OCCUPATION TIMES OF BALLS BY BROWNIAN MOTION WITH DRIFT

51. Introduction and Statement of ResultsLet X ~ {Xt, t 2 0} be a standajrd d-dimensional Brownian motion with drift c startedat fiXed XO ~ x:Xo ~ Wb ct, t 2 0,where Wt is the standard d--dimensional Brownian motion, c E R'(d 2 2) is a fixed vector.Denote by P:(.) the probability meajsure on the path space of X corresponding to initialstate XO = x and drift vector c, with E;(.) the corresponding expection operator. Forsimplity, we shall write Pz(.) and Ex(.) to refer to the case c ~ …     

Some new results on waiting time and busy time in M/G/1 queue

This paper considers an M/G/1 queue with Poisson rate λ > 0 and service time distribution G(t) which is supposed to have finite mean 1/μ. The following questions are first studied: (a) The closed bounds of the probability that waiting time is more than a fixed value; (b)The total busy time of the server, which including the distribution, probability that are more than a fixed value during a given time interval (0, t], and the expected value. Some new and important results are obtained by theories of the classes of life distributions and renewal process.     

Long-time Convergence of Numerical Approximations for Semilinear Parabolic Equations （ Ⅱ ）

In this article we extend ours framework of long-time convergence for numeracal approximations of semihnear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J. , 16( 1 )(2000), 1-28“, to the Gauss-Ledendre full discretization. When apply the result to the CrankNicholson finiteelement full discretization of the Navier-Stokes equations, we can remore the grid-ratio restriction of “Heywood, J. G. and Rannaeher, R., SIAM J. Numer. Anal., 27(1990), 353-384“,and weaken the stability condition on the continuous solution.     

Kinetics of thiol–ene and thiol–acrylate photopolymerizations with real‐time fourier transform infrared

We used real‐time Fourier transform infrared to monitor the conversion of both thiol and ene (vinyl) functional groups independently during photoinduced thiol–ene photopolymerizations. From these results, the stoichiometry of various thiol–ene and thiol–acrylate polymerizations was determined. For thiol–ene polymerizations, the conversion of ene functional groups was up to 15% greater than the conversion of thiol functional groups. For stoichiometric thiol–acrylate polymerizations, the conversion of the acrylate functional groups was roughly twice that of the thiol functional groups. With kinetic expressions for thiol–acrylate polymerizations, the acrylate propagation kinetic constant was found to be 1.5 times greater than the rate constant for hydrogen abstraction from the thiol. Conversions of thiol–acrylate systems of various initial stoichiometries were successfully predicted with this ratio of propagation and chain‐transfer kinetic constants. Thiol–acrylate systems with different initial stoichiometries exhibited diverse network properties. Thiol–ene systems were initiated with benzophenone and 2,2‐dimethoxy‐2‐phenylacetophenone as initiators and were also polymerized without a photoinitiator. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3311–3319, 2001     

晶化时间对ZSM-5分子筛物化性质及催化性能的影响

 考察了ZSM－5分子筛在晶化过程中的变化规律及其在苯与乙烯气相烷基化制乙苯反应中的催化性能．结果表明,当晶化时间为70h时,分子筛晶体开始出现;晶化90h时无定形物相基本消失．晶化时间从90h再延长至150h,ZSM－5分子筛晶粒的大小、形貌和体相硅铝比都基本不变,但分子筛表面的硅铝比逐渐降低．以晶化时间为90h的ZSM－5分子筛原粉为活性组元制备的催化剂,对苯与乙烯气相烷基化制乙苯反应表现出最佳的催化性能．     

Electrostatic Layer‐by‐Layer Assembly of Polycation and DNA Multilayer Films by Real‐time Surface Plasmon Resonance Technique

The assembly of alternating DNA and positively charged poly‐(dimethyldiallylammonium chloride) (PDDA) multilayer films by electrostatic layer‐by‐layer adsorption has been studied. Real time surface plasmon resonance (BIAcore) technique was used to characterize and monitor the formation of multilayer films in solution in real time continuously. The results indicate that the uniform multilayer can be obtained on the poly‐(ethylenimine) (PEI) coated substrate surface. The kinetics of the adsorption of DNA on PDDA surface was also studied by real‐time BIAcore technique, and the observed rate constant was calculated using a Langmuir model (k_obs = (1.28 ± 0.08) × 10^?2s^?1).     

Effect of Calix[4]pyrrole as Addition Reagent on Anions Separation in Capillary Zone Electrophoresis (CZE)

Calixpyrroles, as new macrocyclic receptors, have gain increasing interest in host-guest chemistry. Pioneering work in this area by Sessler and co-workers have evidenced that calix[4]pyrroles are effective anion binding agents and have used for anion binding, sensing and new anion separation technologies1, 2. In this letter, we report that calix[4]pyrroles A, B and C3,4 (Scheme 1) can serve as additives in CZE for the separa- tion of halide ions. Scheme 1 A B C When analyzing anions with…     

捷联惯导姿态更新的四子样旋转矢量优化算法研究

介绍了捷联惯导姿态更新算法中的旋转矢量算法,分析了锥运动环境下数学平台的算法漂移,提出了通过求解矛盾方程组实现四子样旋转矢量算法优化处理的新方法,并对单子样、双子样、三子样、四子样的算法漂移作了对比计算。     

Generating Replications of Chaotic Time Series

This paper addresses the problem of resampling chaotic time series. We propose a method based on resampling distances between nearest neighbours in phase space, so that the resampled time series present the original points differently positioned along the trajectory. This approach allows one to obtain time series with the same length of the original one, so that confidence intervals for Lyapunov exponents, correlation dimension and other invariants would be determined. For its generality this kind of resampling would be applicable to chaotic time series no matter the observations concern natural or life sciences. The method has been tested with common simulated chaotic systems with both clean and noisy data. Short and noisy time series, as the ones we simulated, typically occur in medicine, biology, and social sciences.     

Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties

In this paper, the problem of the robust stabilization for a class of uncertain linear systems with multiple time-varying delays is investigated. The uncertainty is nonlinear time-varying and does not require a matching condition. A memoryless state-feedback controller for the robust stabilization of the system is proposed. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, two sufficient conditions for the stability are derived. Two numerical examples are given to illustrate the proposed method.