BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Mykola Pratsiovytyi (Mykhailo Drahomanov Ukrainian State Universit
 y\; Institute of Mathematics\, Natl. Acad. Sci. Ukraine)
DTSTART:20250123T133000Z
DTEND:20250123T150000Z
DTSTAMP:20260423T024533Z
UID:fran/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/59/">A 
 class of Tribin functions (from idea and interest to motives and fantasies
 )</a>\nby Mykola Pratsiovytyi (Mykhailo Drahomanov Ukrainian State Univers
 ity\; Institute of Mathematics\, Natl. Acad. Sci. Ukraine) as part of Се
 мінар з фрактального аналізу / Fractal analysis s
 eminar\n\n\nAbstract\nThis talk is devoted to the continuum class of conti
 nuous nowhere monotonic functions that generalize non-differentiable Bush 
 and Wunderlich functions\, continuous Cantor projectors\, Tribin functions
 \, etc.\n\nWe consider continuous function $f$ defined by equality\n\\[\n 
  f(x = \\Delta^{s^*}_{\\alpha_1\\alpha_2\\ldots\\alpha_n\\ldots})\n  = \\D
 elta^{2^*}_{b_1b_2\\ldots b_n\\ldots}\,\n\\]\nwhere\n\\[\n  b_1 = \\begin{
 cases}\n    0 & \\text{if $\\alpha_1 \\in A_0 \\neq \\emptyset$}\, \\\\\n 
    1 & \\text{if $\\alpha_1 \\in A \\setminus A_0 \\equiv A_1 \\neq \\empt
 yset$}\,\n  \\end{cases}\n  \\qquad\n  b_{n+1} = \\begin{cases}\n    b_n  
    & \\text{if $\\alpha_{n+1} = \\alpha_n$}\, \\\\\n    1 - b_n & \\text{i
 f $\\alpha_{n+1} \\neq \\alpha_n$}\,\n  \\end{cases}\n\\]\n$A = \\{ 0\, 1\
 , \\ldots\, s - 1 \\}$ is an alphabet\, $s \\geq 3$\, $A_0$ is a subset of
  the alphabet\, $\\Delta^{s^*}_{\\alpha_1\\alpha_2\\ldots\\alpha_n\\ldots}
 $ is an $s$-symbol representation of a number $x \\in [0\, 1]$ that is top
 ologically equivalent to classical $s$-adic representation and $\\Delta^{2
 ^*}_{b_1b_2\\ldots b_n\\ldots}$ is a two-symbol representation that is top
 ologically equivalent to classical binary representation.\n\nIn the talk\,
  we analyze structural\, variational\, integral and differential\, topolog
 ical and metric\, and fractal properties of the function $f$.\n
LOCATION:https://researchseminars.org/talk/fran/59/
END:VEVENT
END:VCALENDAR