• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1193-1200
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• 2013

The center of the Lie group $SU(n)$ is isomorphic to $\mathbb{Z}_n$. If $d$ divides $n$, the quotient $SU(n)/\mathbb{Z}_d$ is also a Lie group. Such groups are locally isomorphic, and their Weyl groups $W(SU(n)/\mathbb{Z}_d)$ are the symmetric group ${\sum}_n$. However, the integral representations of the Weyl groups are not equivalent. Under the mod $p$ reductions, we consider the structure of invariant rings $H^*(BT^{n-1};\mathbb{F}_p)^W$ for $W=W(SU(n)/\mathbb{Z}_d)$. Particularly, we ask if each of them is a polynomial ring. Our results show some polynomial and non-polynomial cases.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.503-515
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• 2011

Let G be a compact connected semisimple Lie group, B the Killing form of the algebra g of G, and g the invariant metric induced by B. Then, we obtain a necessary and sufficient condition for a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) to be projectively flat (resp. Einstein-Weyl). And, we also get that if a left invariant linear connection D with a Weyl structure ($D,\;g,\;{\omega}$) on (G, g) which has symmetric Ricci tensor $Ric^D$ is projectively flat, then the connection D is Einstein-Weyl; but the converse is not true. Moreover, we show that if a left invariant connection D with Weyl structure ($D,\;g,\;{\omega}$) on (G, g) is projectively flat (resp. Einstein-Weyl), then D is a Yang-Mills connection.

• 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.

• Annual Conference of KIPS
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• 2011.04a
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• pp.43-45
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• 2011

Very Long Instruction Word (VLIW) executes multiple instructions in parallel. In order to exploit higher performance, i.e., higher parallelism, VLIW compiler groups as many instructions into one word as possible. In this paper, we show how to construct a VLIW C compiler based on GCC for CDSP32 (Compact Digital Signal Processor 32-bit) which is an embedded DSP processor to issue two instructions in one VLIW. Also, we evaluated the compiler on EEMBC benchmark; the experiment result showed that the total number of dynamic instructions of the VLIW compiler was reduced by 18% on average over without VLIW instruction scheduling.

• 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.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.98-98
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• 2011

We have investigated solar flare probability depending on sunspot classification, its area, and its area change using solar white light data. For this we used the McIntosh sunspot groups with most flare-productive regions : DKI, DKC, EKI, EKC, FKI and FKC. For each group, we classified it into three sub-groups according to sunspot area change : increase, steady, and decrease. For sunspot data, we used the NOAA active region information for 11 years (from January 2000 to December 2010): daily sunspot class and its area corrected for the projection effect. As a result, we find that the mean flare rates and the flare probabilities for the "increase" sub-groups are noticeably higher than those for other sub-groups. In case of the (M+X)-class flares of 'kc' groups, the mean flare rates of the "increase" sub-groups are more than two times than those of the "steady" sub-groups. This is statistical evidence that magnetic flux emergence is an very important for triggering solar flares since sunspot area increase can be a good proxy of magnetic flux emergence. In addition, we have examined the relationship between sunspot area and solar flare probability. For this, we classified each sunspot group into two sub-groups: large and small. In the case of compact group, the solar flare probabilities noticeably increase with its area.

• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.761-790
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• 2021

For given spaces X and Y, let map(X, Y) and map_*(X, Y) be the unbased and based mapping spaces from X to Y, equipped with compact-open topology respectively. Then let map(X, Y ; f) and map_*(X, Y ; g) be the path component of map(X, Y) containing f and map_*(X, Y) containing g, respectively. In this paper, we compute cohomotopy groups of suspended complex plane π^n+m(ΣⁿℂP²) for m = 6, 7. Using these results, we classify path components of the spaces map(ΣⁿℂP², S^m) up to homotopy equivalence. We also determine the generalized Gottlieb groups G_n(ℂP², S^m). Finally, we compute homotopy groups of mapping spaces map(ΣⁿℂP², S^m; f) for all generators [f] of [ΣⁿℂP², S^m], and Gottlieb groups of mapping components containing constant map map(ΣⁿℂP², S^m; *).

• Communications of the Korean Mathematical Society
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• v.23 no.2
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• pp.257-268
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• 2008

Let G and K be compact subgroups of orthogonal groups and $0{\leq}r<x<{\infty}$. We prove that every topological fiber bundle over a definable $C^r$ manifold whose structure group is K admits a unique strongly definable $C^r$ fiber bundle structure up to definable $C^r$ fiber bundle isomorphism. We prove that every G vector bundle over an affine definable $C^rG$ manifold admits a unique strongly definable $C^rG$ vector bundle structure up to definable $C^rG$ vector bundle isomorphism.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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• pp.88.2-88.2
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• 2012

We investigate solar flare occurrence rate and daily flare probability depending on McIntosh sunspot classification, its area, and its area change. For this we use the NOAA active region and GOES solar flare data for 15 years (from January 1996 to December 2010). We consider the most flare-productive 10 sunspot classification: 'Dko', 'Dai', 'Eai', 'Fai', 'Dki', 'Dkc', 'Eki', 'Ekc', 'Fki', and 'Fkc'. Sunspot area and its change can be a proxy of magnetic flux and its emergence/cancellation, respectively. we classify each sunspot group into two sub-groups: 'Large' and 'Small'. In addition, for each group, we classify it into three sub-groups according to sunspot group area change: 'Decrease', 'Steady', and 'Increase'. As a result, in the case of compact groups, their flare occurrence rates and daily flare probabilities noticeably increase with sunspot group area. We also find that the flare occurrence rates and daily flare probabilities for the 'Increase' sub-groups are noticeably higher than those for the other sub-groups. In case of the (M+X)-class flares of 'Dkc' group, the flare occurrence rate of the 'Increase' sub-group is three times higher than that of the 'Steady' sub-group. Mean flare occurrence rates and flare probabilities for all sunspot regions increase with the following order: 'Steady', 'Decrease', and 'Increase'. Our results statistically demonstrate that magnetic flux and its emergence enhance major solar flare occurrence. We are going to forecast solar flares based on these results and NOAA scale.