关于形式三角矩阵环

本文研究形式三角矩阵环R的若干新性质,讨论R-模的伪投射性,给出了形式三角矩阵环R是V-环或半V-环的充要条件.同时,给出了R是PS-环的条件.     

On the structure and representations of non-balanced quantum doubles

For a field k and two finite groups G and X, when G acts on X from the right by group automorphisms, there is a Hopf algebra structure on k-space (kX ^op )* ? kG (see Theorem 2.1), called a non-balanced quantum double and denoted by D _X (G). In this paper, some Hopf algebra properties of D _X (G) are given, the representation types of D _X (G) viewed as a k-algebra are discussed, the algebra structure and module category over D _X (G) are studied. Since the Hopf algebra structure of non-balanced quantum double D _X (G) generalizes the usual quantum double D(G) for a finite group G, all results about D _X (G) in this paper can also be used to describe D(G) as a special case and the universal R-matrix of D _X (G) provides more solutions of Yang-Baxter equation.     

Soliton Solutions,B/icklund Transformations and Lax Pair for a （3 ＋ 1）-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Fluids

Under investigation in this paper is a （3 q- 1）-dimensional variable-coefficient Kadomtsev-Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell polynomials, symbolic computation and auxiliary independent variable, the bilinear forms, soliton solutions, Backlund transformations and Lax pair are obtained. Variable coefficients of the equation can affect the solitonic structure, when they are specially chosen, while curved and linear solitons are illustrated. Elastic collisions between/among two and three solitons are discussed, through which the solitons keep their original shapes invariant except for some phase shifts.     

关于极小子流形全纯量曲率的一个空隙定理

本文证明了欧氏空间RN中的n-维(n＞2)完备极小子流形,若其全纯量曲率小于(π/4@√6)n,则必是n-维平面.此结论改进了文[2,6]中的结果.     

关于一道级数问题解法的思考

部分教材在求f(z)=cotz的Laurant级数展开式时存在疏漏,而借助形式多项式除法和待定系数法可正确求解该问题.     

在物理实验课中开展研究性教学的认识与实践

研究性教学是指教师以课程内容和学生的常识积累为基础,引导学生创造性地运用知识和能力,综合运用研究方法,自主地提出、研究和解决问题,在研讨中达到学习、创造及培养能力等目的的教学形式．从而锻炼学生掌握研究方法,培养研究精神,激励研究的热情．     

Milloux不等式精简形式的推广及应用

主要讨论了Milloux不等式的精简形式的推广问题,借助代数体函数的第二基本定理,得到了关于代数体函数的精简形式的Milloux不等式的一般形式,推广了Milloux不等式的精简形式的结论,并由此得到了关于代数体函数及其导数的涉及拟Borel例外值的性质,推广了亚纯函数的相关性质.     

Sasakian空间形式中具有平行平均曲率向量的C-全实子流形

本文讨论了Sasakian空间形式中具有平行平均曲率向量的C-全实子流形,得到了一个Simons型公式并且改进了S.Yamaguchi等的一个结果.     

透雾连续变焦光学系统的设计

针对透雾连续变焦光学系统的特点,介绍了一种大口径、长焦距、透雾连续变焦光学系统的结构形式选择、系统中各组分相对孔径及初始结构的选取、像差平衡的方法.运用该方法设计的应用于某光电探测设备可见光通道的透雾连续变焦光学系统具有像质好、结构合理、加工装调的工艺性好等优点.     

Low-Dimensional Forest-Like and Desert-Like Fractal Patterns Formed in a DDAN Molecular System

Two kinds of forest-like and desert-like patterns are formed by thermal evaporation of 4-dicyanovinyl-N, Ndimethylamino-1-naphthalene （DDAN） onto SiO2 substrates. Based on thermal kinetics of the molecules on the substrate the transformation between the forest and desert patterns is due to two factors. The first one is the diffusion length, which is related to the deposition rate, the diffusion potential energy barrier and the substrate temperature. The second one is the strong interaction between the two polarity chemical groups of the molecules, which is beneficial to the formation of branches. Totally different patterns are also found on mica substrates, and are attributed to the anisotropic diffusion and the stronger interaction between DDAN molecules and the mica surface.