Correction of eigenvalues estimated by the Legendre–Gauss Tau method

It is known that the accuracy in estimating a large number of eigenvalues deteriorates when the standard numerical methods are applied, because of the sharp oscillatory behavior of the corresponding eigenfunctions. One method which has proved to be efficient in treating such problems is the Legendre–Gauss Tau method. In this paper we present an exponentially fitted version of this method and we develop practical formulae to correct the estimated eigenvalues.     

Nonsmooth analysis of doubly nonlinear evolution equations

In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional, for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a time-discretization scheme with variational techniques. Finally, we discuss an application to a material model in finite-strain elasticity.     

Homogenization of spatially dispersive metamaterial arrays in terms of generalized electric and magnetic polarizations

An anisotropic homogenization theory for spatially dispersive periodic arrays is developed, based on the microscopic Maxwell equations, that yields causal, macroscopic permittivities, and inverse permeabilities for the fundamental Floquet modes of the arrays. (Macroscopic magnetoelectric coefficients are not required.) Reality conditions, reciprocity relations, passivity conditions, and causality relations are derived for these spatially dispersive macroscopic constitutive parameters. A significant feature of the formulation is that the macroscopic permittivities and permeabilities reduce to their anisotropic-continuum definitions in terms of ordinary macroscopic averages at the low spatial and temporal frequencies. In addition, diamagnetic metamaterial arrays require no special considerations or modifications to accommodate their unusual characteristics. A numerical example of a 2D array comprised of circular–cylinder inclusions is given that confirms the theoretical results for the computed electric and magnetic or diamagnetic macroscopic polarizations.     

Regularity and perturbation results for mixed second order elliptic problems

We study a mixed boundary value problem for elliptic second order equations obtaining optimal regularity results under weak assumptions on the data. We also consider the dependence of the solution with respect to perturbations of the boundary sets carrying the Dirichlet and the Neumann conditions.     

The busy period of an M/M/1 queue with balking and reneging

It has been shown by (R.O. Al-Seedy, A.A. El-Sherbiny, S.A. El-Shehawy, S.I. Ammar, Transient solution of the M/M/c queue with balking and reneging, Comput. Math. Appl. 57 (2009) 1280–1285) that a generating function technique can be successfully applied to derive the transient solution for an M/M/c queueing system. In this paper, we further illustrate how this technique can be used to obtain the busy period density function of an M/M/1 queue with balking and reneging. Finally, numerical calculations are presented.     

Interplay of negative pressure and hydrogen chemical effects in CeRhSn from first principles

Investigations within the local spin density functional theory (LSDF) of the intermetallic hydride system CeRhSnH_x were carried out for discrete model compositions in the range 0.33 ≤x_H ≤ 1.33 with the purpose of assessing the change of the cerium valence state in the neighborhood of the experimental hydride composition, CeRhSnH_0.8. In agreement with experiment, the analyses of the electronic and magnetic structures and of the chemical bonding properties point to trivalent cerium for 1 ≤x_H ≤ 1.33. In contrast, for lower hydrogen amounts the hydride system stays in an intermediate-valent state for cerium, like in CeRhSn. The influence of the insertion of hydrogen is addressed from both the volume expansion and chemical bonding effects. The latter are found to have the main influence on the change of Ce valence character. Spin polarized calculations point to a finite magnetic moment carried by the Ce 4f states; its magnitude increases with x_H in the range 1 ≤x_H ≤ 1.33.     

Assessment of Environmental Quantitative Variation of Diosgenin in Fenugreek Seeds via High-Performance Thin-Layer Chromatography Method

JPC – Journal of Planar Chromatography – Modern TLC - Fenugreek is one of the oldest medicinal plants known by mankind. The aim of this study is to evaluate the effect of environmental...     

Synthesis of Selenium(0) and Zinc(II) Biomolecules in Nano-Structured Forms as New Antioxidant Agents: Chemical and Biological Studies

Russian Journal of General Chemistry - In this paper, two new complexes of selenium caffeine, [Se(Caf)4], and zinc α-tocopherol, [Zn(α-Tpl)2(NO3)2], are synthesized. The structures of...