Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
ISSN (print): 1816-9791, ISSN (online): 2541-9005
Founder: Saratov State University
Editor-in-Chief: Kossovich Leonid Yuryevich, Doctor of Physics and Mathematics. sciences, professor
Frequency / Access: 4 issues per year / Open
Included in: White List (3rd level), Higher Attestation Commission List, RISC, Wos, Scopus, zbMath, MathSciNet
The journal is registered in the Federal Service for Supervision of Communications, Information Technology, and Mass Media (Roskomnadzor).
Registration PI № FS77-76640 of 26 August, 2019.
The central aim of the journal is to highlight the results of modern scientific research in the area of mathematics, mechanics and computer science, promoting the development of scientific research and educational activity.
The journal’s objectives are:
publishing original scientific papers with recent results in all the major areas of mathematics, mechanics and computer science;
publishing new original research results in the areas of biomechanics, nanomechanics, machine engineering and modeling;
publishing scientific reviews within the journal themes;
publishing up-to-date information about the field-specific conferences and other scientific events held at Saratov State University;
publishing information on field-specific external conferences;
publishing articles of leading scientists in the areas of mathematics, mechanics, computer science.
Publications are free of charge.
The journal is intended for researchers, university lecturers, students and graduate students.
Journal Themes
Mathematics, including computational mathematics; mechanics, including biomechanics, dynamics and durability of machines, appliances and equipment, mechanical engineering, computer science, computing equipment and control including mathematic modeling, numerical methods and program complexes; methods and systems of information security.
Current Issue
Vol 23, No 4 (2023)
Articles
Wasserstein and weighted metrics for multidimensional Gaussian distributions
Abstract
We present a number of low and upper bounds for Levy – Prokhorov, Wasserstein, Frechet, and Hellinger distances between probability distributions of the same or different dimensions. The weighted (or context-sensitive) total variance and Hellinger distances are introduced. The upper and low bounds for these weighted metrics are proved. The low bounds for the minimum of different errors in sensitive hypothesis testing are proved.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):422-434
422-434
Homogeneous spaces of unsolvable Lie groups that do not admit equiaffine connections of nonzero curvature
Abstract
An important subclass among homogeneous spaces is formed by isotropically-faithful homogeneous spaces, in particular, this subclass contains all homogeneous spaces admitting invariant affine connection. An affine connection is equiaffine if it admits a parallel volume form. The purpose of the work is the local description of the three-dimensional homogeneous spaces that do not admit invariant equiaffine connections of nonzero curvature. We have concerned the case of the unsolvable Lie group of transformations. The basic notions, such as an isotropically-faithful pair, an invariant affine connection, curvature and torsion tensors, Ricci tensor, equiaffine connection are defined. A local study of homogeneous spaces is equivalent to the investigation of pairs consisting of a Lie algebra and its subalgebra. For three-dimensional homogeneous spaces of nonsolvable Lie groups that admit invariant connections of nonzero curvature only, it is determined under what conditions the space does not admit equiaffine connections. Studies are based on the use of properties of the Lie algebras, Lie groups and homogeneous spaces and they mainly have local character. A feature of the methods presented in the work is the application of a purely algebraic approach to the description of homogeneous spaces and connections on them. The results obtained in the work can be used in works on differential geometry, differential equations, topology, as well as in other areas of mathematics and physics, since many fundamental problems in these areas relate to the investigation of invariant objects on homogeneous spaces, the algorithms can be computerized and used for the solution of similar problems in large dimensions.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):435-442
435-442
Orthorecursive expansions generated by the Szego kernel
Abstract
This article considers systems of subspaces of the Hardy space generated by the Szego kernel. The main result of the work is to establish the convergence of orthorecursive expansions with respect to the considered systems of subspaces. Note that the conditions for the convergence of orthorecursive expansions prove to be somewhat more restrictive compared to the previously obtained conditions for the convergence of order-preserving weak greedy algorithms and frame expansions.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):443-455
443-455
Identification of two-dimensional prestress fields in inhomogeneous plates
Abstract
Based on the model of in-plane oscillations of inhomogeneous prestressed plates, the new inverse problems of identifying the components of the prestress tensor via acoustic response probing are considered for the plates with and without holes and inclusions; the prestress components are assumed to be functions of two coordinates. Prestresses were set as a result of solving auxiliary problems of static loading of plates by some initial mechanical load. To solve the main and auxiliary problems of calculating the plates’ displacement functions, a finite element (FE) scheme was developed based on the derived corresponding weak problem statements, implemented in the form of software systems in the FE package FreeFem++. Rectangular plates clamped along one face, both solid and having a hole or a rigid insert, were considered. Inverse problems of identification of three prestress functions depending on two coordinates are formulated on the basis of additional data about the acoustic response on the non-clamped edges of the plates as a result of considering several sets of probing loads at several frequencies. In view of the nonlinearity of the inverse problems under study, an iterative approach was developed to solve them, which combines solving the direct problems for current approximations of the desired functions and the determination of the corresponding corrections from the operator equation built at each iteration. To solve the operator equation, a projection method has been employed that allows one to present the corrections in the form of expansions in terms of some smooth given functions and reduce the problem solution to the study of ill-conditioned SLAEs with respect to sets of the expansion coefficients using the A. N. Tikhonov method. The results of computational experiments on the simultaneous identification of two-dimensional prestress fields corresponding to various types of initial actions on the considered plates are discussed.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):456-471
456-471
Development and approbation of a mobile test bench for mechanical uniaxial compression testing of biological tissues
Abstract
A technique and a prototype of a mobile test bench for conducting experiments on uniaxial compression of biological tissue samples have been developed. The test bench consists of high-precision scales, an electronic caliper with modified grips, and a video camera. With the help of the test bench, a series of experiments (120 in total) was carried out to determine Young's modulus of atherosclerotic plaques and vascular walls removed from the human body no later than a few hours. A database of plaques and artery walls' mechanical characteristics, as close as possible to their real strength properties, has been formed. In addition, regression dependencies linking Hounsfield units and Young’s moduli of atherosclerotic plaques were constructed. The uniaxial compression technique has been verified on the Instron 3342 universal testing machine. Also, to demonstrate the applicability of the developed technique and test bench for uniaxial compression of hard tissues, experiments were conducted with 14 samples of bovine spongy bone.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):472-481
472-481
Stress state near dental implants accounting bone tissues resorption
Abstract
The results of numerical modeling by the boundary integral equations method (BIEM) of the effect of bone tissues resorption on the stress state near screw dental implants under action of normal and inclined compressive loads are presented. The direct version of the BIEM for piecewise homogeneous sub-regions is used. The computation of the implant and the surrounding bone tissues stresses was carried out for plane strain state, assuming the complete bonding of materials at the interface of the implant and bones (osteointegration) and consisted of two stages: 1) analysis of the entire implant structure with smoothed screw join between implant and the surrounding bone tissues; 2) studies of stress distribution taking into account the shape of the screw join of the implant and bone tissues. The model of the first stage of computations consisted of 7 sub-regions corresponding to the parts of the implant structure and bone tissues zones. On the second stage of computations it was assumed that those hollows in the spongy bone, which had formed in a bone after implant penetration, are conformed to the screw thread on the implant. The effect of bone tissues resorption on stresses concentration in the screw join of implants and spongy bone tissue is considered. The creating of computation models was performed on the assumption that the result of bones resorption is the cavity formation around implants. The computations were performed under the assumption that the bone tissues are isotropic and homogeneous elastic materials. It was found that as a result of resoprtion, there is a significant stresses redistribution in bone tissues and the implant with maximum equivalent stresses decreasing in the cortical bone tissue and increasing in spongy bone tissue. The results are presented as the distributions of stress intensity along the sub-regions boundaries of the computational model.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):482-495
482-495
Numerical analysis of the stress-strain state of osteotomies of the first metatarsal bone
Abstract
Deviation of the first toe to the outside, interconnected with the deviation of the first metatarsal bone to the inside, occurs in 46% of patients of the older age group and is called valgus deformity of the first toe. The negative impact of this pathology on the quality of life of patients is the reason for seeking medical help, the gold standard of which is surgical correction, and the basic surgical technique is osteotomy (sawing the bone and fixing its fragments with implants) of the first metatarsal. At the same time, an ideal osteotomy should provide initial stability in the early postoperative period. However, a large number of ways to perform osteotomy, as well as the advantages and disadvantages of each of the surgical techniques, do not allow to consider one of them as the most successful. In this regard, the aim of the work was to develop and validate a biomechanical model of osteotomy of the first metatarsal bone to analyze its stability and reliability depending on the type of osteotomy, the degree of displacement of bone fragments, as well as the number of fastening screws. In this study, biomechanical modeling of the most commonly used variants of osteotomy of the first metatarsal bone of the foot in the surgical treatment of its valgus deformity was carried out. For this purpose, 10 models of osteotomies of a separate first metatarsal bone were created, which were then subjected to static loading to analyze their stress-strain state and assess their success. Successful (stable and reliable) treatment options were identified, as well as unsuccessful ones. Two of the ten options considered were unsuccessful – scarf type osteotomies with displacement of bone fragments by 2/3 of its diameter and fixed with a single screw. It was revealed that osteotomies of the chevron type showed higher stability in comparison with scarf osteotomies. As a result, we note that in this study, numerical experiments were conducted for the first time to compare the stability and strength of the most commonly used variants of osteotomies based on a single bone model. A biomechanical model of scarf osteotomy of the first metatarsal bone has been developed and validated on the basis of mechanical experiments.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):496-511
496-511
Relaxation of residual stresses in surface-hardened rotating prismatic elements of structures under creep conditions
Abstract
A method for solving boundary problems of relaxation of residual stresses in a rotating surface-hardened prismatic specimen under high-temperature creep conditions has been developed. The problem models the stress-strain state of a surface-hardened prismatic rod with one end fixed to an infinitely rigid disk rotating at a constant angular velocity. In the first stage, we solve the problem of reconstructing fields of residual stresses and plastic deformations after the hardening procedure, which play the role of the initial stress-strain state, is solved. In the second stage, we address the problem of relaxation of residual stresses under creep conditions is addressed. A detailed study of the influence of angular velocity on the intensity of residual stress relaxation in different sections along the axial coordinate is carried out for a $10{\times}10{\times}150$ mm prismatic specimen made of EP742 alloy at a temperature of 650$^\circ$C, following ultrasonic mechanical hardening of one of its faces. The analysis of the calculation results revealed that for angular velocities ranging from 1500 rpm to 2500 rpm, a non-trivial effect is observed. The relaxation of residual stresses in more stressed sections experiencing axial tensile stresses due to rotation occurs less intensively than in the “tail” section, where the axial load is zero. The obtained results from this study can be useful in assessing the effectiveness of surface-hardened rotating components under high-temperature creep conditions.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):512-530
512-530
Algorithm for motion detection and gait classification based on mobile phone accelerometer data
Abstract
This paper briefly describes the development of information technology tools using biometric data, in particular, human gait parameters. The problems of assessing gait parameters using a mobile phone accelerometer in real conditions are briefly described. The relevance of this research is substantiated in the field of developing algorithms for assessing biometric gait indicators based on data from wearable devices. The main approaches to the processing of wearable device accelerometer data are considered, the main shortcomings and problems in improving the quality of gait parameter estimation are indicated. The algorithm for processing data from a mobile phone accelerometer is described. In the proposed algorithm, the selection of movement patterns during gait in the recorded data is carried out on the basis of statistical information within the “floating” time window (frequency component with the maximum contribution to the spectrum of the accelerometer signal, the duration of the selected time segments), as well as on the basis of the value of the correlation coefficient, selected time segments. At the stage of data segmentation, the time window of searching of movement segments, as well as the allowable thresholds of selecting movements by their duration, change depending on the individual characteristics of the gait and human activity. The classification of the selected segments according to the nature of gait movements is carried out on the basis of a feed-forward neural network. The sigmoid was used as the activation function for the hidden layers, and the normalized exponential function was used for the output layer. The neural network was trained using the gradient backdescent method with cross entropy as an optimization criterion. Due to the selection of segments with a high correlation coefficient, the classification of data shows the quality of distinguishing movements above 95%.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):531-543
531-543
Optimization of oil field development based on a 3D reservoir model obtained as a result of history matching
Abstract
The paper proposes an approach to optimizing the development of oil fields. The objective function includes weighted squares of development target indicators and regularizing terms, in which the coefficients are searched adaptively. Regularizing terms ensure the fulfillment of restrictions on the optimized parameters and the rapid convergence of the optimization process. When minimizing the objective function, linearization of the target indicators is performed, and the values of the optimized parameters at the next iteration are sought by solving the system of linear algebraic equations obtained from minimizing the quadratic functional. The values of the target indicators and their sensitivity to the parameters being optimized are calculated by fluid dynamic 3D modeling for the oil reservoir model obtained as a result of history matching for the period preceding the optimization period. Calculations are performed in a distributed computing system consisting of multi-core personal computers. To test the proposed approach, a model of a high-viscosity oil field in Tatarstan was used. The optimization was carried out with various weighting factors and desired oil recovery values in the corresponding target indicator. It is shown that the optimized plans provide more efficient development of the oil field compared to the plan used in practice. At the same time, the optimal plan, built on the basis of a reservoir model history-matched at an early stage of development, optimizes development for a model history-matched throughout the entire period of field development. This allows us to conclude that development plans obtained from a model history-matched using a short time period will optimize production characteristics for a real field to about the same extent. The time for solving optimization problems containing about 500 parameters in a distributed computing system was about a day.
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics. 2023;23(4):544-558
544-558