一类广义半无限规划问题的光滑牛顿算法

本文在广义半无限规划问题的最优解集X处满足某些条件的前提下将广义半无限规划问题转化成KKT系统,通过扰动的FB函数,将KKT系统转化为一组光滑函数方程,设计了一个光滑牛顿算法,证明了算法的全局收敛性,并且在光滑函数解集处满足局部误差界条件下证明了算法具有超线性收敛速率.     

Hermite矩阵特征值的新扰动界

本文研究了Hermite矩阵特征值的任意扰动,给出了新的绝对和相对扰动界．所给出的界改进了Hoffman-Wielandt和Kahan早期的结果．     

HR分解的精化扰动界（英文）

给出了HR分解的分量型和范数型的一阶扰动界.对于范数型,新的精化扰动界至少优于已有结果,特别的,新的关于R因子的扰动界远远优于已有的扰动界.     

Banach空间中的Drazin逆的表示和扰动

本文给出了 Ｂａｎａｃｈ空间中 Ｄｒａｚｉｎ逆的表示定理,在一定条件下建立了它的扰动界．     

｜AX—B｜min的J-中心对称解

研究方程｜AX-B｜min的J-中心对称矩阵解,给出通解的一般形式．讨论了最小J-中心对称解及其扰动界,给出J-中心对称解的逼近程度等相关问题的一些结论．     

扰动系统概周期解和有界解的存在性

该文研究扰动系统．在适当条件下给出扰动系统概周期解和有界解的存在性证明．     

3-分片线性NCP函数的滤子QP-free算法

本文定义一个3-分片线性的NCP函数,并对非线性约束优化问题,提出了带有这分片NCP函数的QP-free非可行域算法.根据优化问题的一阶KKT条件,利用乘子和NCP函数,得到非光滑方程,本文给出一个非光滑方程的迭代算法.这算法包含原始-对偶变量,在局部意义下,可看成关于一阶KKT最优条件的的扰动拟牛顿迭代算法.在线性搜索时,这算法采用滤子方法.本文给出的算法是可实现的并具有全局收敛性,且在适当假设下具有超线性收敛性.     

扰动系统的稳定性检测

该文给出了一种对于扰动系统的Ｅ一稳定检测方法，对于离散时间系统，这种稳定性检测还可以通过有限步的代数运算完成．     

一类二次半定规划内点算法的搜索方向

利用牛顿法求解一类二次半定规划的扰动KKT方程组,得出这类二次半定规划原始-对偶路径跟踪算法搜索方向求解的统一形式,以及HKM搜索方向和NT搜索方向存在唯一的充分条件,最后给出了计算搜索方向的表达式,和特殊情况下搜索方向的计算方法.     

Banach代数上广义Drazin逆的扰动

我们利用分块技术得到了扰动后元素广义Drazin可逆的充要条件,还研究了Banach代数上广义Drazin逆的扰动以及给出了扰动界.     

Influence diagnostics for the proportional hazards model

Influence diagnostics based on Cook's curvature diagnostic (1986) are developed for the proportional hazards model. Three perturbation schemes are considered: perturbation of the likelihood, perturbation of the censoring information and perturbation of covariate values.     

Some New Perturbation Bounds for the Generalized Polar Decomposition

The changes in the unitary polar factor under both multiplicative and additive perturbation are studied. A multiplicative perturbation bound and a new additive perturbation bound, in which a different measure of perturbation is introduced, are presented.     

Solutions of evolution inclusions generated by a difference of subdifferentials

An evolution inclusion with the right-hand side containing the difference of subdifferentials of proper convex lower semicontinuous functions and a multivalued perturbation whose values are nonconvex closed sets is considered in a separable Hilbert space. In addition to the original inclusion, we consider an inclusion with convexified perturbation and a perturbation whose values are extremal points of the convexified perturbation that also belong to the values of the original perturbation. Questions of the existence of solutions under various perturbations are studied and relations between solutions are established. The primary focus is on the weakening of assumptions on the perturbation as compared to the known assumptions under which existence and relaxation theorems are valid. All our assumptions, in contrast to the known assumptions, concern the convexified rather than original perturbation.     

Euler-Bernoulli梁的高阶二次摄动解及收敛性讨论

首次用解析的方式给出了Euler-Bernoulli梁后屈曲与非线性弯曲问题的高阶二次摄动解答.假定梁的中线不可伸长，用精确曲率公式与能量变分原理导出了非线性Euler-Bernoulli梁的模型.通过与精确解或高阶摄动解的比较，讨论了二次摄动解答的收敛性及适用域.得到主要结论如下:低阶摄动解适用于描述梁的初始后屈曲阶段及初始非线性弯曲阶段；更高阶次的摄动解适用于描述梁的深度后屈曲以及深度非线性弯曲.从这个意义上去说，该文不仅仅指出某些文献上的部分结果不精确是由于摄动解答超出了其特定的适用域，并且还进一步发展与完善了二次摄动法.     

On the perturbation of the Q‐factor of the QR factorization

This paper gives normwise and componentwise perturbation analyses for the Q‐factor of the QR factorization of the matrix A with full column rank when A suffers from an additive perturbation. Rigorous perturbation bounds are derived on the projections of the perturbation of the Q‐factor in the range of A and its orthogonal complement. These bounds overcome a serious shortcoming of the first‐order perturbation bounds in the literature and can be used safely. From these bounds, identical or equivalent first‐order perturbation bounds in the literature can easily be derived. When A is square and nonsingular, tighter and simpler rigorous perturbation bounds on the perturbation of the Q‐factor are presented. Copyright © 2011 John Wiley & Sons, Ltd.     

圆板非线性理论的一种摄动解

用摄动法分析了几种非线性圆板问题,其所选用的摄动参数,不是某一预先给定的力学量,而是从某些方程中求解得出.这个方法是钱伟长以中心挠度为参数的摄动法的延伸.     

鲁棒稳定多项式的摄动界

鲁棒稳定多项式的摄动界安森建,王恩平（中国科学院系统科学研究所,北京１０００８０）基金项目：国家自然科学基金资助项目．１）作者现在通讯地址：北京大学力学系,邮政编码：１００８７１．１９９２年１月００４日收到,１９９２年４月７日收到第一次修改稿,１９９...     

关于钱氏摄动法的高阶解的计算机求解和收敛性的研究

本文借助于中心受集中载荷圆板小挠度问题的积分方程,获得了摄动参数为中心挠度的任意n阶摄动解的解析式.于是,任意次摄动解的所有待定系数能用计算机求解.因此,获得了相当高阶的摄动解.在此基础上,讨论了钱氏摄动法的渐近性和适用区.     

Perturbation Sensitivity and Limit Loads of Shells

The perturbation sensitivity and its influence on the limit loads of shells are widely discussed phenomena. Both phenomena may be classified with respect to the type of perturbation. As perturbations influence the stability of shells, the identification of unfavourable perturbations is essential. The perturbation energy concept enables to identify unfavourable non–initial perturbation loads and to evaluate the perturbation sensitivity of fundamental states by the perturbation energy. This measure is also the basis for a load–level–specific optimisation of the perturbation sensitivity. Hence, the present paper discusses primarily the perturbation sensitivity of axially loaded cylindrical shells with different boundary conditions. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Subgrid modeling of filtration and dispersion in a fractal porous medium

The equations are obtained for effective coefficients of correlated random fields of permeability and porosity in a fractal porous medium. The fields have log-normal distributions. The refined perturbation theory is formulated that uses some ideas of the Wilson renormalization group. The theoretical results are compared with the results of a direct numerical modeling and the results of the conventional perturbation theory. The advantages of the refined perturbation theory over the conventional perturbation theory are demonstrated.