• Bulletin of the Korean Chemical Society
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• 제13권2호
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• pp.127-131
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• 1992

Changes in network structures of ${\alpha}-Nb_2O_5$ in the X MgO+(1-X) ${\alpha}-Nb_2O_5$ solid solutions occurring as the MgO doping level (X) was varied were investigated by means of infrared spectroscopy and X-ray analysis. X-ray diffraction revealed that all the synthesized specimens have the monoclinic structure. The FT-IR spectroscopy showed that the system investigated forms the solid solutions in which $Mg^{2+}$ ions occupy the octahedral sites in parent crystal lattice. Electrical conductivities were measured as a function of temperature from 600 to $1050{\circ}$ and $P_{O2}$ form $1{\times}10^{-5}$ to $2{\times}10^{-1}$ atm. The defect structure and conduction mechanism were deduced from the results. The $1}n$ value in ${\alpha}{\propto}{P_{O2}^{1}n}}$ is found to be -1/4 with single possible defect model. From the activation energy ($E{\alpha}$ = 1.67-1.73 eV) and the1/n value, electronic conduction mechanism is suggested with a doubly charged oxygen vacancy.

• 한국전기전자재료학회논문지
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• 제15권9호
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• pp.770-775
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• 2002

We present the band lineups of G $e_{1-}$x S $n_{x}$ G $e_{1-}$y S $n_{y(001)}$ heterostructures for the new devices. The energy gap of the bulk G $e_{1-}$x S $n_{x}$ alloy is calculated by taking into account the Vegard's law. The change of the energy gap due to the strain is understood in terms of the deformation Potential theory The valence band offset is obtained from the average bond energy model, where the changes of the band offset due to alloy compositions and strain are included. It is found that Ge/G $e_{1-}$y S $n_{y(001)}$ heterostructure has a staggered lineup type for 0$\leq$0.06 and a straddling one for 0.06$\leq$0.26. Meanwhile, Ge/G $e_{l-y}$ S $n_{y(001)}$ heterostructure has a staggered lineup type for 0$\leq$0.19 and a broken-gap one for 0.19$\leq$0.26. As a result, the various type of the G $e_{1-}$x S $n_{x}$ G $e_{1-}$y S $n_{y(001)}$ heterostructure can be applied for the useful device.evice.

• 대한수학회보
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• 제31권2호
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• pp.193-200
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• 1994

Let x : $M^{n}$ .rarw. $E^{m}$ be an isometric immersion of a manifold $M^{n}$ into the Euclidean space $E^{m}$ and .DELTA. the Laplacian of $M^{n}$ defined by -div.omicron.grad. The family of such immersions satisfying the condition .DELTA.x = .lambda.x, .lambda..mem.R, is characterized by a well known result ot Takahashi (8]): they are either minimal in $E^{m}$ or minimal in some Euclidean hypersphere. As a generalization of Takahashi's result, many authors ([3,6,7]) studied the hypersurfaces $M^{n}$ in $E^{n+1}$ satisfying .DELTA.x = Ax + b, where A is a square matrix and b is a vector in $E^{n+1}$, and they proved independently that such hypersurfaces are either minimal in $E^{n+1}$ or hyperspheres or spherical cylinders. Since .DELTA.x = -nH, the submanifolds mentioned above satisfy .DELTA.H = .lambda.H or .DELTA.H = AH, where H is the mean curvature vector field of M. And the family of hypersurfaces satisfying .DELTA.H = .lambda.H was explored for some cases in [4]. In this paper, we classify space curves x : R .rarw. $E^{3}$ satisfying .DELTA.x = Ax + b or .DELTA.H = AH, and find conditions for such curves to be equivalent.alent.alent.

• 호남수학학술지
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• 제8권1호
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• pp.51-74
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• 1986

The thery of measure is significant in that we extend from it to the theory of integration. AS specific metric outer measures we can take Hausdorff outer measure and Lebesgue-Stieltjes outer measure connecting measure with monotone functions.([12]) The purpose of this paper is to find some properties of Lebesgue-Stieltjes measure by extending it from $R^1$ to $R^n(n{\geq}1)$ $({\S}3)$ and differentiation of the integral defined by Borel measure $({\S}4)$. If in detail, as follows. We proved that if $_n{\lambda}_{f}^{\ast}$ is Lebesgue-Stieltjes outer measure defined on a finite monotone increasing function $f:R{\rightarrow}R$ with the right continuity, then $$_n{\lambda}_{f}^{\ast}(I)=\prod_{j=1}^{n}(f(b_j)-f(a_j))$$, where $I={(x_1,...,x_n){\mid}a_j$<$x_j{\leq}b_j,\;j=1,...,n}$. (Theorem 3.6). We've reached the conclusion of an extension of Lebesgue Differentiation Theorem in the course of proving that the class of continuous function on $R^n$ with compact support is dense in $L^p(d{\mu})$ ($1{\leq$}p<$\infty$) (Proposition 2.4). That is, if f is locally $\mu$-integrable on $R^n$, then $\lim_{h\to\0}\left(\frac{1}{{\mu}(Q_x(h))}\right)\int_{Qx(h)}f\;d{\mu}=f(x)\;a.e.(\mu)$.

• Korean Journal of Mathematics
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• 제30권4호
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• pp.653-663
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• 2022

We study cyclic codes of length n over 𝔽_2^t. Cyclic codes can be viewed as ideals in 𝓡_n = 𝔽_2^t [x]/(xⁿ − 1). It is known that there is a unique generating idempotent for each ideal. Let e(x) ∈ 𝓡_n. If t = 1 or t = 2, then there is a necessary and sufficient condition that e(x) is an idempotent. But there is no known similar result for t ≥ 3. In this paper we give an answer for this problem.

• Korean Journal of Mathematics
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• 제21권3호
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• pp.319-323
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• 2013

Let D be a principal ideal domain, X be an indeterminate over D, D[X] be the polynomial ring over D, and $R_n=D[X]/(X^n)$ for an integer $n{\geq}1$. Clearly, $R_n$ is a commutative Noetherian ring with identity, and hence each nonzero nonunit of $R_n$ can be written as a finite product of irreducible elements. In this paper, we show that every irreducible element of $R_n$ is a primary element, and thus every nonunit element of $R_n$ can be written as a finite product of primary elements.

• 대한수학회지
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• 제52권1호
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• pp.191-207
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• 2015

Let $\mathcal{R}$ be a prime ring of characteristic different from 2, $\mathcal{Q}_r$ be its right Martindale quotient ring and $\mathcal{C}$ be its extended centroid. Suppose that $\mathcal{G}$ is a nonzero generalized skew derivation of $\mathcal{R}$, ${\alpha}$ is the associated automorphism of $\mathcal{G}$, f($x_1$, ${\cdots}$, $x_n$) is a non-central multilinear polynomial over $\mathcal{C}$ with n non-commuting variables and $$\mathcal{S}=\{f(r_1,{\cdots},r_n)\left|r_1,{\cdots},r_n{\in}\mathcal{R}\}$$. If $\mathcal{G}$ acts as a Jordan homomorphism on $\mathcal{S}$, then either $\mathcal{G}(x)=x$ for all $x{\in}\mathcal{R}$, or $\mathcal{G}={\alpha}$.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.549-556
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• 2009

Let $\{(X_{ni}|1{\leq}i{\leq}n,\;n{\geq}1)\}$ be an array of rowwise negatively associated random variables. In this paper we discuss $n^{{\alpha}p-2}h(n)max_{1{\leq}k{\leq}n}|{\sum}_{i=1}^kX_{ni}|/n^{\alpha}{\rightarrow}0$ completely as $n{\rightarrow}{\infty}$ under not necessarily identically distributed with suitable conditions for ${\alpha}$>1/2, 0${\alpha}p{\geq}1$ and a slowly varying function h(x)>0 as $x{\rightarrow}{\infty}$. In addition, we obtain the complete convergence of moving average process based on negative association random variables which extends the result of Zhang (1996).

• 대한금속재료학회지
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• 제47권9호
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• pp.591-596
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• 2009

$TiN_xO_y/TiN_x$ multi-layer thin films with a high resistance(${\sim}k{\Omega}$) were deposited on $SiO_2/Si$ substrates at room temperature by sputtering. The $TiN_x$ thin films show island and smooth surface morphology in samples prepared by ${\alpha}$ and RF magnetron sputtering, respectively. $TiN_xO_y/TiN_x$ multi-layer in has been developed to control temperature coefficient of resistance(TCR) by the incorporation of $TiN_x$ layer(positive TCR) inserted into $TiN_xO_y$ layers(negative TCR). Electrical and structural properties of sputtered $TiN_xO_y/TiN_x$ multi-layer films were investigated as a function of annealing temperature. In order to achieve a stable high resistivity, multi-layer films were annealed at various temperatures in oxygen ambient. Samples annealed at $700^{\circ}C$ for 1 min exhibited good TCR value of approximately $-54 ppm/^{\circ}C$ and a stable high resistivity around $20k{\Omega}/sq$. with good reversibility.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2004년도 하계종합학술대회 논문집(2)
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• pp.605-608
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• 2004

A $Pt/Al_xGa_{l-x}N$ Schottky type Ultra-violet photodetector was modeled and simulated using the commercial SILVACO software program. In the carrier transport, we applied field model and other analytic model to determine the electron saturation velocity and low field mobility for GaN and $Al_xGa_{l-x}N$. A C-Interpreter function was defined to described the mole-fraction for the ternary compound semiconductor such as $Al_xGa_{l-x}N$. As comparing the simulated and experimental results, we found that the simulated result for type-1 has $15.9 nA/cm^2$ of leakage current at 5V. We confirmed a good agreement of photo-current in the UV Photo-detector, while applying the absorption coefficient and reflective index of active $Al_xGa_{l-x}N$ and other layers. There had been an intensive search for the proper refractive indices of the layers.