• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.437-448
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• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• 약학회지
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• 제13권2_3호
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• pp.62-66
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• 1969

Ten new N$^{4}$-furoylsulfonamides were synthesized such as N$^{4}$-furoyl-N$^{1}$-(4,6-dimethyl-2-pyrimidinyl) sulfanilamide (I), N$^{4}$-furoylsulfanilamide (II), N$^{4}$-furoyl-N$^{1}$-(2,6-dimethoxy-4-pyrimidinyl) sulfanilamide (III), N$^{4}$-furoyl-N$^{1}$-(4-methyl-2-pyrimidinyl) sulfanilamide (IV), N$^{4}$-furoyl-N$^{1}$-(6-methoxy-3-pyridazinyl) sulfanilamide (V), N$^{4}$-furoyl-N$^{1}$-2-pyrimidinylsulfanilamide (VI), N$^{4}$-furoyl-N$^{1}$-(3,4-dimethyl-5-isoxazolyl) sulfanilamide (VII), N$^{4}$-furoyl-N$^{1}$-2-thiazoilysulfanilamide (VIII), N$^{4}$-furoyl-N$^{1}$-(5-methoxy-2-pyrimidinyl) sulfanilamide (IX) and N$^{4}$-furoyl-N$^{1}$-(2,6-dimethyl-4-pyrimidinyl) sulfanilamide (X). They were obtained by the action of N$^{1}$-(4,6-dimethyl-2-pyrimidinyl) sulfanilamide, N$^{1}$-(2,6-dimethoxy-4-pyrimidinyl) sulfanilamide, N$^{1}$-(4-methyl-2-pyrimidinyl) sulfanilamide, N$^{1}$-(6-methoxy-3-pyridazinyl) sulfanilamide, N-2-pyrimidinyl sulfanilamide, N$^{1}$-(3,4-dimethyl-5-isoxazolyl) sulfanilamide, N$^{1}$-2-(thiazolysulfanilamide), N$^{1}$-(5-methoxy-2-pyrimidinyl) sulfanilamide and N$^{1}$-(2,6-dimethyl-4-pyrimidinyl) sulfanilamide with furoyl chloride in 4% NaOH solution. Of the above ten compounds, N$^{4}$-furoylsulfathiazole exhibited a good antibacterial action against Staphylococeus aureus and Escherichia coli.

• 한국응용과학기술학회지
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• 제35권3호
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• pp.643-653
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• 2018

본 연구는 고지혈증 모델동물 랫드에서 n-6/n-3가 서로 다른 식이를 급여하였을 때 혈액지질의 대사적 분할에 미치는 작용 메카니즘을 생체 모니터링 기법으로 구명하였다. 총 glycerolipids의 간에서 대사된 cholesteryl $^{14}C$-oleate 비율은 n-6/n-3 비율 4:1, 15:1, 30:1, 대조군 순서로 낮았다(p<0.05). 인지질 분비량은 대조군과 비교할 때 n-6/n-3 비율 4:1, 15:1, 30:1 순서로 높았다(p<0.05). 중성지방 분비량은 대조군과 비교할 때 n-6/n-3 비율 4:1, 15:1, 30:1 순서로 특히, 4:1 처리군에서 낮았다(p<0.05). 총 glycerolipid에 대한 인지질의 분할 비율은 n-6/n-3 비율 4:1, 15:1, 30:1, 대조군 순서로 높았다(p<0.05). 간으로부터 중성지방 분할 비율(%)은 대조군 82.25%와 비교할 때 n-6/n-3 비율 4:1, 15:1, 30:1에서 각각 72.99, 75.93, 78.12%로써 n-6/n-3 비율이 증가할수록 높아졌다(p<0.05). 인지질 분할 비율(%)은 대조군 11.04%와 비교할 때 n-6/n-3 비율 4:1, 15:1, 30:1에서 각 25.15, 18.87, 18.15%로써 n-6/n-3 비율이 증가할수록 낮아졌다(p<0.05).

• East Asian mathematical journal
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• 제25권2호
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• pp.179-196
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• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• East Asian mathematical journal
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• 제24권1호
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.497-503
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• 2005

This paper presents characterizations on the independence of the exponential and Pareto distributions by record values. Let ${X_{n},\;n {\ge1}$ be a sequence of independent and identically distributed(i.i.d) random variables with a continuous cumulative distribution function(cdf) F(x) and probability density function(pdf) f(x). $Let{\;}Y_{n} = max{X_1, X_2, \ldots, X_n}$ for n \ge 1. We say $X_{j}$ is an upper record value of ${X_{n},{\;}n\ge 1}, if Y_{j} > Y_{j-1}, j > 1$. The indices at which the upper record values occur are given by the record times {u(n)}, n \ge 1, where u(n) = $min{j|j > u(n-1), X_{j} > X_{u(n-1)}, n \ge 2}$ and u(l) = 1. Then F(x) = $1 - e^{-\frac{x}{a}}$, x > 0, ${\sigma} > 0$ if and only if $\frac {X_u(_n)}{X_u(_{n+1})} and X_u(_{n+1}), n \ge 1$, are independent. Also F(x) = $1 - x^{-\theta}, x > 1, {\theta} > 0$ if and only if $\frac {X_u(_{n+1})}{X_u(_n)}{\;}and{\;} X_{u(n)},{\;} n {\ge} 1$, are independent.

• Journal of Microbiology and Biotechnology
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• 제20권1호
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• pp.63-70
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• 2010

Novel influenza A (H1N1) is a newly emerged flu virus that was first detected in April 2009. Unlike the avian influenza (H5N1), this virus has been known to be able to spread from human to human directly. Although it is uncertain how severe this novel H1N1 virus will be in terms of human illness, the illness may be more widespread because most people will not have immunity to it. In this study, we compared the codon usage bias between the novel H1N1 influenza A viruses and other viruses such as H1N1 and H5N1 subtypes to investigate the genomic patterns of novel influenza A (H1N1). Totally, 1,675 nucleotide sequences of the hemagglutinin (HA) and neuraminidase (NA) genes of influenza A virus, including H1N1 and H5N1 subtypes occurring from 2004 to 2009, were used. As a result, we found that the novel H1N1 influenza A viruses showed the most close correlations with the swine-origin H1N1 subtypes than other H1N1 viruses, in the result from not only the analysis of nucleotide compositions, but also the phylogenetic analysis. Although the genetic sequences of novel H1N1 subtypes were not exactly the same as the other H1N1 subtypes, the HA and NA genes of novel H1N1s showed very similar codon usage patterns with other H1N1 subtypes, especially with the swine-origin H1N1 influenza A viruses. Our findings strongly suggested that those novel H1N1 viruses seemed to be originated from the swine-host H1N1 viruses in terms of the codon usage patterns.

• 호남수학학술지
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• 제44권1호
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• pp.135-145
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• 2022

This paper aims to investigate characterizations on parameters k₁, k₂, k₃, k₄, k₅, l₁, l₂, l₃, and l₄ to find relation between the class of 𝓗(k, l, m, n, o) hypergeometric functions defined by $$5_F_4\[{\array{k_1,\;k_2,\;k_3,\;k_4,\;k_5\\l_1,\;l_2,\;l_3,\;l_4}}\;:\;z\]=\sum\limits_{n=2}^{\infty}\frac{(k_1)_n(k_2)_n(k_3)_n(k_4)_n(k_5)_n}{(l_1)_n(l_2)_n(l_3)_n(l_4)_n(1)_n}z^n$$. We need to find k, l, m and n that lead to the necessary and sufficient condition for the function zF([W]), G = z(2 - F([W])) and $H_1[W]=z^2{\frac{d}{dz}}(ln(z)-h(z))$ to be in 𝓢^*(2^-r), r is a positive integer in the open unit disc 𝒟 = {z : |z| < 1, z ∈ ℂ} with $$h(z)=\sum\limits_{n=0}^{\infty}\frac{(k)_n(l)_n(m)_n(n)_n(1+\frac{k}{2})_n}{(\frac{k}{2})_n(1+k-l)_n(1+k-m)_n(1+k-n)_nn(1)_n}z^n$$ and $$[W]=\[{\array{k,\;1+{\frac{k}{2}},\;l,\;m,\;n\\{\frac{k}{2}},\;1+k-l,\;1+k-m,\;1+k-n}}\;:\;z\]$$.

• 대한화학회지
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• 제13권3호
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• pp.221-228
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• 1969

Nucleophile의 親核性 添加反應性을 정량적으로 연구하고자 전보에 이어 3,4-methylenedioxy-${\beta}$-nitrostyrene에 대한 n-amyl, n-hexyl, n-Octyl, n-decylamercaptanㅓ의 添加反應速度常數를 측정한 결과 n-amylmercaptide, n-hexylmercaptide, n-octylmercaptide, n-decylmercaptide ino에 대해 각각 2.82${\times}10^8$, 100${\times}10^8$, 2.23${\times}10^8$과 1.77${\times}10^8$ $M^{-2} .sec^{-1}$를 얻었고, n-amyl, n-hexyl, n-Octyl, n-decylmercaptan분자에 대해서는 각각 2.82${\times}10^{-2}$, 1.95${\times}10^{-2}$, 7.08${\times}10^{-2}$과 5.63${\times}10^{-2}$$M^{-1} . sec^{-1}$를 얻었으며, 염기성뿐만 아니라 산성용매 속에서도 그의 반응메카니즘을 잘 설명할 수 있는 반응속도 식도 구하였다.

• 호남수학학술지
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• 제26권4호
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• pp.463-469
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the exponential distribution. Let $\{X_n,\;n{\geq}1\}$ be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function(pdf) f(x). Let $Y_n=max\{X_1,\;X_2,\;{\cdots},\;X_n\}$ for $n{\geq}1$. We say $X_j$ is an upper record value of $\{X_n,\;n{\geq}1\}$, if $Y_j>Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, $n{\geq}1$, where u(n)=min\{j{\mid}j>u(n-1),\;X_j>X_{u(n-1)},\;n{\geq}2\} and u(1) = 1. Suppose $X{\in}Exp(1)$. Then $\Large{E\;\left.{\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}}\right)=\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n)}}}\right)}$ and $\Large{E\;\left.{\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}}\right)=\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m-1)}}{X^s_{u(n-1)}}}\right)}$.