• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.231-241
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• 1991

Recently, many mathematicians([NT], [Ka], [TV], [CW], etc.) studied foliated structures on a smooth manifold with the viewpoint of transversal differential geometry. In this paper, we shall discuss certain hermitian foliations F on a riemannian manifold with a bundle-like metric, that is, their transversal bundles to F have hermitian structures.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.259-263
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• 1996

Let G be a topological group and X a G space. For a given nonequivariant vector bundle over X there does not always exist a G equivariant vector bundle structure. In this paper we find some sufficient conditions for nonequivariant real line bundles to have G equivariant vector bundle structures.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.11-17
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• 2011

We introduce the notion of weak M-precontinuity which is a generalization of M-precontinuity defined between spaces with minimal structures. We also investigate some properties and characterizations for the continuity.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.223-229
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• 2010

We introduce the notion of weak M-semicontinuity which is a generalization of M-semicontinuity defined between spaces with minimal structures. We also investigate some properties and characterizations for such a notion.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.639-646
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• 2013

We investigate the stability of orthogonally additive set-valued functional equation $$F(x+y)=F(x)+F(y)(x{\perp}y)$$ in Hausdorff topology on closed convex subsets of a Banach space.

• The Mathematical Education
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• v.53 no.1
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• pp.57-73
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• 2014

This study investigated the connections of mathematical thinking of students at the second, fourth, and sixth grades with regard to multiplication, fraction, and proportion, all of which have multiplicative structures. A paper-and-pencil test and subsequent interviews were conducted. The results showed that mathematical thinking including vertical thinking and relational thinking was commonly involved in multiplication, fraction, and proportion. On one hand, the insufficient understanding of preceding concepts had negative impact on learning subsequent concepts. On the other hand, learning the succeeding concepts helped students solve the problems related to the preceding concepts. By analyzing the connections between the preceding concepts and the succeeding concepts, this study provides instructional implications of teaching multiplication, fraction, and proportion.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.449-473
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• 2012

In the present paper, we study the relationship between continuous order-representability and the fulfillment of the usual covering properties on topological spaces. We also consider the case of some algebraic structures providing an application of our results to the social choice theory context.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.231-240
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• 2013

We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and of a round 4-sphere.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.171-185
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• 2009

We study fibred Riemannian spaces with almost complex structures which are induced by the almost complex structure or the almost contact structure on the base and fibre. We show that if the total space is a complex space form, then the total space is locally Euclidean. Moreover, we deal with the fibred Riemannian space with various Kaehlerian structures.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.405-423
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• 2023

Let (𝓛, 𝒜) be a complete duality pair. We give some equivalent characterizations of Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures associated to duality pairs and Frobenius pairs. Some rings are described by Frobenius pairs. In addition, we investigate special Gorenstein (𝓛, 𝒜)-projective modules and construct some model structures and recollements associated to them.