Publications
of Department of Algebra
Published
monographies:
- Shchedryk V. Arithmetic of matrices over rings – Kyiv, Akademperiodyka, 2021. − 278 p. − https://doi.org/10.15407/akademperiodika.430.278 pdf.
- Vasyl Fedorchuk, Volodymyr Fedorchuk. Classification of Symmetry Reductions for the Eikonal Equation. – Institute of Mathematics, Pedagogical University, Cracow, Poland; Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of National Academy of Sciences of Ukraine, Lviv, 2018. – 176 p. pdf
- Shchedryk V.P. Factorization of matrices over elementary divisor rings. – Lviv: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NAS of Ukraine, 2017. – 304 p. (in Ukrainian) pdf.
- Petrychkovych V.Ì. Generalized equivalence of
matrices and its collections and factorization of matrices over rings. – L’viv: Pidstryhach Institute for Applied Problems of Mechanics and
Mathematics of the NAS of Ukraine, 2015. – 312 p. pdf.
(in Ukrainian)
- Kazimirs’kii P.S. Factorization of matrix polynomials (second edition revised). – L’viv: Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics of the NAS of
- Shmoilov B. I. Solving of
algebraic equations by continuous fractions. –
- Shmoilov B. I. Continuous
fractions and two classical problems of algebra. –
- Kazimirs’kii P.S. Factorization of matrix polynomials. – K.: Naukova dumka. – 1981. – 224 p. (in Ukrainian)
Publications
in journals:
2024
- Romaniv A. M., Shchedryk V. P.
Adequate Properties of Matrix Divisors // Journal of mathematical sciences.
– 2024. – 279, No 2 – P. 141–150.
https://doi.org/10.1007/s10958-024-07001-7
- Ladzoryshyn
N.B., Petrychkovych V.M. On standard forms of the pairs of matrices over
the ring of Gaussian integers with respect to the (z,k)-equivalence
// Journal of mathematical sciences – 2024. – 279, No 2 – P. 133–140.
https://doi.org/10.1007/s10958-024-07000-8
2023
- Bovdi, V. A., Shchedryk, V. P. Generating solutions of a linear equation and structure of elements of the Zelisko group II // Quaestiones Mathematicae – 2023 – 46 (9) – P. 1789–1798. https://doi.org/10.2989/16073606.2022.2112629
- Fedorchuk V.Ì. and 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
5. Romaniv A. M. On the
Smith normal form of the least common multiple of matrices from some class of
matrices // Journal of mathematical sciences. – 2023. – 277, No. 1. – P. 53–59.
https://doi.org/10.1007/s10958-023-06813-3
- Gatalevych, A. I., Shchedryk V. P. On adequacy of full matrices // Matematychni Studii. – 2023. – 59.2 – P.115–122. https://doi.org/10.30970/ms.59.2.115-122
- Fedorchuk V.M. and 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
- Shavarovskii B.Z. On the triangular form of a polynomial matrix of
simple structure and its invariants with respect to
semi-scalar equivalence // Math. methods and phys.-mech. fields. – 2023. – 66, ¹
1–2. – P. 16–22.
- Prokip V.M.,
Melnyk O.M., Kolyada R.V. On divisibility with remainder of polynomial
matrices over an arbitrary field // Math. methods and phys.-mech. fields. – 2023. – 66, ¹
1–2. – P. 23–39.
- Fedorchuk V.M., Fedorchuk
V.I. On partial preliminary group classification of some class of the
(1+3)-dimensional Monge – Ampère equations. I.
One-dimensional Lie algebras // Math. methods and phys.-mech. fields. –
2023. – 66, ¹ 1–2. – P. 40–47.
2022
11. Petrychkovych V.M. Standard forms of matrices over rings with respect to
different types of equivalences and their applications in theory of the matrix
factorization and matrix equations // Journal of Mathematical Sciences. – 2022.
– 265, No. 3. – P. 345–368.– https://doi.org/10.1007/s10958-022-06057-7.
- Shchedryk V.P. Arithmetic properties of
the solutions of linear equations // Math. methods and phys.-mech. fields. –
2022. – 65, ¹ 3-4. – P. 44–49. (in
Ukrainian)
13. Bovdi V., Shchedryk V. Adequacy of nonsingular matrices over commutative
principal ideal domains – arXiv preprint arXiv:2209.01408, 2022
- Shavarovskii B.Z. On the Triangular Form of 3 X
3-Matrix of Simple Structure Relative to Semiscalar Equivalence // Math. methods and phys.-mech. fields. – 2022. – 65, ¹
3-4. – P. 5–28.
15. Shavarovskii B.Z. Conditions of semiscalar
equivalence of one class 3x3 matrices of simple structure // Journal of
Mathematics. − 2022. − vol. 2022 Article ID 8395922, 13 pages. −
https://doi.org/10.1155/2022/8395922.
16. Fedorchuk V.M. , Fedorchuk V.I. Reduction of
the (1 + 3)-dimensional Inhomogeneous Monge–Ampère equation to
first-order partial differential equations // Ukrainian Mathematical Journal. –
2022. – 74, No. 3. – P. 472–483. – https://doi:10.1007/s11253-022-02076-4.
17. 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)
18. Fedorchuk V.M., Fedorchuk V.I. on
symmetry reduction of the (1+3)-dimensional inhomogeneous Monge – Ampère
equation to algebraic equations // Math. methods and phys.-mech. fields. – 2022. – 65, ¹ 1-2. – P. 58–64.
20. Dzhaliuk N. S. and Petrychkovych V. M. Equivalence of matrices in the
ring M(n,R) and its subrings // Ukrainian Mathematical
Journal. – 2022. – 73, No.12. – P. 1865– 1872. – https://doi.org/10.1007/s11253-022-02034-0.
21. Dzhaliuk N.S. Solutions of
matrix equation AX+YB=C with
triangular coefficients // Journal of Mathematical Sciences. –
2022. – 261, No. 1. – P.
25–32. – https://doi:10.1007/s10958-022-05734-x.
22. Ladzoryshyn N.B., Petrychkovych V.M. The number of standard forms of
matrices over imaginary Euclidean quadratic rings with respect to the (z,k)-equivalence // Matematychni Studii. – 2022. – 57, No. 2. – P. 115–121.
https://doi:10.30970/ms.57.2.115-121
23. Korzhik V. A simple proof of the Map Color Theorem for nonorientable
surfaces // Journal of Combinatorial Theory, Ser. B. – 2022. – Vol. 156. – P. 1
– 17. https://doi.org/10.1016/j.jctb.2022.03.004
24. Prokip V. M. A note on semiscalar equivalence of polynomial matrices //
Electronic Journal of Linear Algebra. – 2022. – V. 38. – P. 195–203.
https://doi.org/10.13001/ela.2022.65
25. Bilous A.M., Gatalevych A.I. Stable range of some classes of
noncommutative rings //
Journal of Mathematical Sciences −
2022. − 261, ¹ 1 − P. 33–40. https://doi.org/
10.1007/s10958-022-05735-w
- Romaniv A.M.,
Dzhaliuk N.S. The structure of the Smith normal form of the greatest common divisor
and
the
least common multiple of the third order matrices over Bezout domains of stable
range 1.5 // Applied problems of mechanics and mathematics. – 2022. – Vol 20. – P. 25–30.
2021
- Ladzoryshyn N. B., Petrychkovych V. M. Standard
form of matrices over quadratic rings with respect to the (z,k)-equivalence and the structure of solutions of bilateral
matrix linear equations. // Journal of
Mathematical Sciences. − 2021. − Vol. 253, No.
1, February. – Ð. 54–62.
https://doi.org/10.1007/s10958-021-05212-w
28. Romaniv A. M., Shchedryk
V. P. Adequate properties of matrix divisors
// Math. methods and phys.-mech. fields – 2021. – 64. – No. 2. – P. 25–31. (in Ukrainian)
- Bovdi V.A., Shchedryk V.P. Generating solutions
of a linear equation and structure of elements of the Zelisko group //
Linear Algebra and Applications. − 2021. − Volume 625. −
P. 55−67. https://doi.org/10.1016/j.laa.2021.04.019
- Ladzoryshyn N. B., Petrychkovych V. M. On standard forms of
pairs of matrices over the ring of gaussian integers with respect to
(z,k)-equivalence // // Math. methods and
phys.-mech. fields. – 2021. – 64,
¹ 4. – P. 18–24. (in Ukrainian).
- Shchedryk V. The left greatest common divisor and the left least common multiple for all solutions of the matrix equation BX = A over a commutative domain of elementary divisors // Ukrainian
Mathematical Journal. − 2021. − 73, No. 2. − P. 303–310.
− https://doi.org/10.1007/s11253-021-01923-0.
32. Shchedryk V. The left greatest common divisor and the left least common multiple for all solutions of the matrix equation BX = A over a commutative domain of elementary divisors // Ukrainian
Mathematical Journal. – 2021. – 73, ¹ 2. – P. 261–267. −
https://doi.org/10.37863/umzh.v73i2.6321. (in Ukrainian)
33. Vasyl Fedorchuk, Volodymyr Fedorchuk. On symmetry reduction and some
classes of invariant solutions of the (1 + 3)-dimensional homogeneous
Monge-Ampère equation. // Proceedings of the
34. Dzhaliuk N.S. Existence of the solution of the Sylvester-type matrix
equation in the ring of block triangular matrices //
Applied problems of mechanics and mathematics. – 2021. – Vol. 19. –
P. 79−83. (in Ukrainian)
35. Dzhaliuk N.S., Petrychkovych V.M. Equivalence of matrices in the ring
M(n,R) and in its subrings // Ukrainian
Mathematical Journal. – 2021. – 73, ¹ 12. –
P. 1612–1618. https://doi.org/10.1007/s11253-021-01923-0. (in Ukrainian)
- Shavarovskii B.Z. Oriented by characteristic
roots reduced matrices in the class of semiscalarly equivalent // Journal
of Mathematics. − 2021. − vol. 2021 Article ID 5592756, 6
pages. − https://doi.org/10.1155/2021/5592756.
- Romaniv A. M. On the
Smith normal form of least common multiple matrices from some class of
matrices // Math. methods and phys.-mech.
fields.
– 2021. – 64, ¹
2. – P. 46–51.
- Romaniv A. M.
Ñonditions for constructing of a square matrix which contains a square
submatrix with given invariant factors // Applied problems of mechanics and
mathematics. – 2021. – Vol. 19 – P. 84–87.
- Shchedryk V.
Classification of Parametric Solutions of One-Sided Matrix Equations by
the Transforming Matrices of Their Characteristic Matrices // Journal of
Mathematical Sciences – 2021 – Vol. 254,
No. 1 – P. 1–7.
https://doi.org/10.1007/ñ10958-021-05283-9
- Prokip V.Ì. Canonical
form of involutory matrices over the domain of principal ideals with
respect to similarity transformations. // Journal of Mathematical Sciences
− 2021. − 258, No. 4 − P. 437–445. https://doi.org/10.1007/s10958-021-05558-1
- Prokip Volodymyr M. On the semi-scalar
equivalence of polynomial matrices over a field // Modeling, Control and
Information Technologies: Proceedings of International scientific and
practical conference. – 2021. – ¹.5. – P. 80–82. https://doi.org/10.31713/MCIT.2021.25
2020
42. Petrychkovych V. M., Zelisko H. V.,. Ladzoryshyn N. B. The
standard form of matrices over the ring of gaussian integers with respect to
(z, k)-equivalence // Applied problems of mechanics and mathematics. − 2020. – 18. – Ð. 5–10. – https://doi.org/10.15407/apmm2020.18.5-10. (in Ukrainian)
- Ladzoryshyn N. B.,
Petrychkovych V. M., Zelisko H. V. Matrix Diophantine equations over
quadratic rings and their solutions // Carpathian Math. Publ. −
2020. −12, ¹2. – Ð. 340–347.
https://doi.org/10.15330/cmp.12.2.368-375
- Shavarovskii B.Z. Reduction to a Canonical Form
of a Third-order Polynomial Matrix with One Characteristic Root by means
of Semiscalarly Equivalent Transformations // Journal of Mathematics, vol.
2020, Article ID 7960987, 10pages, 2020.
https://doi.org/10.1155/2020/7960987
- 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. – 2020. – 63, (2). – P. 7–16.
(in Ukrainian)
- 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. − P. 1178−1195. https://doi.org/10.4236/am.2020.1111080
- Zabavsky B., Romaniv A., Kysil T. Elementary
reduction of matrices over rings of almost stable range 1 // Algebra and
Discrete Mathematics. – 2020. – 29, No. 2. – P. 271–276.
https://dx.doi.org/10.12958/adm1211.
- Prokip V. Semi-scalar equivalence of polynomial
matrices // arXiv preprint https://arxiv.org/pdf/2003.05041.pdf, 2020, 11
pages.
- Prokip V. M. Equivalence of Polynomial Matrices
over a Field // Hot Topics in Linear Algebra. –2020 – Chapter 6. – Ð. 205–232.
- Prokip V. On solvability of the matrix equation
AXB = C over a principal ideal
domain // Modeling, Control and Information Technologies: Proceedings of
International scientific and practical conference. – 2020. – ¹. 4. – Ñ.
47–50. https://doi.org/10.31713/MCIT.2020.09
- Shchedryk V. A greatest common divisor and a least common multiple of
solutions of a linear matrix equation // arXiv preprint
https://arxiv.org/pdf/2011.05173.pdf, 2020, 9 pages.
2019
- Petrychkovych V.M. Standard forms of matrices over rings with
respect to different types of equivalences and their applications in
theory of the matrix factorization and matrix equations // Mat. Metody
Fiz.-Mekh. Polya 62, (4), 7–27, (2019).
- Bovdi V.A., Shchedryk V.P.
Commutative Bezout domains of stable range 1.5 // Linear Algebra and its
Applications. – 2019.
– Volume 568. − P. 127−134.
https://doi.org/10.1016/j.laa.2018.06.012
- Bilous A. Idempotent
matrices over a duo ring // Matematychni Studii. – 2019. – V. 52, No. 3. –
P. 133–137. http://matstud.org.ua/texts/2019/52_2/133-137
- Bilous A. M., Gatalevych A. I. Stable range of some classes of
non-commutative rings // Mat. Metody Fiz.-Mekh. Polya. 62, (2), P. 32–37, (2019). (in Ukrainian)
- Dzhaliuk N. S. Solutions of matrix equation AX+YB=C
with triangular coefficients // Mat. Metody Fiz.-Mekh. Polya. 62, (2), 26–31, (2019). (in
Ukrainian)
- Dzhaliuk Nataliia S.,
Petrychkovych Vasyl' M. Solutions of the matrix linear bilateral
polynomial equation and their structure
// Algebra and Discrete Mathematics. – 2019. –
27, ¹ 2. – P. 243–251.
- Romaniv A. M.,
Dzhaliuk N. S. Some relationships between the invariant factors of matrix and its
submatrix over elementary divisor domains
// Applied
problems of mechanics and mathematics.
– 2019. – 17. – P. 38−41. https://doi.org/10.15407/apmm2019.17.38-41
- 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.
- V.M. Fedorchuk, V.I.
Fedorchuk, On the classification of symmetry reduction and invariant
solutions for the Euler-Lagrange-Born-Infeld equa-tion. // Ukrainian Journal of Physics. −
2019. − Vol. 64, No. 12. − P. 1103−1107. https://doi.org/10.15407/ujpe64.12.1103.
- Shavarovskii B.Z.
Non-singular solutions of one class of matrix equations over a polynomial
ring // Applied problems of mechanics and mathematics. – 2019. – Issue 17.
– P. 17–26.
https://doi.org/10.15407/apmm2019.17.17-26 (in
Ukrainian)
- Shavarovskii B.Z.
Canonical Form of Reduced 3-by-3 Matrix with One Characteristic Root and
with Some Zero Subdiagonal Elements // Journal of Mathematics. −
2019. − Volume 2019, Article ID 7646132, 10 pages. https://doi.org/10.1155/2019/7646132
- Prokip Volodymyr On
Solvability of the Matrix Equation AX–XB=C over Integer Rings // Modeling,
Control and Information Technologies. –2019. – ¹ 3. – Ð.55–58.
https://doi.org/10.31713/MCIT.2019.04
- Prokip V.M. The canonical form of involutory
matrices over the principal ideal domain with respect to similarity
transformation // Mat. Metody Fiz.-Mekh. Polya. – 2019. – 62, ¹ 1. –
P.59–66. (in Ukrainian)
- Prokip V.M. On structure of matrices over a
principal ideal domain with respect to similarity transformation // Proc.
Intern.
- Prokip V.M., Kolyada R.V., Melnyk O.M. About
square roots of matrices over an arbitrary field // Scientific papers UAP.
– 2019. – 59, ¹ 2. – P. 56–64. (in Ukrainian)
- Prokip V. M.
On the Solvability of a System of Matrix Equations AX = B
and BY = A Over Associative
Rings. // Journal of Mathematical Sciences. – 2019. – 238, No.1. – P. 22–31.
https://doi.org/10.1007/s10958-019-04215
- Prokip V. Ì. Structure of Rank-One Matrices Over
the Domain of Principal Ideals Relative to Similarity Transformations. //
Journal of Mathematical Sciences. – 2019. – 236, No.1. – P. 71–82.
https://doi.org/10.1007/s10958-018-4098-0
- Prokip V. Ì. On the divisibility of matrices with
remainder over the domain of principal ideals // Journal of Mathematical
Sciences − 2019. − 243, No.1 − P.
45–55. https://doi.org/10.1007/s10958-019-04524-2
2018
- , Petrychkovych V.M. The
standard form of matrices over quadratic rings with respect
(z,k)-equivalence and structure of
solutions of matrix bilateral linear equations // Mat. Metody Fiz.-Mekh.
Polya. – 2018. – ¹61, (2). – P. 49–56. (in Ukrainian)
- , Petrychkovych V.M. Matrix
linear unilateral and bilateral equations over quadratic rings // Visnyk
of the Lviv Univ. Series Mech. Math. – 2018. – ¹ 85. – P. 32–40.
http://dx.doi.org/10.30970/vmm.2018.85.032-040 (in Ukrainian)
- Romaniv A.M.
On the structure of least common multiple matrices from some class of
matrices // Carpathian Math. Publ. – 2018. – 10, No. 1. – P.
179–184. https://doi.org/10.15330/cmp.10.1.179-184
- Romaniv A. M., Zabavsky B. V., Bilavska S. I.
Adequate properties of the elements with almost stable range 1 of a
commutative elementary divisor domain // Applied
problems of mechanics and mathematics. – 2018. – Issue 16. – P. 33–35.
https://doi.org/10.15407/apmm2018.16.33-35
- Shavarovskii B.Z. Reduced
Triangular Form of Polynomial 3-by-3 Matrices with One Characteristic Root
and Its Invariants // Journal of Mathematics. Volume 2018,
(2018), Article ID 3127984, 6 pages. (http://doi.org/10.1155/2018/3127984).
- Shavarovskii B.Z. About some invariants of polynomial matrices with
respect to semiscalar equivalence // Applied problems of mechanics and mathematics. – 2018. – Issue 16. – P. 14–18.
https://doi.org/10.15407/apmm2018.16.14-18 (in Ukrainian)
- Victor A. Bovdi, Volodymyr P. Shchedryk
Commutative Bezout domains of stable range 1.5, 9 pages. – [Åëåêòðîííèé ðåñóðñ]. Ðåæèì
äîñòóïó: arXiv:1806.04747v1
- Prokip V. M. On the similarity of matrices AB and
BA over a field // Carpathian Mathematical Publications. – 2018. – V. 10.
– ¹ 2. – P. 352–359. https://doi:10.15330/cmp.10.2.352-359
- Shchedryk V. Classification of Parametric
Solutions of One-Sided Matrix Equations by the Transforming Matrices of
Their Characteristic Matrices // Mat. Metody Fiz.-Mekh. Polya. – 2018–
Vol. 61, ¹.3 – P. 7–15. (in Ukrainian)
- Shavarovskii B. Z. Semiscalar equivalence and
quasidiagonal similarity of the matrices // Journal of Mathematical
Science 2018. – 228, ¹ 1. – P.11–25.
https://doi.org/10.1007/s10958-017-3602-2
2017
- Shchedryk V. P. Bezout Rings of Stable Range 1.5
and the Decomposition of a Complete Linear Group into the Product of its
Subgroups // Ukrainian Mathematical Journal – 2017. – 69 – P.138-147. https://doi.org/10.1007/s11253-017-1352-4
- Bilous A. Effective duo rings
// Visnyk of the Lviv Univ. Series Mech. Math. – 2017. – 84. – P. 47–52 (in Ukrainian) http://prima.lnu.edu.ua/faculty/mechmat/Departments/MathVisnykLU/VLUsMath-84/VisnM-84-047.pdf.
- Bilous A., Gatalevych A.I.
2-good abelian and duo rings with conditions of a stable range // Applied
problems of mechanics and mathematics. – 2017. – 15. – P. 16 – 20. (in Ukrainian)
- Petrychkovych V., Dzhaliuk N.
Factorizations in the rings of the block matrices // Bul. Acad.
Stiinte Repub. Mold. Mat. – 2017. – 85,
Number 3. – P. 23–33.
- Petrychkovych V., Dzhaliuk N. Factorizations in
the matrix ring and its subrings of the block matrices // Proceedings The Fourth Conference of Mathematical Society of the
- Ladzoryshyn N.B. Integer
solutions of matrix linear unilateral and bilateral equations over
quadratic rings // Journal of Mathematical Sciences. – 2017. – 223, ¹ 1. – P. 50–59, doi:10.1007/s10958-017-3337-0.
- Romaniv A. M. Least common multiple of one
class of matrices // Applied problems of mechanics and mathematics. – 2017.
– No. 15. – P. 29–34.
- Shavarovskii B.Z. Toeplitz Matrices in
the Problem of Semiscalar Equivalence of Second-Order Polynomial Matrices
//
International Journal of Analysis. Volume 2017, (2017), Article ID
6701078, 14 pages (http://doi.org/10.1155/2017/6701078).
- Shavarovskii B.Z. Conditions of Semiscalar Equivalence of Polynomial
2-by-2 Matrices // Mathematical Bulletin of Taras Shevchenko Scientific
Society. – 2017. – 14. – P. 7–28.
- Shavarovskii B.Z. Block-Diagonal
Similarity and Semisñalar Equivalence of Matrices // Journal of
Mathematical Sciences. – 2017. – 222, No. 1 – P. 35-49.
- Shchedryk V.P. Bezout ring of stable range 1.5 and decomposition
of complete linear group into product its subgroups // Ukrainian
Mathematical Journal. – 2017. – 69, No. 1. – P. 113 – 120 (in
Ukrainian).
- Fedorchuk V.I. On invariant
solutions of some five-dimensional d’Alembert equations // Journal of
Mathematical Sciences. – 2017. – 220, No. 1
– P. 27-37.
- 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.
- Prokip V.M. Triangularization of a pair of
matrices over the domain of principal ideals with minimal quadratic
polynomials. // Journal of Mathematical Sciences. – 2017. – 222, No. 1
– P.50-55.
- Prokip V.M. On divisibility with a remainder of
matrices over a principal ideal domain // Mat. Metody Fiz.-Mekh. Polya. – 2017. – 60, ¹ 2. – P.41–50 (in Ukrainian).
- Prokip V.M. The Structure of Symmetric Solutions
of the Matrix Equation AX=B over a Principal Ideal Domain // Hindawi. International Journal of Analysis. Volume
2017, Article ID 2867354, 7 pages.
2016
- Vasyl Fedorchuk and Volodymyr Fedorchuk., On
Classification of Symmetry Reductions for the Eikonal Equation // Symmetry 2016, 8(6),
51;
32pages, doi:10.3390/sym8060051.
- Romaniv A. M. The greatest
common divisor and lest common multiple of one class of matrices // Visnyk L'viv
Univ. Series Mekh.-Math. – 2016. – Issue 82 – P. 186–191. (in Ukrainian).
- Shavarovskii B.Z. On invariants and
canonical form of matrices of second order with respect to semiscalar
equivalence // Bulet. Acad. de Stinte Republ.
- Prokip V.M. The structure of matrices of rank one
over the domains of principal ideals with respect to similarity
transformation // Mathematical methods and
physico-mechanical fields. – 2016. – 59, No 3. – P. 68–76 (in Ukrainian).
- Prokip V.M. A
structure of symmetric solutions of the matrix equation AX = B over an
arbitrary field // Proc. Intern.
2015
102.
Romaniv A. M. On the Smith
normal form of the greatest common divisor of one class of matrices // Applied problems of mechanics and mathematics. –
2015. – Issue 13 – P. 174–181. (in Ukrainian).
103.
Shchedryk V.P. The
value of matrix on a system of roots of diagonal elements of matrix and its
properties // Applied Problems of Mechanics and Mathematics – 2015.
– 13. – P.
187–194 (in Ukrainian)
104.
Shchedryk V.P.
Bezout rings of stable range 1.5 // Ukrainian
Mathematical Journal. – 2015. – 67,
¹ 6. – P. 960-974.
105.
Romaniv À.Ì., Shchedryk V.P. Least
common right multiple of the matrices with one invariant factor different from
the identity. // Journal of Mathematical Sciences. – 2015. –
208. No 3 – P. 344-354.
106.
Shavarovskii
B. Z. The semiscalar equivalence and
quasi-diagonal similarity of matrices // Mathematical methods and physico-mechanical fields. – 2015. – 58, No 4.
– P. 15–26 (in Ukrainian).
107.
Shavarovskii
B. Z. On
nonsingular solutions of one type of systems of matrix equations // Applied
problems of mechanics and mathematics. 2015. –
Issue. 13. – P. 11–17, (in
Ukrainian).
2014
108.
Petrychkovych
V. M., Ladzoryshyn N.B. Equivalence
of pairs of matrices with relatively prime determinants over quadratic rings of
principal ideals // Bulet. Acad. de Stinte Republ.
109.
Romaniv A. M., Shchedryk
V. P. Greatest common
divisor of matrices one of which is disappear // Ukr. Math. J. –
2014. – 66, No. 3. – P.
425–430.
110.
Prokip V.M. On the solvability
of a system of linear equations over the domain of principal ideals. // Ukr.
Math. J. 66, No. 4, 633-637 (2014).
111.
Prokip V.M. On
solutions of the matrix equation XA0= A1 with prescribed
characteristic polynomials //
Proc. Intern.
2013
112.
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.
113.
Petrychkovych
V. M., Dzhaliuk N.S. Absolute factorization of matrices in the rings of block-triangular matrices. //
Applied problems of mechanics and mathematics.. 11, 36 –
40, (2013) (in
Ukrainian).
114.
Shavarovskii
B. Z. Semisñalar
equivalence of polynomial matrices and
triangular similarity of numerical matrices // Applied problems of
mechanics and mathematics. 2013. – Issue. 11. – P. 63–69. (in Ukrainian).
115.
Fedorchuk V.I. On a partial preliminary group classification of the
nonlinear five-dimensional d’Alembert equation. // Journal
of Mathematical Sciences, – 2013. – 194, No 2
– P. 166-175.
116.
On equivalence of pairs of matrices,
which determinants are primes powers, over quadratic Euclidean rings. Carpathian Mathematical Publications. 5 (1),
63–69, (2013). (in Ukrainian).
117.
Shchedryk V.P.
Generating set of matrices divisors and its properties // Applied problems of mechanics and mathematics. 2013. – Issue. 11. –
P. 70–75. (in Ukrainian).
118.
Prokip V.M. On normal form with
respect to semiscalar equivalence of polynomial matrices over a field. // J.
Math. Sci.,
2012
119.
Petrychkovych
V. M.,
120.
. Petrychkovych V. M., Dzhaliuk N.S. Seniscalar equivalence of polynomial matrices
and tne solutions of the Sylvester matrix polynomial equations. Mathematical
bulletin of the Shevchenko scientific society. 9, 81–88,
(2012) (in Ukrainian).
121.
Petrychkovych
V. M., Dzhaliuk N.S. Solutions of matrix polynomial diophantine
equation. // Applied problems of mechanics and mathematics. 10, 55 –
61, (2012). (in Ukrainian).
122.
Romaniv A. M., Shchedryk
V. P. The greatest
common left divisor and the least common right multiple of second order
matrices // Mathematical bulletin of the Shevchenko scientific
society 9, 269–284, (2012) (in
Ukrainian).
123.
Shchedryk V.P. Commutative
domains of elementary divisors and some properties of their elements // Ukrainian
Mathematical Journal. 2012. – 64, ¹1. – P.
126–139.
124.
Shavarovskii B.Z. Canonical form of polynomial matrices with
all identical elementary divisors // Ukr. Math. J. – 2012. – 64, No. 2. – P.
282–297.
125.
Shavarovskii B.Z. Factorability
of polynomial matrices depending on the powers of their elementary divisors // Zh
Vychisl. Mat. Mat Fiz– 2012. – 52, ¹ 7. – P. 1171–1184. (in Russian)
126.
Shavarovskii
B. Z. On a triangular form of polynomial
matrix and its invariants with respect to semiscalar equivalence // Mathematical methods and physico-mechanical fields. – 2012. – 55, No 3. – P. 7–20. (in Ukrainian).
127.
Shavarovskii
B. Z. Canonical
form for pair of matrices, in which one matrix has pairwise relatively prime
elementary divisors of degree at most two // Applied problems of
mechanics and mathematics. 2012. – Issue. 10. – P. 62–70. (in Ukrainian).
128.
Prokip V.M. Diagonalizability
of matrices over a principal ideal domain. // Ukr. Math. J. 64, No. 2, 316-323
(2012).
129.
Fedorchuk V.M.,
Fedorchuk V.I. Invariant operators of four-dimensional
nonconjugate subalgebras of the Lie algebra of the
Poincaré group P(1,4) // Journal
of Mathematical Sciences – 2012. – 181, ¹3. – P. 305—319
130.
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 noncon-jugate subalgebras of the Lie algebra of the Poincaré group P(1,4) // Scientific bulletin of Uzhorod
university. Series Physic. 32, 112 -120, (2012).
2011
131.
Petrychkovych
V. M.,
132.
Romaniv A. M. Monic
divisors of polynomial matrices over infinite field // Algebra Discrete
Math. – 2011. – 12, No 2. – P. 94–101.
133.
Romaniv A. M. Monic
divisors with canonical diagonal form 
of polynomial matrices
over infinite field // Matematychni Studii. – 2011. – Vol 36, No 1. – P.
12–20. (in Ukrainian).
134.
Shchedryk V. On the
one-side equivalence of matrices with given canonical diagonal form // Algebra
and Discrete Mathematics. – 2011. – 12, ¹2. – Ñ. 102–111
135.
Shchedryk V.P. On
the Interdependence between Invariant Multipliers of a Block-Triangular Matrix
and Its Diagonal Blocks // Mathematical Notes. –
2011. – 90, ¹4. – Ñ. 584 – 596.
136.
Shavarovskii
B. Z On the similarity of matrix polynomials of simple
structure // Applied problems of
mechanics and mathematics. 2011. –
137.
Shavarovskii B.Z. Decomposability of matrix polynomials
with commuting coefficients into a product of linear factors // Ukr. Math. J. – 2011. – 62, No. 8. – P.
1295–1306.
138.
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). // Journal of Mathematical Sciences, – 2012. – 182, No 3 –
P.
305-319.
2010
139.
Petrychkovych
V. M., Dzhaliuk N.S.
Parallel factorizations of matrices over rings and their connections. //
Applied problems of mechanics and mathematics. 2010. –
140.
Romaniv A. M. Unital
divisors with one invariant factor of polynomial matrices // Mathematical methods and physico-mechanical fields. –
2010. – 53,No 4. – P.
35–43. (in Ukrainian).
141.
Shchedryk V.P. On
invariant factors of block-triangular matrices and their diagonal blocks
// Dopovidi NAS of
142.
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. // Journal of
Mathematical Sciences, – 2010. – 170, No 5 – P.
588-593.
2009
143.
Petrychkovych
V. M., Zabavsky B.V. On the stable range of matrix rings Ukrainian Mathematical Journal 61
(11), 1853–1857, (2009).
144.
Petrychkovych
V. M On solvents of matrix polynomial equations and their
number. // Applied problems of mechanics and mathematics. 2009. –
145.
Shchedryk V.
Factorization of matrices over elementary divisor domain // Algebra and
Discrete Mathematics. – 2009. – ¹2. – P.
79–99.
146.
Shavarovskii B.Z. Similarity
Transformations of Decomposable Matrix Polynomials and Related Questions // Computational Mathematics and Mathematical Physics. V. 49, No. 9,
2009. P. 1469–1482.
2008
147.
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.
148.
Romaniv A. M., Shchedryk
V. P. On nonassociated
and monic divisors of polynomial matrices // Applied problems of mechanics and mathematics. –
2008. – Issue. 6. – P. 72–79.
149.
Shchedryk V.P. Some
invariants of transforming matrices // Mathematical studies–
2008. – 29. – P. 121-126 (in Ukrainian).
2007
150.
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.
151.
Petrychkovych
V. M., Dzhaliuk N.S. Factorization of block diagonal and block triangular matrices over principal
ideal rings (with Dzhaliuk N.S). Mathematical
bulletin of the Shevchenko scientific society. 4, 79–89, (2007).
152.
Shavarovskii B.Z. Classes
of Factorable and Unfactorable Polynomial Matrices and Their Relative Position
// Doklady Mathematics . – 2007 – 75,
¹.2. – Ð. 318–321.
153.
Shavarovskii B.Z. On the
Similarity of Matrices of Even Order. // Mathematical Notes. – 81,
no. 3. – 2007. – P. 392–407.
154.
Shavarovskii B.Z. Finding a Complete
Set of Solutions or Proving Unsolvability for Certain Classes of Matrix
Polynomial Equations with Commuting Coefficients // Computational Mathematics
and Mathematical Physics. – 2007. – 47, ¹. 12. – Ð. 1902–1911.
155.
Shavarovskii B.Z. Multiplicative
Structure of a Polynomial Matrix Depending on Its Elementary Divisors// Doklady
Mathematics , 2007. – 76, ¹3. – Ð. 843–847.
2006
156.
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.
157.
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
158.
Petrychkovych
V. M., Zelisko V.R., Ladzoryshyn
N.B. On equivalence of matrices over quadratic Euclidean rings Applied problems of mechanics and mathematics. 4, 16 – 21, (2006). (in Ukrainian).
159.
Shavarovskii B.Z. Solvability of
Matrix Equations in Rings of Quasi-Diagonal Matrices and Similarity of Matrix
Polynomials // Computational Mathematics and Mathematical Physics. – 46.
¹. 8. – 2006. – P. 1283–1292.
2005
160.
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.
161.
Petrychkovych
V. M. Multiplicities of characteristic roots, degrees of
elementary divisors and factorization of polynomial
matrices. Mat. Metody Fiz.-Mekh. Polya 48, (2), 7–17, (2005).
162.
Petrychkovych
V. M. On solutions of matrix polynomial equations and the
similarity of matrices. Mat. Metodi Fiz.-Mekh. Polya. 48, ( 4),
14–19, (2005).
163.
Petrychkovych
V. M.,
164.
Shchedryk V.P. Some determinant
properties of primitive matrices over Bezout B-domain // Algebra and Discrete
Mathematics. – 2005. – ¹2. –P. 46–57.
2004
165.
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.
166.
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.
167.
Petrychkovych
V. M. Generalized equivalence of collections of matrices
and common
divisors of matrices. Algebra and Discrete Mathematics. 2, 84 – 91, (2004).
168.
Petrychkovych
V. M., Zelisko V.R. On common
divisors of polynomial matrices.
Applied problems of mechanics and
mathematics. 2, 56 – 60, (2004).
169.
Petrychkovych
V. M. On divisibility and factorization of
matrices. Mat. Stud. 22, ( 2), 115-120 (2004).
170.
Shavarovskii B.Z. On Some ‘Tame” and “Wild” Aspects of
the Problem of Semiscalar Equivalence of Polynomial Matrices // Mathematical
Notes. – 76, no. 1. – 2004. – P. 111–123.
171.
Shavarovskii B.Z. Solving a System
of Linear Homogeneous Two-Sided Matrix Equations
in Two Unknowns. // Computational Mathematics and Mathematical Physics. – 44.
¹ 11. – 2004. – P. 1853–1866.
2003
172.
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.
173.
Petrychkovych
V. M., Standard form of
pairs of matrices with respect to generalized equivalence. Visnyk Lviv.
Univ., Ser. Mech-Math. 61, 148 –
155, (2003).
174.
Petrychkovych
V. M., Komarnytsky N.Ya.
Structure-theoretical properties of matrices finitely generated principal ideal
rings. Mat.
Metody Fiz.-Mekh. Polya. 46,
(2), 7 – 21, (2003).
175.
Shchedryk V. On
decomposition of complete linear group into product of some its subgroups // Visnyk
Lviv. Univ., Ser. Mech.-Math.
– 2003. – 61. – P. 184–190.
176.
Shavarovskii B.Z. A
Complete System of Invariants with Respect to Similarity for Pairs of Matrices of
Even Order with Characteristic Matrix of Special Smith form // Mathematical
Notes. – 73, no. 6. – 2003. – P. 871–888.
177.
Shavarovskii B.Z. On a Method for
Reducing a Pair of Matrices to Block Diagonal Form by a Similarity
Transformation // Computational Mathematics and Mathematical Physics
. – 43. ¹ 9. – 2003. – P. 1231–1240.
2002
178.
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.
179.
Fedorchuk V, On invariants of
continuous subgroups of the generalized Poincaré group P(1,4) // Universitatis Iagellonicae Acta Mathematica,
Fasciculus XL, 2002, 197-205.
180.
Petrychkovych
V. M.,
181.
Shchedryk V.P. One
class of divisors of matrices over commutative elementary divisor domain //
Mathematical studies. – 2002. – 17, ¹1. – P. 23–28 (in
Ukrainian)
182.
Shchedryk V.P. Non
associated matrix with standard Ô-skeleton // Math. Method. i Fiz. Mekh. Polia. –
2002. – 45, ¹3. – P. 32–44 (in Ukrainian).
2001
183.
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.
184.
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.,
185.
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.
2000
186.
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.
187.
Petrychkovych
V. M. Generalized equivalence of pairs of
matrices. Linear and Multilinear Algebra. 48, (2), 179 – 188, (2000).
188.
Petrychkovych
V. M. Reducibility of pairs of matrices by generalized
equivalent transformations to triangular and diagonal forms and their
applications. Mat. Metody Fiz.-Mekh. Polya. 43, (
2), 15 – 22, (2000).
189.
Shchedryk V.P. Ô-skeleton
of matrices and its properties // Math. Method. i Fiz. Mekh. Polia,
-2000. - 43, ¹ 2. – P. 45-51 (in
Ukrainian).
190.
Shchedryk V.P. On
transforming matrices over some Bezout domains // Math. Method. i Fiz. Mekh. Polia – 2000. –
43, ¹ 1. – Ñ. 36–44 (in Ukrainian).
191.
Shavarovskii B.Z. Factorable
polynomial matrices // Mathematical Notes. – 2000. – 68, ¹4. – Ñ.
507-518
192.
Shavarovskii B.Z. On Semiscalar and Quasidiagonal
Equivalences of Matrices // Ukr. Math. J. – 2000. – 52, No. 10. –
P. 1638–1643.
1999
193.
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.
194.
Petrychkovych
V. M. On the parallel factorization of
matrices over principal ideal rings Journal of Mathematical
Sciences,
195.
Shavarovskii B.Z. Decomposition of polynomial matrices into a direct sum of triangular summands //
Ukr. Math. J. – 1999. – 51, No. 8. –
P. 1291–1295.
196.
Shavarovskii B.Z. On decomposition of polynomial
matrices into direct sum of matrices of smaller order // Reports of the
1998
197.
Shchedryk V.P. Structure
and properties of matrices divisors over commutative elementary divisor domains // Mathematical studies. – 1998. – 10.
–¹2. – Ñ. 115–120 (in Ukrainian).
198.
Shavarovskii B.Z. Reduction of
matrices of equivalent transformations and similarity transformations //
Mathematical Notes. – 1998. – 64, ¹5. – P.
663–673.
1997
199.
Petrychkovych
V. M. A criterion of diagonalizability of a pair of
matrices over the ring of principal ideals by common row and separate column
transformations.Ukr. Math. J. 49, (6), 963–965,
(1997).
200.
Petrychkovych
V. M. Generalized equivalence of pairs of matrices. . Mat.
Stud. 8, (2), 147 – 152, (1997).
1996
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).
1995
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.
1993
Petrychkovych V. M. Decomposition
of polynomial matrices into factors with prescribed canonical diagonal forms Journal of Soviet
Mathematics. 64 (5), 1129–1131, (1993).
Petrychkovych V. M. Semiscalar
equivalence and the Smith normal form of polynomial matrices Journal of Soviet
Mathematics. 66, No.1,
2030–2033, (1993).
1992
Petrychkovych V.
M. Parallel
factorizations of polynomial matrices. Ukrainian
Mathematical Journal 44 (9), 1123–1127,
(1992).
1991
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.
1990
Petrychkovych V. M. Semiscalar
equivalence and the factorization of polynomial matrices Ukrainian
Mathematical Journal. 42, (5),
570–574, (1990).
1986
Petrychkovych V. M., Prokip V.M. Factorization
of polynomial matrices over arbitrary fields. Ukrainian Mathematical Journal. 38, (4), 409–412, (1986).
1985
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.
Petrychkovych V.
M. Cell-triangular and cell-diagonal factorizations of cell-triangular and
cell-diagonal polynomial matrices. Mathematical
Notes. 37, 431–435, (1985).
1984
Petrychkovych V.
M. Linear
divisors and reducibility of polynomial matrices. Ukrainian
Mathematical Journal. 36, (2)
176–181, (1984).
1981
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).
Petrychkovych V.
M. Problems of the factorization of matrix polynomials. Mat. Metody Fiz.-Mekh. Polya 14, 19–26,
(1981).
1980
Petrychkovych V. M. On the number of solutions of a matrix equation. Mat. Metody Fiz.-Mekh. Polya
12, 56–58, (1980).
1979
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).
Petrychkovych V. M. Absolute expansibility of matrix polynomials Mat. Metody
Fiz.-Mekh. Polya 9, 37–41, (1979).
1978
Petrychkovych V. M., Kazimirs' kii P. S. Decomposability of
polynomial matrices into a product of linear factors Mat. Met. Fiz.-Mekh. Polya. 8, 3 – 9, (1978).
1977
Petrychkovych V. M., Kazimirs' kii P. S. On the
equivalence of polynomial matrices Theoretical and
Applied Problems of Algebra and Differential Equations. 61 –
66, (1977).
List of
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
2. Shchedryk V., Bovdi V. Adequacy of nonsingular matrices over
commutative principal ideal domains // Conference UAE Math Day 2023: March 4th,
2023, Organized by
3. Ùåäðèê Â. Ï Ìàòðèö³ òà
ïîâ'ÿçàí³ ç íèìè ãðóïè Çåë³ñêà // Có÷àñí³ ïðîáëåìè ìåõàí³êè òà ìàòåìàòèêè – 2023:
çá³ðíèê íàóêîâèõ ïðàöü / çà çàã. ðåä. àêàä. ÍÀÍ Óêðà¿íè Ð.Ì. Êóøí³ðà òà ÷ë.-êîð. ÍÀÍ Óêðà¿íè Â.Î. Ïåëèõà
[Åëåêòðîííèé ðåñóðñ] // ²íñòèòóò ïðèêëàäíèõ ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. ß.Ñ.
ϳäñòðèãà÷à ÍÀÍ Óêðà¿íè. – 2023. – 452 ñ. – Ðåæèì äîñòóïó: http://iapmm.lviv.ua/mpmm2023/materials/proceedings.mpmm2023.pdf
– Ñ. 403–404. – http://iapmm.lviv.ua/mpmm2023/materials/ma10_12.pdf.
4. Shchedryk V. P. A
parametric 2-decomposition of small order general linear groups over fields // Ukraine
Algebra Conference "At the End of the Year 2023" December 26 27, 2023,
5. 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,
6. 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,
7. Äæàëþê Íàòàë³ÿ, Ïåòðè÷êîâè÷
Âàñèëü. Ðîçâ'ÿçí³ñòü ìàòðè÷íîãî ð³âíÿííÿ AX=YB ó ê³ëüö³ áëî÷íî-òðèêóòíèõ
ìàòðèöü // Có÷àñí³ ïðîáëåìè ìåõàí³êè òà ìàòåìàòèêè – 2023: çá³ðíèê íàóêîâèõ
ïðàöü / çà çàã. ðåä. àêàä. ÍÀÍ
Óêðà¿íè Ð.Ì. Êóøí³ðà òà ÷ë.-êîð. ÍÀÍ Óêðà¿íè Â.Î. Ïåëèõà [Åëåêòðîííèé ðåñóðñ]
// ²íñòèòóò ïðèêëàäíèõ ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. ß.Ñ. ϳäñòðèãà÷à ÍÀÍ
Óêðà¿íè. – 2023. – 452 ñ. – Ðåæèì äîñòóïó: Ñ. 405–406. – http://iapmm.lviv.ua/mpmm2023/materials/ma10_13.pdf
8. Dzhaliuk Nataliia, Petrychkovych
Vasyl'. The Sylvester matrix polynomial equation and its solutions // 14th
Ukraine Algebra Conference, July 3-7, 2023
9. Dzhaliuk Nataliia. Linear
solutions to the bilateral matrix polynomial equations // Ìàòåìàòèêà òà ³íôîðìàö³éí³
òåõíîëî㳿. Ìàòåð³àëè ì³æíàðîäíî¿ íàóêîâî¿ êîíôåðåíö³¿, ïðèñâÿ÷åíî¿ 55-ð³÷÷þ
ôàêóëüòåòó ìàòåìàòèêè òà ³íôîðìàòèêè, 28–30 âåðåñíÿ 2023 ð. – ×åðí³âö³: ×åðí³âåöüêèé
íàö. óí-ò, 2023. – 369 ñ. – Ñ. 47–48.
10. Äæàëþê Í. C. Ðîçâ’ÿçêè ñòåïåíÿ s ìàòðè÷íîãî
ïîëiíîìiàëüíîãî ðiâíÿííÿ Cèëüâåñòðà // Ìàòåð³àëè Äåâ’ÿòíàäöÿòî¿ ì³æíàðîäíî¿ íàóêîâî¿
êîíôåðåíö³¿ ³ìåí³ àêàäåì³êà Ìèõàéëà Êðàâ÷óêà, 11–12 æîâòíÿ 2023 ðîêó, Êè¿â, Êϲ
³ì. ²ãîðÿ ѳêîðñüêîãî. – C. 104–105. – https://matan.kpi.ua/uk/kravchuk-conf-2023/
11. Ëàäçîðèøèí Íàòàë³ÿ, Ïåòðè÷êîâè÷
Âàñèëü. Åêâ³âàëåíòí³ñòü ïàð ìàòðèöü íàä êâàäðàòè÷íèì ê³ëüöåì // Có÷àñí³ ïðîáëåìè ìåõàí³êè òà ìàòåìàòèêè –
2023: çá³ðíèê íàóêîâèõ ïðàöü / çà çàã. ðåä. àêàä. ÍÀÍ Óêðà¿íè Ð.Ì. Êóøí³ðà òà ÷ë.-êîð. ÍÀÍ Óêðà¿íè Â.Î. Ïåëèõà
[Åëåêòðîííèé ðåñóðñ] // ²íñòèòóò ïðèêëàäíèõ ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. ß.Ñ.
ϳäñòðèãà÷à ÍÀÍ Óêðà¿íè. – 2023. – 452 ñ. – Ðåæèì äîñòóïó: http://iapmm.lviv.ua/mpmm2023/materials/proceedings.mpmm2023.pdf
– Ñ. 409−410. – http://iapmm.lviv.ua/mpmm2023/materials/ma10_15.pdf
12. Ladzoryshyn Natalija.
(z,k)-equivalence of pairs of matrices over imaginary Euclidean quadratic rings
// 14th Ukraine Algebra Conference, July 3-7, 2023
1. Ëàäçîðèøèí Í.Á., Ïåòðè÷êîâè÷
Â.Ì. (z,k)-åêâ³âàëåíòí³ñòü îñîáëèâèõ ìàò¬ðèöü íàä
êâàäðàòè÷íèìè åâêë³äîâèìè ê³ëüöÿìè // Ìàòåð³àëè Äåâ’ÿòíàäöÿòî¿ ì³æíàðîäíî¿ íàóêîâî¿
êîíôåðåíö³¿ ³ìåí³ àêàäåì³êà Ìèõàéëà Êðàâ÷óêà, 11–12 æîâòíÿ 2023 ðîêó, Êè¿â, Êϲ
³ì. ²ãîðÿ ѳêîðñüêîãî. – C. 111 − 112. – https://matan.kpi.ua/uk/kravchuk-conf-2023/
2. Ðîìàí³â Àíäð³é. Ðîçêëàä
îáîðîòíî¿ ìàòðèö³ ó äîáóòîê äâîõ ìàòðèöü ³ç çàäàíèìè âëàñòèâîñòÿìè. // Có÷àñí³ ïðîáëåìè
ìåõàí³êè òà ìàòåìàòèêè – 2023: çá³ðíèê íàóêîâèõ ïðàöü / çà çàã. ðåä. àêàä. ÍÀÍ Óêðà¿íè Ð.Ì. Êóøí³ðà
òà ÷ë.-êîð. ÍÀÍ Óêðà¿íè Â.Î. Ïåëèõà [Åëåêòðîííèé ðåñóðñ] // ²íñòèòóò ïðèêëàäíèõ
ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. ß.Ñ. ϳäñòðèãà÷à ÍÀÍ Óêðà¿íè. – 2023. – 452 ñ.
– Ðåæèì äîñòóïó: http://iapmm.lviv.ua/mpmm2023/materials/proceedings.mpmm2023.pdf
– Ñ. 413–414. – http://iapmm.lviv.ua/mpmm2023/materials/ma10_17.pdf
.
3. Romaniv A. Conditions
of existence of a matrix which contains a submatrix with given invariant
factors// 14th Ukraine Algebra Conference, July 3-7, 2023
4. Ðîìàí³â À. Ì. Âëàñòèâ³ñòü îáîðîòíî¿ ìàòðèö³ // Ìàòåð³àëè
Äåâ’ÿòíàäöÿòî¿ ì³æíàðîäíî¿ íàóêîâî¿ êîíôåðåíö³¿ ³ìåí³ àêàäåì³êà Ìèõàéëà
Êðàâ÷óêà, 11–12 æîâòíÿ 2023 ðîêó, Êè¿â, Êϲ ³ì. ²ãîðÿ ѳêîðñüêîãî. – C. 120. –
https://matan.kpi.ua/uk/kravchuk-conf-2023/.
5. Øàâàðîâñüêèé Áîãäàí. Ïîâíà
ñèñòåìà ³íâàð³àíò³â â³äíîñíî íàï³âñêàëÿðíî¿ åêâ³âàëåíòíîñò³ äëÿ 3õ3-ìàòðèö³ ïðîñòî¿
ñòðóêòóðè // Có÷àñí³ ïðîáëåìè ìåõàí³êè òà ìàòåìàòèêè – 2023: çá³ðíèê íàóêîâèõ
ïðàöü / çà çàã. ðåä. àêàä. ÍÀÍ
Óêðà¿íè Ð.Ì. Êóøí³ðà òà ÷ë.-êîð. ÍÀÍ Óêðà¿íè Â.Î. Ïåëèõà [Åëåêòðîííèé ðåñóðñ]
// ²íñòèòóò ïðèêëàäíèõ ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. ß.Ñ. ϳäñòðèãà÷à ÍÀÍ
Óêðà¿íè. – 2023. – 452 ñ. – Ðåæèì äîñòóïó: http://iapmm.lviv.ua/mpmm2023/materials/proceedings.mpmm2023.pdf
– Ñ. 397398. – http://iapmm.lviv.ua/mpmm2023/materials/ma10_08.pdf
6. Shavarovskii Bohdan.The
triangular form of the polynomial 3 × 3-matrix of a simple structure and
its invariants with respect to semiscalar equivalence // 14th Ukraine Algebra
Conference, July 3-7, 2023
7. Ïðîê³ï Âîëîäèìèð, Ìåëüíèê
Îðåñò, Êîëÿäà Ðîñòèñëàâà. Ïðî ïîä³ëüí³ñòü ìíîãî÷ëåííèõ ìàòðèöü íàä ïîëåì // Có÷àñí³
ïðîáëåìè ìåõàí³êè òà ìàòåìàòèêè – 2023: çá³ðíèê íàóêîâèõ ïðàöü / çà çàã. ðåä. àêàä. ÍÀÍ Óêðà¿íè Ð.Ì. Êóøí³ðà
òà ÷ë.-êîð. ÍÀÍ Óêðà¿íè Â.Î. Ïåëèõà [Åëåêòðîííèé ðåñóðñ] // ²íñòèòóò ïðèêëàäíèõ
ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. ß.Ñ. ϳäñòðèãà÷à ÍÀÍ Óêðà¿íè. – 2023. – 452 ñ.
– Ðåæèì äîñòóïó:– Ñ. 389–390. – http://iapmm.lviv.ua/mpmm2023/materials/ma10_04.pdf
8. Prokip V. On canonical
form of matrices with minimal polynomial m(λ)=(λ-α)2.
// 14th
9. Prokip V.M. On
equivalence of polynomial matrices over a field // Ukraine Algebra Conference "At
the End of the Year 2023" December 26
27, 2023,
10. Vasyl Fedorchuk, Volodymyr Fedorchuk. 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 * [
11. Ladzoryshyn N. On the number of standard pairs of pairs of matrices over
the ring of Gaussian integers with respect to (z,k)-equivalence // Conference
of young Scientists “Pidstryhach reading – 2022”. – L’viv,
12. Romaniv A. On property of invariant factors of the matrix and its
submatrix // Conference of young Scientists “Pidstryhach reading – 2022”. –
L’viv,
13. Prokip V.M. About solvability of the matrix equation AX= B over Bezout
domains // In International Scientific Conference Algebraic and Geometric
Methods of Analysis.
14. Prokip V.M. A note on a minimal solution of the matrix polynomial
equation A(λ)X(λ)-Y(λ)B(λ)=C(λ) // International
Algebraic Conference "At the End of the Year" 2022, December 27–28,
2022, Kyiv, Ukraine, Abstracts: Taras Shevchenko National University of Kyiv,
Kyiv, Ukraine. – 73 p. – P. 43
15. 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"
16. 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,
17. Bovdi V., Shchedryk V. The structure of the Zelisko group elements over
factor ring of Bezout domain of stable range 1.5. // The 13th International
Algebraic Conference in
18. Petrychkovych V.M., Dzhaliuk N.S. Application of special triangular
forms of matrices with respect to equivalences of different types to solving
linear matrix equations of Sylvester type // International Algebraic Conference
"At the End of the Year" 2021, December 27–28, 2021, Kyiv, Ukraine,
Abstracts: Kyiv. – 36 p. – P. 20.
19. Dzhaliuk N., Petrychkovych V. Solutions of matrix linear Sylvester type
equations // International Conference in Complex and Functional Analysis
dedicated to the memory of Bohdan Vynnytskyi. September 13–16, 2021,
20. Nataliia Dzhaliuk, Vasyl' Petrychkovych Block matrices, their
equivalences and applications // The 13th International Algebraic Conference in
Ukraine. July 6–9, 2021,
21. Natalija Ladzoryshyn, Vasyl' Petrychkovych. On the number of standard
forms of matrices over imaginary Euclidean quadratic rings with respect to the
(z,k)-equivalence // The 13th International Algebraic Conference in
22. Romaniv A. Divisibility of invariant factors of two matrices and
invariant factors of sum of these matrices // The 13th International Algebraic
Conference in
23. Vasyl Fedorchuk, Volodymyr Fedorchuk. 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
24. Vasyl Fedorchuk, Volodymyr Fedorchuk. On symmetry reduction and some
classes of invariant solutions of the (1+3)-dimensional inhomogeneous
Monge-Ampère equation. // The XV-th International Conference of
Differential Geometry and Dynamical Systems (DGDS-2021) 26 - 29 August 2021 * ONLINE * [
25. Shavarovskii Bohdan Semiscalar equivalence of polynomial 3-by-3 matrices
of simple structure // The 13th International Algebraic Conference in
26. Prokip V. Roth's theorems and similarity of matrices // The 13th
International Algebraic Conference in
27. Prokip V. On the matrix equation AX - YB=C over Bezout domains //
International Online Conference Algebraic and Geometric Methods of Analysis
dedicate to the memory of Yuriy Trokhymchuk (17.03.1928-18.12.2019) (May 25-28,
2021,
28. Prokip V.M. On
solutions of the matrix equation 
// International Algebraic
Conference "At the End of the Year" 2021, December 27–28, 2021,
29. Shchedryk V., Gatalevych A. On adequacy of full matrices over adequate
rings // XI International Skorobohatko Mathematical Conference. October 26−30,
2020,
30. Andriy Romaniv Divisibility of invariant factors of a matrix and its
submatrix // XI International Skorobohatko Mathematical Conference.
October 26−30, 2020,
31. Bohdan Shavarovskii. Canonical form of a reduced matrix with all
non-zero sub-diagonal elements // XI International
Skorobohatko Mathematical Conference. October 26−30, 2020,
32. Prokip V. A note on semiscalar
equivalence of polynomial matrices // XI International Skorobohatko
Mathematical Conference. October 26−30, 2020,
33. Ladzoryshyn N., Petrychkovych V. The standard form of matrices over
imaginary Euclidean quadratic rings with respect to (z,k)-equivalence // XI
International Skorobohatko Mathematical Conference. October 26−30, 2020,
Lviv, Ukraine. Abstracts: Lviv: Pidstryhach Institute for Applied Problems of
Mechanics and Mathematics, 2020. – 130 p. – [Electronic resource]. – Access
mode: http://www.iapmm.lviv.ua/conf_skorob2020/documents/2020tezy.pdf – P. 59.
34. Vasyl Fedorchuk, Volodymyr Fedorchuk. 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 * [
35. Vasyl Fedorchuk, Volodymyr Fedorchuk. On Classification of Symmetry
Reductions for Some P(1,4)-Invariant Partial Differential Equations. XI
International Skorobohatko Mathematical Conference (October 26-30, 2020,
36. Volodymyr Fedorchuk. On Symmetry Reduction and Invariant Solutions of
the Euler-Lagrange-Born-Infeld Equation. XI International Skorobohatko
Mathematical Conference (October 26-30, 2020,
37. Bilous A. Stable range of some classes of non commutative rings // XI
International Skorobohatko Mathematical Conference. October 26−30, 2020,
38. Nataliia Dzhaliuk Equivalence of matrices in the ring of the block
triangular matrices // XI International Skorobohatko Mathematical Conference.
October 26−30, 2020, Lviv, Ukraine. Abstracts: Lviv: Pidstryhach
Institute for Applied Problems of Mechanics and Mathematics, 2020. – 130 p. –
[Electronic resource]. – Access mode:
http://www.iapmm.lviv.ua/conf_skorob2020/documents/2020tezy.pdf – P. 29.
39. Bovdi V., Shchedryk V.P. The structure of
elements of the Zelisko group // 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. – [Electronic resource]. – Access mode:
https://bit.ly/2ZIyqMs – P. 27.
40. V. M. Fedorchuk, V. I. Fedorchuk 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.
– [Electronic resource]. – Access mode: https://bit.ly/2ZIyqMs – P.
34.
41. Prokip V.M. On similarity of families of 2x2 matrices over a field //
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.
– [Electronic resource]. – Access mode: https://bit.ly/2ZIyqMs
– P. 68.
42. Shavarovskii B.Z. Canonical form of a reduced matrix with one zero
sub-diagonal element // 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. – [Electronic resource]. – Access mode: https://bit.ly/2ZIyqMs – P. 74.
43. Petrychkovych V.M., Dzhaliuk N.S. Solvability of the matrix
Sylvester-type equation in the ring of the block triangular matrices // 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.
– [Electronic resource]. – Access mode: https://bit.ly/2ZIyqMs
– P. 63.
44. Romaniv A. M. Properties of the invariant factors of the sum of matrices
// 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. – [Electronic resource]. – Access mode: https://bit.ly/2ZIyqMs– P. 71.
45. Bilous A. Stable range of some classes of non commutative rings //
Conference of young Scientists “Pidstryhach reading – 2020”. – L’viv,
46. Ladzoryshyn N. (z,k)-equivalence of matrices over the ring of Gaussian
integers // Conference of young Scientists “Pidstryhach reading – 2020”. –
L’viv,
47. Romaniv A.M.,
48. Prokip V. On similarity of two families of matrices over a field // International Scientific Conference
Algebraic and Geometric Methods of Analysis, 26-30 may 2020,
49. Ïðîê³ï Â.Ì. Ïðî
êâàäðàòí³ êîðåí³ ìàòðèöü íàä îáëàñòþ ãîëîâíèõ ³äåàë³â // PSC–IMFS–16 (16-òà ³äêðèòà
íàóêîâà êîíôåðåíö³ÿ ²ÌÔÍ), 06–07 ëþòîãî 2020 ðîêó, Ëüâ³â, Óêðà¿íà, Ñ.65–66.
50. Shavarovskii B.Z. Semiscalar equivalence of one class of 3-by-3 matrices
// XII International Algebraic Conference in Ukraine dedicated to the 215th anniversary
of V. Bunyakovsky, July 02–06, 2019, Vinnytsia, Ukraine. – 142 p. – P. 101–102.
51. Shchedryk V. On great common divisors and least common multiple of
matrix equation solutions // XII International Algebraic Conference in Ukraine
dedicated to the 215th anniversary of V. Bunyakovsky, July 2-6, 2019,Vinnytsia,
Ukraine. Abstracts. – Vinnytsia:Vasyl’
52. Nataliia Dzhaliuk. Solutions of the Sylvester matrix equation with
triangular coefficients // The XII International Algebraic Conference in
53. Ladzoryshyn N., Petrychkovych V. (z,k)-equivalence of matrices over
Euclidean quadratic rings and solutions of matrix equation AX+YB=C // Book of
abstracts of the XII International Algebraic Conference in Ukraine dedicated to
the 215th anniversary of V. Bunyakovsky,
July 02 – 06, 2019, Vinnytsia, 2019. – P. 63–64.
54. Ladzoryshyn N. Solutions of the matrix equation AX+BY=C over Euclidean
quadratic rings // Conference of young Scientists “Pidstryhach reading –
2019”.– Lviv,
55. Prokip V. On similarity of tuples of matrices over a field // XII
International Algebraic Conference in Ukraine dedicated to the 215th
anniversary of V. Bunyakovsky, July 2-6, 2019,Vinnytsia, Ukraine. Abstracts. –
Vinnytsia:Vasyl’
56. Romaniv A. Reduction of nonsingular matrices over rings of almost stable
range 1 // XII International Algebraic Conference in Ukraine dedicated to the
215th anniversary of V. Bunyakovsky, July 2-6, 2019,Vinnytsia, Ukraine.
Abstracts. – Vinnytsia:Vasyl’
57. Romaniv A. An element with almost stable range 1 over a commutative
elementary divisor domain // Conference of young Scientists “Pidstryhach
reading – 2019”. – L’viv,
58. V. M. Fedorchuk and V. I. Fedorchuk.
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
59. Bilous A. Diagonability of idempotent matrices over APT ring //
Conference of young Scientists “Pidstryhach reading – 2019”. – L’viv, Ukraine
May 27–29, 2019, L’viv. – [Electronic resource]. – Access mode: (http://iapmm.lviv.ua/chyt2019/abstracts/Bilous.pdf).
60. Bilous A. Diagonability of idempotent matrices
over duo rings // The XII International Algebraic
Conference in
61. Ïðîê³ï Â.Ì. Àëãîðèòì ïîáóäîâè óí³òàëüíîãî ä³ëüíèêà äëÿ ìíîãî÷ëåííî¿
ìàòðèö³ // Òåçè äîïîâ³äåé ì³æíàð. êîíôåðåíö³¿
“Algebraic and geometric methods of analysis” Îäåñà. − 2019. − Ñ.
68 − 69.
62.
63. Kuz A. M., Romaniv A. M., Symotiuk M. M. An analogue of an integral
problem for equations with partial derivatives over a field of p-adic numbers
// Nonlinear analysis problems: VI All-Ukrainian mat. conf. the name of B.V.
Vasilishin: Abstract (26-28 september 2018ð., Ivano-Frankivsk - Mykulychyn). –
Ivano-Frankivsk: 2018. – P. 30.
64. Ladzoryshyn N. The solvability of Diophantine equations over quadratic
rings // 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. 217–218.
65. Romaniv A.M. On the relationship between the Smith normal forms of
matrices and of their least common multiple // Book of abstracts of the
International Scientific Conference “Algebraic and geometric methods of
analysis” (May 30 – June 4, 2018, Odesa, Ukraine). P.53. [Electronic resource].
- Access mode: (http://www.imath.kiev.ua/~topology/conf/agma2018)
66. Romaniv A., Shchedryk V. On stable range of matrix rings over
commutative principal ideal rings // 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: www.iapmm.lviv.ua/mpmm2018. P. 241–242.
67. Shavarovskii B. Improved triangular form of the 3-by-3-matrices with one
characteristic root in the class of semiscalarly equivalent // 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: www.iapmm.lviv.ua/mpmm2018. P. 241–242.
68.
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,
69. Vasyl Fedorchuk, 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:
www.iapmm.lviv.ua/mpmm2018. P. 187.
70. 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. – Access mode: www.iapmm.lviv.ua/mpmm2018. P. 188.
71. 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,
72. Vasyl Fedorchuk, Volodymyr Fedorchuk, On classification of some
non-singular manifolds in the space M(1,3)xR(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 -
73. 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,
74. 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,
75. Vasyl Fedorchuk, Volodymyr Fedorchuk, 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.
76. Vasyl Fedorchuk, and Volodymyr Fedorchuk, 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
77. Prokip Volodymyr On the similarity of matrices AB and BA // 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: www.iapmm.lviv.ua/mpmm2018. P.
260–261.
78. Prokip V.M. About a structure of solutions of the matrix equation AX -
XB = C. Materials of reports International sciences Conferences "Modern
problems of mathematical modeling, computational methods and information
technologies", Rivne , 2018. P.138-139.
79. V.M. Prokip A note on similarity of matrices // // Book of abstracts of
the International Scientific Conference “Algebraic and geometric methods of
analysis” (May 30 – June 4, 2018,
80. Petrychkovych Vasyl', Dzhaliuk Nataliia Factorizations in the matrix
ring and its subrings of the block matrices // The Fourth Conference of
Mathematical Society of the
81. Petrychkovych V.M., Dzhaliuk N.S. A bound on degrees of solutions of the
matrix linear bilateral polynomial equation // Book of abstracts of the XI
International Algebraic Conference in
82. Romaniv A.M. The Smith normal form of the lest common multiples of one
class of matrices // Book of abstracts of the XI International Algebraic
Conference in
83. Shavarovskii B.Z. Improved triangular form of the matrix and its
invariants // Book of abstracts of the XI International Algebraic Conference in
84. Shchedryk V.P. Helmer lemma for Bezout domains of stable range 1.5 //
Book of abstracts of the XI International Algebraic Conference in
85. Romaniv A. On decomposition of matrices from full linear group in the
product matrices from certain its subsets // Conference of young Scientists
“Pidstryhach reading – 2017”. – L’viv,
86. Prokip V.M. On solvability of the matrix equation ÀÕ=XÂ over integral
domains // Book of abstracts of the XI International Algebraic Conference in
87. Prokip V.M. About coexistence of system of matrix equations AX = B ³ BY
= A over commutative rings // PSC–IMFS–13 dedicated to the 125th anniversary
Stefana Banaha. March 30-31, 2017. L'viv,
88. 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. − S.
15. − http:// algebra.up.krakow.pl/II/files/abstrakty.
http://algebra.up.krakow.pl/II/files/abstrakty.pdf.
89. 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,
90. 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
91. Fedorchuk V.M.,
Fedorchuk V.I. Classification of low-dimensional Lie Algebras // Book of
abstracts of the XI International Algebraic Conference in
92. Bilous A. M. Effective duo rings // Book of abstracts of
the XI International Algebraic Conference in Ukraine dedicated to the 75th
anniversary of V.V.Kirichenko, July, 2017, Kyiv, Ukraine – P.23.
93. Romaniv A. M. The Smith normal form of the greatest common divisor of
one class of matrices // Conference of
young Scientists “ Pidstryhach reading –
94. Ïðîêèï Â.Ì. Ñòðóêòóðà ìàòðèö ðàíãà 1 íàä îáëàñòüþ ãëàâíûõ èäåàëîâ
îòíîñèòåëüíî ïðåîáðàçîâàíèÿ ïîäîáèÿ // Àëãåáðà è ëîãèêà. Òåçèñû äîêëàäîâ
Ìåæäóíàð. êîíô., ïîñâÿùåííîé 70-ëåòèþ Â. Ì. Ëåâ÷óêà Êðàñíîÿðñê, 24–29 èþëÿ 2016
ã. Ñ.63–64.
95. Ïðîê³ï Â.Ì. Ïðî ñèìåòðè÷í³ ðîçâ’ÿçêè ë³í³éíèõ ìàòðè÷íèõ ð³âíÿíü íàä îáëàñòþ
ãîëîâíèõ ³äåàë³â // 12 Âiäêðèòà íàóêîâà
êîíôåðåíöiÿ Iíñòèòóòó ïðèêëàäíî¿
ìàòåìàòèêè òà ôóíäàìåíòàëüíèõ íàóê (IÌÔÍ). Çáiðíèê ìàòåðiàëiâ êîíôåðåíöi¿ 2–3 ÷åðâíÿ
2016 ðîêó (Ëüâiâ, Óêðà¿íà). Ñ.41–42.
96. Ïðîê³ï Â.Ì. Ïðî ñòðóêòóðó ñèìåòðè÷íèõ ðîçâ’ÿçê³â ìàòðè÷íîãî ð³âíÿííÿ ÀÕ=Â
// Òåçè äîïîâ³äåé ì³æíàð. Êîíôåð. “Ãåîìåòð³ÿ ³ òîïîëîã³ÿ â Îäåñ³-2016”. Îäåñà,
2-8 ÷åðâíÿ 2016. Ñ. 51.
97. Bilous A.M. Simultaneous reduction of a pair of matrices over some class
of duo rings// X International Algebraic Conference in
98. Ladzoryshyn N., Petrychkovych V. On solutions of the matrix linear
equations AX+YB=C over quadratic rings // Book of abstracts of the X
International Algebraic Conference in Ukraine dedicated to the 70th anniversary
of Yu. A. Drozd, August 20 – 27, 2015, Odessa. – Abstract. – Odessa: TES, 2015.
– P. 61.
99. Ladzoryshyn N.B. The matrix linear unilateral equations over quadratic
rings // Conference of young Scientists “
Pidstryhach reading –
100.
Romaniv A. M. On the
divisibility of the second-order matrices // International V. Skorobohatko
Mathematical Conference (August 25 – 28, 2015,
101.
Romaniv A. M. Greatest common
left divisor of second ordre matrices // Conference
of young Scientists “Pidstryhach reading –
102.
B.Z. Shavarovskii. When
polynomial matrices of second order semiscalarly are equivalent? // X
International Algebraic Conference in
103.
Bogdan Shavarovskii/ On the
canonical form a certain class of matrices of the second order with respect to
the semiscalar equivalence //
International V. Skorobohatko Mathematical Conference (August 25 – 28, 2015,
104.
Shchedryk V.P. Decomposition
of general linear group and ring’s stable range // Book of
abstracts of the X International Algebraic Conference in
Ukraine dedicated to the 70-th anniversary of
Yu. A. Drozd, August 20 – 27,
2015, Odessa. – P. 101.
105.
Volodymyr Prokip. Solutions of
a linear matrix equation XA0 =
A1 with prescribed characteristic polynomials // Oblicza
Algebry. Ogól-nopolska Konferencja Naukowa,
106.
Prokip V.M. Solutions of the
matrix equation XA0 = A1
over domains of principal ideals with prescribed characteristic polynomials //
X International Algebraic Conference in
107.
Volodymyr Prokip. On common
eigenvectors of two matrices over a principal ideal domain // International V.
Skorobohatko Mathematical Conference (August 25 – 28, 2015,
108.
Vasyl Fedorchuk, Volodymyr
Fedorchuk, On classification of reduced equations for the eikonal equation,
International workshop in honor of 70th birthday of Anatoly Nikitin
"Symmetry and Integrability of Equations of Mathematical Physics"
(December 27−28, 2015, Kyiv), Institute of Mathematics of NAS of Ukraine,
http://www.imath.kiev.ua/~appmath/Abstracts2015/FedorchukVas.pdf.
109.
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,
Kraków, Poland.
110.
Vasyl Fedorchuk, O
niektórych zastosowaniach skończenie wymiarowych algebr Lie’go
lokalnych grup Lie’go przekształceń punktowych, abstracty
Ogólnopolskej Konferencji Naukowej "Oblicza Algebry" (Maj
29-31, 2015, Kraków), Uniwersytet Pedagogiczny im. KEN w Krakowie, http://algebra.up.krakow.pl/abstr-all-strona3.pdf,
S.12.
111.
Vasyl Fedorchuk, On
classification of the non-conjugate subalgebras of the Lie algebra of the
Poincare group P(1,4) and symmetry reduction of some differential equations //
International V. Skorobohatko Mathematical Conference (August 25 – 28, 2015,
112.
Ladzoryshyn N.B. The matrix
linear unilateral equations over quadratic rings // Conference of young Scientists
“ Pidstryhach reading – 2015”.– L’viv,
113.
Ladzoryshyn N., Petrychkovych V. On
solutions of the matrix linear equations AX+YB=C over quadratic rings // X
International Algebraic Conference in
114.
Petrychkovych
V.M., Dzhaliuk N.S. Structure
of solutions of the matrix Diofantine polynomial equations // International
Algebraic Conference dedicated to 100th anniversary of L.A.
Kaluzhnin. Book of Abstracts. Jule 7–12, 2014. Kyiv.
– P. 29.
115.
Romaniv A.M. On the least
common right multiples of matrices over an adequate domain // International
Algebraic Conference dedicated to 
anniversary of L.A. Kaluzhnin in
116.
Ladzoryshyn N.B. The integral
solutions of bilateral linear matrix equations over quadratic rings // International
Algebraic Conference dedicated to 100th anniversary of L.A.
Kaluzhnin. Book of Abstracts. Jule 7–12, 2014.
Kyiv.– P. 52.
117.
Ladzoryshyn N.B. Integer
solutions of matrix Diophantine equation over quadratic rings // Conference of
young Scientists “ Pidstryhach reading – 2014”.– L’viv,
118.
B.Z. Shavarovskii.
Quasi-diagonal similarity and semiscalar equivalence of matrices // International
Algebraic Conference dedicated to 100th anniversary of L.A.
Kaluzhnin. Book of Abstracts. Jule 7–12, 2014. Kyiv.
P. 76 – 77.
119.
Shchedryk V. On Bezout rings of stable range 1,5 // Book of
abstracts of the International Algebraic Conference dedicated to 100 anniversary
of L.A. Kaluzhnin, July 7–12, 2014, Taras
Shevchenko National University of Kyiv, Ukraine,
P.77-78.
120.
Prokip V. On
common solutions of matrix equations over an elemen-tary
divisor domain // International
Algebraic Conference dedicated to 100th anniversary of L.A.
Kaluzhnin. Book of Abstracts. Jule 7–12, 2014. Kyiv.
P. 69.
121.
Fedorchuk V.M., Fedorchuk V.I.,
On Invariant Operators of Nonconjugate Subalgebras of the Lie Algebra of the
Poincare Group P(1,4), Book of abstracts of the International Algebraic
Conference dedicated to 100th anniversary of L.A.Kaluzhnin (July 7-12, 2014,
Kyiv, Ukraine), Taras Shevchenko National University of Kyiv, p. 29.
122.
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.
123.
Dzhaliuk
N., Petrychkovych
V. Semiscalar equivalence of polynomial matrices and solutions of the matrix
linear polynomial equations // 9-th International algebraic conference in
124.
Ladzoryshyn N., Petrychkovych
V. Equivalence of pairs of matrices with relatively prime determinants over
quadratic principal ideal rings // 9-th International
algebraic conference in Ukraine, L'viv, July 8-13, 2013: Book of abstracts. –
L'viv, 2013. – P. 109.
125.
Ladzoryshyn N. The matrix
linear bilateral equations over quadratic rings
// International Conference “Modern Problems of Mechanics and
Mathematics”. – L’viv, Ukraine May 21–25, 2013, L’viv. Abstract. – L’viv: YA.
S. Pidstryhach Institute for APMM NAS of Ukraine. – P. 187–189.
126.
À.Ì. Romaniv Greatest common
left divisor of matrices one of which is disappear // Abstract
of 9-th International Algebraic Conference in Ukraine, Jule
5–12, 2013. / Abstract of talks – Lviv: Lviv
Taras Shevchenko National University Ukraine 2013. – p.156.
127.
B.Z. Shavarovskii. Reduction of
polynomial matrices by semiscalar equivalent transformation // 9th
International Algebraic Conference in
128.
Prokip V. Normal form with
respect to similarity of involutory mat-rices
over a principal ideal domain // 9th International Algebraic Con-ference
in
129.
Vasyl M. Fedorchuk, Volodymyr
I. Fedorchuk, On symmetry reduction of some differential equations and
classification of low-dimensional nonconjugate subalgebras of the Lie algebra
of the Poincare group P(1,4), International workshop in honor of Wilhelm
Fushchych "Symmetry and Integrability of Equations of Mathematical
Physics" (December 22−23, 2013, Kyiv), Institute of Mathematics of
NAS of Ukraine, http://www.imath.kiev.ua/~appmath/AbstractsWIF/FedorchukVas2013.pdf
130.
Fedorchuk V.M., Fedorchuk V.I.,
Classification of low-dimensional non-conjugate subalgebras of the Lie algebra
of the Poincare group P(1,4), 9-th International Algebraic Conference in
Ukraine (July 8-13,
131.
Dzhaliuk
N., Petrychkovych
V. On the
minimal degree solutions of the Sylvester matrix polynomial equations // International
mathematical conference: abstracts of talks. – Mykolayiv: Published by
132.
Vasyl` Petrychkovych, Nataliia Dzhaliuk The matrix Diophantine polynomial
equations // International Conference on Algebra dedicated to 100th
anniversary of S.M. Chernikov, August 20-26,
2012, Dragomanov National Pedagogical University, Kiev, Ukraine:
Book of abstracts. – Kiev: Institute of Mathematics of
UNAS, 2012. – P. 116.
133.
B. Shavarovskii. On similarity
of pairs of matrices, in which one matrix has only one elementary divisor // International
mathematical conference: abstracts of talks. – Mykolayiv: Published by
134.
Romaniv A., Shchedryk V. On
Smith normal form of greatest common left divisor and least common right
multiple of matrices // International
mathematical conference: abstracts of talks. – Mykolayiv: Published by
135.
Bogdan Shavarovskii. On
similarity of pairs of matrices, in which one matrix is nonderogatory //
International Conference on Algebra dedicated to 100th
anniversary of S.M. Chernikov, August 20-26,
2012, Dragomanov National Pedagogical University, Kiev, Ukraine:
Book of abstracts. – Kiev: Institute of Mathematics of
UNAS, 2012. – P. 138.
136.
Volodymyr Prokip. Normal form
with respect to similarity of a matrix with minimal polynomial
m(λ)=(λ–α)(λ–β),(α≠β) //
International Conference on Algebra dedicated to 100th
anniversary of S.M. Chernikov, August 20-26,
2012, Dragomanov National Pedagogical University, Kiev, Ukraine:
Book of abstracts. – Kiev: Institute of Mathematics of
UNAS, 2012. – P. 121.
137.
Prokip V.M. Note on the Hermite
normal form // International
Conference dedicated to the 120th anniversary of Stefan Banach,
Lviv, Ukraine, 17–21 September 2012. Abstracts of Reports. –
P. 262.
138.
Bogdan Shavarovskii On the
canonical form for a certain class of matrices with respect to similarity // International
Conference dedicated to the 120th anniversary of Stefan Banach,
Lviv, Ukraine, 17–21 September 2012. Abstracts of Reports. – P. 264.
139.
Romaniv A., Shchedryk V. On
Smith normal form of greatest common left divisor and least common right
multiple of matrices // International
mathematical conference: abstracts of talks. – Mykolayiv: Published by
140.
Volodymyr Shchedryk On
factorizability and associativity of matrices // International Conference on
Algebra dedicated to 100th anniversary of
S.M. Chernikov, August 20-26,
2012, Dragomanov National Pedagogical University, Kiev, Ukraine:
Book of abstracts. – Kiev: Institute of Mathematics of
UNAS, 2012. – P. 139.
141.
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 Poincare group
P(1,4), Íàóêîâèé â³ñíèê Óæãîðîäñüêîãî óí³âåðñèòåòó. Ñåð³ÿ Ô³çèêà. Âèïóñê 32. –
2012. – Ñ. 112–120.
142.
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
143.
Vasyl Fedorchuk,
Volodymyr Fedorchuk, Non-equivalent functional bases of invariants for non-conjugate subgroups of the
Poincaré group P(1,4) in the space M(1,4)×R(u) // International mathematical conference: abstracts of
talks. – Mykolayiv: Published by
144.
Vasyl Fedorchuk,
Volodymyr Fedorchuk, Classification of functional bases of invariants in the
space M(1,3)×R(u) for one- and two- parametrical non-conjugate subgroups
of the Poincaré group P(1,4) // International
Conference dedicated to the 120th anniversary of Stefan Banach,
Lviv, Ukraine, 17–21 September 2012. Abstracts of Reports. –
P. 189.
145.
Petrychkovych
V. M., Dzhaliuk N. S. Factorizations in
rings of block triangular matrices // Book of abstracts
of the 8th International Algebraic Conference in
146.
Prokip V.M. About the normal
form of linear matrix pencils // III International Conference on matrix
methods and operator equations.
147.
Romaniv À. On monic
divisors of polynomial matrices // Book of abstracts of the 8th
International Algebraic Conference in
148.
Fedorchuk Vasyl M., Fedorchuk
Volodymyr I. Classification of the five-dimensional
non-conjugate subalgebras of the Lie algebra of the Poincaré
group P(1,4) // Book of abstracts of the 8th
International Algebraic Conference in
149.
Shavarovskii B. Canonical
forms for matrices under semiscalar equivalence // Book of
abstracts of the 8th International Algebraic Conference in
150.
Shchedryk V. On
elementary divisor rings and properties of its elements // Book of
abstracts of the 8th International Algebraic Conference in
151.
Shchedryk V. Matrices divisors
generated by transformable matrices // Int. Alg. Conf. dedicated to A.V.
Yakovlev. 2010. – S. Peterburg. – Jun 19–24, 2010. Abstracts. S. Peterburg.
– P.153–154.
152.
Kateryna Pavlyk and Oleg Gutik,
On some semigroup constructions //
AAA80 workshop on general algebra in connection with the Workshop on
non-classical algebraic structures, 1-6 June 2010,
153.
Ladzoryshyn N.B. On equivalence
of certain pairs of matrices over quadratic Euclidean rings // XIII
inter¬natio¬nal Scientific Kravchuk mathematical conference. –
154.
B. Shavarovskii On the
invariants of polynomial matrices with respect to semiscalar equivalence // 7
International Algebraic Conference in
155.
Bogdan Shavarovskii Solving a System of Linear Two-Sided Matrix Equations //
Ukrainian Mathematical Congress. –
156.
Shchedryk V. On matrices
reduction by one-side transformations // 7 International Algebraic Conference
in
157.
Shchedryk V. On invariant factors of block-triangular matrix and
its diagonal blocks // Ukrainian Mathematical Congress.
–
158.
Prokip V. M. On semiskalar
equivalence of polynomial matrices over a field // Abstract of 7-th
International Algebraic Conference in
159.
Prokip V.M.On common divisors
of polynomial matrices // Ukrainian Mathematical Congress. –
160.
Petrychkovych V.M. Matrix
polynomial equations and its solutions // 7 International Algebraic Conference
in
161.
Petrychkovych V.M., Zabavsky
B.V. On the stable range of rings of matrices // 7 International Algebraic
Conference in
162.
Petrychkovych V.M.
Matrix polynomials its divisors and structure // Ukrainian Mathematical Congress. –
163.
Dzhalyuk N.S. Equivalence and
factorization of partitioned matrices // 7 International Algebraic Conference
in
164.
Kateryna Pavlyk, Oleg Gutik and
Andriy Reiter On Topological Semigroups of Matrix
Units // The 14th general meeting of European women in
mathematics, Novi Sad, Serbia August 25-28, 2009, Book of Abstracts 2. - P.
36-37.
165.
Ladzoryshyn N.B. On equivalence
of pairs of matrices over quadratic Euclidean rings // Conference of young
Scientists Pidstryhach with Modern Problems of Mechanics and Mathematics. –
L’viv, Ukraine, May 25–27, 2009. – P. 176–177.
166.
Vasyl Fedorchuk, Volodymyr
Fedorchuk, O konstruowaniu klas rownan rozniczkowych z nietrywialnymi grupami
symetrii // III forum matematykow polskich (30.06–02.07 2009,
167.
V.M. Fedorchuk, V.I. Fedorchuk,
On some classes of the partial differential equations with non-trivial symmetry
groups // XVI International Congress on Mathematical Physics,
168.
Shavarovs’kii B. On the class
of factorable polynomial matrices // 6th International Algebraic Conference in
169.
Fedorchuk Vasyl M., Fedorchuk
Volodymyr I. On classification of the four-dimensional decomposable
non-conjugate subalgebras of the Lie algebra of the Poincare group P(1,4) //
6th International Algebraic Conference in
170.
Prokip V. About the uniqueness
solution of the matrix polynomial equation // 6th International Algebraic
Conference in
171.
Shchedryk V.,. Mel’nyk O. On
canonical diagonal form of matrices product // 6th International Algebraic
Conference in
172.
Dzhalyuk N., Petrychkovych V.
Factorizations of partitioned matrices and solutions of linear matrix equations
// 6th International Algebraic Conference in
173.
Petrychkovych V. On factorizations
of matrices over some classes ofrings // International conference ASADE,
Chisineu, August 21-23, 2007. - P.108-109.
174.
Gutik O. V. , Pavlyk K. P.
Topological Brandt λ^0-extensions and H-closed
topological semigroups // 6th International Algebraic Conference in
175.
Zelisko V., Ladzoryshyn N., On
equivalence and factorization of matrices over quadratic rings // 6th
International Algebraic Conference in
176.
Romaniv A., On regular divisors
of polynomial matrices // 6th International Algebraic Conference in
177.
Fedorchuk Vasyl M, Fedorchuk
Volodymyr I. On classification of the four-dimensional decomposable
non-conjugate subalgebras of the Lie algebra of the Poincare group P(1,4) //
6th International Algebraic Conference in
178.
Prokip V. On similarity of a
matrix and its transpos // International Conference on Radicals ICOR-2006, July
30 – August 5, 2006,
179.
Gutik O. V. and Pavlyk K. P. On
Brandt λ^0-Extensions of Topological
Semigroups with Zero // Forth Summer School “Algebra, Topology, Functional and
Stochastic Analysis”, Lviv-Kozyova, July 17-29, 2006. Invited Lectures and Abstracts
of Research Reports. – Lviv-Kozyova, 2006. – P. 139-142.
180.
Fedorchuk Vasyl, Fedorchuk
Volodymyr, On some Applications of Invariant of Continuous Subgroups of the
Poincare Group P(1,4) in Mathematical Physics //
181.
Fedorchuk Vasyl M., Fedorchuk
Volodymyr I. On functional bases of the first-order differential invariants for
non conjugate subgroups of the Poincare group P(1,4)//
182.
Shavarovs’kii B. On the
block-diagonal equivalence of matrices // International Conference on Radicals
ICOR-2006, July 30- August 5, 2006,
183.
Shchedryk V. Unilateral
equivalence of singular martices and singular divisors of matrices //
International Conference on Radicals ICOR-2006, July 30 - August 5, 2006,
184.
Gutik O.V. and Pavlyk K.P. On
absolutely H-closed topological semigroups and Brandt λ^0-extensions
// 5th International Algebraic Conference in
185.
Petrychkovych V.M. Generalized
equivalence of matrices and its collections and factorization of matrices over
rings // 5th International Algebraic Conference in
186.
Prokip V. On common divisors of
matrices over principal ideal domain // 5th International Algebraic Conference
in
187.
Shchedryk V.P. Some determinant
properties of matrices // 5th International Algebraic Conference in
188.
Shavarovs’kii B.Z. On
similarity of some collection of matrices // 5th International Algebraic
Conference in
189.
Fedorchuk Vasyl, Fedorchuk
Volodymyr, On symetry reduction of some new classes of the first-order
differential equations in the space M(1,4)xR(4) //
190.
Gutik O. and Pavlyk K. On
compact congruence-free topological inverse semigroups // International
Conference dedicated to the 125-th anniversary of Hans Hahn, Chernivtsi,
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Symmetry Reduction of Some Closses of the First-Order Differential Equations in
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Prokip V. On a class of
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Fedorchuk V.M., Fedorchuk V.I.
On construction first-order differential equations in the space M(1,3)xR(4)
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Fedorchuk V.M., Fedorchuk V.I.
On differential first-order differential invariants of the continuous subgroups
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199.
Shavarovs`kyj B.Z. Similarity
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Gutik O.V., Pavlyk K. P. On
H-closed topological semigroups and Brandt λ-extensions
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Topological Brandt λ-extensions of absolutely H-closed
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Petrychkovych V.M. On
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Fedorchuk V.Ì.,
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Fedorchuk V.M., Fedorchuk V.I.
Some new differential equations of the first-order in the space M(1,3)xR(u)
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Fedorchuk V.M., Fedorchuk V.I.
On Differential Invariants of First- and Second-Order of the Splitting
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Fedorchuk V.M., Fedorchuk V.I.
On construction of the first-order differential equations in the space M(1,4)x
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Fedorchuk V.M., Fedorchuk V.I.
First-order differential invariants of the splitting subgroups of the Poincare
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Fedorchuk V. On new
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