• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.251-256
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• 1997

We show that a strong system of derivations ${D_0, D_1,\cdots,D_m}$ on a commutative Banach algebra A is contained in the radical of A if it satisfies one of the following conditions for separating spaces; (1) $\partial(D_i) \subseteq rad(A) and \partial(D_i) \subseteq K D_i(rad(A))$ for all i, where $K D_i(rad(A)) = {x \in rad(A))$ : for each $m \geq 1, D^m_i(x) \in rad(A)}$. (2) $(D^m_i) \subseteq rad(A)$ for all i and m. (3) $\bar{x\partial(D_i)} = \partial(D_i)$ for all i and all nonzero x in rad(A).

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.517-523
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• 2007

Let R/I be an Artinian algebra of codimension 3 with Hilbert function H such that $h_{d-1}>h_d=h_{d+1}$. Ahn and Shin showed that A cannot be level if ${\beta}_{1,d+2}(Gin(I))={\beta}_{2,d+2}(Gin(I))$ where Gin(I) is a generic initial ideal of I. We prove that some certain graded Artinian algebra R/I cannot be level if either ${\beta}_{1,d}(I^{lex})={\beta}_{2,d}(I^{lex})+1\;or\;{\beta}_{1,d+1}(I^{lex})={\beta}_{2,d+1}(I^{lex})\;where\;I^{lex}$ is a lex-segment ideal associated to I.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1137-1146
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• 2011

Let {$X_i$, $i{\geq}1$} be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote $S_n={\sum}_{i=1}^n\;X_i$, $M_n=max_{1{\leq}i{\leq}n}\;{\mid}S_i{\mid}$ and $V_n^2={\sum}_{i=1}^n\;X_i^2$. Then for d > -1, we showed that under some regularity conditions, $$\lim_{{\varepsilon}{\searrow}0}{\varepsilon}^2^{d+1}\sum_{n=1}^{\infty}\frac{(loglogn)^d}{nlogn}I\{M_n/V_n{\geq}\sqrt{2loglogn}({\varepsilon}+{\alpha}_n)\}=\frac{2}{\sqrt{\pi}(1+d)}{\Gamma}(d+3/2)\sum_{k=0}^{\infty}\frac{(-1)^k}{(2k+1)^{2d+2}}\;a.s.$$ holds in this paper, where If g denotes the indicator function.

• Korean Journal of Animal Reproduction
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• v.22 no.1
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• pp.89-94
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• 1998

A study was made to investigate the effects of concerning factors with IGF-I recovery on the final IGF-I concentration in the effluent and to establish recovery conditions of IGF-I using liquid emulsion membranes(LEM). D2EHPA was best carrier among Amberlite LA2, Aliquit 336 and D2EHPA for recovery rate of IGF-I. Recovery rate of IGF-I by D2EHPA volume in the oil phase was increased as increasing D2EHPA volume, and optimal volume of D2EHPA was 5% in this experiment. The recovery rate of IGF-I by D2EHPA was increased by the decreasing from pH 7 to pH 4 of external phase. Therefore, optimal pH value was 4.0. Optimal concentrations of sulfuric acid in internal phase, paraffin oil in oil phase and Span 80 for recovery rate of IGF-I were 0.1M, 2.0% and 5%, respectively, and optimal W/O rate was 2. These results suggested that optimal conditions for recovery of IGF-I were D2EHPA(5%) as carrier, pH 4.0, 0.1M sulfuric acid, 2% paraffin oil, 2.0 W/O rate and 5.0% Span 80.

• The Journal of the Acoustical Society of Korea
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• v.11 no.6
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• pp.15-22
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• 1992

i.i.d 신호의고차 모멘트와 스펙트럼의 성질에 대하여 4차까지 고찰하였으며 이의 결과를 이용하 여 2차 Volterra 급수로 표시되고, i.i.d. 입력 신호를 갖는 시불변 비선형 시스테므이 파라메타들을 추정 하는 알고리즘을 시간 영역과 주파수 영역에서 각각 제안하였다. 비록 2차 Volterra 급수가 i.i.d. 입력 신호에 대하여 orthogonal 모델이 아닐지라도 입력 신호의 각종 시간지연에 대한 모멘트나 역행렬의 계 산등이 요구되지 않으며 선형 전달함수와 2차 전달함수를 추정할 수 있는 알고리즘이 존재하는 것을 보 았다.

• Journal of the Korea Society of Computer and Information
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• v.20 no.2
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• pp.63-70
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• 2015

In the absence of a polynomial time algorithm capable of obtaining the exact solutions to it, the domatic number problem (DNP) of dominating set (DS) has been regarded as NP-complete. This paper suggests polynomial-time complexity algorithm about DNP. In this paper, I select a vertex $v_i$ of the maximum degree ${\Delta}(G)$ as an element of a dominating set $D_i,i=1,2,{\cdots},k$, compute $D_{i+1}$ from a simplified graph of $V_{i+1}=V_i{\backslash}D_i$, and verify that $D_i$ is indeed a dominating set through $V{\backslash}D_i=N_G(D_i)$. When applied to 15 various graphs, the proposed algorithm has succeeded in bringing about exact solutions with polynomial-time complexity O(kn). Therefore, the proposed domatic number algorithm shows that the domatic number problem is in fact a P-problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.9-14
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• 2007

A signed 3-partite graph is a 3-partite graph in which each edge is assigned a positive or a negative sign. Let G(U, V, W) be a signed 3-partite graph with $U\;=\;\{u_1,\;u_2,\;{\cdots},\;u_p\},\;V\;=\;\{v_1,\;v_2,\;{\cdots},\;v_q\}\;and\;W\;=\;\{w_1,\;w_2,\;{\cdots},\;w_r\}$. Then, signed degree of $u_i(v_j\;and\;w_k)$ is $sdeg(u_i)\;=\;d_i\;=\;d^+_i\;-\;d^-_i,\;1\;{\leq}\;i\;{\leq}\;p\;(sdeg(v_j)\;=\;e_j\;=\;e^+_j\;-\;e^-_j,\;1\;{\leq}\;j\;{\leq}q$ and $sdeg(w_k)\;=\;f_k\;=\;f^+_k\;-\;f^-_k,\;1\;{\leq}\;k\;{\leq}\;r)$ where $d^+_i(e^+_j\;and\;f^+_k)$ is the number of positive edges incident with $u_i(v_j\;and\;w_k)$ and $d^-_i(e^-_j\;and\;f^-_k)$ is the number of negative edges incident with $u_i(v_j\;and\;w_k)$. The sequences ${\alpha}\;=\;[d_1,\;d_2,\;{\cdots},\;d_p],\;{\beta}\;=\;[e_1,\;e_2,\;{\cdots},\;e_q]$ and ${\gamma}\;=\;[f_1,\;f_2,\;{\cdots},\;f_r]$ are called the signed degree sequences of G(U, V, W). In this paper, we characterize the signed degree sequences of signed 3-partite graphs.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.273-286
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• 2011

Using the fixed point method, we prove the Hyers-Ulam stability of the following quadratic functional equations $${cf\left({\displaystyle\sum_{i=1}^n\;xi}\right)+{\displaystyle\sum_{i=2}^nf}{\left(\displaystyle\sum_{i=1}^n\;x_i-(n+c-1)x_j\right)}\\ {=(n+c-1)\;\left(f(x_1)+c{\displaystyle\sum_{i=2}^n\;f(x_i)}+{\displaystyle\sum_{i in fuzzy Banach spaces.

• Journal of Korean Ophthalmic Optics Society
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• v.15 no.1
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• pp.99-104
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• 2010

Purpose: Difference of refraction result from the method of autorefraction and iTrace were investigaged for the children of elementary school in Asan City. In iTrace method. exclusion of accommodation without cycloplegia was used. Methods: Manifest refractive stale of 42 eyes of 12~13 years old were measured using autorefractor and iTrace. Refractions of far (more than 5 m) and ncar (30 cm) vision were measured using iTrace. All data showed that the spherical equivalent were classified as being in the group 1 (-0.50D < ~ < +1.00D) and 2 (below -0.50D) according 10 refractive errors. Results: Mean spherical equivalent using autorefractor and iTrace (far and near vision) were -1.08D, -0.29D and -2.34D, respectively (p<0.01). Compared with the far vision using iTrace, autorefraction was measured the myopia with -0.50D ~ -1.00D in 52.4% of total eyes. Autorefraction also statistical significant were measured a more myopia than the far vision using iTrace in group I and 2. Conclusions: The difference of refractive errors between autorefraction and iTrace, objective refraction were measured with far vision of more than 5 m were -0.79D. Autoreftaction showed statistically decreased refraction errors than iTrace with far vision.

• Korean Journal of Community Nutrition
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• v.2 no.2
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• pp.133-140
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• 1997

The serum concentrations of the major minerals(calcium, phosphorus, magnesium, sodium, potassium) and trace elements(iron, Zinc, copper manganese)were datermined in 23 breast fed infants living in Eumsung, Choong-buk region. The results obtained are summarized as follows: 1)The mean levels of calcium, phosphorus, magnesium, sodium and potassium of the serum of total subjects were 8.15$\pm$0.33mg/dI, 11.06$\pm$0.16mg/dI, 2.00$\pm$0.14mg/dI, 3.4476$\pm$17.99mg/dI and 9.06$\pm$2.04mg/dI respectively. 2)The serum concentrations of iron, zinc, copper and manganese in total subjects averaged 95.83$\pm$0.33mg/dI, 93.79$\pm$7.06$\mu$g/dI and 98.57$\pm$7.06 $\mu$g/dI and 4.93$\pm$0.62$\mu$g/dI respecitively. 3)Breast fed infants had significantly higher serum calcim, magnesium, sodium and iron concentrations than the formula fed groups. Otherwise, serum potassium, copper and manganese levels in breast milk fed infants were significantly lower than those in formula fed infants. 4) In formula fed infants, serum potassium and copper levels increased increased significantly with months after birth.