Mn(C)中的不可约性

对于Mn(C)(所有n×n矩阵的全体)中的不可约矩阵得到以下结果:对于任意A∈Mn(C),设λ1,λ2,…,λm为A的所有特征值,这里m≤n而且当i≠j时,λi≠λj.则A是不可约的当且仅当任意P∈A'(A),P*=P=P2,有σ(P|ker(A-λ1))=σ(P|ker(A-λ2))=…=σ(P|ker(A-λm))为单点集.     

Von Neumann代数上P点ξ-Lie导子的刻画

设A是没有I_1型中心直和项的von Neumann代数,P∈A是一个非中心的空核投影且其中心包络是I.研究了Von Neumann代数上P点ξ-Lie导子δ,得到了对任意A∈A,存在T∈A使得δ(A)=AT-TA,这里非零数ξ∈F且ξ≠±1.     

一致可积函数的非标准刻画

设(X,A,μ)是内有限可加测度空间.首先给出了S-可积的等价条件,进而给出了一致可积函数的非标准刻画,即可测函数集{fi)i∈I是一致可积的当且仅当对于任意的i∈*I,fi都是S-可积的.     

复矩阵和的Drazin逆

1引 言设Cn×n为n×n复矩阵的集合,对A∈Cn×n,满足rank(Ak+1 )=rank( Ak)的最小非负整数k称为A的指标,记为Ind(A)=κ,则存在唯一矩阵AD∈Cn×n,满足下列矩阵方程组[1]:Ak=Ak+1AD AD=ADAAD AAD=ADAAD称为A的Drazin逆.若Ind(A)=1,则AD称为A的群逆,记为A#.显然Ind(A)=0当且仅当A非奇异,此时AD =A-1.     

复半正定矩阵的奇异值不等式

用Mn表示所有复矩阵组成的集合.对于A∈Mn,σ(A)=(σ1(A),…,σn(A)),其中σ1(A)≥…≥σn(A)是矩阵A的奇异值.本文给出证明:对于任意实数α,A,B∈Mn为半正定矩阵,优化不等式σ(A-|α|B) wlogσ(A+αB)成立,改进和推广了文[5]的结果.     

β(H)上Jordan同构的一个代数不变量:幂等元的集合

令β(H)表示无限维复Hilbert空间H上的所有有界线性算子组成的代数,I(H)是β(H)中所有幂等元的集合.设Φ:β(H)→β(H)是满射.证明了对任意的λ∈{-1,1,2,3,1/2,1/3}及A,B∈β(H),映射Φ满足条件A-λB∈I(H)(=)Φ(A)-λΦ(B)∈I(H)当且仅当Φ是β(H)的Jordan环自同构,即存在H上的连续可逆线性或共轭线性算子T,使得Φ(A)=TAT-1对所有的A∈β(H)成立,或Φ(A)=TA*T-1对所有的A∈β(H)成立.令i表示虚数单位,进而如果Φ也满足条件A-iB∈I(H)(=)Φ(A)-iΦ(B)∈I(H),则Φ是自同构,或是反自同构.     

交错阵空间上保秩等价的线性算子

设F是任意域,n≥4是一个正整数.令Kn(F)是F上n×n交错阵空间.对于A,B∈Kn(F),如果rank A=rank B,则称A和B是秩等价的.本文主要刻画Kn(F)上的保秩等价的线性算子,并给出一些应用.     

关于分担值与正规性的一点注记

本证明了如下定理：设F是区域D内的一族亚纯函数，α是一非零有穷复数，k是一正整数。若对于任意f∈F有在D内f≠0且f与f^(k)分担α，则F在D内正规。     

环的B-稳定正则理想

研究了正则理想是B-稳定的充分和必要条件,并且证明环R的正则理想I是B-稳定的当且仅当对任意的有限生成投射右R-模A,如果A₁和A₂是A的有限生成子模且满足A₁≌A₂,A₁=A₁I以及A₂=A₂I,则存在一个有限生成子模B,使得A=A₁（?）B=A₂（?）B;当且仅当对任意的幂等元e,f∈I,eR≌fR蕴含eR/（eR∩fR）≌fR/（eR∩fR）;当且仅当对任意的a∈1+I,存在一个幂等元e∈I,使得a-e∈∪（R）并且aR∩eR=0.进而构造了相关的例子.     

二阶常微分方程组的极限边值问题解的存在性和唯一性

本文研究二阶非线性常微分方程组=a(t)h(y),=b(t,x)g(y),(S)其中 a:I→R_+=(0,∞),I=[t_0,∞),t_0∈R=(-∞,∞),h:R→R,g:R→R_+和b:I×R→R 均为连续函数,且满足:yh(y)>0(y≠0),h(y)是 y 的递增函数;xb(t,x)≥0,b(t,x)是 x 的不减函数,且对任意固定的 x≠0,在 I 的任意子区间上b(t,x)不恒等于零.我们还假设,对任意的 c≥t_0,α,β∈R,组(S)满足初值条件:x(c)=α,(1)y(c)=β (2)的解存在唯一,且对初值具有连续相依性.我们考虑下面几种极限边值条件:     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].