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    Recent Publications

    Department No.14

     

    1. Fedorchuk V.M., Fedorchuk V.I. On Differential Invariants of First- and Second-Order of the Splitting Subgroups of the Generalized Poincarй Group P(1,4)// Symmetry in Nonlinear Mathematical Physics: Proc. 4th Int. Conf. (Ukr. Math. Congr. Dedicated to 200th Anni­versary of Mykhailo Ostrohrads'kyi), Kyiv, 9–15 July, 2001.– Part 1.– Kyiv: Inst. of Math. of NAS of Ukraine.– 2002.– P. 140–144.– (Proc. Inst. of Math. of NAS of Ukraine.– 2002.– 43, Part 1).
    2. Fedorchuk V.М., Fedorchuk V.I. Subgroup structure of the generalized Poincare group P(1,4) and models with nontrivial symmetry // Математична фізика: Праці Українського математичного конгресу. – 2001. – Київ: Інститут математики НАН України. – 2002. – C. 101–116.
    3. PetrychkovychV. M. On factorizations of matrices over ring // International Algebraic Conference Dedicated to the memory of Z.I.Borevich, St.Petersburg, Russia, September 17‑23, 2002. Abstracts of reports. – St. Pe­ter­burg. –  2002. – Р. 138–139.
    4. Shchedryk V.P. Nonassociative divisors of matrices over elementary divisor ring // Inter­national Algebraic Conference Dedicated to the memory of Z.I.Borevich, St.Petersburg, Russia, September 17‑23, 2002. Abstracts of reports. – St. Pe­tersburg. –Р. 156–158.
    5. Gutik O. V., Rajagopalan M., Sundaresan K. Compact semilattices with open principal filters // J. Austral. Math. Soc. – 2002. – 72, № 2. – P. 349–362.
    6. Fedorchuk V. On invariants of continuous subgroups of the generalized Poincarй group P(1,4) // Universitatis Jagellonicae Acta Mathematica, Fasc. – 2002, Xl. – P. 197–205.
    7. Petrychkovych V.Standard form of pairs of matrices with respect to generalized equi­valence // Visnyk Lviv. Univ., Ser. Mech.-Math. – 2003. – 61. – P. 148–155.
    8. Fedorchuk V.M., Fedorchuk V.I.On new differential equations on the first-order in the space M(1,4)R(4) with non trivial symmetries // Annales Academiae Pedagogicae Cracoviensis, Studia Mathematica. – 2003. – III, Folia 16. – P. 49–53.
    9. Fedorchuk V.M., Fedorchuk V.I.On construction of the first-order differential equations in the space M(1,3)R(4) with non trivial symmetries // Prace Naukove Wyzsej Szkoly Peda­gogizcnej w Czestochowie. Matematyka IX, Czestochowie. – 2003. – P. 35–39.
    10. 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.
    11. Shchedryk V.P., Mel’nyk O.M.Some properties of minors of invertible matrices // Visnyk Lviv Univer., Ser. Mech.-Mat. – 2003. – 61. – P. 129–134.
    12. Gutik O., Pavlyk K.Topological Brandt -extensions of absolutely - closed topological inverse semigroups // Visnyk Lviv. Univ., Ser. Mech.-Math. – 2003. – 61. – P. 98–105.
    13. 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 (Translated from Matematicheskie Zametki. – 73, no. 6. – 2003. – P. 923–941).
    14. 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. № 9. – 2003. – P. 1231–1240 (Translated from Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki. 43, № 9, 2003, Р. 1283–1293).
    15. Shavarovskii B.Z. On Some ‘Tame” and “Wild” Aspects of the Problem of Semiscalar Equivalence of Polynomial Matrices // Mathematical Notes. – 76, no. 1. – 76, no. 1. – 2004. – P. 2004. – P. 111-123 (Translated from Matematicheskie Zametki. – 76, no. 1. – 2004. – P. 119–132).
    16. Shavarovskii B.Z. Solving a System of Linear  Homogeneous Two-Sided Matrix Equations in Two Unknowns. // Computational Mathematics and Mathematical Physics. – 44. № 11. – 2004. – P. 1853–1866 (Translated from Zhurnal Vychislitel’noi Matematiki i Matema­ticheskoi Fiziki. – 44. № 11. – 2004. – P. 1950–1963).
    17.  Petrychkovych V.M.Generalized equivalence of collections of matrices and common divisors of matrices  // Algebra and Discrete Mathematics. – 2004. – No 2. – P. 84 – 91.( A note to my paper “Generalized equivalence of collections of matrices and common divisors of matrices”  // Algebra and Discrete Mathematics. – 2005. – № 2. – P. 94 – 95.)
    18. Fedorchuk V.M., Fedorchuk V.I.On еру differential first-order invariants of the nonspleet­tinng subgroups of the Poincare group P(1,4) // Procideengs of Institute of Mathematics of NAS of Ukraine. – 50, Part 1. – 2004. – P. 85–91.
    19.  Fedorchuk V., Fedorchuk V. Some new differential equations of the first-order in the spaces  M(1,3)ґR(u) and M(1,4)ґR(u)$ with given symmetry groups // Functional Analysis and its Applications, North-Holland Mathematics Studies, Editor: Saul Lubkin, Elsevier. – 197 – 2004. – P. 85–95.
    20. Fedorchuk V. M., Fedorchuk V. I.On the differential first-order invariants for the non-splitting subgroups of the generalized Poincare group~P(1,4) // Annales Academiae Paedagogicae Cracoviensis, Studia Methematica. – 2004. – IV, Folia 23. – P. 65–74.
    21. Banakh T.O. and Gutik O.V. On the continuity of inversion in countably compact inverse topological semigroups // Semigroup Forum. – 2004. – 68, №3. – P. 411–418.
    22. Prokip V. On similarity of matrices over commutative rings  // Linear Algebra and its Application, 2005. – 399. – P. 225–233.
    23. Banakh T., Gutik O. and Rajagopalan M.Compatible algebraic structures on scattered compacta // Topology and its Applications. – 2005. – 153, № 5-6. – P. 710–723.
    24. Gutik O. V.  and Pavlyk K. P.  Topological semigroups of matrix units // Algebra and Discrete mathematics. – 2005. – № 3. – P. 1–17.
    25. Gutik O. V.  and Pavlyk K. P.  On topological semigroups of matrix units // Semigroup Forum. – 2005. – 71. – P. 389 – 400.
    26. Shchedryk V.P. Some determinant properties of primitive matrices over Bezout B-domain // Algebra and Discrete Mathematics. – 2005. – № 2. –P. 46–57.
    27. Gutik O. V.  and Pavlyk K. P.  On Brandt -extensions of semigroups with ze­ro // Mat. methods and phys.-mech. fields. – 2006. – 49, № 3. – P. 26–40.
    28. Shavarovs’kii B. On the block-diagonal equivalence of matrices // International Conference on Radicals ICOR-2006, July 30- August 5, 2006, Kyiv, Ukraine. – Kyiv, 2006. – P. 62–63.
    29. Shchedryk V.Unilateral equivalence of singular matrices and singular divisors of matrices // International Conference on Radicals ICOR-2006, July 30 - August 5, 2006, Kyiv, Ukraine. – Kyiv, 2006. – P. 64–66.
    30. Fedorchuk V.M., Fedorchuk V.I.First-order differential invariants of the splitting subgroups of the Poincare group P(1,4) // Universitatis Iagellonicae Acta Mathematica – 2006. – XLIV. – P. 35–44.
    31. Shavarovskii B.Z. Solvability of Matrix Equations in Rings of Quasi-Diagonal Matrices and Similarity of Matrix Polynomials // Computational Mathematics and Mathematical Physics. – 46. №. 8. – 2006. – P. 1283–1292 (Translated from Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki. – 46. №. 8. – 2006. – P. 1353–1362).
    32. Shavarovskii B.Z. Classes of Factorable and Unfactorable Polynomial Matrices and Their Relative Position // Doklady Mathematics . – 2007 – 75, №.2. – Р. 318-321 (Original Russian Text published in Doklady Akademii Nauk. – 2007. – 413, №. 6. – Р. 738–742).
    33. Shavarovskii B.Z. On the Similarity of Matrices of Even Order. // Mathematical Notes. – 81, no. 3. – 2007. – P. 392-407 (Translated from Matematicheskie Zametki. – 2007. – 81, №. 3. – P. 448–463).
    34. Shavarovskii B.Z. Multiplicative Structure of a Polynomial Matrix Depending on Its Elementary Divisors// Doklady Mathematics , 2007. – 76, №3. – Р. 843-847 (Original Russian Text published in Doklady Akademii Nauk. – 2007. – 417, №. 2. – Р. 175–179).
    35. 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, №. 12. – Р. 1902-1911 (Original Russian Text published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki. – 2007. – 47, №. 12. – Р. 1988–1997.).
    36. Shavarovs’kii B. On the class of factorable polynomial matrices // 6th Internatio­nal Algebraic Conference in Ukraine. Kamyanets-Podilsky, July 1–7, 2007. Abstracts. –Kamyanets-Podilsky, 2007. – P. 187–188.
    37. 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 Ukraine. Kamyanets-Podilsky, July 1–7, 2007. Abstracts. – Kamyanets-Podilsky, 2007. – P. 78–79.
    38. Prokip V. About  the uniqueness solution of the matrix polynomial equation// 6th Inter­natio­nal Algebraic Conference in Ukraine. Kamyanets-Podilsky, July 1–7, 2007. Abstracts. – Kamyanets-Podilsky, 2007. –P.  158–159.
    39. Shchedryk V., Mel’nyk O. On canonical diagonal form of matrices product // 6th Inter­natio­nal Algebraic Conference in Ukraine. Kamyanets-Podilsky, July 1–7, 2007. Abstracts. – Kamyanets-Podilsky, 2007. – P. 188–189.
    40. Dzhalyuk N., Petrychkovych V. Factorizations of partitioned matrices and solutions of linear matrix equations // 6th Inter­natio­nal Algebraic Conference in Ukraine. Kamyanets-Po­dilsky, July 1–7, 2007. Abstracts. – Kamyanets-Podilsky, 2007. – P. 75–76.
    41. Petrychkovych V.  On factorizations of matrices over some classes of rings // International conference ASADE, Chisineu, August 21-23, – 2007. – P.108–109.
    42. Gutik O. V. , Pavlyk K. P. Topological Brandt  λº-extensions and H-closed topological semigroups// 6th Inter­natio­nal Algebraic Conference in Ukraine. Kamyanets-Po­dilsky, July 1–7, 2007. Abstracts. – Kamyanets-Podilsky, 2007. – P. 88–89.
    43. Zelisko V., Ladzoryshyn N.On equivalence and  factorization  of matrices over quadratic rings // 6th Inter­natio­nal Algebraic Conference in Ukraine. Kamyanets-Po­dilsky, July 1–7, 2007. Abstracts. – Kamyanets-Podilsky, 2007. – P. 231–232.
    44. Romaniv A. On regular divisors of polynomial matrices // 6th Inter­natio­nal Algebraic Conference in Ukraine. Kamyanets-Po­dilsky, July 1–7, 2007. Abstracts. – Kamyanets-Podilsky, 2007. – P. 171–172.
    45. Prokip V.M. About the uniqueness Solution of the Matrix Polynomial Equation A(λ)X(λ)-Y(λ)B(λ)=C(λ) // Lobacheskij Journal of Mathematics. – 2008 – 23, №3. – Р.186–191.
    46. Fedorchuk V.M., 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 – Р. 122–132.
    47. Fedorchuk V. M, Fedorchuk V. I.On first-order differential invariants of the non-conjugate subgroups of the Poincare 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. – Р. 431-444.
    48. Fedorchuk V. M., Fedorchuk V. I. On functional bases of the first-order differential invariants for non-conjugate subgroups of the Poincare group P(1,4) // Annales Academiae Paedagogicae Cracoviensis, Studia Mathematica VII. – 2008. – Р.41–50.