სახარე ტბის ფსკერზე დალექილი მარილებიდან უწყლო ნატრიუმის სულფატის მიღების შესწავლა ექსპერიმენტის მათემატიკური დაგეგმვის გზით

This paper considers processes of electric arc damping by automatic switches in the short-circuit mode. Certain conditions for facilitating a successful short-circuit arc damping are shown, such as the limitation of the short-circuit current amplitude by its active resistance, the reduction of the phase shift between current and voltage, and the amplitude loss in returning and restoring voltages. The article features oscillograms of currents and voltages in the short-circuit mode. Anode heating processes are also described within the framework of the process of arc burning (heat saturation mode) and after the change of polarity current transition through zero processes at the cathode in the temperature equalization mode. Mathematical models of processes at the cathode took into account the thermal flows of the ionic component and evaporation. The calculations were carried out with the average values of thermal coefficients for copper, as the arc base moves from contacts to contact holders, which are made of copper and its alloys. The results of the calculations proved the validity of the considered mathematical models of thermal processes at both the cathode and the anode.

This article gives a brief description of the principles of organization of Internet education in the teaching of “Mathematical modeling of information technology and processes” to students on the basis of “Moodle LMS” system distance learning at the Tashkent Pharmaceutical Institute and shows its main features and advantages. Extensive use of educational technologies, optimization, humanization and innovation in the National Program of Personnel Training to solve the tasks of training and educating young people to be highly moral, spiritual and enlightened, conscientious at work, deeply aware of their responsibilities to society and family, competitive, qualified professionals. The organization, management and control of the learning process on the basis of methods is relevant. Nowadays, a wide range of opportunities are being created for students to have fast, plentiful, reliable information and to acquire knowledge independently. In particular, electronic systems allow students to use important information related to science at any distance, depending on their capabilities. “Moodle” open source software complex is a system designed specifically for the management of the educational process using the Internet (Learning management system - LMS). Distance learning is a modern form of organizing the learning process using distance learning technologies. Its development was due to the increase in the number of Internet users, the availability and quality of open learning electronic resources. The use of distance learning technologies undoubtedly has a wide range of advantages: the organization of the learning process in an Internet environment, so the student location does not prevent high-quality training, regardless of the location of the educational institution. Distance learning is based on the principle of independent preparation of students through teacher guidance and allows you to choose a convenient time for lessons. It includes interactive communication between teachers and students, information resources of the educational institution and information resources of the Internet, the rapid delivery of the Internet in electronic form.

The article provides a substantiation of the conceptual model of the production process of special forms of dumplings. It is the first stage in the development of a model of this process as a control object. The purpose of which is to form an objective basis for the development of an effective system for automatic process control. The development of the conceptual model presupposes the specification and description of the properties of control channels and acting disturbances to the level of their mathematical model, which can be implemented in a simulation environment. Problems of identification of the mathematical model of the process of the production of dumplings, i. e. obtaining a mathematical description of processes based on the results of its purposeful experimental research, due to its complexity as a control object.The experimental approach, in this case, gives much more reliable results on the properties of the process. An attempt to obtain such general properties on the basis of experimental data would inevitably lead to the need for very complex and lengthy multifactorial experiments and nontrivial procedures for their processing. But this will leave open the question of the adequacy of the model for those conditions of the process and types of raw materials that were not covered by the experiments. Fundamentally important is the fact that the mathematical model of the process is developed as a model of the control object.Model can be used in two ways. This is due to the fact that in the closed circuits of the SAC, the discrepancy between the models can be considered as a manifestation of uncontrolled coordinate and parametric disturbances. It is in conditions of this kind of disturbances that the SAC must fulfill its functional purpose. The developed mathematical model of the production process of special forms of dumplings will be used by us only in the direction, when it is of great importance not so much quantitative as its qualitative correspondence to the original object.

The underground coal gasification is a continually evolving technology, which converts coal to calorific gas. There are many important parameters in this technology, which are difficult to measure. These parameters include the underground cavity growth, amount gasified coal, and the leakage of input and output gaseous components into the surrounding layers during the coal gasification process. Mathematical modeling of this process is one of the possible alternatives for determining these unknown parameters. In this paper, the structure of the mathematical model of laboratory underground coal gasification process from the material balance aspect is presented. The material balance consists of mass components entering and leaving from the UCG process. The paper shows a material balance in the form of a general mass balance and atomic species balance. The material balance was testing by six UCG laboratory experiments, which were realized in two ex-situ reactors.

In this work a new nonlinear mathematical model of process of three level assimilation which is described by four-dimensional dynamic systems is offered. In case of constancy of coefficients special points of the dynamic system are found. The conditions on constant coefficients for which it is possible to find special points with all four coordinates non-negative are determined. Introducing some dependence among coefficients of the system, two first integrals are derived, and the four-dimensional system is reduced to a two-dimensional one.The sign-variable divergence theorem of a two-dimensional vector field in some one-coherent area of the first quadrant of the phase plane is proved. According to Bendixon’s criterion it is possible to have a closed integral curve completely lying in this area.Introduction. Mathematical modeling of physical processes has a long history. Mathematical modeling of physical processes involves the model adequacy, which is validated by Newton’s non-relative five laws of classical mechanics: mass conservation law; law of conservation of impulse; the law of conservation the momentum of impulse; the first law of thermodynamics, i.e. energy conservation law; the second law of thermodynamics, i.e. entropy conservation law [, , , , ].Creation of mathematical models is more original in social sphere, because, they are more difficult to substantiate [, , ].We created a new direction of mathematical modeling, i.e. “Mathematical Modeling of Information Warfare” [, , ]. In these models two antagonistic sides waging with each other information warfare and also the third peacekeeping side trying to extinguish information warfare are considered. Conditions on model parameters at which the third side will be able to force the conflicted sides to completion of information warfare are found.We also offered mathematical models of forecasting the results of political elections in case of two or three parties. Also models in case of change of selective subjects before the next elections have been considered [, , , , ].We proposed to create new nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (two countries or a country and its legal region) which consider economic or other type of cooperation between different parts of population aimed to the peaceful resolution of conflicts [, ].Taking into consideration the important tendencies in the world, it is important to study demographic and assimilation of social processes through mathematical modeling.In [] we considered a new nonlinear continuous mathematical model of linguistic globalization. Two categories of the world’s population are considered: a category that hinders and a category leading to the dominant position of the English language. With a positive demographic factor of the population, which prevents globalization or a negative demographic factor of the population contributing to globalization, it is shown that the dynamic systems describing these processes allow the existence of two topologically not equivalent phase portraits (a stable node, a limit cycle).It is known that, in the world, a social process of assimilation of languages is hidden. This process, as a rule, considers expansion of an area of the dominating languages (state languages of economically powerful states) at the expenses of less widespread languages (state languages economically of rather weak states).According to this point of view, today, for less widespread languages (including classic languages) the conditions under which there will be no disappearance of the major languages are important, i.e. there will be no full assimilation of people talking in these languages.

Model-to-model: Comparison of mathematical process models of lipase catalysed biodiesel production in a microreactor

A future-oriented approach is the application of Digital Twins for process development, optimization and finally during manufacturing. Digital Twins are detailed virtual representations of bioprocesses with predictive capabilities. In biotechnology, Digital Twins can be used to monitor processes and to provide data for process control and optimization. Central and crucial components of Digital Twins are mathematical process models, which are capable to describe and predict cultivations with high fidelity. Detailed mechanistic models in particular are suitable for both use in Digital Twins and for the development of process control strategies.In this chapter the requirements that process models must fulfil in order to be used for process optimization and finally in Digital Twins will be described. Different types of models, including mechanistic as well as compartmentalized models, are outlined and their application in Digital Twins and for process optimization is explained. Finally, a structured, compartmentalized process model, which was specifically designed for process optimization and has already been used in Digital Twins, is highlighted.

A mathematical model of thermodynamic processes occurring in the arcjet thruster device with using argon for arcjet working process carring out. A comparative analysis of the results of experimental data with theoretical data has been carried out. The purpose of the study is to develop a mathematical model of thermodynamic processes in the arcjet thruster device and simulate the interaction of argon with arc discharge plasma. The comparative analysis of the calculated parameters, thanks to the proximity of electron temperature values with the previously experimentally obtained under the static state in the arcjet thruster device, confirms the reliability of the presented mathematical model of plasma processes and the need for its improvement.

Analysis of the work, which considered the mathematical modeling of the melting process in various industries, currently does not pay attention to modeling the processes of heating and melting of hydrocarbon mixtures, such as vaseline, paraffin, fats, lanolin and others. The issue of optimization of heating and melting processes, calculations of necessary process parameters (speed and depth of thermal front penetration, etc.) and equipment, avoidance of repetition for each hydrocarbon mixture of experimental studies shows the need to develop a mathematical model of these processes. For the method of melting a substance placed in a cylindrical tank, based on the movement of a disc heating element under the action of gravity during melting and overflow of molten substance through the gaps between the disc and the walls of the tank, simulation has been carried out. Simulation of the melt flow in the annular gap is presented, which describes the laminar flow under the influence of the pressure drop and the velocity of the vessel wall relative to the heater, and the melt flow under the heater.

This paper is dealing with the optimization of the bio-scouring process in ultrasound on cotton & cottonised hemp fabrics. The tests were performed using an experimental program designed after a central, rotatable second order compound program with two independent variables CRSCP2IV. The mathematical models of the bio-scouring processes are needed for the optimization of the process parameters. Special knowledge is needed to operate such programs. That is why we also used a simpler yet effective software tool for modeling and decision making, including process optimization, the Fuzzy Inference System (FIS) from Matlab environment. The experimental data processed according to CRSCP2IV in Mathcad were processed in parallel with FIS in Matlab, which has high compatibility with all the important data processing and automate control products and offers numerous dedicated tools.

Providing growing economic needs is impossible without economic development. Economic development is associated with qualitative and structural changes in the economy, education, science, and culture. In accordance with the changes in society, the purpose of economic science also changes. There is a transition from observing the economy to influencing economic processes, their management, planning, forecasting, implementation of specific tasks at individual enterprises within certain terms in accordance with the general goals and interests of the national economy. The level of influence on economic phenomena varies from recommendations to specific methods of quantitative calculation, which provide an objective choice of an economic decision. Scientific management of economic processes can be carried out only on the basis of the application of precise mathematical methods in all spheres of the economy – from the distribution of minerals to the demand for consumer goods and household services, labor needs, planning of logistical tasks, etc. Therefore, the subject of the research is conducting mathematical modeling of an economic phenomenon, analysis of economic processes, using the methodology of economic-mathematical modeling and mathematical programming, with the aim of forecasting and studying one or another aspect of its development in the planning and management system, in information provision, in the possibility taking into account the dynamics of economic processes. The study of various economic phenomena with the help of economic-mathematical models, which are a simplified description and take into account the most significant and determining factors of the studied phenomenon, involves the use of mathematics for a formal description of the most significant relationships between economic variables and objects: conclusions can be obtained by the method of deduction, which are adequate for the object under study; methods of mathematics and statistics make it possible to obtain new knowledge about the researched object; the use of mathematical terminology allows you to accurately and compactly express the statements of economic theory, formulate its concepts and conclusions. The analysis of previous studies shows that the problems of organizing the teaching of mathematical disciplines in higher educational institutions, taking into account modern requirements, were taken care of by scientists: I.P. Vasylchenko, L.P. Husak, G.Ya. Dutka, T.V. Krylova, O.V. Levchuk, L.I. Nichugovska, V.A. Petruk et al. The need to build a holistic methodology for the introduction of higher mathematics, the theory of probabilities and mathematical statistics, mathematical modeling and optimization of economic processes is the key task of the article on the use of economic and mathematical models for the development and implementation of optimal projects for the development of the production and services market. Conclusion: to solve effectively a wide class of problems with appropriate solution methods, covering various problems of development and functioning of real economic systems, it is convenient to develop economic and mathematical models, which, in combination with powerful, high-speed computing equipment and modern software products, will make up decision-making support systems in various sectors of the economy.

The article presents mathematical model of interconnected physical processes on sintering machine during agglomeration of iron ore pellets. The mathematical model uses a system of partial differential equations. Velocity of the horizontal movement of the layer and the vertical velocity of the air movement through the layer as well as phase transition and simple chemical reactions of pellet and air components are taken into account in this model. The purpose of simulation is to determine the time dependency of sinter temperature distributed along the length and height of the layer and then define rational parameters for optimization of metallurgical process. In addition, concentration of sinter and gas components distributed along the height of the layer is computed. The numerical experiment shows that temperature front, which is lower in the layer cross-section, is sharper in comparison with the upper front, where the obtained agglomerate is cooled, as water requires a considerable amount of energy to evaporate. The obtained results are qualitatively consistent with the data in scientific literature.

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Mathematical models of competitive processes in the economy using known universal models that describe the behavior of counterparties in the market are found in this article. The object of research is to build mathematical models of competitive processes in a pair – secondhand dealer, and to process and convert the economic parameters that are necessary for the models. The methods of research use analysing and solving equations for the known and improved universal models that describe the behaviour of contractors in the market. Mathematical package for construction of schedules of dependences is used. The goals are to construct and research the modified model on the basis of mathematical model by Lotka- Volterra and its further development, and to create software product for statistical processing the economic information. Results – the mathematical model manufacturer – secondhand dealer is created, its modified version is received, and with the help of mathematical package Mathcad, researches of models were done. Prospects of the further improvement of models are revealed. The software product is developed, allowing to process the statistical economic information. On the basis of mathematical model by Lotka-Volterra and its further development a mathematical model of several producers and one middleman is created. Its modified version is studied using mathematical package Mathcad. The nonstable behavior of the counterparties is found. For this model some prospects for further improvements is identified.

This paper provides a synthesis of the concept of supply chain optimization. The aim of the research is to identify a supply chain optimization process, the key aspects in carrying out this process, and at the same time to emphasize the advantages that the optimization of companies' processes brings through the mathematical modeling of logistic processes that can be useful in the optimization of supply chains. In the research methodology it is used the Simplex transport algorithm. In a practical situation of a company with 3 warehouses and 4 clients, it allowed optimizing the transport routes and getting a minimal total cost for logistical delivery.