In this paper,we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton■as follows■where is a positive continuous function on,denotes the outward ...In this paper,we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton■as follows■where is a positive continuous function on,denotes the outward unit normal to the boundary,and are two nonnegative constants.We establish some universal inequalities for eigenvalues of this problem.展开更多
Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the syste...Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.展开更多
A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential ...A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function for the Zakharov–Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, tanh(ax) mapping, and Chebyshev nodes, the Zakharov–Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma–Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems.展开更多
Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.I...Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.In a layered model with increasing layer velocity,the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer.If the phase velocity is the same as the P-or S-wave velocity of the layer,which is called the critical mode or critical phase velocity of surface waves,the general solution of the wave equation is not a homogeneous(expressed by trigonometric functions)or inhomogeneous(expressed by exponential functions)plane wave,but one whose amplitude changes linearly with depth(expressed by a linear function).Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode,owing to the singularity at the critical phase velocity.In this study,based on the classical framework of generalized reflection and transmission coefficients,the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity.Therefore,the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem.The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models.In contrast to the normal mode,the eigendisplacement associated with the critical phase velocity exhibits different characteristics.If the phase velocity is equal to the S-wave velocity in the bottom half-space,the eigendisplacement remains constant with increasing depth.展开更多
单主用户信号的出现主要引起多天线接收信号取样协方差矩阵中极值特征值的变化,而多主用户信号的出现则会同时扰动取样协方差矩阵极值特征值和其他特征值,此时,经典的极值特征值检测算法则会表现出次佳的检测性能。针对这一问题,本研究...单主用户信号的出现主要引起多天线接收信号取样协方差矩阵中极值特征值的变化,而多主用户信号的出现则会同时扰动取样协方差矩阵极值特征值和其他特征值,此时,经典的极值特征值检测算法则会表现出次佳的检测性能。针对这一问题,本研究设计了一种基于极值特征值差与特征值几何平均(difference of extreme eigenvalues and geometric average of eigenvalues,DEEGAE)的多主用户信号检测判决规则;提出了一种基于Wishart矩阵特征值统计分布理论的感知判决门限的闭式求解方法。该算法在频谱感知过程中直接利用认知用户的多天线接收数据构造判决规则并实施感知判决,具有全盲检测的优点;通过融合2种极限特征值门限分析结果,提高了非渐近感知条件下感知结果的准确性。Monte-Carlo仿真试验表明,新算法具有比经典的最大最小特征值之比算法和协方差绝对值检测算法更优的多主用户信号检测性能,同时能获得比传统基于最大最小特征值之差及其改进算法更为可靠的检测结果;与此同时,新算法的检测性能随着样本数目以及天线数目的增大而显著提升。展开更多
“沙戈荒”风电经高压直流输电(line commutated converter based high voltage direct current,LCC-HVDC)送至负荷中心消纳场景中,风机采用虚拟同步机控制(virtual synchronous generator control,VSG)可自行构建输出电压和频率,为LCC-...“沙戈荒”风电经高压直流输电(line commutated converter based high voltage direct current,LCC-HVDC)送至负荷中心消纳场景中,风机采用虚拟同步机控制(virtual synchronous generator control,VSG)可自行构建输出电压和频率,为LCC-HVDC提供换相电压。采用虚拟同步机控制的直驱风电场(virtual synchronous generator direct-drive wind farm,VSG-DDWF)接入LCC-HVDC送端换流站近区时,系统次同步振荡(sub-synchronous oscillation,SSO)特性及机理尚未有定论。首先,文章采用模块化小信号建模方法建立了VSG-DDWF接入LCC-HVDC送端近区系统状态空间模型;其次,基于特征值分析法分析了系统SSO特性;然后,通过阻尼路径法揭示VSG-DDWF与LCC-HVDC系统SSO交互作用机理,并分析了风机机侧动态对系统阻尼的影响;最后,分析了风机台数、短路比(Short Circuit Ratio,SCR)、控制器参数对系统阻尼的影响。结果显示,VSG-DDWF同步控制环节主导的SSO模态具有失稳风险,VSG-DDWF与LCC-HVDC间存在SSO交互作用,加剧了系统发生的SSO风险;风机机侧动态会引入负阻尼,并使振荡频率发生偏移;风机网侧外环控制器比例系数减小,短路比增大时,系统SSO模态阻尼减小;VSG-DDWF中风机台数增多,系统SSO模态阻尼先增加后减小。展开更多
基于Wi-Fi感知的室内入侵检测系统是一种无需在移动实体上附加任何设备即可检测移动实体的系统。针对目前检测方法忽略复杂的幅度变化和相位变化引起的潜在影响,提出了融合长短期记忆网络和支持向量机的室内入侵检测新方法LSID(Long Sho...基于Wi-Fi感知的室内入侵检测系统是一种无需在移动实体上附加任何设备即可检测移动实体的系统。针对目前检测方法忽略复杂的幅度变化和相位变化引起的潜在影响,提出了融合长短期记忆网络和支持向量机的室内入侵检测新方法LSID(Long Short-Term Memory and Support Vector Machine Intrusion Detection)。LSID方法采用一种新的特征值建模方式,利用长短期记忆网络可以学习到时序特征并且能捕捉时序信号长期的依赖关系,将信道状态信息真实值与长短期记忆神经网络的预测值之差作为特征值,能更准确地捕捉入侵者对信号状态信息的影响。该检测方法在学校实验室环境下经过多次实验验证,最终检测准确率达到99.21%,通过多组实验比对,结果显示LSID方法具有有效性和可行性,相比于其他入侵检测方法准确率明显提升。展开更多
基金Supported by National Natural Science Foundation of China(11001130,12272062)Fundamental Research Funds for the Central Universities(30917011335).
文摘In this paper,we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton■as follows■where is a positive continuous function on,denotes the outward unit normal to the boundary,and are two nonnegative constants.We establish some universal inequalities for eigenvalues of this problem.
基金This work was supported by the National Natural Science Foundation of China(Grant No.62071248)the Natural Science Foundation of Nanjing University of Posts and Telecommunications(Grant No.NY223109)China Postdoctoral Science Foundation(Grant No.2022M721693).
文摘Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.52171251,U2106225,and 52231011)Dalian Science and Technology Innovation Fund (Grant No.2022JJ12GX036)。
文摘A numerical method is proposed to calculate the eigenvalues of the Zakharov–Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function for the Zakharov–Shabat eigenvalue problem. The mapping can distribute Chebyshev nodes very well considering the gradient for the potential function. Using Chebyshev polynomials, tanh(ax) mapping, and Chebyshev nodes, the Zakharov–Shabat eigenvalue problem is transformed into a matrix eigenvalue problem. This method has good convergence for the Satsuma–Yajima potential and the convergence rate is faster than the Fourier collocation method. This method is not only suitable for simple potential functions but also converges quickly for a complex Y-shape potential. It can also be further extended to other linear eigenvalue problems.
基金supported by the National Natural Science Foundation of China(No.U1839209).
文摘Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.In a layered model with increasing layer velocity,the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer.If the phase velocity is the same as the P-or S-wave velocity of the layer,which is called the critical mode or critical phase velocity of surface waves,the general solution of the wave equation is not a homogeneous(expressed by trigonometric functions)or inhomogeneous(expressed by exponential functions)plane wave,but one whose amplitude changes linearly with depth(expressed by a linear function).Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode,owing to the singularity at the critical phase velocity.In this study,based on the classical framework of generalized reflection and transmission coefficients,the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity.Therefore,the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem.The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models.In contrast to the normal mode,the eigendisplacement associated with the critical phase velocity exhibits different characteristics.If the phase velocity is equal to the S-wave velocity in the bottom half-space,the eigendisplacement remains constant with increasing depth.
文摘单主用户信号的出现主要引起多天线接收信号取样协方差矩阵中极值特征值的变化,而多主用户信号的出现则会同时扰动取样协方差矩阵极值特征值和其他特征值,此时,经典的极值特征值检测算法则会表现出次佳的检测性能。针对这一问题,本研究设计了一种基于极值特征值差与特征值几何平均(difference of extreme eigenvalues and geometric average of eigenvalues,DEEGAE)的多主用户信号检测判决规则;提出了一种基于Wishart矩阵特征值统计分布理论的感知判决门限的闭式求解方法。该算法在频谱感知过程中直接利用认知用户的多天线接收数据构造判决规则并实施感知判决,具有全盲检测的优点;通过融合2种极限特征值门限分析结果,提高了非渐近感知条件下感知结果的准确性。Monte-Carlo仿真试验表明,新算法具有比经典的最大最小特征值之比算法和协方差绝对值检测算法更优的多主用户信号检测性能,同时能获得比传统基于最大最小特征值之差及其改进算法更为可靠的检测结果;与此同时,新算法的检测性能随着样本数目以及天线数目的增大而显著提升。
文摘“沙戈荒”风电经高压直流输电(line commutated converter based high voltage direct current,LCC-HVDC)送至负荷中心消纳场景中,风机采用虚拟同步机控制(virtual synchronous generator control,VSG)可自行构建输出电压和频率,为LCC-HVDC提供换相电压。采用虚拟同步机控制的直驱风电场(virtual synchronous generator direct-drive wind farm,VSG-DDWF)接入LCC-HVDC送端换流站近区时,系统次同步振荡(sub-synchronous oscillation,SSO)特性及机理尚未有定论。首先,文章采用模块化小信号建模方法建立了VSG-DDWF接入LCC-HVDC送端近区系统状态空间模型;其次,基于特征值分析法分析了系统SSO特性;然后,通过阻尼路径法揭示VSG-DDWF与LCC-HVDC系统SSO交互作用机理,并分析了风机机侧动态对系统阻尼的影响;最后,分析了风机台数、短路比(Short Circuit Ratio,SCR)、控制器参数对系统阻尼的影响。结果显示,VSG-DDWF同步控制环节主导的SSO模态具有失稳风险,VSG-DDWF与LCC-HVDC间存在SSO交互作用,加剧了系统发生的SSO风险;风机机侧动态会引入负阻尼,并使振荡频率发生偏移;风机网侧外环控制器比例系数减小,短路比增大时,系统SSO模态阻尼减小;VSG-DDWF中风机台数增多,系统SSO模态阻尼先增加后减小。
文摘基于Wi-Fi感知的室内入侵检测系统是一种无需在移动实体上附加任何设备即可检测移动实体的系统。针对目前检测方法忽略复杂的幅度变化和相位变化引起的潜在影响,提出了融合长短期记忆网络和支持向量机的室内入侵检测新方法LSID(Long Short-Term Memory and Support Vector Machine Intrusion Detection)。LSID方法采用一种新的特征值建模方式,利用长短期记忆网络可以学习到时序特征并且能捕捉时序信号长期的依赖关系,将信道状态信息真实值与长短期记忆神经网络的预测值之差作为特征值,能更准确地捕捉入侵者对信号状态信息的影响。该检测方法在学校实验室环境下经过多次实验验证,最终检测准确率达到99.21%,通过多组实验比对,结果显示LSID方法具有有效性和可行性,相比于其他入侵检测方法准确率明显提升。
