In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We ...In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles.展开更多
Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are...Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.展开更多
针对现有限流设施与策略智能化程度不高,灵活性较差的问题,提出一种基于光流特征描述子的站点限流设施优化方法.首先,根据枢纽内场景特点,设置感兴趣区域(region of interest,ROI),从而降低后续操作的计算量,提高算法的执行效率;然后,...针对现有限流设施与策略智能化程度不高,灵活性较差的问题,提出一种基于光流特征描述子的站点限流设施优化方法.首先,根据枢纽内场景特点,设置感兴趣区域(region of interest,ROI),从而降低后续操作的计算量,提高算法的执行效率;然后,在建立光流特征描述子的基础上,对图片序列进行特征分析;最后,基于人群聚集特征,对经典单分类支持向量机进行调整,并实现超负荷状态的检测.实验结果表明,提出的方法能够对站台人群状态进行准确检测,有效增强限流设施的自动化水平,为轨道交通站点客流组织与管理提供数据支撑和理论依据.展开更多
文摘In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles.
文摘Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.
文摘针对现有限流设施与策略智能化程度不高,灵活性较差的问题,提出一种基于光流特征描述子的站点限流设施优化方法.首先,根据枢纽内场景特点,设置感兴趣区域(region of interest,ROI),从而降低后续操作的计算量,提高算法的执行效率;然后,在建立光流特征描述子的基础上,对图片序列进行特征分析;最后,基于人群聚集特征,对经典单分类支持向量机进行调整,并实现超负荷状态的检测.实验结果表明,提出的方法能够对站台人群状态进行准确检测,有效增强限流设施的自动化水平,为轨道交通站点客流组织与管理提供数据支撑和理论依据.
