The paper considers a mathematical model of the ion-beam etching process. A nonlinear differential equation of first-order ion-beam etching is considered. It has been established that the model equation for ion-beam etching can be reduced to a homogeneous Monge-Ampere equation. Some classes of exact solutions are presented for this equation. A power-law solution is obtained by the method of functional separation of variables, which depends only on a set of constants and does not contain arbitrary functions. Solutions are also found that linearly depend on arbitrary functions of the coordinate variable and the time variable. Assumptions and explicit conditions are formulated on how to select solutions from the families of solutions of the Monge-Ampere equation that correspond to the model process under consideration. A class of nonlinear equations in partial derivatives of the first order is indicated, which can also be reduced to the Monge-Ampere equation. Limitations on the etching rate are established, which allow the ion-beam etching equation to be reduced to a second-order linear hyperbolic equation, for which, by separation of variables, it is possible to obtain a solution in the form of a Fourier series.

Keywords: ion-beam etching equation, Monge-Ampere equation, model solutions, exact solutions

The paper discusses the use of machine learning in relation to natural language processing (sentiment analysis, semantic proximity analysis) to build a recommendation system for the choice of perfumery products. The topic of the work is relevant in view of the growth of the range of manufactured perfumery products and the complexity of its choice by consumers and promotion by manufacturers. The proposed approaches are relevant for solving this problem due to the accumulated textual reviews and reviews of perfumery products on various websites, including online stores.

Keywords: machine learning, natural language, sentiment analysis, distributive semantics, word2vec, recommender systems

The issue of changing scientific interest in the methods of combining images in technical systems is considered. The material is based on the analysis of open publications, patents presented in the scientific electronic library eLibrary for the period 1980 – 2021, as well as not included in it for any reason. The types of sources for formation of image, goals and features of the most common ways of combining are considered. The areas of preferential use methods of combining are given. The issues of image preprocessing to increase the informativeness of the result of the combination are considered.

Keywords: visual data, foundation image, image combination, information combination, image preprocessing

Pipe fittings, which are one of the main elements of any type of pipeline networks, can be used for various purposes: shut-off, reverse, safety, control, separating, shutting off, etc. In order to control the performance of this element, it is necessary to carry out various tests in the prescribed manner, the main ones being pneumatic. This study is devoted to the development of equipment for in-plant pneumatic testing of rotary check valves for pipeline systems of hazardous production facilities with ultra-high parameters of the working environment. For this design of the installation, the simulation of the stress-strain state of the elements of the installation was carried out, as well as the gas-dynamic calculation of the test circuit of the installation.

Keywords: rotary check valve, pipeline fittings, pipeline system, mathematical modeling, finite element method, strength analysis, stress-strain state, computational fluid dynamics, pneumatic testing, technological pneumatic installation

In industrial production, stacker loaders used for loading and transporting goods packed on pallets are quite widely used in warehouse work. Basically, when performing a loading and transport technological operation, the functionality of the stacker is sufficient. When an obstacle appears or pallets are stacked, additional maneuverability is required, as a result of which the overall performance of the loader is lost. As a result of the conducted research, it was found that when bypassing obstacles and laying pallets, the time spent on maneuvering the chassis is up to 13%, while the utilization factor of the loader-stacker in terms of productivity is 0.7. Numerical modeling of the positioning process of the load-handling body of the loading and transport unit was carried out, on this basis, the design of a loader-stacker with expanded functionality was proposed and developed, in particular, the service area increased due to the use of a tripod manipulator and two guide actuators, which reduces the time of the technological operation of loading and unloading pallets in warehouse work. Geometrical, structural and kinematic parameters of the loader mechanism are calculated.

Keywords: numerical simulation, loader-stacker, service area, lifting body, manipulator, hinges, chassis, structural analysis, geometric analysis, kinematic analysis, executive drive, pallet

The article discusses various mechanisms of self-healing of concrete used in the construction of buildings and structures designed for certain operating conditions and the environment, which saves resources and time during maintenance and repair of objects for various purposes. Types of self-healing of concrete: With hollow fibers; Microcapsulation; Expanding additives; Bacteria. Conclusions. Today, progress has been made in understanding the relationship between the structure of materials and their properties. Thanks to the knowledge gained about the structure of materials, the possibility of designing materials of directional quality was considered, which guarantees their compliance with certain operating conditions and the environment.

Keywords: concrete, destruction, self-healing, hollow fibers, microcapsulation, expanding agent, bacteria

The construction of public buildings from a metal frame is always associated with the search for a rational constructive solution that meets not only the dependability requirements, safety, but also architectural and design solutions. Often, the solution to the problem of rationalization of roof construction in public buildings is the use of arched combined systems, since such systems have a number of advantages over simple arches: the survivability of combined systems is higher than simple ones, the possibility of creating complex, architecturally expressive spatial structures, lower material consumption, high load-carrying ability with relatively low weight, etc. The aim of the research is to find a rational construction solution for two arch-cable systems (Hud type system and Radial type system) by comparing in terms of the minimum internal forces, displacements and metal intensity at different ratios of the arch boom and span. Based on the calculation results in the Lira SAPR 2020 software, the most unfavorable loads combinations were determined, deformation schemes of arch systems, displacements, moments and forces were obtained, sections of arches and ties were selected. From ten arched structures of two types considered with different ratios of arch boom to span, the Hub type system with the ratio of arch boom to span f/L = 1/3 and Radial type system with the ratio of boom to span f/L = 1/4 showed the best result in terms of efficient operation and metal intensity.

Keywords: combined systems, arch-cable constructions, simulation of prestress, hub type s

This arcticle are devoted to the modernization of housing and communal system based on the technology of "Smart Grids". The methology of developing an assessment of the effectiveness of the project of the modernization of housing and communal services facilities using the technology of "Smart Grids" is given. It from the publication that the use of "Smart Grids" technology provides energy and economic efficiency in the development of the city's energy system

Keywords: Smart grids, "Smart City", centralized heat supply systems, individual heat supply, evaluation of the economic modernization project, key performance indicators

The system for measuring cargo dimensions is designed for streaming measurement of cargo dimensions, which can be luggage at airports and transshipment bases, various parcels, as well as commercial cargo. The authors of the article developed a structural and functional diagram of a control and measuring system for dynamic measurement of cargo dimensions, and also considered the principles of its operation.

Keywords: control and measuring system, measurements, cargo dimensions, luggage, automated systems

The work updates a strategic approach to maintaining the quality of student performance. In the article "Big Data" is presented as an approach to organizing the data obtained during the educational process. Mining analysis as a Big Data analysis tool. The authors also considered approaches to improving the effectiveness of learning, which allow predicting student performance. Blended learning, as an integration into the educational process, the best opportunities for online and distance learning, provided for the subsequent collection of Big Data for analysis. The application of data mining methods for the development of models for predicting the behavior and academic performance of students is considered. The authors propose student modeling as a key concept in data mining in education, which refers to the qualitative representation of student behavior. Algorithms for data mining are described, classification and clustering are presented as the most common tasks. The CART decision tree algorithm is presented as one of the effective data mining methods needed to predict student performance based on online activity that is stored in the Moodle LMS log file. Finally, it was concluded that the personal contact of an experienced teacher with a student in the educational process can not be replaced by the tools provided by Moodle and similar systems, but due to the growing threats caused by the pandemic, the relevance of distance education is becoming increasingly important.

Keywords: student performance quality, big data, data mining, student modeling, CART decision tree algorithm, Moodle LMS, distance education

One of the most relevant areas in construction is the improvement of methods of reconstruction of buildings and structures. An innovative solution to this issue is considered to be the reinforcement of construction objects with composite materials, in particular, the reinforcement of structures made of natural anisotropic material - wood.

Keywords: wood, carbon fiber, composite, materials, reinforcement, structures, reconstruction, restoration, labor intensity, cost, strength, deformability.

The article discusses the features of identifying novelty in data, as well as general methods for identifying it. Since the absence of noise in the training information is a determining factor for building high-quality classifiers on it in supervised machine learning, such a practically important special case of the search for novelty is considered, when it is determined in separate classes of training data after all outliers have been eliminated in these data. For greater definiteness, when searching for novelty, its geometric interpretation in the space of object feature values.

Keywords: data, classifier, outliers, novelty, novelty detection, geometric approach, statistical criterion

Concrete has unique properties that allow it to occupy a leading position in the market of building materials. General-purpose structural concrete is used for the construction of buildings and structures that can provide sufficient strength and elasticity for load-bearing and enclosing structures. Concrete production technologies are in constant development, inextricably linked with the solution of the most important task – reducing the mass of building materials, and, as a result, reducing the material consumption of construction

Keywords: capital construction, structural concrete, heavy concrete, light structural concrete, resource saving, economic feasibility of using light concrete

The aim of this study was to analyze the possibility of using a mathematical model of logistic regression for the recognition of malignant neoplasms on digital images of the skin. The study used a database containing 6594 digital skin images. At the first stage of the study, digital skin images were segmented to isolate the object under study, in which morphometric and color characteristics corresponding to the parameters of the classical ABCD system were determined. At the second stage, the characteristics were used in the classification into malignant and benign neoplasms using logistic regression. When classifying images, the highest value of the accuracy indicator (67.9 [66.9; 68.8]%) was obtained during classification using logistic regression, built on the basis of the reverse Wald stepwise method. Thus, the logistic regression built on the basis of the reverse stepwise Wald method can be applied in the classification of malignant neoplasms on digital images of the skin, but further research and determination of the optimal parameters are required.

Keywords: mathematical model, digital skin images, logistic regression, image classification, skin cancer

The article proposes a special device to transport earth when building an underground part by the «top-down» and «top and down» technique. The developed device is fully electrically powered. The proposed technology enables to completely exclude nonproductive movements of excavating and transportation devices to relocate the earth from the working site to the dumping site onto trucks above ground. The device is adapted to work as part of the production line when realizing the “top-down” and «top and down» technology. To exclude load lifting mechanisms for lifting and dumping of the earth onto the trucks above ground, it is proposed to use two lifting rails with hoisting equipment fixed on a metal frame.

Keywords: “top and down” technology, earth works, excavation works, subsurface part of a building, earth movement, tier of a subsurface part of a building