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Year 2020, Volume: 8 Issue: 2, 145 - 156, 15.10.2020

Fügen Torunbalcı Aydın

https://doi.org/10.36753/mathenot.621169

Abstract

References

  • [1] William Rowan Hamilton. Elements of Quaternions. Longmans, Green & Company,London, 1866.
  • [2] NJA Sloane. A handbook of integer sequences. 1973.
  • [3] A. F. Horadam. Jacobsthal representation numbers. Fibonacci Quarterly, 34:40–54, 1996.
  • [4] A. F. Horadam. Jacobsthal representation polynomials. Fibonacci Quarterly, 35:137– 148, 1997.
  • [5] F. Koken and D. Bozkurt. On the jacobsthal numbers by matrix methods. Int. J. Contemp. Math. Sciences, 3(13):605–614, 2008.
  • [6] F. Koken and D. Bozkurt. On the jacobsthal-lucas numbers by matrix methods. Int. J. Contemp. Math. Sciences, 3(13):1629–1633, 2008.
  • [7] A. Dasdemir. A study on the jacobsthal and jacobsthal-lucas numbers by matrix method. DUFED Journal of Sciences, 3(1):13–18, 2014.
  • [8] A. Dasdemir. On the jacobsthal numbers by matrix method. Fen Derg, 7(1):69–76, 2012.
  • [9] G. B. Djordjevic. Derivative sequences of generalized jacobsthal and jacobsthal-lucaspolynomials. Fibonacci Quarterly, 38(4):334–338, 2000.
  • [10] G. B. Djordjevic. Generalized jacobsthal polynomials. Fibonacci Quarterly, 38(3):239– 243, 2009.
  • [11] Z. Cerin. Sums of squares and products of jacobsthal numbers. Journal of Integer Se- quences, 10(07.2):5, 2007.
  • [12] Z. Cerin. Formulae for sums of jacobsthal lucas numbers. In Int. Math. Forum, volume 2, pages 1969–1984, 2007.
  • [13] Anetta Szynal-Liana and Iwona Wloch. A note on jacobsthal quaternions. Advances in Applied Clifford Algebras, 26(1):441–447, 2016.
  • [14] Fugen Torunbalcı Aydın and Salim Yuce. A new approach to jacobsthal quaternions.Filomat, 31(18):5567–5579, 2017.
  • [15] Dursun Tasci. On k-jacobsthal and k-jacobsthal-lucas quaternions. JOURNAL OF SCI- ENCE AND ARTS, (3):469–476, 2017.
  • [16] Fugen Torunbalcı Aydın. Dual jacobsthal quaternions. submitted, 2018.
  • [17] William Kingdon Clifford. A preliminary sketch of biquaternions. 1873.
  • [18] AP Kotelnikov. Screw calculus and some of its applications to geometry and mechanics.Annals of Imperial University of Kazan, 1895.
  • [19] E. Study. Geometrie der dynamen. Leipzig, 1903.
  • [20] V. Majernik. Multicomponent number systems. Acta Pyhsica Polonica A, 90(3):491– 498, 1996.
  • [21] Farid Messelmi. DUAL-COMPLEX NUMBERS AND THEIR HOLOMORPHICFUNCTIONS. working paper or preprint, January 2015.
  • [22] Mehmet Ali Gungor and Ayse Zeynep Azak. Investigation of dual-complex fibonacci, dual-complex lucas numbers and their properties. Advances in Applied Clifford Algebras,27(4):3083–3096, 2017.

Dual-complex Jacobsthal Quaternions

Year 2020, Volume: 8 Issue: 2, 145 - 156, 15.10.2020

Fügen Torunbalcı Aydın

https://doi.org/10.36753/mathenot.621169

Abstract

In this paper, dual-complex Jacobsthal quaternions are defined. Also, some algebraic properties of dual-complex Jacobsthal quaternions
which are connected with dual-complex numbers and Lucas numbers are investigated. Furthermore, the Honsberger identity, the d'Ocagne's
identity, Binet's formula, Cassini's identity, Catalan's identity for these quaternions and their real representations are given.
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Keywords

Dual number dual-complex number Jacobsthal number dual-complex Jacobsthal number Jacobsthal quaternion

References

  • [1] William Rowan Hamilton. Elements of Quaternions. Longmans, Green & Company,London, 1866.
  • [2] NJA Sloane. A handbook of integer sequences. 1973.
  • [3] A. F. Horadam. Jacobsthal representation numbers. Fibonacci Quarterly, 34:40–54, 1996.
  • [4] A. F. Horadam. Jacobsthal representation polynomials. Fibonacci Quarterly, 35:137– 148, 1997.
  • [5] F. Koken and D. Bozkurt. On the jacobsthal numbers by matrix methods. Int. J. Contemp. Math. Sciences, 3(13):605–614, 2008.
  • [6] F. Koken and D. Bozkurt. On the jacobsthal-lucas numbers by matrix methods. Int. J. Contemp. Math. Sciences, 3(13):1629–1633, 2008.
  • [7] A. Dasdemir. A study on the jacobsthal and jacobsthal-lucas numbers by matrix method. DUFED Journal of Sciences, 3(1):13–18, 2014.
  • [8] A. Dasdemir. On the jacobsthal numbers by matrix method. Fen Derg, 7(1):69–76, 2012.
  • [9] G. B. Djordjevic. Derivative sequences of generalized jacobsthal and jacobsthal-lucaspolynomials. Fibonacci Quarterly, 38(4):334–338, 2000.
  • [10] G. B. Djordjevic. Generalized jacobsthal polynomials. Fibonacci Quarterly, 38(3):239– 243, 2009.
  • [11] Z. Cerin. Sums of squares and products of jacobsthal numbers. Journal of Integer Se- quences, 10(07.2):5, 2007.
  • [12] Z. Cerin. Formulae for sums of jacobsthal lucas numbers. In Int. Math. Forum, volume 2, pages 1969–1984, 2007.
  • [13] Anetta Szynal-Liana and Iwona Wloch. A note on jacobsthal quaternions. Advances in Applied Clifford Algebras, 26(1):441–447, 2016.
  • [14] Fugen Torunbalcı Aydın and Salim Yuce. A new approach to jacobsthal quaternions.Filomat, 31(18):5567–5579, 2017.
  • [15] Dursun Tasci. On k-jacobsthal and k-jacobsthal-lucas quaternions. JOURNAL OF SCI- ENCE AND ARTS, (3):469–476, 2017.
  • [16] Fugen Torunbalcı Aydın. Dual jacobsthal quaternions. submitted, 2018.
  • [17] William Kingdon Clifford. A preliminary sketch of biquaternions. 1873.
  • [18] AP Kotelnikov. Screw calculus and some of its applications to geometry and mechanics.Annals of Imperial University of Kazan, 1895.
  • [19] E. Study. Geometrie der dynamen. Leipzig, 1903.
  • [20] V. Majernik. Multicomponent number systems. Acta Pyhsica Polonica A, 90(3):491– 498, 1996.
  • [21] Farid Messelmi. DUAL-COMPLEX NUMBERS AND THEIR HOLOMORPHICFUNCTIONS. working paper or preprint, January 2015.
  • [22] Mehmet Ali Gungor and Ayse Zeynep Azak. Investigation of dual-complex fibonacci, dual-complex lucas numbers and their properties. Advances in Applied Clifford Algebras,27(4):3083–3096, 2017.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Fügen Torunbalcı Aydın 0000-0002-4953-1078

Publication Date October 15, 2020
Submission Date September 17, 2019
Acceptance Date October 8, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Torunbalcı Aydın, F. (2020). Dual-complex Jacobsthal Quaternions. Mathematical Sciences and Applications E-Notes, 8(2), 145-156. https://doi.org/10.36753/mathenot.621169
AMA Torunbalcı Aydın F. Dual-complex Jacobsthal Quaternions. Math. Sci. Appl. E-Notes. October 2020;8(2):145-156. doi:10.36753/mathenot.621169
Chicago Torunbalcı Aydın, Fügen. “Dual-Complex Jacobsthal Quaternions”. Mathematical Sciences and Applications E-Notes 8, no. 2 (October 2020): 145-56. https://doi.org/10.36753/mathenot.621169.
EndNote Torunbalcı Aydın F (October 1, 2020) Dual-complex Jacobsthal Quaternions. Mathematical Sciences and Applications E-Notes 8 2 145–156.
IEEE F. Torunbalcı Aydın, “Dual-complex Jacobsthal Quaternions”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 145–156, 2020, doi: 10.36753/mathenot.621169.
ISNAD Torunbalcı Aydın, Fügen. “Dual-Complex Jacobsthal Quaternions”. Mathematical Sciences and Applications E-Notes 8/2 (October 2020), 145-156. https://doi.org/10.36753/mathenot.621169.
JAMA Torunbalcı Aydın F. Dual-complex Jacobsthal Quaternions. Math. Sci. Appl. E-Notes. 2020;8:145–156.
MLA Torunbalcı Aydın, Fügen. “Dual-Complex Jacobsthal Quaternions”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, 2020, pp. 145-56, doi:10.36753/mathenot.621169.
Vancouver Torunbalcı Aydın F. Dual-complex Jacobsthal Quaternions. Math. Sci. Appl. E-Notes. 2020;8(2):145-56.
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