• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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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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• v.15 no.1_2
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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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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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 $m{\geq}2$.

• Applied Chemistry for Engineering
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• v.2 no.4
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• pp.311-329
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• 1991

Electrochemical behavior of surface active Osmium bipyridine complex adsorbed in a monomolecular layer on tin oxide electrodes by the Langmuir-Blodgett method was studied. Theoretical equation of cyclic voltammetry of electrode reactions for redox species adsorbed as monolayer form was discussed by reversible and quasi-reversible waves. The film was transferred onto the $SnO_2$ electrode surface and then amounts of charge on the electrode were measured in the technique of cyclic voltammetry. The electron transfer mediation of these monolayer with $Fe^{2+}$, TEMPOL and others were studied. And the cyclic voltammetry were simulated by taking into account the interaction parameters. From these values, we found it possible to fit almost all measured cyclic voltammograms with these parameters. The recent works and directions using LB method were introduced with various applicable field.

• Bulletin of the Society of Naval Architects of Korea
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• v.11 no.1
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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.