The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vec...The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.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
The authors present their analysis of the differential equation d X(t)/ d t = AX(t)-X T (t)BX(t)X(t) , where A is an unsymmetrical real matrix, B is a positive definite symmetric real matrix, X ∈...The authors present their analysis of the differential equation d X(t)/ d t = AX(t)-X T (t)BX(t)X(t) , where A is an unsymmetrical real matrix, B is a positive definite symmetric real matrix, X ∈R n; showing that the equation characterizes a class of continuous type full feedback artificial neural network; We give the analytic expression of the solution; discuss its asymptotic behavior; and finally present the result showing that, in almost all cases, one and only one of following cases is true. 1. For any initial value X 0∈R n, the solution approximates asymptotically to zero vector. In this case, the real part of each eigenvalue of A is non positive. 2. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a nontrivial constant vector (X 0) . In this case, the eigenvalue of A with maximal real part is the positive number λ=‖(X 0)‖ 2 B and (X 0) is the corresponding eigenvector. 3. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a non constant periodic function (X 0,t) . Then the eigenvalues of A with maximal real part is a pair of conjugate complex numbers which can be computed.展开更多
Edge detection of potential field interpretation is an important task. The traditional edge detection methods have poor ability in outlining weak amplitude anomalies clearly. The resolved edges position is blurred.We ...Edge detection of potential field interpretation is an important task. The traditional edge detection methods have poor ability in outlining weak amplitude anomalies clearly. The resolved edges position is blurred.We purposed new edge detection methods based on directional eigenvalues of potential field gradient tensor for the causative sources. In order to balance strong and weak amplitude anomalies simultaneously,we present one normalization method using different orders of vertical derivatives to improve the new filters. The presented filters were tested on synthetic and real potential field data to verify its feasibility. All of the results have shown that the new edge detection methods can not only display the sources edges precisely and clearly,but also bring out more geological subtle details.展开更多
We calculate the eigenvalues and eigenvectors of a five-qubit isotropic Heisenberg model in an external magnetic field, and give analytical results for the concurrence of two nearest-neighbor qubits. A magnetic field ...We calculate the eigenvalues and eigenvectors of a five-qubit isotropic Heisenberg model in an external magnetic field, and give analytical results for the concurrence of two nearest-neighbor qubits. A magnetic field can eliminate degeneration and change the ground state of the system. Therefore increasing the value of the magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic case.展开更多
A time-series similarity measurement method based on wavelet and matrix transform was proposed,and its anti-noise ability,sensitivity and accuracy were discussed. The time-series sequences were compressed into wavelet...A time-series similarity measurement method based on wavelet and matrix transform was proposed,and its anti-noise ability,sensitivity and accuracy were discussed. The time-series sequences were compressed into wavelet subspace,and sample feature vector and orthogonal basics of sample time-series sequences were obtained by K-L transform. Then the inner product transform was carried out to project analyzed time-series sequence into orthogonal basics to gain analyzed feature vectors. The similarity was calculated between sample feature vector and analyzed feature vector by the Euclid distance. Taking fault wave of power electronic devices for example,the experimental results show that the proposed method has low dimension of feature vector,the anti-noise ability of proposed method is 30 times as large as that of plain wavelet method,the sensitivity of proposed method is 1/3 as large as that of plain wavelet method,and the accuracy of proposed method is higher than that of the wavelet singular value decomposition method. The proposed method can be applied in similarity matching and indexing for lager time series databases.展开更多
In this paper, an error is firstly pointed out in the proof of the main theorems (Theorem 4 and Theorem 6) in [1]. Then the error is corrected and the right proof is given.
The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techn...The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techniques. However, the application of this extended procedure is often hampered by its complexity in computation and by lack of some appropriate theory. In this paper, by use of the empirical processes we established a large sample theory for the robust PP estimators of the principal components and dispersion matrix.展开更多
The interaction of strain and vorticity in compressible turbulent boundary layers at Mach number 2.0 and 4.9 is studied by direct numerical simulation(DNS)of the compressible Navier-Stokes equations.Some fundamental c...The interaction of strain and vorticity in compressible turbulent boundary layers at Mach number 2.0 and 4.9 is studied by direct numerical simulation(DNS)of the compressible Navier-Stokes equations.Some fundamental characteristics have been studied for both the enstrophy producing and destroying regions.It is found that large enstrophy production is associated with high dissipation and high enstrophy,while large enstrophy destruction with moderate ones.The enstrophy production and destruction are also correlated with the dissipation production and destruction.Moreover,the enstrophy producing region has a distinct tendency to be‘sheet-like’structures and the enstrophy destroying region tends to be‘tube-like’in the inner layer.Correspondingly,the tendency to be‘sheet-like’or‘tube-like’structures is no longer obvious in the outer layer.Further,the alignment between the vorticity vector and the strain-rate eigenvector is analyzed in the flow topologies.It is noticed that the enstrophy production rate depends mainly on the alignment between the vorticity vector and the intermediate eigenvector in the inner layer,and the enstrophy production(destruction)mainly on the alignment between the vorticity vector and the extensive(compressive)eigenvector in the outer layer.展开更多
基金the Science Research Foundation of Education Department of ShaanxiProvince (08JK340)the Items of Xi’an University of Architecture and Technology(RC0701JC0718)
文摘The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.
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The authors present their analysis of the differential equation d X(t)/ d t = AX(t)-X T (t)BX(t)X(t) , where A is an unsymmetrical real matrix, B is a positive definite symmetric real matrix, X ∈R n; showing that the equation characterizes a class of continuous type full feedback artificial neural network; We give the analytic expression of the solution; discuss its asymptotic behavior; and finally present the result showing that, in almost all cases, one and only one of following cases is true. 1. For any initial value X 0∈R n, the solution approximates asymptotically to zero vector. In this case, the real part of each eigenvalue of A is non positive. 2. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a nontrivial constant vector (X 0) . In this case, the eigenvalue of A with maximal real part is the positive number λ=‖(X 0)‖ 2 B and (X 0) is the corresponding eigenvector. 3. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a non constant periodic function (X 0,t) . Then the eigenvalues of A with maximal real part is a pair of conjugate complex numbers which can be computed.
基金financially supported by Sino Probe-09-01 Grant No. 201311192Project 2014100 Supported by Graduate Innovation Fund of Jilin University
文摘Edge detection of potential field interpretation is an important task. The traditional edge detection methods have poor ability in outlining weak amplitude anomalies clearly. The resolved edges position is blurred.We purposed new edge detection methods based on directional eigenvalues of potential field gradient tensor for the causative sources. In order to balance strong and weak amplitude anomalies simultaneously,we present one normalization method using different orders of vertical derivatives to improve the new filters. The presented filters were tested on synthetic and real potential field data to verify its feasibility. All of the results have shown that the new edge detection methods can not only display the sources edges precisely and clearly,but also bring out more geological subtle details.
基金project upported by National Natural Science Foundation of China under Grant No.10774108
文摘We calculate the eigenvalues and eigenvectors of a five-qubit isotropic Heisenberg model in an external magnetic field, and give analytical results for the concurrence of two nearest-neighbor qubits. A magnetic field can eliminate degeneration and change the ground state of the system. Therefore increasing the value of the magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic case.
基金Projects(60634020, 60904077, 60874069) supported by the National Natural Science Foundation of ChinaProject(JC200903180555A) supported by the Foundation Project of Shenzhen City Science and Technology Plan of China
文摘A time-series similarity measurement method based on wavelet and matrix transform was proposed,and its anti-noise ability,sensitivity and accuracy were discussed. The time-series sequences were compressed into wavelet subspace,and sample feature vector and orthogonal basics of sample time-series sequences were obtained by K-L transform. Then the inner product transform was carried out to project analyzed time-series sequence into orthogonal basics to gain analyzed feature vectors. The similarity was calculated between sample feature vector and analyzed feature vector by the Euclid distance. Taking fault wave of power electronic devices for example,the experimental results show that the proposed method has low dimension of feature vector,the anti-noise ability of proposed method is 30 times as large as that of plain wavelet method,the sensitivity of proposed method is 1/3 as large as that of plain wavelet method,and the accuracy of proposed method is higher than that of the wavelet singular value decomposition method. The proposed method can be applied in similarity matching and indexing for lager time series databases.
基金Supported by the Natural Scientific Research Foundation of Yunnan Province(2000A0001-1M)the Scientific Foundations of Education Commisison of Yunnan Province(9911126)
文摘In this paper, an error is firstly pointed out in the proof of the main theorems (Theorem 4 and Theorem 6) in [1]. Then the error is corrected and the right proof is given.
基金The researcb was partially supported by the National Natural Science Foundation of China under Grant No.19631040.
文摘The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techniques. However, the application of this extended procedure is often hampered by its complexity in computation and by lack of some appropriate theory. In this paper, by use of the empirical processes we established a large sample theory for the robust PP estimators of the principal components and dispersion matrix.
基金supported by the National Natural Science Foundation of China(Grant Nos.11132010 and 11072236)the 111 Project(GrantNo.B07033)
文摘The interaction of strain and vorticity in compressible turbulent boundary layers at Mach number 2.0 and 4.9 is studied by direct numerical simulation(DNS)of the compressible Navier-Stokes equations.Some fundamental characteristics have been studied for both the enstrophy producing and destroying regions.It is found that large enstrophy production is associated with high dissipation and high enstrophy,while large enstrophy destruction with moderate ones.The enstrophy production and destruction are also correlated with the dissipation production and destruction.Moreover,the enstrophy producing region has a distinct tendency to be‘sheet-like’structures and the enstrophy destroying region tends to be‘tube-like’in the inner layer.Correspondingly,the tendency to be‘sheet-like’or‘tube-like’structures is no longer obvious in the outer layer.Further,the alignment between the vorticity vector and the strain-rate eigenvector is analyzed in the flow topologies.It is noticed that the enstrophy production rate depends mainly on the alignment between the vorticity vector and the intermediate eigenvector in the inner layer,and the enstrophy production(destruction)mainly on the alignment between the vorticity vector and the extensive(compressive)eigenvector in the outer layer.
