• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.13-33
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• 2022

The quaternionic Calabi conjecture was introduced by Alesker-Verbitsky, analogous to the Kähler case which was raised by Calabi. On a compact connected hypercomplex manifold, when there exists a flat hyperKähler metric which is compatible with the underlying hypercomplex structure, we will consider the parabolic quaternionic Monge-Ampère equation. Our goal is to prove the long time existence and C^∞ convergence for normalized solutions as t → ∞. As a consequence, we show that the limit function is exactly the solution of quaternionic Monge-Ampère equation, this gives a parabolic proof for the quaternionic Calabi conjecture in this special setting.

• Journal for History of Mathematics
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• v.20 no.1
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• pp.33-44
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• 2007

This paper examines a historical case- the French Revolution- of conceptual change in mathematics. The case that is a space of possibility gave birth to a new community of mathematical practitioners. Carnot and Monge shared the particular conceptions of the problems, aims, and methods of a field and contributed to found Ecole Polytechnique. I intend to show how Carnot's and Monge's mathematical endeavours responded to social, political and technological developments in French society.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1994.10a
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• pp.36-48
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• 1994

• Journal of Computing Science and Engineering
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• v.3 no.2
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• pp.90-108
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• 2009

In this paper, we present an ontology mediation solution based on the methods frequently used in Formal Concept Analysis. Our approach of mediation is based on the existence of instances associated to two source ontologies, then we can generate concepts in a new ontology if and only if they share the same extent. Hence our approach creates a merged ontology which captures the knowledge of these two source ontologies. The main contributions of this work are (i) to enable the creation of concepts not originally in the source ontologies, (ii) to propose a solution to label these emerging concepts and finally (iii) to optimize the resulting ontology by eliminating redundant or non pertinent concepts. Another contribution of this work is to emphasize that several forms of mediated ontology can be defined based on the relaxation of certain criteria produced from our method. The solution that we propose for tackling these issues is an automatic solution, meaning that it does not require the intervention of the end-user, excepting for the definition of the common set of ontology instances.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1457-1469
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• 2016

In this paper, we study a class of Finsler metric. First, we find some rigidity results of the dually flat (${\alpha}$, ${\beta}$)-metric where the underline Riemannian metric ${\alpha}$ satisfies nonnegative curvature properties. We give a new geometric approach of the Monge-$Amp{\acute{e}}re$ type equation on $R^n$ by using those results. We also get the non-existence of the compact globally dually flat Riemannian manifold.

• Journal of Multimedia Information System
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• v.5 no.2
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• pp.79-82
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• 2018

Due to the handheld holding of smartphones and the presence of light leakage and non-balanced contrast, the detection of the retina area in smartphone-captured fundus images is more challenging than retinography-captured fundus images. This paper presents a computationally efficient image processing pipeline in order to detect and enhance the retina area in smartphone-captured fundus images. The developed pipeline consists of five image processing components, namely point spread function parameter estimation, deconvolution, contrast balancing, circular Hough transform, and retina area extraction. The results obtained indicate a typical fundus image captured by a smartphone through a D-EYE lens is processed in 1 second.

• Proceedings of the Korea Information Processing Society Conference
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• 2006.05a
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• pp.615-618
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• 2006

언어 기반의 형태소 분석에 따라 언어 지식을 국부 문법을 이용하여 그래픽적으로 기술하여 이를 기반으로 한 어휘 정보와 연결 정보를 함께 가지는 어절 사전을 구축하였다.

• Journal of the Korean Mathematical Society
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• v.37 no.2
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• pp.177-191
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• 2000

All scalar CR invariants of weight $\leq$ 6 are explicitly given for 3-dimensional strictly pseudoconvex CR structures, as an application of Fefferman's ambient metric construction and its generalization by he author.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.267-277
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• 2019

In this study, we define the dual surfaces by z = f(u) + g(v) and also classify these surfaces in ${\mathbb{I}}{\frac{1}{3}}$ satisfying some algebraic equations in terms of the coordinate functions and the Laplace operators according to fundamental forms of the surface.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.1011-1018
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• 2022

In this work, magnetic geodesics over the space of Kähler potentials are studied through a variational method for a generalized Landau-Hall functional. The magnetic geodesic equation is calculated in this setting and its relation to a perturbed complex Monge-Ampère equation is given. Lastly, the magnetic geodesic equation is considered over the special case of toric Kähler potentials over toric Kähler manifolds.