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1.
If a graph G decomposes into edge‐disjoint 4‐cycles, then each vertex of G has even degree and 4 divides the number of edges in G. It is shown that these obvious necessary conditions are also sufficient when G is any simple graph having minimum degree at least , where n is the number of vertices in G. This improves the bound given by Gustavsson (PhD Thesis, University of Stockholm, 1991), who showed (as part of a more general result) sufficiency for simple graphs with minimum degree at least . On the other hand, it is known that for arbitrarily large values of n there exist simple graphs satisfying the obvious necessary conditions, having n vertices and minimum degree , but having no decomposition into edge‐disjoint 4‐cycles. We also show that if G is a bipartite simple graph with n vertices in each part, then the obvious necessary conditions for G to decompose into 4‐cycles are sufficient when G has minimum degree at least . 相似文献
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T∞-测度分解定理的进一步讨论 总被引:1,自引:0,他引:1
在对T∞-测度做进一步研究的基础上,得到了(有限或无限)T∞-测度的Hahn分解定理和Jordan分解定理。同时,用一种新方法证明了有限T∞-测度的Lebesgue分解定理。此外,还得到了一些类似于经典测度的结论。 相似文献
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Brian D. Sutton 《Numerical Algorithms》2009,50(1):33-65
An algorithm for computing the complete CS decomposition of a partitioned unitary matrix is developed. Although the existence
of the CS decomposition (CSD) has been recognized since 1977, prior algorithms compute only a reduced version. This reduced
version, which might be called a 2-by-1 CSD, is equivalent to two simultaneous singular value decompositions. The algorithm
presented in this article computes the complete 2-by-2 CSD, which requires the simultaneous diagonalization of all four blocks
of a unitary matrix partitioned into a 2-by-2 block structure. The algorithm appears to be the only fully specified algorithm
available. The computation occurs in two phases. In the first phase, the unitary matrix is reduced to bidiagonal block form,
as described by Sutton and Edelman. In the second phase, the blocks are simultaneously diagonalized using techniques from
bidiagonal SVD algorithms of Golub, Kahan, Reinsch, and Demmel. The algorithm has a number of desirable numerical features.
相似文献
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Binyong SUN 《数学年刊B辑(英文版)》2015,36(3):355-400
A Nash group is said to be almost linear if it has a Nash representation with
a finite kernel. Structures and basic properties of these groups are studied. 相似文献
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关于图的升分解的Alavi猜想 总被引:3,自引:1,他引:2
Y.Alavi等人在1987年定义了图的一种新分解,即“升分解”(ascebding subgraph decomposition),并提出猜想:设自然数n≥2,G是由k个分离的星S_1,S_2,…,S_k构成的图,S_i含有a_i条边,n≤a_i≤2n-2,,则G可升分解为星的并。本文证明了当n=2k+i(i=0,1,2)时猜想成立。 相似文献
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For an ordered k-decomposition
of a connected graph G and an edge e of G, the
-code of e is the k-tuple
where d(e, G
i) is the distance from e to G
i. A decomposition
is resolving if every two distinct edges of G have distinct
-codes. The minimum k for which G has a resolving k-decomposition is its decomposition dimension dim
d
(G). A resolving decomposition
of G is connected if each G
i is connected for 1 i k. The minimum k for which G has a connected resolving k-decomposition is its connected decomposition number cd(G). Thus 2 dim
d
(G) cd(G) m for every connected graph G of size m 2. All nontrivial connected graphs of size m with connected decomposition number 2 or m have been characterized. We present characterizations for connected graphs of size m with connected decomposition number m – 1 or m – 2. It is shown that each pair s, t of rational numbers with 0 < s t 1, there is a connected graph G of size m such that dim
d
(G)/m = s and cd(G)/m = t. 相似文献
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We consider weighted anchored and ANOVA spaces of functions with first order mixed derivatives bounded in . Recently, Hefter, Ritter and Wasilkowski established conditions on the weights in the cases and which ensure equivalence of the corresponding norms uniformly in the dimension or only polynomially dependent on the dimension. We extend these results to the whole range of . It is shown how this can be achieved via interpolation. 相似文献
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朱子云 《应用泛函分析学报》2014,(4):360-373
本文提出了一个基于收入构成差异和收入差距动因的分解框架,旨在量化相关决定因素对居民人均收入省际差距的贡献度.从指标内在关联性维度将居民人均收入指标进行多指标分解,由此导出因变量指标与各自变量之和(或之乘积)之间存在恒等关系的表达式,并引入可导性方差分解法构造了地区间居民收入绝对差距和相对差距的结构与动因分解模型.研究结果表明,驱动2005-2012年中国居民人均收入省际间差距形成和缩小的首要动力是人均设备性资本,其次是非设备性资本与设备性资本比例;人力资本与总人口比例在差距形成和绝对差距缩小中具有显著的推动作用,但在相对差距缩小中表现出明显的抑制效应;非设备性资本产出率在差距形成中具有较大的推动作用,但在差距缩小中表现出巨大的抑制效应;劳动力与人力资本比例在差距形成和绝对差距缩小中具有显著的抑制作用,但在相对差距缩小中表现出巨大的推动作用;产出分配率在差距形成中发挥了较小的抑制作用,但在差距缩小中表现出巨大的遏制作用. 相似文献
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In 1998 Cavenagh [N.J. Cavenagh, Decompositions of complete tripartite graphs into k-cycles, Australas. J. Combin. 18 (1998) 193-200] gave necessary and sufficient conditions for the existence of an edge-disjoint decomposition of a complete equipartite graph with three parts, into cycles of some fixed length k. Here we extend this to paths, and show that such a complete equipartite graph with three partite sets of size m, has an edge-disjoint decomposition into paths of length k if and only if k divides 3m2 and k<3m. Further, extending to five partite sets, we show that a complete equipartite graph with five partite sets of size m has an edge-disjoint decomposition into cycles (and also into paths) of length k with k?3 if and only if k divides 10m2 and k?5m for cycles (or k<5m for paths). 相似文献
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Wael Abu-Shammala Alberto Torchinsky 《Proceedings of the American Mathematical Society》2007,135(9):2839-2843
In this paper we present an atomic decomposition of integrable functions. As an application we compute the distance of in to the Hardy space .
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Hirotaka Akiyoshi 《Proceedings of the American Mathematical Society》2001,129(8):2431-2439
Epstein and Penner give a canonical method of decomposing a cusped hyperbolic manifold into ideal polyhedra. The decomposition depends on arbitrarily specified weights for the cusps. From the construction, it is rather obvious that there appear at most a finite number of decompositions if the given weights are slightly changed. However, since the space of weights is not compact, it is not clear whether the total number of such decompositions is finite. In this paper we prove that the number of polyhedral decompositions of a cusped hyperbolic manifold obtained by the Epstein-Penner's method is finite.
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It is shown that the obvious necessary conditions for the existence of a decomposition of the complete multigraph with n vertices and with λ edges joining each pair of distinct vertices into m‐cycles, or into m‐cycles and a perfect matching, are also sufficient. This result follows as an easy consequence of more general results which are obtained on decompositions of complete multigraphs into cycles of varying lengths. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:42‐69, 2010 相似文献
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We derive an averaging property under the Iwasawa decomposition on a semisimple Lie group of noncompact type based on a limiting property of random walks in the Lie group.
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We show that a complete equipartite graph with four partite sets has an edge-disjoint decomposition into cycles of length k if and only if k≥3, the partite set size is even, k divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least k. We also show that a complete equipartite graph with four even partite sets has an edge-disjoint decomposition into paths with k edges if and only if k divides the number of edges in the equipartite graph and the total number of vertices in the graph is at least k+1. 相似文献