• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.871-888
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• 2018

We study the nonrelativistic limit of the Chern-Simons-Dirac system on ${\mathbb{R}}^{1+2}$. As the light speed c goes to infinity, we first prove that there exists an uniform existence interval [0, T] for the family of solutions ${\psi}^c$ corresponding to the initial data for the Dirac spinor ${\psi}_0^c$ which is bounded in $H^s$ for ${\frac{1}{2}}$ < s < 1. Next we show that if the initial data ${\psi}_0^c$ converges to a spinor with one of upper or lower component zero in $H^s$, then the Dirac spinor field converges, modulo a phase correction, to a solution of a linear $Schr{\ddot{o}}dinger$ equation in C([0, T]; $H^{s^{\prime}}$) for s' < s.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.533-543
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• 2018

Under the symbol ${\Omega}$ is a combination of ${\phi}_i$ ($i=1,2,3,{\ldots},n$) which has a suitable growth condition, for dimension n = 2 and $n{\geq}3$, when the initial data f belongs to homogeneous Sobolev space, we obtain the global $L^q$ estimate for maximal operators generated by operators family $\{S_{t,{\Omega}}\}_{t{\in}{\mathbb{R}}}$ associated with solution to dispersive equations, which extend some results in [27].

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.89-111
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• 2020

In the present paper, we give some characterization of the L₂ maximal estimate for the operator P^t_a,γf(Γ(x, t)) along curve with complex time, which is defined by $$P^t_{a,{\gamma}}f({\Gamma}(x,t))={\displaystyle\smashmargin{2}{\int\nolimits_{\mathbb{R}}}}\;e^{i{\Gamma}(x,t){\xi}}e^{it{\mid}{\xi}{\mid}^a}e^{-t^{\gamma}{\mid}{\xi}{\mid}^a}{\hat{f}}({\xi})d{\xi}$$, where t, γ > 0 and a ≥ 2, curve Γ is a function such that Γ : ℝ×[0, 1] → ℝ, and satisfies Hölder's condition of order σ and bilipschitz conditions. The authors extend the results of the Schrödinger type with complex time of Bailey [1] and Cho, Lee and Vargas [3] to Schrödinger operators along the curves.

• Journal of the Optical Society of Korea
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• v.19 no.2
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• pp.130-135
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• 2015

Based on the extended nonlinear Schr$\ddot{o}$dinger equation, the influences of the filter effect on pulse splitting in a passively mode-locked erbium-doped fiber laser with positive dispersion cavity are investigated theoretically. Numerical results show that, as the bandwidth of the spectral filter decreases, the nonlinear chirp appended to the pulse increases under the combined action of the filter effect of the super-Gaussian spectral filter and the self-phase modulation effect. On further decreasing the bandwidth, the wave breaking of the pulse takes place. In addition, by varying the pump power of the laser or the profile of the spectral filter, the influences of the filter effect on pulse splitting also change accordingly.

• Proceeding of EDISON Challenge
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• 2014.03a
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• pp.15-27
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• 2014

양자화학 (quantum chemistry)을 처음 접했을 때, 이전까지의 고전역학 (classical mechanics)에 익숙한 대다수의 학생들은 양자화학을 받아들이는 데 어려움을 겪는다. 모형계에 양자역학 (quantum mechanics)을 직접 적용하여 봄으로써 생소한 양자 개념에 대한 이해를 도울 수 있다. 본 논문에서는 양자동역학 (quantum dynamics)을 수치적으로 구현하는 계산 프로그램을 모형계에 적용하여 양자 개념을 설명할 수 있는 몇 가지 예를 보이고자 한다. 1 차원 시간의존 슈뢰딩거 방정식 (1-D time-dependent $Schr{\ddot{o}}dinger$ equation)의 해를 얻어 양자동역학을 구현하였으며, 그에 해당하는 고전동역학은 뉴턴 방정식 (Newton's equation)의 해로 얻어졌다. 조화 진동자 퍼텐셜 (harmonic oscillator potential), 모스 진동자 퍼텐셜 (Morse oscillator potential), 이중 우물 퍼텐셜 (double-well potential), 네모 퍼텐셜 장벽 (rectangular potential barrier), 그리고 에카트 퍼텐셜 (Eckart potential)에 대한 계산을 수행하였다. 두 가지 동역학을 비교하기 위하여 계산 결과의 시각화 (visualization)를 이용하고 동역학 특성의 차이를 비교하는 차별화 (differentiation)를 강조한다. 영점에너지 (zero-point energy), 위상어긋남 (dephasing), 터널링 (tunneling), 그리고 반사 (reflection) 현상과 같은 양자동역학의 특징을 고전동역학과 비교함으로써 직관적인 이해를 도울 수 있었다. 이러한 결과는 양자화학에 입문하는 학생들을 대상으로 쓰일 수 있는 효율적인 강의 모델을 제시할 것으로 기대한다.

• JSTS:Journal of Semiconductor Technology and Science
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• v.11 no.4
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• pp.278-286
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• 2011

In this paper, we present a compact model of gate-voltage-dependent quantum effects in short-channel surrounding-gate (SG) metal-oxide-semiconductor field-effect transistors (MOSFETs). We based the model on a two-dimensional (2-D) analytical solution of Poisson's equation using cylindrical coordinates. We used the model to investigate the electrostatic potential and current sensitivities of various gate lengths ($L_g$) and radii (R). Schr$\ddot{o}$dinger's equation was solved analytically for a one-dimensional (1-D) quantum well to include quantum effects in the model. The model takes into account quantum effects in the inversion region of the SG MOSFET using a triangular well. We show that the new model is in excellent agreement with the device simulation results in all regions of operation.

• ETRI Journal
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• v.21 no.4
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• pp.65-82
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• 1999

We present a calculation model for an improved quantitative theoretical analysis of electronic and optical properties of strained-piezoelectric[111] InGaAs/GaAs superlattices (SLs). The model includes a full band-coupling between the four important energy bands: conduction, heavy, light, and spin split-off valence bands. The interactions between these and higher lying bands are treated by the k ${\cdot}$ p perturbation method. The model takes into account the differences in the band and strain parameters of constituent materials of the heterostructures by transforming it into an SL potential in the larger band-gap material region. It self-consistently solves an $8{\times}8$ effective-mass $Schr{\ddot{o}}dinger$ equation and the Hartree and exchange-correlation potential equations through the variational procedure proposed recently by the present first author and applied to calculate optical matrix elements and spontaneous emission rates. The model can be used to further elucidate the recent theoretical results and experimental observations of interesting properties of this type of quantum well and SL structures, including screening of piezoelectric field and its resultant optical nonlinearities for use in optoelectronic devices.