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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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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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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《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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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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Let be the finite field of characteristic p with q elements and its extension of degree n. We prove that there exists a primitive element of that produces a completely normal basis of over , provided that with and . 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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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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H.E.A. Campbell J. Chuai R.J. Shank D.L. Wehlau 《Journal of Pure and Applied Algebra》2019,223(5):2015-2035
Suppose is a field of prime characteristic p and E is a finite subgroup of the additive group . Then E is an elementary abelian p-group. We consider two such subgroups, say E and , to be equivalent if there is an such that . In this paper we show that rational functions can be used to distinguish equivalence classes of subgroups and, for subgroups of prime rank or rank less than twelve, we give explicit finite sets of separating invariants. 相似文献