Fedorchuk Volodymyr Ivanovych

Education: Ivan Franko Lviv State University (speciality - mathematics, 1999), postgraduate study at the Lviv State University (1999-2002)

Scientific degree: Ph.D. Degree

Position: Junior Research Fellow

Research interests: finite-dimensional Lie algebras, differential equations with non-trivial symmetry groups

Field of scientific research: study of structural properties of the finite-dimensional Lie algebras and application of the results obtained for construction and investigation of classes of differential equations invariant with respect to these Lie algebras

Main scientific results:

1.    Construction of classes of first- and second- order differential equations in the space M(1,4)× R(u) with non-trivial symmetry groups.

2.    Equivalence criteria for arbitrary two functional bases of differential invariants of arbitrary finite order of nonconjugate subalgebras of Lie algebras of local Lie groups of point transformations. (With V.M. Fedorchuk).

3.    Construction of non-equivalent functional bases of first-order differential invariants for all nonconjugate subalgebras of the Lie algebra of the group P(1,4). (With V.M. Fedorchuk).

4.    Classification of all nonconjugate subalgebras (dimL ≤ 5) of the Lie algebra of the group P(1,4) in classes of isomorphic subalgebras. (With V.M. Fedorchuk).

1.    Construction of invariant operators (generalized Casimir operators) for all nonconjugate subalgebras (dimL5) of the Lie algebra of the group P(1,4). (With V.M. Fedorchuk).

2.    Partial preliminary group classification for nonlinear five-dimensional dAlembert equation.

3.    Construction of classes of invariant solutions for some five-dimensional dAlembert equations.

4.    Classification of symmetry reductions for the eikonal equation. (With V.M. Fedorchuk).

The results obtained are presented in scientific publications ( articles, abstracts).

Major publications:

1.    Fedorchuk V.I. First-order differential equations in the space M(1,4)×R(u) with nontrivial symmetry groups. (Ukrainian) // Group and analytic methods in mathematical physics (Ukrainian), 283292, Pr. Inst. Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 36, Natsional. Akad. Nauk Ukraini, Inst. Mat., Kiev, 2001.

2.    Fedorchuk V.I. On second-order differential equations in the space M(1,4)×R(u) with nontrivial symmetry groups. (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. 2001. 44, N. 4. . 5256.

3.    Fedorchuk V.M., Fedorchuk I.M. and Fedorchuk V.I. Symmetry reduction of the five-dimensional Dirac equation. (Ukrainian) // Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki, 1999, N 9, P. 2429.

4.    Fedorchuk V.M. and Fedorchuk V.I. Differential invariants of the first order of splitting subgroups of the generalized Poincaré group P(1,4). (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. - 2001.- 44, N 1. - P. 16-21.

5.    Fedorchuk V.M. and Fedorchuk V.I. On first-order differential invariants for splitting subgroups of the generalized Poincaré group P(1,4). (Ukrainian) // Dopov. Nats. Akad. Nauk Ukr. 2002, N 5. P. 3642.

6.    Fedorchuk V.M. and Fedorchuk V.I., On new differential equations of the first-order in the space M(1,4)×R(u) with non-trivial symmetries // Annales Academiae Paedagogicae Cracoviensis, Studia Mathematica III (2003), Folia 16, 49-53.

7.    Vasyl Fedorchuk and Volodymyr Fedorchuk., On the Differential First - Order Invariants of the Non-Splitting Subgroups of the Poincaré group P(1,4) // Proceedings of Institute of Mathematics of NAS of Ukraine. - 2004, 50, Part 1, 85-91.

8.    Vasyl M. Fedorchuk and Volodymyr I. Fedorchuk., On the differential first-order invariants for the non-splitting subgroups of the generalized Poincaré group P(1,4) // Annales Academiae Paedagogicae Cracoviensis, Studia Mathematica IV (2004), Folia 23, 65-74.

9.    Fedorchuk V.M. and Fedorchuk V.I. On functional bases of first-order differential invariants of continuous subgroups of the Poincaré group P(1,4). (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. - 2005. - 48, N 4. - P. 51-58.

10. Fedorchuk V.M. and Fedorchuk V.I., First-order differential invariants of the splitting subgroups of the Poincaré group P(1,4) // Universitatis Iagellonicae Acta Mathematica, 2006, Fasciculus XLIV, 35-44.

11. Fedorchuk V.M. and Fedorchuk V.I. On classification of low-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4). (Ukrainian) // Proceedings of the Institute of Mathematics of NAS of Ukraine, 2006,  3, N 2, 302-308.

12. Fedorchuk V.M. and Fedorchuk V.I. On invariant operators of low-dimension nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4). (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. - 2007. - 50, N 1. - P. 16-23.

13. Fedorchuk V.M.and  Fedorchuk V.I., On functional bases of the first-order differential invariants for non-conjugate subgroups of the Poincaré group P(1,4) // Annales Academiae Paedagogicae Cracoviensis, Studia Mathematica VII (2008), 4150.

14. Fedorchuk V.M. and Fedorchuk V.I. On the equivalence of functional bases of differential invariants of nonconjugate subgroups of local Lie groups of point transformations. (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. 2009. - 52, 2. P. 23-27 ; translation in J. Math. Sci., 170 (2010), no. 5, 588593.

15. Fedorchuk V. M. and Fedorchuk V.I. Invariant operators for four-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4). (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. - 2010. - 53, N 4. - P. 17-27; translated in J. Math. Sci., 181 (2012), no. 3, 305319.

16. Fedorchuk V.I. On a partial preliminary group classification of the nonlinear five-dimensional dAlembert equation. (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. 2012. - 55, N 3. P. 3543; translated in J. Math.Sci., 194 (2013), no. 2, 166175.

17. Vasyl Fedorchuk and Volodymyr Fedorchuk, Invariant Operators of Five-Dimensional Nonconjugate Subalgebras of the Lie Algebra of the Poincaré Group P(1,4) // Abstract and Applied Analysis, vol. 2013, Article ID 560178, 16 pages, 2013. doi:10.1155/2013/560178.

18. Fedorchuk V.I. On invariant solutions of some five-dimensional dAlembert equations. (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. 2014. 57, N 4, 2734. ; translated in Journal of Mathematical Sciences, Vol. 220, No. 1, 27 - 37 (2017).

19. Vasyl Fedorchuk and Volodymyr Fedorchuk., On Classification of Symmetry Reductions for the Eikonal Equation // Symmetry 2016, 8(6), 51; 32pages, doi:10.3390/sym8060051.

 

List of Conference Proceedings:

1.    V.I. Fedorchuk. On Differential Equations of First- and Second-Order in the Space M(1,3)×R(u) with Nontrivial Symmetry Groups //  Proc. of the Fourth Internat. Conf. Symmetry in Nonlinear Mathematical Physics (9-15 July 2001, Kyiv, Ukraine), Proceedings of Institute of Mathematics of NAS of Ukraine, Kyiv,  43, Part 1, 145-148.

2.    Fedorchuk V.M., Fedorchuk I.M. and Fedorchuk V.I. On Symmetry Reduction of the Five-Dimensional Dirac Equation // The Third Internat. Conf. "Symmetry in Nonlinear Mathematical Physics" (July 12-18, 1999, Kyiv, Ukraine), Proceedings of Institute of Mathematics, Kyiv, 2000, V.30, Part 1, P. 103-108.

3.    FedorchukV.M. and Fedorchuk V.I. Subgroup structure of the generalized Poincaré group P(1,4) and models with nontrivial symmetry // Mathematical physics: Proceedings of the Ukrainian mathematical congress - 2001. - Kyiv: Institute of mathematics of NAS of Ukraine, 2002, 101-116.

4.    Fedorchuk V. and Fedorchuk V. Some new differential equations of the first-order in the spaces M(1,3)× R(u) and M(1,4)× R(u) with given symmetry groups // Functional Analysis and its Applications, North-Holland Mathematics Studies, 197, Editor: Saul Lubkin, Elsevier, 2004, 85-95.

5.    Fedorchuk V.I. and Fedorchuk V.M. Symmetry reduction of some classes of the first-order differential equations in the space M(1,4)× R(u) // XIth Slovak-Polish-Czech Mathematical School, Mathematica, Proceedings of the XIth Slovak-Polish-Czech Mathematical School (Ruzomberok, June 2nd-5th, 2004), Pedagogical Faculty of Catholic University in Ruzomberok, P. 37-41.

6.    Fedorchuk V.M. and Fedorchuk V.I. On first-order differential invariants of the non-conjugate subgroups of the Poincaré group P(1,4) // Differential Geometry and its Applications: Proc. 10th Int. Conf. on DGA 2007, in Honour of Leonhard Euler, Olomouc, Czech Republic, 27 - 31 August 2007, World Scientific Publishing Company, 2008, 431-444.

7.    Fedorchuk V.M. and Fedorchuk V.I. On non-equivalent functional bases of first-order differential invariants of the non-conjugate subgroups of the Poincaré group P(1,4) // Acta Physica Debrecina, 2008, XLII, 122-132.

8.    Vasyl M. Fedorchuk and Volodymyr I. Fedorchuk. On some classes of the partial differential equations with non-trivial symmetry groups // Proc. of the XVIth International Congress on Mathematical Physics, edited by Pavel Exner, World Scientific Publishing Co. Pte. Ltd. Singapore, 2010, p. 454.

9.    Vasyl Fedorchuk and Volodymyr Fedorchuk. On non-singular manifolds in the space M(1,3)×R(u) invariant under the non-conjugated subgroups of the Poincaré group P(1,4) // The 7th edition of the Bolyai-Gauss-Lobachevsky conference series. Abstracts book. International Conference on Non-Euclidean Geometry and its Applications (5-9 July 2010, Babe\c{s}-Bolyai University, Cluj-Napoca, Romania), p. 43.

Phone number: (032) 258 96 22

E-mail: volfed@gmail.com