• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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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.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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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].

• Journal of the Korean Chemical Society
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• v.40 no.1
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• pp.50-58
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• 1996

In the presence of metal ions(Co(Ⅱ), Ni(Ⅱ), Sr(Ⅱ), Cu(Ⅱ), Fe(Ⅲ), U(Ⅵ)), the sedimentation of humic acid was increased at constant pH with increasing metal concentration and the strength was increased in the following order: Sr < Ni < Co < Cu < Fe < U. At constant metal concentration, Cu(Ⅱ), Ni(Ⅱ), and Co(Ⅱ) ions caused an increase in sedimentation of humic acid as the solution pH increased, whereas Fe(Ⅲ) and U(Ⅵ) ions caused a decrease. Sr(Ⅱ) ions did not affect the sedimentation even with the variation of pH. The analysis of FT-IR spectra for the sediments prepared from the reaction between humic acid and metal ions showed that metal ions were bound to humic acid to form complexes, suggesting that the metal complexation plays an important role in the sedimentation of humic acid.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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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.

• Journal of the Korean Chemical Society
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• v.28 no.4
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• pp.259-264
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• 1984

The rate constants for the hydrolysis of benzenesulfonylimido phosgene at various pH were determined by ultraviolet spectrophotometry in 1 : 4 dioxane-water mixed solvents at 25$^{\circ}$C and a rate equation which can be applied over a wide pH range was obtained. Based on the Grunwald-Winstein equation, m = 0.4 was obtained. The thermodynamic activation parameters for the hydrolysis were ${\Delta}H^{\neq}$ = 15kcal mol$^{-1}$, ${\Delta}S^{\neq}$ = 21e.u. at pH 4.0 and $ {\Delta}H^{\neq}$ = 8kcal. mol$^{-1}$, ${\Delta}S^{\neq}$ = -39e.u. at pH 11.0, respectively. It was concluded that the hydrolysis of benzenesulfonylimido phosgene in 1 : 4 dioxane-water mixed solvents proceed via nucleophilic addition-elimination.

• Korean Journal of Mathematics
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• v.4 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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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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• v.49 no.3
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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.

• Proceedings of the Korean Nuclear Society Conference
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• 2005.05a
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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.