On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

A theorem on sequentiality and compactness, with its fuzzy extension

An amended proof of a theorem of Franklin's on sequentiality and sequential compactness is presented, and a corresponding fuzzy version formulated using the theory of quasi-coincidence.     

Generalized fractional programming duality: A parametric approach

Using a parametric approach, duality is presented for a minimax fractional programming problem that involves several ratios in the objective function.The first author is thankful to Natural Science and Engineering Research Council of Canada for financial support through Grant A-5319, and the authors are thankful to the anonymous referees for useful suggestions.     

分数布朗运动的新表示

构造了一类新的分数布朗运动模型，它不同于Mandelbrot,Barton及Decreusefond等人所定义的分数布朗运动模型。     

2,3-二羟基萘钼多酸有机衍生物的合成及1H NMR和IR谱学研究

本文对二种新合成的2，3－二羟基萘二钼和四钼多酸有机衍生物[n-Bu)4N]2[Mo2O5(OC10H6O)2](Ⅰ）和[n-Bu)4N]2[Mo4O10(OC10H6O)2(OCH3)2](Ⅱ)进行了红外光谱与核磁共振波谱研究，发现[Mo2O5]^2 中钼氧多桥键的红外振动频率较[Mo4O10(OCH3)2]^2 中钼氧多桥键的红外振动频率红移，而在配合物Ⅱ中2，3－二羟基中芳环的^1H化学位移较配合物Ⅰ中向低场移动。同时还发现含二钼配位中心[Mo2O5]^2 的[Mo2O5(OC10H6O)2]^2-与含四钼配位中心[Mo4O10(OCH3)2]^2 的[Mo4O10(OC10H6O)2(OCH3)2]^2-生成条件的差异仅仅只在反应体系的pH值的微小变化，说明钼多酸有机衍生物阴离子是对体系酸碱度极为敏感的物质。     

标的资产服从几何分数布朗运动的期权定价

本文在M ogens B ladt和T ina H av iid R ydberg无市场假设,仅利用价格过程的实际概率的期权保险精算定价模型的基础上,得出了标的资产服从几何分数布朗运动的欧式期权定价公式,并说明了几何布朗运动是本文的一种特殊情况.     

Fractional-Linear Transformations of Operator Balls; Applications to Dynamical Systems

The operator sets, which are the subject of this paper, have been studied in many papers where, under different restrictions on the generating operators, convexity, compactness in the weak operator topology, and nonemptiness were proved for sets of different classes under study. Then the results obtained were used in these papers to solve several applied problems. Namely, they played the key role in establishing the dichotomy of nonautonomous dynamical systems, with either continuous or discrete time. In the present paper, we generalize and sharpen the already known criteria and obtain several new criteria for convexity, compactness, and nonemptiness of several special operator sets. Then, using the assertions obtained, we construct examples of sets of the form under study which are nonconvex, noncompact in the weak operator topology, as well as empty, and are generated by ＂smooth＂ operators of a special class. The existence problem for such sets remained open until the authors of this paper announced some of its results.     

n维广义函数的集值导数

本文将文献［9］中给出的一维广义函数的集值导数的某些结果，推广到n维情形，并给出一些与优化有关的其他结果．     

Integrated Groups and Smooth Distribution Groups

In this paper, we prove directly that α-times integrated groups define algebra homomorphisms. We also give a theorem of equivalence between smooth distribution groups and α-times integrated groups.     

On error bounds for lower semicontinuous functions

We give some sufficient conditions for proper lower semicontinuous functions on metric spaces to have error bounds (with exponents). For a proper convex function f on a normed space X the existence of a local error bound implies that of a global error bound. If in addition X is a Banach space, then error bounds can be characterized by the subdifferential of f. In a reflexive Banach space X, we further obtain several sufficient and necessary conditions for the existence of error bounds in terms of the lower Dini derivative of f. Received: April 27, 2001 / Accepted: November 6, 2001?Published online April 12, 2002