Systems of generalized vector quasi-variational inclusions and systems of generalized vector quasi-optimization problems in locally FC-uniform spaces

In this paper, we introduce some new systems of generalized vector quasi-variational inclusion problems and system of generalized vector ideal （resp., proper, Pareto, weak） quasi-optimization problems in locally FC-uniform spaces without convexity structure. By using the KKM type theorem and Himmelberg type fixed point theorem proposed by the author, some new existence theorems of solutions for the systems of generalized vector quasi-variational inclusion problems are proved. As to its applications, we obtain some existence results of solutions for systems of generalized vector quasi-optimization problems.

SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS ON PRODUCT FC-SPACES

By applying a maximal element theorem on product FC-space due to author, some new equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in FC-spaces. By using these equilibrium existence theorems, some new existence theorems of solutions for the system of generalized vector quasi-equilibrium problems are established in noncompact product FC-spaces. These results improve and generalize some recent results in literature to product FC-spaces without any convexity structure.

NONEMPTY INTERSECTION THEOREMS AND SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS IN PRODUCT G-CONVEX SPACES

By using an existence theorems of maximal elements for a family of set-valued mappings in G-convex spaces due to the author, some new nonempty intersection theorems for a family of set-valued mappings were established in noncompact product G-convex spaces. As applications, some equilibrium existence theorems for a system of generalized vector equilibrium problems were proved in noncompact product G-convex spaces. These theorems unify, improve and generalize some important known results in literature.

LEVITIN-POYAK WELL-POSEDNESS OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS WITH FUNCTIONAL CONSTRAINTS

In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.

SYSTEM OF GENERALIZED VECTOR VARIATIONAL INEQUALITIES

In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is presented by Kakutani-Fan-Glicksberg fixed point theorem.

MATHEMATICAL PROGRAMS WITH SYSTEM OF GENERALIZED VECTOR QUASI-EQUILIBRIUM CONSTRAINTS IN FC-SPACES

In this article, four new classes of systems of generalized vector quasi-equilibrium problems are introduced and studied in FC-spaces without convexity structure. The notions of Ci（x）-FC-partially diagonally quasiconvex, Ci（x）-FC-quasiconvex, and Ci（x）-FC- quasiconvex-like for set-valued mappings are also introduced in FC-spaces. By applying these notions and a maximal element theorem, the nonemptyness and compactness of solution sets for four classes of systems of generalized vector quasi-equilibrium problems are proved in noncompact FC-spaces. As applications, some new existence theorems of solutions for mathematical programs with system of generalized vector quasi-equilibrium constraints are obtained in FC-spaces. These results improve and generalize some recent known results in literature.

PREDICTION OF MAGNETOCRYSTALLINE ANISOTROPY OF POLYCRYSTALLINE MATERIALS WITH GENERALIZED VECTOR METHOD

The crystallite orientation distribution functions(ODFs)were determined for the surface, 1/4 depth and 1/2 depth layers of a cold-rolled W20 non-oriented silicon steel sheet.By extending the theory of magnetic anisotropy to textured materials with no sample symmetry, the variation of magnetic torque versus directions in the plane of the sheet was further calcu- lated quantitatively,which fits well with the measured torque curve.

GENERIC STABILITY AND EXISTENCE OF ESSENTIAL COMPONENTS OF THE SOLUTION SET FOR THE SYSTEM OF GENERALIZED VECTOR EQUILIBRIUM PROBLEMS

By using Fort theorem the generic stability result for the system of generalized vector equilibrium problems is established. Further, by proving the existence and connectivity of minimal essential set the existence result of essential components in the solution set is derived.

GENERALIZED VECTOR VARIATIONAL-TYPE INEQUALITIES IN FC-SPACES

A class of generalized vector variational-type inequality problems （GVVTIP） are studied in FC-spaces, which includes the most of vector equilibrium problems, vector variational inequality problems, generalized vector equilibrium problems and general- ized vector variational inequality problem as special cases. By using F-KKM theorem, some new existence results for GVVTIP axe established in noncompact FC-space. As consequences, some recent known results in literature are obtained under much weaker assumption.

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMSIN LOCALLY G-CONVEX SPACES

Some classes of generalized vector quasi-equilibrium problems ( in short, GVQEP) are introduced and studied in locally G-convex spaces which includes most of generalized vector equilibrium problems; generalized vector variational inequality problems, quasi-equilibrium problems and quasi-variational inequality problems as special cases. First, an equilibrium existence theorem for one person games is proved in locally G-convex spaces.. As applications, some new existence theorems of solutions for the GVQEP are established in noncompact locally G-convex spaces. These results and argument methods are new and completely different from that in recent literature.

Upper and Lower Semicontinuity of Solution Sets for Parametric Generalized Vector Quasi-equilibrium Problems

In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.

Existence results for generalized vector equilibrium problems with applications

By a coincidence theorem, some existence theorems of solutions are proved for four types of generalized vector equilibrium problems with moving cones. Applications to the generalized semi-infinite programs with the generalized vector equilibrium constraints under the mild conditions are also given. The results of this paper unify and improve the corresponding results in the previous literature.

Existence of Solutions to Generalized Vector Quasi-variational-like Inequalities with Set-valued Mappings

In this paper, we introduce and study a class of generalized vector quasivariational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space.

Generalized Vector Quasi-Variational-Like Inequalities without Monotonity and Compactness

In this paper, some existence theorems of a solution for generalized vector quasivariational-like inequalities without any monotonity conditions in a noncompact topological space setting are proven by the maximal element theorem.

System of Generalized Vector Quasi-Equilibrium Problems in Locally FC-Spaces

A new class of locally finite continuous topological spaces （for short, locally FC-spaces） and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures.

Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems with Discontinuous Mappings

Let X, Y be two finite-dimensional topological vector spaces, Z a Hausdorff topological vector space, K C X and D C Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠θ Let S ： K → 2^K and T ： K → 2^D be two multivalued mappings, and φ ： K × D × K → Y be a trifunction. In this paper, we consider the generalized vector quasi-equilibrium problem, which is formulated by finding X∈ K and y∈ T（x） such that x∈ E S（x） and φ（x,y, u） （∈/） -int C for all u ∈ S（x）. We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo.

Lower Semicontinuity of the Solution Sets to Parametric Generalized Vector Equilibrium Problems

In this paper,by a scalarization method,the lower semicontinuity of the solution mappings to two kinds of parametric generalized vector equilibrium problems involving set-valued mappings is established under new assumptions which are weaker than the C-strict monotonicity.These results extend the corresponding ones.Some examples are given to illustrate our results.

APPLICATION OF GENERALIZED CONVECTIVE VORTICITY VECTOR IN A RAINFALL PROCESS CAUSED BY A LANDFALLING TROPICAL DEPRESSION

A heavy rainfall process, which occurred in Shanghai during 5-6 August, 2001 from a landfalling tropical depression (TD),is examined with a control numerical experiment based on MM5 model. It is found that the contours of generalized equivalent potential temperature (θ*) are almost vertical with respect to horizontal surfaces near the TD center and more densely distributed than those of equivalent potential temperature (θe).Because the atmosphere is non-uniformly saturated in reality, θ* takes the place of θe in the definition of convective vorticity vector (CVV) so that a new vector, namely the generalized convective vorticity vector (CVV*), is applied in this study. Since CVV* can reflect both the secondary circulation and the variation of horizontal moist baroclinicity, the vertical integration of vertical component of CVV* is found, in this study, to represent the rainfall areas in the TD case better than potential vorticity (PV), moist potential vorticity (MPV), generalized moist potential vorticity (Pm), and CVV, with high-value area of CVV* corresponding to heavy-rainfall area. Moreover, the analysis from CVV* implies that the Hangzhou Bay might play an important role in the heavy rain process. A sensitivity experiment without the Hangzhou Bay is then designed and compared with the control run. It is found that the CVV* becomes weaker than that in the control run, implying that the elimination of Hangzhou Bay results in reduced rainfall. Further analyses show that the Hangzhou Bay provides sufficient water vapor and surface heat flux to the TD system, which is very important to the genesis and development of mesoscale cloud clusters around the TD and the associated heavy rainfall.

Robust PolInSAR optimal interferogram estimation method based on generalized scattering vector

For the polarimetric synthetic aperture radar interferometry (PoIInSAR) processing, it is necessary to coregister all the images, including the coregistration of polarimetric SAR images and the coregistration of interferometric SAR images. Otherwise, the performance of the estimated optimal interferograms will be deteriorated. A generalized scattering vector (GSV) model is proposed to execute the PoIInSAR optimal interferograms estimation. The generalized scattering vector is constructed by the Pauli scattering vectors of the processing pixel and the surrounding pixels. Even though there are coregistration errors, all the polarimetric information of the current processing pixel is entirely included in the generalized scattering vector. Therefore, the GSV-based method can automatically recover the optimal scattering mechanisms of the processing pixel with coregistration errors either in interferoemetric channels or polarimetric channels. Theoretical analysis and processing results of simulated PoISARPro data and real PALSAR data validate the effectiveness and correctness of the proposed method.

Continuity of the Solution Mappings for Parametric Generalized Strong Vector Equilibrium Problems

The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.