Modelling the Development Dynamics of Small and Medium-Sized Enterprises in Russia

The paper explores the factors in the development of small and medium-sized entrepreneurship (SME) in Russia over the past 13 years. The purpose of the article is to identify the patterns and current trends in the dynamics of the number of SMEs. The present study carries out correlation and regression analysis of the factors using the statistical data for 2006–2018. The number of the employed and the average nominal wage are the factors that exert a positive effect on the number of small enterprises, whereas tax burden, the weighted average rate for short-term loans and the inflation rate have a negative impact. The research results allowed forecasting the development dynamics of SMEs for 2020–2024. Providing that Russia follows the basic scenario of the socio-economic development and the existing trends persist, the total number of SMEs is expected to grow to 3,636 thousand (1.37 times) by 2024

Normalization of double-circuit overhead line magnetic field inside Khrushchev building

This paper deals with the mitigation of 110 kV double-circuit overhead line magnetic field inside five-story Khrushchev buildings. We show that the magnetic field can exceed the reference level 0.5 μT in 90 % part of living space. To mitigate the magnetic field, we propose the inverted L-shaped grid shield with conductors on the wall and in the attic of the building. Using the analytical model of the grid shield and the numerical simulation, we determine the parameters of the L-shaped grid shield which provides the magnetic field normalization in 97 % part of living space. Further improvement of the grid shield profile, in particular, the placement of some conductors in the basement, allows to reduce the quantity of metal of the shield by 15 % while maintaining the shielding efficiency. Also we consider the magnetic field normalization for the overhead line with a rated current of 500 A. In this case, the quantity of metal of the grid shield increases 2.74 times.У роботі показано, що в п’ятиповерхових будинках хрущовської споруди, розташованих на границях охоронних зон двоколових повітряних ліній електропередачі 110 кВ, величина магнітного поля промислової частоти може перевищувати гранично допустимий рівень 0,5 мкТл в 90 % житлового простору. Для зменшення магнітного поля запропоновано використовувати Г-подібний ґратчастий екран, проводи якого розташовуються на стіні та на горищі будинку. Шляхом аналітичного та чисельного моделювання визначено параметри Г-подібного ґратчастого екрана, застосування якого дає змогу нормалізувати рівень магнітного поля в 97 % житлового простору. Подальше вдосконалення профілю ґратчастого екрана, зокрема, розміщення частини проводів у підвалі, дало змогу зменшити металоємність конструкції на 15 % при збереженні ефективності екранування. Також досліджено можливість нормалізації магнітного поля повітряної лінії з номінальним струмом 500 А. У цьому випадку металоємність ґратчастого екрана збільшується у 2,74 рази

ON THE INFLUENCE OF THE LEVEL OF AN EXTERNAL MAGNETIC FIELD AND THE LENGTH ON THE MAGNETIC MOMENT OF CYLINDRICAL CORES

Purpose. Analysis of inhomogeneous magnetization of long cylindrical permalloy 50N cores by a uniform constant magnetic field and the influence of length and field level on their magnetic moment. Methodology. The magnetostatic field of a non-uniformly magnetized in a uniform magnetic field long cylindrical core of an electromagnet of a spacecraft control system is considered. To calculate this field, a transformation of the integral equation with respect to the density of fictitious magnetic charges, as well as an iterative algorithm for its numerical solution, are proposed. Results. The convergence of the algorithm and the fact that the magnetic moment of the core depends heavily on its length and the level of the external magnetic field is shown. We have made an analysis of the influence of the length of a permalloy 50N core in the entire range of the magnetization curve and the level of a uniform external magnetic field on the axial projection of the magnetic moment of the core. Originality. The use of an almost equal distribution of the axial projection of the resulting magnetic field in the cross sections of the greater part of the cylindrical core and its division into cylindrical elements can significantly reduce the order of the system of algebraic equations approximating the integral equation for the surface density of fictitious magnetic charges for its numerical solution. Practical value. Recommendations regarding the level of the external field created by the electromagnet coil, the increase of the magnetic moment in cases of long cores and the choice of the number of cylindrical elements depending on the length of the core are given

ОБ ЭЛЕКТРОСТАТИЧЕСКОЙ АНАЛОГИИ МАГНИТОСТАТИЧЕСКОГО ПОЛЯ В НЕОДНОРОДНОЙ НАМАГНИЧИВАЮЩЕЙСЯ СРЕДЕ

Purpose. The application in electrostatic analogy of magnetostatics for inhomogeneous magnetized media of two known magnetization models. Methodology. A comparison of basic equations and formulas of electrostatic and magnetostatic field in immoveable isotropic inhomogeneous polarized medium for dipole model and the magnetization model by molecular currents is made. The value-analogues for dipole model of magnetization are established. Results. We have shown that the using of dipole model of magnetization is correct. There is not even formal analogy with electrostatic field in the case of using the magnetization model by molecular currents. The relation between the magnetizations for various models is obtained. It allows us to justify the using magnetization by molecular currents in electrostatic analogy. Originality. The magnetization for dipole model is introduced and the possibility of using magnetization by molecular currents in the formulas for calculating potential magnetostatic field in magnetized medium is substantiated. Practical value. The results allow to obtain correct formulation and solution of the problem of magnetostatic field calculation in inhomogeneous magnetized medium.Сделан анализ применения электростатической аналогии в магнитостатике неоднородных намагничивающихся сред на основе дипольной модели и модели намагничивания молекулярными токами. Показано, что корректным является использование дипольной модели намагничивания. Получено соотношение между намагниченностями для различных моделей, поясняющее применение в электростатической аналогии намагниченности молекулярными токами

ТЕСТИРОВАНИЕ ЧИСЛЕННОГО РЕШЕНИЯ ЗАДАЧИ ОПРЕДЕЛЕНИЯ ИСТОЧНИКОВ МАГНИТОСТАТИЧЕСКОГО ПОЛЯ В НАМАГНИЧИВАЕМОЙ СРЕДЕ

Purpose. Testing of numerical solution algorithm for integral equation for calculation of plane meridian magnetostatic field source distribution at interfaces of piecewise homogeneous magnetized medium by means of electrostatic analogy. Methodology. The piecewise homogeneous medium consists of three regions with different magnetic permeabilities: the shell of arbitrary meridian section, external unlimited medium outside the shell, and the medium inside the shell. For testing external homogeneous magnetic field effect on spherical shell is considered. The analytical solution of this problem on the basis of electrostatic analogy from the solution of the problem uniform electrostatic field effect on dielectric shell is obtained. We have compared results of numerical solution of integral equation with the data obtained by means of analytical solution at the variation of magnetic permeabilities of regions of medium. Results. Integral equation and the algorithm of its numerical solution for calculation of source field distribution at the boundaries of piecewise homogeneous medium is validated. Testing of integral equations correctness for calculation of fictitious magnetic charges distribution on axisymmetric boundaries of piecewise homogeneous magnetized medium and algorithms of their numerical solutions can be carried out by means of analytical solutions of problems of homogeneous electrostatic field effect analysis on piecewise homogeneous dielectric medium with central symmetry of boundaries – single-layer and multilayer spherical shells. In the case of spherical shell in wide range of values of the parameter λk, including close to ± 1, numerical solution of integral equation is stable, and relative error in calculating of fictitious magnetic charges surface density and magnetic field intensity inside the shell is from tenths of a percent up to several percent except for the cases of very small values of these quantities. Originality. The use analytical solutions for problems of calculation of external electrostatic field effect on piecewise homogeneous dielectric bodies for testing integral equations of magnetostatics and algorithms for their numerical solutions. Practical value. The described method of testing integral equations of magnetostatics and their numerical solutions can be used for calculation of magnetic fields of spacecraft control system electromagnets.Выполнена проверка правильности интегрального уравнения второго рода для расчета распределения источников плоскомеридианного магнитостатического поля на границах раздела кусочно-однородной намагничиваемой среды и его численного решения. Для этого использованы электростатическая аналогия и аналитическое решение задачи о воздействии однородного электростатического поля на сферическую диэлектрическую оболочку в кусочно-однородной диэлектрической среде. Подтверждена правильность интегрального уравнения и его численного решения при помощи аппроксимирующей системы алгебраических уравнений. Сделан анализ влияния магнитных проницаемостей однородных областей среды на распределение фиктивных магнитных зарядов на поверхностях и напряженность магнитного поля внутри сферической оболочки

MAGNETIC FIELD NORMALIZATION IN RESIDENTIAL BUILDING LOCATED NEAR OVERHEAD LINE BY GRID SHIELD

This paper deals with the magnetic field mitigation of 110 kV trefoil single-circuit and double-circuit overhead lines by grid shields. The shields under study are made of aluminum conductors connected in parallel. These shields are mounted on the walls of the building. We study the efficiencies of plane and U-shaped grid shields as the dependence from the quantity of metal. As the result, we show that the plane grid shield does not supply the required efficiency of magnetic field mitigation in corner areas of the building. At the same time, the U-shaped grid shield having equivalent quantity of metal allows to mitigate the magnetic field to the reference level 0.5 µT in more than 97 % part of the building