Equivalence of spectral projections in semiclassical limit and a vanishing theorem for higher traces in K-theory

In this paper, we study a refined L2 version of the semiclassical approximation of projectively invariant elliptic operators with invariant Morse type potentials on covering spaces of compact manifolds. We work on the level of spectral projections (and not just their traces) and obtain an information about classes of these projections in K-theory in the semiclassical limit as the coupling constant goes to zero. An important corollary is a vanishing theorem for the higher traces in cyclic cohomology for the spectral projections. This result is then applied to the quantum Hall effect. We also give a new proof that there are arbitrarily many gaps in the spectrum of the operators under consideration in the semiclassical limit.Comment: 41 pages, latex2e, uses xypic package. Minor clarifications made, some references added. Final versio

Semiclassical asymptotics and gaps in the spectra of magnetic Schroedinger operators

In this paper, we study an L2 version of the semiclassical approximation of magnetic Schroedinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence of an arbitrary large number of gaps in the spectrum of these operators, in the semiclassical limit as the coupling constant goes to zero.Comment: 18 pages, Latex2e, more typos correcte

Non-catalytic bromination of benzene: a combined computational and experimental study

The non-catalytic bromination of benzene is shown experimentally to require high 5-14M concentrations of bromine in order to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable (The non-catalytic bromination of benzene is shown experimentally to require high 5-14M concentrations of bromine in order to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable (The non-catalytic bromination of benzene is shown experimentally to require high 5-14M concentrations of bromine in order to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable

Trends of the major porin gene (ompF) evolution

OmpF is one of the major general porins of Enterobacteriaceae that belongs to the first line of bacterial defense and interactions with the biotic as well as abiotic environments. Porins are surface exposed and their structures strongly reflect the history of multiple interactions with the environmental challenges. Unfortunately, little is known on diversity of porin genes of Enterobacteriaceae and the genus Yersinia especially. We analyzed the sequences of the ompF gene from 73 Yersinia strains covering 14 known species. The phylogenetic analysis placed most of the Yersinia strains in the same line assigned by 16S rDNA-gyrB tree. Very high congruence in the tree topologies was observed for Y. enterocolitica, Y. kristensenii, Y. ruckeri, indicating that intragenic recombination in these species had no effect on the ompF gene. A significant level of intra- and interspecies recombination was found for Y. aleksiciae, Y. intermedia and Y. mollaretii. Our analysis shows that the ompF gene of Yersinia has evolved with nonrandom mutational rate under purifying selection. However, several surface loops in the OmpF porin contain positively selected sites, which very likely reflect adaptive diversification Yersinia to their ecological niches. To our knowledge, this is a first investigation of diversity of the porin gene covering the whole genus of the family Enterobacteriaceae. This study demonstrates that recombination and positive selection both contribute to evolution of ompF, but the relative contribution of these evolutionary forces are different among Yersinia species

Uniformization and an Index Theorem for Elliptic Operators Associated with Diffeomorphisms of a Manifold

We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely differential operators with shifts induced by the action of an isometric diffeomorphism. The key to the solution is the method of uniformization: We assign to the nonlocal problem a pseudodifferential operator with the same index, acting in sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah-Singer index theorem.Comment: 16 pages, no figure

Quantization of the Riemann Zeta-Function and Cosmology

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.Comment: 14 pages, corrected typos, references and comments adde

Comparative physical-tribological properties of anti-friction ion-plasma Ti-C-Mo-S coating on VT6 alloy or 20X13 and 40X steels

Results of comparative tests mechanical and tribological properties of solid antifriction Ti-C-Mo-S coating, deposited by magnetron-plasma combined sputtering method on substrates of VT6 titanium alloy, 40X and 20X13 hardened steels are provided. Coating is sputtered using the same conditions and technological regimes on substrates of different materials. However, the friction tests results showed significant difference in tribological characteristics of coating depending on type of material used for substrate, first of all by wear-resistance ability. Authors suppose that this is due to difference between physical properties such as composition and structure of substrate materials that determines hardness and coating adhesion to surface

Metal Ir coatings on endocardial electrode tips, obtained by MOCVD

The present work demonstrates the application of the Metal-Organic Chemical Vapor Deposition technique to fabricate metal iridium coatings onto the pole tips of endocardial electrodes. Using iridium (III) acetylacetonate as volatile precursor, the target coatings were successfully applied to the working surface of cathodes and anodes of pacemaker electrodes in the flow type reactor in hydrogen atmosphere at deposition temperature of 550°C. The coating samples were characterized by means of XRD, SEM, Raman- and XPS-spectroscopies. The formation of non-textured coatings with fractal-like morphology and 7-24 nm crystallite size has been realized. The electrochemical properties of the coatings were investigated by cyclic voltammetry and electrochemical impedance spectroscopy. The charge storage capacity values of the electrochemically activated samples were 17.0-115 mC·cm–2 and 14.4-76.5 mC·cm–2 for measurements carried out in 0.1M sulfuric acid and in phosphate buffer saline solutions, respectively. A comparison of some characteristics of the samples obtained with commercially available cathode of pacemaker electrodes is also presented