Deformations of algebroid stacks

In this paper we consider deformations of an algebroid stack on an étale groupoid. We construct a differential graded Lie algebra (DGLA) which controls this deformation theory. In the case when the algebroid is a twisted form of functions we show that this DGLA is quasiisomorphic to the twist of the DGLA of Hochschild cochains on the algebra of functions on the groupoid by the characteristic class of the corresponding gerbe.     

Molecular Weight Distribution in Living Polymerization Proceeding with Reshuffling of Polymer Segments due to Chain Transfer to Polymer with Chain Scission, 2. Monte Carlo Simulation of Polymer Reshuffling Proceeding with Disproportionation of Chain Functionalities

The method for analyzing the reshuffling of polymer segments developed previously has been extended to systems involving the disproportionation of chain functionalities. The effect of interchain exchange reactions of this type, leading to the redistribution of chain lengths and of the chain functionalities (redistribution of living and dead chain ends), was analyzed by means of the Monte Carlo simulations. In the systems, in which no propagation occurs (monomer concentration equal to zero), a set of polymer chains containing one living and one dead end was taken as an initial material. A series of simulations were performed for systems with differing molecular weight distributions of the starting macromolecules. Uniform (no chain length distribution polymer – all chains are of the same length), Poisson, and the most probable (geometric) distributions were taken into consideration. Although the molecular weight distributions (MWDs) of functionally different chains of the same polymer were different apart from the eventual equilibrium conditions, the overall MWD was very close to that observed in analogous systems without disproportionation. The same was observed concerning MWDs in modeled polymerization systems, in which reshuffling and disproportionation accompanied propagation. Consequently, a method of estimating the ratio of rate constants of propagation and reshuffling (i. e. k_p /k _tr) in the relevant polymerization systems, using the observed polydispersity indexes, was proposed. The extent of disproportionation can be evaluated from the determined relationships of the polydispersity index and of the monofunctional chains fraction as functions of the average number of chain transformations.     

The Baum-Connes conjecture via localisation of categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the Baum-Connes assembly map for other equivariant homology theories. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting.     

Algebraic index theorem

We prove the Atiyah-Singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold.Partially supported by NSF Grant DMS-9101817.     

Electron impact-induced fragmentation of some aminonitropyridines

The fragmentation behaviour of 18 vicinally substituted aminonitropyridines was studied under electron impact conditions. Tbe decomposition patterns were found to be strongly dependent on the position of substituents. The formation of the aza analogue of carbazole seems to affect considerably the fragmentation of 3-nitro-2-phenylaminopyridine.     

Unitarization of Körner-Kuroda model of electromagnetic structure of octet 1/2+ baryons

The Körner-Kuroda model of the electromagnetic structure of octet 1/2⁺ baryons is restored on a more topical physical basis. Electromagnetic radii of baryons under consideration are calculated and compared with other model predictions. By an incorporation of a two-cut approximation of correct form factor analytic properties and nonzero vector-meson widths, the Körner-Kuroda model is unitarized, providing in this manner imaginary parts of the octet 1/2⁺ baryon form factors to be nonzero just starting from a branch point corresponding to the lowest threshold.     

The magnetic field,force and inductance of the system consisting of a thin ellipsoidal coil and a ferromagnetic ellipsoid

The method of separation of variables has been applied to determine the magnetic field of the system consisting of a thin ellipsoidal coil and a ferromagnetic ellipsoid of revolution. The inductance and the force acting between the coil and the ellipsoid are also examined.     

Randomly flashing diffusion: Asymptotic properties

The theory of abstract Markov operators and semigroups is applied for studying asymptotics of a randomly flashing diffusion process. The probability distribution of the process is determined by a set of two partial differential equations and sufficient conditions for the existence of a stationary solution of the equations are formulated, and convergence of solutions to the stationary solution is proved.