Vector variational-like inequalities and non-smooth vector optimization problems

In this paper, we establish relationships between vector variational-like inequality problems and non-smooth vector optimization problems under non-smooth invexity. We identify the vector critical points, the weakly efficient points and the solutions of the non-smooth weak vector variational-like inequality problems, under non-smooth pseudo-invexity assumptions. These conditions are more general than those existing in the literature.     

Focusing properties of Gaussian beam with superimposed left-handed and right-handed helical phase fronts

Vector diffraction theory is employed to investigate the focusing properties of the Gaussian beams with superimposed left-handed and right-handed helical phase fronts theoretically. Numerical simulations show that the intensity distribution in focal region can be altered considerably by adjusting topological charge m corresponding to right-handed helix and topological charge n corresponding to left-handed helix. Many novel focal pattern may occur. It was shown that the focal pattern evolves from one intensity peak to multiple intensity peaks with changing the topological charge m and n, and all the intensity peaks form in a circle. As the number of intensity peaks is the sum of m and n, the focal pattern can be controlled through adjusting the topological charge m and n. And in order to show the possible applications of these alterable foci pattern, some optical gradient force distributions were also calculated and illuminated.     

Effect of spherical aberration on tightly focused cylindrically polarized vortex beams

In this paper attention is given to the effects of primary spherical aberration on the cylindrical polarized vortex beam based on the vector diffraction theory. It is observed that by properly choosing the polarization angle and topological charge one can obtain many novel focal patterns suitable for optical tweezers, laser printing and material process. However, it is observed that the focusing objective with spherical aberration generates structural modification and positional shift of the generated focal structure.     

基于矢量传感器的频率估计算法在水声通信中的应用

本文给出了基于矢量传感器的ESPRIT频率估计算法，并将其应用于频率调制水声通信系统中。与声强频率估计算法相比，ESPRIT频率估计可在小样本的情况下，获得高精度的频率估计。仿真和湖试结果表明，基于矢量传感器的ESPRIT频率估计算法可以提高通信速率并降低对通信系统的带宽要求。本算法对信噪比的要求较高，目前看，较适用于近程高速水声通信。     

Lagrange multipliers for set-valued optimization problems associated with coderivatives

In this paper we investigate a vector optimization problem (P) where objective and constraints are given by set-valued maps. We show that by mean of marginal functions and suitable scalarizing functions one can characterize certain solutions of (P) as solutions of a scalar optimization problem (SP) with single-valued objective and constraint functions. Then applying some classical or recent results in optimization theory to (SP) and using estimates of subdifferentials of marginal functions, we obtain optimality conditions for (P) expressed in terms of Lagrange or sequential Lagrange multipliers associated with various coderivatives of the set-valued data.     

On the Mixed Propagator Approach to ρ-ω Mixing

The mixed propagator (MP) approach to ρ-ω mixing is discussed. It is found that under the pole-approximation assumption the results of MP approach is not compatible both with the effective Lagrangian theory andwith the experiment measurement criterion. To overcome these inconsistent, we propose a new MP approach in whichthe physical states of ρ and ω are determined by the requirement of experimental measurement to meson resonance. Interms of this new MP approach, the EM pion form factor Fπ and form factors of ρo →π0γ and of ω→πo γ are derived.The results of Fπ are in good agreement with data. The form factor of ρo →π0γ exhibits a hidden charge-asymmetryenhancement effect which agrees with the prediction of the effective Lagrangian theory.     

(γ, π0γ) reaction on a nucleus in the GeV region

π⁰γ invariant mass distribution spectrum has been calculated for the (γ, π⁰γ) reaction on¹²C nucleus at 2.5 GeV beam energy. These π⁰ and γ are assumed to originate due to the decay of vector mesons produced in the photonuclear reaction. The nuclear medium effect on vector mesons and the effect of π⁰ rescattering on the π⁰γ invariant mass spectrum have been investigated     

Existence Results for Systems of Vector Equilibrium Problems*

The purpose of this paper is to study systems of vector equilibrium problems. We establish some existence theorems for systems of vector equilibrium problems by using (S)₊-conditions and Kakutani–Fan–Glicksberg fixed point theorem *This work was supported by the Kyungnam University Research Fund 2004     

On Vector Implicit Variational Inequalities and Complementarity Problems

In this paper, two vector implicit variational inequalities and three vector implicit complementarity problems are introduced with a more general order in ordered Banach spaces and the equivalence between them is studied under certain assumptions. Furthermore, some existence theorems of the vector implicit variational inequalities are proved. We answered the open question proposed by Rapcsák [Nonconvex Optim., Appl., Vol. 38, Kluwer Acad. Publ., Dordrecht, 2000, pp. 371–380]. This work was supported by the National Natural Science Foundation of China and the Scientific Research Foundation for the Returned Overseas Chinese, Scholars, State Education Ministry.