• 대한수학회논문집
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• 제15권4호
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• pp.675-681
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• 2000

Let f : M longrightarrow M be a homotopically periodic self-map of a closed surface M. Except for M = $S^2$, the Nielsen number N(f) and the Lefschetz number L(f) of the self-map f are the same. This is a generalization of Kwasik and Lee's result to 2-dimensional case. On the 2-sphere $S^2$, N(f) = 1 and L(f) = deg(f) + 1 for any self-map f : $S^2$longrightarrow$S^2$.

• 충청수학회지
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• 제19권3호
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• pp.275-281
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• 2006

In this article, we establish the stability of the orthogonally cubic type functional equation 2f(x + 2y) + 2f(x - 2y) + 2f(2x)+7[f(x)+f(-x)] = 4f(x)+8[f(x+y)+f(x-y)], $x{\bot}y$ in which ${\bot}$ is the orthogonality in the sense in the R$\ddot{a}$tz.

• 대한수학회지
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• 제33권2호
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• pp.387-397
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• 1996

Let G be a finite group and F be a field of characteristic $p \geq 0$. Let $\Gamma = F^f G$ be a twisted group algebra corresponding to a 2-cocycle $f \in Z^2(G,F^*), where F^* = F - {0}$ is the multiplicative subgroup of F.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1315-1322
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• 2010

Let D be a plane domain whose boundary consists of n components and $C_1$, $C_2$ two boundary components of D. We consider the family $F_1$ of conformal mappings f satisfying f(D) $\subset$ {1 < |w| < ${\mu}(f)$}, $f(C_1)=\{|w|=1\}$, $f(C_2)=\{|w|={\mu}(f)\}$. There are conformal mappings $g_0$, $g_1({\in}F_1)$ onto a radial and a circular slit annulus respectively. We obtain the following theorem, $$\{{\mu}(f)|f\;{\in}\;F_1\}=\{\mu|\mu(g_1)\;{\leq}\;{\mu}\;{\leq}\;{\mu}(g_0)\}$$. And we consider the family $F_n$ of conformal mappings $\tilde{f}$ from D onto a covering surfaces of the Riemann sphere satisfying some conditions. We obtain the following theorems, {$\mu|1$ < ${\mu}\;{\leq}\;{\mu}(g_1)$} ${\subset}\;\{{\mu}(\tilde{f})|\tilde{f}\;{\in}\;F_2\}\;{\subset}\;\{{\mu}(\tilde{f})|\tilde{f}\;{\in}\;F_n\}$ and ${\mu}(\tilde{f})\;{\leq}\;{\mu}(g_0)^n$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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• pp.161-170
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• 2018

In this paper, we introduce and solve the following additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) $${\parallel}f(x+y+z)-f(x)-f(y)-f(z){\parallel}{\leq}{\parallel}{\rho}_1(f(x+z)-f(x)-f(z)){\parallel}+{\parallel}{\rho}_2(f(y+z)-f(y)-f(z)){\parallel}$$, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero complex numbers with ${\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}$ < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (${\rho}_1,{\rho}_2$)-functional inequality (0.1) in complex Banach spaces.

• 대한수학회보
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• 제49권1호
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• pp.135-143
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• 2012

We present two kinds of construction methods for self-dual codes over $\mathbb{F}_2+u\mathbb{F}_2$. Specially, the second construction (respectively, the first one) preserves the types of codes, that is, the constructed codes from Type II (respectively, Type IV) is also Type II (respectively, Type IV). Every Type II (respectively, Type IV) code over $\mathbb{F}_2+u\mathbb{F}_2$ of free rank larger than three (respectively, one) can be obtained via the second construction (respectively, the first one). Using these constructions, we update the information on self-dual codes over $\mathbb{F}_2+u\mathbb{F}_2$ of length 9 and 10, in terms of the highest minimum (Hamming, Lee, or Euclidean) weight and the number of inequivalent codes with the highest minimum weight.

• 대한환경공학회지
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• 제38권6호
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• pp.317-322
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• 2016

PFOS sodium salt ($C_8F_{17}SO_3Na$)는 28일 동안 미생물에 의한 분해가 이루어지지 않은 반면 4종의 대체물질($C_{25}F_{17}H_{32}S_3O_{13}Na_3$, $C_{15}F_9H_{21}S_2O_8Na_2$, $C_{23}F_{18}H_{28}S_2O_8Na_2$, $C_{17}F_9H_{25}S_2O_8Na_2$)은 각각 21.6%, 20.5%, 15.8% 그리고 6.4% 분해가 이루어졌다. Daphnia magna를 이용하여 48시간 동안 수행한 물벼룩급성독성시험에서 sodium salt ($C_8F_{17}SO_3Na$)의 반수영향농도($EC_{50}$)는 54.5 mg/L 인 것으로 확인된 반면 4종의 대체물질은 500.0 mg/L에서 아무런 영향이 나타나지 않았다. 500.0 mg/L에서 PFOS sodium salt($C_8F_{17}SO_3Na$)의 표면장력은 46.2 mN/m이었으며 대체물질 4종의 표면장력은 모두 PFOS sodium salt 보다 우수한 것으로 확인되었다. $C_{23}F_{18}H_{28}S_2O_8Na_2$ (20.9 mN/m)는 가장 낮은 표면장력을 갖고 있었다. 그 다음은 $C_{15}F_9H_{21}S_2O_8Na_2$ (23.4 mN/m), $C_{17}F_9H_{25}S_2O_8Na_2$ (27.3 mN/m) 그리고 $C_{25}F_{17}H_{32}S_3O_{13}Na_3$ (28.2 mN/m) 순인 것으로 확인되었다. 미생물분해시험, 물벼룩급성독성시험 그리고 표면장력측정 결과를 종합해 보면 4종의 PFOS 대체물질($C_{25}F_{17}H_{32}S_3O_{13}Na_3$, $C_{15}F_9H_{21}S_2O_8Na_2$, $C_{23}F_{18}H_{28}S_2O_8Na_2$, $C_{17}F_9H_{25}S_2O_8Na_2$)은 모두 PFOS sodium salt ($C_8F_{17}SO_3Na$) 보다 우수한 것으로 확인되었으며 특히 3종의 대체물질($C_{15}F_9H_{21}S_2O_8Na_2$, $C_{23}F_{18}H_{28}S_2O_8Na_2$, $C_{25}F_{17}H_{32}S_3O_{13}Na_3$)은 미생물분해율이 15.8~21.6%로 상대적으로 높고, 물벼룩급성독성과 표면장력측정이 PFOS sodium salt 보다 상당히 우수하다. 그러므로 이들 4종의 대체물질은 PFOS 대체물질로 활용이 가능할 것으로 판단된다.

• 한국진공학회지
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• 제1권1호
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• pp.145-152
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• 1992

Si surfaces exposed to CHF3/C2F6 gas plasmas ih reactive ion etching (RIE) have been characterized by X-ray photoelectron spectroscopy (XPS). CHF3/C2F6 gas plasma exposure of Si surface leads to the deposition of residual film containing carbon and fluorine. The narrow scan spectra of C 1s show various bonding states of carbon as C-Si, C-F/H, C-CFx(x $\leq$ 3), C-F, C-F2, and C-F3. The chemical bonding states of fluorine are described with F-Si, F-C and F-O. And the oxygen and silicon are also detected. The effects of parameters for reactive ion etching as CHF3/C2F6 gas ratio, RF power, and pressure are investigated.

• 한국방사성폐기물학회:학술대회논문집
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• 한국방사성폐기물학회 2003년도 가을 학술논문집
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• pp.426-430
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• 2003

장수명핵종 소멸처리를 위한 건식분리공정에서 핵분열성물질인 우라늄을 장수명핵종과 분리할 필요가 있다. 본 실험은 $LiF-BeF_2$ 용융염에서 전해제련에 의한 우라늄 금속을 분리하기 위하여 분해전압 측정하였고, 인가전압에 따른 전해특성 파악 및 반응속도를 측정하였다. 측정결과 $500^{\circ}C$에서 $UF_4$와 $LiF-BeF_2$의 분해전압은 각각 -1.4volt와 -1.55volt이었다 우라늄의 전착속도는 우라늄 농도가 높을수록 증가하였다.

• 한국식품영양과학회지
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• 제27권4호
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• pp.693-697
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• 1998

The influence of flavonols from onion skin on xanthine oxidase was investigated. Methanol extract was showed 12.8% of yield, 661.3mg% of flavonoids contents and 88.7% of inhibitory effect on xanthine oxidase F1 and F2 fractions were obtained from the methanol extract by ODS and Sephadex LH-20 chromatography. F1 and F2 fractions flavonols(3-OH free) identified by UV/visible spectroscopy. Inhibitory effect of F1 and F2 on xanthine oxidase were increased with increasing concentration. IC50s of F1 and F2 were 0.95$\mu\textrm{g}$ and 0.67$\mu\textrm{g}$, respectively. To confirm the specificity of F1 and F2 against xanthine oxidase, albumin was added to the reaction mixture. The inhibition of F1 and F2 may be due to specific binding to xanthine oxidase. The modes of their inhibitions were of mixed type with respect to xanthine as a substrate.