### MATHEMATICAL MODEL OF THE FILM BOILING DISTRIBUTION

In the article a mathematical model is constructed for calculation of the running heat wave that transforms the bubble boiling into the film boiling on the surface of a fuel element. Control calculations are carried out that allow to set limits on the minimum step in the spatial coordinate.

Read More### STUDY THE PERFORMANCE OF ALGORITHMS ANIMATION FOR JAVASCRIPT

The article describes the algorithms animation interface elements web applications. The purpose of this article is to investigate the performance of the considered algorithms. The results can be used to develop animation Javascript library.

Read More### PRODUCTION WAVE FUNCTION

The mathematical model of economic branches production dynamics, reflecting change in time under the influence of scientific and technical progress (monotonous processes), and also recessions and rises in wave character (harmonious processes) is developed.

Read More### FREE-FORM SURFACES IN THE MICRO-SURFACE

Microtopography surface plays an important role in the modern problems of production of the product, and covers areas such as mechanical engineering, metallurgy, aviation, manufacturing of precision optics manufacturing implants. The precise definition of the characteristics of the micro-topography surface dependent performance of the manufactured products. Modern production poses new challenges to regulation and quality of the surface, which in turn requires the relevant research. One of the most pressing problems is the regulation of free-form surface microtopography.

Read More### THE INFLUENCE OF NON-UNIFORMITY OF THE NEUTRON FLUX ON THE SIZE OF THE “RHYTHM” TYPE REACTOR PLANT

Although the work on research, improvement and design of the nuclear power plant has been carried out since the middle of the last century, in some points it still remains incomplete and many aspects require further studying. There is always a question of selecting the necessary materials for pipelines, fuel-element cladding, fuel assemblies, and the problem of which fuel and reactor type to choose. The selection of options always depends on the situation, the purpose of the installation, the location and the method of operation. Another important problem is the influence of the composition of various fuels and materials of the reactor core on the long-term operation of the nuclear steam generating plant at the full reactor power raising. Its economic benefit in comparison with other compositions should also be taken into consideration. It is necessary to find a balanced price-quality option.

Read More### STOCHASTIC INDEPENDENCE OF COMPLEX EVENTS

The problem of independence of random events is one of the most important and insufficiently studied in probability theory. The importance of the problem is caused by the mass application of the assumption of independence of factors in practical provisions. The article shows formulas for calculating the conditional probabilities of a sum, the product of events and the opposite event. Two necessary and sufficient conditions for the independence of events have been determined. The obtained results can be used in intelligent decision-making systems.

Read More### THE IMPACT THAT GREENHOUSE CARBON DIOXIDE HAS ON HUMAN

This paper suggests a model that can be used to calculate the impact that atmospheric (greenhouse) carbon dioxide has on human genetic activity, and consequently, on their health. Constituent parts of the human cells which contain DNA demonstrate various resonating frequencies, including those of the IR spectrum; it depends on the structural level of chromosome organisation. It turned out that this resonating frequency of the absorbance spectrum, for example, for the nuclear DNA, concurs with the frequency of the twice degenerate deformation vibrations of the greenhouse carbon dioxide in the IR radiated spectrum. Likewise, concurrence (in the order of values) could be seen at the complying powers of its optical radiation and is absorbed by all the human nuclear DNAs. In this latter case, the numerical value was calculated through dipole approximation, taking into account all human nuclear DNAs. Thus, the greenhouse carbon dioxide affects human. This impact occurs due to the “greenhouse effect” and can occur through the membranes of some particular skin cells. Due to the proximity of the optical powers getting to the human because of the greenhouse effect and the powers radiated by their genome at the same frequency resonance is possible which, consequently, makes possible the impact upon human genetic activity and health.

Read More### VIDEOSTREAM SURVEILLANCE AND FACE RECOGNITION SYSTEM

The article looks into the practical aspects of developing a system of face identification and verification in a videostream. The practical part of this paper is made up of the pilot surveillance system capable of videostream face recognition, and the possibilities of scaling and putting it in operation quickly. For its implementation, advanced (so-termed “state of the art”) machine-learning algorithms were used; and for the creation of the necessary pilot framework, the authors used containerization and data storage tools capable of scaling and grid computing.

Read More### STUDY OF MONOTONIZED DIFFERENCE SCHEMES

The paper considers the possibilities of the practical application of monotonized difference schemes previously proposed by the author. The author introduced the monotonicity condition for a nonmonotonic scheme. It is shown that monotonized schemes can both completely remove oscillations and reduce the amplitude of oscillations without changing the condition of monotony, besides some properties of monotonized schemes are proved. The author provides examples of monotonizing operators and develops a convenient design for solving time-dependent tasks. The results can be generalized to a wider variety of tasks.

Read More### GETTING FORMULAS FOR THE EXTRACTION OF ALL PRIME NUMBERS FROM THE PASCAL’S TRIANGLE

The following arithmetic study presents previously unknown numerical properties of the Pascal’s right-angled triangle and gives the main results of finding its real discriminant for the first time. Precisely, the numerical properties of the truncated Pascal’s triangle for the extraction of all prime numbers were discovered. Then, arithmetic formulas are presented for the direct extraction of all prime numbers. All of the above is possible after the entire class of numerical tables of truncated triangles has been successfully decoded in the cryptographic system. After these results had been achieved, the general method of establishing the simplest numerical properties of symmetric polynomials of power sums became available. It should be specially noted that only recurrent numerical series are used for the generalization of tables and precise determination of the rules for these tables.

Read More### RESEARCH OF PHOTOCATALYTIC ACTIVITY OF BiFe1-xMnxO3 NANOPARTICLES IN DECOMPOSITION OF METHYLENE BLUE

The nanosized multiferroic powders BiFe1-xMnxO3, synthesized by the sol-gel method, are the studied objects. The samples are calcined at appropriate temperatures and within a given period. A study of the absorption spectra in the UV-visible area of the fabricated samples showed that doping with Mn reduces the bandgap (from 2.11 eV to 1.94 eV). This will increase the photocatalytic activity of the BFO material system, which will make the application more practical. The results obtained show that BiFe1-xMnxO3 nanoparticles in this work provide the possibility to decompose methylene blue. When doping Mn in BFO, the decomposition efficiency increases. However, this efficiency is not high.

Read More### ON THE SOLVABILITY OF ONE SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS IN THE SPACE OF FUNCTIONS LIMITED FOR THE ENTIRE AXIS

The issue of unique solvability in the space of functions limited for the entire axis for one system of linear differential equations with unlimited coefficients is considered. When setting tasks, the matrix of coefficients is divided into two matrices, the matrix of “senior” and the matrix of “lower” coefficients. It is assumed that the spectrum of the matrix of “senior” coefficients has an intersection with the imaginary axis. The conditions for the matrix of “lower” coefficients are revealed, the fulfillment of which ensures the unique solvability of the system in the space of functions limited for the entire axis. Revealed conditions are written out using the relationship between the “senior and junior” coefficients of the system.

Read More### NUMERICAL STUDY OF THE INFLUENCE OF INITIAL VOLUME CONTENT OF DISPERSION COMPONENT OF MIXTURE ON THE LEAKAGE OF DUSTY MEDIUM IN VACUUM

The following work mathematically models the flow of homogeneous gas and inhomogeneous medium in the form of a suspending matter of solid particles in gas – gas suspension. The aim of the work is to study the influence of the initial volumetric content of the solid component of the mixture on the process of its flow into a vacuum and to identify its differences from the process of the homogeneous gas leakage into a vacuum. When simulating the outflow process, we took into account the viscosity, compressibility, and thermal conductivity of gas. The mathematical model used in this work implements a continuous methodology for modeling the flow of an inhomogeneous medium. This kind of methodology for modeling the mixture motion involves solving the complete hydrodynamic system of equations of motion for each of the components of the mixture. In contrast, the system of equations of motion of the components of the mixture is connected with components responsible for the inter-phase force and thermal interaction. The system of equations of the mathematical model includes continuity equations for the density of the carrier medium and “average density” of the dispersed component of the mixture. The Navier-Stokes equation was solved to describe the momentum conservation of the carrier medium; the equation of momentum conservation was also written for the dispersed component of the mixture with regard to components responsible for the inter-component interaction. The energy conservation equations for the mixture components were solved, taking into account inter-component heat transfer. The system of equations of the mathematical model, supplemented by boundary conditions, was solved by the explicit finite-difference method of the second order of accuracy.

Read More### MOVEMENT IN VISCOUS MEDIA. TYPES OF RESISTANCE FORCES. DETERMINATION OF RESISTANCE COEFFICIENTS

The process of friction of a rotating solid is studied. A model experiment is performed in which friction in the system is changed using sails oriented at different angles with respect to the airflow. The speed range is determined at which various types of friction play an important role: dry, viscous and aerodynamic, and the main parameters of different types of friction (the moment of dry friction force, coefficient of viscous friction) and the laws of their change depending on the experimental conditions are calculated.

Read More### APPROXIMATION OF PERIODIC FUNCTIONS BY COMPOSITE TWO-POINT HERMITE POLYNOMIALS

This paper deals with polynomial approximating a periodic functions by composite two-point Hermite polynomials. The final formulas of these polynomials, using the function values and its derivatives at a given point, are constructed. The relation of Taylor’s polynomial and two-point polynomials with respect to representation of periodic function is specified. The estimation of proximity, expressed through the evaluation of the derivative of the corresponding order is given. A sufficient condition for the convergence of a sequence of two-point polynomials to a given periodic function is established. Examples are given in which periodic function is approximated by a sequence of two-point Hermite polynomials with data on an errors and its evaluation.

Read More### INVESTMENT PORTFOLIO FORMATION AND ANALYSIS ON EXAMPLE OF TWO SECURITIES

The paper considers the econometric models of stock prices of large domestic companies based on modeling a portfolio of securities and predicting its behavior using mathematical modeling with the elements of probability theory and mathematical statistics. Based on the obtained results, companies and entrepreneurs can build a strategy for investing and buying shares, knowing the likely income from a portfolio of certain types of securities.

Read More### NUMERICAL RESEARCH OF INFLUENCE UNEVEN DISTRIBUTION OF CONCENTRATION OF ONE FROM FRACTIONS OF DISPERSED COMPONENT PER PROCESS PROPAGATION OF SHOCK WAVE FROM HOMOGENEOUS GAS TO TWO-FRACTIONAL GAS-SUSPENSION

The effect of the non-uniform concentration of one of the fractions of a two-fraction gas suspension on the parameters of a shock wave moving from pure gas to a gas suspension is numerically studied. The motion of a direct shock wave in a two-fraction gas suspension was simulated. The finely dispersed fraction of the gas suspension had a uniform initial mass content, while larger particles had an uneven initial mass content along the transverse coordinate. The mathematical model took into account the viscosity of the carrier medium, as well as interphase force and thermal interaction. The equations of the mathematical model were integrated by an explicit finite-difference method.

Read More### NUMERICAL MODELING OF HEAT AND MASS TRANSFER PROCESSES OF LIQUEFIED NATURAL GAS IN CORRUGATED CRYO-TANK

The article discusses a promising model of an LNG fuel tank, which allows increasing the time of drainless storage by means of ensuring a constant degree of filling an isothermal vessel with the liquid phase of the fuel. A technological description of the method for maintaining an unchanged volume fraction of cryogenic fuel in the liquefied state with a corrugated vessel in the form of an axial bellows compensator is performed. The problem of the program calculation is formulated using the finite volume method, which enables describing the distribution of the physical parameters of the two-phase liquid-gas system with regard to the presence of heat influx to the walls of the corrugated vessel under consideration. The results of the numerical experiment of drainless storage of cryo-liquid without bleeding the product into the power supply system of an internal combustion engine are presented, the shortcomings of the analytical study of heat and mass transfer, and LNG hydrodynamics in a cryogenic isothermal tank are revealed.

Read More### FINITE ELEMENT MESH AUTOMATIC GENERATION USING TRIANGULAR SUBDIVISION SCHEMES

We suggest here a new algorithm for triangular finite element mesh generation for NURBS surface represented as a set of control points. We use a modern approach – subdivision techniques, which has many advantages. Two different subdivision schemes are presented here: Modified Butterfly and Loop ones.

Read More### TEACHING MS EXCEL FINANCIAL COMPUTATIONS IN ENGLISH

This article is based on 6 years experience of teaching IT disciplines (in particular, financial computations in MS Excel) in English at International Finance Faculty of the Financial University under the Government of the Russian Federation.

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