• Korean Journal of Mathematics
• /
• v.4 no.1
• /
• pp.45-49
• /
• 1996

Let $F_0$ be the maximal real subfield of $\mathbb{Q}({\zeta}_q+{\zeta}_q^{-1})$ and $F_{\infty}={\cup}_{n{\geq}0}F_n$ be its basic $\mathbb{Z}_p$-extension. Let $A_n$ be the Sylow $p$-subgroup of the ideal class group of $F_n$. The aim of this paper is to examine the injectivity of the natural $mapA_n{\rightarrow}A_m$ induced by the inclusion $F_n{\rightarrow}F_m$ when $m>n{\geq}0$. By using cyclotomic units of $F_n$ and by applying cohomology theory, one gets the following result: If $p$ does not divide the order of $A_1$, then $A_n{\rightarrow}A_m$ is injective for all $m>n{\geq}0$.

• Proceedings of the KSMRM Conference
• /
• 2003.10a
• /
• pp.49-53
• /
• 2003

확산텐서영상(Diffusion Tensor Imaging)의 개념은 1980년대 중반 확산강조영상(Diffusion Weighted Imaging)의 개념이 도입되면서 거의 동시에 도입되었지만 MR 장비의 기계적 한계등으로 인해 최근에야 임상적으로 사용되기 시작했다. 확산텐서영상(DTI)과 확산강조영상(DWI)의 방법론적인 차이점은 단순히 확산강조영상의 경우 세 개의 다른방향 (X-, Y-, Z-축)으로 확산측정용 경사자장을 가하는 반면 확산텐서영상의 경우 이보다 많은 방향 (최소한 6 방향)으로 확산측정용 경사자장을 가한다는 점이다. 이러한 차이로부터 금방 알 수 있는 점은 확산강조영상은 확산텐서영상의 일부라는 점이다. 즉, 확산텐서영상의 경우 더 많은 방향으로 확산측정용 경사자장을 가했으므로 더 많은 정보를 획득할 수 있고 이중 세 개의 방향 (주로 X,Y,Z)에 대한 정보만을 이용하게 되면 확산강조영상이다. 이러한 이유로 확산텐서영상을 획득하면 확산강조영상에서 얻게 되는 방향별 확산강조영상, 등방성(isotropic) 확산강조영상, ADC (Apparent Diffusion Coefficient) map등도 기본적으로 얻게 되므로 추가로 확산강조영상을 획득할 필요가 없다. 본 강의에서는 이러한 확산(텐서)영상의 물리적 원리를 복잡한 수학적 설명보다는 개념 위주로 설명해 보고자 한다.

• Korean Journal of Computational Design and Engineering
• /
• v.10 no.2
• /
• pp.107-113
• /
• 2005

Octree-based algorithm is developed for machining simulation. Most of commercial machining simulators are based on Z map model, which have several limitations to get a high precision in 5 axis machining simulation. Octree representation is three dimensional decomposition method. So it is expected that these limitations be overcome by using octree based algorithm. By using the octree model, storage requirement is reduced. And also recursive subdivision was processed in the boundaries, which reduces useless computation. The supersampling method is the most common form of the anti-aliasing and usually used with polygon mesh rendering in computer graphics. Supersampling technique is applied for advancing its efficiency of the octree algorithm.

• The Pure and Applied Mathematics
• /
• v.6 no.1
• /
• pp.39-45
• /
• 1999

The concept of pseudoLindelof spaces is introduced. It is shown that the followings are equivalent: (a) for any two disjoint zero-sets in X, at least one of them is Lindelof, (b) $\mid$vX{\;}-{\;}X$\mid${\leq}{\;}1$, and (c) for any space T with $X{\;}{\subseteq}{\;}T$, there is an embedding $f{\;}:{\;}vX{\;}{\rightarrow}{\;}vT$ such that f(x) = x for all $x{\;}{\in}{\;}X$ and that if $X{\;}{\times}{\;}Y$ is a z-embedded pseudoLindelof subspace of $vX{\;}{\times}{\;}vY,{\;}then{\;}v(X{\;}{\times}{\;}Y){\;}={\;}vX{\;}{\times}{\;}vY$.

• Honam Mathematical Journal
• /
• v.35 no.2
• /
• pp.303-310
• /
• 2013

In this paper, we first show that $z_{{\kappa}X}:E_{cc}({\kappa}X){\rightarrow}{\kappa}X$ is $z^{\sharp}$-irreducible and that if $\mathcal{G}(E_{cc}({\beta}X))$ is a base for closed sets in ${\beta}X$, then $E_{cc}({\kappa}X)$ is $C^*$-embedded in $E_{cc}({\beta}X)$, where ${\kappa}X$ is the extension of X such that $vX{\subseteq}{\kappa}X{\subseteq}{\beta}X$ and ${\kappa}X$ is weakly Lindel$\ddot{o}$f. Using these, we will show that if $\mathcal{G}({\beta}X)$ is a base for closed sets in ${\beta}X$ and for any weakly Lindel$\ddot{o}$f space Y with $X{\subseteq}Y{\subseteq}{\kappa}X$, ${\kappa}X=Y$, then $kE_{cc}(X)=E_{cc}({\kappa}X)$ if and only if ${\beta}E_{cc}(X)=E_{cc}({\beta}X)$.

• The Bulletin of The Korean Astronomical Society
• /
• v.44 no.2
• /
• pp.49.1-49.1
• /
• 2019

I present the mean metallicity distribution of stars in the Milky Way based on photometry from the Sloan Digital Sky Survey. I utilize an empirically calibrated set of stellar isochrones developed in previous work to estimate the metallicities of individual stars to a precision of 0.2 dex for reasonably bright stars across the survey area. I also obtain more precise metallicity estimates using priors from the Gaia parallaxes for relatively nearby stars. Close to the Galactic mid-plane (|Z| < 2 kpc), a mean metallicity map reveals deviations from the mirror symmetry between the northern and southern hemispheres, displaying wave-like oscillations. The observed metallicity asymmetry structure is almost parallel to the Galactic mid-plane, and coincides with the previously known asymmetry in the stellar number density distribution. This result reinforces the previous notion of the plane-parallel vertical waves propagating through the disk, which have been excited by a massive halo substructure such as the Sagittarius dwarf galaxy plunging through the Milky Way's disk. This work provides evidence that the Gaia phase-space spiral may continue out to |Z| ~ 1.5 kpc.

• The Bulletin of The Korean Astronomical Society
• /
• v.44 no.2
• /
• pp.76.2-76.2
• /
• 2019

Recent observation of the neutron star merger event, GW170817, through both gravitational wave (GW) and electromagnetic wave (EM) observations opened a new way of exploring the universe, namely, multi-messenger astronomy (MMA). One of the keys to the success of MMA is a rapid identification of EM counterpart. We will introduce the strategy for prioritization of GW source host galaxy candidates. Our method relies on recent simulation results regarding plausible properties of GW source host galaxies and the low latency localization map from LIGO/Virgo. We will show the test results for both NS merger and BH merger events using previous events and describe observing strategy with our facilities for GW events during the ongoing LIGO/Virgo O3 run. Finally, we report the result of follow-up observation on, the first neutron star merger event, S190425z, during LIGO/VIrgo O3 run.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.599-612
• /
• 2017

If ${\psi}$ is analytic on the open unit disk $\mathbb{D}$ and ${\varphi}$ is an analytic self-map of $\mathbb{D}$, the weighted composition operator $C_{{\psi},{\varphi}}$ is defined by $C_{{\psi},{\varphi}}f(z)={\psi}(z)f({\varphi}(z))$, when f is analytic on $\mathbb{D}$. In this paper, we study normal, cohyponormal, hyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces. First, for some weighted Hardy spaces $H^2({\beta})$, we prove that if $C_{{\psi},{\varphi}}$ is cohyponormal on $H^2({\beta})$, then ${\psi}$ never vanishes on $\mathbb{D}$ and ${\varphi}$ is univalent, when ${\psi}{\not\equiv}0$ and ${\varphi}$ is not a constant function. Moreover, for ${\psi}=K_a$, where |a| < 1, we investigate normal, cohyponormal and hyponormal weighted composition operators $C_{{\psi},{\varphi}}$. After that, for ${\varphi}$ which is a hyperbolic or parabolic automorphism, we characterize all normal weighted composition operators $C_{{\psi},{\varphi}}$, when ${\psi}{\not\equiv}0$ and ${\psi}$ is analytic on $\bar{\mathbb{D}}$. Finally, we find all normal weighted composition operators which are bounded below.

• The Bulletin of The Korean Astronomical Society
• /
• v.43 no.2
• /
• pp.33.3-34
• /
• 2018

Galaxy clusters contain a diffuse component of stars outside galaxies, that is observed as intracluster light (ICL). Since the ICL abundance increases during various dynamical exchanges of galaxies, the amount of ICL can act as a measurement tool for the dynamical stage of galaxy clusters. There are two prominent ICL formation scenarios; one is related to the brightest cluster galaxy (BCG) major mergers, and the other to the tidal stripping of galaxies. However, it is still under debate as to which is the main ICL formation mechanism. In this study we improve on earlier observational constraints of the ICL origin, by investigating it in a massive fossil cluster at z~0.47. Fossil clusters are believed to be dynamically matured galaxy clusters which have dominant BCGs. Recent simulation studies imply that, BCGs have assembled 85~90% of their mass by z~0.4 (e.g., Contini et al. 2014). Thus our target is an optimal test bed to examine the BCG-related scenario. Our deep images and Multi-Object Spectroscopic observations of the target fossil cluster (Gemini North 2018A) allow us to extract the ICL distribution, ICL color map and ICL fraction to cluster light. We will present a possible constraint of the ICL origin and discuss its connection to the BCG and the host galaxy cluster.

• The Bulletin of The Korean Astronomical Society
• /
• v.40 no.2
• /
• pp.30.2-30.2
• /
• 2015

Abell 2744 is a giant merging cluster, called the Pandora's Cluster, at the redshift of z=0.308 (corresponding to a distance of 1270 Mpc). Taking the advantage of the deep high resolution images in the Hubble Frontier Field program, we study the properties of compact stellar systems including globular clusters and ultracompact dwarfs (UCDs) as well as dwarf galaxies in this cluster. We find a rich population of globular clusters and UCDs in Abell 2744. The spatial distribution of these objects is consistent with the mass map derived from lensing analysis, while showing a significant offset from the X-ray map of hot gas. The faint end of the luminosity function of the galaxies in the red sequence is fit by a flat slope, showing no faint upturn. We discuss these finding in relation with the origin of UCDs, formation of red sequence dwarf galaxies, and formation of the Pandora's cluster.