Internal Oxidant‐Triggered Aerobic Oxygenation and Cyclization of Indoles under Copper Catalysis

A concise synthesis of pyrazolo[1,5‐a]indole derivatives by copper‐catalyzed aerobic oxygenation and cyclization of indoles with oxime acetates is described. This protocol represents an elegant example of N‐1, C‐2, and C‐3 tri‐functionalization of indoles in one‐pot. Mechanistic studies indicate the reaction proceeds through a radical procedure. Oximes as an internal oxidant have been demonstrated to be a driver to initiate aerobic oxidation, which provides a new oxidative pattern for C‐H functionalization even with high atom‐ and step‐economy.     

Sinusoidal synchronization of a Duffing oscillator with a chaotic pendulum

In this Letter, analytical conditions for the sinusoidal synchronization of the pendulum and Duffing oscillator are presented. From the analytical conditions, the invariant domain of such sinusoidal synchronization is determined, and the control parameter map of the synchronicity is achieved. Under specific parameters, numerical illustrations of the partial and full sinusoidal synchronizations of the controlled Duffing oscillator with the pendulum are carried out for a better understanding of such synchronization under specific function constraints. The methodology presented in this Letter is applicable to synchronizations with any specific function constraints.     

欧洲航空超网络的实证分析

本文将机场定义为节点,将航空公司定义为超边,采用超网络方法分析了欧洲航空网络的特征.实证结果表明,这些统计属性的累计概率分布服从指数分布,说明多个随机因素的相互作用导致了该超网络的形成,较小的平均距离和较大的聚集系数表明该超网络符合小世界效应.     

Periodic and chaotic synchronizations of two distinct dynamical systems under sinusoidal constraints

In this paper, periodic and chaotic synchronizations between two distinct dynamical systems under specific constraints are investigated from the theory of discontinuous dynamical systems. The analytical conditions for the sinusoidal synchronization of the pendulum and Duffing oscillator were obtained, and the invariant domain of sinusoidal synchronization is achieved. From analytical conditions, the control parameter map is developed. Numerical illustrations for partial and full sinusoidal synchronizations of chaotic and periodic motions of the controlled pendulum with the Duffing oscillator are carried out. This paper presents how to apply the theory of discontinuous dynamical systems to dynamical system synchronization with specific constraints. The function synchronization of two distinct dynamical systems with specific constraints should be identified only by G-functions. The significance of function synchronization of distinct dynamical systems is to make the synchronicity behaviors hidden, which is very useful for telecommunication synchronization and network security.