矩阵代数上保持与正矩阵的相似性的可加满射

用M_n表示n×n复矩阵代数(n≥2),给出M_n上双边保与正矩阵的相似性的可加满射的完全刻画和分类.     

保持因子交换性的可加映射

设x和y是代数中的两个元.如果存在某个数ξ,使得xy=ξyx,称x和y关于因子ξ交换.给出了标准算子代数间双边保关于因子交换的可加满射的刻画和分类以及C*-代数间保关于因子交换的有界线性满射的刻画和分类.     

保特征2域上上三角矩阵群逆的线性映射

设F是一个特征2且至少含有5个元素的域,n≥2是一个正整数．令Mn（F）和Tn（F）分别F上的全矩阵空间和上三角矩阵空间．我们首先刻划从Tn（F）到Mn（F）的保矩阵群逆的所有线性单射，由此从Tn（F）到自身的所有保矩阵群逆的线性双射被刻划．     

三角矩阵代数上的保交换可加映射

本文研究了三角矩阵代数上保持交换性的可加映射的结构.利用最近Marcoux与Sourour发表在[Linear Alg.Appl.288(1999),89-104]上的一个结果,我们证明了任意域F上的三角矩阵代数Tn(F)(n＞2)上的可加满射ψ双向保交换当且仅当ψ是Tn(F)上一个可加泛函与Tn(F)上某个环自同构或环反自同构之和.     

保域上矩阵群逆的线性算子

设F是特征为2的域,n≥2,Mn(F)为F上全矩阵代数.在这篇文章中我们刻画了Mn(F)上保持矩阵群逆的线性算子的形式.     

保持二次算子的可加映射

设X是具有无限重复度的无限维或维数不小于3的有限维复Banach空间,B(X)是X上全体有界线性算子组成的Banach代数.首先证明了单位算子不能表示成3个平方幂零算子之和,利用算子分块矩阵技巧获得了平方幂零算子的本质特征.以此特征为基础,刻画了B(X)上双边保持二次算子可加满射的结构.     

Von Neumann代数套子代数上保因子交换性的线性映射

对因子von Neumann代数的套子代数上的保单位线性映射Φ:AlgMα→AlgMβ满足AB=ξBA(?)Φ(A)Φ(B)=ξΦ(B)Φ(A)进行了刻画,其中A,B∈AlgMα,ξ∈F,即证明了因子von Neumann代数的套子代数间每个保单位的弱连续线性满射它双边保因子交换性,则映射Φ或者是同构或者是反同构.     

矩阵空间之间的保幂线性映射

在本文中,设C是复数域,n和m是正整数,k为固定的自然数,且k≥2．设Mm(C)为C上m阶全矩阵空间,Sn(C)为C上n阶对称矩阵空间．本文分别刻画了从Sn(C)到Mm(C)和Sn(C)到Sm(C)上的保矩阵k次幂的线性映射．     

域上两类矩阵保逆的诱导映射

令F是一个域,S_n(F)是F上所有n×n上对称矩阵的集合.用T_n(F)记F上所有n阶上三角阵的集合.首先分别给出诱导映射和保逆性的定义.然后改进了关于复对称阵保逆的主要相关结果及其证明,得到了S_n(F)保逆诱导映射的一般形式,最后借助于类序列技术和初等方法刻画了T_n(F)保逆诱导映射.它推广和改进了带有附加条件(f_(ij)(x)=0x=0)的相关结果.     

保持拟可逆性或拟零因子的可加映射

设X和Y是维数大于1的复Banach空间,A和B分别是B(X)和B(Y)中包含有限秩算子的范数闭子代数.A,B∈A,定义A。B=A+B-AB,称。为A,B的拟积.刻画了从A到B的双边保持算子的(左,右)拟可逆性或(左,右,半)拟零因子的可加满射的结构.     

关于域上矩阵广义逆的加法映射

假设F是特征不为2的域,令Mn(F)是F上n×n矩阵的集合.本文证明了f是Mn(F)到自身的矩阵{1}-逆或{1,2}-逆的加法保持算子当且仅当f有:(a)f=0;(b)f(A)=εPAτP-1对任意A∈Mn(F),其中P∈GLn(F),τ-为域F的某个单自同态且x(1)=1,ε=±1;(c)f(A)=εP(Aτ)TP-1对于任意A∈Mn(F),其中τ,ε,P如(b)中一样意义.     

加型一致性毕达哥拉斯模糊偏好关系

在模糊偏好关系两种等价的加型一致性概念基础上,通过简单的数学证明,分析了区间值模糊偏好关系、直觉模糊偏好关系的相应的两种加型一致性并不是等价的.然后,在加型一致性直觉模糊偏好关系的启发下,构造了可以与毕达哥拉斯模糊偏好关系相互转换的两个区间值模糊偏好关系,并利用它们的加型一致性,定义了加型一致性毕达哥拉斯模糊偏好关系,并分析了其与杨艺等定义的加型一致性毕达哥拉斯模糊偏好关系的关系.其次,研究了加型一致性毕达哥拉斯模糊偏好关系的性质以及毕达哥拉斯模糊偏好关系的满意一致性,并给出满意一致性毕达哥拉斯模糊偏好关系下的方案优劣排序算法.最后,通过两个计算实例说明了排序算法可行有效.     

Equality of proofs for linear equality

This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation, those of an equivalence relation, and other properties appropriate for an equality relation in linear logic. The guiding idea is that equality of proofs is induced by coherence, understood as the existence of a faithful functor from a syntactical category into a category whose arrows correspond to diagrams. Edges in these diagrams join occurrences of variables that must remain the same in every generalization of the proof. It is found that assumptions about equality of proofs for equality are parallel to standard assumptions about equality of arrows in categories. They reproduce standard categorial assumptions on a different level. It is also found that assumptions for a preordering relation involve an adjoint situation.      

从对称矩阵代数到全矩阵代数的线性群逆保持

设F是一个特征不为2的域,Mn(F)和Sn(F)分别记F上的n×n全矩阵代数和对称矩阵代数.所有的从Sn(F)到Mn(F)的保群逆的线性映射被刻划,作为一个中间步骤,三个矩阵的同时相似标准形也被证明.这个标准形简化了从Sn(F)到Mn(F)的保群逆的线性映射的刻划.     

The equality relations in scientific computing

The equality relation (more generally, the ordering relations) in floating point arithmetic is the exact translation of the mathematical equality relation. Because of the propagation of round-off errors, the floating point arithmetic is not the exact representation of the theoretical arithmetic which is continuous on the real numbers.This leads to some incoherence when the equality concept is used in floating point arithmetic. A well known example is the detection of a zero element in the pivoting column and equation when applying Gaussian elimination, which is almost impossible in floating point arithmetic.We shall begin by showing the inadequacy of the equality relation used in floating point arithmetic (we will call it floating point equality), and then introduce two new concepts: stochastic numbers and the equality relation between such numbers which will be called the stochastic equality. We will show how these concepts allow to recover the coherence between the arithmetic operators and the ordering relations that was missing in floating point computations.     

Homomorphisms Between Multiplicative Semigroups of Matrices Over Fields

Suppose F is a field, and n, p are integers with 1 ≤ p 〈 n. Let Mn（F） be the multiplicative semigroup of all n × n matrices over F, and let M^Pn（F） be its subsemigroup consisting of all matrices with rank p at most. Assume that F and R are subsemigroups of Mn（F） such that F M^Pn（F）. A map f ： F→R is called a homomorphism if f（AB） = f（A）f（B） for any A, B ∈F. In particular, f is called an endomorphism if F = R. The structure of all homomorphisms from F to R （respectively, all endomorphisms of Mn（F）） is described.     

Bivariate least squares approximation with linear constraints

In this article linear least squares problems with linear equality constraints are considered, where the data points lie on the vertices of a rectangular grid. A fast and efficient computational method for the case when the linear equality constraints can be formulated in a tensor product form is presented. Using the solution of several univariate approximation problems the solution of the bivariate approximation problem can be derived easily. AMS subject classification (2000)  65D05, 65D07, 65D10, 65F05, 65F20     

Minimal representation of convex polyhedral sets

A system of linear inequality and equality constraints determines a convex polyhedral set of feasible solutionsS. We consider the relation of all individual constraints toS, paying special attention to redundancy and implicit equalities. The main theorem derived here states that the total number of constraints together determiningS is minimal if and only if the system contains no redundant constraints and/or implicit equalities. It is shown that the existing theory on the representation of convex polyhedral sets is a special case of the theory developed here.The author is indebted to Dr. A. C. F. Vorst (Erasmus University, Rotterdam, Holland) for stimulating discussions and comments, which led to considerable improvements in many proofs. Most of the material in this paper originally appeared in the author's dissertation (Ref. 1). The present form was prepared with partial support from a NATO Science Fellowship for the Netherlands Organization for the Advancement of Pure Research (ZWO) and a CORE Research Fellowship.     

关于非光滑不变凸多目标规划的Wolfe型对偶

本文讨论定义在Banach空间上的,既具有等式约束又具有不等式约束的,非光滑(F,P)不变凸多目标规划的Wolfe对偶性,Mond-Weir型对偶性可类似讨论之。