Stochastic analysis, rough path analysis and fractional Brownian motions

 In this paper we show, by using dyadic approximations, the existence of a geometric rough path associated with a fractional Brownian motion with Hurst parameter greater than 1/4. Using the integral representation of fractional Brownian motions, we furthermore obtain a Skohorod integral representation of the geometric rough path we constructed. By the results in [Ly1], a stochastic integration theory may be established for fractional Brownian motions, and strong solutions and a Wong-Zakai type limit theorem for stochastic differential equations driven by fractional Brownian motions can be deduced accordingly. The method can actually be applied to a larger class of Gaussian processes with covariance functions satisfying a simple decay condition. Received: 11 May 2000 / Revised version: 20 March 2001 / Published online: 11 December 2001     

继承异常的一种解决方法

继承异常用来描述在并发面向对象语言中继承与并发的冲突．对继承异常做了系统的分析，给出一种新的分类．提出在一并发对象中将同步部分与顺序部分分离，生成两个对象，通过将同步代码放入一单独对象，将继承过程分为顺序部分和同步部分，这种分离大大地减少了继承异常的发生．     

掺铒光纤吸收增加光学双稳态

报道了的掺铒光纤中观测到的吸收增加非线性和无腔光学双稳运转。双稳是低功率的（亚毫瓦级）。分析了掺铒光纤吸收增加双稳态产生的机理     

｜x｜^α的Lagrange插值多项式在零点的收敛速度

S.M.Lozinskii指出了函数｜x｜基于等距节点的Lagrange插值多项式在零点的收敛速度.2000年,M.Revers把S.M.Lozinskii的结果推广到｜x｜~α(0<α1).本文考虑的是把等距节点改为修改的Chebyshev节点,从而把零点处的收敛速度从M.Revers证明的O(n-α)提高O(n-2α).     

完全单半群上同余的两种刻画

给出了完全单半群的相容组和同余结的定义,并利用它们刻画了完全单半群上的同余.     

Effect of nonlinear electrodynamics on shadows of slowly rotating black holes

In this study, we investigate the effect of nonlinear electrodynamics on the shadows of charged, slowly rotating black holes with the presence of a cosmological constant. Rather than the null geodesic of the background black hole spacetime, the trajectory of a photon, as a perturbation of the nonlinear electrodynamic field, is governed by an effective metric. The latter can be derived by analyzing the propagation of a discontinuity of the electromagnetic waveform. Subsequently, the image of the black hole and its shadow can be evaluated using the backward ray-tracing technique. We explore the properties of the resultant black hole shadows of two different scenarios of nonlinear electrodynamics, namely, the logarithmic and exponential forms. In particular, the effects of nonlinear electrodynamics on the optical image are investigated, as well as the image's dependence on other metric parameters, such as the black hole spin and charge. The resulting black hole image and shadow display rich features that potentially lead to observational implications.     

PROGRESS IN THREE-DIMENSIONALLY ORDERED SELF-ASSEMBLY OF COLLOIDAL SiO2 PARTICLES

Three-dimensionally ordered self-assembly of monodispersed colloidal SiO2 particles involving a structure with periodic alternation of refractive indices represents an advanced field of particuology, colloidal chemistry, materials science, optical physics and information science. Study on such self-assembly not only lays the foundation for the development of advanced functional materials, but also is significant in understanding the principles of nano- and micro-scele processes. Recent progress in three-dimensionally ordered self-assembly of colloidal SiO2 particles is reviewedinclusive of the authors‘‘ investigations.     

壳体结构优化及其DDDU(W)新版本

本文建立了壳体结构优化的序列二次规划模型,对八节点等参壳单元做了优化处理,扩充了通用结构优化程序DDDU(W)的功能。文末算例表明了算法的合理性与有效性。