### ALGORITHMS FOR CALCULATING THE SIMULATED HEAT TRANSFER PROCESSES IN CONCRETE AND REINFORCED CONCRETE STRUCTURES WHEN EXPOSED TO HIGH TEMPERATURE

The article considers the algorithm of the calculation process of heating the surface of the concrete and reinforced concrete structures when exposed to elevated temperatures, the algorithm for calculating the distribution process temperature of concrete when heated.

Read More### SPECTRAL ANALYSIS OF THE IMAGE OF THE AMORPHOUS ALLOY NANOSTRUCTURES

This paper we discuss methods of spectral analysis and filtering of electron microscopic images of nanostructures in amorphous alloys. Besides we consider the spectral characteristics evaluation method of objects nanostructures image.

Read More### ABC-ANALYSIS FOR SOLVING ENGINEERING PLANNING AND FORECASTING PROBLEMS

The article is devoted to the application of ABC analysis for solving engineering problems. The object of study is the range of agricultural machinery. The practice presents physico-mathematical models improves the quality of training technical direction.

Read More### ESTIMATES FOR THE SOLUTION IN С0(S12) METRIC OF A QUASILINEAR EQUATION OF GENERAL FORM

The questions of the existence and uniqueness of regular surfaces with the given geometric characteristics in one or another space are analytically equivalent to considering and investigating the unique solvability of partial differential equations on one or another manifold. The paper provides a proof that a priori estimates for the solution of a generalized quasilinear equation on the unit sphere S12 exist. It also considers special cases of a generalized quasilinear equation related to geometric problems.

Read More### ESTIMATION OF THE LEVEL OF DISPERSION IN OPTICAL CABLES IN CONDUCTING THE INPUT CONTROL USING A HOLOGRAPHIC INTERFEROMETER

In conducting incoming control, the analysis of the quality of an optical fiber can be carried out only by assessing the level of dispersion in the optical fiber, therefore, the task of accurately measuring the level of dispersion is the most important. Currently, the level of dispersion of the signal in an optical fiber is estimated on a section of this fiber using a laser emitter that emits a luminous flux of a known intensity and measuring the power of the optical signal at the input and output of the fiber using special devices (for example, a reflector). The holographic interferometer developed by the authors makes it possible to analyze optical fiber more accurate at the lowest cost and, when analyzing on a functioning connection line without significantly increasing its mass-dimensional characteristics.

Read More### ELECTRIC FIELD SIMULATION NEAR METAL NANOPARTICLES

This paper presents the results of studies on the application of the finite difference time domain (FDTD) method for mathematical modeling of disturbances in the electric field strength near gold nanoparticles (NPs) of varying size under irradiation with different excitation wavelengths λ = 532, λ = 632, λ = 785 nm. The authors consider several types of gold NPs differing in size. The values of the maximum electric field value near the particle surface are calculated. These results can be used in the future to simulate multilayer and gold-core nanostructure-optical sensors implemented based on the effect of giant Raman scattering of light, used for the analysis of chemical compounds in low concentrations, macroscopic biological objects.

Read More### SIMULATION OF ELECTRONIC TRANSFER SPATIAL CHARACTERISTICS IN FLASH MEMORY ELEMENTS

Based on the kinetic Monte Carlo method, a numerical simulation of electron transport in silicon short-channel floating-gate MOS transistors, which are the basic element of modern flash memory chips, is performed. This simulation is used to calculate the effect of the gate voltage on the relative value of the tunnel parasitic current that occurs on a floating gate, as well as the average energy and mobility of electrons in the conducting channel of these transistors at different drain voltages. It is shown that for the studied conditions, this effect is significant in the middle section of the conducting channel of the transistor and decreases at the source and drain junctions of the device.

Read More### SOLVING THE INVERSE MIXED BOUNDARY VALUE PROBLEM OF LATTICE FLUID DYNAMICS

The authors consider the inverse mixed boundary value problem of lattice fluid dynamics, in which we need to find the shape of a part of the lattice profile through the velocity distribution given for this part and the velocity distribution on the rest known part of the lattice profile, which is streamlined by a potential flow of ideal frictionless liquid. The authors delve into the case when the required profile is close to the profile of a known lattice with a known flow complex potential. It is assumed that the known part of the lower surface of the profile, except for its plot adjacent to the nose profile, and the form of the rest of the investigated profile is sought, through the distribution of velocity as a function of the arc abscissa of the point of the required profile. We obtained formulas giving a solution to the problem. In the process of solving the problem, the lattice period and the flow velocity streamlining the lattice are determined.

Read More### THE RESEARCH ON THE FAMILIES CONFOCAL ELLIPSES AND HYPERBOLAS THROUGH GEOGEBRA MATHEMATICAL PACKAGE

The article describes setting the families of confocal ellipses and hyperbolas and studying their properties through the GeoGebra mathematical package in the course “Analytic geometry” under the topic “Second-order curve” by the students of a technical college. The primary purpose of the article is to demonstrate the integration of modern information technology into the process of teaching higher mathematics. Using the built-in tools and commands of the GeoGebra environment, the setting and construction of confocal ellipses and hyperbolas are shown step-by-step. Using the dynamic drawings, the author considers the process of “transformation” of one conic into another at different values of the specified parameters. Relying on the properties of a tangent to a second-order curve, the author found and analyzed that the confocal ellipse and the hyperbola intersect at a right angle. The last result is considered for various cases of the mutual arrangement of curves and tangents at the point of their intersection. All the results obtained are justified strictly mathematically.

Read More### 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.

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