共查询到20条相似文献,搜索用时 46 毫秒
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《Discrete Mathematics》2022,345(10):113004
Let G be a graph. We say that G is perfectly divisible if for each induced subgraph H of G, can be partitioned into A and B such that is perfect and . We use and to denote a path and a cycle on t vertices, respectively. For two disjoint graphs and , we use to denote the graph with vertex set and edge set , and use to denote the graph with vertex set and edge set . In this paper, we prove that (i) -free graphs are perfectly divisible, (ii) if G is -free with , (iii) if G is -free, and (iv) if G is -free. 相似文献
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We study the non-linear minimization problem on with , and : where presents a global minimum α at with . In order to describe the concentration of around , one needs to calibrate the behavior of with respect to s. The model case is In a previous paper dedicated to the same problem with , we showed that minimizers exist only in the range , which corresponds to a dominant non-linear term. On the contrary, the linear influence for prevented their existence. The goal of this present paper is to show that for , and , minimizers do exist. 相似文献
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《Discrete Mathematics》2022,345(9):112977
Consider functions , where A and C are disjoint finite sets. The weakly connected components of the digraph of such a function are cycles of rooted trees, as in random mappings, and isolated rooted trees. Let and . When a function is chosen from all possibilities uniformly at random, then we find the following limiting behaviour as . If , then the size of the maximal mapping component goes to infinity almost surely; if , a constant, then process counting numbers of mapping components of different sizes converges; if , then the number of mapping components converges to 0 in probability. We get estimates on the size of the largest tree component which are of order when and constant when , . These results are similar to ones obtained previously for random injections, for which the weakly connected components are cycles and linear trees. 相似文献
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In this paper, we study the existence and concentration behavior of minimizers for , here and where and are constants. By the Gagliardo–Nirenberg inequality, we get the sharp existence of global constraint minimizers of for when , and . For the case , we prove that the global constraint minimizers of behave like for some when c is large, where is, up to translations, the unique positive solution of in and , and . 相似文献
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Roberto Aravire Ahmed Laghribi Manuel ORyan 《Journal of Pure and Applied Algebra》2019,223(1):439-457
Let F be a field of characteristic 2. In this paper we give a complete computation of the kernel of the homomorphism induced by scalar extension, where is a purely inseparable extension (of any degree), is the cokernel of the Artin–Schreier operator given by: , where is the space of absolute m-differential forms over F and d is the differential operator. Other related results are included. 相似文献
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Riccardo Adami Ugo Boscain Valentina Franceschi Dario Prandi 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(4):1095-1113
In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on is essentially self-adjoint in . A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on is never essentially self-adjoint in , if . We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass. 相似文献
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Ruxi Shi 《Journal of Functional Analysis》2019,276(12):3767-3794