In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation...In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory.展开更多
In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which def...In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which define the nonlinear system represent a remarkable mathematical instrument for the control of affine systems. We determine the optimal control which corresponds to the nilpotent operator of the first order. In particular, we obtain the control that minimizes the energy of the given nonlinear system. Applications of this control to bilinear systems with first order nilpotent operator are considered.展开更多
The main purpose of this note is to show that there is a one-to-one corre- spondence between minimal non-nilpotent （resp., locally nilpotent） saturated fusion sys- tems and finite p J-core-free p-constrained minimal...The main purpose of this note is to show that there is a one-to-one corre- spondence between minimal non-nilpotent （resp., locally nilpotent） saturated fusion sys- tems and finite p J-core-free p-constrained minimal non-nilpotent （resp., locally p-nilpotent） groups.展开更多
Hodge和Parshall在文[On the representation theory of Lie triple systems,Trans AmerMath Soc,2002,354(11):4359-4391]中指出,若(T,(-)^([p]))是有限维限制李三系且(-)^([p]):T→T是单射,则T是可交换的.但是,这个结论是不正确的.作...Hodge和Parshall在文[On the representation theory of Lie triple systems,Trans AmerMath Soc,2002,354(11):4359-4391]中指出,若(T,(-)^([p]))是有限维限制李三系且(-)^([p]):T→T是单射,则T是可交换的.但是,这个结论是不正确的.作者证明了它在代数闭域上是成立的,同时,给出了限制李三系可交换的一些条件,并刻画了限制李三系的p-映射和半单元的一些性质.展开更多
文摘In this paper we deal with a cubic near-Hamiltonian system whose unperturbed system is a simple cubic Hamiltonian system having a nilpotent center. We prove that the system can have 5 limit cycles by using bifurcation theory.
文摘In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which define the nonlinear system represent a remarkable mathematical instrument for the control of affine systems. We determine the optimal control which corresponds to the nilpotent operator of the first order. In particular, we obtain the control that minimizes the energy of the given nonlinear system. Applications of this control to bilinear systems with first order nilpotent operator are considered.
基金Supported by the National 973 Project （452101650122） and the National Natural Science Foundation of China （11201194, 11301393）. In addition, the second author was supported by the doctoral foundation of Jiangxi Normal University.
文摘The main purpose of this note is to show that there is a one-to-one corre- spondence between minimal non-nilpotent （resp., locally nilpotent） saturated fusion sys- tems and finite p J-core-free p-constrained minimal non-nilpotent （resp., locally p-nilpotent） groups.
文摘Hodge和Parshall在文[On the representation theory of Lie triple systems,Trans AmerMath Soc,2002,354(11):4359-4391]中指出,若(T,(-)^([p]))是有限维限制李三系且(-)^([p]):T→T是单射,则T是可交换的.但是,这个结论是不正确的.作者证明了它在代数闭域上是成立的,同时,给出了限制李三系可交换的一些条件,并刻画了限制李三系的p-映射和半单元的一些性质.
