• 한국응용과학기술학회지
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• 제23권3호
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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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• 제7권4호
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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.

• 대한수학회보
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• 제59권1호
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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.

• 전기학회논문지
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• 제59권6호
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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.

• 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.

• 폴리머
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• 제31권2호
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• pp.98-104
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• 2007

다양한 분자량의 폴리스티렌을 벤젠/n-헵탄, 1,4-다이옥산/이소프로판올, 1,4-다이옥산/n-헵탄과 같은 3종류의 혼합용매 계에 녹인 뒤 온도 상승에 따른 사슬의 팽창거동을 Flory $\Theta$온도 이상에서 점성도법으로 측정하였다. 온도 상승에 따라 두 종류의 영역, 즉 고분자 사슬이 팽창하는 영역과 수축하는 영역으로 구별되며, 분자량이 클수록 최대팽창온도가 높게 나타났다. 하나의 혼합용매 계 내에서는 $\tau/\tau_c$ 파라미터로 서로 다른 분자량의 사슬 팽창에 대하여 만능성이 나타나지만 서로 다른 혼합용매 계 사이에서는 각각의 기울기를 보임으로써 만능성이 관찰되지 않았다. 그러나 새로운 실험적 $b^{2/3}\tau/\tau_c$ 파라미터를 도입할 경우 모든 혼합용매 계의 사슬 팽창의 데이터들은 하나의 직선 위에 놓임으로써 만능성은 다시 회복되었다. 여기서 $\tau$는 $(T-\Theta)/\Theta$로 $\tau_c$는 $(\Theta-T_c)/T_c$로 각각 정의되며, $T_c$는 임계용액온도를 의미하며, b는 Schultz-Flory 식에서 $1/T_c$의 $1/M_w^{1/2}$에 대한 유효 기울기이다.