Changes

MyWikiBiz, Author Your Legacy — Tuesday December 03, 2024
Jump to navigationJump to search

User:Jon Awbrey/ATLAS (view source)

Revision as of 14:28, 2 July 2007

12,488 bytes added ,  14:28, 2 July 2007
→‎Table 59. Synopsis of Terminology: Restrictive and Alternative Subtypes: copy model table
Line 8,327: Line 8,327:  
o--------------o----------------------o--------------------o----------------------o
 
o--------------o----------------------o--------------------o----------------------o
 
</pre>
 
</pre>
 +
 +
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:left; width:96%"
 +
|+ '''Table 55.  Synopsis of Terminology:  Restrictive and Alternative Subtypes'''
 +
|- style="background:paleturquoise"
 +
! &nbsp;
 +
! Operator
 +
! Proposition
 +
! Map
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Tacit
 +
|-
 +
| Extension
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <math>\epsilon</math> :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <math>\epsilon</math>''J'' :
 +
|-
 +
| 〈''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v''〉&nbsp;&rarr;&nbsp;'''B'''
 +
|-
 +
| '''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>&nbsp;&rarr;&nbsp;'''B'''
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <math>\epsilon</math>''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''B'''<sup>1</sup>]
 +
|}
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Trope
 +
|-
 +
| Extension
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <math>\eta</math> :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; d''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <math>\eta</math>''J'' :
 +
|-
 +
| 〈''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v''〉&nbsp;&rarr;&nbsp;'''D'''
 +
|-
 +
| '''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>&nbsp;&rarr;&nbsp;'''D'''
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <math>\eta</math>''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[d''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''D'''<sup>1</sup>]
 +
|}
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Enlargement
 +
|-
 +
| Operator
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| E :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; d''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| E''J'' :
 +
|-
 +
| 〈''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v''〉&nbsp;&rarr;&nbsp;'''D'''
 +
|-
 +
| '''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>&nbsp;&rarr;&nbsp;'''D'''
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| E''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[d''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''D'''<sup>1</sup>]
 +
|}
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Difference
 +
|-
 +
| Operator
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| D :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; d''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| D''J'' :
 +
|-
 +
| 〈''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v''〉&nbsp;&rarr;&nbsp;'''D'''
 +
|-
 +
| '''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>&nbsp;&rarr;&nbsp;'''D'''
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| D''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[d''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''D'''<sup>1</sup>]
 +
|}
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Differential
 +
|-
 +
| Operator
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| d :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; d''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| d''J'' :
 +
|-
 +
| 〈''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v''〉&nbsp;&rarr;&nbsp;'''D'''
 +
|-
 +
| '''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>&nbsp;&rarr;&nbsp;'''D'''
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| d''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[d''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''D'''<sup>1</sup>]
 +
|}
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Remainder
 +
|-
 +
| Operator
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| r :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; d''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| r''J'' :
 +
|-
 +
| 〈''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v''〉&nbsp;&rarr;&nbsp;'''D'''
 +
|-
 +
| '''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>&nbsp;&rarr;&nbsp;'''D'''
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| r''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[d''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''D'''<sup>1</sup>]
 +
|}
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Radius
 +
|-
 +
| Operator
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <font face=georgia>'''e'''</font> = ‹<math>\epsilon</math>, <math>\eta</math>› :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <font face=georgia>'''e'''</font>''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[''x'',&nbsp;d''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''B'''&nbsp;&times;&nbsp;'''D''']
 +
|}
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Secant
 +
|-
 +
| Operator
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <font face=georgia>'''E'''</font> = ‹<math>\epsilon</math>, E› :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <font face=georgia>'''E'''</font>''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[''x'',&nbsp;d''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''B'''&nbsp;&times;&nbsp;'''D''']
 +
|}
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Chord
 +
|-
 +
| Operator
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <font face=georgia>'''D'''</font> = ‹<math>\epsilon</math>, D› :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|-
 +
| &nbsp;
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <font face=georgia>'''D'''</font>''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[''x'',&nbsp;d''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''B'''&nbsp;&times;&nbsp;'''D''']
 +
|}
 +
|-
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| Tangent
 +
|-
 +
| Functor
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <font face=georgia>'''T'''</font> = ‹<math>\epsilon</math>, d› :
 +
|-
 +
| ''U''<sup>&nbsp;&bull;</sup> &rarr; E''U''<sup>&nbsp;&bull;</sup>&nbsp;,&nbsp;&nbsp;''X''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>&nbsp;,
 +
|-
 +
| (''U''<sup>&nbsp;&bull;</sup> &rarr; ''X''<sup>&nbsp;&bull;</sup>) &rarr; (E''U''<sup>&nbsp;&bull;</sup> &rarr; E''X''<sup>&nbsp;&bull;</sup>)
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| d''J'' :
 +
|-
 +
| 〈''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v''〉&nbsp;&rarr;&nbsp;'''D'''
 +
|-
 +
| '''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>&nbsp;&rarr;&nbsp;'''D'''
 +
|}
 +
|
 +
{| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%"
 +
| <font face=georgia>'''T'''</font>''J'' :
 +
|-
 +
| [''u'',&nbsp;''v'',&nbsp;d''u'',&nbsp;d''v'']&nbsp;&rarr;&nbsp;[''x'',&nbsp;d''x'']
 +
|-
 +
| ['''B'''<sup>2</sup>&nbsp;&times;&nbsp;'''D'''<sup>2</sup>]&nbsp;&rarr;&nbsp;['''B'''&nbsp;&times;&nbsp;'''D''']
 +
|}
 +
|}<br>
    
===Formula Display 12===
 
===Formula Display 12===
Jon Awbrey
12,080

edits

Retrieved from "https://mywikibiz.com/Special:MobileDiff/49235"

Navigation menu