Variations on the Drygas equation and its stability

We study the stability of the Drygas functional equation:

g(xy)+g(xy⁻¹)=2g(x)+g(y)+g(y⁻¹)     

Alternative Cauchy equation in three unknown functions

Aequationes mathematicae - In this paper we deal with the product of two or three Cauchy differences equaled to zero. We show that in the case of two Cauchy differences, the condition of absolute...     

Sulla stabilita' degli omomorfismi e sue applicazioni alle equazioni funzionali

Sono presentati i principali risultati relativi alla stabilità degli omomorfismi e vengono illustrate alcune applicazioni nella risoluzione di equazioni funzionali di Cauchy alternative e non omogenee. The main results concerning the stability of homomorphisms are presented. Then they are used for solving some alternative and inhomogeneous Cauchy functional equations.

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(Conferenza tenuta il 29 febbraio 1988)     

Evaluation of Mercury Levels in Sediment and Soil Samples from Vila Nova River Basin, in Amapá State, Brazil, Using Radiochemical Neutron Activation Analysis

In the present work, results from a survey on mercury concentration in sediments and soils from a gold mining area along the Vila Nova river, in Amapá State, Brazil, are presented. These values were compared with those from the Igarapé Pedra Preta basin, an area unaffected by mining activities. Total mercury contents were determined in the muddy (silt+clay) fraction of the sediments and in the <2 mm fraction of the soils using radiochemical neutron activation analysis (RNAA). The detection limit of the method was 54 µg·kg^–1 for soils and 14 µg·kg^–1 for sediments when 200 mg of sample were analysed. The Hg results obtained from a comparison between our current method (RNAA) and CV AAS are also presented. Mercury levels showed to be very high in the soils and sediments collected in the Vila Nova river (up to 2 mg·kg^–1) when compared to background values (0.3 mg·kg^–1) for this region. An enrichment factor was calculated, using Al as a normalizing factor. It showed values up to 8 in sediments of the Vila Nova river basin, indicating a relatively high degree of pollution as compared to the values of about 1 for the samples of the Igarapé Pedra Pretra basin.     

Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations

In this short paper the core of the direct method for proving stability of functional equations is described in a clear way and in a quite general form.