Syndiotactic polymerization of styrene catalyzed by alkenyl‐substituted cyclopentadienyltitanium trichlorides

CH₂?CHCH₂CpTiCl₃ (1), CH₂?CHCH₂CH₂CpTiCl₃ (2) and CH₃CH₂CH₃CpTiCl₃ (3) have been synthesized and characterized. The influence of the alkenyl substituent groups on the catalyst activities in the syndiotactic polymerization of styrene was investigated. The catalyst activities decreased in the order CH₂?CHCH₂CH₂CpTiCl₃ > CH₃CH₂CH₂CH₂CpTiCl₃ > CH₃CH₂CH₂CpTiCl₃ > CH₂?CHCH₂CpTiCl₃ (Cp?C₅H₄). By using complex 1, the dependence of the activity on the concentration of methylaluminoxane, triisobutylaluminum and diisobutylaluminum hydride was investigated. Copyright © 2003 John Wiley & Sons, Ltd.     

On harmonic analysis of causal operators

We follow the group representation theory approach to define causal operators on Banach modules and present some of their spectral properties.     

On the existence of f-local subgroups in a group

We prove the existence of infinite subgroups with nontrivial locally finite radicals and of locally finite subgroups in the groups with almost finite almost solvable elements of prime orders and in the groups with generally finite elements.     

Hamiltonian torus actions on symplectic orbifolds and toric varieties

In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly, we prove the orbifold versions of the abelian connectedness and convexity theorems. In the second half, we prove that compact symplectic orbifolds with completely integrable torus actions are classified by convex simple rational polytopes with a positive integer attached to each open facet and that all such orbifolds are algebraic toric varieties.

     

四元Heisenberg群上次拉普拉斯算子的m幂次的基本解

本文研究了四元Heisenberg群上次拉普拉斯算子的m幂次的基本解，该结论是Heisenberg群上结果的推广.本文利用了四元Heisenberg群上的Fourier变换理论构造了该群上次拉普拉斯算子的m幂次的基本解，并且给出了基本解的积分表示.     

Alternating subgroups of Coxeter groups

We study combinatorial properties of the alternating subgroup of a Coxeter group, using a presentation of it due to Bourbaki.     

G-spaces and Fixed Point Sets

For a compact connected group G, in a compact free G-space M every closed subset is the fixed point set of an autohomeomorphism if the weight of M is not bigger than that of G. In a compact group with nonsingleton components, every closed subset is the fixed point set of an autohomeomorphism if and only if the weight of the whole group is not bigger than that of the component of the identity.     

Weight functions on groups and an amenability criterion for Beurling algebras

The paper is devoted to the study of weights on groups. A connection between weight functions and harmonic functions is established. A relationship between the weight theory on groups with the “Tychonoff property” and the theory of bounded cohomology is presented. It is proved that the Beurling algebraℓ1 (G, ω) constructed for the weightω is amenable if and only if the groupG is amenable and the weightω is equivalent to a multiplicative characterχ:G→ℝ₊. Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 448–460, September, 1996. This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-00974 and by the INTAS Foundation under grant No. 94-3420.     

Group of Self-Equivalences of Sum Object

In general category, the group of self-equivalences of sum object can decompose as the product of its two subgroups under certain conditions and also several split short exact sequences are obtained. Subsequently, we apply the above results to the category of space under a space and get some results which are dual to those in fibrewise category.     

一类量子环面李代数的自同构群

=C_q[x_1~(±1),x_2~(±1)]为复数域上的非交换环面结合代数,A=\C,Der为的导子李代数．本文研究李代数L_q=DerA的自同构群Aut L_q．