Conditional expectation of integrands and random sets

The conditional expectation of integrands and random sets is the main tool of stochastic optimization. This work wishes to make up for the lack of real synthesis about this subject. We improve the existing hypothesis and simplify the corresponding proofs. In the convex case we especially study the problem of the exchange of conditional expectation and subdifferential operators.     

Algebras of Random Operators Associated to Delone Dynamical Systems

We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C ^*-subalgebra to discuss a Shubin trace formula.     

A multifractal decomposition according to rate of returns

For one‐dimensional simple symmetric random walk, the Hausdorff and packing dimensions of sets of sample paths with prescribed rate of returns to the origin are determined. This gives a multifractal decomposition of the underlying sample space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

闭排队网络中性能势与无穷小实现因子之间的关系

In this paper,the concept of the infinitesimal realization factor is extended to the parameter-dependent performance functions in closed queueing networks. Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced,and the relations between infinitesimal realization factors and these two quantities are discussed. This provides a united framework for both IPA and non IPA approaches. Finally,another physical meaning of the service rate is given.     

关于“信息熵”分析及其应用的研究

本文用Ｓｈａｎｎｏｎ熵函数的观点及最大离散熵原理，探讨了对随机试验项目的优选问题：即压缩某种“不确定性”试验项目的实施与探索．并通过应用实例的计算，获得了满意的聚类效果．这种方法对于信息资料的数据处理及压缩“不确定性“验项目具有普遍意义．     

Model-dependent nature of blowtorch effect on the escape and equilibration rates

We analyze the relaxation behavior of a bistable system when the background temperature profile is inhomogeneous due to the presence of a localized hot region (blowtorch) on one side of the potential barrier. Since the diffusion equation for inhomogeneous medium is model-dependent, we consider two physical models to study the kinetics of such system. Using a conventional stochastic method, we obtain the escape and equilibration rates of the system for the two physical models. For both models, we find that the hot region enhances the escape rate from the well where it is placed while it retards the escape rate from the other well. However, the value of the escape rate from the well where the hot region is placed differs for the two models while that of the escape rate from the other well is identical for both. This work, for the first time, gives a detailed report of the similarities and differences of the escape rates and, hence, exposes the common and distinct features of the two known physical models in determining the way the bistable system relaxes. Received 25 September 2001     

Quasipotentials for simple noisy maps with complicated dynamics

The theory of nonequilibrium potentials or quasipotentials is a physically motivated approach to small random perturbations of dynamical systems, leading to exponential estimates of invariant probabilities and mean first exit times. In the present article we develop the mathematical foundation of this theory for discrete-time systems, following and extending the work of Freidlin and Wentzell, and Kifer. We discuss strategies for calculating and estimating quasipotentials and show their application to one-dimensionalS-unimodal maps. The method proves to be especially suited for describing the noise scaling behavior of invariant probabilities, e.g., for the map occurring as the limit of the Feigenbaum period-doubling sequence. We show that the method allows statements about the scaling behavior in the case of localized noise, too, which does not originally lie within the scope of the quasipotential formalism.     

2+1维SU(2)格点规范场胶球质量的七阶RPA近似

采用无规相近似(RPA)方法,用空心图作为试探波函数,利用Feymann?Hellman定理计算七阶2?+?1维SU(2?)格点规范场的胶球质量,在弱耦合区1/g2?=1.0?–?1.8胶球质量表现出良好的标度行为,基本趋于常数(m/e2?≈1.2?0±0?.0?1)?.     

既不离散也不连续的随机变量

讨论了既不离散也不连续的随机变量 ,并纠正了有关文献中关于连续型随机变量定义中的错误 .     

极性晶体外表面电子的量子像势及其极化子的基态能量

本从与真空接触的存在二支声子的半无限极性晶体表面附近极化子的哈密顿算符入手，应用二支模型理论，分别对GaAs和ZnO两种材料计算了外表面电子的量子像势及其极化子的基态能量，计算结果表明，利用二支模型理论求出的外表面极化子的基态能量与利用一支模型理论求出的外表在面极化子的基态能量相差较大，对GaAs，误差约为31.1%, 对ZnO，误差约为14.8%。