Some refinements of Dade's projective conjecture

In this paper a further refinement of Dade's projective conjecture, due to Boltje, is presented. This new statement includes ideas first published by Isaacs and Navarro as well as the recent contractibility version of Alperin's conjecture introduced by Boltje. Leaning heavily on the work of Robinson, weaker forms of the conjecture are proved in the case of p-solvable groups.     

Group algebras of Kleinian type and groups of units

The algebras of Kleinian type are finite-dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type and the group algebras of Kleinian type. As an application, we characterize the group rings RG, with R an order in a number field and G a finite group, such that the group of units of RG is virtually a direct product of free-by-free groups.     

Lefschetz Formulae for p-Adic Groups

In this paper,Lefschetz formulae for torus actions on p-adic groups are proven. These are similar to comparable formulae for real Lie groups.Applications lie in the realm of dynamical zeta functions.     

Trace Equivalence in SU(2, 1)

In this paper it is shown that one can choose an arbitrarily large number of inconjugate elements of the group Z/2Z*Z/2Z*Z/2Z which have the property that, under all representations of the group in SU(2,1) as a discrete complex hyperbolic ideal triangle group, the elements are hyperbolic and correspond to closed geodesics of equal length on the associated complex hyperbolic surface. This is an analogue of the geometric fact that the multiplicity of the length spectrum of a Riemann surface is never bounded or the equivalent algebraic phenomenon that an arbitrarily large number of conjugacy classes in a free group can have the same trace under all representations in SL(2,R ).     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

Photografting of vinyl polymers onto ultrafine inorganic particles: Photopolymerization of vinyl monomers initiated by AZO groups introduced onto these surfaces

The photografting of polymers onto ultrafine inorganic particles, such as silica and titanium oxide, initiated by azo groups introduced onto these surfaces was investigated. The introduction of azo groups onto the particles was achieved by the reaction of 4,4′-azobis(4-cyanopentanoic acid) with surface isocyanate groups, which were introduced by the treatment with tolylene 2,4-diisocyanate. It was found that the photopolymerization of vinyl monomers, such as methyl methacrylate (MMA), styrene, and N-vinylcarbazole, is initiated by ultrafine particles having azo groups. The corresponding polymers were effectively grafted onto these surfaces through the propagation of the polymer from the surface radicals formed by the photodecomposition of the azo groups: e.g., the percentage of grafting of PMMA and polystyrene onto silica was reached to 112 and 176%, respectively. The percentage of grafting onto silica in the graft polymerization initiated by photodecomposition of surface azo groups was much larger than that initiated by thermal decomposition. Polymer-grafted ultrafine particles thus obtained gave a stable colloidal dispersion in good solvents for the grafted chain. © 1994 John Wiley & Sons, Inc.     

The effect of side substituents on rotation hindrance in polyheteroarylenes

Hindered rotation was considered in calculations of the conformational parameters of a series of polyheteroarylenes with bulky side substituents by the Monte-Carlo method. Within the range of experimental errors, the results of calculations for several polyarylates coincide with the values of conformational rigidity, determined from hydrodynamic experimental data. The proposed procedure was used to estimate the rigidities of a number of polymers with bulky side substuents for which experimental determination is difficult. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1287–1296, July, 1998.     

Oxobenzo[f]benzopyrans as new fluorescent photolabile protecting groups for the carboxylic function

The properties of three oxobenzo[f]benzopyrans as new fluorogenic photolabile protecting groups for the carboxylic function of amino acids were studied. Fluorescent amino acid conjugates were efficiently prepared and characterised. Photodeprotection of these compounds was carried out by irradiation at 300, 350 and 419 nm, the most suitable wavelength being 350 nm, on account of short irradiation times and good deprotection yields.