• 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.

• 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.

• 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.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.739-746
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• 2013

There are several ways to normalize a Haar measure on the orders in a quaternion algebra. In order to understand the arithmetic properties of orders, we study the volumes of orders and compute them for some cases.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.73-82
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• 2013

There are some identities between the representations of Hecke operators defined on a subspace of modular forms associated with orders of a Quaternion algebra. In this paper, we find the identities between the zeta functions attached to these representations.

• Journal of the Optical Society of Korea
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• v.20 no.1
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• pp.42-54
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• 2016

A hybrid color and grayscale images encryption scheme based on the quaternion Hartley transform (QHT), the two-dimensional (2D) logistic map, the double random phase encoding (DRPE) in gyrator transform (GT) domain and the three-step phase-shifting interferometry (PSI) is presented. First, we propose a new color image processing tool termed as the quaternion Hartley transform, and we develop an efficient method to calculate the QHT of a quaternion matrix. In the presented encryption scheme, the original color and grayscale images are represented by quaternion algebra and processed holistically in a vector manner using QHT. To enhance the security level, a 2D logistic map-based scrambling technique is designed to permute the complex amplitude, which is formed by the components of the QHT-transformed original images. Subsequently, the scrambled data is encoded by the GT-based DRPE system. For the convenience of storage and transmission, the resulting encrypted signal is recorded as the real-valued interferograms using three-step PSI. The parameters of the scrambling method, the GT orders and the two random phase masks form the keys for decryption of the secret images. Simulation results demonstrate that the proposed scheme has high security level and certain robustness against data loss, noise disturbance and some attacks such as chosen plaintext attack.

• 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.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1319-1327
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• 2020

In this paper, we find new conjugacy invariants of Sl(3, ℍ). This result is a generalization of Foreman's result for Sl(2, ℍ).

• East Asian mathematical journal
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• v.28 no.5
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• pp.553-559
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• 2012

The noncommutative extension of the complex numbers for the four dimensional real space is a quaternion. R. Fueter, C. A. Deavours and A. Subdery have developed a theory of quaternion analysis. M. Naser and K. N$\hat{o}$no have given several results for integral formulas of hyperholomorphic functions in Clifford analysis. We research the properties of hyperholomorphic functions on $\mathbb{C}^2{\times}\mathbb{C}^2$.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.658-663
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• 2005

This paper presents the steering control algorithm of a locomotion robot using a quaternion. The locomotion robot is to be moved on an irregular floor that can inevitably result in the errors of both position and orientation. Especially the orientation error should be compensated every work in order to adjust the misaligned values of current orientation to those commanded values. In this paper, we propose a new steering control algorithm between the two values by using a quaternion with spherical cubic interpolation. The proposed algorithm is shown to be effective in terms of vibration when compared to a conventional simple compensation without interpolation, by using $MATLAB^{(R)}$ and $VisualNastran4D^{(R)}$.