Ergodic theorem for the two-dimensional super-Brownian motion with super-Brownian immigration

By investigating the related nonlinear equation, the ergodic theorem is obtained for the super-Browni-an with super-Brownian immigration in two dimension.     

Qualitative behaviour of stochastic delay equations with a bounded memory

A dichotomy is proved concerning recurrence properties of the solution of certain stochastic delay equations. If the solution process is recurrent, there exists an invariant measure π on the state space C which is unique (up to a multiplicative constant) and the tail-field is trivial. If π happens to be a probability measure, then for every initial condition, the distribution of the process converges to it as t→∞. We will formulate a sufficient condition for the existence of an invariant probability measure (ipm) in icrnia of Lyapunov junctionals and give two examples, one Heing the stochastic-delay version of the famous logistic equation of population growth. Finally we study approximations of delay equations by Markov chains.     

Spectral rigidity of group actions: Applications to the case gr

We apply a technique to study the notion of spectral rigidity of group actions to a group gr. As an application, we prove that there exist rank one weakly mixing transformations conjugate to its square, thereby giving a positive answer to a well-known question.

     

Construction of the Thermodynamic Jamming Limit for the Parking Process and Other Exclusion Schemes on {\mathbb Z}^{d}

We provide an explicit construction of the thermodynamic jamming limit for the parking process and other finite range exclusion schemes on . By means thereof, a strong law of large numbers for occupation densities is accomplished, and, amongst other results, the so called “super-exponential” (i.e. gamma) decay of pair correlation functions is established. Mathematics Subject Classification (1991): 60K99     

A noncommutative extended de Finetti theorem

The extended de Finetti theorem characterizes exchangeable infinite sequences of random variables as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is a noncommutative version of this theorem.In contrast to the classical result of Ryll-Nardzewski, exchangeability turns out to be stronger than spreadability for infinite sequences of noncommutative random variables. Out of our investigations emerges noncommutative conditional independence in terms of a von Neumann algebraic structure closely related to Popa's notion of commuting squares and Kümmerer's generalized Bernoulli shifts. Our main result is applicable to classical probability, quantum probability, in particular free probability, braid group representations and Jones subfactors.     

一种低阶大气环流模型的全局指数吸引集估计

本文研究一种低阶大气环流模型的全局指数吸引集估计问题。针对具有变参数的大气环流模型,通过广义Lypunov函数方法,给出了模型全局指数吸引集的估计式,此估计式验证了系统的最终一致有界性.     

A new multivariate variability control chart based on a covariance matrix combination

In the field of multivariate quality control, there are many control charts related to the process mean but few options addressing process variability. Variability control charts have two main drawbacks: the first relates to the number of parameters to tune and the second relates to how changes in the mean affect the performance of these charts. Thus, in this paper, we propose a new multivariate variability control chart, called the multivariate exponentially weighted covariance matrix combination, which solves these two problems. The results show that this new chart performs well in the detection of changes in variance when the mean does not change and outperforms other charts when the mean does change.     

Semi-uniform sub-additive ergodic theorems for skew-product quasi-flows

The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are established. By making use of these results, it is feasible to get uniform estimation of the Lyapunov exponent of some special systems even under non-uniform hypotheses     

Equipartition of interval partitions and an application to number theory

We give wider application and simpler proofs of results describing the rate at which the digits of one number-theoretic expansion determine those of another. The proofs are based on general measure-theoretic covering arguments and not on the dynamics of specific maps.

     

修正高斯模型在制备液相色谱收集区间优化中的应用

近年来制备液相色谱得到了越来越广泛的应用。制备液相色谱操作条件的优化对提高其效率及节约成本非常重要。对制备高效液相色谱而言,其样品收集区间的确定及优化是其操作条件优化的重要步骤。该文以修正高斯模型(EMG模型)为理论基础,编写了一个小软件,可有效地帮助用户确定合理的样品收集区间。此软件对制备液相色谱实际应用有积极的指导及参考意义。