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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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Figure 31. Operator Diagram (1)

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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)===

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Figure 32. Operator Diagram (2)

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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)===

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Figure 33-i. Analytic Diagram (1)

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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)===

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Figure 33-ii. Analytic Diagram (2)

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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===

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Figure 34. Tangent Functor Diagram

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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===

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Figure 35. Conjunction as Transformation

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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===

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

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

<pre>

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</pre>

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===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>

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</pre>

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===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 4,358: Line 4,402:

</pre>

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===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)===

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

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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)===

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

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

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</pre>

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===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 4,682: Line 4,738:

</pre>

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===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 4,722: Line 4,782:

</pre>

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===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>

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Figure 40-d. Enlargement of J (Digraph)

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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)===

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

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

<pre>

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</pre>

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===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>

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</pre>

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===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>

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</pre>

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===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>

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

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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===

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

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

<pre>

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</pre>

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===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>

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</pre>

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===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>

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</pre>

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===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>

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Figure 46-d. Differential of J (Digraph)

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

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

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

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

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

<pre>

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</pre>

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

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

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

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

<pre>

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</pre>

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

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

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

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

<pre>

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</pre>

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

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

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

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

<pre>

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Figure 48-d. Remainder of J (Digraph)

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

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

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

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

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

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

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

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

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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===

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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]]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

</pre>

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

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

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

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

</pre>

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

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

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

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

</pre>

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

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

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

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

</pre>

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

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

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

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

</pre>

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

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

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

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

</pre>

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

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

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

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

</pre>

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

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

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

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

</pre>

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

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

===Formula Display 11===

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Figure 61. Propositional Transformation

</pre>

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

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

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

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Figure 62. Propositional Transformation (Short Form)

</pre>

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

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

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

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Figure 63. Transformation of Positions

</pre>

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

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

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

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

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

<pre>

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

</pre>

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

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

===Formula Display 19===

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−

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

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

<pre>

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

</pre>

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

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<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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Changes

User:Jon Awbrey/ATLAS (view source)

Revision as of 15:00, 25 August 2007