New AlDy(Ni,Co) glasses - the influence of pre-aging on decomposition and modelling of the crystallisation

The decomposition of AlDy₆Ni₁₀ and AlDy₈Ni₆Co₂ glasses prepared by melt spinning after different pre-aging regimes was investigated. The modelling of the transformation at the glass transition and the crystallisation was tested by a more general Johnson-Mehl-Avrami-Kolmogorov model and by the determination of the local kinetic parameter. The relaxation was tested with an lnt kinetic model after Gibbs.     

Some characterisations of supported algebras

We give several equivalent characterisations of left (and hence, by duality, also of right) supported algebras. These characterisations are in terms of properties of the left and the right parts of the module category, or in terms of the classes L₀ and R₀ which consist respectively of the predecessors of the projective modules, and of the successors of the injective modules.     

On bimeasurings II

We answer some questions posed in [L. Grunenfelder, M. Mastnak, On bimeasurings, J. Pure Appl. Algebra 204 (2006) 258-269] concerning the universal bimeasuring bialgebra via a construction of suitable subcoalgebras of the universal measuring coalgebra.     

Motivic Serre invariants of curves

In this article, we generalize the theory of motivic integration on formal schemes topologically of finite type and the notion of motivic Serre invariant, to a relative point of view. We compute the relative motivic Serre invariant for curves defined over the field of fractions of a complete discrete valuation ring R of equicharacteristic zero. One aim of this study is to understand the behavior of motivic Serre invariants under ramified extension of the ring R. Thanks to our constructions, we obtain, in particular, an expression for the generating power series, whose coefficients are the motivic Serre invariant associated to a curve, computed on a tower of ramified extensions of R. We give an interpretation of this series in terms of the motivic zeta function of Denef and Loeser.     

The σ<Emphasis Type="Italic">g</Emphasis>-Drazin Inverse and the Generalized Mbekhta Decomposition

In this paper we define and study an extension of the g-Drazin for elements of a Banach algebra and for bounded linear operators based on an isolated spectral set rather than on an isolated spectral point. We investigate salient properties of the new inverse and its continuity, and illustrate its usefulness with an application to differential equations. Generalized Mbekhta subspaces are introduced and the corresponding extended Mbekhta decomposition gives a characterization of circularly isolated spectral sets.     

Trace norm estimates for products of integral operators and diffusion semigroups

We give trace norm estimates for products of integral operators and for diffusion semigroups. These are applied to differences of heat semigroups. A natural example of an integral operator with finite trace which is not trace class is given.     

Mechanism of the reaction of neutral and anionic N-nucleophiles with α-halocarbonyl compounds

N-Acylalkylation of neutral and anionic N-nucleophiles with α-halocarbonyl compounds was investigated by quantum chemical methods in terms of the density functional theory and by experimental methods for 2,3-dihydroimidazo[2,1-b]quinazolin-1(10)H-5-one, its N-anion, and simpler model structures. High reactivity of these reagents is determined primarily by stabilization of transition states (TS) by bridge bonds involving halogen or nitrogen atoms rather than by conjugation, as has been commonly accepted. Bridged TS are formed by both the substitution mechanism S _N 2 and the addition-elimination mechanism. α-Haloalkyl-substituted zwitterions, which are potential intermediates of stepwise N-acylalkylation of neutral N-nucleophiles, do not exist in the isolated state, but they are rather efficiently stabilized upon solvation. These zwitterions, as well as analogous O-anions generated from anionic N-nucleophiles, can serve as intermediates of N-acylalkylation, as was demonstrated by localization of the corresponding TS. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1150–1164, June, 2007.     

Classification of real moduli spaces over genus 2 curves

We classify, in terms of simple algebraic equations, the fixed point sets of the moduli space of stable bundles over genus 2 curves with anti-holomorphic involutions.Research supported by SRF of University of Missouri.