共查询到20条相似文献,搜索用时 15 毫秒
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We construct orthogonal arrays (of strength two) having a row that is repeated times, where is as large as possible. In particular, we consider OAs where the ratio is as large as possible; these OAs are termed optimal. We provide constructions of optimal OAs for any , albeit with large . We also study basic OAs; these are optimal OAs in which . We construct a basic OA with and , provided that a Hadamard matrix of order exists. This completely solves the problem of constructing basic OAs with , modulo the Hadamard matrix conjecture. 相似文献
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Given two graphs and , the maximum possible number of copies of in an -free graph on vertices is denoted by . We investigate the function , where denotes vertex disjoint copies of a fixed graph . Our results include cases when is a complete graph, cycle or a complete bipartite graph. 相似文献
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A well-known result from the 1960 paper of Erdős and Rényi (1960) [2] tells us that the almost sure theory for first order language on the random graph sequence is not complete. Our paper proposes and proves what the complete set of completions of the almost sure theory for should be. The almost sure theory consists of two sentence groups: the first states that all the components are trees or unicyclic components, and the second states that, given any and any finite tree , there are at least components isomorphic to . We define a -completion of to be a first order property , such that if holds for a graph (which indicates that the property described in sentence is satisfied by the graph, and for every sentence in the theory , the property described by is also satisfied by the graph), we can fully describe the first order sentences of quantifier depth that hold for that graph. We show that a -completion specifies the numbers, up to “cutoff” , of the (finitely many) unicyclic component types of given parameters (that only depend on ) that the graph contains. A complete set of -completions is then the finite collection of all possible -completions. 相似文献
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Anna Aksamit Monique Jeanblanc Marek Rutkowski 《Stochastic Processes and their Applications》2019,129(4):1229-1258
We work in the setting of the progressive enlargement of a reference filtration through the observation of a random time . We study an integral representation property for some classes of -martingales stopped at . In the first part, we focus on the case where is a Poisson filtration and we establish a predictable representation property with respect to three -martingales. In the second part, we relax the assumption that is a Poisson filtration and we assume that is an -pseudo-stopping time. We establish integral representations with respect to some -martingales built from -martingales and, under additional hypotheses, we obtain a predictable representation property with respect to two -martingales. 相似文献
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We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium , . The governing equation may be degenerate of p-Laplace type, with . We prove optimal estimates for the blow-up of the gradient of the solution as the distance between the inclusions tends to zero. 相似文献
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《Discrete Mathematics》2022,345(1):112631
For a graph , a total ordering L on V, and a vertex , let be the set of vertices for which there is a path from v to w whose length is 0, 1 or 2 and whose L-least vertex is w. The weak 2-coloring number of G is the least k such that there is a total ordering L on V with for all vertices . We improve the known upper bound on the weak 2-coloring number of planar graphs from 28 to 23. As the weak 2-coloring number is the best known upper bound on the star list chromatic number of planar graphs, this bound is also improved. 相似文献
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We consider the problem of sending a message from a sender to a receiver through an unreliable network by specifying in a protocol what each vertex is supposed to do if it receives the message from one of its neighbors. A protocol for routing a message in such a graph is finite if it never floods with an infinite number of copies of the message. The expected reliability of a given protocol is the probability that a message sent from reaches when the edges of the network fail independently with probability .We discuss, for given networks, the properties of finite protocols with maximum expected reliability in the case when is close to 0 or 1, and we describe networks for which no one protocol is optimal for all values of . In general, finding an optimal protocol for a given network and fixed probability is challenging and many open problems remain. 相似文献
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《Expositiones Mathematicae》2023,41(2):316-332
Let be a connective homology theory. We construct a functorial relative plus construction as a Bousfield localization functor in the category of maps of spaces. It allows us to associate to a pair , consisting of a connected space and an -perfect normal subgroup of the fundamental group , an -acyclic map inducing the quotient by on the fundamental group. We show that this map is terminal among the -acyclic maps that kill a subgroup of . When is an ordinary homology theory with coefficients in a commutative ring with unit , this provides a functorial and well-defined counterpart to a construction by cell attachment introduced by Broto, Levi, and Oliver in the spirit of Quillen’s plus construction. We also clarify the necessity to use a strongly -perfect group in characteristic zero. 相似文献
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Let denote a Hermite process of order and self-similarity parameter . This process is -self-similar, has stationary increments and exhibits long-range dependence. When , it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as . In this paper, we deal with a Vasicek-type model driven by , of the form . Here, and are considered as unknown drift parameters. We provide estimators for and based on continuous-time observations. For all possible values of and , we prove strong consistency and we analyze the asymptotic fluctuations. 相似文献
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《Stochastic Processes and their Applications》2020,130(4):1897-1912
We determine the optimal structure of couplings for the Martingale transport problem between radially symmetric initial and terminal laws on and show the uniqueness of optimizer. Here optimality means that such solutions will minimize the functional where is concave and strictly increasing, and the dimension is arbitrary. 相似文献