共查询到20条相似文献,搜索用时 15 毫秒
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We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献
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We give an elementary proof for Lewis Bowen’s theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our methods also show that for all compact groups K and every free product Γ of infinite amenable groups, the factor Γ?KΓ/K of the Bernoulli action Γ?KΓ by the diagonal K-action is isomorphic with a Bernoulli action of Γ. 相似文献
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We analyze the extent to which a quantum universal enveloping algebra of a Kac–Moody algebra g is defined by multidegrees of its defining relations. To this end, we consider a class of character Hopf algebras defined by the same number of defining relations of the same degrees as the Kac–Moody algebra g. We demonstrate that if the generalized Cartan matrix A of g is connected then the algebraic structure, up to a finite number of exceptional cases, is defined by just one “continuous” parameter q related to a symmetrization of A, and one “discrete” parameter m related to the modular symmetrizations of A. The Hopf algebra structure is defined by n(n−1)/2 additional “continuous” parameters. We also consider the exceptional cases for Cartan matrices of finite or affine types in more detail, establishing the number of exceptional parameter values in terms of the Fibonacci sequence. 相似文献
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A group-word w is called concise if whenever the set of w-values in a group G is finite it always follows that the verbal subgroup w(G) is finite. More generally, a word w is said to be concise in a class of groups X if whenever the set of w-values is finite for a group G∈X, it always follows that w(G) is finite. P. Hall asked whether every word is concise. Due to Ivanov the answer to this problem is known to be negative. Dan Segal asked whether every word is concise in the class of residually finite groups. In this direction we prove that if w is a multilinear commutator and q is a prime-power, then the word wq is indeed concise in the class of residually finite groups. Further, we show that in the case where w=γk the word wq is boundedly concise in the class of residually finite groups. It remains unknown whether the word wq is actually concise in the class of all groups. 相似文献
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The oscillation of solutions of f″+Af=0 is discussed by focusing on four separate situations. In the complex case A is assumed to be either analytic in the unit disc D or entire, while in the real case A is continuous either on (−1,1) or on (0,∞). In all situations A is expected to grow beyond bounds that ensure finite oscillation for all (non-trivial) solutions, and the separation between distinct zeros of solutions is considered. 相似文献
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We exhibit an example of a smooth affine threefold A over a field of characteristic 0 for which there exist non-trivial 2-torsion elements in the Euler class group E(A) vanishing in the weak Euler class group E0(A). This gives a positive answer to a question of the first author and Raja Sridharan. 相似文献
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In 1994 Dias da Silva and Hamidoune solved a long-standing open problem of Erd?s and Heilbronn using the structure of cyclic spaces for derivatives on Grassmannians and the representation theory of symmetric groups. They proved that for any subset A of the p-element group Z/pZ (where p is a prime), at least min{p,m|A|−m2+1} different elements of the group can be written as the sum of m different elements of A. In this note we present an easily accessible simplified version of their proof for the case m=2, and explain how the method can be applied to obtain the corresponding inverse theorem. 相似文献
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By means of a certain module V and its tensor powers in a finite tensor category, we study a question of whether the depth of a Hopf subalgebra R of a finite-dimensional Hopf algebra H is finite. The module V is the counit representation induced from R to H, which is then a generalized permutation module, as well as a module coalgebra. We show that if in the subalgebra pair either Hopf algebra has finite representation type, or V is either semisimple with R∗ pointed, projective, or its tensor powers satisfy a Burnside ring formula over a finite set of Hopf subalgebras including R, then the depth of R in H is finite. One assigns a nonnegative integer depth to V, or any other H-module, by comparing the truncated tensor algebras of V in a finite tensor category and so obtains upper and lower bounds for depth of a Hopf subalgebra. For example, a relative Hopf restricted module has depth 1, and a permutation module of a corefree subgroup has depth less than the number of values of its character. 相似文献
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We extend some known results on radicals and prime ideals from polynomial rings and Laurent polynomial rings to Z-graded rings, i.e, rings graded by the additive group of integers. The main of them concerns the Brown–McCoy radical G and the radical S, which for a given ring A is defined as the intersection of prime ideals I of A such that A/I is a ring with a large center. The studies are related to some open problems on the radicals G and S of polynomial rings and situated in the context of Koethe’s problem. 相似文献
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In this note we study distance-regular graphs with a small number of vertices compared to the valency. We show that for a given α>2, there are finitely many distance-regular graphs Γ with valency k, diameter D≥3 and v vertices satisfying v≤αk unless (D=3 and Γ is imprimitive) or (D=4 and Γ is antipodal and bipartite). We also show, as a consequence of this result, that there are finitely many distance-regular graphs with valency k≥3, diameter D≥3 and c2≥εk for a given 0<ε<1 unless (D=3 and Γ is imprimitive) or (D=4 and Γ is antipodal and bipartite). 相似文献
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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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Mustapha Chellali Teresa W. Haynes Stephen T. Hedetniemi Alice McRae 《Discrete Applied Mathematics》2013
A subset S⊆V in a graph G=(V,E) is a [j,k]-set if, for every vertex v∈V?S, j≤|N(v)∩S|≤k for non-negative integers j and k, that is, every vertex v∈V?S is adjacent to at least j but not more than k vertices in S. In this paper, we focus on small j and k, and relate the concept of [j,k]-sets to a host of other concepts in domination theory, including perfect domination, efficient domination, nearly perfect sets, 2-packings, and k-dependent sets. We also determine bounds on the cardinality of minimum [1, 2]-sets, and investigate extremal graphs achieving these bounds. This study has implications for restrained domination as well. Using a result for [1, 3]-sets, we show that, for any grid graph G, the restrained domination number is equal to the domination number of G. 相似文献