diagram (2)

</pre>

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'''Note.''' The following image was corrupted in transit between software platforms.

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[[Image:Diff Log Dyn Sys -- Figure 33-ii -- Analytic Diagram (2).gif|center]]

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<center>'''Figure 33-ii. Analytic Diagram (2)'''</center>

===Formula Display 4===

Line 4,012: Line 4,104:

Figure 34. Tangent Functor Diagram

</pre>

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'''Note.''' The following image was corrupted in transit between software platforms.

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[[Image:Diff Log Dyn Sys -- Figure 34 -- Tangent Functor Diagram.gif|center]]

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<center>'''Figure 34. Tangent Functor Diagram'''</center>

===Figure 35. Conjunction as Transformation===

Line 4,067: Line 4,165:

Figure 35. Conjunction as Transformation

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 35 -- A Conjunction Viewed as a Transformation.gif|center]]

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<center>'''Figure 35. Conjunction as Transformation'''</center>

===Table 36. Computation of !e!J===

Line 4,140: Line 4,242:

−

===Figure 37-a. Tacit Extension of J (Areal)===

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===Figure 37-a. Tacit Extension of ''J''  (Areal)===

<pre>

Line 4,183: Line 4,285:

</pre>

−

===Figure 37-b. Tacit Extension of J (Bundle)===

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[[Image:Diff Log Dyn Sys -- Figure 37-a -- Tacit Extension of J.gif|center]]

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<center>'''Figure 37-a. Tacit Extension of ''J''  (Areal)'''</center>

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===Figure 37-b. Tacit Extension of ''J''  (Bundle)===

<pre>

Line 4,252: Line 4,358:

</pre>

−

===Figure 37-c. Tacit Extension of J (Compact)===

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[[Image:Diff Log Dyn Sys -- Figure 37-b -- Tacit Extension of J.gif|center]]

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<center>'''Figure 37-b. Tacit Extension of ''J''  (Bundle)'''</center>

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===Figure 37-c. Tacit Extension of ''J''  (Compact)===

<pre>

Line 4,292: Line 4,402:

</pre>

−

===Figure 37-d. Tacit Extension of J (Digraph)===

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[[Image:Diff Log Dyn Sys -- Figure 37-c -- Tacit Extension of J.gif|center]]

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<center>'''Figure 37-c. Tacit Extension of ''J''  (Compact)'''</center>

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===Figure 37-d. Tacit Extension of ''J''  (Digraph)===

<pre>

Line 4,333: Line 4,447:

Figure 37-d. Tacit Extension of J (Digraph)

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 37-d -- Tacit Extension of J.gif|center]]

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<center>'''Figure 37-d. Tacit Extension of ''J''  (Digraph)'''</center>

===Table 38. Computation of EJ (Method 1)===

Line 4,504: Line 4,622:

−

===Figure 40-a. Enlargement of J (Areal)===

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===Figure 40-a. Enlargement of ''J''  (Areal)===

<pre>

Line 4,547: Line 4,665:

</pre>

−

===Figure 40-b. Enlargement of J (Bundle)===

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[[Image:Diff Log Dyn Sys -- Figure 40-a -- Enlargement of J.gif|center]]

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<center>'''Figure 40-a. Enlargement of ''J''  (Areal)'''</center>

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===Figure 40-b. Enlargement of ''J''  (Bundle)===

<pre>

Line 4,616: Line 4,738:

</pre>

−

===Figure 40-c. Enlargement of J (Compact)===

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[[Image:Diff Log Dyn Sys -- Figure 40-b -- Enlargement of J.gif|center]]

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<center>'''Figure 40-b. Enlargement of ''J''  (Bundle)'''</center>

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===Figure 40-c. Enlargement of ''J''  (Compact)===

<pre>

Line 4,656: Line 4,782:

</pre>

−

===Figure 40-d. Enlargement of J (Digraph)===

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[[Image:Diff Log Dyn Sys -- Figure 40-c -- Enlargement of J.gif|center]]

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<center>'''Figure 40-c. Enlargement of ''J''  (Compact)'''</center>

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===Figure 40-d. Enlargement of ''J''  (Digraph)===

<pre>

Line 4,697: Line 4,827:

Figure 40-d. Enlargement of J (Digraph)

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 40-d -- Enlargement of J.gif|center]]

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<center>'''Figure 40-d. Enlargement of ''J''  (Digraph)'''</center>

===Table 41. Computation of DJ (Method 1)===

Line 4,964: Line 5,098:

−

===Figure 44-a. Difference Map of J (Areal)===

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===Figure 44-a. Difference Map of ''J''  (Areal)===

<pre>

Line 5,007: Line 5,141:

</pre>

−

===Figure 44-b. Difference Map of J (Bundle)===

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[[Image:Diff Log Dyn Sys -- Figure 44-a -- Difference Map of J.gif|center]]

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<center>'''Figure 44-a. Difference Map of ''J''  (Areal)'''</center>

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===Figure 44-b. Difference Map of ''J''  (Bundle)===

<pre>

Line 5,076: Line 5,214:

</pre>

−

===Figure 44-c. Difference Map of J (Compact)===

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[[Image:Diff Log Dyn Sys -- Figure 44-b -- Difference Map of J.gif|center]]

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<center>'''Figure 44-b. Difference Map of ''J''  (Bundle)'''</center>

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===Figure 44-c. Difference Map of ''J''  (Compact)===

<pre>

Line 5,117: Line 5,259:

</pre>

−

===Figure 44-d. Difference Map of J (Digraph)===

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[[Image:Diff Log Dyn Sys -- Figure 44-c -- Difference Map of J.gif|center]]

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<center>'''Figure 44-c. Difference Map of ''J''  (Compact)'''</center>

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===Figure 44-d. Difference Map of ''J''  (Digraph)===

<pre>

Line 5,155: Line 5,301:

Figure 44-d. Difference Map of J (Digraph)

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 44-d -- Difference Map of J.gif|center]]

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<center>'''Figure 44-d. Difference Map of ''J''  (Digraph)'''</center>

===Table 45. Computation of dJ===

Line 5,193: Line 5,343:

−

===Figure 46-a. Differential of J (Areal)===

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===Figure 46-a. Differential of ''J''  (Areal)===

<pre>

Line 5,236: Line 5,386:

</pre>

−

===Figure 46-b. Differential of J (Bundle)===

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[[Image:Diff Log Dyn Sys -- Figure 46-a -- Differential of J.gif|center]]

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<center>'''Figure 46-a. Differential of ''J''  (Areal)'''</center>

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===Figure 46-b. Differential of ''J''  (Bundle)===

<pre>

Line 5,305: Line 5,459:

</pre>

−

===Figure 46-c. Differential of J (Compact)===

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[[Image:Diff Log Dyn Sys -- Figure 46-b -- Differential of J.gif|center]]

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<center>'''Figure 46-b. Differential of ''J''  (Bundle)'''</center>

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===Figure 46-c. Differential of ''J''  (Compact)===

<pre>

Line 5,342: Line 5,500:

</pre>

−

===Figure 46-d. Differential of J (Digraph)===

+

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[[Image:Diff Log Dyn Sys -- Figure 46-c -- Differential of J.gif|center]]

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<center>'''Figure 46-c. Differential of ''J''  (Compact)'''</center>

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===Figure 46-d. Differential of ''J''  (Digraph)===

<pre>

Line 5,378: Line 5,540:

Figure 46-d. Differential of J (Digraph)

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 46-d -- Differential of J.gif|center]]

+

<center>'''Figure 46-d. Differential of ''J''  (Digraph)'''</center>

===Table 47. Computation of rJ===

Line 5,439: Line 5,605:

−

===Figure 48-a. Remainder of J (Areal)===

+

===Figure 48-a. Remainder of ''J''  (Areal)===

<pre>

Line 5,482: Line 5,648:

</pre>

−

===Figure 48-b. Remainder of J (Bundle)===

+

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[[Image:Diff Log Dyn Sys -- Figure 48-a -- Remainder of J.gif|center]]

+

<center>'''Figure 48-a. Remainder of ''J''  (Areal)'''</center>

+

===Figure 48-b. Remainder of ''J''  (Bundle)===

<pre>

Line 5,551: Line 5,721:

</pre>

−

===Figure 48-c. Remainder of J (Compact)===

+

+

[[Image:Diff Log Dyn Sys -- Figure 48-b -- Remainder of J.gif|center]]

+

<center>'''Figure 48-b. Remainder of ''J''  (Bundle)'''</center>

+

===Figure 48-c. Remainder of ''J''  (Compact)===

<pre>

Line 5,591: Line 5,765:

</pre>

−

===Figure 48-d. Remainder of J (Digraph)===

+

+

[[Image:Diff Log Dyn Sys -- Figure 48-c -- Remainder of J.gif|center]]

+

<center>'''Figure 48-c. Remainder of ''J''  (Compact)'''</center>

+

===Figure 48-d. Remainder of ''J''  (Digraph)===

<pre>

Line 5,627: Line 5,805:

Figure 48-d. Remainder of J (Digraph)

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 48-d -- Remainder of J.gif|center]]

+

<center>'''Figure 48-d. Remainder of ''J''  (Digraph)'''</center>

===Table 49. Computation Summary for J===

Line 6,228: Line 6,410:

Figure 52. Decomposition of the Enlarged Conjunction EJ = (J, DJ)

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 52 -- Decomposition of EJ.gif|center]]

+

<center>'''Figure 52. Decomposition of E''J'''''</center>

===Figure 53. Decomposition of the Differed Conjunction DJ = (dJ, ddJ)===

Line 6,279: Line 6,465:

Figure 53. Decomposition of the Differed Conjunction DJ = (dJ, ddJ)

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 53 -- Decomposition of DJ.gif|center]]

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<center>'''Figure 53. Decomposition of D''J'''''</center>

===Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators===

Line 6,981: Line 7,171:

Figure 56-a1. Radius Map of the Conjunction J = uv

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 56-a1 -- Radius Map of J.gif|center]]

+

<center>'''Figure 56-a1. Radius Map of the Conjunction ''J'' = ''uv'''''</center>

===Figure 56-a2. Secant Map of the Conjunction J = uv===

Line 7,049: Line 7,243:

Figure 56-a2. Secant Map of the Conjunction J = uv

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 56-a2 -- Secant Map of J.gif|center]]

+

<center>'''Figure 56-a2. Secant Map of the Conjunction ''J'' = ''uv'''''</center>

===Figure 56-a3. Chord Map of the Conjunction J = uv===

Line 7,117: Line 7,315:

Figure 56-a3. Chord Map of the Conjunction J = uv

</pre>

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[[Image:Diff Log Dyn Sys -- Figure 56-a3 -- Chord Map of J.gif|center]]

+

<center>'''Figure 56-a3. Chord Map of the Conjunction ''J'' = ''uv'''''</center>

===Figure 56-a4. Tangent Map of the Conjunction J = uv===

Line 7,185: Line 7,387:

Figure 56-a4. Tangent Map of the Conjunction J = uv

</pre>

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+

[[Image:Diff Log Dyn Sys -- Figure 56-a4 -- Tangent Map of J.gif|center]]

+

<center>'''Figure 56-a4. Tangent Map of the Conjunction ''J'' = ''uv'''''</center>

===Figure 56-b1. Radius Map of the Conjunction J = uv===

Line 7,285: Line 7,491:

Figure 56-b1. Radius Map of the Conjunction J = uv

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 56-b1 -- Radius Map of J.gif|center]]

+

<center>'''Figure 56-b1. Radius Map of the Conjunction ''J'' = ''uv'''''</center>

===Figure 56-b2. Secant Map of the Conjunction J = uv===

Line 7,385: Line 7,595:

Figure 56-b2. Secant Map of the Conjunction J = uv

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 56-b2 -- Secant Map of J.gif|center]]

+

<center>'''Figure 56-b2. Secant Map of the Conjunction ''J'' = ''uv'''''</center>

===Figure 56-b3. Chord Map of the Conjunction J = uv===

Line 7,485: Line 7,699:

Figure 56-b3. Chord Map of the Conjunction J = uv

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 56-b3 -- Chord Map of J.gif|center]]

+

<center>'''Figure 56-b3. Chord Map of the Conjunction ''J'' = ''uv'''''</center>

===Figure 56-b4. Tangent Map of the Conjunction J = uv===

Line 7,585: Line 7,803:

Figure 56-b4. Tangent Map of the Conjunction J = uv

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 56-b4 -- Tangent Map of J.gif|center]]

+

<center>'''Figure 56-b4. Tangent Map of the Conjunction ''J'' = ''uv'''''</center>

===Figure 57-1. Radius Operator Diagram for the Conjunction J = uv===

Line 7,655: Line 7,877:

Figure 57-1. Radius Operator Diagram for the Conjunction J = uv

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 57-1 -- Radius Operator Diagram for J.gif|center]]

+

<center>'''Figure 57-1. Radius Operator Diagram for the Conjunction ''J'' = ''uv'''''</center>

===Figure 57-2. Secant Operator Diagram for the Conjunction J = uv===

Line 7,725: Line 7,951:

Figure 57-2. Secant Operator Diagram for the Conjunction J = uv

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 57-2 -- Secant Operator Diagram for J.gif|center]]

+

<center>'''Figure 57-2. Secant Operator Diagram for the Conjunction ''J'' = ''uv'''''</center>

===Figure 57-3. Chord Operator Diagram for the Conjunction J = uv===

Line 7,795: Line 8,025:

Figure 57-3. Chord Operator Diagram for the Conjunction J = uv

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 57-3 -- Chord Operator Diagram for J.gif|center]]

+

<center>'''Figure 57-3. Chord Operator Diagram for the Conjunction ''J'' = ''uv'''''</center>

===Figure 57-4. Tangent Functor Diagram for the Conjunction J = uv===

Line 7,865: Line 8,099:

Figure 57-4. Tangent Functor Diagram for the Conjunction J = uv

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 57-4 -- Tangent Functor Diagram for J.gif|center]]

+

<center>'''Figure 57-4. Tangent Functor Diagram for the Conjunction ''J'' = ''uv'''''</center>

===Formula Display 11===

Line 8,902: Line 9,140:

Figure 61. Propositional Transformation

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 61 -- Propositional Transformation.gif|center]]

+

<center>'''Figure 61. Propositional Transformation'''</center>

===Figure 62. Propositional Transformation (Short Form)===

Line 8,953: Line 9,195:

Figure 62. Propositional Transformation (Short Form)

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 62 -- Propositional Transformation (Short Form).gif|center]]

+

<center>'''Figure 62. Propositional Transformation (Short Form)'''</center>

===Figure 63. Transformation of Positions===

Line 9,030: Line 9,276:

Figure 63. Transformation of Positions

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 63 -- Transformation of Positions.gif|center]]

+

<center>'''Figure 63. Transformation of Positions'''</center>

===Table 64. Transformation of Positions===

Line 9,220: Line 9,470:

| ''U'' •

|- style="background:paleturquoise"

−

| ''f''''i''‹''x'', ''y''›

+

| rowspan="2" | ''f''''i''‹''x'', ''y''›

|

−

{|

+

{| align="right" style="background:paleturquoise; text-align:right"

+

| ''u'' =

+

|-

+

| ''v'' =

+

|}

|

−

{|

+

{| align="center" style="background:paleturquoise; text-align:center"

−

| ~~u =~~

+

| 1 1 0 0

|-

−

| ~~v =~~

+

| 1 0 1 0

|}

−

|-

|

−

{|

+

{| align="left" style="background:paleturquoise; text-align:left"

−

| x =

+

| = ''u''

|-

−

| y =

+

| = ''v''

−

|}

+

| rowspan="2" | ''f''''j''‹''u'', ''v''›

+

|- style="background:paleturquoise"

|

−

{|

+

{| align="right" style="background:paleturquoise; text-align:right"

−

|

+

| ''x'' =

−

{|

−

~~| 1 1 0 0~~

|-

−

| ~~1 0 1 0~~

+

| ''y'' =

|}

−

|-

|

−

{|

+

{| align="center" style="background:paleturquoise; text-align:center"

| 1 1 1 0

|-

| 1 0 0 1

−

|}

|

−

{|

+

{| align="left" style="background:paleturquoise; text-align:left"

−

|

+

| = ''f''‹''u'', ''v''›

−

{|

−

| = u

|-

−

| = v

+

| = ''g''‹''u'', ''v''›

|}

−

|-

−

|

−

{|

−

~~| = f‹u, v›~~

−

|-

−

~~| = g‹u, v›~~

−

|}

−

|}

−

~~| ''f''''j''‹''u'', ''v''›~~

|-

|

{| cellpadding="2" style="background:lightcyan"

−

| f0

+

| ''f''0

|-

−

| f1

+

| ''f''1

|-

−

| f2

+

| ''f''2

|-

−

| f3

+

| ''f''3

|-

−

| f4

+

| ''f''4

|-

−

| f5

+

| ''f''5

|-

−

| f6

+

| ''f''6

|-

−

| f7

+

| ''f''7

|}

|

Line 9,293: Line 9,532:

| ()

|-

−

|  (x)(y) 

+

|  (''x'')(''y'') 

|-

−

|  (x) y  

+

|  (''x'') ''y''  

|-

−

|  (x)    

+

|  (''x'')    

|-

−

|   x (y) 

+

|   ''x'' (''y'') 

|-

−

|     (y) 

+

|     (''y'') 

|-

−

|  (x, y) 

+

|  (''x'', ''y'') 

|-

−

|  (x  y) 

+

|  (''x''  ''y'') 

|}

|

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| ()

|-

−

|  (u)(v) 

+

|  (''u'')(''v'') 

|-

−

|  (u)(v) 

+

|  (''u'')(''v'') 

|-

−

|  (u, v) 

+

|  (''u'', ''v'') 

|-

−

|  (u, v) 

+

|  (''u'', ''v'') 

|-

−

|  (u  v) 

+

|  (''u''  ''v'') 

|-

−

|  (u  v) 

+

|  (''u''  ''v'') 

|}

|

{| cellpadding="2" style="background:lightcyan"

−

| f0

+

| ''f''0

|-

−

| f0

+

| ''f''0

|-

−

| f1

+

| ''f''1

|-

−

| f1

+

| ''f''1

|-

−

| f6

+

| ''f''6

|-

−

| f6

+

| ''f''6

|-

−

| f7

+

| ''f''7

|-

−

| f7

+

| ''f''7

|}

|-

|

{| cellpadding="2" style="background:lightcyan"

−

| f8

+

| ''f''8

|-

−

| f9

+

| ''f''9

|-

−

| f10

+

| ''f''10

|-

−

| f11

+

| ''f''11

|-

−

| f12

+

| ''f''12

|-

−

| f13

+

| ''f''13

|-

−

| f14

+

| ''f''14

|-

−

| f15

+

| ''f''15

|}

|

{| cellpadding="2" style="background:lightcyan"

−

|   x  y  

+

|   ''x''  ''y''  

|-

−

| ((x, y))

+

| ((''x'', ''y''))

|-

−

|      y  

+

|      ''y''  

|-

−

|  (x (y))

+

|  (''x'' (''y''))

|-

−

|   x     

+

|   ''x''     

|-

−

| ((x) y) 

+

| ((''x'') ''y'') 

|-

−

| ((x)(y))

+

| ((''x'')(''y''))

|-

| (())

Line 9,418: Line 9,657:

|

{| cellpadding="2" style="background:lightcyan"

−

|   u  v  

+

|   ''u''  ''v''  

|-

−

|   u  v  

+

|   ''u''  ''v''  

|-

−

| ((u, v))

+

| ((''u'', ''v''))

|-

−

| ((u, v))

+

| ((''u'', ''v''))

|-

−

| ((u)(v))

+

| ((''u'')(''v''))

|-

−

| ((u)(v))

+

| ((''u'')(''v''))

|-

| (())

Line 9,436: Line 9,675:

|

{| cellpadding="2" style="background:lightcyan"

−

| f8

+

| ''f''8

|-

−

| f8

+

| ''f''8

|-

−

| f9

+

| ''f''9

|-

−

| f9

+

| ''f''9

|-

−

| f14

+

| ''f''14

|-

−

| f14

+

| ''f''14

|-

−

| f15

+

| ''f''15

|-

−

| f15

+

| ''f''15

|}

Line 10,210: Line 10,449:

−

===Figure 69. Difference Map of F = ‹f, g› = ‹((u)(v)), ((u, v))›===

+

===Figure 69. Difference Map of F = ‹f, g› = ‹((u)(v)), ((u, v))›===

<pre>

Line 10,276: Line 10,515:

Figure 69. Difference Map of F = <f, g> = <((u)(v)), ((u, v))>

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 69 -- Difference Map (Short Form).gif|center]]

+

<center>'''Figure 69. Difference Map of F = ‹f, g› = ‹((u)(v)), ((u, v))›'''</center>

===Formula Display 19===

Line 10,314: Line 10,557:

−

===Figure 70-a. Tangent Functor Diagram for F‹u, v› = ‹((u)(v)), ((u, v))›===

+

===Figure 70-a. Tangent Functor Diagram for F‹u, v› = ‹((u)(v)), ((u, v))›===

<pre>

Line 10,399: Line 10,642:

Figure 70-a. Tangent Functor Diagram for F‹u, v› = <((u)(v)), ((u, v))>

</pre>

+

+

[[Image:Diff Log Dyn Sys -- Figure 70-a -- Tangent Functor Diagram.gif|center]]

+

<center>'''Figure 70-a. Tangent Functor Diagram for F‹u, v› = ‹((u)(v)), ((u, v))›'''</center>

===Figure 70-b. Tangent Functor Ferris Wheel for F‹u, v› = ‹((u)(v)), ((u, v))›===

Jon Awbrey

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Revision as of 15:00, 25 August 2007