• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.393-401
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• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.401-409
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• 2010

In this paper, we introduce an iterative method to study oscillatory properties of delay difference equations of the following form ${\nabla}_{\alpha}\;[x(t)\;-\;r(t)x(t\;-\;k)]\;+\;p(t)x(t\;-\;{\tau})\;-\;q(t)x(t\;-\;{\sigma})\;=\;0$, $t\;{\geq}\;t_0$, where $t_0\;{\in}\;\mathbb{R}$, t varies in the real interval ($t_0,\;{\infty}$), $\alpha$ > 0, $\kappa$, $\tau$, ${\sigma}\;{\geq}\;0$, $r\;{\in}\;C\;([t_0-{\alpha},\;{\infty}),\;\mathbb{R}^+$, p, $q\;{\in}\;C\;([t_0,\;{\infty}),\;\mathbb{R}^+)$ and ${\nabla}_{\alpha}x(t)\;=\;x(t)\;-\;x(t\;-\;{\alpha})$ for $t\;{\geq}\;t_0$.

• Proceedings of the Korean Magnestics Society Conference
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• 2008.12a
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• pp.4.2-4.2
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• 2008

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.323-342
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• 2013

Let $C[0,t]$ denote the function space of all real-valued continuous paths on $[0,t]$. Define $Xn:C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}:C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\cdots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\cdots},x(t_n),x(t_{n+1}))$, where $0=t_0$ < $t_1$ < ${\cdots}$ < $t_n$ < $t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions which have the form $${\int}_{L_2[0,t]}{{\exp}\{i(v,x)\}d{\sigma}(v)}{{\int}_{\mathbb{R}^r}}\;{\exp}\{i{\sum_{j=1}^{r}z_j(v_j,x)\}dp(z_1,{\cdots},z_r)$$ for $x{\in}C[0,t]$, where $\{v_1,{\cdots},v_r\}$ is an orthonormal subset of $L_2[0,t]$ and ${\sigma}$ and ${\rho}$ are the complex Borel measures of bounded variations on $L_2[0,t]$ and $\mathbb{R}^r$, respectively. We then investigate the inverse transforms of the function with their relationships and finally prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the products of the conditional Fourier-Feynman transforms of each function.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1385-1394
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• 2016

Let (R, m) be a Noetherian local ring, I, J two ideals of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of lengths of A-cosequences in dimension > k in I defined by Nhan-Hoang [9]. It is first shown that for each $t{\leq}r$ and each sequence $x_1,{\cdots},x_t$ which is an A-cosequence in dimension > k, the set $$\Large(\bigcup^{t}_{i=0}Att_R(0:_A(x_1^{n_1},{\ldots},x_i^{n_i})))_{{\geq}k}$$ is independent of the choice of $n_1,{\ldots},n_t$. Let r be the eventual value of $Width_{>k}(0:_AJ^n)$. Then our second result says that for each $t{\leq}r$ the set $\large(\bigcup\limits_{i=0}^{t}Att_R(Tor_i^R(R/I,\;(0:_AJ^n))))_{{\geq}k}$ is stable for large n.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.167-169
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• 1999

Let R be a Noetherian domain. It is proved that $t$-dimR = 1 if and only if each (proper if R is not a valuation domain) $t$-linked overring D of R is of $t$-dimD = 1 if and only if each integrally closed $t$-linked overring of R is a Krull domain.

• Nuclear Engineering and Technology
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• v.19 no.3
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• pp.169-179
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• 1987

The change of material J-R (J-T) curve with crack extension and J-calculation method was investigated to give experimental and analytical method for reliable J-R (J-T) curve, which was adapted recently as a tool for instability analysis of Nuclear Pressure Vessel. Experiments were carried out by Single Specimen Unloading Compliance Method using 1/2"T, Compact-Tension Type fracture mechanic specimens which were the same size and material as domestic nuclear pressure vessel material surveillance specimens. The results revealed that crack extension up to 25~30% of initial uncracked ligament and JD (Deformation theory J) calculation method, currently being used in NUREG-0744, could give rather reliable material J-R (J-T) curve than the small crack extension and JM (Modified J) calculation method. But as JM results more or less higher J at instability, the application of JM should be considered regarding to the problem of power plant availability.lity.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• Korean Journal of Microbiology
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• v.48 no.3
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• pp.180-186
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• 2012

Pseudomonas aeruginosa, a Gram-negative bacterium, is an ubiquitous and opportunistic human pathogen, which expresses many virulence factors through quorum sensing (QS) regulation. QscR, one of the QS signal receptors of P. aeruginosa, has unique features that make it possible to distinguish QscR from other QS receptors. In the present study, we focused on amino acid residues responsible for such a broad signal specificity of QscR. Thus we constructed mutant QscRs: $QscR_{T72I}$, $QscR_{R132M}$, and $QscR_{T140I}$ by substituting $72^{nd}$ threonine, $132^{nd}$ arginine, and $140^{th}$ threonine residues with isoleucine, methionine, and isoleucine, respectively by site-directed mutagenesis. When we examined the activity of these mutant QscRs, $QscR_{R132M}$ failed to respond to N-3-oxododecanoyl homoserine lactone (3OC12-HSL), but $QscR_{T72I}$ and $QscR_{T140I}$ remained the ability to respond to 3OC12-HSL despite much reduction of the sensitivity. When we treated a variety of acyl-HSLs with different structure, $QscR_{T72I}$ and $QscR_{T140I}$ showed better responsiveness to N-decanoyl HSL (C10-HSL) or N-dodecanoyl HSL (C12-HSL) that has no oxo-moiety at $3^{rd}$ carbon of acyl group than to 3OC12-HSL, and $QscR_{R132M}$ showed no responsiveness to any acyl-HSLs tested here. In addition, $QscR_{T72I}$ and $QscR_{T140I}$ were inhibited by 5f, a QscR inhibitor as similarly as wild type QscR was. These results suggest that while the $130^{th}$ arginine is crucial in both activity and acyl-HSL binding of QscR, the $72^{nd}$ and $140^{th}$ threonines are important in the activity, but they are little responsible for the discrimination of acyl-HSLs or competitive inhibitor.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.487-496
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• 1996

Let f(z) be an entire function. Then the order $\rho(f)$ of f is defined by $$ \rho(f) = \overline{lim}_r\to\infty \frac{log r}{log^+ T(r,f)} = \overline{lim}_r\to\infty \frac{log r}{log^+ log^+ M(r,f)}, $$ where T(r,f) is the Nevanlinna characteristic of f (see [4]), $M(r,f) = max_{$\mid$z$\mid$=r} $\mid$f(z)$\mid$$ and $log^+ t = max(log t, 0)$.