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
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.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)
2. 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)
3. 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)
4. 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)
5. 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)
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., Fedorchuk, V. Ñèìåòð³éíà ðåäóêö³ÿ òà äåÿê³
êëàñè ³íâàð³àíòíèõ ðîçâ’ÿçê³â (1+3)-âèì³ðíîãî îäíîð³äíîãî ð³âíÿííÿ Ìîíæà-Àìïåðà // Proceedings of the
8. 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)
9. 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)
10. 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)
11. 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.
1. 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)
2. 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.
3. Vasyl Fedorchuk and Volodymyr Fedorchuk,
On Classification of Symmetry Reductions
for the Eikonal
Equation // Symmetry 2016, 8(6), 51; 32pages, doi:10.3390/sym8060051.
4. 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).
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
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
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19.
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.
20. 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.
21. 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. 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
2. 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
3. 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.
4. 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 * [
5. 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
6. 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.
7. 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
8. 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
9. 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.
10. 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 * [
11. 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
12. 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
13. 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
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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,
21. 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.
22. 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.
23. 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.
24. 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,
25. 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.
26. 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
27. 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
28. 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)
29. 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.
30. 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.
31. 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.
32. 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.
33. 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.
34. 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.
35. 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.
36. 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.
37. 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.
38. 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,
Phone number: (032) 258
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E-mail: volfed@gmail.com