• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.231-244
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• 2023

We study the modularity and holomorphic anomaly equation for Hodge-Gromov-Witten invariants of elliptic curves.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.455-468
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• 1996

Certain analytic behavior of geometric objects defined on a Riemannian manifold depends on some very crude properties of the manifold. Some of those crude invariants are the volume growth rate, isoperimetric constants, and the likes. However, these crude invariants sometimes exercise surprising control over the analytic behavior.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.695-698
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• 2008

A simple proof of the fact that the j-invariants for Weierstrass equations are invariant under birational transformations which keep the forms of Weierstrass equations is given by finding a non-trivial explicit birational transformation which sends a normalized Weierstrass equation to the same equation.

• Journal of Integrative Natural Science
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• v.10 no.4
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• pp.240-244
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• 2017

We study the behavior of some invariants under completion. We also give a counterexample, which is the same as a counterexample to Ding's Conjecture, to Koh-Lee's Conjecture.

• Journal of Integrative Natural Science
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• v.11 no.2
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• pp.82-86
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• 2018

We show that the (Castelnuovo-Mumford) regularity of a homogeneous Cohen-Macaulay ring agrees with some of the invariants defined the papers, and we study a ring of small index.

• 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.1
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• pp.93-99
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• 2012

Dealternating numbers and alternation numbers measure the distance between the link and an alternating links. In the present article, we show that classical link invariants; the determinant, signature and Alexander polynomial can not detect the almost alternativity of links.

• East Asian mathematical journal
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• v.23 no.2
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• pp.207-212
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• 2007

We describe the class of invertible matrices T such that $TAT^{-1}$ is EPr, for a given EPr matrix A of order n. Necessary and sufficient condition is determined for $TAT^{-1}$ to be EP for an arbitrary matrix A of order n.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.685-692
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• 2012

Consider a hypersurface $M^n$ in $\mathbb{R}^{n+1}$ with $n$ distinct principal curvatures, parametrized by lines of curvature with vanishing Laplace invariants. (1) If the lines of curvature are planar, then there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations Dupin hypersurfaces with constant M$\ddot{o}$bius curvature. (2) If the principal curvatures are given by a sum of functions of separated variables, there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations, Dupin hypersurfaces with constant M$\ddot{o}$bius curvature.

• KIEE International Transaction on Systems and Control
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• v.12D no.1
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• pp.7-11
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• 2002

In this study, fur the shape-based image retrieval, a method using local differential invariants is proposed. This method calculates the differential invariant feature vector at every feature point extracted by Harris comer point detector. Then through vector quantization using LBG algorithm, all feature vectors are represented by a codebook index. All images are indexed by the histogram of codebook index, and by comparing the histograms the similarity between images is obtained. The proposed method is compared with the existing method by performing experiments for image database including various 1100 trademarks.