Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-alge...Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）.展开更多
Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights f...Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.展开更多
This paper studies the state/output synchronization of switched Boolean networks （SBNs） with impulsive effects via the algebraic state space representation （ASSR） approach. First, an algebraic form is established ...This paper studies the state/output synchronization of switched Boolean networks （SBNs） with impulsive effects via the algebraic state space representation （ASSR） approach. First, an algebraic form is established for SBNs with impulsive effects via ASSR. Second, based on the algebraic form, some necessary and sufficient conditions are presented for the state/output synchronization of SBNs with impulsive effects under arbitrary switching signals. Third, two special kinds of switching signals, that is, free switching signal and feedback switching signal, are considered for the state synchroniza-tion of SBNs with impulsive effects. Finally, two illustrative examples are worked out to show the effectiveness of the obtained results.展开更多
Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven...Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.展开更多
This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,i...This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,it is proved that if N, M are non-trivial then RN RM=R if and only if N, M are continuous.展开更多
文摘Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）.
基金National Natural Science Foundation of China (Grant No. 11071200)Natural Science Foundation of Fujian Province of China (Grant No. 2010J01013)
文摘Multilinear commutators and iterated commutators of multilinear fractional integral operators with BMO functions are studied. Both strong type and weak type endpoint weighted estimates involving the multiple weights for such operators are established and the weak type endpoint results are sharp in some senses. In particular, we extend the results given by Cruz-Uribe and Fiorenza in 2003 and 2007 to the multilinear setting. Moreover, we modify the weak type of endpoint weighted estimates and improve the strong type of weighted norm inequalities on the multilinear commutators given by Chen and Xue in 2010 and 2011.
基金The research was supported by the National Natural Science Foundation of China under grant 61503225, the Natural Science Fund for Distinguished Young Scholars of Shandong Province under grant JQ201613, and the Natural Science Foundation of Shandong Province under grant ZR2015FQ003.
文摘This paper studies the state/output synchronization of switched Boolean networks （SBNs） with impulsive effects via the algebraic state space representation （ASSR） approach. First, an algebraic form is established for SBNs with impulsive effects via ASSR. Second, based on the algebraic form, some necessary and sufficient conditions are presented for the state/output synchronization of SBNs with impulsive effects under arbitrary switching signals. Third, two special kinds of switching signals, that is, free switching signal and feedback switching signal, are considered for the state synchroniza-tion of SBNs with impulsive effects. Finally, two illustrative examples are worked out to show the effectiveness of the obtained results.
基金supported by National Natural Science Foundation of China(Grant Nos.11071147,11431010 and 11371278)Natural Science Foundation of Shandong Province(Grant Nos.ZR2010AM003and ZR2013AL013)+1 种基金Shanghai Municipal Science and Technology Commission(Grant No.12XD1405000)Fundamental Research Funds for the Central Universities
文摘Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.
文摘This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,it is proved that if N, M are non-trivial then RN RM=R if and only if N, M are continuous.
