Fedorchuk Vasyl Maksymovych
Education:
postgraduate study
at the
Scientific title: senior researcher
(1990)
Scientific degree: Doctor of Sciences
(1999)
Position: Leading Research Fellow
Scientific
profiles
ORCID: https://orcid.org/0000-0003-0164-2673
Scopus: https://www.scopus.com/authid/detail.uri?authorId=16491124400
Google Scholar: https://nbuviap.gov.ua/bpnu/bpnu_profile.php?bpnuid=BUN0006656
Research interests: finite-dimensional
Lie algebras, differential equations with non-trivial symmetry groups,
application of the local Lie groups of point transformations in theoretical and
mathematical physics
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. Description of all nonconjugate subalgebras of the Lie algebra of the
Poincaré group P(1,4). The conjugation
was considered under the group P(1,4). (With W.I. Fushchych, A.F. Barannyk, L.F. Barannyk).
2. Construction of functional bases of invariants for all nonconjugate
subalgebras of the Lie algebra of the group P(1,4).
3. Symmetry reduction and construction classes of exact solutions for
the following differential equations:
– eikonal equation.
(With I.M. Fedorchuk);
–
Euler-Lagrange-Born-Infeld equation. (With I.M. Fedorchuk) ;
– homogeneous and
inhomogeneous Monge-Ampère equation.
(With O.S. Leibov);
– linear and
nonlinear five-dimensional wave equation;
– five-dimensional Dirac equation.
(With
I.M. Fedorchuk and V.I. Fedorchuk).
4. 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.I. Fedorchuk).
5. 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.I. Fedorchuk).
6. Classification of all
nonconjugate subalgebras (dimL ≤ 5) of the Lie algebra of the group P(1,4) in classes of isomorphic subalgebras. (With V.I. Fedorchuk).
7. 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.I. Fedorchuk).
8. Classification of symmetry
reductions for the eikonal equation. (With V.I. Fedorchuk).
9. Classification of symmetry reductions for
the Euler-Lagrange-Born-Infeld equation. (With V.I. Fedorchuk).
10. Classification of symmetry reductions and
invariant solutions for the (1+3)-dimensional homogeneous and inhomogeneous
Monge-Ampère equati-ons. (With V.I. Fedorchuk).
Major publications:
Monographies
Vasyl Fedorchuk, Volodymyr Fedorchuk. Classification of Symmetry
Reductions for the Eikonal Equation. - Lviv: Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics 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. 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)
7.
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)
8.
Fedorchuk,
V., Fedorchuk, V. Ñèìåòð³éíà ðåäóêö³ÿ òà äåÿê³ êëàñè ³íâàð³àíòíèõ ðîçâ’ÿçê³â
(1+3)-âèì³ðíîãî îäíîð³äíîãî ð³âíÿííÿ Ìîíæà-Àìïåðà // Proceedings of the
International Geometry Center. − 2021. − 14 (3). − 206–218. https://doi.org/10.15673/tmgc.v14i3.2078 (Scopus, 0.603,
Q4)
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. 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.
14. Vasyl Fedorchuk and Volodymyr Fedorchuk, On Classification of Symmetry
Reductions for the Eikonal Equation // Symmetry 2016, 8(6), 51; 32pages, doi:10.3390/sym8060051.
15. 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.
16.
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;
translation in J. Math. Sci., 181 (2012), no. 3,
305–319.
17. 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.
18.
Fedorchuk V.M. and Fedorchuk
V.I., On functional bases of
the first-order differential invariants for nonconjugate subgroups of the Poincaré group P(1,4) // Annales Academiae Paedagogicae Cracoviensis, Studia Mathematica VII (2008), 41–50.
19. 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.
20. 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
21. 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.
22. 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.
23. 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.
24. 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.
25. 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.
26. Fedorchuk
V, On invariants of continuous subgroups of the generalized Poincaré
group P(1,4) // Universitatis Iagellonicae Acta Mathematica, Fasciculus XL,
2002, 197-205.
27. 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.
28. 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.
29. Fedorchuk V.M. Invariants of subgroups of the generalized
Poincaré group P(1,4). (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. - 2000. - 43, N 2. - P. 64-69.
30. 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.
31. Fedorchuk V.M. Symmetry reduction and some exact solutions of a nonlinear five-dimensional
wave equation. (Ukrainian) // Ukrain. Mat. Zh. – 1996. – 48, N 4. – P. 574–577; translation
in Ukrainian Math. J., 48 (1996), no. 4, 636–640 (1997).
32. Fedorchuk V. Symmetry Reduction and
Exact Solutions of the Euler-Lagrange-Born-Infeld, the Multidimensional Monge–Ampère and the Eikonal Equations // J. Nonlinear Math.
Phys. – 1995.– v. 2, N 3–4. – P. 329–333.
33. Fedorchuk V.M., Fedorchuk I.M. and Leibov O.S. Reduction of the Born-Infeld, the Monge-Ampère and the eikonal
equation to linear equations. (Russian) //
Dokl. Akad. Nauk Ukrainy. – 1991,
N 11. – P. 24–26.
34. Fushchich W.I., Barannik A.F., Barannik
L.F. and Fedorchuk V.M. Continuous
subgroups of the Poincaré group
P(1,4) // J. Phys. A: Math. Gen. – 1985. – 18, N 14. – P. 2893–2899.
35. Fedorchuk V.M. Nonsplitting subalgebras
of the Lie algebra of the generalized Poincaré group P(1,4).
(Russian) // Ukrain. Mat. Zh. - 1981. - 33,
N 5. P. 696-700. English translation: Ukrainian Math. J. 33 (1981), no.
5, 535-538 (1982).
36. Fedorchuk V.M. Splitting
subalgebras of the Lie algebra of the generalized Poincaré
group P(1,4) . (Russian) // Ukrain. Mat. Zh. – 1979. – 31, N 6. – P. 717–722. English
translation: Ukrainian Math. J., 31 (1979), no. 6, 554–558 (1980).
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
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
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
15. Fedorchuk
Vasyl. On Symmetry Reduction of Some Partial Differential Equations. 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. – Access mode:
(http://www.iapmm.lviv.ua/mpmm2018/Volume_3.pdf). P. 187.
16. Fedorchuk
Vasyl. On symmetry reduction and invariant solutions of some partial
differential equations. The 32nd International Colloquium on Group Theoretical
Methods in Physics (Group32) (9-13 July 2018, Czech Technical University in
Prague, Czech Republic). Book of Abstracts. - p. 23., http://kmlinux.fjfi.cvut.cz/~burdices/Group32/new-booklet.pdf.
17. 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.
18. 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,
19. 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.
20. 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.
21. Fedorchuk Vasyl. O klasyfikacji niskowymiarowych algebr Liego,
abstrakty Drugiej Ogόlnopolskej Konferencji Naukowej "Oblicza Algebry
II" (Krakόw, 1-4 czerwca, 2017), Uniwersytet Pedagogiczny im. KEN w
Krakowie,\\
http://algebra.up.krakow.pl/II/files/abstrakty.pdf, S. 15.
22. 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.
23. 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.
24. 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.
25. Fedorchuk
Vasyl, Fedorchuk Volodymyr, Classification of reduced equations for the eikonal
equation // Symmetry and Integrability of Equations of Mathematical Physics,
International workshop in honor of Wilhelm Fushchych (December 17-20, 2016,
Kyiv,
26. V.
Fedorchuk, V. Fedorchuk, On symmetry reduction and invariant solutions of some
P(1,4)-invariant differential equations, Abstracts of the 14th Conference
"Mathematics in Technical and Natural Sciences” (September 18-24, 2015,
Kościelisko), Faculty of Applied Mathematics of AGH University of Science
and Technology,
27. 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
28. 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
29. Fedorchuk
V.M, Fedorchuk V.I., Classification of non-singular manifolds in the space
M(1,4)×R(u) invariant under one- and two-dimensional non-conjugate
subalgebras of the Lie algebra of the Poincaré group P(1,4) // 8th Bolyai-Gauss-Lobachevsky
Conference "Non-Euclidean Geometry in Modern Physics and Mathematics"
(Uzhgorod, Ukraine, 22-25 May
2012). Programme and Abstracts.
Uzhgorod, 2012, IEP of the NAS of Ukraine, p. 43.
30. 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.
31. 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.
32. 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.
33. 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.
34. 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.
35. 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.
36. 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,
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and Fedorchuk V.I. Subgroup structure of the generalized Poincaré group
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