In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dyna...In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.展开更多
Based on active control theory, anti-synchronization between two different hyperchaotic systems is investigated. The sufficient conditions for achieving anti-synchronization of two different hyperchaotic systems are d...Based on active control theory, anti-synchronization between two different hyperchaotic systems is investigated. The sufficient conditions for achieving anti-synchronization of two different hyperchaotic systems are derived. Moreover, numerical simulations are presented for hyperehaotic Lorenz-Chen system, hyperchaotic Lorenz-Lu system, and hyperchaotic Chen Lu system to verify the effectiveness and feasibility of the proposed anti-synchronization scheme.展开更多
In this paper,we proved that the infinitesimal generator of a strongly continuous cosine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is ...In this paper,we proved that the infinitesimal generator of a strongly continuous cosine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is a bounded linear operator from X into a bigger space Xθ(not X),then the corresponding 2-order abstract Cauchy problem is uniformly well-posed.展开更多
Validity of adiabatic assumption is discussed within the constrained Hartree-Fock theory for self-conjugate nucleus ~(72)Kr.It is shown that the adiabatic assumption does not provide a correct description for the natu...Validity of adiabatic assumption is discussed within the constrained Hartree-Fock theory for self-conjugate nucleus ~(72)Kr.It is shown that the adiabatic assumption does not provide a correct description for the nature of nucleus when a configuration change is involved.The excited Hartree-Fock states and the continuously-connected constrained Hartree-Fock states are given for the first time by applying the configuration dictated constrained Hartree-Fock theory with Gogny force.The importance of self-consistency between the mean-field and the single particle wave functions is emphasized even when a small number of nucleons are involved in the configuration change.展开更多
The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the...The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p).展开更多
文摘In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.
基金National Natural Science Foundation of China under Grant No.10575082the Natural Science Foundation of Gansu Province under Grant No.3ZS061-A25-014+1 种基金the Natural Science Foundation of NWNU under Grant No.NWNU-KJCXGC-03-17the Scientific Research Foundation of NWNU under Grant No.NWNU-QN-07-41
文摘Based on active control theory, anti-synchronization between two different hyperchaotic systems is investigated. The sufficient conditions for achieving anti-synchronization of two different hyperchaotic systems are derived. Moreover, numerical simulations are presented for hyperehaotic Lorenz-Chen system, hyperchaotic Lorenz-Lu system, and hyperchaotic Chen Lu system to verify the effectiveness and feasibility of the proposed anti-synchronization scheme.
文摘In this paper,we proved that the infinitesimal generator of a strongly continuous cosine operator function is preserved under the time-dependent perturbation in the sun-reflexive case,where the perturbed operator is a bounded linear operator from X into a bigger space Xθ(not X),then the corresponding 2-order abstract Cauchy problem is uniformly well-posed.
基金The project supported in part by the Japanese Society for the Promotion of Science (JSPS) and National Natural Science Foundation of China as the bilateral program between Japan and China.One of the authors (E.G.Zhao) acknowledges the support by National
文摘Validity of adiabatic assumption is discussed within the constrained Hartree-Fock theory for self-conjugate nucleus ~(72)Kr.It is shown that the adiabatic assumption does not provide a correct description for the nature of nucleus when a configuration change is involved.The excited Hartree-Fock states and the continuously-connected constrained Hartree-Fock states are given for the first time by applying the configuration dictated constrained Hartree-Fock theory with Gogny force.The importance of self-consistency between the mean-field and the single particle wave functions is emphasized even when a small number of nucleons are involved in the configuration change.
基金supported by the National Natural Science Foundation of China(No.10871141)
文摘The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p).
