• 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.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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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.

• Journal of Korean Society for Atmospheric Environment
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• v.13 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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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.

• 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.

• 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.

• English Language & Literature Teaching
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• v.12 no.4
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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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• v.17 no.7
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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.

• 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.