• 대한수학회보
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• 제40권2호
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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.

• 대한수학회지
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• 제50권2호
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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 $GL(n,\mathbb{R})$.

• 한국전기전자재료학회논문지
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• 제14권2호
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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.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 1994년도 추계학술대회 논문집
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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.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2011년도 제41회 하계 정기 학술대회 초록집
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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.

• 대한수학회보
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• 제26권1호
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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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• 제17권1호
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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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• 제40권3_4호
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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]].

• 마이크로전자및패키징학회지
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• 제25권3호
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• pp.1-5
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• 2018

본 연구에서는 InGaN/GaN multi quantum well (MQW)에서 Indium (In) 도핑효과에 따른 광전기화학적 특성을 관찰하였다. 기판으로는 Sapphire을 사용하였고, 각 Quantum well (QW)을 구성하고 있는 InGaN의 조성을 다르게 하였다. 투과도 측정 결과 일정한 In 조성을 가진 InGaN/GaN MQW에 비해 각 QW의 In 조성을 다르게 한 InGaN/GaN MQW에서 흡수도가 향상되는 것을 확인할 수 있었다. 이는 각각 다른 In 조성을 가진 InGaN 층이 더 넓은 영역의 스펙트럼 에너지를 가지는 빛을 흡수하기 때문인 것으로 생각된다. 광학적 특성을 평가하기 위해 진행한 상온 photoluminescence (PL) 실험을 진행한 결과, 역시 다양한 In 조성을 가진 InGaN/GaN MQW이 더 넓은 파장에서 발광이 나타나는 것을 확인할 수 있었다. 이들 샘플에 대한 광전기화학적 특성평가를 통하여, gradation In 조성을 가지고 있는 InGaN/GaN MQW이 일정한 In 조성을 가지는 InGaN/GaN MQW에 비해 광전기화학적 물분해 능력이 월등히 향상됨을 확인하였다.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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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)).