Displaying similar documents to “A moment sequence in the q-world”

Algebra of Polynomially Bounded Sequences and Negligible Functions

Hiroyuki Okazaki (2015)

Formalized Mathematics

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In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation...

A q-analogue of complete monotonicity

Anna Kula (2008)

Colloquium Mathematicae

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The aim of this paper is to give a q-analogue for complete monotonicity. We apply a classical characterization of Hausdorff moment sequences in terms of positive definiteness and complete monotonicity, adapted to the q-situation. The method due to Maserick and Szafraniec that does not need moments turns out to be useful. A definition of a q-moment sequence appears as a by-product.

On the correlation of families of pseudorandom sequences of k symbols

Kit-Ho Mak, Alexandru Zaharescu (2016)

Acta Arithmetica

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In an earlier paper Gyarmati introduced the notion of f-correlation for families of binary pseudorandom sequences as a measure of randomness in the family. In this paper we generalize the f-correlation to families of pseudorandom sequences of k symbols and study its properties.

Irreducible Sobol' sequences in prime power bases

Henri Faure, Christiane Lemieux (2016)

Acta Arithmetica

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Sobol' sequences are a popular family of low-discrepancy sequences, in spite of requiring primitive polynomials instead of irreducible ones in later constructions by Niederreiter and Tezuka. We introduce a generalization of Sobol' sequences that removes this shortcoming and that we believe has the potential of becoming useful for practical applications. Indeed, these sequences preserve two important properties of the original construction proposed by Sobol': their generating matrices...