von Neumann代数上的Lie可导映射

设A是不含交换中心投影的von Neumann代数,投影P∈A使得P=0, P=I.称可加映射δ:A→A在Ω∈A Lie可导,若δ([A,B])=[δ(A,δ(B)],■A,B∈A,AB=Ω.该文证明,若Ω∈A满足PΩ=Ω,则δ在ΩLie可导当且仅当存在导子τ:A→A和可加映射f:A→Z(A)使得δ(A)=τ(A)+f(A),■A∈A其中f([A,B)=0,■A,B∈A,AB=Ω.特别地,若A是因子von Neumann代数,Ω∈A满足ker(Ω)≠0或ran(Ω)≠H,则可加映射δ:A→A在ΩLie可导当且仅当δ有上述形式.     

三角代数上的交换零点ξ-Lie可导映射

设u是数域F上的一个三角代数,δ是u上的一个线性映射,ξ∈F且ξ≠1证明了:如果对任意的x,y∈u且xy=yx=0有δ([x,y]_ξ)=[δ(x),y]_ξ+[x,δ(y)]_ξ,则在u上存在一个导子Φ和一个中心元λ使得对任意的x∈u,有δ(x)=Φ(x)+λx.     

因子von Neumann代数上导子的等价刻画

设R是含非平凡幂等元P的素环,C∈R,C=PC.本文证明可加映射△:R→R在C可导,即△(AB)=△(A)B+A△(B),A,B∈R,AB=C当且仅当存在导子δ:R→R,使得△(A)=δ(A)+△(I)A,A∈R.没有I_1型中心直和项的von Neumann代数上的可导映射也有类似结论.利用该结论证明了,若非零算子C∈B(X),使得ran(C)或ker(C)在X中可补,则可加映射△:B(X)→B(X)在C可导当且仅当它是导子.特别地,证明了因子von Neumann代数上的可加映射在任意但固定的非零算子可导当且仅当它是导子.     

含幂等元的环上的Jordan导子的刻画-在零点Jordan可导的可加映射

设A为包含非平凡幂等元且有单位的环(或代数),δ:A→A是可加(或线性)映射.称δ在零点Jordan可导,若δ(A)B+Aδ(B)+δ(B)A+Bδ(A)=0对任意满足AB+BA=0的A,B∈A成立.在一定条件下,证明了δ在零点Jordan可导当且仪当存在可加Jordan导子τ,使得δ(A)=τ(A)+δ(I)A对任意的A∈A成立.利用此结论,完全刻画了因子von Neumann代数上在零点Jordan可导的可加映射.此外,还刻画了一般von Neumann代数和C*代数上在零点Jordan可导的有界线性映射.     

含幂等元的环上的Jordan导子的刻画—在零点Jordan可导的可加映射

设A为包含非平凡幂等元且有单位的环(或代数),δ:A→A是可加(或线性)映射.称δ在零点Jordan可导,若δ(A)B+Aδ(B)+δ(B)A+Bδ(A)=0对任意满足AB+BA=0的A,B∈A成立.在一定条件下,证明了δ在零点Jordan可导当且仅当存在可加Jordan导子τ,使得δ(A)=τ(A)+δ(I)A对任意的A∈A成立.利用此结论,完全刻画了因子von Neumann代数上在零点Jordan可导的可加映射.此外,还刻画了一般von Neumann代数和C~*代数上在零点Jordan可导的有界线性映射.     

素＊-环上非线性保XY-ξYX~＊积

设M是包含非平凡投影P的单位素*-环.证明了非线性双射φ:M→M对所有A,B∈M,满足φ(AB-ξBA*)=φ(A)φ(B)—ξφ(B)φ(A)*.若ξ=1,则φ是线性或共轭线性的*-同构;若ξ≠1,则φ是*-环同构,且对所有A∈M,有φ(ξA)=ξφ(A).     

Von Neumann代数套子代数上保因子交换性的线性映射

对因子von Neumann代数的套子代数上的保单位线性映射Φ:AlgMα→AlgMβ满足AB=ξBA(?)Φ(A)Φ(B)=ξΦ(B)Φ(A)进行了刻画,其中A,B∈AlgMα,ξ∈F,即证明了因子von Neumann代数的套子代数间每个保单位的弱连续线性满射它双边保因子交换性,则映射Φ或者是同构或者是反同构.     

因子von Neumann代数上的非线性*ξ-Lie可导映射

设A是维数大于1的因子von Neumann代数且ξ≠1.本文给出了A上非线性*ξ-Lie可导映射的结构·作为应用,得到了B(H)上非线性*ξ-Lie可导映射的具体形式.     

von Neumann代数上的零点(m,n)-可导映射

研究了von Neumann代数A上的零点(m,n)-可导映射,证明了:对任意固定的非零整数m,n且(m+n)(m-n)≠0,如果线性映射δ:A→A对任意满足AB=0的A,B∈A有mδ(AB)+nδ(BA)=mδ(A)B+mAδ(B)+nδ(B)A+nBδ(A),则δ是导子.     

关于时间序列线性预报问题的单纯形算法

本文考虑稳定时间序列的p阶线性预报问题,提出一个不受异常值影响的数学模型: 其中当k<1及k>n时ξ_k=0。进而将(1)归结为含有自由变量的线性规划问题 min1~Tδ~++1~Tδ~- (2) s.t.Aα+[E,-E][δ~(+T),δ~(-T)]=b,δ~+,δ~-≥0。其中α=[α_1,…,α_p]~T,b=[-ξ_2,…,-ξ_n,0,…,0]~T∈R~(p+n-1),1=[1,…,1]~T∈R~(p+n-1),A是(p+n-1)×p阶Toeplitz矩阵     

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.     

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.     

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

<正>~~     

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.