• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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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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• v.29 no.3
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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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• v.14 no.1_2
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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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.7
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• pp.627-632
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• 2007

Dual quaternion is efficient methodology to express rotation and translation of the vehicle's movements in the unified frame work. Recently, a strapdown inertial navigation algorithm based on dual quaternion was introduced. By comparing and analyzing the classical and dual-quaternion algorithms, this paper proposes a new strapdown inertial navigation algorithm that maintains the accuracy benefit of the dual-quaternion algorithm with considerable computational reduction. Simulation results show the efficiency of the proposed hybrid strapdown navigation algorithm.

• Honam Mathematical Journal
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• v.37 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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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.

• Honam Mathematical Journal
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• v.35 no.4
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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.

• The Pure and Applied Mathematics
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• v.23 no.1
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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.

• Honam Mathematical Journal
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• v.38 no.4
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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.

• Journal of Korea Multimedia Society
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• v.10 no.1
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• pp.36-48
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• 2007

This paper proposed 3D keyframe animation using orientation interpolator. 3D keyframe animation consists of a number of transform nodes that have geometrical node of initial model and several interpolator nodes that represent the object moving. In the proposed algorithm, we randomly selects transform nodes with orientation interpolator node and performs to resample quaternion components for haying uniform key time. And then, watermark bits are embedded into quaternion components with large rotation angles. Experimental results verified that the watermark embedded by the proposed algorithm had good robustness against geometrical attacks and timeline attacks and also PSNR of keyvalue in orientation interpolator node is above 42dB.