关于二阶幂型扩张映射的不动点定理

研究完备度量空间中的二阶幂型扩张映射、改进、推广和统一了文献[2－3]中的主要结果。     

关于膨胀同胚的一个注记

利用符号法则证明了如下结论：设X是Peano连续统，f是X上的膨胀同胚，膨胀常数为c．如果A是X的闭子集，X—A有有限个连通分支，且每个分支的直径小于c，那么X=^ ∞∪n=-∞f^n(A)．作为应用给出了单位闭区间上不存在膨胀同胚的一个新的证明．     

The Nonexistence of Expansive Z^d Actions on Graphs

It is well known that if X is an arc or a circle, then there is no expansive homeomorphism on X. In this paper we prove that there is no expansive Z^d action on X, which answers the two questions raised by us before, In 1979, Mané proved that there is no expansive homeomorphism on infinite dimensional spaces. Contrary to this result, we construct an expansive Z^2 action on an infinite dimensional space. We also construct an expansive Z^2 action on a zero dimensional space but no element in Z^2 is expansive.     

THE APOTP AND NON-WANDERING HOMEOMORPHISM

We introduce the concept of asymptotic pseudo orbit tracing property (APOTP) and obtain a new condition by the APOTP for which a homeomor-phism is a non-wandering homeomorphism.     

具有跟踪性可扩流的吸引子的稳定性

本文证明了紧致流形上具有跟踪性可扩流的链回复吸引子均为若干基本集的并而且关于Hausdorff度量稳定。     

拓扑群在连续统上的膨胀作用

本文把一个同胚的膨胀作用推广到拓扑群的情形,并研究了有限生成离散群 的膨胀作用,得到了如下结果:Z×Z不能膨胀地作用在单位闭区间I上,而自由积 Z★Z可以膨胀地作用在I上.     

Quantum cloning machines and their implementation in physical systems

We review the basic theory of approximate quantum cloning for discrete variables and some schemes for implementing quantum cloning machines. Several types of approximate quantum clones and their expansive quantum clones are intro- duced. As for the implementation of quantum cloning machines, we review some design methods and recent experimental results.     

膨胀土分类的灰色变权聚类法

将灰色变权聚类法应用于膨胀土的分类.结果表明,用灰色变权聚类法对膨胀土的胀缩等级进行分类,其结果更合理、更客观.     

Some relations between Hausdorff-dimensions and entropies

Some relations between the Hausdorff-dimensions and the entropies for expansive homeomorphisms on compact metric spaces are obtained. Project partially supported by the National Natural Science Foundation of China.     

全局极值定理的一个拓广

本文在有限维Ｈｉｌｂｅｒｔ空间上改进了全局极值定理并给出了改进后定理的某些应用．