Some classes of finite homomorphism-homogeneous point-line geometries

In 2006, P. J. Cameron and J. Ne?et?ril introduced the following variant of homogeneity: we say that a structure is homomorphism-homogeneous if every homomorphism between finite substructures of the structure extends to an endomorphism of the structure. In this paper we classify finite homomorphism-homogeneous point-line geometries up to a certain point. We classify all disconnected point-line geometries, and all connected point-line geometries that contain a pair of intersecting proper lines (we say that a line is proper if it contains at least three points). In a way, this is the best one can hope for, since a recent result by Rusinov and Schweitzer implies that there is no polynomially computable characterization of finite connected homomorphism-homogeneous point-line geometries that do not contain a pair of intersecting proper lines (unless P=coNP).     

Experimental investigation and thermodynamic calculation of the Bi-Ga-Sn phase equilibria

Binary thermodynamic data, successfully used for phase diagram calculations of binary systems Bi-Ga, Bi-Sn, and Ga-Sn, were used for prediction of phase equilibria in ternary Bi-Ga-Sn system. The thermodynamic functions, such as enthalpy of formation and activity, were calculated using the Redlich-Kister-Muggianu model and compared with experimental data reported in the literature. The liquidus surface, invariant equilibria and three vertical sections with molar ratio Ga:Sn=1, Bi:Sn=1 and Bi:Ga=1 of the Bi-Ga-Sn ternary system were calculated by the CALPHAD method. Alloys, situated along three calculated vertical sections, were investigated by Differential Scanning Calorimetry (DSC). The experimentally determined phase transition temperatures were compared with calculation results and good mutual agreement was noticed.     

Stochastic analysis of the electromagnetic induction effect on a neuron’s action potential dynamics

Nonlinear Dynamics - The presence of time-varying electromagnetic fields across a neuron cell may cause changes in its electrical characteristics, most notably, in the action potential dynamics....     

High diffusion barrier and piezoelectric nanocomposites based on polyvinylidene fluoride‐trifluoroethylene copolymer and hydrophobized clay

Nanocomposites based on polyvinylidene fluoride–trifluoroethylene copolymer and up to 4 vol % of hydrophobized clay nanoparticles are investigated. The structure, piezoelectric properties, and oxygen permeability of solvent cast films are analyzed before and after annealing above the Curie temperature of the polymer. Exfoliation of the clay takes place at concentrations up to 1 vol %, beyond which it rapidly drops and is absent at a concentration of 4 vol %. The presence of clay does not change the crystallinity of the polymer, but leads to a threefold decrease of the oxygen permeability at a concentration of 0.5 vol %. Annealing at 130 °C increases the crystallinity, the proportion of β phase up to 94%, and the piezoelectric coefficient by 20–40% at clay fractions below 1 vol %. Annealing also leads to a remarkable 3‐ to 10‐fold decrease of O₂ permeability and to intriguing changes of the activation energy for O₂ transport, which decreases from 56 kJ/mol for the as‐cast polymer to below 10 kJ/mol for the polymer and exfoliated composite. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1828–1836     

Cryptanalyzing a novel pseudorandom number generator based on pseudorandomly enhanced logistic map

Nonlinear Dynamics - Dielectric elastomer is a prosperous material in electromechanical systems because it can effectively transform electrical energy to mechanical work. In this paper, the period...     

Corrigendum to “On norms of composition operators acting on Bergman spaces” [J. Math. Anal. Appl. 291 (2004) 189-202]

A theorem and a corollary in the paper cited in the title were stated incorrectly, as was pointed out by Christopher Hammond. We now state correctly and prove both of them. These results still generalize and explain the geometric meaning of the Cowen-Hurst norm formula. We also include additional references and provide an example relevant for further study.     

A Classification of 2-Arc-Transitive Circulants

A graph X is k-arc-transitive if its automorphism group acts transitively on the set of k-arcs of X. A circulant is a Cayley graph of a cyclic group. A classification of 2-arc-transitive circulants is given.     

Walks and regular integral graphs

We establish a useful correspondence between the closed walks in regular graphs and the walks in infinite regular trees, which, after counting the walks of a given length between vertices at a given distance in an infinite regular tree, provides a lower bound on the number of closed walks in regular graphs. This lower bound is then applied to reduce the number of the feasible spectra of the 4-regular bipartite integral graphs by more than a half.Next, we give the details of the exhaustive computer search on all 4-regular bipartite graphs with up to 24 vertices, which yields a total of 47 integral graphs.