Big data processing methods are used to solve various problems, for example, collecting, storing, analyzing, visualizing and interpreting large amounts of information received from various sources: the Internet, mobile applications and social networks. The use of special technologies and tools, such as MapReduce, Hadoop, Spark, speeds up the process due to parallel and distributed data processing. A comparison of data from five geomagnetic observatories included in the international INTERMAGNET network is carried out using visualization, which is one of the components of Big Data technology. In each observatory of the INTERMAGNET network, information about the current state of the Earth's magnetic field is collected using specially certified magnetometric equipment. Quite often the analysis of this information obtained over a long period is of scientific and practical interest. In this case, the information is big data, that is, data that does not fit into the RAM of the computer being used. Graphs of initial observation data for the period from January 1, 2018 to July 31, 2023 are presented. The MatLab system with Big Data methods implemented in it, is used as a toolkit.

The state of the Internet as a repository of information resources is analyzed from the point of view of a bot - a program that collects data for the purpose of monitoring resources, filling a search engine, or other commercial or research purposes. An approach is proposed to describe the problem under study through a set of phenomena that arise when collecting documents on the Internet. The described phenomena must be taken into account when developing monitoring systems or search engines. A number of features that arise during web scraping, harvesting and other cases of using bots to collect data on the Internet are given. The problems of using subdomains, recursive subdomains, dynamically loaded content technologies, search engine optimization of text content and others are described. It is shown that the task of collecting data from Internet resources is not only technological, but also to a greater extent knowledge-intensive, and since research is in an active phase, there is no “out-of-the-box” solution for it. The article will be useful to researchers in the field of Internet development, search engine developers, specialists in data retrieval and Internet technologies, as well as specialists in the field of creation and support of Internet resources and in the field of Internet marketing.

An approach to modeling automatic control systems with variable delay using a shift register is proposed. The types of variable delay are analyzed. The combined variable delay arising due to the variable speed and variable length of the signal transmission path is considered. An algorithm for modeling such a delay is proposed taking into account the initial function based on a shift register. The algorithm is implemented in C++ and can be adapted to the code of a microcontroller or a simulation environment block (for example, Matlab/Simulink).

Results of numerical modeling of the dynamics of measuring instrument verification workplace functioning as a non-stationary service system with relative priorities of the incoming flow of requests, are presented. Estimates of the modeling complexity are given. The possibility of control the system states probabilities under peak loads by controlling intensities over significant periods of time is illustrated. This opportunity can be used for the rational redistribution of production capacities of metrological departments over a given period of time when forming a work schedule for the departments. The ability to control the intensity of verification can be used to ensure certain technical and technological requirements for the workplace for verification of measuring instruments.

An analytical approach to studying countable homogeneous Markov chains is proposed. An algorithm for selective search of input-output operators in z-form is presented. Simple analytical procedures for obtaining probability functions for real and complex conjugate eigenvalues of the transition probability matrix are described. Estimates are given for the boundaries of the onset of a steady state in clock time. Additional results are presented for the steady state using an algorithm for expanding the characteristic determinants. The main calculations are illustrated by assessing the characteristics of Markov chains taking into account the influence of transient dynamics when changing the probabilities of states over the operating interval in clock time. Aspects of calculation reliability when estimating probability values using the proposed approach are also considered.

For a static control object with a variable parameter, the problem of tracking a deterministic reference action with zero error has been solved. An algorithm for the synthesis of a dynamic controller is proposed, which allows a parameterization of variable parameter generators with an unknown state matrix, in which the problem of potential division by zero is solved.

A new method for assessing the hardness of materials by testing their samples for wear by the chord method (“block-on-ring”) is proposed. It is based on the principles of determining hardness with stationary hardness testers and results of a previously performed analysis of the correlation dependence of Mohs hardness on the material resistance to wear. Such dependencies are obtained by measuring the wear segment chord from cutting a disk into a flat sample for a selective set of materials in a wide range of hardness.

As part of technological preparation of production, the technological processes design is a complex and time-consuming task. A hypothesis is put forward about the possibility of using swarm intelligence tools in the task of developing route technology. The features of technological preparation of production are studied; modernization of the technological preparation is aimed at increasing the production process automation, as well as reducing the risk of errors associated with the human factor. A mathematical model for assessing the condition of equipment is presented. An algorithm is been proposed which allows automating the development of routing technology based on graph theory and swarm intelligence algorithms, as well as monitoring the condition of equipment and its readiness to perform the task. It is noted that the use of swarm algorithms can make it possible to work with graphs and build routing technologies with greater data processing speed.