바로가기메뉴

본문 바로가기 주메뉴 바로가기

ACOMS+ 및 학술지 리포지터리 설명회

  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
  • 2024년 07월 03일(수) 13:30
 

logo

DUAL QUATERNIONIC REGULAR FUNCTION OF DUAL QUATERNION VARIABLES

DUAL QUATERNIONIC REGULAR FUNCTION OF DUAL QUATERNION VARIABLES

한국수학교육학회지시리즈B:순수및응용수학 / 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 (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)
SHON, KWANG HO (DEPARTMENT OF MATHEMATICS, PUSAN NATIONAL UNIVERSITY)

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.

참고문헌

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.

한국수학교육학회지시리즈B:순수및응용수학