Proof of two inequalities by means of conditional extremum;

One full condition of conditional extremum;

Solution of conditional extremum of quadric form on hypersurface by using the matrix method

Li Wen-xue puts forward a sufficient condition of conditional extreme value with Lagrange Function,but his proof is wrong.

In the paper,the sufficient conditions for judging the conditional extreme value of multi-function are made out with Hissian matrix,and the mistakes in the literature [3] are pointed out.

Wenxue Li put forward a sufficient condition of conditional extreme value with Lagrange function, but his proof is wrong.

Firstly this paper analyzes the reasons resulting in un-sharing input voltage of the ISOP converter under extreme conditions,then improves input voltage sharing control strategy to realize the input voltage sharing at light-load and output current limiting at short circuit,and a power-adjustable auxiliary circuit is introduced to keep the module input voltage within limits easily and effectively.

For DQ rC ring we have a semi primal DQ rC ring R,if right ideal satisfies the minimal condition, then it is direct sum of simple Artin rings.

In this paper,it is proved that if G∈BW∩N,then G is compactly generated if and only if each l-subgroup of G is closed and(G)satisfies minimal condition.

The main result of this paper is as following: G∈F , G is compactly generated if and only if each l subgroup of G is closed and Γ(G) satisfies minimal condition.