非奇异H-矩阵的新判据

1引言与记号设A=(a_(ij))∈C~(n×n),记N={1,2,…,n},∧_i(?)∧_i(A)=sum from j≠i|a_(ij)|,S_i(?)S_i(A)=sum from j≠i|a_(ij)|,(?)i,j∈N。若|a_(ij)>∧_i(A),(?)i∈N,则称A为严格对角占优矩阵。     

两类对角占优矩阵的特征值分布

§1.引言 由于矩阵特征值分布的重要性,迄今已有许多人对其进行研究,国内这方面的主要工作参见[1]—[5]。本文将进一步研究以下两类矩阵的特征值分布。 定义1 设A=(a_ij)_n×n为n阶复矩阵,记,若对任意都成立,称A∈DD_0(R). 定义2 若2|Rea_(ij)|+|Rea_(ij)|>以Λ_i+Λ_j对任意i≠j,i,j∈N均成立,称A∈SD(R).若|Rea_(ij)|+|Rea_(ij)|≥Λ_i+Λ_j对任意i≠j,i,j∈N均成立,称A∈SD_0(R).     

广义严格对角占优阵的判定程序

1 引言和符号 在本文中,均采用下列符号而不再重申.恒用N表示前n个自然数的集合;而用Mn(C)和Mn(R)分别表示所有n阶复矩阵和所有n阶实矩阵的集合. Z_N={A|A=(a_(ij))_(n×n)∈Mn(R),a_(ij)≤0,i,j∈N,i≠j},I恒表示单位矩阵. 如果A∈Mn(R)且A的所有元素都为非负实数,则称A为非负方阵,并记为A≥0;若A的所有元素都为正数,则称A为正矩阵,并记为A>0. 对A=(a_(ij))(n×n)∈Mn(C),令A_i(A)=sum from j=1 j≠i to n (|a_(ij)|(i=1、2…… n)) ;若把A的非零元用1代替 而得到—个n阶(0,1)矩阵。称为A的导出矩阵。记为;而把A的比较矩阵记为 u(A)=(b_(ij))_(n×n))其中b_(ij)=|a_(ij)|,b_(ij)=-|a_(ij)|(i,j∈N i≠j)     

广义严格对角占优矩阵的迭代判别方法

正1引言设A=(a_(ij))∈C~(n×n),N={1,2,…,n}.记R_i(A)= sum |a_(ij)| from j≠i (i∈N),又记N_1=N_1(A)={i∈N:0|a_(ii)|≤R_i(A)},N_2=N_2(A)={i∈N:|a_(ii)R_i(A)}.定义1设A=(a_(ij))∈C~(n×n),如果|a_(ii)|R_i(A)(i∈N),则称A为严格对角占优矩阵.严格对角占优矩阵的集合记为D.如果存在n阶正对角矩阵D使得AD∈D,则称A为广义严格对角占优矩阵.广义严格对角占优矩阵的集合记为D.     

连对角占优矩阵的一些性质

设A=(a_(ij))_(n×n)∈C~(n,n),.记Λ_i=sum from (i≠1 j≠i) to n(|a_(ij)|,)i=?,称|a_(ii)|≥Λ_i的行为占优行,|a_(ii)|>Λ_i的行为严格占优行,|a_(ii)|<Λ_i的行为非占优行. 若A为对角占优阵,记为A∈D_0;若A为严格对角占优阵,记为A∈E;若A为不可约对角占优阵,记为A∈F;若A为广义对角占优阵,记为A∈GD_0;若A为广义严格对角占优阵,记为A∈GE.     

也谈广义对角占优阵的特征值的分布

设A=(a_(ij))_(n×n)为n阶复矩阵,记 σ_i=sum from j=1,j≠i to n(|a_(ij)|,i=l,2,…,n)。若|a_(ij)|>σ_i(i=1,2,…n),则称A为(按行)严格对角占优阵,记为A∈D,若|a_(ii)|·|a_(jj)|>σ_iσ_j(i≠j,i,j=1,2,…,n)则称A为严格对角乘积占优阵,记为A∈D_p(在〔1〕中此类矩阵称为广义对角占优阵,并记为GD)。若存在非奇对角阵Q=diag(q_l,…,q_n)使Q~(-1)AQ∈D,则称A为准严格对角占优阵,记为A∈D′(见〔2〕)。若存在非奇对角阵Q=diag(q_1,…,q_n)使Q~(-1)AQ∈D_p,则称A为准严格对角乘积占优阵。记为A∈D′_p。     

非奇异H矩阵的充分条件

1 引言 设A=(a_(ij))∈C~(n,n),R_i(A)=sum from j≠i to(|a_(ij)|,i,j∈N={1,2,…,n}。若|a_(ij)|≥R_i(A),i∈N,则称A为对角占优矩阵,记为A∈D_0;若不等式中每个不等号都是严格的,则称A为严格对角占优矩阵,记为A∈D。若存在正对角矩阵X,使得AX∈D,则称A为广义严格对角占优矩阵,记为A∈D。     

非奇异H-矩阵一类新的实用性判据

1引言在计算数学、数学物理、控制论与矩阵论中,非奇异H-矩阵是有着重要应用的一类特殊矩阵,有关其数值判定也一直是矩阵计算的重要课题,不少学者对此进行了研究,得到了许多结果,如文[1]-[10]都给出一些比较实用的判别方法．本文另提出了一些新的实用性判别,进一步改进了文[1]的主要结果．用Cn×n表示n阶复矩阵集,设A=(aij)∈Cn×n,记,若|aii|≥Λi(i=1,2,…,n)(本文用Λi表示Λi(A)),则称A为对角占优矩阵;如果每个不等号都为严格成立,则称A为严格对角占优矩阵,记A∈D;若存在正对角阵X,使得AX为严格对角占优矩阵,则称A为广义严格对角占优阵,记A∈D．设A∈Zn×n={(aij)∈Cn×n|aij≤0,i≠j;i,j∈N},若A=sI-B,s>ρ(B),其中B为非负方阵,ρ(B)表示B的谱半径,则称A为非奇异M-矩阵．若A∈Cn×n的比较矩阵M(A)=(mij)为非奇异M-矩阵,则称A为非奇异H-矩阵,其中     

对称次反对称矩阵的一类反问题

1 引言 用R~(m×n),SR~(n×n),ASR~(n×n),OR~(n×n)分别表示所有m×n实矩阵,n阶实对称矩阵,n阶实反对称矩阵和n阶实正交矩阵组成的集合,I_k表示k阶单位矩阵,S_k表示k阶反序单位矩阵,||A||表示矩阵A的Frobenius范数。若A=(a_(ij))∈R~(n×n),记D_A=diag(a_(11),a_(22),…,a_(nn)),L_A=(l_(ij))∈R_(n×n)其中当i>j时,l_(ij)=a_(ij),当i≤j时,l_(ij)=0,(i,j=1,2,…,n).若A=(a_(ij)),B=(b_(ij))∈R~(m×n),A*B表示A与B的Hadamard乘积,其定义为A*B=(a_(ij)b_(ij))。     

广义对角占优矩阵与M—矩阵的判定准则

广义对角占优矩阵与M—矩阵是计算数学中应用极其广泛的矩阵类。作者在文[1]中证明若A=(α_(ij))∈C~(n×n)为具有非零元素链对角占优阵或A满足:|α_(ii)‖α_(kk)|>Λ_iΛ_k,i,k∈N={1,…,n},则A为广义对角占优矩阵,detA≠0,揭示了文[3],[4]中detA≠0的共同本     

On commutativity of near-rings with generalized derivations

In this paper we prove some theorems of commutativity for near-rings with generalized derivations. As a consequence of the results obtained, we generalize some published results. Also, we give some examples to show that some conditions in some results obtained are not redundant.     

高阶变系数泛函方程解的振动性

讨论了高阶变系数泛函微分方程解的振动性,并给出了这类高阶变系数函数方程解的若干新振动准则.结果推广了目前已有的某些结果.并且给出了在差分方程中的应用.     

Meromorphic solutions of some types of complex differential-difference equations

Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we obtain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.     

FC-空间上的连续选择和邻近选择定理

给出了-些从仿紧拓扑空间到FC-空间的新的连续选择;也给出了-些从仿紧拓扑空间到局部FC-一致空间的新的邻近选择.这些结果改进且推广了-些近来的结论.     

Existence and global attractivity of solutions of a nonlinear functional integral equation

This paper presents some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation, via measure of noncompactness. Our results improve and extend some previous results obtained in other studies. We will also include some examples which show that our results are applicable where the previous ones are not.     

Nontrivial solutions for resonant cooperative elliptic systems via computations of the critical groups

In this paper, we consider a class of resonant cooperative elliptic systems. Based on some new results concerning the computations of the critical groups and the Morse theory, we establish some new results about the existence and multiplicity of solutions under new classes of conditions. It turns out that our main results sharply improve some known results in the literature.     

关于一个奇异Dirichlet问题的注记

The Dirichlet problem to a second order differential equation with some singularities is studied. Some existence results are established to the problem which generalize some results recently obtained by D. O‘Regan by eliminating some superfluous constrains to the problem. Also, some new results have been proven which may provide more useful information for the study of the problem.     

An investigation on ordered algebraic hyperstructures

In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.     

关于AP-内射环和AGP-内射环(英文)

本文研究了AP-内射环和AGP-内射环的von Neumann正则性问题.利用P-内射环和Y J-内射环的研究方法及GW-理想的性质,得到了AP-内射环和AGP-内射环是(强)正则环的一些条件.推广了文献[7,12,14]中的相关结果.     

关于拟GP-内射模

在本文中,我们定义了拟GP-内射模,并且得到了关于它的一些结果.这些结果总结了GP-内射环和拟P-内射模的一些结果.