共查询到20条相似文献,搜索用时 31 毫秒
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《Journal of Discrete Algorithms》2008,6(4):561-569
We present a fixed-parameter algorithm for the Minimum Convex Partition and the Minimum Weight Convex Partition problem. The algorithm is based on techniques developed for the Minimum Weight Triangulation problem. On a set P of n points the algorithm runs in time. The parameter k is the number of points in P lying in the interior of the convex hull of P. 相似文献
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Sujith Vijay 《Journal of Combinatorial Theory, Series A》2012,119(5):1078-1080
Let and where and arbitrarily slowly as . We show that the probability of a random 2-coloring of containing a monochromatic k-term arithmetic progression approaches 1, and the probability of a random 2-coloring of containing a monochromatic k-term arithmetic progression approaches 0, as . This improves an upper bound due to Brown, who had established an analogous result for . 相似文献
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Philippe G. Ciarlet Liliana Gratie Cristinel Mardare 《Comptes Rendus Mathematique》2005,341(3):201-206
The main purpose of this Note is to show how a ‘nonlinear Korn's inequality on a surface’ can be established. This inequality implies in particular the following interesting per se sequential continuity property for a sequence of surfaces. Let ω be a domain in , let be a smooth immersion, and let , , be mappings with the following properties: They belong to the space ; the vector fields normal to the surfaces , , are well defined a.e. in ω and they also belong to the space ; the principal radii of curvature of the surfaces stay uniformly away from zero; and finally, the three fundamental forms of the surfaces converge in toward the three fundamental forms of the surface as . Then, up to proper isometries of , the surfaces converge in toward the surface as . To cite this article: P.G. Ciarlet et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005). 相似文献
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《Journal de Mathématiques Pures et Appliquées》2006,85(1):2-16
Let ω be a domain in and let be a smooth immersion. The main purpose of this paper is to establish a “nonlinear Korn inequality on the surface ”, asserting that, under ad hoc assumptions, the -distance between the surface and a deformed surface is “controlled” by the -distance between their fundamental forms. Naturally, the -distance between the two surfaces is only measured up to proper isometries of .This inequality implies in particular the following interesting per se sequential continuity property for a sequence of surfaces. Let , , be mappings with the following properties: They belong to the space ; the vector fields normal to the surfaces , , are well defined a.e. in ω and they also belong to the space ; the principal radii of curvature of the surfaces , , stay uniformly away from zero; and finally, the fundamental forms of the surfaces converge in toward the fundamental forms of the surface as . Then, up to proper isometries of , the surfaces converge in toward the surface as .Such results have potential applications to nonlinear shell theory, the surface being then the middle surface of the reference configuration of a nonlinearly elastic shell. 相似文献
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Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 相似文献
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Jim Agler Zinaida A. Lykova N.J. Young 《Journal of Mathematical Analysis and Applications》2012,386(1):308-318
We give a new solvability criterion for the boundary Carathéodory–Fejér problem: given a point and, a finite set of target values , to construct a function f in the Pick class such that the limit of as nontangentially in the upper half-plane is for . The criterion is in terms of positivity of an associated Hankel matrix. The proof is based on a reduction method due to Julia and Nevanlinna. 相似文献
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《Computational Geometry》2005,30(1):59-77
The dilation of a geometric graph is the maximum, over all pairs of points in the graph, of the ratio of the Euclidean length of the shortest path between them in the graph and their Euclidean distance. We consider a generalized version of this notion, where the nodes of the graph are not points but axis-parallel rectangles in the plane. The arcs in the graph are horizontal or vertical segments connecting a pair of rectangles, and the distance measure we use is the -distance. The dilation of a pair of points is then defined as the length of the shortest rectilinear path between them that stays within the union of the rectangles and the connecting segments, divided by their -distance. The dilation of the graph is the maximum dilation over all pairs of points in the union of the rectangles.We study the following problem: given n non-intersecting rectangles and a graph describing which pairs of rectangles are to be connected, we wish to place the connecting segments such that the dilation is minimized. We obtain four results on this problem: (i) for arbitrary graphs, the problem is NP-hard; (ii) for trees, we can solve the problem by linear programming on variables and constraints; (iii) for paths, we can solve the problem in time ; (iv) for rectangles sorted vertically along a path, the problem can be solved in time, and a -approximation can be computed in linear time. 相似文献