• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.309-317
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• 2003

In this paper we study the relation of Euler characteristic with respect to cohomology with compact support in F$_{p}$-coefficient for the fibration of ENR's and generalize some properties on proper G-spaces for locally compact Lie group G.G.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.2
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• pp.34.2-34.2
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• 2016

We study the mid-infrared (MIR) properties of galaxies in compact groups and their environmental dependence using the Wide-field Infrared Survey Explorer data. We use a sample of 670 compact groups and their 2175 member galaxies with $M_r$ < -19 and 0.01 < z < 0.0741 from Sohn et al. (2016), which were identified through a friends-of-friends algorithm. We find that the MIR [3.4]-[12] colors of early-type galaxies in compact groups are on average bluer than those of early-type galaxies in clusters. Furthermore, we find that when compact groups have both early- and late-type member galaxies, the MIR colors of the late-type galaxies in those compact groups can be bluer than those of late-type galaxies in clusters. We also find that as background galaxy number densities of compact groups increase, compact group galaxies have higher early-type galaxy fractions and bluer MIR colors. These trends are also seen for background galaxies. However, at a given background density, compact group galaxies always have higher early-type galaxy fractions and bluer MIR colors than the background galaxies. Our findings suggest that the properties of compact group galaxies depend on both internal and external environments of the compact groups, and that galaxy evolution is faster in compact groups than in clusters.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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• pp.48.2-48.2
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• 2012

We present preliminary results of a statistical study on the nuclear activity of compact group galaxies. What triggers Active Galactic Nuclei (AGN) is still a puzzling problem. One of the suggested AGN triggering mechanisms is galaxy-galaxy interaction. Many simulations have shown that gas can be supplied to the center of galaxies during galaxy encounters. In this regard, compact groups of galaxies are an ideal laboratory for studying the connection between galaxy interaction and nuclear activity because of their high densities and low velocity dispersions. We study the environmental dependence of the activity in galactic nuclei using 59 compact groups in the SDSS DR6. Using the emission line data, we classify galaxies in the compact groups. We find that 19% of the compact group galaxies are pure star-forming nuclei, 10% as transition objects, and only 7% of the galaxies in compact groups show the nuclear activity. The AGN fraction of compact group is higher than galaxy clusters, but lower than field environment. Implications of this result will be discussed.

• 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 Mathematical Society
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• v.26 no.1
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• pp.47-52
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• 1989

Methods of Riemannian geometry has played an important role in the study of compact transformation groups. Every effective action of a compact Lie group on a differential manifold leaves a Riemannian metric invariant and the study of such actions reduces to the one involving the group of isometries of a Riemannian metric on the manifold which is, a priori, a Lie group under the compact open topology. Once an action of a compact Lie group is given an invariant metric is easily constructed by the averaging method and the Lie group is naturally imbedded in the group of isometries as a Lie subgroup. But usually this invariant metric has more symmetries than those given by the original action. Therefore the first question one may ask is when one can find a Riemannian metric so that the given action coincides with the action of the full group of isometries. This seems to be a difficult question to answer which depends very much on the orbit structure and the group itself. In this paper we give a sufficient condition that a subgroup action of a compact Lie group has an invariant metric which is not invariant under the full action of the group and figure out some aspects of the action and the orbit structure regarding the invariant Riemannian metric. In fact, according to our results, this is possible if there is a larger transformation group, containing the oringnal action and either having larger orbit somewhere or having exactly the same orbit structure but with an orbit on which a Riemannian metric is ivariant under the orginal action of the group and not under that of the larger one. Recently R. Saerens and W. Zame showed that every compact Lie group can be realized as the full group of isometries of Riemannian metric. [SZ] This answers a question closely related to ours but the situation turns out to be quite different in the two problems.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.143-148
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• 2001

First, we show the finiteness property of the homotopy fixed point set of p-discrete toral group. Let $G_\infty$ be a p-discrete toral group and X be a finite complex with an action of $G_\infty such that X^K$ is nilpotent for each finit p-subgroup K of $G_\infty$. Assume X is $F_\rho-complete$. Then X(sup)hG$\infty$ is F(sub)p-finite. Using this result, we give the condition so that X$^{hG}$ is $F_\rho-finite for \rho-compact$ toral group G.

• Journal of The Korean Astronomical Society
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• v.48 no.6
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• pp.381-398
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• 2015

Dynamical analysis of compact groups provides important tests of models of compact group formation and evolution. By compiling 2066 redshifts from FLWO/FAST, from the literature, and from SDSS DR12 in the fields of compact groups in , we construct the largest sample of compact groups with complete spectroscopic redshifts in the redshift range 0.01 < z < 0.22. This large redshift sample shows that the interloper fraction in the compact group candidates is ~ 42%. A secure sample of 332 compact groups includes 192 groups with four or more member galaxies and 140 groups with three members. The fraction of early-type galaxies in these compact groups is 62%, higher than for the original Hickson compact groups. The velocity dispersions of early-and late-type galaxies in compact groups change little with groupcentric radius; the radii sampled are less than 100 h⁻¹ kpc, smaller than the radii typically sampled by members of massive clusters of galaxies. The physical properties of our sample compact groups include size, number density, velocity dispersion, and local environment; these properties slightly differ from those derived for the original Hickson compact groups and for the DPOSS II compact groups. Differences result from subtle differences in the way the group candidates were originally selected. The abundance of the compact groups changes little with redshift over the range covered by this sample. The approximate constancy of the abundance for this sample is a potential constraint on the evolution of compact groups on a few Gigayear timescale.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.1
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• pp.37.1-37.1
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• 2013

We present a result of a statistical studies on nuclear activities of compact group galaxies. It is suggested that the galaxy interaction can trigger the nuclear activity by producing the gas inflow to the center of galaxies. To understand the connection between galaxy interaction and nuclear activity, we study the fraction of Active Galactic Nuclei (AGN) host galaxies in compact groups, known as the most favored environment for galaxy interaction. We select 59 spectroscopically confirmed compact groups in the SDSS DR6. Using the emission line ratio, we determine the spectral types of compact group galaxies and obtain the fraction of AGN-host galaxies. We compare this fraction with those in other galaxy environments. For the early type galaxies, we find that the AGN fraction of compact group galaxies are lower than field galaxies, but higher than cluster galaxies. On the other hand, the AGN fraction of compact group galaxies is similar to those for field and cluster environment for the late type galaxies. Implications of this result will be discussed.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.717-723
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• 1997

The compact transformation group has been developed with lots of properties. Many properties which are satisfied on G-space for compact group G do not hold for noncompact case. To recover some theory on spaces with noncompact group action we give some restriction on G-spaces. Hence we introduced Cartan G-spaces and proper G-spaces for our goal and we prove some properties on these G-spaces with noncompact G.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.749-755
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• 2010

We investigate biprojectivity of $C_{r}^{*}(G)$ as a $L^1(G)$-bimodule for a locally compact group G. The main results are the following. As a $L^1(G)$-bimodule$C_{r}^{*}(G)$ is biprojective if G is compact and is not biprojective if G is an infinite discrete group or G is a non-compact abelian group.