• 호남수학학술지
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• 제39권3호
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• pp.401-416
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• 2017

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].

• Mass Spectrometry Letters
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• 제2권3호
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• pp.73-75
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• 2011

In the collisionally-activated dissociation of the proton-bound cluster ions of DNA base guanine (G) and cytosine (C), $G{\bullet}{\bullet}H^+{\bullet}{\bullet}C$, the abundance of [$CH^+$] ions was found to be higher than that of [$GH^+$] despite the fact that G has a higher proton affinity than C. This unexpected observation seems to demonstrate another example that the simple kinetic method scheme does not work. We suggest that a kinetic factor or detailed dynamics governing the proton transfer and dissociation should be carefully considered in the applications of the kinetic method to the proton affinity measurements.

• East Asian mathematical journal
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• 제36권1호
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• pp.81-90
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• 2020

Many compartment models assume a kinetically homogeneous amount of materials that have well-stirred compartments. However, based on observations from such processes, they have been heuristically fitted by exponential or gamma distributions even though biological media are inhomogeneous in real environments. Fractional differential equations using a specific kernel in Pharmacokinetic/Pharmacodynamic (PKPD) model are recently introduced to account for abnormal drug disposition. We discuss a tumor growth inhibition (TGI) model using fractional-order derivative from it. This represents a tumor growth delay by cytotoxic agents and additionally show variations in the equilibrium points by the change of fractional order. The result indicates that the equilibrium depends on the tumor size as well as a change of the fractional order. We find that the smaller the fractional order, the smaller the equilibrium value. However, a difference of them is the number of concavities and this indicates that TGI over time profile for fitting or prediction should be determined properly either fractional order or tumor sizes according to the number of concavities shown in experimental data.

• EDISON SW 활용 경진대회 논문집
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• 제5회(2016년)
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• pp.102-107
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• 2016

본 연구에서는 동역학적 격자기반 대정준 Monte Carlo (Kinetic Lattice Grand Canonical Monte Carlo, KLGCMC) 모의실험 방법을 이용하여 비정상 몰분율 효과 (Anomalous mole fraction effect)에 대해서 알아보고자 하였다. 이를 위해 양이온 선택성을 가진 이온채널 모델에서 $NH_4{^+}$와 $Rb^+$의 혼합물에 대하여 몰분율의 변화에 따른 이온전도도를 KLGCMC 모의실험을 이용하여 계산하고, 이를 평균장 이론인 Poisson-Nernst-Planck (PNP)의 결과와 비교해 봄으로써 비정상 몰분율 효과에 대하여 심도 있게 이해하고자 하였다. 본 연구 결과로부터 비정상 몰분율 효과는 이온채널의 이온 선택성에 의해서 발생함을 확인할 수 있었다. 즉, 두 종류 이상의 이온들이 채널 내부로 이동할 때, 이온채널의 이온 선택성에 의해서 각 이온들과 채널 간에 서로 상이한 상호작용을 하게 되고, 이로 인해서 이온 혼합물 조성의 변화, 즉 몰분율의 변화에 대해서 이온 전류가 선형적이 아닌 비선형적으로 변하게 됨을 알 수 있었다.

• Journal of Pharmaceutical Investigation
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• 제35권6호
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• pp.453-460
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• 2005

4-Aminopyridine (AP) is a potassium channel blocker used in the treatment of neurological disorders such as multiple sclerosis and Alzheimer disease. AP‘s window of therapeutic effect appears to correlate with its plasma halflife (3.5 hours). It demonstrates pH-dependent solubility because of a weakly basic drug. In addition, the resulting release from conventional matrix tablets decreases with increasing pH-milieu of the gastrointestinal tract. The aim of this study is to design sustained release matrix tablet containing AP, overcoming this problem. $Eudragit^{\circledR}$ L 100 (EuL) and sodium alginate were used in an effort to achieve pH independent drug release. The effect of sodium alginate and EuL on drug release from matrix tablet was investigated. The drug release behavior from the different tablets was analyzed by $t_{20%},\;t_{40%},\;t_{60%}$, The exponential diffusion coefficient n, kinetic constant K were calculated according to the Korsmeyer-Peppas equation. The drug release from matrix tablets prepared with sodium alginate was decreased with increasing the content of sodium alginate in pH 7.4 while there is no significant difference in pH 1.2. The exponent n values were determined to be approximately 0.5 and 0.8 respectively, in both pH 1.2 and 7.4. These values indicate diffusion-based anomalous mechanism and erosion-based anomalous mechanism, respectively. The drug release from sodium alginate matrix tablets prepared with solid dispersion of EuL containing drug showed a slow drug release in an acidic medium and a more fast drug release in phosphate medium, compared with sodium alginate matrix tablets prepared with physical mixture. These results may be attributed to the gel forming ability of sodium alginate and pH dependent solubility of EuL. Therefore, sustained-release AP matrix tablets using sodium alginate and EuL were successfully prepared.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2012년도 제43회 하계 정기 학술대회 초록집
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• pp.80-81
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• 2012

Recently, one of the critical issues in the etching processes of the nanoscale devices is to achieve ultra-high aspect ratio contact (UHARC) profile without anomalous behaviors such as sidewall bowing, and twisting profile. To achieve this goal, the fluorocarbon plasmas with major advantage of the sidewall passivation have been used commonly with numerous additives to obtain the ideal etch profiles. However, they still suffer from formidable challenges such as tight limits of sidewall bowing and controlling the randomly distorted features in nanoscale etching profile. Furthermore, the absence of the available plasma simulation tools has made it difficult to develop revolutionary technologies to overcome these process limitations, including novel plasma chemistries, and plasma sources. As an effort to address these issues, we performed a fluorocarbon surface kinetic modeling based on the experimental plasma diagnostic data for silicon dioxide etching process under inductively coupled C4F6/Ar/O2 plasmas. For this work, the SiO2 etch rates were investigated with bulk plasma diagnostics tools such as Langmuir probe, cutoff probe and Quadruple Mass Spectrometer (QMS). The surface chemistries of the etched samples were measured by X-ray Photoelectron Spectrometer. To measure plasma parameters, the self-cleaned RF Langmuir probe was used for polymer deposition environment on the probe tip and double-checked by the cutoff probe which was known to be a precise plasma diagnostic tool for the electron density measurement. In addition, neutral and ion fluxes from bulk plasma were monitored with appearance methods using QMS signal. Based on these experimental data, we proposed a phenomenological, and realistic two-layer surface reaction model of SiO2 etch process under the overlying polymer passivation layer, considering material balance of deposition and etching through steady-state fluorocarbon layer. The predicted surface reaction modeling results showed good agreement with the experimental data. With the above studies of plasma surface reaction, we have developed a 3D topography simulator using the multi-layer level set algorithm and new memory saving technique, which is suitable in 3D UHARC etch simulation. Ballistic transports of neutral and ion species inside feature profile was considered by deterministic and Monte Carlo methods, respectively. In case of ultra-high aspect ratio contact hole etching, it is already well-known that the huge computational burden is required for realistic consideration of these ballistic transports. To address this issue, the related computational codes were efficiently parallelized for GPU (Graphic Processing Unit) computing, so that the total computation time could be improved more than few hundred times compared to the serial version. Finally, the 3D topography simulator was integrated with ballistic transport module and etch reaction model. Realistic etch-profile simulations with consideration of the sidewall polymer passivation layer were demonstrated.