Published in The Ramanujan Journal
We give a new proof of a theorem of P. Mihailescu which states that the equation xp − yq = 1 is unsolvable with x, y integral and p, q odd primes, unless the congruences pq ≡ p (mod q2) and qp ≡ q (mod p2) hold.
Published in Journal of Computational Neuroscience
A model of columnar networks of neocortical association areas is studied. The neuronal network is composed of many Hebbian autoassociators, or modules, each of which interacts with a relatively small number of the others, randomly chosen. Any module encodes and stores a number of elementary percepts, or features. Memory items, or patterns, are pecu...
Published in Geometriae Dedicata
We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov structure. We use extensions and classical r-matrices to construct Novikov structures on certain cla...
Published in Journal of Computer-Aided Molecular Design
Electron crystallography determines the structure of membrane embedded proteins in the two-dimensionally crystallized state by cryo-transmission electron microscopy imaging and computer structure reconstruction. Milestones on the path to the structure are high-level expression, purification of functional protein, reconstitution into two-dimensional...
Published in Journal of Materials Science
Crack patterns of 53 nm and 103 nm thick silicon oxide coatings on poly(ethylene terephthalate) films are analyzed under equibiaxial stress loading, by means of a bulging cell mounted under an optical microscope with stepwise pressurization of film specimens. The biaxial stress and strain are modeled from classical elastic membrane equations, and a...
Published in Journal of Materials Science
The thermo-mechanical properties of hyperbranched polymer-epoxy blends and their dependence on hyperbranched polymer shell chemistry were investigated. Hyperbranched polymers were shown to be able to increase resin toughness by inducing both a heterogeneous and homogeneous morphology. While the former was better performing in terms of toughness, th...
Published in Journal of Materials Science
The short-term mechanical strength of platelet-reinforced polymer composites was modeled using classical two-dimensional stress-transfer analysis. The stress field in the platelet and at the platelet/matrix interface was described in the presence of a matrix crack perpendicular to the interface. Modeling takes into account the tensile strength of t...
Published in Geometriae Dedicata
We characterize which permutational wreath products \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G \ltimes W^{(X)}$$\end{document} are finitely presented. This occur...
Published in Journal of Materials Science
The influence of annealing parameters on the martensitic phase transformation in sputter-deposited Ti rich Ni-Ti films is systematically studied by differential scanning calorimetry and by transmission electron microscopy. The annealing temperature range extends from the crystallization temperature of the films up to 900°C. For increasing temperatu...
Published in Journal of Applied Electrochemistry
The influence of an IrO2 interlayer between the Ti substrate and the SnO2–Sb2O5 coating on the electrode service life and on the efficiency of p-chlorophenol (p-CP) oxidation for wastewater treatment has been investigated. The results have shown that if the loading of the SnO2–Sb2O5 coating relative to the IrO2 interlayer loading (γ ratio defined b...
