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邊東壽 弘益大學校 科學技術硏究所 1994 科學技術硏究論文集 Vol.5 No.-
In this paper, we study some topological properties of 3-manifolds. We introduce connected sum, prime decomposition of 3-manifolds. We can know if a 3-manifold M is the connected sum of two manifolds M₁M₂ then the foundamental group of M is the free product of the fundamental groups of M₁and M₂. And we construct some 3-manifolds form surfaces and 1-comlexes.
邊東壽 弘益大學校 科學技術硏究所 2003 科學技術硏究論文集 Vol.14 No.-
The approximation of general continuous functions by some special functions is very important in mathematics and many applied areas. For example, we can approximate a general functions by polynomial functions. It is called Taylor's expansion, we can approximate a general functions by cosine and sine functions. It is called Fourier expansion. In neural networks, a function is approximated by superpositions of sigmoidal fuctions. In this paper we use wavelet function for approximating functions. First we try to find good wavelet functions, and we try to find good method of approximations for general continuous functions.
邊東壽 弘益大學校 科學技術硏究所 1998 科學技術硏究論文集 Vol.9 No.1
If M is a closed surface and φis a homomorhpism on M, then the quation space M ×I / φcan be a fiberwise 3-manifolds. For two homomorphisms φand φ, we find the necessary and sufficient condition that two fiberwised 3-manifolds M ×I / φand M ×I / φare equivalent.
邊東壽 弘益大學校 科學技術硏究所 1997 科學技術硏究論文集 Vol.8 No.-
If F is a compact connected oriented surface and Φ: F → F is a diffeomorphism, then we can construct the 3-manifold Fφ. Then Fφis a fiber bundle over S¹. We find the necessary condition that the 3-manifold Fφhas hyperbolic structures.
邊東壽 弘益大學校 科學技術硏究所 1996 科學技術硏究論文集 Vol.7 No.1
Torus and the real line have affine structures. Hence the cartesian product of these T²× R has affine structures. And we can make a quotient space of T²× R, then the quotient space is a fiber bundle over the circle S¹. We try to find some affine structures on mapping torus on MA.
On The Representation of a finite Cyclic Groups
Byun, Dong-Soo,Park, Jong-Ryal 弘益大學校 1982 弘大論叢 Vol.14 No.2
본 論文에서는 有限循環群의 表現에 關하여 硏究하였다. 먼저 有限群 Z??의 representation ring을 계산하고 그 안의 同値關係에 대한 것을 생각하였고 두 개의 元素를 갖는 순환군 Z₂에서 位相同値關係가 線型同値關係가 같아지는 것을 보였다.
Byun, Dong-Soo 弘益大學校 1977 弘大論叢 Vol.9 No.-
3차원 공간 상에 야성적 곡선의 예를 몇개의 곡선을 연속적으로 연결하여 만들어 보았으며 이것을 이용하여 무한히 많은 야성적 곡선을 만들수 있음을 보였다.
On the Properties of a Closed Surfaces
Byun, Dong-Soo 弘益大學校 1984 弘大論叢 Vol.16 No.2
曲面의 基本群의 性質 두 가지를 생각하였고 또 單純閉曲線이 homology 群의 primitive인 元素를 表示할 수 있음을 보였다.
Represemtation Rings of Compact Lie Groups
Byun, Dong-Soo 弘益大學校 1983 弘大論叢 Vol.15 No.2
本 論文에서는 變換群의 定義와 性質에 關하여 살펴보고 compact Lie群의 表現의 同値關係인 G-호모토피, 位相 및 線形同値關係의 상호관계를 연구하고 이를 同値關係가 같아지는 경우를 알아 보았다.