• Honam Mathematical Journal
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• v.23 no.1
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• pp.113-132
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• 2001

We prove an equality that holds on G-invariant minimal hypersurfaces with constant scalar curvatures in $S^5$.

• Bulletin of the Korean Mathematical Society
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• v.40 no.4
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• pp.693-698
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• 2003

Various operator relationships are shown to be equivalent to the existence of an invariant subspace for an algebra of operators.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.45-53
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• 2000

Existence of a unique invariant probability is considered for a class of Markov processes which may not be irreducible and a functional central limit theorem for a class of nonlinear irreducible uniformly ergodic processes is derived as well.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2393-2396
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• 2005

We present a method to detect on-road vehicle using geometric invariant of feature points on side planes of the vehicle. The vehicles are assumed into a set of planes and the invariant from motion information of features on the plane segments the plane from the theory that a geometric invariant value defined by five points on a plane is preserved under a projective transform. Harris corners as a salient image point are used to give motion information with the normalized correlation centered at these points. We define a probabilistic criterion to test the similarity of invariant values between sequential frames. Experimental results using images of real road scenes are presented.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.339-348
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• 2023

It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right R-module is nilpotent-invariant. We prove that R ≅ R₁ × R₂, where R₁, R₂ are rings which satisfy R₁ is a semi-simple Artinian ring and R₂ is square-free as a right R₂-module and all idempotents of R₂ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right R-modules. Such a module is shown to have isomorphic simple modules eR and fR, where e, f are orthogonal primitive idempotents such that eRf ≠ 0.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.233-240
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• 2008

We present a quantum theorical background of the existence of multi-variable link invariants, for example the Kauffman polynomial, by observing the quantum (sl(2,$\mathbb{C}$), ad)-invariant from the Kontsevich invariant point of view. The background implies that the Kauffman polynomial can be studied by using the sl(N,$\mathbb{C}$)-skein theory similar to the Jones polynomial and the HOMFLY polynomial.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.143-165
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• 2023

For each connected and simply connected three-dimensional non-unimodular Lie group, we classify the left invariant Lorentzian metrics up to automorphism, and study the extent to which curvature can be altered by a change of metric. Thereby we obtain the Ricci operator, the scalar curvature, and the sectional curvatures as functions of left invariant Lorentzian metrics on each of these groups. Our study is a continuation and extension of the previous studies done in [3] for Riemannian metrics and in [1] for Lorentzian metrics on unimodular Lie groups.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.11 s.116
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• pp.1149-1157
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• 2006

Donoho et al. suggested a wavelet thresholding denoising method based on discrete wavelet transform. This paper proposes an improved denoising method using a new thresholding function based on translation-invariant wavelet for underwater acoustic measurement. The conventional wavelet thresholding denoising method causes Pseudo-Gibbs phenomena near singularities due to the lack of translation-invariant of the wavelet basis. To suppress Pseudo-Gibbs phenomena, a denoising method combining a new thresholding function based on the translation-invariant wavelet transform is proposed in this paper. The new thresholding function is a modified hard-thresholding to each node according to the discriminated threshold so as to reject unknown external noise and white gaussian noise. The experimental results show that the proposed method can effectively eliminate noise, extract characteristic information of radiated noise signals.

• Bulletin of the Korean Mathematical Society
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• v.47 no.3
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• pp.563-573
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• 2010

Using the fiberization technique of a shift-invariant space and the matrix characterization of the decomposition of a shift-invariant space of finite length into an orthogonal sum of singly generated shift-invariant spaces, we show that the main result in [13] can be interpreted as a statement about the length of a shift-invariant space, and give a more natural construction of multiwavelet frames from a frame multiresolution analysis of $L^2(\mathbb{R}^d)$.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.141-164
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• 2006

Let $G=O(2){\times}O(2){\times}O(2)$ and let $M^4$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$. In this paper, we prove a property on $M^4$.