The corresponding inverse of functions of multidual complex variables in Clifford analysis

Kim, Ji Eun

doi:10.22436/jnsa.009.06.90

Cited by 6 publications

(4 citation statements)

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“…Lai and Crassidis [10,11] further examined the approach of Martins et al [1,2], and based on the results of studying the derivation of the step derivative along the complex direction for a real function using the Taylor series expansion, a complex step differential approximation and its application to a numerical algorithm were presented (see [12][13][14][15]). Kim et al [16][17][18] investigated the composition and properties of quaternion functions based on the algebraic features of quaternions. They suggested that the definitions of the function limit and the derivative are not uniquely determined by the noncommutativity of the product, which is a typical characteristic of the quaternary function basis.…”

Section: Introductionmentioning

confidence: 99%

Calculation of Two Types of Quaternion Step Derivatives of Elementary Functions

Kim

2021

Mathematics

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We aim to get the step derivative of a complex function, as it derives the step derivative in the imaginary direction of a real function. Given that the step derivative of a complex function cannot be derived using i, which is used to derive the step derivative of a real function, we intend to derive the complex function using the base direction of the quaternion. Because many analytical studies on quaternions have been conducted, various examples can be presented using the expression of the elementary function of a quaternion. In a previous study, the base direction of the quaternion was regarded as the base separate from the basis of the complex number. However, considering the properties of the quaternion, we propose two types of step derivatives in this study. The step derivative is first defined in the j direction, which includes a quaternion. Furthermore, the step derivative in the j+k2 direction is determined using the rule between bases i, j, and k defined in the quaternion. We present examples in which the definition of the j-step derivative and (j,k)-step derivative are applied to elementary functions ez, sinz, and cosz.

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Section: Introductionmentioning

confidence: 99%

Calculation of Two Types of Quaternion Step Derivatives of Elementary Functions

Kim

2021

Mathematics

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“…However, PDQs preserve the noncommutative rule of the product and can express the projection of an arbitrary PDQ onto a plane due to the property of the product for PDQs. We have investigated the properties of the unit of dual numbers (see [8]) and we deal with quaternions by means of the unit of dual numbers. This paper introduces PDQs and some of their basic properties.…”

Section: Introductionmentioning

confidence: 99%

Differentiability of pseudo-dual-quaternionic functions with a differential operator

Kim¹

2018

J. Nonlinear Sci. Appl.

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“…In addition, Kim and Shon [5,6] researched corresponding Cauchy-Riemann systems and the properties of functions with values in special quaternions (such as reduced or split-quaternions) by using a regular function with values in dual split-quaternions and gave properties and calculations of functions of bicomplex variables with the commutative multiplication rule [8]. Kim [3] studied the corresponding inverse of functions of multidual complex variables in Clifford analysis. Now, we give the two different analogous ways of defining a holomorphic function of a split-biquaternionic variable.…”

Section: Introductionmentioning

confidence: 99%