Dyadic Diaphony
نویسندگان
چکیده
1. Introduction. Diaphony (see Zinterhof [13] and Kuipers and Nieder-reiter [6, Exercise 5.27, p. 162]) is a numerical quantity that measures the irregularity of the distribution of sequences in the s-dimensional unit cube [0, 1[
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Dyadic diaphony of digital sequences par
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 Z2, s = 1, 2. These formulae show that for fixed s ∈ {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 diaph...
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In this paper, we estimate the star-diaphony and the diaphony of the Roth sequence and the Zaremba sequence using their L 2-discrepancy formula given by Halton and Zaremba (see 3]), and White (see 17]). The optimal estimates and the exact asymptotic behaviours of the star-diaphony and the diaphony of both sequences are given. Moreover, the exact asymptotic behaviours of the star-diaphony are th...
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The b-adic diaphony is a quantitative measure for the irregularity of distribution of a sequence in the unit interval. In this paper we show that the b-adic diaphony of digital (0, 1)-sequences satisfies a central limit theorem. Further we show a relation between the functions χ δj b and ψb, which appear in the formulas for the classical diaphony and the b-adic diaphony of digital (0, 1)-NUT-se...
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In the following we investigate the limit distribution of the Diaphony created by the Mehler kernel. The classical Diaphony was introduced by Zinterhof [5]. In [6] a Diaphony has been defined for reproducing kernel Hilbert spaces over an abstract set E. The limit distribution of the classical Diaphony has been investigated by H. Leeb [3].
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