• 충청수학회지
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• 제30권4호
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• pp.411-422
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• 2017

Let {$X_{ni}$, $i{\geq}1$, $n{\geq}1$} be an array of rowwise asymptotically negatively associated random variables and {$a_{ni}$, $i{\geq}1$, $n{\geq}1$} an array of constants. Some results concerning complete convergence of weighted sums ${\sum}_{i=1}^{n}a_{ni}X_{ni}$ are obtained. They generalize some previous known results for arrays of rowwise negatively associated random variables to the asymptotically negative association case.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.471-479
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• 2008

Let $R\;{\in}\;C^{m{\times}m}$ and $S\;{\in}\;C^{n{\times}n}$ be nontrivial unitary involutions, i.e., $R^*\;=\;R\;=\;R^{-1}\;{\neq}\;I_m$ and $S^*\;=\;S\;=\;S^{-1}\;{\neq}\;I_m$. We say that $G\;{\in}\;C^{m{\times}n}$ is a generalized reflexive matrix if RGS = G. The set of all m ${\times}$ n generalized reflexive matrices is denoted by $GRC^{m{\times}n}$. In this paper, an efficient method for the least squares solution $X\;{\in}\;GRC^{m{\times}n}$ of the matrix equation AXB = D with arbitrary coefficient matrices $A\;{\in}\;C^{p{\times}m}$, $B\;{\in}\;C^{n{\times}q}$and the right-hand side $D\;{\in}\;C^{p{\times}q}$ is developed based on the canonical correlation decomposition(CCD) and, an explicit formula for the general solution is presented.

• 통합자연과학논문집
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• 제8권4호
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• pp.235-243
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• 2015

Rhodium(I)-complex of $[Rh(CO)_2I_2{^-}]$ catalyzed carbonylation of anhydrous-trimethylamine in the presence of methyl iodide to give DMAC (N,N-dimethylacetamide) in no solvent. The catalyst had been reused 20 times, the analyses and distillation of collected products showed that the yields of DMAC, MAA (N-methylacetamide), and DMF (N,N-dimethylformamide) were 82.3%, 12.6%, and 4.4%. The conversion rate of trimethylamine was 99 % and the selectivity of DMAC was 82.3% with TON (Turnover Number) of 700. Stepwise procedure of inner-sphere reductive elimination for the formation of DMAC was suggested instead of acyl iodide intermediate.

• 대한수학회논문집
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• 제31권4호
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• pp.667-682
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• 2016

In this article we show a recursive method to compute the coefficients of the minimal polynomial of cos($2{\pi}/n$) explicitly for $n{\geq}3$. The recursion is not on n but on the coefficient index. Namely, for a given n, we show how to compute ei of the minimal polynomial ${\sum_{i=0}^{d}}(-1)^ie_ix^{d-i}$ for $i{\geq}2$ with initial data $e_0=1$, $e_1={\mu}(n)/2$, where ${\mu}(n)$ is the $M{\ddot{o}}bius$ function.

• 대한화학회지
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• 제48권3호
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• pp.236-242
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• 2004

25$^{\circ}C$의 순수 물 및 n-부탄올 수용액에서 Dodecylpyridinium chloride(DPC)와 Cetyldimethylethylammonium bromide(CDEAB)의 혼합계면활성제가 나타내는 임계마이셀농도(CMC)와 반대이온결합상수(B)값을 DPC의 겉보기몰분율(${\alpha}_1$)에 따른 변화를 전도도법으로 측정하였다. 이와같이 측정한 CMC값에 비이상적 혼합마이셀화모델을 적용함으로써 여러 가지 열역학적 함수값(($X_i,\;{\gamma}_i,\;C_i,\;a^M_i,\;{\beta},\;and\;{\Delta}H_{mix})$들을 계산하고 분석하였다. 그리고 DPC/CDEAB 혼합계면활성제의 마이셀화에 미치는 n-부탄올의 효과를 조사하기 위하여 n-부탄올의 농도에 따른 열역학 함수값(CMC, B 및 ${\Delta}G_o\;^m$)의 변화를 측정하고 분석하였다.

• Korean Journal of Mathematics
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• 제20권3호
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• pp.307-314
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• 2012

Let M be a left R-module and R be a ring with unity, and $S=\{0,2,3,4,{\ldots}\}$ be a submonoid. Then $M[x^{-s}]=\{a_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ is an $R[x^s]$-module. In this paper we show some properties of $M[x^{-s}]$ as an $R[x^s]$-module. Let $f:M{\rightarrow}N$ be an R-linear map and $\overline{M}[x^{-s}]=\{a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}a_i{\in}M\}$ and define $N+\overline{M}[x^{-s}]=\{b_0+a_2x^{-2}+a_3x^{-3}+{\cdots}+a_nx^{-n}{\mid}b_0{\in}N,\;a_i{\in}M}$. Then $N+\overline{M}[x^{-s}]$ is an $R[x^s]$-module. We show that given a short exact sequence $0{\rightarrow}L{\rightarrow}M{\rightarrow}N{\rightarrow}0$ of R-modules, $0{\rightarrow}L{\rightarrow}M[x^{-s}]{\rightarrow}N+\overline{M}[x^{-s}]{\rightarrow}0$ is a short exact sequence of $R[x^s]$-module. Then we show $E_1+\overline{E_0}[x^{-s}]$ is not an injective left $R[x^s]$-module, in general.

• 대한약리학회지
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• 제30권1호
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• pp.49-57
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• 1994

Oxomemazine이 muscarinic receptor subtypes에 대하여 선택성을 가지는지에 관한 지견을 얻고자, 대뇌, 심실 및 회장 muscarinic receptor에 대한 oxomemazine의 결합성질을 조사, 비교하였다. $[^3H]QNB$ 포화결합실험 결과 세 조직의 muscarinic receptor는 $[^3H]QNB$에 대해서는 affinity가 약 60pM인 단일 receptor인 것으로 추정되었다. 대뇌에서 pirenzepine과 oxomemazine의 $[^3H]QNB$ 결합억제에 대한 Hill coefficient는 각각 0.67 및 0.8로서 대뇌에는 이들 약물에 대하여 affinity가 서로 다른 두 종류의 muscarinic receptor subtypes가 존재하는 것으로 나타났으며, pirenzepine에 대한 high $affinity(M_1)$와 $low affinity(M_2)$ receptor 및 oxomemazine에 대한 high $affinity(O_H)$와 $low\;affinity (O_L)$ receptor의 분포비는 약 60:40 및 40:60이었고, $M_1$과 $M_2$ receptor에 대한 pirenzepine의 $K_i$치는 16nM 및 431 nM, $O_H$와 $O_L$, receptor에 대한 oxomemazine 의 $K_i$치는 80nM 및 1350nM이었다. 그러나 심실과 회장에서 이들 약물의 $[^3H]QNB$ 결합억제에 대한 Hill coefficient는 1에 가까웠다. 심실과 회장 muscarinic receptor에 대한 pirenzepine의 $K_i$치는 850nM 및 250nM, oxomemazine의 $K_i$치는 1460nM 및 670nM로서 대피에서 이들 약물의 low affinity receptor에 대한 $K_i$치에 가까웠다. 즉, muscarinic receptor에 대한 affinity면에서 oxomemazine은 pirenzepine과 같이 대뇌에서 가장 높았으며, 회장에 대해서는 중등도였고, 심실에서 가장 낮았다. 이로 보아 oxomemazine은 $M_1\;receptor$에 선택성이 있는 것으로 추정된다.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.95-101
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• 2014

An n-tuple ($a_1,a_2,{\ldots},a_n$) is symmetric, if $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$. Let $H_n$ = {$(a_1,a_2,{\ldots},a_n)$ ; $a_k$ ${\in}$ {+,-}, $a_k$ = $a_{n-k+1}$, $1{\leq}k{\leq}n$} be the set of all symmetric n-tuples. A symmetric n-sigraph (symmetric n-marked graph) is an ordered pair $S_n$ = (G,${\sigma}$) ($S_n$ = (G,${\mu}$)), where G = (V,E) is a graph called the underlying graph of $S_n$ and ${\sigma}$:E ${\rightarrow}H_n({\mu}:V{\rightarrow}H_n)$ is a function. The restricted super line graph of index r of a graph G, denoted by $\mathcal{R}\mathcal{L}_r$(G). The vertices of $\mathcal{R}\mathcal{L}_r$(G) are the r-subsets of E(G) and two vertices P = ${p_1,p_2,{\ldots},p_r}$ and Q = ${q_1,q_2,{\ldots},q_r}$ are adjacent if there exists exactly one pair of edges, say $p_i$ and $q_j$, where $1{\leq}i$, $j{\leq}r$, that are adjacent edges in G. Analogously, one can define the restricted super line symmetric n-sigraph of index r of a symmetric n-sigraph $S_n$ = (G,${\sigma}$) as a symmetric n-sigraph $\mathcal{R}\mathcal{L}_r$($S_n$) = ($\mathcal{R}\mathcal{L}_r(G)$, ${\sigma}$'), where $\mathcal{R}\mathcal{L}_r(G)$ is the underlying graph of $\mathcal{R}\mathcal{L}_r(S_n)$, where for any edge PQ in $\mathcal{R}\mathcal{L}_r(S_n)$, ${\sigma}^{\prime}(PQ)$=${\sigma}(P){\sigma}(Q)$. It is shown that for any symmetric n-sigraph $S_n$, its $\mathcal{R}\mathcal{L}_r(S_n)$ is i-balanced and we offer a structural characterization of super line symmetric n-sigraphs of index r. Further, we characterize symmetric n-sigraphs $S_n$ for which $\mathcal{R}\mathcal{L}_r(S_n)$~$\mathcal{L}_r(S_n)$ and $$\mathcal{R}\mathcal{L}_r(S_n){\sim_=}\mathcal{L}_r(S_n)$$, where ~ and $$\sim_=$$ denotes switching equivalence and isomorphism and $\mathcal{R}\mathcal{L}_r(S_n)$ and $\mathcal{L}_r(S_n)$ are denotes the restricted super line symmetric n-sigraph of index r and super line symmetric n-sigraph of index r of $S_n$ respectively.

• 대한수학회지
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• 제51권3호
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• pp.463-472
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• 2014

Let R be a ring with identity 1, I(R) be the set of all nonunit idempotents in R and $S_{\ell}$(R) (resp. $S_r$(R)) be the set of all left (resp. right) semicentral idempotents in R. In this paper, the following are investigated: (1) $e{\in}S_{\ell}(R)$ (resp. $e{\in}S_r(R)$) if and only if re=ere (resp. er=ere) for all nilpotent elements $r{\in}R$ if and only if $fe{\in}I(R)$ (resp. $ef{\in}I(R)$) for all $f{\in}I(R)$ if and only if fe=efe (resp. ef=efe) for all $f{\in}I(R)$ if and only if fe=efe (resp. ef=efe) for all $f{\in}I(R)$ which are isomorphic to e if and only if $(fe)^n=(efe)^n$ (resp. $(ef)^n=(efe)^n$) for all $f{\in}I(R)$ which are isomorphic to e where n is some positive integer; (2) For a ring R having a complete set of centrally primitive idempotents, every nonzero left (resp. right) semicentral idempotent is a finite sum of orthogonal left (resp. right) semicentral primitive idempotents, and eRe has also a complete set of primitive idempotents for any $0{\neq}e{\in}S_{\ell}(R)$ (resp. 0$0{\neq}e{\in}S_r(R)$).

• 한국막학회:학술대회논문집
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• 한국막학회 2004년도 Proceedings of the second conference of aseanian membrane society
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• pp.86-89
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• 2004

The present study reports the preparation of a compact ZSM-5 membrane showing high thermal stability and high separation factors, especially n-/i-butane isomers at high temperatures. ZSM-5 membrane was prepared on a porous $\alpha$-Al$_2$O$_3$ tube (an average pore diameter, ca. 100 nm) at 18$0^{\circ}C$ by the seed-assisted crystallization method. The XRD and SEM results showed that a thin zeolite layer (ca. 1 ${\mu}{\textrm}{m}$) was formed on the support surface. The single gas permeances of $N_2$, H$_2$, SF$_{6}$, n-butane, and i-butane were taken at 27$0^{\circ}C$. i-Butane permeance hardly changed after repeated thermal treatments up to 40$0^{\circ}C$, indicating the membrane is thermally stable. On the other hand, other single gas permeances increased when the membrane was further dried at 40$0^{\circ}C$, indicating thermal pretreatment at 27$0^{\circ}C$ could not remove all the adsorbed species in the membrane. i-Butane and SF$_{6}$ permeances were significantly lower than the permeances of smaller molecules, indicating that the membrane has a low concentration of defects. The ideal selectivities at 27$0^{\circ}C$ were 61 for $H_2$/i-butane and 47 for $H_2$/SF$_{6}$. The temperature dependency of n/i-butane ideal selectivities and separation factors for an equimolar n/i-butane mixture was studied. The ideal selectivity showed a maximum of 36 at 30$0^{\circ}C$. The separation factors increased with temperature and reached around 12 at 300-40$0^{\circ}C$, which were much higher than those reported in the literature.ature.