• Bulletin of the Korean Chemical Society
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• 제15권1호
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• pp.64-74
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• 1994

The nonstoichiometric chalcogenides with NaCl-type structure were prepared and the physical and structural properties were studied. The homogeneous range and the structural change were studied based on X-ray powder diffractions using Rietveld-type full-profile fitting technique. Wide homogeneous ranges were observed in Y-S and Y-Se systems, and relatively narrow homogeneous ranges were observed in Yb-S and Yb-Se systems. Both in $Yb_{1-x}S\;and\;Yb_{1-x}Se$, a vacancy ordering transition occurred in (111) plane direction. The ordered superstructure had cubic symmetry(Fm$\bar{3}m) with doubled unit cell "a" parameter compared to the original NaCl-type. The superlattice developed in a continuous second-order transitiion was characterized by the reduced waved vector k= $(a^*+b^*+c^*)/2$. Y-S system had metallic, and YSe, YbSe system had semiconducting properties in their homogeneous ranges. It was observed that the change of electronic transport properties in extended homogeneous range did not depend on the relativeratio of metal to nonmetal, but on the quantities of vacancies.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.45-54
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• 2013

Let $$S^{\pm}_{(n,k)}\;:=\{(a,b,x,y){\in}\mathbb{N}^4:ax+by=n,x{\equiv}{\pm}y\;(mod\;k)\}$$. From the formula $\sum_{(a,b,x,y){\in}S^{\pm}_{(n,k)}}\;ab=4\sum_{^{m{\in}\mathbb{N}}_{m<n/k}}\;{\sigma}_1(m){\sigma}_1(n-km)+\frac{1}{6}{\sigma}_3(n)-\frac{1}{6}{\sigma}_1(n)-{\sigma}_3(\frac{n}{k})+n{\sigma}_1(\frac{n}{k})$, we find the Diophantine solutions for modulo $2^{m^{\prime}}$ and $3^{m^{\prime}}$, where $m^{\prime}{\in}\mathbb{N}$.

• 대한수학회논문집
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• 제11권2호
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• pp.367-375
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• 1996

Suppose the kernel function $\kappa$ belongs to $S(R^2)$ and is symmetric such that $ < \otimes x, \kappa >\geq 0$ for all $x \in S'(R)$. Let A be the class of functions f such that the function f is measurable on $S'(R)$ with $\int_{S'(R)}$\mid$f((I + tK)^{\frac{1}{2}}x$\mid$^2d\mu(x) < M$ for some $M > 0$ and for all t > 0, where K is the integral operator with kernel function $\kappa$. We show that the \lambda$-potential $G_Kf$ of f is a weak solution of $(\lambda I - \frac{1}{2} \tilde{\Xi}_{0,2}(\kappa))_u = f$.

• 충청수학회지
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• 제20권2호
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• pp.117-137
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• 2007

We establish the Hyers-Ulam-Rassias stability of the Pexiderized mixed type quadratic equation $f_1(x+y+z)+f_2(x-y)+f_3(x-z)-f_4(x-y-z)-f_5(x+y)-f_6(x+z)=0$ in the spirit of D. H. Hyers, S. M. Ulam and Th. M. Rassias.

• 한국초전도학회:학술대회논문집
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• 한국초전도학회 2003년도 High Temperature Superconductivity Vol.XIII
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• pp.30-30
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• 2003

• 대한수학회보
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• 제44권2호
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• pp.225-231
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• 2007

Given an injective envelope E of a left R-module M, there is an associative Galois group Gal$({\phi})$. Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope $E[x^{-1}]$ of an inverse polynomial module $M[x^{-1}]$ as a left R[x]-module and we can define an associative Galois group Gal$({\phi}[x^{-1}])$. In this paper we describe the relations between Gal$({\phi})$ and Gal$({\phi}[x^{-1}])$. Then we extend the Galois group of inverse polynomial module and can get Gal$({\phi}[x^{-s}])$, where S is a submonoid of $\mathbb{N}$ (the set of all natural numbers).

• 대한수학회지
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• 제36권6호
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• pp.1133-1143
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• 1999

Chaterji strengthened version of a theorem for martin-gales which is a generalization of a theorem of Marcinkiewicz proving that if $X_n$ is a sequence of independent, identically distributed random variables with $E{\mid}X_n{\mid}^p\;<\;{\infty}$, 0 < P < 2 and $EX_1\;=\;1{\leq}\;p\;<\;2$ then $n^{-1/p}{\sum^n}_{i=1}X_i\;\rightarrow\;0$ a,s, and in $L^p$. In this paper, we probe a version of law of large numbers for double arrays. If ${X_{ij}}$ is a double sequence of random variables with $E{\mid}X_{11}\mid^log^+\mid X_{11}\mid^p\;<\infty$, 0 < P <2, then $lim_{m{\vee}n{\rightarrow}\infty}\frac{{\sum^m}_{i=1}{\sum^n}_{j=1}(X_{ij-a_{ij}}}{(mn)^\frac{1}{p}}\;=0$ a.s. and in $L^p$, where $a_{ij}$ = 0 if 0 < p < 1, and $a_{ij}\;=\;E[X_{ij}\midF_[ij}]$ if $1{\leq}p{\leq}2$, which is a generalization of Etemadi's marcinkiewicz-type SLLN for double arrays. this also generalize earlier results of Smythe, and Gut for double arrays of i.i.d. r.v's.

• 한국정보통신학회논문지
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• 제15권4호
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• pp.773-779
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• 2011

자유전단류(Shear free flow) 가정을 이용한 수상함 항적모델을 잠수함에 적용 결과 잠수함 난류항적 지름은 $x^n,\;({\frac{1}{5}}{\leq}n\;<{\frac{1}{2}})$ 에 비례하였으며, 난류항적의 최소 확산을 가정할 때(${\sigma}=50.25$, 즉 ${\infty}\;x^{1/5}$인 경우), 길이65m, 폭 6.5m 속력 6kts 인 잠수함의 난류항적 반지름은 잠수함 함미로부터 1.2Km 후방에서 약 20m, 10Km 후방에서는 약 30m에 달하였고, 해수면에서 관측 가능한 잠수함 난류항적은 잔잔한 해상상태에서 잠수함 후방 약 15Km에 이르는 것으로 나타났으나 쇄파가 발생하는 악천후에서는 해수면에서 난류항적을 관측하기는 매우 제한되었다. 이는 적어도 서해와 같이 얕은 잠수함 작전환경에서는 잠수함 난류항적이 해수면에서 나타나는 것을 의미하며 SAR와 같은 탐지체계를 이용 시 탐색 가능함을 의미한다.

• Journal of the Korean Statistical Society
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• 제32권3호
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• pp.311-311
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• 2003

This paper contains the following errors. 1. "$I_{\{x>D\}}{\lambda}dt_{p0}(t)s(x)$" should be added to the right hand side of (2.3). 2. "$I_{\{x>D\}}{\lambda}_{p0}(t)s(x)$" should be added to the right hand side of (2.6). 3. "$I_{\{x>D\}}{\lambda}_{p0}s(x)$" should be added to the right hand side of (2.9). 4. In Theorem 2.3 and its proof, "${\lambda}{\int}_{0}^{D}f(y)s(x-y)dy$" appears three times (including one in (2.20)). To each of these, "${\lambda}_{po}s(x)$" should be added. 5. In Remark 2.5, "${\lambda}dt_{p0}/s(x)dx" should be added to "${\int}_{0}^{D}{\lambda}dt\;s(x-y)dxf(y)dy$". As a result of these corrections, a simpler proof of Theorem 2.3 becomes available. Substituting (2.18), (2.21), (2.22) into the left hand side of (2.20) and comparing the result with (2.10), we have the right hand side of (2.20).

• 한국수소및신에너지학회논문집
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• 제10권2호
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• pp.119-130
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• 1999

$Mg_2Ni_{1-x}{^{57}}Fe_x$(x=0.015, 0.03, 0.06, 0.12 and 0.24)합금을 제작하여 $M{\ddot{o}}ssbauer$ 공명에 의한 연구를 하였다. x=0.015, 0.03 합금의 $M{\ddot{o}}ssbauer$ spectrum은 2개의 doublet(doublet 1, 2)을, x=0.06 합금의 spectrum은 2개의 doublet(doublet 1, 2)과 1개의 six-line을, 그리고 x=0.12, 0.24 합금의 spectrum은 six-line만 보인다. x=0.015, 0,03, 0.06 합금의 doublet 1은, 초 상자성 거동을 보여주는 과잉으로 존재하는 일부의 철 때문에 생기는 것으로 판단된다. doublet 2는, $Mg_2Ni$ 상의 Ni에 치환된 철에 기인한 것으로 판단된다. doublet 2의 isomer shift 크기 (0,24 ~ 0.28 mm/s)로 보아 $Fe^{+3}$로 존재함을 추측할 수 있다. 또한 doublet 2의 quadrapole splitting이 영이 아님으로부터 Fe 주위의 전자 배열이 비대칭을 이루고 있음을 알 수 있고, 그 크기 (1.20 ~ 1.38 mm/s)는 산화수 +3의 quadrapole splitting 값에 아주 가까운 값이다. 자기적 초미세 상호 작용을 보여주는 six-line은 합금 속에 들어가지 않는 철 때문에 생긴다. 수소화물화 반웅시킨 x=0.015, 0.03 합금의 $M{\ddot{o}}ssbauer$ spectrum이 six-line을 보였는데, 이로부터 수소화물화 반응으로 인하여 Fe이 편석되었음을 알 수 있다. 수소화물화 반응후 $M{\ddot{o}}ssbauer$ spectrum, 자기장의 함수로서 자화의 변화 측정, Auger electron spectroscopy, electron diffraction pattern 분석 결과, Ni의 편석과 MgO의 형성을 보여주었는데, 이는 수소 속에 들어 있는 미량의 산소가 $Mg_2Ni$와 반응하여 야기된 현상으로 생각된다.