• 대한수학회보
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• 제46권5호
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• pp.857-866
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• 2009

Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and $\mu$, $\nu$ be a pair of generalized derivations on R. If < $\mu^2(x)+\nu(x),\;x^n$ > = 0 for all x $\in$ R, then $\mu$ and $\nu$ are either left multipliers or right multipliers. Let n be a fixed positive integer, R be a noncommutative 2n!-torsion free prime ring with the center $C_R$ and d, g be a pair of derivations on R. If < $d^2(x)+g(x)$, $x^n$ > $\in$ $C_R$ for all x $\in$ R, then d = g = 0. Then we apply these purely algebraic techniques to obtain several range inclusion results of pair of (generalized-)derivations on a Banach algebra.

• 대한수학회보
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• 제50권5호
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• pp.1651-1657
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• 2013

Let R be a prime ring, I a nonzero ideal of R, $d$ a derivation of R, $m({\geq}1)$, $n({\geq}1)$ two fixed integers and $a{\in}R$. (i) If $a((d(x)y+xd(y)+d(y)x+yd(x))^n-(xy+yx))^m=0$ for all $x,y{\in}I$, then either $a=0$ or R is commutative; (ii) If $char(R){\neq}2$ and $a((d(x)y+xd(y)+d(y)x+yd(x))^n-(xy+yx)){\in}Z(R)$ for all $x,y{\in}I$, then either $a=0$ or R is commutative.

• 대한수학회지
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• 제47권5호
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• pp.1097-1106
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• 2010

Let R be a commutative ring with identity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will investigate some ring theoretic properties of R by considering $\Gamma$(R), the zero-divisor graph of R, under the regular action on X by G as follows: (1) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then there is a vertex of $\Gamma$(R) which is adjacent to every other vertex in $\Gamma$(R) if and only if R is a local ring or $R\;{\simeq}\;\mathbb{Z}_2\;{\times}\;F$ where F is a field; (2) If R is a local ring such that X is a union of n distinct orbits under the regular action of G on X, then all ideals of R consist of {{0}, J, $J^2$, $\ldots$, $J^n$, R} where J is the Jacobson radical of R; (3) If R is a ring such that X is a union of a finite number of orbits under the regular action on X by G, then the number of all ideals is finite and is greater than equal to the number of orbits.

• 한국지반환경공학회 논문집
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• 제13권6호
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• pp.51-57
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• 2012

본 연구는 E-beam 공정을 통한 triclosan의 광분해에 대하여 조사하였다. 공정의 최적화는 실험계획법에 의한 회분식 실험을 통해 수행되었다. 실험계획법은 통계적 적용 방안의 하나로 각 인자간의 영향을 고려하기 위해 반응표면을 설계하는 방법이다. 반응은 triclosan의 제거율(%, $Y_1$)과 TOC 제거율(%, $Y_2$)로 적용되었고 두 개의 독립변수로서 triclosan의 농도를 "$x_1$", 조사강도를 "$x_2$"로 설계하였다. 코드화 된 인자에 대한 Triclosan 제거율과 TOC 제거율에 따른 회귀식은 각각 $Y_1=63-12.4335x_1+15.1835x_2+5.8125x{_1}^2-5.6875x{_2}^2-0.75x_1x_2(R^2=95.1%,\;R^2(Adj)=91.7%)$과 $Y_2=46-8.8462x_1+11.7175x_2-0.75x{_1}^2-6.25x{_2}^2(R^2=98.7%,\;R^2(Adj)=97.7%)$로 나타났다. $Y_1$과 $Y_2$에 대한 모델 예측식의 결정계수($R^2$)와 수정결정계수($R{^2}_{(Adj)}$)의 값이 90% 이상으로 나타나 실험적 관찰결과와 잘 부합하였다. 이러한 결과는 회귀모델이 E-beam 공정에서의 인자영향을 잘 설명하며 통계적 적용이 성공적으로 적용된 것으로 판단된다.

• 대한수학회지
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• 제46권5호
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• pp.997-1005
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• 2009

Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and n a fixed positive integer. (i) If (d(x)y+xd(y)+d(y)x+$yd(x))^n$ = xy + yx for all x, y $\in$ I, then R is commutative. (ii) If char R $\neq$ = 2 and (d(x)y + xd(y) + d(y)x + $yd(x))^n$ - (xy + yx) is central for all x, y $\in$ I, then R is commutative. We also examine the case where R is a semiprime ring.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2008년도 하계학술대회 논문집 Vol.9
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• pp.21-22
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• 2008

In the paper, we report several experimental data capable of evaluating the phase transformation characteristics of $Ag_x(Ge_2Sb_2Te_5)_{1-x}$ (x =0, 0.05, 0.1) thin films. The $Ag_x(Ge_2Sb_2Te_5)_{1-x}$ phase change thin films have been prepared by thermal evaporation. The crystallization characteristics of amorphous$Ag_x(Ge_2Sb_2Te_5)_{1-x}$ thin films were investigated by using nano-pulse scanner with 658 nm laser diode (power; 1~17 mW, pulse duration; 10~460 ns) and XRD measurement. It was found that the more Ag is doped, the more crystallization speed was 50 improved. In comparision with $Ge_2Sb_2Te_5$ thin film, the sheet resistance$(R_{amor})$ of the amorphous $Ag_x(Ge_2Sb_2Te_5)_{1-x}$ thin films were found to be lager than that of $Ge_2Sb_2Te_5$ film($R_{amor}$ $\sim10^7\Omega/\square$ and $R_{cryst}$ 10 $\Omega/\square$). That is, the ratio of $R_{amor}/R_{cryst}$ was evaluates to be $\sim10^6$ This is very helpful to writing current reduction of phase-change random acess memory.

• 대한수학회지
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• 제47권5호
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• pp.879-897
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• 2010

Y. Hirano introduced the concept of a quasi-Armendariz ring which extends both Armendariz rings and semiprime rings. A ring R is called quasi-Armendariz if $a_iRb_j$ = 0 for each i, j whenever polynomials $f(x)\;=\;\sum_{i=0}^ma_ix^i$, $g(x)\;=\;\sum_{j=0}^mb_jx^j\;{\in}\;R[x]$ satisfy f(x)R[x]g(x) = 0. In this paper, we first extend the quasi-Armendariz property of semiprime rings to the skew polynomial rings, that is, we show that if R is a semiprime ring with an epimorphism $\sigma$, then f(x)R[x; $\sigma$]g(x) = 0 implies $a_iR{\sigma}^{i+k}(b_j)=0$ for any integer k $\geq$ 0 and i, j, where $f(x)\;=\;\sum_{i=0}^ma_ix^i$, $g(x)\;=\;\sum_{j=0}^mb_jx^j\;{\in}\;R[x,\;{\sigma}]$. Moreover, we extend this property to the skew monoid rings, the Ore extensions of several types, and skew power series ring, etc. Next we define $\sigma$-skew quasi-Armendariz rings for an endomorphism $\sigma$ of a ring R. Then we study several extensions of $\sigma$-skew quasi-Armendariz rings which extend known results for quasi-Armendariz rings and $\sigma$-skew Armendariz rings.

• 한국전기전자재료학회:학술대회논문집
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• 한국전기전자재료학회 2001년도 춘계학술대회 논문집 유기절연재료 전자세라믹 방전플라즈마 연구회
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• pp.157-160
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• 2001

We have investigated the Dielectric and Piezoelectric properties of $xPb(R_{1/2}Ta_{1/2})O_3-(1-x)Pb(Zr_{0.52}Ti_{0.48})O_3$ (R=Al,Y) solid solutions in which R ions are substituted for Al and Y ions. The maximum value of electromechanical coupling factor kp of 55% and 51% were obtained at the composition of 5mol% PAT and 5mol% PYT. However mechanical quality factor$(Q_m)$ had a minimum value of 44 and 69 at the composition of 5mol% PAT and 5mol% PYT. Also, the maximum value of piezoelectctric constant of $d_{33}(329[pC/N])$ and $d_{33}(310[pC/N])$ were obtained at the composition of 5mol% PAT and 5mol% PYT.

• 한국수학교육학회지시리즈A:수학교육
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• 제12권2호
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• 대한수학회보
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• 제52권5호
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• pp.1489-1493
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• 2015

For a subset $E{\subseteq}\mathbb{R}^d$ and $x{\in}\mathbb{R}^d$, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by $$dim_{H,loc}(x,E)=\lim_{r{\searrow}0}dim_H(E{\cap}B(x,r))$$, $$dim_{P,loc}(x,E)=\lim_{r{\searrow}0}dim_P(E{\cap}B(x,r))$$, where $dim_H$ and $dim_P$ denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions $f,g:\mathbb{R}^d{\rightarrow}[0,d]$ with $f{\leq}g$, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.