On classical analogues of free entropy dimension

We define a classical probability analogue of Voiculescu's free entropy dimension that we shall call the classical probability entropy dimension of a probability measure on Rn. We show that the classical probability entropy dimension of a measure is related with diverse other notions of dimension. First, it can be viewed as a kind of fractal dimension. Second, if one extends Bochner's inequalities to a measure by requiring that microstates around this measure asymptotically satisfy the classical Bochner's inequalities, then we show that the classical probability entropy dimension controls the rate of increase of optimal constants in Bochner's inequality for a measure regularized by convolution with the Gaussian law as the regularization is removed. We introduce a free analogue of the Bochner inequality and study the related free entropy dimension quantity. We show that it is greater or equal to the non-microstates free entropy dimension.     

Discrete-time GI/Geo/1 queue with multiple working vacations

Consider the discrete time GI/Geo/1 queue with working vacations under EAS and LAS schemes. The server takes the original work at the lower rate rather than completely stopping during the vacation period. Using the matrix-geometric solution method, we obtain the steady-state distribution of the number of customers in the system and present the stochastic decomposition property of the queue length. Furthermore, we find and verify the closed property of conditional probability for negative binomial distributions. Using such property, we obtain the specific expression for the steady-state distribution of the waiting time and explain its two conditional stochastic decomposition structures. Finally, two special models are presented.      

Algorithmic analysis of theMAP/PH/1 retrial queue

In this paper the distribution of the maximum number of customers in a retrial orbit for a single server queue with Markovian arrival process and phase type services is studied. Efficient algorithm for computing the probability distribution and some interesting numerical examples are presented.     

负关联噪声驱动下单模激光的定态分析

研究了负关联的加法和乘法高斯白噪声驱动下单模激光损失模型的定态情况。文中推导了负关联情况下，定态时的激光场幅的几率分布，光强的平均值，光强的协方差以及光强的偏斜率。并和文献〔１，２〕中正关联时的定态分析作了比较，发现了有意义的新现象。     

抗有机杂质镀镍添加剂对阴极极化性能的影响

研究了有机杂质以及抗有机杂质添加剂对镀镍过程中阴极极化性能的影响．实验结果表明，有机杂质增大了阴极极化，而抗有机杂质添加剂却能减小阴极极化．实验结果还显示，添加剂消除有机杂质污染的效果同其降低阴极极化的能力密切相关     

Markovian network processes: Congestion-dependent routing and processing

A Markovian network process describes the movement of discrete units among a set of nodes that process the units. There is considerable knowledge of such networks, often called queueing networks, in which the nodes operate independently and the routes of the units are independent. The focus of this study, in contrast, is on networks with dependent nodes and routings. Examples of dependencies are parallel processing across several nodes, blocking of transitions because of capacity constraints on nodes, alternate routing of units to avoid congestion, and accelerating or decelerating the processing rate at a node depending on downstream congestion. We introduce a general network process representing the numbers of units at the nodes and derive its equilibrium distribution. This distribution takes the form of a product of functions of vectors in which the arguments of the functions satisfy an interchangeability property. This new type of distribution may apply to other multi-variate processes as well. A basic idea in our approach is a linking of certain micro-level balance properties of the network routing to the processing rates at the nodes. The link is via routing-balance partitions of nodes that are inherent in any network. A byproduct of this approach is a general characterization of blocking of transitions without the restriction that the process is reversible, which had been a standard assumption. We also give necessary and sufficient conditions under which a unit moving in the network sees a time average for the unmoved units (called the MUSTA property). Finally, we discuss when certain flows between nodes in an open network are Poisson processes.This research was sponsored in part by Air Force Office of Scientific Research contract 84-0367.     

How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

CuO—ZnO／Al2O3—TiO2催化剂中TiO2的结构和电子效应

采用XPS,XRD,TPR,TPD和指标反应等方法研究了TiO_2在负载型CuO-ZnO/Al_2O_3-TiO_2催化剂中所起的作用.发现TiO_2起双重作用,即结构效应和电子效应,TiO_2的结构效应主要表现为它改善了CuO在载体上的分布.TiO_2的电子效应表现为它对Cu~0具有吸电子的作用,从而削弱了Cu和S之间的吸附力,使S容易脱除.另外,部分还原形成的Ti~(3+)具有促进CuS中的Cu~(2+)还原为Cu~0的能力,TiO_2的上述效应的综合结果使催化剂的抗硫中毒性能大大增强.     

Corrigendum to “EuBaFe2O5+w: Valence mixing and charge ordering are two separate cooperative phenomena” [J. Solid State Chem. 180 (2007) 148-157]

An error in the expression for the Fe²⁺, Fe³⁺ valence-mixing probability in RBaFe₂O_5+w is acknowledged and correct formula is derived. The new formula slightly improves the least-squares fit to the experimental concentrations of the Mössbauer component Fe^2.5+ as a function of the oxygen-nonstoichiometry parameter w for R=Eu.     

催化裂化USY／ZnO／Al2O3脱硫添加剂的高温水热失活

 对USY／ZnO／Al2O3汽油催化裂化脱硫添加剂经高温水热老化处理前后的脱硫性能进行了考察，发现老化后添加剂的脱硫性能大幅度下降．采用XRD和IR等技术对USY／ZnO／Al2O3添加剂在高温和高温水热条件下失活的原因进行了研究．结果表明，在高温下，ZnO可与USY沸石中的铝发生固相反应生成ZnAl2O4尖晶石，从而造成USY晶体结构崩塌，转变成无定形状态．在ZnO含量较高的条件下，ZnO可继续与USY晶体结构崩塌后生成的无定形的硅和铝的氧化物反应，生成Zn2SiO4硅锌矿和ZnAl2O4尖晶石结构．这一方面使添加剂失去了可形成硫化物吸附中心的ZnO，另一方面破坏了硫化物的裂化活性组分USY，从而造成添加剂脱硫性能下降甚至失去脱硫活性．ZnO对USY的破坏作用主要与温度有关．在USY／ZnO／Al2O3体系中，ZnO被ZnO与Al2O3之间形成的锌铝尖晶石膜固定并与USY隔离，单纯的高温条件对添加剂的破坏不显著，而水蒸气可以促进ZnO的移动，有利于ZnO与USY的接触，因此在高温和有水蒸气存 在的条件下添加剂的结构易遭到破坏．