• Communications of the Korean Mathematical Society
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• v.28 no.1
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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.

• Journal of Information Technology Services
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• v.9 no.4
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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.

• Journal of Information Technology Services
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• v.6 no.1
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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.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.5
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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.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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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.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.4 no.3
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• pp.217-224
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• 2011

This paper proposes DDPT(Dynamic Data Protection Technique) which solves the problem of private information exposure occurring in a dynamic database environment. The DDPT in this paper generates the MAG(Multi-Attribute Generalization) rules using multi-attributes generalization algorithm, and the EC(equivalence class) satisfying the k-anonymity according to the MAG rules. Whenever data is changed, it reconstructs the EC according to the MAC rules, and protects the identification exposure which is caused by the EC change. Also, it measures the information loss rates of the EC which satisfies the ${\ell}$-diversity. It keeps data accuracy by selecting the EC which is less than critical value and enhances private information protection.

• The Transactions of the Korea Information Processing Society
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• v.5 no.1
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• pp.103-110
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• 1998

In case of traditional Rule-Based Reasoning(RBR) and Case-Based Reasoning(CBR), although knowledge is reasoned either by one of them or by the integration of RBR and CBR, there is a problem that much time should be consumed by numerous rules and cases. In order to improve this time-consuming problem, in this paper, a new type of reasoning technique, which is a kind of integration of reduced RB and CB, is to be introduced. Such a new type of reasoning uses Rough Set, by which we can represent multi-meaning and/or random knowledge easily. In Rough Set, solution is to be obtained by its own complementary rules, using the process of RB and CB into equivalence class by the classification and approximation of Rough Set. and then using reduced RB and CB through the integrated reasoning.

• Journal of the Korea Computer Industry Society
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• v.2 no.10
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• pp.1301-1308
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• 2001

In this paper, some interesting aspects of Grzegorczyk classes $\xi\sum{n}$, n$\geq$0 & $\sum$= { 1, 2 } of word-theoretic primitive recursive functions are observed including the classes of its corresponding predicates ($\xi\sum{n}$)* In particular, the small classes $\xi\sum{n}$($n\leq2$) are very incomparable to the corresponding small classes $\xi\sum{n}$ where $\xi\sum{n}$ is the number-theoretic Grzegorczyk classes. As one of some interesting aspects of the small classes, we show that the equivalence problem in $\xi\sum{0}$is undecidable.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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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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• v.46 no.1
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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.