Determining L-functions by twists

Suppose that L₁(s) and L₂(s) are two L-functions whose twists by a set of Dirichlet characters simultaneously vanish (vanish mod p) at a critical point. We examine the extent to which this property determines the L-functions in the cases of L-functions of elliptic curves, of number fields, and of curves over finite fields.     

Magnetotransport and magnetic properties of InAs/Mn digital alloys

We have investigated the magnetic and magneto-transport properties of a systematic sequence of five InAs/Mn digital alloys grown by a combination of molecular beam epitaxy and atomic layer epitaxy. The samples consist of 30 periods of Mn fractional monolayers (ML) (0.17–0.5 ML) separated by 14 ML thick InAs spacer layers in a superlattice configuration. Four samples show n-type electrical conduction while the fifth (0.25 ML Mn) is p-type. Squid magnetization measurements performed on these samples show remnant magnetization above room temperature, which is apparently related to a second phase.     

Sulfur Concentration in Nanoporous Alumina Membrane

Nanoporous alumina membrane prepared by anodic oxidation using sulfuric acid electrolyte was subjected to TG-DTA and X-ray Photoelectron Spectroscopy (XPS or ESCA) to further study the distribution of sulfur. In XPS study, Ar⁺ ion bombardment was performed on the sample to etch the surface at a rate of 3 nm min^-1. As a result, sulfur was found to be concentrated within a depth of 3nm from the surface. The S content of the surface was found to be 2.7±0.5 wt%, and that at a depth of ca. 3 nm and ca. 10 nm was found to be as low as about 0.6±0.11 wt% (5.37±1.0 wt%→ 1.26±0.2wt% SO₂). In TG-DTA, the mass loss of 7.3% was in fair agreement with that calculated on XPS results (7.1±1.2%). This revised version was published online in July 2006 with corrections to the Cover Date.     

On the Stabilization of a Solution of the Cauchy Problem for One Class of Integro-Differential Equations

We consider a solution of the Cauchy problem u(t, x), t > 0, x ∈ R ², for one class of integro-differential equations. These equations have the following specific feature: the matrix of the coefficients of higher derivatives is degenerate for all x. We establish conditions for the existence of the limit lim _t→∞ u(t, x) = v(x) and represent the solution of the Cauchy problem in explicit form in terms of the coefficients of the equation.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 12, pp. 1699 – 1706, December, 2004.     

Dispersion modeling by kinematic simulation: Cloud dispersion model

A new technique has been developed to compute mean and fluctuating concentrations in complex turbulent flows (tidal current near a coast and deep ocean). An initial distribution of material is discretized into any small clouds which are advected by a combination of the mean flow and large scale turbulence. The turbulence can be simulated either by kinematic simulation (KS) or direct numerical simulation. The clouds also diffuse relative to their centroids; the statistics for this are obtained from a separate calculation of the growth of individual clouds in small scale turbulence, generated by KS. The ensemble of discrete clouds is periodically re-discretized, to limit the size of the small clouds and prevent overlapping. The model is illustrated with simulations of dispersion in uniform flow, and the results are compared with analytic, steady state solutions. The aim of this study is to understand how pollutants disperses in a turbulent flow through a numerical simulation of fluid particle motion in a random flow field generated by Fourier modes. Although this homogeneous turbulent is rather a “simple” flow, it represents a building block toward understanding pollutant dispersion in more complex flow. The results presented here are preliminary in nature, but we expect that similar qualitative results should be observed in a genuine turbulent flow.     

A brief review on structural concepts of novel supramolecular proton transfer compounds and their metal complexes

Our research group has been interested in synthesis of proton transfer compounds as new supramolecular synthons for the onepot preparation of self-assembled transition metal complex-organo-networks since 2000. We have focused on the proton delivery from acids, which are considered as suitable proton donors, to amines as proton acceptors. The results were production of several proton transfer ion pairs possessing some remaining donor sites applied for coordination to metallic centers in preparation of metal-organic structures. Some of the complexes showed contributions of both cationic and anionic fragments of the starting ion pair, while some others contained only one of these species as ligand. Much of the investigations on reviewed compounds focused on the concept of supramolecular systems, co-crystallization, stereochemically active lone pairs, coordination polyhedron and mainly on various interactions involve including van der Waals, ion pairing, hydrogen bondings, face to face π-π stackings and edge to face C-H...π, C-O...π, N-H...π, S-O...π, Ti...π and Hg-Cl...π interactions. The mentioned interactions are the most commonly used strategies in the extension of supramolecular structures.     

Synthesis and structure of nanocrystalline La0.50Ba0.50MnO3

Nanocrystalline manganite La_0.50Ba_0.50MnO₃ was synthesized by the soft-chemical method. For this purpose, the sol-gel method was modified and improved. A trihydric saturated alcohol, e.g., glycerol, was suggested as a new organic matrix. The crystal structure of the composite was studied by X-ray powder diffraction at room temperature. A La_0.50Ba_0.50MnO₃ powder annealed in air at T = 500°C is characterized by a perovskite-like cubic structure with the unit-cell parameter a = 3.869 Å. The chemical composition of the sample was studied by electron-probe X-ray microanalysis. The La: Ba: Mn cation ratio in the material was 1: 1: 2. The surface topography was examined with a scanning electron microscope. The crystallite size was ～30 nm. The dependence of the crystal structure and the surface topology on the annealing temperature was studied. The high-temperature treatment in air resulted in the growth of larger, micrometer-size, crystallites.