• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1159-1174
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• 1996

The spectrum of the Laplacian matrix of a graph gives an information of the structure of the graph. For example, the product of non-zero eigenvalues of the characteristic polynomial of the Laplacian matrix of a graph with n vertices is n times of the number of spanning trees of that graph. The characteristic polynomial of the Laplacian matrix of a graph tells us the number of spanning trees and the connectivity of given graph. in this paper, we compute the characteristic polynomial of the Laplacian matrix of a graph bundle when its voltage lie in an abelian subgroup of the full automorphism group of the fibre; in particular, the automorphism group of the fibre is abelian. Also we study a relation between the characteristic polynomial of the Laplacian matrix of a graph G and that of the Laplacian matrix of a graph bundle over G. Some applications are also discussed.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.213-223
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• 2012

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.161-166
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• 2010

For an abelian extension K of ${\mathbb{Q}}$, let $C_W(K)$ be the group of Washington units of K, and $C_S(K)$ the group of Sinnott units of K. A lot of results about $C_S(K)$ have been found while very few is known about $C_W(K)$. This is mainly because elements in $C_S(K)$ are more explicitly defined than those in $C_W(K)$. The aim of this paper is to find a basis of $C_W(K)$ and use it to compare $C_W(K)$ and $C_S(K)$ when K is a subfield of ${\mathbb{Q}}({\zeta}_{p^e})$, where p is a prime.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.4
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• pp.63-68
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• 2005

주어진 시스템에서 정보와 정보흐름에 대한 패턴인식을 하기 위해서는, 정보를 내포하고 있는 문맥이 내용에 따라서 다른 단어나 다른 정보를 추론하여 원래의미를 전달함에 있어 오도할 수 있기 때문에, 문맥의 분해에서 정보 조각의 묶음 형태로 전환하는 작업에서부터 연구는 시작되어야만 한다. 많은 연구자들이 정보의 저장, 재표현, 부호화, 검색 등에 관해 효과적인 방법론을 찾고자 노력해 오고 있다. 유사한 노력의 일환으로 본 논문에서는 군이론과 상황이론을 응용해서 정보 및 정보흐름의 패턴인식에 관한 새로운 모델링 기법을 제안하고자 한다. 정보처리에 관련된 선행연구와 비교해서, 본 연구에서 제안하는 방법은 수학이론인 군이론과 상황이론에서 사용되고 있는 개념과 정의를 사용하였다는 점에서 매우 새로운 접근방법이라 할 수 있다. 본 논문에서는 정보흐름의 패턴인식을 위한 모델링 기법으로 Abelian Pattern Semi-Group을 제시하는데 이러한 접근방법은 최근 중요한 연구 분야가 되고 있는 유비쿼터스 컴퓨팅 환경에서도 활용될 수 있을 것이다.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.99-104
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• 1994

Let R be a left Artinian ring with identity 1 and let G be the group of units of R. It is shown that if G is finite, then R is finite. It is also shown that if 2.1 is a unit in R, then G is abelian if and only if R is commutative.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.47-51
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• 2008

By finding two characters of subgroups of the Heisenberg group $H_{27}$ whose induced characters are same, we prove that the Birch and Swinnerton-Dyer conjectures for two elliptic curves corresponding to the characters are equivalent.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.99-110
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• 1998

In this paper we study cyclic codes in $Z_m$. i.e., ideals in $Z_mG$, G afinite abelian group and we give a classification of such codes. We also sgtudy the minimum Hamming distance and the generalized Hamming weight of BCH codes over $Z_m$.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.71-79
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• 2001

We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.673-693
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• 1997

In this work, the irreducible complex representations of degree 4 of $B_4$, the braid group on 4 strings, are classified. There are 4 families of representations: A two-parameter family of representations for which the image of $P_4$, the pure braid group on 4 strings, is abelian; two families of representations which are the composition of an irreducible representation of $B_3$, the braid group on 3 strings, with a certain special homomorphism $\pi : B_4 \longrightarrow B_3$; a family of representations which are the tensor product of 2 irreducible two-dimensional representations of $B_4$.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.491-502
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• 2005

The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].