Minimal surfaces over stars

A JS surface is a minimal graph over a polygonal domain that becomes infinite in magnitude at the domain boundary. Jenkins and Serrin characterized the existence of these minimal graphs in terms of the signs of the boundary values and the side-lengths of the polygon. For a convex polygon, there can be essentially only one JS surface, but a non-convex domain may admit several distinct JS surfaces. We consider two families of JS surfaces corresponding to different boundary values, namely JS₀ and JS₁, over domains in the form of regular stars. We give parameterizations for these surfaces as lifts of harmonic maps, and observe that all previously constructed JS surfaces have been of type JS₀. We give an example of a JS₁ surface that is a new complete embedded minimal surface generalizing Scherk's doubly periodic surface, and show also that the JS₀ surface over a regular convex 2n-gon is the limit of JS₁ surfaces over non-convex stars. Finally we consider the construction of other JS surfaces over stars that belong neither to JS₀ nor to JS₁.     

On lengths of filling closed geodesics of hyperbolic punctured Riemann spheres

Let S be a Riemann sphere with n ≥ 4 points deleted. In this article we investigate certain filling closed geodesics of S and give quantitative common lower bounds for the hyperbolic lengths of those geodesics with respect to any hyperbolic structure on S (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inverse spectral problems for differential pencils on the half-line with turning points

The inverse spectral problem of recovering pencils of second-order differential operators on the half-line with turning points is studied. We establish properties of the spectral characteristics, give a formulation of the inverse problem, prove a uniqueness theorem and provide a constructive procedure for the solution of the inverse problem.     

FIXED POINT RESULTS ON METRIC-TYPE SPACES

In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.     

Polynomials in operator space theory

The aim of this article is to start a metric theory of homogeneous polynomials in the category of operator spaces. For this purpose we take advantage of the basic fact that the space P^m(E)$P^m(E)$ of all m-homogeneous polynomials on a vector space E can be identified with the algebraic dual of the m  -th symmetric tensor product ⊗^m,sE${\otimes }^{m,s}E$. Given an operator space V, we study several different types of completely bounded polynomials on V   which form the operator space duals of ⊗^m,sV${\otimes }^{m,s}V$ endowed with related operator structures. Of special interest are what we call Haagerup, Kronecker, and Schur polynomials – polynomials associated with different types of matrix products.     

集值Lebesgue—Stieltjes积分

本文首先刻划了B(R_ )上的集值测度,其次建立了(R_ B(R_ ))上的集值Lebesgue-Stieltjes积分.最后,进—步建立了集值随机Lebesgue-Stietjes积分的理论.     

一类含参广义集值拟变分包含组的解的灵敏性分析

本文引入了一类新的含参广义集值拟变分包含组,应用隐预解算子技巧,建立了该类变分包含组与一类不动点问题的等价性,在适当的条件下,分析了含参广义集值拟变分包含组的解的灵敏性,所得结果推广改进了最新文献中的许多结果．     

Banach空间上非Lipschitz映射的渐近行为

设Ｃ是具Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间Ｅ的非空凸闭子集，Ｇ是定向集．｛Ｔ_ｔ：ｔ∈Ｇ｝是Ｃ上的渐近非扩张型映照．本文给出了｛Ｔ_ｔ：ｔ∈Ｇ｝的弱收敛定理．     

Monotonicity of input-output mappings in inverse coefficient and source problems for parabolic equations

This article presents a mathematical analysis of input-output mappings in inverse coefficient and source problems for the linear parabolic equation ut=(kx(x)ux)+F(x,t), (x,t)∈ΩT:=(0,1)×(0,T]. The most experimentally feasible boundary measured data, the Neumann output (flux) data f(t):=−k(0)ux(0,t), is used at the boundary x=0. For each inverse problems structure of the input-output mappings is analyzed based on maximum principle and corresponding adjoint problems. Derived integral identities between the solutions of forward problems and corresponding adjoint problems, permit one to prove the monotonicity and invertibility of the input-output mappings. Some numerical applications are presented.