NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES

By applying the technique of continuous partition of unity and Tychonoff's fixed point theorem,. some new collectively fixed point theorems for a family of set-valued, mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence of abstract economies are also obtained in G convex spaces. Our theorems theorems of improve, unify and generalized many important known results in recent literature.

COINCIDENCE THEOREMS IN PRODUCT G-CONVEX SPACES

By applying the technique of continuous partition of unity, some new coincidence theorems for a better admissible mapping and a family of set-valued mappings defined on the product G-convex spaces are proved. Theorems of this paper improve, unify and generalize many important coincidence theorems and collectively fixed point theorems in recent literature.

Traversable Wormholes and the Brouwer Fixed-Point Theorem

The Brouwer fixed-point theorem in topology states that for any continuous mapping f on a compact convex set into itself admits a fixed point, i.e., a point x0 such that f(x0) = x0. Under suitable conditions, this fixed point corresponds to the throat of a traversable wormhole, i.e., b(r0) = r0 for the shape function b = b(r). The possible existence of wormholes can therefore be deduced from purely mathematical considerations without going beyond the existing physical requirements.

Continuous Selection,Collectively Fixed Points and System of Coincidence Theorems in Product Topological Spaces

Some new continuous selection theorems are first proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product space of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known results in recent literature.

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.

Maximum Correntropy Kalman Filtering for Non-Gaussian Systems With State Saturations and Stochastic Nonlinearities

This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take the form of statemultiplicative noises, are introduced in systems to describe the phenomenon of nonlinear disturbances. To resist non-Gaussian noises, we consider a new performance index called maximum correntropy criterion(MCC) which describes the similarity between two stochastic variables. To enhance the “robustness” of the kernel parameter selection on the resultant filtering performance, the Cauchy kernel function is adopted to calculate the corresponding correntropy. The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy between the system state and its estimate. By taking advantage of an upper bound on the one-step prediction error covariance, a modified MCC-based performance index is constructed. Subsequently, with the assistance of a fixed-point theorem, the filter gain is obtained by maximizing the proposed cost function. In addition, a sufficient condition is deduced to ensure the uniqueness of the fixed point. Finally, the validity of the filtering method is tested by simulating a numerical example.

THE EXISTENCE AND MULTIPLICITY OF k-CONVEX SOLUTIONS FOR A COUPLED k-HESSIAN SYSTEM

In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.

G-凸空间内新的聚合不动点定理及应用

由应用连续单位分解技巧和Tychonoff不动点定理对定义在非紧G＿凸空间的乘积空间上的一族集值映象证明了一些新的不动点定理· 作为应用,对G＿凸空间的乘积空间的一簇子集证明了KyFan型非空交定理;

乘积拓扑空间上的重合点定理(英文)

对定义在无线性结构的非紧乘积拓扑空间上的集值映象簇证明了新的重合点定理.作为特殊情形,得到了集值映象簇的聚合不动点定理.

乘积G-凸空间上两个集值映象簇的重合定理(英文)

利用连续选择定理和乘积局部G 凸一致空间上的聚合不动点定理,对定义在乘积G 凸空间上的两个集值映象簇证明某些新的重合点定理.这些定理改进,统一和推广了最近文献中的很多重合点定理.

判断聚合理论述评——关于社会选择理论的一种新进展

判断聚合理论的核心问题是如何摆脱"不可能性"困境,而"不可能性"困境的标志是包括投票悖论在内的衍申困境。衍申困境直接破坏了基于多数投票规则的集体选择的逻辑合理性,从而向多数投票规则的民主性提出了挑战。为了挽救集体选择的逻辑合理性,判断聚合理论不得不对多数投票规则加以限制甚至摒弃,同时力求避免向独裁规则退化。换言之,该理论在保留判断聚合的逻辑合理性的前提下,尽可能少地丧失聚合规则的民主性。然而,这一努力的结果却是难以令人满意的。

弱FC-KKM映射与聚合不动点定理

在FC-空间中引入和研究了弱FC-KKM映射和具有弱FC-KKM性质的映射类.并在非紧局部FC-空间中对具有弱FC-KKM性质的映射建立了一些新的不动点定理和聚合不动点定理.作为应用,给出了聚合不动点定理在矢量平衡问题组中的应用.

乘积局部FC-一致空间内的聚合不动点定理和应用(英文)

应用在局部FC-一致空间内对紧闭集值映象得到的一个H imm elberg型不动点定理,对定义在局部FC-一致空间的乘积空间上的紧闭集值映象族建立了新的聚合不动点定理.作为应用,在局部FC-一致空间内对具有下和上界的拟平衡问题组得到了解的存在性定理和得到了新的极小极大定理.这些结果推广了文献中的某些已知结果.

一种正项级数敛散性的判别法

介绍了正项级数敛散性根值判别法的一种等价形式。该方法把根值判别法和比值判别法有机地结合起来,能较好地解决一类正项级数敛散性的判别问题。

林权纠纷处理与和谐海西林区构建研究——基于三明林权体制改革的实证分析

随着集体林权制度改革在全国的深入开展,由于确权发证不明、林地价值回归、林业政策变动和人为因素等引发的林权纠纷纷纷呈现。根据科斯定理,解决林权纠纷的重点在于明晰产权,解决权属问题。因此,要有效预防并解决林权纠纷,就要做好清理遗留的林权纠纷、加强相关法律宣传、规范林权纠纷管理工作、完善林地流转定价机制和提高工作人员的专业能力和素质等一系列工作。

抽象凸空间上类K的性质及聚合不动点定理

给出抽象凸空间上映射类K的两个性质,利用已知抽象凸空间上的重叠点定理讨论抽象凸空间上映射的不动点存在问题,得到了若干新的不动点定理,同时进一步给出了抽象凸空间族的乘积空间上映射族的聚合不动点定理.

欧拉定理的推广及其在化学热力学中的应用

给出了广义的欧拉(Euler)定理,讨论了广义的欧拉定理在化学热力学中的某些应用,给出了偏摩尔量集合公式和Gibbs-Duhem方程的严格推导方法及适用条件,指出现行化学热力学和物理化学教科书在推导上述两式过程中的不合理性。

Multiple positive solutions for a class of nonlinear four-point boundary value problem with p-Laplacian

This paper deals with the existence of multiple positive solutions for a class of nonlinear singular four-point boundary value problem with p-Laplacian：{（φ（u′））′＋a（t）f（u（t））=0, 0〈t〈1, αφ（u（0））-βφ（u′（ξ））=0,γφ（u（1））＋δφ（u′（η））0,where φ（x） = ｜x｜^p-2x,p 〉 1, a（t） may be singular at t = 0 and/or t = 1. By applying Leggett-Williams fixed point theorem and Schauder fixed point theorem, the sufficient conditions for the existence of multiple （at least three） positive solutions to the above four-point boundary value problem are provided. An example to illustrate the importance of the results obtained is also given.

Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Differential Equation

In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D~α_(o^+)is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.

EXISTENCE OF SOLUTION FOR BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.