• School Mathematics
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• v.16 no.2
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• pp.303-315
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• 2014

Even though the variety of expressions are dealt with in Korean elementary mathematics, the systematization of the subject matter of expressions is still insufficient. This is basically due to the failure of revealing clearly the identity of expressions dealt with in elementary mathematics. In this paper, as a groundwork to improve this situation, after the classification of signs as elements constituting expressions, in a position to consider elementary mathematics using transitional signs such as ${\square}$, ${\triangle}$, etc and words or phrases in expressions, expressions were defined and classified based on that classification of signs. It can be presented as the conclusion that the following four judgements which helps to promote the systematization of the subject matter of expressions are possible through this definition and classifications. First, by clarifying the identity of the expressions, any mathematical clauses or sentences can be determined whether those are expressions or not. Second, Forms of expressions can be identified. Third, the subject matter of expressions can be identified systematically. Fourth, the hierarchy of the subject matter of expressions can be identified.

• Journal of applied mathematics & informatics
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• v.2 no.1
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• pp.17-24
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• 1995

In this paper we shall prove a new fuzzy continuous selec-tion theorem in a compact convex set and next a fixed point theorem for fuzzy mappings is established.

• Journal of applied mathematics & informatics
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• v.2 no.1
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• pp.33-40
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• 1995

Entropy loss is derived by the scale parameter of Rayleigh distribution. Under this entropy loss we obtain the best invariant estimators and the Bayes estimators of the scale parameter. Also we compare MLE with the proposed estimators.

• Journal of applied mathematics & informatics
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• v.1 no.1
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• pp.49-54
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• 1994

Let f(n) denoted the number of essential parameters which are needed to classify n-dimensional nilpotent Lie Algebras over the complex number field. Then ${\int}(2n){\ge}{\frac{n(n^2-7)}{6}}-2$.

• Journal of applied mathematics & informatics
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• v.1 no.1
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• pp.79-84
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• 1994

The purpose of this paper is to introduce and discuss the concept of ${alpha}$-compactness for fuzzy topological spaces. And we obtain a product theorem for an arbitrary product of ${alpha}$-compact fuzzy spaces.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1163-1178
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• 2012

In this paper, we study the geometry of Einstein half lightlike submanifolds M of a semi-Riemannian space form $\bar{M}(c)$ subject to the conditions: (a) M is screen conformal, and (b) the coscreen distribution of M is a conformal Killing one. The main result is a classification theorem for screen conformal Einstein half lightlike submanifolds of a Lorentzian space form with a conformal Killing coscreen distribution.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1711-1726
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• 2014

In this paper, we study the geometry of indefinite generalized Sasakian space form $\bar{M}(f_1,f_2,f_3)$ admitting a generic lightlike submanifold M subject such that the structure vector field of $\bar{M}(f_1,f_2,f_3)$ is tangent to M. The purpose of this paper is to prove a classification theorem of such an indefinite generalized Sasakian space form.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.225-234
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• 2010

In this paper, we study the geometry of lightlike hypersurfaces of a semi-Riemannian manifold. We prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-vanishing smooth function.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.163-175
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• 2013

In this paper, we prove a classification theorem for Einstein lightlike hypersurfaces M of a Lorentzian space form ($\bar{M}$(c), $\bar{g}$) with a semi-symmetric metric connection subject such that the second fundamental forms of M and its screen distribution S(TM) are conformally related by some non-zero constant.

• Journal for History of Mathematics
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• v.10 no.2
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• pp.11-23
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• 1997

Category theory gives a convenient language for the study of mathematical structures besides its own study. In this paper, we investigate how the abstract structure theory emerged in 1930s affects the study in Topology and eventually becomes a rudiment for the category theory. Moreover, various extensions and universal mapping problems were put in their proper perspective as reflections by the category theory and by its duality principle, coreflections become an interesting subject in Topology, both of which give rise to a new discipline of the categorical topology.