SWKB formalism for confined quantum systems

A formalism is developed to study spatially confined one‐dimensional quantum mechanical systems in the framework of the supersymmetric Wentzel–Kramers–Brillouin (SWKB) method. The approximation technique is applied to estimate the energy eigenvalues of two confined potentials—the harmonic oscillator V(x)=x² and the screened Coulomb potential V(x)=−V₀sech²x. The results thus obtained are found to be in better agreement with the exact numerical values than are those from the ordinary WKB approach. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 267–273, 2000     

Reliable preconditioned iterative linear solvers for some numerical integrators

Implicit time‐step numerical integrators for ordinary and evolutionary partial differential equations need, at each step, the solution of linear algebraic equations that are unsymmetric and often large and sparse. Recently, a block preconditioner based on circulant approximations for the linear systems arising in the boundary value methods (BVMs) was introduced by the author. Here, some circulant approximations are compared and a further new type is considered. Numerical experiments are presented to check the effectiveness of the various approximations that can be used in the underlying block preconditioner. Copyright © 2001 John Wiley & Sons, Ltd.     

弹性基础上环形板的屈曲和过屈曲

基于von Kármán方程,本文利用打靶法系统地讨论了弹性基础上环形板的轴对称屈曲和过屈曲.     

Buckling and post-buckling of annular plates on an elastic foundation

On the basis of von Kárman equations,the axisymmetric buckling and post-bucklingof annular plates on anelastic foundation is(?)tematically discussed byusing shootingmethods.     

光波在左手材料中全折射的理论分析

根据菲涅尔公式,从理论上证明了只有在左右手系两种介质中光波才能发生全折射现象,给出了产生全折射时介质折射率应满足的条件n1=－n2,μ1=－μ2.对n2=－1的负折射率平板的成像进行了分析讨论,此负折射率平板具有透镜的作用.     

Asymptotic formulae for generalized Freud polynomials

We establish the Mehler–Heine type formulae for orthonormal polynomials with respect to generalized Freud weights. Using this type of asymptotics, we can give estimates of the value at the origin of these polynomials and of all their derivatives as well as the asymptotic behavior of the corresponding zeros.     

Personae at play. ‘Men of Mathematics’ in commentary

Mathematical writers, above all, Euclid, tend to present their theorems as decontextualized, abstract propositions, which has become the standard modus of textual presentation in theoretical mathematics. Mathematical commentators, however, provide their readers with personal names and historical facts in order to elucidate problems, provide contexts of discovery, or construct doxographies, among other things. Modern readers have used such information for the construction of histories of science. When we look at these passages, however, we see that personal names and information about mathematicians of the past can serve quite a range of different objectives, such as the strategic self-positioning of the commentator vis-à-vis the past or present of mathematics, the education of the reader, mathematical or moral, the construction of the history of the field, etc. Not only does the commentator present a persona of himself to the reader, he can also turn colleagues and predecessors into personae. This paper attempts to elucidate the practice, by offering four examples of such plays of and with personae, in Pappus, Eutocius, al-Nayrīzī, and Proclus.