Optimality conditions for vector optimization problem to attain strictly efficient solutions are considered in the paper.

In this paper a new concept,the strictly efficient solution, is introduced, the Cone-continuous convex map and the connectedness of the set of strictly efficient solution,are studied further.

In this paper, we introduce a new concept the strictly efficient solution.

In locally-convex topological vector spaces, ε-strict efficient points and ε-strict efficient solutions are introduced.

The rigorous solutions of nonlinear Schrdinger equation,which models the Bose-Einstein condensate,are solved within the framework of the quantum phase-space representation.

Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick,the rigorous solutions of stationary Schro¨dinger equation for one-dimensional harmonic oscillator are solved with the methods of matrix mechanics and wave mechanics respectively.

The rigorous solutions of stationary Schrdinger equation for one-dimensional hydrogen atom are obtained.

As an example, exact solutions of the theory for even-even 18-26O, which are equivalent to the shell-model results for the universal ds-shell interaction are calculated and compared with the corresponding Separable Strength Pairing (SSP) and Equal Strength Pairing (ESP) results.

By using an algebraic method related to su(3) Lie algebra,exact solutions of the eigenvalue problem of the reduced Hamiltonian are derived analytically.

A family of exact solutions of the one-dimensional nonlinear Schrdinger equation is derived, which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential.