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)     

COMMUTATORS OF MULTIPLIER OPERATORS

Denote M~l={ω∈C~∞(R~K\{0}:|ω~((β))(ξ)|≤C_β|ξ|~(l-|β|)},l is an integer.R_((-α))~((m))is the n-foldcomposition of Taylor series remainder operator,m=(m_1,…,m_n)∈Z~n.Z is the set ofnon-negative integers,α∈(R~K)n.DenoteThe main results are as follows:(i) If γ_1,γ_2∈Z~K and l is an integer such that |γ_1|+|γ_2|+l=|m|=m_1+…+m_n,0≤|γ_1|≤{m_4},and ω∈M~l,then we havewhereis a conseant.(ii)In the same sense of notation as in (i),but now|m|=1,we havewhereThese results extend the corresponding ones given by coifman-Meyer in [4] andCohen,J.in [2],and,in a sense,extend those given by Calderón,A.P.in [1].     

Classification of Cartan Matrices of Hyperbolic Type

In the theory of finite dimensional semisimple Lie algebras,it is known thatthe Cartan matrix A=(a_(ij))_i~n, i=1 has the following properties: (1)a_(ii)=2,i=1,…,n; (2)a_(ij)≤0 for i≠j,a_(ij)∈Z; (3)a_(ij)=0 a_(ji)=0. Now if a matrix A=(a_(ij))_i~n,j\j=1 satisfies (1),(2),(3),then A is called     

HIGHER C0MMUTATORS OF PSEUDODIFFERENTIAL OPERATORS

In this paper the following result is established: For a_i, f∈(R~K), i=1, …, n, and T (a, f) (x)=ω(x, D)(multiply from i=1 to n P_(mi)(a_i, x, ·)f(·)),it holds that ‖T(a, f)‖_q≤C‖f‖_(po) multiply from i=1 to n ~m_ia_i‖_(p_4),where a=(a_1, …, a_n), q~(-1)=p_0~(-1)+ sum from i=1 to n p_i~(-1)∈(O, 1), p_i∈(1, ∞)or i, p_i=∞, p_0∈(1, ∞),for an integer m_i≥0, P_(m_1)(a_i, x, y)=a_i(x)-∑ |β|相似文献   

关于矩阵切触有理插值

1 矩阵切触插值连分式 设实区间[a,b]中由不同点组成的插值结点为x_1,x_2,…,x_n,它们的重数分别为a_1,a_2,… ,a_n,M=sum from i=l to n(a_i-1),与之对应的待插值矩阵集为 {A_i~(k):k=0,1,…,a_i-1,i=1,2,…,n,A_i~(k)=A~(k)(x_i)∈R~(d×d)}. 设方阵A=(a_(ij)),它的广义矩阵逆定义为 A~(-1)= A/‖A‖~2 (A≠0) (1.1)     

由谱数据数值稳定地构造实对称带状矩阵

§1.引言 设r,n是正整数并且0r有a_(ij)=0.     

矩阵对角占优性的推广及应用

§1.引言设 A=(a_(ij))_(n×n)为一复矩阵,若有一正向量 d=(d_1,d_2,…,d_n)~T 使得d_i|a_(ij)|≥sum from j≠1 d_j|a_(ij)|,(1)对每一 i∈N={1,2,…,n}都成立,则称 A 为广义对角占优矩阵,记为 A∈D_0~*;如若(1)式中每一不等号都是严格的,则称 A 为广义严格对角占优矩阵,记为 A∈D~*.特别地,当 d=(1,1,…,1)~T 时,A∈D_0~*及 A∈D~*即是通常的对角占优与严格对角占优,分别记作 A∈D_0及 A∈D.利用矩阵的对角占优性质讨论其特征值分布是矩阵论中的重要课题,文献[5]—[10]给出了这方面的重要结果.n 阶实方阵 A 称为 M-矩阵,如果 A具有形式:A=sI-B,s>ρ(B),其中 B 为 n 阶非负方阵,ρ(B)表 B 之谱半径,利用广义严格对角占优的概念,文[1]给出了 M-矩阵的等价表征:若 n 阶实方阵     

主理想环上子群Gr在线性群中的扩群

Suppose R is a principal ideal ring,R~* is a multiplicative group which is composed of all reversible elements in R,and M_n(R),GL(n,R),SL(n,R) are denoted by, M_n(R)={A=(a_(ij))_(n×n)|a_(ij)∈R,i,j=1,2,…,n},GL(n,R) = {g|g∈M_n(R),detg∈R~*},SL(n,R) = {g∈GL(n,R)|det g=1},SL(n,R)≤G≤GL(n,R)(n≥3),respectively, then basing on these facts,this paper mainly focus on discussing all extended groups of G_r={(AB OD)∈G|A∈GL(r,R),(1≤r相似文献   

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.     

RESEARCH ANNOUNCEMENTS ON“MINIMAL TIME CONTROL OF EXACT SYNCHRONIZATION FOR PARABOLIC SYSTEMS”

正1 Introduction and Main Results LetΩ■R~d (with d≥1) be a bounded domain with a C~2 boundary Ω.Letω■Ωbe an open and nonempty subset with its characteristic function χ_ω.Let A■(a_(ij))_(1≤i,j≤n)∈R~(n×n)and B■(b_(ij))_(1≤i≤n,1≤j≤m)∈R~(n×m) be two constant matrices,where n≥2 and m≥1.Let y_0∈L~2(Ω)~n.Consider the controlled linear parabolic system     

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.     

用希尔伯特空间理论讨论傅立叶级数

<正> 函数和它的傅立叶级数之间的关系,常见的有下列四种。命题1 (狄里赫勒定理)若f(x)∈C[-π,π),或在[-π,π]上只有有限个第一类间断点,并且可以把[-π,π]分为f(x)的有限个单调区间,则有f(x)=a_0/2+sum from i=1 to ∞(a_icosix+b_isinix)(1)其中x∈(-π,π)为f(x)的连续点,a_i,b_i为f(x)的傅立叶系数(以下同)。当x∈(-π,π)为f(x)的间断点时,则(1)式友端改为[f(x—0)+f(x+0)]/2。当x=±π时,则(1)式左端改为[f(-π+0)+f(π-0)]/2。命题2 若f(x)∈L_2[-π,π],则对任意确定的n,有||f(x)—a_0/2—sum from i=1 to n(a_1cosix+bsinix)||_2     

索伯列夫空间的有限元迫近

记I_1=(-∞,ξ_1),I_2=(ξ_1,ξ_2),…,I_n=(ξ_(n-1),ξ_n),I_(n 1)=(ξ_n, ∞)。定义H~(m 1)(R,ξ_1,…,ξ_n)={u|u∈H~m(R),在I_i上u∈H~(m 1)(I_i),i=1,…,n 1}。 设μ(x)∈H~m(R),λ(x)∈L~∞(R)。并且满足:1.他们的支集都是R中的有界集合;2·∫_Rμ(x)dx=∫_Kλ(x)dx=1;3.μ(x)满足m-1收敛准则条件,即存在常数b_0=1,b_1,…,     

广义对角占优矩阵的判定

本文给出了广义严格对角占优矩阵的几个判定条件以及等价表征,这些结论分别推广了[3]与[4]的一些结果。作为约定本文总假设;A=(a_(ij))_n×n 表示复矩阵,∧_k=(?)|a_(kj)|当|a(kk)|≠0时,σ_k=(∧_k)/|α_(kk)|,θ_A={s||a_(ss)|≤∧_s,s∈N={1,2,…,n}},J_A={k||a_(kk)>∧_k,k∈N}     

Radius of Starlikeness for Class S(a,n)and Its Extension

This paper obtain that the radius of starlikeness for class S(α,n)in [1] is,tespectivety,where α_ is unique solution of equation (αα)~(1/2)=σwith a in (0.1),and α-[1+(1-2α)r~(2n)]/(1-r~(2n)),σ=[1-(1-2α)r~]/(1+r~).Futhermore,we consider an extension of class S(α,n):Let S(α、β、n)denote the class of functions f(z)=z+α_z~(n+1)+…(n≥1)that are analytie in |z|<1 such that f(z)/g(z)∈p(α,n)[1],where g(z)∈S~*(β)[2].This paper prove that the radius of starlikeness of class S(α,β,n) is given by the smallest positive root(less than 1)of the following equations(1-2α)(1-2β)r~(2)-2[1-α-β-n(1-α)]r~+1=0.0≤α≤α_0,(1-α)[1-(1-2β)r~]-n[r~(1+r~)=0.,α_0≤α<1.where α=[1+(1-2α)r~(2)]/(1-r~(2)(0≤r<1),α_0(?(0,1) is some fixed number.This result is also thecxtension of well-known results[T.Th3] and [8,Th3]     

On an Extension of Hadamard Inequalities for Convex Functions(in English)

设f是区间[a,b]上连续的凸函数，我们证明了Hadamard的不等式 $[f(\frac{{a + b}}{2}) \le \frac{1}{{b - a}}\int_a^b {f(x)dx \le \frac{{f(a) + f(b)}}{2}}$ 可以拓广成对[a,b]中任意n+1个点x_0,\cdots,x_n和正数组p_0,\cdots,p_n都成立的下列不等式 $f(\frac{\sum\limits_{i=0}^n p_ix_i}{\sum\limits_{i=0}^n p_i}) \leq |\Omega|^-1 \int_\Omega f(x(t))dt \leq \frac{\sum\limits _{i=0}^n {p_if(x_i)}}{\sum\limits_{i=0}^n p_i}$ 式中\Omega是一个包含于n维单位立方体的n维长方体，其重心的第i个坐标为$\sum\limits _{j=i}^n p_j /\sum\limits_{j=i-1}^n p_i$,|\Omega|为\Omega的体积，对\Omega中的任意点$t=(t_1,\cdots,t_n)$, $w(t)=x_0(1-t_1)+\sum\limits _{i=1}^{n-1} x_i(1-t_{i+1})\prod\limits_{j = 1}^i {{t_j}} +x_n \prod\limits _{j=1}^n t_j$ 不等式中两个等号分别成立的情形亦已被分离出来。 此不等式是著名的Jensen 不等式的精密化。     

THE GLOBAL SMOOTH SOLUTIONS OF SECOND ORDER QUASILINEAR HYPERBOLIC EQUATIONS WITH DISSIPATIVE BOUNDARY CONDITIONS

The paper deals with the following boundary problem of the second order quasilinear hyperbolic equation with a dissipative boundary condition on a part of the boundary:u_(tt)-sum from i,j=1 to n a_(ij)(Du)u_(x_ix_j)=0, in (0, ∞)×Ω,u|Γ_0=0,sum from i,j=1 to n, a_(ij)(Du)n_ju_x_i+b(Du)u_t|Γ_1=0,u|t=0=φ(x), u_t|t=0=ψ(x), in Ω, where Ω=Γ_0∪Γ_1, b(Du)≥b_0>0. Under some assumptions on the equation and domain, the author proves that there exists a global smooth solution for above problem with small data.     

二维Vilenkin型系统的Dirichlet核的加权平均

对二维Vilenkin型系统,我们定义加权平均极大算子T(i.e.Tf:=supn=(n1,n2)∈P2,β-1n1/n2β|Hnf|),并证明此算子是弱(1,1)型、强(p,p)型(1p∞)以及(H,L)型,其中Hnf表示部分和的加权平均,H表示Hardy空间.借用此结果得到序列Hnf是几乎处处收敛于可积函数f.     

轨形Gromov-Witten不变量沿光滑点的加权涨开公式

本文考虑,当一个紧辛轨形群胚(X,ω)沿着光滑点作加权涨开时,它的形如<α_1,…,α_m,[pt]>_(g,A)~X的轨形Gromov-Witten不变量的变化公式,其中[pt]∈H_(dR)~(2n)(X)是生成元,dimX=2n.我们证明了对于非零A∈H_2(|X|,Z),<α_1,…,α_m,[pt]>_(g,A)~X={_(g_1,pl(A)-e’)~xdimX=4,g≥0,∑((-1)g_1·2)/(2g_1+2)!_(g_2,pl(A)-e’)~xdimX=6,g≥0,_(g_1,pl(A)-e’)~xdimX≥8,g=0其中x是X沿一光滑点的权α=(α_1,…,α_n)的加权涨开,且α_1≥α_i,2≤i≤n.     

两类惯量惟一的对称符号模式

§ 1　 IntroductionA sign pattern(matrix) A is a matrix whose entries are from the set{ +,-,0 } .De-note the setofall n× n sign patterns by Qn.Associated with each A=(aij)∈ Qnis a class ofreal matrices,called the qualitative class of A,defined byQ(A) ={ B =(bij)∈ Mn(R) |sign(bij) =aijfor all i and j} .　　 For a symmetric sign pattern A∈ Qn,by G(A) we mean the undirected graph of A,with vertex set { 1 ,...,n} and (i,j) is an edge if and only if aij≠ 0 .A sign pattern A∈ Qnis a do…