• Journal of Korean Society of Water and Wastewater
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• v.13 no.2
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• pp.34-40
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• 1999

Aerobic night-soil treatment effluent containing high concentration of ammonia nitrogen was treated to remove nitrogen using Bardenpho process with Methanol addition. The objective of this study was to investigate the feasibility of complete nitrogen removal at three different HRTs such as 6.25d, 5d, and 3.75d, respectively. At each HRT, the nitrogen removal efficiencies are 92%, 99% and 97% and the required amount of methanol are 3.05gMeOH/gN, 2.75gMeOH/gN, and 3.38gMeOH/gN, respectively. Specific nitrification rates are decreased proportional to HRT and are $0.022gNH_4^+-N/g\;MLVSS{\cdot}day$, $0.0332gNH_4^+-N/g\;MLVSS{\cdot}day$ and $0.051gNH_4^+-N/g\;MLVSS{\cdot}day$ and specific denitification rate are decreased proportional to HRT and are $0.0210g\;N/gMLVSS{\cdot}day$, $0.0330g\;N/gMLVSS{\cdot}day$ and $0.0525g\;N/gMLVSS{\cdot}day$, respectively.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.923-931
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• 2014

Let x be an element of a group G and be an automorphism of G. Then for a positive integer n, the autocommutator $[x,_n{\alpha}]$ is defined inductively by $[x,{\alpha}]=x^{-1}x^{\alpha}=x^{-1}{\alpha}(x)$ and $[x,_{n+1}{\alpha}]=[[x,_n{\alpha}],{\alpha}]$. We call the group G to be n-auto-Engel if $[x,_n{\alpha}]=[{\alpha},_nx]=1$ for all $x{\in}G$ and every ${\alpha}{\in}Aut(G)$, where $[{\alpha},x]=[x,{\alpha}]^{-1}$. Also, for any integer $n{\neq}0$, 1, a group G is called an n-auto-Bell group when $[x^n,{\alpha}]=[x,{\alpha}^n]$ for every $x{\in}G$ and each ${\alpha}{\in}Aut(G)$. In this paper, we investigate the properties of such groups and show that if G is an n-auto-Bell group, then the factor group $G/L_3(G)$ has finite exponent dividing 2n(n-1), where $L_3(G)$ is the third term of the upper autocentral series of G. Also, we give some examples and results about n-auto-Bell abelian groups.

• BMB Reports
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• v.30 no.5
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• pp.326-331
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• 1997

To construct a competitive ELISA standard curve for the detection of glucose-6-phosphate debydrogenase (G6PD), we used highly purified native G6PD (nG6PD) as both immobilized and soluble antigens and anti-G6PD serum raised against nG6PD as antibody. The polystyrene cuvettes coated with nG6PD were challenged with a mixture of a limiting amount of anti-G6PD serum and various doses of nG6PD as competitors followed by incubation with alkaline phosphatase-anti-IgG conjugate. The competitive ELISA did not exhibit the typical sigmoidal dose-response curve characteristic of competition immunoassays under the optimal concentrations of antigen and antibody. The soluble nG6PD used as competitor failed to effectively inhibit the binding of antibodies to the immobilized nG6PD. The addition of NADP, a cofactor of G6PD enzyme, to coating buffer used for immobilizing nG6PD to the cuvettes and PBS-Tween-BSA buffer for diluting competitors did not improve the inhibition of antibody binding to immobilized nG6PD by soluble n/G6PD. The addition of BSA to coating buffer did not increase inhibition, either. Surprisingly, when partially active G6PD (paG6PD), obtained by repeated freeze-thawing, was used as competitor, the antibody binding to either immobilized nG6PD or immobilized paG6PD was inhibited 49-58%. We conclude that an effective competitive ELISA system with nG6PD enzyme and anti-G6PD serum for the detection of G6PD may not be established due to the poor inhibition of antibody binding to immobilized nG6PD by soluble nG6PD under the present assay conditions and that the inhibition may be improved by using an inactivated enzyme as competitor regardless of the type of immobilized antigen used. These results imply that the immobilized nG6PD may undergo denaturation upon binding to the polystyrene cuvettes and that our anti-G6PD serum may recognize denatured enzyme better than active enzyme.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1439-1443
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• 2010

For a positive integer k $\geq$ 2, the k-bonacci sequence {$g^{(k)}_n$} is defined as: $g^{(k)}_1=\cdots=g^{(k)}_{k-2}=0$, $g^{(k)}_{k-1}=g^{(k)}_k=1$ and for n > k $\geq$ 2, $g^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n-2}+{\cdots}+g^{(k)}_{n-k}$. And the k-Lucas sequence {$l^{(k)}_n$} is defined as $l^{(k)}_n=g^{(k)}_{n-1}+g^{(k)}_{n+k-1}$ for $n{\geq}1$. In this paper, we give a representation of nth k-Lucas $l^{(k)}_n$ by using determinant.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.479-487
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• 2004

Let G be a finite group and N be a normal subgroup of G. We denote by ncc(N) the number of conjugacy classes of N in G and N is called n-decomposable, if ncc(N) = n. Set $K_{G}\;=\;\{ncc(N)$\mid$N{\lhd}G\}$. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X. In this paper we characterise the {1, 3, 4}-decomposable finite non-perfect groups. We prove that such a group is isomorphic to Small Group (36, 9), the $9^{th}$ group of order 36 in the small group library of GAP, a metabelian group of order $2^n{2{\frac{n-1}{2}}\;-\;1)$, in which n is odd positive integer and $2{\frac{n-1}{2}}\;-\;1$ is a Mersenne prime or a metabelian group of order $2^n(2{\frac{n}{3}}\;-\;1)$, where 3$\mid$n and $2\frac{n}{3}\;-\;1$ is a Mersenne prime. Moreover, we calculate the set $K_{G}$, for some finite group G.

• Korean Journal of Plant Taxonomy
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• v.39 no.1
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• pp.42-47
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• 2009

In this study, the somatic chromosome of 14 taxa of Korean Galium L. were investigated. Among them were a few taxa for which the somatic chromosome number was determined for the first time. The somatic chromosome numbers of Korean Galium L. were 2n = 22, 24, 44, 48, 66, 72, 77, 88 and so basic chromosome numbers were x = 11 or 12. Those taxa having the basic chromosome number x = 11 showed polyploidy, including diploid, tetraploid, heptaploid, and octoploid. Tetraploid and hexaploid can be observed in those taxa with the basic number x = 12. The eleven taxa reported 11 for the first time are G. spurium var. echinospermon (Wallr.) Hayek (2n = 44), G. gracilens (A. Gray) Makino (2n = 22), G. pogonanthum Franch. & Sav. (2n = 22, 44), G. trachyspermum A. Gray (2n = 22, 44), G. japonicum (Maxim.) Makino & Nakai (2n = 77), G. trifloriforme Kom. (2n = 44), G. dahuricum Turcz. var. dahuricum (2n = 48, 72), G. dahuricum var. tokyoense (Makino) Cufod. (2n = 22), G. kinuta Nakai & Hara (2n=66), G. verum var. trachycarpum for. nikkoense (Nakai) Ohwi (2n = 44), G. verum var. asiaticum for. pusillum (Nakai) M. Park (2n = 44). The taxa with the same chromosome numbers as previously reported ones were G. boreale L. (2n=22) and G. verum var. asiaticum Nakai for. asiaticum (2n = 44). The chromosome number of G. trifidum L. (2n = 22) was different from the previous report. Two infraspecific taxa of G. dahuricum showed differences in their basic chromosome numbers (x = 11 for G. dahuricum Turcz. var. dahuricum and x = 12 for var. tokyoense (Makino) Cufod. The somatic chromosome number for G. dahuricum Turcz. var. dahuricum was found to be 2n = 48 (tetraploid) or 72 (hexaploid), while that of G. dahuricum var. tokyoense (Makino) Cufod. was found to be 2n = 22 (diploid). Therefore, basic chromosome numbers for members of the genus Galium can be used as valuable characters in delimiting infrageneric sections and investigating interspecific relationships.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.87-104
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• 2008

In this paper we investigate several properties and characteristics of the generalized Fibonacci sequence $\{g_n\}$={a, b, a+b, a+2b, 2a+3b, 3a+5b,...}. This concept is a generalization of the famous Fibonacci sequence. In particular we find the identities of sums and the nth term $g_n$ in detail. Also we find the generalizations of the Catalan's identity and A. Tagiuri's identity about the Fibonacci sequence, and investigate the relation between $g_n$ and Pascal's triangle, and how fast $g_n$ increases. Furthermore, we show that $g_n$ and $g_{n+1}$ are relatively prime if a b are relatively prime, and that the sequence $\{\frac{g_{n+1}}{g_n}\}$ of the ratios of consecutive terms converges to the golden ratio $\frac{1+\sqrt5}2$.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.109-123
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• 2003

A tree is called starlike if it has exactly one vertex of degree greate. than two. In [4] it was proved that two starlike trees G and H are cospectral if and only if they are isomorphic. We prove here that there exist no two non-isomorphic Laplacian cospectral starlike trees. Further, let G be a simple graph of order n with vertex set V(G) : {1,2, …, n} and let H = {$H_1$, $H_2$, …, $H_{n}$} be a family of rooted graphs. According to [2], the rooted product G(H) is the graph obtained by identifying the root of $H_{i}$ with the i-th vertex of G. In particular, if H is the family of the paths $P_k_1,P_k_2,...P_k_2$ with the rooted vertices of degree one, in this paper the corresponding graph G(H) is called the sunlike graph and is denoted by G($k_1,k_2,...k_n$). For any $(x_1,x_2,...,x_n)\;\in\;{I_*}^n$, where $I_{*}$ = : {0,1}, let G$(x_1,x_2,...,x_n)$ be the subgraph of G which is obtained by deleting the vertices $i_1,i_2,...i_j\;\in\;V(G)\;(O\leq j\leq n)$, provided that $x_i_1=x_i_2=...=x_i_j=o.\;Let \;G[x_1,x_2,...x_n]$ be characteristic polynomial of G$(x_1,x_2,...,x_n)$, understanding that G[0,0,...,0] $\equiv$1. We prove that $G[k_1,k_2,...,k_n]-\sum_{x\in In}[{\prod_{\imath=1}}^n\;P_k_i+x_i-2(\lambda)](-1)...G[x_1,x_2,...,X_n]$ where x=($x_1,x_2,...,x_n$);G[$k_1,k_2,...,k_n$] and $P_n(\lambda)$ denote the characteristic polynomial of G($k_1,k_2,...,k_n$) and $P_n$, respectively. Besides, if G is a graph with $\lambda_1(G)\;\geq1$ we show that $\lambda_1(G)\;\leq\;\lambda_1(G(k_1,k_2,...,k_n))<\lambda_1(G)_{\lambda_1}^{-1}(G}$ for all positive integers $k_1,k_2,...,k_n$, where $\lambda_1$ denotes the largest eigenvalue.

• Bulletin of the Korean Mathematical Society
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• v.32 no.1
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• pp.45-56
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• 1995

D. H. Gottlieb [1, 2] studied the subgroups $G_n(X)$ of homotopy groups $\pi_n(X)$. In [5, 7, 10], the authors introduced subgroups $G_n(X, A)$ and $G_n^{Rel}(X, A) of \pi_n(X)$ and $\pi_n(X, A)$ respectively and showed that they fit together into a sequence $$ \cdots \to G_n(A) \longrightarrow^{i_*} G_n(X, A) \longrightarrow^{j_*} G_n^{Rel}(X, A) \longrightarrow^\partial $$ $$ \cdots \to G_1^{Rel}(X, A) \to G_0(A) \ to G_0(X, A) $$ where $i_*, j_*$ and \partial$ are restrictions of the usual homomorphisms of the homotopy sequence $$ \cdot \to^\partial \pi_n(A) \longrightarrow^{i_*} \pi_n(X) \longrightarrow^{j_*} \pi_n(X, A) \to \cdot \to \pi_0(A) \to \pi_0(X) $$.

• Korean Journal of Veterinary Research
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• v.30 no.4
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• pp.407-412
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• 1990

This study was designed to elucidate the effects of administration with dietary iron and fat-free diet on the contents of unsaturated fatty acid in phospholipid molecules, vitamin E contents and malondialdehyde contents in liver, kidney, muscle and testis of the male rats. The rats were divided into 3 experimental groups, namely, control, iron injection and fat-free diet administration groups. The control group was fed with normal diet, iron injection group injected intraperitoneally 20mg of ferric hydroxide/100g of body weight 20 times every 3 days and fat-free diet group administered lipid extraction diet with hexane in normal diet. All experimental groups were maintained for 60 days with feeding on the respective ration. The results obtained were summarized as follows: 1. In the mean contents of unsaturated fatty acid in phospholipid of liver, kidney, muscle and testis among groups, control group was 21.31mg/g, 19.38mg/g, 1.67mg/g, 13.68mg/g, iron injection group was 13.83mg/g, 16.53mg/g, 0.71mg/g, 10.11mg/g and fat-free diet group was 21.07mg/g, 19.38mg/g, 1.49mg/g and 13.40mg/g, respectively. 2. In the mean contents of vitamin E in liver, kidney, muscle and testis among groups, control group was 6.77mg/g, 1.93mg/g, 0.12mg/g, 0.17mg/g, iron injection group was 3.16mg/g, 0.86mg/g, 0.07mg/g, 0.09mg/g and fat-free diet group was 7.41mg/g, 1.50mg/g, 0.11mg/g and 0.16mg/g, respectively. 3. In the mean contents of malondialdehyde in liver, kidney, muscle, testis and serum among groups, control group was 11.29nM/0.1g, 23.25nM/0.1g, 42.47nM/0.1g, 7.01nM/0.1g, 4.33nM/ml, iron injection group was 34.98nM/0.1g, 40.55nM/0.1g, 72.21nM/0.1g, 12.26nM/0.1g, 11.27nM/ml and fat-free diet group was 8.07nM/0.1g, 20.63nM/0.1g, 39.92nM/0.1g, 6.95nM/0.1g and 4.27nM/ml, respectively.