• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.341-349
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• 2003

Let {$x_{nk}\;$\mid$1\;\leq\;k\;\leq\;n,\;n\;\geq\;1$} be an array of random varianbles and $\{a_n$\mid$n\;\geq\;1\}\;and\;\{b_n$\mid$n\;\geq\;1} be a sequence of constants with $a_n\;>\;0,\;b_n\;>\;0,\;n\;\geq\;1. In this paper, for array of row negatively associated(NA) random variables, we establish a general weak law of large numbers (WLLA) of the form (${\sum_{\kappa=1}}^n\;a_{\kappa}X_{n\kappa}\;-\;\nu_{n\kappa})\;/b_n$ converges in probability to zero, as $n\;\rightarrow\;\infty$, where {$\nu_{n\kappa}$\mid$1\;\leq\;\kappa\;\leq\;n,\;n\;\geq\;1$} is a suitable array of constants.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.275-306
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• 2013

For two positive integers $m$ and $n$, let $\mathcal{P}_n$ be the open convex cone in $\mathbb{R}^{n(n+1)/2}$ consisting of positive definite $n{\times}n$ real symmetric matrices and let $\mathbb{R}^{(m,n)}$ be the set of all $m{\times}n$ real matrices. In this paper, we investigate differential operators on the non-reductive homogeneous space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$ that are invariant under the natural action of the semidirect product group $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ on the Minkowski-Euclid space $\mathcal{P}_n{\times}\mathbb{R}^{(m,n)}$. These invariant differential operators play an important role in the theory of automorphic forms on $GL(n,\mathbb{R}){\times}\mathbb{R}^{(m,n)}$ generalizing that of automorphic forms on $GL(n,\mathbb{R})$.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.14 no.2
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• pp.123-129
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• 2001

The optimal high temperature processing conditions for the formation of Ohmic contact of Ti/Al/Pt/Au multiple layers were established for the fabrication of n$^{+}$-GaN/AlGaN/GaN HFET device. Contact resistivity as low as 3.4x10$^{-6}$ ohm-$\textrm{cm}^2$ was achieved by the annealing of the sample at 100$0^{\circ}C$ for 10 sec. using the RTA (Rapid Thermal Annealing) system. The fabricated HFET (Heterostructure Field Effect Transistor) with a structure of n'-GaN/undoped AlGaN/undoped GaN exhibited a low knee voltage of 3.5 V and a maximum source-drain current density of 180 mA/mm at Vg=0V.V.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1994.11a
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• pp.50-53
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• 1994

In this study. we report the properties of optically pumped stimulated emission at room temperature (RT) from column-III nitride semiconductors of GaN, GaInN, AlGaN/GaN double hetero-structure (DH) and AlGaN/GaInN DH which grown by low pressure metal-organic vapor phase epitaxy on sapphire substrate using an AIN buffer-layer. The peak wavelength of the stimulated emission at RT from AlGaN/GaN DH is 370nm and the threshold of excitation pumping power density (P$\_$th/) is about 89㎾/$\textrm{cm}^2$, and they from AlGaN/GaInN DH are 403nm and 130㎾/$\textrm{cm}^2$, respectively. The P$\_$th/ of AlGaN/GaN and AlGaN/GaInN DHs are lower than the bulk materials due to optical confinement within the active layers of GaN and GaInN. The optical gain and the polarization of stimulated emission characteristics are presented in this article.

• Proceedings of the Korean Vacuum Society Conference
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• 2011.08a
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• pp.132-132
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• 2011

The sheet resistance (Rs) of undoped GaN films on AlN/c-plane sapphire substrate was investigated in which the AlN films were grown by R. F. magetron sputtering method. The Rs was strongly dependent on the AlN layer thickness and semi-insulating behavior was observed. To clarify the effect of crystalline property on Rs, the crystal structure of the GaN films has been studied using x-ray scattering and transmission electron microscopy. A compressive strain was introduced by the presence of AlN nucleation layer (NL) and was gradually relaxed as increasing AlN NL thickness. This relaxation produced more threading dislocations (TD) of edge-type. Moreover, the surface morphology of the GaN film was changed at thicker AlN layer condition, which was originated by the crossover from planar to island grains of AlN. Thus, rough surface might produce more dislocations. The edge and mixed dislocations propagating from the interface between the GaN film and the AlN buffer layer affected the electric resistance of GaN film.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.35-42
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• 1989

Let .ohm.$_{n}$ and Pm $t_{n}$ denote the sets of all n*n doubly stochastic matrices and the set of all n*n permutation matrices respectively. For m*n matrices A=[ $a_{ij}$ ], B=[ $b_{ij}$ ] we write A.leq.B(A$a_{ij}$ .leq. $b_{ij}$ ( $a_{ij}$ < $b_{ij}$ ) for all i=1,..,m; j=1,..,n. Let $I_{n}$ denote the identity matrix of order n, let $J_{n}$ denote the n*n matrix all of whose entries are 1/n, and let $K_{n}$=n $J_{n}$. For a complex square matrix A, the permanent of A is denoted by per A. Let $E_{ij}$ denote the matrix of suitable size all of whose entries are zeros except for the (i,j)-entry which is one.hich is one.

• Journal of the Optical Society of Korea
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• v.17 no.1
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• pp.16-21
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• 2013

In this paper, we report the effect of GaN/graded-composition AlGaInN/GaN quantum barriers in active regions on the electrical and optical properties of GaN-based vertical light emitting diodes (VLEDs). By modifying the aluminum composition profile within the AlGaInN quantum barrier, we have achieved improvements in the output power and the internal quantum efficiency (IQE) as compared to VLEDs using conventional GaN barriers. The forward voltages at 350 mA were calculated to be 3.5 and 4.0 V for VLEDs with GaN/graded-composition AlGaInN/GaN barriers and GaN barriers, respectively. The light-output power and IQE of VLEDs with GaN/graded-composition AlGaInN/GaN barriers were also increased by 4.3% and 9.51%, respectively, as compared to those with GaN barriers.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.729-740
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• 2022

Let ℤ be the ring of integers and let ℤ_n be the ring of integers modulo n. Let ℤ(+)ℤ_n be the idealization of ℤ_n in ℤ and let (ℤ(+)ℤ_n)[X]] be either (ℤ(+)ℤ_n)[X] or (ℤ(+)ℤ_n)[[X]]. In this article, we study the zero-divisor graphs of ℤ(+)ℤ_n and (ℤ(+)ℤ_n)[X]]. More precisely, we completely characterize the diameter and the girth of the zero-divisor graphs of ℤ(+)ℤ_n and (ℤ(+)ℤ_n)[X]]. We also calculate the chromatic number of the zero-divisor graphs of ℤ(+)ℤ_n and (ℤ(+)ℤ_n)[X]].

• Journal of the Microelectronics and Packaging Society
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• v.25 no.3
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• pp.1-5
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• 2018

In this study, the effects of indium (In) doping in InGaN/GaN multi quantum well (MQW) on photoelectrochemical (PEC) properties were investigated. Each quantum well (QW) layer with controlled In content were grown on sapphire substrate. Before growth of MQW, GaN growth consisted of various stages in the following order: buffer GaN growth, undoped GaN growth, and Si-doped n-type GaN growth. Absorbance of InGaN/GaN MQW having different In composition was higher than that of the InGaN/GaN MQW having a constant In composition. It indicates that InGaN layer having different In composition absorbs light having a broad spectrum energy. These results are in agreement with those in photoluminescence (PL). After evaluation of PEC properties, it demonstrated that InGaN/GaN MQW having different In composition was improved InGaN/GaN MQW having constant In composition in PEC water splitting ability.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.489-496
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• 2004

We study the h- stability of nonlinear difference system x(n+1) =f(n, x(n)) and its perturbed system y(n+l) =f(n, y(n))+g(n, y(n), Sy(n)).