Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers
We describe the geometry of representation of numbers belonging to (0, 1] by the positive Lüroth series, i.e., special series whose terms are reciprocal of positive integers. We establish the geometrical meaning of digits, give properties of cylinders, semicylinders and tail sets, metric relations;...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2012 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2012
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152235 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers / Yu. Zhykharyeva, M. Pratsiovytyi // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 145–160. — Бібліогр.: 18 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-152235 |
|---|---|
| record_format |
dspace |
| spelling |
Zhykharyeva, Yu. Pratsiovytyi, M. 2019-06-09T06:04:06Z 2019-06-09T06:04:06Z 2012 Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers / Yu. Zhykharyeva, M. Pratsiovytyi // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 145–160. — Бібліогр.: 18 назв. — англ. 1726-3255 2010 MSC:11K55. https://nasplib.isofts.kiev.ua/handle/123456789/152235 We describe the geometry of representation of numbers belonging to (0, 1] by the positive Lüroth series, i.e., special series whose terms are reciprocal of positive integers. We establish the geometrical meaning of digits, give properties of cylinders, semicylinders and tail sets, metric relations; prove topological, metric and fractal properties of sets of numbers with restrictions on use of “digits”; show that for determination of Hausdorff-Besicovitch dimension of Borel set it is enough to use connected unions of cylindrical sets of the same rank. Some applications of L-representation to probabilistic theory of numbers are also considered. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| spellingShingle |
Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers Zhykharyeva, Yu. Pratsiovytyi, M. |
| title_short |
Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| title_full |
Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| title_fullStr |
Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| title_full_unstemmed |
Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| title_sort |
expansions of numbers in positive lüroth series and their applications to metric, probabilistic and fractal theories of numbers |
| author |
Zhykharyeva, Yu. Pratsiovytyi, M. |
| author_facet |
Zhykharyeva, Yu. Pratsiovytyi, M. |
| publishDate |
2012 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
We describe the geometry of representation of numbers belonging to (0, 1] by the positive Lüroth series, i.e., special series whose terms are reciprocal of positive integers. We establish the geometrical meaning of digits, give properties of cylinders, semicylinders and tail sets, metric relations; prove topological, metric and fractal properties of sets of numbers with restrictions on use of “digits”; show that for determination of Hausdorff-Besicovitch dimension of Borel set it is enough to use connected unions of cylindrical sets of the same rank. Some applications of L-representation to probabilistic theory of numbers are also considered.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/152235 |
| citation_txt |
Expansions of numbers in positive Lüroth series and their applications to metric, probabilistic and fractal theories of numbers / Yu. Zhykharyeva, M. Pratsiovytyi // Algebra and Discrete Mathematics. — 2012. — Vol. 14, № 1. — С. 145–160. — Бібліогр.: 18 назв. — англ. |
| work_keys_str_mv |
AT zhykharyevayu expansionsofnumbersinpositivelurothseriesandtheirapplicationstometricprobabilisticandfractaltheoriesofnumbers AT pratsiovytyim expansionsofnumbersinpositivelurothseriesandtheirapplicationstometricprobabilisticandfractaltheoriesofnumbers |
| first_indexed |
2025-12-07T16:01:58Z |
| last_indexed |
2025-12-07T16:01:58Z |
| _version_ |
1850865948548923392 |