Primary abelian <Emphasis Type="Italic">n</Emphasis>-Σ-groups

We prove the following theorem: Any abelian p-group is an n-Σ-group which is a strong ω-elongation of a totally projective group by a p ^ω+n -projective group precisely when it is totally projective. In particular, each p-torsion p ^ω+n -projective n-Σ-group is a direct sum of countable p-groups of length not exceeding ω + n and vice versa. These two claims generalize our recent results in [6] and [7]. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 155–162, April–June, 2007.     

Rn上的非初等变换群及其极限集

该文对高维非初等Mò'bius变换群进行了研究,得到了一些重要性质,给出了几个关于离散准则和代数收敛性的定理.     

On the Patterson–Sullivan Measure for Geometrically Finite Groups Acting on Complex or Quaternionic Hyperbolic Space

The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry.     

Synthesis of polysiltrimethylenes with trimethylsilyl groups in the branch of the main chain

The thermally initiated and platinum-catalyzed polymerization of 1-silacyclobutanes with substitutents containing a trimethylsilyl group was carried out. Soluble, high-molecular-weight, heterochain siltrimethylene polymers were obtained, containing trimethylsilyl groups removed from the main chain by various bridges.A. V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, 117912 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 223–225, January, 1992.     

On the rigidity of sphericalt-designs that are orbits of finite reflection groups

The concept of rigid sphericalt-designs was introduced by Bannai. He conjectured that there is a functionf(t, d) such that ifX is a sphericalt design in thed-dimensional Euclidean space so that |X|>f(t, d), theX is non-rigid. Furthermore, he asked to find examples of rigid but not tight sperical designs. In the present article we shall investigate the case whenX is an orbit of a finite reflection group and prove thatX is rigid iff tight for the groupsA _n ,B _n ,C _n ,D _n ,E ₆,E ₇,F ₄,I ₃.Research was partially supported by Hungarian National Research fund Grant No. 4267.     

Boundary G/G Theory and Topological Poisson–Lie Sigma Model

We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G ^* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky.     

角域上的调和函数与条件Brown运动

设中的角域．该文绘出了A上正调和函数的Martin表示，讨论了极小调和函数与条件Brown运动的一个0—1律之间的关系，并给出了A上极小调和函数的表现形式，     

Light scattering by groups of spherical particles

Light scattering by groups of spherical particles is considered. It is shown that the structure of the groups and their orientational distribution can be judged from the spectrum and polarization of the scattered light. Syktyvkar State University, 55, Oktyabr'skii Ave., Syktyvkar, 167001, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 2, pp. 228–231, March–April, 1997.     

Coverings of Abelian groups and vector spaces

We study the question how many subgroups, cosets or subspaces are needed to cover a finite Abelian group or a vector space if we have some natural restrictions on the structure of the covering system. For example we determine, how many cosets we need, if we want to cover all but one element of an Abelian group. This result is a group theoretical extension of the theorem of Brouwer, Jamison and Schrijver about the blocking number of an affine space. We show that these covering problems are closely related to combinatorial problems, including the so-called additive basis conjecture, the three-flow conjecture, and a conjecture of Alon, Jaeger and Tarsi about nowhere zero vectors.     

一类矩阵群的完全性

用与[1]不同的方法,把文[1]的结论作两方面的推广,其一是把矩阵的阶数从2推广到任意,其二是把有理数域推广到任意特征不是2的可线性化的域.