迹稳定秩1的C~*-代数的稳定有限性与弱迹稳定秩1

主要给出了迹稳定秩1的C~*-代数的稳定有限性,证明了如果A是有单位元迹稳定秩1的C~*-代数,则A是稳定有限的,引入了弱迹稳定秩1的定义,并且证明了如果有单位元的C~*-代数A是迹稳定秩1的,则A是弱迹稳定秩1的．对于单的具有SP性质的有单位元的C~*-代数A,如果A是弱迹稳定秩1的,则A是迹稳定秩1的．同时给出了迹稳定秩1的C~*-代数的一个等价条件,证明了一个有单位元的可分的C~*-代数A是迹稳定秩1的,等价于A=(t_4)limn→∞(A_n,p_n),其中tsr(A_n)=1．     

C~*-代数中的等价

在算子理论和算子代数的研究中,等价是一个很重要的工具,它对K-理论的研究和理解起着很重要的作用.寻找等价关系是研究不变量的一种方法,为了使大家更好的认识和学习C*-代数,我们在本文研究了算子代数中经常用到的代数等价、酉等价、同伦等几种等价之间的关系.     

Quantum Hall Effect on the Hyperbolic Plane in the Presence of Disorder

We study both the continuous model and the discrete model of the quantum Hall effect (QHE) on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper. Here we model impurities, that is we consider the effect of a random or almost periodic potential as opposed to just periodic potentials. The Hall conductance is identified as a geometric invariant associated to an algebra of observables, which has plateaus at gaps in extended states of the Hamiltonian. We use the Fredholm modules defined in Comm. Math. Phys. 190 (1998), 629–673, to prove the integrality of the Hall conductance in this case. We also prove that there are always only a finite number of gaps in extended states of any random discrete Hamiltonian.     

Late-model Ionic Clusters of KNO3 and Their Configurations

Late-model ionic clusters of KNO3 were formed under the conditions of electrospray ionization. A series of peaks of the ionic clusters could be observed in the electrospray ionization mass spectra（ESIMS）. The general formulae of the ionic clusters were deduced to be K^ ＋ （ KNO3 ） m and NO3^-（ KNO3 ）m. By referring to the crystal structure of KNOs , the possible configurations of these new typical ionic clusters were speculated based on the calculated data by means of the Gaussian-94^x computer program.     

噻咯类有机小分子光电材料*

噻咯衍生物由于其特殊的σ*-π*共轭,具有较低的最低未占轨道（LUMO）,使得它在电致发光领域有着极大的应用前景。本文从材料合成的角度综述了1,1,2,3,4,5-六取代的噻咯、硅-桥联稠环体系、联噻吩噻咯和螺噻咯类小分子类光电材料的国内外所取得的一些最新进展,介绍了它们作为发光材料和电子传输材料在电致发光器件中的应用情况,讨论了硅原子的引入怎样调节杂环的电子结构,总结了分子结构的修饰对噻咯电子性能的影响。同时,对该领域的发展提出了一些想法。     

2010年度力学科学处面上项目、青年科学基金和地区科学基金资助情况介绍

<正>经力学专家评审、数理科学部工作会议及基金委员会委务会审议,2010年度力学科学处面上项目、青年科学基金、地区科学基金资助项目已确定(见附表1).现将有关信息公布如下:     

Exactness of one relator groups

A discrete group is -exact if the reduced crossed product with converts a short exact sequence of --algebras into a short exact sequence of -algebras. A one relator group is a discrete group admitting a presentation where is a countable set and is a single word over . In this short paper we prove that all one relator discrete groups are -exact. Using the Bass-Serre theory we also prove that a countable discrete group acting without inversion on a tree is -exact if the vertex stabilizers of the action are -exact.

     

On derivations of algebras with involution

Summary Let X be a complex Hilbert space, let L(X) be the algebra of all bounded linear operators on X, and let A(X) ⊂ L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D: A(X) → L(X) satisfying the relation D(AA*A) = D(A) A*A + AD(A*)A + AA*D(A), for all A ∈ A(X). In this case D is of the form D(A) = AB-BA, for all A∈ A(X) and some B ∈ L(X), which means that D is a derivation. We apply this result to semisimple H*-algebras.     

Remarks onB(H) ⊗B(H)

We review the existing proofs that the min and max norms are different onB(H) ⊗B(H) and give a shortcut avoiding the consideration of non-separable families of operator spaces.     

环上幂等Hermite矩阵的一个特征性质

本文证明了一类上幂等矩阵为Hermite矩阵的充要条件是Range A=RangeA.特别地给出了《美国数学月刊》1996年第4期上征解问题10519号的解答.