THERMAL SCIENCE

International Scientific Journal

Pınar Balki Okullu

,

Hüseyin Kocayiğit

,

Tuba Ağirman Aydin

AN EXPLICIT CHARACTERIZATION OF SPHERICAL CURVES ACCORDING TO BISHOP FRAME AND AN APPROXIMATELY SOLUTION

ABSTRACT
In this paper, spherical curves are studied by using Bishop Frame. First, the differential equation characterizing the spherical curves is given. Then, we exhibit that the position vector of a curve which is lying on a sphere satisfies a third-order linear differential equation. Then we solve this linear differential equation by using Bernstein Series Solution Method.
KEYWORDS
Spherical Curve, Bishop Frame, Bernstein Series Solution Method
PAPER SUBMITTED: 2018-11-01
PAPER REVISED: 2018-12-28
PAPER ACCEPTED: 2019-01-10
PUBLISHED ONLINE: 2019-03-09
DOI REFERENCE: https://doi.org/10.2298/TSCI181101049B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S361 - S370]
REFERENCES
  1. Wong , Y. C., On an Explicit Characterization of Spherical Curves, Proc. Am. Math. Soc., 34 (1972), 1, pp. 239-242
  2. Breuer ,S., Gottlieb, D., Explicit Characterization of Spherical Curves, Proc. Am. Math. Soc., 27 (1971), pp. 126-127
  3. Wong, Y. C., A global formulation of the condition for a curve to lie in a sphere, Monatsh. Math., 67 (1963), 363-365
  4. Mehlum, E., Wimp ,J., Spherical Curves and Quadratic Relationships for Special Functions, Austral. Mat. Soc., 27 ( 1985) pp. 111-124
  5. Kose ,O.,An Expilicit Characterization of Dual Spherical Curves, Doğa Mat. 12 (1998 ), 3, pp. 105-113
  6. Abdel Bakey , R. A.,An Explicit Characterization of Dual Spherical Curve, Commun. Fac. Sci. Univ. Ank. Series, 51 (2002), 2, pp. 1-9
  7. Ilarslan , K., et all., On the explicit characterization of spherical curves in 3-dimensional Lorentzian space, Journal of Inverse and Ill-posed Problems, 11 (2003), 4, pp. 389-397
  8. Kocayigit, H., et all., On the explicit characterization of spherical curves in n-dimensional Euclidean space, Journal of Inverse and Ill-posed Problems, 11 (2003), 3, pp. 245-254
  9. Ayyilidiz, N. , et all., A Characterization of Dual Lorentzian Spherical Curves in the Dual Lorentzian Space, Taiwanese Journal of Mathematics, 11 (2007), 4, pp. 999-1018
  10. Camci, C., et all., On the characterization of spherical curves in 3-dimensional Sasakian spaces, J. Math. Anal. Appl., 342 (2008),pp. 1151-1159
  11. Bishop, L. R., There is More Than one Way to Frame a Curve, Amer. Math. Monthly, 82 (1975), 3, pp. 246-251
  12. Bhatti, ,M.I., Brocken, B., Solutions of Differential Equations in a Bernstein Polynomial Basis, Bhatti Journal of Computational And Applied Mathematics. 205 (2007), pp. 272-280
  13. Işik ,O.R., et all., A rational approximation based on Bernstein polynomials for high order initial and boundary values problems, Applied Mathematics and Computation, 217 (2011), pp. 9438-945
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An explicit characterization of spherical curves according to bishop frame and an approximately solution

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence