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 constructivel...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2020 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188505 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862624848602202112 |
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| author | Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. |
| author_facet | Pratsiovytyi, M.V. Lysenko, I.M. Maslova, Yu.P. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T13:32:44Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188505 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T13:32:44Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| 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 | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188505 |
| work_keys_str_mv | AT pratsiovytyimv groupofcontinuoustransformationsofrealintervalpreservingtailsofg2representationofnumbers AT lysenkoim groupofcontinuoustransformationsofrealintervalpreservingtailsofg2representationofnumbers AT maslovayup groupofcontinuoustransformationsofrealintervalpreservingtailsofg2representationofnumbers |