• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.231-238
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• 2005

In this paper, we study the arithmetic properties of orders in a quaternion algebra over a dyadic local field and we find the mass formula of orders.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.8
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• pp.4005-4025
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• 2019

Copy-move forgery (CMF) in digital images is a detrimental tampering of artefacts that requires precise detection and analysis. CMF is performed by copying and pasting a part of an image into other portions of it. Despite several efforts to detect CMF, accurate identification of noise, blur and rotated region-mediated forged image areas is still difficult. A novel algorithm is developed on the basis of quaternion polar complex exponential transform (QPCET) to detect CMF and is conducted involving a few steps. Firstly, the suspicious image is divided into overlapping blocks. Secondly, invariant features for each block are extracted using QPCET. Thirdly, the duplicated image blocks are determined using k-dimensional tree (kd-tree) block matching. Lastly, a new technique is introduced to reduce the flat region-mediated false matches. Experiments are performed on numerous images selected from the CoMoFoD database. MATLAB 2017b is used to employ the proposed method. Metrics such as correct and false detection ratios are utilised to evaluate the performance of the proposed CMF detection method. Experimental results demonstrate the precise and efficient CMF detection capacity of the proposed approach even under image distortion including rotation, scaling, additive noise, blurring, brightness, colour reduction and JPEG compression. Furthermore, our method can solve the false match problem and outperform existing ones in terms of precision and false positive rate. The proposed approach may serve as a basis for accurate digital image forensic investigations.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.2
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• pp.222-231
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• 2016

This paper proposes a new method achieving computationally efficient attitude reference system for low cost strapdown sensors and microprocessor platform. The main idea in this method is to define and compare velocity differential vectors, geometrically computed from INS and GPS data with different update rate, for generating attitude error measurements which is further used for filter construction. A quaternion based Kalman filter configuration is applied for the attitude estimation with the adapted measurement model of differential vector comparison. Linearized model for Extended Kalman Filter and low pass filtered characteristics of measurement greatly extend the affordability of the proposed algorithm to the field of simple low cost embedded systems. For performance verification, experiment are done employing a practical low cost MEMS IMU and GPS receiver specification. Performance comparison with a high grade navigation system demonstrated good estimation result.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.6
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• pp.393-400
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• 2022

The Divert and Attitude Control System(DACS) used in high-altitude engagements is expensive and complex. In this paper, we design a high-altitude terminal guidance and control loop of guided-missile equipped with a Thrust Vector Control(TVC) that is less expensive and simpler than DACS. The proposed system utilizes a quaternion feedback control technique to track the thrust attitude command converted from the acceleration command of true proportional navigation guidance. The performance analysis of the proposed terminal guidance and control loop is conducted through engagement simulations against ballistic targets at a high altitude.

• 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.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.57-63
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• 2015

We define a hyperholomorphic function with values in split quaternions, provide split hyperholomorphic mappings on ${\Omega}{\subset}\mathbb{C}^2$ and research the properties of split hyperholomorphic functions.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.633-638
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• 1988

In this paper, a zero-velocity update technique to improve navigation accuracy of a SDINS(Strapdown Inertial Navigation System) has been studied. An indirect feedback Kalman filter which includes SDINS error equations based on a quaternion between body-fixed frame and local level navigation frame is employed for processing zero-velocity updates in an on-board navigation filter. Simulation results for land-mobile vehicle show that the zerovelocity update technique make a significant contribution to improving SDINS performance without any external aids.

• International Journal of Precision Engineering and Manufacturing
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• v.8 no.4
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• pp.16-21
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• 2007

Robotic applications, such as automatic fish cutting, require online trajectory planning because the material properties of the object, such as the bone or flesh conditions, are not known in advance. Different trajectories are required when the material properties vary. An effective online trajectory-planning algorithm is proposed using quaternions to determine the position and orientation of a robot manipulator with a spherical wrist. Quaternions are free of representation singularities and permit computationally efficient orientation interpolations. To prevent singular configurations, the exact locations of the kinematic singularities of the PUMA 560 manipulator are derived and geometrically illustrated when a forearm offset exists and the third link length is not zero.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.583-592
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• 2017

The paper gives the regularity of dual quaternionic functions and the dual Cauchy-Riemann system in dual quaternions. Also, the paper researches the polar representation and properties of a dual quaternionic function and their regular quaternionic functions.