In this paper, we study the extremum inequalities of general L_(p)-intersection bodies. In addition, associating with the L_(q)-radial combination and Lq-harmonic Blaschke combination, we establish the Brunn-Minkowski...In this paper, we study the extremum inequalities of general L_(p)-intersection bodies. In addition, associating with the L_(q)-radial combination and Lq-harmonic Blaschke combination, we establish the Brunn-Minkowski type inequalities of general Lp-intersection bodies for dual quermassintegrals, respectively. As applications, inequalities of volume are derived.展开更多
In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvatu...In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.展开更多
In this paper,we introduce the concept of the L_(p,s)-Gaussian surface area measure of a convex body in n-dimensional Euclidean space R^(n) and formulate the corresponding L_(p,s)-Gaussian-Minkowski problem:Given a fi...In this paper,we introduce the concept of the L_(p,s)-Gaussian surface area measure of a convex body in n-dimensional Euclidean space R^(n) and formulate the corresponding L_(p,s)-Gaussian-Minkowski problem:Given a finite Borel measureμon S^(n-1),what are the necessary and sufficient conditions for the existence of a convex body whose L_(p,s)-Gaussian surface area measure equals measure μ?Furthermore,we present a solution to the L_(p,s)-Gaussian-Minkowski problem for the case of even measures.展开更多
In this paper,we introduce the normalized L,mixed intersection body and demonstrate how the normalized L_(p) mixed intersection body operator can be used to obtain the polar body operator as a limit.Moreover,we study ...In this paper,we introduce the normalized L,mixed intersection body and demonstrate how the normalized L_(p) mixed intersection body operator can be used to obtain the polar body operator as a limit.Moreover,we study the L_(p)-Busemann-Petty type problem for the normalized L_(p) mixed intersection bodies.展开更多
We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,i...We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB.展开更多
稀疏恢复(Sparse Recovery,SR)空时自适应信号处理(Space Time Adaptive Processing,STAP)仅需要少量的杂波样本即可有效抑制杂波,但是稀疏恢复空时自适应信号处理依赖于空时字典,当载机运动方向与天线放置方向存在偏航角时,杂波脊偏离...稀疏恢复(Sparse Recovery,SR)空时自适应信号处理(Space Time Adaptive Processing,STAP)仅需要少量的杂波样本即可有效抑制杂波,但是稀疏恢复空时自适应信号处理依赖于空时字典,当载机运动方向与天线放置方向存在偏航角时,杂波脊偏离空时字典格点,出现离格问题,从而导致杂波抑制性能下降。已有的基于l_(1)范数类的离格稀疏恢复算法在存在噪声时性能下降,没有充分利用杂波的稀疏性,文章提出一种基于l_(p)(0<p<1)范数的离格空时自适应处理算法,首先将建立基于空时字典更新的稀疏恢复空时自适应模型,然后将该模型松弛为l_(p)(0<p<1)范数的非凸优化问题,最后利用主函数最大化算法将该优化问题转化成凸优化问题,利用两层迭代求解的方法得到该问题的解,最后利用模型的解估计杂波协方差矩阵。通过仿真实验表明,提出的算法能够提高存在离格问题时的杂波恢复精度,抑制杂波的性能也优于已有的基于变分推断的算法。展开更多
为实现正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统的时域同步,本文利用ZC(Zadoff-Chu)序列提出了类奈曼-皮尔逊检验加权的l_(p)(p=1或2)相关(Neyman-Pearson-like test Weighted l_(p)-Correlation,l_(p)-NPWC...为实现正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统的时域同步,本文利用ZC(Zadoff-Chu)序列提出了类奈曼-皮尔逊检验加权的l_(p)(p=1或2)相关(Neyman-Pearson-like test Weighted l_(p)-Correlation,l_(p)-NPWC)同步算法.分析表明:该算法利用类奈曼-皮尔逊检验能有效抑制多径效应对l_(p)相关同步的影响,特别地,当取p=1时,它对重尾分布噪声及循环前缀导致的伪峰具有极强的鲁棒性.实验及仿真结果均证明了理论分析的正确性和有效性,并表明本文算法相较于现有算法在各种干扰环境中均具有更高的同步精度和性能.展开更多
基金the National Natural Science Foundation of China(11371224)the Innovation Foundation of Graduate Student of China Three Gorges University(2019SSPY146)。
文摘In this paper, we study the extremum inequalities of general L_(p)-intersection bodies. In addition, associating with the L_(q)-radial combination and Lq-harmonic Blaschke combination, we establish the Brunn-Minkowski type inequalities of general Lp-intersection bodies for dual quermassintegrals, respectively. As applications, inequalities of volume are derived.
基金supported by the National Natural Science Foundation of China(12171144,12231006,12122106).
文摘In this paper,the L_(p)chord Minkowski problem is concerned.Based on the results shown in[20],we obtain a new existence result of solutions to this problem in terms of smooth measures by using a nonlocal Gauss curvature flow for p>−n with p≠0.
基金Supported by the National Natural Science Foundation of China(11971080,12371137)。
文摘In this paper,we introduce the concept of the L_(p,s)-Gaussian surface area measure of a convex body in n-dimensional Euclidean space R^(n) and formulate the corresponding L_(p,s)-Gaussian-Minkowski problem:Given a finite Borel measureμon S^(n-1),what are the necessary and sufficient conditions for the existence of a convex body whose L_(p,s)-Gaussian surface area measure equals measure μ?Furthermore,we present a solution to the L_(p,s)-Gaussian-Minkowski problem for the case of even measures.
基金Supported by the Postgraduate Scientific Research Innovation Project of Hunan Province (CX20231033)。
文摘In this paper,we introduce the normalized L,mixed intersection body and demonstrate how the normalized L_(p) mixed intersection body operator can be used to obtain the polar body operator as a limit.Moreover,we study the L_(p)-Busemann-Petty type problem for the normalized L_(p) mixed intersection bodies.
文摘We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB.
文摘稀疏恢复(Sparse Recovery,SR)空时自适应信号处理(Space Time Adaptive Processing,STAP)仅需要少量的杂波样本即可有效抑制杂波,但是稀疏恢复空时自适应信号处理依赖于空时字典,当载机运动方向与天线放置方向存在偏航角时,杂波脊偏离空时字典格点,出现离格问题,从而导致杂波抑制性能下降。已有的基于l_(1)范数类的离格稀疏恢复算法在存在噪声时性能下降,没有充分利用杂波的稀疏性,文章提出一种基于l_(p)(0<p<1)范数的离格空时自适应处理算法,首先将建立基于空时字典更新的稀疏恢复空时自适应模型,然后将该模型松弛为l_(p)(0<p<1)范数的非凸优化问题,最后利用主函数最大化算法将该优化问题转化成凸优化问题,利用两层迭代求解的方法得到该问题的解,最后利用模型的解估计杂波协方差矩阵。通过仿真实验表明,提出的算法能够提高存在离格问题时的杂波恢复精度,抑制杂波的性能也优于已有的基于变分推断的算法。
文摘为实现正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统的时域同步,本文利用ZC(Zadoff-Chu)序列提出了类奈曼-皮尔逊检验加权的l_(p)(p=1或2)相关(Neyman-Pearson-like test Weighted l_(p)-Correlation,l_(p)-NPWC)同步算法.分析表明:该算法利用类奈曼-皮尔逊检验能有效抑制多径效应对l_(p)相关同步的影响,特别地,当取p=1时,它对重尾分布噪声及循环前缀导致的伪峰具有极强的鲁棒性.实验及仿真结果均证明了理论分析的正确性和有效性,并表明本文算法相较于现有算法在各种干扰环境中均具有更高的同步精度和性能.
