• 충청수학회지
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• 제31권4호
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• pp.387-396
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• 2018

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a fixed topology on X and we will regard ${\tau}(X)$ a topological space. Our purpose of this study is to comparison new topologies on the family ${\tau}(X)$ of all topologies induced old one.

• Korean Journal of Mathematics
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• 제22권3호
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• pp.553-565
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• 2014

In this paper, we investigate the properties of Alexandrov fuzzy topologies and join-meet approximation operators. We study fuzzy preorder, Alexandrov topologies join-meet approximation operators induced by Alexandrov fuzzy topologies.We give their examples.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.183-194
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• 2014

In this paper, we investigate the properties of Alexandrov fuzzy topologies and meet-join approximation operators. We study fuzzy preorder, Alexandrov topologies and meet-join approximation operators induced by Alexandrov fuzzy topologies. We give their examples.

• 충청수학회지
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• 제28권3호
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• pp.431-441
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• 2015

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. Our purpose of this study is to give new topologies on the family ${\tau}(X)$ of all topologies induced by old one and its ${\theta}$ topology and to compare them.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제15권1호
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• pp.72-78
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• 2015

Alexandrov topologies are the topologies induced by relations. This paper addresses the properties of Alexandrov topologies as the extensions of strong topologies and strong cotopologies in complete residuated lattices. With the concepts of Zhang's completeness, the notions are discussed as extensions of interior and closure operators in a sense as Pawlak's the rough set theory. It is shown that interior operators are meet preserving maps and closure operators are join preserving maps in the perspective of Zhang's definition.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.655-665
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• 2014

The number of topologies (non-homeomorphic topologies) on a fixed finite set having n elements are now known up to n = 18 (n = 16 respectively) but still no complete formula yet. There are one to one correspondences among topologies, preorders and transitive digraphs on a given finite set. In this article, we enumerate topologies and non-homeomorphic topologies whose underlying graph is a given finite simple graph.

• Journal of Power Electronics
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• 제19권6호
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• pp.1351-1365
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• 2019

This paper proposes two modified Z-source inverter topologies, namely an embedded L-Z-source inverter (EL-ZSI) and a coupled inductor L-Z source inverter (CL-ZSI). The proposed topologies offer a high voltage gain with a reduced passive component count and reduction in source current ripple when compared to conventional ZSI topologies. Additionally, they prevent overshoot in the dc-link voltage by suppressing heavy inrush currents. This feature reduces the transition time to reach the peak value of the dc-link voltage, and reduces the risk of component failure and overrating due to the inrush current. EL-ZSI and CL-ZSI possess all of the inherent advantages of the conventional L-ZSI topology while eliminating its drawbacks. To verify the effectiveness of the proposed topologies, MATLAB/Simulink models and scaled down laboratory prototypes were constructed. Experiments were performed at a low shoot through duty ratio of 0.1 and a modulation index as high as 0.9 to obtain a peak dc-link voltage of 53 V. This paper demonstrates the superiority of the proposed topologies over conventional ZSI topologies through a detailed comparative analysis. Moreover, experimental results verify that the proposed topologies would be advantageous for renewable energy source applications since they provide voltage gain enhancement, inrush current, dc-link voltage overshoot suppression and a reduction of the peak to peak source current ripple.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2000년도 ITC-CSCC -1
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• pp.391-394
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• 2000

In this paper four lossy and one lossless inductance simulator topologies employing a single DO-OTA are presented. For the topologies proposed the inductance $L_{eq}$ and the series resistance $R_{eq}$ are independently adjustable. The topologies employ a single capacitor and are canonic in the number of capacitors. The resistors in the topologies can easily be implemented also with DO-OTAs. In this case the topologies proposed change to DO-OTA-C inductor simulators which is important from the integration point of view. Simulation results are included to verify theory.

• 대한수학회지
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• 제39권1호
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• pp.31-49
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• 2002

An R$^{n}$ -geometry (P$^{n}$ , L) is a generalization of the Euclidean geometry on R$^{n}$ (see Def. 1.1). We can consider some topologies (see Def. 2.2) on the line set L such that the join operation V : P$^{n}$ $\times$ P$^{n}$ \ $\Delta$ longrightarrow L is continuous. It is a notable fact that in the case n = 2 the introduced topologies on L are same and the join operation V : P$^2$ $\times$ P$^2$ \ $\Delta$ longrightarrow L is continuous and open [10, 11]. It is a fundamental topological property of plane geometry, but in the cases n $\geq$ 3, it is no longer true. There are counter examples [2]. Hence, it is a fundamental problem to find suitable topologies on the line set L in an R$^{n}$ -geometry (P$^{n}$ , L) such that these topologies are compatible with the incidence structure of (P$^{n}$ , L). Therefore, we need to study the topologies of the line set L in an R$^{n}$ -geometry (P$^{n}$ , L). In this paper, the relations of such topologies on the line set L are studied.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.445-448
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• 2006

Let N be a normal subgroup of a path-connected topological group (G, $t$). In this paper, the authors consider the existence of path-connectedness in refined topologies in order to address the property of maximal path-connectedness in topological groups. In particular, refinements on $t$ and refinements on the quotient topology on G/N are studied. The preservation of path-connectedness in extending topologies and translation topologies is also considered.