• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.230-241
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• 2010

In the present paper we introduce and study fundamental concepts in the framework of L-fuzzifying topology(so called(2,L)-fuzzy topology)as L-concepts where L is a complete residuated lattice. The concepts of (2,L)-derived, (2,L)-closure, (2,L)-interior, (2,L)-exterior and (2,L)-boundary operators are studied and some results on above concepts are obtained. Also, the concepts of an L-convergence of nets and an L-convergence of filters are introduced and some important results are obtained. Furthermore, we introduce and study bases and subbases in (2,L)-topology. As applications of our work the corresponding results(see[10-11]) are generalized and new consequences are obtained.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.323-331
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• 2004

A new topology in terms of order on fuzzy sets, revealing better the relationship between smooth topology and Chang's fuzzy topology, is presented in the paper. Some basic properties are discussed.

• The Transactions of the Korean Institute of Power Electronics
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• v.24 no.6
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• pp.419-427
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• 2019

Several multilevel converter topologies have been proposed and compared. The three-level (3L) neutral-point-clamped (NPC) topology is promising and widely accepted. However, this topology suffers from uneven loss distribution among switches due to its fixed switching strategy. The 3L active NPC (ANPC) topology, which exhibits improved loss distribution profile, was proposed to address this disadvantage. The 3L T-NPC topology, a hybrid configuration of 2L and 3L NPC topologies, was introduced to address not only the loss distribution problem but also the reduction in the number of switches. In the present research, the application of these three topologies in PMSG-based medium-voltage wind turbines was investigated. The power devices considered were 10 kV IGCTs. Performance was evaluated in terms of a power loss of 10 kV IGCT for each NPC topology, which is a crucial indicator of thermal behavior, reliability, cost, and lifetime of any converter. The comparison was performed using ABB make 10 kV IGCT 5SHY17L9000 and the simulation tool PLECS.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.311-319
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• 1995

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ be the algebra of all bounded linear operaors on $H$. A dual algebra is a subalgebra of $L(H)$ that contains the identity operator $I_H$ and is closed in the $weak^*$ topology on $L(H)$. Note that the ultraweak operator topology coincides with the $weak^*$ topology on $L(H)$ (see [5]).

• Proceedings of the KIPE Conference
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• 2018.11a
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• pp.86-88
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• 2018

The three level(3L) neutral point clamped (NPC) voltage source converter (VSC) topology is widely used for grid interface in high power wind energy due to its superior performance as compared to the two level(2L) VS. However, one of the major drawbacks of this topology is the unequal dispersion of loss and therefore the junction temperature among the power devices. The 3L ANPC topology derived from the NPC topology was proposed to resolve this drawback of unequal loss profile of 3L NPC. The 3L ANPC can work under various switching strategies. In this paper a comparative study of the various switching strategies of 3L ANPC using the recently developed 10kV IGCTs which has the capability to raise the current and voltage rating of the wind turbines is carried out. The comparison is performed using ABB make 10kV IGCT 5SHY17L9000 and PLECs simulations.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.173-180
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• 1994

Let H be a separable, infinite dimensional, compled Hilbert space and let L(H) be the algebra of all bounded linear operators on H. A dual algebra is a subalgebra of L(H) that contains the identity operator $I_{H}$ and is closed in the ultraweak topology on L(H). Note that the ultraweak operator topology coincides with the wea $k^{*}$ topology on L(H)(see [3]). Bercovici-Foias-Pearcy [3] studied the problem of solving systems of simultaneous equations in the predual of a dual algebra. The theory of dual algebras has been applied to the topics of invariant subspaces, dilation theory and reflexibity (see [1],[2],[3],[5],[6]), and is deeply related with properties ( $A_{m,n}$). Jung-Lee-Lee [7] introduced n-separating sets for subalgebras and proved the relationship between n-separating sets and properties ( $A_{m,n}$). In this paper we will study the relationship between direct sum and properties ( $A_{m,n}$). In particular, using some results of [7] we obtain relationship between n-separating sets and direct sum of von Neumann algebras.ras.s.ras.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.79-96
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• 2008

In early 21st century, universities in Korea has been asked the new roles according to the changes of educational and social environment. With Korea's NURI and Brain Korea 21 project support, some chosen research oriented universities now should produce "teacher of teachers". We look 100 years back America's mathematics and see many resemblances between the status of US mathematics at that time and the current status of Korean mathematics, and find some answer for that. E. H. Moore had produced many good research mathematicians through his laboratory teaching techniques. R. L. Moore was his third PhD students. He developed his Texas/Moore method. In this article, we analyze what R. L. Moore had done through his American School of Topology and Moore method. We consider the meaning that early University of Texas case gives us in PBL(Problem Based Learning) process.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.115-127
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• 2009

In the present paper we introduce and study L-pre-$T_0$-, L-pre-$T_1$-, L-pre-$T_2$ (L-pre-Hausdorff)-, L-pre-$T_3$ (L-pre-regularity)-, L-pre-$T_4$ (L-pre-normality)-, L-pre-strong-$T_3$-, L-pre-strong-$T_4$-, L-pre-$R_0$-, L-pre-$R_1$-separation axioms in (2, L)-topologies where L is a complete residuated lattice.Sometimes we need more conditions on L such as the completely distributive law or that the "$\bigwedge$" is distributive over arbitrary joins or the double negation law as we illustrate through this paper. As applications of our work the corresponding results(see[1,2]) are generalized and new consequences are obtained.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.135-147
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• 2015

Owing to the notion of a normal adjacency for a digital product in [8], the study of product properties of digital topological properties has been substantially done. To explain a normal adjacency of a digital product more efficiently, the recent paper [22] proposed an S-compatible adjacency of a digital product. Using an S-compatible adjacency of a digital product, we also study product properties of digital topological properties, which improves the presentations of a normal adjacency of a digital product in [8]. Besides, the paper [16] studied the product property of two digital covering maps in terms of the $L_S$- and the $L_C$-property of a digital product which plays an important role in studying digital covering and digital homotopy theory. Further, by using HS- and HC-properties of digital products, the paper [18] studied multiplicative properties of a digital fundamental group. The present paper compares among several kinds of adjacency relations for digital products and proposes their own merits and further, deals with the problem: consider a Cartesian product of two simple closed $k_i$-curves with $l_i$ elements in $Z^{n_i}$, $i{\in}\{1,2\}$ denoted by $SC^{n_1,l_1}_{k_1}{\times}SC^{n_2,l_2}_{k_2}$. Since a normal adjacency for this product and the $L_C$-property are different from each other, the present paper address the problem: for the digital product does it have both a normal k-adjacency of $Z^{n_1+n_2}$ and another adjacency satisfying the $L_C$-property? This research plays an important role in studying product properties of digital topological properties.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.311-324
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• 1997

We show that if $f \in L^{\infty}(D^n)$ satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of Berezin operator, then f is n-harmonic. And we give some remarks and a conjecture on the space $M_2={f \in L^2(D^2, m \times m)\midBf = f$.