A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU–GPU parallelism are discussed.     

Application of very weak formulation on homogenization of boundary value problems in porous media

Czechoslovak Mathematical Journal - The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard...     

Influence of phenylenediamine additions on the morphology and on the catalytic effect of polyaniline

The influence of para‐, ortho‐, and meta‐phenylenediamine (p‐, o‐, and m‐PDA) additions on the electrochemical synthesis of polyaniline has been investigated by the use of cyclic voltametry. It has been found that small additions (1 and 5 mmol L^?1) of PDA monomers influence significantly the polymerization rate. Whereas p‐PDA increases the polymerization rate, the addition of o‐ or m‐PDA slows it down. Therefore, a different number of potential cycling is necessary to obtain similar thickness of layers. The layers exhibit very different morphology, which changes from “spaghetti‐like” for polyaniline to “sponge‐like” for p‐PDA, to “pebble‐like” for o‐PDA and to “cauliflower‐like” for m‐PDA additions, respectively. The catalytic effect of the synthesized polymer layers has been tested. It has been found that all the layers exhibit catalytic effect in lowering the redox potential of hydroquinone/quinone tested reaction, but the rate of the electrocatalytic reaction varies depending on the PDA monomer added. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1599–1608, 2004     

The development of microparticulate cellulose-based packing materials and evaluation of potential use in capillary electrochromatography

Summary Expanding the range of stationary phases employed in capillary electrochromatography, the development of rigid cellulose-based micro-beads, their physical-chemical modification and their use in capillary electrochromatography are described. Cellulose-based stationary phases have been employed in the normal-phase and the reversed-phase modes. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

On quartic half-arc-transitive metacirculants

Following Alspach and Parsons, a metacirculant graph is a graph admitting a transitive group generated by two automorphisms ρ and σ, where ρ is (m,n)-semiregular for some integers m≥1, n≥2, and where σ normalizes ρ, cyclically permuting the orbits of ρ in such a way that σ ^m has at least one fixed vertex. A half-arc-transitive graph is a vertex- and edge- but not arc-transitive graph. In this article quartic half-arc-transitive metacirculants are explored and their connection to the so called tightly attached quartic half-arc-transitive graphs is explored. It is shown that there are three essentially different possibilities for a quartic half-arc-transitive metacirculant which is not tightly attached to exist. These graphs are extensively studied and some infinite families of such graphs are constructed. Both authors were supported in part by “ARRS – Agencija za znanost Republike Slovenije”, program no. P1-0285.     

Sur les solutions extrémales d'un système incompatible d'équations

Sans résumé     

Morphology of polythiophene and polyphenyl films produced via surface polymerization by ion-assisted deposition

Conducting polymer films are grown by either mass-selected or non-mass-selected, hyperthermal thiophene ions coincident on a surface with a thermal beam of organic monomers of either alpha-terthiophene (3T) or p-terphenyl (3P) neutrals. Previous experiments verified polymerization of both 3T and 3P by 200 eV C(4)H(4)S(+) during surface polymerization by ion-assisted deposition (SPIAD). A wide variety of structures are observed by scanning electron microscopy to form in the SPIAD polythiophene and polyphenyl films. These structures include microscale islands, lamellar structures, fractal-like growth patterns, and nanoscale crystallites. Some of the deposited films diffract X-rays while others show electron micrographs of crystallites. The variation of these patterns with deposition conditions clearly indicate that ion-induced polymerization mediates film morphology through control of ion energy and ion/neutral ratio. Furthermore, these ion-assisted events mediate important thermal processes such as sublimation.     

Nonlinear reynolds equation for lubrication of a rapidly rotating shaft

Using the homogenization theory, we derive the nonlinear Reynolds equation governing the process of lubrication of a slipper bearing with rapidly rotating shaft. We prove that this nonliner lubrication law is an approximation of the full Navier-Stokes equations in a thin cylinder with periodic roughness. The analyticity of the nonlinear function giving the relation between the velocity and the pressure drop is proved. The first term in its Taylor's expansion is the classical linear Reynolds law. Boundary layer correctors are computed.     

On G-arc-regular dihedrants and regular dihedral maps

A graph Γ is said to be G-arc-regular if a subgroup $G \le\operatorname{\mathsf{Aut}}(\varGamma)$ acts regularly on the arcs of Γ. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D _2n of order 2n whose cyclic subgroup C _n ≤D _2n of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D _2n , n odd, are classified.