Some Problems of Supersonic Cavitation Flows

The basic results obtained by the author in the theory of supercavities in compressible fluid have been presented. The modern numerical methods have been applied in this investigation and the basic correlations for shock in water have been considered. The characteristic features of supersonic cavitation flows and their difference from the analogous flows in the air have been noted. The buckling stability of an elastic body moving at a high speed in water has been investigated

Calder\'on-Zygmund operators on Zygmund spaces on domains

Given a bounded Lipschitz domain $D\subset \mathbb{R}^d$ and a Calder\'on-Zygmund operator $T$, we study the relations between smoothness properties of $\partial D$ and the boundedness of $T$ on the Zydmund space $\mathcal{C}_{\omega}(D)$ defined for a general growth function $\omega$. In the proof we obtain a T(P) theorem for the Zygmund spaces, when one checks boundedness not only of the characteristic function, but a finite collection of polynomials restricted to the domain. Also, a new form of extra cancellation property of the even Calder\'on-Zygmund operators in polynomial domains is stated.Comment: 31 page

Gauge theory approach to glass transitions

This theory combines a thermodynamic approach with a dynamic one in order to describe glass transition. Glass transition is regarded as an inaccessible second order phase transition, which is interrupted because of premature critical slowing down, caused by the system's frustration. The frustration-induced vortices are present in the structure besides thermoactivated vortices, and prevent the development of the order parameter fluctuations, that leads to the critical slowing down the system kinetics at some temperature above the phase transition point

Managing stimulation of regional innovation subjects’ interaction in the digital economy

The reported study was funded by RFBR according to the research project No. 18-01000204_a, No. 16-07-00031_a, No. 18-07-00975_a.Purpose: The article is devoted to solving fundamental scientific problems in the scope of the development of forecasting modeling methods and evaluation of regional company’s innovative development parameters, synthesizing new methods of big data processing and intelligent analysis, as well as methods of knowledge eliciting and forecasting the dynamics of regional innovation developments through benchmarking. Design/Methodology/Approach: For regional economic development, it is required to identify the mechanisms that contribute to (or impede) the innovative economic development of the regions. The synergetic approach to management is based on the fact that there are multiple paths of IS development (scenarios with different probabilities), although it is necessary to reach the required attractor by meeting the management goals. Findings: The present research is focused on obtainment of new knowledge in creating a technique of multi-agent search, collection and processing of data on company’s innovative development indicators, models and methods of intelligent analysis of the collected data. Practical Implications: The author developed recommendations before starting the process of institutional changes in a specific regional innovation system. The article formulates recommendations on the implementation of institutional changes in the region taking into account the sociocultural characteristics of the region’s population. Originality/Value: It is the first time, when a complex of models and methods is based on the use of a convergent model of large data volumes processing is presented.peer-reviewe