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...
Збережено в:
| Дата: | 2020 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
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 |
| Теги: |
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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| Резюме: | 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. |
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