三维Leibniz代数的分类

Leibniz代数是比Lie代数更广泛的一类代数,它通常不满足反交换性.在这篇文章里我们确定了维数等于3的Leibniz代数的同构类.     

On weakly cospectral graphs

We prove that any set of pair-wise nonisomorphic strongly connected weakly cospectral pseudodigraphs whose set of nilpotency indices is finite also is finite.     

Testing polycyclicity of finitely generated rational matrix groups

We describe algorithms for testing polycyclicity and nilpotency for finitely generated subgroups of and thus we show that these properties are decidable. Variations of our algorithm can be used for testing virtual polycyclicity and virtual nilpotency for finitely generated subgroups of .

     

幂零矩阵的m次根

主要研究当A是幂零矩阵时,方程Xm=A的性质.我们可以得到一些关于方程Xm=A无解性与A自身的特点之间的关系.     

Structure of finitely generated commutative alternative algebras and special Moufang loops

It is proved that the commutator ideal of the multiplication algebra of a free commutative alternative algebra of rank n is nilpotent of index n ? 1. As a corollary to this fact, the Bruck theorem for special commutative Moufang loops is derived.     

On the residual properties of link groups

We study the residual properties of finitely generated linear groups. Using the methods under consideration, we prove the residual 2-finiteness of the groups of the Whitehead link, the Borromean links (answering a question of Cochran), and some other links. We show also that each link is a sublink of some link whose group is residually 2-finite.     

Becchi-Rouet-Stora-Tyutin quantization and Hamiltonian formalism

An introductory review of BRST hamiltonian formalism is presented. The method of quantization of gauge and string theories is discussed. A few simple examples are presented to illustrate the BRST techniques.     

Convergence in finite precision of successive iteration methods under high nonnormality

This paper is devoted to the analysis of the behaviour, in finite precision arithmetic, of the successive iteration method (SI)x ₀,x _k+1 =Ax _k +b,k ≥ 0 whereA is a real or complex matrix of ordern andx is a real or complex vector of sizen. In exact arithmetic, the behaviour of (SI) is completely understood; there is convergence for anyx ₀ if and only if ρ(A) < 1 where ρ(A) is the spectral radius ofA. When (SI) is run on a computer with finite precision arithmetic, then for certain matricesA, the convergence is not guaranteed in practice when ρ(A) < 1 is true in exact arithmetic. It is clear that the phenomenon should be attributed to the conjunction of two factors :i) the nonnormality ofA andii) the finite precision of the computer arithmetic. We perform a straightforward analysis of the convergence of (SI) in finite precision from which we try to understand the subtle interplay between factorsi) andii) which takes place inside the computer, when the iteration matrixA has a high nonnormality. Why should nonnormality be an issue in finite precision? Because only nonnormal matrices can display a significant amount of spectral instability. Therefore a small perturbation ΔA onA can result in a large perturbation of the spectrum. When the spectral instability ofA is high, it appears that a convergence condition such as ρ(A) < 1 may not be generic enough for finite precision computations.     

ON REDUCIBILITY OF THE SELF-HOMOTOPY EQUIVALENCES OF WEDGE SPACES

Reducibility of the self-homotopy equivalences of wedge spaces is studied and some conditions implying the reducibility are obtained.     

On Lie nilpotent modular group algebras

Let K be a field of characteristic p>0 and let KG be the group algebra of an arbitrary group G over K. It is known that if KG is Lie nilpotent, then its lower as well as upper Lie nilpotency index is at least p+1. The group algebras KG for which these indices are p+1 or 2p or 3p?1 or 4p?2 have already been determined. In this paper, we classify the group algebras KG for which the upper Lie nilpotency index is 5p?3, 6p?4 or 7p?5.