Some remarks on the operator of Foias and Williams

In this paper we study the Foias-Williams operator

where , and is a Hankel operator with symbol . We exhibit a relationship between the similarity of to a contraction and the rate of decay of , the absolute values of the Fourier coefficients of the symbol .

     

About some physical mechanisms of statistics of radiation-induced effects formation and non-linear cell response in low dose area

A new cascade-stochastic approach to solve the direct and inverse problems of radiation-induced effect statistics in track biodetectors is presented in this paper. The analysis of the experimental data has made it possible to establish a non-linear nature of the “dose–effect” dependence in low dose area. For the first time, a new determination of the relative biological efficiency and quality coefficient of ionizing radiation in area of low doses are proposed.     

Periodic optimal control for parabolic Volterra-Lotka type equations

This paper considers the optimal harvesting control of a biological species, whose growth is governed by the parabolic diffusive Volterra-Lotka equation. We prove that such equation with L^∞ periodic coefficients has an unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions, we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed.     

Analysis of corrosion scales formed on steel at high temperatures in hydrocarbons containing model naphthenic acids and sulfur compounds

Corrosive naphthenic acids and sulfur compounds in crude oils present a major challenge for refineries from a corrosion perspective. Although it is accepted that some sulfur compounds may form protective FeS scales on the metal surface and deter corrosion, attempting to correlate the characteristics of FeS scale with its protective properties has not been successful. Given the complex chemical compositions of real crudes, model sulfur compound and model naphthenic acids were used to mimic the corrosion by crude fractions in the present study. The iron sulfide scale formed by the model sulfur/acid compounds was challenged by naphthenic acids under high‐velocity conditions to examine its protectiveness against corrosion. Moreover, the scale was analyzed with transmission electron microscope/energy dispersive X‐ray spectroscopy technique, and a layer of iron oxide formed on the 5Cr steel was found when naphthenic acids were present in the solution. The iron oxide layer appeared to be important for maintaining protection against naphthenic acid corrosion, and further analysis revealed that it was composed of magnetite. Copyright © 2015 John Wiley & Sons, Ltd.