广义C-R组的性质及两个边值问题

本文考虑广义C-R组^[1](H)的解f=u iv jw∈C^2的一些性质，提出与之相关的两个边值问题，用积分方程方法和调和函数性质证明了边值问题解的存在唯一性，并写出解的积分表达式．     

A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

关于Banach空间中凸泛函的广义次梯度不等式

本文在前人^[1,2]的基础之上，以凸泛函的次梯度不等式为工具，将Jensen不等式推广到Banach空间中的凸泛函，导出了Banach空间中的Bochner积分型的广义Jensen不等式，给出其在Banach空间概率论中某些应用，从而推广了文献[3—6]的工作．     

A thermodynamic approach with internal variables using Lagrange formalism. Part I: General framework

We present some reflections on the application of the Lagrangian formalism for continuous media locally uniform subjected to internal irreversible evolutions. The Lagrangian density, defined as the time derivative of a non-equilibrium thermodynamic potential, [Thermodynamics of Relaxation Processes using Internal variables within a Lagrange-formalism. P. Germain’s Anniversary Volume 2000. Contiuum Thermomechanics: the Art and Science of Modeling Matter’s Behaviour, 2000], contains all the symmetry properties of the system. The generalised Lagrange co-ordinates correspond to the state and internal variables of the time derivative of the generalised Gibbs potential. The latter being used within the framework of the De Donder’s method, must also account for the memory effect of the physical medium.This first part is devoted to the thermodynamic framework called the distribution of non-linear relaxations approach (DNLR) developed by C. Cunat on the basis of the generalised Gibbs’ relation.     

Fourier-Feynman transform, convolution and first variation

We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral. This revised version was published online in June 2006 with corrections to the Cover Date.     

On topological properties of the Hartman-Mycielski functor

We investigate some topological properties of a normal functorH introduced earlier by Radul which is some functorial compactification of the Hartman-Mycielski construction HM. We prove that the pair (H X, HMY) is homeomorphic to the pair (Q, σ) for each nondegenerated metrizable compactumX and each denseσ-compact subsetY.     

Effects of poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] on the charge distributions of low‐density polyethylene/polystyrene blends

The effect of the triblock copolymer poly[styrene‐b‐(ethylene‐co‐butylene)‐b‐styrene] (SEBS) on the formation of the space charge of immiscible low‐density polyethylene (LDPE)/polystyrene (PS) blends was investigated. Blends of 70/30 (wt %) LDPE/PS were prepared through melt blending in an internal mixer at a blend temperature of 220 °C. The amount of charge that accumulated in the 70% LDPE/30% PS blends decreased when the SEBS content increased up to 10 wt %. For compatibilized and uncompatibilized blends, no significant change in the degree of crystallinity of LDPE in the blends was observed, and so the effect of crystallization on the space charge distribution could be excluded. Morphological observations showed that the addition of SEBS resulted in a domain size reduction of the dispersed PS phase and better interfacial adhesion between the LDPE and PS phases. The location of SEBS at a domain interface enabled charges to migrate from one phase to the other via the domain interface and, therefore, resulted in a significant decrease in the amount of space charge for the LDPE/PS blends with SEBS. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2813–2820, 2004     

X波段六腔渡越管振荡器的高频特性研究

 从麦克斯韦方程出发，采用时域有限差分法（FDTD）和离散傅里叶变换（DFFT）相结合的方法，通过数值计算得出了六腔开放式谐振腔中前四个谐振频率和场分布，计算出的谐振频率与实验测量结果基本相同。比较了开放腔和封闭腔谐振频率，验证了TEM波吸收边界条件，并在实际编程计算中得以应用。计算结果为六腔渡越管振荡器的机理研究提供了依据。     

非均匀网格时域伪谱算法在超宽带技术中的应用

 与传统时域有限差分算法相比，采用以伪谱方法离散Maxwell微分方程为基础的时域伪谱(PSTD)算法计算大的电尺度电磁场时域问题，将大大提高计算效率，降低内存需求。为了拓宽PSTD算法的应用，近年来，基于网格插值方法的非均匀时域伪谱算法得到了发展。研究的重点是算法中非均匀网格技术的实现及其在时域瞬态脉冲电磁场模拟和高功率超宽带脉冲技术方面的应用。以高斯脉冲为激励源，用该算法计算了多层介质的反射和透射，并通过超宽带脉冲穿墙实验对这一方法的应用进行了验证。模拟和实验结果具有较好的一致性。     

超短脉冲贝塞尔光束的非近轴效应对传输的影响

 对超短脉冲贝塞尔光束在近轴近似和非近轴情况下自由空间中的传输作了研究。结果表明，其空间波形在传输中保持贝塞尔形状不变，不受非近轴效应影响；然而当空间参数较大时，非近轴效应影响超短脉冲贝塞尔光束的时间波形。