Ratushniak Sofiia
Publications
2026
25. Pratsiovytyi M.V., Ratushniak S.P., Vovk Yu.Yu., Goncharenko Ya.V. Fractal functions defined in terms of number representations in systems with a redundant alphabet, Mat. Stud. 65 (2) 2026, 115--126 https://doi.org/10.30970/ms.65.2.115-126
2025
24. Nikorak O.O., Ratushniak S.P. A Continuous projector from the binary representation of
numbers to the continuous $A_2$-representation, Bukovinian Math. Journal. 13, 2 (2025), 39–
46. DOI:https://doi.org/10.31861/bmj2025.02.05
23. Pratsiovytyi M., Lysenko I., Ratushniak S. A two-symbol system of encoding and some of its applications. Algebra and Discrete Mathematics. Vol. 40(2025). Number 1, pp.119-132. http://dx.doi.org/10.12958/adm2395
22. Pratsiovytyi, M. V., & Ratushniak, S. P. Singular distributions of random variables with independent digits of representation in numeral system with natural base and redundant alphabet. Matematychni Studii, 2025, 63(2), 199-209. https://doi.org/10.30970/ms.63.2.199-209
21.Pratsiovytyi O.M.; Ratushniak S.P. On the properties of a certain perturbed binary sequence. Bukovynian Mathematical Journal. 2025, 13 (1) https://doi.org/10.31861/bmj2025.01.10
20. Pratsiovytyi M., Baranovskyi O., Lysenko I., Ratushniak S. Fractal random variables defined by probability distributions of digits of their $G_2$-representation having two bases with different sings, Stochastic and Analytic Structures with Applications. Exploring the World of Mathematical Structures. Springer, Volume 1, P.166-182.
2024
19. Serhiiko D.M., Ratushniak S.P. Singular Functions Associated with Markovian Representation of Numbers, Bukovynian Mathematical Journal, 2024, Vol. 12, No. 2, pp. 211–219. (Category B journal) DOI:https://doi.org/10.31861/bmj2024.02.20.
18. Nazarchuk, V., Vaskevych, S. ³ Ratushniak, S. One continuum class of fractal functionsdefined in terms of $Q^*_s$-representation, Bukovinian Math. Journal.12, 2 (2024), 154–161. (Category B journal) DOI:https://doi.org/10.31861/bmj2024.02.14.
17. Pratsiovytyi M.V., Lysenko I.M., Ratushniak S.P., Tsokolenko O.A., Distribution of unit mass on one fractal self-similar web-type curve, Matematychni Studii, 2024, 62(1), pp. 21–30. DOI 10.30970/ms.62.1.21-30
16.Pratsiovytyi M.V., Lysenko I.M., Ratushniak S.P., Uncountable group of continuous transformations of unit segment preserving tails of $Q_2$-representation of numbers, Proceedings of the International Geometry Center, 2024, 17(2), pp. 133–142.
DOI:10.15673/pigc.v17i2.2755
2023 ð³ê
15.Pratsiovytyi M.V., Vovk Y.Y., Lysenko I.M., Ratushnyak S.P., Superpositions of functions with fractal properties, Journal of Mathematical Sciences (United States) (2023), 273(2), 248–270. DOI: 10.1007/s10958-023-06497-9
14.Pratsiovytyi M., Goncharenko Y., Lysenko I., Ratushniak S., Finite $A_2$-continued fractions in the problems of rational approximations of real numbers, Ukrainian Mathematical Journal, (2023) Vol. 75, no. 6, 972-983. DOI: 10.37863/umzh.v75i6.7413
13.Pratsovytyi M.V., Baranovskyi O. M., Bondarenko O.I., Ratushniak S.P., One class of continuous locally complicated functions related to infinite-symbol Φ-representation of numbers, Matematychni Studii, (2023), 59(2), 123-131. DOI: 10.30970/ms.59.2.123-131
12.Ratushniak S. A Nowhere Monotone Continuous Function Defined in Terms of Chain $A_2$-Representation of Numbers, Bukovynian Mathematical Journal., (2023) 11(1), 126-133.DOI: 10.31861/bmj2023.01.11
11.Ratushniak S.P. A Nowhere Monotone Continuous Function Defined in Terms of Chain A-Representation of Numbers, Bukovynian Mathematical Journal, (2023) Òîì 11, ¹ 2, 236-245.DOI: 10.31861/bmj2023.02.23
10.Pratsovytyi M., Bondarenko O., Lysenko I., Ratushniak S. Continuous Functions with Locally Complex and Fractal Properties Associated with Infinite-Symbol B-Representation of Numbers, Nonlinear Oscillations, (2023), ò. 26, No 3, 408–425.
2022 ð³ê
9.Pratsiovytyi M.V.,Ratushniak S.P.,Symonenko Yu.O.,Shpytuk D.S.Convolution of two singular distributions:classic Cantor type and random variable with independent nine digits,Bukovinian Math.Journal.10,2(2022),204-212. DOI: 10.31861/bmj2022.02.16
8.Pratsovytyi M.V., Bondarenko O.I., Ratushniak S.P., Franchuk K.V. Q-Representations of Real Numbers as a Generalization of Cantor Numeration Systems, Mohylianka Mathematical Journal., (2022) Ò. ¹ 5, 9-18. DOI: 10.18523/2617-7080520229-18
7.Pratsiovytyi M.V., Goncharenko Y.V., Lysenko I.M., Ratushniak S. P., Continued $A_2$-fractions and singular functions, Matematychni Studii, (2022), 58(1), 3-12.DOI: 10.30970/ms.58.1.3-12
2021 ð³ê
6.PratsiovytyiM.V.,GoncharenkoYa.V.,DmytrenkoS.O.,LysenkoI.M.,RatushniakS.P.About one class of functions with fractal properties, Bukovinian Math.Journal.6,1(2021),273-283. DOI: 10.31861/bmj2021.01.23
5.Pratsiovytyi M.V., Goncharenko Ya.V., Dyvliash S.P., Ratushniak S.P., Inversor of digits of $Q_2^*$-representation of numbers, Matematychni Studii, (2021), 55, 37–43. DOI: 10.30970/ms.55.1.37-43
4.Pratsiovytyi M.V., Ratushniak S.P., Continuous nowhere differentiable function with fractal properties defined in terms of $Q_2$-representation, Journal of Mathematical Sciences (United States), (2021), 258, no.5, 670–697. DOI: 10.1007/s10958-021-05573-2
3.Pratsiovytyi M.V., Goncharenko Ya.V., Lysenko I.M., Ratushniak S.P., Fractal functions of exponential type that is generated by the $Q_2^*$-representation of argument, Matematychni Studii, (2021) V.57, No 2, P.133–143. DOI:10.30970/ms.56.2.133-143
2019 ð³ê
2.Pratsiovytyi M.V., Ratushniak S.P., Properties and distributions of values of fractal functions related to $Q_2$-representations of real numbers, Theory of Probability and Mathematical Statistics. 99 (2019), 211-228. DOI: 10.1090/tpms/1091
25. Pratsiovytyi M.V., Ratushniak S.P., Vovk Yu.Yu., Goncharenko Ya.V. Fractal functions defined in terms of number representations in systems with a redundant alphabet, Mat. Stud. 65 (2) 2026, 115--126 https://doi.org/10.30970/ms.65.2.115-126
2025
24. Nikorak O.O., Ratushniak S.P. A Continuous projector from the binary representation of
numbers to the continuous $A_2$-representation, Bukovinian Math. Journal. 13, 2 (2025), 39–
46. DOI:https://doi.org/10.31861/bmj2025.02.05
23. Pratsiovytyi M., Lysenko I., Ratushniak S. A two-symbol system of encoding and some of its applications. Algebra and Discrete Mathematics. Vol. 40(2025). Number 1, pp.119-132. http://dx.doi.org/10.12958/adm2395
22. Pratsiovytyi, M. V., & Ratushniak, S. P. Singular distributions of random variables with independent digits of representation in numeral system with natural base and redundant alphabet. Matematychni Studii, 2025, 63(2), 199-209. https://doi.org/10.30970/ms.63.2.199-209
21.Pratsiovytyi O.M.; Ratushniak S.P. On the properties of a certain perturbed binary sequence. Bukovynian Mathematical Journal. 2025, 13 (1) https://doi.org/10.31861/bmj2025.01.10
20. Pratsiovytyi M., Baranovskyi O., Lysenko I., Ratushniak S. Fractal random variables defined by probability distributions of digits of their $G_2$-representation having two bases with different sings, Stochastic and Analytic Structures with Applications. Exploring the World of Mathematical Structures. Springer, Volume 1, P.166-182.
2024
19. Serhiiko D.M., Ratushniak S.P. Singular Functions Associated with Markovian Representation of Numbers, Bukovynian Mathematical Journal, 2024, Vol. 12, No. 2, pp. 211–219. (Category B journal) DOI:https://doi.org/10.31861/bmj2024.02.20.
18. Nazarchuk, V., Vaskevych, S. ³ Ratushniak, S. One continuum class of fractal functionsdefined in terms of $Q^*_s$-representation, Bukovinian Math. Journal.12, 2 (2024), 154–161. (Category B journal) DOI:https://doi.org/10.31861/bmj2024.02.14.
17. Pratsiovytyi M.V., Lysenko I.M., Ratushniak S.P., Tsokolenko O.A., Distribution of unit mass on one fractal self-similar web-type curve, Matematychni Studii, 2024, 62(1), pp. 21–30. DOI 10.30970/ms.62.1.21-30
16.Pratsiovytyi M.V., Lysenko I.M., Ratushniak S.P., Uncountable group of continuous transformations of unit segment preserving tails of $Q_2$-representation of numbers, Proceedings of the International Geometry Center, 2024, 17(2), pp. 133–142.
DOI:10.15673/pigc.v17i2.2755
2023 ð³ê
15.Pratsiovytyi M.V., Vovk Y.Y., Lysenko I.M., Ratushnyak S.P., Superpositions of functions with fractal properties, Journal of Mathematical Sciences (United States) (2023), 273(2), 248–270. DOI: 10.1007/s10958-023-06497-9
14.Pratsiovytyi M., Goncharenko Y., Lysenko I., Ratushniak S., Finite $A_2$-continued fractions in the problems of rational approximations of real numbers, Ukrainian Mathematical Journal, (2023) Vol. 75, no. 6, 972-983. DOI: 10.37863/umzh.v75i6.7413
13.Pratsovytyi M.V., Baranovskyi O. M., Bondarenko O.I., Ratushniak S.P., One class of continuous locally complicated functions related to infinite-symbol Φ-representation of numbers, Matematychni Studii, (2023), 59(2), 123-131. DOI: 10.30970/ms.59.2.123-131
12.Ratushniak S. A Nowhere Monotone Continuous Function Defined in Terms of Chain $A_2$-Representation of Numbers, Bukovynian Mathematical Journal., (2023) 11(1), 126-133.DOI: 10.31861/bmj2023.01.11
11.Ratushniak S.P. A Nowhere Monotone Continuous Function Defined in Terms of Chain A-Representation of Numbers, Bukovynian Mathematical Journal, (2023) Òîì 11, ¹ 2, 236-245.DOI: 10.31861/bmj2023.02.23
10.Pratsovytyi M., Bondarenko O., Lysenko I., Ratushniak S. Continuous Functions with Locally Complex and Fractal Properties Associated with Infinite-Symbol B-Representation of Numbers, Nonlinear Oscillations, (2023), ò. 26, No 3, 408–425.
2022 ð³ê
9.Pratsiovytyi M.V.,Ratushniak S.P.,Symonenko Yu.O.,Shpytuk D.S.Convolution of two singular distributions:classic Cantor type and random variable with independent nine digits,Bukovinian Math.Journal.10,2(2022),204-212. DOI: 10.31861/bmj2022.02.16
8.Pratsovytyi M.V., Bondarenko O.I., Ratushniak S.P., Franchuk K.V. Q-Representations of Real Numbers as a Generalization of Cantor Numeration Systems, Mohylianka Mathematical Journal., (2022) Ò. ¹ 5, 9-18. DOI: 10.18523/2617-7080520229-18
7.Pratsiovytyi M.V., Goncharenko Y.V., Lysenko I.M., Ratushniak S. P., Continued $A_2$-fractions and singular functions, Matematychni Studii, (2022), 58(1), 3-12.DOI: 10.30970/ms.58.1.3-12
2021 ð³ê
6.PratsiovytyiM.V.,GoncharenkoYa.V.,DmytrenkoS.O.,LysenkoI.M.,RatushniakS.P.About one class of functions with fractal properties, Bukovinian Math.Journal.6,1(2021),273-283. DOI: 10.31861/bmj2021.01.23
5.Pratsiovytyi M.V., Goncharenko Ya.V., Dyvliash S.P., Ratushniak S.P., Inversor of digits of $Q_2^*$-representation of numbers, Matematychni Studii, (2021), 55, 37–43. DOI: 10.30970/ms.55.1.37-43
4.Pratsiovytyi M.V., Ratushniak S.P., Continuous nowhere differentiable function with fractal properties defined in terms of $Q_2$-representation, Journal of Mathematical Sciences (United States), (2021), 258, no.5, 670–697. DOI: 10.1007/s10958-021-05573-2
3.Pratsiovytyi M.V., Goncharenko Ya.V., Lysenko I.M., Ratushniak S.P., Fractal functions of exponential type that is generated by the $Q_2^*$-representation of argument, Matematychni Studii, (2021) V.57, No 2, P.133–143. DOI:10.30970/ms.56.2.133-143
2019 ð³ê
2.Pratsiovytyi M.V., Ratushniak S.P., Properties and distributions of values of fractal functions related to $Q_2$-representations of real numbers, Theory of Probability and Mathematical Statistics. 99 (2019), 211-228. DOI: 10.1090/tpms/1091