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Let be a directed set without maximal element, be an infinite semigroup and be the collection of all functions from into . It is shown that for a commutative semigroup , is a -set with respect to if and only if is a -set with respect to . We investigate the Central Sets Theorem for arbitrary semigroups. In fact the Central Sets Theorem is stated with respect to for arbitrary semigroups. 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
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Hai Q. Dinh Xiaoqiang Wang Hongwei Liu Songsak Sriboonchitta 《Discrete Mathematics》2019,342(11):3062-3078
Let be an odd prime, and be a nonzero element of the finite field . The -constacyclic codes of length over are classified as the ideals of quotient ring in terms of their generator polynomials. Based on these generator polynomials, the symbol-pair distances of all such -constacyclic codes of length are obtained in this paper. As an application, all MDS symbol-pair constacyclic codes of length over are established, which produce many new MDS symbol-pair codes with good parameters. 相似文献
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In this paper, several classes of complete permutation polynomials with the form over are proposed by the AGW criterion and determining the number of solutions of some equations. Our results also enrich constructions of known permutation polynomials. 相似文献
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Hai Q. Dinh Xiaoqiang Wang Hongwei Liu Songsak Sriboonchitta 《Discrete Mathematics》2019,342(5):1456-1470
Let be an odd prime, , be positive integers, be nonzero elements of the finite field such that . In this paper, we show that, for any positive integer , the Hamming distances of all repeated-root -constacyclic codes of length can be determined by those of certain simple-root -constacyclic codes of length . Using this result, Hamming distances of all constacyclic codes of length are obtained. As an application, we identify all MDS -constacyclic codes of length . 相似文献
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In this paper, we will study Ciani curves in characteristic , in particular their standard forms . It is well-known that any Ciani curve is a non-hyperelliptic curve of genus 3, and its Jacobian variety is isogenous to the product of three elliptic curves. As a main result, we will show that if C is superspecial, then belong to and C is maximal or minimal over . Moreover, in this case we will provide a simple criterion in terms of that tells whether C is maximal (resp. minimal) over . 相似文献
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