Places of algebraic function fields in arbitrary characteristic

We consider the Zariski space of all places of an algebraic function field F|K of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime divisors, places of maximal rank, zero-dimensional discrete places) lie dense in this topology. Further, we give several equivalent characterizations of fields that are large, in the sense of F. Pop's Annals paper Embedding problems over large fields. We also study the question whether a field K is existentially closed in an extension field L if L admits a K-rational place. In the appendix, we prove the fact that the Zariski space with the Zariski topology is quasi-compact and that it is a spectral space.     

Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle

We investigate heteroclinic orbits between equilibria and rotating waves for scalar semilinear parabolic reaction-advection-diffusion equations with periodic boundary conditions. Using zero number properties of the solutions and the phase shift equivariance of the equation, we establish a necessary and sufficient condition for the existence of a heteroclinic connection between any pair of hyperbolic equilibria or rotating waves.     

Long Abelian ideals

We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the number of long Abelian ideals is given. We also show that there is a one-to-one correspondence between the long Abelian ideals and B-stable commutative subalgebras in the little adjoint representation of the Langlands dual Lie algebra.     

Rank estimation in reduced-rank regression

Reduced rank regression assumes that the coefficient matrix in a multivariate regression model is not of full rank. The unknown rank is traditionally estimated under the assumption of normal responses. We derive an asymptotic test for the rank that only requires the response vector have finite second moments. The test is extended to the nonconstant covariance case. Linear combinations of the components of the predictor vector that are estimated to be significant for modelling the responses are obtained.     

Polyaniline/12-phosphotungstic acid/V<Subscript>2</Subscript>O<Subscript>5</Subscript> nanocomposite and its platinum analog as oxygen reduction electrocatalysts

A guest-host nanocomposite based on electroconducting polyaniline doped with 12-phosphotungstic acid and V₂O₅ as well as its bifunctional analog containing not more than 5 mass% nanosized platinum were obtained. A study was carried out on the structure of these nanocomposites, their redox characteristics, and electrocatalytic activity in the reduction of oxygen. These nanocomposites were found to display catalytic properties in the electrochemical reduction of oxygen, while the presence of even a slight amount of nanosized platinum in the bifunctional composite leads to a significant increase in its electrocatalytic activity. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 43, No. 5, pp. 307–314, September–October, 2007.     

Sound velocity in alumino-silicate liquids determined up to 2550 K from Brillouin spectroscopy: glass transition and crossover temperatures

Hypersonic longitudinal sound velocities in five silicate and alumino-silicate liquids have been measured between 293 and 2550 K by Brillouin spectroscopy. Together with previous observations for four other glasses and liquids of the system SiO₂-Al₂O₃-CaO-MgO, these results are used to discuss changes in hypersonic velocities in three adjacent temperature domains, i.e., below, in, and above the glass transformation range. The temperature dependence of Brillouin velocities is consistent with the observed variations with temperature of viscosity, density, and mean heat capacity for the same three temperature domains. These variations of physical properties of alumino-silicate liquids are qualitatively in agreement with the Inherent Structure Theory for liquids.     

Model spectral function and superconductivity in BaxK1−xBiO3 (x=0.5-0.7)

The Eliashberg spectral density function is constructed for the superconducting compound Ba_xK_1−xBiO₃ with x=0.5, 0.6, 0.7. The functions, besides yielding some prominent structures, show widely spreading spectra that inhibit lattice instability by yielding not too large values of λ(<1.32). The resulting spectral functions show similar shape as other results, where available, and also successfully reproduce the observed critical temperature, isotope exponent, gap ratio and several other parameters.     

Rank one perturbations at infinite coupling in Pontryagin spaces

In this paper we relate the operators in the operator representations of a generalized Nevanlinna function N(z) and of the function −N(z)⁻¹ under the assumption that z=∞ is the only (generalized) pole of nonpositive type. The results are applied to the Q-function for S and H and the Q-function for S and H^∞, where H is a self-adjoint operator in a Pontryagin space with a cyclic element w, H^∞ is the self-adjoint relation obtained from H and w via a rank one perturbation at infinite coupling, and S is the symmetric operator given by S=H∩H^∞.     

More on Kleinewillinghöfer Types of Flat Laguerre Planes

Polster and Steinke [Result. Math., 46 (2004), 103–122] determined the possible Kleinewillingh?fer types of flat Laguerre planes. These types reflect transitivity properties of groups of certain central automorphisms. We exclude three more types from the list given there with respect to Laguerre homotheties. This yields a complete determination of all possible single types with respect to Laguerre homotheties that can occur in flat Laguerre planes. Building on results by M?urer and Hartmann to characterize ovoidal or miquelian Laguerre planes we further characterize certain flat Laguerre planes in terms of their Kleinewillingh?fer types. Received: January 16, 2007. Revised: July 26, 2007.