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Let χ be an order c multiplicative character of a finite field and a binomial with . We study the twisted classical and T-adic Newton polygons of f. When , we give a lower bound of Newton polygons and show that they coincide if p does not divide a certain integral constant depending on .We conjecture that this condition holds if p is large enough with respect to by combining all known results and the conjecture given by Zhang-Niu. As an example, we show that it holds for . 相似文献
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《Discrete Mathematics》2022,345(11):113058
Given an undirected graph , a conflict-free coloring with respect to open neighborhoods (CFON coloring) is a vertex coloring such that every vertex has a uniquely colored vertex in its open neighborhood. The minimum number of colors required for such a coloring is the CFON chromatic number of G, denoted by .In previous work [WG 2020], we showed the upper bound , where denotes the distance to cluster parameter of G. In this paper, we obtain the improved upper bound of . We also exhibit a family of graphs for which , thereby demonstrating that our upper bound is tight. 相似文献
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
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In this paper, we study the antipode of a finite-dimensional Hopf algebra H with the dual Chevalley property and obtain an annihilation polynomial for the antipode. This generalizes an old result given by Taft and Wilson in 1974. As consequences, we show that 1) the quasi-exponent of H is the same as the exponent of its coradical, that is, ; 2) . 相似文献
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