Unital辛代数的分解

考查了辛代数的分解,在此过程中充分运用了辛代数、李三系、李代数的关系,建立了三者之间的根基关系,并由此证明了unital辛代数的分解.     

An algebraic approach to physical fields

According to the algebraic approach to spacetime, a thoroughgoing dynamicism, physical fields exist without an underlying manifold. This view is usually implemented by postulating an algebraic structure (e.g., commutative ring) of scalar-valued functions, which can be interpreted as representing a scalar field, and deriving other structures from it. In this work, we point out that this leads to the unjustified primacy of an undetermined scalar field. Instead, we propose to consider algebraic structures in which all (and only) physical fields are primitive. We explain how the theory of natural operations in differential geometry—the modern formalism behind classifying diffeomorphism-invariant constructions—can be used to obtain concrete implementations of this idea for any given collection of fields. For concrete examples, we illustrate how our approach applies to a number of particular physical fields, including electrodynamics coupled to a Weyl spinor.     

Is there a stability problem for Bayesian noncommutative probabilities?

A stability condition for Bayesian statistical inference, which Redei [(1992). When can non-commutative statistical inference be Bayesian? International Studies in the Philosophy of Science, 6, 129–132; (1998). Quantum logic in algebraic approach. Dordrecht: Kluwer Academic Publishers] formulated as a rationality constraint holding in classical probability theory, is shown to fail in quantum mechanics. That allegedly challenges a Bayesian interpretation of quantum probabilities. In this paper we demonstrate that Redei's argument does not apply to quantum mechanics. Moreover, we provide a solution to the problem of Bayesian noncommutative statistical inference arising from the violation of stability condition in general probability spaces.     

单纯可适变换Lie群无穷小生成元的代数性质

给出了作用在C^∞流形肘上的单纯可迁变换Lie群G的无穷小生成元的有关概念，得到了与之相关的若干重要代数性质．     

双原子分子光谱的量子代数Uqp（u1,1）模型

本文提出了描述双原子分子振动谱的量子代数Ｕｑｐ（ｕ１，１）模型，通过对Ｈ２的Ｘ＾１∑＾＋Ｒ态的经验数据进行拟合处理验证了模型的适用性。     

复Poisson李群

文章将复李群上的典型复结构扩展到任意的k重向量场上,又结合复李群和Poisson李群的特点,定义了复Possion李群的概念,得到了一些有趣的结论.     

基于分数阶模型的非保守Hamilton系统的Lie对称性研究

为了进一步揭示动力学系统的对称性和守恒量之间的内在联系,基于分数阶模型提出并研究非保守Hamilton系统的Lie对称性与守恒量。首先,依据非保守系统的Hamilton原理导出了基于分数阶模型的Hamilton正则方程。其次,在群的无限小变换下,给出了Lie对称性的确定方程,建立了分数阶模型下非保守Hamilton系统的Lie对称性的定义,并给出Lie对称性导致一类新型分数阶Noether守恒量的条件及其形式。最后,给出一个算例说明结果的应用。     

$\tilde{A}_n$型丛倾斜代数的Cohen-Macaulay Auslander代数的导出等价分类

主要研究了$\tilde{A}_n$型丛倾斜代数的Cohen-Macaulay Auslander代数的导出等价分类问题, 利用Avella-Alamimos和Geiss给出的算法证明了$\tilde{A}_n$型丛倾斜代数的Cohen-Macaulay Auslander代数导出等价的充分必要条件是相应的丛倾斜代数导出等价.     

扭曲重模代数的量子化

以Hopf代数为基础,通过双代数上的一些定义及性质,并结合σ-扭曲理论以及扭重模代数的概念,给出了扭重模代数的一些基本性质,并给出了几个具体例子.然后主要构造了扭重模代数的量子化,并在其上讨论了Smash积的一些性质.最后介绍了Long双代数,Long斜双代数和扭重模代数之间的关系,通过前面的铺垫,得出了他们等价的相关条件.     

T—导子的性质

引进T－导子的概念，刻划了一般代数和算子代数上的T－导子的特征性质。