Simultaneously,when the reachability equals to the satisfiability of the state equation,the following conclusions can be drawn:for every vector X such that M0+ATX>0∧X≥0∧X≠0,there exists t∈Tx satisfying M0 t>,and X is an executable vector.

Linear feasible direction algorithm for calculation of reliability index of structure;

The principle of incorporating relations between parameters and objectives to finding the infeasible directions of searched points in global optimization is studied.

However,the feasible direction strategy for selecting working set may degrade the performance of the kernel cache maintained in standard SMO.

The bases and maximal vectors in Verma module of quantum algebra for type A_2;

The constraint vector extremum problem in real Banach space stated as max{f(x)|x∈D}(where f:X→Y and is discussed and the aItemative theorem is given for general-ized systems in the space.

In this paper, the necessary optimality conditions for vector extremum problems with equality constraint in product of Banach spaces are obtained by using a implicit function theorem in Banach spaces and a theorem of the alternative for subconvexlike vector-valued maps in ordered linear topological spaces.

Under linear space, but without any topological structures, the vector-valued Lagrangian saddle point theorem of vector extremal problems with set-to-set maps is studied.