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.     

An optical measurement of vortex shape at a free surface

We have proposed an optical method of vortex shape measurement based on Fourier transform profilometry (FTP) and verified it by experiment. The results of our experiment proposed in this paper show that FTP can efficiently reconstruct the vortex shape at a free surface and this method is suitable for wide use in studying such problems as liquid shear flow, wake of an object, flow behind a bluff body, and wetting angle.     

O在Au(111)表面吸附的密度泛函理论研究

应用密度泛函理论，本文系统地研究了O在Au(111)表面上的吸附能、吸附结构、功函数、电子密度和投影态密度，给出了覆盖度从0.11ML到1.0ML的范围内，O的吸附特性随覆盖度变化的规律.研究发现O的稳定吸附位为3重面心立方(fcc)洞位，O在fcc洞位的吸附能对覆盖度比较敏感，其值随着覆盖度的增加而减小；O诱导Au(111)表面功函数的变化量与覆盖度成近线性关系，原因是Au表面电子向O偏移，形成表面偶极子；O—Au的相互作用形成成键态和反键态，且反键态都被占据，造成O—Au键很弱，O吸附能较小. 关键词： 表面吸附 Au(111)表面 密度泛函理论 电子特性     

Constructing Invariant Fairness Measures for Surfaces

The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined.     

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.     

Acoustic reflection from a baffled elastic/piezoelectric plate

A finite difference/boundary integral procedure to determine the acoustic reflected pressure from a fluid-loaded bi-laminated plate is described. The bi-laminate is composed of a piezoelectric layer and an elastic layer in contact with the fluid, and is held by an acoustically hard baffle. In the numerical model, the fluid pressure at fluid/solid interface is replaced by a continuum of point sources weighted by the normal acceleration of the elastic plate, and the governing equation system is solved in the solid domain. With the normal acceleration found, the reflected pressure in the fluid is determined by an integral expression involving the Green's function. It is demonstrated that an appropriate applied voltage potential across the piezoelectric layer has the effect of cancelling either the reflected or scattered pressure of the plate at any chosen field points in the fluid. Project supported by the National Natural Science Foundation of China (No. 10172039).