Nizhny Novgorod State University of Architecture and Civil Engineering

This article describes the issue of automated transformation of two-dimensional technical drawings into three-dimensional wireframe models. Existing solutions primarily provide one-way conversion of three-dimensional models into two-dimensional drawings. The paper describes an algorithm for automated processing of projection views based on the use of bounding rectangles to identify projection views and projection vectors to reconstruct projection link lines; an algorithm for generating a wireframe model through analysis of the relationships between cloud points and edge projections onto projection views, taking into account various configurations of supporting lines (lines, ellipses) and expanding the class of modeled bodies to objects bounded by planes and second-order surfaces (ellipsoids, elliptical cylinders, and cones).The obtained results make it possible to significantly reduce the time required to construct a three-dimensional model from two-dimensional drawings of objects for various purposes.

The article explores the impact of the level of geometric detail on the accuracy of modeling physical processes over a digital twin of high-tech facilities. A miniature subsonic wind tunnel is used as an example. The authors have conducted a series of computer simulations with pipe models, varying in the degree of detail: from simplified to the most detailed. By comparing the results of these simulations, the researchers aim to determine the optimal level of model detail to create the most accurate digital twin. The findings are planned to be used to make practical recommendations on the selection of suitable geometric models for the creation of digital twins intended for aerodynamic research. Thus, the aim of the work is to establish the relationship between the complexity of the geometric model and the accuracy of the results of modeling aerodynamic processes in a digital twin. The more accurate the model, the more computing resources will be required, so finding the optimal balance between accuracy and computational efficiency is a key research objective.

The article is devoted to analyzing the possibilities and effectiveness of integrating information technology into classical methods of teaching foreign languages. It considers the main principles of traditional methods, reveals their strengths and weaknesses in the modern educational context. An overview of current IT tools and resources applicable to linguodidactics is provided, ranging from interactive online platforms and multimedia tools to artificial intelligence and virtual reality. Special attention is given to models and practical examples of integrating IT into grammatical, translational, direct, audio-lingual, and communicative teaching methods. The article also presents results from an empirical study that included a survey of teachers and students. This allowed us to assess the current level of application of IT, identify perceived advantages, and main challenges from the perspective of direct participants in the educational process. Based on the data obtained, conclusions are formulated about the potential of blended learning and practical recommendations are proposed to teachers, educational institutions, and developers of IT solutions for further improvement of foreign language teaching methods in the context of digitalization.

In modern machine learning, the efficiency of training is heavily influenced by the choice of optimization algorithm, with preconditioned methods offering significant speed improvements at the cost of increased memory usage. This study explores the trade-off between memory consumption and optimization performance by generalizing the Shampoo preconditioning algorithm to support arbitrarily sized preconditioning matrices, rather than being limited by tensor dimensions. We evaluate this approach on a perceptron trained for a simple regression task, measuring how different preconditioner sizes affect the training speed. Our results reveal a strong positive correlation: larger preconditioners consistently lead to faster learning, although the performance gains scale sublinearly with memory. Our findings provide practical insights into balancing computational resources and training efficiency in adaptive optimization.

A method of searching optimal nodes of approximation realized on the example of Runge function is proposed. The method is based on the use of interpolation algebraic curves in point calculus and is reduced to minimization of the target function of many variables, which provides minimum deviations of the approximating function from the original one. Traditionally, in the process of interpolation, the coefficients of the interpolating function are determined on the basis of the initial points, which does not make it possible to ensure the search for the optimal location of interpolation nodes, since the coordinates of the node points are necessary to determine the coefficients of the interpolating function. The peculiarity of interpolation curves realized in point calculation is that they are obtained by uniform distribution of the parameter along the numerical axis and keep the coordinates of interpolation nodes in the point equation, which makes it possible to set and solve the problem of their optimal location by minimizing the target function. After the realization of the coordinate calculation of the point equation of the interpolation curve, the final result of the approximation of the original function is an algebraic curve given in parametric form, which allows us to use the nonlinearity of space to significantly reduce the degree of the approximating polynomial function. For example, when using Chebyshev nodes, which are considered optimal for approximating the Runge function, at least 20 nodes are needed to achieve a high-quality approximation, which leads to the need to use a polynomial of degree 19. In this case, the MSE is 0.000111. Whereas for the Runge function approximation based on the optimized arrangement of approximation nodes, even when using 6 node points, the MSE is only 0.0000284, which is an order of magnitude lower compared to Chebyshev nodes and allows using two polynomials of degree 5 on each of the coordinate axes instead of one polynomial of degree 19.

The problem of using the boundary model of geometric solids representation in BIM is formulated. A new concept of solid geometric modeling is presented, which allows to define geometric solids as a selected part of space, according to which geometric solids are represented by an organized set of points by analogy with other geometric objects. The mathematical apparatus “Point Calculus” is used for analytical description of geometric solids. Examples of modeling geometric solids in point calculus are given. The advantages of this approach are the possibility of representation of geometric information in BIM in compact vector form and realization of parallel calculations at the level of mathematical apparatus. The prospect of further research is the use of the proposed concept for the representation of various elements of building structures with the subsequent optimization of the representation of geometric objects in the IFC format. This will significantly reduce the volume required for the transfer of geometric information between the systems of information modeling and computer-aided design, increase their performance and radically solve the problem of interoperability of existing BIM software packages.

This paper is devoted to the study of the interaction between nonthermal electrons injected into a flare loop and whistler turbulence in it. The features of redistributions of nonthermal electrons by energy and pitch angle are considered during their interaction with whistlers having spectra of different amplitudes, bandwidths, and central frequencies. We show, in particular, that this interaction results in an efficient and fast (seconds) acceleration of electrons in the energy range of 200–3000 keV, which leads to a significant flattening of their energy spectrum. The most efficient acceleration of high-energy electrons occurs by turbulence with low central frequencies, wide bandwidths, and large amplitudes. In this case, their concentration with energies above 1000 keV can increase by several orders of magnitude.