• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.507-518
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• 2016

In this paper, using forms of conjugations, we give some algebraic properties of bicomplex numbers. We research differential operators, elementary functions and the analogous Cauchy-Riemann system in bicomplex number systems. Also, we investigate the definition and properties of regular functions with values in bicomplex settings in Clifford analysis.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.307-315
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• 2017

In this paper, we aim to compare the differentials with the regularity of the hypercomplex valued functions in Clifford analysis. For three kinds of conjugation of the bicomplex numbers, we define the differentials of the bicomplex number functions by the naive approach. And we investigate some relations of the corresponding Cauchy-Riemann system and the conditions of the differentiable functions in the bicomplex number system.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.101-113
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• 2024

In this paper, we define the generalized tricomplex numbers and give some algebraic properties of them. By using the matrix representation of generalized tricomplex numbers, we determine a motion on the hypersurface M in eight dimensional generalized linear space ℝ⁸_αβγ and show that this is a homothetic motion. Also, for some special cases of the real numbers α, β and γ, we give some examples of homothetic motions in ℝ⁸ and ℝ⁸₄ and obtain some rotational matrices in these spaces, too.