完备格上基于Sup-(J)合成算子的矩阵的平方根

对于完备格L上给定的|I|×|I|的矩阵R,若存在|I|×|I|的L上的矩阵S满足S☉S=R,则称S为R的平方根,其中|I|表示指标集I的基数,☉在本文中指的是sup-(J)合成算子并且(J)是无限Ⅴ分配的保序的算子,本文给出了完备格上基于sup-(J)合成算子的矩阵平方根存在的充要条件以及相应的理论上的算法求解所有的平方根.     

伪统一模与剩余格之间的关系

讨论伪统一模与剩余格之间的关系,证明完备格上无穷∨-分配伪统一模和它的剩余蕴涵算子构成一个完备剩余格,并说明任给一个完备剩余格L=(L,∧,∨,*,e→,,*是无穷∨-分配的伪统一模,→和(?)是*的剩余蕴涵算子.     

算子矩阵的性质(gω)

设M_R=(T R O S)是定义在Banach空间X⊕Y上的2×2上三角算子矩阵,则T和S满足性质(gw)(或性质(gb))推不出M_R满足性质(gw)(或性质(gb)),即使R=0.文章主要利用局部谱理论的知识,研究了Banach空间上2×2上三角算子矩阵在什么情况下满足性质(gb)和性质(gw).     

一类矩阵方程的正交对称解及其最佳逼近

1引言设Rn×m表示所有n×m实矩阵集合,I表示单位矩阵,AT表示矩阵A的转置矩阵, ORn×n={P|PTP=I)表示列正交矩阵集,SORn×n={P|PT=P,P2=I}表示对称正交对称矩阵集．如无特别说明,本文中的矩阵P均指这类对称正交对称矩阵．在Rn×m上定义内积为     

Fourier-Laplace级数的强逼近

设f是Rn(n≥3)中单位球面∑n-1上的可积函数,Sθ(f)是步长为θ∈R的平移算子.σδN(f)是Fourier-Laplace级数的δ阶Ceaaro平均.如果∫π0 |Sθ(f)-f|p/θ2dθ∈ L∞ (∑n- 1 ),则∑∞k=0 |σλk(f)-f|p∈L∞(∑n-1)且∑∞k=0(f)-f|p∈L∞(∑n-1 ),其中Eλk(f)为Cesaro平均σλk的等收敛算子.     

广义Kato分解与Weyl型定理的摄动

称T∈B(H)有广义Kato分解,若存在一对T的闭的不变子空间(M,N)使得H=M⊕Ⅳ,其中T|_M为上半Fredholm算子且具有非负的指标,T|_N是幂零的本文利用算子的广义Kato分解性质,研究了Weyl型定理在紧摄动下的稳定性.此外还研究了2×2上三角算子矩阵的Weyl型定理在紧摄动下的稳定性.     

双蕴含算子及其在Fuzzy关系方程中的应用

本文在全序完备格L上定义了双蕴含算子“(?)”。讨论了L上及L-Fuzzy矩阵上算子“(?)”的若干性质,分别得到了Fuzzy关系方程AX=A(XA=A)及Fuzzy不等方程AX≤A(XA≤A)的解,给出了L-Fuzzy矩阵有广义下逆的一个充分必要条件及幂等阵的两个广义逆。     

一类次正常算子的表示

[1]中提出如下的问题:若S是Hilbert空间H上次正常算子,而且S~*S-SS~*是有限秩算子。能否绐出S的一般形式。当S~*S-SS~*是一秩算子时,S=aI bU_ ,这儿U-是单向平移算子。在[2]中对自对偶次正常算子情况,给出了一个表示。这里我们从另一个角度来部分回答上述问题。 Hilbert空间H上算子S称为次正常算子是指存在一个Hilbert空间R(?)H上正常算子N,NH(?)H,而S=N|H。称N为S的正常延拓,相对于R=H(?)H-,正常算子N有表示     

完备分配格L上的S-幂零矩阵

利用完备分配格L上的s-模定义格L上的矩阵运算,给出这些运算的一些基本性质,并且定义格L上的s-幂零矩阵,给出一些全新的结果.     

R(K)循环的次正常算子的一些结果

设T,S为R(K)循环的次正常算子,R(K)为Dirichlet代数。T的极小正常扩张mne(T)的谱σ(mneT)(?)K。T与S为拟相似。本文完全刻画了T的不变子空间。此外引进了超不变算子,并且给出了S|_M为超不变算子的充要条件。     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.