Liouville theorem

Liouville theorem的基本解释

-

刘维定理

与Liouville theorem相关的网络例句 [注：此内容来源于网络，仅供参考]

Chapter 5 and 6 are concentrated on the fundamental problem how to con-struct finite-dimensional and infinite-dimensional Liouville integrable Hamiltonsystem.Starting from two isospectral problems,Tu's scheme is applied to gen-erate the corresponding CKdV hierarohy and coupled Burgers hievachy,andthey are shown to be Liouville integrable Hamilton systems.Two spectral prob-lems,which contain three and four potentials respectively,are also studied byTu's scheme.Two new Liouville integrable Hamilton hierarchy are estab-lished.A new general approach using Lenard's gradient sequence is presentedto obtain Lax integrable hierarchy and their zero curvature representation,andsome examples are given.The nonlinearization procedure is applied to theeigenvalue problem of coupled Burgerrs hierarchy.It is shown that underBargmann constraint,the spatial part of the Lax pairs is nonlimearized to be afinite-dimensional Liouville completeiy integrable Hamilton system.

第五、六章研究如何从一个谱问题出发构造可积发展方程族及其零曲率表示、Hamilton结构和判断Liouville可积性：通过对二类具有2个位势的等谱问题直接研究，利用屠格式生成了耦合KdV族和耦合Burgers族，并证明它们均为Liouville可积的广义Hamilton方程族；而通过分别具有3个和4个位势的等谱问题，遵循屠格式构造了二族新的Liouville可积的广义Hamilton方程族；给出了利用Lenard梯度递推序列产生发展方程族及其零曲率表示的一种方法，作为应用，讨论了CKdV族，BPT族及耦合Burgers族的产生及其零曲率表示；应用非线性化技巧，证明了在Bargmann约束下，耦合Burgers族的Lax组可被线性化为Liou-ville完全可积的Hamilton系统。

In the first part of this paper, we give some basic concepts of regular Sturm-Liouville problems and some Sturm-Liouville problems with eigenparameter in the boundary conditions and the definition and properties of the Krein space. Using the Krein space, we describe a class of Sturm-Liouville problems with eigenparameter in two boundary conditions and prove that it can generate a self-adjoint operator in Krein space with only point spectrum.

第一部分我们介绍了一些基本概念如正则Sturm-Liouville问题、边界条件含参数的问题、Krein空间等，并利用Krein空间的定义和性质描述了一类参数边界条件的Sturm-Liouville问题，证明它可构造一Krein空间上的自伴算子，并且谱全为点谱。

This paper weakened the Liouville s theorem conditions,and gives the Liouville theorem of a promotion.

弱化了刘维尔定理的条件，给出了刘维尔定理的一个推广。

与Liouville theorem相关的网络解释 [注：此内容来源于网络，仅供参考]

liouville theorem：刘维尔定理

liouville number 刘维尔数 | liouville theorem 刘维尔定理 | lipschitz condition 李普希茨条件

liouville's theorem：刘维定理

linkage连杆机构 | liouville's theorem刘维定理 | liquefaction液化

liouville's theorem：刘维尔定理

Linear instability,线性的不稳定性,113 | Liouville's theorem,刘维尔定理,95-96 | Multiplayer fictitious play,多参与人虚拟行动,37-39

liouville's theorem：吕维耳定理

Liouville equation 吕维耳方程式 | Liouville's theorem 吕维耳定理 | Lockhart and Martinelli correlation 罗(克哈特)?马(蒂乃利)二氏相关式