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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| Дата: | 2020 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1885052023-03-04T01:27:15Z Group of continuous transformations of real interval preserving tails of G₂-representation of numbers Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. 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. 2020 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/188505 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. |
| spellingShingle |
Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. Group of continuous transformations of real interval preserving tails of G₂-representation of numbers Algebra and Discrete Mathematics |
| author_facet |
Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. |
| author_sort |
Pratsiovytyi, M.V. |
| title |
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2020 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
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