A model of interaction between a railway and a seaport has been developed in the presence of a governing body. Interaction functions are described for the proposed model, analytical solutions for the static model are found, and the simulation speed is compared without and with the use of analytics. Next, a dynamic model is considered and an algorithm for finding an equilibrium for this model is proposed. The subsequent use of parallel programming methods will make it possible to plan interaction in this model to a better extent.

Keywords: mathematical model, simulation modeling, Stackelberg equilibrium, hierarchical game, mixed transportation, railway transport, port

Investigation of ways to accelerate the training of neural networks using genetic algorithms and the study of the dependence of the speed of genetic algorithms on the mutation rate. In this study, a program was implemented on the Unity graphics platform using genetic algorithms and mutations to determine their optimal coefficient. The experiment showed that the learning rate really depends on the mutation rate, and the highest learning rate was obtained at 5-7,5%.

Keywords: machine learning, deep learning, genetic algorithm, optimization, neural network, artificial neuron, mutation, artificial intelligence, non-player character, optimization

The purpose of the work is to show the influence of the works of Nikolai Orem on the formation of the science of dynamics. Methods. The paper shows that the study of motion led N. Omer to the conclusion that the sum of the harmonic series, which gives an estimate of the traveled path of a uniformly tired traveler, diverges. This proved that the traveler would walk any arbitrarily long distance. The connection of the model proposed by N. Orem with the zeta function and similar paradoxical models in which the path turns out to be finite, despite the slowdown or acceleration of movement, is considered. Result. The trajectory of the wayfarer Orem is demonstrated according to the Riemann formula. Links to training servers with dynamic models animated in 3D graphics and built using the ""live book"" technology are provided.

Keywords: Orem's wayfarer, zeta function, zeros of the function, Riemann problem

The article describes the possibilities, advantages and differences of machine learning systems without a teacher from template learning. The definition of clustering is also given, indicating the main methods and tasks solved by this machine learning algorithm. The algorithm for recognizing data from documents using OCR technology is described in detail, the goals and objectives of using OCR technology in the business processes of IT companies are formed. The following are tools for solving the problem of recognizing and clustering data from PDF document scans using the Nanonets and Tesseract machine learning libraries. In conclusion, this article describes the advantages and disadvantages of using these libraries in solving the problem of recognizing and clustering data from document scans.

Keywords: machine learning, clustering, data recognition, library Nanonets, library Tesseract

The algorithm and code listing of the developed self-learning chatbot are presented. Able to maintain a conversation with the user, switch to training mode in the absence of the necessary information, analyze the context of the conversation for "forbidden" words. The Trim function is used, which removes extraneous characters represented in the tr property. And also an additional option "Solve arithmetic problems" is implemented in case of a request from the user. When implementing the latter option, a recursive descent algorithm based on three nested recursive functions was used, while the binary tree is filled in. A function has been developed to divide the incoming string into tokens. The chatbot code is developed in C++/C# based on the principles of object-oriented programming with the development of classes.

Keywords: artificial intelligence, machine learning, voice assistant chatbot, learning mode, tokens, recursive descent, binary tree

The main criteria for evaluating the efficiency of operation of heating networks and points are considered, and the task of their modernization through the reconstruction and introduction of digital technologies is set. The following criteria were selected as evaluation criteria: reliability criterion - integral shortage undersupply of thermal energy, thermal energy quality criterion - pressure losses, economic efficiency criterion - technological heat losses in the network, physical condition criterion - network wear coefficient. The parameters of the existing heating network of the district boiler house No. 1111 in Volgograd were analyzed. Using a multicriteria model, taking into account the uncertainty of heat loads, using a multiplicative criterion, the optimal variant of the order of reconstruction and modernization of network sections and heat points was obtained. A mathematical model of the fuzzy set of the decision efficiency criterion is considered, and the modal value of the functional is determined using an algorithm written in the Python language.

Keywords: modernization, criteria for evaluating the efficiency of operation of thermal networks, methods for evaluating decision-making, multi-criteria optimization, criterion for the effectiveness of decision-making, fuzzy set, triangular fuzzy number

The article researches the influence of the length of Ni-nanotubes on the anisotropy of the mechanical properties of nanotubes using the Young's modulus as an example. In this case, the influence on the anisotropy of both the single-crystal symmetry of the structure and the predominant spatial distribution of crystallographic axes is taken into account.

Keywords: anisotropy of mechanical properties, elastic constants, Young's modulus, anisotropy parameter

The assumptions of mathematical models for calculating the crack resistance of reinforced concrete structures are considered. For each of them, an analysis was carried out to determine whether they correspond to reality throughout the entire life cycle of the structure: from the hardening of the concrete mix to destruction. Based on the results of the analysis, it was proposed to use only one single calculation at the level of standards to assess the crack resistance of structures - according to the crack opening width, acrc. So, for example, at a certain value of acrc, the structure will still remain airtight (the cracks will be non-through), and if this value is exceeded, it will not. At the same time, the calculations already available in the norms for limiting permeability and the safety of reinforcement will still remain in demand. At the junction of the theory of damage accumulation and nonlinear fracture mechanics, a compressed algorithm is proposed for possibly taking into account the influence of cracks at all scale levels of the concrete structure, the key for which is the normalization of the statistical parameters of the distribution of discontinuities by diameters, lengths, openings, depths, directions, distances between discontinuities, etc.

Keywords: reinforced concrete, crack resistance, cracking moment, crack width, plasticity coefficient, damageability, non-linear fracture mechanics

The development, development and reorganization of territories for civil construction projects is often associated with problems of control and protection against erosion processes. Territories previously considered inconvenient are now subject to intensive development. The investment attractiveness of such territories is very high, so it is necessary to carry out engineering preparation measures, including those to protect it from erosion processes. Studies show that the most environmentally friendly structures to prevent erosion processes are geocomposite systems created on the basis of anti-erosion geosynthetic materials. But before applying any measures to stabilize erosion processes, it is necessary to understand the process of interaction between the methods used and the surfaces to be protected. The article considers the zoning of coastal slopes, as the most vulnerable to the impact of erosion of territories in cities, on non-flooded, partially flooded and permanently flooded zones. Accordingly, this division was made in order to determine the possible impacts on the structures of geocomposite systems. Each impact (hydraulic, snow, ice) is described using mathematical modeling, indicating methods for calculating the stability of the geocomposite system for the zones identified in the study. It has been established that the strength of a geocomposite system also affects its stability, therefore, when determining the overall stability of a geocomposite system, the concept of its tensile strength is introduced. The presented materials are of great importance in practical application. This is due to the reduction of material and labor costs for the implementation of anti-erosion protection measures when applying the results of this study. Further research is aimed at optimizing the design of anti-erosion protection based on geocomposite systems in order to organize their mass production and create standard industrial designs.

Keywords: erosion protection, geocomposite systems, inconvenient territories, zoning, mathematical modeling, stability of geocomposite systems

The article describes ways to equalize temperature differences in the material after preheating in the heating zone. A mode for changing the temperatures of the material and the furnace channel has been developed. The optimal length of the firing zone and the time of passage of the material were established, at which a constant temperature is maintained on the surface of the material. Values for optimizing the main parameters are given.

Keywords: firing, tunnel kiln, temperature equalization

This paper describes the development of a hybrid system for recognition of various types of personal data in unstructured texts in Russian language. The system is based on neural network and regular expressions. Regular expressions were used to detect structured entities such as telephone and passport numbers. In order to detect named entities, including persons, locations and organizations, the neural network was used. For training and validation, a specialized Russian-language dataset for named entity recognition was created based on Nerus and WiNER labeled datasets. The proposed neural model is using contextualized ELMo embeddings and includes bidirectional LSTM layers with conditional random field layer (ELMo-BiLSTM-CRF). The performance of the resulting model was analyzed on the validation set, including accuracy on individual classes. During the evaluation, 4 different metrics were used, including precision, recall, f1-score and macro-f1. For more detailed analysis, a confusion matrix was created. The resulting hybrid model can be utilized to reduce the cost of storing and processing textual data, as well as preserve user privacy in case of leaks.

Keywords: personal data, natural language processing, named entity recognition, conditional random field, neural network, recurrent neural network, regular expression

Determination of pile bearing capacity located in collapsible soils. This work simulates the tests in the Plaxis 2D software system, and also determines the bearing capacity in accordance with paragraph 9.9 of SP 24.13330.2021 Pile foundations. Modeling of three capacity tests lead to recieve different results according to chosen method of tne results evaluation. Based on the results of the article the imperfection of the current Russian regulatory document in the field of field testing of piles was revealed. However comparing of the test results was made with analytical calculation of pile bearing capacity.

Keywords: collapsible soils, pile bearing capacity, pile tests, finite element modeling, Plaxis

The development of an automatic system for installing a magneto-optical magnetic field sensor in a neutral position has been carried out. Installation in the neutral position is carried out by an automatic piezoelectric drive control system based on a microcontroller. A mathematical model is constructed and numerical simulation of the automatic control system is performed. The results and parameters of the simulation are presented. The developed system provides a significant increase in the autonomy of the sensor, which makes it possible to eliminate or significantly reduce the cost of regulating the sensor.

Keywords: magnetic field sensor, magneto-optical sensor, automatic control system, piezo motor

In the article, the authors examine the problem of ensuring cybersecurity in the modern world in terms of the study of social practices. The implemented cyber attacks are analyzed, and the danger of hacker attacks is shown. With a fair amount of evidence, it can be stated that in the modern world, the risks associated with cyber intrusions can include the loss or disclosure of consumer data, theft or disclosure of intellectual property, as well as the loss of investors as a result of the theft of funds or a decrease in the market value of companies subjected to cyber attacks. It is concluded that cybersecurity is a constantly evolving landscape, and now there is an urgent need to constantly learn from both our own experience and the experience of other companies countering cyber attacks effectively, and it is also important that successful interaction with adversaries in cyberspace requires a constant pursuit of a tactical, operational and strategic initiative.

Keywords: cyber wars, cognitive modeling, cyber attacks, hacker attacks, cyber risks, cyber defense

For the possibility of installing overhead cranes, steel columns of an industrial building are made in steps, with the allocation of crane and crane parts. The basis of the upper and lower parts of the column are steel I-beams with a mismatch of the central axes. As part of the work, variant modeling (using CAD) of a steel column that is part of the U-shaped frames of industrial buildings, consisting of crane and crane parts, was carried out. Various solutions for the difference of the central axes of the crane and crane parts of the column in the model are proposed. The results of static calculation of column elements are obtained. A comparison of the results obtained is made, an analysis of the optimal method of modeling column elements for structural schemes is performed. Based on the calculations performed and the analysis of the results obtained, conclusions are drawn.

Keywords: industrial building, I-beam, finite element method, stress-strain state, node, rod, circuit

The concept of a fibrous material (hereinafter referred to as FM) as a soft structure formed by fiber elements surrounded by air and areas of fiber interaction on touch surfaces is proposed and substantiated. The fiber elements are in a deformed state. The deformation of the fibers is reversible, elastic-elastic. In the areas of interaction between the fibers, the forces of adhesion and dry friction act. The deformation of the fibers leads to the preservation of residual internal energy in the material. At low loads, the FM can change its state reversibly. At high loads, the structure of the interaction sites irreversibly changes. The processes of aging and degradation of FM are gradual irrevocable transitions from one group of states to others. The dynamics of these processes is statistical in nature. Therefore, a Markov model of state change has been developed in the form of several subsets of irrevocable subsets and one ergodic subset of states. At the qualitative level, the possibility of using the proposed model to describe the dynamics of FM aging processes and estimate the duration of this process, taking into account its probabilistic and statistical nature, is shown.

Keywords: fibrous material, aging, soft structure, elasto-elastic deformation, irreversible process, markov model, statistical dynamics

The article considers the process of relaxation of fibrous material after the action of the load on it is completed. A simple model of the relaxation process is constructed in the form of an exponential function, which describes this process quite accurately. It is determined that the relaxation time estimates are robust with respect to the parameter distributions. The constructed relaxation models make it possible to estimate the magnitude of the residual relative strain corresponding to the plastic strain of the material.

Keywords: relaxation, deformation, fibrous material, robustness, Monte Carlo method, exponential model, regression

The results of a study of the effect of hardening the roof of workings of small length, of arbitrary shape, with a cross section of up to 80 m2, with advanced anchoring, which can significantly reduce the displacement of soil outcrops, are presented. The analysis shows that it is not possible to completely eliminate soil fallouts; therefore, a complex of studies of a stress-strain (SSD) soil mass, reinforced with a protective screen, was carried out. Finite element modeling (FEM) has established that advanced anchoring up to 15 m long does not work effectively, since the anchors are located in the zone of soil slippage. Increasing the length of the protective screen anchors to support their ends outside the sliding prism makes it possible to increase the stability of soil outcrops in the face.

Keywords: underground construction, stresses, displacements, hardening, anchoring, modeling, finite element method

In a competitive environment, the definition of an effective strategy for the development of a company acquires great importance and is impossible without the use of mathematical modeling methods. The article proposes a hierarchically organized model of an IT enterprise. The consideration was carried out on the example of Electronic Medicine LLC. The Cobb-Douglas production function is used to describe the firm's activities. Numerical calculations are made by simulation for real input data. The Stackelberg equilibrium is constructed, and the results obtained are analyzed.

Keywords: hierarchical modeling, Stackelberg equilibrium, Cobb-Douglas production function, simulation

This article analyzes the problems of spatial, temporal and phase synchronization in non-cooperative passive bistatic radar coordinate meters, which make it difficult to detect weak objects. The method of time and phase synchronization based on the estimation of the parameters of the direct wave signal and the method of detecting weak objects, which consists of a long coherent accumulation of signal parameters, are investigated. A universal algorithm is proposed, which consists of two stages: extraction of direct wave pulses and parameter estimation. Based on the estimation of parameters and waveform, an algorithm for detecting weak targets based on the generalized Fourier transform is given.

Keywords: non-cooperative passive bistatic radar, algorithm, synchronization, pulse, generalized Fourier transform

The search for orthogonal and quasi-orthogonal matrices is considered as a sequence of setting initial conditions, choosing an implementation method, filtering a set of generated sequences. It is proposed to accelerate the search for matrices by pre-fixing their structure and filtering the generated sequences using the Fourier spectrum. Fixing the structure involves using the symmetry properties of the desired matrices. Filtering allows you to exclude sequences with explicit spectrum outliers when forming blocks of symmetric matrices.

Keywords: mining of matrices, Hadamard matrices, Propus conctruction, filtering sequences

The main maintenance of a diversification of production as activity of subjects of managing is considered. being shown in purchase of the operating enterprises, the organizations of the new enterprises, redistribution of investments in interests of the organization and development of new production on available floor spaces. The most important organizational economic targets of a diversification of management are presented by innovative activity of the industrial enterprise.

Keywords: ideal thread, flexible homogeneous inextensible thread, tension, balance of thread balance, balance on a smooth surface, balance on a rough surface, sag arrow

The article presents a method for calculating short-circuit currents in a DC traction network. The system of group grounding of supports, considered in the article, is equipped with an additional conductor that improves the working conditions of the entire section of the electrified railway by reducing the resistance of the short circuit loop.

Keywords: group grounding of supports, short-circuit current, electrified railway, traction network, fiber-optic communication line.group grounding of supports, short-circuit current, electrified railway, traction network, fiber-optic communication line

The article describes the study of the behavior of the reaction vector in the contact spot of the wheel with the support base when the values of the angle of rotation of the driving wheels vary. To find the dependence of the values, a MATLAB Simulink model was created with software blocks that allow determining the behavior of the reaction vector in the contact spot of the wheel with the support base when the values of the angle of rotation of the driving wheels vary.

Keywords: controllability, mathematical model, wheeled vehicle simulation, wheel tire, wheel rotation angle, MATLAB Simulink

The paper analyzes the thermal regime of a highly functional on-board control unit in an AMg6 aluminum alloy case and compares the obtained data with the thermal regime of a unit with a highly efficient heat sink made of composite materials. The calculation of the thermal field of the block was carried out using CAD tools based on the finite element method with a thermal application in order to assess its performance under given boundary conditions. Based on a comparative analysis of various heat-removing materials of the basic supporting structure, the least heat-stressed system was chosen.

Keywords: thermal regime, highly efficient heat removal, composite materials, on-board equipment, oxygen system, finite element method, mathematical model, computer-aided design system, electrical radio product, printed circuit board