• Proceedings of the Korean Vacuum Society Conference
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• 2014.02a
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• pp.314.1-314.1
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• 2014

The properties of Ni/Au Ohmic contacts formed on nonpolar a-plane GaN grown on r-plane sapphire substrate with different tilt angles are investigated using current-voltage (I-V) measurements. To investigate the effects of pattern direction and size on Ohmic contact properties of a-plane GaN, transmission line method (TLM) patterns are formed either along c-axis and m-axis on nonpolar GaN surface with different size. I-V measurement results show that the size of TLM pattern and formation direction of electrode have an effect on the electrical properties of a-plane GaN. The large sized patterns show the relatively lower sheet resistance compared to the small sized patterns. In addition, the sheet resistance of a-plane GaN along m-axis shows lower values than that along the c-axis. Finally, the effects of miscut angle of r-sapphire substrate ($0.2^{\circ}$, 0.4oand $0.6^{\circ}$) on electrical properties of a-plane GaN will be discussed.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.309-317
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• 2016

As a generalization of an inflection point, we consider a point P on a smooth plane curve C of degree m at which another curve C' of degree n meets C with high intersection multiplicity. Especially, we deal with the existence of two curves of degree m and n meeting at the unique point.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.145-169
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• 2020

Let k be a field of characteristic 0. Let ${\mathfrak{C}}=Spec(k[x,y]/{\langle}f{\rangle})$ be a weighted homogeneous plane curve singularity with tangent space ${\pi}_{\mathfrak{C}}:T_{{\mathfrak{C}}/k}{\rightarrow}{\mathfrak{C}$. In this article, we study, from a computational point of view, the Zariski closure ${\mathfrak{G}}({\mathfrak{C}})$ of the set of the 1-jets on ${\mathfrak{C}}$ which define formal solutions (in F[[t]]² for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal ${\mathcal{N}}_1({\mathfrak{C}})$ defining ${\mathfrak{G}}({\mathfrak{C}})$ as a reduced closed subscheme of $T_{{\mathfrak{C}}/k}$ and obtain applications in terms of logarithmic differential operators (in the plane) along ${\mathfrak{C}}$.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.211-235
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• 2007

In this paper, first we introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grass-mannians $G_2(\mathbb{C}^{m+2})$ from the equation of Gauss and derive a new formula for the Ricci tensor of M in $G_2(\mathbb{C}^{m+2})$. Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$ with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in $G_2(\mathbb{C}^{m+2})$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.601-609
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• 2011

Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ to have pointwise 1-type Gauss map.

• Water for future
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• v.29 no.5
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• pp.139-150
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• 1996

This paper presents the effect of numerical parameters, such as grid size and grid ratio, on the outflow hydrograph of a unit-width plane in the linear Muskingum-Cunge method. The numerical results depend on Courant number C and cell Reynolds number D, two physically and numerically meaningful parameters. As C approache 1 and D increases, the numerical dispersion-relating oscillations are difficult to occur. The numerical oscillations occur in the front of a propagating wave for C < 1, while smaller oscillations occur behind the wave for C > 1 due to the numerical diffusion effect. For a plane with a small value of characteristic reach length L (e.g., a steep plane), the numerical solution of the Muskingum-Cunge method is similar to that of the kinematic wave method, which shows no wave attenuation. However, for a plane with a large value of L (e.g., a mild plane), the Muskingum-Cunge method leads to the diffusion waves which are essentially independent of the Courant number. Accordingly, the Muskingum-Cunge method will be suited for the routing of the catchment with relatively mild slopes.

• Proceedings of the Materials Research Society of Korea Conference
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• 2011.10a
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• pp.21.1-21.1
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• 2011

Vertically aligned single-crystal ZnO nanowires have been successfully grown on c-plane sapphire substrate using chemical vapor deposition (CVD) without catalyst. According to growth temperatures, it was changed ZnO growth characteristic. We investigated the effect of substrate temperatures on the growth ZnO films or nanowires on c-plane (0001) sapphire substrates. The ZnO films were acquired at $500^{\circ}C$, whereas the ZnO nanowires were obtained at $600^{\circ}C$, $700^{\circ}C$, and $800^{\circ}C$. The growth behavior diameter and growth rate of ZnO were changed due to different temperature. As a result of analyzing in-plane residual stress by X-ray diffraction, the optimized condition of ZnO nanowires were at $600^{\circ}C$.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.18 no.3
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• pp.97-100
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• 2008

Polar and non-polar GaN was grown by the HVPE on various substrates and influence of polarity has been investigated. The $10\;{\mu}m$ thickness GaN were grown by HVPE is along A-plane ($11{\bar{2}}0$), C-plane (0001) and M-Plane ($10{\bar{1}}0$) sapphire substrate respectively. Surface properties were observed by optical microscope and atomic force microscopy. High resolution X-ray diffraction (HR-XRD) confirms the wurtzite structure. The donor band exciton peak located at ${\sim}3.4\;eV$ and also located yellow luminescence peak at 2.2 eV. The polarity of the GaN film has a strong influence on the morphology and the optical properties.

• Tunnel and Underground Space
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• v.6 no.2
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• pp.101-121
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• 1996

The thermomechanical characteristics of rocks such as temperature dependency of strength and deformation were experimentally investigated using Iksan granite, Cheonan tonalite and Chung-ju dolomite for proper design and stability analysis of underground structures subjected to temperature changes. For the temperature below critical threshold temperature $T_c$, the variation of uniaxial compressive strength, Young's modulus, Brazilian tensile strength and cohesion with temperature were slightly different for each rock type, but these mechanical properties decreased at the temperatures above $T_c$ by the effect of thermal cracking. Tensile strength was most affected by $T_c$, and uniaxial compressive strength was least affected by $T_c$. To the temperature of 20$0^{\circ}C$ with the confining prressure to 150 kg/$\textrm{cm}^2$, failure limit on principal stress plane and failure envelope on $\sigma$-$\tau$ plane of Iksan granite were continuously lowered with increasing temperature but those of Cheonan tonalite and Chung-ju dolomite showed different characteristics depending on minor principal stress on principal stress plane and normal stress on $\sigma$-$\tau$ plane. The reason for this appeared to be the effect of rock characteristics and confining pressure. Young's modulus was also temperature and pressure dependent, but the variation of Young's modulus was about 10%, which was small compared to the variation of compressive strength. In general, Young's modulus increased with increasing confining pressure and increased or decreased with increasing temperature to 20$0^{\circ}C$ depending on the rock type.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1337-1346
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• 2017

We define Bloch-type spaces of ${\mathcal{C}}^1({\mathbb{H}})$ on the upper half plane H and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator ${\mathcal{C}}_{\phi}$ acting between two Bloch spaces. These obtained results generalize the corresponding known ones to the setting of upper half plane.