• Korean Journal of Mathematics
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• 제19권1호
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• pp.17-24
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• 2011

Let X, Y be vector spaces. It is shown that if an even mapping $f:X{\rightarrow}Y$ satisfies f(0) = 0, and $$2(_{2d-2}C_{d-1}-_{2d-2}C_d)f\({\sum_{j=1}^{2d}}x_j\)+{\sum_{{\iota}(j)=0,1,{{\small\sum}_{j=1}^{2d}}{\iota}(j)=d}}\;f\({\sum_{j=1}^{2d}}(-1)^{{\iota}(j)}x_j\)=2(_{2d-1}C_d+_{2d-2}C_{d-1}-_{2d-2}C_d){\sum_{j=1}^{2d}}f(x_j)$$ for all $x_1$, ${\cdots}$, $x_{2d}{\in}X$, then the even mapping $f:X{\rightarrow}Y$ is quadratic. Furthermore, we prove the Hyers-Ulam stability of the above functional equation in Banach spaces.

• 충청수학회지
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• 제24권4호
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• pp.617-630
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• 2011

Let X, Y be vector spaces, and let r be 2 or 4. It is shown that if an odd mapping $f:X{\rightarrow}Y$ satisfies the functional equation $${\hspace{50}}rf(\frac{\sum_{j=1}^{d}\;x_j} {r})+\;{\sum\limits_{\iota(j)=0,1 \atop {\sum_{j=1}^{d}}\;{\iota}(j)=l}}\;rf(\frac{\sum_{j=1}^{d}{(-1)^{\iota(j)}x_j}}{r}) \\({\ddag}){\hspace{160}}=(_{d-1}C_l-_{d-1}C_{l-1}+1)\;{\sum\limits_{j=1}^{d}\;f(x_j)}$$ then the odd mapping $f:X{\rightarrow}Y$ is additive, and we prove the Cauchy-Rassias stability of the functional equation in Banach modules over a unital $C^*$-algebra. As an application, we show that every almost linear bijection $h:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ of a unital $C^*$-algebra ${\mathcal{A}}$ onto a unital $C^*$-algebra ${\mathcal{B}}$ is a $C^*$-algebra isomorphism when $h(2^nuy)=h(2^nu)h(y)$ for all unitaries $u{\in}{\mathcal{A}}$, all $y{\in}{\mathcal{A}}$, and $n=0,1,2,{\cdots}$.

• 인터넷정보학회논문지
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• 제15권6호
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• pp.77-84
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• 2014

본 연구는 대학에서 이러닝을 활용 수업의 효과에 영향을 미치는 요인들을 탐색하고 요인들 간의 인과관계를 파악하고자 하였다. 이를 위해 2013년 2학기를 기준으로 이러닝 기반의 수업인 사이버 강의에 참여한 학생들 2,091명 중 유효했던 1,732명을 연구 대상으로 하였다. 연구방법은 확인적 요인분석과 구조방정식모형 분석을 활용하였다. 확인적 요인분석을 통해 이러닝 학습효과, 컨텐츠만족요인, 시스템기능요인, 운영지원요인의 네 개의 잠재변인을 도출할 수 있었다. 이들 잠재변인들 간의 구조방정식 모델 분석을 통한 결과는 다음과 같다. 첫째, 이러닝 학습효과와 관련된 주요 요인으로 컨텐츠 요인, 기능요인, 운영지원 요인으로 구분할 수 있었다. 둘째, 이러닝 학습효과에는 운영지원, 컨텐츠 요인이 직접적 영향을 미치는 것으로 나타났다. 하지만 기능요인은 유의하지 않은 것으로 나타났다. 셋째, 컨텐츠 요인에는 기능 및 운영요인이 유의한 영향을 미치는 것으로 나타났다. 넷째, 기능요인 및 운영지원요인은 컨텐츠 요인을 매개로하여 이러닝 학습효과에 간접적 영향을 미치는 것으로 나타났다.

• Journal of Microbiology and Biotechnology
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• 제26권8호
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• pp.1428-1438
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• 2016

In the present work, Arthrobacter sp. 25, a lead-tolerant bacterium, was assayed to remove lead(II) from aqueous solution. The biosorption process was optimized by response surface methodology (RSM) based on the Box-Behnken design. The relationships between dependent and independent variables were quantitatively determined by second-order polynomial equation and 3D response surface plots. The biosorption mechanism was explored by characterization of the biosorbent before and after biosorption using atomic force microscopy (AFM), scanning electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffraction, and Fourier transform infrared spectroscopy. The results showed that the maximum adsorption capacity of 9.6 mg/g was obtained at the initial lead ion concentration of 108.79 mg/l, pH value of 5.75, and biosorbent dosage of 9.9 g/l (fresh weight), which was close to the theoretically expected value of 9.88 mg/g. Arthrobacter sp. 25 is an ellipsoidal-shaped bacterium covered with extracellular polymeric substances. The biosorption mechanism involved physical adsorption and microprecipitation as well as ion exchange, and functional groups such as phosphoryl, hydroxyl, amino, amide, carbonyl, and phosphate groups played vital roles in adsorption. The results indicate that Arthrobacter sp. 25 may be potentially used as a biosorbent for low-concentration lead(II) removal from wastewater.