For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or multi-clustering.In this paper,we study a nonsymmetric multi-par...For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or multi-clustering.In this paper,we study a nonsymmetric multi-particle system with a constant and local cut-off weight.A distributed communication delay is also introduced into both the velocity adjoint term and the cut-off weight.As a new observation,we show that the desired multi-particle system undergoes both flocking and clustering behaviors when the eigenvalue 1 of the adjacency matrix is semi-simple.In this case,the adjacency matrix may lose the connectedness.In particular,the number of clusters is discussed by using subspace analysis.In terms of results,for both the non-critical and general neighbourhood situations,some criteria of flocking and clustering emergence with an exponential convergent rate are established by the standard matrix analysis for when the delay is free.As a distributed delay is involved,the corresponding criteria are also found,and these small time lags do not change the emergent properties qualitatively,but alter the final value in a nonlinear way.Consequently,some previous works[14]are extended.展开更多
In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and ...In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.展开更多
By using Artin-Wedderburn Theorem and the decomp- osition of central edepotent, several results about normality on closed subsets in standard table algebras are generalized to complex semi-simple algebras and the proo...By using Artin-Wedderburn Theorem and the decomp- osition of central edepotent, several results about normality on closed subsets in standard table algebras are generalized to complex semi-simple algebras and the proofs are easier than the original ones.展开更多
Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A ...Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A can be generated by two elements respectively.展开更多
In this paper, we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms. Using this extrapolation formula, we obtain some asymptotic expansions of the Galerkin fini...In this paper, we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms. Using this extrapolation formula, we obtain some asymptotic expansions of the Galerkin finite element method for semi-simple eigenvalue problems of Fredholm integral equations of the second kind and improve the accuracy of the numerical approximations of the corresponding eigenvalues. Some numerical experiments ave carried out to demonstrate the effectiveness of our new method and to confirm our theoretical results.展开更多
基金supported by the National Natural Science Foundation of China(11671011).
文摘For a collective system,the connectedness of the adjacency matrix plays a key role in making the system achieve its emergent feature,such as flocking or multi-clustering.In this paper,we study a nonsymmetric multi-particle system with a constant and local cut-off weight.A distributed communication delay is also introduced into both the velocity adjoint term and the cut-off weight.As a new observation,we show that the desired multi-particle system undergoes both flocking and clustering behaviors when the eigenvalue 1 of the adjacency matrix is semi-simple.In this case,the adjacency matrix may lose the connectedness.In particular,the number of clusters is discussed by using subspace analysis.In terms of results,for both the non-critical and general neighbourhood situations,some criteria of flocking and clustering emergence with an exponential convergent rate are established by the standard matrix analysis for when the delay is free.As a distributed delay is involved,the corresponding criteria are also found,and these small time lags do not change the emergent properties qualitatively,but alter the final value in a nonlinear way.Consequently,some previous works[14]are extended.
文摘In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.
基金Supported by the National Natural Science Foundation of China(11571129)Educational Commission of Hubei Province(D20132804)
文摘By using Artin-Wedderburn Theorem and the decomp- osition of central edepotent, several results about normality on closed subsets in standard table algebras are generalized to complex semi-simple algebras and the proofs are easier than the original ones.
文摘Suppose that F is a field of characteristic zero and (ⅰ) D is a finite-dimensional central division algabra over F; (ⅱ) A is a finite-dimensional semi-simple algabra over F. It is proved that as F-algebras, D and A can be generated by two elements respectively.
基金the Governor's Special Foundation of Guizhou Province for Outstanding Scientific Education Personnel (No.[2005]155),China
文摘In this paper, we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms. Using this extrapolation formula, we obtain some asymptotic expansions of the Galerkin finite element method for semi-simple eigenvalue problems of Fredholm integral equations of the second kind and improve the accuracy of the numerical approximations of the corresponding eigenvalues. Some numerical experiments ave carried out to demonstrate the effectiveness of our new method and to confirm our theoretical results.
