• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.857-866
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.5
• /
• pp.1651-1657
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.1097-1106
• /
• 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.

• Journal of the Korean GEO-environmental Society
• /
• v.13 no.6
• /
• pp.51-57
• /
• 2012

This study investigated on the photolytic degradation of Triclosan by E-beam process. The optimization of process was investigated during a series of batch experiments by design of experiments(DOEs). The DOE was one of the statistical application that was used for designed the response surface to determine the effects of each parameters. The responses were applied as removal rate of Triclosan(%, $Y_1$) and TOC removal rate(%, $Y_2$). Two independent variables were concentration of Triclosan and irradiation intensity that were designed as "$x_1$" and irradiation intensity was designed as "$x_2$". The regression equation in coded parameter between the Triclosan removal efficiencies(%) and TOC removal efficiencies(%) was $Y_1=63-12.4335x_1+15.1835x_2+5.8125x{_1}^2-5.6875x{_2}^2-0.75x_1x_2(R^2=95.1%,\;R^2(Adj)=91.7%)$ and $Y_2=46-8.8462x_1+11.7175x_2-0.75x{_1}^2-6.25x{_2}^2(R^2=98.7%,\;R^2(Adj)=97.7%)$, respectively. The model predictions agreed well with the experimentally observed results $R^2$ and $R^2(Adj)$ over 90% within both of $Y_1$ and $Y_2$. This result shows that the regression model express well about the effects of parameters on E-beam process and the statistical method was successfully applied.

• Journal of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.997-1005
• /
• 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.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2008.06a
• /
• pp.21-22
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.879-897
• /
• 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.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2001.05c
• /
• pp.157-160
• /
• 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.

• The Mathematical Education
• /
• v.12 no.2
• /
• pp.5-12
• /
• 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....

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1489-1493
• /
• 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.