• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1133-1143
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• 1999

Chaterji strengthened version of a theorem for martin-gales which is a generalization of a theorem of Marcinkiewicz proving that if $X_n$ is a sequence of independent, identically distributed random variables with $E{\mid}X_n{\mid}^p\;<\;{\infty}$, 0 < P < 2 and $EX_1\;=\;1{\leq}\;p\;<\;2$ then $n^{-1/p}{\sum^n}_{i=1}X_i\;\rightarrow\;0$ a,s, and in $L^p$. In this paper, we probe a version of law of large numbers for double arrays. If ${X_{ij}}$ is a double sequence of random variables with $E{\mid}X_{11}\mid^log^+\mid X_{11}\mid^p\;<\infty$, 0 < P <2, then $lim_{m{\vee}n{\rightarrow}\infty}\frac{{\sum^m}_{i=1}{\sum^n}_{j=1}(X_{ij-a_{ij}}}{(mn)^\frac{1}{p}}\;=0$ a.s. and in $L^p$, where $a_{ij}$ = 0 if 0 < p < 1, and $a_{ij}\;=\;E[X_{ij}\midF_[ij}]$ if $1{\leq}p{\leq}2$, which is a generalization of Etemadi's marcinkiewicz-type SLLN for double arrays. this also generalize earlier results of Smythe, and Gut for double arrays of i.i.d. r.v's.

• Proceedings of the Korean Society of Applied Pharmacology
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• 1994.04a
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• pp.171-171
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• 1994

Cephem ring의 C-7위치에 aminothiazoly lmethoxyimino기를 가진 화합물들이 항균활성을 증가시키고, G(-)균의 외막투과성을 촉진시킬뿐 아니라 광범위항균 spectrum을 갖게 하고 $\beta$-lactamase에 안정하며 PBP(penicillin binding protein)에 대한 결합친화성을 증가시킨다는 보고에 따라 본 저자는 C-7위치에 cefotaxime구조와 같이 aminothiazolylmethoxyimino acetamido moiety를 고정시키고 항균활성을 증가시키기 위하여 약리활성이 기대되는 5-(substituted)-2H-tetrazole유도체들을 합성하여 C-3 위치에 도입시킨 새로운 화합물 7$\beta$-〔(z)-2-(2-aminothiazol-4-yl)-2_(methoxyimino)acetamido〕-3-〔5-(substituted)tetrazol-2-yl〕 methyl-3-cephem-4-carboxylic acid 유도체를 합성하여 B. subtilis ATCC 6633, M. luteus ATCC 1004, E. coli KCTC 1039, E. coli ESS, K. pncumonia KCTC 1560, P. aeruginosa IF0 13130, S. typhimurium KCTC 1925, S. typhimurium SL 1102, 및 C. albicans ATCC 10231 등의 균과 fungus에 대하여 기존의 cefotaxime과 cefazoline을 대조물질로 사용하여 항균력을 비교하였다. 이들 화합물들은 대체적으로 M. luteus ATCC 6633, E. coli ESS, S. typhimurium SL 1102 균에 대해서는 cefotaxime보다 항균력이 우수하였으나 P. aeruginosa IF0 13130에 대해서는 항균력이 저하되었고 cefazolin보다는 대체적으로 항균력이 우수하였다.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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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$0{\neq}e{\in}S_r(R)$).

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.271-279
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• 1995

In 1986, Fabry, Mawhin and Nkashama [1] have considered periodic solutios for Lienard equation $$ (1_s) x" + f(x)x' + g(t,x) = s, $$ where s is a real parameter, f and g are continuous functions, and g is $2\pi$-periodic in t and have proved that if $$ (H) lim_{$\mid$x$\mid$\to\infty} g(t,x) = \infty uniformly in t \in [0,2\pi], $$ there exists $s_1 \in R$ such that $(1_s)$ has no $2\pi$periodic solution if $s< s_1$, and at least one $2\pi$-periodic solution if $s = s_1$, and at least two $2\pi$-periodic solutions if $s > s_1$.s_1$.

• East Asian mathematical journal
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• v.17 no.2
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• pp.367-374
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• 2001

Northcott and McKerrow proved that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-1}]$ is an injective left R[x]-module. Park generalized Northcott and McKerrow's result so that if R is a left noetherian ring and E is an injective left R-module, then $E[x^{-S}]$ is an injective left $R[x^S]$-module, where S is a submonoid of $\mathbb{N}$($\mathbb{N}$ is the set of all natural numbers). In this paper we extend the injective property to the Laurent power series module so that if R is a ring and E is an injective left R-module, then $E[[x^{-1},x]]$ is an injective left $R[x^S]$-module.

• Molecules and Cells
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• v.27 no.3
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• pp.329-336
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• 2009

To evaluate the involvement of translation initiation factors eIF4E and eIFiso4E in Chilli veinal mottle virus (ChiVMV) infection in pepper, we conducted a genetic analysis using a segregating population derived from a cross between Capsicum annuum 'Dempsey' containing an elF4E mutation ($pvr1^2$) and C. annuum 'Perennial' containing an elFiso4E mutation (pvr6). C. annuum 'Dempsey' was susceptible and C. annuum 'Perennial' was resistant to ChiVMV. All $F_1$ plants showed resistance, and $F_2$ individuals segregated in a resistant-susceptible ratio of 166:21, indicating that many resistance loci were involved. Seventy-five $F_2$ and 329 $F_3$ plants of 17 families were genotyped with $pvr1^2$ and pvr6 allele-specific markers, and the genotype data were compared with observed resistance to viral infection. All plants containing homozygous genotypes of both $pvr1^2$ and pvr6 were resistant to ChiVMV, demonstrating that simultaneous mutations in elF4E and eIFiso4E confer resistance to ChiVMV in pepper. Genotype analysis of $F_2$ plants revealed that all plants containing homozygous genotypes of both $pvr1^2$ and pvr6 showed resistance to ChiVMV. In protein-protein interaction experiments, ChiVMV viral genome-linked protein (VPg) interacted with both eIF4E and eIFiso4E. Silencing of elF4E and eIFiso4E in the VIGS experiment showed reduction in ChiVMV accumulation. These results demonstrated that ChiVMV can use both eIF4E and eIFiso4E for replication, making simultaneous mutations in eIF4E and eIFiso4E necessary to prevent ChiVMV infection in pepper.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.157-163
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• 2014

Let {$X_i$, $1{\leq}i{\leq}n$} be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cumulative distribution function F(x) and probability density function f(x) and $E(X^2)$ < ${\infty}$. The random variables X + Y and $\frac{(X-Y)^2}{(X+Y)^2}$ are independent if and only if X and Y have gamma distributions. In addition, the random variables $S_n$ and $\frac{\sum_{i=1}^{m}(X_i)^2}{(S_n)^2}$ with $S_n=\sum_{i=1}^{n}X_i$ are independent for $1{\leq}m$ < n if and only if $X_i$ has gamma distribution for $i=1,{\cdots},n$.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.55-60
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• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.