共查询到20条相似文献,搜索用时 62 毫秒
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For every real numbers , with , the curve parametrized by valued in with components: has image contained in the CR-umbilical locus: of the ellipsoid of equation , where the CR-umbilical locus of a Levi nondegenerate hypersurface is the set of points at which the Cartan curvature of M vanishes. 相似文献
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《Discrete Mathematics》2007,307(3-5):544-553
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Let and be a sufficiently large real number. In this paper, we prove that, for almost all , the Diophantine inequality is solvable in primes . Moreover, we also investigate the problem of six primes and prove that the Diophantine inequality is solvable in primes for sufficiently large real 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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For positive integers with , let ICKPD denote a canonical Kirkman packing of order missing one of order . In this paper, it is shown that the necessary condition for existence of an ICKPD, namely , is sufficient with a definite exception , and except possibly when , and . 相似文献
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Let G be a graph with n vertices and edges, and let be the Laplacian eigenvalues of G. Let , where . Brouwer conjectured that for . It has been shown in Haemers et al. [7] that the conjecture is true for trees. We give upper bounds for , and in particular, we show that the conjecture is true for unicyclic and bicyclic graphs. 相似文献
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We discuss dimension theory in the class of all topological groups. For locally compact topological groups there are many classical results in the literature. Dimension theory for non-locally compact topological groups is mysterious. It is for example unknown whether every connected (hence at least 1-dimensional) Polish group contains a homeomorphic copy of . And it is unknown whether there is a homogeneous metrizable compact space the homeomorphism group of which is 2-dimensional. Other classical open problems are the following ones. Let be a topological group with a countable network. Does it follow that ? The same question if is a compact coset space. We also do not know whether the inequality holds for arbitrary topological groups and which are subgroups of -compact topological groups. The aim of this paper is to discuss such and related problems. But we do not attempt to survey the literature. 相似文献
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Marcin Pilipczuk Michał Pilipczuk Riste Škrekovski 《Discrete Applied Mathematics》2012,160(16-17):2484-2490
The well-known conjecture of Vizing on the domination number of Cartesian product graphs claims that for any two graphs and , . We disprove its variations on independent domination number and Barcalkin–German number, i.e. Conjectures 9.6 and 9.2 from the recent survey Bre?ar et al. (2012) [4]. We also give some extensions of the double-projection argument of Clark and Suen (2000) [8], showing that their result can be improved in the case of bounded-degree graphs. Similarly, for rainbow domination number we show for every that , which is closely related to Question 9.9 from the same survey. We also prove that the minimum possible counterexample to Vizing’s conjecture cannot have two neighboring vertices of degree two. 相似文献