共查询到20条相似文献,搜索用时 31 毫秒
1.
《Discrete Mathematics》2020,343(2):111658
A well known result in the analysis of finite metric spaces due to Gromov says that given any metric space there exists a tree metric on such that is bounded above by twice . Here is the hyperbolicity of , a quantity that measures the treeness of 4-tuples of points in . This bound is known to be asymptotically tight.We improve this bound by restricting ourselves to metric spaces arising from filtered posets. By doing so we are able to replace the cardinality appearing in Gromov’s bound by a certain poset theoretic invariant which can be much smaller thus significantly improving the approximation bound.The setting of metric spaces arising from posets is rich: For example, every finite metric graph can be induced from a filtered poset. Since every finite metric space can be isometrically embedded into a finite metric graph, our ideas are applicable to finite metric spaces as well.At the core of our results lies the adaptation of the Reeb graph and Reeb tree constructions and the concept of hyperbolicity to the setting of posets, which we use to formulate and prove a tree approximation result for any filtered poset. 相似文献
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Émeline Schmisser 《Stochastic Processes and their Applications》2019,129(12):5364-5405
In this article, we consider a jump diffusion process , with drift function , diffusion coefficient and jump coefficient . This process is observed at discrete times . The sampling interval tends to 0 and the time interval tends to infinity. We assume that is ergodic, strictly stationary and exponentially -mixing. We use a penalized least-square approach to compute adaptive estimators of the functions and . We provide bounds for the risks of the two estimators. 相似文献
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《Discrete Mathematics》2020,343(1):111641
A graph is called -induced-saturated if does not contain an induced copy of , but removing any edge from creates an induced copy of and adding any edge of to creates an induced copy of . Martin and Smith studied a related problem, and proved that there does not exist a -induced-saturated graph, where is the path on 4 vertices. Axenovich and Csikós gave examples of families of graphs for which -induced-saturated graph exists, and asked if there exists a -induced-saturated graph when . Our aim in this short note is to show that there exists a -induced-saturated graph. 相似文献
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We provide new characterizations of Sobolev ad BV spaces in doubling and Poincaré metric spaces in the spirit of the Bourgain–Brezis–Mironescu and Nguyen limit formulas holding in domains of . 相似文献
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In this paper we consider the curves defined over and give a positive answer to a conjecture about a divisibility condition on L-polynomials of the curves . Our proof involves finding an exact formula for the number of -rational points on for all n, and uses a result we proved elsewhere about the number of rational points on supersingular curves. 相似文献
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Michael Giudici S.P. Glasby Cai Heng Li Gabriel Verret 《Journal of Pure and Applied Algebra》2019,223(3):1217-1226
Let Γ be a finite G-vertex-transitive digraph. The in-local action of is the permutation group induced by a vertex-stabiliser on the set of in-neighbours of the corresponding vertex. The out-local action is defined analogously. Note that and may not be isomorphic. We thus consider the problem of determining which pairs are possible. We prove some general results, but pay special attention to the case when and are both quasiprimitive. (Recall that a permutation group is quasiprimitive if each of its nontrivial normal subgroups is transitive.) Along the way, we prove a structural result about pairs of finite quasiprimitive groups of the same degree, one being (abstractly) isomorphic to a proper quotient of the other. 相似文献
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Lukas Prader 《Journal of Pure and Applied Algebra》2019,223(6):2371-2381
Let R be an affine domain of characteristic zero with finite quotients. We prove that a polynomial map over R is surjective if and only if it is surjective over , the completion of R with respect to , for every maximal ideal . In fact, the completions may be replaced by arbitrary subrings containing R. We use this result to yield a characterization of surjective polynomial maps, and remark that there does not exist a similar principle for injective polynomial maps. 相似文献
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Susumu Kubo 《Journal of Pure and Applied Algebra》2019,223(1):72-85
We consider tropical polynomials in nr variables, divided into n blocks of r variables, and especially r-symmetric tropical polynomials, which are invariant under the action of the symmetric group on the blocks. We define a set of basic r-symmetric tropical polynomials and show that the basic 2-symmetric tropical polynomials give coordinates on more efficiently than known polynomials. Moreover, we present special cases for where the basic polynomials separate orbits. 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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In the present paper, we give an answer to a question which is closely related to doubly warped product of Finsler metrics: ‘‘For each n, is there an n-dimensional Finsler manifold , admitting a non-constant smooth function f on M such that ?”. We relate the preceding mentioned condition to different concepts appeared and studied in Finsler geometry. We introduce and investigate the notion of a semi concurrent vector field on a Finsler manifold. We show that some special Finsler manifolds admitting such vector fields turn out to be Riemannian. We prove that Tachibana's characterization of Finsler manifolds admitting a concurrent vector field leads to Riemannian metrics. Various examples for conic Finsler spaces that admit semi-concurrent vector field are presented. 相似文献
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L. Emily Cowie Hans-Christian Herbig Daniel Herden Christopher Seaton 《Journal of Pure and Applied Algebra》2019,223(1):395-421
Let V be a finite-dimensional representation of the complex circle determined by a weight vector . We study the Hilbert series of the graded algebra of polynomial -invariants in terms of the weight vector a of the -action. In particular, we give explicit formulas for as well as the first four coefficients of the Laurent expansion of at . The naive formulas for these coefficients have removable singularities when weights pairwise coincide. Identifying these cancelations, the Laurent coefficients are expressed using partial Schur polynomials that are independently symmetric in two sets of variables. We similarly give an explicit formula for the a-invariant of in the case that this algebra is Gorenstein. As an application, we give methods to identify weight vectors with Gorenstein and non-Gorenstein invariant algebras. 相似文献
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We investigate a sharp Moser–Trudinger inequality which involves the anisotropic Dirichlet norm on for . Here F is convex and homogeneous of degree 1, and its polar represents a Finsler metric on . Under this anisotropic Dirichlet norm, we establish the Lions type concentration-compactness alternative. Then by using a blow-up procedure, we obtain the existence of extremal functions for this sharp geometric inequality. 相似文献
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Fangqin Ye 《Indagationes Mathematicae》2019,30(4):706-716
In this paper, we construct a class of weighted Bergman spaces such that they can generate in the sense of Möbius invariance. is also equal to the intersection of these spaces. Applying the relation between and these spaces, we show that the characterization via higher order derivatives does not hold for some of these weighted Bergman spaces. 相似文献
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《Indagationes Mathematicae》2019,30(5):930-942
We extend the notions of -convexity and -concavity for Banach ideals of measurable functions following an asymptotic procedure. We prove a representation theorem for the spaces satisfying both properties as the one that works for the classical case: each almost -convex and almost -concave space is order isomorphic to an almost--space. The class of almost--spaces contains, in particular, direct sums of (infinitely many) -spaces with different norms, that are not in general -convex – nor -concave –. We also analyze in this context the extension of the Maurey–Rosenthal factorization theorem that works for -concave operators acting in -convex spaces. In this way we provide factorization results that allow to deal with more general factorization spaces than -spaces. 相似文献