On the (WGb,φ; α)− diaphony of the nets of Halton- Zaremba constructed over finite groups
Journal
Italian Journal of Pure and Applied Mathematics
Date Issued
2023-10
Author(s)
Dimitrievska Ristovska, Vesna
Grozdanov, Vassil
Abstract
In the present paper, the authors introduce an arithmetic based on finite groups with respect to arbitrary bijections. This algebraic background is used to construct the function system W_Gb,φb of the Walsh functions over the set G_b of groups with respect to the set φb of bijections. The developed algebraic base is also used to introduce a wide class of two-dimensional nets Gb,φbZ κ,µ b,ν of type of Halton-Zaremba. Four concrete nets of this class are constructed and graphically illustrated. The so-called (W_Gb,φ; α)−diaphony is applied as an appropriate tool for studying the nets of the introduced class. An exact formula for the (W_Gb,φ; α)−diaphony of the nets of class Gb,φbZ κ,µ b,ν is presented. This formula allows us to show the influence of the vector α on the exact order of the (W_Gb,φ; α)−diaphony of these nets.
File(s)![Thumbnail Image]()
Loading...
Name
it jou nasha stat 2023.pdf
Description
Italian journal 2023-50, pp. 1-26
Size
5.06 MB
Format
Adobe PDF
Checksum
(MD5):fd9a12463c2165002dc3a6dc64ae77fe