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Thomas Andreae 《Journal of Graph Theory》2002,39(4):222-229
For a graph A and a positive integer n, let nA denote the union of n disjoint copies of A; similarly, the union of ?0 disjoint copies of A is referred to as ?0A. It is shown that there exist (connected) graphs A and G such that nA is a minor of G for all n??, but ?0A is not a minor of G. This supplements previous examples showing that analogous statements are true if, instead of minors, isomorphic embeddings or topological minors are considered. The construction of A and G is based on the fact that there exist (infinite) graphs G1, G2,… such that Gi is not a minor of Gj for all i ≠ j. In contrast to previous examples concerning isomorphic embeddings and topological minors, the graphs A and G presented here are not locally finite. The following conjecture is suggested: for each locally finite connected graph A and each graph G, if nA is a minor of G for all n ? ?, then ?0A is a minor of G, too. If true, this would be a far‐reaching generalization of a classical result of R. Halin on families of disjoint one‐way infinite paths in graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 39: 222–229, 2002; DOI 10.1002/jgt.10016 相似文献
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One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities. 相似文献
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A new numerical method called linearized and rational approximation method is presented to solve non‐linear evolution equations. The utility of the method is demonstrated for the case of differentiation of functions involving steep gradients. The solution of Burgers' equation is presented to illustrate the effectiveness of the technique for the solution of non‐linear evolution equations exhibiting nearly discontinuous solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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An analogy between social and hydrodynamic processes is developed. The relation of the state system to the passionarity theory suggested by L. N. Gumilev is discussed. 相似文献
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Andrzej Skowronski Kunio Yamagata 《Proceedings of the American Mathematical Society》2004,132(3):659-667
We prove that a large class of self-injective algebras of tilted type is invariant under stable equivalences of module categories.
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Zhi Shui HU Chun SU 《数学学报(英文版)》2007,23(7):265-1270
Let {X(t), t ≥ 0} be a Lévy process with EX(1) = 0 and EX^2(1) 〈 ∞. In this paper, we shall give two precise asymptotic theorems for {X(t), t 〉 0}. By the way, we prove the corresponding conclusions for strictly stable processes and a general precise asymptotic proposition for sums of i.i.d. random variables. 相似文献
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二阶Melnikov函数及其应用 总被引:2,自引:0,他引:2
在Melnikov函数的种种应用中,目前常见到的仅是一阶形式。本文具体推导了二阶Melnikov函数的分析表达,提出了临界情况下考察双曲鞍点的稳定流形与不稳定流形相对位置的二阶判据,并成功地用于环面vanderPol方程的研究中。 相似文献
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