Spectral corrections for Sturm–Liouville problems

The numerical solution of the Sturm–Liouville problem can be achieved using shooting to obtain an eigenvalue approximation as a solution of a suitable nonlinear equation and then computing the corresponding eigenfunction. In this paper we use the shooting method both for eigenvalues and eigenfunctions. In integrating the corresponding initial value problems we resort to the boundary value method. The technique proposed seems to be well suited to supplying a general formula for the global discretization error of the eigenfunctions depending on the discretization errors arising from the numerical integration of the initial value problems. A technique to estimate the eigenvalue errors is also suggested, and seems to be particularly effective for the higher-index eigenvalues. Numerical experiments on some classical Sturm–Liouville problems are presented.     

Approximation inL 2 Sobolev spaces on the 2-sphere by quasi-interpolation

In this article we consider a simple method of radial quasi-interpolation by polynomials on the unit sphere in ℝ³, and present rates of covergence for this method in Sobolev spaces of square integrable functions. We write the discrete Fourier series as a quasi-interpolant and hence obtain convergence rates, in the aforementioned Sobolev spaces, for the discrete Fourier projection. We also discuss some typical practical examples used in the context of spherical wavelets.     

Repolarization studies in amorphous and polycrystalline silicon

A procedure has been developed to extract qualitative and quantitative information on the muonium fractions, in particular the Mu^* fraction, in polycrystalline and amorphous materials from their longitudinal field repolarization curves. Preliminary results for amorphous silicon suggests that both the Mu^* and Mu^* fractions here are generally lower than in crystalline silicon at temperatures below 200K, but the Mu^* fraction may survive to room temperature in this disordered host.     

The enthalpy of formation of tungsten thiotetrafluoride

The enthalpy of hydrolysis of solid tungsten thiotetrafluoride, WF(in4)S, in aqueous sodium hydroxide solution is -528.2 kJ mo1^-1. Hence its standard enthalpy of formation has been calculated to be -1150.5 kJ mo1^-1.     

Canonical basis linearity regions arising from quiver representations

In this paper we show that there is a link between the combinatorics of the canonical basis of a quantized enveloping algebra and the monomial bases of the second author [Math. Z. 237 (2001) 639] arising from representations of quivers. We prove that some reparametrization functions of the canonical basis, arising from the link between Lusztig's approach to the canonical basis and the string parametrization of the canonical basis, are given on a large cone by linear functions arising from these monomial bases for a quantized enveloping algebra.     

Finite generation of Ext for a generalization of D-Koszul algebras

In this paper we study the finite generation of Ext-algebras of a class of algebras called δ-resolution determined algebras. We characterize the δ-resolution determined algebras which are monomial algebras. If Λ is a graded algebra such that the associated monomial algebra is δ-resolution determined, we classify when the Ext-algebra of Λ is finitely generated.     

Shakedown analyses for rolling and sliding contact problems

There is a range of problems where repeated rolling and sliding contact occurs over a half space of an elastic–perfectly plastic material. For such problems shakedown and limit analysis provide significant advantages over other forms of analysis when a global understanding of deformation behaviour is required. In this paper, a recently developed numerical upper bound method, the Linear Matching Method (LMM), for shakedown analyses is applied to the solution of a problem previously considered by Ponter et al. [Ponter, A.R.S., Hearle, A.D., Johnson, K.L., 1985. J. Mech. Phys. Solids 33 (4), 339–362] for a moving Hertzian contact, with sliding friction. This semi-analytic solution is an upper bound based on certain specific kinematic assumptions. We show that the Ponter, Hearle and Johnson solution is a reasonable approximate solution for a circular contact area but is less accurate for an elliptic contact area. For an elliptic contact area LLM solutions converge to the line contact solution. The effect of the non-coincidence of the direction of travel and slide is also investigated.     

Ionic potential analysis of RHEED rocking curves from fluoride structures

Rocking curves of reflection high energy electron diffraction from MnF₂ and CaF₂(1 1 1) surfaces have been calculated with ionic scattering potentials. The potentials were derived from tabulated X-ray scattering factors and expressed in the Doyle-Turner representation. The Coulomb potential of the ions was introduced into the calculations of diffracted intensity using dynamical diffraction theory. Comparison of the calculated and measured rocking curves for CaF₂(1 1 1) surface confirmed that it is bulk terminated; the correction to volume average potential was found to be 1.1 eV (much less than when using atomic potentials). Analysis of the rocking curves from ultra-thin MnF₂ layers on CaF₂(1 1 1) indicated that MnF₂ inherits the cubic lattice of fluorides up to a thickness of three molecular layers.     

Recent advances in electrochemical sensors based on chiral and nano-sized imprinted polymers

General scheme of enantiomeric molecular imprinting. Reprinted from [21^?] with permission from Elsevier.

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