Aligning with the ongoing search for quantum spin liquids(QSLs),identifying QSLs in Kitaev magnets has attracted significant research interest during the past decade.Nevertheless,it remains a significant challenge.One...Aligning with the ongoing search for quantum spin liquids(QSLs),identifying QSLs in Kitaev magnets has attracted significant research interest during the past decade.Nevertheless,it remains a significant challenge.One of the major difficulties is that Kitaev QSL is typically fragile to competing interactions such as off-diagonal exchanges,which are ubiquitous in real materials owing to spin-orbit coupling and crystal-field effects.This,in turn,generates many intriguing field-induced novel phases and the thermal Hall effect.In this review,we focus on the interplay between the Kitaev interaction and off-diagonal Γ and Γ′exchange from a numerical perspective.The review discusses certain representative exotic phases such as𝛤spin liquid,nematic ferromagnet,spin-flop phase,and distinct chiral spin states with spontaneous time-reversal symmetry breaking.It also presents quantum phase diagrams of anisotropic Kitaev-Γ chains that exhibit kaleidoscopy for both ordered and disordered phases.展开更多
Driven by advancements in mobile internet technology,images have become a crucial data medium.Ensuring the security of image information during transmission has thus emerged as an urgent challenge.This study proposes ...Driven by advancements in mobile internet technology,images have become a crucial data medium.Ensuring the security of image information during transmission has thus emerged as an urgent challenge.This study proposes a novel image encryption algorithm specifically designed for grayscale image security.This research introduces a new Cantor diagonal matrix permutation method.The proposed permutation method uses row and column index sequences to control the Cantor diagonal matrix,where the row and column index sequences are generated by a spatiotemporal chaotic system named coupled map lattice(CML).The high initial value sensitivity of the CML system makes the permutation method highly sensitive and secure.Additionally,leveraging fractal theory,this study introduces a chaotic fractal matrix and applies this matrix in the diffusion process.This chaotic fractal matrix exhibits selfsimilarity and irregularity.Using the Cantor diagonal matrix and chaotic fractal matrix,this paper introduces a fast image encryption algorithm involving two diffusion steps and one permutation step.Moreover,the algorithm achieves robust security with only a single encryption round,ensuring high operational efficiency.Experimental results show that the proposed algorithm features an expansive key space,robust security,high sensitivity,high efficiency,and superior statistical properties for the ciphered images.Thus,the proposed algorithm not only provides a practical solution for secure image transmission but also bridges fractal theory with image encryption techniques,thereby opening new research avenues in chaotic cryptography and advancing the development of information security technology.展开更多
Given a positive integer n and the residue class ring Z_(n)=Z/nZ,we set Z_(n)^(x)to be the group of units in Z_(n),i.e.,Z_(n)^(x)={x∈Z_(n):ged(x,n)=1}.Let N_(m)(n)be the number of solutions of x_(1)^(4)+…+x_(m)^(4)...Given a positive integer n and the residue class ring Z_(n)=Z/nZ,we set Z_(n)^(x)to be the group of units in Z_(n),i.e.,Z_(n)^(x)={x∈Z_(n):ged(x,n)=1}.Let N_(m)(n)be the number of solutions of x_(1)^(4)+…+x_(m)^(4)≡0(mod n)with x_(1),…,x_(m)∈Z_(n)^(x).In this note,we determine an explicit expression of N_(m)(n).This extends the results of Sun and Yang in 2014.展开更多
A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are con...A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.展开更多
We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that t...We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that the heat kernel in higher dimensions converges rapidly. We also compute the constants involved in the estimate for the 1-dimensional heat kernel. Furthermore, we discuss the general case of on-diagonal estimates for the heat kernel.展开更多
In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the nu...Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.展开更多
This study was conducted to analyze the effect of joint type, and numbers and types of dovetail keys on diagonal tension and compression performance of corner joints in a furniture frame. Joint members were cut from w...This study was conducted to analyze the effect of joint type, and numbers and types of dovetail keys on diagonal tension and compression performance of corner joints in a furniture frame. Joint members were cut from white fir lumber. Butted and mitered joints were constructed with one and two dovetail key（s） with butterfly and H shapes. Joints were glued by polyvinyl acetate （PVAc） and cynoacrylate （CA）. Compression capacity of joints was higher than diagonal tension. Mitered joints were stronger than butted ones. Butterfly dovetail keys were superior to H shape keys. Double keys performed better than single key. Experimental joints glued with PVAc were stronger than those glued with CA glue and control specimens. In terms of strength, butterfly dovetailed joints were comparable with doweled joints.展开更多
The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covarian...The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.展开更多
A study of bispectral analysis in gearbox condition monitoring is presented.The theory of bispectrum and quadratic phase coupling (QPC) is first introduced, and then equationsfor computing bispectrum slices are obtain...A study of bispectral analysis in gearbox condition monitoring is presented.The theory of bispectrum and quadratic phase coupling (QPC) is first introduced, and then equationsfor computing bispectrum slices are obtained. To meet the needs of online monitoring, a simplifiedmethod of computing bispectrum diagonal slice is adopted. Industrial gearbox vibration signalsmeasured from normal and tooth cracked conditions are analyzed using the above method. Experimentsresults indicate that bispectrum can effectively suppress the additive Gaussian noise andchracterize the QPC phenomenon. It is also shown that the 1-D bispectrum diagonal slice can capturethe non-Gaussian and nonlinear feature of gearbox vibration when crack occurred, hence, this methodcan be employed to gearbox real time monitoring and early diagnosis.展开更多
In order to enhance the robustness and contrast in the minimum variance(MV) beamformer, adaptive diagonal loading method was proposed. The conventional diagonal loading technique has already been used in the MV beamfo...In order to enhance the robustness and contrast in the minimum variance(MV) beamformer, adaptive diagonal loading method was proposed. The conventional diagonal loading technique has already been used in the MV beamformer, but has the drawback that its level is specified by predefined parameter and without consideration of input-data. To alleviate this problem, the level of diagonal loading was computed appropriately and automatically from the given data by shrinkage method in the proposed adaptive diagonal loaded beamformer. The performance of the proposed beamformer was tested on the simulated point target and cyst phantom was obtained using Field II. In the point target simulation, it is shown that the proposed method has higher lateral resolution than the conventional delay-and-sum beamformer and could be more robust in estimating the amplitude peak than the MV beamformer when acoustic velocity error exists. In the cyst phantom simulation, the proposed beamformer has shown that it achieves an improvement in contrast ratio and without distorting the edges of cyst.展开更多
The interaction of diagonal waves with perforated-wall breakwater partially filled with rock fill is studied using the linear potential theory. By means of the matched eigenfunction expansion method, an analytical met...The interaction of diagonal waves with perforated-wall breakwater partially filled with rock fill is studied using the linear potential theory. By means of the matched eigenfunction expansion method, an analytical method is presented to calculate the reflection coefficient and the wave force coefficient of the breakwater. The calculated results of the reflection coefficient for limiting cases are the same to the existing results. The main effect factors of the reflection coefficient and the wave force coefficient are analyzed by numerical examples. With the increasing of thickness of rock fill, the wave force coefficient on the perforated wall generally decreases, while the reflection coefficient increases. With the increasing of the incident angle of the wave, the reflection coefficient of the breakwater first decreases, reaches its minimum, and then increases monotonously.展开更多
In this paper, the nonnull moments and the distributions of the likelihood ratio criterion for testing the equality of diagonal blocks with blockwise independence under certain alternatives have derived.
A new algorithm is proposed for joint diagonalization. With a modified objective function, the new algorithm not only excludes trivial and unbalanced solutions successfully, but is also easily optimized. In addition, ...A new algorithm is proposed for joint diagonalization. With a modified objective function, the new algorithm not only excludes trivial and unbalanced solutions successfully, but is also easily optimized. In addition, with the new objective function, the proposed algorithm can work well in online blind source separation （BSS） for the first time, although this family of algorithms is always thought to be valid only in batch-mode BSS by far. Simulations show that it is a very competitive joint diagonalization algorithm.展开更多
In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） al...In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.展开更多
Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive integer.Let F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of H...Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive integer.Let F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of Hasse-Davenport theorem,an explicit formula for the number of solutions of cubic diagonal equation x_(1)^(3)+x_(2)^(3)+…+x_(n)^(3)=c over Fqis given,where c∈F_(q)^(*)and p≡1(mod 3).This extends earlier results.展开更多
The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identica...The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.展开更多
Inspired by total variation(TV), this paper represents a new iterative algorithm based on diagonal total variation(DTV) to address the computed tomography image reconstruction problem. To improve the quality of a reco...Inspired by total variation(TV), this paper represents a new iterative algorithm based on diagonal total variation(DTV) to address the computed tomography image reconstruction problem. To improve the quality of a reconstructed image, we used DTV to sparsely represent images when iterative convergence of the reconstructed algorithm with TV-constraint had no effect during the reconstruction process. To investigate our proposed algorithm, the numerical and experimental studies were performed, and rootmean-square error(RMSE) and structure similarity(SSIM)were used to evaluate the reconstructed image quality. The results demonstrated that the proposed method could effectively reduce noise, suppress artifacts, and reconstruct highquality image from incomplete projection data.展开更多
We propose a novel neural network based on a diagonal recurrent neural network and chaos, and its structure and learning algorithm are designed. The multilayer feedforward neural network, diagonal recurrent neural net...We propose a novel neural network based on a diagonal recurrent neural network and chaos, and its structure and learning algorithm are designed. The multilayer feedforward neural network, diagonal recurrent neural network, and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map. The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks.展开更多
基金supported by the National Program on Key Research Projects(Grant No.MOST2022YFA1402700)the National Natural Science Foundation of China(Grant Nos.12304176,12274187,12247183,and 12247101)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20220876)partially supported by the High-Performance Computing Platform of Nanjing University of Aeronautics and Astronautics。
文摘Aligning with the ongoing search for quantum spin liquids(QSLs),identifying QSLs in Kitaev magnets has attracted significant research interest during the past decade.Nevertheless,it remains a significant challenge.One of the major difficulties is that Kitaev QSL is typically fragile to competing interactions such as off-diagonal exchanges,which are ubiquitous in real materials owing to spin-orbit coupling and crystal-field effects.This,in turn,generates many intriguing field-induced novel phases and the thermal Hall effect.In this review,we focus on the interplay between the Kitaev interaction and off-diagonal Γ and Γ′exchange from a numerical perspective.The review discusses certain representative exotic phases such as𝛤spin liquid,nematic ferromagnet,spin-flop phase,and distinct chiral spin states with spontaneous time-reversal symmetry breaking.It also presents quantum phase diagrams of anisotropic Kitaev-Γ chains that exhibit kaleidoscopy for both ordered and disordered phases.
基金supported by the National Natural Science Foundation of China(62376106)The Science and Technology Development Plan of Jilin Province(20250102212JC).
文摘Driven by advancements in mobile internet technology,images have become a crucial data medium.Ensuring the security of image information during transmission has thus emerged as an urgent challenge.This study proposes a novel image encryption algorithm specifically designed for grayscale image security.This research introduces a new Cantor diagonal matrix permutation method.The proposed permutation method uses row and column index sequences to control the Cantor diagonal matrix,where the row and column index sequences are generated by a spatiotemporal chaotic system named coupled map lattice(CML).The high initial value sensitivity of the CML system makes the permutation method highly sensitive and secure.Additionally,leveraging fractal theory,this study introduces a chaotic fractal matrix and applies this matrix in the diffusion process.This chaotic fractal matrix exhibits selfsimilarity and irregularity.Using the Cantor diagonal matrix and chaotic fractal matrix,this paper introduces a fast image encryption algorithm involving two diffusion steps and one permutation step.Moreover,the algorithm achieves robust security with only a single encryption round,ensuring high operational efficiency.Experimental results show that the proposed algorithm features an expansive key space,robust security,high sensitivity,high efficiency,and superior statistical properties for the ciphered images.Thus,the proposed algorithm not only provides a practical solution for secure image transmission but also bridges fractal theory with image encryption techniques,thereby opening new research avenues in chaotic cryptography and advancing the development of information security technology.
基金Supported by the Natural Science Foundation of Henan Province(232300420123)the National Natural Science Foundation of China(12026224)。
文摘Given a positive integer n and the residue class ring Z_(n)=Z/nZ,we set Z_(n)^(x)to be the group of units in Z_(n),i.e.,Z_(n)^(x)={x∈Z_(n):ged(x,n)=1}.Let N_(m)(n)be the number of solutions of x_(1)^(4)+…+x_(m)^(4)≡0(mod n)with x_(1),…,x_(m)∈Z_(n)^(x).In this note,we determine an explicit expression of N_(m)(n).This extends the results of Sun and Yang in 2014.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62105004 and 52174141)the College Student Innovation and Entrepreneurship Fund Project(Grant No.202210361053)+1 种基金Anhui Mining Machinery and Electrical Equipment Coordination Innovation Center,Anhui University of Science&Technology(Grant No.KSJD202304)the Anhui Province Digital Agricultural Engineering Technology Research Center Open Project(Grant No.AHSZNYGC-ZXKF021)。
文摘A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc.
文摘We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that the heat kernel in higher dimensions converges rapidly. We also compute the constants involved in the estimate for the 1-dimensional heat kernel. Furthermore, we discuss the general case of on-diagonal estimates for the heat kernel.
文摘In this paper, we provide some new necessary and sufficient conditions for generalized diagonally dominant matrices and also obtain some criteria for nongeneralized dominant matrices.
文摘Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.
文摘This study was conducted to analyze the effect of joint type, and numbers and types of dovetail keys on diagonal tension and compression performance of corner joints in a furniture frame. Joint members were cut from white fir lumber. Butted and mitered joints were constructed with one and two dovetail key（s） with butterfly and H shapes. Joints were glued by polyvinyl acetate （PVAc） and cynoacrylate （CA）. Compression capacity of joints was higher than diagonal tension. Mitered joints were stronger than butted ones. Butterfly dovetail keys were superior to H shape keys. Double keys performed better than single key. Experimental joints glued with PVAc were stronger than those glued with CA glue and control specimens. In terms of strength, butterfly dovetailed joints were comparable with doweled joints.
文摘The derivation of a diagonally loaded sample-matrix inversion （LSMI） algorithm on the busis of inverse matrix recursion （i.e.LSMI-IMR algorithm） is conducted by reconstructing the recursive formulation of covariance matrix. For the new algorithm, diagonal loading is by setting initial inverse matrix without any addition of computation. In addition, a corresponding improved recursive algorithm is presented, which is low computational complexity. This eliminates the complex multiplications of the scalar coefficient and updating matrix, resulting in significant computational savings. Simulations show that the LSMI-IMR algorithm is valid.
基金This project is supported by 95 Pan Deng Program of China (No.PD952l908) National Key Basic Research Special Foundation of China (No.Gl998020320)Provincial Natural Science Foundation of Hubei, China (No.2000J125)
文摘A study of bispectral analysis in gearbox condition monitoring is presented.The theory of bispectrum and quadratic phase coupling (QPC) is first introduced, and then equationsfor computing bispectrum slices are obtained. To meet the needs of online monitoring, a simplifiedmethod of computing bispectrum diagonal slice is adopted. Industrial gearbox vibration signalsmeasured from normal and tooth cracked conditions are analyzed using the above method. Experimentsresults indicate that bispectrum can effectively suppress the additive Gaussian noise andchracterize the QPC phenomenon. It is also shown that the 1-D bispectrum diagonal slice can capturethe non-Gaussian and nonlinear feature of gearbox vibration when crack occurred, hence, this methodcan be employed to gearbox real time monitoring and early diagnosis.
基金Project(2013GZX0147-3)supported by the Science and Technology Pillar Program of Sichuan Province,China
文摘In order to enhance the robustness and contrast in the minimum variance(MV) beamformer, adaptive diagonal loading method was proposed. The conventional diagonal loading technique has already been used in the MV beamformer, but has the drawback that its level is specified by predefined parameter and without consideration of input-data. To alleviate this problem, the level of diagonal loading was computed appropriately and automatically from the given data by shrinkage method in the proposed adaptive diagonal loaded beamformer. The performance of the proposed beamformer was tested on the simulated point target and cyst phantom was obtained using Field II. In the point target simulation, it is shown that the proposed method has higher lateral resolution than the conventional delay-and-sum beamformer and could be more robust in estimating the amplitude peak than the MV beamformer when acoustic velocity error exists. In the cyst phantom simulation, the proposed beamformer has shown that it achieves an improvement in contrast ratio and without distorting the edges of cyst.
基金The Natural Science Foundation of Shandong Province under contract No.Q2008F01the Specialized Research Fund for the Doctoral Program of Higher Education under contract No.200804231006the Found of Shandong Province Key Laboratory of Ocean Engineering
文摘The interaction of diagonal waves with perforated-wall breakwater partially filled with rock fill is studied using the linear potential theory. By means of the matched eigenfunction expansion method, an analytical method is presented to calculate the reflection coefficient and the wave force coefficient of the breakwater. The calculated results of the reflection coefficient for limiting cases are the same to the existing results. The main effect factors of the reflection coefficient and the wave force coefficient are analyzed by numerical examples. With the increasing of thickness of rock fill, the wave force coefficient on the perforated wall generally decreases, while the reflection coefficient increases. With the increasing of the incident angle of the wave, the reflection coefficient of the breakwater first decreases, reaches its minimum, and then increases monotonously.
文摘In this paper, the nonnull moments and the distributions of the likelihood ratio criterion for testing the equality of diagonal blocks with blockwise independence under certain alternatives have derived.
基金supported partly by the Key Program of National Natural Science Foundation of China (U0635001U0835003)+3 种基金the National Natural Science Foundation of China (60505005 60674033 60774094)the Natural Science Fundof Guangdong Province (05006508).
文摘A new algorithm is proposed for joint diagonalization. With a modified objective function, the new algorithm not only excludes trivial and unbalanced solutions successfully, but is also easily optimized. In addition, with the new objective function, the proposed algorithm can work well in online blind source separation （BSS） for the first time, although this family of algorithms is always thought to be valid only in batch-mode BSS by far. Simulations show that it is a very competitive joint diagonalization algorithm.
基金supported by the National Natural Science Foundation of China(6167145361201379)Anhui Natural Science Foundation of China(1608085MF123)
文摘In view of the low performance of adaptive asymmetric joint diagonalization（AAJD）, especially its failure in tracking high maneuvering targets, an adaptive asymmetric joint diagonalization with deflation（AAJDd） algorithm is proposed. The AAJDd algorithm improves performance by estimating the direction of departure（DOD） and direction of arrival（DOA） directly, avoiding the reuse of the previous moment information in the AAJD algorithm.On this basis, the idea of sequential estimation of the principal component is introduced to turn the matrix operation into a constant operation, reducing the amount of computation and speeding up the convergence. Meanwhile, the eigenvalue is obtained, which can be used to estimate the number of targets. Then, the estimation of signal parameters via rotational invariance technique（ESPRIT） algorithm is improved to realize the automatic matching and association of DOD and DOA. The simulation results show that the AAJDd algorithm has higher tracking performance than the AAJD algorithm, especially when the high maneuvering target is tracked. The efficiency of the proposed method is verified.
基金Supported by the Natural Science Foundation of Henan Province(232300420123)the National Natural Science Foundation of China(12026224)the Research Center of Mathematics and Applied Mathematics,Nanyang Institute of Technology。
文摘Let Fqbe the finite field,q=p^(k),with p being a prime and k being a positive integer.Let F_(q)^(*)be the multiplicative group of Fq,that is F_(q)^(*)=F_(q){0}.In this paper,by using the Jacobi sums and an analog of Hasse-Davenport theorem,an explicit formula for the number of solutions of cubic diagonal equation x_(1)^(3)+x_(2)^(3)+…+x_(n)^(3)=c over Fqis given,where c∈F_(q)^(*)and p≡1(mod 3).This extends earlier results.
文摘The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.
基金supported in part by the National Natural Science Foundation of China(No.61401049)the Chongqing Foundation and Frontier Research Project(Nos.cstc2016jcyjA0473,cstc2013jcyjA0763)+3 种基金the Graduate Scientific Research and Innovation Foundation of Chongqing,China(No.CYB16044)the Strategic Industry Key Generic Technology Innovation Project of Chongqing(No.cstc2015zdcy-ztzxX0002)China Scholarship Councilthe Fundamental Research Funds for the Central Universities Nos.CDJZR14125501,106112016CDJXY120003,10611CDJXZ238826
文摘Inspired by total variation(TV), this paper represents a new iterative algorithm based on diagonal total variation(DTV) to address the computed tomography image reconstruction problem. To improve the quality of a reconstructed image, we used DTV to sparsely represent images when iterative convergence of the reconstructed algorithm with TV-constraint had no effect during the reconstruction process. To investigate our proposed algorithm, the numerical and experimental studies were performed, and rootmean-square error(RMSE) and structure similarity(SSIM)were used to evaluate the reconstructed image quality. The results demonstrated that the proposed method could effectively reduce noise, suppress artifacts, and reconstruct highquality image from incomplete projection data.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61173183,60973152,and 60573172)the Superior University Doctor Subject Special Scientific Research Foundation of China (Grant No. 20070141014)the Natural Science Foundation of Liaoning Province,China (Grant No. 20082165)
文摘We propose a novel neural network based on a diagonal recurrent neural network and chaos, and its structure and learning algorithm are designed. The multilayer feedforward neural network, diagonal recurrent neural network, and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map. The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks.
