On Some Integral Equations in Hilbert Space with an Application to the Theory of Elasticity

A Volterra type integral equation in a Hilbert space with an additional linear operator L and a spectral parameter depending on time is considered. If the parameter does not belong to the spectrum of L unconditional solvability of the considered problem is proved. In the case where the initial value of the parameter coincides with some isolated point of the spectrum of the operator L sufficient conditions for solvability are established. The obtained results are applied to the partial integral equations associated with a contact problem of the theory of elasticity.     

甲型H1N1流感的死亡率高吗——Bayes计量分析框架下的建模与估算

在全球甲型H1N1流感大流行背景下,本文在充分考虑各国甲流感死亡率可能存在个体混合效应、独立效应、相关效应及空间相关效应基础上,运用Bayes计量分析框架下的模型选择标准确定描述各国甲流感死亡率的最优模型,并基于该模型对不同国家甲流感死亡率进行估算。结果显示:个体独立、空间相关效应模型能很好拟合各国甲流感疫情统计数据,利用该模型估算的全球甲流感平均死亡率为0.577%。     

The dependence of critical parameter bounds on the monotonicity of a Newton sequence

Summary A new method is proposed for the inclusion of the critical parameter ^* of some convex operator equationu=Tu (appearing e.g. in thermal explosion theory). It is based on the fact that for a fixed Newton's method starting with a suitable subsolution is not monotonically if and only if >^*. Several numerical examples arising from nonlinear boundary value problems illustrate the efficiency of the method.     

Affine Ebenen und Tupelsysteme

Zusammenfassung Es werden zwei neue Koordinatisierungsmethoden für affine Ebenen gegeben, und zwar durch homogene bzw. stark balancierte Tupelsysteme. Ihre Brauchbarkeit wird u.a. demonstriert an einer Charakterisierung der Kollineationsgruppen einer affinen Ebene mit der Eigenschaft (R) Für alle i l enthält der Stabilisator von i nur Perspektivitäten mit Zentrum i. Außerdem wird der Satz bewiesen: Für eine Elation der geraden Ordnung d in einer projektiven Ebene der Ordnung v gilt 2d|v. Dieses Resultat impliziert schon bekannte Ergebnisse von Hughes (d=2) und Hall.

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We give two new coordinatization methods for affine planes by means of homogeneous (resp. strong balanced) tuple systems. Their usefulness is demonstrated by proving a characterization of collineation groups of an affine plane with the property (R): The stabilizer of every i l contains only perspectivities with centre i. Besides, we prove: If a projective plane of order v contains an elation of even order d then 2d|v. This implies known results of Hughes (d=2) and Hall.

     

La méthode de Kikuchi appliquée aux équations de von Karman

Resumé Le but de cet article est l'étude de l'approximation numérique des solutions non-triviales des équations de Von Karman pour le flambage d'une plaque mince encastrée. S'inspirant de la méthode de Kikuchi pour des problèmes quasi-linéaires du second ordre, on propose une méthode itérative d'éléments finis qui donne des approximations des solutions de norme «petite» qui bifurquent de la solution triviale au voisinage d'une valeur propre simple du problème linéarisé. On démontre la convergence et on obtient des estimations de l'erreur.

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Application of Kikuchi's method to the von Karman equations

Summary The aim of this article is to study the numerical approximation of non-trivial solutions of the Von Karman equations for the buckling of a thin elastic clamped plate. Following Kikuchi's method for second order quasilinear problems, we propose an iterative finite element method which produces approximations of non-trivial solutions of small norm which bifurcate from the trivial solution near simple eigenvalues of the linearised problem. The convergence is proved and error estimates are obtained.

     

Conjugate points at infinity in infinite dimensional teichmüller spaces

We show in this article that there exists conjugate points at infinity in infinite dimensional Teichmüller spaces.     

Functions averages over the roots of unity,cauchy problems and addition formulas

An averaging operator over the roots of unity is defined on a class of analytic functions and its algebraic and analytic properties are investigated. A Cauchy like integral formula for this is obtained. This operator and its properties are then employed to solve higher order Cauchy problems, to derive addition formulas for hypergeometric functions and to obtain integral representations for special classes of hypergeometric functions.     

Reconstruction of Hp -Functions: Best Approximation,Regularization and Optimal Error Estimates

Let U be the open unit disc of the complex plane. We explicitly construct the best pointwise approximation for determining a function in the Hardy space H ^p (U) from measured data at a countable set of points in U whenever the data is exact. A regularization scheme is given to deal with the case of nonexact data. Moreover, optimal error estimates are also studied.     

Boundary behavior of monotone Sobolev functions on John domains in a metric space

This article deals with weighted boundary limits of monotone Sobolev functions on bounded s-John domains in a metric space.     

On linear extremal problems in the class of schlicht functions

The form of the Schiffer differential equation puts severe restrictions on the class of functions that can occur as extremal functions for arbitrary coefficient-functionals of finite degree. Theorem 1 characterizes the algebraic extremal functions for coefficient-functionals of finite degree. Furthermore it is shown that the extremal function either is an algebraic function or it must possess a non-isolated singularity, or must have a transcendental branch-point. The results are closely related to the Malmquist-Yosida theorems. However Nevanlinna's Theory of Value Distribution is not the mainly used tool but the special form of the Schiffer differential equation and the multiplicity of certain values together with the Great Picard Theorem are exploited.