Group of continuous transformations of real interval preserving tails of G₂-representation of numbers
In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs g₀ < 1 and g₁ = g₀ − 1. Transformations (bijections of the set to itself) of interval [0, g₀] preserving tails of this representation of numbers are studied. We prove constructively th...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2020 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188505 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Group of continuous transformations of real interval preserving tails of G₂-representation of numbers / M.V. Pratsiovytyi, I.M. Lysenko, Yu.P. Maslova // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 99–108. — Бібліогр.: 10 назв. — англ. |
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Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. 2023-03-03T16:00:12Z 2023-03-03T16:00:12Z 2020 Group of continuous transformations of real interval preserving tails of G₂-representation of numbers / M.V. Pratsiovytyi, I.M. Lysenko, Yu.P. Maslova // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 99–108. — Бібліогр.: 10 назв. — англ. 1726-3255 DOI:10.12958/adm1498 2010 MSC: 11H71, 26A46, 93B17 https://nasplib.isofts.kiev.ua/handle/123456789/188505 In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs g₀ < 1 and g₁ = g₀ − 1. Transformations (bijections of the set to itself) of interval [0, g₀] preserving tails of this representation of numbers are studied. We prove constructively that the set of all continuous transformations from this class with respect to composition of functions forms an infinite non-abelian group such that increasing transformations form its proper subgroup. This group is a proper subgroup of the group of transformations preserving frequencies of digits of representations of numbers. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Group of continuous transformations of real interval preserving tails of G₂-representation of numbers Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers |
| spellingShingle |
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. |
| title_short |
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers |
| title_full |
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers |
| title_fullStr |
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers |
| title_full_unstemmed |
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers |
| title_sort |
group of continuous transformations of real interval preserving tails of g₂-representation of numbers |
| author |
Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. |
| author_facet |
Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. |
| publishDate |
2020 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs g₀ < 1 and g₁ = g₀ − 1. Transformations (bijections of the set to itself) of interval [0, g₀] preserving tails of this representation of numbers are studied. We prove constructively that the set of all continuous transformations from this class with respect to composition of functions forms an infinite non-abelian group such that increasing transformations form its proper subgroup. This group is a proper subgroup of the group of transformations preserving frequencies of digits of representations of numbers.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188505 |
| citation_txt |
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers / M.V. Pratsiovytyi, I.M. Lysenko, Yu.P. Maslova // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 99–108. — Бібліогр.: 10 назв. — англ. |
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