共查询到20条相似文献,搜索用时 46 毫秒
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《Journal de Mathématiques Pures et Appliquées》2005,84(11):1496-1514
In this paper we obtain a new regularity criterion for weak solutions to the 3-D Navier–Stokes equations. We show that if any one component of the velocity field belongs to with , , then the weak solution actually is regular and unique. 相似文献
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Let be the number of numerical semigroups of genus . We present an approach to compute by using even gaps, and the question: Is it true that ? is investigated. Let be the number of numerical semigroups of genus whose number of even gaps equals . We show that for and for ; thus the question above is true provided that for . We also show that coincides with , the number introduced by Bras-Amorós (2012) in connection with semigroup-closed sets. Finally, the stronger possibility arises being the golden number. 相似文献
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Boštjan Brešar 《Discrete Mathematics》2017,340(10):2398-2401
A long-standing Vizing’s conjecture asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers; one of the most significant results related to the conjecture is the bound of Clark and Suen, , where stands for the domination number, and is the Cartesian product of graphs and . In this note, we improve this bound by employing the 2-packing number of a graph into the formula, asserting that . The resulting bound is better than that of Clark and Suen whenever is a graph with , and in the case has diameter 2 reads as . 相似文献
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Michel Vasquez 《Comptes Rendus Mathematique》2006,342(3):157-160
Until 2003 no chromatic numbers () for the queen graphs were available for except where n is not a multiple of 2 or 3. In this research announcement we present an exact algorithm which provides coloring solutions for and 32 such as . Then we prove that there exists an infinite number of values for n such that or , and . To cite this article: M. Vasquez, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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《Discrete Mathematics》2007,307(9-10):1115-1135
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Jeong-Hyun Kang 《Discrete Mathematics》2018,341(1):96-103
The vertices of Kneser graph are the subsets of of cardinality , two vertices are adjacent if and only if they are disjoint. The square of a graph is defined on the vertex set of with two vertices adjacent if their distance in is at most 2. Z. Füredi, in 2002, proposed the problem of determining the chromatic number of the square of the Kneser graph. The first non-trivial problem arises when . It is believed that where is a constant, and yet the problem remains open. The best known upper bounds are by Kim and Park: for 1 (Kim and Park, 2014) and for (Kim and Park, 2016). In this paper, we develop a new approach to this coloring problem by employing graph homomorphisms, cartesian products of graphs, and linear congruences integrated with combinatorial arguments. These lead to , where is a constant in , depending on . 相似文献
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In this paper, we show that the largest and smallest eigenvalues of a sample correlation matrix stemming from independent observations of a -dimensional time series with iid components converge almost surely to and , respectively, as , if and the truncated variance of the entry distribution is “almost slowly varying”, a condition we describe via moment properties of self-normalized sums. Moreover, the empirical spectral distributions of these sample correlation matrices converge weakly, with probability , to the Mar?enko–Pastur law, which extends a result in Bai and Zhou (2008). We compare the behavior of the eigenvalues of the sample covariance and sample correlation matrices and argue that the latter seems more robust, in particular in the case of infinite fourth moment. We briefly address some practical issues for the estimation of extreme eigenvalues in a simulation study.In our proofs we use the method of moments combined with a Path-Shortening Algorithm, which efficiently uses the structure of sample correlation matrices, to calculate precise bounds for matrix norms. We believe that this new approach could be of further use in random matrix theory. 相似文献