A note on quaternion matrices and split quaternion matrix pencils

In this paper, localization theorems for left and right eigenvalues of a quaternion matrix are presented. Some differences between quaternion matrices and split quaternion matrices are summarized. A counter example for Gerschgorin theorems for left and right eigenvalues of a split quaternion matrix is given. Finally, a method for finding right eigenvalues of a split quaternion matrix pencil is presented.     

AC conductivity and dielectric behavior of bulk Furfurylidenemalononitrile

AC conductivity and dielectric behavior for bulk Furfurylidenemalononitrile have been studied over a temperature range (293–333 K) and frequency range (50–5×10⁶ Hz). The frequency dependence of ac conductivity, σ_ac, has been investigated by the universal power law, σ_ac(ω)=Aω^s. The variation of the frequency exponent (s) with temperature was analyzed in terms of different conduction mechanisms, and it was found that the correlated barrier hopping (CBH) model is the predominant conduction mechanism. The temperature dependence of σ_ac(ω) showed a linear increase with the increase in temperature at different frequencies. The ac activation energy was determined at different frequencies. Dielectric data were analyzed using complex permittivity and complex electric modulus for bulk Furfurylidenemalononitrile at various temperatures.     

Non-Autonomous Evolution Equations on Nonsmooth Domair

The solution of a stationary boundary value problem on a domain with conical points has singularities near these points. Here we first consider existence results in appropriate weighted Sobolev spaces in order to incorporate the singularities. We secondly use these results to prove existence, uniqueness and regularity of solutions of non-autonomous second order evolution equations on such domains.     

New ordered MAX phase Mo_2 TiAlC_2: Elastic and electronic properties from first-principles

First-principles computation on the basis of density functional theory(DFT) is executed with the CASTEP code to explore the structural, elastic, and electronic properties along with Debye temperature and theoretical Vickers' hardness of newly discovered ordered MAX phase carbide Mo_2TiAlC_2. The computed structural parameters are very reasonable compared with the experimental results. The mechanical stability is verified by using the computed elastic constants. The brittleness of the compound is indicated by both the Poisson's and Pugh's ratios. The new MAX phase is capable of resisting the pressure and tension and also has the clear directional bonding between atoms. The compound shows significant elastic anisotropy. The Debye temperature estimated from elastic moduli(B, G) is found to be 413.6 K. The electronic structure indicates that the bonding nature of Mo_2TiAlC_2 is a mixture of covalent and metallic with few ionic characters. The electron charge density map shows a strong directional Mo–C–Mo covalent bonding associated with a relatively weak Ti–C bond.The calculated Fermi surface is due to the low-dispersive Mo 4d-like bands, which makes the compound a conductive one.The hardness of the compound is also evaluated and a high value of 9.01 GPa is an indication of its strong covalent bonding.     

Amplitude equation for the stochastic reaction‐diffusion equations with random Neumann boundary conditions

In this paper, we consider a quite general class of reaction‐diffusion equations with cubic nonlinearities and with random Neumann boundary conditions. We derive rigorously amplitude equations, using the natural separation of time‐scales near a change of stability and investigate whether additive degenerate noise and random boundary conditions can lead to stabilization of the solution of the stochastic partial differential equation or not. The nonlinear heat equation (Ginzburg–Landau equation) is used to illustrate our result. Copyright © 2015 John Wiley & Sons, Ltd.     

A collocation method of lines for two‐sided space‐fractional advection‐diffusion equations with variable coefficients

We present the method of lines (MOL), which is based on the spectral collocation method, to solve space‐fractional advection‐diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the SFADEs consist of both left‐ and right‐sided fractional derivatives. To do so, we begin by introducing a new set of basis functions with some interesting features. The MOL, together with the spectral collocation method based on the new basis functions, are successfully applied to the SFADEs. Finally, four numerical examples, including benchmark problems and a problem with discontinuous advection and diffusion coefficients, are provided to illustrate the efficiency and exponentially accuracy of the proposed method.     

Role of recording geometry in the performance of spectral diversity filters with spherical beam volume holograms

We present experimental demonstrations of spectral diversity filters with spherical beam volume holograms for multimodal multiplex spectroscopy. Major properties of filters under diffuse-light illumination are discussed. The comparisons of spectral diversity between the transmission geometry holograms and the reflection geometry holograms are also studied. The results show that there is a trade-off between the degree of the spatial coherence of the source and the spectral diversity of the filter. We also conclude that the reflection geometry holograms have better spectral diversity and less sensitivity to the spatial coherence of the source.     

Analytical design of photonic band-gap fibers and their dispersion characteristics

The paper essentially deals with the analysis of photonic band-gap fibers in analogy with the electron wave motion in periodic crystal lattice. As such, the analyses are based on Bloch formulation. The dispersion characteristics of such fibers are presented by considering some illustrative values of design parameters. The effect of design parameters on the dispersion characteristics is also presented in terms of the variation of widths of allowed and forbidden bands of band-gap fibers. It is found that the number of allowed bands increases with the increase in difference between refractive indices of different layers. Further, widths of the allowed and forbidden bands increase with the increase in layer thickness.