Semiconvergence in distribution of random closed sets with application to random optimization problems

The paper considers upper semicontinuous behavior in distribution of sequences of random closed sets. Semiconvergence in distribution will be described via convergence in distribution of random variables with values in a suitable topological space. Convergence statements for suitable functions of random sets are proved and the results are employed to derive stability statements for random optimization problems where the objective function and the constraint set are approximated simultaneously. The author is grateful to two anonymous referees for helpful suggestions.     

An implicit method for linear ill‐posed problems with perturbed operators

An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems, and then the optimal convergence rate can also be obtained by an a posteriori strategy. The convergence results show that the algorithm is a robust regularization method. Copyright © 2006 John Wiley & Sons, Ltd.     

Mixed Elastico-Plasticity Problems with Partially Unknown Boundaries

In this paper,we study mixed elastico-plasticity problems in which part of the boundary is known,while the other part of the boundary is unknown and is a free boundary.Under certain conditions,this problemcan be transformed into a Riemann-Hilbert boundary value problem for analytic functions and a mixed boundaryvalue problem for complex equations.Using the theory of generalized analytic functions,the solvability of theproblem is discussed.     

The statement and numerical solution of an optimization problem in X-ray tomography

A nonclassical problem is considered for the transport equation with coefficients depending on the energy of radiation. The task is to find the discontinuity surfaces for the coefficients of the equation from measurements of the radiation flux leaving the medium. For this tomography problem, an optimization problem is stated and numerically analyzed. The latter consists in determining the radiation energy that ensures the best reconstruction of the unknown medium. A simplified optimization problem is solved analytically.     

Exceptional set of a representation with fractional powers

We prove that for any given c, 1 < c < 17/11, almost all natural numbers are representable in the form [x ^c] + [p ^c], where x is a natural number and p is a prime.     

Mass‐lumping or not mass‐lumping for eigenvalue problems

In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003     

对于工学硕士的《数理统计》教学的研究

工学硕士的《数理统计》教学 ,要根据工学硕士的培养目标和数理统计课程的特点编写教材、确定讲授内容和授课方式 .力求使学员掌握处理随机数据的思考方法 ,培养解决问题、分析问题和善于应用知识的能力 .改革《数理统计》教学 ,实现和普及多媒体教学是时代发展的趋势 .     

Asymptotic Correction of More Sturm–Liouville Eigenvalue Estimates

The asymptotic correction technique of Paine, de Hoog and Anderssen can dramatically improve the accuracy of finite difference or finite element eigenvalues at negligible extra cost if closed form expressions are available for the errors in a simpler related problem. This paper gives closed form expressions for the errors in the eigenvalues of certain Sturm–Liouville problems obtained by various methods, thereby increasing the range of problems for which asymptotic correction can achieve maximum efficiency. It also investigates implementation of the method for more general problems.     

Asymptotic Methods Applied to Contact Problems

Asymptotic methods for contact problems are expounded. Some typical integral equations are considered     

Balanced contributions for TU games with awards and applications

Calleja et al. [Calleja, P., Borm, P., Hendrickx, R., 2005. Multi-issue allocation situations. European Journal of Operational Research 164, 730–747] introduced multi-issue allocation situations with awards. In this paper, we extend the classical model of cooperative games with transferable utility to the cooperative games with transferable utility and awards. We define a run-to-the-bank rule for cooperative games with transferable utility and awards and characterise it in terms of a property of balanced contributions. We apply our main result to bankruptcy problems and multi-issue allocation situations with awards.