• 대한수학회지
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• 제43권5호
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• pp.1129-1142
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• 2006

In this paper, we estimate area of tube in a CBA(0)-space with extendible geodesics. As its application, we obtain an upper bound of systole in a nonsimply connected space of nonpositive curvature. Also, we determine a relative growth of a ball in a CBA(0)-space to the corresponding ball in Euclidean plane.

• 대한수학회보
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• 제50권4호
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• pp.1099-1108
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• 2013

We define the Mannheim curve in a 3-dimensional Riemannian manifold, which is a generalization of the Mannheim curve in Euclidean space. In particular, we study the Mannheim curves and their partner curves in 3-dimensional space forms.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.297-310
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• 2005

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness is completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.445-463
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• 2019

Let C[0, T] denote the space of continuous real-valued functions on [0, T]. On the space C[0, T], we introduce a Banach algebra of series of functions which are generalized Fourier-Stieltjes transforms of measures of finite variation on the product of simplex and Euclidean space. We evaluate analytic Feynman integrals of the functions in the Banach algebra which play significant roles in the Feynman integration theory and quantum mechanics.

• East Asian mathematical journal
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• 제24권1호
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• pp.7-10
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• 2008

We prove a localization theorem of Azukawa pseudometric at a local plurisubharmonic peak point of a domain in the complex Euclidean space.

• 대한수학회지
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• 제31권3호
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• pp.429-437
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• 1994

Let $M^n$ be a connected hypersurface in Euclidean (n + 1)-space $E^{n+1}$, and let $G : G^n \longrightarrow S^n(1) \subset E^{n+1}$ be its Gauss map.

• East Asian mathematical journal
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• 제14권2호
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• pp.269-279
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• 1998

For a codimension 1 submanifold in a Euclidean 2n-space, the degree of the gauss map mod 2 is the semi-characteristic of the manifold in $Z_2$ coefficient.

• 충청수학회지
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• 제27권3호
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• pp.403-404
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• 2014

• 디지털콘텐츠학회 논문지
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• 제10권3호
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• pp.423-431
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• 2009

영상을 검색하는 데에는 형태, 색상, 질감 등 여러 가지 특징을 사용 할 수 있다. 그 중 가장 활발한 연구가 이루어지고 있는 분야가 형태 정보와 색상 정보를 이용하는 분야이다. 형태 정보를 이용하는 검색 방법에는 2D 모멘트와 푸리에변환 등의 방법이 유명하다. 또 다른 방법으로는 CSS(Curvature Scale Space)가 있는데, 이는 윤곽선 정보를 이용하여 윤곽선의 굴곡을 2D 그래프로 표현하여 그 그래프의 극대점을 특징 값으로 사용하여 영상을 비교 검색하는 방법이다. 기존 CSS 방법에는 몇 가지 문제점이 있어서 본 논문에서는 기존 방법을 향상시킨 ICSS 방법을 사용하여 영상을 검색한다. 색상 정보를 이용하는 방법에는 RGB 색상정보를 이용하는 방법과 HSI 색상정보를 이용하는 방법 등이 있는데 본 논문에서는 HSI 색상정보를 이용하여 색상 히스토그램으로 표현한 후 영상의 비교 척도로 사용하였다. 영상의 유사도를 측정하는 방법으로는 유클리디언 디스턴스를 주로 사용하는데, 본 논문에서는 정확도와 검색 시간을 단축시키고자 DTW를 사용하여 영상의 유사도를 측정하였고, 유클리디언 디스턴스를 사용했을 때와 비교하여 성능 향상 결과를 보인다.

• International Journal of Control, Automation, and Systems
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• 제2권1호
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• pp.107-117
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• 2004

A new algorithm for planning a collision-free path based on an algebraic curve as well as the concept of path space is developed. Robot path planning has so far been concerned with generating a single collision-free path connecting two specified points in a given robot workspace with appropriate constraints. In this paper, a novel concept of path space (PS) is introduced. A PS is a set of points that represent a connection between two points in Euclidean metric space. A geometry mapping (GM) for the systematic construction of path space is also developed. A GM based on the 2$^{nd}$ order base curve, specifically Bezier curve of order two is investigated for the construction of PS and for collision-free path planning. The Bezier curve of order two consists of three vertices that are the start, S, the goal, G, and the middle vertex. The middle vertex is used to control the shape of the curve, and the origin of the local coordinate (p, $\theta$) is set at the centre of S and G. The extreme locus of the base curve should cover the entire area of actual workspace (AWS). The area defined by the extreme locus of the path is defined as quadratic workspace (QWS). The interference of the path with obstacles creates images in the PS. The clear areas of the PS that are not mapped by obstacle images identify collision-free paths. Hence, the PS approach converts path planning in Euclidean space into a point selection problem in path space. This also makes it possible to impose additional constraints such as determining the shortest path or the safest path in the search of the collision-free path. The QWS GM algorithm is implemented on various computer systems. Simulations are carried out to measure performance of the algorithm and show the execution time in the range of 0.0008 ~ 0.0014 sec.