Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2018, Cilt: 3 Sayı: 2, 9 - 22, 30.08.0208

Tuba Agirman Aydin Mehmet Sezer Huseyin Kocayigit

Öz

Kaynakça

  • [1] A. Magden, O. Köse, ¨ On The Curves Of Constant Breadth In E4 Space, Turk J. Math.,(21), (1997), 277-284.
  • [2] A.P. Mellish, Notes On Differential Geometry, Ann Of Math. (2)32, no.1, (1931), 181-190.
  • [3] F. Reuleaux, The Kinematics Of Machinery, Trans. By Kennedy A.B.W., Dover Pub. (1963), New York.
  • [4] H. Gluck. Higher Curvatures of Curves In Euclidean Space, Proc. Amer. Math. Montly,(73)(1966),699-704.
  • [5] H.H. Hacisalihoglu, Diferensiyel Geometri, Ankara Universitesi Fen Fak¨ultesi, (1993), Ankara, 269s.
  • [6] J. Walrave, Curves and Surfaces In Minkowski Space, Ph. D. Thesis (1995), K. U. Leuven, Faculty Of Sciences, Leuven. [7] L. Euler, De Curvis trangularibis, Acta Acad. Petropol, (1778, 1780), 3-30.
  • [8] M. Fujivara, On Space Curves of Constant Breadth, Thoku Math. J.(5), (1914), 179-184.
  • [9] M. Onder, H. Kocayi˘git, E. Candan, Differential Equations Characterizing Timelike and Spacelike Curves of Constant Breadth ˙In Minkowski 3-Space E. J. Korean Math. Soc.(48), no.4, (2011), 849-866.
  • [10] M. Sezer, Differential Equations Characterizing Space Curves of Constant Breadth and A Criterion For These Curves, Doga TU J. Math., 13 (2), (1989), 70-78.
  • [11] M. Sezer, Integral Characterizations For A System of Frenet Like Differential Equations and Applications, E. U. Faculity of Science, Series Of Scientific Meetings, (1), (1991), 435-444.
  • [12] M.I. Bhatti, B. Brocken, Solutions of Differential Equations ˙In A Bernstein Polynomial Basis. Journal of Computational And Applied Mathematics. (205), (2007), 272-280.
  • [13] O.R. Isik, M. Sezer and Z. Güney, A rational approximation based on Bernstein polynomials for high order initial and boundary values problems, Applied Mathematics and Computation, 217, (2011), 9438-9450.
  • [14] O. Köse, Düzlemde Ovaller ve Sabit Genislikli Egrilerin bazı özellikleri, Doga Bilim Dergisi, Seri B, (2), (1984), 119-126. [15] O. Köse, On Space Curve of Constant Breadth, Doga TU J. Math.,(1), (1986), 11-14.
  • [16] T.A. Aydin, Differential Equations Characterizing Curves of Constant Breadth And Spherical Curves In En-Space and Their Solutions, Ph. D. Thesis (2014), Mugla Sıtkı Koc¸man Universty, Mugla.
  • [17] V. Dannon, Integral Characterizations And The Theory of Curves, Proc. Amer. Math. Soc.,(4), (1981), 600-602.
  • [18] Z. Akdogan, A. Magden, Some Characterization of Curves of Constant Breadth In En Space, Turk J. Math.,(25), (2001), 433-444.

Bernsteinn polynomials approach to determine timelike curves of constant breadth in Minkowski 3-space

Yıl 2018, Cilt: 3 Sayı: 2, 9 - 22, 30.08.0208

Tuba Agirman Aydin Mehmet Sezer Huseyin Kocayigit

Öz

In this study, we first show that the system of Frenet-like differential equation characterizing timelike curves of constant
breadth is equivalent to a third order, linear, differential equation with variable coefficients. Then, by using a rational approximation
based on Bernstein polynomials, we obtain the set of solution of the mentioned differential equation under the given initial conditions.
Furthermore, we discuss that the obtained results are useable to determine timelike curves of constant breadth in Minkowski 3-space
E1
3.

Anahtar Kelimeler

Timelike curve of constant breadth Bernstein polynomials Linear differential equations

Kaynakça

  • [1] A. Magden, O. Köse, ¨ On The Curves Of Constant Breadth In E4 Space, Turk J. Math.,(21), (1997), 277-284.
  • [2] A.P. Mellish, Notes On Differential Geometry, Ann Of Math. (2)32, no.1, (1931), 181-190.
  • [3] F. Reuleaux, The Kinematics Of Machinery, Trans. By Kennedy A.B.W., Dover Pub. (1963), New York.
  • [4] H. Gluck. Higher Curvatures of Curves In Euclidean Space, Proc. Amer. Math. Montly,(73)(1966),699-704.
  • [5] H.H. Hacisalihoglu, Diferensiyel Geometri, Ankara Universitesi Fen Fak¨ultesi, (1993), Ankara, 269s.
  • [6] J. Walrave, Curves and Surfaces In Minkowski Space, Ph. D. Thesis (1995), K. U. Leuven, Faculty Of Sciences, Leuven. [7] L. Euler, De Curvis trangularibis, Acta Acad. Petropol, (1778, 1780), 3-30.
  • [8] M. Fujivara, On Space Curves of Constant Breadth, Thoku Math. J.(5), (1914), 179-184.
  • [9] M. Onder, H. Kocayi˘git, E. Candan, Differential Equations Characterizing Timelike and Spacelike Curves of Constant Breadth ˙In Minkowski 3-Space E. J. Korean Math. Soc.(48), no.4, (2011), 849-866.
  • [10] M. Sezer, Differential Equations Characterizing Space Curves of Constant Breadth and A Criterion For These Curves, Doga TU J. Math., 13 (2), (1989), 70-78.
  • [11] M. Sezer, Integral Characterizations For A System of Frenet Like Differential Equations and Applications, E. U. Faculity of Science, Series Of Scientific Meetings, (1), (1991), 435-444.
  • [12] M.I. Bhatti, B. Brocken, Solutions of Differential Equations ˙In A Bernstein Polynomial Basis. Journal of Computational And Applied Mathematics. (205), (2007), 272-280.
  • [13] O.R. Isik, M. Sezer and Z. Güney, A rational approximation based on Bernstein polynomials for high order initial and boundary values problems, Applied Mathematics and Computation, 217, (2011), 9438-9450.
  • [14] O. Köse, Düzlemde Ovaller ve Sabit Genislikli Egrilerin bazı özellikleri, Doga Bilim Dergisi, Seri B, (2), (1984), 119-126. [15] O. Köse, On Space Curve of Constant Breadth, Doga TU J. Math.,(1), (1986), 11-14.
  • [16] T.A. Aydin, Differential Equations Characterizing Curves of Constant Breadth And Spherical Curves In En-Space and Their Solutions, Ph. D. Thesis (2014), Mugla Sıtkı Koc¸man Universty, Mugla.
  • [17] V. Dannon, Integral Characterizations And The Theory of Curves, Proc. Amer. Math. Soc.,(4), (1981), 600-602.
  • [18] Z. Akdogan, A. Magden, Some Characterization of Curves of Constant Breadth In En Space, Turk J. Math.,(25), (2001), 433-444.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Tuba Agirman Aydin

Mehmet Sezer Bu kişi benim

Huseyin Kocayigit Bu kişi benim

Yayımlanma Tarihi 30 Ağustos 208
Yayımlandığı Sayı Yıl 2018 Cilt: 3 Sayı: 2

Kaynak Göster

APA Agirman Aydin, T., Sezer, M., & Kocayigit, H. Bernsteinn polynomials approach to determine timelike curves of constant breadth in Minkowski 3-space. Communication in Mathematical Modeling and Applications, 3(2), 9-22.
AMA Agirman Aydin T, Sezer M, Kocayigit H. Bernsteinn polynomials approach to determine timelike curves of constant breadth in Minkowski 3-space. CMMA. 3(2):9-22.
Chicago Agirman Aydin, Tuba, Mehmet Sezer, ve Huseyin Kocayigit. “Bernsteinn Polynomials Approach to Determine Timelike Curves of Constant Breadth in Minkowski 3-Space”. Communication in Mathematical Modeling and Applications 3, sy. 2 : 9-22.
EndNote Agirman Aydin T, Sezer M, Kocayigit H Bernsteinn polynomials approach to determine timelike curves of constant breadth in Minkowski 3-space. Communication in Mathematical Modeling and Applications 3 2 9–22.
IEEE T. Agirman Aydin, M. Sezer, ve H. Kocayigit, “Bernsteinn polynomials approach to determine timelike curves of constant breadth in Minkowski 3-space”, CMMA, c. 3, sy. 2, ss. 9–22.
ISNAD Agirman Aydin, Tuba vd. “Bernsteinn Polynomials Approach to Determine Timelike Curves of Constant Breadth in Minkowski 3-Space”. Communication in Mathematical Modeling and Applications 3/2, 9-22.
JAMA Agirman Aydin T, Sezer M, Kocayigit H. Bernsteinn polynomials approach to determine timelike curves of constant breadth in Minkowski 3-space. CMMA.;3:9–22.
MLA Agirman Aydin, Tuba vd. “Bernsteinn Polynomials Approach to Determine Timelike Curves of Constant Breadth in Minkowski 3-Space”. Communication in Mathematical Modeling and Applications, c. 3, sy. 2, ss. 9-22.
Vancouver Agirman Aydin T, Sezer M, Kocayigit H. Bernsteinn polynomials approach to determine timelike curves of constant breadth in Minkowski 3-space. CMMA. 3(2):9-22.
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