Generalized Smash Products

In this paper．we study the ring #(D．B)and obtain two very interesting results. First we prove in Theorem 3 that the category of rational left BU-modules is equivalent to both the category of #-rational left modules and the category of all(B．D)-Hopf modules BM^D．Cai and Chen have proved this result in the case B=D=A．Secondly they have proved that if A has a nonzero left integral then A#A^*rat is a dense subring of Endk(A)．We prove that #(A,A) is a dense subring of Endk(Q),where Q is a certain subspace of #(A．A)under the condition that the antipode is bijective(see Theorem18).This condition is weaker than the condition that A has a nonzero integral.It is well known the antipode is bijective in case A has a nonzero integral．Furthermore if A has nonzero left integral,Q can be chosen to be A(see Corollary 19)and #(A,A)is both left and right primitive.Thus A#A^*rat #(A,A)-Endk(A)．Moreover we prove that the left singular ideal of the ring #(A,A)is zero．A corollary of this is a criterion for A with nonzero left integral to be finite-dimensional,namely the ring #(A,A)has a finite uniform dimension．     

关于拟赋值环的一个刻画

Let R be a commutative ring without nil-factor. In this paper, we discuss the problem of quasi-valuation ring presented in the reference “Wang Shianghaw, On quasi-valuation ring, Northeast People‘s Univ. Natur. Sci. J., (1)(1957), 27-40”,when the quotient field of R is an algebraic number field or an algebraic function field, and we obtain a characterization of quasi-valuation rings.     

Classification of Hardy Submodules and Characteristic Space Theory（A Brief and Selective Survey）

This paper is a brief and selective survey on classification of Hardy Submodules over the polydisk. The survey reports some progress in classification of Hardy submodules.     

On ＂Problems on von Neumann Algebras by R. Kadison, 1967＂

A brief summary of the development on Kadison‘s famous problems (1967) is given. A new set of problems in von Neumann algebras is listed.     

An型扭双指标代数

给出了F (Δ)-有限的A_n型偏序集的扭双指标代数的完全分类     

动力学椭圆代数Aq,p,(^π)(∧gln)的Drinfeld流

从推广的Yang-Baxter关系"RLL=LLR*"出发,利用高秩高斯分解,得到了动力学椭圆代数Aq,p,^π(∧gln)及其对应的Drinfeld流.其中R,R*是A(1)n-1面模型对应的谱参数有一关于代数中心平移的动力学R矩阵.     

改进的同步迭代算法在光声血管成像中的应用

光声成像结合了光学成像和声学成像的优点，是一种高分辨率，高对比度的无损伤医学成像技术.一种改进的同步迭代算法应用于光声图像重建.仿真和模拟结果表明，与传统的代数迭代算法相比，在90°，135°，180°的有限场光声成像中，此算法对测量误差的校正和迭代次数的收敛上具有较大的优势，图像重建的速度和成像质量都有了明显的提高.实验中，一种圆形扫描结构的光声成像装置，用于180°的有限场扫描，利用改进的同步迭代算法，重建出了高对比度和高分辨率（60μm）的鸡胚胎光声血管图像.实验证明，这种算法的应用，大幅度减少了数据采集时间，为光声成像技术运用于实时监测血流灌注和肿瘤光动力治疗的血管损伤效应提供了潜在的应用价值. 关键词： 光声成像 有限角度 代数迭代算法 光声血管成像     

可积开边界条件下的q形变玻色子模型

利用代数Bethe Ansatz方法在可积开边界条件下推广了q形变玻色子模型，得到可积开边界条件下此模型的哈密顿量及其本征方程.该工作可为在更小尺度下研究具有相互作用的玻色子系统提供有效的理论基础. 关键词： 代数Bethe Ansatz q形变玻色子模型')" href="#">q形变玻色子模型 开边界 可积系统     

物理解题中的数形结合思想

在数学领域中，数形结合是一种非常重要的思想方法，通过它，可使复杂的几何问题数字化，亦可使抽象的代数问题几何化，从而拓宽了解决数学问题的基本方法．在物理学研究中，有时要通过一定的数学手段总结出物理规律，有时又要在已建立的物理规律基础上利用数学工具进行分析归纳，从而得出新的结论．因此，物理学与数学存在很大的联系．     

Discrete Integrable Couplings of the Volterra Lattice

A practicable way to construct discrete integrable couplings is proposed by making use of two types of semi-direct sum Lie algebras. As its application, two kinds of discrete integrable couplings of the Volterra lattice are worked out.