In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map...In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map S(z,ζ) which do not depends holomorphic on z∈D in Koppelman formula is obtained and the L s norm estimates for the solution operators are the same as that [10] in forms.展开更多
Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates...Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ.展开更多
We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpol...We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.展开更多
It is assumed that reconfigurable intelligent surface(RIS)is a key technology to enable the potential of mmWave communications.The passivity of the RIS makes channel estimation difficult because the channel can only b...It is assumed that reconfigurable intelligent surface(RIS)is a key technology to enable the potential of mmWave communications.The passivity of the RIS makes channel estimation difficult because the channel can only be measured at the transceiver and not at the RIS.In this paper,we propose a novel separate channel estimator via exploiting the cascaded sparsity in the continuously valued angular domain of the cascaded channel for the RIS-enabled millimeter-wave/Tera-Hz systems,i.e.,the two-stage estimation method where the cascaded channel is separated into the base station(BS)-RIS and the RIS-user(UE)ones.Specifically,we first reveal the cascaded sparsity,i.e.,the sparsity exists in the hybrid angular domains of BS-RIS and the RIS-UEs separated channels,to construct the specific sparsity structure for RIS enabled multi-user systems.Then,we formulate the channel estimation problem using atomic norm minimization(ANM)to enhance the proposed sparsity structure in the continuous angular domains,where a low-complexity channel estimator via Alternating Direction Method of Multipliers(ADMM)is proposed.Simulation findings demonstrate that the proposed channel estimator outperforms the current state-of-the-arts in terms of performance.展开更多
In this paper,we study the accuracy of delay-Doppler parameter estimation of targets in a passive radar using orthogonal frequency division multiplexing(OFDM)signal.A coarse-fine joint estimation method is proposed to...In this paper,we study the accuracy of delay-Doppler parameter estimation of targets in a passive radar using orthogonal frequency division multiplexing(OFDM)signal.A coarse-fine joint estimation method is proposed to achieve better estimation accuracy of target parameters without excessive computational burden.Firstly,the modulation symbol domain(MSD)method is used to roughly estimate the delay and Doppler of targets.Then,to obtain high-precision Doppler estimation,the atomic norm(AN)based on the multiple measurement vectors(MMV)model(MMV-AN)is used to manifest the signal sparsity in the continuous Doppler domain.At the same time,a reference signal compensation(RSC)method is presented to obtain highprecision delay estimation.Simulation results based on the OFDM signal show that the coarse-fine joint estimation method based on AN-RSC can obtain a more accurate estimation of target parameters compared with other algorithms.In addition,the proposed method also possesses computational advantages compared with the joint parameter estimation.展开更多
In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing ac...In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing accuracy-conserving(SIAC)filter is a post-processing technique to enhance the accuracy of the discontinuous Galerkin(DG)solutions.This work is the essential step to extend the SIAC filter to the moving mesh for nonlinear problems.By the post-processing theory,the negative norm estimates are vital to get the superconvergence error estimates of the solutions after post-processing in the L2 norm.Although the SIAC filter has been extended to nonuniform mesh,the analysis of fil-tered solutions on the nonuniform mesh is complicated.We prove superconvergence error estimates in the negative norm for the ALE-DG method on moving meshes.The main dif-ficulties of the analysis are the terms in the ALE-DG scheme brought by the grid velocity field,and the time-dependent function space.The mapping from time-dependent cells to reference cells is very crucial in the proof.The numerical results also confirm the theoreti-cal proof.展开更多
In this article, the authors give a typical integral's bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F(p, q, s, k) space in theunit ball of Cn are given.
The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The me...The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A (α l ), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi collinearity of A. According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.展开更多
Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0...Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0(F,B)becomes a complete random normed module,which has played an important role in the process of applications of random normed modules to the theory of Lebesgue-Bochner function spaces and random operator theory.Let V be a closed convex subset of B and L^0(F,V)the set of equivalence classes of strong random elements from(?,F,P)to V.The central purpose of this article is to prove the following two results:(1)L^0(F,V)is L^0-convexly compact if and only if V is weakly compact;(2)L^0(F,V)has random normal structure if V is weakly compact and has normal structure.As an application,a general random fixed point theorem for a strong random nonexpansive operator is given,which generalizes and improves several well known results.We hope that our new method,namely skillfully combining measurable selection theorems,the theory of random normed modules,and Banach space techniques,can be applied in the other related aspects.展开更多
In this paper,we address the problem of multiple frequency-hopping(FH)signal parameters estimation in the presence of random missing observations.A space-time matrix with random missing observations is acquired by a u...In this paper,we address the problem of multiple frequency-hopping(FH)signal parameters estimation in the presence of random missing observations.A space-time matrix with random missing observations is acquired by a uniform linear array(ULA).We exploit the inherent incomplete data processing capability of atomic norm soft thresholding(AST)to analyze the space-time matrix and complete the accurate estimation of the hopping time and frequency of the received FH signals.The hopping time is obtained by the sudden changes of the spatial information,which is implemented as the boundary to divide the time domain signal so that each segment of the signal is a superposition of time-invariant multiple components.Then,the frequency of multiple signal components can be estimated precisely by AST within each segment.After obtaining the above two parameters of the hopping time and the frequency of signals,the direction of arrival(DOA)can be directly calculated by them,and the network sorting can be realized.Results of simulation show that the proposed method is superior to the existing technology.Even when a large portion of data observations is missing,as the number of array elements increases,the proposed method still achieves acceptable accuracy of multi-FH signal parameters estimation.展开更多
Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model...Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model-observation discrepancies are quantified. Commonly used parameter estimation techniques based on least-squares minimization of the model-observation discrepancies assume that the discrepancies are quantified with the L<sup>2</sup>-norm applied to a discrepancy function. While techniques based on such an assumption work well for many applications, other applications are better suited for least-squared minimization approaches that are based on other norm or inner-product induced topologies. Motivated by an application in the material sciences, the new alternative least-squares approach is defined and an insightful analytical comparison with a baseline least-squares approach is provided.展开更多
多输入多输出(Multiple-Input Multiple-Output,MIMO)雷达在阵元故障时虚拟阵列输出数据矩阵会出现大量的整行数据丢失,由于阵列接收数据矩阵的不完整而导致对波达方向(Direction of Arrival,DOA)的估计性能恶化。大多数低秩矩阵填充算...多输入多输出(Multiple-Input Multiple-Output,MIMO)雷达在阵元故障时虚拟阵列输出数据矩阵会出现大量的整行数据丢失,由于阵列接收数据矩阵的不完整而导致对波达方向(Direction of Arrival,DOA)的估计性能恶化。大多数低秩矩阵填充算法要求缺失数据随机分布于不完整的矩阵中,无法适用于整行缺失数据的恢复问题。为此,提出了一种基于低秩块Hankel矩阵正则化的阵元故障MIMO雷达DOA估计方法。首先,通过奇异值分解(Singular Value Decomposition,SVD)降低虚拟阵列输出矩阵的维度,以减少计算复杂度。然后,对降维数据矩阵建立基于块Hankel矩阵正则化的低秩矩阵填充模型,在该模型中将MIMO雷达降维数据矩阵排列成块Hankel矩阵并施加Schatten-p范数作为正则项。最后,结合交替方向乘子法(Alternate Direction Multiplier Method,ADMM)求解该模型,获得完整的MIMO雷达降维数据矩阵。仿真结果表明,所提方法能够有效恢复降维数据矩阵中的整行数据缺失,具有较高的DOA估计精度和实时性,在阵元故障率低于50.0%时DOA估计精度优于现有方法。展开更多
文摘In this paper,we discussed the local integral solution operators of imhomogeneous Cauchy Riemann equations on an open set with piecewise C k boundary in C n,as a generalization of the solution opertators for Leray map S(z,ζ) which do not depends holomorphic on z∈D in Koppelman formula is obtained and the L s norm estimates for the solution operators are the same as that [10] in forms.
基金Supported by Natural Science Fundation of Anhui Province (07021019)Education Committee of AnhuiProvince (KJ2007A009 KJ2008B244)
文摘Let F be a C^∞ curve in IR^n and μ be the measure induced by Lebesgue measure on F, multiplied by a smooth cut-off function. In this paper, we will prove some mixednorm estimates based on the average decay estimates of the Fourier transform of μ.
基金This research is supported by the Foundation for Talents for Next Century of Shandong University
文摘We’ll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.
文摘It is assumed that reconfigurable intelligent surface(RIS)is a key technology to enable the potential of mmWave communications.The passivity of the RIS makes channel estimation difficult because the channel can only be measured at the transceiver and not at the RIS.In this paper,we propose a novel separate channel estimator via exploiting the cascaded sparsity in the continuously valued angular domain of the cascaded channel for the RIS-enabled millimeter-wave/Tera-Hz systems,i.e.,the two-stage estimation method where the cascaded channel is separated into the base station(BS)-RIS and the RIS-user(UE)ones.Specifically,we first reveal the cascaded sparsity,i.e.,the sparsity exists in the hybrid angular domains of BS-RIS and the RIS-UEs separated channels,to construct the specific sparsity structure for RIS enabled multi-user systems.Then,we formulate the channel estimation problem using atomic norm minimization(ANM)to enhance the proposed sparsity structure in the continuous angular domains,where a low-complexity channel estimator via Alternating Direction Method of Multipliers(ADMM)is proposed.Simulation findings demonstrate that the proposed channel estimator outperforms the current state-of-the-arts in terms of performance.
基金supported by the National Natural Science Foundation of China(6193101562071335)+1 种基金the Technological Innovation Project of Hubei Province of China(2019AAA061)the Natural Science F oundation of Hubei Province of China(2021CFA002)。
文摘In this paper,we study the accuracy of delay-Doppler parameter estimation of targets in a passive radar using orthogonal frequency division multiplexing(OFDM)signal.A coarse-fine joint estimation method is proposed to achieve better estimation accuracy of target parameters without excessive computational burden.Firstly,the modulation symbol domain(MSD)method is used to roughly estimate the delay and Doppler of targets.Then,to obtain high-precision Doppler estimation,the atomic norm(AN)based on the multiple measurement vectors(MMV)model(MMV-AN)is used to manifest the signal sparsity in the continuous Doppler domain.At the same time,a reference signal compensation(RSC)method is presented to obtain highprecision delay estimation.Simulation results based on the OFDM signal show that the coarse-fine joint estimation method based on AN-RSC can obtain a more accurate estimation of target parameters compared with other algorithms.In addition,the proposed method also possesses computational advantages compared with the joint parameter estimation.
基金the fellowship of China Postdoctoral Science Foundation,no:2020TQ0030.Y.Xu:Research supported by National Numerical Windtunnel Project NNW2019ZT4-B08+1 种基金Science Challenge Project TZZT2019-A2.3NSFC Grants 11722112,12071455.X.Li:Research supported by NSFC Grant 11801062.
文摘In this paper,we present the negative norm estimates for the arbitrary Lagrangian-Eulerian discontinuous Galerkin(ALE-DG)method solving nonlinear hyperbolic equations with smooth solutions.The smoothness-increasing accuracy-conserving(SIAC)filter is a post-processing technique to enhance the accuracy of the discontinuous Galerkin(DG)solutions.This work is the essential step to extend the SIAC filter to the moving mesh for nonlinear problems.By the post-processing theory,the negative norm estimates are vital to get the superconvergence error estimates of the solutions after post-processing in the L2 norm.Although the SIAC filter has been extended to nonuniform mesh,the analysis of fil-tered solutions on the nonuniform mesh is complicated.We prove superconvergence error estimates in the negative norm for the ALE-DG method on moving meshes.The main dif-ficulties of the analysis are the terms in the ALE-DG scheme brought by the grid velocity field,and the time-dependent function space.The mapping from time-dependent cells to reference cells is very crucial in the proof.The numerical results also confirm the theoreti-cal proof.
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘In this article, the authors give a typical integral's bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F(p, q, s, k) space in theunit ball of Cn are given.
文摘The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A (α l ), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi collinearity of A. According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.
基金This work was supported by National Natural Science Foundation of China(11571369)。
文摘Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0(F,B)becomes a complete random normed module,which has played an important role in the process of applications of random normed modules to the theory of Lebesgue-Bochner function spaces and random operator theory.Let V be a closed convex subset of B and L^0(F,V)the set of equivalence classes of strong random elements from(?,F,P)to V.The central purpose of this article is to prove the following two results:(1)L^0(F,V)is L^0-convexly compact if and only if V is weakly compact;(2)L^0(F,V)has random normal structure if V is weakly compact and has normal structure.As an application,a general random fixed point theorem for a strong random nonexpansive operator is given,which generalizes and improves several well known results.We hope that our new method,namely skillfully combining measurable selection theorems,the theory of random normed modules,and Banach space techniques,can be applied in the other related aspects.
文摘In this paper,we address the problem of multiple frequency-hopping(FH)signal parameters estimation in the presence of random missing observations.A space-time matrix with random missing observations is acquired by a uniform linear array(ULA).We exploit the inherent incomplete data processing capability of atomic norm soft thresholding(AST)to analyze the space-time matrix and complete the accurate estimation of the hopping time and frequency of the received FH signals.The hopping time is obtained by the sudden changes of the spatial information,which is implemented as the boundary to divide the time domain signal so that each segment of the signal is a superposition of time-invariant multiple components.Then,the frequency of multiple signal components can be estimated precisely by AST within each segment.After obtaining the above two parameters of the hopping time and the frequency of signals,the direction of arrival(DOA)can be directly calculated by them,and the network sorting can be realized.Results of simulation show that the proposed method is superior to the existing technology.Even when a large portion of data observations is missing,as the number of array elements increases,the proposed method still achieves acceptable accuracy of multi-FH signal parameters estimation.
文摘Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model-observation discrepancies are quantified. Commonly used parameter estimation techniques based on least-squares minimization of the model-observation discrepancies assume that the discrepancies are quantified with the L<sup>2</sup>-norm applied to a discrepancy function. While techniques based on such an assumption work well for many applications, other applications are better suited for least-squared minimization approaches that are based on other norm or inner-product induced topologies. Motivated by an application in the material sciences, the new alternative least-squares approach is defined and an insightful analytical comparison with a baseline least-squares approach is provided.
文摘多输入多输出(Multiple-Input Multiple-Output,MIMO)雷达在阵元故障时虚拟阵列输出数据矩阵会出现大量的整行数据丢失,由于阵列接收数据矩阵的不完整而导致对波达方向(Direction of Arrival,DOA)的估计性能恶化。大多数低秩矩阵填充算法要求缺失数据随机分布于不完整的矩阵中,无法适用于整行缺失数据的恢复问题。为此,提出了一种基于低秩块Hankel矩阵正则化的阵元故障MIMO雷达DOA估计方法。首先,通过奇异值分解(Singular Value Decomposition,SVD)降低虚拟阵列输出矩阵的维度,以减少计算复杂度。然后,对降维数据矩阵建立基于块Hankel矩阵正则化的低秩矩阵填充模型,在该模型中将MIMO雷达降维数据矩阵排列成块Hankel矩阵并施加Schatten-p范数作为正则项。最后,结合交替方向乘子法(Alternate Direction Multiplier Method,ADMM)求解该模型,获得完整的MIMO雷达降维数据矩阵。仿真结果表明,所提方法能够有效恢复降维数据矩阵中的整行数据缺失,具有较高的DOA估计精度和实时性,在阵元故障率低于50.0%时DOA估计精度优于现有方法。