拓扑向量空间中锥拟凸映射的若干性质

本文针对拓扑向量空间中锥拟凸映射类 ,利用Minkowski泛函研究其若干性质 ,Karamardian定理是本文所得结论的一个特例 .     

一类非线性分数阶泛函微分方程的正解的存在性

本文研究了一类非线性分数阶泛函微分方程.利用锥拉伸与锥压缩不动点定理,得到这类分数阶泛函微分方程的正解的存在性,推广了马如云的结果.     

线性锥系统的Tucker型相容性定理

为了将线性规划中的基础理论之一的Tucker定理推广到一般线性锥系统上,应用对偶锥的概念和线性锥系统的Farkas引理,给出了一般线性系统的Tucker定理,所得结果显示含齐次线性不等式组的线性锥系统和它的对偶系统都存在Tucker定理,且Tucker定理结论的表达式基本相同,这为进一步研究锥规划提供了便利.     

广义锥-s次类凸向量优化的标量化和鞍点定理

讨论序拓扑向量空间中的约束向量优化问题.在广义锥-s次类凸假设下,得到了向量优化问题关于δ-弱有效解的标量化定理和Lagrange泛函的鞍点定理.     

一类非线性中立型分数阶泛函微分方程正解的存在性(英文)

本文考虑一类非线性中立型分数阶泛函微分方程.利用锥拉伸与锥压缩不动点定理对问题进行讨论,得到了这类中立型分数阶泛函微分方程正解的存在性.     

锥拟凸集值映射与集值映射的锥半连续性

本文借助锥界集定义了一种新的锥拟凸集值映射,并且利用广义Minkowski泛函讨论了锥半连续及锥外上半连续集值映射的锥拟凸性．     

锥线性算子的延拓定理

建立了一种锥分离定理,据此证明了锥线性算子的延拓定理,作为应用,给出了正线性算子的延拓定理。     

实线性锥距离空间和不动点定理

给出了实线性锥距离空间的概念,其中锥距离取值到没有拓扑结构的实线性空间,并在实线性锥距离空间中建立了几个新的不动点定理.利用非线性标量化函数证明了这些不动点定理与距离空间中相应形式的不动点定理等价.我们的结果改进了锥距离空间中的一些现有不动点定理.     

锥Pf的若干性质

利用实赋范线性空间E上非零连续线性泛函f,确定了E上半序关系和锥Pf,证明了锥Pf的几个性质,给出了H ilbert空间中Pf的对偶锥的表现形式及由Pf确定的H ilbert投影距离与T hom pson距离.     

锥体积泛函与仿射不等式(英文)

本文研究了凸多胞形的锥体积泛函.利用投影体以及Lutwak、杨和张最近所建立的仿射等周不等式,得到了刻划平行四边形特征的一个崭新不等式和用锥体积泛函以及投影体的体积所表达的关于配极体体积的严格下界.     

Intervallfunktionale vom GAUSS-LEGENDRE-Typ

A general class of quadrature formulas is discussed where the usual point functionals are replaced by interval functionals. The quadrature formulas of this type with highest possible degree of exactness are minimizing a certain functional. This leads to an existence theorem for arbitrary weights, which must comply with some necessary condition only. Besides, this minimum property enables us to calculate the nodes of such quadrature formulas very effectively.     

Fixed Point Theorem of Cone Expansion and Compression of Functional Type

The fixed point theorem of cone expansion and compression of norm type is generalized by replacing the norms with two functionals satisfying certain conditions to produce a fixed point theorem of cone expansion and compression of functional type. We conclude with an application verifying the existence of a positive solution to a discrete second-order conjugate boundary value problem.     

Qualitative and infinitesimal robustness of tail-dependent statistical functionals

The main goal of this article is to introduce a new notion of qualitative robustness that applies also to tail-dependent statistical functionals and that allows us to compare statistical functionals in regards to their degree of robustness. By means of new versions of the celebrated Hampel theorem, we show that this degree of robustness can be characterized in terms of certain continuity properties of the statistical functional. The proofs of these results rely on strong uniform Glivenko-Cantelli theorems in fine topologies, which are of independent interest. We also investigate the sensitivity of tail-dependent statistical functionals w.r.t. infinitesimal contaminations, and we introduce a new notion of infinitesimal robustness. The theoretical results are illustrated by means of several examples including general L- and V-functionals.     

Localization of limit sets and stability of systems of the neutral type with nonmonotone Lyapunov functionals

We suggest new approaches to the study of the asymptotic stability of equilibria for equations of the neutral type. Nonmonotone indefinite Lyapunov functionals are used. We investigate the localization of solutions with respect to the level surfaces of a Lyapunov functional and a functional estimating the derivative of the Lyapunov functional along the solutions. By using solution localization tests, we obtain new conditions for the asymptotic stability of equilibria for equations of the neutral type with bounded right-hand side. We present asymptotic stability tests that do not impose any a priori stability condition on the difference operator. A generalization of the Barbashin–Krasovskii theorem for nonmonotone indefinite Lyapunov functionals is proved for autonomous equations.     

?B-值广义泛函值函数可微性的刻画

In this paper, we discuss fuzzy simplex and fuzzy convex hull, and give several representation theorems for fuzzy simplex and fuzzy convex hull. In addition, by giving a new characterization theorem of fuzzy convex hull, we improve some known results about fuzzy convex hull.     

Convex risk functionals: Representation and applications

We introduce the family of law-invariant convex risk functionals, which includes a wide majority of practically used convex risk measures and deviation measures. We obtain a unified representation theorem for this family of functionals. Two related optimization problems are studied. In the first application, we determine worst-case values of a law-invariant convex risk functional when the mean and a higher moment such as the variance of a risk are known. Second, we consider its application in optimal reinsurance design for an insurer. With the help of the representation theorem, we can show the existence and the form of optimal solutions.     

高阶拉氏乘子法和弹性理论中更一般的广义变分原理

作者曾指出[1],弹性理论的最小位能原理和最小余能原理都是有约束条件限制下的变分原理采用拉格朗日乘子法,我们可以把这些约束条件乘上待定的拉氏乘子,计入有关变分原理的泛函内,从而将这些有约束条件的极值变分原理,化为无条件的驻值变分原理.如果把这些待定拉氏乘子和原来的变量都看作是独立变量而进行变分,则从有关泛函的驻值条件就可以求得这些拉氏乘子用原有物理变量表示的表达式.把这些表达式代入待定的拉氏乘子中,即可求所谓广义变分原理的驻值变分泛函.但是某些情况下,待定的拉氏乘子在变分中证明恒等于零.这是一种临界的变分状态.在这种临界状态中,我们无法用待定拉氏乘子法把变分约束条件吸收入泛函,从而解除这个约束条件.从最小余能原理出发,利用待定拉氏乘子法,企图把应力应变关系这个约束条件吸收入有关泛函时,就发生这种临界状态,用拉氏乘子法,从余能原理只能导出Hellinger-Reissner变分原理[2],[3],这个原理中只有应力和位移两类独立变量,而应力应变关系则仍是变分约束条件,人们利用这个条件,从变分求得的应力中求应变.所以Hellinger-Reissner变分原理仍是一种有条件的变分原理.     

Morse Theory on Banach Space Its Applications to Partial Differential Equations

The author introduces a definition about the nondegeneracy of critical points of a differentiable functional defined on a Banach space. Thus the Morse theory is estabished to these functionals on a Banach space with an equivalent differentiable norm. And by use of the Morse inequalities an exension of three critical point theorem due to Krasnoselski, Castro, Lazer and the author is provided. As an application, the multiple solutions of a quasilinear elliptic boundary value problems studied.     

Stationary Solutions of Fokker-Planck Equations with Nonlinear Reaction Terms in Bounded Domains

Using an operator approach, we discuss stationary solutions to Fokker-Planck equations and systems with nonlinear reaction terms. The existence of solutions is obtained by using Banach, Schauder and Schaefer fixed point theorems, and for systems by means of Perov’s fixed point theorem. Using the Ekeland variational principle, it is proved that the unique solution of the problem minimizes the energy functional, and in case of a system that it is the Nash equilibrium of the energy functionals associated to the component equations.

     

A two-point boundary-value problem for gyroscopic systems in some Lorentzian manifolds

We study the dynamics of gyroscopic systems of relativistic type with multivalued action functionals. We assume that Lorentzian configuration manifolds have the structure of the twisted product. The solvability of the two-point boundary-value problem for such systems was proved earlier only in the case of a limited Lorentzian distance from the initial point to the final one. In this work we obtain a new existence theorem. According to this theorem, the specified distance to attainable points may be arbitrarily large. The result is applied to the dynamics of a charged test particle in the external space-time of the Reissner-Nordström black hole.