We obtain the global weighted estimates for Jacobian J（x,f） and its subdeterminants, as well as the components of K-quasiconformal mappings in L^p （μ）-averaging domains. To develop these estimates, both local and...We obtain the global weighted estimates for Jacobian J（x,f） and its subdeterminants, as well as the components of K-quasiconformal mappings in L^p （μ）-averaging domains. To develop these estimates, both local and global weighted Ponincaré inequalities for differential forms are established.展开更多
A clustering algorithm based on Sparse Projection (SP), called Sparse Projection Clus- tering (SPC), is proposed in this letter. The basic idea is applying SP to project the observed data onto a high-dimensional spars...A clustering algorithm based on Sparse Projection (SP), called Sparse Projection Clus- tering (SPC), is proposed in this letter. The basic idea is applying SP to project the observed data onto a high-dimensional sparse space, which is a nonlinear mapping with an explicit form and the K-means clustering algorithm can be therefore used to explore the inherent data patterns in the new space. The proposed algorithm is applied to cluster a complete artificial dataset and an incomplete real dataset. In comparison with the kernel K-means clustering algorithm, the proposed algorithm is more efficient.展开更多
The dynamics anMysis of recurrent neural networks （RNNs） is a first and necessary step for any practical applications of them. In the present paper, the easily verified theorem is found to ascertain the asymptotical...The dynamics anMysis of recurrent neural networks （RNNs） is a first and necessary step for any practical applications of them. In the present paper, the easily verified theorem is found to ascertain the asymptotical stability for generic RNN model with projection mapping under the critical condition that a discriminant matrix defined by the networks is semi-positive definite. The results given here not only improve deeply upon the existing relevant critical as well as non-critical dynamics conclusions in literature, but also can be used in the practical application of RNNs directly.展开更多
We discuss Ky Fan's theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operat...We discuss Ky Fan's theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors.展开更多
文摘We obtain the global weighted estimates for Jacobian J（x,f） and its subdeterminants, as well as the components of K-quasiconformal mappings in L^p （μ）-averaging domains. To develop these estimates, both local and global weighted Ponincaré inequalities for differential forms are established.
基金Supported by the National Natural Science Foundation of China (No.60872123)the Joint Fund of the National Natural Science Foundation and the Guangdong Provin-cial Natural Science Foundation (No.U0835001)
文摘A clustering algorithm based on Sparse Projection (SP), called Sparse Projection Clus- tering (SPC), is proposed in this letter. The basic idea is applying SP to project the observed data onto a high-dimensional sparse space, which is a nonlinear mapping with an explicit form and the K-means clustering algorithm can be therefore used to explore the inherent data patterns in the new space. The proposed algorithm is applied to cluster a complete artificial dataset and an incomplete real dataset. In comparison with the kernel K-means clustering algorithm, the proposed algorithm is more efficient.
基金supported by the National Nature Science Foundation of China under Grant Nos.11101327,11471006,and 11171270the National Basic Research Program of China(973 Program)under Grant No.2013C13329406the Fundamental Research Funds for the Central Universities under Grant Nos.xjj20100087 and 2011jdhz30
文摘The dynamics anMysis of recurrent neural networks （RNNs） is a first and necessary step for any practical applications of them. In the present paper, the easily verified theorem is found to ascertain the asymptotical stability for generic RNN model with projection mapping under the critical condition that a discriminant matrix defined by the networks is semi-positive definite. The results given here not only improve deeply upon the existing relevant critical as well as non-critical dynamics conclusions in literature, but also can be used in the practical application of RNNs directly.
基金supported by National Natural Science Foundation of China(Grant No.11371221)the Specialized Research Foundation for the Doctoral Program of Higher Education of China(Grant No.20123705110001)the Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province
文摘We discuss Ky Fan's theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors.
