 Roman O. POPOVYCH



Current address: Faculty of Mathematics,
University of Vienna, OskarMorgensternPlatz 1, 1090 Vienna, Austria
Office: OskarMorgensternPlatz 1, room 03.133
Phone: +43 1 4277 50632 (office)
Fax: +43 1 4277 50620 (office)
Secondary Address:
Department of Mathematical Physics,
Institute of Mathematics,
National Academy of Sciences of Ukraine,
3 Tereshchenkivs'ka Street, 01004 Kyiv, Ukraine
Phone: +380 44 234 63 22 (office)
Fax: +380 44 235 2010 (office)
Academic Degrees and Titles:
Prof. in Math.: 2017, Institute of Mathematics, NAS of Ukraine, Kyiv
D.Sc. in Math.: 2009, Institute of Mathematics, NAS of Ukraine, Kyiv (Consultant Prof. A.M. Samoilenko)
[pdf of the thesis (in Ukrainian)]
Senior Reseacher: 2005, Institute of Mathematics, NAS of Ukraine, Kyiv
Ph.D. in Math.: 1992, Institute of Mathematics, NAS of Ukraine, Kyiv (Supervisor Prof. W.I. Fushchych)
M.Sc. in Math.: 1989, Taras Shevchenko Kyiv State University (Supervisor Prof. W.I. Fushchych)
Professional Experience:
1992till now
Junior Researcher, Researcher, Senior Researcher, Leading Researcher at the
Department of Mathematical Physics (former Department of Applied Research), Institute of Mathematics, NAS of Ukraine, Kyiv
2018till now
Senior Postdoc, Standalone project P30233 of FWF, Faculty of Mathematics, University of Vienna
2019
Postdoc, Standalone project P29177 of FWF, Faculty of Mathematics, University of Vienna
20132018
Principal investigator, Standalone project P25064 of FWF,
Wolfgang Pauli Institute, Vienna
20082013
Principal investigator, Standalone project P20632 of FWF,
Faculty of Mathematics, University of Vienna, and Wolfgang Pauli Institute, Vienna
20062008
Principal investigator, Lise Meitner project of FWF,
Faculty of Mathematics, University of Vienna
19891992
PhD Student, Institute of Mathematics, Kyiv
Area of Expertise
Symmetry analysis of differential equations and applications, Lie algebras
Awards and Grants
Standalone project P25064 of FWF (2013)
Standalone project P20632 of FWF (2008)
Lise Meitner project M923N13 of FWF (2005)
Prize of President of Ukraine for Young Scientists (2001)
Former D.Sc. Candidates
Vyacheslav Boyko,
thesis: "Generalized Casimir operators, singular reduction modules and symmetries of differential equations" (2018),
Institute of Mathematics, NAS of Ukraine, Kyiv
Former PhD Students
Célestin Kurujyibwami (jointly with Prof. P. BasarabHorwath),
Admissible transformations and the group classification of Schrödinger equations,
Doctoral Thesis, Linköping Studies in Science and Technology. Dissertation No. 1846, Linköping University, 2017.
Oleksandr Pocheketa, thesis: "Extended group analysis of generalized Burgers equations" (2016), Institute of Mathematics, NAS of Ukraine, Kyiv
Elsa Maria Dos Santos CardosoBihlo, thesis: "Group analysis and invariant parameterization in dynamic meteorology" (2014), University of Vienna
Alexander Bihlo (jointly with Prof. M. Hantel), thesis: "Symmetry methods in the atmospheric sciences" (2010), University of Vienna
Olena Vaneeva, thesis: "Group classification and nonclassical symmetries of reactiondiffusion equations" (2008), Institute of Mathematics, NAS of Ukraine, Kyiv
Maryna Nesterenko (jointly with Prof. A.G. Nikitin), thesis: "Contractions and realizations of Lie algebras" (2007), Institute of Mathematics, NAS of Ukraine, Kyiv
Maxim Lutfullin (jointly with Prof. A.G. Nikitin), thesis: "Realizations of lowdimensional Lie algebras and invariant systems of nonlinear differential equations" (2005),
Institute of Mathematics, NAS of Ukraine, Kyiv
Former Master Students
Célestin Kurujyibwami (jointly with Prof. P. BasarabHorwath),
Group classification of linear Schrödinger equations by the algebraic method,
Licentiate Thesis, Linköping Studies in Science and Technology. Thesis No. 1743, Linköping University, 2016.
Editorial Boards and Organizing Committees
Associate Editor of the
Journal of Mathematical Analysis and Applications
(2009till now)
Associate Editor of the refereed online journal SIGMA
''Symmetry, Integrability and Geometry: Methods and Applications''
(2005till now)
Member of Local Organizing Committee of the International Conference Series
''
Symmetry in Nonlinear Mathematical Physics''
(1995, 1997, 1999, 2001, 2003, 2005, 2007, 2009, Kyiv, Ukraine)
Member of Organizing Committee of the International Workshop Series
''Group Analysis of Differential Equations and Integrable Systems''
(2005, 2006, 2007, 2008, 2010, 2012, 2014, 2016, 2018, Cyprus)
Member of Scientific Committee of the International Workshop
''A Century of Noether's Theorem and Beyond''
(30 November 2 December 2018, Opava, Czech Republic)
Member of Scientific Committee of the 11th and 12th Conferences
''Mathematics in Technical and Natural Sciences''
(812 September 2010 and 410 September 2011, Krynica, Poland)
Member of Organizing Committee of the International Workshop
''Symmetries and integrability of equations of mathematical physics''
in honor of Professor Wilhelm Fushchych
(1819 December 2011, Kyiv, Ukraine)
Member of Scientific Committee of the Fifth International School and Workshop "QFT and Hamiltonian Systems" (2026 May 2006, Calimanesti, Romania)
Referee
Acta Applicandae Mathematicae
Acta Mechanica
Applied Mathematics Letters
Electronic Journal of Differential Equations (EJDE)
IMA Journal of Applied Mathematics
Journal of Engineering Mathematics
Journal of Mathematical Analysis and Applications
Journal of Mathematical Physics
Journal of Nonlinear Mathematical Physics
Journal of Physics A: Mathematical and Theoretical
manuscripta mathematica
Mathematical Methods in the Applied Sciences
Modern Physics Letters B
Nonlinear Analysis A: Theory and Methods
Nonlinear Dynamics
Nonlinearity
Physics Letters A
Proceedings of Royal Society A
Reports on Mathematical Physics
Reviews in Mathematical Physics
etc.
Reviewer
Mathematical Review
Mathematical Zenterblatt
Participation at International Conferences and Workshops
Conference ''Dynamics, Geometry and Analysis: 20 years of Mathematical Institute in Opava''
(813 September 2019, Hradec nad Moravicí, Czech Republic)
International Workshop Series
''Group Analysis of Differential Equations and Integrable Systems''
(27 October 2005, 2528 September 2006, 45 October 2007, Nicosia, Cyprus; 2630 October 2008, 610 June 2010, 1721 June 2012, Protaras, Cyprus;
1519 June 2014, 1217 June 2016, 1014 June 2018, Larnaka, Cyprus)
International Workshop
''A Century of Noether's Theorem and Beyond''
(30 November 2 December 2018, Opava, Czech Republic)
''Workshop on Integrable Nonlinear Equations'' (1824 October 2015, Mikulov, Czech Republic)
International Workshop
''Symmetries and integrability of equations of mathematical physics''
in honor of Professor Wilhelm Fushchych
(1819 December 2011; 2124 December 2013; Kyiv, Ukraine)
''2012 Canadian Mathematical Society (CMS) Winter Meeting,
Session ''Symmetries of Differential and Difference Equations''
(89 December 2012, Montréal, Canada)
11th and 12th Conferences
''Mathematics in Technical and Natural Sciences''
(812 September 2010 and 410 September 2011, Krynica, Poland)
International Conference Series
''Symmetry in Nonlinear Mathematical Physics''
(38 July 1995; 713 July 1997; 1218 July 1999; 915 July 2001; 2329 June 2003; 2026 June 2005; 2430 June 2007; 2127 June 2009; Kyiv, Ukraine)
Applications of Computer Algebra (ACA2008),
the session
Symbolic Symmetry Analysis and Its Applications
(2730 July 2008, RISC, Castle of Hagenberg, Austria)
MMVII Symmetries and Mechanics Conference
(2427 September 2007, Novi Sad, Serbia)
Fifth International School and Workshop "QFT and Hamiltonian Systems" (2026 May 2006, Calimanesti, Romania)
IV International Symposium Quantum Theory and Symmetries
(1521 August 2005, Varna, Bulgaria)
International Workshop on Nonlinear Partial Differential Equations
(516 December 2004, Tehran, Iran)
International Conference in Modern Group Analysis (MOGRAN X)
(2431 October 2004, Larnaca, Cyprus)
11th Regional Conference on Mathematical Physics and Mathematics
(36 May 2004, Tehran, Iran)
NATO ASI 2003 "Data Fusion for Situation Monitoring, Incident Detection, Alert and Response Management"
(1829 August 2003, Tsakhkadzor, Armenia)
10th International Conference on Symmetry Methods in Physics
(1319 August 2003, Yerevan, Armenia)
Invited Scientific Visits
Mathematical Institute in Opava, Silesian University in Opava
(Opava, Czech Republic, 620 October 2014; 1122 May 2015; 1 November 2016 31 March 2017; 2 September 2018 28 February 2019; 1314 November 2019)
Department of Mathematics and Statistics, University of Cyprus
(Nicosia, Cyprus, 2004, 2005, 2006, 2007, 2008, 2010; 29 September 15 October 2013; 24 September 11 October 2015; 1323 October 2016; 526 October 2017; 23 September 16 October 2019)
Abdus Salam International Centre for Theoretical Physics (ICTP)
(Trieste, Italy, 1728 April 2019)
Department of Mathematics and Statistics, Memorial University
(St. John's, Canada, 627 September 2016; 31 August 28 September 2017)
Department of Mathematics, Linköping University,
(Linköping, Sweden, 329 November 2013; 2127 February 2016; 28 May 4 June 2017)
Faculty of Applied Mathematics, AGH University of Science and Technology
(Krakow, Poland, 69 April 2017)
Department of Mathematics and Statistics, University of Saskatchewan
(Saskatoon, Canada, 1015 June 2013; 216 November 2014; 217 September 2015)
Department of Mathematics and Statistics, McGill University
(Montréal, Canada, 2329 April 2013)
Faculty of Engineering, Katholieke Universiteit Leuven, Campus Kortrijk
(Belgium, Kortrijk, 28 May 1 June 2012)
Centre de Recherches Mathématiques, Universite de Montréal
(Montréal, Canada, 2004)
Institute for Studies in Theoretical Physics and Mathematics (IPM)
(Tehran, Iran, 6 September 22 October, 2003; 26 April 24 May 2004)
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research
(Dubna, Russia, 2003)
PUBLICATIONS
*** Popovych, Roman O. = Popovych, R.O. = Popovych, R. = Popovich, R.E. = Popovich, R.Y. = Popovich, R.Ye. = Popowych, R.O. = Popovich, R.O. = Popowych, Roman

Popovych R.O. and Cheviakov A.F.,
Variational symmetries and conservation laws of the wave equation in one space dimension,
Appl. Math. Lett. 104 (2020), 106225, 7 pp.,
arXiv:1912.03698.

Opanasenko S., Boyko V. and Popovych R.O.,
Enhanced group classification of nonlinear diffusionreaction equations with gradientdependent diffusion,
J. Math. Anal. Appl. 484 (2020), 123739, 30 pp.,
arXiv:1804.08776.

Opanasenko S., Bihlo A., Popovych R.O. and Sergyeyev A.,
Extended symmetry analysis of isothermal noslip drift flux model,
Phys. D 402 (2020), 132188, 16 pp.,
arXiv:1705.09277.

Popovych R.O. and Bihlo A.,
Inverse problem on conservation laws,
Phys. D 401 (2020), 132175, 16 pp.,
arXiv:1705.03547.

Vaneeva O.O., Bihlo A. and Popovych R.O.,
Equivalence groupoid and group classification of a class of nonlinear wave and elliptic equations,
arXiv:2002.08939, 38 pp.

Kontogiorgis S., Popovych R.O. and Sophocleous C.,
Enhanced symmetry analysis of twodimensional Burgers system,
Acta Appl. Math. 163 (2019), 91128,
arXiv:1709.02708.

Bihlo A., Dos Santos CardosoBihlo E. and Popovych R.O.,
Differential invariants for a class of diffusion equations,
Symmetry and Integrability of Equations of Mathematical Physics,
Collection of Works of Institute of Mathematics, Kyiv, 16 (2019), no. 1, 5065,
arXiv:1909.00477.

Bihlo A. and Popovych R.O.,
Zerothorder conservation laws of twodimensional shallow water equations with variable bottom topography,
arXiv:1912.11468, 22 pp.

Bihlo A., Poltavets N. and Popovych R.O.,
Lie symmetries of twodimensional shallow water equations with variable bottom topography,
arXiv:1911.02097, 24 pp.

Opanasenko S., Bihlo A. and Popovych R.O.,
Equivalence groupoid and group classification of a class of variablecoefficient Burgers equations,
arXiv:1910.13500, 20 pp.

Bihlo A., Dos Santos CardosoBihlo E. and Popovych R.O.,
Invariant parameterization of geostrophic eddies in the ocean,
arXiv:1908.06345, 21 pp.

Vaneeva O.O., Popovych R.O. and Sophocleous C.,
Enhanced symmetry analysis of twodimensional degenerate Burgers equation,
arXiv:1908.01877, 26 pp.

Opanasenko S., Bihlo A., Popovych R.O. and Sergyeyev A.,
Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal noslip drift flux model,
arXiv:1908.00034, 33 pp.

Popovych R.O. and Sakhnovich A.,
GBDT and explicit solutions for the matrix coupled dispersionless equations (local and nonlocal cases),
arXiv:1907.08258, 31 pp.

Boyko V.M., Kunzinger M. and Popovych R.O.,
Parameterdependent linear ordinary differential equations and topology of domains,
arXiv:1901.02059, 26 pp.

Kurujyibwami C., BasarabHorwath P. and Popovych R.O.,
Algebraic method for group classification of (1+1)dimensional linear Schrödinger equations,
Acta Appl. Math. 157 (2018), 171203,
arXiv:1607.04118.

Opanasenko S. and Popovych R.O.,
Generalized symmetries and conservation laws of (1+1)dimensional KleinGordon equation,
arXiv:1810.12434, 16 pp.

Pocheketa O.A. and Popovych R.O.,
Extended symmetry analysis of generalized Burgers equations,
J. Math. Phys. 58 (2017), 101501, 28 pp.,
arXiv:1603.09377.

Opanasenko S., Bihlo A. and Popovych R.O.,
Group analysis of general BurgersKortewegde Vries equations,
J. Math. Phys. 58 (2017), 081511, 37 pp.,
arXiv:1703.06932.

Bihlo A. and Popovych R.O.,
Group classification of linear evolution equations,
J. Math. Anal. Appl. 448 (2017), 9821005,
arXiv:1605.09251.

Boyko V.M., Kunzinger M. and Popovych R.O.,
Singular reduction modules of differential equations,
J. Math. Phys. 57 (2016), 101503, 34 pp.,
arXiv:1201.3223.

Bihlo A., Dos Santos CardosoBihlo E. and Popovych R.O.,
Invariant and conservative parameterization schemes,
Chapter 28 in Parameterization of Atmospheric Convection. Vol. 2. Current Issues and New Theories,
Imperial College Press, London, 2015, pp. 483524.

Bihlo A., Dos Santos CardosoBihlo E. and Popovych R.O.,
Algebraic method for finding equivalence groups,
J. Phys.: Conf. Ser. 621 (2015) 012001, 17 pp.,
arXiv:1503.06487.

Boyko V.M., Popovych R.O. and Shapoval N.M.,
Equivalence groupoids of classes of linear ordinary differential equations and their group classification,
J. Phys.: Conf. Ser. 621 (2015) 012002, 17 pp.,
arXiv:1403.6062.

Vaneeva O.O., Popovych R.O. and Sophocleous C.,
Group analysis of BenjaminBonaMahony equations with time dependent coefficients,
J. Phys.: Conf. Ser. 621 (2015) 012016, 13 pp.
arXiv:1506.08137.

Dos Santos CardosoBihlo E. and Popovych R.O.,
On the ineffectiveness of constant rotation in the primitive equations and their symmetry analysis,
arXiv:1503.04168, 15 pp.

Pocheketa O.A., Popovych R.O. and Vaneeva O.O.,
Group classification and exact solutions of variablecoefficient generalized Burgers equations with linear damping,
Appl. Math. Comput. 243 (2014) 232244,
arXiv:1308.4265.

Vaneeva O.O., Popovych R.O. and Sophocleous C.,
Equivalence transformations in the study of integrability,
Phys. Scr. 89 (2014), 038003, 9 pp.,
arXiv:1308.5126.

Bihlo A., Dos Santos CardosoBihlo E. and Popovych R.O.,
Invariant parameterization and turbulence modeling on the betaplane,
Phys. D 269 (2014), 4862,
arXiv:1112.1917.

Dos Santos CardosoBihlo E. and Popovych R.O.,
Complete point symmetry group of the barotropic vorticity equation on a rotating sphere,
J. Engrg. Math. 82 (2013), 3138,
arXiv:1206.6919.

Pocheketa O.A. and Popovych R.O.,
Reduction operators of Burgers equation,
J. Math. Anal. Appl. 398 (2013), 270277,
arXiv:1208.0232.

Boyko V.M., Popovych R.O. and Shapoval N.M.,
Lie symmetries of systems of secondorder linear ordinary differential equations with constant coefficients,
J. Math. Anal. Appl. 397 (2013), 434440,
arXiv:1203.0387.

Boyko V.M. and Popovych R.O.,
Reduction operators of the linear rod equation,
Proceedings of the Sixth International Workshop "Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, June 1721, 2012),
University of Cyprus, Nicosia, 2013, 1729.

Vaneeva O.O., Popovych R.O. and Sophocleous C.,
Group classification of the Fisher equation with timedependent coefficients,
Proceedings of the Sixth International Workshop "Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, June 1721, 2012),
University of Cyprus, Nicosia, 2013, 225237.

Bihlo A. and Popovych R.O.,
Invariant discretization schemes for the shallowwater equations,
SIAM J. Sci. Comput. 34 (2012), no. 6, B810B839,
arXiv:1201.0498.

Bihlo A., Dos Santos CardosoBihlo E. and Popovych R.O.,
Complete group classification of a class of nonlinear wave equations,
J. Math. Phys. 53 (2012), 123515, 32 pp.,
arXiv:1106.4801.

Pocheketa O.A. and Popovych R.O.,
Reduction operators and exact solutions of generalized Burgers equations,
Phys. Lett. A 376 (2012), 28472850,
arXiv:1112.6394.

Popovych R.O. and Bihlo A.,
Symmetry preserving parameterization schemes,
J. Math. Phys. 53 (2012), 073102, 36 pp.,
arXiv:1010.3010.

Vaneeva O.O., Popovych R.O. and Sophocleous C.,
Extended group analysis of variable coefficient reactiondiffusion equations with exponential nonlinearities,
J. Math. Anal. Appl. 396 (2012), 225242,
arXiv:1111.5198.

Bihlo A. and Popovych R.O.,
Lie reduction and exact solutions of vorticity equation on rotating sphere,
Phys. Lett. A 376 (2012), 11791184,
arXiv:1112.3019.

Kunzinger M. and Popovych R.O.,
Generalized conditional symmetries of evolution equations,
J. Math. Anal. Appl. 379 (2011), 444460,
arXiv:1011.0277.

Bihlo A. and Popovych R.O.,
Lie symmetry analysis and exact solutions of the quasigeostrophic twolayer problem,
J. Math. Phys. 52 (2011), 033103, 24 pp.,
arXiv:1010.1542.

Dos Santos CardosoBihlo E., Bihlo A. and Popovych R.O.,
Enhanced preliminary group classification of a class of generalized diffusion equations,
Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 36223638,
arXiv:1012.0297.

Vaneeva O.O., Popovych R.O. and Sophocleous C.,
Reduction operators of variable coefficient semilinear diffusion equations with an exponential source,
Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 610, 2010, Protaras, Cyprus), University of Cyprus, Nicosia, 2011, 207219,
arXiv:1010.2046.

Bihlo A. and Popovych R.O.,
Point symmetry group of the barotropic vorticity equation,
Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 610, 2010, Protaras, Cyprus), University of Cyprus, Nicosia, 2011, 1527,
arXiv:1009.1523.

Boyko V.M. and Popovych R.O.,
Simplest potential conservation laws of linear evolution equations,
Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 610, 2010, Protaras, Cyprus), University of Cyprus, Nicosia, 2011, 2839,
arXiv:1008.4851.

Popovych D.R. and Popovych R.O.,
Lowest dimensional example on nonuniversality of generalized InönüWigner contractions,
J. Algebra 324 (2010), 27422756,
arXiv:0812.1705.

Popovych R.O. and Sergyeyev A.,
Conservation laws and normal forms of evolution equations,
Phys. Lett. A 374 (2010), 22102217,
arXiv:1003.1648.

Popovych R.O. and Vaneeva O.O.,
More common errors in finding exact solutions of nonlinear differential equations. I,
Commun. Nonlinear Sci. Numer. Simul. 15 (2010), 38873899,
arXiv:0911.1848.

Ivanova N.M., Popovych R.O. and Sophocleous C.,
Group analysis of variable coefficient diffusionconvection equations. I. Enhanced group classification,
Lobachevskii J. Math. 31 (2010), 100122,
arXiv:0710.2731.

Popovych R.O., Kunzinger M. and Eshraghi H.,
Admissible transformations and normalized classes of nonlinear Schrödinger equations,
Acta Appl. Math. 109 (2010), 315359,
arXiv:mathph/0611061.

Bihlo A. and Popovych R.O.,
Symmetry justification of Lorenz' maximum simplification,
Nonlinear Dynam. 61 (2010), 101107,
arXiv:0805.4061.

Bihlo A. and Popovych R.O.,
Lie symmetries and exact solutions of barotropic vorticity equation,
J. Math. Phys. 50 (2009), 123102, 12 pp.,
arXiv:0902.4099.

Popovych D.R. and Popovych R.O.,
Equivalence of diagonal contractions to generalized IWcontractions with integer exponents,
Linear Algebra Appl. 431 (2009), 10961104,
arXiv:0812.4667.

Bihlo A. and Popovych R.O.,
Symmetry analysis of barotropic potential vorticity equation,
Commun. Theor. Phys. 52 (2009), 697700,
arXiv:0811.3008.

Vaneeva O.O., Popovych R.O. and Sophocleous C.,
Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source,
Acta Appl. Math. 106 (2009), 146,
arXiv:0708.3457.

Ivanova N.M., Popovych R.O., Sophocleous C. and Vaneeva O.O.,
Conservation laws and hierarchies of potential symmetries for certain diffusion equations,
Physica A 388 (2009), 343356,
arXiv:0806.1698.

Boyko V.M., Patera J. and Popovych R.O.,
Invariants of Lie Algebras via Moving Frames,
Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (2630 October 2008, Protaras, Cyprus), University of Cyprus, Nicosia, 2009, 3644,
arXiv:0904.4462.

Vaneeva O.O., Popovych R.O. and Sophocleous C.,
Reduction operators of variable coefficient semilinear diffusion equations with a power source,
Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (2630 October 2008, Protaras, Cyprus), University of Cyprus, Nicosia, 2009, 191209,
arXiv:0904.3424.

Kunzinger M. and Popovych R.O.,
Is a nonclassical symmetry a symmetry?,
Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (2630 October 2008, Protaras, Cyprus), University of Cyprus, Nicosia, 2009, 107120,
arXiv:0903.0821.

Kunzinger M. and Popovych R.O.,
Singular reduction operators in two dimensions,
J. Phys. A 41 (2008), 505201, 24 pp.,
arXiv:0808.3577.

Kunzinger M. and Popovych R.O.,
Potential conservation laws,
J. Math. Phys. 49 (2008), 103506, 34 pp.,
arXiv:0803.1156.

Popovych R.O. and Samoilenko A.M.,
Local conservation laws of secondorder evolution equations,
J. Phys. A 41 (2008), 362002, 11 pp.,
arXiv:0806.2765.

Popovych R.O.,
Reduction operators of linear secondorder parabolic equations,
J. Phys. A 41 (2008), 185202, 31 pp.,
arXiv:0712.2764.

Rajaee L., Eshraghi H. and Popovych R.O.,
Multidimensional quasisimple waves in weakly dissipative flows,
Physica D 237 (2008), 405419.

Boyko V.M., Patera J. and Popovych R.O.,
Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements,
Linear Algebra Appl. 428 (2008), 834854,
arXiv:0706.2465.

Popovych R.O., Kunzinger M. and Ivanova N.M.,
Conservation laws and potential symmetries of linear parabolic equations,
Acta Appl. Math. 100 (2008), 113185,
arXiv:0706.0443.

Popovych R.O., Vaneeva O.O. and Sophocleous C.,
Exact solutions of a remarkable fin equation,
Appl. Math. Lett. 21 (2008), 209214,
arXiv:mathph/0610017.

Vaneeva O.O., Johnpillai A.G., Popovych R.O. and Sophocleous C.,
Group analysis of nonlinear fin equations,
Appl. Math. Lett. 21 (2008), 248253,
arXiv:mathph/0610006.

Boyko V.M., Patera J. and Popovych R.O.,
Invariants of triangular Lie algebras with one nilindependent diagonal element,
J. Phys. A 40 (2007), 97839792,
arXiv:0705.2394.

Boyko V.M., Patera J. and Popovych R.O.,
Invariants of triangular Lie algebras,
J. Phys. A 40 (2007), 75577572,
arXiv:0704.0937.

Ivanova N.M. and Popovych R.O.,
Equivalence of conservation laws and equivalence of potential systems,
Internat. J. Theoret. Phys. 46 (2007), 26582668,
arXiv:mathph/0611032.

Vaneeva O.O., Johnpillai A.G., Popovych R.O. and Sophocleous C.,
Enhanced group analysis and conservation laws of variable coefficient reactiondiffusion equations with power nonlinearities,
J. Math. Anal. Appl. 330 (2007), 13631386,
arXiv:mathph/0605081.

Popovych R.O., Vaneeva O.O and Ivanova N.M.,
Potential nonclassical symmetries and solutions of fast diffusion equation,
Phys. Lett. A 362 (2007), 166173,
arXiv:mathph/0506067.

Boyko V.M., Patera J. and Popovych R.O.,
Invariants of Lie algebras with fixed structure of nilradicals,
J. Phys. A 40 (2007), 113130,
arXiv:mathph/0606045.

Nesterenko M. and Popovych R.O.,
Contractions of lowdimensional Lie algebras,
J. Math. Phys. 47 (2006), 123515, 45 pp.,
arXiv:mathph/0608018.

Popovych R.O.,
Direct methods of construction of conservation laws,
Physics AUC 16(II) (2006), 8194.

Popovych R.O.,
Classification of admissible transformations of differential equations,
Collection of Works of Institute of Mathematics, Kyiv, 3 (2006), no. 2, 239254.

Popovych R.O.,
Nogo theorem on reduction operators of linear secondorder parabolic equations,
Collection of Works of Institute of Mathematics, Kyiv, 3 (2006), no. 2, 231238.

Boyko V.M., Patera J. and Popovych R.O.,
Computation of invariants of Lie algebras by means of moving frames,
J. Phys. A 39 (2006), 57495762,
arXiv:mathph/0602046.

Popovych R.O.,
Normalized classes of nonlinear Schrödinger equations,
Proceedings of the VI International Workshop "Lie theory and its application to physics" (1521 August, 2005, Varna, Bulgaria),
Bulg. J. Phys. 33(s2) (2006), 211222.

Popovych R.O. and Ivanova N.M.,
Hierarchy of conservation laws of diffusionconvection equations,
J. Math. Phys. 46 (2005), 043502, 22 pp.,
arXiv:mathph/0407008.

Popovych R.O. and Ivanova N.M.,
Potential equivalence transformations for nonlinear diffusionconvection equations,
J. Phys. A 38 (2005), 31453155,
arXiv:mathph/0402066.

Eshraghi H., Abedini Y. and Popovych R.O.,
Effect of external sources on finite time singularity,
Physica Scripta 71 (2005), 5259.

Ivanova N.M., Popovych R.O. and Eshraghi H.,
On symmetry properties of nonlinear Schrödinger equations with potentials,
Proceedings of Third Summer School in Modern Mathematical Physics (2031 August, 2004, Zlatibor, Serbia and Montenegro),
Sveske Fiz. Nauka 18(A1) (2005), 451456.

Ivanova N.M., Popovych R.O. and Sophocleous C.,
Conservation laws of variable coefficient diffusionconvection equations,
Proc. of 10th International Conference in Modern Group Analysis (MOGRAN X) (Larnaca, Cyprus, 2004), University of Cyprus, Nicosia, 2005, 107113,
arXiv:mathph/0505015.

Popovych R.O. and Eshraghi H.,
Admissible point transformations of nonlinear Schrödinger equations,
Proc. of 10th International Conference in Modern Group Analysis (MOGRAN X) (Larnaca, Cyprus, 2004), University of Cyprus, Nicosia, 2005, 167174.

Nesterenko M. and Popovych R.O.,
Realizations of real unsolvable lowdimensional Lie algebras,
in Proceedings of the Third Voronoi Conference on Analytic Number Theory and Spatial Tessellations,
Editors H. Syta, A. Yurachkivsky and P. Engel,
Proceedings of Institute of Mathematics, Kyiv 55 (2005), 163168,
arXiv:mathph/0510015.

Popovych R.O., Ivanova N.M. and Eshraghi H.,
Group classification of (1+1)dimensional Schrödinger equations with potentials and power nonlinearities,
J. Math. Phys. 45 (2004), no. 8, 30493057,
arXiv:mathph/0311039.

Popovych R.O. and Ivanova N.M.,
New results on group classification of nonlinear diffusionconvection equations,
J. Phys. A 37 (2004), no. 30, 75477565,
arXiv:mathph/0306035.

Popovych R.O., Ivanova N.M., Eshraghi H.,
Lie symmetries of (1+1)dimensional cubic Schrödinger equation with potential,
in Proceedings of Fifth International Conference ''Symmetry in Nonlinear Mathematical Physics''
(2329 June, 2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A. Yehorchenko,
Proceedings of Institute of Mathematics, Kyiv 50 (2004), Part 1, 219223,
[pdf],
arXiv:mathph/0310039.

Popovych R.O., Boyko V.M., Nesterenko M.O. and Lutfullin M.W.,
Realizations of real lowdimensional Lie algebras,
J. Phys. A 36 (2003), no. 26, 73377360,
arXiv:mathph/0301029v3.

Popovych R.O., Boyko V.M., Nesterenko M.O. and Lutfullin M.W.,
Realizations of real lowdimensional Lie algebras,
arXiv:mathph/0301029v7, 39 pp.
(extended and revised version of paper J. Phys. A 36 (2003), no. 26, 73377360).

Popovych R. and Boyko V.,
Differential invariants of oneparameter group of local transformations: one independent variable,
Nonlinear Oscilations 5 (2002), no. 2, 218223 (in Ukrainian).

Popovych R. and Boyko V.,
Differential invariants and application to Riccatitype systems,
in Proceedings of Fourth International Conference
''Symmetry in Nonlinear Mathematical Physics'' (915 July, 2001, Kyiv),
Editors A.G. Nikitin, V.M. Boyko and R.O. Popovych,
Proceedings of Institute of Mathematics, Kyiv 43 (2002), Part 1, 184193
[pdf],
arXiv:mathph/0112057.

Lutfullin M. and Popovych R.,
Realizations of real 4dimensional solvable decomposable Lie algebras,
in Proceedings of Fourth International Conference ''Symmetry in Nonlinear Mathematical Physics''
(915 July, 2001, Kyiv), Editors A.G. Nikitin, V.M. Boyko and R.O. Popovych,
Proceedings of Institute of Mathematics, Kyiv 43 (2002), Part 2, 466468.
[pdf]

Boyko V. and Popovych R.,
On differential invariants in the space of two variables,
Dopov. Nats. Akad. Nauk Ukr., 2001, no. 5, 710 (in Ukrainian).

Boyko V. and Popovych R.,
Differential invariants of oneparameter Lie groups,
in Group and Analytic Methods in Mathematical Physics,
Proceedings of Institute of Mathematics, Kyiv 36 (2001), 5162 (in Ukrainian).
[pdf]

Popovych R.O. and Cherniha R.M.,
Complete classification of Lie symmetries of system of nonlinear twodimensional Laplace equations,
in Group and Analytic Methods in Mathematical Physics,
Proceedings of Institute of Mathematics, Kyiv 36 (2001), 212221.
[pdf]

Popovych R. and Boyko V.,
On group classification Galilei invariant equations of second order,
in Book of Abstract of Ukrainian Mathematical Congress (2224 August, 2001, Kyiv),
Kyiv, Institute of Mathematics, Section 5 (Math. Phys.), 2001, 2526 (in Ukrainian).

Nikitin A.G. and Popovych R.O.,
Group classification of nonlinear Schrödinger equations,
Ukr. Math. J. 53 (2001), no. 8, 12551265,
arXiv:mathph/0301009.

Popovych R.O. and Yehorchenko I.A.,
Group classification of generalized eikonal equations,
Ukr. Math. J. 53 (2001), no. 11, 15131520.

Popovych R.O. and Yehorchenko I.A.,
Group classification of generalized eikonal equations,
arXiv:mathph/0112055, 14 pp.
(extended and revised version of paper Ukr. Math. J. 53 (2001), no. 11, 15131520).

Popovych R. and Boyko V.,
Differential invariants of oneparameter group of local transformation and integration of Riccati equation,
Vestnik Samarskogo gosudarstvennogo universiteta 18 (2001), no. 4, 4956 (in Russian).
[pdf]

Popovych R.O.,
Equivalence of Qconditional symmetries under group of local transformation,
in Proceedings of the Third International Conference ''Symmetry in Nonlinear Mathematical Physics'',
Eds. A. Nikitin and V. Boyko, Proceedings of Institute of Mathematics, Kyiv 30 (2000), Part 1, 184189
[pdf],
arXiv:mathph/0208005.

Popovych G.V. and Popovych R.O.,
Flows of incompressible fluids with linear vorticity,
J. Appl. Math. Mech. 63 (1999), no. 3, 369374.
[pdf]

Zhdanov R.Z., Tsyfra I.M. and Popovych R.O.,
A precise definition of reduction of partial differential equations,
J. Math. Anal. Appl. 238 (1999), no. 1, 101123,
arXiv:mathph/0207023.

Vasilenko O.F. and Popovych R.O.,
On class of reducing operators and solutions of evolution equations,
Vestnik PGTU, 1999, no. 8, 269273 (in Russian).

Popovych R.O.,
On a class of Qconditional symmetries and solutions of evolution equations,
in Symmetry and Analytic Methods in Mathematical Physics,
Proceedings of Institute of Mathematics, Kyiv 19 (1998), 194199 (in Ukrainian).
[pdf]

Popovych R.O. and Korneva I.P.,
On the Qconditional symmetry of the linear ndimensional heat equation,
in Symmetry and analytic methods in mathematical physics,
Proceedings of Institute of Mathematics, Kyiv 19 (1998), 200211 (in Ukrainian).
[pdf]

Popovych G.V. and Popovych R.O.,
On NavierStokes fields with linear vorticity,
Ukr. Math. J. 49 (1997), no. 9, 12231229 (in Ukrainian);
translation in Ukr. Math. J. 49 (1997), no. 9, 13771385.

Popovych R.O.,
On reduction and Qconditional (nonclassical) symmetry,
in Proceedings of the Second International Conference
''Symmetry in Nonlinear Mathematical Physics'' (Kyiv, July 713, 1997),
Editors M.I. Shkil', A.G. Nikitin, V.M. Boyko, Kyiv, Institute of Mathematics,
2 (1997), 437443 [pdf],
arXiv:mathph/0207015.

Popovych V.O. and Popovych R.O.,
Solutions of NavierStokes equations represented as sums of exponents,
Proceedings of the III International conference
''Asymptotical and Qualitative Methods in Theory of Nonlinear Oscillations''
(Kyiv: Acad. Sci. Ukraine, Inst. Math.), 1997, 139140 (in Ukrainian).

Korneva I.P. and Popovych R.O.,
On compatibility of system of nonlinear Laplace equation and generalized HamiltonJacobi equation,
Proceedings of the VI International conference named acad. M.P. Kravchuk
(Kyiv: National Tech. University of Ukraine), 1997, 220 (in Ukrainian).

Popovych R.O. and Popovych V.O.,
On the NavierStokes equation with the additional condition u^1_1=u^3=0,
Ukr. Math. J. 48 (1996), no. 10, 13631374 (in Ukrainian);
translation in Ukr. Math. J. 48 (1996), no. 10, 15461560.

Popovych H.V. and Popovych R.O.,
Solutions of Euler equations which have linear vorticity,
Vestnik PGTU, 1996, no. 2, 255260 (in Russian).

Popovych R.O.,
On generalization of potential flows,
Proceedings of the V International conference named acad. M.P. Kravchuk
(Kyiv: National Tech. University of Ukraine), 1996, 352 (in Ukrainian).

Popovych R.O.,
On Lie reduction of the NavierStokes equations,
J. Nonlinear Math. Phys. 2 (1995), no. 34, 301311
[pdf].

Popovych R.O.,
On the symmetry and exact solutions of a transport equation,
Ukr. Math. J. 47 (1995), no. 1, 121125 (in Ukrainian);
translation in Ukr. Math. J. 47 (1995), no. 1, 142148.

Popovych V.O. and Popovych R.O.,
Exact solutions of NavierStokes equations for shear flows,
Akad. Nauk Ukrainy Inst. Mat. Preprint no. 8, 1995, 24 pages (in Ukrainian).

Fushchych W.I., Popovych R.O.,
Symmetry reduction and exact solutions of the NavierStokes equations. II,
J. Nonlinear Math. Phys. 1 (1994), no. 2, 158188
[pdf],
arXiv:mathph/0207016
or [pdf].

Fushchych W.I., Popovych R.O.,
Symmetry reduction and exact solutions of the NavierStokes equations. I,
J. Nonlinear Math. Phys. 1 (1994), no. 1, 75113
[pdf],
arXiv:mathph/0207016
or [pdf].

Fushchych W.I., Popovych R.O. and Popovych G.V.,
Ansätze of codimension one for the NavierStokes field and reduction of the NavierStokes equations,
Dopov. Nats. Akad. Nauk Ukr., 1994, no. 4, 3744
[pdf].

Fushchych W.I. and Popovych R.O.,
Symmetry reduction and exact solutions of NavierStokes equations,
Preprint no. 7, Kyiv, Institute of Mathematics, 1993, 56 p.

Popovych R.O.,
On solutions of the NavierStokes equations expressed via solutions of the heat equation,
in Symmetry analysis of equations of mathematical physics, Kyiv, Institute of Mathematics, Editor W.I. Fushchych, 1992, 9092.

Fushchych W. I., Shtelen W.M. and Popovych R.O.,
On the reduction of NavierStokes equations to linear heat equations,
Dopov. Nats. Akad. Nauk Ukr., 1992, no. 2, 2330 (in Ukrainian)
[pdf].

Popovych R.O.,
General solution of NavierStokes equations with an additional condition,
Dopov. Nats. Akad. Nauk Ukr., 1992, no. 4, 2124 (in Ukrainian).

Fushchych W.I. and Popovych R.O.,
Symmetry reduction of the NavierStokes equations to linear twodimensional systems of equations,
Dopov. Nats. Akad. Nauk Ukr., 1992, no. 8, 2937
[pdf].

Fushchych W.I., Shtelen W.M., Serov M.I. and Popovych R.O.,
Qconditional symmetry of the linear heat equation,
Dopov. Nats. Akad. Nauk Ukr., 1992, no. 12, 2833
[pdf].

Popovych R.O.,
On general solutions and symmetry of NavierStokes equations with additional condition $(\vec u\cdot\nabla)\vec u=\vec 0$,
Proceedings of the International conference dedicated the memory
of acad. M.P. Kravchuk (Kyiv: Acad. Sci. Ukraine, Inst. Math.), 1992, 163
(in Ukrainian).

Popovych R.O.,
Symmetry properties of an integrodifferential equation of Hartree type,
in Algebrotheoretic analysis of equations in mathematical physics,
Kyiv, Institute of Mathematics, 1990, 5053 (in Russian).

Goncharenko V.M., Popovych R.E., Popovych G.V. and Halikov D.,
Method of boundary integral equations in problem on steadystate oscillations of elastic body with cracks,
UkrNIINTI Preprint. no. 2684Uk89, 1989, 27 pages (in Russian).

Goncharenko V.M., Popovych R.E.,
On problem of difraction of plane monochromatic wave on crack of finite length,
UkrNIINTI Preprint. no. 2685Uk89, 1989, 20 pages (in Russian).

Ayvazova L.S., Goncharenko V.M., Goncharenko M.I. and Popovych R.E.,
On heat deformation arising upon laser irradiation of rigid body,
UkrNIINTI Preprint. no. 2686Uk89, 1989, 20 pages (in Russian).
EDITORIAL ACTIVITIES

Boyko V.M., Vaneeva O.O., Nesterenko M.O., Nikitin A.G. and Popovych R.O. (Eds.),
Symmetry and Integrability of Equations of Mathematical Physics,
Collection of Works of Institute of Mathematics, Kyiv, 16 (2019), no. 1, 204 pp.

Vaneeva O.O., Sophocleous C., Popovych R.O., Boyko V.M. and Damianou P.A. (Eds.),
Seventh International Workshop: Group Analysis of Differential Equations and Integrable Systems (GADEIS VII)
1519 June 2014, Larnaca, Cyprus,
J. Phys.: Conf. Ser. 621 (2015).

Maharaj S.D., Moyo S., Popovych R. (Eds.),
Special issue on the tercentenary of the LaplaceRungeLenz vector,
J. Engrg. Math. 82 (2013) issue 1.

Vaneeva O.O., Sophocleous C., Popovych R.O., Leach P.G.L., Boyko V.M. and Damianou P.A. (Eds.),
Proceedings of the Sixth International Workshop "Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, June 1721, 2012),
University of Cyprus, Nicosia, 2013, 248 pp.

N.M. Ivanova, Leach P.G.L., Popovych R.O., Sophocleous C. and Damianou P.A. (Editors),
Proceedings of Fifth Workshop "Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, June 610, 2010),
University of Cyprus, Nicosia, 2011, 240 pp.

Ivanova N.M., Popovych R.O., Sophocleous C., Damianou P. and Nikitin A.G. (Editors),
Proceedings of Fourth Workshop "Group Analysis of Differential Equations and Integrable Systems" (Protaras, Cyprus, October 2630, 2008),
University of Cyprus, Nicosia, 2009, 256 pp.

Boyko V.M., Nikitin A.G. and Popovych R.O. (Editors), Symmetry and
Integrability of Equations of Mathematical Physics
(Dedicated to the 70th Anniversary of Professor W.I. Fushchych),
Collection of Works of Institute of Mathematics, Kyiv 3 (2006), no. 2, 400 pp.

Boyko V.M., Gorbachuk M.L., Lukovs'kyi I.O., Nikitin A.G., Popovych R.O., Samoilenko A.M. (Editors),
W.I.
Fushchych, Selected Works, Kyiv, Naukova Dumka, 2005, 448 pp.

Nikitin A.G., Boyko V.M., Popovych R.O. and Yehorchenko I.A. (Editors),
Proceedings
of Fifth International Conference ''Symmetry in Nonlinear Mathematical
Physics'' (2329 June, 2003, Kyiv), Proceedings of Institute of
Mathematics, Kyiv 50 (2004), Parts 13, 1528 pp.

Nikitin A.G., Boyko V.M. and Popovych R.O. (Editors),
Proceedings
of Fourth International Conference ''Symmetry in Nonlinear Mathematical
Physics'' (915 July, 2001, Kyiv), Proceedings of Institute of Mathematics,
Kyiv 43 (2002), Parts 12, 784 pp.

Boyko V.M., Lykova O.B., Popovych R.O. and Pustovoitov M.O. (Editors), Outlines of History of Mathematics and Mathematical Sciences
(on the Occasion of Ninetieth Birthday of O.M. Bogolyubov), Proceedings
of Institute of Mathematics, Kyiv 39 (2001), 160 pp.

Boyko V.M., Nikitin A.G. and Popovych R.O. (Editors),
Group and Analytic Methods in Mathematical Physics, Proceedings of Institute
of Mathematics, Kyiv 36 (2001), 324 pp. You can download pdf
(1.63 Mb) or pdfbooklet
(1.53 Mb).

Bogolyubov O.M., Popovych R.O. and Pustovoitov M.O. (Editors),
Mathematics and the Mathematical Sciences in Ukraine in the Twentieth Century
(Proceedings of the International Summer Scientific School held in Kam'yanets'Podil's'kii, July 17, 1999),
Proceedings of Institute of Mathematics, Kyiv 34 (2001), 240 pp.

Vasilenko O.F., Popovych G.V. and Vertsanova E.V.,
Handbook on solving problems of mathematical programming (Editor: Popovych R.O.),
Kyiv, MAUP, 1999, 200 pp.

Nikitin A.G., Lopatin O.K., Boyko V.M., Zhdanov R.Z.,
Popovych R.O. and Cherniha R.M. (Editors), Symmetry and Analytic Methods
in Mathematical Physics, Proceedings of Institute of Mathematics,
Kyiv 19 (1998), 280 pp. You can download pdf
(1.35 Mb) or pdfbooklet
(1.27 Mb).

Bogolyubov O.M., Vyvrot T.M., Koshlyakov V.M., Pustovoitov M.O. and Popovych R.O. (Editors),
The Institute of Mathematics. Outlines of Its Development,
Proceedings of Institute of Mathematics, Kyiv 17 (1997), 248 pp.
Selected invited seminar talks

Conditional symmetries of linear partial differential equations with two independent variables,
14 November 2019, Seminar on differential geometry and its applications,
Mathematical Institute in Opava, Silesian University in Opava
(Opava, Czech Republic)

Computation of contractions of Lie algebras,
18 April 2019, Mathematics Seminar Afternoon,
Abdus Salam International Centre for Theoretical Physics (ICTP) (Trieste, Italy)

Equivalence groups and equivalence groupoids of classes of differential equations,
21 September 2017, Colloquium of Department of Mathematics and Statistics,
Memorial University (St. John's, Canada)

Inverse problem on conservation laws: theory and applications,
6 April 2017, Seminar "Nonlinear differential equations: symmetries, ansatzes, solutions",
Faculty of Applied Mathematics, AGH University of Science and Technology (Krakow, Poland)

Pointtransformation structures on classes of differential equations,
14 February 2017, Ostrava Seminar on Mathematical Physics,
Department of Mathematics, University of Ostrava (Czech Republic)

Inverse problems on conservation laws and conservative parameterizations,
26 September 2016, Colloquium of Department of Mathematics and Statistics,
Memorial University (St. John's, Canada)

Contractions of Lie algebras,
20 September 2016, Seminar of Department of Mathematics and Statistics,
Memorial University (St. John's, Canada)

Inverse problems on conservation laws of differential equations,
11 September 2015, Math and Stats Colloquium, Department of Mathematics and Statistics,
University of Saskatchewan (Saskatoon, Canada)

Equivalence groupoids of classes of differential equations,
3 October 2013, Mathematics and Statistics Seminar, Department of Mathematics and Statistics,
University of Cyprus (Nicosia, Cyprus)

Point transformations in classes of differential equations,
11 June 2013, Math and Stats Colloquium, Department of Mathematics and Statistics,
University of Saskatchewan (Saskatoon, Canada)

Local conservation laws of differential equations: algorithms and further development,
24 April 2013, CRM Applied Mathematics Seminar, Department of Mathematics and Statistics,
McGill University (Montréal, Canada)

Invariant discretization schemes for the shallowwater equations,
30 May 2012, SYMMHD miniworkshop,
Faculty of Engineering, Katholieke Universiteit Leuven, Campus Kortrijk (2930 May 2012, Kortrijk, Belgium)
ΐρο³πΰνςσπΰ σ β³δδ³λ³ μΰςεμΰςθχνξΏ τ³ηθκθ ²νρςθςσςσ μΰςεμΰςθκθ ΝΐΝ ΣκπΰΏνθ