### COMPUTER SIMULATION OF SPECTROSCOPY OF INFRARED ABSORPTION AND RAMAN SCATTERING OF LIGHT IN GASE UNDER THE INFLUENCE OF HYDROSTATIC COMPRESSION

The paper contains the results of computer simulation of infrared absorption spectroscopy and Raman scattering of light in GaSe under hydrostatic compression. The theory of the electron density functional was used as the main approach. The oscillatory properties were calculated using the perturbation theory of the electron density functional. It is shown that Raman scattering values change from pressure and show linear dependence. The shear rates are calculated. The obtained data are in accord with the published experimental results. This enables us to consider this approach as promising for the study of such materials and may lead, in the long term, to expanding the field of applicability of gallium selenide as a non-linear optical element by fine tuning the properties with the help of hydrostatic compression.

Read More### EXISTENCE AND UNIQUENESS OF THE CAUCHY PROBLEM FOR A WIDE CLASS OF EREDITARY OSCILLATORS

In this paper, using the elements of the theory of functional analysis (fixed-point theorem), the existence and uniqueness of the Cauchy problem for a special class of integral and differential equations with difference kernels in the form of power functions is justified. The initial integral and differential equation with the help of derivatives of fractional order in the sense of Gerasimov-Caputo is reduced to an equation, describing a wide class of fractal oscillators or oscillators with memory.

Read More### NEW APPROACH TO ACCELERATING THE METHOD OF D-MORPH FOR THE SEARCH OF OPTIMUM QUANTUM CONTROL

The article introduces new corrections of various orders of smallness to the D-MORPH method for finding the optimal control of a quantum system in the problem of realizing the desired unitary evolution by using the complete expression of the derivative of the operator exponent defined on the Lie algebra. Inclusion of the corrections with regard to information on the commutators of the Hamiltonian system into the method leads to faster identification of optimal control, even in comparison with the improved version of the method published by the author earlier.

Read More### APPLICATION OF LINEAR PROGRAMMING TO THE TASKS OF LOGICAL ALGEBRA

Significant variables of Boolean functions are found in the article with the help of linear programming. Boolean functions are checked for monotonicity and linearity.

The problem of the shortest covering of a Boolean matrix is generalized, as is the problem of the shortest covering of a Boolean matrix with a given defect. Generalized problem of the shortest covering is reduced to the problem of linear programming. As a consequence we obtain a linear programming problem, to which the classical problem of the shortest covering of a Boolean matrix is reduced.

Examples are given where problems of the theory of Boolean functions are solved with the help of linear programming.

### NEW APPROACH TO ACCELERATING THE METHOD OF D-MORPH FOR THE SEARCH OF OPTIMUM QUANTUM CONTROL

The article introduces new corrections of various orders of smallness to the D-MORPH method for finding the optimal control of a quantum system in the problem of realizing the desired unitary evolution by using the complete expression of the derivative of the operator exponent defined on the Lie algebra. Inclusion of the corrections with regard to information on the commutators of the Hamiltonian system into the method leads to faster identification of optimal control, even in comparison with the improved version of the method published by the author earlier.

Read More### USING THE CONTROLLERS OF AUTOMATION OF MICROSOFT OFFICE APPLICATIONS IN THE MANAGEMENT ACTIVITY OF HIGH SCHOOL DEPARTMENTS

In order to optimize the interaction between the Educational-methodical management (EMM) and the departments of the university, a computer system is proposed that allows to automate the information processes associated with the calculation of the load of the departments and the distribution of training assignments. Using a remote server made possible to collect the department’s information in one repository and quickly obtain a general and detailed picture of the load calculations and its distribution throughout the university. The practical implementation of the system accelerated the solution of various organizational tasks and the adoption of managerial decisions. The system allowed to more strictly control digital material related to the organization of the educational process at the department. The subsystem of generation of various documents on the side of the EMM and on the side of the department allowed to fully automate the preparation of a number of everyday documents electronically, eliminating in many cases excessive paperwork.

Read More### MATHEMATICAL MODELING OF THE DYNAMICS OF MASS- AND HEAT TRANSFER IN EJECTION AND INJECTION PROCESSES

The dynamics of the considered class of objects and water treatment systems in the general case is described by linear or linearized differential equations with partial derivatives and constant or variable coefficients, the existence and uniqueness of the solution of which are provided by necessary and sufficient linear boundary conditions.

The same mathematical description has, in particular, the processes of heat and mass transfer used by technological processes at water treatment facilities. Taking into account the interrelation of heat and mass transfer, determination of the generalized dynamic characteristics of these processes will allow solving the problems of analysis and synthesis of an automated or automatic control system for such units, as well as the tasks of improving technology and upgrading equipment in order to improve quality characteristics of products, reduce energy costs for its production and enhance the productivity of technological units.

Read More### CHARACTERISTIC POLYNOMIALS OF BOOLEAN FUNCTIONS

In this article we introduce the notion of a characteristic polynomial of a Boolean function having a given polarization of variables and consider a method for representing a Boolean function by the Reed-Muller polynomial (the canonical polarized polynomial) using the characteristic polynomial of this function.

It is proved that the values of the characteristic polynomial coincide with the corresponding coefficients of the Reed-Muller polynomial and a linear algorithm for finding the coefficients of the Reed-Muller polynomial is presented.

We also consider positively polarized characteristic polynomials and problems associated with them, including checking whether the Boolean function belongs to the class of linear functions.

Examples of the application of characteristic polynomials to the determination of Reed-Muller polynomials, the extension of a partial Boolean function to a linear function and the verification of a Boolean function for linearity are given.

Read More### APPLICATION OF ROBOTICAL SETS IN PHYSICAL EXPERIMENTS

A robotic LEGO type set is used in two physical experiments. The first experiment is related to the phenomenon of sliding a permanent magnet over a non-magnetic conducting plate. High-precision automated measurement of the sliding time allowed confirming the constancy of the sliding speed and determining its magnitude. In the second experiment, the sliding of three steel balls of different diameters along a shoot was considered. The measurement of the sliding time showed that it is the same for all balls. With an accuracy of up to 5%, a factor of 0.4 is determined in the moment of the balls inertia.

Read More### APPLICATION OF LYAPUNOV’S QUADRATIC FUNCTIONS IN SOLVING APPLIED DYNAMIC PROBLEMS

In the following paper, we propose a technique for determining the moment of the end of the transient process when the parameters of a continuous dynamic system are changed on the basis of the application of the direct Lyapunov method, based on the estimation of the regions of attraction of equilibrium states. For an estimate of the region the trajectory of the system does not leave with time, we take a neighborhood of the equilibrium state where the first derivative of the Lyapunov function is negative. The Lyapunov function is chosen in the form of a positive definite quadratic form, where the negative sign of its first derivative is provided with a given margin due to a linear system.

Read More### INFLUENCE OF THERMAL PROCESSING ON QUALITY OF PRODUCTS SURFACE MADE OF QUARTZ GLASS

Silicon-oxygen tetrahedra is the basis of a strong surface in silicate glasses. They are nanostructures for macro-formations, which are called globules. The smaller the size of globules is, the stronger is the surface, because more siloxane bonds form between them. This factor affects the quality of the product surface, which improves the inductance of the resonator circuit, and therefore, increases the Q factor. The size of globules is provided by means of annealing technology. The tempering process takes place at a temperature gradient of 300 °C per hour. A further change of the cooling temperature leads to the formation of cracks. Experiments carried out with the help of the Vickers method and the method of a recumbent drop on distilled water and glycerin showed that the greatest strength of the surface is achieved in resonators annealed in the temperature range 950 – 1080 °C, and the Q factor takes the maximum value.

Read More### EJECTION AND INJECTION OF REAGENTS IN WATER TREATMENT TECHNOLOGIES

A water treatment system provides for the introduction of various reagents into it. The main technological methods for introducing reagents into disinfected water are ejection and injection. This article analyzes both of these methods. A technique for calculating high-efficiency ejectors is developed. The laboratory and production tests carried out by the authors established the best proportions of the internal section longitudinal dimensions – they ensure the maximum effective value of the ejection coefficient.

Read More### CONSTRUCTION OF THE CONDITION-EXTREMAL LYAPUNOV FUNCTIONS IN STUDIES OF THE TRAJECTORIES BEHAVIOR OF CONTINUOUS DYNAMIC SYSTEMS ON A PLANE

The paper presents the solution of the problem of constructing a conditionally extremal Lyapunov function for a continuous dynamical system described by a system of second-order differential equations. This is a quadratic Lyapunov function, which guarantees the minimality of the time before the linearization of a trajectory in a neighborhood of the equilibrium state of the system, into the section of the Lyapunov function inscribed in a given band. With respect to the quadratic Lyapunov function, it is assumed that the condition of equality of the ratio of the modulus minimum of the first derivative of the Lyapunov function on the section to the value of the function itself to a given number is fulfilled. A conditional-extremal Lyapunov function is sought as a quadratic Lyapunov function of the class under consideration, the cross-section of which, inscribed in the strip, is the trajectory of a system linearized in a neighborhood of the equilibrium state with a given initial point.

Read More### INFLUENCE OF CALCINATION REGIMES ON PHASE FORMATION AND MAGNETIC PROPERTY OF NANOPOWDERS BiFeO3 SYNTHESIZED BY SOL-GEL METHOD USING CITRIC ACID

Nano-sized multiferroic BiFeO3 (BFO) powders were synthesized by sol-gel method using citric acid as a chelating agent. Samples were calcinated at different temperatures and in different time periods. The phase analysis of the samples was carried out by X-ray diffractometry (XRD). A morphology of BiFeO3 powder particles was investigated with scanning electron microscope (SEM). Room temperature magnetic hysteresis (M-H) measurements were carried out using a vibrating sample magnetometer. The results show that BFO phase composition of powders calcinated at 600 ºC for 11 to 12 hours and at 700 ºC for 10 hours was highest, powder morphology of the sample heated at 600 ºC for 12 hours was the best, magnetic characteristics of samples heated at 600 ºC for 12 hours and at 700 ºC for 10 hours were better than the rest.

Read More### TEMPERATURE INFLUENCE ON MAGNETOSTATIC WAVES DISPERSION IN YTTRIUM IRON GARNET FILMS

The dispersion relations for surface and volume magnetostatic waves (MSW) propagating in an infinite ferrite film magnetized to saturation by a longitudinal constant magnetic field was obtained in the magnetostatic approximation of electrodynamics. The frequency spectrum dependence on the magnitude of the constant magnetic field and the direction of the wave vector of surface (MSSW) and backward volume (MSBVW) magnetostatic waves is analyzed. The temperature influence on the spectrum and dispersion characteristics of the MSW is considered.

Read More### METHODS FOR EVALUATION OF THE INTENSITY OF AGRICULTURAL PRODUCTION BASED ON THE THEORY OF FUZZY SETS

The authors propose the model for calculating the integrated assessment of the intensification of agricultural production in the region based on the theory of fuzzy sets. The indicators of the two groups were used as the evaluation criteria: the level of intensification of agricultural production and the level of economic efficiency of the intensification of agricultural production. The method allowed to obtain the estimate of the level of intensification of the agro-industrial complex in the Rostov region and to give recommendations on its increase.

Read More### STUDY OF MAGNETO-ELECTRIC EFFECT IN MULTILAYER STRUCTURE OF GALLIUM ARSENIDE-NICKEL-TIN-NICKEL

The article contains the results of the magneto-electric effect study in a multilayer nickel-tin-nickel structure obtained by means of electroplating on a substrate of gallium arsenide. The paper describes the technology of manufacturing multilayer structures and experimental results of the frequency dependence of the magneto-electric effect. It is shown that the use of tin as an intermediate layer reduces mechanical stresses arising from the incommensurability of the phases which enables obtaining qualitative structures with a thickness of the nickel layer of the order of 70 microns. Resulting structures have good adhesion between the layers and a high Q-factor.

Read More### LOCATING MINIMAL FRAMING ORIENTED TREE GRAPHS

The article considers a generalized problem of a minimal framing tree graph, that is, a problem with asymmetric matrix of weight coefficients of arcs where the solution is an oriented tree graph. The article includes mathematical models of quadratic programming, including a model with a minimum number of linear constraints the generalized minimal framing tree graph problem is reduced to. We consider finding the minimal framing tree graph when the number of the root, transit, or hanging vertex is given, as well as the case of several conditions. Examples are provided; mathematical models are solved with the help of the Excel.

Read More### STOCHASTIC KINETIC MODEL OF PRICE FORMATION

The article considers the problem of numerical estimation of functional from the solution of a system of non-linear Boltzmann type equations occurring in the stochastic kinetic model of asset price formation. This topic is relevant due to the constant increase in the volume of high-frequency trading at financial markets. This leads to the necessity to improve trading algorithms, taking into account the stochasticity of the price series parameters such as drift and volatility, as well as the behavior of traders during the trading session. The authors proposed an integral equation of the second kind associated with the linear multi-particle model of the behavior dynamics of a set of traders (vendors and buyers) at the exchange for the initial probabilistic price model. To estimate the functionals from the solution of the obtained equation, it is proposed to use the apparatus of the weighted Monte Carlo algorithms. Developed statistical algorithms will be applied to build the price forecast inside the trading session in real time mode. The combination of the short-term forecast based on the kinetic model and the long-term forecast of price series based on the stochastic dynamic model will be the mathematical basis of the adaptive intellectual system. This system, based on historical and current market data, will automatically create personal financial recommendations.

Read More### ON REPRESENTATION OF A STABLE ELEMENT OF A FREE NILPOTENT GROUP

In order to find a nontrivial stable element of a free nilpotent group, it is necessary to isolate all possible types of basic commutators that are later used to build a candidate for a stable element. The article is devoted to the description of three kinds of switches; each of them is closely related to the other two. For example, if the representation of a stable element includes commutators of one of the types, then the remaining species must be represented in the expansion of this element. We consider a free nilpotent group of rank 3 and of order 12.

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