• East Asian mathematical journal
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• 제18권2호
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• pp.271-282
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• 2002

Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

• 대한화학회지
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• 제38권2호
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• pp.108-121
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• 1994

OV-1701 모세관 컬럼과 OV-1모세관 컬럼을 사용하여 컬럼온도 150, 180, $210^{\circ}C$에서 알칸, 방향족, 알코올, 아민, 케톤, 알데히드 및 고리 화합물의 머무름 지표값을 구하였다. 기능기에 의한 머무름 인자(GRF)와 구조변화에 따른 머무름 인자(SRF)는 기능기가 없는 비교 화합물로부터 계산하였다. f번째 기능기에 따른 $GRF_f$를 구하는 식은 $GRF_f\;=\;I_{obs}-(100Z +\sum\limits_{i{\neq}f}GRF_i+{\sum}SRF_i$)와 같다. 마찬가지로 f번째의 구조변화에 따른 $SRF_i$를 구하는 식은 $SRF_f\;=\;I_{obs}-(100Z + {\sum}GRFi + \sum\limits_{i{\neq}f}SRF_i$)와 같다. 계산된 머무름 지표값과 측정값과의 차이는 OV-1701컬럼에서는 ${\pm}2$, OV-1컬럼에서는 ${\pm}3$이내였다. 또한 온도변화에 따른 기능기와 구조변화에 따른 머무름 인자 $\Delta_{ xi}$와 $\Delta_{ yi}$값을 기능기가 없는 비교 화합물 로부터 계산하였다. f번째 기능기에 따른 $GRF_f$를 구하는 식은 ${\Delta}x_f$ = $\Delta'/^{\circ}C+ \sum\limits_{i{\neq}f}{\Delta}xi +{\sum}{\Delta}yi$ 와 같다. 마찬가지로 f번째의 구조변화에 따른$SRF_f$를 구하는 식은 ${\Delta}yi ={\Delta}'/^{\circ}C+{\sum}{\Delta}xi + \sum\limits_{i{\neq}f}{\Delta}yi$와 같다. 계산된 ${\Delta}xi$ 값과 측정값과의 오차는 OV-1701 컬럼에는 ${\pm}18%$, OV-1컬럼에는 ${\pm}17%$였다.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.205-215
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• 2009

Sufficient conditions for the existence of at least one solution of the boundary value problems for higher order nonlinear difference equations $\{{{{{\Delta^n}x(i-1)=f(i,x(i),{\Delta}x(i),{\cdots},\Delta^{n-2}x(i)),i{\in}[1,T+1],\atop%20{\Delta^m}x(0)=0,m{\in}[0,n-3],}\atop%20\Delta^{n-2}x(0)=\phi(\Delta^{n-1}(0)),}\atop%20\Delta^{n-1}x(T+1)=-\psi(\Delta^{n-2}x(T+1))}\$. are established.

• 한국컴퓨터정보학회논문지
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• 제17권11호
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• pp.189-196
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• 2012

본 논문은 동적 경제급전의 최적화 문제를 풀기 위해 교환 알고리즘을 제안하였다. 제안된 알고리즘은 첫 번째로, 발전단가 $C_i^{max}/P_i^{max}$가 비싼 발전기는 가동을 중지시키는 개념을 도입하여 총 요구량 $P_d$와 총 발전량 ${\Sigma}P_i$의 균형을 맞추었다. 다음으로 발전량을 $P_i=P_i{\pm}{\Delta}$, (${\Delta}$=1.0, 0.1, 0.01, 0.001)에 대해 $_{max}[F(P_i)-F(P_i-{\Delta})]$ > $_{min}[F(P_j+{\Delta})-F(P_j)]$, $i{\neq}j$이면 $P_i=P_i-{\Delta}$, $P_j=P_j+{\Delta}$로 발전량을 교환하는 방법을 적용하였다. 동적 경제급전 문제의 시험사례에 제안된 알고리즘을 적용한 결과 기존의 휴리스틱 알고리즘 최적화 발전비용을 크기 감소시켜 경제적인 이익을 극대화 시켰다.

• 대한수학회지
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• 제15권1호
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• pp.59-61
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• 1978

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

• 한국자기공명학회논문지
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• 제2권2호
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• pp.141-151
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• 1998

Human annexin I is a member of annexin family of calcium dependent phospholipid binding proteins, which have been implicated in various physiological roles including phospholipase A2(PLA2) inhibition, membrane fusion and calcium channel activity. In this work, the structure of N-terminally truncated human annexin I ({{{{ DELTA }}-annexin I) and its interactions with Ca2+, ATP and cAMP were studied at atomic level by using nuclear magnetic resonance (NMR) spectroscopy. The effect of Ca2+ binding on the structure of {{{{ DELTA }}-annexin I was investigated. The addition of Ca2+ to {{{{ DELTA }}-annexin I caused some changes in 13C NMR spectra. Carbonyl carbon resonances of some histidines were significantly broadened by Ca2+ binding. However, in the case of methionine, phenylalanine, and tyrosin, small changes could be observed. We found that ATP and cAMP bind {{{{ DELTA }}-annexin I, and the binding ratio of ATP to {{{{ DELTA }}-annexin I is 1. These results are well consistent with the report that cAMP and ATP interact with annexin I, and affect the calcium channels formed by annexin I. Because {{{{ DELTA }}-annexin I is a large protein with 35 kDa molecular weight, site-specific (carbonyl-13C) labeling technique was used to study the interaction sites of {{{{ DELTA }}-annexin I with Ca2+. NMR study was focused on the carbonyl carbon resonances of tyrosine, phenylalanine, methionine and histidine residues of {{{{ DELTA }}-annexin I because the number of these amino acids is small in the amino acid sequence of {{{{ DELTA }}-annexin I.

• 멤브레인
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• 제8권3호
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• pp.157-169
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• 1998

폴리이미드(6FDA-p-TeMPD) 비대칭막을 습식 상분리법으로 제조하는데 있어서 그 구조에 미치는 용매 (DMAc, NMP, 1,4-dioxane)와 비용매($H_2O$, Methanol, n-hexane)의 영향을 고찰하였다. 고분자/용매/비용매 분리 속도를 예측함으로써 생성된 비대칭막의 구조를 해석하였다. 용해도 곡선이 용매-고분자 축에 가깝고, 응결값이 작으며, 광투과도가 즉시 감소하고, 용해도 계수차가 $\Delta \delta_{S-NS} > \Delta \delta_{P-NS} > \Delta \delta_{P-S}$ 순이면 생성막은 고분자 결절의 불연속 결집속에 finger-like pore가 형성되었다. 용해도 곡선이 용매-고분자 축에서 멀고, 응결값이 크며, 상분리 시간이 길고, 용해도 계수차 $\Delta \delta_{i-j}$ 가 $\Delta \delta_{P-NS} >(\Delta \delta_{S-NS} < > \Delta \delta_{P-S})$ 일때, 생성되는 막은 미소 고분자 결절구가 치밀하게 응집된 표피가 있으며, 고분자 연속상 스폰지층에 macropore가 발달되었다. 용해도 곡선이 용매-고분자 축으로부터 멀리 떨어지고, 응결값이 대단히 크며, 상분리 시간이 길고, 용해도 계수차 $\Delta \delta_{i-j}$가 $\Delta \delta_{S-NS} > (\Delta \delta_{P-NS}$\lessgtr$)\Delta \delta_{P-S}$인 경우는 고분자 미소 결절의 두터운 응집층과 다음에 성근 결절응집층이 나타났다.

• Journal of the Korean Statistical Society
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• 제10권
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• pp.97-104
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• 1981

It is shown that a lattice distribution defined on a set of n lattice points $L(n,\delta) = {\delta,\delta+1,...,\delta+n-1}$ is a distribution induced from the distribution of convolution of independently and identically distributed (i.i.d.) uniform [0,1] random variables. Also the m-th moment of the lattice distribution is obtained in a quite different approach from Park and Chung (1978). It is verified that the distribution of the sum of n i.i.d. uniform [0,1] random variables is completely determined by the lattice distribution on $L(n,\delta)$ and the uniform distribution on [0,1]. The factorial mement generating function, factorial moments, and moments are also obtained.

• Journal of the Korean Statistical Society
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• 제32권3호
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• pp.299-309
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• 2003

Let ${\pi}_1,...,{\pi}_{k}$k($\geq$2) independent logistic populations such that the cumulative distribution function (cdf) of an observation from the population ${\pi}_{i}$ is $$F_{i}\;=\; {\frac{1}{1+exp{-\pi(x-{\mu}_{i})/(\sigma\sqrt{3})}}},\;$\mid$x$\mid$<\;{\infty}$$ where ${\mu}_{i}(-{\infty}\; < \; {\mu}_{i}\; <\; {\infty}$ is unknown location mean and ${\delta}^2$ is known variance, i ＝ 1,..., $textsc{k}$. Let ${\mu}_{[k]}$ be the largest of all ${\mu}$'s and the population ${\pi}_{i}$ is defined to be 'good' if ${\mu}_{i}\;{\geq}\;{\mu}_{[k]}\;-\;{\delta}_1$, where ${\delta}_1\;>\;0$, i = 1,...,$textsc{k}$. A selection procedure based on sample median is proposed to select a subset of $textsc{k}$ logistic populations which includes all the good populations with probability at least $P^{*}$(a preassigned value). Simultaneous confidence intervals for the differences of location parameters, which can be derived with the help of proposed procedures, are discussed. If a population with location parameter ${\mu}_{i}\;<\;{\mu}_{[k]}\;-\;{\delta}_2({\delta}_2\;>{\delta}_1)$, i ＝ 1,...,$textsc{k}$ is considered 'bad', a selection procedure is proposed so that the probability of either selecting a bad population or omitting a good population is at most 1­ $P^{*}$.

• 대한수학회보
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• 제50권4호
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• pp.1303-1314
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• 2013

An injective coloring of a graph G is an assignment of colors to the vertices of G so that any two vertices with a common neighbor receive distinct colors. A graph G is said to be injectively $k$-choosable if any list $L(v)$ of size at least $k$ for every vertex $v$ allows an injective coloring ${\phi}(v)$ such that ${\phi}(v){\in}L(v)$ for every $v{\in}V(G)$. The least $k$ for which G is injectively $k$-choosable is the injective choosability number of G, denoted by ${\chi}^l_i(G)$. In this paper, we obtain new sufficient conditions to be ${\chi}^l_i(G)={\Delta}(G)$. Maximum average degree, mad(G), is defined by mad(G) = max{2e(H)/n(H) : H is a subgraph of G}. We prove that if mad(G) < $\frac{8k-3}{3k}$, then ${\chi}^l_i(G)={\Delta}(G)$ where $k={\Delta}(G)$ and ${\Delta}(G){\geq}6$. In addition, when ${\Delta}(G)=5$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{17}{7}$, and when ${\Delta}(G)=4$ we prove that ${\chi}^l_i(G)={\Delta}(G)$ if mad(G) < $\frac{7}{3}$. These results generalize some of previous results in [1, 4].