Irregularities of distribution with respect to strips

Summary A lower bound is established for the strip discrepancy of a broad class of point distributions. The bound implies unbounded strip discrepancy for equally weighted point distributions under favorable conditions. The methods of proof use notions from integral geometry.     

猜想M(2k,k+1)=3k-1+[(k-1)/2]的反例

Brualdi与Jung在[1]中研究了一类具有固定线和k的n×n矩阵上的最大跳跃数M(n,k),并提出猜想M(2k, k + 1) = 3k - 1 + [(k-1)/2].本文给出了这一猜想的两个反例．     

The mapping properties of the radiosity operator along an edge

In this article we study the radiosity operator along an edge between two adjacent half‐planes. First we show that the radiosity operator is invertible in a whole scale of anisotropic Sobolev spaces. In the absence of any shadows we are able to derive regularity properties of the solution, which depend only on the angle between the half‐planes, the reflectivity coefficients and the right‐hand side. This work can be considered as a supplement to the article of Rathsfeld (Mathematical Methods in the Applied Sciences 1999; 22 : 217–241). Copyright © 2002 John Wiley & Sons, Ltd.     

Stability Properties of Feynman's Operational Calculus for Exponential Functions of Noncommuting Operators

Stability properties of Feynman's operational calculus are addressed in the setting of exponential functions of noncommuting operators. Applications of some of the stability results are presented. In particular, the time-dependent perturbation theory of nonrelativistic quantum mechanics is presented in the setting of the operational calculus and application of the stability results of this paper to the perturbation theory are discussed.     

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.     

Integral Inequalities and Global Solutions of Semilinear Evolution Equations

A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.     

Luminescent properties of Ce in MSO4 (M: Ca, Sr and Ba) and the effect of Na co-doping

The optical properties of Ce³⁺ in CaSO₄, SrSO₄ and BaSO₄ are reported. The Ce³⁺ ion shows 4f⁰5d¹→²F_5/2,²F_7/2 luminescence in all three sulphates. Co-doping with Na⁺ does not change the local surrounding of the Ce³⁺ ion, but enhances the amount of Ce³⁺ ions built in. Under optical excitation, besides the typical Ce³⁺ doublet emission in the ultraviolet spectral region, band emission around 445 nm was observed. This band emission was not assigned to emission from a Ce³⁺ centre, but to emission from an impurity-trapped exciton. Under X-ray excitation, both Ce³⁺ emission and an emission band around 380 nm was observed. This band was assigned to emission from a self-trapped exciton.     

K_(1,n)-free图具有给定性质的[a,b]-因子的一个充分条件

图G称为K1,n-free图,如果它不含K1,n作为其导出子图.对K1,n-free图具有给定性质的[a,b]-因子涉及到最小度条件进行了研究,得到一个充分条件.     

Approximate Inverse Preconditioners for Some Large Dense Random Electrostatic Interaction Matrices

A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners of otherwise similar construction, and especially so when the preconditioners are very sparse. AMS subject classification (2000) 65F10, 65R20, 65F35, 78A30     

Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture

By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems.