• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.149-163
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• 2018

In recent years, the study of slice Dirac operators has attracted more and more attention in the literature. In this paper, Almansitype decompositions for null solutions to the iterated slice Dirac operator and the generalized slice Dirac operator are obtained without a star-like domain centered at the origin. As applications, we investigate Riquier type problems and Dirichlet type problems in the theory of slice monogenic functions.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.83-95
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• 2024

The Quaternionic Dirac operator proves instrumental in tackling various challenges within spectral geometry processing and shape analysis. This work involves the introduction of the quaternionic Dirac operator on a symplectic submanifold of an exact symplectic product manifold. The self adjointness of the symplectic quaternionic Dirac operator is observed. This operator is verified for spin ${\frac{1}{2}}$ particles. It factorizes the Hodge Laplace operator on the symplectic submanifold of an exact symplectic product manifold. For achieving this a new complex structure and an almost quaternionic structure are formulated on this exact symplectic product manifold.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.201-208
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• 2015

This paper reviews recent mathematical progresses made on the study of the initial-value problem for nonlinear Dirac equations in one space dimension. We also prove the global existence of solutions to some nonlinear Dirac equations and propose a model problem (3.6).

• Journal of Sensor Science and Technology
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• v.27 no.3
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• pp.204-208
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• 2018

Monolayer graphene grown via chemical vapor deposition (CVD) is recognized as a promising material for sensor applications owing to its extremely large surface-to-volume ratio and outstanding electrical properties, as well as the fact that it can be easily transferred onto arbitrary substrates on a large-scale. However, the Dirac voltage of CVD-graphene devices fabricated with transferred graphene layers typically exhibit positive shifts arising from transfer and photolithography residues on the graphene surface. Furthermore, the Dirac voltage is dependent on the channel lengths because of the effect of metal-graphene contacts. Thus, large and nonuniform Dirac voltage of the transferred graphene is a critical issue in the fabrication of graphene-based sensor devices. In this work, we propose a fabrication process for graphene field-effect transistors with Dirac voltages close to zero. A vacuum annealing process at $300^{\circ}C$ was performed to eliminate the positive shift and channel-length-dependence of the Dirac voltage. In addition, the annealing process improved the carrier mobility of electrons and holes significantly by removing the residues on the graphene layer and reducing the effect of metal-graphene contacts. Uniform and close to zero Dirac voltage is crucial for the uniformity and low-power/voltage operation for sensor applications. Thus, the current study is expected to contribute significantly to the development of graphene-based practical sensor devices.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1579-1589
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• 2014

We study the Dirac spectrum on compact Riemannian spin manifolds M equipped with a metric connection ${\nabla}$ with skew torsion $T{\in}{\Lambda}^3M$ in the situation where the tangent bundle splits under the holonomy of ${\nabla}$ and the torsion of ${\nabla}$ is of 'split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.907-910
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• 1999

본 논문에서는 고 농도로 불순물이 주입된 영역에서 전자 및 정공 농도를 정교하게 구현하기 위해 Fermi-Dirac 분포함수를 고려한 포아송 방정식의 이산화 방법을 제안하였다. Fermi-Dirac 분포를 근사시키기 위해서 Least-Squares 및 점근선 근사법을 사용하였으며 Galerkin 방법을 근간으로 한 유한 요소법을 이용하여 포아송 방정식을 이산화하였다. 구현한 모델을 검증하기 위해 전력 BJT 시료를 제작하여 자체 개발된 소자 시뮬레이터인 BANDIS를 이용하여 모의 실험을 수행한 결과, 상업용 2차원 소자 시뮬레이터인 MEDICI에 비해 최대 4%이내의 상대 오차를 보였다.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1445-1461
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• 2021

The aim of this paper is to show the local well-posedness of 2 dimensional Dirac equations with power type and Hartree type nonlin-earity derived from honeycomb structure in H^s for s > $\frac{7}{8}$ and s > $\frac{3}{8}$, respectively. We also provide the smoothness failure of flows of Dirac equations.

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.999-1021
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• 2023

Using the results in the paper [12], we give an estimate for the first positive and negative Dirac eigenvalue on a 7-dimensional Sasakian spin manifold. The limiting case of this estimate can be attained if the manifold under consideration admits a Sasakian Killing spinor. By imposing the eta-Einstein condition on Sasakian manifolds of higher dimensions 2m + 1 ≥ 9, we derive some new Dirac eigenvalue inequalities that improve the recent results in [12, 13].

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.365-373
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• 2008

We prove a lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold depending on the scalar curvature as well as a chosen Codazzi tensor. The inequality generalizes the classical estimate from [2].

• Honam Mathematical Journal
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• v.44 no.4
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• pp.485-503
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• 2022

In this work, a discontinuous singular Dirac system is studied. For this system, a spectral function is constructed. Finally, by using the spectral function, a spectral expansion formula is given.