混沌与SS混沌不等价

构造了是混沌但不是ＳＳ混沌的极小子转移,从而证明对于限制在测度中心上的紧系统而言,混沌一般地不等价于 ＳＳ混沌．     

几乎周期性与SS混沌集

引进正则移位不变集的概念,证明了有正则移位不变集的紧致系统在几乎周期点集中存在SS混沌集,特别地,具有正拓扑熵的区间映射在几乎周期点集中存在SS混沌集.     

几乎周期性与SS混沌集

引进正则移位不变集的概念,证明了有正则移位不变集的紧致系统在几乎周期点集中存在SS混沌集,特别地,具有正拓扑熵的区间映射在几乎周期点集中存在SS混沌集.     

拓扑熵为零且Schweizer-Smítal混沌的极小子转移

构造了具有零拓扑熵且为Schweizer-Smital混沌的极小子转移,从而证明对一般紧系统而言,正拓扑熵与发生在测度中心上的Schweizer-Smital混沌不等价.     

正拓扑熵与紊动不等价——一类极小子转移

本文构造一类具有零拓扑熵的紊动极小子转移,从而证明了正拓扑熵与发生在测度中心上的紊动不等价。     

关于一个混沌但非S-S混沌的子转移的一点注记

In this paper we prove that the minimal chaotic but not S-S chaotic subshifts are also uinquely ergodic and have zero topological entropy.     

∑上的非弱几乎周期的回复点集和SS混沌集

该文对单边符号空间上的转移自映射进行了讨论,证明了在非弱几乎周期的回复点集上存在不可数的SS混沌集.     

Chen混沌系统的非线性全局同步控制

研究了Chen提出的一个新的混沌系统的混沌同步问题,利用非线性控制方法设计了三种混沌同步控制器,并用李雅普诺夫方法证明了在混沌控制器作用下,驱动、响应混沌系统可以实现全局同步.数值仿真结果表明,所设计的三种混沌控制器都能有效的实现混沌同步,并且具有很强的鲁棒性.     

Logistic混沌系统分形特性研究

对Logistic序列进行研究,利用Matlab数值模拟,通过计算不同初值、不同参数对应的混沌序列的计盒维数,得出结论:只要在数据充分的情况下,Logistic系统的分形维数基本由参数λ决定,与系统初值无关;同时计盒维数并非像熵一样随Logistic系统的参数λ增大而增大.     

Involution Semigroups Are Not Globally Determined

The purpose of this paper is to present an example of nonisomorphic involution semigroups which are globally isomorphic, i.e. which have isomorphic power algebras (elements of which are the nonempty subsets of the original algebras). As an immediate consequence, we obtain that (involution) semirings are not globally determined. September 7, 1999     

There Are Not Too Many Magic Configurations

A finite planar point set P is called a magic configuration if there is an assignment of positive weights to the points of P such that, for every line l determined by P, the sum of the weights of all points of P on l equals 1. We prove a conjecture of Murty from 1971 and show that if a set of n points P is a magic configuration, then P is in general position, or P contains n−1 collinear points, or P is a special configuration of 7 points. The research by Rom Pinchasi was supported by a Grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development.     

Aubin—Nitsche Estimates Are Equivalent to Compact Embeddings

In this short note we show that having an Aubin–Nitsche type estimate (a superconvergence estimate in a weaker norm for a convergent Galerkin method) is equivalent to having compact injection of the space into its completion with the weaker norm.     

关于线性方程组同解的条件

讨论线性方程组同解的条件,得到了两个线性方程组同解的充分必要条件.     

Odd Crossing Number and Crossing Number Are Not the Same

The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtain the odd crossing number. We show that there is a graph for which these two concepts differ, answering a well-known open question on crossing numbers. To derive the result we study drawings of maps (graphs with rotation systems).     

For Rewriting Systems the Topological Finiteness Conditions FDT and FHT are Not Equivalent

A finite rewriting system is presented that does not satisfythe homotopical finiteness condition FDT, although it satisfiesthe homological finiteness condition FHT. This system is obtainedfrom a group G and a finitely generated subgroup H of G througha monoid extension that is almost an HNN extension. The FHTproperty of the extension is closely related to the FP₂ propertyfor the subgroup H, while the FDT property of the extensionis related to the finite presentability of H. The example systemseparating the FDT property from the FHT property is then obtainedby applying this construction to an example group.