Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

A note on minimization problems and multistep methods

Summary. We use the qualitative properties of the solution flow of the gradient equation to compute a local minimum of a real-valued function . Under the regularity assumption of all equilibria we show a convergence result for bounded trajectories of a consistent, strictly stable linear multistep method applied to the gradient equation. Moreover, we compare the asymptotic features of the numerical and the exact solutions as done by Humphries, Stuart (1994) and Schropp (1995) for one-step methods. In the case of -stable formulae this leads to an efficient solver for stiff minimization problems. Received July 10, 1995 / Revised version received June 27, 1996     

Vector potential theory on nonsmooth domains in R<Superscript>3</Superscript> and applications to electromagnetic scattering

We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for L^p-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.     

Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 1996     

Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution

Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper bounds on spectral gaps. Received: 10 June 1996 / In revised form: 9 August 1996     

The Jacobian and the Ginzburg-Landau energy

We study the Ginzburg-Landau functional for , where U is a bounded, open subset of . We show that if a sequence of functions satisfies , then their Jacobians are precompact in the dual of for every . Moreover, any limiting measure is a sum of point masses. We also characterize the -limit of the functionals , in terms of the function space B2V introduced by the authors in [16,17]: we show that I(u) is finite if and only if , and for is equal to the total variation of the Jacobian measure Ju. When the domain U has dimension greater than two, we prove if then the Jacobians are again precompact in for all , and moreover we show that any limiting measure must be integer multiplicity rectifiable. We also show that the total variation of the Jacobian measure is a lower bound for the limit of the Ginzburg-Landau functional. Received: 15 December 2000 / Accepted: 23 January 2001 / Published online: 25 June 2001     

激光调Q CAI

从激光调Q速率方程出发,分析推导了激光调Q过程中,腔内光子数与工作物质内反转粒子数间的关系.再根据激光调Q的过程中,对腔Q值控制方式不同,将激光调Q技术分为:转镜调Q、声光调Q、电光调Q、饱和吸收调Q和脉冲透射式调Q.用C语言进行了激光调Q CAI软件的开发研制,获得了将文学、图形、动画和计算融为一体的,直观而生动地将调Q的理论和过程再现于屏幕的CAI课件.介绍了课件的内容、结构及其特点.     

Spline collocation for strongly elliptic equations on the torus

Summary We prove convergence and error estimates in Sobolev spaces for the collocation method with tensor product splines for strongly elliptic pseudodifferential equations on the torus. Examples of applications include elliptic partial differential equations with periodic boundary conditions but also the classical boundary integral operators of potential theory on torus-shaped domains in three or more dimensions. For odd-degree splines, we prove convergence of nodal collocation for any strongly elliptic operator. For even-degree splines and midpoint collocation, we find an additional condition for the convergence which is satisfied for the classical boundary integral operators. Our analysis is a generalization to higher dimensions of the corresponding analysis of Arnold and Wendland [4].     

QN-spaces, wQN-spaces and covering properties

The main results of the paper are as follows: covering characterizations of wQN-spaces, covering characterizations of QN-spaces and a theorem saying that Cp(X) has the Arkhangel'ski?ˇ property (α₁) provided that X is a QN-space. The latter statement solves a problem posed by M. Scheepers [M. Scheepers, Cp(X) and Arhangel'ski?ˇ's αi-spaces, Topology Appl. 89 (1998) 265-275] and for Tychonoff spaces was independently proved by M. Sakai [M. Sakai, The sequence selection properties of Cp(X), Preprint, April 25, 2006]. As the most interesting result we consider the equivalence that a normal topological space X is a wQN-space if and only if X has the property S₁(Γshr,Γ). Moreover we show that X is a QN-space if and only if Cp(X) has the property (α₀), and for perfectly normal spaces, if and only if X has the covering property (β₃).