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In the context of intensive growth in e-commerce volumes and an increase in the number of returns, the task of improving the efficiency of logistics management, including both direct and reverse flows, is becoming relevant. Reversible processes are particularly complex, due to the need to determine the real return reasons, which directly determine the choice of route nodes. The aim of the article is to develop a multi-model method for situational managing logistics flows in e-commerce, characterized by a comprehensive solution to the interrelated tasks of analysis of customer requests for returns and multi-criteria routing of material flows. To classify the return reasons, an intuitionistic fuzzy random forest was used, since it allows for the uncertainty, incompleteness, and inconsistency of customer data to be taken into account by using intuitionistic fuzzy sets and an ensemble of decision trees. To optimize routes in both forward and reverse logistics, the earthworm algorithm was used, thanks to a balanced approach to global and local search using two mechanisms of reproduction and Cauchy mutation. The proposed multi-model method is implemented as a software in the Python and integrated with corporate information systems and data warehouse. The results of his testing showed that the combined use of a text data processing tools, intuitionistic fuzzy random forest and an earthworm algorithm allows us to the development of an effective logistics management system. Customer request analysis and route optimization reduce operating costs for processing returns, while accumulated statistics on their causes provide the basis for proactively adjusting product policies and increasing the redemption rate.

The effectiveness of modern cities’ functioning depends on the level of development and connectivity of large spatially distributed systems, such as built-up spaces, road networks, engineering infrastructures, and information-communication networks. The consistency of structures of these systems directly affects residents’ access to infrastructure facilities. Urban ­SDS structures evolve under the influence of natural, historical, and anthropogenic factors, demonstrating signs of statistical self-similarity characteristic of stochastic fractal objects. Therefore, applying methods from fractal geometry to study the dynamics of development and self-organization of urban ­SDS has significant potential for planning and modeling transformations of city territories. Classical approaches of fractal analysis are focused on studying general patterns and global characteristics of ­SDS at the city-wide scale. Such data is useful for strategic and tactical planning but insufficient for forming an objective picture at the intra-city territorial units level. To overcome these limitations, it is proposed to perform spatial discretization of the studied ­SDS and obtain two-dimensional maps of spatial fractal data that can be effectively mapped. Building upon the cartograms implemented in the ­DCFA method, a technology for creating schematic maps is proposed, which reflect the distribution of quantitative assessments of fractal dimensionality in the studied urban ­SDS. For quantitatively assessing consistency, a difference map between spatial datasets of the investigated systems is suggested. Additionally, a procedure for calculating an effective sequence of cell sizes for implementing the box-counting algorithm is presented. An example of analyzing the coherence between road networks and urban development in Zelenograd using the proposed procedure is provided.

When considering the motion of statically unstable objects, such as a cyberphysical system in the form of a seven-link exoskeleton mechanism, the problem of adhesion to the supporting surface plays a significant role during anthropoid walking. This is because operating conditions change during movement: gait phases alternate, the characteristics of the supporting surface change, and external disturbances occur. To improve stability and prevent slippage, it is necessary to consider the characteristics of foot motion. Therefore, the presence of weighty inertial feet ensures the novelty and relevance of the proposed model. This paper presents a model of a cyber-physical system for an exoskeleton mechanism moving in a vertical plane and creating the prerequisites for implementing a situational approach to movement control. The model includes seven moving links connected by hinges, ensuring the maximum approximation of the model to a real exoskeleton. The objective of the study is to develop and describe algorithms for designing motion control for an exoskeleton mechanism using a software method, taking into account situational parameters, applying a previously developed method for controlling a robotic anthropoid mechanism in the form of programmable movements. The testing of the developed algorithms was carried out in the Wolfram Mathematica environment using mathematical modeling tools, numerical methods and visualization. In the course of the work, a model of an exoskeletal mechanism with seven movable links was developed, including weighty feet moving in a vertical plane. The originality of the development lies in the use of angles between the links when describing the model and the use of rotation matrices of the coordinate axes when composing a system of differential equations. A mathematical model of the presented link of the exoskeletal mechanism and algorithms for solving direct and inverse dynamics problems for it have been developed. A motion visualization routine has been created that allows you to demonstrate the motion process of the model in question in accordance with the specified functions. The necessity of taking into account situational parameters when using an exoskeleton is shown. The relevance of using fuzzy logic methods and neural networks to optimize modeling while adapting to environmental uncertainty is described.

A game-theoretic model of oligopoly with reflexive player behavior and quantity conjectural variations is proposed. The model generalizes two types of player reflexion –symmetric and asymmetric. It allows to describe the forecasts regarding competitors’ actions more flexibly and to study a wider range of market equilibrium options. For symmetric reflexions, the model is examined in terms of the influence of reflexivity rank and the number of players, revealing the dependence of equilibria on the depth of players’ strategic thinking. For asymmetric reflexions, the model is analyzed depending on the type of representation and the number of players. The goal of the study is to develop a method for calculating conjectural variations for both symmetric and asymmetric player representations. Unlike existing methods for calculating conjectural variations, which ignore the interactions between the number of players and the depth and type of reflexivity, this study yields new results for linear demand and cost functions. These results have significant practical implications and allow for the calculation of game equilibria with arbitrary reflexivity ranks and an arbitrary number of players, while also taking into account the type of reflexion of the analyzed player. This expands the toolkit for modeling real-world market situations. Thus, this study makes a significant contribution to the development of reflexive game theory by offering an adequate mathematical framework for analyzing strategic interactions in oligopoly settings, taking into account the heterogeneous expectations of players, which is necessary for forecasting market dynamics. To visualize the analytical results, graphical interpretations of the patterns of change in hypothetical variations are presented, which are used to formulate conclusions.

In the Interval Method of Target Solution Displacement the problem formulation can be refined by an expert at any step of the interactive solution search process, based on the analysis of intermediate results and situation portraits (target, current, and achieved). The best approximation to a feasible solution can be found even with an inconsistent system of constraints. At all stages of computation, IMTSD operates not with boundaries but with real-number segments as integral objects. IMTSD allows the integration of domain expert knowledge (represented in the form of mandatory and guiding requirements for the solution) with a formalized step-by-step search for feasible solutions. The step-by-step human-in-the-loop solution search scheme enables the expert (or an intelligent robot) to: analyse constraint violations; evaluate the feasibility and effectiveness of solutions; input directives that guide the search (“increase”, “decrease”, “fix” the right-hand sides of selected constraints); adjust the priorities of selected constraints and the levels of applied data and solution precision; modify the problem formulation by adding/removing constraints, changing the number of main variables, and updating constraint coefficients. Numerical experiments have demonstrated the high efficiency of IMTSD in solving complex situational planning problems under uncertainty. An example of using IMTSD to solve the resource allocation problem in emergency situation is presented. IMTSD is considered as a contribution to the methodological arsenal of technologies for solving practically significant linear situational planning problems.

Assessment of the economic efficiency of using digital assets in production processes is important both for industrial enterprises themselves and for government authorities implementing measures to encourage the introduction of digital technologies by enterprises within the framework of the Strategy for the Development of the Manufacturing Industry of the Russian Federation, as well as for development institutions when selecting projects within the framework of technological development programs. The purpose of the study was to develop an econometric model for evaluating the effectiveness of using digital assets, which makes it possible to quantify their impact on labor productivity and operating costs based on panel data from Russian manufacturing enterprises for 2019–2024. A statistical verification of the specification and quality of the constructed panel regression models was carried out using formal statistical tests (Hausmann, Breusch – Pagan, VIF). The estimates obtained allow us to quantify the impact of digital assets on the dynamics of key performance indicators. The essence of digital assets is defined as a set of digital resources and technologies used by an enterprise that automate data analysis, forecasting, and decision support operations. To build the model, the author’s integral index of digital assets has been developed, taking into account investment, technological, analytical and integration components. When writing the article, the methods of generalization and classification, comparative and econometric analysis were used. The conclusion is made about the practical significance and potential users of the developed models, the directions of their further improvement.

The problem of recognizing human body activities by analyzing data obtained from inertial measurement units using artificial neural networks is consired. The feature of this study is using of only five angular coordinates defined by a planar five-link human model for movement analysis. Furthermore, in addition to walking, athletic exercises movements are analyzed. Both long-term and short-term movements (for example, Start of walking or sitting down) are recognized. Activities recognition is used in human-machine interfaces, as well as in sports, to assess the number and technique of performing exercises. Movement analysis is also used in medicine, for example, in the treatment of Parkinson’s disease. The purpose of this work is to develop a method for recognizing short-term and long-term movements based on data from wearable inertial sensors, without the influence of vertical axis body position, with a recognition accuracy of over 98%. Five measuring modules are attached to the human body using elastic belts. One module is placed on the person’s chest, the others are attached to the sides of the thighs and shins. Each module uses a microelectromechanical sensor MPU-6050 with a specialized digital signal processor for motion processing (DMP) used to pre-process and filter data coming directly from the 3-axis gyroscope and accelerometer. Then the data from the modules is transmitted wirelessly to the receiving device and then to a personal computer, where they are finally processed and stored for subsequent classification. In the course of the work, a data set was collected that, in addition to common states (standing and sitting positions, walking), included sports exercises that primarily involve the leg muscles (squatting, step-ups). Using video recording carried out during the motion capture process, the areas where the movements are performed were marked on the obtained data. Several neural network configurations (fully connected, convolutional, and recurrent) were used to classify the movements. The highest accuracy of combine recognition of long-term and short-term movements (98–99% F1-score) was achieved using convolutional neural networks. In the work process, it was found that the duration of the analyzed movement fragment has effect on recognition accuracy. This accuracy was achieved using 2-second recording fragments.

Reviewing manuscripts of articles in scientific journals is often complicated by insufficiently thorough preparation of the presented material. In addition to the irremovable reasons due to the low substantive (scientific) level and the lack of significant results, a significant contribution is made by the authors’ insufficient familiarity with the existing canons and rules for organizing the text of the article and the style of presentation. Despite the fact that a single standard that does not depend on the specifics of specific areas of scientific knowledge, the cultural environment and publishing traditions is impossible, it is quite possible to build a kind of “supporting structure” that would set the vector for applying the creative efforts of the author to build an information image of the scientific result obtained by researchers. The work sets out the conceptual foundations of an approach to manuscript design that is sufficiently general and meets the requirements for adequate exposure of key research results offered by the authors to the attention of the scientific community. The basic limitation is the subject of the work, which can be identified as the development of new mathematical methods and tools designed to solve practical problems in various fields of activity. Taking into account the specified specifics of the scientific orientation of the works and, accordingly, the profile of the scientific journal, as well as the technology for working with applications adopted in a particular editorial office, basic concepts are postulated, methodological rules are formulated on the most significant points, and normative markers are provided to help authors in matters of the structural organization of the manuscript, the choice of presentation style and means of presentation. The proposed material is the result of a generalization and systematization of the authors’ long-term practical experience, directly related to the publication of works on the designated scientific topics.