Uniform fourth order difference scheme for a singular perturbation problem

Summary The numerical solution of a nonlinear singularly perturbed two-point boundary value problem is studied. The developed method is based on Hermitian approximation of the second derivative on special discretization mesh. Numerical examples which demonstrate the effectiveness of the method are presented.This research was partly supported by NSF and SIZ for Science of SAP Vojvodina through funds made available to the U.S.-Yugoslav Joint Board on Scientific and Technological Cooperation (grants JF 544, JF 799)     

Lattice-point examples for a question of Erdős

Here we establish a set of eight points in general position in the plane, i.e. no three on a line, no four on a circle, and they determine 7 distinct distances, so that, thei-th distance occursi times,i = 1, 2, , 7. The points are embedded in a triangular net, and the distances are not ordered by size or in any other way. We shall show that some known and unknown examples forn < 8 with the above properties may also be lattice points of a similar net.Research (partially) supported by the Hungarian National Foundation for Scientific Research (OTKA) grant, no. 1808.     

A fourth order method for a singular two-point boundary value problem

Recently, Chawla et al. described a second order finite difference method for the class of singular two-point boundary value problems:

Stability properties of collocation methods

Lower bounds for are given for which equidistant s-point collocation methods areA()-stable for arbitrarys.     

Adaptive boundary element methods for strongly elliptic integral equations

Summary Integral operators are nonlocal operators. The operators defined in boundary integral equations to elliptic boundary value problems, however, are pseudo-differential operators on the boundary and, therefore, provide additional pseudolocal properties. These allow the successful application of adaptive procedures to some boundary element methods. In this paper we analyze these methods for general strongly elliptic integral equations and obtain a-posteriori error estimates for boundary element solutions. We also apply these methods to nodal collocation with odd degree splines. Some numerical examples show that these adaptive procedures are reliable and effective.This work was carried out while Dr. De-hao Yu was an Alexander-von-Humboldt-Stiftung research fellow at the University of Stuttgart in 1987, 1988     

What do multistep methods approximate?

Summary Standard analysis of multistep methods for ODE's assumes the application of an initialization routine that generates the starting points. Here ak-step method is considered directly as a mappingR ^kn R ⁿ . It is shown to approximate a mapping which is expressible directly in terms of the flow of the vector field. Some useful properties of that mapping are shown and for strictly stable methods these are applied to the question of invariant circles near a hyperbolic periodic solution.     

Convolution quadrature and discretized operational calculus. I

Numerical methods are derived for problems in integral equations (Volterra, Wiener-Hopf equations) and numerical integration (singular integrands, multiple time-scale convolution). The basic tool of this theory is the numerical approximation of convolution integrals

On the generation and annealing of dangling bond defects in hydrogenated amorphous silicon

We show that, through the diffusive re-arrangement of Si-H bonds, the a-SiH lattice is able to establish thermal equilibrium between the densities of band tail trapped charge carriers and dangling bond defects. When this equilibrium is disturbed by changes in temperature, carrier injection or illumination, dangling bond defects have to be generated or annealed out via H-diffusion processes. Based on the concept of charge-induced bond breaking, we develop a mathematical formalism for the diffusive re-arrangement of Si-H bonds and show that our formalism can account for a variety of observations that have been made in the context of defect-generation and annealing experiments.     

Influence of end reflectivity on gain saturation in a planar distributed feedback laser

An approximate method for the analysis of planar-waveguide distributed-feedback lasers is extended to include a nonvanishing reflectivity at the ends of the structure. An index grating structure with parasitic losses is investigated. An expression for the small-signal gain coefficient ^0MN as a function of the output power P ^MNout normalized to the saturation power P ^s , coupling coefficient K, complex reflectivity R of end reflectors, and waveguide parameters is presented.     

缬草根化学成分的研究

本文报道了湖南花坦县产的缬草根的化学成分，用气相色谱－色谱－计算机联用和波谱技术鉴定了缬草根中的４４个组分，其中乙酸里哪醇酯，２－蒈烯，马拶铃烯，瓦伦烯，香橙烯，愈创木烯，异尼醇，乙酸金合欢酯，邻苯二甲酸二异辛酯，６，１３－二甲基－十四烷酸和２－甲基十六烷酸甲酯等化合物是在缬草根中首次发现的，对缬草根中的氨基酸和微量元素也进行了测定。