This paper studies the nonzero normal vector fields of immersions homotopic to a map g: Mn→N2n-1. In the case of the stable normal bundle of g being orientable, rather complete results are obtained.
Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT)...Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.展开更多
In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normaliza...In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normalization of analytically integrable differential systems. Then we present a new result on the equivalent characterization of the existence of the first integrals of an analytic differential systems near a nonhyperbolic singularity. Finally we pose some open problems on this subject.展开更多
选择静止无功补偿器(static var compensator,SVC)或其它类型的并联型无功补偿装置的安装地点对提高电力系统电压稳定性是一个重要而实际的课题。该文提出一种采用向量场正规形理论,以非线性参与因子为依据,确定SVC安装位置的新方法。...选择静止无功补偿器(static var compensator,SVC)或其它类型的并联型无功补偿装置的安装地点对提高电力系统电压稳定性是一个重要而实际的课题。该文提出一种采用向量场正规形理论,以非线性参与因子为依据,确定SVC安装位置的新方法。由于所提出的方法可计及电力系统非线性特性对电压稳定性的影响,因此与线性化分析方法相比,该文提出的方法在系统具有强非线性特性的条件下,仍能准确选择SVC的有效安装地点。为验证所提出方法的有效性,将所提出的方法用于New England39节点系统,确定在系统中使用SVC的最有效位置,通过对几种情况下系统电压稳定性指标的比较,验证所提出方法的有效性。展开更多
提出了利用向量场正规形方法分析电力系统在不同运行条件下的非线性行为,以非线性参与因子衡量节点对静态电压稳定性的重要程度,并以此确定电力系统中无功补偿设备的有效安装位置。在New England 39节点系统上进行了算例分析,验证了该...提出了利用向量场正规形方法分析电力系统在不同运行条件下的非线性行为,以非线性参与因子衡量节点对静态电压稳定性的重要程度,并以此确定电力系统中无功补偿设备的有效安装位置。在New England 39节点系统上进行了算例分析,验证了该方法的正确性和有效性。展开更多
电网结构是电力系统安全稳定运行的一个重要因素。为研究不同负荷节点对电压稳定性所具有的不同影响程度,首先应用向量场正规形理论分析电力系统潮流方程,提出了以节点电压非线性参与因子作为依据衡量负荷节点影响电压稳定性的程度的方...电网结构是电力系统安全稳定运行的一个重要因素。为研究不同负荷节点对电压稳定性所具有的不同影响程度,首先应用向量场正规形理论分析电力系统潮流方程,提出了以节点电压非线性参与因子作为依据衡量负荷节点影响电压稳定性的程度的方法。该方法可计及电力系统非线性特性对电压稳定性的影响,因此与线性化分析方法相比,该方法在系统具有强非线性特性的条件下,仍能准确识别负荷节点的重要程度。然后用该方法研究了New England 39节点系统中不同负荷节点对电压稳定性的影响,通过对系统电压稳定性指标的比较,验证了所提出方法的有效性。展开更多
文摘This paper studies the nonzero normal vector fields of immersions homotopic to a map g: Mn→N2n-1. In the case of the stable normal bundle of g being orientable, rather complete results are obtained.
基金supported by National Natural Science Foundation of China(No.61171145)Shanghai Educational Development Fundation(No.12ZZ083)
文摘Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.
基金supported by the NNSF of China Grant 11271252the RFDP of Higher Education of China grant 20110073110054the FP7-PEOPLE-2012-IRSES-316338 of Europe
文摘In this paper we first summarize our results published in recent years and their sketch proofs on local integrability,which are on the characterization of local integrability and on the existence of analytic normalization of analytically integrable differential systems. Then we present a new result on the equivalent characterization of the existence of the first integrals of an analytic differential systems near a nonhyperbolic singularity. Finally we pose some open problems on this subject.
文摘选择静止无功补偿器(static var compensator,SVC)或其它类型的并联型无功补偿装置的安装地点对提高电力系统电压稳定性是一个重要而实际的课题。该文提出一种采用向量场正规形理论,以非线性参与因子为依据,确定SVC安装位置的新方法。由于所提出的方法可计及电力系统非线性特性对电压稳定性的影响,因此与线性化分析方法相比,该文提出的方法在系统具有强非线性特性的条件下,仍能准确选择SVC的有效安装地点。为验证所提出方法的有效性,将所提出的方法用于New England39节点系统,确定在系统中使用SVC的最有效位置,通过对几种情况下系统电压稳定性指标的比较,验证所提出方法的有效性。
文摘电网结构是电力系统安全稳定运行的一个重要因素。为研究不同负荷节点对电压稳定性所具有的不同影响程度,首先应用向量场正规形理论分析电力系统潮流方程,提出了以节点电压非线性参与因子作为依据衡量负荷节点影响电压稳定性的程度的方法。该方法可计及电力系统非线性特性对电压稳定性的影响,因此与线性化分析方法相比,该方法在系统具有强非线性特性的条件下,仍能准确识别负荷节点的重要程度。然后用该方法研究了New England 39节点系统中不同负荷节点对电压稳定性的影响,通过对系统电压稳定性指标的比较,验证了所提出方法的有效性。
