Äæàëþê Íàòàë³ÿ Ñåìåí³âíà

(Dzhaliuk Nataliia Semenivna)

Îñâ³òà: Äðîãîáèöüêèé äåðæàâíèé ïåäàãîã³÷íèé óí³âåðñèòåò iìåí³ ²âàíà Ôðàíêà (ñïåö³àëüí³ñòü – ìàòåìàòèêà òà ³íôîðìàòèêà, 2001 ð.), àñï³ðàíòóðà ²ÏÏÌÌ ³ì. ß.Ñ.ϳäñòðèãà÷à ÍÀÍ Óêðà¿íè (01.01.06–àëãåáðà ³ òåîð³ÿ ÷èñåë, 2009 ð.)

Íàóêîâèé ñòóï³íü: êàíäèäàò ô³çèêî–ìàòåìàòè÷íèõ íàóê (01.01.06–àëãåáðà ³ òåîð³ÿ ÷èñåë, 2010 ð.)

Â÷åíå çâàííÿ: äîöåíò, ñòàðøèé äîñë³äíèê (ñïåö³àëüí³ñòü 111 Ìàòåìàòèêà, ç 2024ð.)

Ïîñàäà: ñòàðøèé íàóêîâèé ñï³âðîá³òíèê

 ²íñòèòóò³: ç 2001 ð.

Ïðîô³ë³ íàóêîâöÿ:

            ORCID:                                  https://orcid.org/0000-0001-5114-3296

            Scopus:                                   https://www.scopus.com/authid/detail.uri?authorId=57203801361

            Google Scholar:                     https://nbuviap.gov.ua/bpnu/bpnu_profile.php?bpnuid=BUN0023678

Îáëàñòü íàóêîâèõ ³íòåðåñ³â: ë³í³éíà àëãåáðà, çîêðåìà ìíîãî÷ëåíí³ ìàòðèö³ òà ìàòðè÷í³ ð³âíÿííÿ; ìàòðèö³ íàä êîìóòàòèâíèìè ê³ëüöÿìè

Äåÿê³ ç ïóáë³êàö³é:

 

1.     Dzhaliuk N.S., Petrychkovych V.M. Matrix linear bilateral equations over different domains, methods for the construction of solutions, and description of their structure // Journal of Mathematical Sciences. – 2024. – 282, No.5. – P. 616–645. https://doi.org/10.1007/s10958-024-07206-w (Scopus, 0.523, Q3)

2.     Dzhaliuk N.S., Petrychkovych V.M. Kronecker product of matrices and solutions of Sylvester-type matrix polynomial equations // Matematychni Studii. – 2024. – 61, No.2. – P. 115–122. https://doi.org/10.30970/ms.61.2.115-122 (Scopus, 0.675, Q3)

3.     Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì. Ìàòðè÷í³ ë³í³éí³ ð³çíîñòîðîíí³ ð³âíÿííÿ íàä ð³çíèìè îáëàñòÿìè, ìåòîäè ïîáóäîâè ðîçâ'ÿçê³â òà îïèñ ¿õíüî¿ ñòðóêòóðè // Ìàòåìàòè÷í³ ìåòîäè ³ ô³çèêî–ìåõàí³÷í³ ïîëÿ. – 2022. – Âèï. 65, ¹ 1–2. – Ñ. 18–41. (êàòåãîð³ÿ «À»)

4.     Ðîìàí³â À.Ì., Äæàëþê Í.Ñ. Ñòðóêòóðà ôîðìè Ñì³òà íàéá³ëüøîãî ñï³ëüíîãî ä³ëüíèêà òà íàéìåíøîãî ñï³ëüíîãî êðàòíîãî ìàòðèöü òðåòüîãî ïîðÿäêó íàä îáëàñòÿìè Áåçó ñòàá³ëüíîãî ðàíãó 1,5 // Ïðèêëàäí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè. – 2022. – Âèï. 20. – Ñ. 25–30.

5.     Dzhaliuk N.S., 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. (Scopus, 0.726, Q3)

6.     Dzhaliuk N.S. Solutions of the matrix equation AX + YB = C with triangular coefficients // Journal of Mathematical Sciences. – 2022. – 261, No. 1. – P. 25–32.– https://doi.org/10.1007/s10958–022–05734–x. (Scopus, 0.534, Q3)

7.     Äæàëþê Í.Ñ. ²ñíóâàííÿ ðîçâ’ÿçêó ìàòðè÷íîãî ð³âíÿííÿ òèïó Ñèëüâåñòðà ó ê³ëüö³ áëî÷íî–òðèêóòíèõ ìàòðèöü // Ïðèêëàäí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè. – 2021. – Âèï. 19. – Ñ. 79−83.

8.     Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì. Åêâiâàëåíòíiñòü ìàòðèöü ó êiëüöi M(n,R) òà â éîãî ïiäêiëüöÿõ // Óêð. ìàò. æóðí. – 2021. – 73, ¹ 12. – P. 1612–1618. DOI: 10.37863/umzh.v73i12.6858 (êàòåãîð³ÿ «À»)

9.     Äæàëþê Í. Ñ. Ðîçâ’ÿçêè ìàòðè÷íîãî ð³âíÿííÿ AX + YB = C ç òðèêóòíèìè êîåô³ö³ºíòàìè // Ìàò. ìåòîäè òà ô³ç.–ìåõ. ïîëÿ. – 2019. – 62, ¹ 2. – Ñ. 26–31. (êàòåãîð³ÿ «À»)

10.  Romaniv A. M., Dzhaliuk N. S. Some relationships between the invariant factors of matrix and its submatrix over elementary divisor domains // Ïðèêëàäí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè. – 2019. – Âèï. 17. – Ñ. 38−41.

11.  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. (Scopus, 0.782, Q3)

12.  Petrychkovych Vasyl', Dzhaliuk Nataliia Factorizations in the matrix ring and its subrings of the block matrices // The Fourth Conference of Mathematical Society of the Republic of Moldova: dedicated to the centenary of Vladimir Andrunachievici (1917–1997): Proceedings CMSM 4, June 28 – July 2, 2017 Chisinau / ed.: Mitrofan Choban [et al.]. Chisinau: Institute of Mathematics and Computer science, 2017 (CEP USM). P.143–146.

13.  Petrychkovych V., Dzhaliuk N. Factorizations in the rings of the block matrices // Bul. Acad. Stiinte Repub. Mold. Mat. – 2017. – Number 3 (85). – P. 23–33. (Scopus, 0.649, Q4).

14.  Dzhaliuk N.S., Petrychkovych V.M. The structure of solutions of the matrix linear unilateral polynomial equation with two variables // Carpathian Math. Publ. – 2017. – 9, No. 1. – P. 48–56. (Web of Science, Q4)

15.  Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì. Àáñîëþòíà ðîçêëàäí³ñòü íà ìíîæíèêè ó ê³ëüöÿõ êë³òêîâî–òðèêóòíèõ ìàòðèöü // Ïðèêëàäí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè. – 2013. – Âèï. 11. – Ñ. 36–40.

16.  Dzhaliuk N.S., Petrychkovych V.M. The matrix linear unilateral and bilateral equations with two variables over commutative rings // International Scholarly Research Network, ISRN Algebra. – Volume 2012. – Article ID 205478, 14 pages, doi: 10.5402/2012/205478.

17.  Äæàëþê Í., Ïåòðè÷êîâè÷ Â. Íàï³âñêàëÿðíà åêâ³âàëåíòí³ñòü ïîë³íîì³àëüíèõ ìàòðèöü òà ðîçâ'ÿçóâàííÿ ìàòðè÷íèõ ïîë³íîì³àëüíèõ ð³âíÿíü Ñèëüâåñòðà // Ìàòåìàòè÷íèé â³ñíèê ÍÒØ. – 2012. – ò.9. – Ñ. 81–88.

18.  Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì. Ðîçâ’ÿçêè ìàòðè÷íîãî ä³îôàíòîâîãî ïîë³íîì³àëüíîãî ð³âíÿííÿ // Ïðèêëàäí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè. – 2012. – Âèï. 10. – Ñ. 55–61.

19.  Äæàëþê Í.Ñ. Êë³òêîâî–ä³àãîíàëüíî ïàðàëåëüí³ ôàêòîðèçàö³¿ ìàòðèöü íàä îáëàñòÿìè ãîëîâíèõ ³äåàë³â // ³ñíèê Íàö³îíàëüíîãî óí³âåðñèòåòó "Ëüâ³âñüêà ïîë³òåõí³êà", Ô³çèêî–ìàòåìàòè÷í³ íàóêè. – 2012. – ¹ 740. – Ñ. 5–10.

20.   Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì. Ìàòðè÷í³ ä³îôàíòîâ³ ð³âíÿííÿ AX+BY=C // Êàðïàòñüê³ ìàòåìàòè÷í³ ïóáë³êàö³¿. – 2011. – Ò. 3, ¹ 2. – Ñ. 40 – 47.

21.  Äæàëþê Í.Ñ. Àñîö³éîâí³ñòü ôàêòîðèçàö³é êë³òêîâî–òðèêóòíèõ ìàòðèöü òà ¿õ ä³àãîíàëüíèõ êë³òîê íàä êîìóòàòèâíèìè îáëàñòÿìè ãîëîâíèõ ³äåàë³â // Ïðèêëàäí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè. – 2011. – Âèï. 9. – Ñ. 82–86.

22.  Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì. Ïàðàëåëüí³ ôàêòîðèçàö³¿ ìàòðèöü íàä ê³ëüöÿìè òà ¿õ çâ’ÿçêè // Ïðèêëàäí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè. – 2010. – Âèï. 8. – Ñ. 7–17.

23.  Äæàëþê Í.Ñ. Îäíîçíà÷í³ñòü êë³òêîâî–òðèêóòíèõ ôàêòîðèçàö³é ìàòðèöü íàä ê³ëüöÿìè ãîëîâíèõ ³äåàë³â // Äîïîâ³ä³ ÍÀÍ Óêðà¿íè. – 2010. – ¹ 1. – Ñ. 7 – 12.

24.  Äæàëþê Í. Ñ., Îïèñ ïàðàëåëüíèõ ôàêòîðèçàö³é ìíîãî÷ëåííèõ ìàòðèöü // Íàóê. â³ñíèê Óæãîðîä. óí–òó. Ñåð. ìàòåì. ³ ³íôîðì. – Óæãîðîä: ÓæÍÓ, 2009. – Âèï. 19. – Ñ. 31 – 37.

25.  Äæàëþê Í. Ñ., Ñï³ëüí³ ä³ëüíèêè êë³òêîâî–òðèêóòíèõ ìàòðèöü íàä ê³ëüöÿìè ãîëîâíèõ ³äåàë³â // Ïðèêëàäí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè. – 2009. – Âèï. 7. – Ñ. 86 – 90.

26.  Íàòàë³ÿ Äæàëþê, Âàñèëü Ïåòðè÷êîâè÷, Ôàêòîðèçàö³ÿ êë³òêîâî–ä³àãîíàëüíèõ òà êë³òêîâî–òðèêóòíèõ ìàòðèöü íàä ê³ëüöÿìè ãîëîâíèõ ³äåàë³â // Ìàòåìàòè÷íèé â³ñíèê ÍÒØ. – 2007 ð. – ò. 4. – ñ. 79–89.

27.  Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì., Ïðî ðîçâ’ÿçêè ìàòðè÷íèõ ìíîãî÷ëåííèõ ð³âíÿíü ³ ïîä³áí³ñòü ìàòðèöü // Ìàòåìàòè÷í³ ìåòîäè ³ ô³çèêî–ìåõàí³÷í³ ïîëÿ. – 2005. – Âèï.48, ¹4. – Ñ.14–19.

28.  Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì., Ïðî ñï³ëüí³ óí³òàëüí³ ä³ëüíèêè ìíîãî÷ëåííèõ ìàòðèöü ³ç çàäàíîþ êàíîí³÷íîþ ä³àãîíàëüíîþ ôîðìîþ // Ìàòåìàòè÷í³ ìåòîäè ³ ô³çèêî–ìåõàí³÷í³ ïîëÿ. – 2002. – Âèï.45, ¹3. – C.7.–13.

Àâòîðåôåðàò äèñåðòàö³¿:

Äæàëþê Í. Ñ. Ôàêòîðèçàö³ÿ ìàòðèöü íàä ïîë³íîì³àëüíèìè òà áëèçüêèìè äî íèõ ê³ëüöÿìè: Àâòîðåô. äèñ. ... êàíä. ô³ç.–ìàò. íàóê. – Ëüâ³â, 2010. – 19 ñ.

Ïóáë³êàö³¿ çà âèñòóïàìè íà êîíôåðåíö³ÿõ:

1.     Nataliia Dzhaliuk, Vasyl’ Petrychkovych Solutions of a given degree for the matrix linear bilateral polynomial equations // Ukraine Mathematics Conference "At the End of the Year 2024," December 16–18, 2024, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine, Book of Abstracts. – 92 ñ. – P. 23. – https://sites.google.com/knu.ua/aey2024/abstracts

2.     Dzhaliuk Nataliia, Sylvester-type Matrix Polynomial Equations and Solutions of a Prescribed Degree // 3rd International Symposium on Current Developments in Fundamental and Applied Mathematics Sciences 02-05 September 2024, Istanbul, Turkey. Abstract and Full Text Symposium Book. ISBN 978-625-97879-0-9. – 290 p. – P. 109. –https://atabulut.atauni.edu.tr/atabulut/index.php/s/bUAy5E7j1iZOfgX

3.     Dzhaliuk Nataliia, Petrychkovych Vasyl' On uniqueness of Sylvester-type matrix polynomial equation's solution // ̳æíàðîäíà êîíôåðåíö³ÿ ïðèñâÿ¬÷åíà 145-ð³÷÷þ ç äíÿ íàðîäæåííÿ Ãàíñà Ãàíà, 23–27 âåðåñíÿ 2024 ð., ×åðí³âö³. – ×åðí³âö³: ×åðí³âåöüêèé íàö. óí-ò ³ìåí³ Þð³ÿ Ôåäüêîâè÷à, 2024. – 184 ñ. – C. 126–127. – https://hahn.chnu.edu.ua/media/odbldmui/book-of-abstracts.pdf

4.     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

5.     Dzhaliuk Nataliia, Petrychkovych Vasyl'. The Sylvester matrix polynomial equation and its solutions // 14th Ukraine Algebra Conference, July 3–7, 2023 Sumy, Ukraine. Book of Abstracts: Sumy State Pedagogical University named after A.S. Makarenko, Sumy, Ukraine. – 150 p. – P. 54

6.     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.

7.     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/

8.     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.

9.     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, Drohobych, Ukraine. Book of Abstracts: Drohobych State Pedagogical University of Ivan Franko, Drohobych, Ukraine. – 67 p. – P. 15.

10.  Nataliia Dzhaliuk, Vasyl' Petrychkovych Block matrices, their equivalences and applications // The 13th International Algebraic Conference in Ukraine. July 6–9, 2021, Taras Shevchenko National University of Kyiv. Book of Abstracts: Taras Shevchenko National University of Kyiv, Kyiv, Ukraine. – 94 p. Ðåæèì äîñòóïó äî ðåñóðñó: https://bit.ly/3hcTbKe – P. 34.

11.  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. – Ðåæèì äîñòóïó äî ðåñóðñó: http://www.iapmm.lviv.ua/conf_skorob2020/documents/2020tezy.pdf – P. 29.

12.  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. – Ðåæèì äîñòóïó äî ðåñóðñó: https://bit.ly/2ZIyqMs– P. 63.

13.  Romaniv A.M., Dzhaliuk N.S. Some connections between invariant factors of matrix and its submatrix // International Scientific Conference Algebraic and Geometric Methods of Analysis, 26–30 may 2020, Odesa, Ukraine. – 131 p. – Ðåæèì äîñòóïó äî ðåñóðñó: https://www.imath.kiev.ua/~topology/conf/agma2020/agma–2020–abstracts/agma2020–theses.pdf – P. 57.

14.  Nataliia Dzhaliuk. Solutions of the Sylvester matrix equation with triangular coefficients // The XII International Algebraic Conference in Ukraine dedicated to the 215th anniversary of V.Bunyakovsky. July 02–06, 2019, Vinnytsia, Ukraine. Abstracts / Vinnytsia: Vasyl' Stus Donetsk National University, 2019. – 142 p. – P. 28–29. http://jiac.donnu.edu.ua/article/view/6933/6964

1.     Äæàëþê Íàòàë³ÿ, Ïåòðè÷êîâè÷ Âàñèëü Òðèêóòí³ ðîçâ'ÿçêè ìàòðè÷íîãî ð³âíÿííÿ AX+YB=C // Ñó÷àñí³ ïðîáëåìè ìåõàí³êè òà ìàòåìàòèêè: çá³ðíèê íàóêîâèõ ïðàöü ó 3–õ ò. / çà çàã.ðåä. À.Ñ. Ñàìîéëåíêà òà Ð.Ì. Êóøí³ðà [Åëåêòðîííèé ðåñóðñ] // ²íñòèòóò ïðèêëàäíèõ ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. ß.Ñ. ϳäñòðèãà÷à ÍÀÍ Óêðà¿íè. – 2018. – Ò.3. – Ðåæèì äîñòóïó äî ðåñóðñó: www.iapmm.lviv.ua/mpmm2018. – C. 197–198.

2.     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 Ukraine dedicated to the 75th anniversary of V.V.Kirichenko (July, 2017, Kyiv, Ukraine). P.99.

3.     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.

4.     Äæàëþê Íàòàë³ÿ, Ïåòðè÷êîâè÷ Âàñèëü Ôàêòîðèçàö³¿ â ê³ëüöÿõ êë³òêîâî–ä³àãîíàëüíèõ ìàòðèöü // Ñó÷àñí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè:  3–õ ò. / ï³ä çàãàëüíîþ ðåäàêö³ºþ Ð.Ì. Êóøí³ðà, Á.É. Ïòàøíèêà. – Ëüâ³â: ²íñòèòóò ïðèêëàäíèõ ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. ß.Ñ.ϳäñòðèãà÷à ÍÀÍ Óêðà¿íè, 2013. – Ò.3. – Ñ. 181–183.

5.     Dzhaliuk N., Petrychkovych V. Semiscalar equivalence of polynomial matrices and solutions of the matrix linear polynomial equations // 9–th International algebraic conference in Ukraine, L'viv, July 8–13, 2013: Book of abstracts. – L'viv, 2013. – P. 57.

6.     Äæàëþê Í., Ïåòðè÷êîâè÷ Â. Ôàêòîðèçàö³¿ êë³òêîâî–òðèêóòíèõ ìàòðèöü òà ¿õ ÷èñëî // International Conference dedicated to the 120th anniversary of Stefan Banach, Lviv, Ukraine, 17–21 September 2012. Abstracts of Reports. – P. 268.

7.     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.

8.     Dzhaliuk N., Petrychkovych V. On the minimal degree solutions of the Sylvester matrix polynomial equations // International mathematical conference: abstracts of talks. – Mykolayiv: Published by Mykolayiv V.O. Suchomlinsky National University, 2012. – P. 138.

9.     Äæàëþê Í.Ñ. Êë³òêîâî–ä³àãîíàëüíî ïàðàëåëüí³ ôàêòîðèçàö³é ìàòðèöü íàä îáëàñòÿìè ãîëîâíèõ ³äåàë³â // Ìàòåð³àëè êîíôåðåíö³¿ ìîëîäèõ ó÷åíèõ «Ï³äñòðèãà÷³âñüê³ ÷èòàííÿ – 2012» (23–25 òðàâíÿ 2012 ð., Ëüâ³â) – Ñ. 32–35. – [Åëåêòðîííèé ðåñóðñ]. Ðåæèì äîñòóïó: http://www.iapmm.lviv.ua/chyt2012/materials/12.pdf

10.  Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì. Îäíîçíà÷í³ñòü êë³òêîâî–ä³àãîíàëüíî ïàðàëåëüíèõ ôàêòîðèçàö³é ìàòðèöü // Äåñÿòà â³äêðèòà íàóêîâà êîíôåðåíö³ÿ ²ÌÔÍ: Çá³ðíèê ìàòåð³àë³â òà ïðîãðàìà êîíôåðåíö³¿ [«PSCIMFS–10»], (Ëüâ³â, 17–18 òðàâíÿ 2012 ð.) / Íàö³îíàëüíèé óí³âåðñèòåò «Ëüâ³âñüêà ïîë³òåõí³êà». — Ëüâ³â: Âèäàâíèöòâî Ëüâ³âñüêî¿ ïîë³òåõí³êè, 2012. — C. A32 – [Åëåêòðîííèé ðåñóðñ]. Ðåæèì äîñòóïó: http://psc–imfs.conference.lviv.ua/messages/psc–imfs–10–proceedings_175x250.pdf

11.  Äæàëþê Í.Ñ., Ïåòðè÷êîâè÷ Â.Ì. Êë³òêîâî–òðèêóòí³ ìàòðèö³ ç àáñîëþòíîþ âèä³ëþâàí³ñòþ ìíîæíèê³â // ×îòèðíàäöÿòà ì³æíàðîäíà íàóêîâà êîíôåðåíö³ÿ ³ìåí³ àêàäåì³êà Ì. Êðàâ÷óêà, 19–21 êâ³òíÿ, 2012 ð., Êè¿â: Ìàòåð³àëè êîíô. Ò. 2. Àëãåáðà. Ãåîìåòð³ÿ. Ìàòåìàòè÷íèé òà ÷èñåëüíèé àíàë³ç. – Êè¿â: ÍÒÓÓ Êϲ, 2012. – Ñ. 87.

12.  Äæàëþê Í.Ñ. Àñîö³éîâí³ñòü ôàêòîðèçàö³é êë³òêîâî–òðèêóòíèõ ìàòðèöü // ²V Êîíôåðåíö³ÿ ìîëîäèõ ó÷åíèõ ³ç ñó÷àñíèõ ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ìåí³ àêàäåì³êà ß.Ñ.ϳäñòðèãà÷à, 24–27 òðàâíÿ 2011ð., Ëüâ³â. / Òåçè äîïîâ³äåé. – Ëüâ³â: ²íñòèòóò ïðèêëàäíèõ ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. ß. Ñ. Ï³äñòðèãà÷à ÍÀÍ Óêðà¿íè, 2011. – Ñ. 241–242.

13.  Petrychkovych V. M., Dzhaliuk N. S. Factorizations in rings of block triangular matrices // 8–ìà ̳æíàðîäíà àëãåáðà¿÷íà êîíôåðåíö³ÿ â Óêðà¿í³: çá³ðíèê òåç. – Ëóãàíñüê: Âèäàâíèöòâî Ëóãàíñüêîãî íàö³îíàëüíîãî óí³âåðñèòåòó ³ìåí³ Òàðàñà Øåâ÷åíêà, 2011. – Ñ. 159.

14.  Ïåòðè÷êîâè÷ Â. Ì., Äæàëþê Í.Ñ. Ìàòðè÷í³ ä³îôàíòîâ³ ð³âíÿííÿ // ̳æíàð. ìàòåì. êîíô. ³ì. Â. ß. Ñêîðîáîãàòüêà, 1923 âåðåñíÿ 2011 ð.: òåçè äîïîâ. – Ëüâ³â, 2011. – Ñ. 161.

15.  Ïåòðè÷êîâè÷ Â. Ì., Äæàëþê Í.Ñ. Îäíîçíà÷í³ñòü ðîçâ’ÿçê³â ìàòðè÷íèõ ë³í³éíèõ îäíîá³÷íèõ ïîë³íîì³àëüíèõ ð³âíÿíü â³ä äâîõ çì³ííèõ // Âñåóêðà¿íñüêà íàóêîâà êîíôåðåíö³ÿ “Çàñòîñóâàííÿ ìàòåìàòè÷íèõ ìåòîä³â â íàóö³ ³ òåõí³ö³”, 25 – 26 ëèñòîïàäà 2011 ð.: Çá³ðíèê òåç äîïîâ. – Ëóöüê, 2011. – Ñ. 70–72.

16.  Dzhalyuk N. S. Equivalence and factorizations of partitioned matrices // 7th Inter­natio­nal Algebraic Conference in Ukraine, 18 – 23 August, 2009: Abstract of talks. – Kharkov, 2009. – Ð. 49.

17.  Äæàëþê Í. Ñ. ijëüíèêè ìíîãî÷ëåííèõ ìàòðèöü ç óìîâîþ ïàðà­ëåëüíîñò³ // Êîíôåðåíö³ÿ ìîëîäèõ ó÷åíèõ ³ç ñó÷àñíèõ ïðîáëåì ìåõàí³êè ³ ìàòåìàòèêè ³ì. àêàä. ß. Ñ. Ï³äñòðèãà÷à, 25 – 27 òðàâíÿ, 2009 ð.: òåçè äîïîâ. – Ëüâ³â, 2009. – Ñ. 168 – 170.

18.  Äæàëþê Í. Ñ. Ïðî ôàêòîðèçàö³¿ êë³òêîâî–òðèêóòíèõ ìàòðèöü òà ¿õ îäíî­çíà÷í³ñòü // Äâàíàäöÿòà ì³æíàðîäíà íàóêîâà êîíôåðåíö³ÿ ³ìåí³ àêàäåì³êà Ì. Êðàâ÷óêà, 15 – 17 òðàâ., 2008 ð.: ìàòåð³àëè êîíô. – Ê.: ÒΠ„Çàäðóãà”, 2008. – Ñ. 600.

19.  Íàòàë³ÿ Äæàëþê, Âàñèëü Ïåòðè÷êîâè÷ Ïðî ñï³ëüí³ ä³ëüíèêè êë³òêîâî–òðèêóòíèõ ìàòðèöü // ̳æíàð. íàóê. êîíô. “Ñó÷àñí³ ïðîáëåìè ìåõàí³êè ³ ìàòåìàòèêè”, ïðèñâÿ÷åíà 80–ð³÷÷þ â³ä äíÿ íàðîäæåííÿ àêàäåì³êà ÍÀÍÓ ß. Ñ. ϳäñòðèãà÷à òà 30–ð³÷÷þ çàñíîâàíîãî íèì ²ÏÏÌÌ, 25 – 29 òðàâíÿ 2008 ð., Ëüâ³â: â 3–õ òîìàõ. – Ëüâ³â, 2008. – Ò. 3. – Ñ. 184 – 185.

20.  Íàòàë³ÿ Äæàëþê, Âàñèëü Ïåòðè÷êîâè÷ Ôàêòîðèçàö³¿ êë³òêîâî–òðèêóòíèõ ö³ëî÷èñåëüíèõ ìàòðèöü // ̳æíàð. ìàòåì. êîíô. ³ì. Â. ß. Ñêîðîáîãàòüêà, 24 – 28 âåðåñíÿ 2007 ð.: òåçè äîïîâ. – Ëüâ³â, 2007. – Ñ. 88.

21.  Nataliya Dzhalyuk, Vasyl’ Petrychkovych Factorizations of partitioned matrices and solutions of linear matrix equations // 6th Inter­natio­nal Algebraic Conference in Ukraine, 17 July, 2007: Abstracts of talks.Kamyanets–Podilsky, 2007. – P. 7576.

Íàâ÷àëüíî-ìåòîäè÷í³ ïðàö³:

1.     Åëåêòðîííèé íàâ÷àëüíî-ìåòîäè÷íèé êîìïëåêñ «Âèùà ìàòåìàòèêà (ç³ ñêîðî÷åíèì òåðì³íîì íàâ÷àííÿ) ²Á²Ñ». Ñåðòèô³êàò ¹ 04651 ïðî âèçíàííÿ ³íôîðìàö³éíîãî ðåñóðñó: íîìåð òà äàòà ðåºñòðàö³¿: E41-143-299/2022 â³ä 29.04.2022, ó ³ðòóàëüíîìó ñåðåäîâèù³ Ëüâ³âñüêî¿ ïîë³òåõí³êè ìåòîäè÷íîþ ïðàöåþ (ÁÄ-ê). Àâòîðè: Äæàëþê Í.Ñ., Ðîìàí³â À.Ì., Ñàëî Ò.Ì., Ô³ëåâè÷ Ï.Â. – 310 ñ. https://vns.lpnu.ua/course/view.php?id=10649

2.     Åëåêòðîííèé íàâ÷àëüíî-ìåòîäè÷íèé êîìïëåêñ «Âèùà ìàòåìàòèêà». Ñåðòèô³êàò ¹ 03999 ïðî âèçíàííÿ ³íôîðìàö³éíîãî ðåñóðñó:  íîìåð òà äàòà ðåºñòðàö³¿: E41-143-351/2021 â³ä 13.05.2021, ó ³ðòóàëüíîìó ñåðåäîâèù³ Ëüâ³âñüêî¿ ïîë³òåõí³êè ìåòîäè÷íîþ ïðàöåþ (ÅÅ-ê). Àâòîðè: Äæàëþê Í.Ñ., Áîáèê ².Î., Êâ³ò Ð.²., Ñàëî Ò.Ì. – 270 ñ. http://vns.lpnu.ua/course/view.php?id=10810

3.     Âèùà ìàòåìàòèêà: ìåòîäè÷í³ âêàç³âêè äî ïðàêòè÷íèõ ðîá³ò, ïðèêëàäè òà çàäà÷³ äëÿ ñòóäåíò³â áàçîâîãî íàïðÿìêó “Åëåêòðîåíåðãåòèêà, åëåêòðîòåõí³êà òà åëåêòðîìåõàí³êà” (ç³ ñêîðî÷åíèì òåðì³íîì íàâ÷àííÿ) / Óêë.: Í.Ñ. Äæàëþê, ².Î. Áîáèê, ².². Âîëÿíñüêà, Î.². Ìëèíêî, À.Ì. Ðîìàí³â, Í.². Ñòðàï – Ëüâ³â: Âèäàâíèöòâî Ëüâ³âñüêî¿ ïîë³òåõí³êè, 2020. – 96 ñ.

 

Íàóêîâî-ïîïóëÿðí³ ïóáë³êàö³¿:

Äæàëþê Í. Ñ. Àëãåáðà åëåìåíòàðíà // Âåëèêà óêðà¿íñüêà åíöèêëîïåä³ÿ. URL: https://vue.gov.ua/Àëãåáðà åëåìåíòàðíà (äàòà ïóáë³êàö³¿: ñåðïåíü 2019ð.).

Òåëåôîí ñëóæáîâèé: (032) 258 96 22

Email: nataliya.dzhalyuk@gmail.com