A priori tests of a stochastic mode reduction strategy

Several a priori tests of a systematic stochastic mode reduction procedure recently devised by the authors [Proc. Natl. Acad. Sci. 96 (1999) 14687; Commun. Pure Appl. Math. 54 (2001) 891] are developed here. In this procedure, reduced stochastic equations for a smaller collections of resolved variables are derived systematically for complex nonlinear systems with many degrees of freedom and a large collection of unresolved variables. While the above approach is mathematically rigorous in the limit when the ratio of correlation times between the resolved and the unresolved variables is arbitrary small, it is shown here on a systematic hierarchy of models that this ratio can be surprisingly big. Typically, the systematic reduced stochastic modeling yields quantitatively realistic dynamics for ratios as large as 1/2. The examples studied here vary from instructive stochastic triad models to prototype complex systems with many degrees of freedom utilizing the truncated Burgers–Hopf equations as a nonlinear heat bath. Systematic quantitative tests for the stochastic modeling procedure are developed here which involve the stationary distribution and the two-time correlations for the second and fourth moments including the resolved variables and the energy in the resolved variables. In an important illustrative example presented here, the nonlinear original system involves 102 degrees of freedom and the reduced stochastic model predicted by the theory for two resolved variables involves both nonlinear interaction and multiplicative noises. Even for large value of the correlation time ratio of the order of 1/2, the reduced stochastic model with two degrees of freedom captures the essentially nonlinear and non-Gaussian statistics of the original nonlinear systems with 102 modes extremely well. Furthermore, it is shown here that the standard regression fitting of the second-order correlations alone fails to reproduce the nonlinear stochastic dynamics in this example.     

Capillary Electrophoresis Chiral Separation for Enantiomeric Purity Determination of a Basic Drug in Pharmaceutical Formulations

Capillary electrophoresis using a running buffer composed of β-cyclodextrin as the chiral selector and ethanolamine mesylate at pH 9.6 is being used to monitor the stereochemical stability of a hydrophobic drug, containing two chiral centers, in two different formulated self-emulsifying drug delivery system (SEDDS) products. The separation takes place in less than 25 min. Strategies for enhancing the method reproducibility and detection sensitivity in the lower potency formulation are presented. The results demonstrating the specificity, assay precision, recovery, linearity and range achieved during the method validation experiments are presented in this paper.Presented at: CE in the Biotechnology and Pharmaceutical Industries: 7th Symposium on the Practical Applications for the Analysis of Proteins, Nucleotides and Small Molecules, Montreal, Canada, August 12–16, 2005.     

Emden方程的Mei对称性、Lie对称性和Noether对称性

研究Emden动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Emden方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一个例子说明结果的应用. 关键词： Emden动力学方程 Mei对称性 Noether对称性 Lie对称性     

准晶体中八方晶系点群的对称性与矩阵表示

从理论上对准晶体中八方晶系各点群进行了研究.运用八方晶系各点群的极赤投影图,列出了各点群的所有对称操作;填出了固有点群822的群乘表.运用坐标变换和群论在自定义的八方坐标系中,推导出八方晶系点群所有对称操作的矩阵.这32个3×3矩阵的结构是相当简洁的,它们的矩阵元只有5种可能取值:0,±1,±2.其中2是反映八方晶系准晶体所具有的准周期性的特殊无理数.     

生化分析仪光学系统的研究与设计

光学系统是自动生化分析仪的核心部件,其性能的好坏将直接影响整机性能。根据生化分析的检测要求,通过理论分析和实验对该仪器光学系统的各个部分进行了研究和设计。实现了两种设计方案,通过实验分析选择了较优的方案。     

PVK∶DBVP掺杂体系的能量转移及发光性质的研究

研究了不同比例的PVK与齐聚PPV衍生物DBVP掺杂体系的能量转移和发光特性.通过对PVK,DBVP及PVK:DBVP掺杂体系的UV-vis,PL和PLE光谱的研究,分析了PVK与DBVP之间的能量转移过程.利用PVK在体系中类似于溶剂的分散作用,制备了结构为ITO/PEDOT/PVK:DBVP/LiF/Al的电致发光器件,研究了掺杂体系的电致发光性能.结果表明,在掺杂体系的光致发光和电致发光中,PVK的发射被有效地抑制,PVK与DBVP之间发生了非常有效的能量转移,通过调节PVK与DBVP的比例,可以获得蓝色和绿色发光,同时可以改善器件的发光性能,当PVK与DBVP的重量比为1∶2时,器件的绿色发光效率达到1·06cd/A,此时发光亮度为52cd/m2.     

Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system

For a discrete linear stochastic dynamical system, computation of the response matrix to the external action from a subspace using given observational data is examined. An algorithm is proposed and substantiated that makes it possible to improve the numerical accuracy and to reduce the amount of observational data compared to the general case where an arbitrary external action is allowed. As an illustration, a discrete system arising in the analysis of a linear stochastic dynamical continuous-time system is considered more thoroughly. Some numerical results are presented.     

2-fold and 3-fold mixing: why 3-dot-type counterexamples are impossible in one dimension

V.A. Rohlin asked in 1949 whether 2-fold mixing implies 3-fold mixing for a stationary process (ξ_i )_i2ℤ, and the question remains open today. In 1978, F. Ledrappier exhibited a counterexample to the 2-fold mixing implies 3-fold mixing problem, the socalled 3-dot system, but in the context of stationary random fields indexed by ℤ². In this work, we first present an attempt to adapt Ledrappier's construction to the onedimensional case, which finally leads to a stationary process which is 2-fold but not 3-fold mixing conditionally to the σ-algebra generated by some factor process. Then, using arguments coming from the theory of joinings, we will give some strong obstacles proving that Ledrappier's counterexample can not be fully adapted to one-dimensional stationary processes.     

运用量子约束动力学对具有耗散的量子位的追踪控制

在有限温度环境内，量子约束动力学及其追踪控制可使退相干系统的相干性稳定一段时间.约束方程产生的控制场能够按量子比特的动力学状态进行控制(量子动力学轨道的反馈控制)；依靠量子比特的这种反馈效应，可使量子位稳定在设定的时间内.同时，在量子位的稳定方面，温度扮演一种消极的角色. 关键词： 量子约束动力学 耗散量子位的控制 追踪控制 量子比特的反馈效应     

用自适应脉冲微扰引导混沌系统到周期解

用自适应脉冲微扰方法控制的系统的某个系统变量作为驱动,设计了一种自适应控制器方法对两个或多个响应混沌系统进行脉冲微扰,引导这些系统从混沌运动到低周期运动,实现同时控制多个混沌系统到不同的周期态. 当选择相同的自适应控制器输入变量实施脉冲微扰时,还可控制两个或多个混沌系统达到不同的周期态同步. 通过对R?ssler混沌系统的仿真研究证实了方法的有效性. 关键词： 混沌控制 系统参量 自适应控制器 脉冲微扰 周期态同步