a Pole voltage waveforms (VA20 and VA40) for modulation index 0.4 (middle trace is A-phase voltage waveform) x-axis: 1 div.=10ms, y-axis: 1 div.= 100V b Normalized harmonic spectrum for pole voltage of Fig. 9a c A-pha...a Pole voltage waveforms (VA20 and VA40) for modulation index 0.4 (middle trace is A-phase voltage waveform) x-axis: 1 div.=10ms, y-axis: 1 div.= 100V b Normalized harmonic spectrum for pole voltage of Fig. 9a c A-phase current and phase voltage for modulation index 0.4 (reference space vector is in inner layer)展开更多
a Pole voltage waveforms (VA20 and VA40) for modulation index 0.4 (middle trace is A-phase voltage waveform) x-axis: 1 div.=10ms, y-axis: 1 div.= 100V b Normalized harmonic spectrum for pole voltage of Fig. 9a c A-pha...a Pole voltage waveforms (VA20 and VA40) for modulation index 0.4 (middle trace is A-phase voltage waveform) x-axis: 1 div.=10ms, y-axis: 1 div.= 100V b Normalized harmonic spectrum for pole voltage of Fig. 9a c A-phase current and phase voltage for modulation index 0.4 (reference space vector is in inner layer)展开更多
A new method based on the iterative adaptive algorithm(IAA)and blocking matrix preprocessing(BMP)is proposed to study the suppression of multi-mainlobe interference.The algorithm is applied to precisely estimate the s...A new method based on the iterative adaptive algorithm(IAA)and blocking matrix preprocessing(BMP)is proposed to study the suppression of multi-mainlobe interference.The algorithm is applied to precisely estimate the spatial spectrum and the directions of arrival(DOA)of interferences to overcome the drawbacks associated with conventional adaptive beamforming(ABF)methods.The mainlobe interferences are identified by calculating the correlation coefficients between direction steering vectors(SVs)and rejected by the BMP pretreatment.Then,IAA is subsequently employed to reconstruct a sidelobe interference-plus-noise covariance matrix for the preferable ABF and residual interference suppression.Simulation results demonstrate the excellence of the proposed method over normal methods based on BMP and eigen-projection matrix perprocessing(EMP)under both uncorrelated and coherent circumstances.展开更多
In this study,the problem of bundle adjustment was revisited,and a novel algorithm based on block matrix Cholesky decomposition was proposed to solve the thorny problem of self-calibration bundle adjustment.The innova...In this study,the problem of bundle adjustment was revisited,and a novel algorithm based on block matrix Cholesky decomposition was proposed to solve the thorny problem of self-calibration bundle adjustment.The innovation points are reflected in the following aspects:①The proposed algorithm is not dependent on the Schur complement,and the calculation process is simple and clear;②The complexities of time and space tend to O(n)in the context of world point number is far greater than that of images and cameras,so the calculation magnitude and memory consumption can be reduced significantly;③The proposed algorithm can carry out self-calibration bundle adjustment in single-camera,multi-camera,and variable-camera modes;④Some measures are employed to improve the optimization effects.Experimental tests showed that the proposed algorithm has the ability to achieve state-of-the-art performance in accuracy and robustness,and it has a strong adaptability as well,because the optimized results are accurate and robust even if the initial values have large deviations from the truth.This study could provide theoretical guidance and technical support for the image-based positioning and 3D reconstruction in the fields of photogrammetry,computer vision and robotics.展开更多
Cloud computing provides powerful processing capabilities for large-scale intelligent Internet of things(IoT)terminals.However,the massive realtime data processing requirements challenge the existing cloud computing m...Cloud computing provides powerful processing capabilities for large-scale intelligent Internet of things(IoT)terminals.However,the massive realtime data processing requirements challenge the existing cloud computing model.The edge server is closer to the data source.The end-edge-cloud collaboration offloads the cloud computing tasks to the edge environment,which solves the shortcomings of the cloud in resource storage,computing performance,and energy consumption.IoT terminals and sensors have caused security and privacy challenges due to resource constraints and exponential growth.As the key technology of IoT,Radio-Frequency Identification(RFID)authentication protocol tremendously strengthens privacy protection and improves IoT security.However,it inevitably increases system overhead while improving security,which is a major blow to low-cost RFID tags.The existing RFID authentication protocols are difficult to balance overhead and security.This paper designs an ultra-lightweight encryption function and proposes an RFID authentication scheme based on this function for the end-edge-cloud collaborative environment.The BAN logic proof and protocol verification tools AVISPA formally verify the protocol’s security.We use VIVADO to implement the encryption function and tag’s overhead on the FPGA platform.Performance evaluation indicates that the proposed protocol balances low computing costs and high-security requirements.展开更多
In order to alleviate the shortcomings of most blind deconvolution algorithms,this paper proposes an improved fast algorithm for blind deconvolution based on decorrelation technique and broadband block matrix.Althougt...In order to alleviate the shortcomings of most blind deconvolution algorithms,this paper proposes an improved fast algorithm for blind deconvolution based on decorrelation technique and broadband block matrix.Althougth the original algorithm can overcome the shortcomings of current blind deconvolution algorithms,it has a constraint that the number of the source signals must be less than that of the channels.The improved algorithm deletes this constraint by using decorrelation technique.Besides,the improved algorithm raises the separation speed in terms of improving the computing methods of the output signal matrix.Simulation results demonstrate the validation and fast separation of the improved algorithm.展开更多
In this paper, we present a method how to get the expression for the group inverse of 2×2 block matrix and get the explicit expressions of the block matrix (A C B D) under some conditions.
This work essentially consists in inverting in an exact, explicit, and original way the pentadiagonal Toeplitz matrix or tridiagonal block matrix resulting from the discretization of the two-dimensional Laplace operat...This work essentially consists in inverting in an exact, explicit, and original way the pentadiagonal Toeplitz matrix or tridiagonal block matrix resulting from the discretization of the two-dimensional Laplace operator. This method is an algorithm facilitating the resolution of a large number of problems governed by PDEs involving the Laplacian in two dimensions. It guarantees high precision and high efficiency in solving various differential equations.展开更多
In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq...In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.展开更多
In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domai...In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domain. Based on the shear gradient operator, we extend the total variation(TV) norm to the shear total variation(STV) norm by adding two shear gradient terms. Subsequently, we introduce a shear total variation deblurring model. Experimental results are provided to validate the ability of the STV norm to capture the detailed information. Leveraging the Block Circulant with Circulant Blocks(BCCB) structure of the shear gradient matrices, the alternating direction method of multipliers(ADMM) algorithm can be used to solve the proposed model efficiently. Numerous experiments are presented to verify the performance of our algorithm for non-blind image deblurring.展开更多
For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such a...For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices. Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices for some typical matrices from the real-world applications.展开更多
Interference suppression is a challenge for radar researchers, especially when mainlobe and sidelobe interference coexist. We present a comprehensive anti-interference approach based on a cognitive bistatic airborne r...Interference suppression is a challenge for radar researchers, especially when mainlobe and sidelobe interference coexist. We present a comprehensive anti-interference approach based on a cognitive bistatic airborne radar. The risk of interception is reduced by lowering the launch energy of the radar transmitting terminal in the direction of interference;main lobe and sidelobe interferences are suppressed via cooperation between the two radars. The interference received by a single radar is extracted from the overall radar signal using multiple signal classification(MUSIC), and the interference is cross-located using two different azimuthal angles. Neural networks allowing good, non-linear nonparametric approximations are used to predict the location of interference, and this information is then used to preset the transmitting notch antenna to reduce the likelihood of interception. To simultaneously suppress mainlobe and sidelobe interferences, a blocking matrix is used to mask mainlobe interference based on azimuthal information, and an adaptive process is used to suppress sidelobe interference. Mainlobe interference is eliminated using the data received by the two radars. Simulation verifies the performance of the model.展开更多
We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the F...We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the Feng spectrum)of the whole operator matrix and that of its entries.In addition,the connection between the Furi-Martelli-Vignoli spectrum of the whole operator matrix and that of its Schur complement is presented by means of Schur decomposition.展开更多
The Moore-Penrose inverse of a block k-circulant matrix whose blocks are arbitrary matrices are obtained when k has unit modulus. In the meantime. explicit formulae for finding group inverses of certain specified k-ci...The Moore-Penrose inverse of a block k-circulant matrix whose blocks are arbitrary matrices are obtained when k has unit modulus. In the meantime. explicit formulae for finding group inverses of certain specified k-circulant matrices are also given.展开更多
Yamdrok melange occurs south of, and parallel to, the Yarlung—Zangbo ophiolites, extending several hundreds of kilometres with a width of several to tens of kilometres. Areas near Baisa and Rilang in the Gyangze dist...Yamdrok melange occurs south of, and parallel to, the Yarlung—Zangbo ophiolites, extending several hundreds of kilometres with a width of several to tens of kilometres. Areas near Baisa and Rilang in the Gyangze district were chosen for detailed investigation in this study. Three months of field mapping (1∶1000 and 1∶50000) has been followed by laboratory investigation to extract radiolarians from cherty blocks and matrix material. Laboratory work is continuing..Field investigations in the Baisa area near Gyangze indicate the presence of three melange facies:broken formation, matrix\|rich facies, and block\|in\|matrix melange. Broken formation is characterized by disruption of layering by means of boudinage and pinching\|and\|swelling and dispersal of blocks within the finer\|grained shales due to layer\|parallel extension. Broken formation occurs mostly as dispersed but more\|or\|less traceable lenses within a foliated matrix. A transition from broken formation to typical block\|in\|matrix melange is observed in the field. Further disruption of broken formation leads to the formation of typical block\|in\|matrix melange either, by later shearing, or by suspected mud diapirism. Matrix\|rich facies is characterized by a dominance of shale matrix containing small granules of sandstone and other lithologies. This facies commonly is subject to later deformation, with disruption of the primary foliation into sigmoidal structures. Block\|in\|matrix facies is the most common melange facies and is characterized by blocks of different sizes, shapes and lithologies either encased in, or floating on, relatively finer\|grained arenaceous\|argillaceous matrix. Blocks range in size from several centimeters to several hundreds of meters, and have various shapes from phacoidal, elongate, to irregular. The blocks are mainly composed of varicolored cherts, greywacke and limestone as well as igneous rocks including serpentinite and basalt breccia. The matrix is mainly composed of dark argillaceous shales and siliceous shales, and partly of yellowish green greywacke. The injection or intrusion of mud matrix into blocks is quite common in this melange facies.展开更多
In this paper,we propose a shear high-order gradient(SHOG)operator by combining the shear operator and high-order gradient(HOG)operator.Compared with the HOG operator,the proposed SHOG operator can incorporate more di...In this paper,we propose a shear high-order gradient(SHOG)operator by combining the shear operator and high-order gradient(HOG)operator.Compared with the HOG operator,the proposed SHOG operator can incorporate more directionality and detect more abundant edge information.Based on the SHOG operator,we extend the total variation(TV)norm to shear high-order total variation(SHOTV),and then propose a SHOTV deblurring model.We also study some properties of the SHOG operator,and show that the SHOG matrices are Block Circulant with Circulant Blocks(BCCB)when the shear angle isπ/4.The proposed model is solved efficiently by the alternating direction method of multipliers(ADMM).Experimental results demonstrate that the proposed method outperforms some state-of-the-art non-blind deblurring methods in both objective and perceptual quality.展开更多
A contiguous derivation of radius and center of the insphere of a general tetrahedron is given. Therefore a linear system is derived. After a transformation of it the calculation of radius and center can be separated ...A contiguous derivation of radius and center of the insphere of a general tetrahedron is given. Therefore a linear system is derived. After a transformation of it the calculation of radius and center can be separated from each other. The remaining linear system for the center of the insphere can be solved after discovering the inverse of the corresponding coefficient matrix. This procedure can also be applied in the planar case to determine radius and center of the incircle of a triangle.展开更多
The matrix Wiener algebra,W_(N):=M_(N)(W)of order N>0,is the matrix algebra formed by N×N matrices whose entries belong to the classical Wiener algebraWof functions with absolutely convergent Fourier series.A ...The matrix Wiener algebra,W_(N):=M_(N)(W)of order N>0,is the matrix algebra formed by N×N matrices whose entries belong to the classical Wiener algebraWof functions with absolutely convergent Fourier series.A block-Toeplitz matrix T(a)=[A_(i,j)]i,j≥0is a block semi-infinite matrix such that its blocks A_(i,j) are finite matrices of order N,A_(i,j)=A^(r,s) whenever i-j=r-s and its entries are the coefficients of the Fourier expansion of the generator a:T→M_(N)(C).Such a matrix can be regarded as a bounded linear operator acting on the direct sum of N copies of L^(2)(T).We show that exp(T(a))differes from T(exp(a))only in a compact operator with a known bound on its norm.In fact,we prove a slightly more general result:for every entire function f and for every compact operator E,there exists a compact operator F such that f(T(a)+E)=T(f(a))+F.We call these T(a)+E′s matrices,the quasi block-Toeplitz matrices,and we show that via a computation-friendly norm,they form a Banach algebra.Our results generalize and are motivated by some recent results of Dario Andrea Bini,Stefano Massei and Beatrice Meini.展开更多
In this paper, we make further discussions and improvements on the results presented in the previously published work ＂Block H-matrices and spectrum of block matrices＂. Furthermore, a new bound for eigenvalues of bl...In this paper, we make further discussions and improvements on the results presented in the previously published work ＂Block H-matrices and spectrum of block matrices＂. Furthermore, a new bound for eigenvalues of block matrices is given with examples to show advantages of the new result.展开更多
文摘a Pole voltage waveforms (VA20 and VA40) for modulation index 0.4 (middle trace is A-phase voltage waveform) x-axis: 1 div.=10ms, y-axis: 1 div.= 100V b Normalized harmonic spectrum for pole voltage of Fig. 9a c A-phase current and phase voltage for modulation index 0.4 (reference space vector is in inner layer)
文摘a Pole voltage waveforms (VA20 and VA40) for modulation index 0.4 (middle trace is A-phase voltage waveform) x-axis: 1 div.=10ms, y-axis: 1 div.= 100V b Normalized harmonic spectrum for pole voltage of Fig. 9a c A-phase current and phase voltage for modulation index 0.4 (reference space vector is in inner layer)
基金The National Natural Science Foundation of China(No.U19B2031).
文摘A new method based on the iterative adaptive algorithm(IAA)and blocking matrix preprocessing(BMP)is proposed to study the suppression of multi-mainlobe interference.The algorithm is applied to precisely estimate the spatial spectrum and the directions of arrival(DOA)of interferences to overcome the drawbacks associated with conventional adaptive beamforming(ABF)methods.The mainlobe interferences are identified by calculating the correlation coefficients between direction steering vectors(SVs)and rejected by the BMP pretreatment.Then,IAA is subsequently employed to reconstruct a sidelobe interference-plus-noise covariance matrix for the preferable ABF and residual interference suppression.Simulation results demonstrate the excellence of the proposed method over normal methods based on BMP and eigen-projection matrix perprocessing(EMP)under both uncorrelated and coherent circumstances.
基金National Natural Science Foundation of China(Nos.41571410,41977067,42171422)。
文摘In this study,the problem of bundle adjustment was revisited,and a novel algorithm based on block matrix Cholesky decomposition was proposed to solve the thorny problem of self-calibration bundle adjustment.The innovation points are reflected in the following aspects:①The proposed algorithm is not dependent on the Schur complement,and the calculation process is simple and clear;②The complexities of time and space tend to O(n)in the context of world point number is far greater than that of images and cameras,so the calculation magnitude and memory consumption can be reduced significantly;③The proposed algorithm can carry out self-calibration bundle adjustment in single-camera,multi-camera,and variable-camera modes;④Some measures are employed to improve the optimization effects.Experimental tests showed that the proposed algorithm has the ability to achieve state-of-the-art performance in accuracy and robustness,and it has a strong adaptability as well,because the optimized results are accurate and robust even if the initial values have large deviations from the truth.This study could provide theoretical guidance and technical support for the image-based positioning and 3D reconstruction in the fields of photogrammetry,computer vision and robotics.
基金supported in part by the “Pioneer” and “Leading Goose” R&D Program of Zhejiang (Grant No. 2022C03174)the National Natural Science Foundation of China (No. 92067103)+4 种基金the Key Research and Development Program of Shaanxi (No.2021ZDLGY06- 02)the Natural Science Foundation of Shaanxi Province (No.2019ZDLGY12-02)the Shaanxi Innovation Team Project (No.2018TD007)the Xi’an Science and technology Innovation Plan (No.201809168CX9JC10)National 111 Program of China B16037
文摘Cloud computing provides powerful processing capabilities for large-scale intelligent Internet of things(IoT)terminals.However,the massive realtime data processing requirements challenge the existing cloud computing model.The edge server is closer to the data source.The end-edge-cloud collaboration offloads the cloud computing tasks to the edge environment,which solves the shortcomings of the cloud in resource storage,computing performance,and energy consumption.IoT terminals and sensors have caused security and privacy challenges due to resource constraints and exponential growth.As the key technology of IoT,Radio-Frequency Identification(RFID)authentication protocol tremendously strengthens privacy protection and improves IoT security.However,it inevitably increases system overhead while improving security,which is a major blow to low-cost RFID tags.The existing RFID authentication protocols are difficult to balance overhead and security.This paper designs an ultra-lightweight encryption function and proposes an RFID authentication scheme based on this function for the end-edge-cloud collaborative environment.The BAN logic proof and protocol verification tools AVISPA formally verify the protocol’s security.We use VIVADO to implement the encryption function and tag’s overhead on the FPGA platform.Performance evaluation indicates that the proposed protocol balances low computing costs and high-security requirements.
基金Natural Science Fund of Anhui Province of China (050420101)
文摘In order to alleviate the shortcomings of most blind deconvolution algorithms,this paper proposes an improved fast algorithm for blind deconvolution based on decorrelation technique and broadband block matrix.Althougth the original algorithm can overcome the shortcomings of current blind deconvolution algorithms,it has a constraint that the number of the source signals must be less than that of the channels.The improved algorithm deletes this constraint by using decorrelation technique.Besides,the improved algorithm raises the separation speed in terms of improving the computing methods of the output signal matrix.Simulation results demonstrate the validation and fast separation of the improved algorithm.
基金Supported by the Fund for Postdoctoral of China(2015M581688)Supported by the National Natural Science Foundation of China(11371089)+2 种基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education(20120092110020)Supported by the Natural Science Foundation of Jiangsu Province(BK20141327)Supported by the Foundation of Xuzhou Institute of Technology(XKY2014207)
文摘In this paper, we present a method how to get the expression for the group inverse of 2×2 block matrix and get the explicit expressions of the block matrix (A C B D) under some conditions.
文摘This work essentially consists in inverting in an exact, explicit, and original way the pentadiagonal Toeplitz matrix or tridiagonal block matrix resulting from the discretization of the two-dimensional Laplace operator. This method is an algorithm facilitating the resolution of a large number of problems governed by PDEs involving the Laplacian in two dimensions. It guarantees high precision and high efficiency in solving various differential equations.
文摘In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.
基金Supported by Open Fund of Key Laboratory of Anhui Higher Education Institutes (CS2021-07)the National Natural Science Foundation of China (61701004)Outstanding Young Talents Support Program of Anhui Province (gxyq2021178)。
文摘In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domain. Based on the shear gradient operator, we extend the total variation(TV) norm to the shear total variation(STV) norm by adding two shear gradient terms. Subsequently, we introduce a shear total variation deblurring model. Experimental results are provided to validate the ability of the STV norm to capture the detailed information. Leveraging the Block Circulant with Circulant Blocks(BCCB) structure of the shear gradient matrices, the alternating direction method of multipliers(ADMM) algorithm can be used to solve the proposed model efficiently. Numerous experiments are presented to verify the performance of our algorithm for non-blind image deblurring.
文摘For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices. Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices for some typical matrices from the real-world applications.
基金Supported by the National Natural Science Foundation of China(2 0 0 0 CG0 1 0 3) the Fund of"The Developing Program for Outstanding Person"in NPUS & T Innovation Foundation for Young Teachers of Northwestern Polytechnical University.
文摘In this paper, the spectrum and characteristic polynomial for a special kind of symmetric block circulant matrices are given.
文摘Interference suppression is a challenge for radar researchers, especially when mainlobe and sidelobe interference coexist. We present a comprehensive anti-interference approach based on a cognitive bistatic airborne radar. The risk of interception is reduced by lowering the launch energy of the radar transmitting terminal in the direction of interference;main lobe and sidelobe interferences are suppressed via cooperation between the two radars. The interference received by a single radar is extracted from the overall radar signal using multiple signal classification(MUSIC), and the interference is cross-located using two different azimuthal angles. Neural networks allowing good, non-linear nonparametric approximations are used to predict the location of interference, and this information is then used to preset the transmitting notch antenna to reduce the likelihood of interception. To simultaneously suppress mainlobe and sidelobe interferences, a blocking matrix is used to mask mainlobe interference based on azimuthal information, and an adaptive process is used to suppress sidelobe interference. Mainlobe interference is eliminated using the data received by the two radars. Simulation verifies the performance of the model.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11561048 and 11761029)the Natural Science Foundation of Inner Mongolia,China(Grant Nos.2019MS01019 and 2020ZD01)。
文摘We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the Feng spectrum)of the whole operator matrix and that of its entries.In addition,the connection between the Furi-Martelli-Vignoli spectrum of the whole operator matrix and that of its Schur complement is presented by means of Schur decomposition.
文摘The Moore-Penrose inverse of a block k-circulant matrix whose blocks are arbitrary matrices are obtained when k has unit modulus. In the meantime. explicit formulae for finding group inverses of certain specified k-circulant matrices are also given.
文摘Yamdrok melange occurs south of, and parallel to, the Yarlung—Zangbo ophiolites, extending several hundreds of kilometres with a width of several to tens of kilometres. Areas near Baisa and Rilang in the Gyangze district were chosen for detailed investigation in this study. Three months of field mapping (1∶1000 and 1∶50000) has been followed by laboratory investigation to extract radiolarians from cherty blocks and matrix material. Laboratory work is continuing..Field investigations in the Baisa area near Gyangze indicate the presence of three melange facies:broken formation, matrix\|rich facies, and block\|in\|matrix melange. Broken formation is characterized by disruption of layering by means of boudinage and pinching\|and\|swelling and dispersal of blocks within the finer\|grained shales due to layer\|parallel extension. Broken formation occurs mostly as dispersed but more\|or\|less traceable lenses within a foliated matrix. A transition from broken formation to typical block\|in\|matrix melange is observed in the field. Further disruption of broken formation leads to the formation of typical block\|in\|matrix melange either, by later shearing, or by suspected mud diapirism. Matrix\|rich facies is characterized by a dominance of shale matrix containing small granules of sandstone and other lithologies. This facies commonly is subject to later deformation, with disruption of the primary foliation into sigmoidal structures. Block\|in\|matrix facies is the most common melange facies and is characterized by blocks of different sizes, shapes and lithologies either encased in, or floating on, relatively finer\|grained arenaceous\|argillaceous matrix. Blocks range in size from several centimeters to several hundreds of meters, and have various shapes from phacoidal, elongate, to irregular. The blocks are mainly composed of varicolored cherts, greywacke and limestone as well as igneous rocks including serpentinite and basalt breccia. The matrix is mainly composed of dark argillaceous shales and siliceous shales, and partly of yellowish green greywacke. The injection or intrusion of mud matrix into blocks is quite common in this melange facies.
基金Supported by the National Natural Science Foundation of China(61701004)Outstanding Young Talents Support Program of Anhui Province(gxyq2021178)+1 种基金Open Fund of Key Laboratory of Anhui Higher Education Institutes(CS2021-07)Program of University Mathematics Teaching Research and Development Center(CMC20200301)。
文摘In this paper,we propose a shear high-order gradient(SHOG)operator by combining the shear operator and high-order gradient(HOG)operator.Compared with the HOG operator,the proposed SHOG operator can incorporate more directionality and detect more abundant edge information.Based on the SHOG operator,we extend the total variation(TV)norm to shear high-order total variation(SHOTV),and then propose a SHOTV deblurring model.We also study some properties of the SHOG operator,and show that the SHOG matrices are Block Circulant with Circulant Blocks(BCCB)when the shear angle isπ/4.The proposed model is solved efficiently by the alternating direction method of multipliers(ADMM).Experimental results demonstrate that the proposed method outperforms some state-of-the-art non-blind deblurring methods in both objective and perceptual quality.
文摘A contiguous derivation of radius and center of the insphere of a general tetrahedron is given. Therefore a linear system is derived. After a transformation of it the calculation of radius and center can be separated from each other. The remaining linear system for the center of the insphere can be solved after discovering the inverse of the corresponding coefficient matrix. This procedure can also be applied in the planar case to determine radius and center of the incircle of a triangle.
文摘The matrix Wiener algebra,W_(N):=M_(N)(W)of order N>0,is the matrix algebra formed by N×N matrices whose entries belong to the classical Wiener algebraWof functions with absolutely convergent Fourier series.A block-Toeplitz matrix T(a)=[A_(i,j)]i,j≥0is a block semi-infinite matrix such that its blocks A_(i,j) are finite matrices of order N,A_(i,j)=A^(r,s) whenever i-j=r-s and its entries are the coefficients of the Fourier expansion of the generator a:T→M_(N)(C).Such a matrix can be regarded as a bounded linear operator acting on the direct sum of N copies of L^(2)(T).We show that exp(T(a))differes from T(exp(a))only in a compact operator with a known bound on its norm.In fact,we prove a slightly more general result:for every entire function f and for every compact operator E,there exists a compact operator F such that f(T(a)+E)=T(f(a))+F.We call these T(a)+E′s matrices,the quasi block-Toeplitz matrices,and we show that via a computation-friendly norm,they form a Banach algebra.Our results generalize and are motivated by some recent results of Dario Andrea Bini,Stefano Massei and Beatrice Meini.
基金Project supported by the National Natural Science Foundation of China (No.10671164)Important Project Foundation of Hunan Education Department (No.06A070)
文摘In this paper, we make further discussions and improvements on the results presented in the previously published work ＂Block H-matrices and spectrum of block matrices＂. Furthermore, a new bound for eigenvalues of block matrices is given with examples to show advantages of the new result.
