Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m ...Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.展开更多
In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piec...In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piecewise algebraic sets, and turn theisomorphism and classifying problem of piecewise algebraic sets into the isonorphismand classifying problem of commutative algebras.展开更多
In this paper, the author proves the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras. This is used to investigate isomorphisms between quasi-Banach algebras.
In this paper, epidemic spread with the staged progression model on homogeneous and heterogeneous networks is studied. First, the epidemic threshold of the simple staged progression model is given. Then the staged pro...In this paper, epidemic spread with the staged progression model on homogeneous and heterogeneous networks is studied. First, the epidemic threshold of the simple staged progression model is given. Then the staged progression model with birth and death is also considered. The case where infectivity is a nonlinear function of the nodes＇ degree is discussed, too. Finally, the analytical results are verified by numerical simulations.展开更多
文摘Both the global exponential stability and the existence of periodic solutions for a class of recurrent neural networks with continuously distributed delays （RNNs） are studied. By employing the inequality α∏k=1^m bk^qk≤1/r ∑qkbk^r＋1/rα^r（α≥0,bk≥0,qk〉0,with ∑k=1^m qk=r-1,r≥1, constructing suitable Lyapunov r k=l k=l functions and applying the homeomorphism theory, a family of simple and new sufficient conditions are given ensuring the global exponential stability and the existence of periodic solutions of RNNs. The results extend and improve the results of earlier publications.
文摘In this paper , we define the piecewise algebraic sets by using multivariatespline functions and discuss their irreducibility and isomorphism problem. We presenttwo equivalent conditions for the irreducibility of piecewise algebraic sets, and turn theisomorphism and classifying problem of piecewise algebraic sets into the isonorphismand classifying problem of commutative algebras.
基金the Korea Research Foundation (No. KRF-2005-041-C00027).
文摘In this paper, the author proves the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras. This is used to investigate isomorphisms between quasi-Banach algebras.
基金supported by Hong Kong Polytechnic University Grant via a Council Competitive Earmarked Research Grant(CERG) under Grant No.PolyU 5279//08Ethe National Natural Science Foundation of China under Grant Nos.11005001 and 11072136+1 种基金the 211 Project of Anhui University under Grant No.2009QN003A,KJTD002Bsupported by Shanghai Leading Academic Discipline Project under Grant No.S30104
文摘In this paper, epidemic spread with the staged progression model on homogeneous and heterogeneous networks is studied. First, the epidemic threshold of the simple staged progression model is given. Then the staged progression model with birth and death is also considered. The case where infectivity is a nonlinear function of the nodes＇ degree is discussed, too. Finally, the analytical results are verified by numerical simulations.
