Hilbert空间稠定闭线性算子的Moore-Penrose正交广义逆的扰动分析

主要研究Hilbert空间具有闭值域的稠定闭线性算子的Moore-Penrose正交广义逆的扰动,并且在原有的第一类,第二类扰动的基础上定义了第三类和第四类扰动,并得到了相应的性质和结论.     

属性测度μ_x(A)的扰动问题及属性扰动算子研究

提出了属性测度 μx的扰动概念 ,使得对属性集的描述更加符合客观实际 .在此基础上定义了扰动属性区间集、属性测度区间和属性扰动算子 ,为属性数学的进一步发展拓宽了空间 .     

TD型扰动值模糊正规子群

将幂等扰动范数TD引入到扰动值空间上,以此为基础定义了TD型扰动值模糊正规子群,并研究了其性质与结构特征,从而拓广了扰动模糊集的代数结构理论。     

A Class of Nonlinear Singularly Perturbed Problems for Reaction Diffusion Equations with Boundary Perturbation

A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems is studied using the theory of differential inequalities.     

The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations with a boundary perturbation

The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.     

R0-代数的扰动模糊子代数和扰动模糊MP滤子

把扰动模糊集理论应用在R_0-代数上,给出R_0-代数的扰动模糊子代数,扰动模糊MP滤子的概念,讨论R_0-代数上扰动模糊子代数的等价刻画和扰动模糊MP滤子的若干性质;研究了扰动模糊MP滤子的同态像和逆像。     

知识的属性扰动与属性扰动定理

By using the dynamic characteristic of one direction S-rough sets(one direction singular rough sets) and dual of one direction S-rough sets(dual of one direction singular rough sets),the concepts of attribute disturbance of knowledge,the attribute disturbance degree of knowledge,and the disturbance coefficient of knowledge are given.By employing these concepts,the cardinal order theorem of the attribute disturbance knowledge,the unit circle theorem of the attribute disturbance knowledge,and the discernib...     

A SINGULARLY PERTURBED EIGENVALUE ROBIN PROBLEM WITH TURNING POINT OF HIGHER ORDER

A singularly perturbed eigenvalue Robin problem with turning point of higher order is studied, which can describe some heat conduction phenomena. Using the method of Langer transformation, the uniformly asymptotic solution of the equation is obtained, which is expressed by Bessel function, and the eigenvalue and eigenfunction of the problem are given, and then the known result is generalized.     

单链需求扰动下竞争供应链决策模型研究

突发事件经常导致需求扰动,致使供应链运营出现失调.以两条竞争供应链组成的供应链系统为研究对象,建立了供应链竞争基准模型.引入偏差惩罚成本,构建了竞争供应链应对单链需求扰动的均衡模型,给出了不同扰动程度下生产数量及零售价格的应对策略.研究发现,在一定的扰动程度内,原生产计划都具有鲁棒性,鲁棒性范围依赖于价格交叉弹性系数和偏离惩罚成本,其大小与需求扰动源无关.     

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．     

关于特征值的Hoffman-Wielandt型相对扰动界

本文主要研究了关于特征值的Hoffman-wielandt型相对扰动界，改进了LiRC和Ipsen I等人关于这方面的相应结果．     

任意矩阵的特征值的扰动估计

设A和B是两个任意的n阶方阵,其特征值分别为{λ_1,…,λ_n}和{μ_1,…,μ_n}.本文对此两组特征值的如下“距离”的界给出了若干估计: B对于A的谱改变量 A与B的特征值的改变量这里的结果包含了Bauer-Fike定理,并且优于Kahan-Parlett/Jiang定理及Chu,施和肖所得出的结果.     

矩阵特征值的几个扰动定理

1 引言 设A∈C~(n×m),B∈C~(m×m)(m≤n),它们的特征值分别为{λ_k}_(k=1)~n和{μ_k}_(k=1)~m.令 R=AQ-QB (1)这里Q∈C~(n×m)为列满秩矩阵.Kahan研究了矩阵A在C~(n×m)上的Rayleigh商的性质,证明了下列定理:设A为Hermite矩阵,Q为列正交矩阵,即Q~HQ=I,而B=Q~HAQ,则存在 1,2,… ,n的某个排列π,使得 {sum from j=1 to m │μ_j-λ_(π(j))│~2}~(1/2)≤2~(1/2)‖R‖_F (2)其中R如(1)所示,‖·‖_F为矩阵的Frobenius范数.刘新国在[2]中将此定理推广到B为可对角化矩阵的情形,并且还建立了较为一般的扰动定理:设A为正规矩阵,B为可对角化矩阵;存在非奇异矩阵G,使得G~(-1)BG为对角阵,则存在1,2,…,n的某个排列π,使得 │μ_j-λ_(π(j))│≤2(2~(1/2))nK(G)_(σ_m~(-1))‖R‖_F,j=1,2,…,m. (3)     

THE SINGULARLY PERTURBED NONLINEAR ELLIPTIC SYSTEMS IN UNBOUNDED DOMAINS

Abstract. The singularly perturbed problems for elliptic systems in unbounded domains are considered. Under suitable conditions and by using the comparison theorem the existence and asymptotic behavior of solution for the boundary value problems studied,     

具有边界摄动的拟线性Robin问题

A class of quasilinear Robin problems with boundary perturbation are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the boundary value problem is studied.     

Sylvester方程在矩阵扰动分析中的应用

§1.引言 矩阵扰动分析的研究对于矩阵论的发展及数值分析问题计算结果的分析和处理都有重要意义.有关特征值、广义特征值及最小二乘问题的主要研究结果均含于[1]中,[5]运用二次方程根的判别法通过对代数Ricatti方程的解的估计给出了QR分解因子及Cholesky因子的扰动分析,但论证方法及所得结果都比较复杂且所求条件很强.[3]和     

Bogdanov-Takens系统的三次齐次扰动

对Bogdanov-Takens向量场的三次齐次扰动系统进行了讨论，得到了当其前二阶Melnikov函数恒为0时，则其后各阶Melnikov函数一定为0，且对于小的扰动参数，此系统为可积的或为Hamilton的；并对M1（h)≠0和M1(h)≡0，M2(h)≠0两种情形该系统的分岔结构给出了较全面的结论。     

一类矩阵特征值的扰动

本文讨论可正规化矩阵和可对称化矩阵特征值的扰动。所谓可正规化矩阵和可对称化矩阵分别指相似于正规矩阵和Hermite矩阵的矩阵。