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JORDAN-VON NEUMANN TYPE FUNCTIONAL INEQUALITIES

  • Kwon, Young Hak;Lee, Ho Min;Sim, Jeong Soo;Yang, Jeha;Park, Choonkil
    • 충청수학회지
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    • 제20권3호
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    • pp.269-277
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    • 2007
  • It is shown that $f:\mathbb{R}{\rightarrow}\mathbb{R}$ satisfies the following functional inequalities (0.1) ${\mid}f(x)+f(y){\mid}{\leq}{\mid}f(x+y){\mid}$, (0.2) ${\mid}f(x)+f(y){\mid}{\leq}{\mid}2f(\frac{x+y}{2}){\mid}$, (0.3) ${\mid}f(x)+f(y)-2f(\frac{x-y}{2}){\mid}{\leq}{\mid}2f(\frac{x+y}{2}){\mid}$, respectively, then the function $f:\mathbb{R}{\rightarrow}\mathbb{R}$ satisfies the Cauchy functional equation, the Jensen functional equation and the Jensen quadratic functional equation, respectively.

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ON A LIE RING OF GENERALIZED INNER DERIVATIONS

  • Aydin, Neset;Turkmen, Selin
    • 대한수학회논문집
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    • 제32권4호
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    • pp.827-833
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    • 2017
  • In this paper, we define a set including of all $f_a$ with $a{\in}R$ generalized derivations of R and is denoted by $f_R$. It is proved that (i) the mapping $g:L(R){\rightarrow}f_R$ given by g (a) = f-a for all $a{\in}R$ is a Lie epimorphism with kernel $N_{{\sigma},{\tau}}$ ; (ii) if R is a semiprime ring and ${\sigma}$ is an epimorphism of R, the mapping $h:f_R{\rightarrow}I(R)$ given by $h(f_a)=i_{{\sigma}(-a)}$ is a Lie epimorphism with kernel $l(f_R)$ ; (iii) if $f_R$ is a prime Lie ring and A, B are Lie ideals of R, then $[f_A,f_B]=(0)$ implies that either $f_A=(0)$ or $f_B=(0)$.

QUADRATIC (ρ1, ρ2)-FUNCTIONAL EQUATION IN FUZZY BANACH SPACES

  • Paokant, Siriluk;Shin, Dong Yun
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제27권1호
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    • pp.25-33
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    • 2020
  • In this paper, we consider the following quadratic (ρ1, ρ2)-functional equation (0, 1) $$N(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y)-{\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y))-{\rho}_2(4f({\frac{x+y}{2}})+f(x-y)-f(x)-f(y)),t){\geq}{\frac{t}{t+{\varphi}(x,y)}}$$, where ρ2 are fixed nonzero real numbers with ρ2 ≠ 1 and 2ρ1 + 2ρ2≠ 1, in fuzzy normed spaces. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (ρ1, ρ2)-functional equation (0.1) in fuzzy Banach spaces.

$CHF_3/C_2F_6$ 플라즈마에 의한 실리콘 표면 잔류막의 특성 (The Characteristics of Residual Films on Silicon Surface $CHF_3/C_2F_6$ Reactive Ion Etching)

  • 권광호;박형호;이수민;강성준;권오준;김보우;성영권
    • 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.

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$LiF-BeF_2$ 용융염계에서 전해제련에 의한 우라늄 회수 (Recovery of Uranium in $LiF-BeF_2$ Molten Salt System by Electrowinning)

  • 우문식;김응호;유재형
    • 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$$LiF-BeF_2$의 분해전압은 각각 -1.4volt와 -1.55volt이었다 우라늄의 전착속도는 우라늄 농도가 높을수록 증가하였다.

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양파껍질에서 분리한 플라보놀의 Xanthine Oxidase 저해기작 (Inhibition of Xanthine Oxidase by Flavonols from Onion Skin)

  • 서형주;나경수;배송환;손홍수;정수현
    • 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.

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FUNCTIONAL EQUATIONS IN THREE VARIABLES

  • Boo, Deok-Hoon;Park, Chun-Gil;Wee, Hee-Jung
    • 충청수학회지
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    • 제17권2호
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    • pp.169-190
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    • 2004
  • Let r, s be nonzero real numbers. Let X, Y be vector spaces. It is shown that if a mapping f : $X{\rightarrow}Y$ satisfies f(0) = 0, and $$sf(\frac{x+y{\pm}z}{r})+f(x)+f(y){\pm}f(z)=sf(\frac{x+y}{r})+sf(\frac{y{\pm}z}{r})+sf(\frac{x{\pm}z}{r})$$, or $$sf(\frac{x+y{\pm}y}{r})+f(x)+f(y){\pm}f(z)=f(x+y)+f(y{\pm}z)+f(x{\pm}z)$$ for all x, y, $z{\in}X$, then there exist an additive mapping A : $X{\rightarrow}Y$ and a quadratic mapping Q : $X{\rightarrow}Y$ such that f(x) = A(x) + Q(x) for all $x{\in}X$. Furthermore, we prove the Cauchy-Rassias stability of the functional equations as given above.

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各種 燐化合物溶媒 抽出系에 있어서 4f 및 5f 系列 元素의 抽出速度 및 分配率의 溫度依存性 (Extraction Rate and Temperature Dependency of Distribution Ratio of 4f and 5f Series Element in the Various Phosphorus Compounds)

  • 이진택
    • 대한화학회지
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    • 제13권3호
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    • pp.199-204
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    • 1969
  • 4f 및 5f 系列 元素의 溶媒抽出에 있어서 分配速度를 測定해 본 結果 4f 系列의 前半部와 後半部 間에 明白한 差異를 볼 수 있었다. 三價의 Am 및 Cm은 4f 系列의 前半部와 類似함을 알았다. 또한 分配率과 抽出溫度와의 關係를 檢討해 본 結果 抽出系에 따라 獨特한 增加 또는 減少傾向이 나타났으며 또한 Chelate 抽出系에 있어서는 原子番號 存在性이 있음을 알았다

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다이나믹 전류보상기를 이용한 V/f 제어 유도전동기 드라이브 시스템의 안정도 향상 (Stability Improvement of a V/f Controlled Induction Motor Drive System using a Dynamic Current Compensator)

  • 정강률
    • 대한전기학회논문지:전기기기및에너지변환시스템부문B
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    • 제53권6호
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    • pp.402-408
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    • 2004
  • This paper proposes the novel V/f control method to improve the stability of a V/f controlled induction motor drive system. The conventional V/f control method used in the proposed V/f control method is a vector-based method that is slightly different from the existing conventional V/f control method. The proposed control method uses a dynamic current compensator to improve the stability of a V/f controlled induction motor drive system. This proposed method is easy to implement and completely eliminates the motor oscillation phenomenon causing the instability of a V/f controlled induction motor drive system, especially when the system is driven near the resonant frequency in steady-state with light load. Additionally, this paper analyzes theoretically the instability of a V/f controlled induction motor drive system and shows the validity of the Proposed V/f control method through simulation and experimental results.

ADDITIVE ρ-FUNCTIONAL INEQUALITIES

  • LEE, SUNG JIN;LEE, JUNG RYE;SEO, JEONG PIL
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제23권2호
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    • pp.155-162
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    • 2016
  • In this paper, we solve the additive ρ-functional inequalities (0.1)${\parallel}f(x+y)+f(x-y)-2f(x){\parallel}$ $\leq$ ${\parallel}{\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$, where ρ is a fixed complex number with |ρ| < 1, and (0.2) ${\parallel}2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$ $\leq$ ${\parallel}{\rho}f(x+y)+f(x-y)-2f(x){\parallel}$, where ρ is a fixed complex number with |ρ| < 1. Furthermore, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces.