A universal solution to an applied problem related to the study of deviations occurring in the joints of manipulation robots, for example, due to elastic deformations or gaps in them, is proposed. A mathematical (dynamic) model obtained by the Lagrange–Euler method is presented, making it possible to investigate such deviations. Six generalized coordinates, three linear and three angulars, were used to describe the variations of each joint in the dynamic model. This made it possible to introduce into consideration joints with six degrees of freedom (6-DOF joints). In addition, mathematical models for external forces acting on the links of manipulation robots are presented. When composing matrices of coefficients of equations of motion, elements identically equal to zero were excluded, which significantly increased the computational efficiency of these equations. The dynamic model based on the obtained equations can be used in the computer simulation of manipulation robots.

To predict the spread of the new coronavirus infection COVID-19, the critical values of spread indicators have been determined for deciding on the introduction of restrictive measures using the city of Moscow as an example. A model was developed using classical methods of mathematical modeling based on exponential regression, the accuracy of the forecast was estimated, and the shortcomings of mathematical methods for predicting the spread of infection for more than two weeks. As a solution to the problem of the accuracy of long-term forecasts for more than two weeks, two models based on machine learning methods are proposed: a recurrent neural network with two layers of long short-term memory (LSTM) blocks and a 1-D convolutional neural network with a description of the choice of an optimization algorithm. The forecast accuracy of ML models was evaluated in comparison with the exponential regression model and one another using the example of data on the number of COVID-19 cases in the city of Moscow.

Recently, we have seen the rapidly growing popularity of unmanned aerial vehicles. This is due to some advantages, namely portability, the ability to fly over hard-to-reach areas without human intervention. They are also widely used for commercial purposes, agriculture, delivery, automation in warehouses. The potential of unmanned aerial vehicles is vast and demonstrates promising opportunities. However, when using these devices, the issue of safety is acute. This article presents a developed software application that is used to improve the efficiency of flight research of groups of unmanned aerial vehicles, based on a new method for assessing flight safety by comparing the complexity of specified air routes. A practical approach to modeling and evaluating the search for a safe way is proposed. A suitable method of research is computer and simulation modeling. It is suggested to use the spectrum of dynamic characteristics of the sequence as a formal attribute for analyzing routes. The method is illustrated by an example of comparing air trajectories according to the flight safety criterion. The software application is intended for use in the educational process when training specialists in transport security, robotics, and system analysis.

The problem evaluated in this study is related to the optimization of a budget of an industrial enterprise using simulation methods of the production process. Our goal is to offer a universal and straightforward methodology for simulating a production budget at any level of complexity by presenting it in a specific form. The calculation of such production schemes, in most enterprises, is currently done manually, which significantly limits the possibilities for optimization. This article proposes a model based on the Monte Carlo method to automate the budgeting process. The application of this model is described using an example of a typical meat processing enterprise. Approbation of the model showed its high applicability and the ability to transform the process of making management decisions and the potential to increase the profits of the enterprise, which is unattainable using other methods. As a result of the study, we present a methodology for modeling industrial production that can significantly speed up the formation and optimization of an enterprise’s budget. In our demonstration case, the profit increased by over 30 percentage points.

An algorithm for parallel calculations in a dynamic model of manipulation robots obtained by the Lagrange–Euler method is developed. Independent components were identified in the structure of the dynamic model by its decomposition. Using the technology of object-oriented programming, classes corresponding to the structures of the selected components of the dynamic model were described. The algorithmization of parallel computing is based on the independence of the calculation of objects of individual classes and the sequence of matrix operations. The estimation of the execution time of parallel algorithms, the resulting acceleration, and the efficiency of using processors is given.

A model of a layered hierarchically constructed composite is presented, the structure of which demonstrates the properties of similarity at different scales. For the proposed model of the composite, fractal analysis was carried out, including an assessment of the permissible range of scales, calculation of fractal capacity, Hausdorff and Minkovsky dimensions, calculation of the Hurst exponent. The maximum and minimum sizes at which fractal properties are observed are investigated, and a quantitative assessment of the complexity of the proposed model is carried out. A software package is developed that allows calculating the fractal characteristics of hierarchically constructed composite media. A qualitative analysis of the calculated fractal characteristics is carried out.