• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.147-159
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• 2013

Hamada ([8]) and Maruta ([17]) proved the minimum length $n_3(6,\;d)=g_3(6,\;d)+1$ for some ternary codes. In this paper we consider such minimum length problem for $q{\geq}4$, and we prove that $n_q(6,\;d)=g_q(6,\;d)+1$ for $d=q^5-q^3-q^2-2q+e$, $1{\leq}e{\leq}q$. Combining this result with Theorem A in [4], we have $n_q(6,\;d)=g-q(6,\;d)+1$ for $q^5-q^3-q^2-2q+1{\leq}d{\leq}q^5-q^3-q^2$ with $q{\geq}4$. Note that $n_q(6,\;d)=g_q(6,\;d)$ for $q^5-q^3-q^2+1{\leq}d{\leq}q^5$ by Theorem 1.2.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.421-426
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• 2007

The problem of vertex labeling with a condition at distance two in a graph, is a variation of Hale's channel assignment problem, which was first explored by Griggs and Yeh. For positive integer $p{\geq}q$, the ${\lambda}_{p,q}$-number of graph G, denoted ${\lambda}(G;p,q)$, is the smallest span among all integer labellings of V(G) such that vertices at distance two receive labels which differ by at least q and adjacent vertices receive labels which differ by at least p. Van den Heuvel and McGuinness have proved that ${\lambda}(G;p,q){\leq}(4q-2){\Delta}+10p+38q-24$ for any planar graph G with maximum degree ${\Delta}$. In this paper, we studied the upper bound of ${\lambda}_{p,q}$-number of some planar graphs. It is proved that ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+2(2p-1)$ if G is an outerplanar graph and ${\lambda}(G;p,q){\leq}(2q-1){\Delta}+6p-4q-1$ if G is a Halin graph.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.419-425
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• 2008

For $q^5-q^3-q^2-q+1{\leq}d{\leq}q^5-q^3-q^2$, we prove the non-existence of a $[g_q(6,d),6,d]_q$ code and we give a $[g_q(6,d)+1,6,d]_q$ code by constructing appropriate 0-cycle in the projective space, where $g_q (k,d)={{\sum}^{k-1}_{i=0}}{\lceil}\frac{d}{q^i}{\rceil}$. Consequently, we have the minimum length $n_q(6,d)=g_q(6,d)+1\;for\;q^5-q^3-q^2-q+1{\leq}d{\leq}q^5-q^3-q^2\;and\;q{\geq}3$.

• Korean Chemical Engineering Research
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• v.54 no.1
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• pp.101-107
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• 2016

This paper investigates the feasibility of applying the jet loop reactor for the neutralization of alkaline wastewater using carbon dioxide ($CO_2$). In this study, pH changes and $CO_2$ removal characteristics were examined by changing influent flow rate of alkaline wastewater (initial pH=10.1) and influent $CO_2$ flow rates. Influent flow rates of alkaline wastewater ($Q_{L,in}$) ranged between 0.9 and 6.6 L/min, and inlet gas flow rate ($Q_{G,in}$) of 1 and 6 L/min in a lab-scale continuous flow jet loop reactor. The outlet pH of wastewater was maintained at 7.2 when the ratio ($Q_{L,in}/Q_{G,in}$) of $Q_{L,in}$ and $Q_{G,in}$ was 1.1. However, the $CO_2$ removal efficiency and the outlet pH of wastewater were increased when $Q_{L,in}/Q_{G,in}$ ratio was higher than 1.1. Throughout the experiments, the maximum $CO_2$ removal efficiency and the outlet pH of wastewater were 98.06% and 8.43 at the condition when $Q_{G,in}$ and $Q_{L,in}$ were 2 L/min and 4 L/min, respectively.

• 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 $T/Q_1$.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.12 no.5
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• pp.493-498
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• 2019

This study deals with the analysis of the technology association rules between CPC codes of the Internet of Things(IoT) patent, the core of the Fourth Industrial Revolution ICT-based technology. The association rules between CPC codes were extracted using R, an open source for data mining. To this end, we analyzed 369 of the 605 patents related to the Internet of Things filed with the Patent Office until July 2019, with a complex CPC code, up to the subclass-level. As a result of the technology association rules, CPC codes with high support were [H04W ${\rightarrow}$ H04L](18.2%), [H04L ${\rightarrow}$ H04W](18.2%), [G06Q ${\rightarrow}$ H04L](17.3%), [H04L ${\rightarrow}$ G06Q](17.3%), [H04W ${\rightarrow}$ G06Q](9.8%), [G06Q ${\rightarrow}$ H04W](9.8%), [G06F ${\rightarrow}$ H04L](7.9%), [H04L ${\rightarrow}$ G06F](7.9%), [G06F ${\rightarrow}$ G06Q](6.2%), [G06Q ${\rightarrow}$ G06F](6.2%). After analyzing the technology interconnection network, the core CPC codes related to technology association rules are G06Q and H04L. The results of this study can be used to predict future patent trends.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.155-167
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• 2007

A graph G is called to be a 2-degree integral subgraph of a q-tree if it is obtained by deleting an edge e from an integral subgraph that is contained in exactly q - 1 triangles. An added-vertex q-tree G with n vertices is obtained by taking two vertices u, v (u, v are not adjacent) in a q-trees T with n - 1 vertices such that their intersection of neighborhoods of u, v forms a complete graph $K_{q}$, and adding a new vertex x, new edges xu, xv, $xv_{1},\;xv_{2},\;{\cdots},\;xv_{q-4}$, where $\{v_{1},\;v_{2},\;{\cdots},\;v_{q-4}\}\;{\subseteq}\;K_{q}$. In this paper we prove that a graph G with minimum degree not equal to q - 3 and chromatic polynomial $$P(G;{\lambda})\;=\;{\lambda}({\lambda}-1)\;{\cdots}\;({\lambda}-q+2)({\lambda}-q+1)^{3}({\lambda}-q)^{n-q-2}$$ with $n\;{\geq}\;q+2$ has and only has 2-degree integral subgraph of q-tree with n vertices and added-vertex q-tree with n vertices.

• Journal of the Korean Wood Science and Technology
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• v.38 no.4
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• pp.359-374
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• 2010

This study was carried out to investigate the chemotaxonomical correlation and chemical constituents of domestic Quercus spp. barks. The barks of Q. mongolica, Q. aliena, Q. serrata, Q. acutissima, Q. dentata, and Q. variabilis were collected in the experimental forest of Kangwon National University. The combined extracts were successively fractionated with n-hexane, methylene chloride and ethyl acetate using a separation funnel. A portion of the ethyl acetate and H2O soluble materials of each species were chromatographed on a Sephadex LH-20 column using various aqueous MeOH and EtOH-hexane as washing solvents. Spectrometric analysis such as NMR and MS, including TLC, were performed to characterize the structures of the isolated compounds. Ellagic acid (0.03 g), (+)-catechin (4.59 g), taxifolin (3.35 g), and glucodistylin (20.52 g) were isolated from Q. mongolica bark. Gallic acid (0.18 g), (+)-catechin (8.52 g), (+)-gallocatechin (0.09 g), taxifolin (0.54 g), and glucodistylin (3.28 g) were characterized from Q. acutissima bark. Gallic acid (0.38 g), ellagic acid (0.11 g), (+)-catechin (2.01 g), (+)-gallocatechin (0.12 g), and glucodistylin (0.39 g) were identified from Q. dentata bark. Ellagic acid (1.51 g), (+)-catechin (21.91 g), and glucodistylin (3.91 g) were purified from Q. aliena bark. Ellagic acid (0.84 g), (+)-catechin (0.82 g), taxifolin (4.02 g), and glucodistylin (21.50) were isolated from Q. serrata bark. Gallic acid (0.24 g), caffeic acid (0.05 g), (+)-catechin (0.32 g), and glucodistylin (0.65 g) were purified from Q. variabilis bark. (+)-Catechin and glucodistylin were isolated from all the barks. Glucodistylin can be a taxonomic index on Quercus spp.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.239-268
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• 2015

Let Q be a finite quiver and $G{\subseteq}Aut(\mathbb{k}Q)$ a finite abelian group. Assume that $\hat{Q}$ and ${\Gamma}$ are the generalized Mckay quiver and the valued graph corresponding to (Q, G) respectively. In this paper we discuss the relationship between indecomposable $\hat{Q}$-representations and the root system of Kac-Moody algebra $g({\Gamma})$. Moreover, we may lift G to $\bar{G}{\subseteq}Aut(g(\hat{Q}))$ such that $g({\Gamma})$ embeds into the fixed point algebra $g(\hat{Q})^{\bar{G}}$ and $g(\hat{Q})^{\bar{G}}$ as a $g({\Gamma})$-module is integrable.

• Honam Mathematical Journal
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• v.17 no.1
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• pp.7-14
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• 1995

The purpose of this study is to construct the structure of the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$, which conforms to Stellmacher's [4] Pushing Up. The main idea of this paper comes from Stellmacher's [4] Pushing Up. Stelhnacher considered Pushing Up under a finite p-group. This paper, however, considers Pushing Up under the connected Lie group G with its Lie algebra $g=rad(g){\oplus}sl(2, \mathbb{F})$. In this paper, $O_p(G)$ in [4] is Q=exp(q), where q=nilrad(g) and a Sylow p-subgroup S in [7] is S=exp(s), where $s=q{\oplus}\{\(\array{0&*\\0&0}\){\mid}*{\in}\mathbb{F}\}$. Showing the properties of the connected Lie group and the subgroups of the connected Lie group with relations between a connected Lie group and its Lie algebras under the exponential map, this paper constructs the subgroup series C_z(G)