• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.383-399
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• 2020

Following Matsumoto's definition of continuous orbit equivalence for one-sided subshifts of finite type, we introduce the notion of orbit equivalence to canonically associated dynamical systems, called the limit dynamical systems, of self-similar groups. We show that the limit dynamical systems of two self-similar groups are orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids. We also show that the equivalence class of Cuntz-Pimsner groupoids and the stably isomorphism class of Cuntz-Pimsner algebras of self-similar groups are invariants for orbit equivalence of limit dynamical systems.

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.359-364
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• 2015

We present smooth simply connected closed 4k-dimensional manifolds N := N_k, for each k ∈ {2, 3, ⋯}, with distinct symplectic deformation equivalence classes [[ω_i]], i = 1, 2. To distinguish [[ω_i]]’s, we used the symplectic Z invariant in [4] which depends only on the symplectic deformation equivalence class. We have computed that Z(N, [[ω₁]]) = ∞ and Z(N, [[ω₂]]) < 0.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1457-1482
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• 2017

Let S and R be rings and $_SC_R$ a (faithfully) semidualizing bimodule. We introduce and study C-weak flat and C-weak injective modules as a generalization of C-flat and C-injective modules ([21]) respectively, and use them to provide additional information concerning the important Foxby equivalence between the subclasses of the Auslander class ${\mathcal{A}}_C$ (R) and that of the Bass class ${\mathcal{B}}_C$ (S). Then we study the stability of Auslander and Bass classes, which enables us to give some alternative characterizations of the modules in ${\mathcal{A}}_C$ (R) and ${\mathcal{B}}_C$ (S). Finally we consider an open question which is closely relative to the main results ([11]), and discuss the relationship between the Bass class ${\mathcal{B}}_C$(S) and the class of Gorenstein injective modules.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07b
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• pp.388-390
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• 2005

최근 소프트웨어 가 점 점 복잡해 짐 에 따라 다양한 상황에 대한 테스트의 중요도도 함께 증가하지만, 다양한 상황을 모두 고려하여 테스트하는 것은 많은 시간과 비용을 요구한다. 본 논문에서는 이러한 복잡한 시스템의 테스트를 위해 Orthogonal Array와 Equivalence Class 기법을 이용하여 test suite의 중복성을 낮추는 효율적인 test set을 생성하는 기법을 제안한다. 이렇게 제안된 기법을 OMA DRM(Digital Rights Management) System에 적용한 사례를 통해 기법의 우수성을 보인다.

• East Asian mathematical journal
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• v.17 no.1
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• pp.57-70
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• 2001

In this paper, we introduce a class of generalized quasivariational inclusions for fuzzy mappings and show its equivalence with a class of fixed point problems. Using this equivalence, we develop the Mann and Ishikawa type perturbed iterative algorithms for this class of generalized quasivariational inclusions. Further, we prove the existence of solutions for the class of generalized quasivariational inclusions and discuss the convergence criteria for the perturbed algorithms.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.20-29
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• 2009

In this paper, by using the definition of fuzzy equivalence relations introduced by Dib and Youssef, we obtain fuzzy analogues of many results concerning ordinary equivalence relations. Moreover, we investigate fuzzy analogues of many results concerning relationships between ordinary equivalence relations and ordinary functions. In particular, we obtain the fuzzy-canonical decomposition of a fuzzy function.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.291-315
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• 2006

By using the new concepts of fuzzy equivalence relations and fuzzy partitions which Dib and Youssef introduced, we obtains fuzzy analogues of many results concerning ordinary equivalence relations and partitions. Also, we give some examples.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.960-964
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• 2004

During system resource improvement process that based on Object-Oriented technology could be affect to the continuous system performance if lack appropriate management and control objects mechanism. This paper proposes a methodology to support continuous system performance and its stability. The adoption is based on Java Container Framework and Collections Framework for object collection. Also includes Software Engineering, Object Migration and Multiple Class Loaders mechanism accommodate to construct Continuous Migration Container (CMC). CMC is a runtime environment provides interfaces for management and control to support upgrading object process. Upgrade object methodology of CMC can be divided into two phase are object equivalence checking and object migration process. Object equivalence checking include object behavior verification and functional conformance verification before object migration process. In addition, CMC use Multiple Class Loaders mechanism to support reload effected classes instead of state transfer in migration process while upgrading object. These operations are crucial for system stability and enhancement efficiency.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.549-554
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• 2014

We present a smooth simply connected closed eight dimensional manifold with distinct symplectic deformation equivalence classes [[${\omega}_i$]], i = 1, 2 such that the symplectic Z invariant, which is defined in terms of the scalar curvatures of almost K$\ddot{a}$hler metrics in [5], satisfies $Z(M,[[{\omega}_1]])={\infty}$ and $Z(M,[[{\omega}_2]])$ < 0.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.781-802
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• 2020

For a fixed semi-Wakamatsu-tilting module _AT, we generalize the concepts of Auslander class, Bass class, and investigate many homological properties of such classes. Moreover, we establish an equivalence between the class of ∞-T-cotorsionfree modules and a subclass of the class of T-adstatic modules. Finally, a similar version of Auslander-Bridger approximation theorem and a nice property of relative cotranspose are obtained.