The study is devoted to the development of electronic and distance learning tools for mastering the skills of applying mathematical methods by specialists in the field of automated systems development. The concept (structure) of an automated information system (AIS) for managing the life cycle of exercises to study optimization methods has been developed and schematically presented. An important element of decision support in the AIS is software simulators (training and training components) that generate exercise options and automatically check them based on the properties of mathematical models of optimization problems. An algorithmic and prototype software for the training subsystem for monitoring the skills of solving optimization problems have been developed. Variations in the interfaces for constructing a mathematical model for an optimization problem by a student when performing an exercise in the AIS are demonstrated. Building a model in the interface and, accordingly, the complexity of the exercise depends on the number of model parameters that can be changed by the student. The simulator provides an integral assessment of the student's actions when performing the task. The introduction of the simulator into the digital educational environment of the university will automate and simplify the implementation of current and intermediate control of knowledge and skills in the disciplines studied.

Keywords: optimization problems, mathematical programming, decision support, software simulator, mathematical modeling of systems and processes, visual modeling

Two capacitive methods of measuring the linear density of one-dimensional fibrous products are considered. The sensitivity of the measurement results to variations in the geometric and physical parameters of the measuring device for the differential and resonance measurement methods is estimated. A weak, almost linear dependence of the measurement error on parameter variations in a wide variation range is established. The good suitability of both methods for measuring the linear density of one-dimensional products by the capacitive method and the high correlation between the measured value and the measurement results are substantiated.

Keywords: fibrous materials, one-dimensional products, linear density, capacitive measurement method, capacitive method, differential circuit, resonant measurement circuit, parameter variations

The paper considers the issue of using a computer vision system to control the quality of products in the control algorithm of a mechatronic sorting station. Shoe products are chosen as an example. The developed system is based on machine learning methods for image recognition by segmentation. As a result, a neural network model was created, and a program was written for identifying and selecting objects using a camera for subsequent sorting of defective products. The program contains three modules: initialization for declaring all variables, models, classes, video stream from the camera; the main module, containing an internal loop for each segmented object; a subroutine for completing the work. The introduction of computer vision into the control algorithm increases the efficiency and flexibility of the quality control system, and improves the accuracy of measuring the parameters of objects for their subsequent sorting.

Keywords: mechatronic station, sorting, computer vision, image segmentation, neural network training, control algorithm

In this work, we present the development and analysis of a feature model for dynamic handwritten signature recognition to improve its effectiveness. The feature model is based on the extraction of both global features (signature length, average angle between signature vectors, range of dynamic characteristics, proportionality coefficient, average input speed) and local features (pen coordinates, pressure, azimuth, and tilt angle). We utilized the method of potentials to generate a signature template that accounts for variations in writing style. Experimental evaluation was conducted using the MCYT_Signature_100 signature database, which contains 2500 genuine and 2500 forged samples. We determined optimal compactness values for each feature, enabling us to accommodate signature writing variability and enhance recognition accuracy. The obtained results confirm the effectiveness of the proposed feature model and its potential for biometric authentication systems, presenting practical interest for information security specialists.

Keywords: dynamic handwritten signature, signature recognition, biometric authentication, feature model, potential method, MCYT_Signature_100, FRR, FAR

During the research, a new prestressing system was developed for carbon fiber reinforced polymer plates to reinforce damaged steel beams. A parametric analysis was performed using finite element modeling. The results showed that satisfactory amplification efficiency can be achieved using the new pre-voltage system. The prestressed carbon fiber significantly increased the performance when bending beams at the elastic and elastic-plastic stages due to the use of high-strength carbon fiber plates. In addition, as the pre-voltage level increased, the amplification efficiency increased. A simple increase in the area or modulus of elasticity of the carbon fiber plate slightly improved the hardening efficiency, while the simultaneous application of prestressing clearly increases the hardening efficiency.

Keywords: reinforcement, steel beam, prestressing, new system, carbon fiber plate

The article focuses on methods for reducing high inductance in power supply circuits using one of the IC substrate topologies with a high-speed interface as an example. The interface in question operates at a speed of 28.25 Gbit/s and imposes strict requirements on the parameters of the power supply inductance. The presented solutions are aimed at ensuring low values ​​of power supply inductance in conditions of high layout density and power integrity requirements for modern data transfer interfaces.

Keywords: power supply inductor, power system, low noise power supply, power supply impedance, analog power supply, serial interface, high speed interface, organic substrate, IC packaging

The presented article reveals the issue of using waste from the automotive industry of rubber products as one of the possible ways to improve the quality of asphalt pavement and, accordingly, reduce the number of repair activities and material costs for their implementation and increase the service life of the roadway. The tests carried out show that the asphalt-concrete mixture using a modifier based on active rubber powder demonstrates the best mechanical and operational characteristics. The strength and elasticity of asphalt concrete increases, as well as the abrasion resistance decreases, which leads to a longer use time of this web. Such changes in the characteristics of the roadway have a positive effect on the economic side of the issue. Improving the quality of the finished product increases the time intervals between repair actions, which reduces material and resource costs. The adhesion of the road to the rubber of cars is improved.

Keywords: asphalt concrete, asphalt mix, automobile waste, rubber crumb, modifier, active rubber powder

The paper proposes a method for calculating the area of a flat area from a photograph based on the use of mathematical analysis methods. To calculate the area, a curved integral of the second kind is used along a closed contour bounding the area under consideration. Defining the boundary in the form of a Bezier spline reduces the calculation of a curved integral to the calculation of several definite integrals from the Bernstein basis polynomials. An explicit form is obtained for integrals of Bernstein basis polynomials. For a third-order Bezier spline, a formula is derived for calculating the area of the area in terms of the coordinates of the reference points of the Bezier curves.

Keywords: cubic spline, Bernstein basis polynomials. Bezier curve, Bezier spline, Green's formula, beta function, gamma function

The article describes the methodology for constructing a regression model of occupancy of paid parking zones taking into account the uneven distribution of sessions during the day and the behavioral characteristics of two groups of clients - the regression model consists of two equations that take into account the characteristics of each group. In addition, the process of creating a data model, collecting, processing and analyzing data, distribution of occupancy during the day is described. Also, the methodology for modeling a phenomenon whose distribution has the shape of a bell and depends on the time of day is given. The results can be used by commercial enterprises managing parking lots and city administrations, researchers when modeling similar indicators that demonstrate a normal distribution characteristic of many natural processes (customer flow in bank branches, replenishment and / or withdrawal of funds during the life of replenished deposits, etc.).

Keywords: paid parking, occupancy, regression model, customer behavior, behavioral segmentation, model robustness, model, forecast, parking management, distribution

within the framework of the conducted research, the task of controlling a robot of a parallel structure was considered. This paper presents a model of a 3-RPR type flat parallel robot in the Matlab package, developed for conducting computational experiments. Implementation of two types motion trajectories have been simulated in order to determine the optimal structure of the position regulators of the drive joint used in the robot control system. Six structure of regulators were compared: three classical ones: PD, PID, PDD and three of their fractional-degree analogues: FOPD, FOPID, FOPDD. The FOMCON tool was used to model fractional-degree regulators. The best results for type 3-PPR robot were shown by a control system with a FOPID regulator, which indicates the expediency of using fractional-degree regulators to control parallel robots.

Keywords: parallel robot, inverse kinematics problem, 3-RPR robot, computational experiment, working out the trajectory of movement, control system accuracy, fractional-degree regulator, parametric optimization of the regulator, comparative modeling, FOMCON tool

A review of various approaches used to model the contact interaction between the grinding wheel grain and the surface layer of the workpiece during grinding is presented. In addition, the influence of material properties, grinding parameters and grain morphology on the contact process is studied.

Keywords: grinding, grain, contact zone, modeling, grinding wheel, indenter, micro cutting, cutting depth

The article is devoted to the automation of the process of managing road construction works at a manufacturing enterprise. Among the means of communication in Russia, highways are in the first place in terms of length. Construction of new roads, repair and bringing the existing roads to regulatory requirements is a complex process that can be characterized as a project. The process of project-oriented management of road construction works is formalized, project limitations are defined. The enlarged milestones of project-oriented management of road construction works are highlighted, including the stages of initialization and implementation. The categories of system users and their functions are defined. A class diagram of the information system for managing road construction works is provided. An algorithm for the operation of an automated system for managing road construction works based on a project-oriented approach is developed and described in detail. Formalization of the calculation of the percentage of project readiness is carried out based on the significance coefficient. Examples of implementing the algorithm stages in the information system and generating analytical reports in the system are given. The reports generated in the system are described in detail. The economic efficiency of the proposed automation system is substantiated.

Keywords: road construction works, project-oriented management, highway, automation, reporting, significance coefficient, project, project resources, performance indicator, construction, repair

The article presents a method for protecting transmitted images in instant messengers using time-based one-time passwords (TOTP). An additional level of protection is offered based on a combination of image masking using orthogonal matrices and two-factor authentication based on TOTP. A prototype Python application has been developed and tested using the gRPC remote procedure protocol to ensure secure data exchange between the client and the server. The results of the implementation of the proposed method in preventing unauthorized access to confidential images are presented.

Keywords: information security, messenger, messaging, communications, instant messaging systems, one-time password

The paper considers a method for obtaining gypsum foam based on various compositions of dry mixtures, including a foaming agent, various sorbents, and gypsum binder. Expanded vermiculite, perlite sand, and crushed expanded clay gravel were used as sorbents. The most effective sorbent of the above is the crushing waste from the production of expanded clay gravel. As studies have shown, foam gypsum with a density of 250 kg/m3 and a strength of 0.9 MPa can be obtained.

Keywords: Dry mix, adsorption, gypsum foam, gypsum binders, sorbent, expanded clay sand, vermiculite, perlite, foaming agent

The article examines the transition of universities from data warehouses to data lakes, revealing their potential in processing big data. The introduction highlights the main differences between storage and lakes, focusing on the difference in the philosophy of data management. Data warehouses are often used for structured data with relational architecture, while data lakes store data in its raw form, supporting flexibility and scalability. The section ""Data Sources used by the University"" describes how universities manage data collected from various departments, including ERP systems and cloud databases. The discussion of data lakes and data warehouses highlights their key differences in data processing and management methods, advantages and disadvantages. The article examines in detail the problems and challenges of the transition to data lakes, including security, scale and implementation costs. Architectural models of data lakes such as ""Raw Data Lake"" and ""Data Lakehouse"" are presented, describing various approaches to managing the data lifecycle and business goals. Big data processing methods in lakes cover the use of the Apache Hadoop platform and current storage formats. Processing technologies are described, including the use of Apache Spark and machine learning tools. Practical examples of data processing and the application of machine learning with the coordination of work through Spark are proposed. In conclusion, the relevance of the transition to data lakes for universities is emphasized, security and management challenges are emphasized, and the use of cloud technologies is recommended to reduce costs and increase productivity in data management. The article examines the transition of universities from data warehouses to data lakes, revealing their potential in processing big data. The introduction highlights the main differences between storage and lakes, focusing on the difference in the philosophy of data management. Data warehouses are often used for structured data with relational architecture, while data lakes store data in its raw form, supporting flexibility and scalability. The section ""Data Sources used by the University"" describes how universities manage data collected from various departments, including ERP systems and cloud databases. The discussion of data lakes and data warehouses highlights their key differences in data processing and management methods, advantages and disadvantages. The article examines in detail the problems and challenges of the transition to data lakes, including security, scale and implementation costs. Architectural models of data lakes such as ""Raw Data Lake"" and ""Data Lakehouse"" are presented, describing various approaches to managing the data lifecycle and business goals. Big data processing methods in lakes cover the use of the Apache Hadoop platform and current storage formats. Processing technologies are described, including the use of Apache Spark and machine learning tools. Practical examples of data processing and the application of machine learning with the coordination of work through Spark are proposed. In conclusion, the relevance of the transition to data lakes for universities is emphasized, security and management challenges are emphasized, and the use of cloud technologies is recommended to reduce costs and increase productivity in data management.

Keywords: data warehouse, data lake, big data, cloud storage, unstructured data, semi-structured data