It is important to analyze the distribution of strain rate near the stagnation point for understanding the mechanic and heat behaviors of the material during explosive welding.

The calculation of stagnation point position of straight pipeline section with both movable ends and L-type pipeline section with bend at one end and bellows type expansion joint at other end is discussed.

In allusion to Funar Conjecture :"If a random triangle lies in a closed unit square,then its inscribed circle s radius,r≤(5-1)/4",an equivalent minimum problem about a function of 2-variables is studied;the stagnation point and its value,value on the boundary of the function of 2-variables are studied,the equivalent problem is proved correct,so the Funar Conjecture is proved correct.

Based on those ba- sic theories , the critical point method of optimal polarization is given and reinforced at length .

Darboux s theoryis used t prove that the extreme ualue of univariate function is its maximum or minimum when it has only one critical point.

This article deals with problems of extreme value of tribasic and dual functions in the cases of infinite stationary point,offers a determined approach to extreme value,and,with it,gives a proof of several inequalities.

Using Taylor Theorem,we generalize the second sufficient conditions for extreme point and inflection point,and give the classification for a large class of stationary point.

The extreme value of binary function at f_(xx)f_(yy)-f~2_(xy)=0 is judged by its direction derivative which follows ray starting from stable point and passing point P at every point P in noncentral neighborhood of stable point.

To the mixed effects models which the number of support points is equal to the number of parameters, we construct D-optimal block designs.