共查询到20条相似文献,搜索用时 62 毫秒
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本文证明对于满足强分离条件的自相似集E,存在一个闭凸集达到它的最大密度.即存在一个闭凸集V■E0(|V|0),使得sup{μ(U)/|U|s:U■E0}=μ(V)/|V|s,其中U为闭集,E0表示自相似集E的闭凸壳,μ表示E上的唯一自相似概率测度.作为应用,我们给出命题"满足强分离开集条件的自相似集具有最优几乎处处覆盖"的一个新证明. 相似文献
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Haudorff测度与等径不等式 总被引:1,自引:0,他引:1
对于:Hausdorff维数为s>0的满足开集条件的自相似集E(?)Rn(n>1),我们引入等径不等式Hs|E(X)≤|X|s,以及使该不等式等号成立而直径大于0的极限集U(?)Rn.这里,Hs|E(·)是限制到集合E上的s维Hausdorff测度,而|X|指集合X在欧氏度量下的直径.当s=n时,n维球是唯一的极限集;当s∈(1,n)时,除去一些反面例子以外,我们对上述等径不等式的极限集的基本性质所知甚少.可以看出,这些不等式与Hs(E)的准确值的计算有密切联系.作为特例,我们将考虑Sierpinski垫片,指出计算这一典型自相似集的In2/In3维Hausdorff测度准确值的困难何在.由此可以大致推想,为什么除去平凡情形以外,至今还没有一个具体的满足开集条件而维数大于1的自相似集的:Hausdorff测度准确值被计算出来. 相似文献
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设E是Hausdorff测度正有限的广义齐次自相似集,本文证明了s维Hausdorff测度是E上唯一的非扩张概率测度. 相似文献
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设E是Hausdorff测度正有限的广义齐次自相似集,本文证明了s维Hausdorff测度是E上唯一的非扩张概率测度. 相似文献
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关于自相似集的Hausdorff测度的一个判据及其应用 总被引:6,自引:1,他引:5
讨论了满足开集条件的自相似集。对于此类分形,用自然覆盖类估计它的Hausdorff测度只能得到一个上限,因而如何判断某一个上限就是它的Hausdorff测度的准确值是一个重要的问题。本文给出了一个判据。作为应用,统一处理了一类自相似集,得到了平面上的一个Cantor集-Cantor尘的Hausdorff测度的准确值,并重新计算了直线上的Cantor集以及一个Sierpinski地毯的Hausdorff测度。 相似文献
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本文给出了直线上Marion集的Hausdorff测度的一个有效计算方法,并通过几个实例得出如何利用此方法计算出直线上分形的Hausdorff测度的精确值. 相似文献
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闭模糊集构成凸模糊集的充要条件 总被引:4,自引:1,他引:3
本文通过引入弱拟凸模糊集的概念,针对欧几里空间上的闭模糊集,给出了它构成凸模糊集的一个充要条件,从而丰富了凸模糊集的理论及其应用。 相似文献
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对于整数k,θ≥3,β≥1,称k个元素集合S为(k;β,θ)0自由集,如果S的最小元素为0且它没有互不相同的元素aij∈S(1≤j≤θ使得∑j=1θ-1aij=βaiθ成立,S的最大元素记为max(S).反平均数定义为λ(k;β,θ)=min{max(S):S是(k;β,θ)0自由集}.给出反平均数λ(k;β,θ)的2个界. 相似文献
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We prove the following theorems:
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- It is consistent with ZFC that there exists a - set which is not perfectly meager in the transitive sense.
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- Every set which is perfectly meager in the transitive sense has the property.
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- The product of two sets perfectly meager in the transitive sense has also that property.
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Khodr Shamseddine 《Journal of Mathematical Analysis and Applications》2010,368(1):281-292
Two topologies on the Levi-Civita field R will be studied: the valuation topology induced by the order on the field, and another weaker topology induced by a family of seminorms, which we will call weak topology. We show that each of the two topologies results from a metric on R, that the valuation topology is not a vector topology while the weak topology is, and that R is complete in the valuation topology while it is not in the weak topology. Then the properties of both topologies will be studied in details; in particular, we give simple characterizations of open, closed, and compact sets in both topologies. 相似文献
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For a given graph G, if the vertices of G can be partitioned into an independent set and an acyclic set, then we call G a near-bipartite graph. This paper studies the recognition of near-bipartite graphs. We give simple characterizations for those near-bipartite graphs having maximum degree at most 3 and those having diameter 2. We also show that the recognition of near-bipartite graphs is NP-complete even for graphs where the maximum degree is 4 or where the diameter is 4. 相似文献
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Computing the minimal covering set 总被引:1,自引:0,他引:1
We present the first polynomial-time algorithm for computing the minimal covering set of a (weak) tournament. The algorithm draws upon a linear programming formulation of a subset of the minimal covering set known as the essential set. On the other hand, we show that no efficient algorithm exists for two variants of the minimal covering set–the minimal upward covering set and the minimal downward covering set–unless P equals NP. Finally, we observe a strong relationship between von Neumann–Morgenstern stable sets and upward covering on the one hand, and the Banks set and downward covering on the other. 相似文献
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On the Simple Connectivity of Fatou Components 总被引:1,自引:0,他引:1
We shall show that for certain holomorphic maps, all Fatou components are simply connected. We also discuss the relation
between wandering domains and singularities for certain meromorphic maps.
Received May 8, 2002, Accepted May 24, 2002 相似文献