MyWikiBiz, Author Your Legacy — Wednesday November 27, 2024
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, 13:08, 19 June 2007
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| First, the enlargement map (or the secant transformation) E''G'' = ‹E''G''<sub>1</sub>, E''G''<sub>2</sub>› : E''U''<sup> •</sup> → E''X''<sup> •</sup> is defined by the following set of component equations: | | First, the enlargement map (or the secant transformation) E''G'' = ‹E''G''<sub>1</sub>, E''G''<sub>2</sub>› : E''U''<sup> •</sup> → E''X''<sup> •</sup> is defined by the following set of component equations: |
| | | |
− | <pre> | + | <br><font face="courier new"> |
− | o-------------------------------------------------o
| + | {| align="center" border="1" cellpadding="12" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:left; width:96%" |
− | | | | + | | |
− | | EG_i = G_i <u + du, v + dv> | | + | {| align="left" border="0" cellpadding="12" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:left; width:100%" |
− | | | | + | | width="8%" | E''G''<sub>''i''</sub> |
− | o-------------------------------------------------o
| + | | width="4%" | = |
− | </pre> | + | | width="88%" | ''G''<sub>''i''</sub>‹''u'' + d''u'', ''v'' + d''v''› |
| + | |} |
| + | |} |
| + | </font><br> |
| | | |
| Second, the difference map (or the chordal transformation) D''G'' = ‹D''G''<sub>1</sub>, D''G''<sub>2</sub>› : E''U''<sup> •</sup> → E''X''<sup> •</sup> is defined in component-wise fashion as the boolean sum of the initial proposition ''G''<sub>''i''</sub> and the enlarged proposition E''G''<sub>''i''</sub>, for ''i'' = 1, 2, according to the following set of equations: | | Second, the difference map (or the chordal transformation) D''G'' = ‹D''G''<sub>1</sub>, D''G''<sub>2</sub>› : E''U''<sup> •</sup> → E''X''<sup> •</sup> is defined in component-wise fashion as the boolean sum of the initial proposition ''G''<sub>''i''</sub> and the enlarged proposition E''G''<sub>''i''</sub>, for ''i'' = 1, 2, according to the following set of equations: |