数字技术与科技进步

本文讨论并提出数字技术与数学科学的内在联系 .并根据实际的分析和研究 ,认为数字化技术只是信息化促进科技发展的一个阶段 ,尽管数字技术已经并将继续推动科技和生产力的发展速度     

The Likelihood of the Parameters of a Continuous Time Vector Autoregressive Model

This paper provides a method of constructing the likelihood function of the parameters of a continuous time vector autoregressive model on the basis of discrete data without requiring the restrictions extant methods impose on the data that are capable of being rejected by a statistical test. In particular, the method does not rely on a steady-state assumption that can rule out unit root processes; it allows for weak assumptions on the innovations; and it allows for a mixture of skip-sampled and temporally-aggregated data. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ergodic Properties of the Non-Markovian Langevin Equation

We discuss the dissipative dynamics of a classical particle coupled to an infinitely extended heat reservoir. We announce a number of results concerning the ergodic properties of this model. The novelty of our approach is that it extends beyond Markovian dynamics to the case where the Langevin equation is driven by colored noise. Our method works in arbitrary space dimension, and for fully nonlinear systems.     

On computing average cost optimal policies with application to routing to parallel queues

The Approximating Sequence Method for computation of average cost optimal stationary policies in denumerahle state Markov decision chains, introduced in Sennott (1994), is reviewed. New methods for verifying the assumptions are given. These are useful for models with multidimensional state spaces that satisfy certain mild structural properties. The results are applied to four problems in the optimal routing of packets to parallel queues. Numerical results are given for one of the models.     

Hydrophobic guar gum derivatives prepared by controlled grafting processes

Introduction of polyalkoxyalkyleneamide grafts to guar gum produces a new water soluble guar derivative. Modification of either guar gum or hydroxyopropyl guar is achieved in a three‐step process: carboxymethylation with sodium chloroacetate, esterification with dimethyl sulfate (DMS) and amidation with a series of polyalkoxyalkyleneamines. The process was followed using infrared spectroscopy; the grafted guar derivatives were characterized using ¹H NMR. A series of hydroxypropyl guar (HPR) derivatives with degrees of carboxymethylations ranging from 0.2–0.3 were modified with polyalkoxyalkyleneamines with molecular weights ranging from 300 to 3000. The ratio of oxypropylene to oxoethylene units in the polyalkoxyalkyleneamines was varied from 9/1 to 8/58 to adjust the hydrophobicity of the grafts. Aqueous solutions of the graft copolymers exhibit viscosities one to two orders of magnitude lower than the corresponding solutions of the parent guar gum. Copyright © 2007 John Wiley & Sons, Ltd.     

Cost-Effective Migration from Sub-Lambda to Wavelength-Based Metro Networks

This article will discuss the importance of hybrid coexistence of sub-lambda grooming with wavelength-based services for driving down costs and maximizing the use of metro bandwidth, as well as enabling next-generation lambda-based services. The article will also address migration to all optical metro networks.     

Acousto-optic modulation in magnetised diffusive semiconductors

The modulation of an intense electromagnetic beam induced by the acousto-optic (AO) effect has been analysed in a transversely magnetised semiconductor-plasma medium. The effect of carrier diffusion on the threshold field and gain profile of the modulated wave has been extremely investigated using coupled mode theory. The origin of the AO interaction is assumed to lie in the induced nonlinear diffusion current density of the medium. By considering the modulation process as a four wave parametric interaction an expression for effective third-order AO susceptibility describing the phenomena has been deduced. The modulation is greatly modified by propagation characteristics such as dispersion and diffraction due to dielectric relaxation of the acoustic mode. The threshold pump field and the steady state growth rates are estimated from the effective third-order polarisation in the plasma medium. Analytical estimation reveals that in the presence of enhanced diffusion due to excess charge carriers the modulated beam can be effectively amplified in a dispersionless acoustic wave regime. The presence of an external dc magnetic field is found to be favourable for the onset of diffusion induced modulational amplification of the modulated wave in heavily doped regime. Received 5 November 2001     

On the rate of convergence to equilibrium in the Becker-Döring equations

We provide an explicit rate of convergence to equilibrium for solutions of the Becker-Döring equations using the energy/energy-dissipation relation. The main difficulty is the structure of equilibria of the Becker-Döring equations, which do not correspond to a Gaussian measure, such that a logarithmic Sobolev-inequality is not available. We prove a weaker inequality which still implies for fast decaying data that the solution converges to equilibrium as e^−ct1/3.     

基于半导体光放大器交叉增益调制(SOA-XGM)波长变换器仿真研究

本文在PTDS(Photonic Transimission Design Suite)软件仿真平台上对基于半导体光放大器交叉增益调制(SOA-XGM)的波长变换器的变换特性作了仿真实验研究,仿真并分析了输入信号光功率、输入探测光功率、偏置电流和SOA的结构参量等因素对变换信号的消光比(ER)、Q值及误码率(BER)的影响关系.研究结果对优化设计SOA-XGM波长变换器有一定的参考价值.