• Bulletin of the Korean Chemical Society
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• v.15 no.1
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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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• v.31 no.1_2
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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 $m^{\prime}{\in}\mathbb{N}$.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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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 $(\lambda I - \frac{1}{2} \tilde{\Xi}_{0,2}(\kappa))_u = f$.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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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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• v.13
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• pp.30-30
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• 2003

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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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).

• Journal of the Korean Mathematical Society
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• v.36 no.6
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.15 no.4
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• pp.773-779
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• 2011

The width of a submarine's turbulent wake, using Shear-free and Ship wake theory, is proportional to $x^n,\;({\frac{1}{5}}{\leq}n<{\frac{1}{2}})$ If we assume submarine's length, width, velocity are 65m, 6.5m, 6kts respectively, and the minimum diffusion of turbulent wake ; ${\infty}\;x^{1/5}$, the width of wake behind the submarine is about 20m at 1.2km, 30m at 15km when there is no breaking waves on the sea surface. However, in the case of breaking waves, it is very limited to identify submarine's wake on the sea surface because wind generated turbulent wake has higher turbulent kinetic energy than that of submarine's wake. As a result, there is a high possibility to detect submarine's wake on the sea surface in the shallow water such as the Yellow-Sea using a proper detection method such as SAR. This means that in anti-submarine operations, non-acoustic sea surface serveillance applied turbulent wake will be very effective way to detect a submarine in near future. To do this we have to develop exact theory of submarine's turbulent wake above all.

• Journal of the Korean Statistical Society
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• v.32 no.3
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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).

• Transactions of the Korean hydrogen and new energy society
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• v.10 no.2
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• pp.119-130
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• 1999

After preparing $Mg_2Ni_{1-x}{^{57}}Fe_x$(x=0.015, 0.03, 0.06, 0.12 and 0.24) alloys, they were studied by $M{\ddot{o}}ssbauer$ resonance. The $M{\ddot{o}}ssbauer$ spectra of x=0.015 and 0.03 alloys exhibit two doublets (doublet 1, 2). That of x=0.06 alloys shows two doublets (doublet 1,2) and one six-line, and those of x=0.12 and 0.24 alloys have only one six-line. The doublet 1 for x=0.015, 0.03 and 0.06 alloys is considered to result from a fraction of Fe in excess showing a superparamagnetic behavior. The doublet 2 is considered to result from the Fe substituted for Ni in the $Mg_2Ni$ phase. The values of isomer shift 0.24 ~ 0.28 mm/s suggest that the iron exist in the state $Fe^{+3}$. The result that the quadrapole splitting of the doublet 2 is not zero shows that the distribution of electrons around the iron is asymmetric. Their values for the doublet 2, 1.20 ~ 1.38 mm/s, approach the value of quadrapole for the oxidation number +3. The six-line showing the magnetic hyperfine interactions results from the iron which has not substituted the nickel in the $Mg_2Ni$ phase. The $M{\ddot{o}}ssbauer$ spectra of the hydrided alloys with x=0.015 and 0.03 show six-line. This suggests that the iron segregates with the hydriding reaction. The analysis results of the $M{\ddot{o}}ssbauer$ spectrum, the variation of magnetization with magnetic field, Auger electron spectroscopy and electron diffraction show the segregation of Ni and the formation of MgO. This is considered to result from the reaction of the $Mg_2Ni$ phase with the oxygen contained in the hydrogen as impurity.