A fractional-order phase-locked loop(PLL)with a time-delay is firstly proposed on the basis of the fact that a capacitor has memory.The existence of Hopf bifurcation of the fractional-order PLL with a time-delay is in...A fractional-order phase-locked loop(PLL)with a time-delay is firstly proposed on the basis of the fact that a capacitor has memory.The existence of Hopf bifurcation of the fractional-order PLL with a time-delay is investigated by studying the root location of the characteristic equation,and the bifurcated periodic solution and its stability are studied simply by using"pseudo-oscillator analysis".The results are checked by numerical simulation.It is found that the fractional-order PLL with a time-delay reduces the locking time,and it minimizes the amplitude of the bifurcated periodic solution when the order is properly chosen.展开更多
汉诺塔(Tower of Hanoi)问题源于印度一个古老传说,据此做成了益智游戏,蕴含大量的数学思想与方法.本文采用矩阵描述汉诺塔状态和圆盘移动过程,将圆盘从一个位置移动到另一个位置转化为矩阵的加法,进而构造由若干可能状态矩阵组成的图...汉诺塔(Tower of Hanoi)问题源于印度一个古老传说,据此做成了益智游戏,蕴含大量的数学思想与方法.本文采用矩阵描述汉诺塔状态和圆盘移动过程,将圆盘从一个位置移动到另一个位置转化为矩阵的加法,进而构造由若干可能状态矩阵组成的图的邻接矩阵,计算其幂矩阵,由此很方便地求得完成汉诺塔游戏的所有可能的圆盘移动方案,求解过程简单,含义清晰,易于理解和实现.展开更多
利用2020年春节期间(1月21~28日)广州市21个空气质量监测站气象和空气污染物数据及其中4个监测点位的单颗粒气溶胶质谱仪(single particle aerosol mass spectrometer,SPAMS)数据,研究烟花爆竹燃放对广州市及11个行政区空气质量的影响,...利用2020年春节期间(1月21~28日)广州市21个空气质量监测站气象和空气污染物数据及其中4个监测点位的单颗粒气溶胶质谱仪(single particle aerosol mass spectrometer,SPAMS)数据,研究烟花爆竹燃放对广州市及11个行政区空气质量的影响,并基于SPAMS建立了烟花爆竹快速溯源方法,分析了烟花爆竹源单颗粒化学成分.结果表明,烟花爆竹燃放对燃放区及禁止燃放区的空气质量都造成显著影响,广州市PM_(2.5)、PM_(10)和SO_(2)质量浓度在除夕夜间迅速升高.烟花爆竹集中燃放时段(1月25日01:00~06:00),主要影响了增城区、白云区、黄埔区及天河区部分区域的空气质量.建立了基于SPAMS以Al^(+)为示踪物及最快5 min时间分辨率的烟花爆竹快速溯源方法.烟花爆竹源颗粒主要颗粒类型是左旋葡聚糖、富钾和矿物质类颗粒.烟花爆竹源颗粒含有丰富的硝酸盐,但不利于铵盐的形成.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 10825207the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘A fractional-order phase-locked loop(PLL)with a time-delay is firstly proposed on the basis of the fact that a capacitor has memory.The existence of Hopf bifurcation of the fractional-order PLL with a time-delay is investigated by studying the root location of the characteristic equation,and the bifurcated periodic solution and its stability are studied simply by using"pseudo-oscillator analysis".The results are checked by numerical simulation.It is found that the fractional-order PLL with a time-delay reduces the locking time,and it minimizes the amplitude of the bifurcated periodic solution when the order is properly chosen.
文摘汉诺塔(Tower of Hanoi)问题源于印度一个古老传说,据此做成了益智游戏,蕴含大量的数学思想与方法.本文采用矩阵描述汉诺塔状态和圆盘移动过程,将圆盘从一个位置移动到另一个位置转化为矩阵的加法,进而构造由若干可能状态矩阵组成的图的邻接矩阵,计算其幂矩阵,由此很方便地求得完成汉诺塔游戏的所有可能的圆盘移动方案,求解过程简单,含义清晰,易于理解和实现.
