• 충청수학회지
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• 제17권1호
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• pp.29-45
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• 2004

We prove the Cauchy-Rassias stability of cyclic functional equations in Banach modules over a unital $C^*$-algebra.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.343-361
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• 2004

We prove the generalized Hyers-Ulam-Rassias stability of cyclic functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with cyclic functional equations in Banach algebras.

• 대한수학회보
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• 제54권6호
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• pp.2165-2182
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• 2017

Let G be a group and $\mathbb{C}$ the field of complex numbers. Suppose ${\sigma}:G{\rightarrow}G$ is an endomorphism satisfying ${{\sigma}}({{\sigma}}(x))=x$ for all x in G. In this paper, we first determine the central solution, f : G or $G{\times}G{\rightarrow}\mathbb{C}$, of the functional equation $f(xy)+f({\sigma}(y)x)=2f(x)+2f(y)$ for all $x,y{\in}G$, which is a variant of the quadratic functional equation. Using the central solution of this functional equation, we determine the general solution of the functional equation f(pr, qs) + f(sp, rq) = 2f(p, q) + 2f(r, s) for all $p,q,r,s{\in}G$, which is a variant of the equation f(pr, qs) + f(ps, qr) = 2f(p, q) + 2f(r, s) studied by Chung, Kannappan, Ng and Sahoo in [3] (see also [16]). Finally, we determine the solutions of this equation on the free groups generated by one element, the cyclic groups of order m, the symmetric groups of order m, and the dihedral groups of order 2m for $m{\geq}2$.

• 공업화학
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• 제2권4호
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• pp.311-329
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• 1991

산화주석전극 위에 LB 법에 의해 단분자층상으로 흡착된 양친매성 Os 착체의 전기화학적 거동을 살펴보았다. 또한 단분자막형태로 흡착된 redox 종의 전극반응의 이론식을 가역, 비가역, 준가역파에 대하여 검토하였고, 이들막이 진공증착된 $SnO_2$ 전극 위로 전이될 때, 그 전극에서 흐른 전체 전하를 cyclic voltammogram 의 그림적분법에 의해 구하였다. 그리고 이들 단분자막을 이용한 전자이동 중개반응의 응용면도 $Fe^{2+}$, TEMPOL 등을 이용해 해석하였다. 이들 측정된 cyclic voltammogram을 이론식으로부터 유도하여 분자들간의 상호작용 parameter를 고려해서 simultation 하였다. 이들로부터 구해진 parameter 들은 측정된 cyclic voltammogram 과 거의 일치함을 확인할수 있었다. 마지막으로 LB 법을 이용한 최근의 연구동향 및 응용분야를 소개하였다.

• 대한조선학회지
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• 제11권1호
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• pp.27-34
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• 1974

This study is aimed at a validation of the vigilance simulation model which was proposed earlier (2). The model estimates a perceived danger value, an alertness level and the probability of detection at a given elapsed time of vigilance. Twenty-nine male and seven female subjects were given a simple task. They were asked to detect a number(four numbers out of six digits in the telephone directory which have the probability of occurrence in the range of 0.0010-0.0018) in six different experimental conditions, for periods of two to three hours. Analysis of the experiments showed that although the mean detection rate varied slightly in two hours, the within-subject variance and the number of cyclic performance fluctuations increased significantly. A primal factor that affects the performance seems to be the frequency of target occurrence. By curve fitting, the relation between the probability of detection and the percentages of danger event occurrence was derived; $y=0.50(1-{\varepsilon}^{-50x^2})+0.39$. Assuming the equation represents the normal detection rate(100% performance), the Relative Vigilance Performance Rating was calculated. This rating method could be a useful criterion in selecting and training of the vigilance personnel. The results show that the simulation model is a good estimator of human a performance when the probability of danger occurrence is greater than 0.0015; it gives a good reference for improving the vigilance system. Suggestions are made that (1) the validity of proposed functional equations over the extended range of danger probability be studied, (2) an analysis of the cyclic fluctuations of the alertness level be accomplished, and (3) the cost functions of detection reliability be included in any future model.