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1.
关于一致模糊横贯拟阵的研究   总被引:1,自引:0,他引:1  
"模糊横贯拟阵'的反例"~([1])一文指出不是所有模糊集族的模糊部分横贯都能构成一个模糊拟阵的模糊独立集族。本文找到一类满足"一致性"条件的模糊集族,其模糊部分横贯全体一定能组成一个模糊拟阵的模糊独立集族(称这类模糊拟阵为一致模糊横贯拟阵);然后详细讨论了一致模糊横贯拟阵的基本序列、导出拟阵序列和模糊基等许多性质;还讨论了一致模糊横贯拟阵与准模糊图拟阵的关系,与正规模糊拟阵的关系;最后证明了一致模糊横贯拟阵是一类准模糊图拟阵。  相似文献   

2.
关于模糊横贯拟阵表示的初步研究   总被引:1,自引:0,他引:1  
本文首先讨论了模糊子集族的全体模糊部分横贯能够形成模糊横贯拟阵的条件,得到两个充要条件。第一个充要条件使用截短模糊子集族来进行描述;第二个充要条件是通过部分横贯的指标集单射兼容这个概念来描述。然后研究了模糊横贯拟阵的表示形式,得到了三个结论。一是任何模糊横贯拟阵都有"精简表示",而且构造了从一个表示寻找精简表示的方法;二是模糊横贯拟阵的表示的模糊子集个数不小于导出拟阵的最大秩;三是一致模糊横贯拟阵的任何表示都包含"最小表示",也给出了求这个"最小表示"的方法。  相似文献   

3.
本文用Furstenberg族研究了弱混合系统的攀援集.证明了:对于每一个有不动点的离散弱混合系统(X,f)而言,存在一个不变的稠密的(τF_(inf),F_(inf))-攀援集;对于每一个弱混合的有任意周期的周期点的周期吸附系统(X,f)而言,存在一个不变的稠密的(τF_(inf),τF_(inf))-攀援集,其中τF_(inf)为非负整数集的全体thick集组成的集族,F_(inf)为非负整数集的全体无限子集组成的集族。  相似文献   

4.
模糊横贯拟阵的再研究   总被引:2,自引:0,他引:2  
本文首先推广模糊横贯拟阵概念,定义了更为广泛的模糊横贯拟阵;然后,通过模糊拟阵导出集合函数概念,证明了所有模糊横贯拟阵都是闭模糊拟阵;利用这个闭性,研究了模糊横贯拟阵的基本序列和导出拟阵序列特性;通过这两个特性和"截短模糊集族"概念,得到了模糊横贯拟阵的独立模糊集和模糊基的等价刻画;借助建立"子集族串"概念,找到了模糊集族的全部模糊部分横贯能够组成模糊横贯拟阵的一个等价刻画。  相似文献   

5.
文献[1]、文献[2]、文献[3]、文献[4]和文献[5]推广横贯概念定义了模糊横贯,并认为一个模糊集族的全体模糊部分横贯构成一个模糊拟阵[6](称为"模糊横贯拟阵")。本文举出一个反例,说明某些模糊集族的全体模糊部分横贯不能构成模糊拟阵;然后,详细分析了出现这种情况的原因,指出文献[1]、文献[2]、文献[3]、文献[4]和文献[5]得出这个结论的证明方法是错误的。  相似文献   

6.
杨存基 《数学学报》2010,53(1):187-198
Stallard曾经用一族特殊的整函数说明了:超越整函数的Julia集的Hausdorff维数可以无限接近1.本文证明了该函数族的随机迭代的Julia集的Hausdorff维数也可无限接近于1.另一方面,对任意自然数M及任意实数d∈(1,2),本文给出了M个元素的整函数族其随机迭代的Julia集的Hausdorff维数等于d.  相似文献   

7.
本文给出了一种方法用于构造k-紧优双环网络无限族(k≥1),并用此方法构造出了4族3-紧优无限族,3族新的4-紧比无限族,3族5-紧优无限族及2族6-紧优无限族.  相似文献   

8.
对论域U上一般知识引入了知识交派生概念,研究了知识交派生集族的性质,证明了在论域U有限且给定知识对并关闭时,知识交派生集族形成一个拓扑。举例说明了论域U无穷且知识对任意并关闭时,其有限交派生集族不必形成一个拓扑。我们还给出了有穷论域上知识交派生的有效算法,证明了这种算法确实给出了交派生集族。  相似文献   

9.
设G为简单图,若G的点子集S与图中的每个团都有非空的交,则称S是图G的一个团横贯集,这里G的团是指图中的极大完全子图且至少包含两个点.图G的最小团横贯集所含点的数目称为G的团横贯数,记作τC(G).如果G的每条边至少包含在一个t阶完全子图中且τC(G)≤|V(G)|/t,则称G具有〈t〉一性质.提出了平面图分离4-团的概念.首先证明了最大度不超过5的平面图具有〈t〉-性质.其次,对任意平面图G,若它不含分离4-团且每条边都包含在一个4-团之中,得到了它的横贯数的上界和独立数的可达下界.  相似文献   

10.
双环网络是计算机互连网络和通讯系统的一类重要拓扑结构.1993年,李乔等人提出一个系统的构造方法,构造出69类0紧优和33类1紧优双环网络的无限族,并提出研究下述问题:求k(k>1)紧优双环网络的无限族.2003年,徐俊明等人给出一个4紧优双环网络的无限族.本文首先证明从每一个具体的0紧优双环网络出发,都可以构造若干0紧优双环网络无限族;结合同余方程组理论和数论中的素数理论,给出若干求一般k(k≥0)紧优双环网络无限族(包括非单位步长双环网络无限族)的方法.  相似文献   

11.
Abstract. We show that if every three members of a finite disjoint family of unit disks in the plane have a line transversal, then there is a line transversal to all except at most 12 disks in the family. We derive an analogous result for translates of a general compact convex set, with the constant equal to 47.  相似文献   

12.
   Abstract. We show that if every three members of a finite disjoint family of unit disks in the plane have a line transversal, then there is a line transversal to all except at most 12 disks in the family. We derive an analogous result for translates of a general compact convex set, with the constant equal to 47.  相似文献   

13.
A colorful theorem on transversal lines to plane convex sets   总被引:1,自引:0,他引:1  
We prove a colorful version of Hadwiger’s transversal line theorem: if a family of colored and numbered convex sets in the plane has the property that any three differently colored members have a transversal line that meet the sets consistently with the numbering, then there exists a color such that all the convex sets of that color have a transversal line. All authors are partially supported by CONACYT research grant 5040017.  相似文献   

14.
We prove the following: If a finite family of unit (radius) disks has the property that the distance between every pair of centres is greater than 4/3 and every subset of at most five disks has a common transversal line, then all disks have a common transversal line.  相似文献   

15.
若在中心附近的闭轨线都具有相同的周期,则此中心称为等时中心. 时间可逆多项式系统的等时中心问题是一类公开问题. 为了构造性地解决这一难题,讨论一类范围更广的时间可逆解析动力系统, 给出相应横截交换系统的递推公式,此公式可以用于等时中心条件的推导. 在递推公式的基础上,以吴特征集方法为工具,给出一类时间可逆三次系统具有横截交换系统的充要条件.  相似文献   

16.
Rough sets are efficient for data pre-processing during data mining. However, some important problems such as attribute reduction in rough sets are NP-hard and the algorithms required to solve them are mostly greedy ones. The transversal matroid is an important part of matroid theory, which provides well-established platforms for greedy algorithms. In this study, we investigate transversal matroids using the rough set approach. First, we construct a covering induced by a family of subsets and we propose the approximation operators and upper approximation number based on this covering. We present a sufficient condition under which a subset is a partial transversal, and also a necessary condition. Furthermore, we characterize the transversal matroid with the covering-based approximation operator and construct some types of circuits. Second, we explore the relationships between closure operators in transversal matroids and upper approximation operators based on the covering induced by a family of subsets. Finally, we study two types of axiomatic characterizations of the covering approximation operators based on the set theory and matroid theory, respectively. These results provide more methods for investigating the combination of transversal matroids with rough sets.  相似文献   

17.
Let U be a family of sets having a finite number of infinte members. A proof is given for a theorem of Brualdi and Scrimger regarding the existence of a transversal of U, and this theorem is used to obtain necessary and sufficient conditions for U to have a partial transversal of prescribed finite defect. The dual of the Brualdi-Scrimger result is discussed.  相似文献   

18.
There are two conditions which are known to be necessary for the existence of a transversal in any family of sets, but both are sufficient only if the family is countable. This paper proves that these conditions are always equivalent to each other. The families which are compatible with these conditions are characterised, in the sense that each of their subfamilies possesses a transversal if it satisfies the conditions. Using this, a conjecture of Podewski and Steffens is proved.  相似文献   

19.
A family of hypergraphs is exhibited which have the property that the minimum cardinality of a transversal is equal to the maximum cardinality of a matching. A result concerning domination and independence in trees which generalises a recent result of Meir and Moon is deduced.  相似文献   

20.
A geometric permutation induced by a transversal line of a finite family ℱ of disjoint convex sets in ℝd is the order in which the transversal meets the members of the family. We prove that for each natural k, each family of k permutations is realizable (as a family of geometric permutations of some ℱ) in ℝd for d ≥ 2k – 1, but there is a family of k permutations which is non-realizable in ℝd for d ≤ 2k – 2.  相似文献   

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