Reconstruction of the shape of object with near field measurements in a half-plane

We consider a mathematical problem modelling some characteristics of near field optical microscope.We take a monofrequency line source to illuminate a sample with constant index of refraction and use the scattered field data measured near the sample to reconstruct the shape of it. Mixed reciprocity relation and factorization method are applied to solve our problem.Some numerical examples to show the feasibility of the method are presented.     

On consistency measures of linguistic preference relations

Inspired by the concept of deviation measure between two linguistic preference relations, this paper further defines the deviation measure of a linguistic preference relation to the set of consistent linguistic preference relations. Based on this, we present a consistency index of linguistic preference relations and develop a consistency measure method for linguistic preference relations. This method is performed to ensure that the decision maker is being neither random nor illogical in his or her pairwise comparisons using the linguistic label set. Using this consistency measure, we discuss how to deal with inconsistency in linguistic preference relations, and also investigate the consistency properties of collective linguistic preference relations. These results are of vital importance for group decision making with linguistic preference relations.     

A new sharpened version of the Neuberg–Pedoe inequality

In this work, we present a new sharpened version of the classical Neuberg–Pedoe inequality. As an application, the following improved Neuberg–Pedoe inequality is derived:

     

基于灰色关联分析的财产保险公司偿付能力的模糊综合评判

为解决财产保险公司的偿付能力的评价问题,建立了基于灰色关联分析的模糊综合评判模型.选取了2003-2005年我国8家财产保险公司的相关数据,用灰色关联分析中的点关联系数求解隶属度得出评判矩阵,用范数灰关联度法确定因素集中各因素的权重,从而对其偿付能力进行模糊综合评判,得出各公司的偿付能力所属的类别.并对评语集中各评语赋予适当的权重,对所研究的8家财产保险公司依据其偿付能力的情况进行了排序.     

岩土强度与变形关系的理论剖析

深入浅出地阐述了岩土强度与变形关系，并对一些令人困惑的问题进行了讨论和作出可能的解释。     

A Test of Multivariate Independence Based on a Single Factor Model

A test of the independence of two sets of variables is developed to have high power against a special family of dependence. In this each set of variables has the structure of a single factor model and the dependence is solely via the correlation γ between the underlying latent variables. This is a model with only one nonzero canonical correlation. It is shown that a test based on the maximum likelihood estimate of γ is appreciably more powerful than that based on r₁, the largest sample canonical correlation. If, however, the model is used, not just as a family of alternatives but as the basis for interpretation, and if substantial cross-correlation is present then the procedure is essentially equivalent to the use of r₁.     

On congruences and ideals of partially ordered quasigroups

Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.     

Structure relations for monic orthogonal polynomials in two discrete variables

In this paper, extensions of several relations linking differences of bivariate discrete orthogonal polynomials and polynomials themselves are given, by using an appropriate vector–matrix notation. Three-term recurrence relations are presented for the partial differences of the monic polynomial solutions of admissible second order partial difference equation of hypergeometric type. Structure relations, difference representations as well as lowering and raising operators are obtained. Finally, expressions for all matrix coefficients appearing in these finite-type relations are explicitly presented for a finite set of Hahn and Kravchuk orthogonal polynomials.     

Theory of quantum fluctuations and the Onsager relations

A microscopic model is constructed within the theory of normal fluctuations for quantum systems, yielding an irreversible dynamics satisfying the Onsager relations. The property of return to equilibrium and the principle of minimal entropy production are proved.