Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A POLAR REPRESENTATION OF A REGULARITY OF A DUAL QUATERNIONIC FUNCTION IN CLIFFORD ANALYSIS

  • Kim, Ji Eun (Department of Mathematics Dongguk University) ;
  • Shon, Kwang Ho (Department of Mathematics Pusan National University)
  • Received : 2016.03.08
  • Published : 2017.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

The paper gives the regularity of dual quaternionic functions and the dual Cauchy-Riemann system in dual quaternions. Also, the paper researches the polar representation and properties of a dual quaternionic function and their regular quaternionic functions.

Keywords

References

  1. W. K. Clifford, Preliminary sketch of bi-quaternions, Proc. London Math. Soc. 4 (1873), 381-395.
  2. K. Daniilidis, Hand-eye calibration using dual quaternions, Int. J. Rob. Res. 18 (1999), no. 3, 286-298. https://doi.org/10.1177/02783649922066213
  3. Z. Ercan and S. Yuce, On Properties of the Dual Quaternions, Eur. J. Pure Appl. Math. 4 (2011), no. 2, 142-146.
  4. G. Helzer, Special Relativity with acceleration, Amer. Math. Monthy 107 (2000), no. 3, 215-237.
  5. J. Kajiwara, X. D. Li, and K. H. Shon, Regeneration in complex, quaternion and Clifford analysis, In Finite or Infinite Dimensional Complex Analysis and Applications, pp. 287-298, Springer US, New York, USA, 2004.
  6. J. Kajiwara, X. D. Li, and K. H. Shon, Function spaces in complex and Clifford analysis, In Finite or Infinite Dimensional Complex Analysis and Applications, pp. 127-155, Springer US, New York, USA, 2006.
  7. B. Kenwright, A beginners guide to dual-quaternions: what they are, how they work, and how to use them for 3D character hierarchies, wscg.zcu.cz/wscg2012/short/a29-full.pdf.
  8. B. Kenwright, Inverse kinematics with dual-quaternions, exponential-maps, and joint limits, Int. J. Adv. Sys. 6 (2013), no. 1-2.
  9. J. E. Kim, S. J. Lim, and K. H. Shon, Regular functions with values in ternary number system on the complex Clifford analysis, Abstr. Appl. Anal. 2013 (2013), Artical ID 136120, 7 pages.
  10. J. E. Kim, S. J. Lim, and K. H. Shon, Regularity of functions on the reduced quaternion field in Clifford analysis, Abstr. Appl. Anal. 2014 (2014), Artical ID 654798, 8 pages.
  11. J. E. Kim and K. H. Shon, The Regularity of functions on Dual split quaternions in Clifford analysis, Abstr. Appl. Anal. 2014 (2014), Artical ID 369430, 8 pages.
  12. J. E. Kim and K. H. Shon, Polar Coordinate Expression of Hyperholomorphic Functions on Split Quater-nions in Clifford Analysis, Adv. Appl. Clifford Algebr. 25 (2015), no. 4, 915-924. https://doi.org/10.1007/s00006-015-0541-1
  13. J. E. Kim and K. H. Shon, Coset of a hypercomplex numbers in Clifford analysis, Bull. Korean Math. Soc. 52 (2015), no. 5, 1721-1728. https://doi.org/10.4134/BKMS.2015.52.5.1721
  14. J. E. Kim and K. H. Shon, Properties of regular functions with values in bicomplex numbers, Bull. Korean Math. Soc. 53 (2016), no. 2, 507-518. https://doi.org/10.4134/BKMS.2016.53.2.507
  15. J. E. Kim and K. H. Shon, Inverse Mapping Theory on Split Quaternions in Clifford Analysis, To appear in Filomat.
  16. K. Nono, Hyperholomorphic functions of a quaternion variable, Bull. Fukuoka Univ. Ed. 32 (1983), 21-37.
  17. E. Pennestri and R. Stefanelli, Linear algebra and numerical algorithms using dual numbers, Multibody Syst. Dyn. 18 (2007), no. 3, 323-344. https://doi.org/10.1007/s11044-007-9088-9
  18. J. Plucker, On a new geometry of space, Phil. Trans. Roy. Soc. Lond. 155 (1865), 725-791. https://doi.org/10.1098/rstl.1865.0017
  19. R. M. Porter, Quaternionic linear and quadratic equations, J. Nat. Geom. 11 (1997), no. 2, 101-106.
  20. E. Study, Geometrie der Dynamen, Leipzig, Germany, 1903.