Research Interests Infinite-Dimensional Topology
Fractal Geometry
Fractal Measures
Idempotent Measures
Fractal Geometry
Fractal Measures
Idempotent Measures
Scientific Training December 2022 January 2023
Ivano-Frankivsk National University of Oil and Gas, Ivano-Frankivsk
Department of Computer Systems and Networks
Advisor: Prof. Stepan Melnychuk
April 2017 June 2017
University of Rzeszow, Rzeszow, POL
Department of Functional Analysis
Advisor: Prof. Mykhailo Zarichnyi
October 2013 November 2013
Ivan Franko Lviv National University, Lviv
Department of Geometry and Topology
Advisor: Prof. Mykhailo Zarichnyi
Ivano-Frankivsk National University of Oil and Gas, Ivano-Frankivsk
Department of Computer Systems and Networks
Advisor: Prof. Stepan Melnychuk
April 2017 June 2017
University of Rzeszow, Rzeszow, POL
Department of Functional Analysis
Advisor: Prof. Mykhailo Zarichnyi
October 2013 November 2013
Ivan Franko Lviv National University, Lviv
Department of Geometry and Topology
Advisor: Prof. Mykhailo Zarichnyi
Main Publications Books:
- Natalia Mazurenko. Fractal Geometry, Ivano-Frankivsk, 2010, 65 p. (in Ukrainian)
[image] 
[read on issuu] - Mazurenko N., Mykytsey O., Cherkovskyi T. Workbook in Discrete Math, Ivano-Frankivsk, 2016, 81 p. (in Ukrainian) [image] [read on issuu]
- Mazurenko N., Sobkovych R. School Geometry in Problems,
Ivano-Frankivsk, 2018, 281 p. (in Ukrainian)[image] [read on issuu] - Mazurenko N., Sobkovych R. School Algebra in Problems. Part I,
Ivano-Frankivsk, 2019, 332 p. (in Ukrainian)[image] [read on issuu]
Articles:
- Zarichnyi M., Mazurenko N. (In)homogeneous invariant compact convex sets of probability measures, Proc. of Int.Geom.Center Vol., 12 (2019), no. 4, 60–68.
[download] - Zarichnyi M., Mazurenko N. Invariant Idempotent Measures, Carpathian Math. Publ., 2018, 10(1), 172–178. [download]
- Zarichnyi M., Mazurenko N. Idempotent Ultrametric Fractals, Visnyk Lviv Univ. Ser. Mech-Math., 2014. [download]
- Banakh T., Mazurenko N. The topology of systems of hyperspaces determined by dimension functions, Topology, 48 (2009), 43-53. [download]
- Mazurenko N. Uncountable Absorbing Systems related to the Hausdorff Dimension, Mat. Stud., 31 (2009), no 2, 195-203. [download]
- Mazurenko N. Поглинаючі системи у функціональному просторі, пов’язані з виміром Гаусдорфа, Мат. Студії, 23 (2005), № 2, 207-216. [download]
- Mazurenko N. Absorbing systems in the Hilbert cube related to Hausdorff and covering dimension, Мат. методи та фіз.-мех. поля, 47 (2004), № 4, 18-26.
[download] - Mazurenko N. Топологія гіперпросторів континуумів заданого виміру Гаусдор-фа в скінченновимірному кубі, Наук. Вісник Чернівецького унів. Математика, 228 (2004), 60-65. [download]
- Mazurenko N. Absorbing sets related to Hausdorff dimension, Visnyk Lviv Univ. Ser. Mech-Math. 61 (2003), 121-128. [download]
- Mazurenko N. On invariant inclusion hyperspaces for iterated function systems, Mat. Stud., 17 (2002), no. 2, 211-214. [download]
- Мазуренко Н., Никифорчин O. Спектральний аналіз формальних граматик, Вісник Прикарпатського університету. Математика. Фізика. Хімія, Вип.1, 1999. С.87-97. [download]
Conference Talks- Invariant ∗-measures, International scientific online conference “Algebraic and geometric methods of analysis”, May 29 – June 1, 2023, Odesa, Ukraine. (with M. Zarichnyi)
- On (in)homogeneous fractals generated by *-measures, International online conference “Current trends in abstract and applied analysis”, May 12-15, 2022, Ivano-Frankivsk, Ukraine. (with Kh. Sukhorukova, M. Zarichnyi)
- Hyperspaces of convex sets related to idempotent mathematics, International scientific online conference “Algebraic and geometric methods of analysis”, May 25-28, 2021, Odesa, Ukraine. (with M. Zarichnyi)
- Spaces of probability measures and box dimension, International scientific online conference “Algebraic and geometric methods of analysis”, May 26-30, 2020, Odesa, Ukraine. (with M. Zarichnyi)
- Invariant idempotent measures in topological spaces, Intern. Conf. In Functional Analysis dedicated to the 125th ann. of Stefan Banach, September 2017, Lviv, Ukraine. (with M. Zarichnyi)
- On ultrametric fractals generated by max-plus closed convex sets of idempotent measures, Intern. Conf. “Modern advances in Geometry and Topology”, September 2016, Kharkiv, Ukraine.
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