An extension of gap functions for a system of vector equilibrium problems with applications to optimization problems

In this paper, the notion of gap functions is extended from scalar case to vector one. Then, gap functions and generalized functions for several kinds of vector equilibrium problems are shown. As an application, the dual problem of a class of optimization problems with a system of vector equilibrium constraints (in short, OP) is established, the concavity of the dual function, the weak duality of (OP) and the saddle point sufficient condition are derived by using generalized gap functions. This work was supported by the National Natural Science Foundation of China (10671135) and the Applied Research Project of Sichuan Province (05JY029-009-1).     

Optimality and duality in multiobjective fractional programming involving ρ-semilocally type I-preinvex and related functions

Optimality conditions are obtained for a nonlinear fractional multiobjective programming problem involving η-semidifferentiable functions. Also, a general dual is formulated and a duality result is proved using concepts of generalized ρ-semilocally type I-preinvex functions.     

Spatial decay in a double diffusive convection problem in Darcy flow

This paper deals with a model of time-dependent double diffusive convection in Darcy flow. In particular it is concerned with the spatial decay of solutions when the flow is confined to a semi-infinite cylinder. Decay bounds for an energy expression are derived.     

压差式矢量水听器方位估计中的干扰抵消

矢量水听器由于能获取声场中标量（声压）和矢量（振速）信息，因此单个的矢量水听器就可实现目标方位估计。单个矢量水听器是利用信号的声压和质点振速之间相关性进行信号方位估计，但是当存在干扰，并且干扰和信号之间相关时，如果对运用能量流进行方位估计的方法不加改进，则会出现很大的误差，甚至出现错误的估计。本文提出一种存在已知噪声干扰情况下的干扰抵消方法，并针对该方法进行了仿真试验，最后运用湖试数据进行了验证。结果表明，该方法能有效地减弱相千千柑对信号的影响，实现对信号的方位估计。     

Generalized 3G theorem and application to relativistic stable process on non-smooth open sets

Let G(x,y) and GD(x,y) be the Green functions of rotationally invariant symmetric α-stable process in Rd and in an open set D, respectively, where 0<α<2. The inequality GD(x,y)GD(y,z)/GD(x,z)?c(G(x,y)+G(y,z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c=c(D)∈(0,∞), then we say that the 3G theorem holds in D. In this paper, we establish a generalized version of 3G theorem when D is a bounded κ-fat open set, which includes a bounded John domain. The 3G we consider is of the form GD(x,y)GD(z,w)/GD(x,w), where y may be different from z. When y=z, we recover the usual 3G. The 3G form GD(x,y)GD(z,w)/GD(x,w) appears in non-local Schrödinger operator theory. Using our generalized 3G theorem, we give a concrete class of functions belonging to the non-local Kato class, introduced by Chen and Song, on κ-fat open sets. As an application, we discuss relativistic α-stable processes (relativistic Hamiltonian when α=1) in κ-fat open sets. We identify the Martin boundary and the minimal Martin boundary with the Euclidean boundary for relativistic α-stable processes in κ-fat open sets. Furthermore, we show that relative Fatou type theorem is true for relativistic stable processes in κ-fat open sets. The main results of this paper hold for a large class of symmetric Markov processes, as are illustrated in the last section of this paper. We also discuss the generalized 3G theorem for a large class of symmetric stable Lévy processes.     

On Basic Constraint Qualifications for Infinite System of Convex Inequalities in Banach Spaces

The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.     

A Partial Differential Inequality in Geological Models

Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation.This limiter happens to satisfy a stationary scalar hyperbolic inequality,within a constraint,for which the authors prove the existence and the uniqueness of the solution.Actually,this solution is shown to be the maximal element of a convenient convex set of functions.The existence proof is obtained thanks to the use of a numerical scheme.     

向量变分不等式的严格可行性问题

本篇文章首先定义了向量变分不等式的严格可行点概念,其次在假设了映射是强(D)-伪单调的情况下,证明了向量变分不等式解集非空有界与其严格可行点存在的等价性问题,推广了在数量变分不等式上得到的相应结果．     

Determination of generalized quadrangles with distinct elation points

In this paper, we classify the finite generalized quadrangles of order (s,t), s,t > 1, which have a line L of elation points, with the additional property that there is a line M not meeting L for which {L, M} is regular. This is a first fundamental step towards the classification of those generalized quadrangles having a line of elation points. Mathematics Subject Classification (2000): 51E12, 51E20, 20B25, 20E42     

Continuous spectral decompositions of Abelian group actions on -algebras

Let G be a locally compact Abelian group. Following Ruy Exel, we view Fell bundles over the Pontrjagin dual group of G as continuous spectral decompositions of G-actions on C^*-algebras. We classify such spectral decompositions using certain dense subspaces related to Marc Rieffel's theory of square-integrability. There is a unique continuous spectral decomposition if the group acts properly on the primitive ideal space of the C^*-algebra. But there are also examples of group actions without or with several inequivalent spectral decompositions.