顺从性在动力系统中一直是一个热点课题。这一概念最初是由冯诺依曼针对离散群而提出来的,时至今日,已经拓展到数学的许多领域。但是,关于群满足顺从性的一系列等价条件在国内一直没有系统性的整理,国外相关文献又存在定理证明简略难懂...顺从性在动力系统中一直是一个热点课题。这一概念最初是由冯诺依曼针对离散群而提出来的,时至今日,已经拓展到数学的许多领域。但是,关于群满足顺从性的一系列等价条件在国内一直没有系统性的整理,国外相关文献又存在定理证明简略难懂、文献分散的情况。并且这些条件之间的联系国内外均未提及。因此,本文旨在系统完整的梳理群满足顺从性的相关等价条件并分析它们之间的内在联系。通过文献研究法梳理了可数离散群满足顺从性的常见等价条件,包括存在正定函数点点逼近单位函数、Følner条件和Reiter性质等。在此基础上,分析了它们之间的内在联系并得到关系图。Amenability has always been a hot topic in dynamical systems theory. This concept was first proposed by von Neumann for discrete groups, which has been extended to many areas of mathematics. However, the equivalent conditions of amenability have not been systematically sorted out in China, and the proof of relevant theorems in foreign literature is simple and difficult to understand and scattered. Besides, the relations between them are also not mentioned. Therefore, the purpose of this paper is to systematically and completely comb out the equivalence conditions of compliance and analyze the internal relations between them. We get the common equivalent conditions of the amenability for countable discrete groups by literature research, including the positive definite function tend pointwise to the unit function, Følner condition, Reiter property and so on. On this basis, we analyze the internal relations between them and get the relationship diagram between them.展开更多
This paper presents a detailed analysis of the complex flow beneath two impinging jets aligned with a low-velocity crossflow which is relevant for the future F-35 VSTOL configuration, and provides a quantitative pictu...This paper presents a detailed analysis of the complex flow beneath two impinging jets aligned with a low-velocity crossflow which is relevant for the future F-35 VSTOL configuration, and provides a quantitative picture of the main features of interest for impingement type of flows. The experiments were carried out for a Reynolds number based on the jet exit conditions of Rej = 4.3 × 10^4, an impingement height of 20.1 jet diameters and for a velocity ratio between the jet exit and the crossflow VR = V/Uo of 22.5. The rear jet is located at S = 6 D downstream of the first jet. The results show a large penetration of the first （upstream）jet that is deflected by the crossflow and impinges on the ground, giving rise to a ground vortex due to the collision of the radial wall and the crossflow that wraps around the impinging point like a scarf. The rear jet （located downstream） it is not so affected by the crossflow in terms of deflection, but due to the downstream wall jet that flows radially from the impinging point of the first jet it does not reach the ground. The results indicate a new flow pattern not yet reported so far, that for a VSTOL aircraft operating in ground vicinity with front wind or small forward movement may result in enhanced under pressures in the aft part of the aircraft causing a suction down force and a change of the pitching moment towards the ground.展开更多
文摘顺从性在动力系统中一直是一个热点课题。这一概念最初是由冯诺依曼针对离散群而提出来的,时至今日,已经拓展到数学的许多领域。但是,关于群满足顺从性的一系列等价条件在国内一直没有系统性的整理,国外相关文献又存在定理证明简略难懂、文献分散的情况。并且这些条件之间的联系国内外均未提及。因此,本文旨在系统完整的梳理群满足顺从性的相关等价条件并分析它们之间的内在联系。通过文献研究法梳理了可数离散群满足顺从性的常见等价条件,包括存在正定函数点点逼近单位函数、Følner条件和Reiter性质等。在此基础上,分析了它们之间的内在联系并得到关系图。Amenability has always been a hot topic in dynamical systems theory. This concept was first proposed by von Neumann for discrete groups, which has been extended to many areas of mathematics. However, the equivalent conditions of amenability have not been systematically sorted out in China, and the proof of relevant theorems in foreign literature is simple and difficult to understand and scattered. Besides, the relations between them are also not mentioned. Therefore, the purpose of this paper is to systematically and completely comb out the equivalence conditions of compliance and analyze the internal relations between them. We get the common equivalent conditions of the amenability for countable discrete groups by literature research, including the positive definite function tend pointwise to the unit function, Følner condition, Reiter property and so on. On this basis, we analyze the internal relations between them and get the relationship diagram between them.
文摘This paper presents a detailed analysis of the complex flow beneath two impinging jets aligned with a low-velocity crossflow which is relevant for the future F-35 VSTOL configuration, and provides a quantitative picture of the main features of interest for impingement type of flows. The experiments were carried out for a Reynolds number based on the jet exit conditions of Rej = 4.3 × 10^4, an impingement height of 20.1 jet diameters and for a velocity ratio between the jet exit and the crossflow VR = V/Uo of 22.5. The rear jet is located at S = 6 D downstream of the first jet. The results show a large penetration of the first （upstream）jet that is deflected by the crossflow and impinges on the ground, giving rise to a ground vortex due to the collision of the radial wall and the crossflow that wraps around the impinging point like a scarf. The rear jet （located downstream） it is not so affected by the crossflow in terms of deflection, but due to the downstream wall jet that flows radially from the impinging point of the first jet it does not reach the ground. The results indicate a new flow pattern not yet reported so far, that for a VSTOL aircraft operating in ground vicinity with front wind or small forward movement may result in enhanced under pressures in the aft part of the aircraft causing a suction down force and a change of the pitching moment towards the ground.
基金Supported by the Natural Science Foundations of China(10771059)Natural Science Foundations of Hunan Province(05JJ10001)+1 种基金Program for New Century Excellent Talents in University(04-0783)Program for Hengyang Normal University(08B06)
