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Algebra and Discrete Mathematics, 2016, Volume 22, Issue 1, Pages 102–115 (Mi adm577)  

This article is cited in 2 scientific papers (total in 2 papers)

RESEARCH ARTICLE

Transformations of (0,1](0,1] preserving tails of ΔμΔμ-representation of numbers

Tetiana M. Isaieva, Mykola V. Pratsiovytyi

Institute of Physics and Mathematics, National Pedagogical Mykhailo Drahomanov University, 9 Pyrohova St., Kyiv, 01601, Ukraine
Full-text PDF (353 kB) Citations (2)
References:
Abstract: Let μ(0,1)μ(0,1) be a given parameter, ν1μν1μ. We consider ΔμΔμ-representation of numbers x=Δμa1a2anx=Δμa1a2an belonging to (0,1](0,1] based on their expansion in alternating series or finite sum in the form:
x=n(BnBn)Δμa1a2an,
where Bn=νa1+a3++a2n11μa2+a4++a2n2, Bn=νa1+a3++a2n11μa2+a4++a2n, aiN. This representation has an infinite alphabet {1,2,}, zero redundancy and N-self-similar geometry.
In the paper, classes of continuous strictly increasing functions preserving “tails” of Δμ-representation of numbers are constructed. Using these functions we construct also continuous transformations of (0,1]. We prove that the set of all such transformations is infinite and forms non-commutative group together with an composition operation.
Keywords: Δμ-representation, cylinder, tail set, function preserving “tails” of Δμ-representation of numbers, continuous transformation of (0,1] preserving “tails” of Δμ-representation of numbers, group of transformations.
Received: 10.04.2016
Revised: 10.08.2016
Bibliographic databases:
Document Type: Article
MSC: 11H71, 26A46, 93B17
Language: English
Citation: Tetiana M. Isaieva, Mykola V. Pratsiovytyi, “Transformations of (0,1] preserving tails of Δμ-representation of numbers”, Algebra Discrete Math., 22:1 (2016), 102–115
Citation in format AMSBIB
\Bibitem{IsaPra16}
\by Tetiana~M.~Isaieva, Mykola~V.~Pratsiovytyi
\paper Transformations of $(0,1]$ preserving tails of~$\Delta^{\mu}$-representation of numbers
\jour Algebra Discrete Math.
\yr 2016
\vol 22
\issue 1
\pages 102--115
\mathnet{http://mi.mathnet.ru/adm577}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3573547}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000392708800007}
Linking options:
  • https://www.mathnet.ru/eng/adm577
  • https://www.mathnet.ru/eng/adm/v22/i1/p102
  • This publication is cited in the following 2 articles:
    1. M. V. Pratsiovytyi, I. M. Lysenko, Yu. P. Maslova, “Group of continuous transformations of real interval preserving tails of G2-representation of numbers”, Algebra Discrete Math., 29:1 (2020), 99–108  mathnet  crossref
    2. M. Pratsiovytyi, A. Chuikov, “Continuous distributions whose functions preserve tails of an a-continued fraction representation of numbers”, Random Operators Stoch. Equ., 27:3 (2019), 199–206  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Algebra and Discrete Mathematics
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