A nodal coupling of finite and boundary elements

This article presents and analyzes a simple method for the exterior Laplace equation through the coupling of finite and boundary element methods. The main novelty is the use of a smooth parametric artificial boundary where boundary elements fit without effort together with a straight approximate triangulation in the bounded area, with the coupling done only in nodes. A numerically integrated version of the algorithm is also analyzed. Finally, an isoparametric variant with higher order is proposed. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 555–570, 2003     

Exact and approximate solutions to the Schrödinger equation for the harmonic oscillator with a singular perturbation

I obtain exact solutions for the quantum-mechanical harmonic oscillator with a perturbation potential which belongs to a class of polynomial functions of 1/r. I show that some of the eigenfunctions enable the calculation of expectation values in closed form and are therefore suitable trial functions for the application of the variational method to related nonsolvable problems.     

Indirect spectrophotometric determination of cyanide

A spectrophotometric method for cyanide based on its inhibition of the colour formation reaction between nickel(II) and 3-(4,5-dimethyl-2-thiazolylazo)-2,6-dihydroxybenzoic acid has been developed, and allows the determination of down to 0.1 g of cyanide. Most of the interferences can be avoided by displacement of the hydrogen cyanide using an arsine generator.     

Titanosilicates as Supports for an Enzymatic Alcoholysis Reaction

Novel [Cr^III(amp)(bipy)(Cl)] (1) (H₂amp = N-(hydroxyphenyl)salicyldimine; bipy = 2,2-bipyridyl) and [Cr^III(app)(bipy)(Cl)]⁺ (2) (H₂app = N-(hydroxyphenyl)pyridine-2-carboxaldimine; bipy = 2,2-bipyridyl) complexes have been synthesized and characterized by physico-chemical methods. Complexes 1 and 2 have been employed as catalysts in the oxidation of both saturated and unsaturated hydrocarbons using tert-butylhydroperoxide (t-BuOOH). The significance of the results with respect to oxo-functionalization of C-H bonds both in unsaturated and saturated hydrocarbons is noted.     

Some remarks on the homogenization of the dam problem

The homogenization of the dam problem is discussed in the general weak formulation by means of the technique of correctors. In the two special cases of horizontal layers and of the isotropic coefficients with separated variables the problem is solved. However, in general, the unsaturated region is not stable for the homogenization, as a counterexample by Alt shows.