可交换随机变量序列的随机极限定理

本文讨论了可交换随机变量序列{X_n:n≥1}的极限定理,得到了可交换随机变量序列的随机强大数律及加权和定理,并推广了文[4]中的结果.     

Super-Brownian motion with reflecting historical paths. II. Convergence of approximations

We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([1]) converges in probability to the “super-Brownian motion with reflecting historical paths.” This solves an open problem posed in [1], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [1] for all subsequential limits–they obviously hold for the unique limit found in the present paper.Mathematics Subject Classification (2000): Primary 60H15, Secondary 35R60Supported in part by NSF Grant DMS-0071486, Israel Science Foundation Grants 12/98 and 116/01 - 10.0, and the U.S.-Israel Binational Science Foundation (grant No. 2000065).     

Formula 1 – A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students

In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple^®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.This revised version was published online in September 2005 with corrections to the Cover Date.     

Quadratic Integrals of Motion for the Systems of Identical Particles

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in Hamilton-Jacobi equation is clarified.     

从一道运动学题目的求解谈坐标系选取的重要性

通过比较一道典型运动学题目的近似求解方法与精确求解方法，探讨坐标系选取对研究曲线运动的重要性．     

Asymptotic Methods Applied to Contact Problems

Asymptotic methods for contact problems are expounded. Some typical integral equations are considered     

背景光光伏效应对屏蔽-光伏空间孤子的影响

在光伏晶体两端外加一恒定的直流偏压，背景光的光伏效应对形成屏蔽-光伏孤子的空间电荷场没有影响，但对晶体中的电流有影响.如果外电源的电动势是恒定的，则背景光的光伏效应与外电路的电阻协同起作用，可以通过晶体两端的电压降影响晶体中的空间电荷场，进而影响空间孤子的宽度.在一定的条件下甚至可以实现亮、暗孤子的转换. 关键词： 屏蔽-光伏 空间孤子 孤子宽度 亮暗孤子转换     

神经网络在大型复杂武器装备质量综合评价排序中的应用

从大型复杂武器装备系统的具体特点出发,运用基于神经网络的评价方法,构建了大型复杂武器装备质量综合评价模型。实证分析的结果表明该方法得出的结果与实际情况相符。     

Quantum information processing in optical images

Optical images can be used to transport, store and process information in a parallel way. We discuss different results obtained in the domain of ‘quantum imaging’, aiming at exploiting at the same time the quantum properties of optical images and their intrinsic parallelism. We define the notion of standard quantum limit (SQL) in optical resolution, set by the quantum noise of usual coherent light, and show that it can be much lower than the diffraction limit. We also prove that this limit can be circumvented by especially designed nonclassical and multimode light. We present an experiment showing that OPOs oscillating inside an exactly confocal cavity actually produce such transverse multimode nonclassical light. We finally describe another experiment which has surpassed the SQL in the case of beam positioning, both in the 1D and 2D cases.     

The influence of temperature gradients on the kinetic boundary layer problem for a condensing droplet

We extend an earlier method for solving kinetic boundary layer problems to the case of particles moving in aspatially inhomogeneous background. The method is developed for a gas mixture containing a supersaturated vapor and a light carrier gas from which a small droplet condenses. The release of heat of condensation causes a temperature difference between droplet and gas in the quasistationary state; the kinetic equation describing the vapor is the stationary Klein-Kramers equation for Brownian particles diffusing in a temperature gradient. By means of an expansion in Burnett functions, this equation is transformed into a set of coupled algebrodifferential equations. By numerical integration we construct fundamental solutions of this equation that are subsequently combined linearly to fulfill appropriate mesoscopic boundary conditions for particles leaving the droplet surface. In view of the intrinsic numerical instability of the system of equations, a novel procedure is developed to remove the admixture of fast growing solutions to the solutions of interest. The procedure is tested for a few model problems and then applied to a slightly simplified condensation problem with parameters corresponding to the condensation of mercury in a background of neon. The effects of thermal gradients and thermodiffusion on the growth rate of the droplet are small (of the order of 1%), but well outside of the margin of error of the method.