• Publications of The Korean Astronomical Society
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• v.22 no.4
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• pp.103-111
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• 2007

On the formulation frameworks of linearly perturbed spacetime and weak gravitational lensing(WGL) we studied the statistical properties of a bundle of light rays propagating through stochastic gravitational wave background(SGWB). For this we considered the SGWB as tensor perturbations of linearly perturbed Friedmann spacetime. Using the solution of null geodesic deviation equation(NGDE) we related the convergence, shear and rotation deformation spectra of WGL with the strain spectra of SGWB. Adopting the astrophysical and cosmological SGWB strain spectra which were already known we investigated the approximated spectral forms of convergence, shear and rotation of WGL.

• Proceedings of the IEEK Conference
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• 2000.07a
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• pp.482-485
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• 2000

A modified watershed transform is proposed which is context-free marker-controlled and minima imposition-free to reduce the over-segmentation and to speedup the transform. In contrast to the conventional methods in which a priori knowledge, such as flat zones, zones of homogeneous texture, and morphological distance, is required for marker extraction, context-free marker extraction is proposed by using the attention operator based on the GST (generalized symmetry transform). By using the context-free marker, the proposed watershed transform exploit marker-constrained labeling to speedup the computation and to reduce the over-segmentation by eliminating the unnecessary geodesic reconstruction such as the minima imposition and thereby eliminating the necessity of the post-processing of region merging. The simulation results show that the proposed method can extract context-free markers inside the objects from the complex background that includes multiple objects and efficiently reduces over-segmentation and computation time.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.35-56
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• 2015

In this paper, we classify all nonconstant smooth CR maps from a sphere $S_{n,1}{\subset}\mathbb{C}^n$ with n > 3 to the Shilov boundary $S_{p,q}{\subset}\mathbb{C}^{p{\times}q}$ of a bounded symmetric domain of Cartan type I under the condition that p - q < 3n - 4. We show that they are either linear maps up to automorphisms of $S_{n,1}$ and $S_{p,q}$ or D'Angelo maps. This is the first classification of CR maps into the Shilov boundary of bounded symmetric domains other than sphere that includes nonlinear maps.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.1
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• pp.53.2-53.2
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• 2011

A small number of active galactic nuclei are known to exhibit prominent double peak emission profiles indicating the presence of a relativistic accretion disk model. Using a Monte Carlo technique, we compute the linear polarization of a double peaked broad emission line. A Keplerian accretion disk is adopted for the double peak emission line region and the Schwarzschild geometry is assumed in the emission region. Far from the accretion disk where flat Minkowski geometry is appropriate, we place a scattering region in the shape of a spherical shell sliced. We generate a line photon in the accretion disk in an arbitraray direction in the local rest frame and follow the geodesic of the photon until it hits the scattering region. The profile of the polarized flux is mainly determined by the relative location of the scattering region with respect to the emission source. When the scattering region is in the polar direction, the linear degree of polarization also shows a double peak structure. Under a favorable condition we show that up to 1% of linear degree of polarization may be obtained.

• Journal of Electrical Engineering and Technology
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• v.7 no.6
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• pp.1001-1008
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• 2012

Non-destructive testing (NDT) is a technique used in science and industry to evaluate the properties of a material without causing damage. In this paper we propose a method for segmenting radiographic images of welding in order to extract the welding defects which may occur during the welding process. We study different methods of level set and choose the model adapted to our application. The methods presented here take the property of local segmentation geodesic active contours and have the ability to change the topology automatically. The computation time is considerably reduced after taking into account a new level set function which eliminates the re-initialization procedure. Satisfactory results are obtained after applying this algorithm both on synthetic and real images.

• Proceedings of the Korean Information Science Society Conference
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• 2012.06c
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• pp.362-363
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• 2012

본 논문에서는 한 장의 실제 나무 영상이 주어졌을 시, 사실적인 3차원 나무 모델링(modeling) 및 자가생장(self-growth) 표현을 위한 방법을 소개하도록 한다. 스켈레톤기반의 간략화(skeleton-based abstraction)를 이용하여 동일한 나무 몸통(trunk)을 갖는 다양한 나무 모델생성과 함께 나무의 다면체구조(manifold structure)를 고려한 지오데식 커널(geodesic kernel)을 이용하여 나무의 자가생장을 표현한다. 나무의 자가생장은 사전 정의된 나무 굵기, 전체 크기, 그리고 가지증식 순서정보와 같은 상대적 성장정보(allometric information)를 동시 이용하여 상대적인 나무 생장(allometric tree growth)을 표현하도록한다. 한편, 보여지지않는 나무 가지와 잎들에 대해선, 나무구조는 로컬하게 자기유사성(local self-similarity)을 갖는다라는 고전적인 절차적(conventional procedural) 가정을 이용하여 자동적으로 생성토록한다. 실제영상을 이용한 몇몇들의 실험을 통해 보다 효과적으로 나무 모델 및 생장 표현이 가능함을 보여주도록한다.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.733-743
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• 2012

For the "Hopf bundle" $S^1{\rightarrow}S^{2n,1}{\rightarrow}\mathbb{C}H^n$, horizontal lifts of simple closed curves are studied. Let ${\gamma}$ be a piecewise smooth, simple closed curve on a complete totally geodesic surface $S$ in the base space. Then the holonomy displacement along ${\gamma}$ is given by $$V({\gamma})=e^{{\lambda}A({\gamma})i}$$ where $A({\gamma})$ is the area of the region on the surface $S$ surrounded by ${\gamma}$; ${\lambda}=1/2$ or 0 depending on whether $S$ is a complex submanifold or not. We also carry out a similar investigation for the complex Heisenberg group $\mathbb{R}{\rightarrow}\mathcal{H}^{2n+1}{\rightarrow}\mathbb{C}^n$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1539-1550
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• 2019

We classify minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles and ruled constant mean curvature (cmc) surfaces in ${\mathbb{S}}^3$. First we show that minimal surfaces in ${\mathbb{S}}^3$ which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric ${\mathbb{S}}^1$-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in ${\mathbb{S}}^3$ up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in ${\mathbb{S}}^3$(cf. Theorem 3).

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.453-463
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• 2021

In this study, tubular surfaces that play an important role in technological designs in various branches are examined for the case of the base curve is not satisfying the fundamental theorem of the differential geometry. In order to give an alternative perspective to the researches on tubular surfaces, the modified orthogonal frame is used in this study. Firstly, the relationships between the Serret-Frenet frame and the modified orthogonal frame are summarized. Then the definitions of the tubular surfaces, some theorems, and results are given. Moreover, the fundamental forms, the mean curvature, and the Gaussian curvature of the tubular surface are calculated according to the modified orthogonal frame. Finally, the properties of parameter curves of the tubular surface with modified orthogonal frame are expressed and the tubular surface is drawn according to the Frenet frame and the modified orthogonal frame.