Applied Mathematics and Control Sciences

The range of application of the ejector pumps for industry is extensive. The ejector pumps are used for gas, liquid and the multicomponent or multiphase mixtures transport. The stream-flow devices (pumps, compressors) has several advantages, for example: simple design, schema without moving parts, high reliability. Possibility of working with multiphase mixtures for ejectors determines their usage in the oil and gas mining systems as part of pumping stations for oil and gas pipe transport. Hydrodynamic of the stream-flow devices, which are used for oil and gas pipe transport, was researched good over a span of last years. This allows create optimal design of flow channel for ejectors. However, in the real life, in the working process of pumping station, is the flow unstable with the random occurrence of the gas and liquid slugs. Известно, что при перекачке газов длина камеры смешения должна быть значительно больше, чем при перекачке жидкости. In this way, creating design of ejectors for both effective gas and oil transport is very difficult problem. It is known that a length of the ejectors mixing section should be longer by gas transport than by liquid transport. In this paper was presented variant of the ejector’s flow channel with variable geometry, which was designed as the moving conical body in diffuser section. In this configuration, the annular conical channel between conical body and inner surface of diffuser is propagation of the mixing section and allows to effective mixing of components in ejectors with the short cylindrical mixing section actually. The diffuser’s function - converting kinetic energy of flow to pressure energy - holds because the surface area of annular channel increases in flow direction. The move of conical body in diffuser allows to control of the fluid transport efficiency. Researches are made as numerical flow simulation with CFD STAR-CCM+. This gives the possibility to the detail research all mixing processes with the analysis of the velocity, pressure and volume of fraction fields and flow.

The color component of an image is the basic information about the image. Color determines the mood of an image, its concept, and can also serve as a semantic accent. Obtaining information about the color component of an image is necessary when solving various kinds of tasks. For example, the task of finding similar images according to the content, as information about the color component can be combined with other metadata of the image and more fully describe its concept. In this paper authors describe the physical representation of color, the most popular digital representations of color, ways of extracting color components of an image, such as color histograms, quantization, coherent vectors and K -means, and ways of comparing color components of images, such as Euclidean distance, cosine distance, Manhattan distance, Chebyshev distance, Jaccard index, correlation analysis, Pearson's agreement test and Bhattacharya distance. It is suggested that the use of histogram comparison and vector comparison methods is acceptable for comparing the color components of images, since color histograms can be written in vector form. The authors conduct an experiment in which a human expert reviews combinations of color component acquisition and comparison methods and completes a test protocol based on the criteria highlighted by the authors. The criteria were based on the human interpretability of the results of the methods of determining and comparing the color component. On the basis of the experiment it has been determined that the best of the methods of comparison of color components of the definition images considered in the article is the correlation analysis of color histograms of images, which have been extracted in a quantized color space, because this approach meets all the criteria for testing and keeps the greatest amount of information about the color component.

The task of training artificial neural networks (ANNs) for the diagnosis of Alzheimer's disease based on the magnetic susceptibility of 10 brain veins under conditions of limited initial data (81 patients) is considered. In a recent study, fully-connected ANNs with one and two hidden layers were successfully trained in a recent study after reducing the number of veins to 4 and determining the number of synaptic connections comparable to a neural network based on a decision root. The known results gave rise to the hypothesis that training ANNs on the same data without preprocessing would also yield high-quality neural networks. To assess the quality of ANNs, the following indicators were used: mean square errors of training and generalization (testing), coefficients of determination (R2) on the sets of values used in training and generalization (testing), as well as the number of trained ANNs satisfying a certain value of the above indicators. For graphical representation of the results of repeated experiments on training and testing of ANNs, a new graph is proposed to visualize the quality of ANNs. Thus, the paper demonstrates the quality indicators of 800 ANNs trained without data preprocessing, among which there were 7 neural networks with one hidden layer and 9 neural networks with two hidden layers, for each of which 50 experiments were conducted. For comparison, we present the quality indices of 2400 ANNs trained with preprocessing.

The relevance of the use of thermal power plants for the generation of thermal and electric energy on the territory of the Russian Federation is revealed, taking into account its geographical and climatic features. The substantiation of the importance of the process of maintenance and repair in relation to boiler units, which are operated at thermal power plants, is given. Difficulties accompanying the practical implementation of this process are identified. The influence of the identified difficulties on the existing shortcomings in the process of maintenance and repair of boiler equipment and the technological pipelines connecting them and pipelines of steam and hot water is shown. The goal of the study is set, which is aimed at eliminating the identified objective difficulties and the tasks are formulated, the solution of which will contribute to the achievement of the goal. The necessity of developing specialized software for managing the process of maintenance and repair of equipment and pipelines of boiler units of combined heat and power plants is substantiated. The methodology of the work is based on the development of digital models of pipelines and boiler equipment, as well as algorithms aimed at processing the parameters of digital models. The software implementation of the developed models and algorithms is made by means of object-oriented programming in the form of a client-server application for the Windows operating system. The description of the results of software development aimed at solving the set tasks is given. Examples of some dialog boxes accompanying the functioning of the developed software are given, as well as examples of created digital models of boiler equipment and their individual elements. The practical application of the research results contributes to an increase in the degree of digitalization of industrial production in general and energy production in particular. The results obtained in the framework of this work, in the form of software, can be used to accompany the process of maintenance and repair of boiler equipment of combined heat and power plants. With appropriate adaptation, the results obtained can also be applied to boiler equipment, pipelines and apparatus that are used in the chemical, petrochemical and oil refining industries.

The development of a visual prototype of an application in a single queue for service is given. The pre-image connects the accounting for the growth of losses due to the duration of waiting with such sides of the importance of the application as urgency and priority. Varieties of change of urgency in time are discussed. The possibility of interpreting service as a lasting good is considered. On this basis, it is proposed to use relative losses as the main measure for determining the place of an application in the queue - the ratio of losses due to waiting to the duration of service. The example shows that the order in which service requests arrive depends on the time when the service facility starts accessing the queue and on the ratio of the service durations of individual requests. For the case of returning the service facility to the request after a forced interruption, the possibility of rivalry with it by other requests in the queue that have not yet arrived for servicing is considered. The possibility of working with the queue when servicing in small parts with a change in serviced requests is shown. For this type of work, expressions for step-by-step calculations are given. Calculations are made for two complicated cases of servicing a queue of five requests with a contradictory combination of the initial data of requests. A diagram of the switching of service facilities between requests is given. Taking into account the four sides of the description of the request in the queue at once provides the prototype with greater flexibility than most widely used queuing disciplines. The proposed prototype can be taken as a basis for building multi-parameter models of applications and algorithms for automatic control of the queue of applications for social, economic and computational applications.

The analysis of the functions of demand and costs of mobile operators leading in the telecommunications market is carried out. Methods used in the study: mathematical modeling, regression analysis, optimization. The Russian telecommunications market is an oligopoly, which makes it possible to analyze the dynamics of the development of the three dominant firms (MTS, Megafon and VimpelCom), since they are the ones that influence the market to a greater extent. Various models of demand and costs are considered in accordance with the dynamics of the development of the telecommunications market. Analysis of a number of weighted average voice communication prices depending on the total volume of voice traffic of services showed the presence of linear and power-law models of the inverse demand function in 2002-2021. The functions of the costs of mobile operators are considered and the direct dependence of costs on the volume of voice traffic is revealed. Cost functions and demand functions have a linear and power-law character in different periods of operator development, which indicates different types of scale expansion effects. The regularity of the influence of price dynamics on market growth is established: a power-law downward trend in prices stimulated intensive market growth, a linear downward trend contributed to smooth growth, and an increasing trend corresponding to the Giffen effect caused stagnation; it is proved that the concentration of the telecommunications market mainly determines the change in the market price of communication services; the principles of the impact of the scale-up effect on the change in the company's market share are defined: the constant return on scale-up can lead to both an increase and a narrowing of the operator's market share, depending on whether the company increases the pace of investment or reduces; the positive effect of scale-up, as a rule, causes an increase in the operator's market share, and the negative effect leads to a reduction in market share/ The conducted research can be used for further analysis of the actual data and trends of demand functions and costs functions of telecommunications market companies.