共查询到20条相似文献,搜索用时 31 毫秒
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Wojciech S. Ożański 《Journal of Functional Analysis》2019,276(10):2990-3013
The surface growth model, , is a one-dimensional fourth order equation, which shares a number of striking similarities with the three-dimensional incompressible Navier–Stokes equations, including the results regarding existence and uniqueness of solutions and the partial regularity theory. Here we show that a weak solution of this equation is smooth on a space-time cylinder Q if the Serrin condition is satisfied, where are such that either or , . 相似文献
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Joachim Toft 《Applied and Computational Harmonic Analysis》2019,46(1):154-176
We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator is a Schatten-q operator from to and r-nuclear operator from to when for suitable p, q and r in . 相似文献
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Lionel Nguyen Van Thé 《Expositiones Mathematicae》2019,37(2):192-199
Say that a graph is representable in if there is a map from its vertex set into the Euclidean space such that iff and are both edges or both non-edges in . The purpose of this note is to present the proof of the following result, due to Einhorn and Schoenberg in Einhorn and Schoenberg (1966): if finite is neither complete nor independent, then it is representable in . A similar result also holds in the case of finite complete edge-colored graphs. 相似文献
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《Discrete Mathematics》2022,345(3):112706
The power of a graph , , is the graph whose vertex set is V and in which two distinct vertices are adjacent if and only if their distance in G is at most k. This article proves various eigenvalue bounds for the independence number and chromatic number of which purely depend on the spectrum of G, together with a method to optimize them. Our bounds for the k-independence number also work for its quantum counterpart, which is not known to be a computable parameter in general, thus justifying the use of integer programming to optimize them. Some of the bounds previously known in the literature follow as a corollary of our main results. Infinite families of graphs where the bounds are sharp are presented as well. 相似文献
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We define additive G-codes over finite fields. We prove that if C is an additive G-code over with duality M then its dual with respect to this duality is an additive G-code. We prove that if M and are two dualities, then and are equivalent codes. Finally, we study the existence of self-dual codes for a variety of dualities and relate them to formally self-dual and linear self-dual codes. 相似文献
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In this paper we study the existence of homomorphisms using semidefinite programming. Specifically, we use the vector chromatic number of a graph, defined as the smallest real number for which there exists an assignment of unit vectors to its vertices such that when . Our approach allows to reprove, without using the Erdős–Ko–Rado Theorem, that for the Kneser graph and the -Kneser graph are cores, and furthermore, that for there exists a homomorphism if and only if divides . In terms of new applications, we show that the even-weight component of the distance -graph of the -cube is a core and also, that non-bipartite Taylor graphs are cores. Additionally, we give a necessary and sufficient condition for the existence of homomorphisms when . Lastly, we show that if a 2-walk-regular graph (which is non-bipartite and not complete multipartite) has a unique optimal vector coloring, it is a core. Based on this sufficient condition we conducted a computational study on Ted Spence’s list of strongly regular graphs (http://www.maths.gla.ac.uk/ es/srgraphs.php) and found that at least 84% are cores. 相似文献
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Xiang He 《Journal of Pure and Applied Algebra》2019,223(2):794-817
Let X and be closed subschemes of an algebraic torus T over a non-archimedean field. We prove the rational equivalence as tropical cycles in the sense of [11, §2] between the tropicalization of the intersection product and the stable intersection , when restricted to (the inverse image under the tropicalization map of) a connected component C of . This requires possibly passing to a (partial) compactification of T with respect to a suitable fan. We define the compactified stable intersection in a toric tropical variety, and check that this definition is compatible with the intersection product in [11, §2]. As a result we get a numerical equivalence between and via the compactified stable intersection, where the closures are taken inside the compactifications of T and . In particular, when X and have complementary codimensions, this equivalence generalizes [15, Theorem 6.4], in the sense that is allowed to be of positive dimension. Moreover, if has finitely many points which tropicalize to , we prove a similar equation as in [15, Theorem 6.4] when the ambient space is a reduced subscheme of T (instead of T itself). 相似文献
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After a brief review of the existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bring a PB to its canonical form under equivalence. We then focus on PBs of of the form , where n and d are positive integers and . Our contributions include two nonexistence results: (1) If q is even and sufficiently large and , then is not a PB of . (2) If , q is sufficiently large and , then is not a PB of under certain additional conditions. (1) partially confirms a recent conjecture by Tu et al. (2) is an extension of a previous result with . 相似文献
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Let be the finite field with q elements and let . It was conjectured that for integers and , the polynomial is a permutation polynomial of if and only if (i) and , or (ii) and . In the present paper we confirm this conjecture. 相似文献
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We consider four classes of polynomials over the fields , , , , , , , where . We find sufficient conditions on the pairs for which these polynomials permute and we give lower bounds on the number of such pairs. 相似文献
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《Discrete Mathematics》2022,345(8):112902
For a simple graph G, denote by n, , and its order, maximum degree, and chromatic index, respectively. A graph G is edge-chromatic critical if and for every proper subgraph H of G. Let G be an n-vertex connected regular class 1 graph, and let be obtained from G by splitting one vertex of G into two vertices. Hilton and Zhao in 1997 conjectured that must be edge-chromatic critical if , and they verified this when . In this paper, we prove it for . 相似文献
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Let q be a perfect power of a prime number p and be an elliptic curve over given by the equation . For a positive integer n we denote by the number of rational points on E (including infinity) over the extension . Under a mild technical condition, we show that the sequence contains at most 10200 perfect squares. If the mild condition is not satisfied, then is a perfect square for infinitely many n including all the multiples of 12. Our proof uses a quantitative version of the Subspace Theorem. We also find all the perfect squares for all such sequences in the range and . 相似文献