• Korean Journal of Mathematics
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• 제16권3호
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• pp.323-334
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• 2008

We define injective and projective representations of quivers with two vertices with n arrows. In the representation of quivers we denote n edges between two vertices as ${\Rightarrow}$ and n maps as $f_1{\sim}f_n$, and $E{\oplus}E{\oplus}{\cdots}{\oplus}E$ (n times) as ${\oplus}_nE$. We show that if E is an injective left R-module, then $${\oplus}_nE{\Longrightarrow[50]^{p_1{\sim}p_n}}E$$ is an injective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $p_i(a_1,a_2,{\cdots},a_n)=a_i,\;i{\in}\{1,2,{\cdots},n\}$. Dually we show that if $M_1{\Longrightarrow[50]^{f_1{\sim}f_n}}M_2$ is an injective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are injective left R-modules. We also show that if P is a projective left R-module, then $$P\Longrightarrow[50]^{i_1{\sim}i_n}{\oplus}_nP$$ is a projective representation of $Q={\bullet}{\Rightarrow}{\bullet}$ where $i_k$ is the kth injection. And if $M_1\Longrightarrow[50]^{f_1{\sim}f_n}M_2$ is an projective representation of a quiver $Q={\bullet}{\Rightarrow}{\bullet}$ then $M_1$ and $M_2$ are projective left R-modules.

• 호남수학학술지
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• 제36권2호
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• pp.253-261
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• 2014

In this paper, we first will show that for any space X and any Wallman sublattice $\mathcal{A}$ of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}$, (${\Phi}^{-1}_{\mathcal{A}}(X)$, ${\Phi}_{\mathcal{A}}$) is the minimal quasi-F cover of X if and only if (${\Phi}^{-1}_{\mathcal{A}}(X)$, ${\Phi}_{\mathcal{A}}$) is a quasi-F cover of X and $\mathcal{A}{\subseteq}\mathcal{Q}_X$. Using this, if X is a locally weakly Lindel$\ddot{o}$f space, the set {$\mathcal{A}|\mathcal{A}$ is a Wallman sublattice of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}$ and ${\Phi}^{-1}_{\mathcal{A}}(X)$ is the minimal quasi-F cover of X}, when partially ordered by inclusion, has the minimal element $Z(X)^{\sharp}$ and the maximal element $\mathcal{Q}_X$. Finally, we will show that any Wallman sublattice $\mathcal{A}$ of $\mathcal{R}(X)$ with $Z(X)^{\sharp}{\subseteq}\mathcal{A}{\subseteq}\mathcal{Q}_X$, ${\Phi}_{\mathcal{A}_X}:{\Phi}^{-1}_{\mathcal{A}}(X){\rightarrow}X$ is $z^{\sharp}$-irreducible if and only if $\mathcal{A}=\mathcal{Q}_X$.

• 대한수학회지
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• 제54권6호
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• pp.1733-1757
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• 2017

Let $R={\oplus}_{{\alpha}{\in}{\Gamma}}R_{\alpha}$ be an integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$, ${\bar{R}}$ be the integral closure of R, H be the set of nonzero homogeneous elements of R, C(f) be the fractional ideal of R generated by the homogeneous components of $f{\in}R_H$, and $N(H)=\{f{\in}R{\mid}C(f)_v=R\}$. Let $R_H$ be a UFD. We say that a nonzero prime ideal Q of R is an upper to zero in R if $Q=fR_H{\cap}R$ for some $f{\in}R$ and that R is a graded UMT-domain if each upper to zero in R is a maximal t-ideal. In this paper, we study several ring-theoretic properties of graded UMT-domains. Among other things, we prove that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of $R_{N(H)}$ is extended from a homogeneous ideal of R, if and only if ${\bar{R}}_{H{\backslash}Q}$ is a graded-$Pr{\ddot{u}}fer$ domain for all homogeneous maximal t-ideals Q of R, if and only if ${\bar{R}}_{N(H)}$ is a $Pr{\ddot{u}}fer$ domain, if and only if R is a UMT-domain.

• 대한전자공학회논문지TC
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• 제45권6호
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• pp.27-33
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• 2008

차수가 h인 다항식 ${\hbar}(x){\in}F_q[x]$에서, $x-s_1,\;x-s_2,\;{\cdots},\;x-s_n$에 의해 생성된 $\(F_q[x]/({\hbar(x))\)*$의 multiplicative subgroup의 크기를 결정하는 것은 대단히 중요한 과제이다. 여기서 $\{s_1,\;s_2,\;{\cdots},\;s_n\}{\sebseteq}F_q$이고 모든 i 에 대해서, ${\hbar}(x){\neq}0$이다. 지금까지 알려진 asymptotic lower bound는 $(rh)^{O(1)}\(2er+O(\frac{1}{r})\)^h$이며, 여기서 $r=\frac{n}{h}$이고 e(=2.718...)는 natural logarithm의 기저이다. 본 논문에서는, coding theory 문제와 연계해서 더 낳은 lower bound인 $(rh)^{O(1)}\(2er+{\frac{e}{2}}{\log}r-{\frac{e}{2}}{\log}{\frac{e}{2}}+O{(\frac{{\log}^2r}{r})}\)^h$를 증명하고자 한다. 여기서 log는natural logarithm을 나타내며, 또한 이방식의 제약점에 대해서도 논의한다.

• 호남수학학술지
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• 제26권1호
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• pp.45-59
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• 2004

In this paper we obtain the general solution the functional equation $a^2f(\frac{x-2y}{a})+f(x)+2f(y)=2a^2f(\frac{x-y}{a})+f(2y).$ The type of the solution of this equation is Q(x)+A(x)+C, where Q(x), A(x) and C are quadratic, additive and constant, respectively. Also we prove the stability of this equation in the spirit of Hyers, Ulam, Rassias and $G\check{a}vruta$.

• 대한수학회논문집
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• 제12권2호
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.

• 대한수학회논문집
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• 제19권4호
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• pp.775-778
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• 2004

The authors aim at obtaining an interesting result for a special summation formula for $_{6F_5}$(1), by comparing two generalized Watson's theorems on the sum of a $_{3F_2}$ obtained earlier by Mitra and Lavoie et. al.

• 대한기계학회논문집B
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• 제24권8호
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• pp.1038-1045
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• 2000

An experimental study was carried out to delineate the flow characteristics in a closed countescurrent two-phase thermo syphon with concentric tubes. This is to be installed in the HANARO research reactor as a part of a Cold Neutron Source(CNS). In the present investigation, experiments ata room temperature with Freon-II3 as a moderator were performed. Results show that, based on the magnitude of pressure fluctuation, the flow regimes could be divided into 4 distinct ones in the ($V_f,\;Q_i$) plane, where $V_f$ represents the volume of the charged liquid and $Q_i$ the heat load: a stable flow regime, an oscillatory flow regime, a restablized flow regime and a dryout flow regime. For $V_f$>2.5l, the flow is stable at low $Q_i$. However, as $Q_i$ increases, the flow becomes oscillatory and finally restablizes As $V_f$ increases, the oscillation amplitude decreases, reaching to the restablized flow region at low $Q_i$, and the liquid level in the moderator cell remains high. In the oscillatory flow regimes, for a fixed VI; the oscillating period of time varies with $Q_i$, having a minimum value at a certain value of $Q_i$. The heat load, where the oscillating period of time is minimum, decreases as $V_f$ increases.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2003년도 춘계학술대회 논문집 센서 박막재료 반도체 세라믹
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• pp.277-281
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• 2003

Effects of $CaF_2$ addition as a filler on the high frequency dielectric properties and sintering of CaO-$Al_2O_3-SiO_2-B_2O_3$(CASB) and ZnO-MgO-$B_2O_3-SiO_2$(ZMBS) glass composites were investigated. The optimal glass composition in the CASB system was 33.0CaO-$17.0Al_2O_3-35.0SiO_2-15.0B_O_3$(in wt%). The corresponding dielectric properties were k=8.1 and $Q{\times}fo$=1,200GHz. The sintering temperature was $800{\mu}m$. In case of 2MBS system, 25.0ZnO-25.0MgO-20.0$B_2O_3-30.0SiO_2$(in wt%) glass showed k=6.8 and $Q{\times}fo$=5,200GHz when it was sintered at $750^{\circ}C$. The maximum amount of $CaF_2$ in the CASB and 2MBS glass system without any detrimental effect on the sintering was 25.0 v/o and 15.0 v/o, respectively. The addition of $CaF_2$ in the glass systems improved the high frequency dielectric properties. In case of CASB+$CaF_2$ composite, k was 7.1 and $Q{\times}fo$ was 2,300GHz. And in case of 2MBS+$CaF_2$ composite, k was 5.9 and $Q{\times}fo$ was 8,100GHz. $CaF_2$ addition also reduced sintering temperature. Effects of $CaF_2$ on the dielectric and sintering properties was analyzed in terms of viscosity and crystallization behavior changes due to the interaction between $CaF_2$ and the glass systems.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2005년도 하계학술대회 논문집 Vol.6
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• pp.363-364
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• 2005

LTCC(low temperature co-fired ceramics)용 glass/ceramic 복합체를 제조하기 위해 3종류 의 glass를 선정하고 filler로 $Al_2O_3$ 와 $TiO_2$를 사용하여 glass frit에 따른 소결 및 유전 특성에 대하여 조사하였다. Glass frit은 lead-borosilicate(PBS), zinc-borosilicate(ZBS), bismuth-borosilicate(BBS) glass 조성을 사용하였고 1100~$1400^{\circ}C$에서 melting시킨 후 quenching하여 frit화하였다. $Al_2O_3$와 $TiO_2$ filler에 10~50 vol%로 glass frit을 각각 혼합한 후 600~$950^{\circ}C$에서 2시간 동안 소결한 결과 50 vol% glass frit 일 때 $900^{\circ}C$ 이하에서 소성이 가능하였다. 유전특성은 $900^{\circ}C$에서 $Al_2O_3$-50vol%PBS($\varepsilon_{r}$=8.8, $Q{\times}f_o$=4,900, $\tau_f$=-24), $Al_2O_3$-50vol% ZBS($\varepsilon_{r}$=5.7, $Q{\times}f_o$=17,800, $\tau_f$=-21), $Al_2O_3$-50vol%BBS($\varepsilon_{r}$=11.1, $Q{\times}f_o$= 2,080, $\tau_f$=-48), $TiO_2$-50vol%PBS($\varepsilon_{r}$=18.6, $Q{\times}f_o$=3,800, $\tau_f$=+135), $TiO_2$-50vol%ZBS($\varepsilon_{r}$=36.4, $Q{\times}f_o$= 7,500, $\tau_f$=+159), $TiO_2$-50vol%BBS($\varepsilon_{r}$=56.4, $Q{\times}f_o$=520, $\tau_f$=+119)을 나타내었다. 따라서 LTCC용 기판재료 및 마이크로파 유전체로 응용이 가능한 것으로 확인되었다.