• 대한수학회지
• /
• 제54권1호
• /
• pp.117-139
• /
• 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.

• 대한수학회보
• /
• 제56권3호
• /
• pp.681-689
• /
• 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 ${\mathbb{S}}^{n+1}$.

• 한국보육지원학회지
• /
• 제9권1호
• /
• pp.201-220
• /
• 2013

본 연구는 협력적인 탐구과정이 요구되는 과학활동에 초점을 맞추어, 성격 유형별 소집단과학협동학습이 유아의 과학적 능력에 어떠한 영향을 미치는지 알아보고자 하였다. 이를 위해 전라북도 J시에 소재한 S유치원과 J유치원 만 5세를 대상으로 K-ABC 인지능력 검사와 MMTIC 성격유형 검사를 통해 각 기관별로 15명씩 총 30명을 EI지표에 따라 E(외향성)집단과 I(내향성) 집단의 성격유형 동질집단과 EI 혼합집단인 이질집단으로 구성하였다. 자료 분석은 과학적 태도는 공변량분석(ANCOVA), 과학적 지식 발달은 빈도 분석을 하였다. 연구결과 첫째, 소집단 협동학습에서 성격 유형별 동질집단과 이질집단 간 과학적 지식발달에 차이가 나타났다. 둘째, 소집단 협동학습에서 성격 유형별 동질집단과 이질집단 간과학적 태도에도 차이가 나타났다. Scheffe 사후검증을 실시한 결과 E동질집단과 I동질집단 간에 유의한 차이가 있었으나 I동질집단과 이질집단, E동질집단과 이질집단 간에는 차이가 없었고, I동질집단이 과학적 태도 향상에 가장 효과적인 집단구성이었다.

• 대한수학회보
• /
• 제54권4호
• /
• pp.1229-1240
• /
• 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
• /
• 제28권11호
• /
• pp.1902-1909
• /
• 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.

• 대한수학회보
• /
• 제56권1호
• /
• pp.253-263
• /
• 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 ${\nabla}_{\xi}h=2f{\phi}h$, $f{\in}{\mathbb{R}}$.

• 대한수학회보
• /
• 제32권1호
• /
• pp.115-121
• /
• 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.

• 충청수학회지
• /
• 제19권3호
• /
• pp.291-297
• /
• 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.

• 대한수학회보
• /
• 제60권6호
• /
• pp.1607-1620
• /
• 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.

• 대한수학회보
• /
• 제50권2호
• /
• pp.667-674
• /
• 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.