• 대한수학회논문집
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• 제28권1호
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• pp.63-69
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• 2013

On any semigroup S, there is an equivalence relation ${\phi}^S$, called the locally equivalence relation, given by a ${\phi}^Sb{\Leftrightarrow}aSa=bSb$ for all $a$, $b{\in}S$. In Theorem 4 [4], Tiefenbach has shown that if ${\phi}^S$ is a band congruence, then $G_a$ := $[a]_{{\phi}^S}{\cap}(aSa)$ is a group. We show in this study that $G_a$ := $[a]_{{\phi}^S}{\cap}(aSa)$ is also a group whenever a is any idempotent element of S. Another main result of this study is to investigate the relationships between $[a]_{{\phi}^S}$ and $aSa$ in terms of semigroup theory, where ${\phi}^S$ may not be a band congruence.

• 한국IT서비스학회지
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• 제9권4호
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• pp.219-229
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• 2010

The Green's equivalence relations have played a fundamental role in the development of semigroup theory. They are concerned with mutual divisibility of various kinds, and all of them reduce to the universal equivalence in a group. Boolean matrices have been successfully used in various areas, and many researches have been performed on them. Studying Green's relations on a monoid of boolean matrices will reveal important characteristics about boolean matrices, which may be useful in diverse applications. Although there are known algorithms that can compute Green relations, most of them are concerned with finding one equivalence class in a specific Green's relation and only a few algorithms have been appeared quite recently to deal with the problem of finding the whole D or J equivalence relations on the monoid of all $n{\times}n$ Boolean matrices. However, their results are far from satisfaction since their computational complexity is exponential-their computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and the size of the monoid of all $n{\times}n$ Boolean matrices grows exponentially as n increases. As an effort to reduce the execution time, this paper shows an isomorphism between the R relation and L relation on the monoid of all $n{\times}n$ Boolean matrices in terms of transposition. introduces theorems based on it discusses an improved algorithm for the J relation computation whose design reflects those theorems and gives its execution results.

• 한국IT서비스학회지
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• 제6권1호
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• pp.151-158
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• 2007

D-class computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and search for equivalent $n{\times}n$ Boolean matrices according to a specific equivalence relation. It is easy to see that even multiplying all $n{\times}n$ Boolean matrices with themselves shows exponential time complexity and D-Class computation was left an unsolved problem due to its computational complexity. The vector-based multiplication theory shows that the multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices can be done much more efficiently. However, D-Class computation requires computation of equivalent classes in addition to the efficient multiplication. The paper discusses a theory and an algorithm for efficient D-class computation, and shows execution results of the algorithm.

• 전자공학회논문지B
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• 제32B권5호
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• pp.671-682
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• 1995

In this paper, we propose a multimedia query language MQL which defines and manipulates multimedia data as integration of monomedia data in time and space. The MQL is designed for a multimedia data model, called the object-relationship model, and based on the multimedia object calculus which formally describes operations on multimedia data. The SQL- like syntax for class definition and object manipulation, such as retrieval, insert, update, and delete, is defined. We show how the MQL can represent the user queries using composite temporal-spatial class structures and various relationships, such as equivalence and sequence.

• 대한수학회지
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• 제45권3호
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• pp.621-630
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• 2008

In this paper, we provide a complete list of 177 equivalence classes of primitive even 2-regular quaternary positive definite quadratic forms and their discriminants. All of them have class number 1.

• 한국정보전자통신기술학회논문지
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• 제4권3호
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• pp.217-224
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• 2011

본 논문에서는 동적 데이터베이스 환경에서 발생할 수 있는 개인 정보 노출 문제를 해결할 수 있는 동적 데이터 보호 기법(Dynamic Data Protection Technique)을 제안하였다. 본 논문에서 제안한 DDPT은 다중 속성 일반화 알고리즘을 이용해 MAG(Multi-Attribute Generalization) 규칙을 생성하고, 그 MAG 규칙에 따라 k-anonymity를 만족하는 EC(Equivalence Class)를 생성한다. 그리고 데이터 변경 시 MAG 규칙에 따라 EC를 재구성 하도록 하여, EC의 변경으로 인한 식별 노출을 방지할 수 있다. 또한, ${\ell}$-diversity를 만족하는 EC의 정보손실 정도를 측정하고, 임계치 이하의 EC를 선정해서 데이터의 정확성을 유지함으로써 개인 정보 보호를 향상시켰다.

• 한국정보처리학회논문지
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• 제5권1호
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• pp.103-110
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• 1998

기존의 규칙베이스 추론(Rule-Based REasoning : RBR)과 사례베이스 추론 (Case-Base : CB)가 통합되어 추론되고 있지만, 많은 수의 규칙(Rule)과 사례(Case)에 의해 추론 시간이 많이 걸리는 단점이 있다. 본 논문에서는 이런 단점을 해결하기 위하여, 다중 의미 또는 불확실한 지식을 쉽게 표현할 수 있는 라프집합 (Rough Set)을 이용하여 RB와 CB를 간략화한 새로운 추론 방법을 제안한다. 라프집합의 식별(classification)과 근사(aprroximation)개념을 이용하여, RB와 CB를 통치 클래스(equivalence class)로 분류하여 각각을 각략화하고, 간략화된 RB와 CB를 이용하여 통합 추론하여, 상호 보완적인 역할에 의해 결정 해를 얻고자 하는 것이다.

• 한국컴퓨터산업학회논문지
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• 제2권10호
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• pp.1301-1308
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• 2001

이 논문에서는 기존의 number-theoretic 순환함수와 연계된 word-theoretic 순환함수 및 술어(predicates)들의 Grzegorzyk 클래스를 논한다. 특히 small 클래스 $\xi\sum{n}$($n\leq2$)에서의 특성은 그에 대응하는 number-theoretic small 클래스 $\xi\sum{n}$과는 매우 틀린 특성을 보인다 [2]. 흥미 있는 문제 중의 하나인 $\xi\sum{0}$ 등급에서의 동치문제는 undecidable 임을 증명한다.

• 대한수학회보
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• 제41권2호
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• pp.241-256
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• 2004

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.

• Kyungpook Mathematical Journal
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• 제46권1호
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• pp.145-152
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• 2006

In this paper, we study a class of strongly nonlinear implicit complementarity problems in the setting of Hilbert spaces H (not necessarily Hilbert lattices). By using the property of the projection and a suitable change of variables, we establish the equivalence between the strongly nonlinear implicit complementarity problem and the fixed point problem in H. Moreover, we use this equivalence and the fixed point theorem of Boyd and Wong to prove the existence and uniqueness of solutions for the strongly nonlinear implicit complementarity problem in H.