Banach空间中一类扰动优化问题最优解的特征与存在性

设(X,‖·‖)是Banach空间,x∈X,Z是X的非空子集,J是Z→R的下半连续下有界函数．本文研究扰动优化问题min_(z∈Z)(J(z)+‖x-z‖)(记作(J,x)-inf)的最优解的特征和最优解的存在性等问题．我们引入J－太阳集的概念,同时在Z是J-太阳集的情形下,给出了扰动优化问题(J,x)-inf的最优解的“Kolmogorov”型特征刻画．并借助于集合的若干紧性概念和最优值函数的方向导数研究了扰动优化问题(J,x)-inf的最优解的存在性．     

关于Columbus问题大扰动情形的完全解

本文在大扰动普遍情形下,按照连续系统的直接方法解答了Columbus问题。所得理论结果和Kelvin实验结果精确一致。至此,Columbus问题得到较完善的解决。     

次酉极因子在酉不变范数下的相对扰动界

设A是一个m×n阶复矩阵,分解A=QH称为广义极分解,如果Q是m×n次酉极因子且H为n×n半正定的Hermite矩阵．本文获得了次酉极因子在任意酉不变范数下的几个相对扰动界,在某种意义上,相对扰动界比R．C．Li等获得的绝对扰动界要好．     

单机排序中关于完工前总损失的应急管理

该文研究了扰动环境下的关于完工前总损失的单机排序问题, 也就是这样一个问题: 在时刻 t , 一部分工件已经完工了, 一个扰动发生了, 在这种情形下, 原来的排序已经不是最优排序甚至是不可行排序了. 因此就需要对未完成的工件找一个新的排序. 作者采用的方法与大多数重新排序问题所不同的是: 模型里包含了原始排序与新排序之间的偏差所造成的损失. 作者主要研究了在原始排序中加权最短加工时间规则(WSPT)是最优排序的情形. 根据扰动的类型, 应急管理策略的类型以及目标函数, 研究了几个问题. 对于每个问题, 作者找到了最优排序或者得出了一些重要结果.     

有限理性下参数最优化问题解的稳定性

主要研究有限理性下参数最优化问题解的稳定性. 即在两类扰动即目标函数及可行集二者, 目标函数、可行集及参数三者分别同时发生扰动的情形下, 对参数最优化问题引入一个抽象的理性函数, 分别建立了参数最优化问题的有限理性模型M, 运用``通有'的方法, 得到了上述两种扰动情形下相应的有限理性模型M的结构稳定性及对\varepsilon-平衡(解)的鲁棒性, 即有限理性下绝大多数的参数最优化问题的解都 是稳定的, 并以一个例子说明所得的稳定性结果均是正确的.     

非紧致实半单纯Lie代数的最大非半单纯子代数

<正> ■在[1]中已经完全解决了复牛单纯 Lie 代数的最大非半单纯子代数的共轭分类问题.紧致实半单纯 Lic 代数的所有不共轭的最大非半单纯子代数也早已有 Borel A.et Sicbenthal J.在[2]中决定.但不论在复的情形还是在实紧致的情形,上述最大非半单纯子代数的根不必区别它是紧致的还是非紧致的.而对于非紧致实半单纯Lie 代数,它的最大非半单纯子代数的根有紧致与非紧致之別.     

气体动力学燃烧模型的广义Riemann问题

考察了在(x,t)平面上原点(t＞0)的邻域内气体动力学燃烧模型的广义Riemann问题．在改进的熵条件下构造了此问题的唯一解．它们是自相似ZND燃烧模型的极限．发现对某些情形,广义Riemann问题的解与相应的Riemann问题的解有本质的不同．特别地,扰动会使得相应Riemann问题的强爆轰波转化为由预压激波点燃的弱爆燃波．在一些情形,尽管相应的Riemann解中不含燃烧波,扰动后燃烧波会出现．这反映了未燃气体的不稳定性．     

一类齐次线性微分方程复振荡的特例和结果

发现一类k(≥2)阶齐次线性微分方程存在唯一的情形具有k个无零点的线性无关解,同时得到这类方程复振荡的一个普遍结果,由此,完整解决了在超越整函数时这类方程的复振荡理论,而在多项式时回答了Bank的问题。     

极大η-单调集值映射的一个性质

本文着重研究了在什么条件下集值映射I λT的值域是全空间Rn这一问题,其中I是恒等映射,λ>0是任意给定的常数,T是一个极大η-单调的集值映射．文中主要结果部分地解决了C．-H．Lee,Q．H．Ansari和J．-C．Yao在2000年提出的一个公开问题．此外,针对真下半连续泛函的η-次微分映射,也讨论了上述问题．     

一类四次椭圆Hamilton向量场在三次多项式下的扰动

本文研究一类四次椭圆Hamilton向量场在所有三次多项式下的扰动,证明了如下结论: (1)除全局中心外,围绕一个中心定义的Abel积分的孤立零点的个数不超过12; (2)存在一个三次系统,它在扰动前属于一个鞍点环的情形,而在扰动后至少存在3个极限环.     

On the growth factor in Gaussian elimination for generalized Higham matrices

A Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite. We prove that, for such A, the growth factor in Gaussian elimination is less than 3. Moreover, a slightly larger bound holds true for a broader class of complex matrices A=B+iC, where B and C are Hermitian and positive definite. Copyright © 2002 John Wiley & Sons, Ltd.     

关于矩阵多项式特征值界的注记

本文讨论矩阵多项式特征值定域问题.首先对Higham和Tisseur[Linear Algebra Appl.,358(2003),5-22]得到的结果给出较详细的比较.然后利用分块矩阵谱半径的估计给出了获取特征值界的一种新办法.利用这种新办法,不但可以简明地得出很多已有的界,且对椭圆及双曲矩阵多项式得出了特征值的新的界.     

REAL AND COMPLEX OPERATOR IDEALS

Abstract

The powerful concept of an operator ideal on the class of all Banach spaces makes sense in the real and in the complex case. In both settings we may, for example, consider compact, nuclear, or 2-summing operators, where the definitions are adapted to each other in a natural way. This paper deals with the question whether or not that fact is based on a general philosophy. Does there exists a one-to-one correspondence between “real properties” and “complex properties” defining an operator ideal? In other words, does there exist for every real operator ideal a uniquely determined corresponding complex ideal and vice versa?

Unfortunately, we are not abel to give a final answer. Nevertheless, some preliminary results are obtained. In particular, we construct for every real operator ideal a corresponding complex operator ideal and for every complex operator ideal a corresponding real one. However, we conjecture that there exists a complex operator ideal which can not be obtained from a real one by this construction.

The following approach is based on the observation that every complex Banach space can be viewed as a real Banach space with an isometry acting on it like the scalar multiplication by the imaginary unit i.     

图的预解Estrada指标的界的估计（英文）

n阶图G的子图中心度,即后来著名的Estrada指标定义为EE（G）=∑_（i=1）~N e~（λ2）.其中λ_1,λ_2……λ_n为图G的特征值.作为复杂网络的一种中心性测度和一种分子结构描述符,Estrada指标在许多研究领域有着广泛的应用.最近,Estrada和High-ama引进了一种新的复杂网络中心度,即∑_（i=1）~n n-1n-1λ_i：他们称之为预解中心度,后来又被称为预解Estrada指标.本文主要利用图G的顶点数和边数给出了图G的预解Estrada指标的若干界.     

A version of Turán’s problem for positive definite functions of several variables

We present a systematic approach to solving the problem of affine homogeneity of real hypersurfaces in the three-dimensional complex space. This question is an important part of the general problem of holomorphic classification of homogeneous real hypersurfaces in three-dimensional complex spaces. In contrast to the two-dimensional case, the whole problem (just as its affine part) has not yet been fully studied, although there exist a large number of examples of homogeneous manifolds. We study only the class of tubular type surfaces, which is defined by conditions imposed on the 2-jet of their canonical equations and generalizes the class of tube manifolds. We discuss the procedure of describing all matrix Lie algebras corresponding to the homogeneous manifolds under consideration. In the class that we study, we distinguish four cases depending on the third-order Taylor coefficients of the canonical equations; in three of these cases, the Lie algebras and the corresponding affine homogeneous surfaces are completely described. The key point of the proposed approach is the solution of a large system of quadratic equations that corresponds to each of the homogeneous surfaces.     

Computing a partial generalized real Schur form using the Jacobi–Davidson method

In this paper, a new variant of the Jacobi–Davidson (JD) method is presented that is specifically designed for real unsymmetric matrix pencils. Whenever a pencil has a complex conjugate pair of eigenvalues, the method computes the two‐dimensional real invariant subspace spanned by the two corresponding complex conjugated eigenvectors. This is beneficial for memory costs and in many cases it also accelerates the convergence of the JD method. Both real and complex formulations of the correction equation are considered. In numerical experiments, the RJDQZ variant is compared with the original JDQZ method. Copyright © 2007 John Wiley & Sons, Ltd.     

Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.     

李超代数上的不变双线性型

本文通过定义李超代数上的形心和零次形心来考察其性质.证明了二次李超代数(G,B)上的不变数积的集合和其形心中的可逆B-超对称元素的集合之间存在一一对应.而对实单李超代数分为两种不同的类型:或者是一个忽略了复结构的复李超代数或者是一个复单李超代数的实形式.     

Buchstaber Invariants of Universal Complexes

Davis and Januszkiewicz introduced (real and complex) universal complexes to give an equivalent definition of characteristic maps of simple polytopes,which now can be seen as "colorings".The author derives an equivalent definition of Buchstaber invariants of a simplicial complex K,then interprets the difference of the real and complex Buchstaber invariants of K as the obstruction to liftings of nondegenerate simplicial maps from K to the real universal complex or the complex universal complex.It was proved by Ayzenberg that real universal complexes can not be nondegenerately mapped into complex universal complexes when dimension is 3.This paper presents that there is a nondegenerate map from 3-dimensional real universal complex to 4-dimensional complex universal complex.     

Blocks of monodromy groups in complex dynamics

Motivated by a problem in complex dynamics, we examine the block structure of the natural action of iterated monodromy groups on the tree of preimages of a generic point. We show that in many cases, including when the polynomial has prime power degree, there are no large blocks other than those arising naturally from the tree structure. However, using a method of construction based on real graphs of polynomials, we exhibit a non-trivial example of a degree 6 polynomial failing to have this property. This example settles a problem raised in a recent paper of the second author regarding constant weighted sums of polynomials in the complex plane. We also show that degree 6 is exceptional in another regard, as it is the lowest degree for which the monodromy group of a polynomial is not determined by the combinatorics of the post-critical set. These results give new applications of iterated monodromy groups to complex dynamics.