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ISSN : 1226-0657

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Vol.23 No.1

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DUAL QUATERNIONIC REGULAR FUNCTION OF DUAL QUATERNION VARIABLES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2016, v.23 no.1, pp.97-104
https://doi.org/10.7468/jksmeb.2016.23.1.97
KIM, JI EUN
SHON, KWANG HO
KIM,, J. E. , & SHON,, K. H. (2016). DUAL QUATERNIONIC REGULAR FUNCTION OF DUAL QUATERNION VARIABLES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 23(1), 97-104, https://doi.org/10.7468/jksmeb.2016.23.1.97

Abstract

We give representations of differential operators and rules for addition and multiplication of dual quaternions. Also, we research the notions and properties of a regular function and a corresponding harmonic function with values in dual quaternions of Clifford analysis.

keywords
quaternion, dual number, regular function, differentiable, Clifford analysis.

Reference

1.

Deakin, M.A.B.;. (1966). Functions of a dual or duo variable. Math. Mag., 39(4), 215-219. 10.2307/2688085.

2.

Deavours, C.A.;. (1973). The Quaternion Calculus. Amer. Math. Monthly, 80, 995-1008. 10.2307/2318774.

3.

Ferdinands, T.;Kavlie, L.;. (2009). A Beckman-quarles type theorem for laguerre transforma-tions in the dual plane. RHIT Undergrad. Math. J., 10(1).

4.

Fueter, R.;. (1935). Die Funktionentheorie der Differentialgleichungen Δu = 0 und ΔΔu = 0 mit vier reellen Variablen. Comment. math. Helv., 7, 307-330.

5.

Fueter, R.;. (1936). Über die analytische Darstellung der regulären Funktionen einer Quaternio-nenvariablen. Comment. math. Helv., 8, 371-378.

6.

Hamilton, W.R.;. Elements of Quaternions.

7.

Joly, C.J.;. A Manual of Quaternions.

8.

Kajiwara, J.;Li, X.D.;Shon, K.H.;. (2004). Regeneration in complex, quaternion and Clifford analysis (287-298). Proc. the 9th International Conf. on Finite or Infinite Dimensional Complex Analysis and Applications, Adv. Complex Anal. Appl..

9.

Kajiwara, J.;Li, X.D.;Shon, K.H.;. (2006). Function spaces in complex and Clifford analysis, Inhomogeneous Cauchy Rie-mann system of quaternion and Clifford analysis in ellipsoid (127-155). Proc. the 14th Inter-national Conf. on Finite or Infinite Dimensional Complex Analysis and Applications.

10.

Kim, J.E.;Lim, S.J.;Sho, K.H.;. (0000). Regular functions with values in ternary number system on the complex Clifford analysis. Abstr. Appl. Anal., 2013.

11.

Kim, J.E.;Lim, S.J.;Shon, K.H.;. (0000). Regularity of functions on the reduced quaternion field in Clifford analysis. Abstr. Appl. Anal., 2014.

12.

Kim, J.E.;Shon, K.H.;. (2015). Polar Coordinate Expression of Hyperholomorphic Functions on Split Quaternions in Clifford Analysis. Adv. Appl. Clifford Alg., 25(4), 915-924. 10.1007/s00006-015-0541-1.

13.

Kim, J.E.;Shon, K.H.;. (0000). The Regularity of functions on Dual split quaternions in Clifford analysis. Abstr. Appl. Anal., 2014.

14.

Kim, J.E.;Shon, K.H.;. (2015). Coset of hypercomplex numbers in Clifford analysis. Bull. Korean Math. Soc., 52(5), 1721-1728. 10.4134/BKMS.2015.52.5.1721.

15.

Kim, J.E.;Shon, K.H.;. (2015). Inverse Mapping Theory on Split Quaternions in Clifford Analysis. Filomat, .

16.

Sudbery, A.;. (1979). Quaternionic Analysis. Math. Proc. Cambridge Philos. Soc., 85, 199225.

17.

Tait, P.G.;. An Elementary Treatise on Quaternions.

18.

Yaglom, M.;. Complex numbers in geometry.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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