• Journal of the Korean Applied Science and Technology
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• v.23 no.3
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• pp.185-191
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• 2006

It is desirable to have an accurate expression on the temperature dependence of surface(or interfacial) tension ${\sigma}$, because most of the interfacial thermodynamic functions can be derived from it. There have been proposed several equations on the temperature dependence of the surface tension, ${\sigma}(T)$. Among them $E{\ddot{o}}tv{\ddot{o}}s$ equation and the one modified by Katayama, which is called Katayama equation, for improving accuracies of $E{\ddot{o}}tv{\ddot{o}}s$ equation close to critical points, have been most well-known. In this article Katayama equation is interpreted on the basis of the cell model to understand the nature of the equation. The cell model results in an expression very similar to Katayama equation. This implies that, although $E{\ddot{o}}tv{\ddot{o}}s$ and Katayama equations were obtained on the basis of experimental results, they have a sound theoretical background. The Katayama equation is also modified with the phase volume replaced with a critical scaling expression. The modified Katayama equation becomes a power-law equation with the exponent slightly different from the value obtained by critical-scaling theory. This implies that Katayama equation can be replaced by a critical-scaling equation which is proven to be accurate.

• Bulletin of the Korean Chemical Society
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• v.7 no.4
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• pp.283-288
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• 1986

A nonlinear analysis is presented for the treatment of fluctuations near the critical point in the presence of diffusion in the Schlogl models. The two time scaling method is used to obtain an evolution equation for the amplitude of fluctuations. It is shown that the fluctuations decay to zero in the stable region and they are enhanced to a finite value as time goes to infinity in the unstable region.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.241-263
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• 2022

We consider a nonlinear Schrödinger equation with critical frequency, (P_𝜀) : 𝜀²∆v(x) - V(x)v(x) + |v(x)|^p-1v(x) = 0, x ∈ ℝ^N, and v(x) → 0 as |x| → +∞, for the infinite case as described by Byeon and Wang. Critical means that 0 ≤ V ∈ C(ℝ^N) verifies Ƶ = {V = 0} ≠ ∅. Infinite means that Ƶ = {x₀} and that, grossly speaking, the potential V decays at an exponential rate as x → x₀. For the semiclassical limit, 𝜀 → 0, the infinite case has a characteristic limit problem, (P_inf) : ∆u(x)-P(x)u(x) + |u(x)|^p-1u(x) = 0, x ∈ Ω, with u(x) = 0 as x ∈ Ω, where Ω ⊆ ℝ^N is a smooth bounded strictly star-shaped region related to the potential V. We prove the existence of an infinite number of solutions for both the original and the limit problem via a Ljusternik-Schnirelman scheme for even functionals. Fixed a topological level k we show that v_k,𝜀, a solution of (P_𝜀), subconverges, up to a scaling, to a corresponding solution of (P_inf ), and that v_k,𝜀 exponentially decays out of Ω. Finally, uniform estimates on ∂Ω for scaled solutions of (P_𝜀) are obtained.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.6
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• pp.1095-1102
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• 2010

This paper presents an equalizer reducing CCI(cell-to-cell interference) in MLC NAND flash memory. High growth of the flash memory market has been driven by two combined technological efforts that are an aggressive scaling technique which doubles the memory density every year and the introduction of MLC(multi level cell) technology. Therefore, the CCI is a critical factor which affects occurring data errors in cells. We introduced an equation of CCI model and designed an equalizer reducing CCI based on the proposed equation. In the model, we have been considered the floating gate capacitance coupling effect, the direct field effect, and programming methods of the MLC NAND flash memory. Also we design and verify the proposed equalizer using Matlab. As the simulation result, the error correction ratio of the equalizer shows about 20% under 20nm NAND process where the memory channel model has serious CCI.

• 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.

• Polymer(Korea)
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• v.31 no.2
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• pp.98-104
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• 2007

The expansion behavior of polystyrene (PS) chains with various molecular weights has been investigated above Flory $\Theta$temperature by viscometry after dissolving in the three different mixed solvents systems such as benzene/n-heptane, 1,4-dioxane/isopropanol, and 1,4-dioxane/n-heptane. Two different regimes are observed as increasing temperature: one regime is for the expansion of chain and the other is for the contraction. For the higher molecular weight sample of PS, the higher peak temperature showing its maximum expansion is obtained. Within a certain system of Ps/mixed solvents, the $\tau/\tau_c$ parameter shows universality for the variation of molecular weight. But while each system of Ps/mixed solvents has shown its own different slope, the universality breaks down in the overall system of mixed solvents. However after introducing a new empirical $b^{2/3}\tau/\tau_c$ parameter, all data points of three different systems have dropt on one master curve and the universality of chain expansion has recovered again. Here $\tau$ and $\tau_c$ are defined as $(T-\Theta)/\Theta$ and $(\Theta-T_c)/T_c$, respectively and $T_c$ is the critical solution temperature, and b of Schultz-Flory equation is corresponding to the effective slope in the plot of $1/T_c$ against $1/M_w^{1/2}$.