The Kuhn-Tucker type necessary optimality conditions under this constraint qualification are derived.

A note on necessary optimality conditions for a class of generalized fractional programming;

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.

In this paper,by using a implicit function theorem in Banach spaces the necessary optimality conditions for mathematical programming problems with equality constraints in the product of Banach spaces are established.

Moreover,the necessary optimality conditions in mathematical programming problem with equality and inequality constraints of Lipschitz functions are derived with the help of Ekeland variational principle on Riemannian manifolds.

Several typys of alkali-aggregate reaction and its mechanism was introduced, then the essential conditions of the reaction were also pointed out.

In this paper,by using reflective function method for secondary nonlinear differential system,we obtain secondary nonlinear differential system to have the linear reflection function necessary and sufficient condition and the essential condition.

The effects of monsoon wind stress, continental slope topology andbottom friction as essential conditions to form monsoon upwind flow and as diagnosticcriteria are discussed.