• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.645-648
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• 2005

Let K be a Galois extension of a field F with G = Gal(K/F). Let L be an extension of F such that $K\;{\otimes}_F\;L\;=\; N_1\;{\oplus}N_2\;{\oplus}{\cdots}{\oplus}N_k$ with corresponding primitive idempotents $e_1,\;e_2,{\cdots},e_k$, where Ni's are fields. Then G acts on $\{e_1,\;e_2,{\cdots},e_k\}$ transitively and $Gal(N_1/K)\;{\cong}\;\{\sigma\;{\in}\;G\;/\;{\sigma}(e_1)\;=\;e_1\}$. And, let R be a commutative F-algebra, and let P be a prime ideal of R. Let T = $K\;{\otimes}_F\;R$, and suppose there are only finitely many prime ideals $Q_1,\;Q_2,{\cdots},Q_k$ of T with $Q_i\;{\cap}\;R\;=\;P$. Then G acts transitively on $\{Q_1,\;Q_2,{\cdots},Q_k\},\;and\;Gal(qf(T/Q_1)/qf(R/P))\;{\cong}\;\{\sigma{\in}\;G/\;{\sigma}-(Q_1)\;=\;Q_1\}$ where qf($T/Q_1$) is the quotient field of $T/Q_1$.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.115-129
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• 2005

In this paper, we give a digital graph-theoretical approach of the study of digital images with relation to a simplicial complex. Thus, a digital graph $G_k$ with some k-adjacency in ${\mathbb{Z}}^n$ can be recognized by the simplicial complex spanned by $G_k$. Moreover, we demonstrate that a graphically $(k_0,\;k_1)$-continuous map $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}}^{n_1}$ can be converted into the simplicial map $S(f):S(G_{k_0}){\rightarrow}S(G_{k_1})$ with relation to combinatorial topology. Finally, if $G_{k_0}$ is not $(k_0,\;3^{n_0}-1)$-homotopy equivalent to $SC^{n_0,4}_{3^{n_0}-1}$, a graphically $(k_0,\;k_1)$-continuous map (respectively a graphically $(k_0,\;k_1)$-isomorphisim) $f:G_{k_0}{\subset}{\mathbb{Z}}^{n_0}{\rightarrow}G_{k_1}{\subset}{\mathbb{Z}^{n_1}$ induces the group homomorphism (respectively the group isomorphisim) $S(f)_*:{\pi}_1(S(G_{k_0}),\;v_0){\rightarrow}{\pi}_1(S(G_{k_1}),\;f(v_0))$ in algebraic topology.

• Journal of Ginseng Research
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• v.35 no.1
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• pp.86-91
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• 2011

Ginsenoside (G)-F1 is an enzymatic metabolite generated from G-Rg1. Although this metabolite has been reported to suppress platelet aggregation and to reduce gap junction-mediated intercellular communication, the modulatory activity of G-F1 on the functional role of skin-derived cells has not yet been elucidated. In this study, we evaluated the regulatory role of G-F1 on the cellular responses of B16 melanoma cells. G-F1 strongly suppressed the proliferation of B16 cells up to 60% at 200 ${\mu}g/mL$, while only diminishing the viability of HEK293 cells up to 30%. Furthermore, G-F1 remarkably induced morphological change and clustering of B16 melanoma cells. The melanin production of B16 cells was also significantly blocked by G-F1 up to 70%. Interestingly, intracellular signaling events involved in cell proliferation, migration, and morphological change were up-regulated at 1 h incubation but down-regulated at 12 h. Therefore, our results suggest that G-F1 can be applied as a novel anti-skin cancer drug with anti-proliferative and anti-migration features.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.91-103
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• 2007

In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by $f(x{\ast}y)+f(x{\ast}y^{-1})-2g(x)-2g(y)={\varphi}(x,y)$, $f(x{\ast}y)+g(x{\ast}y^{-1})-2h(x)-2k(y)={\varphi}(x,y)$, where (G, *) is a group, X is a real or complex Hausdorff topological vector space and f, g, h, k are functions from G into X.

• The Journal of the Korea Contents Association
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• v.2 no.2
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• pp.91-97
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• 2002

Let (X, F, g) be a fuzzy measure space. Then for any h$\in$ $L^{0}$ (X) , a$\in$[0 , 1] , and $A\in$F ∫$_{A}$aㆍh($\chi$)┬g＝aㆍ∫$_{A}$h($\chi$)┬g with the t-seminorm ┬(x, y)= xy. And we prove that the Seminormed fuzzy integral has some linearity properties only for ｛0,1｝-classes of fuzzy measure as follow, For any f, h$\in$ $L^{0}$ ($\chi$), any a, b$\in$R+: af＋bh$\in$ $L^{0}$ ($\chi$)⇒ ∫$_{A}$(af＋bh)┬g＝a∫$_{A}$f┬g＋b∫$_{A}$h┬g; if and only if g is a probability measure fulfilling g(A) $\in$｛0, 1｝ for all $A\in$F.n$F.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.103-114
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• 2008

In this paper, we investigate the superstability problem for the pexiderized cosine functional equations f(x+y) +f(x−y) = 2g(x)h(y), f(x + y) + g(x − y) = 2f(x)g(y), f(x + y) + g(x − y) = 2g(x)f(y). Consequently, we have generalized the results of stability for the cosine($d^{\prime}Alembert$) and the Wilson functional equations by J. Baker, $P.\;G{\check{a}}vruta$, R. Badora and R. Ger, and G.H. Kim.

• Journal of Ginseng Research
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• v.45 no.6
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• pp.695-705
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• 2021

Background: Ginsenosides have beneficial effects on several airway inflammatory disorders primarily through glucocorticosteroid-like anti-inflammatory activity. Among inflammatory cells, eosinophils play a major pathogenic role in conferring a risk of severe refractory diseases including chronic rhinosinusitis (CRS). However, the role of ginsenosides in reducing eosinophilic inflammation and CRS pathogenesis is unexplored. Methods: We investigated the therapeutic efficacy and underlying mechanism of ginsenoside F1 (G-F1) in comparison with those of dexamethasone, a representative glucocorticosteroid, in a murine model of CRS. The effects of G-F1 or dexamethasone on sinonasal abnormalities and infiltration of eosinophils and mast cells were evaluated by histological analyses. The changes in inflammatory cytokine levels in sinonasal tissues, macrophages, and NK cells were assessed by qPCR, ELISA, and immunohistochemistry. Results: We found that G-F1 significantly attenuated eosinophilic inflammation, mast cell infiltration, epithelial hyperplasia, and mucosal thickening in the sinonasal mucosa of CRS mice. Moreover, G-F1 reduced the expression of IL-4 and IL-13, as well as hematopoietic prostaglandin D synthase required for prostaglandin D2 production. This therapeutic efficacy was associated with increased NK cell function, without suppression of macrophage inflammatory responses. In comparison, dexamethasone potently suppressed macrophage activation. NK cell depletion nullified the therapeutic effects of G-F1, but not dexamethasone, in CRS mice, supporting a causal link between G-F1 and NK cell activity. Conclusion: Our results suggest that potentiating NK cell activity, for example with G-F1, is a promising strategy for resolving eosinophilic inflammation in CRS.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.607-618
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• 2015

An L(2; 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all non-negative integers such that ${\mid}f(u)-f(v){\mid}{\geq}2$ if d(u, v) = 1 and ${\mid}f(u)-f(v){\mid}{\geq}1$ if d(u, v) = 2. The ${\lambda}$-number of G, denoted ${\lambda}(G)$, is the smallest number k such that G admits an L(2, 1)-labeling with $k=\max\{f(u){\mid}u{\in}V(G)\}$. In this paper, we consider the square of a cycle and provide exact value for its ${\lambda}$-number. In addition, we also completely determine its edge span.

• KOREAN JOURNAL OF CROP SCIENCE
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• v.7 no.1
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• pp.145-151
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• 1969

To make clear the species of Korean Asiatic cotton, 21 Asiatic cotton varieties collected from China, Manchuria, Japan and Korea and preserved at suwon Crop Experiment Station were crossed to the tester stocks and cytological studies were made for their $F_1$ pollen mother cells. The results were summarized as follows: 1. In the all $F_1$ hybrids between the 21 collections and G. herbaceum tester stocks always one ring-four association was observed. 2. In the $F_1$ hybrids between additional 5 collections and G. arboreum tester stock ring-four or chain-four was not observed. 3. In the $F_1$ hybrids between G. herbaceum tester stocks and between G. arboreum tester stocks no ring-four or chain-four was observed, while in the $F_1$ hybrids between G. herbaceum tester stock and G. arboreum tester stock always one ring-four was observed. In the $F_1$ hybrids between collections also no ring-four or chain-four was observed. 4. From above results and together with the results reported in previous paper the species of Asiatic collections was inferred to the D.U. Gerstel's G. arboreum and their race was inferred to the J. Hutcinson's G. arboreum L. race sinense.

• Food Science and Preservation
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• v.6 no.4
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• pp.495-499
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• 1999

The free sugars in leaf and root of dandelion were composed of sucrose, glucose and fructose. The contents of total free sugars was higher in root than those in leaf. The oxalic acid, citric acid and malic acid contents of leaf was 45.4, 3.6, 2.7mg/100g-f.w., respectively. And the oxalic acid, citric acid and malic acid contents of root was 34.6, 2.1, 1.6mg/100g-f.w., respectively. Total free organic acid content of leaf was higher than that of root. The major free amino acids of dandelion were aspartic acid, serine, asparagine, glutamic acid, glycine, valine, isoleucine and content of glutamic acid was highest in free amino acids. The contents of vitamin A in leaf and root of dandelion was 135.4 and 34.1$\mu\textrm{g}$/100g-f.w., respectively. The contents of vitamin C in leaf and root of dandelion was 67.4 and 4.6 mg/100g-f.w., respectively.