• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.87-94
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• 2000

In this paper we shall de ne a concept of ${\pi}_1$-category for a map relative to a subset which is a generalization of both the category for a map and the ${\pi}_1$-category of a space, and study some properties of the ${\pi}_1$-category for a map relative to a subset.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.1-17
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• 2004

In this paper, the concept of semi-compatibility in Menger space is introduced and it is used to prove results on the existence of a unique common fixed point of four self-maps. These results are a very wide improvement of Mishra [8], Dedeic and Sarapa [3, 4], Cain and Kasril [1], and Sehgal and Bharucha Reid [10].

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.59-63
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• 2010

In this paper, we introduce the concept of weakly-ultra-${\alpha}{\psi}$-separation of two sets in a topological space using ${\alpha}{\psi}$-open sets. The ${\alpha}{\psi}$-closure and the ${\alpha}{\psi}$-kernel are defined in terms of this weakly ultra-${\alpha}{\psi}$-separation. We also investigate some of the properties of the ${\alpha}{\psi}$-kernel and the ${\alpha}{\psi}$-closure.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.109-117
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• 2010

In this paper, we define the concept of a c-net and study the convergence of c-nets. Also we show that a c-net in a topological space X has a convergent sub-c-net if and only if X is a $Lindel{\ddot{o}}f$ space, if every $G_{\delta}$ set is open in X.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.565-572
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• 2016

In this paper, the concept of $PC^{\star}$-closed sets is introduced. $PC^{\star}$-closed sets contain $pre^*_I$-open and $pre^*_I$-closed sets, ${\mathcal{RPC}}_I$ and $pre^*_I$-closed sets, ${\mathcal{RPC}}_I$ and weakly $I_{rg}$-closed sets.

• East Asian mathematical journal
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• v.27 no.4
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• pp.453-470
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• 2011

Arithmetic education is based not only on concept but also fundamentally on intuition. Pestalozzi understood time, a Kant's transcendental intuition, as numbers, a form of cognition, so that he considered intuition essential in arithmetic education. Pestalozzi and Herbart also recommended the intuitive arithmetic education. Significance of the arithmetic education based on intuition resides in the fact that arithmetic, an expression of nature and the world, is succeeded to modern arithmetic education because numbers, a cornerstone of mathematics, are symbolized as a law of mind reasoning.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.627-633
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• 2015

In this paper, we generalize the concept of the energy of Seidel matrix S(G) which denoted by S^α(G) and obtain some results related to this matrix. Also, we obtain an upper and lower bound for S^α(G) related to all of graphs with |detS(G)| ≥ (n - 1); n ≥ 3.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1153-1167
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• 2005

In this paper, all rings and all near-rings R are associative, all modules are right R-modules. For a near-ring R, we consider representations of R as R-groups. We start with a study of AGR rings and their properties. Next, for any right R-module M, we define a new concept GM module and investigate the commutative property of faithful GM modules and some characterizations of GM modules. Similarly, for any near-ring R, we introduce an R-group with MR-property and some properties of MR groups.

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.709-718
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• 2002

Observing that each Tychonoff space X has the minimal basically disconnected cover (ΛX, Λ$\sub$X/) and the .realcompact-ification $\upsilon$X, we introduce a concept of stable $\sigma$Z(X)#-ultrafilters and give internal characterizations of Tychonoff spaces X for which Λ($\upsilon$X) : $\upsilon$(ΛX).

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.661-679
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• 1995

The concept of the structure conformal vector field C on a Sasakian manifold M is defined. The existence of such a C on M is determined by an exterior differential system in involution. In this case M is a foliate manifold and the vector field C enjoys the property to be exterior concurrent. This allows to prove some interesting properties of the Ricci tensor and Obata's theorem concerning isometries to a sphere. Different properties of the conformal Lie algebra induced by C are also discussed.