关于微分同胚的一个充分必要条件

确定两个流形是否C^r-微分同胚是微分流形研究中的重要课题,本文定义了反层的概念,给出了反层范畴,由此找到两个微分流形,C^r-微分同胚的特征刻画,于是给出了一种较以往更优的判定法．     

关于高等代数题解的五种方法

介绍处理高等代数习题的标准形式化方法、公理化方法、模型转换方法、形式统一性方法和形态联想方法,并给出实例加以说明.     

Geometric Property （T）

This paper discusses“geometric property （T）”. This is a property of metric spaces introduced in earlier works of the authors for its applications to K-theory. Geometric property （T） is a strong form of “expansion property”, in particular, for a sequence （Xn） of bounded degree finite graphs, it is strictly stronger than （Xn） being an expander in the sense that the Cheeger constants h（Xn） are bounded below. In this paper, the authors show that geometric property （T） is a coarse invariant, i.e., it depends only on the large-scale geometry of a metric space X. The authors also discuss how geometric property （T） interacts with amenability, property （T） for groups, and coarse geometric notions of a-T-menability. In particular, it is shown that property （T） for a residually finite group is characterised by geometric property （T） for its finite quotients.     

Graphic Sequences with an A-Connected Realization

A non-increasing sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) of non-negative integers is said to be graphic if it is the degree sequence of a simple graph G on n vertices. Let A be an (additive) abelian group. An extremal problem for a graphic sequence to have an A-connected realization is considered as follows: determine the smallest even integer \({\sigma (A, n)}\) such that each graphic sequence \({\pi = (d_1, d_2, \ldots, d_n)}\) with d _n ≥ 2 and \({\sigma (\pi) = d_1 + d_2 + \cdots +d_n \ge \sigma (A, n)}\) has an A-connected realization. In this paper, we determine \({\sigma (A, n)}\) for |A| ≥ 5 and n ≥ 3.     

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS I

In this paper,authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically selfsimilar measure.     

Phase conjugator with two coherent beams in a BaTiO3:Ce crystal

A phase conjugator which includes two coherent beams that are incident upon one of a-faces of a BaTiO3:Ce crystal without internal reflection is performed experimentally. Based on the four-wave mixing, the mechanism of this conjugator is investigated numerically. In comparison with the corresponding self-pumped phase conjugator, the phase-conjugate behavior of this conjugator is established much more quickly, its phase conjugate reflectivity is greater in some cases and the intensity threshold is lower by over two orders of magnitude. The configuration of this conjugator is easy to perform because the output response exists over a wide range of angular and lateral positions of the two incident beams on the crystal.     

变时滞关联大系统的镇定控制

基于Liapunov理论,针对关联矩阵的不同分解,建立了变时滞线性关联大系统分散镇定的充分条件。同时,还给出了一种局部无记忆状态反馈控制律的设计方法,所考虑的时滞皆为变时滞。     

系统Hα中F(S)的一个分划及一种升级算法

研究王国俊提出的系统Hα中F(S)的分划问题,利用可达广义重言式的概念给出F(S)的一个关于同余的分划,并给出了各类间的一种升级算法,证明在系统Hα中,重言式不可能由对非重言式进行有限次升级算法得到。     

亚正定矩阵的Bergstrom型不等式

首先证明亚正定矩阵的一个偏序,利用该偏序得到了亚正定矩阵的一些Bergstrom型不等式,推广了近期关于亚正定矩阵行列式不等式的一些结果.     

圆柱贮箱液体非线性晃动的多维模态分析方法

将Faltinsen等提出的多维模态理论应用到求解圆柱贮箱液体非线性晃动问题中．根据Narimanov-Moiseiev的三阶渐近假设关系,通过选取主导模态以及确定它们的阶次关系,将一般形式的无穷维模态系统降为五维渐近模态系统,即描述自由液面波高的广义坐标之间相互耦合的二阶非线性常微分方程组．通过对这个模态系统的数值积分,得到了与以前的理论分析和实验结果相吻合的非线性现象．研究结果表明,多维模态方法是用来求解液体非线性晃动动力学的一个很好的工具．在我们的下一步工作中,将继续发展这种方法,用来研究更为复杂的晃动问题．