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We first give an example of a rigid structure of computable dimension 2 such that the unique isomorphism between two non-computably isomorphic computable copies has Turing degree strictly below , and not above . This gives a first example of a computable structure with a degree of categoricity that does not belong to an interval of the form for any computable ordinal α. We then extend the technique to produce a rigid structure of computable dimension 3 such that if , , and are the degrees of isomorphisms between distinct representatives of the three computable equivalence classes, then each . The resulting structure is an example of a structure that has a degree of categoricity, but not strongly. 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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We study ground states of two-component Bose–Einstein condensates (BEC) with trapping potentials in , where the intraspecies interaction and the interspecies interaction ?β are both attractive, , , and β are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated -critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as , where () is fixed and w is the unique positive solution of in . The semi-trivial limit behavior of ground states is tackled in the companion paper [12]. 相似文献
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Let be a finite field of cardinality , which is a finite chain ring, and is an odd positive integer. For any , an explicit representation for the dual code of any -constacyclic code over of length is given. And some dual codes of -constacyclic codes over of length 14 are constructed. For the case of , all distinct self-dual -constacyclic codes over of length are determined. 相似文献
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《Discrete Mathematics》2020,343(10):112010
Let be the -partite multigraph in which each part has size , where two vertices in the same part or different parts are joined by exactly edges or edges, respectively. It is proved that there exists a maximal set of edge-disjoint Hamilton cycles in for , the upper bound being best possible. The results proved make use of the method of amalgamations. 相似文献
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In the papers (Benoumhani 1996;1997), Benoumhani defined two polynomials and . Then, he defined and to be the polynomials satisfying and . In this paper, we give a combinatorial interpretation of the coefficients of and prove a symmetry of the coefficients, i.e., . We give a combinatorial interpretation of and prove that is a polynomial in with non-negative integer coefficients. We also prove that if then all coefficients of except the coefficient of are non-negative integers. For all , the coefficient of in is , and when some other coefficients of are also negative. 相似文献
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《Discrete Mathematics》2022,345(10):113000
Let be a finite field with elements and , where n, m and k are positive integers with and . In this paper, motivated by a recent work of Li, Xiong and Zeng (Li et al. (2021) [12]), we further study the boomerang uniformity of by using similar ideas and carrying out particular techniques in solving equations over finite fields. As a consequence, we generalize Li, Xiong and Zeng's result from the case of m being odd and to that of both and being odd. 相似文献
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We study elliptic surfaces corresponding to an equation of the specific type , defined over the finite field for a prime power . It is shown that if defines a curve that is maximal over then the rank of the group of sections defined over on the elliptic surface is determined in terms of elementary properties of the rational function . Similar results are shown for elliptic surfaces given by using prime powers and curves . Finally, for each of the forms used here, existence of curves with the property that they are maximal over is discussed, as well as various examples. 相似文献
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Very recently, Tu et al. presented a sufficient condition on , see Theorem 1.1, such that is a class of permutation polynomials over with and m odd. In this present paper, we prove that the sufficient condition is also necessary. 相似文献
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We consider subordinators in the domain of attraction at 0 of a stable subordinator (where ); thus, with the property that , the tail function of the canonical measure of , is regularly varying of index as . We also analyse the boundary case, , when is slowly varying at 0. When , we show that converges in distribution, as , to the random variable . This latter random variable, as a function of , converges in distribution as to the inverse of an exponential random variable. We prove these convergences, also generalised to functional versions (convergence in ), and to trimmed versions, whereby a fixed number of its largest jumps up to a specified time are subtracted from the process. The case produces convergence to an extremal process constructed from ordered jumps of a Cauchy subordinator. Our results generalise random walk and stable process results of Darling, Cressie, Kasahara, Kotani and Watanabe. 相似文献