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Dergiler / Journal of Engineering Technology and Applied Sciences / 2023 / Cilt: 8 Sayı: 3

On Hybrid Curves

Mücahit Akbıyık(BEYKENT UNIVERSITY)0000-0002-0256-1472
Sayfa
119–130
Yayın Tarihi
2023-12-31
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

However, we present the Frenet-Serret frame formulae of a non-lightlike hybrid curve in R^4 and an illustrative example for all theorems of the paper with MATLAB 2016a codes.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we first define the vector product in a special analog Minkowski Geometry (R^3,<>) which is identified with the space of spatial hybrids.
📊
Temel Bulgular & Veri:Next, we derive the Frenet-Serret frame formulae for a three dimensional non-parabolic curve by using the spatial hybrids and the vector product.
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Sonuç & Katkı:However, we present the Frenet-Serret frame formulae of a non-lightlike hybrid curve in R^4 and an illustrative example for all theorems of the paper with MATLAB 2016a codes.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hybrid numbers · Curvatures · Frenet-Serret frame formulae

Abstract

In this paper, we first define the vector product in a special analog Minkowski Geometry (R^3,<>) which is identified with the space of spatial hybrids. Next, we derive the Frenet-Serret frame formulae for a three dimensional non-parabolic curve by using the spatial hybrids and the vector product. However, we present the Frenet-Serret frame formulae of a non-lightlike hybrid curve in R^4 and an illustrative example for all theorems of the paper with MATLAB 2016a codes.

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Bu Makaleye Atıf Yap

Akbıyık, M. (2023). On Hybrid Curves. Journal of Engineering Technology and Applied Sciences, Cilt: 8 Sayı: 3, 119–130. https://doi.org/10.30931/jetas.1338660

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Kaynakça (16)

  1. Bharathi, K., Nagaraj, M., "Quaternion valued function of a real variable Serret–Frenet formulae", Indian J. Pure Appl. Math. 16 (1985): 741–756.
  2. Coken, A.C., Tuna, A., "On the quaternionic inclined curves in the semi-Euclidean space ", Appl. Math. Comput. 155 (2004): 373-389.
  3. Dağdeviren, A., Yüce, S., "Dual quaternions and dual quaternionic curves", Filomat 33(4) (2019): 1037–1046.
  4. Ohashi, M., "G 2-Congruence theorem for curves in purely imaginary octonions and its application", Geom Dedicata 163 (2013): 1–17.
  5. Özdemir, M., "Introduction to Hybrid Numbers", Adv. Appl. Clifford Algebras 28(11) (2018).
  6. Özdemir, M., "Finding Roots of a 2×2 real matrix using De Moivre’s formula", Advances in Applied Clifford Algebras 29(2) (2019).
  7. Öztürk, İ., Özdemir, M., "Similarity of hybrid numbers", Mathematical Methods in Applied Sciences 43(15) (2020): 8867-8881.
  8. Akbıyık, M., S. Yamaç Akbıyık, E. Karaca, F. Yılmaz, "De Moivre’s and Euler Formulas for matrices of hybrid numbers", Axioms 2021, 10, 213.
  9. Szynal-Liana, A., "The Horadam Hybrid Numbers", Discussiones Mathematicae General Algebra and Applications 38 (2018): 91–98.
  10. Kızılateş, C., "A new generalization of Fibonacci hybrid and Lucas hybrid numbers", Chaos, Solitons & Fractals 130 (2020): 109449.
  11. Bharathi, K., Nagaraj, M., "Quaternion valued function of a real variable Serret–Frenet formulae", Indian J. Pure Appl. Math. 16 (1985): 741–756.
  12. Coken, A.C., Tuna, A., "On the quaternionic inclined curves in the semi-Euclidean space ", Appl. Math. Comput. 155 (2004): 373-389.
  13. Dağdeviren, A., Yüce, S., "Dual quaternions and dual quaternionic curves", Filomat 33(4) (2019): 1037–1046.
  14. Ohashi, M., "G 2-Congruence theorem for curves in purely imaginary octonions and its application", Geom Dedicata 163 (2013): 1–17.
  15. Szynal-Liana, A., "The Horadam Hybrid Numbers", Discussiones Mathematicae General Algebra and Applications 38 (2018): 91–98.
  16. Kızılateş, C., "A new generalization of Fibonacci hybrid and Lucas hybrid numbers", Chaos, Solitons & Fractals 130 (2020): 109449.