Furthermore,it has been proved that among the equichordal bodies,the star dual of ball gets the minimal volume.

In this paper,we define the concepts of the star semirings of no star factor ,the star semimodules of no star factor, the dual star semimodules and the reflexive star semimodules in the basis of the star system which is introduced by Professor CHNE Pei-ci ,and obtain some properties.

Lagrangian duality for vector optimization of set-valued maps;

Study on risk measures-duality method;

Optimality and duality for minimax fractional problems;

Fuzzy subgradient algorithm for solving Lagrangian relaxation dual problem;

A dual characterization for Benson proper efficiency;

The generalization of a dual J.M.Child inequality;

Apply of Symmetry and Antithesis in day-to-day Teaching Activities in Science and Technology Aesthetics;

Tai Ji and Antithesis--Research of Psychology and Rhetoric,Series 4;

In Chinese classical poems, "antithesis" is a widely used means to reflect the contrasting parts of the world, achieving beauty in form and in sense.

Under the condition of P-reflexivity,a dual pair(X,P) is uniformly smooth(uniformly convex) if and only if its strong dual pair(X′,P′) is uniformly convex(uniformly smooth).

We improve the definitions of uniformly convex,locally uniformly convex,strong convex and very convex for the dual pair (X,P) and discuss the mutual relations of these concepts.