• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.773-785
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• 2022

In this paper, we propose the notion of a distance between n points, called a g-metric, which is a further generalized G-metric. Indeed, it is shown that the g-metric with dimension 2 is the ordinary metric and the g-metric with dimension 3 is equivalent to the G-metric.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.169-176
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• 1997

The purpose of this note is to compare two known results related to the lifting problem of an action of a topological group G on a G-space X to a coverring space of X.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.13-23
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• 2022

Let G be a semialgebraic group not necessarily compact. Let M be a proper semialgebraic G-set whose orbit space has a semialgebraic structure. In this paper, we prove the embeddability of M into a G-representation space when G is linear.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1231-1252
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• 2006

In this paper we shall explicitly calculate the formula of the algebraic presentation of an embedding of the Teichmiiller space ${\Im}(M)$ into the Goldman space g(M). From this algebraic presentation, we shall show that the Goldman's length parameter on g(M) is an isometric extension of the Fenchel-Nielsen's length parameter on ${\Im}(M)$.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.1
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• pp.55.4-56
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• 2017

Complex organic molecules (COMs) are commonly detected in star forming regions and considered important species since they are seeds of prebiotic molecules. Although COMs form in ice mantles on dust grains, they are preferentially detected in the gas phase. The origin of the gaseous COMs highly depends on the circumstance of each star forming region. Therefore, the distribution of COMs emission reflects the physical and chemical conditions of the region. We present the newly detected COMs, especially methanol emission lines toward two massive star forming regions, G19.61-0.23 and G75.78+0.34 in the Atacama Large Millimeter/submillimeter Array Band 3 observations during the Cycle 2 phase. Multiple transitions of methanol are detected in both regions but show different emission morphology. The origin of the desorption (e.g. shocks or high energy photons) is discussed.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.1
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• pp.34.1-34.1
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• 2017

The GMT-Consortium Large Earth Finder (G-CLEF) is the very first light instrument of the Giant Magellan Telescope (GMT). The instrument is a fiber feed, optical band echelle spectrograph that is capable of extremely precise radial velocity measurement, and has been being developed through the international consortium consisted of five astronomical institutes including Smithsonian Astrophysical Observatory (SAO), Observatories of the Carnegie Institution of Washington (OCIW), and Korea Astronomy and Space Science Institute (KASI). The Preliminary Design Review (PDR) for the G-CLEF was held in Cambridge, Massachusetts in April 2015. It is scheduled to have Critical Design Review (CDR) in March 2018. Flexure Control Camera (FCC) is one of the KASI's major contributions to the G-CLEF project. In this presentation, we describe the current critical design status, and structural and thermo-elastic analyses results on the G-CLEF FCC.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.635-646
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• 2024

In this research work, we introduce and investigate four innovative types of soft spaces, pushing the boundaries of traditional spatial concepts. These new types of soft spaces are named as soft T_b space, soft T^#_b space, soft T^##_b space and soft_αT^#_b space. Through rigorous analysis and experimentation, we uncover and propose distinct characteristics that define and differentiate these spaces. In this research work, we have established that every soft $T_{\frac{1}{2}}$ space is a soft _αT^#_b space, every soft T_b space is a soft _αT^#_b space, every soft T^#_b space is a soft _αT^#_b space, every soft T_b space is a soft T^#_b space, every soft T^#_b space is a soft T^##_b space, every soft $T_{\frac{1}{2}}$ space is a soft ^#T_b space and every soft T_b space is a soft #T_b space.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.391-397
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• 2017

In this note we extend our previous result about the structure of the dual of a crossed product $C^*$-algebra $A{\rtimes}_{\sigma}G$, when G is a finite group. We consider the space $\tilde{\Gamma}$ which consists of pairs of irreducible representations of A and irreducible projective representations of subgroups of G. Our goal is to endow $\tilde{\Gamma}$ with a topology so that the orbit space e $G{\backslash}{\tilde{\Gamma}}$ is homeomorphic to the dual of $A{\rtimes}_{\sigma}G$. In particular, we will show that if $\widehat{A}$ is Hausdorff then $G{\backslash}{\tilde{\Gamma}}$ is homeomorphic to $\widehat{A{\rtimes}_{\sigma}G}$.

• Kyungpook Mathematical Journal
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• v.45 no.1
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• pp.45-53
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• 2005

A basis of the cycle space C (G) is d-fold if each edge occurs in at most d cycles of C(G). The basis number, b(G), of a graph G is defined to be the least integer d such that G has a d-fold basis for its cycle space. MacLane proved that a graph G is planar if and only if $b(G)\;{\leq}\;2$. Schmeichel showed that for $n\;{\geq}\;5,\;b(K_{n}\;{\bullet}\;P_{2})\;{\leq}\;1\;+\;b(K_n)$. Ali proved that for n, $m\;{\geq}\;5,\;b(K_n\;{\bullet}\;K_m)\;{\leq}\;3\;+\;b(K_n)\;+\;b(K_m)$. In this paper, we give an upper bound for the basis number of the semi-strong product of a bipartite graph with a cycle.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.245-259
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• 2007

We define and study a concept of $T^f$-space for a map, which is a generalized one of a T-space, in terms of the Gottlieb set for a map. We show that X is a $T_f$-space if and only if $G({\Sigma}B;A,f,X)=[{\Sigma}B,X]$ for any space B. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain a sufficient condition to having a lifting $T^{\bar{f}}$-structure on $E_k$ of a $T^f$-structure on X. Also, we define and study a concept of co-$T^g$-space for a map, which is a dual one of $T^f$-space for a map. We obtain a dual result for a principal cofibration $i_r:X{\rightarrow}C_r$ induced by $r:X^{\prime}{\rightarrow}X$ from ${\iota}:X^{\prime}{\rightarrow}cX^{\prime}$.