Risk map as a tool of the effective management of the company, the goal of a risk map, methods, quantitative evaluation and modeling of risk maps for the successful activity of organization are viewed in this article.

A method of solving symmetric polynomials of two variables is presented in the article. Several of such problems have been solved. There are very hard problems among them which were included in Mathematical Olympiads.

There has been researched the temperature field in the refractory bricks of the furnace. As a result, there has been received a scheme of temperature distribution in the furnace wall in the presence of installed water – cooled caissons.

The mathematical education of a pripary schoolchild is one of the directions at primary school. It gives an opportunity to a schoolchild to master successfully the program of secondary and high school. The question of education actions formation for junior schoolchildren through geometric training is considered in this article.

The main purpose of the new test materials: tests, test items is an objective assessment of the level of mastery of knowledge , skills and abilities , relevant state general education standards in mathematics and the ability to apply them in real life ( in extracurricular life situations ). The article deals with technology making control gauges in mathematics at the secondary school, is an example of the development of such a meter

An interdisciplinary connection in the school learning process is a necessary condition for successful teaching. Properly executed drawing of geometric shapes according to the rules of rectangular projection is one of the solutions of mathematical problems in geometry. Such ways of construction as the replacement of the projection planes, rotation and alignment demonstrate finding out of an actual size of a segment and a plane.

In this article the study of knowledge control patterns in math class with the help of computer-based testing. Displaying several models of construction of test tasks . Highlight the advantages of computer-based testing. The theoretical foundations of mathematical modeling.

This article mainly deals with the role of healthy lifestyle in strengthening pupils` health. The relevance of the issue of healthy lifestyle modeling arises out of the fact that heath is one of the most significant life values of a person and a guarantee of his or her welfare longevity. Currently, due to the low life expectancy of people, it is crucial to foster the meaning of health as the main value in one`s life and importance and necessity of health preservation from the early childhood. Life preservation requires dedicated and persistent efforts from every person. Herewith, it is necessary to understand one fact: life preservation is a personal prerogative. If one is to always be healthy one must remember that it requires persistent, dedicated and considerable efforts. Therefore, it is crucial to have a long course of personal conduct that designates the general culture of our labour and rest management, rational combination of physical and mental workload, sensible nutrition, active leisure and good quality sleep, and, moreover, skills of safe conduct in different dangerous emergencies. All of it composes the system of healthy lifestyle.

The article presents a study of the effect of a resistor in a network neutral point from 6 to 35 kV on the conductive electromagnetic interference with the ground-fault current. A mathematical model is proposed.

The article deals with the application of information and communication technologies in the teaching of mathematics. These technologies contribute to the development of independent thinking, help to rationally use time, form interdisciplinary communication.

This article reveals the possibility of solving life situations with combinatorial coefficients and shows the practicality of applying formulas on the theory of probability and mathematical statistics. The solution of tasks with combinatorial coefficients consists mainly in the decomposition of these coefficients by the basic formulas and their manipulations.

In this article on the materials of "Gamma" LLP and with the help of Rational Rose visual modeling of processes for automation of the service center is conducted.

The article considers basic principles and approaches for creation of an electronic textbook, the stages of introduction of information and communication technologies in the learning process. The main stages of creating an electronic publication in accordance with the requirements for the development of a modern textbook are presented.

This article describes the ways in which students can develop logical thinking skills. Currently, any form of the exam takes precedence over logic. Accordingly, the article grouped logical tasks and provided their solutions.

The paper is devoted to solving logistics problems based on information technologies. Petri net-based modeling is proposed as a solution method. The paper describes solution of the problem of supply chain management based on the Petri net.

The article is devoted to solving the optimization problem of finding an energy-efficient mode operation of one of the types of energy-intensive industries with the properties nonlinearity, inertia, and isolation. An optimization model based on a genetic algorithm is considered as a solution method. Moreover, the calculation of the fitness function for the selection of chromosomes is proposed to be calculated on the basis of fuzzy logic

The article provides a mathematical description of an induction motor with a device for indirect control of the electromagnetic moment and angular velocity of an induction motor in an electric drive, which allows substantiating on its basis a method for controlling the output variables of an asynchronous electric motor. A simulation model of an induction motor with an indirect control device for the output variables of an induction motor and the main results of the study are presented.

The article is devoted to the task of automating the assessment of the electrical safety level of electrical installations based on the determination of the electrical resistivity of soil layers ρ in specific climatic conditions. The soil ρ value depends on many factors, which can vary significantly during the year. Therefore, the decision was made using modeling based on one of the areas of artificial intelligence: fuzzy logic.

In the article presents the results of studies on the effect of temperature and pressure on the chloride sublimation of zinc and lead from converter dusts of steel production. Currently, an objective necessity is the development of dust utilization technologies for converter steel production, with its further use in production and production of by-products. The use of dust allows not only to save natural raw materials, but also increases production efficiency and improves the environmental situation. The content of non-ferrous metals in dusts makes it difficult to process and use them in agglomeration or in blast furnace production, while the iron content in converter dusts (sludges) makes it possible to use them as promising metallurgical raw materials. Therefore, for a more complete processing of dusts, extraction of non-ferrous metals from them is proposed. The purpose of this work was to determine the possibility of extracting zinc and lead from sludges of the converter production by the method of chloride sublimation. We used dust containing: 86,3 % Fe2O3, 3,5 % FeO, 0,9 % Al2O3, 1,6 % CaO, 0,9 % MgO, 1,1 % MnO, 0,8 % SiO2, 4,4 % ZnO, 0,5 % PbO. The study was conducted in the temperature range 200-1600 degrees C and pressures of 0,01; 0,1 and 1 bar based on a complete thermodynamic analysis using the HSC – 5.1 software package. Finnish metallurgical company Outokumpu, based on the principle of minimum Gibbs energy. According to the results of the studies, it was found that, at normal pressure, lead chloride sublimationbegins at a temperature of 600 degrees С, and zinc - at 900 degrees С: a decrease in pressure to 0,01 bar reduces the temperature to 500 degrees С and 700 degrees С, respectively; lead chloride sublimation under equal conditions is more complete than zinc; To achieve zinc chloride distillation at the level of 90-96 %, the process must be carried out at 1145-1200 degrees С and pressure from logP = -2 to 1,2 bar, while the degree of lead chloride distillation is 99,8-100 %.

When managing a filling station chain, it is necessary to solve the following tasks in dynamics: determining the volume of purchases by types of oil products sold and redistributing the available volume of various types of oil products to filling station chain. The peculiarity of this control task is that the replenishment of the storage of oil products is carried out centrally, and the sale of each type of fuel is carried out at separate filling stations of the network, that is, in many points. At the same time, the volume of each type of fuel sold by each station of the network should be taken into account separately, taking into account the seasonal demand for a specific oil product. In addition to modeling demand, information is needed on the volume of petroleum products that can be purchased from suppliers with the possibility of increasing or decreasing the volume of purchases due to demand. To solve this problem, a list of suppliers of a specific type of oil product with a possible range of supply volumes must be determined. In the proposed model, an attempt is made to solve the above problems. To solve them, a management model was developed, which was implemented using the Visual Studio C # programming environment and MS SQLServer DBMS. When developing the structure of the database tables, the task of managing a network of filling stations based on the Petri net was taken into account: that is, the database tables provided for storing information on the volumes of supplies of petroleum products, the volume of sales of each type of petroleum product, as well as the time of deliveries and sales. To solve the problem of centralized procurement for all types of fuel, the database provided tables with information about suppliers and possible volumes of supplies by them of various types of petroleum products. To solve the problems of forecasting demand, the model includes algorithms for predicting the volume of sales of petroleum products based on the accumulated time series of data for each type of fuel separately. The forecasting was carried out in order to assess the required volumes of purchases of oil products for the coming period. The prediction algorithms are implemented using two methods: linear approximation and exponential smoothing. Both algorithms take into account the seasonality of demand.

The article is devoted to the mathematical modulation of a complex of experimental data obtained in the process of experimental studies of processed cheese products, processed by mathematical methods. The purpose of this study is to establish the type and amount of the melting salt that promotes the formation of the plastic structure of the processed cheese product. The analysis of scientific research in the field of food technologies showed that mathematical modeling is used in the following areas: clarification of the modes of technological processes, design of recipes and assessment of the quality of finished products, as well as forecasting the shelf life of new products when they are put into production. The most relevant in describing the processes of food production are models of multivariate variance-regression analysis using methods of mathematical planning of the experiment. The authors carried out mathematical modeling and established graphical dependencies characterizing the degree of influence of the regulated factors X1 and X2 on the controlled ones that determine the quality and safety of processed cheese products. It is important that the mathematical analysis of the graphical dependences of the rheological parameters on the adjustable factors indicates the reliability of the data obtained. It is concluded that an increase in the melting salt dose leads to an increase in the – limit shear stress, which reflects the nature and state of the consistency of the processed cheese product. The process of normalization of the controlled factors by the maximum value was carried out. Graphical dependencies were built and regression analysis was performed, the results of which allow an objective assessment of the degree of influence of the type and dose of the melting salt on the chemical and organoleptic characteristics of the test products. The authors have proven that the optimal efficiency of transforming the structure of the constituent components of the recipe into a plastic structure of a processed cheese product that is stable during storage is provided by a combination of adjustable factors X1 (Solva 85) and X2 (Solva 120) taken in a ratio of 1: 1, with a total amount of 1,2 mas.%. At the same time, the quality indicators of the experimental products are characterized by the following values of the controlled factors: У1 – 1280 Pa; У2 – 9 points, У3 – 9,301 (2,0-2,2109 colony forming units /g).

Basic problem: the Republic of Kazakhstan is a platform for implementing innovative projects in all spheres of the economy, providing the younger generation with resource centers, technological parks, agricultural equipment, industrial technologies and scientific and educational complexes. The main goal of such actions is to activate scientific research, increase the technological potential of the industrial sectors of the national economy, and stimulate the development of innovative activities in the field of research and development. The problems of developing an entrepreneurial culture are a cornerstone issue that combines a combination of motivational principles for generating and promoting ideas, activating youth entrepreneurship as the flagship of the future economy, and a complex epidemiological situation in the world that hinders not only the development of entrepreneurship, but also the course of all socio-economic processes in society. Purpose: The purpose of this study is to identify the problems of youth entrepreneurship and find ways to solve them in accordance with the principles and methods of implementation, including the unit economics. Methods: the research Area focuses on economic modeling techniques that are successfully used in international practice to determine the profitability of business models, taking into account the effect of the production of a unit of goods / services or a single client / customer. The implementation of this approach is facilitated by the use of traditional methods of scientific research, such as analysis, comparison, and a graphical method for visualizing the results obtained; quantification method and parametric method as an evaluation tool that allows formalizing the procedure for evaluating the performance of unit economics models. Results and their significance: when considering business models in relation to youth entrepreneurship, attention is paid to the skills and competencies that students who study the disciplines of the entrepreneurial block in higher education receive. The proposed methods of unit economics are actively used in the development and promotion of startups, as an integral part of business plans. It is concluded that youth business has started to play a crucial role in solving socio-economic problems, such as creating new jobs and reducing the unemployment rate, and training qualified personnel. The set of proposed measures provides additional opportunities and increases the influence of youth entrepreneurship, which becomes the basis for unlocking its potential.

The main problem: The article deals with the issues of hiding text information in a graphic file. A formula for hiding text information in image pixels is proposed. A steganography scheme for embedding secret text in random image pixels has been developed. Random bytes are pre-embedded in each row of pixels in the source image. As a result of the operations performed, a key image is obtained. The text codes are embedded in random bytes of pixels of a given RGB channel. To form a secret message, the characters of the ASCII code table are used. Demo encryption and decryption programs have been developed in the Python 3.5.2 programming language. A graphic file is used as the decryption key. Purpose: To develop an algorithm for embedding text information in random pixels of an image. Methods: Among the methods of hiding information in graphic images, the LSB method of hiding information is widely used, in which the lower bits in the image bytes responsible for color encoding are replaced by the bits of the secret message. Analysis of methods of hiding information in graphic files and modeling of algorithms showed an increase in the level of protection of hidden information from detection. Results and their significance: Using the proposed steganography scheme and the algorithm for embedding bytes of a secret message in a graphic file, protection against detection of hidden information is significantly increased. The advantage of this steganography scheme is that for decryption, a key image is used, in which random bytes are pre-embedded. In addition, the entire pixel bits of the container image are used to display the color shades. It can also be noted that the developed steganography scheme allows not only to transmit secret information, but also to add digital fingerprints or hidden tags to the image.

Currently, the problems of environmental safety are facing society. The industry develops every year. In this critical economic situation, the oil industry is a stimulant for the economic sector in Azerbaijan. The level of development of this industry is also relevant due to other reasons: sociological, technological and features of the economy of Azerbaijan. The production activity of oil processing, concentrating harmful substances and energy, is a source of man-made danger and pollution of the natural environment. The risk management process mainly consists of three stages - risk safety analysis, risk assessment, which is carried out in comparison of calculated and actual risk levels, the so-called acceptable risk levels and the adoption of appropriate regulations and management decisions. One of the factors that should be taken into account when assessing risk and safety is to determine the necessary costs. Since these costs are paid directly to the company, they try to minimize them as much as possible, which reduce the accuracy of risk assessment. One of the objectives of the study is to determine the optimal value of the necessary costs. It is established that the less reliable the method, the lower is the cost of its implementation. The methodological basis of the work was scientific works on these problems of scientists-economists, mathematicians on safety and risk assessment at industrial enterprises. When developing the presented methodology, computational algorithms developed by Dow Chemical were used. This company has collected a large volume of material on accident statistics, taking into account damages. Based on the obtained and experimentally verified data, a system of indices has been developed, an assessment of various indicators for qualitative and quantitative risk assessment of oil refineries. The analysis of the technogenic danger of oil refineries makes it possible to determine ecological and economic losses and choose rational possibilities of acceptable risk. The required costs, depending on the level of risk, are determined based on an increase in the accuracy of calculating the probability of occurrence of the cause of risks. The article examines the relationship between the expected level of risk and economic losses during oil refining in separate technological units, which allow determining the required level of risk and the expected economic damage.

Singularly perturbed partial differential equations with small parameters with higher derivatives deserve special attention, which often arise in a variety of applied problems and are used in describing mathematical models of diffusion processes, absorption taking into account small diffusion, filtration of liquids in porous media, chemical kinetics, chromatography, heat and mass transfer, hydrodynamics and many other fields. It is necessary to consider the creation of an asymptotic classification of solutions of singularly perturbed equations using a well-known approach to solving the boundary value problem. In this case, the singular problem is understood as the problem of constructing the asymptotics of the solution of the Cauchy problem for a system of ordinary differential equations with a small parameter with a large derivative. The asymptotics of the solution in all cases is based on the last time interval or the construction of a boundary value problem for a system with a weak clot in an asymptotically large time interval. Purpose - to construct and substantiate the asymptotics of solving a singular initial problem for a system of two nonlinear ordinary differential equations with a small parameter; To date, a number of methods have been developed for constructing asymptotic expansions of solutions to various problems. This is the method of boundary functions developed in the works of A.B. Vasilyeva, M.I. Vishik, L.A. Lusternik, V.F. Butuzov; the regularization method of S. A. Lomov, methods of averaging, VKB, splicing of asymptotic decompositions of A.M. Ilyin and others. All the above methods allow us to obtain asymptotic expansions of solutions for wide classes of equations. At the same time, such singularly perturbed problems often arise, to which ready-made methods are not applicable or do not allow to obtain an effective result. Therefore, the development of methods for solving equations remains a very urgent problem. As a result of the study, an algorithm for constructing an asymptotic classification of the initial solution of the problem with a singular perturbation is given, and approaches to estimating the residual term are also shown.

It is known that an increase in the volume of production in any sphere of production as a consequence increases the intensity of anthropogenic impact on the environment, including the atmosphere. This problem is especially typical for oil refineries. On the one hand, this is due to the complexity of oil refining processes and the release of various hydrocarbon compounds into the atmosphere during processing. Therefore, when implementing sustainable ecological and economic development in the Azerbaijani regions that are associated with oil refining, an increase in the volume of products should not create an increase in environmental impact. This problem is considered one of the factors directly affecting the economic situation of the enterprise, as well as creating certain environmental, social and economic problems for society as a whole. The purpose is to study the possibility of using the correlation-regression method in solving the problem of determining the presence of the decapling effect. The relationship between the volume of petroleum products produced and the amount of pollutants released into the atmosphere is random and is characterized by stochastic and statistical dependence. At the same time, on the basis of a mutual comparison of the methods of correlation and regression analysis and the method of production function, the effectiveness of correlation and regression analysis is determined. The methodological basis of the work was the scientific works of scientists-economists, mathematicians providing the definition of the decoupling effect at industrial enterprises. In the presented methodology, the obtained estimates of the performed in real time vary depending on the values of the set parameter. When developing the presented methodology, the STATISTIKA software package was used. This program was developed by StatSoft. Based on the obtained and experimentally verified data, the equation of linear regression dependence is determined. During the research, it was found that in some cases it is not possible to evaluate the statistical characteristics of a random variable or it is accompanied by serious errors. Therefore, when processing data, instead of mathematical expectations and variances, we used selective mathematical expectations and variances. The analysis of the ecological and economic situation of oil refineries based on correlation and regression analysis allows us to determine the presence of the decapling effect. The obtained correlation coefficient between the volume of production oil products and the volume of emissions into the atmosphere shows that there is no statistically significant relationship between these parameters. Thus, there is an achievement of the decoupling effect between the production of petroleum products and the volume of emissions of pollutants into the atmosphere.

Local self-government bodies are an integral mechanism of the foundation of a democratic state. In the modern system of public relations, one of the most important places is occupied by general economic relations, namely local self-government. Without a developed system of local self-government, legislative and real opportunities, it is very difficult to independently create market-democratic structures to solve economic, social, domestic, cultural and other issues at the local level. Local self-government bodies are a special level of government, which combines two principles: public and state. In the practice of Constitutional and administrative law, it is important to determine the place and nature of local self-government and to establish balanced relations between State authorities and self-government bodies, on the one hand, with local representative offices and structures. The purpose of the article isto study the role and place of local self-government in modern society, to develop practical recommendations on the formation and prospects for the development of local authorities in Kazakhstan. When writing an article, the following methods are used: description, analysis and synthesis, justification, logical modeling, system analysis, etc. When studying the formation of local self-government, as well as the functional management system, the method of structural and analytical analysis was used. The conclusions and recommendations obtained as a result of the conducted research can be used: in the practical activities of maslikhats and akimats of the Republic of Kazakhstan, civil servants; in the process of studying at courses in higher educational institutions, as well as for further general theoretical and applied research.

Main problem: Today electronic information is one of the important resources in the management system. Electronic information resources are not only means, but also control flows. For example, any instruction or instruction in the management system is actually a guide to action. At the same time, for example, data on the movement of an object (employees, goods, money, etc.) are information resources, the storage and accounting of which is the basis of the organizational process. Large flows of information require their structuring, and operations on them become time-consuming. One of the ways to solve this problem is the development and implementation of an information system. Purpose: To analyze and design an information system using specialized tools designed to optimize the implementation of the above stages of software system development, using the example of a real business process. Methods: The article discusses the methodologies of CASE tools designed to automate software development processes, namely, the first two stages of the life cycle: analysis and design of a software product. The analysis and design of the business process functionality is carried out using the IDEF0 functional modeling methodology. The design of the database structure of the information system was carried out using the methodology of semantic (information) modeling IDEF1X. Description of the scenario of the designed software for a real business process is carried out using the dynamic modeling methodology IDEF3. Results and their significance: The article substantiates the relevance of the use of modern CASE-technologies in the process of analyzing and designing a future information system, as well as for the purpose of possible optimization on the example of a real business process "Inventory accounting". As a result, a comprehensive business process model was built using tools based on CASE-methodologies. The resulting model, as well as the description of its construction, is a clear example of the use of CASE technologies for software developers, as well as system analysts and IT specialists.

The main problem: Modern research in the development of fermented milk products is focused on increasing the bioavailability of milk components, as well as the use of bacterial components of sourdough, which increase health properties. The use of the fermentation process of skimmed milk with a combined starter consisting of traditional for cottage cheese and starter cultures of probiotic cultures immobilized in a gel of biopolymers is very important. Purpose: The purpose of this study is to determine the optimal amount of starter, consisting of an association of probiotic cultures immobilized in a gel of biopolymers (membranes) to be added to fermented skimmed milk in order to enrich it with functional ingredients. Methods: A one-factor experiment was used. The culture association Propionibacterium freudenreichii subsp. was used as a regulatory factor. Shermanii, Bifidobacterium lactis and Streptococcus thermophilus, immobilized in a biopolymer gel, added to skimmed milk in the form of membranes (determined as a percentage of the mass of fermented milk). Controlled factors are the main indicators characterizing the efficiency of the skim milk fermentation process; these are active acidity, the logarithm of the number of viable cells of bifidobacteria, the logarithm of the number of viable cells of propionic acid bacteria, and organoleptic evaluation. Results and their significance: Based on the results of a mathematical analysis of the totality of values of controlled factors depending on the amount of starter cultures of probiotic cultures, mathematical models were built to determine the degree of influence of the starter on the quality indicators of the product, using the Table Curve 3D-v4 mathematical computer program.

Main problem: It is very important for each company to obtain an industrial certificate, which makes it possible to get into the Register of Domestic Manufacturers, as they expect to receive large orders. With the receipt of an industrial certificate, their prospects for participation in various tenders and purchases will significantly increase, where they can show their abilities, compete with domestic producers, and also have an advantage over importers. Since July 1, 2019, the industrial certificate has become mandatory for participation in public procurement. Corresponding changes to the rules for public procurement were made by the Ministry of Finance of the Republic of Kazakhstan. Taking into account the experience of the «Rules for determining the country of origin of goods, issuing a certificate of origin of goods and canceling its validity», approved by Order of the Acting Minister for Investment and Development of the Republic of Kazakhstan dated February 24, 2015. No. 155», it becomes clear that the document does not take into account a number of «narrow» specifics of individual industries. Purpose: development of amendments and additions to the «Rules for the formation and maintenance of the register of domestic producers of goods, works and services, as well as the issuance of an Industrial Certificate» for the subsequent possibility of obtaining an Industrial Certificate by a chemical industry enterprise for the production of mineral fertilizers. Methods: study and analysis of literary sources, statistics and modeling of the procedure for issuing an Industrial Certificate. Results and their significance: the problems of application were studied, ways to solve these problems were found, and amendments and additions to the “Rules for the formation and maintenance of the register of domestic producers of goods, works and services, as well as the issuance of an industrial certificate” were developed. At the moment, the Rules need to be carefully finalized. It is necessary to consider this issue together with authorized state bodies, associations and business representatives, since obtaining an Industrial Certificate will directly affect participation in public procurement, and, accordingly, the economy of the Republic of Kazakhstan.

Based on the psychological aspect of the concept of "qualification", the article analyzes the main directions of the formation of methodological qualifications of future teachers of mathematics and advanced training in pedagogical universities. It is possible to achieve high-quality teaching of geometric subjects in higher educational institutions by using methodological and meaningful methods in organizing the educational process. The creation of a certain structure of the educational process, the definition of teaching methods and means, the careful selection of subject content were determined by the specific principles of pedagogy. Basically, these principles are the real achievements of modern pedagogy and are constantly changing. The existing system of didactic principles can be gradually changed and expanded The purpose is to choose the main didactic principles and to offer a scientific-methodological basis for improving the methodological preparation of future mathematics teachers in the Pedagogical University for solving and teaching geometrical problems. In this regard, interviews, questionnaires, analysis of the curriculum and its content, as well as discussions with experienced teachers and methodologists in teaching geometry were conducted; pedagogical control and diagnostics of the educational process were carried out. In order to test the effectiveness of the methods proposed by us, pedagogical experiments were carried out. The entire system of training future teachers of mathematics faces new challenges related to the implementation of effective didactic principles for teaching geometry in pedagogical universities. First of all, it is the principle of mastering innovative teaching methods of the future teacher of mathematics and the principle of mastering new pedagogical and information technologies of education. The results of the study can be used as a methodological basis for further research on the professional orientation of teaching mathematics in universities.

Main problem: the article is devoted to the issue of designing basic recipes for dairy products using mathematical modeling methods. The author analyzed the problems in the field of food technology and concluded that mathematical modeling is used in the following areas: clarification of technological process modes, designing recipes and assessing the quality of finished products, as well as predicting the shelf life of new products when they are put into production. The use of dihydroquercetin as a drug that prevents the oxidation of milk fat in the design of dairy products is substantiated. Mathematical modeling was carried out on the basis of experimental and analytical material obtained in laboratory and production conditions. Based on the maximum value of the objective functions, the optimal normalized mixtures and the maximum allowable concentration of dihydroquercetin were selected. The analysis of the received mathematical dependences and models is carried out, the system of linear equations is made. Purpose: to study the effect of natural bioflavonoid antioxidant on the oxidative processes of milk fat and the viability of lactic acid cultures and their associations by mathematical modeling in order to use it in the technology of a new product; conduct an analysis of mathematical dependencies and models, compose a system of linear equations. Methods: the article uses the method of mathematical analysis and the matrix method. Results and their significance: a mathematical model was developed for the dependence of the viability of probiotic cultures on the mass fraction of dihydroquercetin when designing recipes for a creamy-protein curd product, a matrix of the chemical composition of dairy ingredients was presented, and a system of linear equations for basic recipes was compiled. In the course of the study, the spatial configurations of dihydroquercetin, as well as its effect on the oxidative processes of milk fat, were studied. Mathematical modeling of experimental data on the study of the effect of dihydroquercetin on the viability of microorganisms with probiotic properties was carried out. The normalization of the complex of obtained results on the study of the influence of the mass fraction of dihydroquercetin on the fermentation process was studied. Controlled factors characterizing the process of fermentation of model media with dihydroquercetin have been determined. A rationing of the dihydroquercetin complex of more than 0.50% was established; the target function decreases to its minimum value of 0.53 with a mass fraction of dihydroquercetin of 1.00%.

The ideas of accelerated disclosure of the spiritual, intellectual and professional potential of a person have always been occupied by scientists and teachers (Ya.A. Komensky, K.D. Ushinsky, V.A. Sukhomlinsky, Ya. Korchak, A.S. Makarenko, A. Kunanbayev, Y. Altynsarin and others). Modern innovative teachers are guided by a personality-oriented approach, the ideas of subject-subject relations, and generational cooperation. Georgian teacher Sh. A. Amonashvili wrote: «humanitarian pedagogy perceives the child by his nature. He sees the infinity of the child, understands his cosmic quality and prepares him for the service of humanity throughout his life. It establishes the personality of the child through the determination of his will and builds pedagogical systems, the procedural of which predetermines love, optimism and high spiritual morality. Humanitarian pedagogical thinking seeks to take on something enormous, and this is the power of educational systems and processes that have arisen in its bowels». In order to realize the value of self-disclosure of innovative abilities of students, ensuring the role of a teacher, it is necessary to recognize the intellectual reflexive mechanism of a person as the main subject of Education. The purpose of the article is to identify innovative methods and models of pedagogical activity for the cultivation of innovative abilities of students, which determine the development of the country. The study used methods such as analysis, generalization, synthesis, modeling of scientific sources.

Main problem: achievement of socio-economic sustainability in each locality depends on coordinated actions of executive and representative authorities, which should be focused on creating appropriate conditions for ensuring social standards and improving quality of life of rural population, as well as the development of main economic basis – agricultural production. In this context, in today’s reality, the urgent problem of sustainable development of rural settlements is provision of appropriate industrial and social infrastructure, because systemic development of rural regions depends on this rural infrastructure, which acts as an element of territorial socio-economic subsystem. Purpose: identification and studying of key factors that determines and contributes to balanced development of industrial and social infrastructure of rural regions of country in context of sustainable development goals and objectives. According to the results of the study, the main distinctive features of sustainable development of rural areas are determined due to the provision of industrial and social infrastructure of rural regions, which has a correlation with the level and quality of life of the rural population, as well as the final results of agricultural production. Methods: general methodological principles, systematic approach and empirical methods of economic cognition act as methodological basis for implementation of this study: economic and statistical models, forecasting and modeling, methods of induction and deduction, synthesis, and also logical methods. Results and their significance: results of research can be used as a practical basis in activity of local executive bodies and local self-government bodies. Their use is possible for scientific substantiation of development and implementation of comprehensive plans for development of industrial and social infrastructure of rural areas of region within framework of Regional Development Plan, focused on qualitative improvement of economic basis of villages and the well-being of all segments of rural population.

The present stage of development of power systems is characterized by the need to increase their intelligence, that is, the formation of an environment capable of solving the problems of effective management of all components included in the power system. One of the features of modern energy systems is an active consumer, that is, a consumer who has the opportunity to optimize the schedule of loading their capacities, planning energy consumption, intellectualization of energy consumption. In addition to the fact that there are digital systems for collecting, processing and presenting information, as well as transmitting this information via the Internet, to solve the most difficult task of managing power systems, it is necessary to develop a large number of models adequate to real processes that can describe the processes taking place in the power system under consideration. The purpose is to develop models capable of adequately describing the interrelated processes occurring in the considered elements of the power system, as well as in the aggregate of related elements; development of methods that allow solving problems of effective control of elements of energy systems on the basis of the proposed intelligent models. To solve the problem of increasing the intelligence of the power system, nonlinear adaptive models of electrical complexes of an energy-intensive enterprise included in the power system were developed on the basis of balance equations and artificial intelligence methods. The production of alumina with the properties of inertia, nonlinearity and closure is chosen as the production under consideration. This type of production was chosen as the most difficult to predict due to the unpredictability of changes in energy consumption during the transition to other modes of its operation, associated, for example, with the receipt of raw materials with a different chemical composition for processing. Static and dynamic models of energy consumption of electrotechnical complexes with continuous inertial nonlinear closed production based on artificial intelligence methods have been developed, which makes it possible to eliminate the need to use long time series of retrospective data. For the considered type of continuous energy-intensive production, dynamic characteristics of energy consumption and technological processes are obtained from the main controlled parameters, which make it possible to predict emergency situations and partly man-made disasters. On the basis of a genetic algorithm, a multiparametric optimization problem of energy management of continuous production has been solved, taking into account technological parameters and cost factors.

The article contains the results of a research work devoted to an important problem - the development, production and delivery to the consumer of fermented dairy products of a healthy diet fortified (enriched) with milk protein, a vitamin-mineral complex, and probiotics and prebiotics. Purpose is based on mathematical modeling of experimental data, to determine an effective fermented food system for use as the basis of a fortified (enriched) curd product for a healthy specialized diet; to develop a recipe and technology for its production; to study the nutritional, biological and energy value of a new product. Modern technologies and equipment were used in experimental studies: ultrafiltration, fortification, etc. The studies were carried out by standard physicochemical, microbiological methods in three to five repetitions. Mathematical and statistical processing of experimental data was carried out using the program "Statistica-6.0". A recipe and technology for the production of a curd product for a healthy specialized diet has been developed. Its nutritional, biological and energy value has been studied. The developed recipe and biotechnological parameters for the production of the curd product were tested in the industrial conditions of the leading enterprise JSC "Lyubinskiy MKK". The quality and safety of the curd product was studied in the laboratory of techno-chemical control of FGANU "VNIMI" (Moscow).

Main problem: local self-government bodies are an integral mechanism of the foundation of a democratic state. In the modern system of public relations, one of the most important places is occupied by general economic relations, namely local self-government. Without a developed system of local self-government, legislative and real opportunities, it is very difficult to independently create market-democratic structures to solve economic, social, domestic, cultural and other issues at the local level. Local self-government bodies are a special level of government, which combines two principles: public and state. In the practice of Constitutional and administrative law, it is important to determine the place and nature of local self-government and to establish balanced relations between State authorities and self-government bodies, on the one hand, with local representative offices and structures. Purpose: to study the role and place of local self-government in modern society, to develop practical recommendations on the formation and prospects for the development of local authorities in Kazakhstan. Methods: when writing an article, the following methods are used: description, analysis and synthesis, justification, logical modeling, system analysis, etc. When studying the formation of local self-government, as well as the functional management system, the method of structural and analytical analysis was used. The results and their significance: the conclusions and recommendations obtained as a result of the conducted research can be used: in the practical activities of maslikhats and akimats of the Republic of Kazakhstan, civil servants; in the process of studying at courses in higher educational institutions, as well as for further general theoretical and applied research.

Main problem: the globalization of the information sphere has led to a significant increase in the volume of stored and processed information. To increase the processing speed and provide information to the recipient, it is logical to increase the power of the equipment on which the information is processed. But such a path also leads to an increase in financial costs for continuous modernization or complete updating of computer equipment and application software. Purpose: an alternative solution to increasing the capacity of hardware and software may be to optimize the process of organizing data storage, and already at the stage of information analysis. At the initial stages of the task, a huge amount of information is collected and processed, which needs to be classified, to identify essential and non-essential information flows for the information system being developed, etc. The quality of functioning of the developed information system as a whole and its individual modules in particular will depend on how correctly and fully the structuring and systematization of data will be carried out. Methods: modern methodologies of conceptual design of information systems shift the emphasis from software implementation to analysis and modeling of the production environment. The tools used in the process of conceptual modeling allow you to automate the main part of the processes, including the development of program code in the format of templates (patterns), including the preparation of documentation for the software product being developed. Since modern methodologies and tools are based on the use of powerful graphical tools, this significantly increases the visibility and simplifies the process of making adjustments to the information system project, actually using the "Drag-and-Drop" technology. This allows you to redistribute the time spent on the implementation of the first stages of information system development, allocating more time to the analysis and design of the software environment at an abstract, conceptual level. Results and their significance: the stages of analysis and design do not require large financial costs and are more variable. Information at these stages is easier to adjust and change than, for example, at the stage of writing program code. In addition, it is at these stages that the most active interaction between the developer and the customer is carried out, where maximum visibility and variability of the project of the future information system is required. And the use of modern software design methodologies significantly increases the efficiency of the first stages of information system design.

The main problem: In the context of the rapid development of the digital economy, where technological innovations become the engine of progress, the role of planning in the management function acquires new dimensions and comes to the fore. Digital transformation not only redefines business models, but also requires organizations to reconsider their approaches to strategic and operational planning. Planning, as an integral part of management, is becoming a key tool for enterprises to adapt to the rapidly changing conditions inherent in the digital age. In this context, effective planning does not just foresee the future, but is a catalyst for innovation, risk management and achieving strategic goals in the context of digital dynamics. The purpose of the article is to study the transformation of the planning function in modern management in the digital economy. Methods: The research is based on a thorough analysis of the works of both domestic and foreign scientists devoted to the problems of choosing and using intra-company planning tools in the context of digitalization of the economy. To achieve the goals of the research, systematic and functional approaches of scientific cognition, as well as various methods of scientific analysis and synthesis were applied. In particular, modeling methods were actively used, which made it possible to explore in more depth the interrelationships and the impact of selected intra-company planning tools on the efficiency of enterprises in a new digital context. Results and their significance: The article examines the key aspects of changes in planning caused by the introduction of digital technologies, automation and data analytics. The authors analyze the impact of the digital economy on decision-making processes, long-term and short-term planning, and also emphasize the need to adapt management methods for effective navigation in the modern business environment.

Main problem: Monitoring the reliability of the foundation of roads, buildings and engineering structures is an important aspect of geophysical research. Modeling of geological heterogeneities is relevant. Moreover, the use of computer modeling in this problem is associated with computational costs. Purpose: Analysis of the vertical electrical sounding (VES) method for modeling the physical properties of soil and their changes when exposed to elastic vibrations. Methods: To achieve the goal, the vertical electrical sounding (VES) method was used, using a one-dimensional model of the geological environment. The direct VES problem was solved by calculating the Hankel integral. Results and their significance: The study made it possible to model a large number of soil layers using the VES method. The results obtained make it possible to determine the parameters of detected objects and changes in the characteristics of the controlled environment when exposed to elastic vibrations. The significance of the results lies in the possibility of improving the method for modeling the physical properties of soil and taking into account their changes under the influence of elastic vibrations, which helps to increase the efficiency and accuracy of monitoring the reliability of the foundation.

Main problem: One of the priority directions for improving the management system at the enterprise is the organization of effective interaction between strategic and operational management through the formation of a mechanism for their interaction, orienting operational management to achieve strategic goals and objectives. In market conditions, issues of interaction between strategic and operational production management are particularly relevant, allowing solving complex economic problems of the enterprise related to the rational use of resources involved in production, reducing production costs, improving the quality of products, optimizing production potential in order to increase the efficiency of the entire enterprise as a whole and its structural divisions. The role of the mechanism of interaction between strategic and operational production management also lies in the possibility of coordinating those final strategic goals that the enterprise strives for with the actual internal production capabilities. The purpose of this article is to study the issues of interaction between operational and strategic management of an enterprise in a market environment. The theory and modern practice of production management in a competitive environment show that the implementation of operational production management is a natural stage in the implementation of strategic management, therefore, there is a close relationship between them, which manifests itself in their interaction. Methods: The methods of analysis and generalization, the method of systematic and comparative analysis, structural and functional method, economic and mathematical methods, graphical and tabular method were used in the work. Results and their significance: the authors consider the theoretical aspects of the relationship between strategic and operational production management at an enterprise in a competitive environment. There is a low level of compliance of operational tasks of production with the strategic goals of development of domestic enterprises and the special role of information systems designed to link operational and strategic management tasks together. Accordingly, the key aspects of information technology implementation are investigated, including the need for employee training, strategic communications planning, information flow management and the use of data analytics. Examples of successful application of information technologies in various industries and organizations are given.