• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.67-75
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• 1984

Let X be a topological space. We consider a groupoid G over X and the quotient groupoid G/N for any normal subgroupoid N of G. The concept of groupoid (topological groupoid) is a natural generalization of the group(topological group). An useful example of a groupoid over X is the foundamental groupoid .pi.X whose object group at x.mem.X is the fundamental group .pi.(X, x). It is known [5] that if X is locally simply connected, then the topology of X determines a topology on .pi.X so that is becomes a topological groupoid over X, and a covering space of the product space X*X. In this paper the concept of the locally simple connectivity of a topological space X is applied to the groupoid G over X. That concept is defined as a term '1-connected local subgroupoid' of G. Using this concept we topologize the groupoid G so that it becomes a topological groupoid over X. With this topology the connected groupoid G is a covering space of the product space X*X. Further-more, if ob(.overbar.G)=.overbar.X is a covering space of X, then the groupoid .overbar.G is also a covering space of the groupoid G. Since the fundamental groupoid .pi.X of X satisfying a certain condition has an 1-connected local subgroupoid, .pi.X can always be topologized. In this case the topology on .pi.X is the same as that of [5]. In section 4 the results on the groupoid G are generalized to the quotient groupoid G/N. For any topological groupoid G over X and normal subgroupoid N of G, the abstract quotient groupoid G/N can be given the identification topology, but with this topology G/N need not be a topological groupoid over X [4]. However the induced topology (H) on G makes G/N (with the identification topology) a topological groupoid over X. A final section is related to the covering morphism. Let G$_{1}$ and G$_{2}$ be groupoids over the sets X$_{1}$ and X$_{2}$, respectively, and .phi.:G$_{1}$.rarw.G$_{2}$ be a covering spimorphism. If X$_{2}$ is a topological space and G$_{2}$ has an 1-connected local subgroupoid, then we can topologize X$_{1}$ so that ob(.phi.):X$_{1}$.rarw.X$_{2}$ is a covering map and .phi.: G$_{1}$.rarw.G$_{2}$ is a topological covering morphism.

• 한국초전도학회:학술대회논문집
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• v.12
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• pp.31-31
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• 2002

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.491-506
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• 2006

In this paper, we extend the concept of the group ${\varepsilon}(X)$ of self homotopy equivalences of a space X to that of an object in the category of pairs. Mainly, we study the group ${\varepsilon}(X,\;A)$ of pair homotopy equivalences from a CW-pair (X, A) to itself which is the special case of the extended concept. For a CW-pair (X, A), we find an exact sequence $1\;{\to}\;G\;{\to}\;{\varepsilon}(X,\;A)\;{to}\;{\varepsilon}(A)$ where G is a subgroup of ${\varepsilon}(X,\;A)$. Especially, for CW homotopy associative and inversive H-spaces X and Y, we obtain a split short exact sequence $1\;{\to}\;{\varepsilon}(X)\;{\to}\;{\varepsilon}(X{\times}Y,Y)\;{\to}\;{\varepsilon}(Y)\;{\to}\;1$ provided the two sets $[X{\wedge}Y,\;X{\times}Y]$ and [X, Y] are trivial.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.181-189
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• 2011

Let G be a group and X be a nonempty set and H be a subgroup of G. For a given ${\phi}_G\;:\;G{\times}X{\rightarrow}X$, a group action of G on X, we define ${\phi}_H\;:\;H{\times}X{\rightarrow}X$, a subgroup action of H on X, by ${\phi}_H(h,x)={\phi}_G(h,x)$ for all $(h,x){\in}H{\times}X$. In this paper, by considering a subgroup action of H on X, we have some results as follows: (1) If H,K are two normal subgroups of G such that $H{\subseteq}K{\subseteq}G$, then for any $x{\in}X$ ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}_H}(x)$) = ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}_K}(x)$) = ($orb_{{\phi}_K}(x)\;:\;orb_{{\phi}_H}(x)$); additionally, in case of $K{\cap}stab_{{\phi}_G}(x)$ = {1}, if ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}H}(x)$) and ($orb_{{\phi}_K}(x)\;:\;orb_{{\phi}_H}(x)$) are both finite, then ($orb_{{\phi}_G}(x)\;:\;orb_{{\phi}_H}(x)$) is finite; (2) If H is a cyclic subgroup of G and $stab_{{\phi}_H}(x){\neq}$ {1} for some $x{\in}X$, then $orb_{{\phi}_H}(x)$ is finite.

• Journal of Genetic Medicine
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• v.6 no.1
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• pp.67-73
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• 2009

Purpose : In spite of the karyotype and phenotype diversity in Turner syndrome patients, there are few reports about such differences in Korea. We reviewed the data of chromosome abnormalities, clinical manifestations, and comorbidities of Turner syndrome patients in Kyungpook National University Hospital to compare them to the recent hypotheses about sex chromosome gene loci related to Turner symptoms. Materials and Methods : We identified the cytologic findings of 92 patients with Turner syndrome and the clinical findings of 62 patients among them. Results : 54.3 percent of patients had 45,X while 45.7 percent showed other karyotype combinations (45,X/46,XX, 45,X/46,XX/47,XXX, 46,X,del(Xp), 46,X,del(Xq), 45,X/46,X,del(Xq), 46,X,i(Xq), 45,X/46,X,i (Xq)). The Turner symptoms found included short neck, high arched palate, broad chest, Madelung deformity, short metacarpals, scoliosis, cubitus valgus, low hair line, webbed neck, edematous extremities, pigmented nevus, and sexual infantilism. The specific diseases associated Turner syndrome included renal abnormalities, congenital heart disease, hearing defects, diabetes mellitus, hyperlipidemia, and decreased bone density. The phenotype of the mosaicism group was milder than that of the monosomy group. In the case of 46,X,del(Xp) and 45,X/46,X,del(Xq) groups, all had skeletal abnormalities, but the 46,X,del(Xq) group had none. In the case of 46,X,del(Xp) group, all showed short statures and skeletal abnormalities, but no sexual infantilism was observed. In the case of 46,X,i(Xq) and 45,X/46,X,i(Xq) groups, they all showed delayed puberty and had primary amenorrhea. Conclusion : It is important to study karyotype-phenotype correlations in patients with Turner syndrome to obtain interesting information about the genotype-phenotype correlations related to the X chromosome.

• Current Photovoltaic Research
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• v.11 no.2
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• pp.39-43
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• 2023

Carrier-selective contacts (CSCs) solar cells are considerably attractive on highly efficient crystalline silicon heterojunction (SHJ) solar cells due to their advantages of high thermal tolerance and the simple fabrication process. CSCs solar cells require a hole selective contact (HSC) layer that selectively collects only holes. In order to selectively collect holes, it must have a work function characteristic of 5.0 eV or more when contacted with n-type Si. The VO_x, NiO_x, and CuI_x thin films were fabricated and analyzed respectively to confirm their potential usage as a hole-selective contact (HSC) layer. All thin films showed characteristics of band-gap engergy > 3.0 eV, work function > 5.0 eV and minority carrier lifetime > 1.5 ms.

• BMB Reports
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• v.46 no.2
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• pp.86-91
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• 2013

Glucose effects on the vegetative growth of Dictyostelium discoideum Ax2 were studied by examining oxidative stress and tetrahydropteridine synthesis in cells cultured with different concentrations (0.5X, 7.7 g $L^{-1}$; 1X, 15.4 g $L^{-1}$; 2X, 30.8 g $L^{-1}$) of glucose. The growth rate was optimal in 1X cells (cells grown in 1X glucose) but was impaired drastically in 2X cells, below the level of 0.5X cells. There were glucose-dependent increases in reactive oxygen species (ROS) levels and mitochondrial dysfunction in parallel with the mRNA copy numbers of the enzymes catalyzing tetrahydropteridine synthesis and regeneration. On the other hand, both the specific activities of the enzymes and tetrahydropteridine levels in 2X cells were lower than those in 1X cells, but were higher than those in 0.5X cells. Given the antioxidant function of tetrahydropteridines and both the beneficial and harmful effects of ROS, the results suggest glucose-induced oxidative stress in Dictyostelium, a process that might originate from aerobic glycolysis, as well as a protective role of tetrahydropteridines against this stress.

• Journal of the Korean Ceramic Society
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• v.40 no.4
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• pp.346-349
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• 2003

Microwave dielectric characteristics and physical properties of the new Zr$_{1-x}$ (Bn$_{1}$3/Nb$_{2/3}$)xTi $O_4$ (0.2$\leq$x$\geq$ 1.0) system have been investigated as a function of the amount of Bn$_{1}$3/Nb$_{2/3}$ $O_2$substitution. With increasing Bn$_{1}$3/Nb$_{2/3}$ $O_2$ content (x), two phase regions were observed: $\alpha$-Pb $O_2$ solid solution (x<0.4), mixture of the rutile type Zn$_{1}$3/Nb$_{2/3}$Ti $O_4$ and the $\alpha$-Pb $O_2$ solid solution (x$\geq$0.4). In the$\alpha$-Pb $O_2$solid solution region below x<0.4, the Q.f$_{0}$ value sharply increased and the Temperature Coefficient of the Resonant Frequency(TCF) decreased with increasing Bn$_{1}$3/Nb$_{2/3}$ $O_2$ contents while dielectric constant (K) showed nearly same value. In the mixture region above x$\geq$4, the dielectric constant and TCF increased with increasing Bn$_{1}$3/Nb$_{2/3}$ $O_2$ content. Zr$_{1-x}$ (Zn$_{1}$3/Nb$_{2/3}$)xTi $O_4$ materials have excellent microwave dielectric properties with K=44.0, Q.f$_{0}$ : 41000 GHz and TCF =-3.0 ppm/$^{\circ}C$ at x=0.35.=0.35. x=0.35.=0.35.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.109-115
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• 2020

Recently, Lesieutre constructed a 6-dimensional projective variety X over any field of characteristic zero whose automorphism group Aut(X) is discrete but not finitely generated. As an application, he also showed that X is an example of a projective variety with infinitely many non-isomorphic real structures. On the other hand, there are also several finiteness results of real structures of projective varieties. The aim of this short paper is to give a sufficient condition for the finiteness of real structures on a projective manifold in terms of the structure of the automorphism group. To be more precise, in this paper we show that, when X is a projective manifold of any dimension≥ 2, if Aut(X) does not contain a subgroup isomorphic to the non-abelian free group ℤ ∗ ℤ, then there are only finitely many real structures on X, up to ℝ-isomorphisms.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1371-1385
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• 2019

Given a topological space X and a non-negative integer k, ${\varepsilon}^{\sharp}_k(X)$ is the set of all self-homotopy equivalences of X that do not change maps from X to an t-sphere $S^t$ homotopically by the composition for all $t{\geq}k$. This set is a subgroup of the self-homotopy equivalence group ${\varepsilon}(X)$. We find certain homotopic tools for computations of ${\varepsilon}^{\sharp}_k(X)$. Using these results, we determine ${\varepsilon}^{\sharp}_k(M(G,n))$ for $k{\geq}n$, where M(G, n) is a Moore space type of (G, n) for a finitely generated abelian group G.