-symmetry for (r,s)-hypergeometric series

Contiguous operators for a two-parameter analogue of hypergeometric series are constructed. These represent a two-parameter quantum enveloping algebra introduced by Takeuchi.     

Further results on large sets of disjoint group‐divisible designs with block size three and type 2n41

Large sets of disjoint group‐divisible designs with block size three and type 2ⁿ4¹ were first studied by Schellenberg and Stinson because of their connection with perfect threshold schemes. It is known that such large sets can exist only for n ≡0 (mod 3) and do exist for all odd n ≡ (mod 3) and for even n=24m, where m odd ≥ 1. In this paper, we show that such large sets exist also for n=2^k(3m), where m odd≥ 1 and k≥ 5. To accomplish this, we present two quadrupling constructions and two tripling constructions for a special large set called ^*LS(2ⁿ). © 2002 Wiley Periodicals, Inc. J Combin Designs 11: 24–35, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10032     

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.     

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.