• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.117-139
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• 2017

This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.681-689
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• 2019

The $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is an orbit of a subgroup of the $M{\ddot{o}}bius$ transformation group of ${\mathbb{S}}^{n+1}$. In this note, We prove that a compact $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is the image of a $M{\ddot{o}}bius$ transformation of the isometric homogeneous submanifold in ${\mathbb{S}}^{n+1}$.

• Korean Journal of Childcare and Education
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• v.9 no.1
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• pp.201-220
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• 2013

This study focused on science activities that need collaborative inquiry process and evaluate the effects of small group's science cooperative learning according to personality types on young children's science activities. The subjects are 30 five-year-old kindergarteners. They have been divided equally into three groups, extroversion(E), interversion(I), and heterogeneous group of EI mixed group depending on EI indicators through K-ABC cognitive ability tests and MMTIC personality types targeting. Both of groups have 10 members each. For data analysis, scientific attitude was analyzed with ANCOVA, scientific knowledge development was done with frequency analysis. As a result, first there was a difference in scientific knowledge development between the homogeneous group and heterogeneity group in small group's cooperative learning. Through the results of a Scheffe post-hoc test, there was a significant difference between E and I homogeneous groups but there was no difference between I homogeneous group and the heterogeneity group, and between E homogeneous group and the heterogeneity group, I homogeneous group had the most effective group composition in scientific attitude improvement.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1229-1240
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• 2017

This paper presents a systematic study of the abstract harmonic analysis over spaces of complex measures on homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Then we study abstract harmonic analysis of complex measures over the left coset space G/H.

• Bulletin of the Korean Chemical Society
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• v.28 no.11
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• pp.1902-1909
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• 2007

This account reports an overview of our findings in homogeneous Pd-catalyzed reactions. Herein we describe the new design in reactions of Group 14 element compounds and in homogeneous nanosize Pd catalysts. In the early stages of our study, we developed Pd-catalyzed transformations of allylic esters with disilanes, silylcyanides and acylsilanes to the corresponding silylation, cyanation and acylation products, respectively. We also developed a Pd-catalyzed three component coupling reaction of Group 14 element compounds involving 1,3-diene and acid chlorides to form β,γ-unsaturated ketone as a single product. Recently, we focus our attention on modifying the catalytic environment by nanosize Pd in order to improve the performance of Pd catalysts. These nanosystems realize efficient catalytic environment with remarkable enhancement in catalytic activity and unprecedented selectivity.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.253-263
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• 2019

Let M be a curvature homogeneous or ball-homogeneous non-$coK{\ddot{a}}hler$ almost $coK{\ddot{a}}hler$ 3-manifold. In this paper, we prove that M is locally isometric to a unimodular Lie group if and only if the Reeb vector field ${\xi}$ is an eigenvector field of the Ricci operator. To extend this result, we prove that M is homogeneous if and only if it satisfies ${\nabla}_{\xi}h=2f{\phi}h$, $f{\in}{\mathbb{R}}$.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.115-121
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• 1995

We define a group of homogeneous type G which is a more general setting than $R^n$. This group G forms a natural habitat for extensions of many of the objects studied in Euclidean harmonic analysis.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.291-297
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• 2006

We find unit Killing vectors and homogeneous geodesics on the Lie group with Lie algebra $\mathbf{a}{\oplus}_p\mathbf{r}$, where $\mathbf{a}$ and $\mathbf{r}$ are abelian Lie algebra of dimension n and 1, respectively.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1607-1620
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• 2023

In this paper, we mainly study the problem of the existence of homogeneous geodesics in sub-Finsler manifolds. Firstly, we obtain a characterization of a homogeneous curve to be a geodesic. Then we show that every compact connected homogeneous sub-Finsler manifold and Carnot group admits at least one homogeneous geodesic through each point. Finally, we study a special class of ℓ^p-type bi-invariant metrics on compact semi-simple Lie groups. We show that every homogeneous curve in such a metric space is a geodesic. Moreover, we prove that the Alexandrov curvature of the metric space is neither non-positive nor non-negative.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.667-674
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• 2013

Considering a special double-cover Q of the symmetric group of degree 3, we show that a proper non-regular approximate symmetry occurs from its quasigroup homogeneous space. The weak compatibility of any two elements of Q is completely characterized in any such quasigroup homogeneous space of degree 4.