Goy Taras


associate professor


MainBiographyResearch activity

Taras Goy, associate professor, was born in 1969, graduated from the Vasyl Stefanyk Precarpathian National University in 1993, speciality “Mathematics and Computer Sciences”.

He studied in postgraduate school at the Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine, Department of Mathematical Physics. In 1998 he defended his Ph.D. dissertation on “Nonlocal boundary value problem for partial differential equations and systems”. In the years 1999–2001 – assistant professor of Department of Mathematical Analysis and Differential Equations, Vasyl Stefanyk Precarpathian National University. Since 2002, associate professor of Department of Differential Equations and Applied Mathematics.

He provides teaching courses “Differential Equations”, “Variational calculus and optimization methods”.

E-mail: taras.goy@pnu.edu.ua

Taras Goy was born at December 24, 1969 in Kalush, Ivano-Frankivsk region, Ukraine.

In 1977-1987 he studied in secondary school number 12 and 16 of Ivano-Frankivsk.

In 1988-1993 he studied at the specialty “Mathematics and Computer Sciences”, Faculty of Physics and Mathematics of Vasyl Stefanyk Precarpathian University. He received a master’s degree with honors, qualification – the mathematician, teacher. Theme of master thesis – “Problems with nonlocal boundary value problem for hyperbolic equations with variables coefficients”, scientific adviser – professor Bohdan Ptashnyk (Lviv, Ukraine).

In 1993–1996 he studied in postgraduate school at the at the Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Department of Mathematical Physics.

In 1998 he defended his thesis for the degree Ph. D. in a specialized academic council of Yuriy Fedkovych Chernivtsi University. Theme of the Ph. D. dissertation “Nonlocal boundary value problem for partial differential equations and systems” Scientific adviser – Doctor of Physical and Mathematical Sciences, Professor Bohdan Ptashnyk (Lviv, Ukraine).

In 1999-2001 he worked as an assistant at the Department of Mathematical Analysis and Differential Equations of Vasyl Stefanyk Precarpathian National University.

Since 2002, he works as associate professor at the Department of Differential Equations and Applied Mathematics Vasyl Stefanyk Precarpathian National University.

In 2010 he passed the scientific training at the Department of Differential Equations of Ivan Franko National University of Lviv. In 2015 he passed the scientific training at the Department of Mathematics of Ivano-Frankivsk National Technical University of Oil and Gas.

Research interests: special numbers and polynomials, combinatorial number theory, determinants, permanents and other special matrix functions.

Member of Editorial Board of the journals: Carpathian Mathematical Publications (Scopus, Web of Science),  JP Journal of Algebra, Number Theory and Applications  (Web of Science).

Research papers
indexed in Scopus or Emerging Sources Citation Index
(Web of Science)

  1. Goi T.P., Ptashnik B.I. Problem with nonlocal conditions for weakly nonlinear hyperbolic equations, Ukrainian Math. J. (1997), 49(2), 204–215.
  2. Goi T.P., Ptashnik B.I. Nonlocal boundary-value problems for systems of linear partial differential equations with variable coefficients, Ukrainian Math. J. (1997), 49(11), 1659–1670.
  3. Goy T.P., Zatorsky R.A. New integral functions generated by rising factorial powers, Carpathian Math. Publ. (2013), 5(2), 217–224.
  4. Goy T.P. Special functions generated by rising and central factorial powers, Vestn. Tomsk. Gos. Univ. Mat. Mekh. (2016), 2(40), 19–32.
  5. Zatorsky R., Goy T. Parapermanents of triangular matrices and some general theorems on number sequences. J. Integer Seq. (2016), 19, Article 16.2.2.
  6. Goy T., Zatorsky R. Infinite linear recurrence relation and superposition of linear recurrence equations. J. Integer Seq. (2017), 20(5), Article 17.5.3.
  7. Goy T. On determinants and permanents of some Toeplitz-Hessenberg matrices whose entries are Jacobsthal numbers. Eurasian Math. J. (2018), 9(4), 61–67.
  8. Goy T.P., Negrych M., Savka I.Ya. On nonlocal boundary value problem for the equation of motion of a homogeneous elastic beam with pinned-pinned ends. Carpathian Math. Publ. (2018), 10(1), 105–113.
  9. Goy T. Horadam sequence through recurrent determinants of tridiagonal matrix. Kragujevac J. Math. (2018), 42(4), 527–532.
  10. Goy T. On new identities for Mersenne numbers. Appl. Math. E-Notes (2018), 18, 100–105.
  11. Goy T. Some families of identities for Padovan numbers. Proc. Jangjeon Math. Soc. (2018), 21(3), 413–419.
  12. Goy T. Fibonacci and Lucas numbers via the determinants of tridiagonal matrix. Notes Number Theory Discrete Math. (2018), 24(1), 103–108.
  13. Goy T.P. On some fibinomial identities. Chebyshevskii Sb. (2018), 19(2), 56–66.
  14. Goy T. On identities with multinomial coefficients for Fibonacci-Narayana sequence. Ann. Math. Inform. (2018), 49, 75–84.
  15. Goy T., Shattuck M. Determinant formulas of some Toeplitz-Hessenberg matri­ces with Catalan entries. Proc. Indian Acad. Sci. Math. Sci. (2019), 129, Article 46.
  16. Goy T., Shattuck M. Fibonacci and Lucas identities using Toeplitz–Hessenberg matrices. Appl. Appl. Math. (2019), 14 (2), 699–715.
  17. Goy T. Pell numbers identities from Toeplitz-Hessenberg determinants and permanents. Novi Sad J. Math. (2019), 49(2), 87–94.
  18. Goy T., Zatorsky R. On Oresme numbers and their connection with Fibonacci and Pell numbers. Fibonacci Quart. (2019), 57(3), 238–245.
  19. Goy T., Shattuck M. Determinants of Toeplitz-Hessenberg matrices with gene­ralized Fibonacci entries. Notes Number Theory Discrete Math. (2019), 25(4), 83–95.
  20. Goy T., Shattuck M. Some Toeplitz-Hessenberg determinant identities for the tetranacci numbers. J. Integer Seq. (2020), 23, Article 20.6.8.
  21. Goy T. Combinatorial properties of Boubaker polynomials. Math. Probl. Eng. (2020), 2020, Article ID 1528639.
  22. Goy T., Shattuck M. Determinant identities for Toeplitz-Hessenberg matrices with tribonacci number entries. Trans. Comb. (2020), 9(2), 89–109.
  23. Frontczak R., Goy T. Mersenne-Horadam identities using generating functions. Carpathian Math. Publ. (2020), 12(1), 34–45.
  24. Goy T., Zatorsky R. Hessenberg matrices: their properties and some appli­cations, Hot Topics in Linear Algebra, edited by I. Kyrchei, Nova Science Publishers, New York, 2020, 163–204.
  25. Goy T., Shattuck M. Fibonacci-Lucas identities and the generalized Trudi formula. Notes Number Theory Discrete Math. (2020), 26(3), 203–217.
  26. Goy T., Sharyn S. A note on Pell-Padovan numbers and their connection with Fibonacci numbers. Carpathian Math. Publ. (2020), 12(2), 280-288.
  27. Frontczak R., Goy T. Combinatorial sums associated with balancing and Lucas-balancing polynomials. Ann. Math. Inform. (2020), 52, 97–105.
  28. Frontczak R., Goy T. General infinite series evaluations involving Fibonacci numbers and the Riemann zeta function. Mat. Stud. (2021), 55(2), 115–123.
  29. Frontczak R., Goy T. More Fibonacci-Bernoulli relations with and without balancing polynomials. Math. Commun. (2021), 26(2), 215–226.
  30. Goy T., Shattuck M. Determinant formulas of some Hessenberg matrices with Jacobsthal entries, Applications and Applied Mathematics: An International J. (2021), 16 (2), 191–213.
  31. Adegoke K., Frontczak R., Goy T. Partial sum of the products of the Horadam numbers with subscripts in arithmetic progression, Notes on Number Theory and Discrete Mathematics. (2021), 27 (2), 54–63.
  32. Adegoke K., Frontczak R., Goy T. Special formulas involving polygonal numbers and Horadam numbers, Carpathian Math. Publ. (2021), 13(2), 207–216.
  33. Frontczak R., Goy T. Lucas-Euler relations using balancing and Lucas-balancing polynomials, Kyungpook Math. J. (2021), 61(3), 473–486.
  34. Frontczak R., Goy T. Chebyshev-Fibonacci polynomial relations using generating functions, Integers: Electronic Journal of Combinatorial Number Theory. (2021), 21, A 100, 15 p.
  35. Adegoke K., Frontczak R.,Goy T. Some special sums with squared Horadam numbers and generalized tribonacci numbers, Palestine J. Math. (2022), 11(1), 66-73.
  36. Adegoke K., Frontczak R., Goy T. Binomial tribonacci sums, Discrete Math. Lett. (2022), 8, 30-37.
  37. Frontczak R., Goy T., Shattuck M. Identities relating six members of the Fibonacci family of sequences, Carpathian Math. Publ. (2022), 14(1), 6-19.
  38. Frontczak R., Goy T., Shattuck M. Fibonacci-Lucas-Pell-Jacobsthal relations. Ann. Math. Inform. (2022), 54, doi: 10.33039/ami.2022.01.002.
  39. Adegoke K., Frontczak R., Goy T. On a family of infinite series with reciprocal Catalan numbers, Axioms (2022), 11(4), 165.
  40. Adegoke K., Frontczak R., Goy T. Recurrence relations for the squares the Horadam numbers and some associated consequen­ces, Tatra Mt. Math. Publ. (2022), 82(1), 17–28.
  41. Adegoke K., Frontczak R., Goy T. Fibonacci–Catalan series, Integers (2022), 22, A110.
  42. Adegoke K., Frontczak R., Goy T. Additional Fibonacci–Bernoulli relations, Res. Math. (2022), 30(2), 3–17.
  43. Adegoke K., Frontczak R., Goy T. Reciprocal series involving Ho­radam numbers, Ukrainian Math. J. (2023), 75(3), 335–346.
  44. Goy T., Shattuck M. Determinants of some Hessenberg–Toeplitz matrices with Motzkin number entries, J. Integer Seq. (2023), 26, Article 23.3.4.
  45. Goy T., Shattuck M. Hessenberg-Toeplitz matrix determinants with Schröder and Fine number entries, Carpathian Math. Publ. (2023), 15(2), 420–436.
  46. Goy T., Shattuck M. Determinant identities for the Catalan, Motzkin and Schröder numbers, Art Discrete Appl. Math. (2024), 7(1), #P1.09.