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Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)

Revision as of 15:24, 3 May 2012

5,836 bytes added ,  15:24, 3 May 2012
→‎Current Work
Line 1,142: Line 1,142:     
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
−
|+ style="height:30px" | <math>\text{Table 42.} ~~ \text{Higher Ascent Sign Relation} ~ \operatorname{Ref}^1 L(A)\!</math>
+
|+ style="height:30px" | <math>\text{Table 44.} ~~ \text{Higher Import Sign Relation} ~ \operatorname{HI}^1 L(A)\!</math>
 
|- style="height:40px; background:#f0f0ff"
 
|- style="height:40px; background:#f0f0ff"
 
| <math>\text{Object}\!</math>
 
| <math>\text{Object}\!</math>
Line 1,212: Line 1,212:  
| valign="bottom" width="33%" |
 
| valign="bottom" width="33%" |
 
<math>\begin{matrix}
 
<math>\begin{matrix}
 +
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 
{}^{\langle} \text{A} {}^{\rangle}
 
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\end{matrix}</math>
 +
|-
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\end{matrix}</math>
 +
|-
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
 
{}^{\langle} \text{B} {}^{\rangle}
 
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle} \text{i} {}^{\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 +
\end{matrix}</math>
 +
|-
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
 
\\
 
\\
−
{}^{\langle} \text{u} {}^{\rangle}
+
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
 
\end{matrix}</math>
 
\end{matrix}</math>
 
| valign="bottom" width="33%" |
 
| valign="bottom" width="33%" |
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\end{matrix}</math>
 
\end{matrix}</math>
 
| valign="bottom" width="33%" |
 
| valign="bottom" width="33%" |
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\end{matrix}</math>
 
\end{matrix}</math>
 
|}
 
|}
Line 1,245: Line 1,338:     
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
 
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
−
|+ style="height:30px" | <math>\text{Table 43.} ~~ \text{Higher Ascent Sign Relation} ~ \operatorname{Ref}^1 L(B)\!</math>
+
|+ style="height:30px" | <math>\text{Table 45.} ~~ \text{Higher Import Sign Relation} ~ \operatorname{HI}^1 L(B)\!</math>
 
|- style="height:40px; background:#f0f0ff"
 
|- style="height:40px; background:#f0f0ff"
 
| <math>\text{Object}\!</math>
 
| <math>\text{Object}\!</math>
Line 1,315: Line 1,408:  
| valign="bottom" width="33%" |
 
| valign="bottom" width="33%" |
 
<math>\begin{matrix}
 
<math>\begin{matrix}
 +
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 
{}^{\langle} \text{A} {}^{\rangle}
 
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\end{matrix}</math>
 +
|-
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{A} {}^{\rangle}
 +
\end{matrix}</math>
 +
|-
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{A} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{A} {}^{\rangle} & )
 +
\\
 +
( & \text{A} & , & {}^{\langle} \text{u} {}^{\rangle} & , & {}^{\langle} \text{u} {}^{\rangle} & )
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\end{matrix}</math>
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
{}^{\langle} \text{B} {}^{\rangle}
 +
\\
 +
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
 
{}^{\langle} \text{B} {}^{\rangle}
 
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle} \text{i} {}^{\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 +
\end{matrix}</math>
 +
|-
 +
| valign="bottom" width="33%" |
 +
<math>\begin{matrix}
 +
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{B} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
 +
\\
 +
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{B} {}^{\rangle} & )
 
\\
 
\\
−
{}^{\langle} \text{u} {}^{\rangle}
+
( & \text{B} & , & {}^{\langle} \text{i} {}^{\rangle} & , & {}^{\langle} \text{i} {}^{\rangle} & )
 
\end{matrix}</math>
 
\end{matrix}</math>
 
| valign="bottom" width="33%" |
 
| valign="bottom" width="33%" |
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\end{matrix}</math>
 
\end{matrix}</math>
 
| valign="bottom" width="33%" |
 
| valign="bottom" width="33%" |
 
<math>\begin{matrix}
 
<math>\begin{matrix}
−
{}^{\langle\langle} \text{A} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{B} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{i} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\\
 
\\
−
{}^{\langle\langle} \text{u} {}^{\rangle\rangle}
+
{}^{\langle} \text{B} {}^{\rangle}
 
\end{matrix}</math>
 
\end{matrix}</math>
 
|}
 
|}
Jon Awbrey
12,080

edits

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