• East Asian mathematical journal
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• v.37 no.3
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• pp.307-317
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• 2021

In this paper, we deal with a problem to determine the type of automorphisms of the unit disc in ℂ in terms of intrinsic geometry. We will characterize the hyperbolicity and parabolicity of automorphism by the distance function of the Poincaré metric.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.643-652
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• 2022

In this paper, we will describe affine homogeneous domains in the complex plane. For this study, we deal with the Lie algebra of infinitesimal affine transformations, a structure of the hyperbolic metric involved with affine automorphisms. As a consequence, an affine homogeneous domain is affine equivalent to the complex plane, the punctured plane or the half plane.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.7
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• pp.1072-1077
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• 2017

Mean-reverting analysis refers to a way of estimating the underlining tendency after new data has evoked the variation in the equilibrium state. In this paper, we propose a new method to interpret the specular portraits of Premature Ventricular Contraction(PVC) arrhythmia by applying K-means unsupervised learning algorithm on electrocardiogram(ECG) data. Aiming at this purpose, we applied a mean-reverting model to analyse Heart Rate Variability(HRV) in terms of the modified poincare plot by considering PVC rhythm as the component of disrupting the homeostasis state. Based on our experimental tests on MIT-BIH ECG database, we can find the fact that the specular patterns portraited by K-means clustering on mean-reverting HRV data can be more clearly visible and the Euclidean metric can be used to identify the discrepancy between the normal sinus rhythm and PVC beats by the relative distance among cluster-centroids.