Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extrac...Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.展开更多
Based on the resulting Lax pairs of the generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge...Based on the resulting Lax pairs of the generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using Darboux transformation, the generalized odd-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given.展开更多
Under improper transformations,the traditional transformation laws for cross products,the permutation tensor,and rotations are incorrect.For a cross product,using a counter-example the left-hand rule is proved wrong.T...Under improper transformations,the traditional transformation laws for cross products,the permutation tensor,and rotations are incorrect.For a cross product,using a counter-example the left-hand rule is proved wrong.The unique rule for a cross product is the right-hand rule.Coordinate systems have handedness,while a cross product is frame-indifference.Since the permutation tensor is defined as a triple product including a cross product,the law for the permutation tensor is false.For a rotation,its pseudovector representation is incorrect,because the mirror is an auxiliary device to produce the virtual image rather than a new coordinate system or reference frame.展开更多
Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light＇s orbital angular momentum degree of freedom...Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light＇s orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light＇s orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup.展开更多
The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a p...The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.展开更多
By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Ni...By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a-1xdto be a complete permutation polynomial over Fp4 k, where d =(p4k-1)/(pk-1)+ 1 and a ∈ F*p4k. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.展开更多
We present novel vector permutation and branch reduction methods to minimize the number of execution cycles for bit reversal algorithms.The new methods are applied to single instruction multiple data(SIMD) parallel im...We present novel vector permutation and branch reduction methods to minimize the number of execution cycles for bit reversal algorithms.The new methods are applied to single instruction multiple data(SIMD) parallel implementation of complex data floating-point fast Fourier transform(FFT).The number of operational clock cycles can be reduced by an average factor of 3.5 by using our vector permutation methods and by 1.1 by using our branch reduction methods,compared with conventional im-plementations.Experiments on MPC7448(a well-known SIMD reduced instruction set computing processor) demonstrate that our optimal bit-reversal algorithm consistently takes fewer than two cycles per element in complex array operations.展开更多
Digital image steganography technique based on hiding the secret data behind of cover image in such a way that it is not detected by the human visual system.This paper presents an image scrambling method that is very ...Digital image steganography technique based on hiding the secret data behind of cover image in such a way that it is not detected by the human visual system.This paper presents an image scrambling method that is very useful for grayscale secret images.In this method,the secret image decomposes in three parts based on the pixel’s threshold value.The division of the color image into three parts is very easy based on the color channel but in the grayscale image,it is difficult to implement.The proposed image scrambling method is implemented in image steganography using discrete wavelet transform(DWT),singular value decomposition(SVD),and sorting function.There is no visual difference between the stego image and the cover image.The extracted secret image is also similar to the original secret image.The proposed algorithm outcome is compared with the existed image steganography techniques.The comparative results show the strength of the proposed technique.展开更多
The diffusion layers in substitution-permutation network（SPN） block ciphers are almost invertible linear transformations, which is optimal if the branch number reaches the maximum value. The method of constructing i...The diffusion layers in substitution-permutation network（SPN） block ciphers are almost invertible linear transformations, which is optimal if the branch number reaches the maximum value. The method of constructing involutory optimal diffusion layers is proposed based on the Cauchy matrix, which can decrease the cost of implementation. The analysis to experimental results indicates that the diffusion layer ensures the security of the SPN block cipher against differential cryptanalysis（DC） and linear cryptanalysis（LC）, and decreases half the cost of implementation.展开更多
基金supported financially by FundamentalResearch Program of Shanxi Province(No.202103021223056).
文摘Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.
基金the Science Fundation for Young Teachers of Southwest University(No.SWUQ2006028)
文摘Based on the resulting Lax pairs of the generalized coupled KdV soliton equation, a new Darboux transformation with multi-parameters for the generalized coupled KdV soliton equation is derived with the help of a gauge transformation of the spectral problem. By using Darboux transformation, the generalized odd-soliton solutions of the generalized coupled KdV soliton equation are given and presented in determinant form. As an application, the first two cases are given.
基金National Natural Science Foundation of China(No.51978166)the Research Fund of Sanjiang University(No.2018SJKY005)。
文摘Under improper transformations,the traditional transformation laws for cross products,the permutation tensor,and rotations are incorrect.For a cross product,using a counter-example the left-hand rule is proved wrong.The unique rule for a cross product is the right-hand rule.Coordinate systems have handedness,while a cross product is frame-indifference.Since the permutation tensor is defined as a triple product including a cross product,the law for the permutation tensor is false.For a rotation,its pseudovector representation is incorrect,because the mirror is an auxiliary device to produce the virtual image rather than a new coordinate system or reference frame.
基金supported by the Fundamental Research Funds for the Central Universitiesthe National Natural Science Foundation of China(Grant Nos.11374008,11374238,11374239,and 11534008)
文摘Quantum algorithms provide a more efficient way to solve computational tasks than classical algorithms. We experimentally realize quantum permutation algorithm using light＇s orbital angular momentum degree of freedom. By exploiting the spatial mode of photons, our scheme provides a more elegant way to understand the principle of quantum permutation algorithm and shows that the high dimension characteristic of light＇s orbital angular momentum may be useful in quantum algorithms. Our scheme can be extended to higher dimension by introducing more spatial modes and it paves the way to trace the source of quantum speedup.
基金Project supported by the National Natural Science Foundation of China (No.10271106)the Education Commission of Zhejiang Province of China (No.20030342).
文摘The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.
基金supported by National Natural Science Foundation of China(Grant Nos.61272481 and 61402352)the China Scholarship Council,Beijing Natural Science Foundation(Grant No.4122089)+1 种基金National Development and Reform Commission(Grant No.20121424)the Norwegian Research Council
文摘By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a-1xdto be a complete permutation polynomial over Fp4 k, where d =(p4k-1)/(pk-1)+ 1 and a ∈ F*p4k. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.
文摘We present novel vector permutation and branch reduction methods to minimize the number of execution cycles for bit reversal algorithms.The new methods are applied to single instruction multiple data(SIMD) parallel implementation of complex data floating-point fast Fourier transform(FFT).The number of operational clock cycles can be reduced by an average factor of 3.5 by using our vector permutation methods and by 1.1 by using our branch reduction methods,compared with conventional im-plementations.Experiments on MPC7448(a well-known SIMD reduced instruction set computing processor) demonstrate that our optimal bit-reversal algorithm consistently takes fewer than two cycles per element in complex array operations.
基金This work was supported by Taif university Researchers Supporting Project Number(TURSP-2020/114),Taif University,Taif,Saudi Arabia.
文摘Digital image steganography technique based on hiding the secret data behind of cover image in such a way that it is not detected by the human visual system.This paper presents an image scrambling method that is very useful for grayscale secret images.In this method,the secret image decomposes in three parts based on the pixel’s threshold value.The division of the color image into three parts is very easy based on the color channel but in the grayscale image,it is difficult to implement.The proposed image scrambling method is implemented in image steganography using discrete wavelet transform(DWT),singular value decomposition(SVD),and sorting function.There is no visual difference between the stego image and the cover image.The extracted secret image is also similar to the original secret image.The proposed algorithm outcome is compared with the existed image steganography techniques.The comparative results show the strength of the proposed technique.
文摘The diffusion layers in substitution-permutation network（SPN） block ciphers are almost invertible linear transformations, which is optimal if the branch number reaches the maximum value. The method of constructing involutory optimal diffusion layers is proposed based on the Cauchy matrix, which can decrease the cost of implementation. The analysis to experimental results indicates that the diffusion layer ensures the security of the SPN block cipher against differential cryptanalysis（DC） and linear cryptanalysis（LC）, and decreases half the cost of implementation.
