Decidability of Chaos for Some Families of Dynamical Systems

We show that the existence of positive Lyapounov exponents and/or SRB measures are undecidable (in the algorithmic sense) properties within some parametrized families of interesting dynamical systems: the quadratic family and Hénon maps. Because the existence of positive exponents (or SRB measures) is, in a natural way, a manifestation of chaos, these results may be understood as saying that the chaotic character of a dynamical system is undecidable. Our investigation is directly motivated by questions asked by Carleson and Smale in this direction.     

Bounds for f-Divergences Under Likelihood Ratio Constraints

In this paper we establish an upper and a lower bound for the f-divergence of two discrete random variables under likelihood ratio constraints in terms of the Kullback-Leibler distance. Some particular cases for Hellinger and triangular discrimination, ²-distance and Rényi's divergences, etc. are also considered.     

Quantum-Logics-Valued Measure Convergence Theorem

In this paper, the following quantum-logic valued measure convergence theorem is proved: Let (L ₁, 0, 1) be a Boolean algebra, (L ₂, , , 0, 1) be a quantum logic and { _n : n N} be a sequence of s-bounded (L ₂, , , 0, 1)-valued measures which are defined on (L ₁, 0, 1). If for each a (L ₁, 0, 1), { _n (a)} _{n N} is an order topology Cauchy sequence, when {v(a)} convergent to 0, { _n (a)} is order topology convergent to 0 for each n N, where v is a nonnegative finite additive measure which is defined on (L ₁, 0, 1), then when {v(a)} convergent to 0, { _n (a)} are order topology convergent to 0 uniformly with respect to n N.     

A representation of the characteristic function of a stable probability measure on certain TV spaces

In this paper, a Lévy-Khintchine type representation of the characteristic function of a K-regular stable probability measure on real locally convex topological vector spaces, satisfying certain conditions, is presented.     

Gibbs States on Space-time

Gibbs states on path spaces of the form C infinite stochastic differential equations of gradient type or as thermodynamic limits constructed with help of the method of cluster expansions.     

Intermittency generated by attracting and weakly repelling fixed points

Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay between a superexponentially attracting fixed point and an exponentially repelling fixed point. In this article we consider a closely related family of random systems with exponentially fast attraction to and polynomially fast repulsion from two fixed points, and show that such a phase transition still exists. The method of the proof however is different and relies on the construction of a suitable invariant set for the transfer operator.     

全身麻醉患者恢复期躁动的原因分析

目的分析全身麻醉患者恢复期发生躁动的原因,并探讨全麻患者恢复期躁动的预防措施。方法选取2014年12月至2016年7月期间在东莞市东城医院麻醉科接受全麻手术治疗的200例患者,统计恢复期躁动发生率、发生躁动的原因、各种原因导致躁动的发生率和严重程度,并总结预防措施。结果 200例全麻手术患者中共24例(12.00%)恢复期发生躁动,发生躁动的原因包括疼痛、气管导管刺激、导尿管刺激、药物残留、循环功能障碍,其中疼痛导致的躁动发生率为41.67%,与其他原因导致的躁动发生率比较存在的差异均具有统计学意义(P<0.05),由循环功能障碍导致的躁动程度最严重。结论导致全麻患者恢复期发生躁动的原因较多,躁动程度轻重不一,临床工作者应积极分析全麻患者恢复期发生躁动的原因,制定具有针对性的预防措施。     

Besov spaces via wavelets on metric spaces endowed with doubling measure,singular integral,and the T1 type theorem

The aim of this paper is twofold. We first establish the Besov spaces on metric spaces endowed with a doubling measure, via the remarkable orthonormal wavelet basis constructed recently by T. Hytönen and O. Tapiola, and characterize the dual spaces of these Besov spaces. Second, we prove the T1 type theorem for the boundedness of Calderón–Zygmund operators on these Besov spaces. Finally, we introduce a new class of Lipschitz spaces and characterize these spaces via the Littlewood–Paley theory. Copyright © 2016 John Wiley & Sons, Ltd.