Nearby Cycles and the Dold–Kan Correspondence

The purpose in this article is to develop the formalism of nearby cycles for simplicial sheaves of abelian groups. In doing so, we utilize the cohomology groups of simplicial sheaves introduced by Brown and Gersten. A key role in our constructions is played by the Dold–Kan correspondence.     

Correlation of CSF neuroinflammatory molecules with leptomeningeal cortical subcortical white matter fractional anisotropy in neonatal meningitis

It has been previously hypothesized that the high fractional anisotropy (FA) values in leptomeningeal cortical subcortical white matter (LCSWM) regions of neonatal brain with bacterial meningitis is due to the presence of adhesion molecules in the subarachnoid space, which are responsible for adherence of inflammatory cells over the subarachnoid membrane. The aim of this study was to look for any relationship between FA values in LCSWM regions and various neuroinflammatory molecules (NMs) in cerebrospinal fluid (CSF) measured in neonates with bacterial meningitis. Diffusion tensor imaging was performed on 18 term neonates (median age, 10.5 days) having bacterial meningitis and 10 age-/sex-matched healthy controls. CSF enzyme-linked immunosorbent assay was performed to quantify NMs [soluble intracellular adhesion molecules (sICAM), tumor necrosis factor-alpha (TNF-alpha) and interleukin-1beta (IL-1beta)]. Significantly increased FA values were observed in LCSWM regions of the patients compared to controls. A significant positive correlation was observed between FA values in LCSWM regions and NMs [sICAM (r=0.67, P=.006), TNF-alpha (r=0.69, P=.005) and IL-1beta (r=0.82, P=.000)] in CSF of these patients. No difference in FA values (P=.99) in LCSWM regions was observed between patients with sterile (0.12+/-0.02) and culture-positive CSF study (0.12+/-0.02). FA may be used as noninvasive surrogate marker of NMs in neonatal meningitis in assessing therapeutic response in future.     

Heat Transport in Ordered Harmonic Lattices

We consider heat conduction across an ordered oscillator chain with harmonic interparticle interactions and also onsite harmonic potentials. The onsite spring constant is the same for all sites excepting the boundary sites. The chain is connected to Ohmic heat reservoirs at different temperatures. We use an approach following from a direct solution of the Langevin equations of motion. This works both in the classical and quantum regimes. In the classical case we obtain an exact formula for the heat current in the limit of system size N→∞. In special cases this reduces to earlier results obtained by Rieder, Lebowitz and Lieb and by Nakazawa. We also obtain results for the quantum mechanical case where we study the temperature dependence of the heat current. We briefly discuss results in higher dimensions.     

Green's function approach to study the propagation of SH‐wave in piezoelectric layer influenced by a point source

Green's function technique serves as a powerful tool to find the particle displacements due to SH‐wave propagation in layer of a shape different from the space between two parallel planes. Therefore, the present paper undertook to study the propagation of SH‐wave in a transversely isotropic piezoelectric layer under the influence of a point source and overlying a heterogeneous substrate using Green's function technique. The coupled electromechanical field equations are solved with the aid of Green's function technique. Expression for displacements in both layer and substrate, scalar potential and finally the dispersion relation is obtained analytically for the case when wave propagates along the direction of layering. Numerical computations are carried out and demonstrated with the aid of graphs for six different piezoelectric materials namely PZT‐5H ceramics, Barium titanate (BaTiO₃) ceramics, Silicon dioxide (SiO₂) glass, Borosilicate glass, Cobalt Iron Oxide (CoFe₂O₄), and Aluminum Nitride (AlN). The effects of heterogeneity, piezoelectric and dielectric constants on the dispersion curve are highlighted. Moreover, comparative study is carried out taking the phase velocity for different piezoelectric materials on one hand and isotropic case on the other. Dispersion relation is reduced to well‐known classical Love wave equation with a view to illuminate the authenticity of problem. Copyright © 2017 John Wiley & Sons, Ltd.     

An improvement on the maximum number of -dominating independent sets

Erdős and Moser raised the question of determining the maximum number of maximal cliques or, equivalently, the maximum number of maximal independent sets in a graph on vertices. Since then there has been a lot of research along these lines. A -dominating independent set is an independent set such that every vertex not contained in has at least neighbors in . Let denote the maximum number of -dominating independent sets in a graph on vertices, and let . Nagy initiated the study of . In this study, we disprove a conjecture of Nagy using a graph product construction and prove that for any even we have We also prove that for any we have improving the upper bound of Nagy.     

A new substitution–diffusion based image cipher using chaotic standard and logistic maps

In this paper, we propose a new loss-less symmetric image cipher based on the widely used substitution–diffusion architecture which utilizes chaotic standard and logistic maps. It is specifically designed for the coloured images, which are 3D arrays of data streams. The initial condition, system parameter of the chaotic standard map and number of iterations together constitute the secret key of the algorithm. The first round of substitution/confusion is achieved with the help of intermediate XORing keys calculated from the secret key. Then two rounds of diffusion namely the horizontal and vertical diffusions are completed by mixing the properties of horizontally and vertically adjacent pixels, respectively. In the fourth round, a robust substitution/confusion is accomplished by generating an intermediate chaotic key stream (CKS) image in a novel manner with the help of chaotic standard and logistic maps. The security and performance of the proposed image encryption technique has been analyzed thoroughly using various statistical analysis, key sensitivity analysis, differential analysis, key space analysis, speed analysis, etc. Results of the various types of analysis are encouraging and suggest that the proposed image encryption technique is able to manage the trade offs between the security and speed and hence suitable for the real-time secure image and video communication applications.     

The Mordell-Weil bases for the elliptic curve y2 = x3 − m2x + m2

Czechoslovak Mathematical Journal - Let Dm be an elliptic curve over ? of the form y2 = x3 ? m2x + m2, where m is an integer. In this paper we prove that the two points P?1 =...