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Year 2019, Volume: 2 Issue: 3, 180 - 184, 30.12.2019

Mehmet Ali Güngör , Elma Kahramani

Abstract

References

  • [1] J. Cockle On a new imaginary in algebra, London-Dublin-Edinburgh Philosophical Magazine 3(34) (1849), 37-47.
  • [2] I. M. Yaglom, A simple non-Euclidean geometry and its physical basis, Springer-Verlag New York, 1979.
  • [3] S. Yüce, Z. Ercan, On properties of the dual quaternions, European Journal of Pure and Applied Mathematics 4(2) (2011), 142-146.
  • [4] G. Sobczyk The hyperbolic number plane, The College Math. J., 26(4) (1995), 268-280.
  • [5] F. Catoni, R. Cannata, V. Catoni, P. Zampetti, Hyperbolic trigonometry in two-dimensional space-time geometry, Nuovo Cimento della Societa Italiana di Fisica B 118 (2003), 475-491.
  • [6] S. Yüce, N. Kuruo˜glu , One-parameter plane hyperbolic motions, Adv. Appl. Clifford Alg. 18(2) (2018), 279-285.
  • [7] M. Akar, S. Yüce, S. Sahin, On the Dual Hyperbolic Numbers and the Complex Hyperbolic Numbers, Journal of Computer Science Computational Mathematics, 8(1) (2018), 279-285.
  • [8] S. Ersoy, M. Akyiğit, One-parameter homothetic motion in the hyperbolic plane and Euler-Savary formula, Adv. Appl. Clifford Alg. 21(2) (2011), 297-317.
  • [9] D. P. Mandic, V. S. L. Goh, Hyperbolic valued nonlinear adaptive filters: noncircularity, widely linear and neural models, John Wiley-Sons., 2009.
  • [10] G. Helzer, Special relativity with acceleration, Amer. Math. Monthy 107(3) (2000), 219-237.
  • [11] W. K. Clifford, Preliminary sketch of bi-quaternions, Proc. London Math. Soc. 4 (1873), 381-395.
  • [12] E. Study, Geometrie der dynamen, Leipzig, Germany, 1903.
  • [13] E. Cho, De-Moivreâ˘AZ´s formula for quaternions, Appl. Math. Lett. 11(6) (1998), 33-35.
  • [14] H. Kabadayı, Y. Yaylı, De-Moivre’s formula for dual quaternions, Kuwait J. Sci. Technol. 38(1) (2011), 15-23.
  • [15] I. A. Kösal, A note on hyperbolic quaternions, Universal Journal Of Mathematics and Applications 1(3) (2018), 155-159.
  • [16] V. Majernik, Multicomponent number systems, Acta Physics Polonica A 3(90) (1996), 491-498.
  • [17] F. Messelmi, Dual-hyperbolic numbers and their holomorphic functions, (2015), https://hal.archives-ouvertes.fr/hal-01114178.

De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers

Year 2019, Volume: 2 Issue: 3, 180 - 184, 30.12.2019

Mehmet Ali Güngör , Elma Kahramani

Abstract

In this study, we generalize the well-known formulae of de-Moivre and Euler of hyperbolic numbers to dual-hyperbolic numbers. Furthermore, we investigate the roots and powers of a dual-hyperbolic number by using these formulae. Consequently, we give some examples to illustrate the main results in this paper.

Keywords

Dual number Hyperbolic number

References

  • [1] J. Cockle On a new imaginary in algebra, London-Dublin-Edinburgh Philosophical Magazine 3(34) (1849), 37-47.
  • [2] I. M. Yaglom, A simple non-Euclidean geometry and its physical basis, Springer-Verlag New York, 1979.
  • [3] S. Yüce, Z. Ercan, On properties of the dual quaternions, European Journal of Pure and Applied Mathematics 4(2) (2011), 142-146.
  • [4] G. Sobczyk The hyperbolic number plane, The College Math. J., 26(4) (1995), 268-280.
  • [5] F. Catoni, R. Cannata, V. Catoni, P. Zampetti, Hyperbolic trigonometry in two-dimensional space-time geometry, Nuovo Cimento della Societa Italiana di Fisica B 118 (2003), 475-491.
  • [6] S. Yüce, N. Kuruo˜glu , One-parameter plane hyperbolic motions, Adv. Appl. Clifford Alg. 18(2) (2018), 279-285.
  • [7] M. Akar, S. Yüce, S. Sahin, On the Dual Hyperbolic Numbers and the Complex Hyperbolic Numbers, Journal of Computer Science Computational Mathematics, 8(1) (2018), 279-285.
  • [8] S. Ersoy, M. Akyiğit, One-parameter homothetic motion in the hyperbolic plane and Euler-Savary formula, Adv. Appl. Clifford Alg. 21(2) (2011), 297-317.
  • [9] D. P. Mandic, V. S. L. Goh, Hyperbolic valued nonlinear adaptive filters: noncircularity, widely linear and neural models, John Wiley-Sons., 2009.
  • [10] G. Helzer, Special relativity with acceleration, Amer. Math. Monthy 107(3) (2000), 219-237.
  • [11] W. K. Clifford, Preliminary sketch of bi-quaternions, Proc. London Math. Soc. 4 (1873), 381-395.
  • [12] E. Study, Geometrie der dynamen, Leipzig, Germany, 1903.
  • [13] E. Cho, De-Moivreâ˘AZ´s formula for quaternions, Appl. Math. Lett. 11(6) (1998), 33-35.
  • [14] H. Kabadayı, Y. Yaylı, De-Moivre’s formula for dual quaternions, Kuwait J. Sci. Technol. 38(1) (2011), 15-23.
  • [15] I. A. Kösal, A note on hyperbolic quaternions, Universal Journal Of Mathematics and Applications 1(3) (2018), 155-159.
  • [16] V. Majernik, Multicomponent number systems, Acta Physics Polonica A 3(90) (1996), 491-498.
  • [17] F. Messelmi, Dual-hyperbolic numbers and their holomorphic functions, (2015), https://hal.archives-ouvertes.fr/hal-01114178.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehmet Ali Güngör 0000-0003-1863-3183

Elma Kahramani 0000-0002-4017-0931

Publication Date December 30, 2019
Acceptance Date December 6, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Güngör, M. A., & Kahramani, E. (2019). De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers. Conference Proceedings of Science and Technology, 2(3), 180-184.
AMA Güngör MA, Kahramani E. De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers. Conference Proceedings of Science and Technology. December 2019;2(3):180-184.
Chicago Güngör, Mehmet Ali, and Elma Kahramani. “De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers”. Conference Proceedings of Science and Technology 2, no. 3 (December 2019): 180-84.
EndNote Güngör MA, Kahramani E (December 1, 2019) De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers. Conference Proceedings of Science and Technology 2 3 180–184.
IEEE M. A. Güngör and E. Kahramani, “De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers”, Conference Proceedings of Science and Technology, vol. 2, no. 3, pp. 180–184, 2019.
ISNAD Güngör, Mehmet Ali - Kahramani, Elma. “De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers”. Conference Proceedings of Science and Technology 2/3 (December 2019), 180-184.
JAMA Güngör MA, Kahramani E. De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers. Conference Proceedings of Science and Technology. 2019;2:180–184.
MLA Güngör, Mehmet Ali and Elma Kahramani. “De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers”. Conference Proceedings of Science and Technology, vol. 2, no. 3, 2019, pp. 180-4.
Vancouver Güngör MA, Kahramani E. De-Moivre and Euler Formulae for Dual-Hyperbolic Numbers. Conference Proceedings of Science and Technology. 2019;2(3):180-4.
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