Morgan-Voyce Polynomial Approach for Quaternionic Space Curves of Constant Width

• Autorzy: Aydin Tuba Ağirman , Ayazoğlu Rabil , Kocayiğit Hüseyin

Identyfikatory

DOI

10.2478/fcds-2021-0005

• Języki publikacji: EN

Abstrakty

EN

The curves of constant width are special curves used in engineering, architecture and technology. In the literature, these curves are considered according to different roofs in different spaces and some integral characterizations of these curves are obtained. However, in order to examine the geometric properties of curves of constant width, more than characterization is required. In this study, firstly differential equations characterizing quaternionic space curves of constant width are obtained. Then, the approximate solutions of the differential equations obtained are calculated by the Morgan-Voyce polynomial approach. The geometric properties of this curve type are examined with the help of these solutions.

Słowa kluczowe

EN

curve of constant width; quaternionic space curve; Morgan-Voyce polynomial approach

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2021
• Tom: Vol. 46, No. 1
• Strony: 71--83
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Aydin Tuba Ağirman

• Faculty of Education, Bayburt University, Bayburt, Turkey

autor

Ayazoğlu Rabil

• Faculty of Education, Bayburt University, Bayburt, Turkey

autor

Kocayiğit Hüseyin

• Department of Mathematics, Celal Bayar University, Manisa, Turkey

Bibliografia

• [1] Akdoğan Z., Mağden A., Some characterization of curves of constant-breadth in En space, Turkısh Journal of Mathematics, 25, 2001, 433-444.
• [2] Demir S., Özdaş K., Serret–Frenet formulas by real quaternions, Süleyman Demirel University, Journal of Science Institute, 9, 2005, 1-7.
• [3] Hacısalihoğlu H.H., Motion geometry and quaternions theory, Gazi University, Faculty of Arts and Sciences Publications, Ankara, 1983.
• [4] Hacısalihoğlu H.H., Differential geometry I, Ankara university Pres, Ankara, 1998.
• [5] Hamilton W.R., Lectures on Quaternions, 1853.
• [6] Karadağ M., Sivridağ A.İ., Univariate quaternion-valued functions and tendency lines, Erciyes University Journal of Science Institute, 13, 1997, 23-36.
• [7] Mağden A., Yılmaz S., On the curves of constant-breadth in four dimensional Galilean space, International Mathematical Forum, 9, 2014, 1229-1236.
• [8] O’neil B., Elementary differantial geometry, Academic Pres, Newyork, 1966.
• [9] Önder M., Kocayiğit H., Candan E., Differential equations characterizing timelike and spacelike curves of constant-breadth in Minkowski 3-space, Journal of the Korean Mathematical Society, 48, 2011, 849-866.
• [10] Özel M., Kürkçü Ö.K., Sezer M., Morgan-Voyce matrix method for generalized functional integro-differential equations of volterra-type, Journal of Science and Arts, 2, 2019, 295-310.
• [11] Öztürk G., Kişi İ., Büyükkütük S., Constant Ratio Quaternionic Curves in Euclidean Spaces, Advances in Applied Clifford Algebras, 27, 2017, 1659–1673.
• [12] Resnikoff H.L., On Curves and Surfaces of Constant Width, arXiv: Differential Geometry, 2015, 1-48.
• [13] Sezer M., Differential equations characterizing space curves of constant-breadth and a criterion for these curves, Doğa Tr J Math, 1989, 69-78.
• [14] Soyfidan T., Parlatıcı H., Güngör M.A., On The Quaternionic Curves According to Parallel Transport Frame, TWMS Journal of Pure and Applied Mathematics, 4, 2013, 194-203.
• [15] Swamy M.N.S., Properties of the polynomial defined by Morgan-Voyce. The Fibonacci Quarterly, 4, 1966, 73-81.
• [16] Türkyılmaz B., Gürbüz B., Sezer M., Morgan-Voyce polynomial approach for solution of high-order linear differential-difference equations with residual error estimation, Düzce University Journal of Science & Technology, 4, 2016, 252-263.
• [17] Zhu C., Zheng C., Shu L., Han G., A survey on coverage and connectivity issues in wireless sensor networks, Journal Network and Computer Applications, 35, 2012, 619-632.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).