Araştırma Makalesi
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Yıl 2020, , 130 - 142, 29.09.2020

Fügen Torunbalcı Aydın

https://doi.org/10.33434/cams.680381
Cited By: 1

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, , 130 - 142, 29.09.2020

Fügen Torunbalcı Aydın

https://doi.org/10.33434/cams.680381
Cited By: 1

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 Makaleler
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

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.

Cited By

On the dual quaternion geometry of screw motions
Analele Universitatii "Ovidius" Constanta - Seria Matematica
https://doi.org/10.2478/auom-2023-0035

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