Simulation reconstruction of the pilot ejection process using the K-36DM ejection seat

In the context of globalization processes, the professional activity of future economists is characterized by dynamism, complexity and uncertainty of conditions. Informatization and fundamentalization of knowledge provide relevance to such components of professional competence of the future economist as the ability to think analytically, solve predictive tasks using software products, implement economic and mathematical modeling using modern information systems, apply computer data processing technologies to solve economic problems. This provides the importance of mathematical training, as one of the fundamental, which primarily forms the skills of abstract thinking, analysis and synthesis. Thus, a new function of an educational institution arises in the process of providing educational services - the formation of a competence model of professional education of specialists. The article substantiates the expediency of introducing mathematical modeling based on Mathcad in the process of forming professional competence of future economists. The essence of the concepts of "professional competence" and "mathematical competence" of future economists are considered. It is argued that mathematical training is an important component of professional competence. Today, it is the results of mathematical modeling of real processes that generate the most progressive directions of development in science and technology. Therefore, the concept of an economic-mathematical model plays a fundamental role in the training of economists. The formation of professional competence of future economists, anticipating the integration of professional and personal development, should be carried out using mathematical modeling, starting with junior courses. However, despite the fact that the mathematical model of the process or phenomenon being studied in economics is always its generalized abstract reflection, the mathematical apparatus used is usually quite cumbersome. This is a significant obstacle in strengthening the applied orientation of mathematics in the first years. In our opinion, one of the effective ways to eliminate certain contradictions is the introduction of information technologies The purpose of this publication is to substantiate the feasibility of introducing mathematical modeling based on Mathcad in the process of forming professional competence of future economists, to determine the main didactic requirements and explore the impact of technology on the main components of mathematical training: motivational-value, cognitive, operational-activity, communicative. On the basis of what was studied, we concluded that for a specific specialty it is worth highlighting professionally significant topics, questions, concepts of classical sections of mathematics, which have their application in professionally-oriented disciplines. The introduction from the first course of professional-oriented tasks related to the specialty, even at the level of the simplest models, allows you to implement the principle of continuity in learning. Since the new content of mathematical disciplines becomes a reliable base for the study of professionally-oriented, within which more complex models are studied, with the help of which the key problems of the future profession are solved In the process of mathematical training of specialists, we used the universal integrated system Mathcad, which allows you to simply and visually enter the original data, carry out the traditional mathematical description of solutions and get the results of calculations using graphical interpretation. This made it possible to consider the simplest mathematical models and, using a complex mathematical apparatus, to develop universal models and algorithms. The main mathematical models of economic systems that are appropriate to consider in mathematical courses are highlighted. Examples of mathematical modeling based on Mathcad are given. The advantages of introducing mathematical modeling into the process of professional training are demonstrated. On the basis of the study, conclusions were drawn that mathematical modeling based on Mathcad allows to improve the main components of the process of mathematical preparation: - motivational and value (the formation of a sustained interest in the mastery of mathematical knowledge and information technology with a view to their application in professional and research activities); - cognitive (obtaining fundamental knowledge from the classical sections of mathematics and the ability to apply them in the process of mathematical modeling) - operational-activity (self-realization in professional activity by means of mathematical modeling based on the integration of knowledge across professional-oriented and mathematical disciplines using information technologies); - communicative (possession of ways of presenting the results of its activity-communicative (possession of ways of presenting the results of its activities). The study showed that the introduction of mathematical modeling should provide the following didactic requirements: - a fairly correct idea of ​​the teacher about the holistic picture of the future educational and professional activities of the student; - definition of goals and purpose of the introduced new content in the content of mathematical disciplines; - Compliance of the learning task with the ideas of the personal approach (updating the personal functions of specialists, consistency with the problems of practical training in production); - approbation of the skills and skills produced in practice. This allows you to organize student-centric education.

Ethanol is one of the most promising alternative fuels for Ukraine. To convert existing projects of power and cogeneration plants based on gas turbine engines (GTEs) operating on petroleum products and natural gas to ethanol, as well as for their design and performance calculation, it is necessary to have a mathematical model of the working process of GTE combustor. The object of the study is the working process of the GTE combustor fueling on ethanol. The subject of the study is a mathematical model of the working process of GTE combustor fueling on ethanol. The work aims to improve a mathematical model of the working process of a GTE combustor fueling on ethanol by changing the algorithm for calculation of the fuel air ratio, considering thermal dissociation, and a correctly formulated equivalent chemical reaction path of the combustion process. To achieve the aim, the following tasks were solved: based on the use of experimental values of specific isobaric heat capacities of combustion products, which are a function of temperature and pressure, a mathematical model of the working process of the GTE combustor was improved ("simplified" mathematical model); based on the solution of the system of equations of chemical thermodynamics, a mathematical model of the working process of the GTE combustor was developed ("complex" mathematical model); the results of calculation by "simplified" mathematical model of the working process of the GTE combustor were compared with the "complex" one. The following results were obtained: the difference in the calculation of the combustion products' thermodynamic parameters between the developed mathematical models was less than 1.2% for the three modes of the General Electric CF6-80A engine. Conclusion: the "simplified" mathematical model of the working process of the GTE combustor fueling on ethanol was improved. A feature of the model is the implicit consideration of the effect of thermal dissociation and correctly formulated equivalent chemical reaction path of the combustion process by using experimental values of specific isobaric heat capacities of combustion products. This will improve the accuracy of fuel air ratio calculation and other thermodynamic parameters of GTE combustor mathematical models fueling on ethanol, without significantly complicating the model algorithm.

The vertical motion of a flat material bent in a fold on a base plate between rotating pairs of shafts is investigated in the article. Roller pairs are located one above the other, and the distance between them is equal to the height of the base plate. The technological process is analytically considered to determine the energy consumption for the stable operation of the roller machine. Four cases of the state of the base plate during its movement between the pairs of shafts are considered. According to the conditions of the technological process, the positions of the base plate at the entrance between the bottom roller pair, between two pairs of shafts, at the exit between the bottom roller pair and the upper roller pair were studied. In the study, Newton's second law was used, and differential equations describing the technological process were obtained. Based on the solutions obtained, graphs of the dependence of the base plate velocity on the force of gravity and the friction coefficient were built. Graphical results were analyzed. Based on the results of calculations and graphs, the base plate motion at constant velocity was theoretically substantiated in the four cases considered.KeywordsPair of shaftsFlat materialBase plateGravityCoefficient of frictionExternal pressureReaction forceGrip zoneVelocityTime

Mathematical and optimization modelling in desalination: State-of-the-art and future direction

Clasiffication and Analysis of Typical Structures of Dynamic Systems of Machining of Low-Rigidity Shafts

A mathematical model of the desorption process based on the synthesised technological topology of the regeneration process gas components NH3 and CO2, was developed. The logical principle methodology of the mathematical modelling of desorption processes was worked out in detail. The mathematical model of the process, including the following: - The synthesized technological scheme of the desorption of components NH3 and CO2, with all the necessary requirements and limitations of the mathematical model; - The relevant multicomponent systems which exist in the process were defined in which the interphase transformation occurs; - The considered units (aparatus) are defined which make up the basic technological topology of the process; - Desorption processes in towers with different types of trays were defined and mathematically described; - The cooling process and condensation of gas phase in a complex multicomponent system was of the gas phase in a complex multicomponent system was defined and mathematically described. Many variants of the process were analyzed by using developed model with the aim of determining the relevant functional dependences between some basic parameters of the process. They will be published in the second part of this study.

CFD modeling of thermal processes in the firebox and heat load distribution on the screen surface firebox

Alexander G. Madera - Professor, Department of Mathematics of the Faculty of Economics, National Research University Higher School of EconomicsAddress: 20, Myasnitskaya Street, Moscow, 101000, Russian FederationE-mail: amadera@hse.ru This paper is devoted to mathematical modeling and optimization of business processes and process systems under conditions of uncertainty. At present, modeling of business processes is mainly descriptive, which does not allow quantitative modeling and optimization in the design of processes and process systems. In addition, the existing methods of decision-making in business processes are based on the assumption that the decisive factors are deterministic. Despite uncertainty of the real processes caused by the uncertainty of future costs of resources, the market environment, economy, finances, etc,, the factors of an uncertain future are either not taken into account, or are believed to be the same as those observed currently. In this paper, a stochastic interval mathematical optimization model is developed. This model allows us to simulate in a quantitative way the business processes and process systems in which they take place, taking into account the uncertainties of the future state of the economy, finances, market environment, costs of resources, as well as future realization of chances and risks related to the productive, supporting, and service processes. The criterion for optimality of the model is the maximization of the smallest deviation of the projected chances and risks, which makes it possible to make the best decision in the case that the most unfavorable conditions for the business process occur in the future. The criterion of optimality adopted in the mathematical model takes into account not only the uncertainty of the future state of the economy, finance, and market environment, but also the psychology of decision-making and the subjective nature of judgments and estimates. We present a concept and method for estimating the inductive (logical, subjective) probabilities of the occurrence of uncertain predicted business process factors. The models and methods developed in the paper make it possible to carry out mathematical modeling and optimization of business processes in a variety of activities without restrictions on the complexity of the structural model of the business process, the qualitative and quantitative composition of the connections in the process systems. On their basis, a software package for the quantitative design of business processes and process systems under conditions of uncertainty can be developed.

The article explores the vital subject of optimizing business process management, which is essential for enhancing the efficiency and competitiveness of enterprises. The study evaluates various perspectives, including economic, engineering, and managerial aspects, and underscores the importance of mathematical models over descriptive models in achieving precise and effective optimization. Descriptive models, despite their widespread use, do not guarantee optimal outcomes. The article emphasizes the need for mathematical models to accurately optimize business processes, considering various criteria and constraints. This approach aims to address the limitations of current descriptive models and advocates for the development of specific mathematical models to manage business process optimization under uncertainty. Key findings reveal that optimization in business process management has a significant impact on enterprise efficiency, productivity, and competitiveness. The process approach, which concentrates on enhancing individual business processes, is highlighted as a crucial paradigm in modern management. The research calls for further investigations to develop mathematical models that can deliver more reliable and precise optimization results, especially in uncertain conditions. In conclusion, the article supports the transition from descriptive to mathematical models in optimizing business process management to achieve maximum efficiency and competitiveness in enterprises. Future research will focus on developing mathematical optimization models for business processes, particularly those related to new product development under uncertain conditions. This shift is anticipated to offer more accurate and effective solutions for optimizing business processes in a dynamic and unpredictable business environment. Furthermore, the article highlights the need for continuous development and application of mathematical approaches to ensure that business processes are optimized effectively. It stresses the importance of incorporating various optimization criteria and constraints to achieve the best possible outcomes. By transitioning to mathematical models, businesses can better navigate the complexities and uncertainties inherent in today's competitive landscape, leading to improved performance and sustainable growth.

The analysis of the oscillatory process in a linear system of spring oscillators from several spherical bodies is carried out. The case is considered when one end of the system is fixed, and force acts on the opposite end. The cause of oscillations is the initial displacement of one or more bodies from the equilibrium state or an external load. It is shown that at a sufficiently large amplitude of the oscillations, neighboring bodies can come into contact with each other, as a result of which their velocities will change stepwise in accordance with the laws of conservation of kinetic energy and conservation of momenta. The mathematical model of the process is presented in the form of a system of second-order differential equations. The solution to the problem was obtained using the numerical Rung-Kutta method. For calculations, a program was developed in the C ++ algorithmic language, which allows you to build phase portraits taking into account the collision of neighboring elements, as well as determine the time dependences of the deviation and the speed of this deviation of each body. Variant calculations showed that the possibility of using a mathematical or physical model of the oscillatory process is determined by the ratio of the maximum amplitude to the diameter of the balls. If this ratio is much less than unity, you can use the model of mathematical oscillators. Otherwise, it is necessary to apply the model of physical oscillators. The adequacy of the physical model is maintained under any initial conditions and for any external load. The magnitude of the jumps usually increases in the direction from the first to the last oscillator, to which the force is applied. Fracture on the graph of the time dependence of the deviations of the balls from the equilibrium position at low load is usually manifested to a small extent. In this case, you should refer to the analysis of the phase portrait. Key words: oscillatory process, mathematical model, oscillator, phase portrait, physical oscillator.

The paper contains a proposal an original, extended mathematical model of an automatic system of human vision reaction to a forcing light pulse. A comprehensive mathematical model of the vision process was proposed in the form of an equation described in the frequency (dynamics) domain. Mathematical modelling of human senses is very important. It enables better integration of automation systems with a human cooperating with them, also as an automation system. This provides the basis for reasoning based on a mathematical model instead of intuitive reasoning about human reactions to visual stimuli. A block diagram of the proposed system with five human reaction paths is given. The following can be distinguished in the scheme: the main track consisting of: the transport delay of the eye reaction, the transport delay of the afferent nerves, the inertia of the brain with a preemptive action, the transport delay of the centrifugal nerves and the inertial and transport delay of the neuromotor system. In addition, the scheme of the system includes four tracks of negative feedback of motor and force reactions: upper eyelid, lower eyelid, pupil and lens. In the proposed model, the components of each path along with their partial mathematical models are given and discussed. For each reaction path, their overall mathematical models are also given. Taking into account the comprehensive models of all five reaction paths, a complete mathematical model of the automatic system of human reaction to a forcing light impulse is proposed. The proposed mathematical model opens up many possibilities for synchronizing it with mathematical models of many mechatronics and automation systems and their research. Optimizing the parameters of this model and its synchronization with specific models of automation systems is difficult and requires many numerical experiments. This approach enables the design of automation systems that are better synchronized with human reactions to existing stimuli and the selection of optimal parameters of their operation already in the design phase. The proposed model allows, for example, accurate determination of difficulty levels in computer games. Another example of the use of the proposed model is the study of human reactions to various situations generated virtually, for example in flight simulators and other similar ones.

Mathematical modeling of processes occurring in the biotechnological system, including those describing the interaction of functional microorganisms with contaminating microflora, is currently a promising scientific direction. The article discusses the issues of system analysis of the processes occurring in the biotechnological system during fermentation. By "microbiological system" is meant a microbiological process consisting of two subsystems or populations of microorganisms. During a given technological process, these populations interact with each other by using a common resource. Systems analysis and mathematical modeling of microbiological processes is a complex task. It is necessary to take into account a lot of factors, such as the simultaneous occurrence of several non-stationary processes; many state parameters, including analysis of the links between them; change in real time of technological parameters, in particular, the main resource, consideration of various properties of microbial populations affecting the behavior of microbiological systems (mortality, fertility, the existence of extraneous microflora, etc.), and other factors that have a direct impact on the quality of the finished product. In turn, a quantitative analysis of these interactions will lead to the development of scientifically based methods and approaches that minimize the effect of contamination. The analysis was carried out and a system model was constructed reflecting the entire spectrum of interactions between useful and extraneous populations of microorganisms in the production of bakery products. The presented system model allows to continue the study of the questions posed in the work, by further studying its components.

Unmanned aerial vehicles are by far the most promising military and civilian systems. There is a tendency to increase the efforts of a number of leading countries in the development of unmanned aerial vehicles and their complexes. The mathematical model of any system reflects in one way or another its real properties, including the existing limitations. It has been found that one of the most favorable and efficient methods for constructing mathematical models of automatic control systems is to develop them using transfer functions. In order to solve this problem, the article deals with the composition of the control system of a drone. A mathematical model consisting of the joint design of the unmanned aerial vehicle and its automatic control system has been synthesized. The description of the proposed mathematical model of the system is based on the representation of a linear continuous system by the difference equations obtained using the Tustin relation. The mathematical model proposed in the article can be used for the study of typical aircraft whose course management system is built according to the considered structure. The practical significance of the obtained results is the possibility of applying the developed mathematical model to study the dynamics of the change of state and to set up the system of automatic control of the course of the unmanned aerial vehicle through computer simulation. Prospects for further research in this area are computer simulation of an unmanned aerial vehicle control system and estimation of the accuracy of the mathematical model developed.

This work deals with a two-dimensional mathematical model of the micellar flooding process. It includes up to six components: oil, water, surfactant, polymer, and monovalent and divalent cations in two immiscible phases. We also incorporate the effects of adsorption, dispersion, inaccessible' pore volume, cation exchange and mass transfer between phases. The differential equations are solved by finite differences. Numerical dispersion is reduced by using two-point upstream weighting of concentration and saturation. Results from one-dimensional experiments indicate the model can be applied to displacements characterized by moderate dispersion levels. To approximate the time level, a procedure similar "to the IMPES technique is applied. The mechanism of oil mobilization by the micellar fluid is simulated by changing the relative permeabilities as the residual oil" saturation is reduced. The capillary-number concept is employed to correlate residual oil saturation with interfacial tension. Experimental data for a one-dimensional system were reproduced by the model with reasonable accuracy. Model performance was further analyzed by studying the effects of grid orientation, dispersion level and time-step size. It is concluded that cartesian grids can have a pronounced effect on the computed results, depending on their orientation. From a practical standpoint, time-step size limitations to guarantee tability are not so restrictive as to prevent one-dimensional; or small pilot-type, two-dimensional areal simulations. Introduction Micellar flooding is one of several enhanced recovery methods for recovering oil left after a waterflood. It involves injection of a micellar fluid into a reservoir to mobilize the oil by reducing the capillary forces that trap it in the pores. It has been demonstrated, in both laboratory and field tests, that residual oil saturation can be further reduced beyond waterflood values by this technique (1–8). Some of the more important considerations of the process are phase behaviour, adsorption, cation exchange, capillary number and dispersion effects. A few mathematical models of the process have been developed which include some of these concepts (9–14). Most of these models have been made for the purpose of translating laboratory results. However, they generally are not suitable for predicting field-scale tests due to various simplifying assumptions made in their development. Furthermore, they are mostly limited to one-dimensional flow*. For field-scale applications, two-dimensional geometry must be considered. Also, capillary and gravitational forces cannot be overlooked. Similarly, the dispersive transport of the miscible components should be included. In this study, a two-dimensional, two-phase micellar flooding simulator is presented. The model includes up to six components-oil, water, surfactant, polymer, sodium and calcium. The flow of the two immiscible phases is governed by Darcy's Law, and hydrodynamic dispersion is permitted between the components within a phase. Phase behaviour is accounted for by allowing the oil, water and surfacant to partition between phases. Ion exchange, adsorption, inaccessible pore volume and capillary number are incorporated. The results obtained with the simulator are compared with published data. A history match with a laboratory test was executed, and the effects of relative permeability and phase behaviour were analyzed.

The mathematical model of the mutual synchronization system, having ring form structure and composed of n (n ∈ N) oscillators, is investigated. The mathematical model of the system is the matrix differential equation with delayed argument. The solution of the matrix differential equation with delayed argument is obtained applying the Lambert function method. Using obtained solution, the transients in the system are examined. The results of calculations, received by the Lambert function method, are compared with the results, obtained by the exact method of consequent integration.Keywordssynchronization systemdifferential equationsdelayed argumentsLambert function