On the universal regularity of the numbers of generalized recurrence sequence and solutions to its characteristic equation of second order

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dc.citation.epage33
dc.citation.issue1
dc.citation.spage27
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorКособуцький, П. С.
dc.contributor.authorKosobutskyy, P.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2021-01-19T09:50:00Z
dc.date.available2021-01-19T09:50:00Z
dc.date.created2019-02-28
dc.date.issued2019-02-28
dc.description.abstractУ роботі досліджено закономірності відношень коефіцієнтів , αn βn послідовностей {αn} і {βn}, які формуються в процесі степеневого перетворення (декомпозиції) виду φn=αn ×φ+βn ділянці додатних і від’ємних показників n.
dc.description.abstractIn this work shows that the classical oscillations of the ratio of neighboring members of the Fibonacci sequences are valid for arbitrary directions on the plane of the phase coordinates, approaching, to a maximum, the solutions to the characteristic quadratic equation at a given point. The values of the solutions to the characteristic equation along the satellites are asymptotically close to their integer values of the corresponding root lines.
dc.format.extent27-33
dc.format.pages7
dc.identifier.citationKosobutskyy P. On the universal regularity of the numbers of generalized recurrence sequence and solutions to its characteristic equation of second order / P. Kosobutskyy // Computer Design Systems. Theory and Practice. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 1. — No 1. — P. 27–33.
dc.identifier.citationenKosobutskyy P. On the universal regularity of the numbers of generalized recurrence sequence and solutions to its characteristic equation of second order / P. Kosobutskyy // Computer Design Systems. Theory and Practice. — Lviv : Lviv Politechnic Publishing House, 2019. — Vol 1. — No 1. — P. 27–33.
dc.identifier.doidoi.org/10.23939/cds2019.01.027
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/55844
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofComputer Design Systems. Theory and Practice, 1 (1), 2019
dc.relation.references1. Kosobutskyy P. Modelling of electrodynamic Systems by the Method of Binary Seperation of Additive Parameter in Golden Proportion. Jour. of Electronic Research and Application, 2019,3(3), р. 8–12,
dc.relation.references2. Kosobutskyy P. et.al. Physical principles of Optimization of the Static Regime of a Cantilever-Type Powereffect Sensor with a Constant Rectangular Cross Section. Jour. of Electronic Research and Application, 2018, 2(5), р. 11–15.
dc.relation.references3. Vorobyov N. Fibonacci Numbers. Moscow,1961.
dc.relation.references4. R. Dunlap. The golden ratio and Fibonacci numbers. World Scientific Publishing Co. Pte. Ltd. 1997
dc.relation.references5. Vajda S. (1989) Fibonacci & Lucas Numbers, and the Golden Section. Theory and Applications. Ellis Horwood limited.
dc.relation.references6. Koshy T. (2001) Fibonacci and Lucas numbers with application, A Wiley-Interscience Publication: New York.
dc.relation.references7. Horadam A. Basic Properties of a Certain Generalized Sequence of Numbers. Fibonacci Quarterly, 3.3(1965), рр. 161–176.
dc.relation.references8. Larcombe P. Horadam Sequences: A Survey Update and Extension , Bulletin of the ICA, Vol. 80 (2017), 99–118.
dc.relation.references9. F. Gatta, A. D’amico. Sequences {Hn} for which Hn+1/Hn approaches the Golden Ratio. Fibonacci Quarterly, 46/47.4 (2008/2009), рр. 346–349.
dc.relation.references10. Ozvatan M., Pashev O. Generalized Fibonacci Sequences and Binnet-Fibonacci Curves. arXiv:1707.09151v1 [math.HO] 28 Jul 2017. https://arxiv.org/pdf/1707.09151.pdf
dc.relation.references11. Szakacs T. K-order Linear Recursive Sequences and the Golden Ratio. Fibonacci Quarterly, 55.5 (2017), рр. 186–191.
dc.relation.references12. Shneider R. Fibonacci numbers and the golden ratio. VarXiv:1611.07384v1 [math.HO] 22 Nov 2016.
dc.relation.referencesen1. Kosobutskyy P. Modelling of electrodynamic Systems by the Method of Binary Seperation of Additive Parameter in Golden Proportion. Jour. of Electronic Research and Application, 2019,3(3), r. 8–12,
dc.relation.referencesen2. Kosobutskyy P. et.al. Physical principles of Optimization of the Static Regime of a Cantilever-Type Powereffect Sensor with a Constant Rectangular Cross Section. Jour. of Electronic Research and Application, 2018, 2(5), r. 11–15.
dc.relation.referencesen3. Vorobyov N. Fibonacci Numbers. Moscow,1961.
dc.relation.referencesen4. R. Dunlap. The golden ratio and Fibonacci numbers. World Scientific Publishing Co. Pte. Ltd. 1997
dc.relation.referencesen5. Vajda S. (1989) Fibonacci & Lucas Numbers, and the Golden Section. Theory and Applications. Ellis Horwood limited.
dc.relation.referencesen6. Koshy T. (2001) Fibonacci and Lucas numbers with application, A Wiley-Interscience Publication: New York.
dc.relation.referencesen7. Horadam A. Basic Properties of a Certain Generalized Sequence of Numbers. Fibonacci Quarterly, 3.3(1965), rr. 161–176.
dc.relation.referencesen8. Larcombe P. Horadam Sequences: A Survey Update and Extension , Bulletin of the ICA, Vol. 80 (2017), 99–118.
dc.relation.referencesen9. F. Gatta, A. D’amico. Sequences {Hn} for which Hn+1/Hn approaches the Golden Ratio. Fibonacci Quarterly, 46/47.4 (2008/2009), rr. 346–349.
dc.relation.referencesen10. Ozvatan M., Pashev O. Generalized Fibonacci Sequences and Binnet-Fibonacci Curves. arXiv:1707.09151v1 [math.HO] 28 Jul 2017. https://arxiv.org/pdf/1707.09151.pdf
dc.relation.referencesen11. Szakacs T. K-order Linear Recursive Sequences and the Golden Ratio. Fibonacci Quarterly, 55.5 (2017), rr. 186–191.
dc.relation.referencesen12. Shneider R. Fibonacci numbers and the golden ratio. VarXiv:1611.07384v1 [math.HO] 22 Nov 2016.
dc.relation.urihttps://arxiv.org/pdf/1707.09151.pdf
dc.rights.holder© Національний університет „Львівська політехніка“, 2019
dc.rights.holder© Kosobutskyy P., 2019
dc.subjectпропорція нерівного поділу цілого
dc.subjectдекомпозиція
dc.subjectрекурентні послідовності чисел Фібоначчі
dc.subjectформула Біне
dc.subjectGolden ratio
dc.subjectPhidias number
dc.subjectthe quadratic equation
dc.subjectsecond order recursive sequence
dc.subject.udc004.451(86)
dc.subject.udcУДК 512.8
dc.titleOn the universal regularity of the numbers of generalized recurrence sequence and solutions to its characteristic equation of second order
dc.title.alternativeПро закономірності формування рекурентних послідовностей {αn} і {βn} в декомпозиції φn=αn ×φ+βn
dc.typeArticle

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Комп'ютерні системи проектування теорія і практика. – 2019. – Том 1, № 1