A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the s...A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.展开更多
The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the minimal annihilating polyn...The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the minimal annihilating polynomial, and a set of linearly independent eigenvectors from the decomposition in disjoint cycles of the permutation naturally associated to the matrix.展开更多
The paper presents an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time varying bias. In particular it refers to parallel tank oscillato...The paper presents an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time varying bias. In particular it refers to parallel tank oscillators of which the energy restoring can be modeled through a train of current pulses. Since Floquet eigenvectors are acknowledged to give a correct decomposition of noise perturbations along the stable orbit in oscillator's space state, an analytical and compact model of their displacement can provide useful criteria for designers. The goal is to show, in a simplified case, the achievement of oscillators design oriented by eigenvectors. To this aim, minimization conditions of the effect of stationary and time varying noise as well as the contribution of jitter noise introduced by driving electronics are deduced from analytical expression of eigenvectors displacement.展开更多
We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful atta...We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful attack of this code are also computed. For multi-sender authentication code,it allows a group of senders to construct an authenticated message for a receiver such that the receiver can verify authenticity of the received message.展开更多
Every matrix is similar to a matrix in Jordan canonical form,which has very important sense in the theory of linear algebra and its engineering application.For a matrix with multiplex eigenvalues,an algorithm based on...Every matrix is similar to a matrix in Jordan canonical form,which has very important sense in the theory of linear algebra and its engineering application.For a matrix with multiplex eigenvalues,an algorithm based on the singular value decomposition(SVD) for computing its eigenvectors and Jordan canonical form was proposed.Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues.It is superior to MATLAB and MATHEMATICA.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
Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leadi...Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leading principal submatrix Vn and a bordered matrix of Vn. Recurrence formula are given for the characteristic polynomial of W2＋n＋1 . The eigenvectors of W2＋n＋1 are proved to be symmetric or skew symmetric. For W2n＋1 , it is found that its eigenvalues are zero and the square roots of the eigenvalues of a bordered matrix of Vn2. And the eigenvectors of W2n＋1 , which the corresponding eigenvahies are opposite in pairs, have close relationship.展开更多
This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quater...This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.展开更多
The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices...The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.展开更多
The paper presents an analytical derivation of Floquet eigenvalues and eigenvectors for a class of harmonic phase and quadrature oscillators. The derivation refers in particular to systems modeled by two parallel RLC ...The paper presents an analytical derivation of Floquet eigenvalues and eigenvectors for a class of harmonic phase and quadrature oscillators. The derivation refers in particular to systems modeled by two parallel RLC resonators with pulsed energy restoring. Pulsed energy restoring is obtained through parallel current generators with an impulsive characteristic triggered by the resonators voltages. In performing calculation the initial hypothesis of the existence of stable oscillation is only made, then it is verified when both oscillation amplitude and eigenvalues/eigenvectors are deduced from symmetry conditions on oscillator space state. A detailed determination of the first eigenvector is obtained. Remaining eigenvectors are hence calculated with realistic approximations. Since Floquet eigenvectors are acknowledged to give the correct decomposition of noise perturbations superimposed to the oscillator space state along its limit cycle, an analytical and compact model of their behavior highlights the unique phase noise properties of this class of oscillators.展开更多
立体摄影技术可实现三维海浪的连续观测,但目前基于立体摄影海浪观测数据开展二维海浪方向谱估计的研究却相对匮乏,从而束缚了立体摄影技术在海洋观测中的进一步深入应用。鉴于此,本文基于中国海洋大学微波遥感实验室开发的立体摄影海...立体摄影技术可实现三维海浪的连续观测,但目前基于立体摄影海浪观测数据开展二维海浪方向谱估计的研究却相对匮乏,从而束缚了立体摄影技术在海洋观测中的进一步深入应用。鉴于此,本文基于中国海洋大学微波遥感实验室开发的立体摄影海浪观测系统,并结合海浪方向谱阵列测量的扩展本征矢方法,系统性研究了基于立体摄影海浪观测数据反演二维海浪方向谱的可行性,并分析了不同海面采样点阵列排列方式、采样点间距及观测误差等因素对二维海浪方向谱反演结果的影响。立体摄影实测海浪数据反演结果显示:阵列中采样点间距小于1/3波浪的波长,海面采样点阵列排列方式为五边形时可得到较好的海浪方向谱反演结果。通过将立体摄影数据反演所得二维海浪方向谱与Signature1000型声学多普勒波浪流速剖面仪(Acoustic Doppler Wave and Current Profiler, AWAC)测量结果进行比较,结果显示二者具有较高的相关性和良好的一致性。立体摄影所得有效波高、平均波向和AWAC测量的有效波高、平均波向的相关系数分别为0.988和0.983,平均偏差分别为0.029 m和0.010°,均方根误差分别为0.089 m和8.844°。展开更多
基金Project supported by the Mathematical Tianyuan Foundation of China (No. 10626019)
文摘A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.
文摘The spectral properties of special matrices have been widely studied, because of their applications. We focus on permutation matrices over a finite field and, more concretely, we compute the minimal annihilating polynomial, and a set of linearly independent eigenvectors from the decomposition in disjoint cycles of the permutation naturally associated to the matrix.
文摘The paper presents an approximated and compact derivation of the mutual displacement of Floquet eigenvectors in a class of LC tank oscillators with time varying bias. In particular it refers to parallel tank oscillators of which the energy restoring can be modeled through a train of current pulses. Since Floquet eigenvectors are acknowledged to give a correct decomposition of noise perturbations along the stable orbit in oscillator's space state, an analytical and compact model of their displacement can provide useful criteria for designers. The goal is to show, in a simplified case, the achievement of oscillators design oriented by eigenvectors. To this aim, minimization conditions of the effect of stationary and time varying noise as well as the contribution of jitter noise introduced by driving electronics are deduced from analytical expression of eigenvectors displacement.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61179026)the Fundamental Research of the Central Universities of China Civil Aviation University of Science Special(Grant No.3122016L005)
文摘We construct one multi-sender authentication code by algebraic combination method from eigenvalues and eigenvectors of the matrix over nite elds. Some parameters and the probabilities of three kinds of successful attack of this code are also computed. For multi-sender authentication code,it allows a group of senders to construct an authenticated message for a receiver such that the receiver can verify authenticity of the received message.
文摘Every matrix is similar to a matrix in Jordan canonical form,which has very important sense in the theory of linear algebra and its engineering application.For a matrix with multiplex eigenvalues,an algorithm based on the singular value decomposition(SVD) for computing its eigenvectors and Jordan canonical form was proposed.Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues.It is superior to MATLAB and MATHEMATICA.
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.
基金The Fundamental Research Funds for the Central Universities, China (No.10D10908)
文摘Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leading principal submatrix Vn and a bordered matrix of Vn. Recurrence formula are given for the characteristic polynomial of W2＋n＋1 . The eigenvectors of W2＋n＋1 are proved to be symmetric or skew symmetric. For W2n＋1 , it is found that its eigenvalues are zero and the square roots of the eigenvalues of a bordered matrix of Vn2. And the eigenvectors of W2n＋1 , which the corresponding eigenvahies are opposite in pairs, have close relationship.
文摘This paper aims to present, in a unified manner, the algebraic techniques of eigen-problem which are valid on both the quaternions and split quaternions. This paper studies eigenvalues and eigenvectors of the v-quaternion matrices by means of the complex representation of the v-quaternion matrices, and derives an algebraic technique to find the eigenvalues and eigenvectors of v-quaternion matrices. This paper also gives a unification of algebraic techniques for eigenvalues and eigenvectors in quaternionic and split quaternionic mechanics.
文摘The eigenvectors of a fuzzy matrix correspond to steady states of a complex discrete-events system, characterized by the given transition matrix and fuzzy state vectors. The descriptions of the eigenspace for matrices in the max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra have been presented in previous papers. In this paper, we investigate the monotone eigenvectors in a max-T algebra, list some particular properties of the monotone eigenvectors in max-Lukasiewicz algebra, max-min algebra, max-nilpotent-min algebra, max-product algebra and max-drast algebra, respectively, and illustrate the relations among eigenspaces in these algebras by some examples.
文摘The paper presents an analytical derivation of Floquet eigenvalues and eigenvectors for a class of harmonic phase and quadrature oscillators. The derivation refers in particular to systems modeled by two parallel RLC resonators with pulsed energy restoring. Pulsed energy restoring is obtained through parallel current generators with an impulsive characteristic triggered by the resonators voltages. In performing calculation the initial hypothesis of the existence of stable oscillation is only made, then it is verified when both oscillation amplitude and eigenvalues/eigenvectors are deduced from symmetry conditions on oscillator space state. A detailed determination of the first eigenvector is obtained. Remaining eigenvectors are hence calculated with realistic approximations. Since Floquet eigenvectors are acknowledged to give the correct decomposition of noise perturbations superimposed to the oscillator space state along its limit cycle, an analytical and compact model of their behavior highlights the unique phase noise properties of this class of oscillators.
文摘立体摄影技术可实现三维海浪的连续观测,但目前基于立体摄影海浪观测数据开展二维海浪方向谱估计的研究却相对匮乏,从而束缚了立体摄影技术在海洋观测中的进一步深入应用。鉴于此,本文基于中国海洋大学微波遥感实验室开发的立体摄影海浪观测系统,并结合海浪方向谱阵列测量的扩展本征矢方法,系统性研究了基于立体摄影海浪观测数据反演二维海浪方向谱的可行性,并分析了不同海面采样点阵列排列方式、采样点间距及观测误差等因素对二维海浪方向谱反演结果的影响。立体摄影实测海浪数据反演结果显示:阵列中采样点间距小于1/3波浪的波长,海面采样点阵列排列方式为五边形时可得到较好的海浪方向谱反演结果。通过将立体摄影数据反演所得二维海浪方向谱与Signature1000型声学多普勒波浪流速剖面仪(Acoustic Doppler Wave and Current Profiler, AWAC)测量结果进行比较,结果显示二者具有较高的相关性和良好的一致性。立体摄影所得有效波高、平均波向和AWAC测量的有效波高、平均波向的相关系数分别为0.988和0.983,平均偏差分别为0.029 m和0.010°,均方根误差分别为0.089 m和8.844°。
