• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1757-1771
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• 2017

Let K be a field and G be a group of its automorphisms. It follows from Speiser's generalization of Hilbert's Theorem 90, [10] that any K-semilinear representation of the group G is isomorphic to a direct sum of copies of K, if G is finite. In this note three examples of pairs (K, G) are presented such that certain irreducible K-semilinear representations of G admit a simple description: (i) with precompact G, (ii) K is a field of rational functions and G permutes the variables, (iii) K is a universal domain over field of characteristic zero and G its automorphism group. The example (iii) is new and it generalizes the principal result of [7].

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.507-509
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• 2015

This work aims to study the evolution of galaxies, located in the dense environment of the NGC 4095 compact group, which have recession velocities 6,000 < v ($km\;s^{-1}$) < 8,000. Imaging observations for BV $R_c$ broad-band, and [$S\small{II}$] and red-continuum narrow-band were carried out with the 2.4 m Thai National Telescope (TNT) at Doi Inthanon, Chiang Mai, Thailand. The sample contains 13 galaxies, consisting of 8 spirals, 4 ellipticals and 1 irregular morphological type. Late type galaxies tend to be bluer than early type galaxies. The results show that most of the late type galaxies have ongoing star formation activity, which could be triggered by galaxy-galaxy or tidal interactions, and that young massive stars in these galaxies cause their colors to be bluer than the early type galaxies.

• 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 ${\mathbb{S}}^{n+1}$.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.367-377
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• 2022

Let G be a non-discrete locally compact abelian group, and 𝜇 be a transformable and translation bounded Radon measure on G. In this paper, we construct a Segal algebra S_𝜇(G) in L¹(G) such that the generalized Poisson summation formula for 𝜇 holds for all f ∈ S_𝜇(G), for all x ∈ G. For the definitions of transformable and translation bounded Radon measures and the generalized Poisson summation formula, we refer to L. Argabright and J. Gil de Lamadrid's monograph in 1974.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.1-8
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• 2016

In this paper, we get a complete condition for a group homomorphism of a compact Lie group with an arbitrarily given left invariant Riemannian metric into another Lie group with a left invariant metric to be a harmonic map, and then obtain a necessary and sufficient condition for a group homomorphism of (SU(2), g) with a left invariant metric g into the Heisenberg group (H, $h_0$) to be a harmonic map.

• Journal of the Korean Mathematical Society
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• v.15 no.2
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• pp.163-165
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• 1979

• Bulletin of the Korean Mathematical Society
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• v.24 no.1
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• pp.41-41
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• 1987

• Journal of the Korean Mathematical Society
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• v.26 no.1
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• pp.27-32
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• 1989

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.691-699
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• 1997

The following statement is known as the generalized Hilbert-Smith conjecture : If G is a compact group and acts effectively on a manifold, then G is a Lie group. In this paper we prove that the generalized Hilbert-Smith conjecture is equivalent to the following : A known, but has never been published before.

• The Journal of Korean Obstetrics and Gynecology
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• v.15 no.4
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• pp.17-31
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• 2002

Objective : This study was carried out to investigate the effects of the hormones and cytokines associated with bone metabolism in ovariectomized rats. Method : Twenty-four Female-Sprague-Dawley rats were divided into sham operated(normal) group, ovariectomized(control)group, ovariectomized and treated with extract Caraganae Sinicae Radix(treated) group. Each group was investigated the changes of body weight at 3,5,7weeks after treatment, and femur weight, femur/body weight, thickness of compact bone of body of femur, area of cancellous bone of distal epiphysis of femur, serum estrogen, serum calcitonin, serum parathormone, serum Tumor Necrosis $Factor-{\alpha}$, serum $lnterleukin-1{\beta}$ at 7weeks after treatment. The results were summerized as follows; 1. The treated group showed significant change in body weight compared with the control group at 5,7weeks after treatment. 2. The treated group revealed significant increases in femur/body weight compared with the control group. 3. The treated group showed a little thicker compact bone of body of femur than the control group. 4. The area of cancellous bone of distal epiphysis of femur in treated group was increased significantly compared with control group. 5. The level of serum estrogen showed no change compared with control group. 6. The level of serum calcitonin showed no change compared with control group. 7. The level of serum parathormone was decreased in treated group significantly compared with control group. 8. The level of serum $TNF-{\alpha}$ was decreased in treated group significantly compared with control group. 9. The level of serum $interleukin-1{\beta}$ showed no change compared with control group. The results indicate that Caraganae Sinicae Radix inhibits bones resorption in ovariectomized rats by it's lowering effects on serum parathormone and $TNF-{\alpha}$.