• 대한수학회보
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• 제48권6호
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• pp.1169-1182
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• 2011

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form $$-div(h(x){\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+b(x){\mid}u{\mid}^{p-2}u=f(x,\;u),\;p{\geq}2$$ in an unbounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, with sufficiently smooth bounded boundary ${\partial}{\Omega}$, where $h(x){\in}L_{loc}^1(\overline{\Omega})$, $\overline{\Omega}={\Omega}{\cup}{\partial}{\Omega}$, $h(x){\geq}1$ for all $x{\in}{\Omega}$. The proof of main results rely essentially on the arguments of variational method.

• 대한수학회논문집
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• 제21권2호
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• pp.261-272
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• 2006

In this paper, we define the sequence spaces: $[V,{\lambda},f,p]_0({\Delta}^r,E,u),\;[V,{\lambda},f,p]_1({\Delta}^r,E,u),\;[V,{\lambda},f,p]_{\infty}({\Delta}^r,E,u),\;S_{\lambda}({\Delta}^r,E,u),\;and\;S_{{\lambda}0}({\Delta}^r,E,u)$, where E is any Banach space, and u = ($u_k$) be any sequence such that $u_k\;{\neq}\;0$ for any k , examine them and give various properties and inclusion relations on these spaces. We also show that the space $S_{\lambda}({\Delta}^r, E, u)$ may be represented as a $[V,{\lambda}, f, p]_1({\Delta}^r, E, u)$ space. These are generalizations of those defined and studied by M. Et., Y. Altin and H. Altinok [7].

• 대한화학회지
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• 제40권1호
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• pp.50-58
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• 1996

일정한 pH에서 Co(II), Ni(II), Sr(II), Cu(II), Fe(III) 및 U(VI) 등의 금속이온농도가 증가할 수록 흄산의 침적율이 증가하였으며, Sr

• 대한수학회논문집
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• 제12권2호
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.

• 대한수학회지
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• 제55권2호
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• pp.373-390
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• 2018

In this paper we study the small-data scattering of the d dimensional fractional $Schr{\ddot{o}}dinger$ equations with d = 2, 3, $L{\acute{e}}vy$ index 1 < ${\alpha}$ < 2 and Hartree type nonlinearity $F(u)={\mu}({\mid}x{\mid}^{-{\gamma}}{\ast}{\mid}u{\mid}^2)u$ with max(${\alpha}$, ${\frac{2d}{2d-1}}$) < ${\gamma}{\leq}2$, ${\gamma}$ < d. This equation is scaling-critical in ${\dot{H}}^{s_c}$, $s_c={\frac{{\gamma}-{\alpha}}{2}}$. We show that the solution scatters in $H^{s,1}$ for any s > $s_c$, where $H^{s,1}$ is a space of Sobolev type taking in angular regularity with norm defined by ${\parallel}{\varphi}{\parallel}_{H^{s,1}}={\parallel}{\varphi}{\parallel}_{H^s}+{\parallel}{\nabla}_{{\mathbb{S}}{\varphi}}{\parallel}_{H^s}$. For this purpose we use the recently developed Strichartz estimate which is $L^2$-averaged on the unit sphere ${\mathbb{S}}^{d-1}$ and utilize $U^p-V^p$ space argument.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.51-64
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• 1996

In this paper we investigate the existence of weak solutions of a nonlinear beam equation under Dirichlet boundary condition on the interval $-\frac{\pi}{2}<x<\frac{\pi}{2}$ and periodic condition on the variable $t$, $u_{tt}+u_{xxxx}=p(x,t,u)$. We show that if $p$ satisfies condition $(p_1)-(p_3)$, then the nonlinear beam equation possesses at least one weak solution.

• 대한화학회지
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• 제28권4호
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• pp.259-264
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• 1984

1 : 4 dioxane-물의 혼합용매중에서 benzenesulfonylimido phosgene의 가수분해 반응속도 상수를 자외선 분광법으로 측정하여 넓은 pH범위에서 잘 맞는 반응속도식을 구하였다. Grunwald-Winstein식에 적용하여 pH4.0에서 m=0.4의 값을 얻었으며 열역학적 활성화 파라미터 값은 pH4.0에서 ${\Delta}H^{\neq}$ = 15kcal/mol과 $ {\Delta}S^{\neq}$ =-21e.u 그리고 pH10.0에서는 $ {\Delta}H^{\neq}$ = 8kcal/mol, ${\Delta}S^{\neq}$ = -39e.u.이었다. 이와 같은 결과로부터 잘 알려져 있지않은 benzenesulfonylimido phosgene의 친핵성 첨가-제거 반응메카니즘을 정량적으로 잘 설명할 수 있었다.

• 대한수학회논문집
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• 제27권3호
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• pp.557-564
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• 2012

This study concerns the existence of positive solution for the following nonlinear system $$\{-div(|x|^{-ap}|{\nabla}u|^{p-2}{\nabla}u)=|x|^{-(a+1)p+c_1}({\alpha}_1f(v)+{\beta}_1h(u)),x{\in}{\Omega},\\-div(|x|^{-bq}|{\nabla}v|q^{-2}{\nabla}v)=|x|^{-(b+1)q+c_2}({\alpha}_2g(u)+{\beta}_2k(v)),x{\in}{\Omega},\\u=v=0,x{\in}{\partial}{\Omega}$$, where ${\Omega}$ is a bounded smooth domain of $\mathbb{R}^N$ with $0{\in}{\Omega}$, 1 < $p,q$ < N, $0{{\leq}}a<\frac{N-p}{p}$, $0{{\leq}}b<\frac{N-q}{q}$ and $c_1$, $c_2$, ${\alpha}_1$, ${\alpha}_2$, ${\beta}_1$, ${\beta}_2$ are positive parameters. Here $f,g,h,k$ : $[0,{\infty}){\rightarrow}[0,{\infty})$ are nondecresing continuous functions and $$\lim_{s{\rightarrow}{\infty}}\frac{f(Ag(s)^{\frac{1}{q-1}})}{s^{p-1}}=0$$ for every A > 0. We discuss the existence of positive solution when $f,g,h$ and $k$ satisfy certain additional conditions. We use the method of sub-super solutions to establish our results.

• Nuclear Engineering and Technology
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• 제49권3호
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• pp.534-540
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• 2017

The adsorption of uranium (VI) by calcium alginate beads was examined by batch experiments. The effects of environmental conditions on U (VI) adsorption were studied, including contact time, pH, initial concentration of U (VI), and temperature. The alginate beads were characterized by using scanning electron microscopy, transmission electron microscopy, X-ray photoelectron spectroscopy, and Fourier transform infrared spectroscopy. Fourier transform infrared spectra indicated that hydroxyl and alkoxy groups are present at the surface of the beads. The experimental results showed that the adsorption of U (VI) by alginate beads was strongly dependent on pH, the adsorption increased at pH 3~7, then decreased at pH 7~9. The adsorption reached equilibrium within 2 minutes. The adsorption kinetics of U (VI) onto alginate beads can be described by a pseudo first-order kinetic model. The adsorption isotherm can be described by the Redlich-Peterson model, and the maximum adsorption capacity was 237.15 mg/g. The sorption process is spontaneous and has an exothermic reaction.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 2005년도 춘계학술발표회
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• pp.311-312
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• 2005

The precipitation of U(VI) in the presence of phosphate and carbonate was investigated in the pH range of 4 to 13 and the following was obtained as a result of this experimental condition. U(VI) precipitates as a $NaUO_{2}PO_{4}$ at pH<9 but as mixtures of phosphate, hydroxides and/or carbonate at pH>9. The portion of the phosphate in the precipitate decreases almost linearly to near zero with an increasing pH in the range of 9 to 13. The U(VI) phosphate is dissolved by the carbonate complex formation at pH<10.5. The ternary complex of a carbonate and phosphate is not found.