Convergence of Discrete Snakes

The discrete snake is an arborescent structure built with the help of a conditioned Galton-Watson tree and random i.i.d. increments Y. In this paper, we show that if and , then the discrete snake converges weakly to the Brownian snake (this result was known under the hypothesis ). Moreover, if this condition fails, and the tails of Y are sufficiently regular, we show that the discrete snake converges weakly to an object that we name jumping snake. In both case, the limit of the occupation measure is shown to be the integrated super-Brownian excursion. The proofs rely on the convergence of the codings of discrete snake with the help of two processes, called tours.     

Closed maps on metric spaces

The following result is proved: Let Y be the image of a metric space X under a closed map f. Then every ?f^-1(y) is Lindelöf if and only if Y has a point-countable k-network.     

Nonhomogeneous markov chains with desired properties - the nearest markovian model

A new class of operators performing an optimization (optimization operators or, simply, optimators) which generate transition matrices with required properties such as ergodicity, recurrence etc., is considered and their fundamental features are described. Some criteria for comparing such operators by taking into account their strenght are given and sufficient conditions for both weak and strong ergodicity are derived. The nearest Markovian model with respect to a given set of observed probability vectors is then defined as a sequence of transition matrices satisfying certain constraints that express our prior knowledge about the system. Finally, sufficient conditions for the existence of such a model are given and the related algorithm is illustrated by an example.     

Objectification problem,CHSH inequalities for a system of two spin-1/2 particles

The weak objectification and Bell/CHSH inequalities are studied for a particular type of set of states of two spin-1/2 particles. The restriction on interference term which allows Bell/CHSH inequalities to be satisfied are found out.     

BCI—代数的弱直和与正则可裂同态

本文引入正则可裂同态、正则可裂正合序列等概念,刻画了BCI-代数的弱直和并讨论了弱直和与外直和的关系.     

拓扑空间中的弱连通集

强连通条件较强，因而这种强连通空间就较少，例如实数空间R就不是强连通的，而且，强连通无法推广到强连通分支，针对强连通给出了一种条件较弱的弱连通，它具有一些强连通所不具有的性质且可将其推广到弱连通分支。     

The probability approach to numerical solution of nonlinear parabolic equations

A number of new layer methods for solving semilinear parabolic equations and reaction‐diffusion systems is derived by using probabilistic representations of their solutions. These methods exploit the ideas of weak sense numerical integration of stochastic differential equations. In spite of the probabilistic nature these methods are nevertheless deterministic. A convergence theorem is proved. Some numerical tests are presented. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 490–522, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10020