From our analytic study of the Templator

This functin does not give you the correct curve in MATHEMATICA 

[Graphics:../Images/templator_gr_69.gif]

This is the analytic relation between fo, K and ku to find the zero manifold of the  trace of R with MATHEMATICA 

[Graphics:../Images/templator_gr_70.gif]
[Graphics:../Images/templator_gr_71.gif]

[Graphics:../Images/templator_gr_72.gif]

[Graphics:../Images/templator_gr_73.gif]
[Graphics:../Images/templator_gr_74.gif]
[Graphics:../Images/templator_gr_75.gif]

[Graphics:../Images/templator_gr_76.gif]

Comparison between exact and the second order approximation 

[Graphics:../Images/templator_gr_77.gif]

[Graphics:../Images/templator_gr_78.gif]

[Graphics:../Images/templator_gr_79.gif]

Converted by Mathematica      November 14, 2000