Stochastic Methods for Ill-Posed Problems

This paper is devoted to the numerical analysis of ill-posed problems of evolution equations in Banach spaces using certain classes of stochastic one-step methods. The linear stability properties of these methods are studied. Regularisation is given by the choice of the regularisation parameter as = , where _n is the stepsize and provides the convergence on smooth initial data. The case of the approximation of well-posed problems is also considered.     

Comparison of chemical effects of UV radiation from spark discharge in air and a low-pressure mercury lamp

The chemical effects of UV radiation from atmospheric-pressure spark discharge and a DBK-9 low-pressure mercury lamp in distilled water and aqueous solutions of hydrogen peroxide and tryptophan have been studied. Reactive species generated in water by the both radiation sources are HO ₂ ^· radicals, acid residue ions NO ₂ ^? and NO ₃ ^? , and ammonium ions. The yield of HO ₂ ^· radicals has appeared to be the same for both sources, (1.1–1.2) × 10^?6 mol L^?1 s^?1. This is confirmed by measurements of the degradation kinetics of tryptophan, which can be destroyed by HO ₂ ^· radicals. The pH of water monotonically decreases with time during the spark discharge treatment. In the case of the mercury lamp, the pH varies insignificantly because of the competition of NH ₄ ⁺ alkali ions with the acid residues. UV radiation plays the major role in the decomposition of hydrogen peroxide.     

Alteration in the surface properties of direct-current discharge-treated tetrafluoroethylene-vinylidene fluoride copolymer films

A change in the contact properties of the surface of tetrafluoroethylene-vinylidene fluoride copolymer films by a dc discharge treatment has been studied, depending on the treatment time and the discharge current. It has been shown that the treatment of the films at the anode and cathode leads to a significant decrease in the contact angle and an increase in the total surface energy and its polar term. The change in the contact properties of the plasma-modified films during storage and heating has been studied as well. The experiments have shown that the formation of polyconjugated structures and crosslinking of macromolecules take place in the film surface layer during long-term treatment at the anode (>60 s, 50 mA), processes that result in an acetone-insoluble layer. The composition and surface structure of the films have been examined by Fourier-transform IR spectroscopy and X-ray photoelectron spectroscopy. The formation of new oxygen-containing groups and double bonds on the polymer surface and crosslinking of macromolecules in the case of anode treatment have been revealed. It has been found experimentally that the discharge treatment increases the peel strength in the Scotch® 810/copolymer film system.