• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.351-359
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• 2019

In this paper, we introduce a modification of extremally disconnected spaces which is said to be m-extremally disconnected. And we obtain many characterizations of m-extremally disconnected spaces. The concepts of ${\ast}$-extremally disconnected spaces, ${\ast}$-hyperconnected spaces, and generalized hyperconnectedness are as examples for this paper.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.173-205
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• 2021

The spherical buildings associated with absolutely simple algebraic groups of relative rank 2 are all Moufang polygons. Tits polygons are a more general class of geometric structures that includes Moufang polygons as a special case. Dagger-sharp Tits n-gons exist only for n = 3, 4, 6 and 8. Moufang octagons were classified by Tits. We show here that there are no dagger-sharp Tits octagons that are not Moufang. As part of the proof it is shown that the same conclusion holds for a certain class of dagger-sharp Tits quadrangles.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.227-253
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• 2023

In this article, we generalize the results discussed in [6] by introducing a genus to generic fibers of Lefschetz fibrations. That is, we give families of relations in the mapping class groups of genus-1 surfaces with boundaries that represent rational homology disk smoothings of weighted homogeneous surface singularities whose resolution graphs are 3-legged with a bad central vertex.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.885-892
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• 2010

In this paper we study the structures and properties of a single cycle T-finction, whose theory has been lately proposed by Klimov and Shamir. Any cryptographic system based on T-functions may be insecure. Some of the TSC-series stream ciphers have been successfully attacked by some attacks. So it is important to analyze every aspect of a single cycle T-function. We study some properties on a single cycle T-function and we show some examples are single cycle T-functions by these properties, whose proof is easier than existing methods.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.575-588
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• 2023

In the present paper, we consider a kind of generalized hyperbolic geometric flow which has a gradient form. Firstly, we establish the existence and uniqueness for the solution of this flow on an n-dimensional closed Riemannian manifold. Then, we give the evolution of some geometric structures of the manifold along this flow.

• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.161-181
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• 2024

We describe the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one and its geometric structures in terms of the Hitchin map and a flat degeneration of the moduli space of Higgs bundles on an elliptic curve.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.493-511
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• 2024

We introduce invariant rigged null hypersurfaces of indefinite almost contact manifolds, by paying attention to those of indefinite nearly α-Sasakian manifolds. We prove that, under some conditions, there exist leaves of the integrable screen distribution of the ambient manifolds admitting nearly α-Sasakian structures.

• Research in Mathematical Education
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• v.27 no.1
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• pp.151-156
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• 2024

Mathematics Classrooms that Students Love, Grade 1: Numbers and Operations is a book that reviews student-centered educational strategies in mathematics, contrasting the teacher-centered approach. The book included lesson plans, transcriptions, and annotated comments for imperative instructional practices. Drawing from a range of effective instructional practices, it explores how student engagement and enjoyment in mathematics can be fostered through innovative lesson structures, activities, and discussions.

• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.673-692
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• 2024

In this work, an alternative fashion of the multi-Jensen is introduced. The structures of the multi-Jensen and the multi-Euler-Lagrange-Jensen mappings are described. In other words, the system of n equations defining each of the mentioned mappings is unified as a single equation. Furthermore, by applying a fixed point theorem, the Hyers-Ulam stability for the multi-Euler-Lagrange-Jensen mappings in the setting of Banach spaces is established. An appropriate counterexample is supplied to invalidate the results in the case of singularity for multiadditive mappings.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.309-325
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• 2009

The purpose of the study was to investigate the differences between Korean mathematics textbooks and CPMP textbooks in the view of conceptual network, structure of mathematical contents, instructional design, and teaching and learning environment to explore the implications for mathematics education in Korea. According to the results, Korean textbooks emphasized the mathematical structures and conceptual network, on the other hand, CPMP textbooks focused on making connections between mathematical concepts and corresponding real life situations as well as mathematical structures. And generalizing mathematical concepts at the symbolic level was very important objective in Korean textbooks, but in the CPMP textbooks, investigating mathematical ideas and solving problems in diverse contexts including real- life situations were considered very important. Teachers using Korean textbooks preferred an explanatory teaching method with the use of concrete manipulatives and student worksheet, however, teachers using CPMP textbooks emphasized collaborative group activities to communicate mathematical ideas and encouraged students to use graphing calculators when they explore mathematical concepts and solve problems.