Ph.D., associate professor |

Makhnei Oleksandr – associate professor, was born in 1977, graduated from the Vasyl Stefanyk Precarpathian National University in 1999, speciality “Mathematics”. He studied in postgraduate school at the National University “Lviv Polytechnic”. In 2005 he defended his Ph.D. dissertation on “Singular quasidifferential operators on a finite interval”. In the years 2003-2008 – assistant professor of mathematical analysis at the Vasyl Stefanyk Precarpathian National University. Since 2008 – associate professor of differential equations and applied mathematics.

He provides teaching standard and special courses “Systems of computer mathematics”, “Mathematical modeling”, “Algorithms and data structures”, “Simulation modeling”, “System programming”, “Web programming”, “Web technologies”, “Differential and integral equations”, “LaTeX publishing system”, “Optimal project management”, “Computer modeling and optimization”, “Computer tools for mathematical modeling”, “Applied problems of graph theory”.

Research interests: boundary value problems for singular differential and qusidifferential equations.

E-mail: oleksandr.makhnei@pnu.edu.ua, makhney1@yahoo.com

Oleksandr Makhnei was born at February 22, 1977 in Ivano-Frankivsk (Ukraine).

In 1994-1999 he studied at the specialty “mathematics” of Faculty of Physics and Mathematics of Vasyl Stefanyk Precarpathian University. He received a master’s degree with honors, qualification – the mathematician, teacher. Theme of master thesis – “Integral and quasidifferential equations of Volterra-Stieltjes type”, scientific adviser – professor Roman Tatsii (Lviv, Ukraine).

In 1999-2002 he studied in postgraduate school at the National University “Lviv Polytechnic” (Department of Structural Mechanics).

In 2003-2005 he worked as an assistant at the Department of Theoretical and Experimental Physics of Vasyl Stefanyk Precarpathian National University.

In March 4, 2005 he defended his thesis for the degree Ph. D. in a specialized academic council of Odessa I. I. Mechnikov National University. Theme of the Ph. D. dissertation – “Singular quasidifferential operators on a finite interval”. Scientific adviser – Doctor of Physical and Mathematical Sciences, Professor Roman Tatsii (Lviv, Ukraine).

In 2005-2008 he worked as an assistant at the Department of Mathematical Analysis and Applied Mathematics Vasyl Stefanyk Precarpathian National University. Since 2008 he works as associate professor at the Department of Differential Equations and Applied Mathematics Vasyl Stefanyk Precarpathian National University.

In 2011 he received the academic status of associate professor of differential equations and applied mathematics.

In 2010 he passed the scientific training at the department of differential equations of Ivan Franko National University of Lviv. In 2015 he passed the scientific training at the department of mathematics of Ivano-Frankivsk National Technical University of Oil and Gas. In 2020 he passed the scientific training at the department of applied mathematics and information technologies of Yuriy Fedkovich Chernivtsi National University.

**ORCID ID:** orcid.org/0000-0003-3048-5910

**Publications**

There are published over fifty scientific papers, one monograph, two textbooks on the recommendation of the Ministry of Education and Science of Ukraine, two manuals on the recommendation of the Scientific Council of the Faculty, a collection of tests, guidelines. Below is a list of publications and electronic versions of some of them.

**Monography:**

1. Makhnei O., Tatsii R. Singular quasidifferential operators on a finite interval. Ivano-Frankivsk : Simyk, 2012. 360 p. (in Ukrainian)

**Textbooks:**

1. Golota V. Probability Theory and Mathematical Statistics. Computer workshop / Golota V., Novosyadlyi S., Makhnei O. Ivano-Frankivsk : Prospect Precarpathian Univ, 2006. 104 p.

2. Goy T., Makhnei O. Differential and Integral Equations. Ivano-Frankivsk : Simyk, 2012. 356 p. (in Ukrainian, for the direction of “Physics”, “Applied Physics”)

3. Goy T., Makhnei O. Differential equations. Ivano-Frankivsk : Simyk, 2012. 352 p. (in Ukrainian, for the direction of “Computer Science”, “Applied Mathematics”)

4. Makhnei O., Goy T. Mathematical software of automation of applied research: Tutorial. Ivano-Frankivsk : Simyk, 2013. 304 p. (in Ukrainian)

5. Collection of tests for applicants on the educational qualification of Specialist in “Applied Mathematics” / [P. Vasylyshyn, V. Gavrilko, T. Hoi et al.]; Ed. R. Zatorsky, O. Makhnei. Ivano-Frankivsk : Golinei, 2014. 204 p. (in Ukrainian)

6. Makhnei O. Mathematical modeling: Tutorial. Ivano-Frankivsk : Suprun V., 2015. 372 p. (in Ukrainian)

7. Goy T., Makhnei O. Workshop on differential equations. Part 1. Differential equations of the first order. Ivano-Frankivsk: Golinei, 2017. 116 p. (in Ukrainian)

8. Goy T., Makhnei O., Negrych M., Simotiuk M. Workshop on differential equations. Part 2. Differential equations of higher orders, systems of differential equations. Ivano-Frankivsk: Golinei, 2019. 176 p. (in Ukrainian)

9. Goy T., Makhnei O. Differential and integral equations. View. 3rd, ex. Ivano-Frankivsk: Vasyl Stefanyk Precarpathian National University, 2021. 248 p. (in Ukrainian)

10. Goy T. P., Makhney O. V. Differential equations. Ivano-Frankivsk: Vasyl Stefanyk Precarpathian National University, 2021. 357 p. (in Ukrainian)

11. Makhnei O. Workshop on mathematical modeling. Ivano-Frankivsk: Golinei, 2022. 172 p. (in Ukrainian)

**Guidelines:**

1. Makhnei O. Laboratory workshop in Maple: guidelines for laboratory classes. Ivano-Frankivsk : CIT Vasyl Stefanyk Precarpathian National University, 2010. 32 p. (in Ukrainian)

2. Makhnei O. Laboratory workshop on simulation modeling in GPSS: guidelines for laboratory classes. Ivano-Frankivsk : CIT Vasyl Stefanyk Precarpathian National University, 2010. 36 p. (in Ukrainian)

3. Makhnei O. Laboratory workshop on simulation modeling in GPSS. Part 2: guidelines for laboratory classes. Ivano-Frankivsk: Golinei, 2012. 32 p. (in Ukrainian)

4. Makhnei O. Mathematical modeling: guidelines. Ivano-Frankivsk : Golinei, 2014. 36 p. (in Ukrainian)

5. Makhnei O. Laboratory workshop on mathematical software: methodical recommendations for conducting laboratory classes. Ivano-Frankivsk : Golinei, 2016. 32 p. (in Ukrainian)

6. Makhnei O. LaTeX workshop: methodical recommendations for independent work of students. Ivano-Frankivsk : Golinei, 2018. 36 p. (in Ukrainian)

7. Makhnei O. Laboratory workshop on simulation modeling in GPSS. Part 1: guidelines for laboratory classes. Ivano-Frankivsk : Golinei, 2020. 40 p. (in Ukrainian)

8. Makhnei O. Laboratory workshop on system programming: guidelines for conducting laboratory classes. Ivano-Frankivsk: Golinei, 2022. 28 p. (in Ukrainian)

9. Mazurenko V., Makhney O. The theory of automatic control: laboratory workshop on the educational discipline. Ivano-Frankivsk: Golinei, 2023. 32 p. (in Ukrainian)

**Scientific articles:**

1. Makhnei O. On properties of solutions of a generalized qusidifferential second-order equation / Makhnei O. // Bulletin of the National University “Lviv Polytechnic”. Applied Mathematics. – 2000. – No. 407. – P. 77-81. (in Ukrainian)

2. Makhnei O. Asymptotics of eigenvalues and eigenfunctions of a singular differential operator on a finite interval / Makhnei O. // Mathematical methods and physical and mechanical fields. – 2001. – Vol. 44, No. 2. – P. 17-25. (in Ukrainian)

3. Makhnei O. Green function of a singular differential operator and its properties / Maknnei O. // Mathematical Studies. – 2002. – Vol. 18, No. 2. – P. 147-156. (in Ukrainian)

4. Makhnei O. Generalized nonself-adjoint operator of the second order on the semi-axis / Makhnei O., Tatsii R. // Bulletin of Lviv University. Mechanical and Mathematical Series. – 2002. – Vol. 60. – P. 92-101. (in Ukrainian)

5. Makhnei O. Asymptotics of eigenvalues and eigenfunctions of a singular quasidifferential operator on a finite interval / Makhnei O., Tatsii R. // Differential equations. – 2003. – Vol. 39, No. 8. – P. 1098-1105. (in Russian)

6. Makhnei O. Eigenfunctions expansions for a singular quasidifferential operator with simple eigenvalues / Makhnei O., Tatsii R. // Mathematical methods and physical and mechanical fields. – 2004. – Vol. 47, No. 3. – P. 16-27. (in Ukrainian)

7. Makhnei O. The structure of Cauchy function of a vector quasidifferential equation / Makhnei O., Tatsii R. // Mathematical Studies. – 2004. – Vol. 21, No. 2. – P. 221-224.

8. Makhnei O. Eigenfunctions expansions for a singular differential operator / Makhnei O. // Mathematical methods and physical and mechanical fields. – 2004. – Vol. 47, No. 4. – P. 88-94. (in Ukrainian)

9. Makhnei O. Asymptotics of solutions of a singular quasidifferential equation on a finite interval / Makhnei O. // Proceedings of the National University “Lviv Polytechnic”, Physics and mathematics. – 2004. – No. 518. – P. 38-51. (in Ukrainian)

10. Makhnei O. Eigenfunctions expansions for a singular quasidifferential operator with simple eigenvalues / Makhnei O., Tatsii R. // Dyfferential equations. – 2006. – Vol. 42, No. 2. – P. 193-201.

11. Makhnei O. Green Function of a boundary value problem for a vector singular differential equation / Makhnei O. // Bulletin of Precarpathian University. Math. Physics. – 2007. – Vol. 3. – P. 38-45. (in Ukrainian)

12. Makhnei O. Asymptotics of eigenvalues of boundary value problem for a vector singular quasidifferential equation / Makhnei O., Tatsii R. // Bulletin of Odessa National University. Mat. and mech. – 2007. – Vol. 12, No. 7. – P. 110-120. (in Ukrainian)

13. Makhnei O. Asymptotic behavior of eigenvalues and eigenfunctions of a boundary value problem for a singular quasidifferential equation / Makhnei O., Tatsii R. // Mathematical Studies. – 2008. – Vol. 29, No. 2. – P. 165-174. (in Ukrainian)

14. Makhnei O. Green function of a boundary value problem for a vector quasidifferential equation with measures and its properties / Makhnei O., Tatsii R. // Collection of scientific papers: Actual problems of mathematics. – Grodno, 2008. – P. 120-133. (in Russian)

15. Makhnei O. Asymptotics of the eigenvalues of a boundary value problem for a vector singular differential equation / Makhnei O., Tatsii R. // Differential Equations. – 2009. – Vol. 45, No 6. – P. 805-813.

16. Makhnei O. Green function of a boundary value problem for a singular quasidifferential equation / Makhnei O. // Bulletin of the National University “Lviv Polytechnic”, Physics and mathematics. – 2009. – No. 643. – P. 64-72. (in Ukrainian)

17. Makhnei O. Asymptotics of fundamental system of solutions of a differential equation with measures on the semiaxis / Makhnei O. // Bulletin of the National University “Lviv Polytechnic”, Physics and mathematics. – 2010. – No. 687. – P. 82-90.

18. Makhnei O. Eigenfunctions expansions for a vector singular differential operator with simple eigenvalues / Makhnei O., Tatsii R. // Carpathian mathematical publications. – 2011. – Vol. 3, No. 1. – P. 94-105. (in Ukrainian)

19. Makhnei O. Green function of a boundary value problem for a vector singular quasidifferential equation / Makhnei O., Tatsii R. // Bulletin of the National University “Lviv Polytechnic”, Physics and mathematics. – 2011. – No. 718. – P. 70-77.

20. Makhnei O. Asymptotics of a fundamental solution system for a quasidifferential equation with measures on the semiaxis // Mathematical Carpathian publications. 2014. Vol. 6, No. 1. P. 113-122.

21. Makhnei O. V. Boundary problem for the singular heat equation // Mathematical Carpathian publications. 2017. Vol. 9, No. 1. P. 86–91. (doi:10.15330/cmp.9.1.86-91)

22. Makhnei O. V. Mixed problem for the singular partial differential equation of parabolic type // Mathematical Carpathian publications. 2018. Vol. 10, No. 1. P. 165–171. (doi:10.15330/cmp.10.1.165-171)

23. Makhnei O. V. Mixed problem for the partial differential equation of parabolic type with measures // Mathematical methods and physical and mechanical fields. 2018. Vol. 61, No. 4. P. 49–55. (in Ukrainian)

24. Makhnei O., Pylypiv V., Zatorskii R. m-submultisets and m-permutations of multisets elements // Carpathian Math. Publ. 2021. V. **13,** No. 1. P. 240–258. (https://doi.org/10.15330/cmp.13.1.240-258)

25. Makhnei O. V. Mixed problem for the differential equation of parabolic type with measures. J. Math. Sci. 2021. V. **256**, No. 4. P. 416–425. (https://doi.org/ 10.1007/s10958-021-05435-x)

26. Zatorskyi R. A., Makhney O. V., Pylypiv V. M. Algebroids and combinatorial interpretations. Precarpathian Bulletin of the Shevchenko Scientific Society. Number. 2022. No. 17(64). P. 58-64. (https://doi.org/10.31471/2304-7399-2022-17(64)-58-64) (in Ukrainian)

**Materials and abstracts of conferences** – 26 items.