• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.389-398
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• 2018

In this paper we obtain the condition for the existence of Ricci solitons in nonflat quaternion space form by using Eisenhart problem. Also it is proved that if (g, V, ${\lambda}$) is Ricci soliton then V is solenoidal if and only if it is shrinking, steady and expanding depending upon the sign of scalar curvature. Further it is shown that Ricci soliton in semi-symmetric quaternion space form depends on quaternion sectional curvature c if V is solenoidal.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.7
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• pp.2981-2996
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• 2020

With the increasing amount of splicing images, many detection schemes of splicing images are proposed. In this paper, a splicing detection scheme for color image based on the quaternion discrete cosine transform (QDCT) is proposed. Firstly, the proposed quaternion Markov features are extracted in QDCT domain. Secondly, the proposed quaternion Markov features consist of global and local quaternion Markov, which utilize both magnitude and three phases to extract Markov features by using two different ways. In total, 2916-D features are extracted. Finally, the support vector machine (SVM) is used to detect the splicing images. In our experiments, the accuracy of the proposed scheme reaches 99.16% and 97.52% in CASIA TIDE v1.0 and CASIA TIDE v2.0, respectively, which exceeds that of the existing schemes.

• East Asian mathematical journal
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• v.33 no.3
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• pp.309-315
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• 2017

In this paper, we investigate the regularities of the hyper-complex valued functions of the split quaternion variables. We define several differential operators for the split qunaternionic function. We research several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the corresponding Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion 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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1401-1409
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• 2016

In complex analysis, the Bergman kernels for two biholomorphically equivalent complex domains satisfy the transformation formula. Recently new Bergman theory of slice regular functions of the quaternion variables has been investigated. In this paper we construct the transformation formula of the slice Bergman kernels under slice biregular functions in the setting of the quaternion variables.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.611-632
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• 2009

The orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study the arithmetic properties of optimal embeddings of orders in a quaternion algebra over a dyadic local field.

• East Asian mathematical journal
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• v.31 no.1
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• pp.119-126
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• 2015

The aim of this paper is to research certain properties of conic regular functions of conic quaternion variables in $\mathbb{C}^2$. We generalize the properties of conic regular functions and the Cauchy theorem of conic regular functions in conic quaternion analysis.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.65-74
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• 2015

In this paper, we provide the notions of dual quaternions and their algebraic properties based on matrices. From quaternion analysis, we give the concept of a derivative of functions and and obtain a dual quaternion Cauchy-Riemann system that are equivalent. Also, we research properties of a regular function with values in dual quaternions and relations derivative with a regular function in dual quaternions.

• 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.