Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.

Software Products for Modelling and Simulation in Materials Science

Models and software products have been developed for modelling, simulation and prediction of different correlations in materials science, including 1. the correlation between processing parameters and properties in titanium alloys and ?-titanium aluminides; 2. time–temperature–transformation (TTT) diagrams for titanium alloys; 3. corrosion resistance of titanium alloys; 4. surface hardness and microhardness profile of nitrocarburised layers; 5. fatigue stress life (S–N) diagrams for Ti–6Al–4V alloys. The programs are based on trained artificial neural networks. For each particular case appropriate combination of inputs and outputs is chosen. Very good performances of the models are achieved. Graphical user interfaces (GUI) are created for easy use of the models. In addition interactive text versions are developed. The models designed are combined and integrated in software package that is built up on a modular fashion. The software products are available in versions for different platforms including Windows 95/98/2000/NT, UNIX and Apple Macintosh. Description of the software products is given, to demonstrate that they are convenient and powerful tools for practical applications in solving various problems in materials science. Examples for optimisation of the alloy compositions, processing parameters and working conditions are illustrated. An option for use of the software in materials selection procedure is described.

Novel oxidation products from guanine nucleosides reacted with dimethyldioxirane.

Treatment of guanosine or 2'-deoxyguanosine with dimethyldioxirane, followed by heating in aqueous solution, generates respectively 4-amidinocarbamoyl-5-hydroxyimidazole (1) or its 2-(2,3,4-trihydroxybutyl) derivative (2).

Advanced glycation end products induce blood-retinal barrier dysfunction in normoglycemic rats

Advanced glycation end products (AGEs) have been implicated in the progressive vascular dysfunction which occurs during diabetic retinopathy. In the current study we have examined the role of these adducts in blood-retinal barrier (BRB) breakdown and investigated expression of the vasopermeabilizing agent vascular endothelial growth factor (VEGF) in the retina. When normoglycemic rats were injected with AGE-modified albumin daily for up to 10 days there was widespread leakage of FITC-dextran and serum albumin from the retinal vasculature when compared to control animals treated with nonmodified albumin. Ultrastructural examination of the vasculature revealed areas of attenuation of the retinal vascular endothelium and increased vesicular organelles only in the AGE-exposed rats. Quantitative RT-PCR and in situ hybridization demonstrated a significant increase in retinal VEGF mRNA expression (P <0.05). These results suggest that AGEs can initiate BRB dysfunction in nondiabetic rats and a concomitant increase in retinal VEGF expression. These findings may have implications for the role of AGEs in the pathogenesis of diabetic retinopathy.

On subspace lattices I. Closedness type properties and tensor products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.

Quantum manifestations of scattering orbits in the scaled spectrum of a non-hydrogenic atom in crossed fields

Evidence for scattering closed orbits for the Rydberg electron of the singly excited helium atom in crossed electric and magnetic fields at constant scaled energy and constant scaled electric field strength has been found through a quantum calculation of the photo-excitation spectrum. A particular 3D scattering orbit in a mixed regular and chaotic region has been investigated and the hydrogenic 3D closed orbits composing it identified. To the best of our knowledge, this letter reports the first quantum calculation of the scaled spectrum of a non- hydrogenic atom in crossed fields.