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SUMMARY:Mykola Pratsiovytyi (Mykhailo Drahomanov Ukrainian State Universit
 y\; Institute of Mathematics\, Natl. Acad. Sci. Ukraine)\, Sofiia Ratushni
 ak (Institute of Mathematics\, Natl. Acad. Sci. Ukraine\; Mykhailo Drahoma
 nov Ukrainian State University)\, and Volodymyr Yelahin (Institute of Math
 ematics\, Natl. Acad. Sci. Ukraine)
DTSTART:20240215T133000Z
DTEND:20240215T150000Z
DTSTAMP:20260423T021606Z
UID:fran/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/49/">Un
 countability (continuum cardinality) of the group of continuous transforma
 tions of interval that preserve tails of two-symbol representation of numb
 ers</a>\nby Mykola Pratsiovytyi (Mykhailo Drahomanov Ukrainian State Unive
 rsity\; Institute of Mathematics\, Natl. Acad. Sci. Ukraine)\, Sofiia Ratu
 shniak (Institute of Mathematics\, Natl. Acad. Sci. Ukraine\; Mykhailo Dra
 homanov Ukrainian State University)\, and Volodymyr Yelahin (Institute of 
 Mathematics\, Natl. Acad. Sci. Ukraine) as part of Семінар з фр
 актального аналізу / Fractal analysis seminar\n\n\nAbstra
 ct\nWe consider continuous transformations that preserve tails\nof represe
 ntations\, namely\, of classic binary\, negabinary\,\n$Q_2$-representation
 \, $G_2$-representation and other. Solutions of\nsome class of equations r
 elated to left and right shift operators are\ngiven. For arbitrary number 
 from the unit interval\, we construct the\ncorresponding continuous transf
 ormation preserving tails. This is a\ncrucial point to prove that the grou
 p of continuous transformations\npreserving tails is uncountable.\n
LOCATION:https://researchseminars.org/talk/fran/49/
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