• 대한수학회지
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• 제54권1호
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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.

• 대한수학회지
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• 제41권6호
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• pp.1101-1114
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• 2004

We generalize a result of Dror Farjoun and Zabrodsky on the relationship between fixed point sets and homotopy fixed point sets, which is related to the generalized Sullivan Conjecture. As an application, we discuss extension problems considering actions on homogeneous spaces of p-compact groups.

• 한국대기환경학회지
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• 제13권1호
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• pp.51-63
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• 1997

Total suspended particulate matters in the ambient air were analyzed for eight chemical elements (Ca, Co, Cu, Fe, Mn, Pb, Si, and Zn) using an x-ray fluorescence spectrometry (XRF) at the Kyung Hee University - Suwon Campus during 1989 to 1994. To use these data as basis for source identification study, membership of each sample was selected to represent one of the well defined sample groups. The data sets consisting of 83 objects and 8 variables were initially separated into two groups, fine (d$_{p}$<3.3 ${\mu}{\textrm}{m}$) and coarse particle groups (d$_{p}$>3.3 ${\mu}{\textrm}{m}$). A hierarchical clustering method was examined to obtain possible member of homogeneous sample classes for each of the two groups by transforming raw data and by applying various distances. A disjoint principal component analysis was then used to define homogeneous sample classes after deleting outliers. Each of five homogeneous sample classes was determined for the fine and the coarse particle group, respectively. The data were properly classified via an application of logarithmic transformation and Euclidean distance concept. After determining homogeneous classes, correlation coefficients among eight chemical variables within all the homogeneous classes for calculated and meteorological variables (temperature. relative humidity, wind speed, wind direction, and precipitation) were examined as well to intensively interpret environmental factors influencing the characteristics of each class for each group. According to our analysis, we found that each class had its own distinct seasonal pattern that was affected most sensitively by wind direction.ion.

• 대한수학회지
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• 제39권1호
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• pp.61-75
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• 2002

Under the cancellation property and the Lipschitz condition on kernels, we prove that the Marcinkiewicz integrals defined on a homogeneous group H are bounded from $H^1$(H) to $L^1$(H), from $L_{c}$ $^{\infty}$(H) to BMO (H), and from $L^{p}$ (H) to $L^{p}$ (H) for 1 < p < $\infty$ assuming the $L^{q}$ -boundedness for some q > 1.for some q > 1.

• 대한수학회보
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• 제54권4호
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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.

• 충청수학회지
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• 제19권3호
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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.

• 대한수학회보
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• 제60권6호
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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.

• 영어어문교육
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• 제12권4호
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• pp.185-210
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• 2006

This study has two purposes. First, it aims to suggest an appropriate approach to English writing education for Korean high school students in a cooperative learning situation. It also aims to suggest what type of learner grouping, either homogeneous or heterogeneous, is appropriate by comparing the learners' writing abilities and the changes of their affective factors after being exposed to cooperative EFL writing instruction. Two homogeneous classes were selected and instructed to write in English for 11 weeks. One was composed of homogeneous small groups based on the students' writing scores, and the other was composed of heterogeneous small groups, again based on the students' writing scores. The results showed that the improvement between the two class types was quite different across different proficiency levels. For example, although there is little difference between the homogeneous and the heterogeneous classes of low and intermediate-level learners in writing ability improvement, high-level students showed a significant difference between the classes. In addition, it was found that class participation correlated significantly to writing ability improvement. Cooperative learning was proved to be an effective writing instructional approach to encourage learners' interest and increase their self-confidence; however, the results did not show any significant differences in learners' affective domain between the homogeneous and the heterogeneous classes. Similarly, the learners' grouping preference was not affected by the grouping method.

• Macromolecular Research
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• 제17권7호
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• pp.506-515
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• 2009

We synthesized a series of polystyrene derivatives containing various side chain terminal moieties, such as phenoxymethyl, 4-methoxyphenoxymethyl, 4-fluorophenoxymethyl, 4-methylphenoxymethyl, and 4-trifluoromethoxyphenoxymethyl groups, using polymer analogous reactions, in order to investigate the effect of the side group on their liquid crystal (LC) alignment behaviors. The polymers containing 4-fluorophenoxymethyl, 4-methylphenoxymethyl, or 4-trifluoromethoxyphenoxymethyl side groups had lower surface energy values and the LC cells fabricated using the unrubbed films of these polymers showed homeotropic LC alignment behavior. The LC cells fabricated using the rubbed films of the polymers containing phenoxymethyl or 4-fluorophenoxymethyl groups showed homogeneous planar LC alignment behavior in which the LCs were aligned perpendicular to the rubbing direction. This homogeneous planar and perpendicular alignment behavior was ascribed to the favorable anisotropic interactions between the LC molecules and the side groups preferentially oriented perpendicular to the rubbing direction.

• 한국보육지원학회지
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• 제9권1호
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• pp.201-220
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• 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.