Uniformly convergent difference schemes for singularly perturbed parabolic diffusion-convection problems without turning points

We consider first the initial-boundary value problem for the parabolic equation

Biological generation of tritiated vitamin D3 metabolites and their purification by high-performance liquid chromatography

Summary A simple, reproducible method for the biological synthesis of tritiated 24,25-dihydroxycholecalciferol, 25,26-dihydroxycholecalciferol and 1,25-dihydroxycholecalciferol is described. Kidney homogenates from both vitamin D deficient and replete chicks were usedin vitro to generate these dihydroxylated metabolites using 25 (23,24-³H) hydroxycholecalciferol as the substrate. Tritiated products were purified by Sephadex LH 20 chromatography followed by high-performance liquid chromatography; the identity of each metabolite was established by chromatography with authentic crystalline preparations.Presented at the Symposium organised by the Chromatography Discussion Group, held at Hatfield Lodge on 29 November 1979.     

Differential inhibition of postnatal brain,spinal cord and body growth by a growth hormone antagonist

Background  

Growth hormone (GH) plays an incompletely understood role in the development of the central nervous system (CNS). In this study, we use transgenic mice expressing a growth hormone antagonist (GHA) to explore the role of GH in regulating postnatal brain, spinal cord and body growth into adulthood. The GHA transgene encodes a protein that inhibits the binding of GH to its receptor, specifically antagonizing the trophic effects of endogenous GH.     

Single on-chip gold nanowires for electrochemical biosensing of glucose

The development of glucose diagnostic devices with low detection limits is of key importance in diabetes-related research. New highly sensitive sensors are required for non-invasive detection of glucose in bodily fluids, other than blood, and an electrochemical sensor based on a single gold nanowire for rapid, reliable and quantitative detection of low glucose concentrations (10 μM-1 mM), is presented in this paper. Single gold nanowire devices are fabricated at silicon chip substrates using a hybrid electron beam-photolithography approach. Critical dimensions of the nanowires are characterised using a combination of scanning electron and atomic force microscopies. Fabricated nanowire devices are characterised by direct electrical probing and cyclic voltammetry to explore functionality. The voltammetric detection of glucose was performed using ferrocene monocarboxylic acid as an oxidising mediator in the presence of glucose oxidase. The biosensor can be applied to the quantification of glucose in the range of 10 μM-100 mM, with an extremely high sensitivity of 7.2 mA mM(-1) cm(-2) and a low detection limit of 3 μM (S/N = 3). The sensor demonstrated high selectivity towards glucose with negligible interference from other oxidizable species including uric acid, ascorbic acid, mannose, fructose, salicylic acid (Aspirin) and acetaminophen (Paracetamol).     

Transfer measurements for the Ti+Ni systems at near barrier energies

Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies. Coupled channel calculations incorporating couplings to 2⁺ and 3⁻ states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer were carried out for ^46,48Ti+⁶¹Ni systems. The present paper gives the results of these studies.     

A finite element method for a singularly perturbed boundary value problem

Summary We examine the problem:u+a(x)u–b(x)u=f(x) for 0<x<1,a(x)>0,b(x)>, ² = 4>0,a, b andf inC ² [0, 1], in (0, 1],u(0) andu(1) given. Using finite elements and a discretized Green's function, we show that the El-Mistikawy and Werle difference scheme on an equidistant mesh of widthh is uniformly second order accurate for this problem (i.e., the nodal errors are bounded byCh ², whereC is independent ofh and ). With a natural choice of trial functions, uniform first order accuracy is obtained in theL (0, 1) norm. On choosing piecewise linear trial functions (hat functions), uniform first order accuracy is obtained in theL ¹ (0, 1) norm.     

L 1 andL ∞ Uniform convergence of a difference scheme for a semilinear singular perturbation problem

Summary A nonlinear difference scheme is given for solving a semilinear singularly perturbed two-point boundary value problem. Without any restriction on turning points, the solution of the scheme is shown to be first order accurate in the discreteL ¹ norm, uniformly in the perturbation parameter. When turning points are excluded, the scheme is first order accurate in the discreteL norm, uniformly in the perturbation parameter.Partly supported by the Arts Faculty Research Fund of University College, Cork     

Scaled discrete derivatives of singularly perturbed elliptic problems

Numerical approximations to the solution of a singularly perturbed elliptic convection–diffusion problem in two space dimensions are generated using a monotone finite difference operator on a tensor product of piecewise‐uniform Shishkin meshes. The bilinear interpolants of these numerical approximations are parameter‐uniformly convergent to the solution of the continuous problem, in the pointwise maximum norm. In this article, discrete approximations to the first derivatives of the solution are shown to be globally first‐order (up to logarithmic factors) uniformly convergent, when the errors are scaled within the analytical layers of the continuous problem. Numerical results are presented to illustrate the theoretical error bounds established in an appropriated weighted C¹–norm. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 225–252, 2015