The parameter uniform numerical method for singularly perturbed parabolic reaction–diffusion problems on equidistributed grids

This article presents the study of singularly perturbed parabolic reaction–diffusion problems with boundary layers. To solve these problems, we use a modified backward Euler finite difference scheme on layer adapted nonuniform meshes at each time level. The nonuniform meshes are obtained by equidistribution of a positive monitor function, which involves the second-order spatial derivative of the singular component of the solution. The equidistributing monitor function at each time level allows us to use this technique to non-linear parabolic problems. The truncation error and the stability analysis are obtained. Parameter–uniform error estimates are derived for the numerical solution. To support the theoretical results, numerical experiments are carried out.     

Synthesis and characterization of submicron-sized mesoporous aluminosilicate spheres

Mesoporous aluminosilicate spheres of 0.3–0.4 Μm diameter, with different Si/Al ratios, have been prepared by surfactant templating. Surface area of these materials is in the 510–970 m² g^-1 range and pore diameter in the 15–20 ? range.     

Synthesis and structure of a new [6.6]metacyclophane with enediyne bridges

[reaction: see text] Synthesis and structure of a novel [6.6]metacyclophane with enediyne bridges is reported.     

Synthesis of sulfur-bridged piperazinediones by reaction of 3,6-dibromo-1,4-dimethyl-2,5-piperazinedione with geminal dithiols

The reaction of several geminal dithiols with 3,6-dibromo-1,4-dimethyl-2,5-piperazinedione gave in good yields piperazinedione derivatives substituted at the 3,6-position with a geminal dithiol-bridging group. These sulfur-bridged piperazinediones formally represent derivatives of the 2,4-dithia-6,8-diaza-7,9-dioxobicyclo[3.2.2]nonane ring system. Attempts to transform these sulfur-bridged piperazinediones to 3,6-epidithiopiperazinediones by removal of the bridging group common to the sulfur functionality were unsuccessful. Studies also are reported of addition of thioacetic acid to 3,6-dimethylene-2,5-piperazinedione to give 3,6-diacetylthio-3,6-dimethyl-2,5-piperazinedione. Conversion of the 3,6-diacetylthio derivative to the epithiopiperazinedione ring system yielded a mixture of epimono- and epidithiopiperazinediones.     

Vibration of rectangular plates with time-dependent boundary conditions

A general method of solution for the vibration of rectangular plates with any type of time-dependent boundary conditions is developed by an extension of the method of Mindlin and Goodman [1]. For illustration, the problems of a plate with different time-dependent boundary conditions are solved and the closed form solutions for the transverse deflections of the plate are obtained. The non-dimensionalized transverse deflections, ($\text{w}\text{a}$) at the middle of the plate are evaluated numerically for different dimensions of the plate and different forcing functions. These are presented graphically against the non-dimensionalized time, T, for three cases and tabulated for other cases.     

Temperature dependence of the ESR spectra of Mn2+ in iron pyrite (FeS2)

The first observation of the ESR spectra of Mn²⁺, entering substitutionally for Fe²⁺ in the Van Vleck paramagnet FeS₂ (polycrystals), is reported. The data from 5 to 295 K fits the spin-Hamiltonian $\text{h}{}_{\mathrm{s}}\text{= gβ}\text{H}\text{·}\text{S}$ + $\text{[S}{}^{\mathrm{<mtext>2</mtext>}}{}_{\mathrm{z}}\text{?}\text{1}\text{3}\text{S(S + 1)] + A}\text{S}\text{·}\text{I}$, with g = 2.000 ± 0.001, A/β = ?95.0 ± 0.5 Oe and D/β varying from 50 Oe (5K) to 59 Oe (295 K). The temperature dependence of D can be described in terms of a single phonon-mode with frequency ? 145 cm^?1.