• Bulletin of the Korean Chemical Society
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• v.22 no.9
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• pp.969-974
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• 2001

Model calculations for small molecules Li2, F2, LiF and BF have been performed at the Dirac-Fock level of theory using Dirac-Coulomb and Dirac-Coulomb-Magnetic Hamiltonians with various basis sets. In order to understand what may happen when the relativity becomes significant, the value of c, speed of light, is varied from the true value of 137.036 a.u. to 105 (nonrelativistic case) and also to 50 and 20 a.u. (exaggerated relativistic cases). Qualitative trends are discussed with special emphasis on the effect of the magnetic part of the Breit interaction term. The known relativistic effects on bonding such as the bond length contraction or expansion are demonstrated in this model study. Total energy, $\pi-orbital$ splitting, bond length, bond dissociation energy and dipole moment are calculated, and shown to be modified in a uniform direction by the effect of the magnetic term. Inclusion of the magnetic term raises the total energy, increases the bond length, reduces the $\pi-orbital$ splitting, increases the bond dissociation energy, and mitigates the changes in dipole moment caused by the Dirac term.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1037-1049
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• 2015

It is well-known that the spectrum of a $spin^{\mathbb{C}}$ Dirac operator on a closed Riemannian $spin^{\mathbb{C}}$ manifold $M^{2k}$ of dimension 2k for $k{\in}{\mathbb{N}}$ is symmetric. In this article, we prove that over an odd-dimensional Riemannian product $M^{2p}_1{\times}M^{2q+1}_2$ with a product $spin^{\mathbb{C}}$ structure for $p{\geq}1$, $q{\geq}0$, the spectrum of a $spin^{\mathbb{C}}$ Dirac operator given by a product connection is symmetric if and only if either the $spin^{\mathbb{C}}$ Dirac spectrum of $M^{2q+1}_2$ is symmetric or $(e^{{\frac{1}{2}}c_1(L_1)}{\hat{A}}(M_1))[M_1]=0$, where $L_1$ is the associated line bundle for the given $spin^{\mathbb{C}}$ structure of $M_1$.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.949-966
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• 2009

We proved in [10] that Friedrich's estimate [5] for the first eigenvalue of the Dirac operator can be improved when a Codazzi tensor exists. In the paper we further prove that his estimate can be improved as well via a well-chosen divergencefree symmetric tensor. We study the geometric implication of the new first eigenvalue estimates over Sasakian spin manifolds and show that some particular types of spinors appear as the limiting case.

• Proceedings of the IEEK Conference
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• 2001.06b
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• pp.157-160
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• 2001

소자 내부의 전위와 전자 및 정공 의사 페르미 준위에 따른 반송자의 정확한 농도를 얻기 위해 Fermi-Dirac통계를 구현하는 방법을 제시하였다. 또한 Fermi-Dirac통계를 고려하여 반도체 방정식을 이산화하는 방법을 제안한다. 제안된 방법을 검증하기 위해 전력 바이폴라 접합 트랜지스터를 제작하였으며 모의 실험 결과 컬렉터-에미터 전압 대 컬렉터 전류는 현재 업계에서 상용화된 소자의 실측치와 비교하여 최대 15%이내의 상대오차를 보였다.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.333-340
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• 2013

In this paper, we prove that on a K$\ddot{a}$hler spin foliatoin of codimension $q=2n$, any eigenvalue ${\lambda}$ of type $r(r{\in}\{1,{\cdots},[\frac{n+1}{2}]\})$ of the basic Dirac operator $D_b$ satisfies the inequality ${\lambda}^2{\geq}\frac{r}{4r-2}\;{\inf}_M{\sigma}^{\nabla}$, where ${\sigma}^{\nabla}$ is the transversal scalar curvature of $\mathcal{F}$.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.437-443
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• 2001

In this paper the inverse problems for the Dirac Operator are studied. A set of values of eigenfunctions in some internal point and spectrum are taken as a data. Uniqueness theorems are obtained. The approach that was used in the investigation of inverse problems for interior spectral data of the Sturm-Liouville operator is employed.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1347-1370
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• 2016

On a closed eta-Einstein Sasakian spin manifold of dimension $2m+1{\geq}5$, $m{\equiv}0$ mod 2, we prove a new eigenvalue estimate for the Dirac operator. In dimension 5, the estimate is valid without the eta-Einstein condition. Moreover, we show that the limiting case of the estimate is attained if and only if there exists such a pair (${\varphi}_{{\frac{m}{2}}-1}$, ${\varphi}_{\frac{m}{2}}$) of spinor fields (called Sasakian duo, see Definition 2.1) that solves a special system of two differential equations.

• Nuclear Engineering and Technology
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• v.1 no.2
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• pp.103-106
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• 1969

A new representation for the Dirac equation, which may be appropriate to describe the interaction of the charged particle with the electric field, is derived by introducing a gauge-independent unitary transformation. It is shown that in this representation the effective Hamiltonian without potentials has a new feature in the non-relativistic limit.

• 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.

• Journal of the Korean Physical Society
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• v.73 no.11
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• pp.1631-1636
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• 2018

Unpolarized 1.047-GeV proton inelastic scatterings from the Ni isotopes $^{62}Ni$ and $^{64}Ni$ are analyzed phenomenologically employing an optical potential model and the first-order collective model in the relativistic Dirac coupled channel formalism. The Dirac equations are reduced to $Schr{\ddot{o}}dinger-like$ second-order differential equations, and the effective central and spin-orbit optical potentials are analyzed by considering the mass-number dependence. The multistep excitation via the $2^+$ state is found to be important for the $4^+$ state excitation in the ground state rotational band for proton inelastic scatterings from the Ni isotopes. The calculated deformation parameters for the $2^+$ and the $4^+$ states of the ground state rotational band and for the first $3^-$ state are found to agree pretty well with those obtained from nonrelativistic calculations.