Wavelets are widely used in various fields of science and technology for processing 1D signals and multidimensional images. However, technical information processing devices are developing more slowly than the amount of digital data is growing. Computational latency is the most important characteristic of such devices. This paper proposes an implementation of the Winograd method with a convolution step 2 to reduce the latency of wavelet image processing. The proposed scheme for implementing calculations has reduced the asymptotic computational complexity of wavelet processing of 2D images to 53% compared to the direct implemettaion method. A theoretical assessment of the computing device characteristics showed a reduction in latency of up to 67%. A promising direction for further research is the hardware implementation of the proposed approach on modern microelectronic devices.

Keywords: image processing, Winograd method, digital filtering, computational delay, wavelet transform, convolution with step

The activities of modern enterprises and organizations are becoming increasingly complex, which complicates decision-making tasks. In this regard, the issues related to the integration of innovative information technologies in the field of decision-making are being updated. One of these technologies is artificial intelligence, the main advantages of which are the ability to solve time-consuming tasks and perform analysis based on big data in real time. The purpose of the work is to analyze the methods of applying artificial intelligence technologies in the theory of decision-making. The paper considers the fundamental factors associated with the work of artificial intelligence, prospects and current trends in its development in solving decision-making problems. The scientific value of the article consists in an attempt to systematize knowledge regarding the use of intelligent technologies in decision-making theory. The materials of the article can be useful for modern software developers and the management of organizations.

Keywords: artificial intelligence, algorithm, data analysis, decision-making, model, information technology

In this article we present a novel algorithm for detecting moving objects using a stationary camera, which is based on statistical background modeling using edge segments. Traditional algorithms that rely on pixel intensity struggle in dynamic environments due to their inability to handle sudden changes in lighting conditions. These algorithms also tend to produce ghosting artifacts when a sudden change occurs in the scene. To address this issue, edge-based features that are robust to intensity variations and noise have been introduced. However, existing methods that rely on individual edge pixels suffer from scattered edge pixels and cannot effectively utilize shape information. Additionally, traditional segment-based methods struggle with variations in edge shape and may miss moving edges that are close to the background edges. In contrast to conventional approaches, our proposed method constructs the background model using regular training frames that may include moving objects. Furthermore, it avoids the generation of ghosting artifacts. Additionally, our method employs an automatic adaptive threshold for each background edge distribution to facilitate matching. This enhances the robustness of our approach to changes in illumination, camera movement, and background motion. Experimental results demonstrate that our method outperforms other techniques and efficiently detects moving edges despite the aforementioned challenges.

Keywords: motion detection, edges, canny edge detector, gaussian of color, gaussian of gradient magnitude, normal distribution, adaptive thresholds, statistical map

Analyses for the current publishes show that the problem of forecast water overflowing is actual and often causing a lot health threaten and other dangerouses. This article offers computing, analysis and development the regression model of the level of Ia river. The final model correspont the real data with proper level. The final calculation means that this model could be used for real forecast for defend the people from water's overflow.

Keywords: model, simulation, river, water level, flood, emergency, forecast, statistics, monitoring, analysis, iya river, Irkutsk region

A combinatorial problem - the problem of finding the set of all formal concepts of formal concepts is considered. The computational complexity of the problem is that the number of formal concepts depends exponentially on the size of the initial formal context. in the article to solve this problem, an algorithm for fragmentation and defragmentation of the formal context is given, based on the method of decomposing the formal context into fragments. The essence of the method is that the original formal context is divided into various fragments. The fragments have different sizes and a non-empty intersection. Each fragment is subsequently considered as a formal context and can again be subject to decomposition. As a result, a finite set of fragments is formed. Then formal concepts are found in each fragment and combined to form the desired set of all formal concepts of the formal context. The method is “non-distorting”: when dividing the context into fragments, new formal concepts are not formed and the sought-for concepts are not lost. The results of computational experiments are presented, showing the effectiveness of the developed algorithm.

Keywords: formal concepts analisys, fragmentation algorithm, formal context, object-attribute table, combinatorial problem, the problem of finding the set of all formal concepts

In this study, an analysis of the time series was conducted using a class of shift functions for arithmetic and geometric progressions, along with their synchronization using logarithmic decrement. The closing prices of IBM company stocks were taken as the examined data for each trading day. The shift functions of geometric and arithmetic progressions revealed almost-proportions and almost-periods in the examined data. These detected patterns emphasize the importance of applying shift functions in the analysis of time series, allowing the extraction of internal patterns and periodic fluctuations that might go unnoticed with standard analysis methods. Computing the minima and corresponding values of the geometric progression enabled the identification of almost-periods in the data. These results not only confirmed visual observations but also enhanced our understanding of the internal patterns of the time series. The findings underscore the effectiveness of applying methods for analyzing time series based on almost-proportions and metric techniques. These approaches play a crucial role in uncovering hidden patterns and subtle periodicities in data, providing a fundamental foundation for more accurate analysis and successful forecasting.

Keywords: nearly-proportionalities, synchronization of geometric progression, empirical data, geometric progression, shift functions

The article considers the issue of studying the deviation of geometric parameters of a curved surface and a facet surface approximating it. The approximating surface was constructed by triangulation. To obtain adequate results when approximating a surface, it is necessary that the geometric parameters of the approximated surface differ minimally from the parameters of the faceted surface. One of the most important geometric parameters of a surface is its normal at a given point. The deviation of the normals of the given and approximating surfaces significantly affects the calculation error.

Keywords: curved surface, faceted surface, normal to the surface, linear frame, tinted image, plane compartment

In connection with the revival of interest in wooden housing construction in Russia, the creation of specialized software systems for the calculation and design of buildings and structures made of wood is becoming relevant. One of the most popular systems in the world is light-frame housing construction. As one of the possible tools for automated design of light-frame wooden buildings, this article presents the FrameCAD program, developed at the Department of Metal, Wood and Plastic Structures of the Don State Technical University. Some of its capabilities are presented, allowing you to design wall fences of light-frame buildings, beamed wooden floors, perform calculations of individual frame elements taking into account the requirements of current regulatory documents and automatically generate albums of drawings of wooden structures in the domestic NormCAD program, as well as specifications for them factory made. FrameCAD has been tested in the design of a number of objects. The software product is developed by engineers who have many years of experience in the actual design and construction of light-frame buildings. It continues to be improved and supplemented, and in the future it may become a replacement for similar foreign complexes.

Keywords: wooden structures, software package, wall panels, beam overlap, automated calculation

A numerical simulation was used to investigate heat transfer in plate-fin radiators with round fillet profiles of various depths, including 0.55 mm, 1.1 mm, and 1.5 mm. The issue of flowing air around a radiator with a mass flow rate of 10-3 to 4·10-3 кг/с and a temperature of 293 K was solved. The radiator was heated using a heater, whose temperature was set from 323 to 353 K. Changes in heat flow, pressure drop, and energy efficiency indicator were shown depending on the air mass flow, according to the calculation results. The research findings indicate that the radiator featuring round fillet profiles and a depth of 1.65 mm exhibits the highest heat flow and energy efficiency indicators, as well as the lowest pressure drop.

Keywords: radiator, cooling system, numerical modeling, computational fluid dynamics, heat transfer, heat flow, pressure drop, energy efficiency, calculation, electronics

Tests to determine the seismic stability of elements of pipeline systems, in particular pipeline fittings, are included in the list of those necessary to confirm the operability of the element. In this study, a stand was developed for testing to determine the seismic stability of butterfly check valves, which are a type of pipeline fittings. A finite element analysis was carried out, data on maximum deformations, stresses and displacements of structural elements were obtained, and the response of the installation table to seismic impact was calculated. The resulting displacement values of the table structure do not exceed the limit values specified by the technical requirements and do not lead to distortion of the structure or destruction of joints, which makes it possible to move from design to manufacturing and commissioning of the stand.

Keywords: vibration tests, seismic resistance test bench, pipeline, pipeline valves, swing back gate, mathematical modeling, finite element method, strength calculation, simulation modeling, stress-strain state

The effectiveness of the modified Fourier method associated with the use of orthogonal splines is shown when solving the problem of dynamics of a circular membrane with an elliptical hole. A posteriori estimates of the accuracy of the obtained approximate solutions complement the previously proven theoretical convergence of the algorithm and characterize the high accuracy of solutions to the problem of membrane dynamics with a curved boundary. The differences between the approximate solutions of the problem presented in the form of finite series decrease with an increase in the number of grid nodes used in calculations.

Keywords: Fourier method, orthogonal splines, finite series, dynamics of membrane, a posteriori estimation

In this paper, a physics-informed neural network containing natural gradient descent is proposed to solve the boundary value problem of the Poisson equation. Machine learning methods used in solving partial differential equations are an alternative to the finite element method. Traditional numerical methods for solving differential equations are not capable of solving arbitrary problems of mathematical physics with equivalent efficiency, unlike machine learning methods. The loss function of the neural network is responsible for the accuracy of solving initial and boundary value problems of partial differential equations. The more efficiently the loss function is minimized, the more accurate the resulting solution is. The most traditional optimization algorithm is adaptive moment estimation, which is still used in deep learning today. However, this approach does not guarantee achieving a global minimum of the loss function. We propose to use natural gradient descent with the Dirichlet distribution which increase the accuracy of solving the Poisson equation.

Keywords: natural gradient descent, Poisson equation, Fisher matrix, finite element method, neural networks

The aim of this study is mathematical modelling of the southern part of the Siberian craton using the finite element method. The task of the study is to carry out mathematical modelling of the stress-strain state of the visco-elastic-plastic medium of the Yakutsk-Vilyui large eruptive province on the basis of the boundary value problem. Hypothesis of the study: the possibility of using the results of numerical study to determine the zones of mineral dislocations. In the southern part of the craton, on the territory of the Republic of Sakha-Yakutia, there are the richest oil and gas fields, the largest of which is the Ust-Vilyuyskoye field located in the southern part of the craton. Research method: numerical experiment carried out by the method of mathematical modelling. Results achieved: finite element studies were carried out, the possibility of using numerical methods was determined, the stress-strain state of the plate was analysed, and the locations of anomalies of dislocations of craton rocks were determined to identify potential oil and gas bearing fields.

Keywords: craton, mathematical modeling, stress-strain state, geophysics, geotectonics, stretching, igneous province, material models, Hardening Soil model, finite element method, mineral dislocation

Prism spectral devices have a spectrum-variable dispersion and therefore a nonlinear relationship between the wavelength and the position of spectral lines on the focal surface of a spectral monochromator device, which makes it difficult to calibrate such devices in terms of wavelengths and dispersion.Most often, the well-known Hartmat formula is used for graduation. However, the accuracy of its calculation is satisfactory only in a limited spectral range, and therefore the calculation is carried out on overlapping areas no wider than 200 nm with averaging in overlapping zones. Averaging gives a calibration curve (and, accordingly, a dispersion curve) with gaps at the joints. In this paper, we consider the possibility of using a single calibration for the entire spectrum region, providing smooth, continuous calibration curves. The best result is obtained by using the Hartmann formula for the entire spectral range, after which a set of deviations of the calibration points is determined. This set is interpolated by a polynomial of an arbitrarily chosen order n using the least squares method.

Keywords: monochromator, spectrum, calibration, dispersion, Hartmann formula, interpolation, polynomial

This work examines the applicability of a specific force field model – ANI-2x – to the polymer polyphenylene sulfide. The order of the actions taken is given and, as a result, the radial distribution function of sulfur atoms in systems with different temperatures is compared. It was shown that qualitatively the ANI-2x field correctly describes the situation during the transition through the glass transition temperature.

Keywords: poluphenylene sulfide, classic molecular dynamics, machine learning, force field, potential, polymer, computer simulation, model

The article considers an approach to solving the problem of optimizing the speed of aggregating queries to a continuous range of rows of a PostgreSQL database table. A program module based on PostgreSQL Extensions is created, which provides construction of a segment tree for a table and queries to it. Increased query speed by more than 80 times for a table of 100 million records compared to existing solutions.

Keywords: PostgreSQL, segment tree, query, aggregation, optimization, PosgreSQL Extensions, asymptotics, index, build, get, insert

This article analyzes data processing problems for training a neural network. The first stage of model training - feature extraction - is discussed in detail. The article discusses the method of mel-frequency cepstral coefficients. The spectrum of the voice signal was plotted. By multiplying the vectors of the signal spectrum and the window function, we found the signal energy that falls into each of the analysis windows. Next, we calculated the mel-frequency cepstral coefficients. The use of a chalk scale helps in audio analysis tasks and is used in training neural networks when working with speech. The use of mel-cepstral coefficients significantly improved the quality of recognition due to the fact that it made it possible to see the most informative coefficients. These coefficients have already been used as input to the neural network. The method with mel-frequency cepstral coefficients made it possible to reduce the input data for training, increase productivity, and improve recognition clarity.

Keywords: machine learning, data preprocessing, audio analysis, mel-cepstral coefficients, feature extraction, voice signal spectrum, Fourier transform, Hann window, discrete cosine transform, short Fourier transform

This article examines the previously studied linear in factors and non-linear in parameters modular regression model containing unary module operations. Through the use of binary, ternary, ..., l-ary module operations, a generalization of modular regression was proposed for the first time. A special case of generalization is considered - regression with a multiary operation modulus. The problem of accurately estimating such a model using least absolute deviations is reduced to a mixed integer 0-1 linear programming problem. Using data on farm productivity built into the Gretl econometric package, classical linear regression and modular regression with a multivariate operation were built. The quality of approximation of the proposed modular regression turned out to be higher than the quality of the linear model.

Keywords: regression analysis, modular regression, least absolute deviations, multiary operation modulus, mixed integer 0-1 linear programming problem

Using numerical modeling, we performed studies of the influence of the angle of inclination of the plates of the regenerative heat exchanger element on the heating time and pressure drop. The studies were conducted for models of heat exchange elements with lengths of 6 and 20 mm. Depending on the length of the element, the angle of inclination of the plates was: 10°, 20°, 30°, 40° (at L=6 mm) and 3°, 6°, 9°, 12° (at L=20 mm). At the boundary of the calculation area, the air flow velocity and temperature were established, namely 1 and 3 m/s, and 303 and 973 K. The research results demonstrated that increasing the angle of inclination of the plates helped reduce the heating time of the regenerator by 38.56-49.1%, depending on the length of the heat exchange element, the speed and temperature of the air flow.

Keywords: heat recovery, honeycomb heat exchanger, numerical modeling, calculation, heating time, pressure drop, heat exchanger geometry, angle of plate, air flow velocity, air flow temperature

Based on recent developments in the field of parallel computing, in particular at the SYCL abstraction level, the use of optimal parallel computing tools for building applications in the field of computational and applied mathematics is being considered. Examples are given of both simple computational algorithms and computations using mathematical libraries for computational linear algebra.

Keywords: parallel code,heterogeneous enviroment, intel data parallel c++, intel oneapi, sycl, onemkl, fpga accelerator, gpu accelerator

The paper proposes mathematical models that make it possible to describe the electrical conductivity of a nanocomposite based on carbon nanotubes, taking into account the waviness effect and the dispersion index. The model takes into account the contribution of various parameters, such as the concentration of nanotubes, the length, diameter and orientation of the tubes, as well as the electrical properties of the nanocomposite matrix. Using the proposed model, numerical experiments were carried out to evaluate the effects of waviness and dispersion index on the electrical conductivity of the nanocomposite. Comparisons of model data with experimental data are presented, confirming the adequacy and accuracy of the model. The results obtained can be used to optimize the process of creating nanocomposites based on carbon nanoturbines, as well as to increase the efficiency of their use in various fields, including electronics and energy.

Keywords: mathematical modeling, software package, nanocomposites, electrical conductivity, carbon nanotubes, computational experiment

The article presents the development of a software tool for modeling the influence of physical processes occurring in a single-mode optical fiber as a result of bending deformation. Model of bending deformation of single-mode optical fiber is considered. Classical and refined models of deformation and their influence on the optical fiber params are given. The initial data required to implement the software tool is discussed in detail. The development of the modeling program was gradually considered. The specifics of the implemented program obtained during the computational experiment are indicated.

Keywords: mathematical modeling, optical fiber, bending deformation, modeling of deformed fiber behavior, computational experiment, software

Using numerical simulation, we carried out studies on the effect of the length of a porous heat exchanger on the deposition of dust particles. The heat exchanger models with lengths of 5, 10, 20 and 30 mm were the subject of the studies. At the boundaries of the computational domain, we set the air velocity at 0.1, 1, and 5 m/s and the diameter of dust particles from 10-7 to 10-4 m. Research results have shown that with increasing length of the porous heat exchanger, the efficiency of dust particle deposition increases. This can lead to a decrease in the thermal and hydraulic characteristics of the heat exchanger.

Keywords: porous media, heat exchanger, numerical simulation, calculation, deposition of dust particles, heat exchanger length, air flow velocity, particle diameter, air cooling, microelectronics

Methods of computer formation of the equations of motion of multibody systems with a tree structure and algorithms for their reduction to the normal form of ordinary differential equations are considered. The equations of motion are written using Hamilton's formalism for an extended set of state variables of a mechanical system. The equations are presented in a compact visual form. Recursive formulas for determining all coefficients of equations are written out. Algorithms for reducing these equations to Hamilton equations in generalized coordinates and generalized momenta are presented. An algorithm for solving the obtained equations of motion for multibody systems using the LTDL-elimination is presented. Formulas are written that allow one to calculate the amount of arithmetic operations required to bring the equations of motion to normal form using the considered algorithms. On the basis of these formulas, a comparative analysis of the efficiency of algorithms for rigid bodies systems of various structures and with various types of connections between bodies is carried out. The results of the analysis are presented in the form of diagrams. The diagrams highlight areas in which the advantage of one or another method is manifested, depending on the type of mechanical system.

Keywords: multibody systems, equations of motion, dynamics, canonical momenta, mathematical modeling, computational efficiency

The problem of flexible vibrations of a rectangular orthotorque plate clamped along the contour is considered. The general solution of the problem, which satisfies the vibartion equation identically, is constructed on the basis of the superposition method in the form of two Fourier series. Clamped boundary conditions lead to a homogeneous infinite system of linear algebraic equations with respect to unknown coefficients in the general solution. The uniqueness of a bounded non-trivial solution of an infinite system for the natural frequency is proved, the asymptotics of the unknowns are found, and an effective solution algorithm is constructed. Examples of the numerical implementation of the developed algorithm for calculating the natural frequencies and natural modes of the plate vibrations are given.

Keywords: plate, vibrations, natural frequencies, planar forces, superposition method, infinite system of linear equations, asymptotics