Master Equation and Fokker–Planck Equation: Comparison of Entropy and of Rate Constants

A usual approximation of the master equation is provided by the Fokker–Planck equation. For chemical systems with one species, we prove generally that the prediction of the rate constant of the metastable state given by the Master equation and the Fokker–Planck approximation differ exponentially with respect to the size of the system. We show that this is related to the fact that the entropy of the metastable state is not described correctly by the Fokker–Planck equation. We prove that the rate given by the Fokker–Planck equation overestimates that rate given by the Master equation.     

基于步进电机非线性折射率测控系统设计

提出了一个基于步进电机非线性折射率测控系统.整个系统以AT89C51单片机为核心,设计了步进电机驱动电路,光电探测电路和A/D转换电路实现对非线性折射率的测量.用VC++6.0编写了上位机软件,实现单片机与上位机通信,对测量数据的分析、处理以及对整个测控系统的控制.     

Inhibition of premixed and nonpremixed flames with phosphorus-containing compounds

The inhibition/extinction of various flames—premixed stoichiometric C₃H₈/air, nonpremixed counterflow CH₄/O₂/N₂, and nonpremixed coflow n-heptane/air cup-burner flames doped with a number of phosphorus-containing compounds (PCCs)—has been investigated experimentally. More than 20 PCCs (organic phosphates, phosphonates, phosphates) and their fluorinated derivatives were studied. All PCCs exhibited similar dependencies in burning velocities, extinction strain rates, and extinction volume fractions of CO₂ upon PCC loading in the range of mole fractions of 0–7000 ppm within an experimental deviation of ± 5%. This confirms that the inhibition effectiveness of the PCCs is influenced by the phosphorus content in the PCC molecule rather than by the structure of the molecule. The burning velocity of a stoichiometric C₃H₈/air mixture and the extinction strain rate of a nonpremixed counterflow CH₄/O₂/N₂ flame doped with trimethylphosphate were calculated. Satisfactory agreement between experimental and modeling results confirms the conclusion that the reactions of phosphorus oxyacids with radicals are responsible for flame inhibition.     

类Be氩离子振子强度和跃迁光谱

研究了类Ｂｅ氩离子内壳层电子光电离的激发能级，寿命和辐射速率，谱线波长和振子强度，并给出了位于“水窗”波段的谱线波长和谱线强度。     

Multivariate Exponential Distributions with Constant Failure Rates

In this paper a multivariate failure rate representation based on Cox's conditional failure rate is introduced, characterizations of the Freund–Block and the Marshall–Olkin multivariate exponential distributions are obtained, and generalizations of the Block–Basu and the Friday–Patil bivariate exponential distributions are proposed.     

计算机辅助的数字通信频谱分析

从Fourier级数出发 ,到任意闭区间上可积函数的Fourier分析 ,给出了数字信号Fourier分析的理论基础。以字符“b”为例 ,建立了严格的数学模型 ,严密推导了Fourier系数表达式。阐明了Fourier级数的“项”和“n阶Fourier级数”(前n项和 )的概念。详尽地分析了信道通频带B与Fourier阶数n(展开式“保留”项 )的关系。借助计算机计算了n≤ 10 0时各Fourier级数项和前n项和 ,并用Plot将计算结果绘成曲线 ,获得n≤10 0时各级Fourier展开曲线。与数字信号对照 ,Fourier级数的取项与波形的关系显而易见 ,特别是n取值较小时 ,Fourier级数取项少 ,波形失真严重 ;所以在B一定时传输速率不能过高 ,否则 ,由于波形失真而导致信号出错。     

参数的E Bayes估计法及其应用

提出了参数的一种估计方法—— E Bayes估计法 ,对寿命服从指数分布的产品 ,在失效率的先验分布为 Gamma分布时 ,给出了失效率的 E Bayes估计和多层 Bayes估计 ,并在此基础上给出了失效率和可靠度的 E Bayes估计的性质 .结合实际问题进行了计算 ,结果表明提出的 E Bayes估计法可行且便于应用 .     

Some New Results for McKean’s Graphs with Applications to Kac’s Equation

The main goal of the present paper is to sharpen some results about the error made when the Wild sums, used to represent the solution of the Kac analog of Boltzmann’s equation, are truncated at the n-th stage. More precisely, in Carlen, Carvalho and Gabetta (J. Funct. Anal. 220: 362–387 (2005)), one finds a bound for the above-mentioned error which depends on (an ^Λ+ε). On the one hand, it is shown that Λ, the least negative eigenvalue of the linearized collision operator, is the best possible exponent. On the other hand, ε is an extra strictly positive number and a a positive coefficient which depends on ε too. Thus, it is interesting to check whether ε can be removed from the above bound. According to the aforesaid reference, this problem is studied here by means of the probability distribution of the depth of a leaf in a McKean random tree. In fact, an accurate study of the probability generating function of such a depth leads to conclude that the above bound can be replaced with (a′ n ^Λ).     

A New General Equation of the Polarographic Waves

A new general equation of the polarographic waves that improves the accuracy of the analysis has been obtained. The theoretical approach has been developed for Current Sampled DC Polarography or TAST Polarography, and can be used to study reversible, irreversible and quasi‐reversible waves. In order to facilitate the use of the new equation proposed, we have developed a computer program, TOP v1.0. This version works on Windows 32 bits systems (95/98/NT/Xp).     

残酸对原油脱水的影响及处理

酸对原油的破乳具有较大的影响,盐酸的存在使原油脱水发生困难,特别是在稠油中,脱水效率降低;土酸对原油脱水影响比盐酸更大,脱出水颜色发黑,发黄,有大量底渣存在;残酸对原油的脱水影响最大,脱水速度减慢,水色不清,过渡带加长.针对酸化后原油pH值较低的特点,选择碳酸钠作碱化剂,复配低温2#破乳剂,进行了室内实验和现场试验,结果表明:原油脱水效果明显,脱出水颜色清,油水过渡带清晰,保证返排液的pH值保持在6～8的范围内,使原油含水质量分数低于2%.