Fedorchuk Volodymyr Ivanovych
Education:
Scientific degree: Ph.D. Degree (01.01.02 – differential equations, 2016) ( thesis:
"Group classification of non-linear five-dimensional D'Alembert equations
and first-order differential invariants of
non-conjugate subgroups of the Poincare group P(1,4)")
Position: Junior Research
Fellow
In Institute: from 2005
Scientific
profiles
ORCID: https://orcid.org/0000-0002-5248-7776
Scopus: https://www.scopus.com/authid/detail.uri?authorId=54943523000
Google Scholar: https://nbuviap.gov.ua/bpnu/bpnu_profile.php?bpnuid=BUN0021573
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).
5. Construction
of invariant operators (generalized Casimir
operators) for all nonconjugate
subalgebras (dimL ≤ 5) of the Lie algebra of the group P(1,4). (With V.M. Fedorchuk).
6. Partial
preliminary group classification for nonlinear five-dimensional d’Alembert
equation.
7. Construction
of classes of invariant solutions for some five-dimensional d’Alembert
equations.
8. Classification
of symmetry reductions for the eikonal equation. (With V.M. Fedorchuk).
9. Classification of symmetry reductions for the
Euler-Lagrange-Born-Infeld equation. (With V.M. Fedorchuk).
10. Classification of symmetry reductions and invariant
solutions for the (1+3)-dimensional homogeneous and inhomogeneous
Monge-Ampère equati-ons. (With V.M. Fedorchuk).
Some of the important
publications:
Monographies
Vasyl Fedorchuk,
Volodymyr Fedorchuk. Classification of Symmetry Reductions for the Eikonal
Equation. - Lviv: Pidstryhach IAPMM of NAS of
Papers:
1. Fedorchuk V.M., Fedorchuk V.I. On the Symmetry Reduction
of the (1+3)-Dimensional Inhomogeneous Monge–Ampère Equation to
Algebraic Equations // Journal of Mathematical Sciences. – 2024. – 282, No.5. –
P. 668–677. https://doi.org/10.1007/s10958-024-07208-8 (Scopus, Q3)
2. Fedorchuk V.Ì., Fedorchuk V.I. On the Classification of
Symmetry Reductions for the (1+3)-Dimensional Monge-Ampère Equation. //
Journal of Mathematical Sciences. – 2023. – 272, No. 1. – P. 1–13.
https://doi.org/10.1007/s10958-023-06395-0 (Scopus, 0.302, Q3)
3. Fedorchuk V.M., Fedorchuk V.I. On the Construction and
Classification of the Common Invariant Solutions for Some P(1,4) - Invariant
Partial Differential Equations // Applied Mathematics. – 2023 – Vol. 14, No.11
– P. 728–747. https://doi.org/10.4236/am.2023.1411044 (Scopus, 0.228, Q4)
4. Fedorchuk V.M., Fedorchuk V.I. On partial preliminary
group classification of some class of the (1+3)–dimensional Monge – A
mpère equations. I. One–dimensional Lie algebras // Mat. Metody
Fiz.–Mekh. Polya. – 2023. – 66, ¹ 1–2. – P. 40–47. (in Ukrainian)
5. Fedorchuk V.M., Fedorchuk V.I. on symmetry reduction of
the (1+3)–dimensional inhomogeneous Monge – Ampère equation to algebraic
equations // Mat. Metody Fiz.–Mekh. Polya.
– 2022. – 65, ¹ 1–2. – P. 58–64.
(in Ukrainian)
6. Fedorchuk V.M., Fedorchuk V.I. On reduction of the
(1+3)-dimensional inhomogeneous Monge-Ampère equation to the first-order
partial differential equations // Ukr. Math. J. – 2022. – 74, No. 3. – P.
418–426. – https://doi:10.37863/umzh.v74i3.6996. (in Ukrainian)
7. Fedorchuk V.M. , Fedorchuk V.I. Reduction of the (1 +
3)-dimensional Inhomogeneous Monge–Ampère equation to first-order
partial differential equations // Ukr. Mat. J. – 2022. – 74, No. 3. – P.
472–483. – https://doi:10.1007/s11253-022-02076-4. (Scopus, 0.726, Q3)
8. Fedorchuk, V., Fedorchuk, V. Ñèìåòð³éíà ðåäóêö³ÿ òà äåÿê³
êëàñè ³íâàð³àíòíèõ ðîçâ’ÿçê³â (1+3)-âèì³ðíîãî îäíîð³äíîãî ð³âíÿííÿ Ìîíæà-Àìïåðà
// Proceedings of the
9. Fedorchuk V.M., Fedorchuk V.I. On the classification of
symmetry reductions for the (1+3)-dimensional monge – ampère equation //
Mat. Metody Fiz.-Mekh. Polya. 63, (2), 7–16, (2020). (in Ukrainian)
10. Fedorchuk V.M. and Fedorchuk V.I. On Symmetry Reduction
of the (1 + 3)-Dimensional Inhomogeneous Monge-Ampère Equation to the
First-Order ODEs // Applied Mathematics, 2020, 11, 1178–1195. https://doi.org/10.4236/am.2020.1111080.
(Google Scholar, 0.507, Q4)
11. Fedorchuk V.M., Fedorchuk V.I. On the classification of
symmetry reduction and invariant solutions for the Euler-Lagrange-Born-Infeld
equation. // Ukrainian Journal of
Physics.
− 2019. − 64, ¹ 12. − P. 1103−1107.https://doi.org/10.15407/ujpe64.12.1103
(Scopus, 0.333, Q4)
12. Fedorchuk V.M., Fedorchuk V.I., On symmetry reduction of
the Euler–Lagrange–Born–Infeld equation to linear ODEs // Symmetry and Integrability
of Equations of Mathematical Physics, Collection of Works of Institute of
Mathematics, Kyiv. − 2019. − 16, ¹ 1. − P. 193−202.
13. Fedorchuk V.I. On the invariant
solutions of some five-dimensional D’Alembert equations // Journal of
Mathematical Sciences. – 2017. – 220. No 1 – P. 27–37.
https://doi.org/10.1007/s10958-016-3165-7 (Scopus, Web of Science, Q3, 0.517)
14. Fedorchuk V. and Fedorchuk V. On classification of
symmetry reductions for partial differential equations // Collection of the
works dedicated to 80th of anniversary of B.J. Ptashnyk, Pidstryhach Institute
for Applied Problems of Mechanics and Mathematics of NAS of Ukraine, Lviv,
2017. – P. 241–255.
15. Vasyl Fedorchuk and Volodymyr Fedorchuk,
On Classification of Symmetry Reductions for the Eikonal Equation // Symmetry 2016, 8(6), 51; 32pages, doi:10.3390/sym8060051.
16. Fedorchuk V.I. On invariant solutions of some
five-dimensional d’Alembert equations. (Ukrainian) // Mat. Metodi Fiz.-Mekh.
Polya. – 2014. – 57, N 4, 27–34. ; translated in Journal of Mathematical
Sciences, Vol. 220, No. 1, 27 - 37 (2017).
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 a partial preliminary group
classification of the nonlinear five-dimensional d’Alembert equation.
(Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. – 2012. - 55, N 3. – P.
35–43; translated in J. Math.Sci., 194 (2013), no. 2, 166–175.
19. 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, 305–319.
20. 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, ¹ 2. – P. 23-27 ; translation in J. Math. Sci., 170
(2010), no. 5, 588–593.
21. 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), 41–50.
22. 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.
23. 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
24. 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.
25. 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.
26. 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.
27. 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.
28. 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.
29. 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. 36–42.
30. 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.
31.
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. 24–29.
32. 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. – Ñ. 52–56.
33. 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), 283–292, Pr. Inst.
Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 36, Natsional. Akad. Nauk Ukraini, Inst. Mat.,
Conference proceedings
1. Vasyl
Fedorchuk, Volodymyr Fedorchuk. On the construction and classification of the
common invariant solutions for the (1 + 3)-dimensional
Euler-Lagrange-Born-Infeld and homogeneous Monge-Ampere equations //
International scientific online conference «Algebraic and geometric methods of
analysis», May 27-30, 2024,
2. Vasyl
Fedorchuk, Volodymyr Fedorchuk, On the construction of the common invariant
solutions for some P(1,4)-invariant partial differential equations //
International conference dedicated to the 145th anniversary of the birth of
Hans Hahn, September 23–27, 2024, Chernivtsi. – Chernivtsi:
3. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On Classification of Symmetry Reductions for Some
P(1,4)-Invariant Partial Differential Equations. Symmetry 2023 - The 4th
International Conference on Symmetry (21 – 23 June, 2023, AXA Convention Centre
Barcelona, Spain). Program and Abstract Book, p.49. https://symmetry2023.sciforum.net/events_files/766/customs/af8bdf95fc6ca8768ff2b5bbc213cf7f.pdf
4. Fedorchuk
Vasyl, Fedorchuk Volodymyr. Classification of symmetry reductions for some
P(1,4)-invariant partial differential equations. // Int. Scientific Conference
“Current Problems of Mechanics and Mathematics – 2023” (May 23–25, 2023, Lviv,
Ukraine) http://iapmm.lviv.ua/mpmm2023/materials/proceedings.mpmm2023.pdf, P.
376. http://iapmm.lviv.ua/mpmm2023/materials/ma09_02.pdf
5. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On partial preliminary group classification of some
class of (1 + 3)-dimensional Monge-Ampere equations. Two-dimensional Abelian
Lie algebras // International Online Conference Algebraic and geometric methods
of analysis (May 29 June 31, 2023, Odesa-Kyiv, Ukraine)}
https://imath.kiev.ua/~topology/conf/agma2023/contents/abstracts/texts/fedorchuk/fedorchuk.pdf.
6. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On symmetry reduction of the (1+3)-dimensional
Inhomogeneous Monge-Ampère equation to algebraic equation. The XVI-th
International Conference of Differential Geometry and Dynamical Systems (
DGDS-2022 ), (1 - 4 September 2022) * ONLINE * [
7. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On patrial preliminary group classification of some
class of (1+3)-dimensional Monge-Ampere equations. I. One-dimensional Lie
algebras // Workshop "Symmetry and Integrability of Equations of
Mathematical Physics" December 23-24, 2022, Kyiv, Ukraine.
http://www.imath.kiev.ua/~appmath/Abstracts2022/Fedorchuk.pdf
8. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On patrial preliminary group classification of some
class of (1+3)-dimensional Monge-Ampere equations. One-dimensional Galilean Lie
algebras // International Scientific Conference "Algebraic and Geometric
Methods of Analysis" Odesa, Ukraine May 24-27, 2022.
http://imath.kiev.ua/~topology/conf/agma2022/contents/abstracts/texts/fedorchuk/fedorchuk.pdf
– P. 16–17.
9. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On symmetry reduction and some classes of invariant
solutions of the (1+3)-dimensional inhomogeneous Monge-Ampère equation.
The XV-th International Conference of Differenti-al Geometry and Dynamical
Systems (DGDS-2021) 26 - 29 August 2021 * ONLINE * [Bucharest, Romania]. The
booklet of abstracts. p.5 http://www.mathem.pub.ro/dept/dgds-21/dgds-21.htm
10. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On symmetry reduction and some classes of invariant
solutions of the (1 + 3)-dimensional homogeneous Monge-Ampère equation.
// International On line Conference Algebraic and Geometric Methods of Analysis
dedicate to the memory of Yuriy Trokhymchuk (17.03.1928-18.12.2019) (May 25-28,
2021, Odesa, Ukraine). Book of Abstracts. p.36 https://www.imath.kiev.ua/~topology/conf/agma2021/contents/agma2021-abstracts.pdf
11. Fedorchuk
V. M., Fedorchuk V. I. On some applications of classication of low-dimensional
Lie algebras // Book of abstracts of the International mathematical conference
dedicated to the 60th anniversary of the department of algebra and mathematical
logic of Taras Shevchenko National University of Kyiv, 14-17 July 2020, Kyiv,
Ukraine. – 93 p. – Ðåæèì äîñòóïó äî ðåñóðñó: https://bit.ly/2ZIyqMs – P. 34.
12. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On symmetry reduction and some classes of invariant
solutions of the (1+3)-dimensional Monge-Ampère equation. The XIV-th
International Conference of Differential Geometry and Dynamical Systems (
DGDS-2020 ) 27 -29 August 2020 * ONLINE * [
13. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On Classification of Symmetry Reductions for Some
P(1,4)-Invariant Partial Differential Equations. XI International Skorobohatko
Mathematical Conference (October 26-30, 2020, Lviv, Ukraine). Book of
Abstracts. p.31.
http://www.iapmm.lviv.ua/conf_skorob2020/documents/2020tezy.pdf
14. Fedorchuk
Volodymyr. On Symmetry Reduction and Invariant Solutions of the
Euler-Lagrange-Born-Infeld Equation. XI International Skorobohatko Mathematical
Conference (October 26-30, 2020, Lviv, Ukraine). Book of Abstracts. p.32.
http://www.iapmm.lviv.ua/conf_skorob2020/documents/2020tezy.pdf
15. Fedorchuk
V. M. and Fedorchuk V. I. On
classification of symmetry reductions and invariant solutions for the
Euler-Lagrange-Born-Infeld equation // Book of Abstracts. Kiev, Bogolyubov
Institute for Theoretical Physics of NAS of Ukraine, 2019, P.10.
https://indico.bitp.kiev.ua/event/3/attachments/1/83/abstr_bgl_2019.pdf
16. Fedorchuk
Vasyl, Fedorchuk Volodymyr. On classification of some non-singular manifolds in
the space M(1,3)× R(u) and symmetry reduction of the eikonal equation.
The XII-th International Conference of Differential Geometry and Dynamical
Systems (DGDS-2018) (30 August - 2 September 2018, the Callatis High-School in
the city Mangalia - Romania). Abstracts. - p. 1., http://www.mathem.pub.ro/dept/dgds-18/dgds-18.htm.
17.
Fedorchuk V.M., Fedorchuk V.I. On symmetry
reduction of some partial differential equations. VI All-Ukrainian B.V. Vasylyshyn mathematical conference "Nonlinear problems of analysis" (26-28 september 2018, Ivano-Frankivsk - Mykulychyn). Book of Abstracts. Ivano-Frankivsk, Vasyl Stefanyk Precarpathian National University, 2018. – p. 63.
18. Fedorchuk
Vasyl, Fedorchuk Volodymyr, On classification of symmetry reductions for the
Euler–Lagrange–Born–Infeld equation // Symmetry and Integrability of Equations
of Mathematical Physics, International workshop on the occasion of the fortieth
anniversary of the Department of Applied Research (nowadays the Department of
Mathematical Physics) (December 21-24, 2018, Kyiv, Institute of Mathematics of
NAS of Ukraine).
https://www.imath.kiev.ua/~appmath/Abstracts2018/Fedorchuk.html.
19.
Fedorchuk
Vasyl and Fedorchuk Volodymyr. On
Classification of Symmetry Reductions for Partial Differential Equations \\
www.mdpi.com/2504-3900/2/1/85; \\ Proceedings 2018, 2(1), 85; https://doi.org/10.3390/proceedings2010085.
20. Volodymyr Fedorchuk, On some invariant
solutions for the Euler–Lagrange–Born–Infeld equation // Symmetry and
Integrability of Equations of Mathematical Physics, International workshop on
the occasion of the fortieth anniversary of the Department of Applied Research
(nowadays the Department of Mathematical Physics) (December 21-24, 2018, Kyiv,
Institute of Mathematics of NAS of Ukraine). https://www.imath.kiev.ua/~appmath/Abstracts2018/FedorchukV.html.
21.
Volodymyr
Fedorchuk. On Symmetry Reduction of the Eikonal Equation. Modern problems of Mechanics and Mathematics: collection of scientific
papers in 3 vol. / Edited by A.Ì. Samoilenko, R.M. Kushnir [Electronic resource] //
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NAS of
Ukraine. – 2018. – Vol. 3. – p. 188.
http://www.iapmm.lviv.ua/mpmm2018/Volume
3.pdf.
22.
Fedorchuk V.². On symmetry reduction and invariant solutions of the
eikonal equation. VI All-Ukrainian B.V. Vasylyshyn
mathematical conference "Nonlinear problems
of analysis" (26-28 september 2018, Ivano-Frankivsk - Mykulychyn). Book of Abstracts. Ivano-Frankivsk,
23.
Fedorchuk
Vasyl, Fedorchuk Volodymyr. On
Ñlassification of Symmetry Reductions for Partial Differential Equations,
Program and Abstract Book. Symmetry 2017: The 1st International
Conference on Symmetry (16-18 October 2017, Parc Cientific de Barcelona,
Spain), MDPI, p. 168.
24. Fedorchuk
V.M. , Fedorchuk V.I. On Classification
of Some Non-Singular Manifolds In the Space M(1,3) ×R(u). // BGL17: 10th
Bolyai-Gauss-Lobachevski Conference on Non-Euclidean Geometry and its
Applications. (Aug 20–26, 2017 Gyöngyös, Hungary). https://indico.cern.ch/event/586799/attachments/1400831/2353974/bgl17_preliminary_agenda.pdf.
25.
Fedorchuk
V.M., Fedorchuk V.I. Classification of low-dimensional Lie Algebras, Abstracts
of the 11th International Algebraic Conference in Ukraine dedicated to the 75th
anniversary of V.V.Kirichenko (July 3-7, 2017, Kyiv, Ukraine), Taras Shevchenko
National University of Kyiv, p. 42.
26.
Fedorchuk Volodymyr I. On invariant solutions
of the five-dimensional Liouville equation // Symmetry and Integrability of
Equations of Mathematical Physics, International workshop in honor of Wilhelm
Fushchych (December 17-20, 2016, Kyiv,
27.
Fedorchuk V.I. On Exact Solutions of Some
P(1,4)-Invariant d'Alembert Equations // International conference of young
mathematicians (Kuiv, 3–6 June 2015): Book of abstracts. – Kyiv, 2015. – P.
118.
28.
Vasyl
Fedorchuk, Volodymyr Fedorchuk, On Symmetry Reduction of Some P(1,4)-invariant
Differential Equations, Abstracts of The XVIth International Conference is
Dedicated to 70th Anniversary of Professor Jan J. Sławianowski (June 6-11,
2014, Varna, Bulgaria), Institute of Biophysics, Bulgarian Academy of Sciences,\\
http://www.bio21.bas.bg/conference/Conference\_files/abstr2014/Fedorchuk.pdf
29.
Fedorchuk V.M., Fedorchuk V.I. Classification
of low-dimensional noncon-jugate subalgebras of the Lie algebra of the
Poincaré group P(1,4), 9-th
Inter-national Algebraic Conference in
30. Fedorchuk
V.I. On the preliminary group classification of the
nonlinear five-dimensional d'Alembert equation // Conference of young Scientists “ Pidstryhach
reading”.– L’viv, Ukraine, May 23–25, 2012, L’viv. – [Electronic resource]. –
Access mode: http://iapmm.lviv.ua/chyt2012/materials/48.pdf (Ukrainian)
31. Vasyl
M. Fedorchuk, Volodymyr I. Fedorchuk, Classification of the five-dimensional
non-conjugate subalgebras of the Lie algebra of the Poincaré group
P(1,4), 8th International Algebraic Conference in Ukraine (July
5-12, 2011, Lugansk, Ukraine), Book of abstracts, Lugansk, Lugansk Taras
Shevchenko National University, p. 160.
32. 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.
33. 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.
34. 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.
35. 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.
36. 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.
37. 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.
38. Fedorchuk
V.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.
39. 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
in Kyiv, Ukraine), Proceedings of Institute of Mathematics, Kyiv, 2000, V.30,
Part 1, P. 103-108.
40. 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,
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