Conditional expectation of integrands and random sets

The conditional expectation of integrands and random sets is the main tool of stochastic optimization. This work wishes to make up for the lack of real synthesis about this subject. We improve the existing hypothesis and simplify the corresponding proofs. In the convex case we especially study the problem of the exchange of conditional expectation and subdifferential operators.     

A UNICITY THEOREM FOR ENTIRE FUNCTIONS OF SEVERAL COMPLEX VARIABLES

A unicity theorem concerning the total derivative for entire functions of several complex variables is proved.     

Continuous modified Newton’s-type method for nonlinear operator equations

A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with the trajectory starting at some initial point x ₀ and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated. Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003 This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks DAAD for support     

A Distributional Approach to Multiple Stochastic Integrals and Transformations of the Poisson Measure

We study a class of ‘nonpoissonian’ transformations of the configuration space and the corresponding transformations of the Poisson measure. For some class of Poisson measures we find conditions which are sufficient for the transformed measure (which in general is nonpoissonian) to be absolutely continuous with respect to the initial Poisson measure and get the expression for the corresponding Radon–Nikodym derivative. To solve this problem we use a distributional approach to Poisson multiple stochastic integrals.     

高立体选择合成N,N′-取代-双-(反式-β,γ-二取代-γ-丁内酰胺)的简便方法(英文)

顺式 -1 -甲氧羰基 -2 -芳基 -6 ,6 -二甲基 -5 ,7-二氧螺环 [2 ,5 ]-4 ,8-辛二酮与联苯二胺 ( 0 )或 4 ,4′-亚甲基二苯胺 ( 1 )在二氯甲烷中 ,4 0℃搅拌反应合成得到化合物 0和 1 ,干燥后进一步在二甲苯中回流即可得到N,N′-取代 -双 -(反式 -β,γ-二取代 -γ-丁内酰胺 ) ( 0或 1 ) ,得率高 ,立体选择性好 ,方法简便     

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.     

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。     

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．     

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     

二层多目标规划的最优性条件

本文在集值优化的框架下提出了一个二层多目标规划模型（BLMOP）.利用集值映射的相依导数和相依上导数,给出了几个有关（BLMOP）的弱有效解的必要或充分最优性条件.