Shadowing for actions of some finitely generated groups

We introduce a notion of shadowing property for actions of finitely generated groups and study its basic properties. We formulate and prove a shadowing lemma for actions of nilpotent groups. We construct an example of a faithful linear action of a solvable Baumslag-Solitar group and show that the shadowing property depends on quantitative characteristics of hyperbolicity. Finally we show that any linear action of a non-abelian free group does not have the shadowing property.Comment: 18 page

Periodic shadowing and Ω\Omega-stability

We show that the following three properties of a diffeomorphism $f$ of a smooth closed manifold are equivalent: (i) $f$ belongs to the $C^1$-interior of the set of diffeomorphisms having periodic shadowing property; (ii) $f$ has Lipschitz periodic shadowing property; (iii) $f$ is $\Omega$-stable.Comment: 21 page

Features of X-ray Absorption Densitometry of Large-size Objects with Variable Thickness

Features of formation and processing of the primary radiometric signals in the digital high-energy X-ray absorption densitometers for the homogeneous objects with variable thickness are examined. The densitometer's equation based on the polynomial approximation of the object's ray thickness dependence from its mass thickness is proposed. Guidance to select the capacity of the analog-digital converter is given. There is one example of the densitometer's equation coefficients calculation to examine the carbon, aluminum and steel wares with the mass density from 15 to 80 g/cm{2}. It was shown that disagreement of the experimental and estimated values of the ray thickness for the similar mass thicknesses of the testing object is conditioned by the scattered radiation. On the high-energy digital radiography set with the X-ray source - the betatron MIB-4.5/9 the accuracy of the experimental estimation of the density was within 0.0086 g/cm{3} for the steel ware thickness from 25 to 100 mm

High-Energy X-ray Radiation Registration Model

It is proved the necessity for carrying out computing experiments according to the mean value and the square of registered X-ray photons absorbed energy of in a scintillation detector. The offered imitation model of the transfer and registration of high-energy X-ray radiation in a sensing volume of CsI and CdWO[4] scintillation detectors is based on a Monte Carlo method. The model considers leakage of secondary photons and electrons. It is offered approaches to justification of adequacy of the developed model of a high-energy X-ray radiation registration

Informativeness Improvement of Hardness Test Methods for Metal Product Assessment

The paper presents a combination of theoretical suggestions, results, and observations allowing to improve the informativeness of hardness testing process in solving problems of metal product assessment while in operation. The hardness value of metal surface obtained by a single measurement is considered to be random. Various measures of location and scattering of the random variable were experimentally estimated for a number of test samples using the correlation analysis, and their close interaction was studied. It was stated that in metal assessment, the main informative characteristics of hardness testing process are its average value and mean-square deviation for measures of location and scattering, respectively

Application of dual energy method for non-destructive testing of materials designed to work in extreme conditions

The description of the dual energy method (DEM) for non-destructive testing (NDT) of materials and products is presented. It highlights the key factors that determine its accuracy and performance and shows the possibilities for its further improvement. The correlation between the quantum noise level and the DEM precision of the effective atomic number was found