追本溯源：2022年新高考Ⅱ卷第21题解法探究

通过对试题的研究,采用解析几何常规方法,从设直线和点入手,运用设而不求的思想解决问题;也可以从新教材中寻找本题的突破点,根据条件联想中点弦问题,利用点差法,并研究弦中点轨迹方程;还可以利用直线参数方程解决问题.通过思维导图的形式呈现解题思路,在解法中发现规律,拓展结论,从而实现从常规解法到妙解的突破.通过试题的深度研究,找到学生的困难所在,为后续的教学做好铺垫,经历解题的研究过程,引导学生学会如何去探索一个题,如何做到一题多解、举一反三.     

Structure Identification of Nonlinearly Coupled Complex Networks with Non-Delayed and Delayed Coupling

Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identifying the topology of general nonlinearly-coupled complex network models that are either non-delayed or delayed coupled. Simulation results are also presented to illustrate the effectiveness of the method.     

CONSENSUS OF THE SECOND-ORDER MULTI-AGENT SYSTEMS WITH AN ACTIVE LEADER AND COUPLING TIME DELAY

This article investigates the consensus problem of the second-order multi-agent systems with an active leader and coupling time delay in direct graph. One decentralized state control rule is constructed for each agent to track the active leader and it is proved that the proposed control scheme enables the consensus to be obtained when the adjacency topology is fixed/switched. Simulation results show effectiveness of the proposed theoretical analysis.     

大学物理实验中发散思维的引导与训练

发散性思维是创新能力的基础。大学物理实验是理工类学生最早接触的实验,在分析现存物理实验教学模式存在问题的基础上,将发散性思维训练作为大学物理实验课堂的目标之一,提出了课堂发散性思维训练的三种方式。最后通过某个具体的物理实验,对实验教学中的发散思维训练内容及过程进行了说明。     

Adaptive Consensus Problem of Leader-Follower Multi-Agent System

We consider the adaptive consensus problem for leader-follower multi-agent systems with time delay coupling. Under the condition that the interconnection graph of the agents is directed and balanced, a neighbor-based consensus protocol with adaptive feedback gain is proposed for the follower agents to track the leader. The stability is performed based on the Lyapunov stability theorem. Some simulation examples are provided to show the efficiency of the control scheme.