共查询到20条相似文献,搜索用时 937 毫秒
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For bipartite graphs , the bipartite Ramsey number is the least positive integer so that any coloring of the edges of with colors will result in a copy of in the th color for some . In this paper, our main focus will be to bound the following numbers: and for all for and for Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result. 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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In 1965 Erd?s introduced : is the smallest integer such that every is the sum of s distinct primes or squares of primes where a prime and its square are not both used. We prove that for all sufficiently large s, , and the set of s with the equality has the density 1. 相似文献
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Given a graph , the Turán function is the maximum number of edges in a graph on vertices that does not contain as a subgraph. Let be integers and let be a graph consisting of triangles and cycles of odd lengths at least 5 which intersect in exactly one common vertex. Erd?s et al. (1995) determined the Turán function and the corresponding extremal graphs. Recently, Hou et al. (2016) determined and the extremal graphs, where the cycles have the same odd length with . In this paper, we further determine and the extremal graphs, where and . Let be the smallest integer such that, for all graphs on vertices, the edge set can be partitioned into at most parts, of which every part either is a single edge or forms a graph isomorphic to . Pikhurko and Sousa conjectured that for and all sufficiently large . Liu and Sousa (2015) verified the conjecture for . In this paper, we further verify Pikhurko and Sousa’s conjecture for with and . 相似文献
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Le Thi Phuong Ngoc Nguyen Anh Triet Nguyen Thanh Long 《Nonlinear Analysis: Real World Applications》2010,11(4):2479-2501
In this paper, we consider the following nonlinear Kirchhoff wave equation (1) where , , , , , are given functions and . First, combining the linearization method for nonlinear term, the Faedo–Galerkin method and the weak compact method, a unique weak solution of problem (1) is obtained. Next, by using Taylor’s expansion of the function around the point up to order , we establish an asymptotic expansion of high order in many small parameters of solution. 相似文献
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Masatoshi Fujii Ritsuo Nakamoto Keisuke Yonezawa 《Linear algebra and its applications》2013,438(4):1580-1586
The grand Furuta inequality has the following satellite (SGF;), given as a mean theoretic expression:where is the -geometric mean and () is a formal extension of . It is shown that (SGF; ) has the Löwner–Heinz property, i.e. (SGF; ) implies (SGF;t) for every . Furthermore, we show that a recent further extension of (GFI) by Furuta himself has also the Löwner–Heinz property. 相似文献
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In this paper, we show that for any fixed integers and , the star-critical Ramsey number for all sufficiently large . Furthermore, for any fixed integers and , as . 相似文献
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Ping Sun 《Discrete Mathematics》2012,312(24):3649-3655
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Haïm Brezis Petru Mironescu 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(5):1355-1376
We investigate the validity of the Gagliardo–Nirenberg type inequality
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with . Here, are non negative numbers (not necessarily integers), , and we assume the standard relationsBy the seminal contributions of E. Gagliardo and L. Nirenberg, (1) holds when are integers. It turns out that (1) holds for “most” of values of , but not for all of them. We present an explicit condition on which allows to decide whether (1) holds or fails. 相似文献