非自治动力系统的原像熵

本文对紧致度量空间上的连续自映射序列应用生成集和分离集引入了点原像熵、原像分枝熵以及原像关系熵等几类原像熵的定义并进行了研究.主要结果是:(1) 证明了这些熵都是等度拓扑共轭不变量.(2)讨论了这些原像熵之间及它们与拓扑熵之间的关系,得到了联系这些熵的不等式.(3)证明了对正向可扩的连续自映射序列而言, 两类点原像熵相等,原像分枝熵与原像关系熵也相等.(4)证明了对(a).由闭Riemann 流形上的一个扩张映射经充分小的C1-扰动生成的自映射序列,以及(b).有限图上等度连续的自映射序列,有零原像分枝熵.     

Quantum Pseudo-Telepathy

Quantum information processing is at the crossroads of physics, mathematics and computer science. It is concerned with what we can and cannot do with quantum information that goes beyond the abilities of classical information processing devices. Communication complexity is an area of classical computer science that aims at quantifying the amount of communication necessary to solve distributed computational problems. Quantum communication complexity uses quantum mechanics to reduce the amount of communication that would be classically required. Pseudo-telepathy is a surprising application of quantum information processing to communication complexity. Thanks to entanglement, perhaps the most nonclassical manifestation of quantum mechanics, two or more quantum players can accomplish a distributed task with no need for communication whatsoever, which would be an impossible feat for classical players. After a detailed overview of the principle and purpose of pseudo-telepathy, we present a survey of recent and not-so-recent work on the subject. In particular, we describe and analyse all the pseudo-telepathy games currently known to the authors. Supported in Part by Canada’s Natural Sciences and Engineering Research Council (NSERC), the Canada Research Chair programme and the Canadian Institute for Advanced Research (CIAR). Supported in part by a scholarship from Canada’s NSERC. Supported in part by Canada’s NSERC Québec’s Fonds de recherche sur la nature et les technologies (FQRNT), the CIAR and the Mathematics of Information Technology and Complex Systems Network (MITACS).     

Image numerique simultanee d'une famille d'operateurs sur l'espace de Hilbert

We establish some convexity properties of the numerical range for a family of operators on a Hilbert space lying in an uniform dual algebra.     

Analysis of a dynamic unilateral contact problem for a cracked viscoelastic body

This work deals with the mathematical analysis of a dynamic unilateral contact problem with friction for a cracked viscoelastic body. We consider here a Kelvin-Voigt viscoelastic material and a nonlocal friction law. To prove the existence of a solution to the unilateral problem with friction, an auxiliary penalized problem is studied. Several estimates on the penalized solutions are given, which enable us to pass to the limit by using compactness results.     

原子发射光谱内标法测量误差的研究

证明了原子发射光谱内标法的测量误差。当分析线和内标线的相对强度等于1时，测量误差最小。     

天然高分子表面活性剂

综述了淀粉、纤维素和壳聚糖类表面活性剂的合成方法、性质及功能。