The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we first study properties oflk,singular values of rea...The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we first study properties oflk,singular values of real rectangular tensors. Then, a necessary and sufficient condition for the positive definiteness of partially symmetric rectangular tensors is given. Furthermore, we show that the weak Perron-Frobenius theorem for nonnegative partially symmetric rectangular tensor keeps valid under some new conditions and we prove a maximum property for the largest lk,S-singular values of nonnegative partially symmetric rectangular tensor. Finally, we prove that the largest lk,s- singular value of nonnegative weakly irreducible partially symmetric rectangular tensor is still geometrically simple.展开更多
We give a Brualdi-type Z-eigenvalue inclusion set of tensors,and prove that it is tighter than the inclusion set given by G.Wang,G.L.Zhou,and L.Caccetta[Discrete Contin.Dyn.Syst.Ser.B,2017,22:187–198]in a special cas...We give a Brualdi-type Z-eigenvalue inclusion set of tensors,and prove that it is tighter than the inclusion set given by G.Wang,G.L.Zhou,and L.Caccetta[Discrete Contin.Dyn.Syst.Ser.B,2017,22:187–198]in a special case.We also give an inclusion set for l^k,s-singular values of rectangular tensors.展开更多
针对传统被动式检测方法存在较大检测盲区(Non-detection Zone,NDZ)、阈值难以确定以及易受电能质量扰动影响的缺陷,研究了一种基于奇异值分解(Singular Value Decomposition,SVD)和神经网络的被动式孤岛检测方法。该方法首先对公共连接...针对传统被动式检测方法存在较大检测盲区(Non-detection Zone,NDZ)、阈值难以确定以及易受电能质量扰动影响的缺陷,研究了一种基于奇异值分解(Singular Value Decomposition,SVD)和神经网络的被动式孤岛检测方法。该方法首先对公共连接点(Point of Common Coupling,PCC)处电压和逆变器输出电流进行S变换,提取相应的谐波幅值后,对其进行SVD并构成特征向量,最后运用BP神经网络对孤岛以及非孤岛情况进行分类识别。仿真结果表明,该方法可以有效检测出功率平衡情况下发生的孤岛,而且能防止电能质量扰动对检测准确性的影响,具有很高的准确性、可靠性和实用性。展开更多
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371109, 11426075）, the Natural Science Foundation of Heilongjiang Province （No. QC2014C001）, and the Fundamental Research Funds for the Central Universities.
文摘The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we first study properties oflk,singular values of real rectangular tensors. Then, a necessary and sufficient condition for the positive definiteness of partially symmetric rectangular tensors is given. Furthermore, we show that the weak Perron-Frobenius theorem for nonnegative partially symmetric rectangular tensor keeps valid under some new conditions and we prove a maximum property for the largest lk,S-singular values of nonnegative partially symmetric rectangular tensor. Finally, we prove that the largest lk,s- singular value of nonnegative weakly irreducible partially symmetric rectangular tensor is still geometrically simple.
基金This work was supported in part by the National Natural Science Foundation of China(Grant No.11801115)the Youth Science Foundation of Heilongjiang Province of China(No.QC2018002)the Fundamental Research Funds for Central Universities.
文摘We give a Brualdi-type Z-eigenvalue inclusion set of tensors,and prove that it is tighter than the inclusion set given by G.Wang,G.L.Zhou,and L.Caccetta[Discrete Contin.Dyn.Syst.Ser.B,2017,22:187–198]in a special case.We also give an inclusion set for l^k,s-singular values of rectangular tensors.
文摘针对传统被动式检测方法存在较大检测盲区(Non-detection Zone,NDZ)、阈值难以确定以及易受电能质量扰动影响的缺陷,研究了一种基于奇异值分解(Singular Value Decomposition,SVD)和神经网络的被动式孤岛检测方法。该方法首先对公共连接点(Point of Common Coupling,PCC)处电压和逆变器输出电流进行S变换,提取相应的谐波幅值后,对其进行SVD并构成特征向量,最后运用BP神经网络对孤岛以及非孤岛情况进行分类识别。仿真结果表明,该方法可以有效检测出功率平衡情况下发生的孤岛,而且能防止电能质量扰动对检测准确性的影响,具有很高的准确性、可靠性和实用性。
