非Chetaev型非完整可控力学系统的Noether-形式不变性

基于函数对时间的全导数采用沿系统的运动轨线方式, 研究非Chetaev型非完整可控力学系统的Noether-形式不变性. 给出非Chetaev型非完整可控力学系统的Noether-形式不变性的定义和判据. 由Noether-形式不变性同时得到了Noether守恒量和新型守恒量. 并举例说明结果的应用. 关键词： 非Chetaev型非完整系统 可控力学系统 Noether-形式不变性 守恒量     

Conformal invariance and Hojman conservedquantities of first order Lagrange systems

In this paper the conformal invariance by infinitesimal transformations of first order Lagrange systems is discussed in detail. The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given. Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.     

Lagrange系统的共形不变性与Hojman守恒量

研究了一般完整Lagrange系统在无限小变换下的共形不变性,推导出共形不变性的确定方程,并且找到在特殊无限小变换下的共形不变性并且是Lie对称性的共形因子,接下来导出Lagrange系统的运动微分方程共形不变时的Hojman守恒量,并给出应用算例. 关键词： Lagrange系统 共形不变性 Hojman守恒量 确定方程     

Conformal invariance and conserved quantity of Hamilton systems

This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.     

非完整系统的形式不变性与Hojman守恒量

研究非完整力学系统的形式不变性导致的非Noether守恒量——Hojman守恒量. 在时间不变的特殊无限小变换下，给出非完整系统形式不变性的确定方程、约束限制方程和附加限制方程，提出并定义弱（强）形式不变性的概念. 研究特殊形式不变性导致特殊Lie对称性的条件，由系统的特殊形式不变性，得到相应完整系统的Hojman守恒量以及非完整系统的弱Hojman守恒量和强Hojman守恒量. 给出两个经典例子说明结果的应用. 关键词： 分析力学 非完整系统 形式不变性 非Noether守恒量 Hojman守恒量     

奇异非线性Sturm-Liouville边值问题正解的全局结构

该文利用拓扑方法讨论一类非线性Sturm-Liouville边值问题\[\left\{\begin{array}{lcl}-u'=\lambda f(x, u),\\\alpha_0 u(0)+\beta_0 u'(0)=0,\ \ \alpha_1 u(1)+\beta_1 u'(1)=0;\end{array}\right.\]作者在非线性项不奇异和奇异两种情况下研究了上述问题正解解集的全局结构,在非线性项$f$不满足条件f(x,u)≥0(u≥0)时 获得了正解的存在性.     

Structure Identification of Nonlinearly Coupled Complex Networks with Non-Delayed and Delayed Coupling

Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identifying the topology of general nonlinearly-coupled complex network models that are either non-delayed or delayed coupled. Simulation results are also presented to illustrate the effectiveness of the method.     

THE CAUCHY PROBLEM OF THE HARTREE EQUATION

In this paper, we systematically study the wellposedness, illposedness of the Hartree equation, and obtain the sharp local wellposedness, the global existence in Hs, s≥1 and the small scattering result in Hs for 2 〈γ〈 n and s ≥ 2/γ - 1. In addition, we study the nonexistence of nontrivial asymptotically free solutions of the Hartree equation.     

高阶线性常微分方程组在弱拓扑下的连续性

引进了一类Fredholm积分算子并证明其在弱拓扑下有连续性. 根据这个基本观点,对于高阶线性常微分方程组的解和由解定义出的一系列重要的量证明了很强的连续性结果, 即在最弱的L¹空间的弱拓扑下是连续的. 这些量包括分析学中的特征值和动力系统中的Lyapunov指数和旋转数等. 所得结果将导致一系列非常有意义的非常规类型的变分问题.     

模糊粗糙近似算子的拓扑性质

考虑论域上一二元关系所决定的模糊粗糙近似算子的拓扑性质,证明了任一自反二元关系可以决定一模糊拓扑.并且,当二元关系自反对称时,该模糊拓扑中的元是开集当且仅当它是闭集;当二元关系自反传递时,该模糊拓扑的闭包与内部算子恰为模糊粗糙上、下近似算子.