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．     

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.     

Internal Rotation of the Methyl Group in Cations of Toluene Derivatives

The potential of the internal rotation of the methyl group was determined for o-, m-, and p-fluorotoluene cations by pulsed field ionization spectroscopy. The potential of the internal rotational motion was also surveyed for other toluene derivative cations. It was found that the barrier height generally increases by ionization. The increase in the barrier height has been discussed in connection with the reduction of the internal rotational constant B by ionization. The geometrical distortion of the methyl group during the internal rotation has been suggested.     

实时实现MPEG2运动估计的DSP处理系统

本文根据ＭＰＥＧ２的图像标准与要求，利用若干大规模集成电路芯片，设计了实时实现活动图像运动估计的ＤＳＰ处理系统板，通过序列图像的测试，证明其工作正常，性能可靠，完全符合ＭＰＥＧ２的技术规范，从而为我国近期实现ＭＰＥＧ２的编解码系统、乃至ＨＤＴＶ实验系统在硬件方面打下了良好的基础。     

RATTI“R362/S”倍捻机导丝机构往复动程的分析

本文对“R362/S”倍捻机卷绕头往复导丝机构行程缩短原理进行了分析和数值计算,得出了导丝动程缩短规律。通过分析指出了一些在设计上值得我们借鉴的优点,并提出了某些改进的设想。     

产生特殊聚焦图形的二元光学元件

通过面积编码将伽博（Gabor)波带片的透过率函数的余弦分布等效为二元分布，研制了能产生各种特殊聚焦图形的二元光学元件。根据透镜聚焦的物理原理制作的二元振幅型波带片可以方便地产生多种聚焦线，给出了相应的实验结果，并讨论了改善聚焦效果的优化条件。     

Model-dependent nature of blowtorch effect on the escape and equilibration rates

We analyze the relaxation behavior of a bistable system when the background temperature profile is inhomogeneous due to the presence of a localized hot region (blowtorch) on one side of the potential barrier. Since the diffusion equation for inhomogeneous medium is model-dependent, we consider two physical models to study the kinetics of such system. Using a conventional stochastic method, we obtain the escape and equilibration rates of the system for the two physical models. For both models, we find that the hot region enhances the escape rate from the well where it is placed while it retards the escape rate from the other well. However, the value of the escape rate from the well where the hot region is placed differs for the two models while that of the escape rate from the other well is identical for both. This work, for the first time, gives a detailed report of the similarities and differences of the escape rates and, hence, exposes the common and distinct features of the two known physical models in determining the way the bistable system relaxes. Received 25 September 2001