• East Asian mathematical journal
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• v.18 no.2
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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 $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

• Journal of the Korean Chemical Society
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• v.38 no.2
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• pp.108-121
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• 1994

The retention indices of branched-chain alkane, benzene ring, alcohol, amine, ketone, aldehyde and cyclic compounds were measured at 150, 180 and $210^{\circ}C$ on OV-1701 and OV-1 capillary columns. The group retention factors (GRF) of the substituents and the st` ructure retention factors (SRF) of the molecular structure change are derived from the retention indices of reference compounds and series of homologues. The $GRF_f$ equation of `f'th substituent is $GRF_f\;=\;I_{obs}-(100Z + \sum\limits_{i{\neq}f}GRF_i$ + {\sum}$SRF_i$)and the SRFf equation of `f'th molecular structure group is $SRF_f\;=\;I_{obs}-(100Z + {\sum}GRFi + \sum\limits_{i{\neq}f}SRF_i$). The predicted retention indices for those compound were in agreement, within the error of $\pm2$ and $\pm3%$, with the observed values that were obtained using the OV-1701 and OV-1 capillary column, respectively. The $\Delta$ xi of the substituents and $\Delta$ yi of the molecular structure change according to temperature change are derived from the $\Delta'/^{\circ}C$ of reference compounds and series of homologues. The $\Delta$ xi equation of the `f'th substituent is ${\Delta}x_f = {$\Delta}'/^{\circ}C+ \sum\limits_{i{\neq}f}\Delta$ xi + {\sum}{\Delta}yi\;and\;{\Delta}yi$ equation of the `f'th molecular structure group is ${\Delta}y_f$ = {\Delta}'/^{\circ}C+{\sum}{\Delta}xi +\sum\limits_{i{\neq}f}{\Delta}yi$. The predicted $\Delta'/^{\circ}C$ for these compounds were in agreement, within the error of ${\pm}18%$ and 17%, with the observed values that were obtained using the OV-1701 and OV-1 capillary column, respectively.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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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.

• Journal of the Korea Society of Computer and Information
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• v.17 no.11
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• pp.189-196
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• 2012

This paper proposes Swap algorithm for solving Dynamic Economic Dispatch (DED) problem. The proposed algorithm initially balances total load demand $P_d$ with total generation ${\Sigma}P_i$ by deactivating a generator with the highest unit generation cost $C_i^{max}/P_i^{max}$. It then swaps generation level $P_i=P_i{\pm}{\Delta}$, (${\Delta}$=1.0, 0.1, 0.01, 0.001) for $P_i=P_i-{\Delta}$, $P_j=P_j+{\Delta}$ provided that $_{max}[F(P_i)-F(P_i-{\Delta})]$ > $_{min}[F(P_j+{\Delta})-F(P_j)]$, $i{\neq}j$. This new algorithm is applied and tested to the experimental data of Dynamic Economic Dispatch problem, demonstrating a considerable reduction in the prevalent heuristic algorithm's optimal generation cost and in the maximization of economic profit.

• Journal of the Korean Mathematical Society
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• v.15 no.1
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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 ${\delta}$.

• Journal of the Korean Magnetic Resonance Society
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• v.2 no.2
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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.

• Membrane Journal
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• v.8 no.3
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• pp.157-169
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• 1998

The effects of solvents (DMAc, NMP, 1,4-dioxane) and nonsolvents ($H_2O$, Methanol, n-hexane) on the morphology of 6FDA-p-TeMPD polyimide membrane, prepared by the wet phase inversion method, were studied. In the polymer/solvent/nonsolvent ternary system, the binodal curve, the coagulation value and the relative light transmission were measured, and the solubility parameter difference was calculated. The onset state and rate of liquid-liquid alemixing were predicted and the morphology of membrane was analyzed. It is found that the finger-like pores are formed within discontinuous polymer nodules when the binoclal curve is close to the polymer-solvent (P-S) axis, the coagulation value is small, the reduction of light transmission is easy to occur and the order of solubility parameter difference ($\Delta \delta_{i-j}$) is $\Delta \delta_{S-NS} > \Delta \delta_{P-NS} > \Delta \delta_{P-S}$. The dense skin with small nodules and the sponge type sublayer with macrovoid are formed in the case that the binodal curve is distant from the P-S axis, the onset time of liquid-liquid demixing is long and the order of $\Delta \delta_{i-j}$ is $\Delta \delta_{P-NS} >(\Delta \delta_{S-NS} < > \Delta \delta_{P-S})$. The thick layer of fine nodule coagulation and loosely grown sublayer of nodules appear when the binodal curve is distant from the P-S axis, the onset time of liquid-liquid demixing is very long and the order of $\Delta \delta_{i-j}$가 $\Delta \delta_{S-NS} > (\Delta \delta_{P-NS}$\lessgtr$ > (\Delta \delta_{P-NS} < >)\Delta \delta_{P-S}$ ).

• Journal of the Korean Statistical Society
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• v.10
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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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• v.32 no.3
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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 $P^{*}$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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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].