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Yıl 2020, Cilt: 3 Sayı: 3, 130 - 142, 29.09.2020

Fügen Torunbalcı Aydın

https://doi.org/10.33434/cams.680381

Öz

Kaynakça

  • [1] W. R. Hamilton, Elements of Quaternions, Longmans, Green and Co., London, (1866).
  • [2] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions. American Math. Monthly. 70(3)(1963), 289-291.
  • [3] M. R. Iyer, A note on Fibonacci quaternions. Fibonacci Quart., 7(3) (1969), 225-229.
  • [4] M. R. Iyer, Some results on Fibonacci quaternions, Fibonacci Quart.. 7 (1969), 201-210.
  • [5] E. Verner, Jr. Hoggatt, Fibonacci and Lucas Numbers, The Fibonacci Association, (1969).
  • [6] M. N. Swamy, On generalized Fibonacci quaternions, Fibonacci Quart., 11(5) (1973), 547-550.
  • [7] A. L. Iakin, Generalized Quaternions of higher order, Fibonacci Quart., 15(4) (1977), 343-346.
  • [8] A. L. Iakin, Generalized Quaternions with quaternion components, Fibonacci Quart., 15 (1977), 350-352.
  • [9] C. J. Harman, Complex Fibonacci numbers, Fibonacci Quart., 19(1) (1981), 82-86.
  • [10] A. F. Horadam, Quaternion recurrence relations, Ulam Quarterly. 2(2) (1993), 23-33.
  • [11] A. F. Horadam, A generalized Fibonacci sequence, Amer. Math. Month., 68(5) (1961), 455-459.
  • [12] L. Kula, Y. Yaylı, Split Quaternions and rotations in semi-Euclidean space, J. Korean Math. Soc. 44(6) (2007), 1313-1327.
  • [13] E. Ata, Y. Yaylı, Dual quaternions and dual projective spaces, Chaos Solitons Fractals, 40(3) (2009), 1255-1263.
  • [14] S. Halıcı, On Fibonacci quaternions, Adv. Appl. Clifford Algebr., 22(2) (2012), 321-327.
  • [15] S. Halıcı, On Complex Fibonacci Quaternions, Adv. Appl. Clifford Algebr., 23 (2013), 105-112.
  • [16] M. Akyigit, H. H. Kosal and M. Tosun, Split Fibonacci quaternions, Adv. Appl. Clifford Algebr., 23(3) (2013), 535-545.
  • [17] K. S. Nurkan, and A. I. Guven, Dual Fibonacci quaternions, Adv. Appl. Clifford Algebr., (2014) doi: 10.1007/s00006-014- 0488-7
  • [18] V. Majernik, Quaternion formulation of the Galilean space-time transformation, Acta Phy. Slovaca., 56(1) (2006), 9-14.
  • [19] V. Majernik, Galilean transformation expressed by the dual four-component numbers, Acta Phy. Polonica A., 87(6) (1995), 919-923.
  • [20] Z. Ercan, S. Yuce, On properties of the dual quaternions, Eur. J. Pure Appl. Math., 4(2) (2011), 142-146.
  • [21] B. Artmann, The concept of Number: From Quaternions to Modals and topological Fields, Ellis Horwood, Chicherster, (1988).
  • [22] S. Yuce, F. Torunbalcı Aydın, A new aspect of dual Fibonacci quaternions, Adv. Appl. Clifford Algebr., 26(2) (2016), 873-884.
  • [23] N. J. A. Sloane, A Handbook of Integer Sequences, New York, Press, (1973).
  • [24] A. F. Horadam, Jacobsthal and Pell Curves, Fibonacci Quart., 26 (1988), 79-83.
  • [25] A. F. Horadam, Jacobsthal Representation Numbers, Fibonacci Quart., 34 (1996), 40-54.
  • [26] A. F. Horadam, Jacobsthal representation polynomials, Fibonacci Quart., 35 (1997), 137-148.
  • [27] F. Koken, D. Bozkurt, On the Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sci., 3 (13), 605-614 (2008)
  • [28] F. Koken, D. Bozkurt, On the Jacobsthal-Lucas numbers by matrix methods, Int. J. Contemp. Math. Sci., 3(13) (2008), 1629-1633.
  • [29] A. Das¸demir, On the Jacobsthal numbers by matrix method, SDU J. Sci., 71 (2012), 69-76.
  • [30] G. B. Djordjevid, Generalized Jacobsthal polynomials, Fibonacci Quart., 38 (2009), 239-243.
  • [31] Z. Cerin, Sums of squares and products of Jacobsthal numbers, J. Integer Seq., 10 (2007), Article 07.2.5,.
  • [32] Z. Cerin, Formulae for sums of Jacobsthal-Lucas numbers, Int. Math. Forum., 2(40) (2007), 1969-1984.
  • [33] A. Szynal-Liana, I. Włoch, A note on Jacobsthal quaternions, Adv. Appl. Clifford Algebr., 26(1) (2016), 441-447.
  • [34] F. Torunbalcı Aydın, S. Yuce, A new approach to Jacobsthal quaternions, Filomat, 31(18) (2017), 5567-5579.
  • [35] D. Tascı, On k-Jacobsthal and k-Jacobsthal-Lucas quaternions, J. Sci. Arts, 3 (2017), 469-476.
  • [36] G. Cerda-Morales, Identities for third order Jacobsthal quaternions, Adv. Appl. Clifford Algebr., 27(2) (2017), 1043–1053.
  • [37] G. Cerda-Morales, On k-Jacobsthal and k-Jacobsthal-Lucas quaternions, J. Math. Sci. Model., 1(2) (2018), 73-79.

Dual Jacobsthal Quaternions

Yıl 2020, Cilt: 3 Sayı: 3, 130 - 142, 29.09.2020

Fügen Torunbalcı Aydın

https://doi.org/10.33434/cams.680381

Öz

In this paper, dual Jacobsthal quaternions were defined. Also, the relations between dual Jacobsthal quaternions which connected with Jacobsthal and Jacobsthal-Lucas numbers were investigated. Furthermore, Binet's formula, Honsberger identity, D'ocagne's identity, Cassini's identity and Catalan's identity for these quaternions were given.                                                                                                                                                                                                                                                                                               

Anahtar Kelimeler

Jacobsthal number Jacobsthal-Lucas number Jacobsthal quaternion dual jacobsthal quaternion

Kaynakça

  • [1] W. R. Hamilton, Elements of Quaternions, Longmans, Green and Co., London, (1866).
  • [2] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions. American Math. Monthly. 70(3)(1963), 289-291.
  • [3] M. R. Iyer, A note on Fibonacci quaternions. Fibonacci Quart., 7(3) (1969), 225-229.
  • [4] M. R. Iyer, Some results on Fibonacci quaternions, Fibonacci Quart.. 7 (1969), 201-210.
  • [5] E. Verner, Jr. Hoggatt, Fibonacci and Lucas Numbers, The Fibonacci Association, (1969).
  • [6] M. N. Swamy, On generalized Fibonacci quaternions, Fibonacci Quart., 11(5) (1973), 547-550.
  • [7] A. L. Iakin, Generalized Quaternions of higher order, Fibonacci Quart., 15(4) (1977), 343-346.
  • [8] A. L. Iakin, Generalized Quaternions with quaternion components, Fibonacci Quart., 15 (1977), 350-352.
  • [9] C. J. Harman, Complex Fibonacci numbers, Fibonacci Quart., 19(1) (1981), 82-86.
  • [10] A. F. Horadam, Quaternion recurrence relations, Ulam Quarterly. 2(2) (1993), 23-33.
  • [11] A. F. Horadam, A generalized Fibonacci sequence, Amer. Math. Month., 68(5) (1961), 455-459.
  • [12] L. Kula, Y. Yaylı, Split Quaternions and rotations in semi-Euclidean space, J. Korean Math. Soc. 44(6) (2007), 1313-1327.
  • [13] E. Ata, Y. Yaylı, Dual quaternions and dual projective spaces, Chaos Solitons Fractals, 40(3) (2009), 1255-1263.
  • [14] S. Halıcı, On Fibonacci quaternions, Adv. Appl. Clifford Algebr., 22(2) (2012), 321-327.
  • [15] S. Halıcı, On Complex Fibonacci Quaternions, Adv. Appl. Clifford Algebr., 23 (2013), 105-112.
  • [16] M. Akyigit, H. H. Kosal and M. Tosun, Split Fibonacci quaternions, Adv. Appl. Clifford Algebr., 23(3) (2013), 535-545.
  • [17] K. S. Nurkan, and A. I. Guven, Dual Fibonacci quaternions, Adv. Appl. Clifford Algebr., (2014) doi: 10.1007/s00006-014- 0488-7
  • [18] V. Majernik, Quaternion formulation of the Galilean space-time transformation, Acta Phy. Slovaca., 56(1) (2006), 9-14.
  • [19] V. Majernik, Galilean transformation expressed by the dual four-component numbers, Acta Phy. Polonica A., 87(6) (1995), 919-923.
  • [20] Z. Ercan, S. Yuce, On properties of the dual quaternions, Eur. J. Pure Appl. Math., 4(2) (2011), 142-146.
  • [21] B. Artmann, The concept of Number: From Quaternions to Modals and topological Fields, Ellis Horwood, Chicherster, (1988).
  • [22] S. Yuce, F. Torunbalcı Aydın, A new aspect of dual Fibonacci quaternions, Adv. Appl. Clifford Algebr., 26(2) (2016), 873-884.
  • [23] N. J. A. Sloane, A Handbook of Integer Sequences, New York, Press, (1973).
  • [24] A. F. Horadam, Jacobsthal and Pell Curves, Fibonacci Quart., 26 (1988), 79-83.
  • [25] A. F. Horadam, Jacobsthal Representation Numbers, Fibonacci Quart., 34 (1996), 40-54.
  • [26] A. F. Horadam, Jacobsthal representation polynomials, Fibonacci Quart., 35 (1997), 137-148.
  • [27] F. Koken, D. Bozkurt, On the Jacobsthal numbers by matrix methods, Int. J. Contemp. Math. Sci., 3 (13), 605-614 (2008)
  • [28] F. Koken, D. Bozkurt, On the Jacobsthal-Lucas numbers by matrix methods, Int. J. Contemp. Math. Sci., 3(13) (2008), 1629-1633.
  • [29] A. Das¸demir, On the Jacobsthal numbers by matrix method, SDU J. Sci., 71 (2012), 69-76.
  • [30] G. B. Djordjevid, Generalized Jacobsthal polynomials, Fibonacci Quart., 38 (2009), 239-243.
  • [31] Z. Cerin, Sums of squares and products of Jacobsthal numbers, J. Integer Seq., 10 (2007), Article 07.2.5,.
  • [32] Z. Cerin, Formulae for sums of Jacobsthal-Lucas numbers, Int. Math. Forum., 2(40) (2007), 1969-1984.
  • [33] A. Szynal-Liana, I. Włoch, A note on Jacobsthal quaternions, Adv. Appl. Clifford Algebr., 26(1) (2016), 441-447.
  • [34] F. Torunbalcı Aydın, S. Yuce, A new approach to Jacobsthal quaternions, Filomat, 31(18) (2017), 5567-5579.
  • [35] D. Tascı, On k-Jacobsthal and k-Jacobsthal-Lucas quaternions, J. Sci. Arts, 3 (2017), 469-476.
  • [36] G. Cerda-Morales, Identities for third order Jacobsthal quaternions, Adv. Appl. Clifford Algebr., 27(2) (2017), 1043–1053.
  • [37] G. Cerda-Morales, On k-Jacobsthal and k-Jacobsthal-Lucas quaternions, J. Math. Sci. Model., 1(2) (2018), 73-79.
Toplam 37 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Fügen Torunbalcı Aydın 0000-0002-4953-1078

Yayımlanma Tarihi 29 Eylül 2020
Gönderilme Tarihi 27 Ocak 2020
Kabul Tarihi 22 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 3

Kaynak Göster

APA Torunbalcı Aydın, F. (2020). Dual Jacobsthal Quaternions. Communications in Advanced Mathematical Sciences, 3(3), 130-142. https://doi.org/10.33434/cams.680381
AMA Torunbalcı Aydın F. Dual Jacobsthal Quaternions. Communications in Advanced Mathematical Sciences. Eylül 2020;3(3):130-142. doi:10.33434/cams.680381
Chicago Torunbalcı Aydın, Fügen. “Dual Jacobsthal Quaternions”. Communications in Advanced Mathematical Sciences 3, sy. 3 (Eylül 2020): 130-42. https://doi.org/10.33434/cams.680381.
EndNote Torunbalcı Aydın F (01 Eylül 2020) Dual Jacobsthal Quaternions. Communications in Advanced Mathematical Sciences 3 3 130–142.
IEEE F. Torunbalcı Aydın, “Dual Jacobsthal Quaternions”, Communications in Advanced Mathematical Sciences, c. 3, sy. 3, ss. 130–142, 2020, doi: 10.33434/cams.680381.
ISNAD Torunbalcı Aydın, Fügen. “Dual Jacobsthal Quaternions”. Communications in Advanced Mathematical Sciences 3/3 (Eylül 2020), 130-142. https://doi.org/10.33434/cams.680381.
JAMA Torunbalcı Aydın F. Dual Jacobsthal Quaternions. Communications in Advanced Mathematical Sciences. 2020;3:130–142.
MLA Torunbalcı Aydın, Fügen. “Dual Jacobsthal Quaternions”. Communications in Advanced Mathematical Sciences, c. 3, sy. 3, 2020, ss. 130-42, doi:10.33434/cams.680381.
Vancouver Torunbalcı Aydın F. Dual Jacobsthal Quaternions. Communications in Advanced Mathematical Sciences. 2020;3(3):130-42.
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