不动泛系定理的新研究:泛浑沌和泛怪引子

关于浑沌、引子、怪引子等的研究是非线性分析中的重要课题.文[1]在泛系方法论的框架下,讨论了这些问题,提出了泛浑沌、泛引子和泛怪引子的概念,这些概念去掉了诸如连续性、紧性等条件,突出反映了一集合上的二元关系的性质.已有的研究结果指出,泛浑沌、泛引子和泛怪引子分别对应于某个特定的泛系算子作用下的不动子集.本文继续文[1、2]的工作,探讨了存在这类泛系不动子集的条件以及它们的构造和相互间的联系.     

Pansystems Whole-Part Relation Analysis and Triple Covering Systems

Let A_n={1,2,…,n} and let ％={B_1,B_2,…,B_r} where B_1、B_2,…, B_r are subsets of A_n each of size m. is said to cover all the triples (i, j, k), 1≤i2/3, then V(m, n) is a function of the fraction m/n only and the values of V(m, n) are determined for all m, n with m/n≥2/3. The value of V(m, n) for m/n<2/3 is also discussed.     

泛系局整关系分析与三元复盖系统

我们于1985年8月至1986年2月,在我校试验站进行了卷帘式、有窗式和无窗式(不装空调)三种猪舍的对比试验和观测,结果表明: 1.正北京地区,用上述三种猪舍饲养30～90kg的猪,各舍试猪日增重和饲料利用率,在夏秋冬三季均无显著差异; 2.卷帘舍夏季通风好,有利于防暑,但冬季保温较差;无窗舍夏季通风差,较闷热,冬季保温虽好,但湿度较大;有窗舍夏季防暑和冬季保温均较好; 3.无窗舍除大跨度空调猪舍外,小跨度自然通风光照猪舍不易采用;卷帘舍在北京及其以南地区可用于小跨度育肥及成年猪舍;有窗舍可用于饲养各种猪     

具有大的奇围长的符号图的圆环染色（英文）

图G的一个圆环r-染色(r≥2)是将G的每个顶点v对应到一个周长为r的圆上的点的一个映射f,使得对于G中任意的边xy,f(x)和f(y)在圆上的距离不小于1.G的圆环色数χ_c(G)是G存在圆环r-染色的最小实数r.符号图的圆环染色和图的圆环染色基本相同,不同的是对于负边xy,我们要求f(x)和f(y)的对点在圆上的距离不小于1.符号图(G,σ)的圆环色数是使得(G,σ)在圆环r-染色的最小实数r.本文证明:对于任意正整数k和实数ε> 0,存在整数g使得对于任意树宽至多为k的符号图(G,σ),如果(G,-σ)的负围长至少是g,那么(G,σ)的圆环染色数至多是2+ε.     

An approach on fixed pansystems theorems: Panchaos and strange panattractor

The investigations about chaos, attractor and strange attractor are main subjects in nonlinear analysis. Under the framework of pansystems methodology, reference [1] discussed these problems and introduced the concepts of panchaos, panattractor and strange panattractor. These concepts omitted the condition of continuity, compactness, etc. and put stress on the properties of binary relations on a set. A certain obtained result indicates that panchaos, panattractor and strange panattractor correspond respectively to fixed subsets of certain pansystems operators. This paper continues the investigation of [1,2], discusses the existence of these pansystems fixed subsets, their construction and interrelations.The authors appreciate Associate Research Fellow Qin Guo-guang for his discussion on related problems.     

AN APPROACH ON FIXED PANSYSTEMS THEOREMS:PANCHAOS AND STRANGE PANATTRACTOR

The investigations about chaos,attractor and strange attractor are main subjects innon-linear analysis.Under the framework of pansystems methodology,reference[1]discussed these problems and introduced the concepts of panchaos.panattractor andstrange panattractor.These concepts omitted the condition of continuity,compactness.etc.and put stress on the properties of binary relations on a set.A certain obtained resultindicates that panchaos.panattractor and strange panattractor correspond respectively tofixed subsets of certain pansy(?)tems operators.This paper continues the investigation of[1,2],discusses the existence of these pansystems fixed subsets,their construction andinterrelations.