极大加代数的对称代数S上互补基本矩阵

主要研究了极大加代数的对称代数S上互补基本矩阵,给出本征积的概念,证明了S上的Laplace定理,由此推出所有互补基本矩阵的行列式相等,且任意两个互补基本矩阵的行列式中的非零项均一一对应相等.在一个互补基本矩阵的行列式中,对于确定非零项的任一置换,给出了在另一个互补基本矩阵的行列式中找到置换使其确定相同非零项的方法.     

极大加可约矩阵的谱与周期时间向量的关系

提出了极大加代数上可约矩阵特征值的缺失值及冗余值的概念,得到了相应的定理;对特征值与周期时间向量分量之间的关系作了深入的研究.     

一类算子矩阵特征值的代数指标和代数重数

自伴算子特征值的几何重数与代数重数相等,但对于非自伴算子不一定成立,这主要是特征值的代数指标起着决定性的作用.讨论了一类非自伴算子矩阵特征值的几何重数,代数指标与代数重数.     

二次自伴矩阵多项式阵的特征值

系统地论证了二次自伴矩阵多项式特征值,特征向量的性质.给出了二次自伴矩阵多项式特征值与任一非零向量所对应的二次多项式根之间的大小关系;精确地给出了二次自伴矩阵多项式是负定时参数的界;简化了二次自伴矩阵多项式的符号特征是正(负)的特征值对应特征向量间可以是线性无关等定理的证明.     

幂等矩阵的性质及其推广

首先对幂等矩阵的简单性质进行了归纳总结,接着论证了幂等矩阵的等价条件及其特征值的取值范围,并讨论了幂等矩阵与实对称矩阵的关系、幂等矩阵与其伴随矩阵的特征值和特征向量的对应关系及幂等矩阵在群逆中的一个性质.最后讨论了幂等矩阵的两种分解形式.     

用试验数据修正质量矩阵,阻尼矩阵与刚度矩阵

讨论用试验数据修正振动系统的双对称质量矩阵,阻尼矩阵与刚度矩阵的问题.依据特征方程,质量矩阵,阻尼矩阵与刚度矩阵的双对称性,利用代数二次特征值反问题的理论和方法,研究了这个问题解的存在性与惟一性,提出了修正质量矩阵,阻尼矩阵与刚度矩阵的一个新方法.利用矩阵的奇异值分解和矩阵的Kronecker乘积研究了方程的双对称解.给出了二次特征值反问题双对称解的一般表达式,讨论了对任意给定矩阵的最佳逼近问题,并给出了问题的最佳逼近解.     

方阵秩与零特征值代数重数相关性探讨

利用方阵的特征方程和Jordan标准型,可得出方阵的秩R、零特征值代数重数r、几何重数s之间存在的两个关系式．即n-r≤R〈n和R=n-s．而这两个关系式又可用于简化方阵特征值和秩的求解．揭示矩阵零特征值代数重数与矩阵秩之间的内在必然联系．     

关于矩阵和与矩阵积的特征值的关系

本文给出了两个矩阵积的迹与其特征值之间的若干等价关系,并推广到两个矩阵和的情形.     

Q-矩阵第一特征值估计的Monte Carlo方法

本文对给定的可逆马氏链所对应的 Q-矩阵给出了它的第一非零特征值的 Monte Carlo估计方法 .具体做法是通过增加一个状态构造一个新的可逆马氏链 ,然后利用增加状态的击中时分布去估计第一非零特征值 .     

具有不同特征值的Hermitian矩阵及其应用

研究了具有k个不同特征值的Hermitian矩阵,给出了邻接矩阵和(规范)拉普拉斯矩阵的图具有k个不同特征值的代数刻画.     

一种无穷和的定义、性质及其在马尔科夫链中的应用

对形式级数 ∑ui无穷和的定义进行了推广 ,给出蔡查罗无穷和的概念 ,讨论了它们之间的关系 .对正项级数、交错级数的蔡氏收敛性做了完整的讨论 .并将其应用于马尔科夫链的渐近性态的研究 ,得到了更为简洁、完整的结果     

Modules with the Direct Summand Sum Property

The present work gives some characterizations of R-modules with the direct summand sum property (in short DSSP), that is of those R-modules for which the sum of any two direct summands, so the submodule generated by their union, is a direct summand, too. General results and results concerning certain classes of R-modules (injective or projective) with this property, over several rings, are presented.     

Comtrans algebras, Thomas sums, and bilinear forms

A comtrans algebra is said to decompose as the Thomas sum of two subalgebras if it is a direct sum at the module level, and if its algebra structure is obtained from the subalgebras and their mutual interactions as a sum of the corresponding split extensions. In this paper, we investigate Thomas sums of comtrans algebras of bilinear forms. General necessary and sufficient conditions are given for the decomposition of the comtrans algebra of a bilinear form as a Thomas sum. Over rings in which 2 is not a zero divisor, comtrans algebras of symmetric bilinear forms are identified as Thomas summands of algebras of infinitesimal isometries of extended spaces, the complementary Thomas summand being the algebra of infinitesimal isometries of the original space. The corresponding Thomas duals are also identified. These results represent generalizations of earlier results concerning the comtrans algebras of finite-dimensional Euclidean spaces, which were obtained using known properties of symmetric spaces. By contrast, the methods of the current paper involve only the theory of comtrans algebras.Received: 30 March 2004     

ESSENTIALLY FINITELY INDECOMPOSABLE ABELIAN p-GROUPS

Abstract

An abelian p-group C is said to be essentially finitely indecomposable (efi) if given any decomposition of G as the direct sum of a family of subgroups, there exists a positive integer n such that all but at moat a finite number of subgroups of this family are bounded by n. We look at examples and related questions. We prove that a reduced abelian p-group G is efi if and only if G modulo its elements of infinite height is efi. In the proof of this we obtain the following result which is of independent interest: Let A be a reduced p-group with a summand K such that K is a direct sum of cyclic groups. Let B be a basic subgroup of A. Then B contains a subgroup C such that C is a summand of A and the final rank of C is equal to the final rank of K.     

Hardy-Hilbert型不等式的一个加强

改进了Hlder不等式,并利用加强的Hlder的不等式对联系β函数的带参数的Hardy-Hilbert型不等式进行了改进,建立一个新的形如sum from n=1 to ∞ sum from m=1 to ∞(ambn/(m+n)λ)/相似文献   

Painless Breakups—Efficient Demixing of Low Rank Matrices

Journal of Fourier Analysis and Applications - Assume we are given a sum of linear measurements of s different rank-r matrices of the form $$\varvec{y}= \sum _{k=1}^{s} \mathcal {A}_k...     

WEAKLY CONTINUOUS AND C2-RINGS

A ring R is called right weakly continuous if the right annihilator of each element is essential in a summand of R, and R satisfies the right C2-condition (every right ideal that is isomorphic to a direct summand of R is itself a direct summand). We show that a ring R is right weakly continuous if and only if it is semiregular and J(R) = Z(R _R ). Unlike right continuous rings, these right weakly continuous rings form a Morita invariant class. The rings satisfying the right C2-condition are studied and used to investigate two conjectures about strongly right Johns rings and right FGF-rings and their relation to quasi-Frobenius rings.     

Matrices over a commutative ring as sums of three idempotents or three involutions

Motivated by Hirano-Tominaga’s work on rings for which every element is a sum of two idempotents and by de Seguins Pazzis’s results on decomposing every matrix over a field of positive characteristic as a sum of idempotent matrices, we address decomposing every matrix over a commutative ring as a sum of three idempotent matrices and, respectively, as a sum of three involutive matrices.     

Summations of linear recurrent sequences

We give an extension of Sister Celine’s method of proving hypergeometric sum identities that allows it to handle a larger variety of input summands. In particular, we extend the summand to powers of a C-finite sequence times a hypergeometric term. We then apply this to several problems. Some of these applications give new results, and some reprove already known results in an automated way.     

Error bounds in approximations of random sums using gamma-type operators

In this work we deal with approximations of compound distributions, that is, distribution functions of random sums. More specifically, we obtain a discrete compound distribution by replacing each summand in the initial random sum by a discrete random variable whose probability mass function is related to a well-known inversion formula for Laplace transforms [cf. Feller, W., 1971. An Introduction to Probability Theory and its Applications, vol. II, second edn. Wiley, New York]. Our aim is to show the advantages that this method has in the context of compound distributions. In particular we give accurate error bounds for the distance between the initial random sum and its approximation when the individual summands are mixtures of gamma distributions.