Scattering theory for a class of non-selfadjoint extensions of symmetric operators

This work deals with the functional model for a class of extensions of symmetric operators and its applications to the theory of wave scattering. In terms of Boris Pavlov's spectral form of this model, we find explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices. On the basis of these formulae, we are able to construct wave operators and derive a new representation for the scattering matrix for pairs of such extensions in both self-adjoint and non-self-adjoint situations.Comment: 32 pages; This is the continuation of arXiv:1703.06220 (and formerly contained in v1); this version is as accepted by the journal (Operator Theory: Advances and Applications

Improving the competitiveness of rural areas in the aspect of rural tourism development

The main objective of this research is carrying out the analysis of actually used and potential opportunities for development of agrotourism in the Omsk region (Russia). For that it was applied the tool that allow to compare the assessment of the potential for agrotourism development in various rural areas. Based on the results of the analysis, the region of the Southern forest-steppe zone has the highest potential for the development of agro-tourism. Based on the results of the rating assessment, the leader is the Kalachinsky District. However, based on the results of the conducted evaluations, it is possible to judge the existence of conditions for the development of agro-tourism in all areas of the Omsk region. The obtained results allowed giving recommendations on increasing the level of development of agrotourism in the Omsk region.info:eu-repo/semantics/publishedVersio

Functional model for boundary-value problems and its application to the spectral analysis of transmission problems

We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We provide explicit formulae for the resolvents of the associated extensions of symmetric operators in terms of the associated generalised Dirichlet-to-Neumann maps, which can be utilised in the analysis of the properties of parameter-dependent problems as well as in the study of their spectra.Comment: 30 pages, 1 figur

Influence of ultrasonic treatment on electromagnetic characteristics of composites based on multiwall carbon nanotubes at wide range of frequencies (100 Hz - 258 GHz)

In the present paper, we investigated microwave properties of polymer composites based on multiwall carbon nanotubes. The multiwall carbon nanotubes used in the composite were about 9.4 nm and 18.4 nm in diameter. The results show that the ultrasonic treatment modifies the dielectric properties of the composite. The dependence of the real and imaginary parts of the permittivity of sonication time is non linear. The results showed that composite material based on nanotubes with a diameter of 9.4 nm has a dispersive region of dielectric permittivity at the range about 10 GHz

Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions

Using a generalisation of the classical notion of Dirichlet-to-Neumann map and the related formulae for the resolvents of boundary-value problems, we analyse the asymptotic behaviour of solutions to a "transmission problem" for a high-contrast inclusion in a continuous medium, for which we prove the operator-norm resolvent convergence to a limit problem of "electrostatic" type for functions that are constant on the inclusion. In particular, our results imply the convergence of the spectra of high-contrast problems to the spectrum of the limit operator, with order-sharp convergence estimates.Comment: 15 pages, 1 figure. Continuation of: arXiv:1907.08144. As accepted by: Math. Note