共查询到20条相似文献,搜索用时 875 毫秒
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Let X be a complex nonsingular projective 3-fold of general type. We show that there are positive constants c, and such that and for all . 相似文献
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Let be a polynomial of degree n and for any complex number α, let denote the polar derivative of with respect to α. In this paper, we present an integral inequality for the polar derivative of a polynomial. Our theorem includes as special cases several interesting generalisations and refinements of Erdöx–Lax theorem. 相似文献
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Let and be the adjacency matrix and the degree matrix of a graph , respectively. The matrix is called the signless Laplacian matrix of . The spectrum of the matrix is called the Q-spectrum of . A graph is said to be determined by its Q-spectrum if there is no other non-isomorphic graph with the same Q-spectrum. In this paper, we prove that all starlike trees whose maximum degree exceed are determined by their Q-spectra. 相似文献
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A note on two source location problems 总被引:1,自引:1,他引:0
We consider Source Location () problems: given a capacitated network , cost and a demand for every , choose a min-cost so that holds for every , where is the maximum flow value from v to S. In the directed variant, we have demands and and we require and . Undirected is (weakly) NP-hard on stars with for all v except the center. But, it is known to be polynomially solvable for uniform costs and uniform demands. For general instances, both directed an undirected admit a -approximation algorithms, where D is the sum of the demands; up to constant this is tight, unless P = NP. We give a pseudopolynomial algorithm for undirected on trees with running time , where . This algorithm is used to derive a linear time algorithm for undirected with . We also consider the Single Assignment Source Location () where every should be assigned to a single node . While the undirected is in P, we give a -approximation algorithm for the directed case, and show that this is tight, unless P = NP. 相似文献
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Shi-Chao Chen 《Comptes Rendus Mathematique》2018,356(11-12):1081-1084
Let and be the coefficients of the Rogers–Ramanujan identities. We obtain asymptotic formulas for the number of odd values of for odd n, and for even n, which improve Gordon's results. We also obtain lower bounds for the number of odd values of for even n, and for odd n. 相似文献
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《Discrete Mathematics》2006,306(19-20):2572-2581
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Adam Salminen 《Journal of Algebra》2008,319(11):4559-4574
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Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and the term rank of G, by and , respectively. It was conjectured [C. van Nuffelen, Amer. Math. Monthly 83 (1976) 265–266], for any graph G, . The first counterexample to this conjecture was obtained by Alon and Seymour [J. Graph Theor. 13 (1989) 523–525]. Recently, Fishkind and Kotlov [Discrete Math. 250 (2002) 253–257] have proved that for any graph G, . In this Note we improve Fishkind–Kotlov upper bound and show that . To cite this article: S. Akbari, H.-R. Fanaï, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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A. Mimouni 《Journal of Algebra》2009,321(5):1497-1509
In this paper, we will present new developments in the study of the links between the cardinality of the sets of all overrings of R, of all semistar operations of finite character when finite to the Krull dimension of an integral domain R. In particular, we prove that if , then R has at most distinct maximal ideals. Moreover, R has exactly maximal ideals if and only if . In this case R is a Prüfer domain with exactly two maximal ideals and Y-graph spectrum. We also give a complete characterizations for local domains R such that , and nonlocal domains R with for , , and . Examples to illustrate the scopes and limits of the results are constructed. 相似文献