Martingale property of empirical processes

It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.

     

Logarithmic asymptotics of solutions of the large deviation problem for the boltzmann equation with small transfer of momentum

For the Boltzmann equation with small transfer of momentum, we derive a system of nonlinear integral-differential equations describing the logarithmic asymptotics of the solution to the Cauchy problem in the domain at the distanceO(1) from the support of the initial condition.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 73–94, July, 1998.This research was partially supported by INTAS-RFBR under grant No. 95-91 in the case of the first author, and by INTAS under grant No. 96-0698 in the case of the second author.     

HPLC法测定阿奇霉素葡萄糖注射液中阿奇霉素的含量

利用高效液相色谱法，以VP-ODS型色谱柱，乙腈-异丙醇-水-氨水（60：25：15：0.1)为流动相，于210nm波长处测定了阿奇霉素葡萄糖注射液中阿奇霉素葡萄糖注射液中阿奇霉素的含量。阿奇霉素的浓度在0.75-1.75mg/mL线性关系良好，线性方程的A=881910.4c-16208.2，相关系数r=0.9999。阿奇霉素的平均回收率为99.59%，测定结果的相对标准偏差为1.31%。     

股票市场监管策略的一个随机模型

研究了股市在一段有可能给社会造成危害的上涨行情中，管理者监管股市的问题＋根据股市的运行规律，建立了一个随机最优化模型，讨论了参数对解的影响，并得出了一些对股市监管有意义的结论．     

Measurement of small-signal and large-signal responses of packaged laser modules at high temperature

In this paper, the pulsed injection method is extended to measure the chip temperature of various packaged laser modules, such as the DFB laser modules, the FP laser modules, and the EML laser modules. An optimal injection condition is obtained by investigating the dependence of the lasing wavelength on the width and period of the injection pulse in a relatively wide temperature range. The small-signal frequency responses and large-signal performances of packaged laser modules at different chip temperature are measured. The adiabatic small-signal modulation characteristics of packaged LD are first extracted. In the large-signal measurement, the effects of chip temperature, bias current and driving signal on the performances of the laser modules are discussed. It has been found that the large-signal performances of the EML modules depend on the different red-shift speeds of the DFB and EAM sections as chip temperature varying, and the optimal characteristics may be achieved at higher temperature.     

ECR-SFC轴向注入系统聚束器效率的研究

为了减少目前SFC轴向注入系统中聚束器杂散电场对束流轴向注入效率的影响, 提高新系统中SFC的束流俘获效率, 参考原始设计, 对目前聚束器的电极结构进行了设计改进. 两种情况下的聚束器杂散场对注入效率影响的计算表明, 改进后0B02的聚束效率较目前有较大提高. 同时计算了束流空间电荷效应对聚束效率的影响, 据此对新SFC轴向注入系统中聚束器的位置进行了重新调整.     

大非线性相移下光学非线性Z扫描特性的研究

采用高斯分解法(GD)对大非线性相移下的Z扫描特性进行了分析，通过对数值算法的优化，将GD推广到对脉冲入射激光下大非线性相移下的Z扫描理论分析.对不同条件下大非线性相移Z扫描曲线峰谷结构的比较，发现在大非线性相移的情况下，Z扫描曲线的峰和谷随透过光阑或入射光强变化表现出某些新的特性.随着透过光阑孔径的增加，Z扫描曲线峰的变化要明显快于谷的变化，而且在谷明显存在的情况下，峰很快消失.采用皮秒脉冲激光下的纯二硫化碳实验对理论结果加以验证，实验结果和理论分析相一致.我们的分析结果对大非线性相移下Z扫描测量有一定的指导性意义，避免在大非线性相移下对Z扫描结果产生错误的分析. 关键词： 大非线性相移 高斯分解法 Z扫描     

Measurement and prediction of solubilities and diffusion coefficients of carbon dioxide in starch–water mixtures at elevated pressures

The solubility and diffusion coefficient of carbon dioxide in intermediate‐moisture starch–water mixtures were determined both experimentally and theoretically at elevated pressures up to 16 MPa at 50 °C. A high‐pressure decay sorption system was assembled to measure the equilibrium CO₂ mass uptake by the starch–water system. The experimentally measured solubilities accounted for the estimated swollen volume by Sanchez–Lacombe equation of state (S‐L EOS) were found to increase almost linearly with pressure, yielding 4.0 g CO₂/g starch–water system at 16 MPa. Moreover, CO₂ solubilities above 5 MPa displayed a solubility increase, which was not contributed by the water fraction in the starch–water mixture. The solubilities, however, showed no dependence on the degree of gelatinization (DG) of starch. The diffusion coefficient of CO₂ was found to increase with concentration of dissolved CO₂, which is pressure‐dependent, and decrease with increasing DG in the range of 50–100%. A free‐volume‐based diffusion model proposed by Areerat was employed to predict the CO₂ diffusivity in terms of pressure, temperature, and the concentration of dissolved CO₂. S‐L EOS was once more used to determine the specific free volume of the mixture system. The predicted diffusion coefficients showed to correlate well with the measured values for all starch–water mixtures. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 607–621, 2006     

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.     

Fast Fourier Continuous Cyclic Voltammetry at Gold Ultramicroelectrode in Flowing Solution for Determination of Ultra Trace Amounts of Penicillin G

In this work, for the first time a fast continuous cyclic voltammetry was used as a highly sensitive detection method for Penicillin G in a flow‐injection system. A special computer‐based numerical calculation method (using Fast Fourier Transformation) is introduced here for enhancing the analyte signal and noise reduction. During the measurements, the potential waveform (consists of potential steps for cleaning, stripping and potential ramp) was continuously applied on an Au disk microelectrode (with a radius 12.5 μm in radius). The stripping time was less than 200 ms. Effects of rest potential, sweep rate, and delay time on the sensitivity of the method were investigated. The limit of detection of the method was 1.0 × 10^?11 M. The detection limit of the method is 660 times lower than the most sensitive reported method. The relative standard deviation of the method at 1.0×10^?7 M of Penicillin G was 2.7% for 10 runs.