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Let and be two integers with and . For a graph and a vertex of , we use to denote the degree of in . Define to be the minimum value of , where is an independent set of with . This paper proves the following conjecture proposed by Gould et al. (2018). If is a graph of sufficiently large order with , then contains vertex-disjoint cycles. 相似文献
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Modified function projective synchronization (MFPS), which generalizes many kinds of synchronization form, has received great attention recently. Based on the active control method and adaptive control technique, a general formula for designing the controllers is proposed to achieve adaptive MFPS, which corrects several incomplete results that have been reported recently. In addition, this paper derives the sufficient condition for parameter identification, which was not mentioned in much of the relevant literature concerning MFPS. Furthermore, we extend the MFPS scheme to the cases that the drive and response systems come with non-identical structures. The proposed method is both theoretically rigorous and practically feasible, which has the merits that it can not only achieve the full-state MFPS but also identify the fully unknown parameters in the synchronization process. The theoretical results are successfully applied to three typical illustrative cases: the adaptive MFPS of two identical 4-D hyperchaotic systems with unknown parameters in the response system, the adaptive MFPS between a 5-D hyperchaotic system and a 4-D hyperchaotic system with unknown parameters in the drive system and the adaptive MFPS between a 3-D chaotic system and a 4-D hyperchaotic system when the parameters in the drive system and response system are all unknown. For each case the controller functions and parameter update laws are well designed in detail. Moreover, the corresponding numerical simulations are presented, which agree well with the theoretical analysis. 相似文献
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In this paper, the partial and full chaotic synchronizations of two nonlinear gyroscope systems with/without noise are investigated. From analytical conditions for synchronization and non-synchronization of two gyroscope systems, the parameter characteristic study is completed for a better understanding of the synchronization dynamics of two gyroscope dynamical systems. The boundaries of the parameter map for synchronization are determined by the onset and vanishing conditions of synchronization. The simple feedback control can make the noised gyroscope system synchronizing with chaotic behaviors of the expected gyroscope system. The methodology presented in this paper is different from other techniques for synchronization. The partial synchronization is an important phenomenon to be observed in engineering applications. 相似文献
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A novel memristive chaotic circuit is proposed by replacing the Chua’s diode in modified Chua’s circuit with a smooth active memristor, and the corresponding memristive model is analyzed and validated. The equilibrium point set, dissipativity and stability of this new chaotic circuit are developed theoretically. The dynamic characteristics for the new system are presented by means of phase diagrams, Lyapunov exponents, bifurcation diagrams and Poincaré maps. The coexistence of the memristive system is carried out from the perspective of asymmetric coexistence and symmetry coexistence. In addition, the coexistence of multiple states is studied by a more direct method with initial value as the system variable to gain a more intuitive observation. The circuit model of the memristive chaotic system is designed through Multisim simulation software. Finally, the memristive chaotic sequence is used to encrypt the image, and the influence of multistability on the encryption is investigated by the histogram, correlation and key sensitivity. The results show that the proposed new memristive chaotic system has high security. 相似文献
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水润滑尾轴承摩擦磨损性能是影响船舶工作性能的主要因素之一,合理预测水润滑尾轴承工作过程中的摩擦系数对其性能评估具有重要意义.目前对于水润滑尾轴承摩擦系数的理论计算公式已经存在.但由于销盘试验下无法有效获取当量半径,公式在销盘试验条件下的实用性不佳.对此在总结了边界润滑条件下,水润滑尾轴承摩擦机理的基础上,通过在CBZ-1销盘试验机上进行大量试验来进行当量半径等效参数计算公式的总结与摩擦系数经验公式的验证.研究结果表明:(a)在使用理论摩擦系数计算公式的前提下,当量半径等效参数公式拟合合理,具备较高准确性;(b)试验材料的理论摩擦系数与实际摩擦系数误差较小,为同类型试验摩擦性能研究提供了理论与试验基础;(c)水润滑尾轴承材料在工作过程中的摩擦力来源主要分为滞后摩擦力、犁沟摩擦力以及黏着摩擦力.当其处于边界润滑状态下时,滞后摩擦力为主要的摩擦力来源.该研究为水润滑尾轴承的等效当量半径在销盘试验条件下的应用提供了试验基础. 相似文献
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Internal Oxidant‐Triggered Aerobic Oxygenation and Cyclization of Indoles under Copper Catalysis
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Dr. Huawen Huang Jinhui Cai Dr. Xiaochen Ji Dr. Fuhong Xiao Ya Chen Prof. Dr. Guo‐Jun Deng 《Angewandte Chemie (International ed. in English)》2016,55(1):307-311
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. 相似文献
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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. 相似文献
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Fuhong Min 《Physics letters. A》2011,375(34):3080-3089
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. 相似文献