Spectral Measures of Spiked Random Matrices

Journal of Theoretical Probability - We study two spiked models of random matrices under general frameworks corresponding, respectively, to additive deformation of random symmetric matrices and...     

两类模糊数判断矩阵的转换关系及一致性研究

研究了三角模糊数互反和互补判断矩阵的相互转换和一致性问题.提出了三角模糊数互反判断矩阵完全一致性的定义以及三角模糊数互补判断矩阵加性一致性和乘性一致性的定义,给出了两类模糊数判断矩阵相互转化的公式,论证了转换公式对判断矩阵一致性的保持关系.最后,基于一致性模糊数判断矩阵元素和排序权值的关系,建立了两个方案排序的非线性规划模型.     

Additive Maps Preserving Moore-Penrose Inverses of Matrices on Symmetric Matrix Spaces

Suppose F is a field of characteristic not 2. Let M_nF and S_nF be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from S_nF to S_nF (respectively, M_nF) preserving Moore-Penrose inverses of matrices are characterized. We first characterize all additive Moore-Penrose inverse preserving maps from S_nF to M_nF, and thereby, all additive Moore-Penrose inverse preserving maps from S_nF to itself are characterized by restricting the range of these additive maps into the symmetric matrix space.     

Additive preconditioning in matrix computations

We combine our novel SVD-free additive preconditioning with aggregation and other relevant techniques to facilitate the solution of a linear system of equations and other fundamental matrix computations. Our analysis and experiments show the power of our algorithms, guide us in selecting most effective policies of preconditioning and aggregation, and provide some new insights into these and related subjects. Compared to the popular SVD-based multiplicative preconditioners, our additive preconditioners are generated more readily and for a much larger class of matrices. Furthermore, they better preserve matrix structure and sparseness and have a wider range of applications (e.g., they facilitate the solution of a consistent singular linear system of equations and of the eigen-problem). (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

区间数互补判断矩阵的性质及相关问题研究

研究了区间数互补判断矩阵的性质问题。利用区间数互反判断矩阵与区间数互补判断矩阵之间的转换关系，给出了乘性一致性与加性一致性区间数互补判断矩阵的定义，并研究了一致性区间数判断矩阵的一些特殊性质；同时给出了区间数互补判断矩阵满意一致性的一个简单的判断方法与算法。文章的最后，通过一个例子来说明这个算法的有效性。     

Additive endomorphisms of rings

We characterize finite rings all of whose additive endomorphisms are multiplicative also.This work was supported by Alabama State University Faculty Research Grant R-78-6.     

可加乘积模型的研究

文章将乘积模型推广为可加乘积模型,延伸了正测量数据的适用范围.方法具有更强的灵活性,同时也可避免维数祸根问题.文中主要采用B样条逼近技术、最小乘积相对误差(LPRE)方法,研究非参数函数的估计问题.并在一些条件下,证明了非参数函数具有最优收敛速度.最后,通过数值模拟和实例分析,比较了提出的方法和其它几种方法的有限样本表现,验证了新方法的有效性.     

Additive and Multiplicative Expansions in Multidimensional Local Fields

The paper is a continuation of the authors' previous paper on the topology of higher local fields. A useful class of systems of topological generators for the additive and multiplicative groups is described. Bibliography: 3 titles.     

Additive Patterns in Multiplicative Subgroups

The study of sum and product problems in finite fields motivates the investigation of additive structures in multiplicative subgroups of such fields. A simple known fact is that any multiplicative subgroup of size at least q ^3/4 in the finite field F _q must contain an additive relation x + y = z. Our main result is that there are infinitely many examples of sum-free multiplicative subgroups of size Ω(p ^1/3) in prime fields F _p . More complicated additive relations are studied as well. One representative result is the fact that the elements of any multiplicative subgroup H of size at least q ^3/4+o(1) of F _q can be arranged in a cyclic permutation so that the sum of any pair of consecutive elements in the permutation belongs to H. The proofs combine combinatorial techniques based on the spectral properties of Cayley sum-graphs with tools from algebraic and analytic number theory.     

多类型复发事件下变系数加性乘积比率回归模型

本文基于多类型复发事件数据,讨论了一个新的加性乘积比率回归模型,该模型包括两部分,其中第一部分为可加Aalen模型,其中协变量影响为加性的且与时间有关.第二部分为Cox回归模型,其中协变量有乘性影响.利用估计方程的方法,给出了该模型中未知参数和非参数函数的一种估计方法,并利用现代经验过程理沦证明了所得估计的相合性和渐近正态性.     

含有治愈部分的可加危险模型的估计

最近可加危险(AH)模型被广泛地应用于生存分析数据,模型的协变量可以假设为时间独立或时间相关的.基于混合治愈模型,有界累计危险治愈模型和"不正确"的比例危险模型.本文将上述的可乘危险模型延伸到可加的危险模型,这里的模型可以允许含治愈部分的生存数据的存在."不正确"的AH模型的识别和参数估计也将在本文给出讨论.     

Additive and multiplicative tolerance in multiobjective linear programming

We consider a multiobjective linear program. We propose a procedure for computing an additive and multiplicative (percentage) tolerance in which all the objective function coefficients may simultaneously and independently vary while preserving the efficiency of a given solution. For a nondegenerate basic solution, the procedure runs in polynomial time.     

Estimating Additive Character Sums for Fuchsian Groups

In the usual construction of non-holomorphic Eisenstein series, for a general Fuchsian group, a multiplicative character may be included. The properties of these series are well known. Here we instead include an additive character and develop the properties of the resulting series. We pay particular attention to additive characters that are non-cuspidal, i.e., that are not zero on some parabolic generators. These series may be used to estimate certain additive character sums. For example, asymptotics for a weighted sum over group elements that counts the number of appearances of a fixed generator of the Fuchsian group are obtained.     

The Polynomial Method for Random Matrices

We define a class of “algebraic” random matrices. These are random matrices for which the Stieltjes transform of the limiting eigenvalue distribution function is algebraic, i.e., it satisfies a (bivariate) polynomial equation. The Wigner and Wishart matrices whose limiting eigenvalue distributions are given by the semicircle law and the Marčenko–Pastur law are special cases. Algebraicity of a random matrix sequence is shown to act as a certificate of the computability of the limiting eigenvalue density function. The limiting moments of algebraic random matrix sequences, when they exist, are shown to satisfy a finite depth linear recursion so that they may often be efficiently enumerated in closed form. In this article, we develop the mathematics of the polynomial method which allows us to describe the class of algebraic matrices by its generators and map the constructive approach we employ when proving algebraicity into a software implementation that is available for download in the form of the RMTool random matrix “calculator” package. Our characterization of the closure of algebraic probability distributions under free additive and multiplicative convolution operations allows us to simultaneously establish a framework for computational (noncommutative) “free probability” theory. We hope that the tools developed allow researchers to finally harness the power of infinite random matrix theory.     

Additive and multiplicative perturbation bounds for the Moore-Penrose inverse

In this paper, we obtain the additive and multiplicative perturbation bounds for the Moore-Penrose inverse under the unitarily invariant norm and the Q - norm, which improve the corresponding ones in [P.Å. Wedin, Perturbation theory for pseudo-inverses, BIT 13(1973)217-232].     

Additive properties of subgroups of finite index in fields

In this paper, we confirm a conjecture of Bergelson and Shapiro concerning subgroups of finite index in multiplicative groups of fields which have maximal additive dimension. We also show that the natural extension of subgroups Gp of prime index p inside Q^? and additive dimension p+1 to the case where p is replaced by a composite integer n leads to subgroups of bounded additive dimension on a set of positive integers n of asymptotic density 1.     

上三角矩阵代数上的可加保极小秩映射

The additive mappings that preserve the minimal rank on the algebra of all n × n upper triangular matrices over a field of characteristic 0 are characterized.     

Additive Decomposition of Real Matrices

The orthogonal orbit ${\cal O}(A)$ of an n × n real matrix A is the set of real matrices of the form $P^t \ AP$ where $P^t P = I_n$ . We show that $A/ \| A\|$ is an affine sum of four orthogonal matrices, and note that $A^t$ can always be written as an affine combination of no more than 2 n m 1 matrices in ${\cal O}(A)$ . This improves some recent results of Zhan, and answers some of his questions. Other related results are also discussed.     

基于最大满意度的区间混合判断矩阵排序方法

区间混合判断矩阵对表达决策者的判断信息很有帮助,然而区间混合判断矩阵尚未引起学者的足够重视.定义了一致性乘型区间混合判断矩阵和一致性加型区间混合判断矩阵,并基于最大满意度的思想,提出了求解区间混合判断矩阵的乘型和加型最大满意度模型和一致性指标,分析讨论了最大满意度模型的优点,最后通过算例验证了该模型的正确性和适用性,具有一定的理论和实际应用价值.     

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.