The precise L^(p) norm of a class of Forelli-Rudin type operators on the Siegel upper half space is given in this paper.The main result not only implies the upper L^(p) norm estimate of the Bergman projection,but also...The precise L^(p) norm of a class of Forelli-Rudin type operators on the Siegel upper half space is given in this paper.The main result not only implies the upper L^(p) norm estimate of the Bergman projection,but also implies the precise L^(p) norm of the Berezin transform.展开更多
针对核范数正则约束使得矩阵低秩性不足、奇异值分解对大规模数据计算代价大、传统优化算法需人为调试最优参数的问题,提出一种基于Schatten-p范数和近端交替线性最小化算法的深度可学习子空间聚类算法。首先,通过Schatten-p范数作为低...针对核范数正则约束使得矩阵低秩性不足、奇异值分解对大规模数据计算代价大、传统优化算法需人为调试最优参数的问题,提出一种基于Schatten-p范数和近端交替线性最小化算法的深度可学习子空间聚类算法。首先,通过Schatten-p范数作为低秩正则项,使得子空间聚类系数矩阵更好地满足低秩结构;其次,利用Schatten-p范数的矩阵分解格式,避免了SVD计算代价大的不足;最后,针对传统优化算法须人为调整参数的问题,根据激活函数和稀疏正则项的对应关系,建立深度学习网络框架,通过数据自适应学习得到最优参数集。在MNIST手写数字、Amsterdam Library of Object Images和ORL人脸三个数据集上进行聚类的数值实验,结果表明:提出的子空间聚类算法相比于谱聚类、低秩子空间聚类和稀疏子空间聚类算法有更好的聚类性能。展开更多
For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the s...For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the sense of L^p norm.When the systems are disturbed by bounded external noises,robustness of the PDα-type algorithm is firstly analyzed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral.Then,convergence of the algorithm is discussed for the systems without any external noise.The results demonstrate that,under some given conditions,both convergence and robustness can be guaranteed during the entire time interval.Simulations support the correctness of the theory.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.
For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and th...For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.展开更多
The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of no...The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.展开更多
To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the infl...To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the influence of noise and extract the edge information of the image.The new edge extractor is used as the adaptive function and the weighting function of the l_(p) norm variational model to control the noise reduction ability of the model,and a new model 1 is obtained.Considering that the new model 1 only uses the gradient mode as the image feature operator,which is insufficient to express the image texture information,a new level set curvature gradient variational model 2 combined with the edge extractor is proposed.The new model 2 uses the idea of minimum curvature of the level set of clear images to obtain noise reduction images.By coupling new model 1 and new model 2 to smooth the noise and protect more textures,a new Non-local level set denoising model(NLSDM)for image noise reduction is obtained.The experimental results show that compared with the noise reduction model,the new model has significantly improved the peak signal-to-noise ratio and structural similarity,and the effect of noise reduction and edge preservation is better.展开更多
基金supported by the National Natural Science Foundation of China(11801172,11771139,12071130)supported by the Natural Science Foundation of Zhejiang Province(LQ21A010002)supported by the Natural Science Foundation of Zhejiang Province(LY20A010007).
文摘The precise L^(p) norm of a class of Forelli-Rudin type operators on the Siegel upper half space is given in this paper.The main result not only implies the upper L^(p) norm estimate of the Bergman projection,but also implies the precise L^(p) norm of the Berezin transform.
文摘针对核范数正则约束使得矩阵低秩性不足、奇异值分解对大规模数据计算代价大、传统优化算法需人为调试最优参数的问题,提出一种基于Schatten-p范数和近端交替线性最小化算法的深度可学习子空间聚类算法。首先,通过Schatten-p范数作为低秩正则项,使得子空间聚类系数矩阵更好地满足低秩结构;其次,利用Schatten-p范数的矩阵分解格式,避免了SVD计算代价大的不足;最后,针对传统优化算法须人为调整参数的问题,根据激活函数和稀疏正则项的对应关系,建立深度学习网络框架,通过数据自适应学习得到最优参数集。在MNIST手写数字、Amsterdam Library of Object Images和ORL人脸三个数据集上进行聚类的数值实验,结果表明:提出的子空间聚类算法相比于谱聚类、低秩子空间聚类和稀疏子空间聚类算法有更好的聚类性能。
基金supported by the National Natural Science Foundation of China(61201323)the Special Fund Project for Promoting Scientific and Technological Innovation in Xuzhou City(KC18013)the Cultivation Project of Xuzhou Institute of Technology(XKY2017112)
文摘For a class of fractional-order linear continuous-time switched systems specified by an arbitrary switching sequence,the performance of PDα-type fractional-order iterative learning control(FOILC)is discussed in the sense of L^p norm.When the systems are disturbed by bounded external noises,robustness of the PDα-type algorithm is firstly analyzed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral.Then,convergence of the algorithm is discussed for the systems without any external noise.The results demonstrate that,under some given conditions,both convergence and robustness can be guaranteed during the entire time interval.Simulations support the correctness of the theory.
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.
基金The NSF (Q1107107) of Jiangsu Educational Commission.
文摘For a convex set-valued map between p-normed (0 < p < 1) spaces, we give a criterion for its inverse to be locally Lipschitz of order p. From this we obtain the Robinson-Ursescu Theorem in p-normed spaces and the open mapping and closed graph theorems for closed convex set-valued maps.
基金supported by the Natural Science Foundation of Yibin University(No.2009Z03)
文摘The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.
基金funded by National Nature Science Foundation of China,grant number 61302188.
文摘To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the influence of noise and extract the edge information of the image.The new edge extractor is used as the adaptive function and the weighting function of the l_(p) norm variational model to control the noise reduction ability of the model,and a new model 1 is obtained.Considering that the new model 1 only uses the gradient mode as the image feature operator,which is insufficient to express the image texture information,a new level set curvature gradient variational model 2 combined with the edge extractor is proposed.The new model 2 uses the idea of minimum curvature of the level set of clear images to obtain noise reduction images.By coupling new model 1 and new model 2 to smooth the noise and protect more textures,a new Non-local level set denoising model(NLSDM)for image noise reduction is obtained.The experimental results show that compared with the noise reduction model,the new model has significantly improved the peak signal-to-noise ratio and structural similarity,and the effect of noise reduction and edge preservation is better.
