• 대한수학회보
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• 제42권3호
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• pp.639-652
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• 2005

We find the class number of orders in a quaternion algebra over a dyadic local field.

• East Asian mathematical journal
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• 제29권3호
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• pp.293-302
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• 2013

We research properties of ternary numbers and hyperholomorphic functions with values in $\mathbb{C}$(2). We represent reduced quaternion numbers and obtain some propertries in dual reduced quaternion systems in view of Clifford analysis. Moreover, we obtain Cauchy theorems with respect to dual reduced quaternions.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.81-96
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• 2004

The level-m scaled circulant factor matrix over the complex number field is introduced. Its diagonalization and spectral decomposition and representation are discussed. An explicit formula for the entries of the inverse of a level-m scaled circulant factor matrix is presented. Finally, an algorithm for finding the inverse of such matrices over the quaternion division algebra is given.

• 한국항공우주학회지
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• 제35권7호
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• pp.627-632
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• 2007

근래에 들어 관성항법 알고리즘의 성능 향상에 이체 쿼터니언(dual quaternion)이 새로이 적용되기 시작하였다. 이체 쿼터니언은 선형 미분방정식으로 계산하는 쿼터니언을 회전운동과 병진운동을 동시에 취급하는 이체수(dual number) 체계로 확장한 형태이다. 본 논문에서는 기존의 관성항법 알고리즘과 근래에 소개된 이체 쿼터니언 알고리즘을 분석하여 두 알고리즘의 장점을 결합한 새로운 형태의 정밀 이체 쿼터니언 알고리즘을 제안하였다. 제안된 혼합 알고리즘은 기존 알고리즘과 유사한 수치적 연산량으로 이체 쿼터니언의 알고리즘과 유사한 정확도 향상을 얻을 수 있다. 시뮬레이션을 통하여 제안된 혼합 알고리즘의 연산량 및 정확도를 평가하였다.

• Nonlinear Functional Analysis and Applications
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• 제29권3호
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• pp.913-927
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• 2024

In this paper, we represent regular functions on ternary theory in the view of quaternion. By expressing quaternions using ternary number theory, a new form of regular function, called E-regular, is defined. From the defined regular function, we investigate the properties of the appropriate hyper-conjugate harmonic functions and corresponding Cauchy-Riemann equations by pseudo-complex forms.

• 호남수학학술지
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• 제37권4호
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• pp.559-567
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• 2015

This paper gives the expression of dual quaternions and provides differential operators in dual quaternions. The paper also represents the derivative of dual quaternion-valued functions by using a corresponding Cauchy-Riemann system in dual quaternions.

• 대한수학회논문집
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• 제10권3호
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• pp.583-602
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• 1995

With the theory of a certain type of orders in a Quaternion algebra, we construct Brandt matrices and theta series. As a application, we calculate the class number of a certain type of orders in a Quanternion algebra with the trace formular of Brandt matrices.

• 호남수학학술지
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• 제35권4호
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• pp.809-817
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• 2013

We research properties of a corresponding Cauchy theorem of hyperholomorphic functions in an open set of product complex spaces, in the sense of complex Clifford analysis.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권1호
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• pp.97-104
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• 2016

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.

• 호남수학학술지
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• 제38권4호
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• pp.675-683
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• 2016

We give the representation of Fibonacci quaternions for convenient calculus. We research the corresponding properties of Fibonacci quaternions and some examples of a function with values in modified Fibonacci quaternions.