Please use this identifier to cite or link to this item: http://ena.lp.edu.ua:8080/handle/ntb/55844
Title: On the universal regularity of the numbers of generalized recurrence sequence and solutions to its characteristic equation of second order
Other Titles: Про закономірності формування рекурентних послідовностей {αn} і {βn} в декомпозиції φn=αn ×φ+βn
Authors: Кособуцький, П. С.
Kosobutskyy, P.
Affiliation: Національний університет “Львівська політехніка”
Lviv Polytechnic National University
Bibliographic description (Ukraine): Kosobutskyy 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.
Bibliographic description (International): Kosobutskyy 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.
Is part of: Computer Design Systems. Theory and Practice, 1 (1), 2019
Issue: 1
Issue Date: 28-Feb-2019
Publisher: Видавництво Львівської політехніки
Lviv Politechnic Publishing House
Place of the edition/event: Львів
Lviv
DOI: doi.org/10.23939/cds2019.01.027
UDC: 004.451(86)
УДК 512.8
Keywords: пропорція нерівного поділу цілого
декомпозиція
рекурентні послідовності чисел Фібоначчі
формула Біне
Golden ratio
Phidias number
the quadratic equation
second order recursive sequence
Number of pages: 7
Page range: 27-33
Start page: 27
End page: 33
Abstract: У 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.
In 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.
URI: http://ena.lp.edu.ua:8080/handle/ntb/55844
Copyright owner: © Національний університет „Львівська політехніка“, 2019
© Kosobutskyy P., 2019
URL for reference material: https://arxiv.org/pdf/1707.09151.pdf
References (Ukraine): 1. 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,
2. 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.
3. Vorobyov N. Fibonacci Numbers. Moscow,1961.
4. R. Dunlap. The golden ratio and Fibonacci numbers. World Scientific Publishing Co. Pte. Ltd. 1997
5. Vajda S. (1989) Fibonacci & Lucas Numbers, and the Golden Section. Theory and Applications. Ellis Horwood limited.
6. Koshy T. (2001) Fibonacci and Lucas numbers with application, A Wiley-Interscience Publication: New York.
7. Horadam A. Basic Properties of a Certain Generalized Sequence of Numbers. Fibonacci Quarterly, 3.3(1965), рр. 161–176.
8. Larcombe P. Horadam Sequences: A Survey Update and Extension , Bulletin of the ICA, Vol. 80 (2017), 99–118.
9. 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.
10. 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
11. Szakacs T. K-order Linear Recursive Sequences and the Golden Ratio. Fibonacci Quarterly, 55.5 (2017), рр. 186–191.
12. Shneider R. Fibonacci numbers and the golden ratio. VarXiv:1611.07384v1 [math.HO] 22 Nov 2016.
References (International): 1. 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,
2. 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.
3. Vorobyov N. Fibonacci Numbers. Moscow,1961.
4. R. Dunlap. The golden ratio and Fibonacci numbers. World Scientific Publishing Co. Pte. Ltd. 1997
5. Vajda S. (1989) Fibonacci & Lucas Numbers, and the Golden Section. Theory and Applications. Ellis Horwood limited.
6. Koshy T. (2001) Fibonacci and Lucas numbers with application, A Wiley-Interscience Publication: New York.
7. Horadam A. Basic Properties of a Certain Generalized Sequence of Numbers. Fibonacci Quarterly, 3.3(1965), rr. 161–176.
8. Larcombe P. Horadam Sequences: A Survey Update and Extension , Bulletin of the ICA, Vol. 80 (2017), 99–118.
9. 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.
10. 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
11. Szakacs T. K-order Linear Recursive Sequences and the Golden Ratio. Fibonacci Quarterly, 55.5 (2017), rr. 186–191.
12. Shneider R. Fibonacci numbers and the golden ratio. VarXiv:1611.07384v1 [math.HO] 22 Nov 2016.
Content type: Article
Appears in Collections:Комп'ютерні системи проектування теорія і практика. – 2019. – Том 1, № 1



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