Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Spectrum of positive entropy multidimensional dynamical systems with a mixed time

It is shown that if an abelian countable group is such that is a finite group and every aperiodic positive entropy action of on a Lebesgue probability space has a countable Haar spectrum in the subspace , where denotes the Pinsker -
algebra of , then every aperiodic positive entropy action of on has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.

     

HYPERFINITE TRANSVERSAL THEORY. II

We continue the investigation of validity of Hall's theorem in the case of the Loeb space of an internal, uniformly distributed, hyperfinite measure space initiated in1992 by the author. Some new classes of graphs are introduced for which the measure theoretic version of Hall's theorem still holds.

     

Carleson measure characterization of Bloch functions

We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f B if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized Carleson measure;f B ₀ if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized vanishing Carleson measure, whereD f( > 0) is the fractional derivative of analytic functionf of order, m denotes the normalised Lebesgue measure.Supported partly by the Young Teacher Natural Science Foundation of Shandong Province.     

获取路面谱的一种新方法

通过理论分析和实际路面的测量,阐述了直接在汽车车桥上安装传感器测量路面谱的一种简便方法,并通过与用五轮仪测量路面谱方法的结果对比,得出了此种方法在一般汽车性能试验中的实际应用价值．     

多维OU型Markov过程的弱对偶半群及其无穷小算子

研究多维ＯＵ型Ｍａｒｋｏｖ过程的不变测度、参考测度、弱对偶半群及其无穷小算子．说明了ＯＵ型Ｍａｒｋｏｖ过程不变概率测度和弱对偶半群的存在唯一性,Ｌéｖｙ过程Ａｔ的不变测度不一定是由它产生的ＯＵ型Ｍａｒｋｏｖ过程的不变测度,以及Ｌｅｂｅｓｇｕｅ测度ｍ和极限分布ξ在ｓｕｐｐξ＝Ｒｄ的条件下都是ＯＵ型Ｍａｒｋｏｖ过程的参考测度．     

一个基于可能性理论的推理模式

在可能性理论的基础上,提出了一种新的将经典的假言推理作为它的特例的推理模式,其推理机制是借助于基于max-min合成的矩阵积来实现的.所得结果在一定程度上对不精确推理具有理论上的意义.     

Lipophilicity in PK design: methyl, ethyl, futile

Lipophilicity, often expressed as distribution coefficients (log D) in octanol/water, is an important physicochemical parameter influencing processes such as oral absorption, brain uptake and various pharmacokinetic (PK) properties. Increasing log D values increases oral absorption, plasma protein binding and volume of distribution. However, more lipophilic compounds also become more vulnerable to P450 metabolism, leading to higher clearance. Molecular size and hydrogen bonding capacity are two other properties often considered as important for membrane permeation and pharmacokinetics. Interrelationships among these physicochemical properties are discussed. Increasing size (molecular weight) often gives higher potency, but inevitably also leads to either higher lipophilicity, and hence poorer dissolution/solubility, or to more hydrogen bonding capacity, which limits oral absorption. Differences in optimal properties between gastrointestinal absorption and uptake into the brain are addressed. Special attention is given to the desired lipophilicity of CNS drugs. In examples using -blockers, Ca channel antagonists and peptidic renin inhibitors we will demonstrate how potency and pharmacokinetic properties need to be balanced.     

Hepatobiliary excretion and brain distribution of caffeine in rats using microdialysis

To investigate the pharmacokinetic mechanism of hepatobiliary excretion and brain distribution of caffeine, this study uses a method based on microdialysis technique and liquid chromatography that allows continuous and concurrent in vivo monitoring of extracellular caffeine in the blood, brain and bile of anesthetized rats following the administration of caffeine (3 or 10 mg/kg, i.v.) through the femoral vein. Dialysates of the blood, brain and bile were directly injected onto the liquid chromatographic system and no further clean-up procedures were required. The study design consisted of two groups of six rats in parallel: the rats of the control group received caffeine (3 or 10 mg/kg, i.v.) alone and those of the cyclosporine treated-group were injected cyclosporine (10 mg/kg, i.v.) 10 min prior to caffeine administration (3 or 10 mg/kg, i.v.). The decline of caffeine in the blood, brain striatum and bile suggested that caffeine had rapid exchange and equilibration between the peripheral compartment and the central nervous system. In addition, the results indicated that caffeine underwent hepatobiliary excretion and was distributed into brain. When cyclosporine was co-administered, the pharmacokinetic parameters were not significantly altered. The results of this study reveal that the pharmacokinetic mechanism of hepatobiliary excretion and brain distribution of caffeine might not relate to P-glycoprotein.