Nonlinear second-order equations with functional implicit impulses and nonlinear functional boundary conditions

In this paper we deal with nonlinear second-order boundary value problems with impulses. The impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear. In both cases functional dependence on the solution is allowed. The existence results follow from the existence of a pair of well-ordered lower and upper solutions.     

Shadowing with multidimensional time in Banach spaces

We study linear dynamical systems with multidimensional time in Banach spaces. Using Taylor functional calculus we prove that under additional assumptions hyperbolic systems have shadowing property.     

A Fubini theorem

Let I₀ be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I₀ and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Ros?anowski-Shelah stating that I₀ on N² strongly violates the countable chain condition.     

Silicon etching in Cl2 environment

The ion-beam-assisted etching of silicon in Cl₂ environment is considered. The theoretically calculated dependences of silicon etching rate on the flux of Cl₂ molecules at different ion current densities are compared with experimentally measured. The composition of the adsorbed layer is determined. It is found that SiCl₂ molecules prevail in the adsorbed layer. The reciprocal of relative concentration of SiCl₂ molecules in the adsorbed layer linearly depends on the ion-to-neutral flux ratio.     

Non-specific antitumoral activity of staphylococcal enterotoxins

St. aureus enterotoxins A and B possess an antitumour effect. After intraperitoneal inoculation they decrease the size and in some cases prevent the development of the human hypernephroma in the cheek pouch of golden hamsters. The effect of enterotoxins may possibly consist in inducing the production of endogenous immune interferon which activates the host immune system and enhances the rejection of heterologous tumour cells.     

Controlled-resistance loads for induction heating applications using thin non-magnetic metallic layers

The design of controlled-resistance loads for domestic induction heating applications using thin non-magnetic conductive layers is described. Thin metallic layers are fabricated using the phase vapour deposition technique. Such layers would enable vessels, the inductive behaviour of which was similar to those fabricated with conventional ferromagnetic bulk materials, to be manufactured. Optimum layer thickness is investigated using an analytical impedance model of the complete induction system     

Cauchy-Born Rule and the Stability of Crystalline Solids： Dynamic Problems

We study continuum and atomistic models for the elastodynamics of crystalline solids at zerotemperature.We establish sharp criterion for the regime of validity of the nonlinear elastic wave equationsderived from the well-known Cauchy-Born rule.