This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic...This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.展开更多
An eigenvector method for ranking alternatives whose measurements are given as vague values is provided. Firstly, a positive matrix is constructed which is defined as evaluation information matrix （EIM）. Based on fo...An eigenvector method for ranking alternatives whose measurements are given as vague values is provided. Firstly, a positive matrix is constructed which is defined as evaluation information matrix （EIM）. Based on four assumptions for evaluating alternatives, a ranking eigenvector is defined. And then it is proved, based on positive matrix theory, that the EIM＇s eigenvector corresponding to the maximal eigenvalue is the ranking vector. For alternatives whose characteristics are presented by vague sets, the proposed techniques can evaluate the degree of suitability to which an alternative satisfies the decision-maker＇ s requirement efficiently.展开更多
For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding t...For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding to the largest eigenvalue of A(G)(resp. Q(G)). In this paper, an upper bound and lower bound for the sum of the squares of the entries of the principal eigenvector of Q(G) corresponding to the vertices of an independent set are obtained.展开更多
In this paper, the author investigates the existence of eigenvectors of system of Hammerstein integral equations in Banach spaces by means of fixed point index theory. He also gives some applications to a system of S ...In this paper, the author investigates the existence of eigenvectors of system of Hammerstein integral equations in Banach spaces by means of fixed point index theory. He also gives some applications to a system of S turm-Liouville problems of ordinary differential equations.展开更多
Time eigenvectors and time operator are constructed from energy eigenvectors of system.Some features of them are described.Their applications to harmonic oscillating system and to double wave description of system are...Time eigenvectors and time operator are constructed from energy eigenvectors of system.Some features of them are described.Their applications to harmonic oscillating system and to double wave description of system are discussed.展开更多
The orthogonality of eigenvector is a precondition to compute the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method. For a linear multi-rigid-flexible-body system, ...The orthogonality of eigenvector is a precondition to compute the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method. For a linear multi-rigid-flexible-body system, the eigenfunction does not satisfy the orthogonality under ordinary meaning. A new concept--augmented eigenvector is introduced, which is used to overcome the orthogonality problem of eigenvectors of linear multi-rigid-flexible-body system. The constitution method and the orthogonality of augmented eigenvector are expatiated. After the orthogonality of augmented eigenvector is acquired, the coupling of coordinates in dynamics equations can be released, which makes it possible to analyze exactly the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method.展开更多
为识别城市轨道交通网络关键站点并研究其多年演化,构建基于截断奇异值分解(truncated singular value decomposition,TSVD)的关键站点识别方法,选取北京市2011—2019年早高峰时段的OD数据,通过关键特征向量分析网络客流演变并对城轨网...为识别城市轨道交通网络关键站点并研究其多年演化,构建基于截断奇异值分解(truncated singular value decomposition,TSVD)的关键站点识别方法,选取北京市2011—2019年早高峰时段的OD数据,通过关键特征向量分析网络客流演变并对城轨网络中关键站点进行识别,将其与复杂网络方法的识别结果进行对比。分析表明:TSVD法能很好地应用于考虑OD分布的网络关键站点识别,识别结果能更好代表网络客流的空间分布。从识别结果看,北京轨道交通关键站点空间布局呈现多中心发展趋势,如西北西二旗,西南丰台科技园等站点逐步形成网络客流中心并相互联系;东南土桥、东北俸伯等站点也初步呈现网络客流中心的特征。展开更多
As same as the conventional inverse synthetic aperture radar（ISAR）, the compressed ISAR also requires the echo signal based motion compensation, which consists of the range alignment and the phase autofoeusing. A ph...As same as the conventional inverse synthetic aperture radar（ISAR）, the compressed ISAR also requires the echo signal based motion compensation, which consists of the range alignment and the phase autofoeusing. A phase autofocusing algorithm for compressed ISAR imaging is presented. In the algorithm, phase autofocusing for the sparse ISAR echoes is accomplished using the eigenvector method. Experimental results validate the effectiveness of the algorithm.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10962004and11061019)'Chunhui Program' Ministry of Education(Grant No.Z2009-1-01010)+3 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20070126002)the Doctoral Foundation of Inner Mongolia(Grant No.2009BS0101)the Natural Science Foundation of Inner Mongolia(Grant No.2010MS0110)the Cultivation of Innovative Talent of '211Project'of Inner Mongolia University
文摘This paper deals with the completeness of the eigenvector system of a class of operator matrices arising from elasticity theory, i.e., symplectic eigenvector expansion theorem. Under certain conditions, the symplectic orthogonality of eigenvectors of the operator matrix is demonstrated. Based on this, a necessary and sufficient condition for the completeness of the eigenvector system of the operator matrix is given. Furthermore, the obtained results are tested for the free vibration of rectangular thin plates.
基金Sponsored by the Basic Research Foundation of Beijing Institute of Technology(BIT-UBF-20070842009)
文摘An eigenvector method for ranking alternatives whose measurements are given as vague values is provided. Firstly, a positive matrix is constructed which is defined as evaluation information matrix （EIM）. Based on four assumptions for evaluating alternatives, a ranking eigenvector is defined. And then it is proved, based on positive matrix theory, that the EIM＇s eigenvector corresponding to the maximal eigenvalue is the ranking vector. For alternatives whose characteristics are presented by vague sets, the proposed techniques can evaluate the degree of suitability to which an alternative satisfies the decision-maker＇ s requirement efficiently.
文摘For a simple connected graph G, let A(G) and Q(G) be the adjacency matrix and signless Laplacian matrix, respectively of G. The principal eigenvector of A(G)(resp.Q(G)) is the unit positive eigenvector corresponding to the largest eigenvalue of A(G)(resp. Q(G)). In this paper, an upper bound and lower bound for the sum of the squares of the entries of the principal eigenvector of Q(G) corresponding to the vertices of an independent set are obtained.
文摘In this paper, the author investigates the existence of eigenvectors of system of Hammerstein integral equations in Banach spaces by means of fixed point index theory. He also gives some applications to a system of S turm-Liouville problems of ordinary differential equations.
基金Supported by the National Natural Science Foundation of China.
文摘Time eigenvectors and time operator are constructed from energy eigenvectors of system.Some features of them are described.Their applications to harmonic oscillating system and to double wave description of system are discussed.
文摘The orthogonality of eigenvector is a precondition to compute the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method. For a linear multi-rigid-flexible-body system, the eigenfunction does not satisfy the orthogonality under ordinary meaning. A new concept--augmented eigenvector is introduced, which is used to overcome the orthogonality problem of eigenvectors of linear multi-rigid-flexible-body system. The constitution method and the orthogonality of augmented eigenvector are expatiated. After the orthogonality of augmented eigenvector is acquired, the coupling of coordinates in dynamics equations can be released, which makes it possible to analyze exactly the dynamic responses of linear multi-rigid-flexible-body system using the classical modal analysis method.
文摘为识别城市轨道交通网络关键站点并研究其多年演化,构建基于截断奇异值分解(truncated singular value decomposition,TSVD)的关键站点识别方法,选取北京市2011—2019年早高峰时段的OD数据,通过关键特征向量分析网络客流演变并对城轨网络中关键站点进行识别,将其与复杂网络方法的识别结果进行对比。分析表明:TSVD法能很好地应用于考虑OD分布的网络关键站点识别,识别结果能更好代表网络客流的空间分布。从识别结果看,北京轨道交通关键站点空间布局呈现多中心发展趋势,如西北西二旗,西南丰台科技园等站点逐步形成网络客流中心并相互联系;东南土桥、东北俸伯等站点也初步呈现网络客流中心的特征。
基金Supported by the National Natural Science Foundation of China(61071165)the Program for NewCentury Excellent Talents in University(NCET-09-0069)the Defense Industrial Technology Development Program(B2520110008)~~
文摘As same as the conventional inverse synthetic aperture radar（ISAR）, the compressed ISAR also requires the echo signal based motion compensation, which consists of the range alignment and the phase autofoeusing. A phase autofocusing algorithm for compressed ISAR imaging is presented. In the algorithm, phase autofocusing for the sparse ISAR echoes is accomplished using the eigenvector method. Experimental results validate the effectiveness of the algorithm.
