In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14...In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.展开更多
混沌压缩感知是一种利用混沌系统实现非线性测量,通过混沌脉冲同步和参数估计技术实现信号重构的压缩感知理论。针对混沌压缩感知重构系统中采用l1范数正则化信号系数导致在信号稀疏水平较高时重构性能急剧下降的问题,利用lp(0 p 1)范...混沌压缩感知是一种利用混沌系统实现非线性测量,通过混沌脉冲同步和参数估计技术实现信号重构的压缩感知理论。针对混沌压缩感知重构系统中采用l1范数正则化信号系数导致在信号稀疏水平较高时重构性能急剧下降的问题,利用lp(0 p 1)范数来正则化信号系数,将重构系统中的非线性约束l1范数最小化问题替换为非线性约束lp范数最小化问题,并提出-正则迭代再加权非线性最小二乘算法进行求解。以Henon混沌为例,研究了频域稀疏信号的重构性能,数值模拟表明lp范数正则化能够准确重构出比l1范数正则化时稀疏水平更高的信号。展开更多
It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially norm...It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.展开更多
文摘In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.
文摘混沌压缩感知是一种利用混沌系统实现非线性测量,通过混沌脉冲同步和参数估计技术实现信号重构的压缩感知理论。针对混沌压缩感知重构系统中采用l1范数正则化信号系数导致在信号稀疏水平较高时重构性能急剧下降的问题,利用lp(0 p 1)范数来正则化信号系数,将重构系统中的非线性约束l1范数最小化问题替换为非线性约束lp范数最小化问题,并提出-正则迭代再加权非线性最小二乘算法进行求解。以Henon混沌为例,研究了频域稀疏信号的重构性能,数值模拟表明lp范数正则化能够准确重构出比l1范数正则化时稀疏水平更高的信号。
基金supported by National Natural Science Foundation of China (Grant No. 41974140)the PetroChina Prospective,Basic,and Strategic Technology Research Project (No. 2021DJ0606)
基金supported by the Joint funding project of the National Natural Science Foundation of Chinathe China Civil Aviation Administration (No.U1733119)civil aviation science and Technology project (No.20150220)
文摘It is proved that there is only one L^P-matricially normed space of dimension 1 and that quotient spaces of L^P-matricially normed spaces are also L^P-matricially normed spaces. Some properties of L^P-matricially normed spaces are given.