Application of numerical and physical modeling in designing of an X-ray luminescence separator intended for separation of ores containing luminescent minerals

The paper demonstrates the application of numerical and physical modeling to justify the design of the X-ray fluorescence separator’s material handling system. The Rocky DEM software package is a numerical modeling tool that uses the discrete element method as a mathematical apparatus. In order to increase the efficiency of the X-ray luminescence separation, the authors suggest including an additional element in the separator’s material handling system, i.e., a drum spreader that combines a handling device and an actuating mechanism. It was found out that the best loading of the drum spreader cells, in which the number of several pieces in one cell is reduced by at least 15%, is provided by a Vibrating feeder conveyor with a triangular cross-section of the profiled part of the tray compared with the tray of parabolic cross-section. In addition, the triangular section provides a double decrease in the number of pieces with rotational movement around their axes and, accordingly, an increase of at least 5% in the average velocity of the ore flow movement along the tray. The simulation of the material handling system has shown the need to reduce the height of the end partition of the drum spreader between the cells to 45 mm, which eliminates the collision of ore pieces with the partition and subsequently, their movement in the direction of rotation of the drum spreader on its outer surface, as well as the unpredictable escape of the ore pieces beyond the working space of the separator.

Sunflower Seed Cake and Larvae MassRheological Properties Analysis During Pressing WithVarying Temperature, Pressure and Oil Content

For the successful implementation of alternative protein sourcesforbiorefinery, optimization of the process parameters is crucial. Knowledge of the rheological propertiesis necessary for the design and development of appropriate equipment and process calculations.The objective of this research was to evaluate the effect of the following pre-treatments: temperature, pressure andeffect of initial oil content on the rheological properties of sunflower seedcake and larvae tissue. The rheological behavior of two protein sourceswas determined by using a rotational viscometer with a hydraulic system and thermostatic bath attached to the equipment. Using the mathematical apparatus and experimental data it was observed that the plastic viscosity of the sunflower seed cake corresponded to the viscosity of the vegetable oil, which confirmed the Bingham rheology assumption put forward in this work. For the larvae mass, a Hershey Buckley fluid model was proposed.A positive linear relationship was found for pressure and a negativelinear relationship was found for the oil content of the sunflower seed cake and larvae tissue on shear stress. Keywords: rheological property, sunflower seed cake, larvae, pulsed electricaldischarge, viscoplasticity flow, Bingham model, modelling

Simplest Flow Queuing Models for LEO Satellite System

The relevance of the work is associated with the active deployment of low-orbit communication systems and the expansion of research in the field of corresponding satellite systems. A promising low-orbit communication system based on relay satellites with the function (RSRFs) of routing message packets is considered. The low earth orbit communications systems use the BGP protocol and the AAA functionality at the ground station. For assessing the characteristics of RSRF inter-satellite paths, a scenario was created for the message packets arrival from a group of inter-satellite paths to one subscriber path. The corresponding analytical models have been developed using the mathematical apparatus of queuing systems with the simplest flows of requests and exponential distribution of the service time. The RSRF characteristics of a promising low-orbit communication system are predicted. It is proposed to make the mathematical apparatus of analytical models more complicated to take into account the dynamics of displacements and failures of the RSRF in a low-orbit communication system.

IMPLEMENTATION OF ADAPTIVE PRODUCT CUSTOMIZATION PROCESSES IN MASS PRODUCTION

The article presents the results of research and implementation of adaptive calibration systems used in setting up mass-produced products. The proposed method allows you to speed up the tuning of the HF transceiver. In the process of tuning, with the help of a neural network, an adaptive correction of the approximating function of the incident wave sensor is made according to the accumulated data, which makes it possible to reduce the time for tuning the transceiver. The introduction of the mathematical apparatus of neural networks can be applied in the process of mass production for other products.

FORMATION OF MATHEMATICAL APPARATUS OF METHODS OF FIRE AND EXPLOSION SAFETY CONTROL OF LANDFILL

The authors analyze the fire and explosion hazards of solid waste disposal facilities, taking into account current trends in the introduction of biogas (methane) collection and utilization systems. Methane is considered an alternative energy source for power plants. The authors determined the initial and limiting conditions of the mathematical apparatus of the method of combating fire and explosion hazards of solid waste disposal facilities based on the results of analysis and synthesis of factors of occurrence and spread of man-caused danger, existing mathematical models, and methods of counteracting man-caused danger. This is the basis for the further development of appropriate emergency response techniques. During the analysis, the authors found that humidity, the temperature of the landfill (household waste), the presence of sufficient oxygen at some point in time initiate the formation of explosive concentrations of methane in the array and contribute to the spread of hazards in landfills or dumps. The specific weight of the organic component, the value of the density of the array, the height of the landfill affect the process of counteracting the danger, namely the prevention of dangerous events and prevention of emergency from the object to the highest level of distribution (local level), primarily in the first group priorities, such as the number of victims and injured civilians and specialists of the units of the State Emergency Service of Ukraine. The team of authors has defined a system of equations of connection of the existence of the mathematical device taking into account initial and boundary conditions. A system of communication equations is determined taking into account the initial and boundary conditions of the mathematical apparatus, which allows to further develop a control algorithm for emergency response related to fire and explosion hazardous landfills close to settlements.

Probabilistic Combinatorial Model of the Epidemic for a University

The aim of the research was to identify the main causes of infection of teachers and students in a university. Two probabilistic combinatorial problems are considered analytically to determine the probabilities and rates of infection of teachers and students in a university as a result of the appearance of infected persons among the contingent of students. The mathematical apparatus of probability theory and combinatorics is used to solve the problems. For the factorials of combinations arising in the structure, the asymptotic Stirling’s formula is used. Convergent series arise in the final formulas, reflecting the multiplicity of scenarios of the probabilistic approach. Analytical formulas for the sums of series, probabilities and rates of infection of teachers and students are obtained. It is shown that the infection of teachers and students occurs through «dangerous» spatially close contacts, when a teacher and a student talk at a distance of less than 0.5 meter. It is impossible to exclude such contacts in the students’ environment during full-time study. Among teachers, there is also a less probable classroom mechanism of infection through the volume of air infected with viruses.

System-dynamic model of power redistribution among several subjects

A simple model simulating the redistribution of decision-making functions between the state, business, bureaucracy and regional elites is presented. The methodological basis of the work is system-dynamic modeling. The model is implemented in the specialized program Powersim Studio 10. A diagram of stocks and flows is considered, all elements of which were compared with certain political science concepts. The mathematical apparatus of the model is described. Some results of computer experiments are presented: these results indicate the operability and interpretability of the model.

STUDY OF DYNAMIC MODES OF THE SPEED-OPTIMIZED ELECTRIC DRIVE CONTROL SYSTEM UNDER CONDITIONS OF ALTER THE DESIGN VOLTAGE AMPLITUDE

The relevance of the work is due to the need to adapt the methods of the theory of optimal control to modern technical capabilities. The complexity of optimization of control systems by variational methods led to the creation of the N–i switching method. It is characterized by the simplicity of the mathematical apparatus, however, certain methodological aspects encourage research aimed at improving this method with a focus on software implementation. The purpose of this study is to develop the mathematical apparatus of the N–i switching method by developing a technique for correcting the settings of cascade structure relay systems for speed control of electric drives, based on the use of empirically obtained data. To achieve this goal, the following tasks were solved in the work: the parameters of the mathematical model of the electric drive were calculated, on which a series of numerical experiments were performed under the conditions of varying the calculated amplitude of the voltage of the power converter, which made it possible to reveal a stable pattern of changes in the speed of the system depending on the coefficient of the calculated voltage; built a calibration diagram, which is designed to determine the correction factor in the entire range of speed control. The revealed regularity is based on the indirect influence of the varied parameters on the conditions of controllers switching, the moments of occurrence and the nature of their sliding modes. The result of the work is a method for correcting the parameters of relay controllers, which brings the duration of the speed control of the electric drive closer to the empirically set optimal value. Its implementation does not require the involvement of large additional resources and provides an improvement in the quality of transient processes. The empirical component of the proposed optimization method consists not in the direct selection of one of the key parameters of the system, but in the preliminary refinement of the initial data, which is effective within the used synthesis method. The prospect of this study is an analytical solution to the problem of determining the correction coefficient, which will contribute to the practical application of the proposed optimization algorithm.

Limit theorems for Floyd's triangle: a new approach to not a new problem

Floyd's triangle is often presented to computer science students as an exercise or example to illustrate the concepts of text formatting and loop constructs. The paper proposes to look at an object from a different angle and to examine limit theorems for the numbers of generalized Floyd's triangles. Tasks of this type can be used as exercises in study programs of mathematics and informatics (couses of probability theory and combinatorics). It would help to master the appropriate proof techniques and mathematical apparatus. The article proposes a series of possible problems and their proof schemes.

PREDICTION OF THE OCCURRENCE AND DEVELOPMENT OF FATAL VASCULAR COMPLICATIONS IN COVID-19 USING FUZZY MATHEMATICAL MODELS

Целью исследования является разработка метода прогнозирования возникновения и развития тромботических осложнений (тромботических прецедентов), провоцируемых действием новой коронавирусной инфекции (COVID-19) на организм человека, позволяющего усовершенствовать лечебно-диагностические мероприятия для пациентов с данной патологией. В качестве базового математического аппарата была выбрана методология синтеза гибридных нечетких решающих правил, хорошо зарекомендовавшая себя в процессе решения задач с нечётким описанием исследуемых классов со структурой данных аналогичной решаемой в работе задачи. В ходе проводимых исследований были синтезированы математические модели прогнозирования возникновения и развития тромботических прецедентов. Экспертное оценивание и математическое моделирование показали, что уверенность в правильном принятии решений по прогнозу появления и развития исследуемого класса тромботических осложнений превышает величину 0,9. В работе получены нечёткие математические модели прогнозирования возникновения и развития тромботических прецедентов у людей с подтверждённой коронавирусной инфекцией, для которой ведущим фактором риска является вторичный антифосфолипидный синдром с возникновением микроангиопатии. В ходе проведенных исследований была показана целесообразность использования полученных результатов в практике работы таких врачей, как иммунологи, инфекционисты, пульмонологи, кардиологи и сердечно-сосудистые хирурги The aim of the study is to develop a method for predicting the occurrence and development of thrombotic complications (thrombotic precedents) provoked by the action of a new coronavirus infection (COVID-19) on the human body, which allows improving therapeutic and diagnostic measures for patients with this pathology. The methodology of synthesis of hybrid fuzzy decision rules was chosen as the basic mathematical apparatus, which proved itself well in the process of solving problems with a fuzzy description of the classes under study with a data structure similar to the problem being solved in the work. In the course of the research, mathematical models for predicting the occurrence and development of thrombotic precedents were synthesized. Expert evaluation and mathematical modeling have shown that confidence in the correct decision-making on the prognosis of the occurrence and development of the studied class of thrombotic complications exceeds 0.9. The paper presents fuzzy mathematical models for predicting the occurrence and development of thrombotic precedents in people with confirmed coronavirus infection, for which the leading risk factor is secondary antiphospholipid syndrome with the occurrence of microangiopathy. In the course of the conducted studies, the expediency of using the results obtained in the practice of such doctors as immunologists, infectious disease specialists, pulmonologists, cardiologists and cardiovascular surgeons was shown