• International Journal of Fuzzy Logic and Intelligent Systems
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• 제12권3호
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• pp.232-237
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• 2012

We introduce the notion of (L, e)-filters with fuzzy partially order e on complete residuated lattice L. We investigate (L, e)-filters induced by the family of (L, e)-filters and functions. In fact, we study the initial and final structures for the family of (L, e)-filters and functions. From this result, we define the product and co-product for the family of (L, e)-filters and functions.

• Journal of the Optical Society of Korea
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• 제7권1호
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• pp.34-37
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• 2003

Outside the photonic bandgap of two-dimensional square lattice photonic crystals, we found spectral regions in which light coupling from the air is forbidden. This uncoupling spectral region originates from the anisotropy of the photonic crystals. A two-dimensional square photonic crystal has a complete total bandgap (forbidden region in both TE and TM modes) with hole radius ranging from 0.15 to 0.45 times a lattice constant.

• 대한수학교육학회지:수학교육학연구
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• 제13권1호
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• pp.57-75
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• 2003

The goal of this paper is to offer material which make mathematising Fruedenthal(1991) proposed be experienced through the process of teaching and learning mathematics. In this paper, the number of unit squares a diagonal passes through for an m$\times$n lattice rectangle is studied and its generalization is discussed. Through this discussion, the adaptability of this material Is analysed. Especially, beyond inductional conjecture, the number of unit squares is studied by more complete way, and generalization in 3-dimension and 4-dimension are tried. In school mathematics, it is enough to generalize in 3-dimension. This material is basically appropriate for teaching and learning mathematising in math classroom. In studying the number of unit squares and unit cubes, some kinds of mathematising are accompanied. Enough time are allowed for students to study unit squares and unit cubes to make them experience mathematising really. To do so, it is desirable to give students that problem as a task, and make them challenge that problem for enough long time by their own ways. This material can be connected to advanced mathematics naturally in that it is possible to generalize this problem in n-dimension. So, it is appropriate for making in-service mathematics teachers realize them as a real material connecting school mathematics and advanced mathematics.

• 충청수학회지
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• 제13권1호
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• pp.109-118
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• 2000

In this paper, we introduce strict extensions on a ${\delta}$-frame, and show that if L is a regular strong ${\delta}$-frame, then $\mathcal{T}_XL$ is regular ${\delta}$-frame.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.95-100
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• 1998

In this note we consider some basic facts concerning abstract M spaces and investigate extremal structure of the unit ball of bounded linear functionals on $\sigma$-complete abstract M spaces.

• Korean Journal of Mathematics
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• 제20권2호
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• pp.193-212
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• 2012

We investigate the properties of fuzzy connections. We find generating functions which induce fuzzy connections. In particular, we show that their connections relate to fuzzy relations.

• 대한수학회지
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• 제36권6호
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• pp.1091-1113
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• 1999

In this paper, we first classify the possible configurations of fibrations which are not semi-stable on extremal elliptic K3 surfaces. Then we give a complete list of extremal elliptic K3 surfaces whose singular fibers are all not of type $I_n$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권2호
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• pp.113-120
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• 2014

In this paper, we first show that for any space X, there is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) and that the subspace {${\alpha}{\mid}{\alpha}$ is a fixed ${\sigma}Z(X)^{\sharp}$-ultrafilter} of the Stone-space $S(Z({\Lambda}_X)^{\sharp})$ is the minimal basically disconnected cover of X. Using this, we will show that for any countably locally weakly Lindel$\ddot{o}$f space X, the set {$M{\mid}M$ is a ${\sigma}$-complete Boolean subalgebra of $\mathcal{R}$(X) containing $Z(X)^{\sharp}$ and $s_M^{-1}(X)$ is basically disconnected}, when partially ordered by inclusion, becomes a complete lattice.

• Progress in Superconductivity
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• 제7권1호
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• pp.64-68
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• 2005

We fabricated Ni-based alloy substrates for YBCO coated conductor using powder metallurgy. Tungsten and copper were selected as alloy elements due to their mutual solubility to the base element of nickel. The alloying elements were mixed with nickel using ball milling and dried in air. The powder mixtures were packed in a rubber mold, cold isostatic pressed 200 MPa and made into rods. The compacted rods were sintered at $1150^{\circ}C$ for 6 hours for densification. It was confirmed by neutron diffraction experiment that W and Cu atoms made complete solid solution with Ni. Lattice constant of nickel alloy increased by $0.004{\AA}$ for 1at. $\%$ W in Ni-W alloy, $0.0006{\AA}$ for 1 at. $\%$ Cu in Ni-W-Cu alloy.

• 충청수학회지
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• 제26권1호
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• pp.53-69
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• 2013

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. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.