共查询到20条相似文献,搜索用时 23 毫秒
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《Discrete Mathematics》2022,345(1):112668
The following optimal stopping problem is considered. The vertices of a graph G are revealed one by one, in a random order, to a selector. He aims to stop this process at a time t that maximizes the expected number of connected components in the graph , induced by the currently revealed vertices. The selector knows G in advance, but different versions of the game are considered depending on the information that he gets about . We show that when G has N vertices and maximum degree of order , then the number of components of is concentrated around its mean, which implies that playing the optimal strategy the selector does not benefit much by receiving more information about . Results of similar nature were previously obtained by M. Lasoń for the case where G is a k-tree (for constant k). We also consider the particular cases where G is a square, triangular or hexagonal lattice, showing that an optimal selector gains cN components and we compute c with an error less than 0.005 in each case. 相似文献
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Clément Charpentier Simone Dantas Celina M.H. de Figueiredo Ana Furtado Sylvain Gravier 《Discrete Mathematics》2019,342(5):1318-1324
A seminal result by Nordhaus and Gaddum states that for every graph of order , where is the complement of and is the chromatic number. We study similar inequalities for and , which denote, respectively, the game chromatic number and the game coloring number of . Those graph invariants give the score for, respectively, the coloring and marking games on when both players use their best strategies. 相似文献
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A revised Yau's Curvature Difference Flow is considered to deform one convex curve to another one . It is proved that this flow exists globally on time interval and the evolving curve, preserving its convexity and bounded area A, converges to a fixed limiting curve (congruent to ) as time tends to infinity, where is the area bounded by the target curve . 相似文献
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A new criterion for the existence of positive solutions of the second-order delayed differential equation , is given with applications to linear equations. Open problems for future research are formulated. 相似文献
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We consider the pseudo-Euclidean space , , with coordinates and metric , , where at least one is positive, and also tensors of the form , such that are differentiable functions of x. For such tensors, we use Lie point symmetries to find metrics that solve the Ricci curvature and the Einstein equations. We provide a large class of group-invariant solutions and examples of complete metrics defined globally in . As consequences, for certain functions , we show complete metrics , conformal to the pseudo-Euclidean metric g, whose scalar curvature is . 相似文献
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Calvin Deng 《Discrete Mathematics》2019,342(2):540-545
We extend a method of Olsson and Bessenrodt to determine the number of even partitions that are simultaneously -core and -core. When and are distinct primes, this also determines the number of self-associate characters of that are simultaneously defect 0 for and . 相似文献
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《Journal of Pure and Applied Algebra》2022,226(8):106948
Let be a Henselian discrete valued field with residue field of characteristic , and be the Brauer p-dimension of K. This paper shows that if , for some . It proves that if and only if . 相似文献
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We consider a reaction–diffusion–advection equation of the form: for , where is a -periodic function, is a -periodic Fisher–KPP type of nonlinearity with changing sign, is a free boundary satisfying the Stefan condition. We study the long time behavior of solutions and find that there are two critical numbers and with , and , such that a vanishing–spreading dichotomy result holds when ; a vanishing–transition–virtual spreading trichotomy result holds when ; all solutions vanish when or . 相似文献
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We consider subordinators in the domain of attraction at 0 of a stable subordinator (where ); thus, with the property that , the tail function of the canonical measure of , is regularly varying of index as . We also analyse the boundary case, , when is slowly varying at 0. When , we show that converges in distribution, as , to the random variable . This latter random variable, as a function of , converges in distribution as to the inverse of an exponential random variable. We prove these convergences, also generalised to functional versions (convergence in ), and to trimmed versions, whereby a fixed number of its largest jumps up to a specified time are subtracted from the process. The case produces convergence to an extremal process constructed from ordered jumps of a Cauchy subordinator. Our results generalise random walk and stable process results of Darling, Cressie, Kasahara, Kotani and Watanabe. 相似文献
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