On the spectral sequence constructors of Guichardet and Stefan

The concept of a spectral sequence constructor is generalised to Hopf Galois extensions. The spectral sequence constructions that are given by Guichardet for crossed product algebras are also generalised and shown to provide examples. It is shown that all spectral sequence constructors for Hopf Galois extensions construct the same spectral sequence.     

Embedding of Dynamical Symmetry Groups U(1, 1) and U(2) of a Free Particle on AdS 2 and S 2 into Parasupersymmetry Algebra

Using two different types of the laddering equations realized simultaneously by the associated Gegenbauer functions, we show that all quantum states corresponding to the motion of a free particle on AdS ₂ and S ² are splitted into infinite direct sums of infinite-and finite-dimensional Hilbert subspaces which represent Lie algebras u(1, 1) and u(2) with infinite- and finite-fold degeneracies, respectively. In addition, it is shown that the representation bases of Lie algebras with rank 1, i.e., gl(2, C), realize the representation of nonunitary parasupersymmetry algebra of arbitrary order. The realization of the representation of parasupersymmetry algebra by the Hilbert subspaces which describe the motion of a free particle on AdS ₂ and S ² with the dynamical symmetry groups U(1, 1) and U(2) are concluded as well.     

Local automorphisms of operator algebras on Banach spaces

In this paper we extend a result of Semrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Semrl's paper.

     

Tensor Products of Quantum Structures and Their Applications in Quantum Measurements

Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.     

强流束在二极磁铁中的非线性传输—Lie代数分析

 用Lie代数方法分析了带电粒子束在二极磁铁中的非线性传输，包含了空间电荷效应。粒子在相空间中的分布采用K V分布。轨迹分析的结果做到二级近似，根据需要，还可以扩展到三级或更高级近似。在分析中，将磁铁沿中心轨道分成若干小段。在每个小段上利用所得公式进行轨迹计算，得到自洽的解。然后重复此过程，作下一小段的计算，直到最后一个小段为止。     

On Quasiclassical Field Theories Invariant with Respect to a Lie Group

Mathematical Notes -     

On characterization of Poisson and Jacobi structures

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids.     

电子储存环中插入元件的非线性束流动力学的Lie代数方法

介绍了用能保证哈密顿系统“辛”性质的Lie映射方法来研究电子储存环中的插入元件对束流动力学的影响.并以此方法对合肥光源中将要安装的波荡器UD?–?1对储存环的影响作了初步的研究     

On numerical ranges and roots

Existence of the fractional powers is established in Banach algebra setting, in terms of the numerical ranges of elements involved. The behavior of the spectra and (for Hermitian ∗-algebras satisfying some additional hypotheses) the ∗-numerical range under taking these powers also is investigated.