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Preventing soil degradation is an important task of modern agrarian science. Preservation and increase in beneficial soil microflora are a precondition for satisfactory ecological functioning of soil and its fertility. The purpose of this study was to investigate the dynamics of beneficial soil microflora in winter wheat crops under the impact of mineral fertilisers and Agrobacterium radiobacter on the lands of the south of Ukraine. The study was conducted in threefold replication in the conditions of the Kherson region in 2016- 2020 in the experimental fields of the Institute of Climate-Smart Agriculture of the National Academy of Agrarian Sciences of Ukraine. The study used a systematic design, and the following factors were investigated: no fertiliser and Agrobacterium radiobacter; N120P90; N90P60 + Agrobacterium radiobacter; N120P90 + Agrobacterium radiobacter. The study on the microflora composition in the soil layer at 0-30 cm was carried out in the main stages of winter wheat growth and development through the inoculation of nutritious environment. Statistical analysis was performed using the methods of analysis of variance, correlation, and regression analysis. Dynamic changes in the soil biota composition under the influence of the studied factor were established. The slightest response to mineral fertilisers and bacterial preparation application was in ammonifying bacteria, while the strongest response was in cellulosedegrading microorganisms. The winter wheat harvesting revealed a decrease in the number of ammonifying bacteria in the soil, while the number of nitrifying and cellulose-degrading microflora increased significantly. Regression models for the prediction of the number of nitrifying bacteria and cellulose-degrading microorganisms, developed based on experimental data, have great accuracy (the error is 3.78% and 7.79%), and allow determining the adverse effect of phosphorus fertiliser on the microflora of dark-chestnut soil. The study has no analogues in Ukraine and expands theoretical knowledge about the influence of mineral fertilisers and bacterial preparation, containing Agrobacterium radiobacter, on the composition of beneficial microflora of the dark-chestnut soil

On the basis of mathematical modelling of electromagnetic processes, electrical losses in the metal frames of the two-inductor induction channel furnace in a wide range of specific electrical conductivity of the non-magnetic material of the frames were determined. Research was conducted for two options for sectioning the lower frame of the furnace (vertical and horizontal) and two values of the phase angle between the voltages on the inductors (0 and 180 electrical degrees). For these cases, losses in furnace frames made of ferromagnetic material (construction carbon steel and magnetic stainless steel) were also calculated. Recommendations are presented on the selection of the frame material, the sectioning option and the phase angle between the voltages, which ensure minimal electrical losses. Ref. 13, fig. 4.

Our investigations show that electrochemical corrosion of copper is faster than electrochemical corrosion of aluminium at temperatures below 180°C and electric current density 3,000 A/m2 (or 30 A/dm2=3 mA/mm2). We have obtained that aluminium anodes (cylindrical or spherical) dissolve into concentrated NaCl solution during electrolysis more rapidly with temperature increasing while copper anodes (cylindrical or spherical) dissolve more slowly with temperature increasing from room temperature to temperature 180°C. Electric current value also increases with temperature increasing. Really, such result is unexpected. General quantity of the H+ and Cl- ions decreases during electrolysis at all temperatures since the H2 and Cl2 gases are formed near electrodes. It decreases electric current value on 1.3%. General quantity of the Cu+ and Cu2+ ions decreases with temperature increasing too. We guess that one reason only should be for electric current value increasing: average charge of copper ions increases from +1 at room temperature to +1.5 at 100°C and to +2 at 180°C while charge of aluminium ions remains the same +3. Corresponding mathematical model is proposed for the analysis, and literature experimental data are used too.

Modern approaches to automatic control of crude oil dewatering and desalting are predominantly model-free, and described model-based systems lack precise mathematical description. Not a single research provides a dynamic input-output model for electric dehydrator, suitable for control system development. As far as electric dehydrator, which is the main plant to control in the process, is a non-linear system with distributed parameters, a need for linearization arises. The aim of present study is to compare different methods for obtaining approximate transfer function of an electric dehydrator from graphical experimental data.

On the basis of the formulated mathematical model for the study of electromagnetic processes in a two-phase (two-inductor) induction channel furnace, electrical losses in the metal frameworks of the furnace were calculated for vari-ous options for their sectioning. The influence of the phase angle between the voltages feeding the inductors of the fur-nace on the distribution of specific and integral losses in the frames is determined. Practical recommendations for re-ducing these losses in order to increase the efficiency of melting furnaces are presented. Ref. 5, fig. 5.

Purpose. Railway safety during the operation of freight cars largely depends on the reliability, fatigue resistance and durability of the cast bearing elements of the three-element bogie, especially the side frames. Premature failure of cast frames occurs mainly due to undetected latent defects in the foundry. To eliminate these problems, it is advisable to develop an alternative native all-welded side frame for a bogie with an axle load of 23.5 tnf, which can be interchangeable with the cast structure. Methodology. Mathematical modelling approaches were used to determine the stress-strain state of an all-welded structure under the influence of regulated loads and to assess its strength in accordance with current national and modern world standards. Findings. Prototypes of the all-welded side frame structure were subjected to accelerated fatigue tests. The tests have experimentally proved that the cyclic durability of the developed side frame is significantly (2...4 times) higher than the cyclic durability of cast side frames. Originality. A comparative analysis of the permissible stress amplitudes in different zones of the all-welded side frame during long-term operation based on 107 load cycles in accordance with the current standard for the strength of railway cars and modern approaches to determining the fatigue resistance of welded joints showed the insufficient conservatism of the national standard for assessing the fatigue strength of welded joints, which was taken into account when developing a new design of the all-welded side frame. Practical value. In addition to increasing reliability, possible increase in overhaul mileage and warranty period of side frames by ensuring a high level of fatigue resistance and durability, the welded structure can ensure the accuracy of the base frame size, reduce the weight of unsprung masses, which should reduce wheel wear and improve the running characteristics of railway carriage bogies. Reducing the cost of introducing all-welded side frames into mass production compared to the use of foundry technology for the manufacture of these structures and the fact that the cost of manufacturing an all-welded side frame is generally competitive with a cast structure is also one of the important advantages of our developme

The generalized mathematical model of wheeled platforms straight motions on the ideal horizontal plane under speeding-up from the state of rest mode is proposed, and the controls satisfying the restrictions of motion jerks are find. The pure mechanical and electromechanical wheeled platforms are considered, as well as the computer simulations of the researched processes are made. The jerks restrictions are reduced to limiting the value of the wheeled platform acceleration time derivative. The proposed approaches are based on the holonomic systems mechanics and on the electromechanical analogies allowing to consider the different kinds of the wheeled platforms taking into account the electric on-board systems like the drive electric motors and the control systems by using the Lagrange equations of second kind. The examples of the proposed approaches using to define the controls satisfying the jerks restrictions under speeding-up from the state of rest are considered for the pure mechanical and electromechanical wheeled platforms. It is obtained the inequality allowing to chose the instantly supplied driving mechanical couple which will provide the admissible jerks of the motion of the wheeled platform under speeding-up from the state of rest. It is shown that the rolling friction and the viscous damping are the principal causes of the wheeled platforms jerks under speeding-up from the state of rest. It is obtained the inequality defining the voltage instantly supplied on the drive electric motors which will provide the admissible jerks of the motion of the electromechanical wheeled platform during speeding-up from the state of rest, and it is shown that the proposed general approaches are suitable for considering the different kinds of wheeled platforms. The computer simulations of the processes of speeding-up from the state of rest for the electromechanical wheeled platform are considered to show results correctness and to illustrate satisfying the restrictions of the motion jerks. The obtained results of the computer simulations are in the full agreement with the well-known fundamental property inherent for the wheeled platforms. The results for the jerks show that the maximum value of the jerk is really at the initial time as was suggested before, and it is shown that the jerks values at the initial time obtained by using the computer simulations are in full agreement with the theoretically defined correspondent exact values. The big jerks of the considered electromechanical wheeled platform are due to the voltage instantly supplying on the drive electric motors at the initial time, and it is understandable that limiting of such instantly supplied voltage value cannot provide any wished small jerks. The smooth time depending for the voltages supplying on the drive electric motors are required to provide any wished small jerks of the electromechanical wheeled platforms.

The phenomena of the formation of local defects and cracks in asphalt concrete pavements of roads and bridges are most often observed in climatic zones with large temperature differences during their seasonal and daily changes. To a large extent, this is due to the heterogeneity of the thermomechanical properties of the materials of the coating layers and the base. To prevent these phenomena, reinforcing rods and meshes are introduced into the coating structure. In this work, using the theory of thermoelasticity, it is shown by the method of mathematical modelling that in cases of incompatibility of the thermomechanical characteristics of asphalt concrete materials and reinforcement, additional localized thermal stresses arise in its small vicinity, which, even at moderate temperatures, can reach critical values and lead to local defects and cracks. Since these defects are latent, they cannot always be detected in practice. The presented results of analytic calculation validated these conclusions. They can be used in both road building and composite design.

The designs of screw conveyors contain safety clutches that ensure the avoidance of breakdowns in emergencies (e.g., when the auger is jammed). Therefore, the choice of these clutches is a relevant scientific problem, which is related to the calculation of the maximum torque of the auger. The purpose of this study was to develop a method for calculating the maximum torque when the auger of a screw conveyor is jammed. The method developed in this paper article is based on the use of an artificial neural network trained using the “learning with a teacher” technology. The training and test data set for the artificial neural network was obtained by conducting machine experiments, each of which consisted in the numerical integration of a nonlinear differential equation and the determination of the value of the maximum moment in the elastic connection of the dynamic system based on the obtained solution. The specified differential equation is obtained based on the equation of motion of the non-jammed part of the conveyor (drive, gears, clutch) and the Kloss equation, which corresponds to the model of the mechanical characteristics of the conveyor asynchronous motor. The statistical significance of the results of an artificial neural network was proved by analysing the values of approximation quality indicators. A brief analysis of the influence of the stiffness of the elastic connection of the dynamic conveyor system and the drive gear ratio, as well as the overloading capacity of the engine on the maximum moment that occurs when the screw is jammed, was performed. The practical significance of the results obtained is related to the software implementation of the method, which allows engineers to effectively select safety clutches upon designing screw conveyors.

Formulation of the problem. Formulation of the problem. Mathematical modelling is a very important component of mathematics education, because by applying the mathematical theories to practical needs of our everyday life increases the student interest for mathematics. The main steps of the mathematical modelling process include analysis of the given real world problem, formulation of the problem and construction of the mathematical model (mathematization), solution and control of the model and implementation of the final mathematical results to the real situation. Mathematization possesses the greatest difficulty among the steps of the MM process, because it involves a deep abstracting process, which is not always easy to be achieved by a non-expert. It is sometimes, however, the transition from the solution of the model to the real world (control and/or implementation of the model) that presents difficulties for students too. An example is given to illustrate this remark. Materials and methods. In this paper soft sets are used as tools for developing a model for assessing human activities in a parametric manner and an example is presented (assessment of football players performance) to illustrate its applicability under real situations. A soft set, being a parametrized family of subsets of the universal set of the discourse, is a generalization of the concept of fuzzy set designed on the purpose of dealing with the existing uncertainty in a parametric manner. The theory of soft sets has found many and important applications to several sectors of the human activity like decision making, parameter reduction, data clustering and data dealing with incompleteness, etc. Results. The soft set assessment model is applied for evaluating student mathematical modelling skills with respect to the parameters excellent, very good, good, mediocre, and failed. It serves both for assessing the general performance of a student class and the individual performance of each student with respect to the steps of the mathematical modelling process. Conclusions. The constructed in this paper model is very useful in cases where the assessment has qualitative rather than quantitative characteristics and could also be applied to a variety of other cases for assessing human and/or machine (e.g. computer programs) activities.

Recently, there has been a massive drying of conifers all over the world. In North America and Siberia, there are millions of hectares of shrunken plantings; in Europe, pines and firs have been drying up over the past two decades. Furthermore, considerable damage is caused to woody plants by phyto-pest and phyto-diseases, since mass reproduction of Ips typographus Linnaeus, Ips acuminatus Gyllenhal has been observed in Europe in recent years, Dendroctonus micans Kud – in North America, Polygraphus proximus Blandford – in East Asia. Nematodes also cause significant damage to pine forests. Among phyto-diseases, Heterobasidion annosum (Fr.) Bref. harmfully affects Pinus sylvestris L. The appearance of foci of shrunken trees in different parts of the globe indicates the global nature of processes associated with cyclical planetary processes and climate change. This study describes climate changes in the research region for 1961-2020. According to the analysis, it was found that for 2009-2020, considerable damage to pine plantations in Zhytomyr Polissia is caused among needle-eating insects – Panolis flammea Denis & Schiffermuller, Diprion pini L., Neodiprion sertifer Geoffroy; among other pests – Aradus cinnamomeus Panz, Dendrolimus pini L., Bupalus piniarius L. The greatest harmful effect that pineries have recently sustained has been caused by Diprion pini L. It was also found out that among phyto-diseases suffered by the pine forests, significant damage has been done by Heterobasidion annosum (Fr.) Bref., with the damaged area of 13.0-14.2 thousand hectares. Hydrothermal analysis was performed for 2009-2020. The influence of solar activity on the number of phyto-pest and diseases is analysed. This paper provides the estimate of the amount of CO2 emissions is given for 2009-2020. It was found that since 2014, the amount of carbon dioxide emissions has decreased from 1.5 million tonnes to 0.6 million tonnes. Correlation analysis of all indicators indicated a high mutual influence between the area of trees damaged by insect pest, root sponge, the Wolf number, and CO2 emissions to the environment. Mathematical dependences are obtained to predict the influence of the W number on damage to pineries by forest pests and diseases in the conditions of Zhytomyr Polissia

The approach to the formalization of the generation of problem situations applicable to the development of tutoring programs consisting of many tasks is considered. The main errors arising during the software-based generation of parameters are specified. Mathematical modeling of parametrical generation algorithms examined by examples of tasks that make up complex tests on mathematics for secondary schools. The parametric generation method proposed in the article allows getting the large quantitative variations in task problem situations. Thereby, every learner will get a personal unique set of tasks. The structure and functionality of web-tests complex consisting of tasks generated via the proposed method are described. The subject of research in the article is the process of computer training in mathematics. The goal is to develop a method for task generation for mathematical disciplines. Tasks. Research and analysis of the set of mathematical problems. Parameterization of each task and development method and algorithms for automated generation parameters with the determination of incorrect combinations of parameters or problem situations that have no solution. Estimation of borders of admissible for approximate answers. Evaluation of the user solution of a single task and a sequence of tasks. The general objective of the work is to make the software product consisting of a sequence of mathematics tasks. The software should have an extended user interface for the graphical presentation of various problem situations in various mathematical topics. The program must be accessible via the Internet. The following results were obtained: developed methods and algorithms of task generation, which provide correct problem situations and unique parameter sets for each user; described the program complex structure and developed the software system of mathematical web-tests provides two levels of difficulty. Conclusion. The scientific novelty lies in the development of the method of task generation for interactive web tests on the mathematics and its computer implementation with the possibility of graphical representation of tasks and checking of tasks correctness.

This paper is devoted to solving an important task of the food industry - the rational use of food raw materials, including gelling agents of various origins. The innovative strategy of this study is based on the possibility of using gelatin and modified potato or pea starch, as a cheap ingredient in the production of gel semi-finished products and confectionery based on traditional, but expensive raw materials such as agar and agar from Furcellaria - furcelaran. Food gelatin (Ukraine), agar (Germany), furcelaran (Estonia), modified potato starch OPV-1 (Ukraine), modified potato starch Farinex VA-40 (Netherlands), modified pea starch Emden ESH-15 (Germany) were used in the work. The experimental study has been performed concerning the strength of gel-forming heterogeneous systems ‘gelatin - MS - agar – water’ and ‘gelatin - MS - fercellaran – water’, and homogeneous systems: ‘agar - water’, ‘fursalaran - water’, ‘gelatin – water’. Mathematical models have been obtained that relate the strength of the investigated gel-forming systems to the mass concentration of their components. The equation has been obtained that allows calculating the mass concentration of the components of the studied gel-forming compositions with the given level of strength of systems. It is shown that for a given level of strength of a heterogeneous gel-forming system there is an optimal concentration of its components in terms of the least full cost of the system. The equation that allows to calculate the optimal concentration of components of a heterogeneous gel-forming system has been obtained. The adequate mathematical model for forecasting the strength of modelling systems of gel-forming, depending on the mass concentration of components is obtained. It is envisaged to formulate the initial requirements for the parameters of gel-forming, which will allow obtaining an integral elastic structure at optimum duration of the technological process, by modelling the systems of gel-forming, as a technological system, within the framework of the functioning of individual subsystems (the creation of prescription concentrations and ratios of gel-forming agents). The obtained mathematical models can be used for the analysis of other heterogeneous gel-forming compositions in the presence of the data on the strength of such systems depending on the concentration of components.

Three-dimensional mathematical model for study of electromagnetic field of induction channel furnace with inductors’ given voltages has been formulated. The adequacy of the mathematical model has been confirmed by means of com-parison of calculated electromagnetic parameters with experimental data obtained on industrial furnace. For two-phase induction channel-type furnace the influence of phase angle between inductors’ voltages on energy and electro-magnetic furnace parameters have been determined. References 5, figures 4, table.

Purpose of this study was to develop the main components of a model of an adaptive information system for predicting crop productivity. Methods. To conduct research on the establishment of the basic structural elements of an adaptive information model for predicting the productivity of basic crops used the method of constructing dynamic models. Results. A detailed analysis of conceptual approaches to the construction of mathematical agricultural models is carried out and the main advantages and disadvantages of modern analogues are established. It is determined that the adaptive information model is based solely on the needs of the plant and actually on the need to provide these needs with available resources in order to obtain consistently high yields with high quality indicators. The hardware and software complex must have a feedback relationship between its basic structural elements, because it significantly improves the accuracy of predicting plant productivity. Data based on the operation of certain mechanisms or indicators of weather conditions and their forecasts are used for decision making, however, if they are substantially changed, decisions about individual technology elements are reviewed. The software should be related to the economic part and should take into account market conditions and forecast data when making recommendations. In the case of low purchase prices for products, we recommend that certain agrotechnical operations (say vegetation feeding) be applied or not, in the case of significant change in growing conditions - when the application of these agro-measures will be ineffective due to the negative effects of drought, etc. Conclusions. Adaptive information system for forecasting productivity in the technological process of growing crops is formed on the basis of a model consisting of three modules of characteristics – the resultant and two components. At each subsequent stage of implementation of the model, the resulting feature becomes component, with the maximum contribution to the resulting feature of the next module.

Purpose. This work involves the development of a numerical model for the calculation of areas of thermal damage to people in the event of solid propellant burning at the industrial site. Methodology. An equation expressing the law of energy conservation was used to solve the problem of determining the areas of thermal shock of people at the industrial site. A potential flow model was used to calculate the airflow velocity field in the presence of buildings at the industrial site where an emergency occurs. The numerical solution of the two-dimensional equation for the velocity potential is derived using the Liebmann method. This numerical model takes into account the uneven velocity field of the wind flow that is formed near industrial buildings. An implicit difference splitting scheme was used to numerically solve the energy equation. The physical splitting of a two-dimensional energy equation into a system of one-dimensional equations describing the temperature transfer in one coordinate direction has been carried out previously. At each splitting step, the unknown temperature value is determined by an explicit point-to-point computation scheme. Based on the numerical model built, the code using the FORTRAN algorithm language is created. Findings. Based on the developed numerical model, a computational experiment was conducted to evaluate the risk of thermal damage to people at the industrial site where solid propellants are produced. The dangerous areas for personnel are identified. Originality. An efficient numerical model has been developed to calculate the zones of thermal pollution in case of solid propellant burning. Practical value. Based on the developed mathematical model, a computer program was created, which allows performing serial calculations for determining the zones of thermal damage during emergencies at the chemically hazardous objects. The mathematical model developed can be used to design an emergency response plan for chemically hazardous objects.

Purpose. Increasing the traffic intensity in large cities requires the implementation of plans to improve the air quality in accordance with the Procedure for the implementation of state monitoring in the field of atmospheric air protection. To develop and justify the measures to reduce air pollution and negative impact on the environment and public health in decision-making information systems, it is necessary to process large amounts of available heterogeneous information and use mathematical decision-making models. The paper proposes a mathematical decision-making model for evaluating the effectiveness of air quality management plans in cities with high emissions of mobile pollution sources. Methodology. For air quality management problems in cities, a methodology is used for constructing mathematical models of decision-making under emission parameters uncertainty due to incomplete data on vehicles` emissions and their distribution over the city. The structure of data flows in the information system is considered in accordance with the requirements of modern environmental decision support systems, during which the management bodies have the opportunity to take into account different social and economic criteria. Findings. Analysis of national statistics showed an increase in the contribution of mobile sources to the structure of urban air pollution. Information technologies and optimization models are considered that make it possible to quickly assess the impact of vehicles and their traffic on atmospheric air quality in cities and make strategic decisions on planning measures to improve it. Originality. The structure of an information system and a decision-making model for air quality management are proposed based on the multi-criteria optimization of emission parameters using the construction of “source – receptor” matrix in the network area for modelling air pollution of a city’s territory with motor vehicle emissions. Practical value. The model could be used at the stage of designing municipal environmental monitoring systems and developing plans for improving atmospheric air quality in urban agglomerations.

Purpose. Emissions from mine ventilation system can create intensive atmosphere air pollution. As a rule, a huge amount of dust from mine fan enters atmosphere low layers. An important task is the development of methods to assess levels of the atmosphere pollution near mines and settlements. To solve this problem it is important to have physically proved mathematical models. Nowadays to predict the atmosphere pollution near settlements which are effected by mine fan the empirical model OND–86 is used. This model does not take into account many important physical factors. So, the purpose of this study is the development of quick computing mathematical model to predict the atmosphere pollution in case of dust emissions from mine fan. Methodology. To predict levels of the atmosphere pollution in case of mine fan work 3D equation of dust convective – diffusive flow was used. This equation takes into account gravity fallout, wind velocity, atmosphere turbulent diffusion, location of dust emission source. To sole modeling equation the implicit difference scheme of splitting was used. Findings. Developed mathematical model allows quick prediction of the level of atmosphere pollution in case of dust emissions from mine ventilation fan. The models allow to obtain zones of contamination near settlements which are situated in vicinity of mine. Originality. The developed mathematical model takes into account a number of physical factors, which at the present time are not considered on the days when prediction of the atmosphere pollution in settlements near mine is carried out. Practical value. On the basis of the developed mathematical model program code was created. This code can be used for evaluation of atmosphere pollution in settlements which are effected mine fan emissions.

Purpose. The important problem in the field of ecological safety and industrial safety is providing of normal microclimate in dead-end mine working. In these regions of the mine methane gas can be accumulated and as a result explosion may take place. So, to avoid these accidents it is important to ventilate appropriately dead-end mine working. The purpose of the work is development of quick computing mathematical model to obtain information about dead-end mine working ventilation process. Methodology. The process of dead-end mine working ventilation computing is separated in two stages. At the first stage the velocity flow field is computed in the dead-end mine working. We consider the situation when the suction tube is situated in this region. To solve this problem the fluid dynamics model of inviscid gas flow was used. At the second stage of the computational modeling the convective- diffusive equation of admixture transfer was used. The equation takes into account non-uniform flow field in the dead end mine workings. Findings. The developed numerical model was coded using FORTRAN language. The developed computer code allows to perform numerical experiment to assess the efficiency of suction tube implementation to decrease methane gas concentration in dead-end mine working. Originality. The developed numerical model takes into account physical factors, which are not considered nowadays in the empirical models, which are used for solving the problems of dead-end mine working ventilation. It allows taking into account the geometrical form of the dead-end mine working. Practical value. The developed computer program allows to perform calculations to assess the efficiency of suction system used for the ventilation of the dead-end mine working.

A mathematical model that describes heat and mass transfer processes in an induction channel furnace is presented. Using the example of a two-phase channel furnace with standard form of channels, the influence of the phase angle between the voltages supplying the furnace inductors on the thermal state of the liquid metal is considered. Values of this angle, which provide minimal melt overheating in channels in comparison with furnace bath have been determined. Ways of intensification of heat and mass transfer processes in two-phase channel furnace have been suggested. References 9, figures 4. [ABSTRACT FROM AUTHOR]

Biological tissues and their artificial substitutes are composed by different fibers and possess complex viscoelastic properties. Here the most popular 3-element and 5-element rheological models of human soft tissues as viscoelastic bodies are considered accounting for the time delay between the load and mechanical respond of the material.The obtained data compared to the experimental curves got on the vessel wall and heart tissues.

Проблематика. Більшість моделей фінансових та економічних процесів вирізняються значною обчислювальною складністю, а побудова прогнозів прийнятної якості для цих процесів на потрібний часовий горизонт – великою трудомісткістю. Тому розробка і впровадження ефективних інструментів прогнозного моделювання фінансових та економічних процесів є однією з актуальних і практично значимих задач. У роботі розглядається питання моделювання та прогнозування нелінійних нестаціонарних процесів у макроекономіці та фінансах із використанням методики, в основу якої покладені принципи системного аналізу, такі як ієрархічне моделювання, врахування невизначеностей, оптимізація характеристик за допомогою комплексних критеріїв, а також структурно-параметрична адаптація. Застосування запропонованої методики дає змогу покращити якість прогнозування за рахунок виявлення особливостей досліджуваного процесу й адаптації моделі до нових даних тощо. Мета дослідження. Розроблення методики для прогнозного моделювання нестаціонарних процесів у фінансах і макро-економіці із використанням статистичних даних та її реалізація у відповідній комп’ютерній системі. Методика реалізації. Методика базується на технологіях попередньої обробки статистичних даних, спрямованих на усунення можливих невизначеностей, застосуванні кореляційного аналізу для оцінювання структури моделі та виборі методів оцінювання параметрів моделей, обчисленні оцінок прогнозів і генеруванні альтернативних рішень. Це дає можливість об’єктивно оцінювати результати, одержані на кожному етапі розв’язку задачі моделювання нелінійних нестаціонарних процесів у макро-економіці та фінансах. У дослідженні пропонується оригінальна методика визначення структури моделі з подальшим її впровадженням в інформаційну систему підтримки прийняття рішень. Результати дослідження. Для вибраних фінансових і макроекономічних процесів було побудовано відповідні моделі. Висока якість кінцевого результату аналізу даних і прогнозування досягнута завдяки реалізації оцінювання одержаних результатів із використанням статистичних критеріїв якості на кожному етапі обробки даних, побудови моделей і прогнозування, а також завдяки можливості адаптації моделей до нових даних через повторний аналіз статистичних характеристик досліджуваних процесів і застосування комбінованих критеріїв адекватності моделей та якості оцінок прогнозів і зручному представленню проміжних та кінцевих результатів. Висновки.Запропонована методика використана для прогнозного моделювання окремих макроекономічних та фінансових процесів України. Отримані результати свідчать про те, що її можна успішно використовувати для розв’язання практичних задач побудови моделей і прогнозів нелінійних нестаціонарних процесів в умовах невизначеностей різних типів, які зазвичай доводиться розглядати під час моделювання та прогнозування, використовуючи статистичні дані.

Purpose. The existing mathematical models of unsteady heat processes in a passenger car do not fully reflect the thermal processes, occurring in the car wits a heating system. In addition, unsteady heat processes are often studied in steady regime, when the heat fluxes and the parameters of the thermal circuit are constant and do not depend on time. In connection with the emergence of more effective technical solutions to the life support system there is a need for creating a new mathematical apparatus, which would allow taking into account these features and their influence on the course of unsteady heat processes throughout the travel time. The purpose of this work is to create a mathematical model of the heat regime of a passenger car with a heating system that takes into account the unsteady heat processes. Methodology. To achieve this task the author composed a system of differential equations, describing unsteady heat processes during the heating of a passenger car. For the solution of the composed system of equations, the author used the method of elementary balances. Findings. The paper presents the developed numerical algorithm and computer program for simulation of transitional heat processes in a locomotive traction passenger car, which allows taking into account the various constructive solutions of the life support system of passenger cars and to simulate unsteady heat processes at any stage of the trip. Originality. For the first time the author developed a mathematical model of heat processes in a car with a heating system, that unlike existing models, allows to investigate the unsteady heat engineering performance in the cabin of the car under different operating conditions and compare the work of various life support systems from the point of view their constructive solutions. Practical value. The work presented the developed mathematical model of the unsteady heat regime of the passenger car with a heating system to estimate the efficiency of unsteady, transitional temperature states in passenger cars, taking into account the design features of the heating system and the regulatory requirements. This allows the development and implementation of optimal technical characteristics of heating appliances and the construction of an algorithm for controlling their operation in accordance with operating conditions, taking into account the thermal inertia of the car in the transitional modes of heating, on the basis of mathematical modeling.

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Copyright of Nanosistemi, Nanomateriali, Nanotehnologii is the property of G.V. Kurdyumov Institute for Metal Physics, N.A.S.U and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Accidents occurring on railway track of 1520 nun are often associated with the fracture of cast load-carrying elements of three-element freight car trucks. The level of quality and endurance of such truck elements as side frame and truck bolster, which are traditionally manufactured by casting technology, are insufficient, so it is advisable to use welding technology to manufacture the mentioned parts of sheet rolled metal in order to increase the fatigue resistance characteristics. The development of a new all-welded structure of side frame of a three-element freight car truck with an axial load of 23.5 tc was carried out on the basis of widespread use of mathematical modelling to determine the stress-strain state of welded elements of the truck under the action of a regulated range of loads and to evaluate the strength according to the valid standards and modem global approaches. The technology of assembly and welding, as well as the appropriate specialized equipment for manufacture of a developed design of welded side frame were created. Two test specimens were manufactured and accelerated fatigue tests were carried out. the results of which showed a significant increase in endurance and vitality under operational cyclic loads as compared to designs of existing cast side frames. Taking into account high values of reliability, availability and manufacturability, ability of a significant reduction in unsprung weight and increase in dimensional accuracy, the welded structure of the side frame of a three-element freight car truck is very promising for its implementation on railway track of 1520 mm. [ABSTRACT FROM AUTHOR]

A complex of mathematical models and their computer means for numerical prediction of the kinetics of temperature fields, phase and structural states, mechanical stresses and deformations in layer-by-layer formation of typical products of titaniumbased alloys was developed. On the typical examples of electron beam surfacing of T-shaped beam structures of titanium VT6 alloy produced with the help of xBeam 3D Metal Printer technology, the peculiarities of their kinetics depending on the technological parameters of production were investigated. The influence of the thickness of the substrate on regularities of the temperature field development during layer-by-layer formation of beam elements and on the structural state of the metal after complete cooling was shown. On the example of forming a thick-walled T-shape product it was shown, that an important factor, that allows obtaining a low level of residual stresses, is the optimization of the delay time between the surfacing of each of the beads to provide the conditions of uniform cooling of the structure. [ABSTRACT FROM AUTHOR]

Copyright of Technical Electrodynamics / Tekhnichna Elektrodynamika is the property of National Academy of Sciences of Ukraine, Institute of Electrodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The problem of intensive pollution of the Caspian Sea has been continued to be one of the most significant and serious for the region. The rising of pollution level of the Caspian Sea coast with oil hydrocarbons has a particular concern. The purpose of this paper is to assess the pollution degree of the Caspian coast with petroleum hydrocarbons. The idea of the author is to provide a comprehensive analysis of the environmental destructive factors of the oil production process on natural complexes, including the effect of chemical pollution of the water basin with petroleum hydrocarbons on local hydrobionts. Methods of mathematical modeling of the oil films spreading on the water surface aimed to the prediction of the influence area, and methods of toxicological studies and assessment of the dose-effect relationship have been used. It was determined that the waters of the Caspian Sea, associated with offshore oil production, are areas of increased environmental risk. In the cases the concentration of hydrocarbons is above 1 mg / l, physiological changes are observed in the majority of dominant groups of hydrobionts. Areas of increased risk level for marine ecosystems caused by gas and oil industry development are connected with north and west-south parts of the Caspian Sea. The obtained results can be used to develop programs to ensure the environmental safety of the studied region.

Copyright of Metallophysics & Advanced Technologies / Metallofizika i Novejsie Tehnologii is the property of G.V. Kurdyumov Institute for Metal Physics, N.A.S.U and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Today increase in volumes of accumulation of a household waste acts as a global serious problem. Ukraine occupies one of the first places on the list in the world by garbage quantity per capita. Already about 7% of the territory in the country are under municipal solid waste, besides more than 52 million tons of household waste are annually formed. In this regard, sharply raises the question of the stability of landfills after their closure for further use as a basis for engineering constructions and designs. Aim: The aim of this research is to establish the dependence of settlement of the closed landfill on the properties of the underlying soil, as well as the landfill slope angle to predict the possibility of using it as a basis for construction. Materials and Methods: The phased load of landfill by waste layers and angle of inclination were taken into account during the research. The covering and underlying layers are described by Coulomb-Mohr model. The body of landfill was modeled as a weak ground considering its creep. The Soft Soil Creep (SSC) model was applied for this. The finite elements method was used for numerical solution of the problem. Results: In this work the mathematical model of sedimentation of municipal solid waste constructed for the first time, taking into account geometrical and physical and mechanical parameters of landfill and soil base, which will allow further prediction the use of landfill for building structures on it for various purposes. As a result of researches was found that with decreasing of inclination angle of the landfill slope there is a significant decrease in settlement. Thus, while reducing the angle from 75° to 30° the settlement is reduced by 5...22% depending on the type of soil foundation. The largest landfill reduction is observed for the least dense soil (sand).

Purpose. Development of mathematical models of adjustable electrical drives with high-phase order induction motors for their merits analysis at static and dynamical modes. Methodology. At the mathematical modeling main kinds of physical processes taking place in the high-phase order induction motors are considered: electromagnetic, electromechanical, energetic, thermal, mechanical, vibroacoustic ones. Besides, functional as well as mass, frame and value indicators of frequency converters are taking into account which permits to consider technical and economical aspects of the adjustable induction electrical drives. Creation of high-phase order induction motors’ modifications in possible on the base of a stock 3-phase motors of basic design. Polyphase supply of induction motors is guaranteed by a number of the adjustable electrical drives’ power circuits. Results. Modelling of a number of adjustable electrical drives with induction motors of different phase number working on the same load by its character, value and required adjustment range is carried out. At the utilization of the family of characteristics including mechanical ones at different adjustment parameters on which loading mechanism’s characteristics are superimposed regulation curves representing dependences of electrical, energetic, thermal, mechanical, vibroacoustic quantities on the motors’ number of revolutions are obtained. Originality. The proposed complex models of adjustable electrical drives with high-phase order induction motors give a possibility to carry out the grounded choice of the drive’s acceptable variant. Besides, they can be used as design models at the development of adjustable high-phase order induction motors. Practical value. The investigated change of vibroacoustic indicators at static and dynamical modes has been determined decrease of these indicators in the drives with number of phase exceeding 3.

In paper selected problems from wide range of development work which have been carried out by authors on crankshaft design improvement of IC engines have been presented. Heat treatment is technological treatment, which determines crankshaft utilisation properties. Great wear resistance of crankshaft operation surface (crank-pin, main journal) determines its durability and reliability, increasing engine life. In paper mathematical model characteristic has been given, allowing for heat treatment process simulation of crankshafts and experimental investigations which verify analytical model have been presented, too. Great consistence of calculation results and experiment has been obtained.

Copyright of Technical Electrodynamics / Tekhnichna Elektrodynamika is the property of National Academy of Sciences of Ukraine, Institute of Electrodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper presents the analysis of the yoghurt market in Ukraine, the consumer preferences of Ukrainians while choosing yoghurt with fillers were presented, the segmental distribution of yoghurt consumption patterns depending on the type of filling was given. The enhancement prospects of the range of yoghurt and yoghurt drinks with grain ingredients were outlined, the expediency of development of innovative technologies of combined dairy-grain yoghurt drinks with fillers having balanced chemical composition was justified. The prospects of dairy and plant feedstocks combining for the creation of novel foodstuffs with balanced chemical composition were shown. The choice of raw ingredients for the development of end products - yoghurt base, cheese whey, rice flour for baby food and pumpkin filling with sugar was substantiated; the value of raw ingredients was analyzed; their impact on human health was outlined. The mathematical modelling of the component composition of dairy-grain yoghurt drinks with fillers was fulfilled in the Microsoft Excel environment. As the result of the mathematical modelling four production formulas were developed for manufacturing of yoghurt drinks with the ratio of proteins, fats, carbohydrates - 1 : 1 : 4, corresponding to modern requirements of nutritiology for healthy nutrition of adult humans. The chemical composition of yoghurt drinks was estimated on the basis of reference data on the composition of the used raw ingredients; the mass fraction of proteins in the end products will amount to 2.001 ... 2.264%; the mass fractions of fats and carbohydrates - 2.003… 2.265 and 8.001…9.048% respectively. The content of dairy and plant proteins, milk and plant fats in the drinks and the content of mono-, di- and polysaccharides were defined. It was shown that the combination of dairy and plant raw materials will make it possible to produce yoghurt drinks fortified with soluble and insoluble polysaccharides - cellulose, hemicellulose, pectin, and natural stabilizer - rice starch, which mass fraction will amount to 1.763 ... 2.805%. The amino acid composition of proteins of combined dairy-grain yoghurt drinks was computed; it was shown that the end products will not contain limiting amino acids due to combining dairy and plant raw materials, while the control sample - yoghurt - is limited in sulfur-containing amino acids (the amino acid score is 94.3%). [ABSTRACT FROM AUTHOR]

Copyright of Technical Electrodynamics / Tekhnichna Elektrodynamika is the property of National Academy of Sciences of Ukraine, Institute of Electrodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Objective: determining of the functional activity of mice bone marrow hematopoietic progenitor cells, cultivated in gel diffusion chambers, on the stages of hematopoiesis recovery after their prolonged irradiation in the lethal dose in a comparative aspect with the method of colony forming in spleen using mathematical model., Materials and Methods: The method of cell cultivation in gel diffusion chambers, cytological methods, mathematical modeling, and statistical methods of research were used. Bone marrow samples extracted from the femur of mice irradiated with a total dose of 8 Gy with a power 0.0028 Gy/min were cultivated in diffusion chambers with semi solid agar in the abdominal cavity of CBA recipient mice., Results: Comparative analysis of the colonyforming efficiency of progenitor cells (CFU) was carried out during cultivation in gel diffusion chambers in the process of hematopoiesis recovery for 30 days, as well as in the spleen of lethally irradiated animals, in accordance with the mathematical model. Analysis of colony forming kinetics in gel diffusion chambers after prolonged exposure to ionizing radiation indicated the biphasic nature of hematopoiesis recovery. Thus, in the first few days after the irradiation a drop in the number of CFU is observed compared to the control, which continues until the 9th day. Subsequently there is a sharp increase in the number of CFU in cell culture, which continues until the complete recovery of hematopoiesis. The obtained data, recalculated per mouse femur, correspond to the results of colony forming in the spleen of irradiated animals, described by K. S. Chertkov and taken as a basis while developing our mathematical model, as well as to its parameters, which describe the process of hematopoiesis recovery., Conclusions: Conformity of the indices obtained during the cultivation using the method of gel diffusion chambers of mice bone marrow prolongedly irradiated at a total dose of 8 Gy with a power 0.0028 Gy/min, to the results of colony forming in spleen of lethally irradiated mice, which were the basis for mathematical model development, is the evidence of the feasibility of using a mathematical model to assess the process of hematopoiesis recovery by progenitor cells of different maturation levels, and the experimental approach of CFU growing in gel diffusion chambers can be considered as an additional method of researching the hematopoiesis recovery along with the spleen colony method., (D. I. Bilko, R. V. Boiko, I. Z. Russu, I. S. Dyagil, N. M. Bilko.)