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.     

关于限制李超代数的分解

代数$A$ 称为不可分解的,如果 $A$ 不能分解成理想的直和.文中将证明满足$C(L_{\bar{0}})=C(L)=\{0\}$的限制李超代数能够分解成不可分解限制理想的直和,这种分解在不计理想次序的前提下是唯一的.而且还证明了限制李超代数的一些结果.     

Separating points of measures on effect algebras

We prove the existence of separating points for every countable family of nonatomic σ-additive modular measures on a σ-complete lattice ordered effect algebra.      

Strengthened semidefinite programming bounds for codes

We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n; this is based on a result of de Klerk et al. (Math Program, 2006) about the regular ∗-representation for matrix ∗-algebras. The Delsarte bound for A(n,d) is the first bound in the hierarchy, and the new bound of Schrijver (IEEE Trans. Inform. Theory 51:2859–2866, 2005) is located between the first and second bounds in the hierarchy. While computing the second bound involves a semidefinite program with O(n ⁷) variables and thus seems out of reach for interesting values of n, Schrijver’s bound can be computed via a semidefinite program of size O(n ³), a result which uses the explicit block-diagonalization of the Terwilliger algebra. We propose two strengthenings of Schrijver’s bound with the same computational complexity. Supported by the Netherlands Organisation for Scientific Research grant NWO 639.032.203.     

Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation. This is applied to investigate homomorphisms between quasi-Banach algebras. The concept of Hyers-Ulam-Rassias stability originated from Th.M. Rassias' stability theorem that appeared in his paper [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300].     

Left, right, and inner socles of associative systems

We investigate the basic properties of the different socles that can be considered in not necessarily semiprime associative systems. Among other things, we show that the socle defined as the sum of minimal (or minimal and trivial) inner ideals is always an ideal. When trivial inner ideals are included, this inner socle contains the socles defined in terms of minimal left or right ideals. This revised version was published online in June 2006 with corrections to the Cover Date.     

Quantization of lie Bialgebras via the Formality of the operad of Little Disks

We give a proof of the Etingof–Kazhdan theorem on quantization of Lie bialgebras based on the formality of the chain operad of little disks and show that the Grothendieck–Teichmüller group acts non-trivially on the corresponding quantization functors. Partially supported by an NSF Grant and A. Sloan Research Fellowship Received: November 2004 Revision: April 2006 Accepted: May 2006