共查询到20条相似文献,搜索用时 26 毫秒
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M. A. Seoud 《International Journal of Mathematical Education in Science & Technology》2013,44(7):871-881
This note discusses some set equations, using set matrices, i.e. matrices whose entries are sets. 相似文献
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d-小波集 总被引:1,自引:0,他引:1
李卫华 《应用泛函分析学报》2004,6(1):80-82
引入 d-小波集的定义 ,得到了一个 Lebesgue可测子集 E是 d-小波集的六个等价条件 . 相似文献
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基于新集对分析的粗糙集模型 总被引:5,自引:0,他引:5
首先,在这篇文章里两个集合里的元素被分为三个相对独立的部分来研究。接下来,一种定量信息——元素数目被用来描述这两个集合间的关系,然后提出了基于元素数目的新集对分析思想;另一方面,引用含糊集中真隶属度和假隶属度的概念,提出了一种模糊集对联系度。然后,这两种集对分析思想分别被用到粗糙集理论中作为粗糙集模型的一种推广,此外还讨论了一些相关的性质。 相似文献
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A set function is a function whose domain is the power set of a set, which is assumed to be finite in this paper. We treat a possibly nonadditive set function, i.e., a set function which does not satisfy necessarily additivity, ?(A) + ?(B) = ?(A ∪ B) forA ∩ B = ∅, as an element of the linear space on the power set. Then some of the famous classes of set functions are polyhedral in that linear space, i.e., expressed by a finite number of linear inequalities. We specify the sets of the coefficients of the linear inequalities for some classes of set functions. Then we consider the following three problems: (a) the domain extension problem for nonadditive set functions, (b) the sandwich problem for nonadditive set functions, and (c) the representation problem of a binary relation by a nonadditive set function, i.e., the problem of nonadditive comparative probabilities. 相似文献
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J. Mather and A. Fathi defined Ma(n)ié set and Aubry set, which are the important invariant sets in positive definite Lagrangian system, in different ways.They use variational principle and Weak KAM theory respectively. In this paper we provide a proof of the equivalence between the two kinds of definitions, and generalize A. Fathi's definition. In the end of the paper, we calculate the Ma(n)é set and Aubry set for a single pendulum system. 相似文献
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H.J Ryser 《Journal of Combinatorial Theory, Series A》1982,32(2):162-177
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引入实值函数关于有界闭凸值测度的集值积分,并讨论了集值积分的收敛定理,证明了当集值测度为有界闭凸集值的有界变差集值测度时,关于弱紧凸集值测度的积分性质对有界闭凸集值测度仍然保持.推广了实值函数关于弱紧凸值测度的积分. 相似文献
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O.L. Mangasarian 《Journal of Global Optimization》2002,24(4):473-480
Characterization of the containment of a polyhedral set in a closed halfspace, a key factor in generating knowledge-based support vector machine classifiers [7], is extended to the following: (i) containment of one polyhedral set in another; (ii) containment of a polyhedral set in a reverse-convex set defined by convex quadratic constraints; (iii) Containment of a general closed convex set, defined by convex constraints, in a reverse-convex set defined by convex nonlinear constraints. The first two characterizations can be determined in polynomial time by solving m linear programs for (i) and m convex quadratic programs for (ii), where m is the number of constraints defining the containing set. In (iii), m convex programs need to be solved in order to verify the characterization, where again m is the number of constraints defining the containing set. All polyhedral sets, like the knowledge sets of support vector machine classifiers, are characterized by the intersection of a finite number of closed halfspaces. 相似文献
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根据度量空间中极限点和链等价点的定义,给出度量G-空间中G-极限点和G-链等价点的概念,并在度量G-空间中研究了它们的动力学性质,得到了G-极限点和G-链等价点的一些结果,这些结果丰富了度量G-空间中G-极限点和G-链等价点的理论. 相似文献
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Andreas Dress 《Annals of Combinatorics》2009,13(2):193-198
In phylogenetic combinatorics, the analysis of split systems is a fundamental issue. Here, we observe that there is a canonical
one-to-one correspondence between split systems on the one, and “even” set systems on the other hand, i.e., given any finite
set X, we show that there is a canonical one-to-one correspondence between the set P (S (X ) ){\mathcal P (\mathcal S (X ) )} consisting of all subsets S{\mathcal S} of the set S (X){\mathcal S (X)} of all splits of the set X (that is, all 2-subsets {A, B}{\{A, B\}} of the power set P (X){\mathcal P (X)} of X for which A ⋃ B = X and A ⋂ B = 0̸ hold) and the set P even (P (X)){\mathcal P ^{even} (\mathcal P (X))} consisting of all subsets E of the power set P (X){\mathcal P (X)} of X for which, for each subset Y of X, the number of proper subsets of Y contained in E is even. 相似文献
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A set partition is called “gap-free” if its block sizes form an interval. In other words, there is at least one block of each size between the smallest and largest block sizes. Let B(n) and G(n), respectively, denote the number of partitions and the number of gap-free partitions of the set [n]. We prove that 相似文献
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Alexander Engström 《Discrete and Computational Geometry》2008,40(3):357-364
The Hom complexes were introduced by Lovász to study topological obstructions to graph colorings. The vertices of Hom(G,K
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) are the n-colorings of the graph G, and a graph coloring is a partition of the vertex set into independent sets. Replacing the independence condition with any
hereditary condition defines a set partition complex. We show how coloring questions arising from, for example, Ramsey theory
can be formulated with set partition complexes.
It was conjectured by Babson and Kozlov, and proved by Čukić and Kozlov, that Hom(G,K
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) is (n−d−2)-connected, where d is the maximal degree of a vertex of G. We generalize this to set partition complexes. 相似文献
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The inertia-preservers of several sets of matrices are identified. The sets include: all real matrices, all complex matrices, triangular matrices, real symmetric matrices and Hermitian matrices. 相似文献