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线性随机泊松系统基于Padé近似的随机泊松积分子

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中国科学院大学学报（中英文） 2021年第2期38卷 160-170页

作者：王鹏钧王丽瑾中国科学院大学数学科学学院北京100049

利用Padé近似,得到线性随机泊松系统的一类随机泊松积分子。证明数值格式的均方收敛阶,及其对泊松结构和Casimir函数的保持。数值实验验证了数值格式的均方收敛阶及保结构特性。

关键词：随机泊松积分子均方收敛阶 Padé近似泊松结构 Casimir函数

纤维丛Poisson结构及其在力学上的应用

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新疆工学院学报 1996年第1期17卷 6-9页

作者：王宝勤陈春丽新疆师范大学数学系乌鲁木齐830053

本文利用Schouten－Nijenhuis括号在切丛上引进一种Poisson结构，运用这个结构定义了Poisson括号，再用Poisson括号表达了分析力学中一系列内容。

关键词：纤维丛分析力学泊松结构

Co-Poisson structures on polynomial Hopf algebras

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Science China Mathematics 2018年第5期61卷 813-830页

作者： Qi Lou Quanshui Wu School of Mathematical Sciences Fudan University

The Hopf dual H~? of any Poisson Hopf algebra H is proved to be a co-Poisson Hopf algebra provided H is noetherian. Without noetherian assumption, unlike it is claimed in literature, the statement does not hold. It is proved that there is no nontrivial Poisson Hopf structure on the universal enveloping algebra of a non-abelian Lie algebra. So the polynomial Hopf algebra, viewed as the universal enveloping algebra of a finite-dimensional abelian Lie algebra, is considered. The Poisson Hopf structures on polynomial Hopf algebras are exactly linear Poisson structures. The co-Poisson structures on polynomial Hopf algebras are characterized.Some correspondences between co-Poisson and Poisson structures are also established.

关键词：泊松结构 Hopf 代数学多项式合作有限维证明通用

Realization of Poisson enveloping algebra

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Frontiers of Mathematics in China 2018年第4期13卷 999-1011页

作者： Can ZHU Yaxiu WANG College of Science University of Shanghai for Science and Technology Shanghai 200093 China

为泊松代数学，泊松模块的范畴等价于它包围的泊松的模块范畴代数学，在此包围的泊松代数学是联合的。在这篇文章，为多项式代数学 S 上的泊松结构，我们首先构造泊松代数学 R，然后证明包围的泊松 S 的代数学对 R 的使量子化的通用包... 详细信息

为泊松代数学，泊松模块的范畴等价于它包围的泊松的模块范畴代数学，在此包围的泊松代数学是联合的。在这篇文章，为多项式代数学 S 上的泊松结构，我们首先构造泊松代数学 R，然后证明包围的泊松 S 的代数学对 R 的使量子化的通用包围代数学的专门化同形，因此，是 R 的变丑量子化。

关键词：现代数学泊松结构范畴等价量子化多项式模块

Some Evolution Hierarchies Derived from Self-dual Yang-Mills Equations

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Communications in Theoretical Physics 2011年第11期56卷 856-872页

作者：张玉峰韩耀宗 College of Science China University of Mining and Technology Department of Mathematics City University of Hong Kong

We develop in this paper a new method to construct two explicit Lie algebras E and F.By using aloop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations,we obtain an expanding integrablemodel of the Giachetti-Johnson (GJ)hierarchy whose Hamiltonian structure can also be derived by using the traceidentity.This provides a much simplier construction method in comparing with the tedious variational identity approach.Furthermore,the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra g_N.As an application,we apply the loop algebra E of the Lie algebra E to obtain a kind of expanding integrable model ofthe Kaup-Newell (KN)hierarchy which,consisting of two arbitrary parameters a and f3,can be reduced to two nonlinearevolution equations.In addition,we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model ofthe BT hierarchy whose Hamiltonian structure is the same as using the trace identity.Finally,we deduce five integrablesystems in R3 based on the self-dual Yang-Mills equations,which include Poisson structures,irregular lines,and thereduced equations.

关键词：演化方程 Hamilton结构扩展可积模型 loop代数演变层次结构线性代数泊松结构