Van der Corput sequences towards general (0,1)–sequences in base b

Henri Faure

Displaying similar documents to “Van der Corput sequences towards general (0,1)–sequences in base b”

Weak multipliers for generalized van der Corput sequences

Florian Pausinger (2012)

Journal de Théorie des Nombres de Bordeaux

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Generalized van der Corput sequences are onedimensional, infinite sequences in the unit interval. They are generated from permutations in integer base $b$ and are the building blocks of the multi-dimensional Halton sequences. Motivated by recent progress of Atanassov on the uniform distribution behavior of Halton sequences, we study, among others, permutations of the form $P (i) = a i (mod b)$ for coprime integers $a$ and $b$ . We show that multipliers $a$ that either divide $b - 1$ or $b + 1$ generate van der Corput sequences...

Basic Properties and Concept of Selected Subsequence of Zero Based Finite Sequences

Yatsuka Nakamura, Hisashi Ito (2008)

Formalized Mathematics

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Here, we develop the theory of zero based finite sequences, which are sometimes, more useful in applications than normal one based finite sequences. The fundamental function Sgm is introduced as well as in case of normal finite sequences and other notions are also introduced. However, many theorems are a modification of old theorems of normal finite sequences, they are basically important and are necessary for applications. A new concept of selected subsequence is introduced. This concept...

Double Sequences and Limits

Noboru Endou, Hiroyuki Okazaki, Yasunari Shidama (2013)

Formalized Mathematics

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Double sequences are important extension of the ordinary notion of a sequence. In this article we formalized three types of limits of double sequences and the theory of these limits.

Dyadic diaphony of digital sequences

Friedrich Pillichshammer (2007)

Journal de Théorie des Nombres de Bordeaux

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The dyadic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit cube. In this paper we give formulae for the dyadic diaphony of digital $(0, s)$ -sequences over $ℤ_{2}$ , $s = 1, 2$ . These formulae show that for fixed $s \in {1, 2}$ , the dyadic diaphony has the same values for any digital $(0, s)$ -sequence. For $s = 1$ , it follows that the dyadic diaphony and the diaphony of special digital $(0, 1)$ -sequences are up to a constant the same. We give the exact asymptotic order of the dyadic diaphony...

A criterion for non-automaticity of sequences.

Schlage-Puchta, Jan-Christoph (2003)

Journal of Integer Sequences [electronic only]

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On some remarkable properties of the two-dimensional Hammersley point set in base 2

Peter Kritzer (2006)

Journal de Théorie des Nombres de Bordeaux

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We study a special class of $(0, m, 2)$ -nets in base 2. In particular, we are concerned with the two-dimensional Hammersley net that plays a special role among these since we prove that it is the worst distributed with respect to the star discrepancy. By showing this, we also improve an existing upper bound for the star discrepancy of digital $(0, m, 2)$ -nets over $ℤ_{2}$ . Moreover, we show that nets with very low star discrepancy can be obtained by transforming the Hammersley point set in a suitable way. ...