On the Method of Solution for the Non-Homogeneous Generalized Riemann-Hilbert Boundary Value Problems

This paper studies the non-homogeneous generalized Riemann-Hilbert(RH)problems involving two unknown functions.Using the uniformization theorem,such problems are transformed into the case of homogeneous type.By the theory of classical boundary value problems,we adopt a novel method to obtain the sectionally analytic solutions of problems in strip domains,and analyze the conditions of solvability and properties of solutions in various domains.

ON A GENERALIZED MODULUS OF CONVEXITY AND UNIFORM NORMAL STRUCTURE

In this article, the authors study a generalized modulus of convexity, δ（α） （ε）. Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ε, 0 ≤e≤ 1, such that δ^（α）（1＋ε ） 〉 （1- α）ε.

Generalized constrained multiobjective games in locally FC-uniform spaces

A new class of generalized constrained multiobjective games is introduced and studied in locally FC-uniform spaces without convexity structure where the number of players may be finite or infinite and all payoff functions get their values in an infinite-dimensional space. By using a Himmelberg type fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of weak Paxeto equilibria for the generalized constrained multiobjective games are established in locally FC-uniform spaces. These theorems improve, unify and generalize the corresponding results in recent literatures.

Characterization of Generalized Uniform Distribution through Expectation

Normally the mass of a root has a uniform distribution but some have different uniform distributions named Generalized Uniform Distribution (GUD). The characterization result based on expectation of function of random variable has been obtained for generalized uniform distribution. Applications are given for illustrative purpose including a special case of uniform distribution.

Comparison of Uniform and Kernel Gaussian Weight Matrix in Generalized Spatial Panel Data Model

Panel data combine cross-section data and time series data. If the cross-section is locations, there is a need to check the correlation among locations. ρ and λ are parameters in generalized spatial model to cover effect of correlation between locations. Value of ρ or λ will influence the goodness of fit model, so it is important to make parameter estimation. The effect of another location is covered by making contiguity matrix until it gets spatial weighted matrix (W). There are some types of W—uniform W, binary W, kernel Gaussian W and some W from real case of economics condition or transportation condition from locations. This study is aimed to compare uniform W and kernel Gaussian W in spatial panel data model using RMSE value. The result of analysis showed that uniform weight had RMSE value less than kernel Gaussian model. Uniform W had stabil value for all the combinations.

EQUILIBRIUM EXISTENCE FOR MULTI-LEADER-FOLLOWER GENERALIZED CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY FC-UNIFORM SPACES

In this article, we introduce and study some new classes of multi-leader-follower generalized constrained multiobjective games in locally FC-uniform spaces where the number of leaders and followers may be finite or infinite and the objective functions of the followers obtain their values in infinite-dimensional spaces. Each leader has a constrained correspondence. By using a collective fixed point theorem in locally FC-uniform spaces due to author, some existence theorems of equilibrium points for the multi-leader-follower generalized constrained multiobjective games are established under nonconvex settings. These results generalize some corresponding results in recent literature.

A New System of Generalized Variational Inclusions Involving H-η-monotone Operators in Uniformly Smooth Banach Spaces

In this paper, we introduce and study a new system of generalized vari- ational inclusions involving H-η-monotone operators in uniformly smooth Banach spaces. Using the resolvent operator technique associated with H-η-monotone opera- tors, we prove the approximation solvability of solutions using an iterative algorithm. The results in this paper extend and improve some known results from the literature.

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications(Ⅰ)

First, the notions of the measure of noncompactness and condensing setvalued mappings are introduced in locally FC-uniform spaces without convexity structure. A new existence theorem of maximal elements of a family of set-valued mappings involving condensing mappings is proved in locally FC-uniform spaces. As applications, some new equilibrium existence theorems of generalized game involving condensing mappings are established in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Some further applications of our results to the systems of generalized vector quasi-equilibrium problems will be given in a follow-up paper.

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.

NEW SYSTEMS OF GENERALIZED QUASI-VARIATIONAL INCLUSIONS IN FC-SPACES AND APPLICATIONS

In this paper, we study some new systems of generalized quasi-variational inclusion problems in FC-spaces without convexity structure.By applying an existence theorem of maximal elements of set-valued mappings due to the author, some new existence theorems of solutions for the systems of generalized quasi-variational inclusion problems are proved in noncompact FC-spaces. As applications, some existence results of solutions for the system of quasi-optimization problems and mathematical programs with the systems of generalized quasi-variational inclusion constraints are obtained in FC-spaces.

Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain

A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn（f; t） of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove that an operator Wn（f; t） with the new kernel function converges uniformly to any continuous function f（t） ∈ Cn（Ω） （the space of all continuous functions with period Ω） on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.

Global Well-posedness of the Generalized Long-short Wave Equations

In the present paper, we investigate the well-posedness of the global solutionfor the Cauchy problem of generalized long-short wave equations. Applying Kato＇s methodfor abstract quasi-linear evolution equations and a priori estimates of solution,we get theexistence of globally smooth solution.

On the generalized Cauchy function and new Conjecture on its exterior singularities

This article studies on Cauchy’s function f （z） and its integral, （2πi）J[ f （z）] ≡ ■C f （t）dt/（t z） taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x ＋ iy plane consisted of the simply connected open domain D ＋ bounded by C and the open domain D outside C. （1） With f （z） assumed to be C n （n ∞-times continuously differentiable） z ∈ D ＋ and in a neighborhood of C, f （z） and its derivatives f （n） （z） are proved uniformly continuous in the closed domain D ＋ = [D ＋ ＋ C]. （2） Cauchy’s integral formulas and their derivatives z ∈ D ＋ （or z ∈ D ） are proved to converge uniformly in D ＋ （or in D = [D ＋C]）, respectively, thereby rendering the integral formulas valid over the entire z-plane. （3） The same claims （as for f （z） and J[ f （z）]） are shown extended to hold for the complement function F（z）, defined to be C n z ∈ D and about C. （4） The uniform convergence theorems for f （z） and F（z） shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle ｜z｜ = 1 such that the four general- ized Hilbert-type integral transforms are proved. （5） Further, the singularity distribution of f （z） in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . （6） A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. （7） Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. （8） Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f （z） in domain D , based on the continuous numerical value of f （z） z ∈ D ＋ = [D ＋ ＋ C], is presented for resolution as a conjecture.

A PROJECTION-TYPE ALGORITHM FOR SOLVING GENERALIZED MIXED VARIATIONAL INEQUALITIES

We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom（f）, where f ： Rn --RU{＋∞} is a proper func- tion. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.

A Generalized Layered Radiative Transfer Model in the Vegetation Canopy

In this paper, a generalized layered model for radiation transfer in canopy with high vertical resolution is developed. Differing from the two-stream approximate radiation transfer model commonly used in the land surface models, the generalized model takes into account the effect of complicated canopy morphology and inhomogeneous optical properties of leaves on radiation transfer within the canopy. In the model, the total leaf area index （LAI） of the canopy is divided into many layers. At a given layer, the influences of diffuse radiation angle distributions and leaf angle distributions on radiation transfer within the canopy are considered. The derivation of equations serving the model are described in detail, and these can deal with various diffuse radiation transfers in quite broad categories of canopy with quite inhomogeneons vertical structures and uneven leaves with substantially different optical properties of adaxial and abaxial faces of the leaves. The model is used to simulate the radiation transfer for canopies with horizontal leaves to validate the generalized model. Results from the model are compared with those from the two-stream scheme, and differences between these two models are discussed.

Consistency Conditions and Constraints on Generalized f(R) Gravity with Arbitrary Geometry-Matter Coupling

We study the consistency conditions of the generalized f （ R） gravity by extending f （ R） gravity with non-minimal coupling to the generalized f（R） with arbitrary geometry-matter coupling. Specifically, we discuss the two particular models of generalized f（R） by means of consistency conditions. It is found that the second model is not physically viable so as to be ruled out. Moreover, we further constrain the first model using the Dolgov- Kawasaki stability criterion, and give the value ranges of the parameters in the first model It is worth stressing that our results include the ones in f（R） gravity with non-minimal coupling as the special case of Q（Lm） = Lm.

ON A GENERALIZED GEOMETRIC CONSTANT AND SUFFICIENT CONDITIONS FOR NORMAL STRUCTURE IN BANACH SPACES

In this paper, we introduce a new geometric constant C;（a, X） of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, we present several sufficient conditions for normal structure of a Banach space in terms of this new constant, the generalized James constant, the generalized Garc′?a-Falset coefficient and the coefficient of weak orthogonality of Sims. Our main results of the paper generalize some known results in the recent literature.

基于通用生成函数法的CFRP防撞梁碰撞可靠性设计优化

为满足汽车耐撞性与轻量化的要求,对碳纤维增强复合材料(CFRP)防撞梁进行可靠性优化设计(RBDO)。以CFRP防撞梁关键控制点横坐标、厚度以及铺层角度为设计变量,以碰撞力峰值为约束条件,以比吸能最大为目标构建优化模型。采用拉丁超立方法与克里金(Kriging)代理模型法相结合拟合出目标及约束函数的Kriging近似模型,采用通用生成函数(UGF)-直接映射法来进行碰撞可靠性优化设计。结果表明:在随机变量非正态、功能函数高度非线性的情况下,传统矩方法无法保证收敛,蒙特卡罗法精度最高但计算成本过大,使用UGF进行可靠性分析优化时收敛稳定,在保证精度的同时效率较高;引入非均匀聚类技术的UGF法效率进一步提高,采用UGF法得到的优化结果相较于初始目标值优化幅度达21.6%,达到预期效果。

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.

Simulation and uniform design-based automatic generation of risk scenarios

This paper presents a methodology for automatically generating risk scenarios for dynamic reliability applications in which some dynamic characteristics(e.g.,the order,timing and magnitude of events,the value of relevant process parameters and initial conditions) have a significant influence on the evolution of the system.The main idea of the methodology is:(i) making the system model "express itself" through simulation by having the model driven by an elaborated simulation engine;(ii) exploiting uniform design to pick out a small subset of representative design points from the space of relevant dynamic characteristics;(iii) for each selected design point,employing a depth-first systematic exploration strategy to cover all possible scenario branches at each branch point.A highly dynamic example adapted from the literature(a chemical batch reactor) is studied to test the effectiveness of the proposed methodology.