High efficiency video coding (HEVC) transform algorithm for residual coding uses 2-dimensional (2D) 4 × 4 transforms with higher precision than H.264's 4 ×4 transforms, resulting in increased hardware c...High efficiency video coding (HEVC) transform algorithm for residual coding uses 2-dimensional (2D) 4 × 4 transforms with higher precision than H.264's 4 ×4 transforms, resulting in increased hardware complexity. In this paper, we present a shared architecture that can compute the 4 ~4 forward discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) of HEVC using a new mapping scheme in the video processor array structure. The architecture is implemented with only adders and shills to an area-efficient design. The proposed architecture is synthesized using ISE 14.7 and implemented using the BEE4 platform with the Virtex-6 FF1759 LX550T field programmable gate array (FPGA). The result shows that the video processor array structure achieves a maximum operation frequency of 165.2 MHz. The architecture and its implementation are presented in this paper to demonstrate its programmable and high performance.展开更多
A new reflection approach for field distribution measurement of ultrasonic transducers was investigated. Instead of a point-like reflection target (rigid sphere) or thin wires (line-like targets), a line response ...A new reflection approach for field distribution measurement of ultrasonic transducers was investigated. Instead of a point-like reflection target (rigid sphere) or thin wires (line-like targets), a line response function of experimental knife-edge distribution combined with the inverse Abel transforms was used to estimate the lateral beam distributions of ultrasonic transducers. The measurement steps were as follows:① A knife-edge was scanned perpendicularly to acoustic beam axis of the transducer using an ultrasonic C-scan system to obtain its ultrasonic image line response function, ② the transverse beam distribution was solved by the inverse Abel transforms, and ③ experiments were performed to obtain the lateral beam profiles of two transducers, with and without focus, and the results were compared with those from a hydrophone. The results showed that this method was effective for ultrasonic field measurement and could be as a substitute for hydrophone in most cases.展开更多
A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Four...A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum展开更多
The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography (CT), which creates the possibility for dose reduction. In this paper, a filtered-bac...The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography (CT), which creates the possibility for dose reduction. In this paper, a filtered-backprojection (FBP) algorithm based on the Radon inversion transform is presented to deal with the three-dimensional (3D) local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography (ATRACT), not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.展开更多
Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Usin...Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.展开更多
Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find on approximation to f(t) by the use of the dassical Jacobi polynomials. The main contribution of our work is the development of a...Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find on approximation to f(t) by the use of the dassical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series ex-pansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.展开更多
A fast Cholesky decomposition and a fast inverse Cholesky decomposition method for A T A are presented,where A is an m×n rectangular Toeplitz block matrix,we give the FCD algorithm for computing...A fast Cholesky decomposition and a fast inverse Cholesky decomposition method for A T A are presented,where A is an m×n rectangular Toeplitz block matrix,we give the FCD algorithm for computing R , and the FICD algorithm for computing R -1 ,both allow for an efficient parallel implementation,for solving a least squares problem and require only O(mn) operations.展开更多
Since its inception in the 1970s,multi-dimensional magnetic resonance(MR)has emerged as a powerful tool for non-invasive investigations of structures and molecular interactions.MR spectroscopy beyond one dimension all...Since its inception in the 1970s,multi-dimensional magnetic resonance(MR)has emerged as a powerful tool for non-invasive investigations of structures and molecular interactions.MR spectroscopy beyond one dimension allows the study of the correlation,exchange processes,and separation of overlapping spectral information.The multi-dimensional concept has been re-implemented over the last two decades to explore molecular motion and spin dynamics in porous media.Apart from Fourier transform,methods have been developed for processing the multi-dimensional time-domain data,identifying the fluid components,and estimating pore surface permeability via joint relaxation and diffusion spectra.Through the resolution of spectroscopic signals with spatial encoding gradients,multi-dimensional MR imaging has been widely used to investigate the microscopic environment of living tissues and distinguish diseases.Signals in each voxel are usually expressed as multi-exponential decay,representing microstructures or environments along multiple pore scales.The separation of contributions from different environments is a common ill-posed problem,which can be resolved numerically.Moreover,the inversion methods and experimental parameters determine the resolution of multi-dimensional spectra.This paper reviews the algorithms that have been proposed to process multidimensional MR datasets in different scenarios.Detailed information at the microscopic level,such as tissue components,fluid types and food structures in multi-disciplinary sciences,could be revealed through multi-dimensional MR.展开更多
A 3D temperature field reconstruction method using the colored background oriented schlieren(CBOS)method is proposed to address image blurring due to the different refractive index of the multi-wavelength light and si...A 3D temperature field reconstruction method using the colored background oriented schlieren(CBOS)method is proposed to address image blurring due to the different refractive index of the multi-wavelength light and significant errors produced when the traditional background oriented schlieren(BOS)method is applied to high-temperature gas.First,the traditional method is employed to reconstruct the non-uniform 3D temperature field.Second,the CBOS method is applied to correct the distortion.Then,by analyzing the correlation coefficient among different color points of the colored background pattern,the non-uniform temperature field is reconstructed much more accurately.Finally,the experimental results are verified by applying the Runge-Kutta ray-tracing method and the thermocouple contact measurement method.The maximum average temperature error of the CBOS-reconstructed temperature field is 12.92°C,compared with the thermocouples.Therefore,an accurate three-dimensional reconstruction of the temperature field can be achieved by the proposed method effectively.展开更多
Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harm...Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.展开更多
A newly revised inverse scattering transform(IST) for the derivative nonlinear Schrdinger(DNLS+) equation with non-vanishing boundary condition(NVBC) and normal group velocity dispersion is proposed by introduc...A newly revised inverse scattering transform(IST) for the derivative nonlinear Schrdinger(DNLS+) equation with non-vanishing boundary condition(NVBC) and normal group velocity dispersion is proposed by introducing a suitable affine parameter in Zakharov-Shabat integral kern.The explicit breather-type one-soliton solution,which can reproduce one pure soliton at the de-generate case and one bright soliton solution at the limit of van-ishing boundary,has been derived to verify the validity of the revised IST.展开更多
This paper deals with a unified and novel approach for analyzing the frequency and time domain performance of grounding systems.The proposed procedure is based on solving the full set of Maxwell's equations in the...This paper deals with a unified and novel approach for analyzing the frequency and time domain performance of grounding systems.The proposed procedure is based on solving the full set of Maxwell's equations in the frequency domain,and enables the exact computation of very near fields at the surface of the grounding grid,as well as far fields,by simple and accurate closed-form expressions for solving Sommerfeld integrals.In addition,the soil ionization is easily considered in the proposed method.The frequency domain responses are converted to the time domain by fast inverse Laplace transform.The results are validated and have shown acceptable accuracy.展开更多
The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–...The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. Then the Riemann–Hilbert problem corresponding to the reflection-less case is solved.As applications, multi-soliton solutions are obtained for the coupled Sasa–Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons.展开更多
In this paper,a time-frequency associated multiple signal classification(MUSIC)al-gorithm which is suitable for through-wall detection is proposed.The technology of detecting hu-man targets by through-wall radar can b...In this paper,a time-frequency associated multiple signal classification(MUSIC)al-gorithm which is suitable for through-wall detection is proposed.The technology of detecting hu-man targets by through-wall radar can be used to monitor the status and the location information of human targets behind the wall.However,the detection is out of order when classical MUSIC al-gorithm is applied to estimate the direction of arrival.In order to solve the problem,a time-fre-quency associated MUSIC algorithm suitable for through-wall detection and based on S-band stepped frequency continuous wave(SFCW)radar is researched.By associating inverse fast Fouri-er transform(IFFT)algorithm with MUSIC algorithm,the power enhancement of the target sig-nal is completed according to the distance calculation results in the time domain.Then convert the signal to the frequency domain for direction of arrival(DOA)estimation.The simulations of two-dimensional human target detection in free space and the processing of measured data are com-pleted.By comparing the processing results of the two algorithms on the measured data,accuracy of DOA estimation of proposed algorithm is more than 75%,which is 50%higher than classical MUSIC algorithm.It is verified that the distance and angle of human target can be effectively de-tected via proposed algorithm.展开更多
Some results and developments on the extension of the inverse scattering transform to solve non-linear evolution equations in one time and two space dimensions are described.
The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokho...The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.展开更多
The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the ...The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.展开更多
In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples ar...In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems.展开更多
In this paper, we consider the trace of generalized operators and inverse Weyl transformation.First of all we repeat the definition of test operators and generalized operators given in [18],denoting L~2(R) by H.
Let be the quaternion Heisenberg group, and let P be the affine automorphism group of . We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on...Let be the quaternion Heisenberg group, and let P be the affine automorphism group of . We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on L2( ). A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on . . A Semyanistyi-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth. In addition, we obtain an inversion formula of the Radon transform associated with the sub-Laplacian on .展开更多
基金supported by the National Natural Science Foundation of China (61272120,61602377,61634004)the Shaanxi Provincial Co-Ordination Innovation Project of Science and Technology (2016KTZDGY02-04-02)the National Science and Technology Major Project of China (2016ZX03001003-006)
文摘High efficiency video coding (HEVC) transform algorithm for residual coding uses 2-dimensional (2D) 4 × 4 transforms with higher precision than H.264's 4 ×4 transforms, resulting in increased hardware complexity. In this paper, we present a shared architecture that can compute the 4 ~4 forward discrete cosine transform (DCT) and inverse discrete cosine transform (IDCT) of HEVC using a new mapping scheme in the video processor array structure. The architecture is implemented with only adders and shills to an area-efficient design. The proposed architecture is synthesized using ISE 14.7 and implemented using the BEE4 platform with the Virtex-6 FF1759 LX550T field programmable gate array (FPGA). The result shows that the video processor array structure achieves a maximum operation frequency of 165.2 MHz. The architecture and its implementation are presented in this paper to demonstrate its programmable and high performance.
文摘A new reflection approach for field distribution measurement of ultrasonic transducers was investigated. Instead of a point-like reflection target (rigid sphere) or thin wires (line-like targets), a line response function of experimental knife-edge distribution combined with the inverse Abel transforms was used to estimate the lateral beam distributions of ultrasonic transducers. The measurement steps were as follows:① A knife-edge was scanned perpendicularly to acoustic beam axis of the transducer using an ultrasonic C-scan system to obtain its ultrasonic image line response function, ② the transverse beam distribution was solved by the inverse Abel transforms, and ③ experiments were performed to obtain the lateral beam profiles of two transducers, with and without focus, and the results were compared with those from a hydrophone. The results showed that this method was effective for ultrasonic field measurement and could be as a substitute for hydrophone in most cases.
文摘A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum
基金Project supported by the National High Technology Research and Development Program of China (Grant No. 2012AA011603)
文摘The local reconstruction from truncated projection data is one area of interest in image reconstruction for com- puted tomography (CT), which creates the possibility for dose reduction. In this paper, a filtered-backprojection (FBP) algorithm based on the Radon inversion transform is presented to deal with the three-dimensional (3D) local recon- struction in the circular geometry. The algorithm achieves the data filtering in two steps. The first step is the derivative of projections, which acts locally on the data and can thus be carried out accurately even in the presence of data trun- cation. The second step is the nonlocal Hilbert filtering. The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm. Compared with the approximate truncation resistant algorithm for computed tomography (ATRACT), not only it has a comparable ability to restrain truncation artifacts, but also its reconstruction efficiency is improved. It is about twice as fast as that of the ATRACT. Therefore, this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.
基金Supported by the Foundation of the National Natural Science of China( No.1 0 0 71 0 39) and the Foundation of Edu-cation Commission of Jiangsu Province
文摘Let X=Rn +×R denote the underlying manifold of polyradial functions on the Heisenberg group H n. We construct a generalized translation on X=Rn +×R, and establish the Plancherel formula on L2(X,dμ). Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.
文摘Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find on approximation to f(t) by the use of the dassical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series ex-pansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.
文摘A fast Cholesky decomposition and a fast inverse Cholesky decomposition method for A T A are presented,where A is an m×n rectangular Toeplitz block matrix,we give the FCD algorithm for computing R , and the FICD algorithm for computing R -1 ,both allow for an efficient parallel implementation,for solving a least squares problem and require only O(mn) operations.
基金supported by the National Natural Science Foundation of China(No.61901465,82222032,82172050).
文摘Since its inception in the 1970s,multi-dimensional magnetic resonance(MR)has emerged as a powerful tool for non-invasive investigations of structures and molecular interactions.MR spectroscopy beyond one dimension allows the study of the correlation,exchange processes,and separation of overlapping spectral information.The multi-dimensional concept has been re-implemented over the last two decades to explore molecular motion and spin dynamics in porous media.Apart from Fourier transform,methods have been developed for processing the multi-dimensional time-domain data,identifying the fluid components,and estimating pore surface permeability via joint relaxation and diffusion spectra.Through the resolution of spectroscopic signals with spatial encoding gradients,multi-dimensional MR imaging has been widely used to investigate the microscopic environment of living tissues and distinguish diseases.Signals in each voxel are usually expressed as multi-exponential decay,representing microstructures or environments along multiple pore scales.The separation of contributions from different environments is a common ill-posed problem,which can be resolved numerically.Moreover,the inversion methods and experimental parameters determine the resolution of multi-dimensional spectra.This paper reviews the algorithms that have been proposed to process multidimensional MR datasets in different scenarios.Detailed information at the microscopic level,such as tissue components,fluid types and food structures in multi-disciplinary sciences,could be revealed through multi-dimensional MR.
基金Supported by the National Natural Science Foundation of China(52005500)Foundation of Tianjin Educational Committee(2018KJ242)Basic Science-Research Funds of National University(3122019088)。
文摘A 3D temperature field reconstruction method using the colored background oriented schlieren(CBOS)method is proposed to address image blurring due to the different refractive index of the multi-wavelength light and significant errors produced when the traditional background oriented schlieren(BOS)method is applied to high-temperature gas.First,the traditional method is employed to reconstruct the non-uniform 3D temperature field.Second,the CBOS method is applied to correct the distortion.Then,by analyzing the correlation coefficient among different color points of the colored background pattern,the non-uniform temperature field is reconstructed much more accurately.Finally,the experimental results are verified by applying the Runge-Kutta ray-tracing method and the thermocouple contact measurement method.The maximum average temperature error of the CBOS-reconstructed temperature field is 12.92°C,compared with the thermocouples.Therefore,an accurate three-dimensional reconstruction of the temperature field can be achieved by the proposed method effectively.
基金Project supported by the National Natural Science Foundation of China (No.10172038)
文摘Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.
基金Supported by the National Natural Science Foundation of China(10775105)
文摘A newly revised inverse scattering transform(IST) for the derivative nonlinear Schrdinger(DNLS+) equation with non-vanishing boundary condition(NVBC) and normal group velocity dispersion is proposed by introducing a suitable affine parameter in Zakharov-Shabat integral kern.The explicit breather-type one-soliton solution,which can reproduce one pure soliton at the de-generate case and one bright soliton solution at the limit of van-ishing boundary,has been derived to verify the validity of the revised IST.
文摘This paper deals with a unified and novel approach for analyzing the frequency and time domain performance of grounding systems.The proposed procedure is based on solving the full set of Maxwell's equations in the frequency domain,and enables the exact computation of very near fields at the surface of the grounding grid,as well as far fields,by simple and accurate closed-form expressions for solving Sommerfeld integrals.In addition,the soil ionization is easily considered in the proposed method.The frequency domain responses are converted to the time domain by fast inverse Laplace transform.The results are validated and have shown acceptable accuracy.
基金Supported by the National Natural Science Foundation of China under Project Nos.11331008 and 11171312the Collaborative Innovation Center for Aviation Economy Development of Henan Province
文摘The inverse scattering transform of a coupled Sasa–Satsuma equation is studied via Riemann–Hilbert approach. Firstly, the spectral analysis is performed for the coupled Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. Then the Riemann–Hilbert problem corresponding to the reflection-less case is solved.As applications, multi-soliton solutions are obtained for the coupled Sasa–Satsuma equation. Moreover, some figures are given to describe the soliton behaviors, including breather types, single-hump solitons, double-hump solitons, and two-bell solitons.
文摘In this paper,a time-frequency associated multiple signal classification(MUSIC)al-gorithm which is suitable for through-wall detection is proposed.The technology of detecting hu-man targets by through-wall radar can be used to monitor the status and the location information of human targets behind the wall.However,the detection is out of order when classical MUSIC al-gorithm is applied to estimate the direction of arrival.In order to solve the problem,a time-fre-quency associated MUSIC algorithm suitable for through-wall detection and based on S-band stepped frequency continuous wave(SFCW)radar is researched.By associating inverse fast Fouri-er transform(IFFT)algorithm with MUSIC algorithm,the power enhancement of the target sig-nal is completed according to the distance calculation results in the time domain.Then convert the signal to the frequency domain for direction of arrival(DOA)estimation.The simulations of two-dimensional human target detection in free space and the processing of measured data are com-pleted.By comparing the processing results of the two algorithms on the measured data,accuracy of DOA estimation of proposed algorithm is more than 75%,which is 50%higher than classical MUSIC algorithm.It is verified that the distance and angle of human target can be effectively de-tected via proposed algorithm.
文摘Some results and developments on the extension of the inverse scattering transform to solve non-linear evolution equations in one time and two space dimensions are described.
基金supported in part by NSFC(11975145 and 11972291)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17 KJB 110020)。
文摘The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.
基金supported by the National Natural Science Foundation of China under Grant No.11975306the Natural Science Foundation of Jiangsu Province under Grant No.BK20181351+1 种基金the Six Talent Peaks Project in Jiangsu Province under Grant No.JY-059the Fundamental Research Fund for the Central Universities under the Grant Nos.2019ZDPY07 and 2019QNA35。
文摘The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.
文摘In this paper, the modification of double Laplace decomposition method is pro- posed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems.
文摘In this paper, we consider the trace of generalized operators and inverse Weyl transformation.First of all we repeat the definition of test operators and generalized operators given in [18],denoting L~2(R) by H.
基金supported by National Natural Science Foundation of China(Grant Nos.10971039 and 11271091)the second author is supported by National Natural Science Foundation of China(Grant No.10990012)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.2012000110059)
文摘Let be the quaternion Heisenberg group, and let P be the affine automorphism group of . We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on L2( ). A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on . . A Semyanistyi-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth. In addition, we obtain an inversion formula of the Radon transform associated with the sub-Laplacian on .