• 호남수학학술지
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• 제40권1호
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• pp.139-153
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• 2018

Let $P{\geq}3$ be an integer and let ($U_n$) denote generalized Fibonacci sequence defined by $U_0=0$, $U_1=1$ and $U_{n+1}=PU_n-U_{n-1}$ for $n{\geq}1$. In this study, when P is odd, we solve the equation $U_n=11x^2+1$. We show that only $U_1$ and $U_2$ may be of the form $11x^2+1$.

• 대한수학회지
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• 제35권2호
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• pp.465-490
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• 1998

In this paper, we consider the existence and asymptotic behavior of solutions of the following problem: $u_{tt}$ -(t, x) - (∥∇u(t, x)∥(equation omitted) ＋ ∥∇v(t, x) (equation omitted)$^{\gamma}$ $\Delta$u(t, x)＋$\delta$│ $u_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$│u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], $v_{tt}$ (t, x) - (∥∇uu(t, x) (equation omitted) ＋ ∥∇v(t, x) (equation omitted)sup ${\gamma}$/ $\Delta$v(t, x)＋$\delta$ │ $v_{t}$ (t, x)│sup p-1/ $u_{t}$ (t, x) = $\mu$ u(t, x) $^{q-1}$u(t, x), x$\in$$\Omega$, t$\in$[0, T], u(0, x) = $u_{0}$ (x), $u_{t}$ (0, x) = $u_1$(x), x$\in$$\Omega$, u(0, x) = $v_{0}$ (x), $v_{t}$ (0, x) = $v_1$(x), x$\in$$\Omega$, u│∂$\Omega$=v│∂$\Omega$=0 T > 0, q > 1, p $\geq$1, $\delta$ > 0, $\mu$ $\in$ R, ${\gamma}$ $\geq$ 1 and $\Delta$ is the Laplacian in $R^{N}$.X> N/.

• Plant Biotechnology Reports
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• 제5권3호
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• pp.289-295
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• 2011

The SpoU family of proteins catalyzes the methylation of transfer RNAs (tRNAs) and ribosomal RNAs (rRNAs). We characterized a putative tRNA/rRNA methyltransferase, VaSpoU1 of the SpoU family, from Viscum album (mistletoe). VaSpoU1 and other plant SpoU1s exhibit motifs of the SpoU methylase domain that are conserved with bacterial and yeast SpoU methyltransferases. VaSpoU1 transcripts were detected in the leaves and stems of V. album. VaSpoU1-GFP fusion proteins localized to both chloroplasts and mitochondria in Arabidopsis protoplasts. Sequence analysis similarly predicted that the plant SpoU1 proteins would localize to chloroplasts and mitochondria. Interestingly, mitochondrial localization of VaSpoU1 was inhibited by the deletion of a putative N-terminal presequence in Arabidopsis protoplasts. Therefore, VaSpoU1 may be involved in tRNA and/or rRNA methylation in both chloroplasts and mitochondria.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.955-961
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• 2009

In this paper, we establish some characterizations which is satisfied by the independence of the upper record values from the Pareto distribution. We prove that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(m)}}$ and $X_{U(m)}$, $1\;{\le}\;m\;<\;n$ are independent. We show that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0 if and only if $\frac{X_{U(n)}+X_{U{(n+1)}}}{X_{U(n)}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent. And we characterize that $X\;{\in}\;PAR(1,\;{\beta})$, $\beta$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(n)}+X_{U{(n+1)}}}$ and $X_{U(n)}$, $n\;{\ge}\;1$ are independent.

• 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 applied mathematics & informatics
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• 제34권3_4호
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• pp.269-284
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• 2016

In this paper, we firstly use Krasnosel'skii fixed point theorem to investigate positive solutions for the following three-point boundary value problems for p-Laplacian with a parameter $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+{\lambda}f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1), λ > 0 is a parameter. Then we use Leggett-Williams fixed point theorem to study the existence of three positive solutions for the fractional boundary value problem $({\phi}_P(D^{\alpha}_{0}+u(t)))^{\prime}+f(t, u(t))=0$, 0$D^{\alpha}_{0}+u(0)=u(0)=u{\prime}{\prime}(0)=0$, $u^{\prime}(1)={\gamma}u^{\prime}(\eta)$ where ϕ_p(s) = |s|^p−2s, p > 1, $D^{\alpha}_{0^+}$ is the Caputo's derivative, α ∈ (2, 3], η, γ ∈ (0, 1).

• 대한수학회보
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• 제50권5호
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• pp.1513-1521
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• 2013

In this paper we will study cyclic codes over some special rings: $\mathbb{F}_q[u]/(u^i)$, $\mathbb{F}_q[u_1,{\ldots},u_i]/(u^2_1,u^2_2,{\ldots},u^2_i,u_1u_2-u_2u_1,{\ldots},u_ku_j-u_ju_k,{\ldots})$, and $\mathbb{F}_q[u,v]/(u^i,v^j,uv-vu)$, where $\mathbb{F}_q$ is a field with $q$ elements $q=p^r$ for some prime number $p$ and $r{\in}\mathbb{N}-\{0\}$.

• 공업화학
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• 제24권3호
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• pp.227-230
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• 2013

$(U_{1-x}Nd_x)O_2$ 소결체를 $500^{\circ}C$에서 산화하여 얻은 $(U_{1-x}Ndx)_3O_8$ 분말의 상변화를 $900{\sim}1500^{\circ}C$의 공기 중에서 고온 산화 열처리를 하여 조사하였다. $1100^{\circ}C$ 이상의 온도로 산화 열처리할 경우에 Nd 농도가 높은 $(U_{1-y}Nd_y)O_{2+z}$ 상과 $U_3O_8$ 상이 생성됨을 확인하였으며, 산화 열처리 온도가 높아질수록 $(U_{1-y}Nd_y)O_{2+z}$ 상에서의 Nd 농도는 감소하였다. 산화 열처리 온도의 증가에 따라서 $U_3O_{8-w}$ 입자로부터 $(U_{1-y}Nd_y)O_{2+z}$ 입자로의 U 양이온 및 Nd 양이온이 두 입자의 계면을 통해 농도 구배에 따른 확산에 의해서 $(U_{1-y}Nd_y)O_{2+z}$ 상 내에 U의 농도는 증가하고 Nd의 농도는 감소하게 된다. 이러한 현상은 산화 열처리 온도증가에 따라서 $U_3O_8$ 상에 대한 $(U_{1-y}Nd_y)O_{2+z}$ 상의 X-선 회절피크의 적분강도비 증가와 $(U_{1-y}Nd_y)O_{2+z}$ 상의 입자가 커지는 것과 연관하여 해석할 수 있었다.

• 충청수학회지
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• 제30권1호
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• pp.1-13
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• 2017

We introduce the concepts of (${\mathcal{T}}^{{\mu}{\gamma}},{\mathcal{U}}^{{\mu}{\gamma}}$)-double (r, s)(u, v)-preclosures and (${\mathcal{T}}^{{\mu}{\gamma}},{\mathcal{U}}^{{\mu}{\gamma}}$)-double (r, s)(u, v)-preinteriors. Using the notions, we investigate some of characteristic properties of double pairwise (r, s)(u, v)-precontinuous mappings.

• 대한수학회지
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• 제47권3호
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• pp.547-572
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• 2010

We study existence of positive solutions of the classical nonlinear Schr$\ddot{o}$dinger equation $-{\Delta}u\;+\;V(x)u\;-\;f(x,\;u)\;-\;H(x)u^{2*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$. In fact, we consider the following more general quasi-linear Schr$\ddot{o}$odinger equation $-div(|{\nabla}u|^{m-2}{\nabla}u)\;+\;V(x)u^{m-1}$ $-f(x,\;u)\;-\;H(x)u^{m^*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$, where m $\in$ (1, n) is a positive number and $m^*\;:=\;\frac{mn}{n-m}\;>\;0$, is the corresponding critical Sobolev embedding number in $\mathbb{R}^n$. Under appropriate conditions on the functions V(x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.