On fractional powers of the Bessel operator on a semiaxis

In this paper we study fractional powers of the Bessel differential operator defined on a semiaxis. Some important properties of such fractional powers of the Bessel differential operator are proved. They include connections with Legendre functions for kernel representations, fractional integral operators of Liouville and Saigo, Mellin transform and index laws. Possible applications are indicated to differential equations with fractional powers of the Bessel differential operator.Comment: English version (pp. 1--8) and Russian version (pp. 9--18

Research on the possibility of extending the shelf life of cheese raw material and heat-treated cheese by their freezing for further use in HoReCa

The article presents the results of a study of the regularities of changes in the functional properties and quality indicators of heat-treated cheeses made from frozen cheese raw material or frozen after thermomechanical processing for further use in HoReCa. The objects of the study were: Caliatta cheese — a semi-hard ripening cheese intended as the main raw material in the production of heat-treated cheese, as well as heat-treated «pizzacheese», subjected to freezing at temperatures of minus 14 ±2 °Cand minus 55 ±2 °Cand low-temperature storage at a temperature of minus 14 ±2 °Cfor 270 days, followed by defrosting at a temperature of 20 ±2 °C. To confirm the possibility of using the freezing technique in order to increase the shelf life of both the original cheese raw material and heat-treated cheese, their microbiological and physicochemical indicators were determined by standardized methods. Studies of structural and mechanical (rheological) properties were carried out on a Weissenberg rheogoniometer, recording changes in the elastic modulus (G’) and dynamic viscosity (h’). The length of the cheese thread, as one of the main functional properties of the «pizza-cheese», was assessed with a fork test after baking. Organoleptic characteristics were assessed by flavor, texture and appearance. Research results have shown that low-temperature storage of frozen cheese can be considered as a way to retard biological and physicochemical changes, which is a safe way to increase shelf life. Freezing cheese raw material increases the length of the cheese thread in proportion to the temperature and duration of the low-temperature storage. When obtaining heat-treated cheese from both unfrozen and frozen cheese raw material, a significant deterioration in the desired functional properties is observed. Thus, the receipt of heat-treated cheese from the original cheese raw material for further use in the production of pizza is justified only by economic feasibility. Freezing «pizza-cheese» at a temperature of minus 55 ±2 °C, made from unfrozen cheese raw material, ensures the preservation of functional properties and increases the shelf life up to 150 days

Boundary Zonal Flow in Rotating Turbulent Rayleigh-Bénard Convection

For rapidly rotating turbulent Rayleigh–Bénard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one, whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like Ra1/4Ek2/3 where the Ekman number Ek decreases with increasing rotation rate

Application of integral transforms composition method (itcm) to obtaining transmutations via integral transforms with bessel functions in kernels

In this paper we apply the Integral Transforms Composition Method (ITCM) in order to derive compositions of integral transforms with Bessel functions in kernels, and obtain norm estimates and other properties of such composition transform

Comparison of simulation and analytical models for the distribution of a group of agents moving in random directions

This study focused on simulation and analytical models of a multidimensional random walk of many agent

Local polarization reversal in KTP single crystals

The research was made possible in part by RFBR (grant 16-02-00724) and by President of Russian Federation grant for young scientists (Contract 14.Y30.17.2837-MK). The equipment of the Ural Center for Shared Use “Modern nanotechnology” Ural Federal University was used

Fractional powers of bessel operator and its numerical calculation

The article discusses the fractional powers of the Bessel operator and their numerical implementation. An extensive literature is devoted to the study of fractional powers of the Laplace operator and their application