Department of Mathematics and Physics

nltu2

Natalia Protsakh, Sc.D., Assoc.Prof.
Tel: +38(032) 258 42 40, +38(032) 258 42 58
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79057, Lviv, Gen.Chuprynky St. 105, room 801-812

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+38(032) 258 42 40,
+38(032) 258 42 58

https://nltu.edu.ua/index.php/instytuty/imakit/kafedra-matematyky-i-fizyky

protsakh

Head of the Department,
Doctor of Physical and Mathematical Sciences, prof.

Natalia Protsakh



The Department of Mathematics and Physics was organized on January 2, 2019 as the merger of the Departments of Higher Mathematics and Physics, and was involved into the structure of the SRI IMAKIT of the NLTU of Ukraine. Associate professors  Ph.D. Volodymyr Salapak  and, since July 2019,   Sc.D. Natalia Protsakh were appointed to the head of the Department.

The Department of Higher Mathematics was founded in 1945. In different years it was headed by: M.O. Zaretsky, G.L. Buymola, V.D. Bilyj, K.I. Chumak (1959–1972), V.M. Gnatykiv (1972–1988), T.R. Yaskevych (1988–1995), M.M.Stadnyk (1995–2018).

The teaching process was provided by: V.M. Hnatykiv, O.P. Khomiakevych, S.V. Grytsay, E.I. Trush, V.A. Skorodynskyy, B.I. Galashevskyy, M.K. Artamonov, B.V. Lysyk, S.G. Senyk, I.S. Tkach, M.K. Rudenko, I.I. Osipova, O.F. Girnyak, T.R. Yaskevych, B.M. Hnidets, I.F. Soltys, L.F. Boyko, O.Yu. Yushkevych, I.O. Goy, G.V. Gurnyak, V.M. Onyshkevych, I. Gorbachevskyy, O.Ye.  Korkuna,  I. Didukh, O.Yu. Turchyn, N.P. Protsakh.

The Department of Physics was one of the first departments founded in the structure of the Faculty of Forestry of the Lviv Forestry Institute in 1945. D.P. Dyatlov (1945–1958) was its organizer and the first head. Formation of educational and laboratory base was continued by the heads of the department  K.F. Guba (1958–1960), M.Ya. Brown (1960–1962), D.I. Tretyak (1962–1964), A.Ya. Kubetskyi, T.I. Gorbatyy, B.P. Yarema (1964–1967); Vajdanych (1967–1983, 1993–2004), Z.P. Chorniy (1983-1993, 2004–2015), V.M. Salapak (2015-2019).

In different years assoc. prof. N.D. Dovha, S.K. Zherebetskyy , H. K. Maksymovych, G. M. Pentsak, M.I. Batih, N. P. Belyaninova, A. I. Krysa, L. O. Tkachenko, Yu. M. Kyzylov .G.O. Shchur, M.S. Kobrynovych  I.B. Pirko. B.M .Yatsyk, Yu.M. Oryshchyn, M.S. Kobrynovych, O.R. Onufriv, V.M. Salapak, M.V. Dyachuk were doing their scientific and teaching activities.

  1. Natalia Protsakh, Sc.D., Assoc.Prof. (head of department)
  2. Volodymyr Salapak, Ph.D., Assoc.Prof. (deputy head of department)
  3. Ihor Horbachevskyy, Ph.D., Assoc.Prof.
  4. Ivan Didukh, Ph.D., Assoc.Prof.
  5. Mykhajlo Kobrynovych, Ph.D., Assoc.Prof.
  6. Volodymyr Onyshkevych, Ph.D., Assoc.Prof.
  7. Oleh Onufriv, Ph.D., Assoc.Prof.
  8. Ivan Soltys, Ph.D., Assoc.Prof.
  9. Olha Turchyn, Ph.D., Assoc.Prof.
  10. Mykola Dyachuk, Senior teacher

Mandatory courses:

  • Higher Mathematics.
  • Algebra and Geometry
  • Mathematical Analysis
  • Differential Equations
  • Theory of Probability and Random Processes
  • Theory of Information and Coding
  • Higher and Applied Mathematics
  • Physics
  • Theoretical mechanics

Elective courses:

  • Theory of Probability and Random Processes
  • Theory of Probability

  • boundary value problems for nonlinear evolutionary equations;
  • mathematical modeling of contact interaction of friction pairs;
  • tense state in elastic bodies with foreign inclusions;
  • determination of durability and durability of elastic and elastic-plastic bodies subjected to static and cyclic loading;
  • investigation of color centers in crystals of divalent metal halides.

1. Protsakh N.P., Ptashnyk B.Y. Nonlinear ultraparabolic equations and variational
inequalities. [Monograph] – K.: «Naukova dumka», 2017. – 278 p. (in Ukrainian)
2. Protsakh N.P. Higher mathematics (3) Compex variable functions and integral
transformations. Methodical instructions and tasks for homework of students of specialty
6.050202 "Automation and computer integrated technologies" – Lviv, UNFU. – 2016.– 75 pp. (in
Ukrainian)
3. Buhrii O.M., Protsakh N.P. Fundamentals of differential equations: theory, examples and
problems: [textbook]. —Lviv: Publisher I. Chizhykov, 2011. - 348 pp. (in Ukrainian)
4. Adamovsky A., Onyshkevych V. Linear programming: Practicum for bachelour students of
specialties: “Economics”, “Accounting and Taxation” and “Management”. – Lviv: UNFU.
2018. – 59 pp. (in Ukrainian)

5. Adamovsky A., Onyshkevych V. Theory of probability and mathematical statistics:
Practicum for bachelour students of specialties: “Management”, “Economics” and
“Accounting and Taxation”. – Lviv: UNFU. 2018. – 86 pp. (in Ukrainian)
6. Turchyn O., Onyshkevych V., Soltys I. Workshop in Higher Mathematics for bachelour
students of distance education of all specialties . Part 1. – Lviv: UNFU. 2016. – 53 p. (in
Ukrainian)
7. Osarkiv I.M., Sokolovskyi I.A., Dadak R.M., Somar H.V., Dereh O.I., Kobrynovych M.S.
Fundamentals of technology: theory and practice of thermal processes of forest complex
production. Monography. Lviv: 2013. 112 p.
8. Protsakh N.P. Problem of determining of minor coefficient and right-hand side function in
semilinear ultraparabolic equation // Mat. Stud. – 2018. – V. 50, No 1. – P. 60 – 74.
9. Protsakh N. Determining of right-hand side of higher order ultraparabolic equation // Open
Mathematics. – 2017. – V. 15(1). – P. 1048–1062.
10. Protsakh N. Problem for a weakly nonlinear ultraparabolic equation with three unknown
functions of different arguments on the right-hand side // J. Math. Sci. – 2016. – V. 217, No 4. –
476-514.
11. Protsakh N. Inverse problem for semilinear ultraparabolic equation of higher order //
Mathematica Bohemica. – 2015. – V. 140, № 4. – P. 395–404.
12. Protsakh N. P. Inverse problem for a semilinear ultraparabolic equation with unknown
right-hand side// Ukrainian mathematical Journal. –- 2014. –- V. 66, № 3. –- P. 371–390.
13. Protsakh N.P. Inverse problem of the determination of minor coefficient of semilinear
ultraparabolic equation // Visnyk LNU.– 2017, issue. 83.– P.164-178. (in Ukrainian)
14. Protsakh N.P. Initial-boundary value problem for special type nonlinear ultraparabolic
equation // Non-classical boundary value problems of the theory of differential equations
(dedicated to the 80th anniversary of prof. B.Y..Ptashnyk), 2017. -P.199-206. (in Ukrainian)
15. Lavrenyuk S.P., Protsakh N.P. Solvability of the boundary value problems for nonlinear
ultraparabolic equations// Preprint NAS of Ukraine, I.Ya. Pidstryhach IAPMM ;№ 1-08,
2008.–79 pp. (in Ukrainian)
16. Lavrenyuk S., Protsakh N. Boundary value problem for nonlinear ultraparabolic equation
in unbounded with respect to time variable domain, Tatra Mt. Math. Publ., volume 38, 2007,
131–146.
17. Protsakh N.P. Problem for third order nonlinear hyperbolic equation in unbounded owith
respect to spatial variable domain // Nauk. Visnyk ChNU: Mathematics. ChNU. – 2006. – issue
314-315. – P. 143 – 149. (in Ukrainian)
18. Lavrenyuk S.P. Protsakh N. P. Variational ultraparabolic inequalities, Ukrainian
Mathematical Journal, volume 56(12), 2004, 1915–1931.
19. Protsakh N. P., A mixed problem for a nonlinear evolution equation with a second-order
time derivative in generalized Lebesgue spaces, Mat. Stud., volume 16(2), 2001, 157–168.
20. Stadnyk M.M., Horbachevskyy I.Ya. A Limit Equilibrium of Quasi brittle Materials with
Thin Inclusions. Delegate Manual. 10th International Conference of Fracture (Hawaii, USA, 2-6
December, 2001). - Honolulu: ElsevierScience. - P. 395.
21. Volchok I.P., Stadnyk M.M., Slyn'ko G.I., Horbachevskyy I.Y. On the Estimation of a Tensile
Strength for Cast-irons with Phosphide Eutectic Inclusions. - Proc. 14-th Bienniel
ConferenceonFracture - ECF14 (Cracow, Poland, 8-13 September, 2002) - EMAS-publishing. Vol.
III. - P. 519-526.
22. Hasiy O., Horbachevsky I. Determination of stresses in materials with evaporated coatings
// Scientific Journal of the Ternopil National Technical University, 2018, № 4 (92), pp. 24-33

23. Timar I., Szulim G., Scukin V., Turchyn O. Qusistatic thermal elastic task for
layer–halfspace system with local pulsed heating // GÉP, 2007. V.58, No 12. – P. 39-42.
24. Turchyn I., Turchyn O. Transient plane waves in multilayered half-space. Acta mechanica et
automatica. – 2013, Vol 7. No 1 (23). P. 5357.
25. Marchenko G.P., Soltys I.F. About surface fracture of rail by action of residual stresses.
Proceeding of International Scientific Conference “Modern problems of thermomechanics”.
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics. Lviv , 22-24.09.2016. –
2 p.
26. O.M. Udovytskyi, I.F. Soltys. The study of dynamic processes the transportation by chain
conveyor. Scientific Bulletin of UNFU. 2017, 27 (4), p. 144-147.
27. Volodymyr Onyshkevych. Mathematical modelling of wear in a plane problem about
contact of punch and elastic half-plane. Mathematical problems of mechanics of
nonhomogeneous structures: Collection of scientific papers. Lviv: Pidstryhach Institute for applied
problems of mechanics and mathematics. 2019.– Fifth issue.– p. 187-188 (in Ukrainian)
28. Volodymyr Onyshkevych. Modelling of wear in the plane contact of rectangular punch and
elastic half-plane. 14-th International Symposium of Ukrainian Mechanical Engineers in Lviv, 23-
24.05.2019. Proceedings.– Lviv: KINPATRI LTD. 2019. – p. 38-40 (in Ukrainian)
29. Onyshkevych V.M., Sulym G.T. Consideration of wear in plane contact of rectangular
punch and elastic half-plane. V International Scientific Conference “Modern Problems of
Mechanics”, 28-30.08.2019, Kyiv, Ukraine. Proceedings.– p. 67 (in Ukrainian)
30. Georgiy Sulym, Volodymyr Onyshkevych. Plane contact of rectangular punch and elastic
half-plane with due account of wear. 6-th International Scientific-Technical Conference “Theory
and Practice Of Rational Projecting, Producing and Exploitation Of Machine-Building
Constructions, 25-26.10.2018, Lviv, Ukraine. Proceedings.– Lviv: KINPATRI LTD. 2018. – p. 74-
75 (in Ukrainian)
31. Volodymyr Onyshkevych. Plane contact problem for rectangular punch and elastic half-
plane with due account of wear. Modern Problems of Mechanics and Mathematics: Collection of
scientific papers. Lviv: Pidstryhach Institute for applied problems of mechanics and mathematics.
2018.– Vol. 2.– p. 74-75 (in Ukrainian) [Electronic resours] www.iapmm.lviv.ua/mpmm2018
32. Onyshkevych V.M., Sulym G.T. The problem about thermoelastic contact of half-plane and
rectangular punch with heat generation account of friction. IV International Scientific
Conference “Modern Problems of Mechanics”, 28-30.08.2017, Kyiv, Ukraine. Proceedings.– p. 72
(in Ukrainian)
33. Onyshkevych V.M., Sulym G.T. The problem about thermoelastic contact of half-plane and
rectangular punch with heat generation account of friction. Bulletin of Taras Shevchenko
National University of Kyiv. Series: Physics & Mathematics. – 2017. – Vol.3 – p. 165-168 (in
Ukrainian)
34. Onyshkevych V.M., Gapalyak Kh.O. Taking into account stochastic in the imitative
modelling of ecologic-economic processes. Materials of IV International Scientific-Practical
Conference “Scientific Design, Leading Technologies, Innovations”, 6-8.05.2017, Praha-Brno-
Kyiv. – NDISR– p. 197-203 (in Ukrainian)
35. Volodymyr Onyshkevych, Georgiy Sulym. Thermoelastic contact of half-plane with
rectangular punch with heat generation account of friction. Modern Problems of
Thermomechanics: Collection of scientific papers. Lviv: Pidstryhach Institute for applied problems
of mechanics and mathematics. 2016.– p. 202-203 (in Ukrainian) [Electronic resours]
www.iapmm.lviv.ua/MPT2016
36. Sulym G.T., Onyshkevych V.M. The thermoelastic contact of a half-plane with the
rectangular rigid punch in the case of heat providing on its external surface. III International

Scientific Conference “Modern Problems of Mechanics”, 27-29.08.2015, Kyiv, Ukraine.
Proceedings.– p. 80 (in Ukrainian)
37. Sulym G.T., Onyshkevych V.M. The thermoelastic contact of a half-plane with the
rectangular rigid punch in the case of heat providing on its external surface.. Bulletin of Taras
Shevchenko National University of Kyiv. Series: Physics & Mathematics. – 2015. – Special issue –
p. 255-260 (in Ukrainian)
38. Krochuk A.S., Onufriv O.R., Chornyi Z.P. Characteristic Properties of Radiation
ColoringMechanism in MeFX Compounds (Me = Sr, Ba; X = Cl, Br) // Phys.Stat.Sol. (B). -
1989- v.154,No.1. - P. K9 - K12.
39. Stadnik V.I., Andrievsky B.V., Onufriv O.R., Karplyuk L.T. Band structure and refraction of
LiRbSO4 crystals. // Optics and Spectroscopy. -2016.- Vol.121, №2 - p.306-311
40. M.Ya.Rudysh, M.G.Brik, O.R.Onufriv, M.Piasecki, V.Yo.Stadnyk, P.A.Shchepanskyi. Ab
initio study of crystal structure and physical properties of chalcopyrite Cu Ga (S2) x (Se2) 1-x
solid solution. In Ukrainian-Polish-Lithuanian Meeting on Physics of Ferroelectrics. 18-20
September 2018. Uzhhorod, Ukraine.
41. V.Yo.Stadnyk, P.A.Shchepanskyi, R.S.Brezvin, M.Ya.Rudysh, Z.A.Kohut, O.R.Onufriv,
Ya.P.Kost. On Isotropic Points and Potassium Ammonium Sulfate Crystals. Crystallography
Reports. -2019.-Vol.64, №5 –pp. 765-770.
42. Kachan, S.I., Salapak, V.M., Nahurskiy, O.A., Pirko, I.B. Control of radiation sensitivity of
the oxygen-containing fluorite crystals. Acta Physica Polonica A, 2018, V.133(4): p.824-828.
43. Chornij, Z.P., Pirko, I.B., Salapak, V.M., Panasyuk, M.R. FD-centers in fluorite crystals
doped with alkali metals. Journal of Physical Studies, 2012, 16(1): 1602 1-8.
44. Chornyi, Z.P., Pirko, I.B., Salapak, V.M. Study on radiation sensitivity of SrCI2-K crystals.
Functional Materials, 2011, 18(2): 206-210.
45. Chornyi, Z.P., Pirko, I.B., Salapak, V.M., Kachan, S.I., Kushnir T.M. Relaxation properties of
defect complexes in SrCl2-Tl+. Functional Materials, 2004, 11: 696-701.
46. Chornyi, Z.P., Kravchuk, I.M., Kachan, S.I., Shchur, G.O., Salapak, V.M. Reorientation of
M+A-centres in CaF2: Me+crystals Physica Status Solidi (B), 2001, 223: 757-765.
47. Z.Chorniy, W.Vaidanitc, M. Kobrynovytch, I.Pirko. X-rayind Luminescence and the
colour centres in crystals BaX (X = Cl, Br, I). Book of Abstracts 6 European Conference
of Luminescent Detectors and Transformers of ionising Radiation LUMDETR 2006, lviv, p.
194.
48. Stadnyk M. M., Riznychuk R. V., Didukh I. V. Life estimation for fatique crack nucleation
and growth at the notch root // Advances in fracture resistance in materials / Edited by V. V.
Panasyuk, P. Rama Rao and others. – New Delhi: Tata McGraw – Hill Publishing Соmpany
Limited, 1996. – V. 1. – P. 121–127.
49. Stadnyk M., Didukh I. Estimation of the durability of pipe elements at the stage of fatigue
growth of surface halfeliptic crack // Visnyk Lviv, Univ. -Mech.- mat. series. 2010.-No. 73. -
P.23-29. (in Ukrainian)
50. Z.Chorniy, N.Diyachuk, I.Pirko, V.Salapak. Luminescence of autolokalized exitons in
crystals BaCl 2 . Electronics and information technology, 2016, issue 6, p. 45-53. (in Ukrainian)
51. Z.Chorniy, I.Pirko, N.Diyachuk, N. Kobrynovitch, M. Panasiuk, V.Salapak. Self-trapped hole
in the crystals BaCl 2 . Electronics and information technology, 2015, issue 5, p. 61-72. (in
Ukrainian)
52. Z.Chornij, I.Pirko, V.Salapak, N.Dyachuk,. Radiation process in crystals with poind defects
in dipole type. One dimentional model. Electronics and information technology, 2013, issue 3, p.
70-78. (in Ukrainian)

53. Z.Chornij, M. Panasiuk, N.Diyachuk, I.Pirko, V.Salapak. Generation (Tl 0 -Tl 2+ ) –
complementary pairs in Alkali-Halide crystals. Electronics and information technology, 2014,
issue 4, p. 81-87. (in Ukrainian)
54. Osarkiv I.M., Basalyha Y.V., Kuleshnyk Y.F., Sokolovskyi I.A., Kobrynovych M.S. Diagnosis
of wood properties in technological processes of woodworking. Scientific edition. Lviv:
Panorama Publishing House, 2003. 228 p.
55. Chorniy Z.P., Shchur G.O., Kobrynovych M.S. Panasiuk M.R. Investigation of the efficiency
of electron capture by impurity-vacancy dipoles in SrCl 2 crystals. – Kyiv: Physical Electronic,
1985, 108-111 pp.
56. Chorniy Z.P., Zherebetskyi S.K., Kobrynovych M.S., Salapak V.M. Atomic centers of color in
SrCl 2 – Tl crystals. Collection of scientific works "100 years of Engineer-Economical Faculty of
Lviv Polytechnic", Lviv, 1996.
57. Krynytskyi G.T., Vaidanych V.I., Zaika V.K., Kobrynovych M.S. Influence of chronic ionized
irradiation on the Pinus Sylvestris L. functioning. Physical Collection of SciTechSch, vol. 4,
2001, 401-407 pp.
58.Osarkiv I.M., Kobrynovych M.S. Thermodynamic characteristics of wood in drying
processes. Scientific Bulletin. Lviv, UkrDLTU (UNFU), 2003, issue. 13.1, 106-112 pp.
59.Chorniy Z., Vaidanitc W., Kobrynovytch M., Pirko I. X-raying Luminescence and the colour
centres in crystals BaX (X = Cl, Br, I). Book of Abstracts 6 European Conference of
Luminescent Detectors and Transformers of ionizing Radiation LUMDETR 2006, Lviv, p. 194.
60.Chorniy Z.P., Pirko I.B., Solonok V.M., Kobrynovych M.S., Diachuk M.V. Activation centers
of color in BaCl 2 –Pb crystals. Scientific Bulletin of NLTU of Ukraine: collection of scientific and
technical works. - 2014 - issue. 24.3, 321326 pp.
61.Chorniy Z.P., Vaidanych. V.I, Maksymovych H.K., Shchur G.O., Kobrynovych M.S.
Investigation of F A -F transformations in BaCl 2 Me + crystals. Proceedings of All-Union
conference in radiation physics and chemistry of ionic cr. Riga: Salaspils, 1983. p. 306.
62.Chorniy Z.P., Vaidanych. V.I, Maksymovych H.K., Kobrynovych M.S. Thallium glow centers
in crystals of divalent metal halides. Proceedings of All-Union meeting on luminescence non
organic crystals / Rivne, 1984, p. 119.
63.Dubelt S.P., Tsal N.O., Chorniy Z.P., Kobrynovych M.S. Luminescence and color centers in
crystals with a fluorite structure doped with manganese. Proceedings of All-Union Feofilov
Symposium on Crystal Electroscopy. Sverdlovsk, 1985, p. 87.
64.Chornyi Z.P., Govor M.V., Krochuk A.S., Salapak V.M., Kobrinovytch M.S.
Thermostimulated rekombination cyelikon mechanirm SrCl 2 - Me + crystals Simposium
“EXCOM-94”. Darvin, Astralia, 1994. (in English)
65.Krynytskyi G.T., Vaidanych V.I., Zaika V.K., Kobrynovych M.S. Influence of chronic
incorporated radiation on the functioning of common pine. Proceedings of the II International
Scientific Symposium. Ternopil, 2000, p. 253-255.
66.Vaidanych. V.I, Dovha N.D., Pentsak G.M. Kobrynovych M.S. Features of teaching of physics
by specialists of technical specialties in the conditions of realization of modern integration
processes. Proceedings of the All-Ukrainian Scientific and Methodological Conference. Kryvyi
Rih, 2004, vol. 2, no.4, 7276 pp.
67.М. М. Stadnyk, I. V.Didukh. An estimation of life time of the thick-wall tubs and the
tubular welding joints at the stage of fatigue surface semielliptical crack propagation //
Scientific Bulletin of UNFU. – 2017. – Vol. 27. – No.9. –P.74-78.
68.. М. М. Stadnyk, I. V.Didukh. The mathematical model growth of surface semielliptical
crack in elastoplastic body under cyclic loading// Scientific Bulletin of UNFU. – 2007. –
Vol.17. – No.5. –P.220-226.

69. М. М. Stadnyk, I. V.Didukh. The calculation model of assessing the residual life time
of tubular elements under cyclic loading// Modern Problems of Mechanics and Mathematics:
In 3 volume. - Lviv, 2008. - V. 2. - P.295-297.
70. М. М. Stadnyk, I. V.Didukh. An estimation of the life time of tubular structural elements
at the stage of fatigue surface semielliptical crack propagation // Visnyk of the Lviv University.
Series Mechanics and Mathematics. 2010. Issue 73.- P.23-29.

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