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Pratsiovytyi, M. V.; Lysenko, I. M.; Maslova, Yu. P.; Trebenko, O. O.

\(G\)-representation of real numbers and some of its applications. (English. Ukrainian original) Zbl 1532.11106

J. Math. Sci., New York 277, No. 2, 298-310 (2023); translation from Neliniĭni Kolyvannya 25, No. 4, 377-387 (2022).
MSC:  11K55
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\textit{M. V. Pratsiovytyi} et al., J. Math. Sci., New York 277, No. 2, 298--310 (2023; Zbl 1532.11106); translation from Neliniĭni Kolyvannya 25, No. 4, 377--387 (2022)
Full Text: DOI
Pratsiovytyi, M.; Goncharenko, Ya.; Lysenko, I.; Ratushnyak, S.

Finite \(A_2\)-continued fractions in the problems of rational approximations of real numbers. (English. Ukrainian original) Zbl 1537.11108

Ukr. Math. J. 75, No. 6, 972-983 (2023); translation from Ukr. Mat. Zh. 75, No. 6, 849-858 (2023).
Reviewer: Takao Komatsu (Hangzhou)
MSC:  11K50 28A80 11K55
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\textit{M. Pratsiovytyi} et al., Ukr. Math. J. 75, No. 6, 972--983 (2023; Zbl 1537.11108); translation from Ukr. Mat. Zh. 75, No. 6, 849--858 (2023)
Full Text: DOI
Pratsiovytyi, M. V.; Vovk, Yu. Yu.; Lysenko, I. M.; Ratushnyak, S. P.

Superpositions of functions with fractal properties. (English. Ukrainian original) Zbl 07723990

J. Math. Sci., New York 273, No. 2, 248-270 (2023); translation from Neliniĭni Kolyvannya 24, No. 4, 498-517 (2021).
MSC:  28Axx 26Axx 11Kxx
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\textit{M. V. Pratsiovytyi} et al., J. Math. Sci., New York 273, No. 2, 248--270 (2023; Zbl 07723990); translation from Neliniĭni Kolyvannya 24, No. 4, 498--517 (2021)
Full Text: DOI
Artemovych, O. D. (ed.); Bezushchak, O. O. (ed.); Dixon, M. R. (ed.); Drushlyak, M. G. (ed.); Grigorchuk, R. I. (ed.); Kurdachenko, L. A. (ed.); Lukashova, T. D. (ed.); Oliynyk, A. S. (ed.); Oliynyk, B. V. (ed.); Otal, J. (ed.); Petravchuk, A. P. (ed.); Pratsiovytyi, M. V. (ed.); Pypka, O. O. (ed.); Subbotin, I. Ya. (ed.); Tylyshchak, O. A. (ed.); Zatorsky, R. A. (ed.); Zhuchok, A. V. (ed.); Zhuchok, Yu. V. (ed.)

Mykola M. Semko (dedicated to the 65th Birthday). (English) Zbl 07710060

Algebra Discrete Math. 34, No. 1, C-F (2022).
MSC:  00Bxx 16-XX 20-XX
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\textit{O. D. Artemovych} (ed.) et al., Algebra Discrete Math. 34, No. 1, C-F (2022; Zbl 07710060)
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Pratsiovytyi, M. V.; Goncharenko, Ya. V.; Lysenko, I. M.; Svynchuk, O. V.

On one class of singular nowhere monotone functions. (English. Ukrainian original) Zbl 1504.26012

J. Math. Sci., New York 263, No. 2, 268-281 (2022); translation from Neliniĭni Kolyvannya 23, No. 4, 502-512 (2020).
Reviewer: Peter Massopust (München)
MSC:  26A27 26A30
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\textit{M. V. Pratsiovytyi} et al., J. Math. Sci., New York 263, No. 2, 268--281 (2022; Zbl 1504.26012); translation from Neliniĭni Kolyvannya 23, No. 4, 502--512 (2020)
Full Text: DOI
Pratsiovytyi, M. V.; Ratushniak, S. P.

Continuous nowhere differentiable function with fractal properties defined in terms of \(Q_2\)-representation. (English. Russian original) Zbl 1482.26002

J. Math. Sci., New York 258, No. 5, 670-697 (2021); translation from Neliniĭni Kolyvannya 23, No. 2, 231-252 (2020).
MSC:  26A27 28A80
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\textit{M. V. Pratsiovytyi} and \textit{S. P. Ratushniak}, J. Math. Sci., New York 258, No. 5, 670--697 (2021; Zbl 1482.26002); translation from Neliniĭni Kolyvannya 23, No. 2, 231--252 (2020)
Full Text: DOI
Lukovs’kiy, I. O.; Makarov, V. L.; Perestyuk, M. O.; Boichuk, O. A.; Parasyuk, I. O.; Antonyuk, O. V.; Tkachenko, V. I.; Petryshyn, R. I.; Prats’ovytyi, M. V.; Stanzhyts’kyi, O. M.; Ronto, M. I.

Academician Anatolii Mykhailovych Samoilenko (02.01.1938–04.12.2020). (English. Ukrainian original) Zbl 1470.01027

Ukr. Math. J. 73, No. 1, 1-5 (2021); translation from Ukr. Mat. Zh. 73, No. 1, 3-8 (2021).
MSC:  01A70
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\textit{I. O. Lukovs'kiy} et al., Ukr. Math. J. 73, No. 1, 1--5 (2021; Zbl 1470.01027); translation from Ukr. Mat. Zh. 73, No. 1, 3--8 (2021)
Full Text: DOI
Pratsiovytyi, M. V.; Ratushniak, S. P.

Properties and distributions of values of fractal functions related to \(Q_2\)-representations of real numbers. (English. Ukrainian original) Zbl 1453.28014

Theory Probab. Math. Stat. 99, 211-228 (2019); translation from Teor. Jmovirn. Mat. Stat. 99, 187-202 (2018).
MSC:  28A80 26A30 60E05
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\textit{M. V. Pratsiovytyi} and \textit{S. P. Ratushniak}, Theory Probab. Math. Stat. 99, 211--228 (2019; Zbl 1453.28014); translation from Teor. Jmovirn. Mat. Stat. 99, 187--202 (2018)
Full Text: DOI
Prats’ovytyi, M. V.; Svynchuk, O. V.

Spread of values of a Cantor-type fractal continuous nonmonotone function. (English. Ukrainian original) Zbl 1459.26005

J. Math. Sci., New York 240, No. 3, 342-357 (2019); translation from Neliniĭni Kolyvannya 21, No. 1, 116-130 (2018).
Reviewer: Antonio Linero Bas (Murcia)
MSC:  26A30 26A45 28A99 60E05
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\textit{M. V. Prats'ovytyi} and \textit{O. V. Svynchuk}, J. Math. Sci., New York 240, No. 3, 342--357 (2019; Zbl 1459.26005); translation from Neliniĭni Kolyvannya 21, No. 1, 116--130 (2018)
Full Text: DOI
Markitan, V. P.; Prats’ovytyi, M. V.; Savchenko, I. O.

Superfractality of the set of incomplete sums of one positive series. (English. Ukrainian original) Zbl 1477.40002

Ukr. Math. J. 70, No. 10, 1619-1634 (2019); translation from Ukr. Mat. Zh. 70, No. 10, 1403-1416 (2018).
Reviewer: Chryssoula Ganatsiou (Larissa)
MSC:  40A05 28A80 60E05
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\textit{V. P. Markitan} et al., Ukr. Math. J. 70, No. 10, 1619--1634 (2019; Zbl 1477.40002); translation from Ukr. Mat. Zh. 70, No. 10, 1403--1416 (2018)
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Zamrii, Irina V.; Prats’ovytyi, M. V.

Singularity of the digit inversor for the \(Q_3\)-representation of the fractional part of a real number, its fractal and integral properties. (English. Ukrainian original) Zbl 1342.28025

J. Math. Sci., New York 215, No. 3, 323-340 (2016); translation from Neliniĭni Kolyvannya 18, No. 1, 55-70 (2015).
MSC:  28A80
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\textit{I. V. Zamrii} and \textit{M. V. Prats'ovytyi}, J. Math. Sci., New York 215, No. 3, 323--340 (2016; Zbl 1342.28025); translation from Neliniĭni Kolyvannya 18, No. 1, 55--70 (2015)
Full Text: DOI
Prats’ovytyĭ, M. V.; Khvorostina, Yu. V.

A random variable whose digits in the \(\widetilde {L}\)-representation have the Markovian dependence. (English. Ukrainian original) Zbl 1331.60029

Theory Probab. Math. Stat. 91, 157-168 (2015); translation from Teor. Jmovirn. Mat. Stat. 91, 143-153 (2014).
MSC:  60E05
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\textit{M. V. Prats'ovytyĭ} and \textit{Yu. V. Khvorostina}, Theory Probab. Math. Stat. 91, 157--168 (2015; Zbl 1331.60029); translation from Teor. Jmovirn. Mat. Stat. 91, 143--153 (2014)
Full Text: DOI
Prats’ovytyĭ, M. V.; Savchenko, I. O.

The distributions of random incomplete sums of a series with positive terms satisfying the property of non-linear homogeneity. (English. Ukrainian original) Zbl 1346.60053

Theory Probab. Math. Stat. 91, 145-155 (2015); translation from Teor. Jmovirn. Mat. Stat. 91, 133-142 (2014).
MSC:  60G30 60G50 28A78 28A80 11K55
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\textit{M. V. Prats'ovytyĭ} and \textit{I. O. Savchenko}, Theory Probab. Math. Stat. 91, 145--155 (2015; Zbl 1346.60053); translation from Teor. Jmovirn. Mat. Stat. 91, 133--142 (2014)
Full Text: DOI
Klymchuk, S. O.; Makarchuk, O. P.; Prats’ovytyi, M. V.

Frequency of a digit in the representation of a number and the asymptotic mean value of the digits. (English. Ukrainian original) Zbl 1314.60035

Ukr. Math. J. 66, No. 3, 336-346 (2014); translation from Ukr. Mat. Zh. 66, No. 3, 302-310 (2014).
MSC:  60C05 28A80 11A63
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\textit{S. O. Klymchuk} et al., Ukr. Math. J. 66, No. 3, 336--346 (2014; Zbl 1314.60035); translation from Ukr. Mat. Zh. 66, No. 3, 302--310 (2014)
Full Text: DOI
Prats’ovytyi, M. V.; Makarchuk, O. P.

Distribution of random variable represented by a binary fraction with three identically distributed redundant digits. (English. Ukrainian original) Zbl 1320.60043

Ukr. Math. J. 66, No. 1, 86-98 (2014); translation from Ukr. Mat. Zh. 66, No. 1, 79-88 (2014).
MSC:  60E05
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\textit{M. V. Prats'ovytyi} and \textit{O. P. Makarchuk}, Ukr. Math. J. 66, No. 1, 86--98 (2014; Zbl 1320.60043); translation from Ukr. Mat. Zh. 66, No. 1, 79--88 (2014)
Full Text: DOI
Prats’ovytyi, M. V.; Kalashnikov, A. V.

Self-affine singular and nowhere monotone functions related to the \(Q\)-representation of real numbers. (English. Ukrainian original) Zbl 1297.26007

Ukr. Math. J. 65, No. 3, 448-462 (2013); translation from Ukr. Mat. Zh. 65, No. 3, 405-417 (2013).
MSC:  26A30
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\textit{M. V. Prats'ovytyi} and \textit{A. V. Kalashnikov}, Ukr. Math. J. 65, No. 3, 448--462 (2013; Zbl 1297.26007); translation from Ukr. Mat. Zh. 65, No. 3, 405--417 (2013)
Full Text: DOI
Prats’ovytyĭ, M. V.; Kyurchev, D. V.

Singularity of the distribution of a random variable represented by an \(A_2\)-continued fraction with independent elements. (Ukrainian, English) Zbl 1224.60021

Teor. Jmovirn. Mat. Stat. 81, 139-154 (2009); translation in Theory Probab. Math. Stat. 81, 159-175 (2010).
Reviewer: Mikhail P. Moklyachuk (Kyïv)
MSC:  60E05 11K55 11K50 26A30 28A80
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\textit{M. V. Prats'ovytyĭ} and \textit{D. V. Kyurchev}, Teor. Ĭmovirn. Mat. Stat. 81, 139--154 (2009; Zbl 1224.60021); translation in Theory Probab. Math. Stat. 81, 159--175 (2010)
Full Text: DOI
Dmytrenko, S. O.; Kyurchev, D. V.; Prats’ovytyi, M. V.

\(A_2\)-continued fraction representation of real numbers and its geometry. (Ukrainian, English) Zbl 1224.11066

Ukr. Mat. Zh. 61, No. 4, 452-463 (2009); translation in Ukr. Math. J. 61, No. 4, 541-555 (2009).
Reviewer: A. N. Kochubei (Kyïv)
MSC:  11K50 28A80 60D05
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\textit{S. O. Dmytrenko} et al., Ukr. Mat. Zh. 61, No. 4, 452--463 (2009; Zbl 1224.11066); translation in Ukr. Math. J. 61, No. 4, 541--555 (2009)
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Baranovskyi, Oleksandr; Pratsiovytyi, Mykola; Torbin, Grygoriy

On Lebesgue measure and fractal dimension of sets related to the first Ostrogradsky expansion. (English) Zbl 1335.11065

Laurinčikas, Antanas (ed.) et al., Voronoï’s impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22–28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine (ISBN 978-966-02-4891-5/pbk; 978-966-02-4890-8/set). 191-194 (2008).
MSC:  11K55 11K50
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\textit{O. Baranovskyi} et al., in: Voronoï's impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22--28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine. 191--194 (2008; Zbl 1335.11065)
Pratsiovytyi, Mykola; Kyurchev, Dmytro

On \(A_2\)-continued fraction expansion. (English) Zbl 1335.11064

Laurinčikas, Antanas (ed.) et al., Voronoï’s impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22–28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine (ISBN 978-966-02-4891-5/pbk; 978-966-02-4890-8/set). 181-190 (2008).
MSC:  11K50 11A55
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\textit{M. Pratsiovytyi} and \textit{D. Kyurchev}, in: Voronoï's impact on modern science. Book 4, Volume 1. Proceedings of the 4th international conference on analytic number theory and spatial tessellations, Kyiv, Ukraine, September 22--28, 2008. Kyiv: Institute of Mathematics, NAS of Ukraine. 181--190 (2008; Zbl 1335.11064)
Goncharenko, Ya. V.; Prats’ovytyj, M. V.; Torbin, G. M.

Fractal properties of some Bernoulli convolutions. (Ukrainian, English) Zbl 1224.60082

Teor. Jmovirn. Mat. Stat. 79, 34-49 (2008); translation in Theory Probab. Math. Stat. 79, 39-55 (2009).
Reviewer: Mikhail P. Moklyachuk (Kyïv)
MSC:  60G30 11K55 28A80
PDFBibTeX XMLCite
\textit{Ya. V. Goncharenko} et al., Teor. Ĭmovirn. Mat. Stat. 79, 34--49 (2008; Zbl 1224.60082); translation in Theory Probab. Math. Stat. 79, 39--55 (2009)
Full Text: DOI
Baranovs’kyj, O. M.; Prats’ovytyj, M. V.; Torbin, H. M.

Topological and metric properties of sets of real numbers with conditions on their expansions in Ostrogradskii series. (Ukrainian, English) Zbl 1150.11027

Ukr. Mat. Zh. 59, No. 9, 1155-1168 (2007); translation in Ukr. Math. J. 59, No. 9, 1281-1299 (2007).
Reviewer: Anatoly N. Kochubei (Kyïv)
MSC:  11K55 11A67 11K50 60C05
PDFBibTeX XMLCite
\textit{O. M. Baranovs'kyj} et al., Ukr. Mat. Zh. 59, No. 9, 1155--1168 (2007; Zbl 1150.11027); translation in Ukr. Math. J. 59, No. 9, 1281--1299 (2007)
Full Text: DOI
Prats’ovytyj, M. V.; Baranovs’kyj, O. M.

Properties of distributions of random variables with independent differences of sequential elements of Ostrogradsky series. (Ukrainian, English) Zbl 1074.60014

Teor. Jmovirn. Mat. Stat. 70, 131-143 (2004); translation in Theory Probab. Math. Stat. 70, 147-160 (2005).
MSC:  60E05 26A30 11A67 11K55
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\textit{M. V. Prats'ovytyj} and \textit{O. M. Baranovs'kyj}, Teor. Ĭmovirn. Mat. Stat. 70, 131--143 (2005; Zbl 1074.60014); translation in Theory Probab. Math. Stat. 70, 147--160 (2005)
Prats’ovytyj, M. V.; Torbin, G. M.

Fractal geometry and transformations preserving the Hausdorff-Besicovitch dimension. (Ukrainian) Zbl 1098.60003

Ukrainian mathematical congress – 2001, Kiev, Ukraine, August 21–23, 2001. Proceedings. Section 2. Dynamical analysis. Kyïv: Instytut Matematyky NAN Ukraïny (ISBN 966-02-3009-5). 77-93 (2003).
MSC:  60A10 28A78 60E05 28A80
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\textit{M. V. Prats'ovytyj} and \textit{G. M. Torbin}, in: Ukraïns'kyj matematychnyj kongres -- 2001. Pratsi. Sektsiya 2. Dynamichni systemy. Kyïv: Instytut Matematyky NAN Ukraïny. 77--93 (2003; Zbl 1098.60003)
Prats’ovytyj, M. V.; Baranovs’kyj, O. M.

Application of the Ostrogradsky series for the analytical representation of distributions of random variables and random mappings. (Ukrainian) Zbl 1097.60002

Ukrainian mathematical congress – 2001, Kiev, Ukraine, August 21–23, 2001. Proceedings. Section 2. Dynamical analysis. Kyïv: Instytut Matematyky NAN Ukraïny (ISBN 966-02-3009-5). 59-76 (2003).
MSC:  60E05 26A30 11A67 11K55
PDFBibTeX XMLCite
\textit{M. V. Prats'ovytyj} and \textit{O. M. Baranovs'kyj}, in: Ukraïns'kyj matematychnyj kongres -- 2001. Pratsi. Sektsiya 2. Dynamichni systemy. Kyïv: Instytut Matematyky NAN Ukraïny. 59--76 (2003; Zbl 1097.60002)
Prats’ovytyj, M. V.; Kosopl’otkina, O. V.

The fractal properties of the spectrum of the superposition of singular distribution functions. (Ukrainian, English) Zbl 1050.60013

Teor. Jmovirn. Mat. Stat. 67, 122-129 (2002); translation in Theory Probab. Math. Stat. 67, 135-144 (2003).
Reviewer: N. M. Zinchenko (Kyïv)
MSC:  60E99
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\textit{M. V. Prats'ovytyj} and \textit{O. V. Kosopl'otkina}, Teor. Ĭmovirn. Mat. Stat. 67, 122--129 (2002; Zbl 1050.60013); translation in Theory Probab. Math. Stat. 67, 135--144 (2003)
Goncharenko, Ya. V.; Prats’ovytyj, M. V.; Torbin, G. M.

Topological metric and fractal properties of the convolution of two singular distributions with independent binary digits. (Ukrainian, English) Zbl 1051.60013

Teor. Jmovirn. Mat. Stat. 67, 9-19 (2002); translation in Theory Probab. Math. Stat. 67, 11-22 (2003).
Reviewer: N. M. Zinchenko (Kyïv)
MSC:  60E05 28A80
PDFBibTeX XMLCite
\textit{Ya. V. Goncharenko} et al., Teor. Ĭmovirn. Mat. Stat. 67, 9--19 (2002; Zbl 1051.60013); translation in Theory Probab. Math. Stat. 67, 11--22 (2003)
Goncharenko, Ya. V.; Prats’ovytyj, M. V.; Torbin, G. M.

Fractal properties of the set of points of non-differentiability of absolutely continuous and singular distribution functions. (Ukrainian, English) Zbl 1027.60005

Teor. Jmovirn. Mat. Stat. 65, 25-32 (2000); translation in Theory Probab. Math. Stat. 65, 27-35 (2002).
Reviewer: Mikhail Moklyachuk (Kyïv)
MSC:  60E05 28A80
PDFBibTeX XMLCite
\textit{Ya. V. Goncharenko} et al., Teor. Ĭmovirn. Mat. Stat. 65, 25--32 (2000; Zbl 1027.60005); translation in Theory Probab. Math. Stat. 65, 27--35 (2002)

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