bluuebunny/crossref_metadata_2025 huggingface dataset:
Quasi-Gasdynamic Model and Numerical Algorithm for Describing Mixtures of Different Fluids
Authors: Elizarova T. G. , Shil’nikov E. V.
Published: April 2024

An elegant and easy-to-implement numerical algorithm for simulating flows of homogeneous gas mixtures with component temperatures and velocities assumed to be equal is constructed and tested. The algorithm yields monotone density profiles for the components even if their specific heat ratios are widely different. The algorithm can be used to simulate some flows of gas–liquid mixtures.
Four Classes of Definite Integrals about Hyperbolic and Trigonometric Functions
Authors: Li C. , Chu W.
Published: April 2024

By establishing recurrence relations and then determining boundary values, we examine four classes of definite integrals of xm over higher powers of cosh x, sinh x, cos x and sin x in denominators. They are explicitly evaluated in terms of the logarithm function, the Riemann zeta function and its variants, such as Dirichlet beta function and Legendre’s chi-function.
Solution Blow-Up and Global Solvability of the Cauchy Problem for the Equation of Moderately Long Longitudinal Waves in a Viscoelastic Rod
Authors: Umarov Kh. G.
Published: April 2024

The Cauchy problem for a nonlinear Sobolev-type differential equation modeling moderately long small-amplitude longitudinal waves in a viscoelastic rod is investigated in a space of continuous functions defined on the entire number line that have limits at infinity. Conditions for the existence of a global solution and for finite time solution blow-up are examined.
Constructive Algorithm to Vectorize P ⊗ P Product for Symmetric Matrix P
Authors: Glushchenko A. I. , Lastochkin K. A.
Published: April 2024

A constructive algorithm to compute elimination L and duplication D matrices for the operation of P ⊗ P vectorization when P = PT is proposed. The matrix L, obtained according to such algorithm, allows one to form a vector that contains only unique elements of the mentioned Kronecker product. In its turn, the matrix D is for the inverse transformation. A software implementation of the procedure to compute the matrices L and D is developed. On the basis of the mentioned results, a new operation vecu(.) is defined for P ⊗ P in case P = PT and its properties are studied. The difference and advantages of the developed operation in comparison with the known ones vec(.) and vech(.) vecd(.)) in case of vectorization of P ⊗ P when P = PT are demonstrated. Using parameterization of the algebraic Riccati equation as an example, the efficiency of the operation vecu (.) to reduce overparameterization of the unknown parameter identification problem is shown.
Refined Schemes for Computing the Dynamics of Elastoviscoplastic Media
Authors: Golubev V. I. , Nikitin I. S.
Published: April 2024

For a stable numerical solution of the system of equations governing an elastoviscoplastic continuous medium model, a second-order explicit-implicit scheme is proposed. An explicit approximation is used for the equations of motion, and an implicit approximation, for the constitutive relations containing a small relaxation time parameter in the denominator of the nonlinear free terms. A second-order implicit approximation for isotropic and anisotropic elastoviscoplastic models is constructed to match the orders of approximation of the explicit elastic and implicit adjustment steps. Refined formulas for correcting the stress deviators after the elastic step are derived for various viscosity function representations. The resulting solutions of the second-order implicit approximation for the stress deviators of the elastoviscoplastic equations admit passage to the limit as the relaxation time tends to zero. The correcting formulas obtained via this passage to the limit can be treated as regularizers of the numerical solutions to the elastoplastic systems.
Grid Convergence Analysis of Grid-Characteristic Method on Chimera Meshes in Ultrasonic Nondestructive Testing of Railroad Rail
Authors: Kozhemyachenko A. A. , Favorskaya A. V.
Published: April 2024

A three-dimensional direct problem of ultrasonic nondestructive testing of a railroad rail treated as a linear elastic medium is solved by applying a grid-characteristic method on curved structured Chimera and Cartesian background meshes. The algorithm involves mutual interpolation between Chimera and Cartesian meshes that takes into account the features of the transition from curved to Cartesian meshes in three-dimensional space. An analytical algorithm for generating Chimera meshes is proposed. The convergence of the developed numerical algorithms under mesh refinement in space is analyzed. A comparative analysis of the full-wave fields of the velocity modulus representing the propagation of a perturbation from its source is presented.
Existence of a Solution to Lamb’s Initial-Boundary Value Problem with a Limiting Value of Poisson’s Ratio
Authors: Kravtsov A. V.
Published: April 2024

The paper considers a Lamb’s initial-boundary value problem for an elastic half-space in the case when Poisson’s ratio takes the limiting value of 1/2. The existence of a classical solution in the form of an iterated improper integral in the case of axial symmetry is proved.
Numerical and Analytical Investigation of Shock Wave Processes in Elastoplastic Media
Authors: Wang L. , Menshov I. S. , Serezhkin A. A.
Published: April 2024

The Wilkins model for an elastoplastic medium is considered. A theoretical analysis of discontinuous solutions under the assumption of one-dimensional uniaxial strain is performed. In this approximation, the material equations for the deviator stress tensor components are integrated exactly, and only the conservative part of the governing equations remains, which makes it possible to derive a class of exact analytical solutions for the model. To solve the full nonconservative system of equations (without assuming the uniaxial strain), a Godunov-type numerical method is developed, which uses an approximate Riemann solver based on integrating the system of equations along a path in the phase space. A special choice of path is proposed that reduces the two-wave HLL approximation to the solution of a linear equations. Numerical and exact analytical solutions are compared for a number of problems with various regimes of shockwave processes.
Determining the Spectrum of Eigenvalues and Eigenfunctions for the Bernoulli–Euler Equation with Variable Coefficients by the Peano Method
Authors: Zakharov D. D. , Nikitin I. S.
Published: April 2024

The paper considers the problem of determining the natural frequencies and eigenwaves of transverse vibrations for the Bernoulli–Euler equation with variable coefficients. Such problems arise both in the case of complex geometry of a vibrating solid and in the case of functionally graded materials or the accumulation of damage in a classical elastic material. Solutions of boundary value problems are constructed using the expansion in Peano series. Under broad assumptions, the uniform convergence of Peano series is shown and estimates of the residual terms are obtained. Examples of the numerical implementation of the proposed procedure are given for bending vibrations of a rod with certain parameters of a variable cross section (geometric heterogeneity) and elastic modulus distribution (physical heterogeneity). Numerical examples are focused on assessing the geometric and elastic properties of samples in an experimental study of the fatigue strength of alloys during high-frequency cyclic tests based on the general principle of point resonant loading. The method proposed for solving problems of resonant vibrations for the Bernoulli–Euler equation can be used in the design of new promising cyclic test schemes and mathematical modeling of fatigue failure processes under high-frequency resonant vibrations.
SOLVING NONLINEAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND WITH DISCONTINUOUS KERNELS BY USING THE OPERATIONAL MATRIX METHOD
Authors: Amirkhizi Simin Aghaei , Mahmoudi Yaghoub , Shamloo Ali Salimi
Published: April 2024

A numerical method to solve the nonlinear Volterra integral equations of the first kind with discontinuous kernels is proposed. Usage of operational matrices for this kind of equation is a cost-efficient scheme. Shifted Legendre polynomials are applied for solving Volterra integral equations with discontinuous kernels by converting the equation to a system of nonlinear algebraic equations. The convergence analysis is given for the approximated solution and numerical examples are demonstrated to denote the precision of the proposed method.
Discontinuity Structures and Solitary Waves in Electromagnetic Hydrodynamics Associated with Linear and Nonlinear Alfvén Wave Resonances
Authors: Bakholdin I. B.
Published: April 2024

Nondissipative and weakly dissipative discontinuity structures are considered. A special numerical method for studying periodic waves is used. The location of branches of periodic solutions is investigated. Solitary waves and nondissipative discontinuity structures are sought as limiting solutions. It is found that, in addition to the resonance of long Alfvén waves with short fast and slow magnetosonic waves, there is also resonance with long waves, which leads to the occurrence of hybrid-type solitary waves and hybrid-type discontinuity structures. Partial differential equations are solved to find out if the found structures are actually observed.
SOFT COMPUTING ARTICIAL INTELLIGENCE OF SCHRöDINGER TIME INDEPENDENT EQUATION ARISES IN WHEELER-DEWITT MODEL OF QUANTUM COSMOLOGY
Authors: Basat Najam Ul , Asghar Mahmoona
Published: April 2024

Schrödinger time independent equation arises in Wheeler–DeWitt model of quantum cosmology to develop a wave function for the corrections of cosmologies. In this work, k=0 rödinger–Wheeler–DeWitt model is developed by using canonical transformation to transformed Hamiltonian equation. The exact solutions for flat universe () model is presented and then soft computing technique through Levenberg–Marquardt backpropagation neural networks (LMB-NNs) is implemented. The data set of the flat universe model is generated for four different cases of separation constant B with step size 0.1 by Mathematica and imported into LMB-NNs for training, testing, and validation of the our proposed technique. The performance of LMB-NNs is provided by the validation of mean square error, error histogram, and regression analysis. The Statistical analysis; mean, minimum, maximum, and standard deviation, is also presented.
Analysis of the Influence of Quantum Effects on Optical Characteristics of Plasmonic Nanoparticles Based on the Discrete Sources Method
Authors: Eremin Yu. A. , Lopushenko V. V.
Published: April 2024

The discrete sources method is adapted to the study of surface quantum effects based on mesoscopic boundary conditions with Feibelman parameters. A comparative analysis of the influence of bulk nonlocal effects and surface effects on optical characteristics of gold and silver nanoparticles is carried out using the generalized nonlocal optical response model. It is established that allowance for the nonlocal effect in the noble metals always leads to a reduced amplitude of the surface plasmon resonance (SPR) and its blue shift, while the surface effect depends substantially on the geometry of the particles. To a large degree, the mesoscopic boundary conditions recover the SPR amplitude as compared with the bulk nonlocal effect. This difference is especially noticeable in the field enhancement factor on the surface of the particles. Additionally, substantial differences in the SPR behavior for gold and silver particles are found in the case of mesoscopic boundary conditions.
Blow-Up of the Solution to the Equation for Nonlinear Beam Vibrations with Allowance for Transverse Deformation Effects
Authors: Umarov Kh. G.
Published: April 2024

Beam vibrations with allowance for deformation effects in the transverse direction are modeled using a nonlinear Sobolev-type differential equation, for which the Cauchy problem is investigated in the space of continuous functions. Conditions for solution blow-up on a finite time interval are considered.
A Novel Fitted Method for a Class of Singularly Perturbed Differential-Difference Equations with Small Delay Exhibiting Twin Layer or Oscillatory Behaviour
Authors: Alam Javed , Prasad Hari Shankar , Ranjan Rakesh
Published: April 2024

A new exponentially fitted three term method is developed for the numerical treatment of a class of linear second order singularly perturbed differential-difference equations (SPDDEs) which involves the small delay in un-differentiated term. The solution of such equations with the interval and boundary conditions exhibits twin layer or oscillatory behaviour. The method uses the Taylor’s series expansion for constructing an equivalent valid version of the original problem first and then, to derive a new three term finite difference recurrence relationship/scheme. The non-uniformity in the solution is resolved by the introduction of a suitable fitting parameter in the derived new scheme. Finally the resulting system of algebraic equations is solved by the well known “discrete invariant algorithm.” Method is analyzed for the stability and convergence, and the theory is illustrated by solving several test example problems. Computational results are tabulated and compared to show the applicability, accuracy and efficiency of the method. Theory and computation show that the method is able to approximate the solution very well with second order convergence rate.
Stability Analysis of Polymerization Fronts
Authors: Joundy Y. , Rouah H. , Taik A.
Published: April 2024

In this article, we study the influence of certain parameters on the stability conditions of the reaction front in a liquid medium. The mathematical model consists of the heat equation, the concentration equation and the Navier–Stockes equation under the Boussinesq approximation. An asymptotic analysis was performed using the approximation proposed by Zeldovich and Frank–Kamentskii to obtain the interface problem. A stability analysis was carried out to obtain a linearized problem which will be solved numerically using a multiquadric radial basis function method to find the convective threshold. This will allow us to conclude the effect of each parameter on the stability of the front, in particular the amplitude and the resonance frequency.
Density Function-Based Trust Region Algorithm for Approximating Pareto Front of Black-Box Multiobjective Optimization Problems
Authors: Ju K. H. , O Y. B. , Rim K.
Published: April 2024

In this paper, we consider a black-box multiobjective optimization problem, whose objective functions are computationally expensive. We propose a density function-based trust region algorithm for approximating the Pareto front of this problem. At every iteration, we determine a trust region and then in this trust region, select several sample points, at which are evaluated objective function values. In order to obtain non-dominated solutions in the trust region, we convert given objective functions into one function: scalarization. Then, we construct quadratic models of this function and the objective functions. In current trust region, we find optimal solutions of all single-objective optimization problems with these models as objectives. After that, we remove dominated points from the set of obtained solutions. In order to estimate the distribution of non-dominated solutions, we introduce a density function. By using this density function, we obtain the most “isolated” point among the non-dominated points. Then, we construct a new trust region around this point and repeat the algorithm. We prove convergence of proposed algorithm under the several assumptions. Numerical results show that even in case of tri-objective optimization problems, the points generated by proposed algorithm are uniformly distributed over the Pareto front.
Evolution of the Shape of a Gas Cloud during Pulsed Laser Evaporation into Vacuum: Direct Simulation Monte Carlo and the Solution of a Model Equation
Authors: Morozov A. A. , Titarev V. A.
Published: April 2024

The dynamics of gas expansion during nanosecond laser evaporation into vacuum is studied. The problem is considered in an axisymmetric formulation for a wide range of parameters: the number of evaporated monolayers and the size of the evaporation spot. To obtain a reliable numerical solution, two different kinetic approaches are used—the direct simulation Monte Carlo method and solution of the BGK model kinetic equation. The change in the shape of the cloud of evaporated substance during the expansion process is analyzed. The strong influence of the degree of rarefaction on the shape of the forming cloud is shown. When a large number of monolayers evaporate, good agreement with the continuum solution is observed.
COLOR PERCEPTION AND ITS CODING IN SIMIAN NEOCORTEX
Authors: Aseyev N. A.
Published: April 2024

Perception of color by human and nonhuman primates is a complex problem, which is studied not only by neurophysiology, but also by neighboring fields of science such as psychophysiology, psycholinguistics, and even philosophy. With neurophysiology as a starting point, I review contributions of adjacent fields in understanding of the primates’ color space encoding. All known at the moment neurophysiologic mechanisms of color perception by primates are reviewed and a hypothetical way of color stimuli processing is proposed, suggesting at a final stage involvement of conceptual (gnostic) neurons encoding only colors of visual stimuli.
SECOND-ORDER VISUAL MECHANISMS: REVIEW OF RESEARCH
Authors: Babenko V. V.
Published: April 2024

The review is devoted to the analysis of studies aimed at studying second-order visual filters as a mechanism for preattentive grouping of local visual information by striate neurons (first-order filters). The development of ideas about possible mechanisms for combining primary visual features is analyzed, with the emphasis on studies of the properties of second-order filters. The questions of spatial organization and principles of interaction of filters of the first and second orders are considered. The results indicating the multichannel nature of the pooling mechanism and possible relationship between the frequency and orientation settings of the filters of the first and second order are described. A model for organizing filters of the second order is presented, possible neurophysiological correlates of these mechanisms are analyzed, role of the second-order mechanisms in visual perception is considered.
PARADIGM CHANGE IN COGNITIVE SCIENCES
Authors: Knyazev G. G.
Published: April 2024

Since the 1950s, the dominant paradigm in the cognitive sciences has been cognitivism, which emerged as an alternative to behaviorism, and predominantly views cognitive processes as various kinds of “computations” similar to those performed by the computer. Despite significant advances made in the last quarter of the 20th century within this paradigm, it does not satisfy many scientists because it could not adequately explain some features of cognitive processes. Connectionism, which emerged somewhat later, recognizes the role of computational processes, but as their basis considers a neural network, which is a much better model of brain functioning than Turing-type computations. Neural networks, unlike the classical computer, demonstrate robustness and flexibility in the face of real-world problems, such as increased input noise, or blocked parts of the network. They are also well suited for tasks requiring the parallel resolution of multiple conflicting constraints. Despite this, the analogy between the functioning of the human brain and artificial neural networks is still limited due to radical differences in system design and associated capabilities. Parallel to the paradigms of cognitivism and connectionism, the notions that cognition is a consequence of purely biological processes of interaction between the organism and the environment have developed. These views, which have become increasingly popular in recent years, have taken shape in various currents of the so-called enactivism. This review compares the theoretical postulates of cognitivism, connectionism, and enactivism, as well as the predictive coding paradigm and the free energy principle.
EFFECT OF GLYCOLYSIS SUPRESSION ON ULTRASTRUCTURE OF THE HIPPOCAMPAL GIANT SYNAPSES
Authors: Zhuravleva Z. N. , Malkov A. E. , Popova I. Yu.
Published: April 2024

Suppression of glycolysis in the rat hippocampal formations was induced by daily intracerebroventricular injection of 2-deoxy-D-glucose for 10 days. Using electron microscopy, a disturbance of morphological interactions of axonal terminals of granular neurons with perisynaptic astrocytic processes was found. At the same time, both the determinant ultrastructural characteristics of giant synapses and two types of functional contacts (asymmetric chemical active zones with dendritic spines and symmetric adhesive junctions with dendrites) were retained. However, they showed morphological signs of a weakening of synaptic processes, which were expressed in a decrease in the number of intraterminal active zones, clustering of synaptic vesicles, and their removal from neurotransmitter release sites. Compared to the norm, an increase in the number of small mitochondria with an electron-dense matrix and the evidence of initiation of glycogen synthesis in the form of glycosomes were found in the giant terminals. The data obtained indicate that the giant synapses of the hippocampal mossy fibers are a plastic, self-correcting system that is able to function by adapting its own bioenergetic metabolism, when brain glycolysis is suppressed.
FORMATION OF PROSOCIAL BEHAVIOR AND ITS NEUROPHYSIOLOGICAL MECHANISMS IN EARLY CHILDHOOD
Authors: Pavlenko V. B. , Orekhova L. S. , Portugalskaya A. A. , Mikhailova A. A.
Published: April 2024

From a very early age children are capable on prosocial acts: giving objects, comforting and sharing with other people. This review considers modern research on the patterns and neurophysiological mechanisms of helping behavior (HB) formation in early childhood, including the results of the authors’ own work. Methods for HB researching in infants and young children are presented. The factors of development and neurophysiological mechanisms of instrumental, empathic and altruistic HB, and the role of empathy in these kinds of behaviors are analyzed. We also described data about involvement of various brain structures (for example, the mirror system as extended part of sensorimotor and emotional neural networks) in implementation of HB. The importance of research into the mechanisms of prosocial behavior for the full-fledged upbringing and education of children in the conditions of modern society is emphasized.
THE DORSAL LATERAL GENICULATE NUCLEUS: ANATOMY, HISTOLOGY, ONTOGENESIS
Authors: Mikhalkin А. А. , Merkulyeva N. S.
Published: April 2024

Review is devoted to the structure and function of the main visual thalamic nucleus – dorsal part of the lateral geniculate nucleus, and its formation during prenatal and postnatal ontogenesis. The structure and ontogeny of the related structures (retinal ganglion cells and visual cortex, and their projections) are also reviewed. Particular attention is paid to the morphological and functional differences between X, Y, and W parallel channels, and to the development of different layers of the dorsal the lateral geniculate nucleus.
INDICES OF NEUROPLASTICITY AND FUNCTIONAL REORGANIZATION IN MOTOR FUNCTIO RECOVERY AFTER STROKE
Authors: Fedotova I. R. , Bobrov P. D. , Kondur A. A.
Published: April 2024

The paper reviews data on changes of various indices calculated from multi-channel EEG, MRI, fMRI, and DTI data obtained from post-stroke patients during motor function recovery. The indices are most frequently discussed in literature on the topic of both motor rehabilitation in general and using BCI-based procedures in particular. The dynamics of the indices considered reflects the changes in interhemispheric imbalance during movement, the contribution of different areas and their interaction during motor execution as well as structural reorganization. The role of damaged and intact hemispheres and particular areas in motor recovery is discussed.
WORKING MEMORY OF MACACA MULATTA MONKEYS FOR COLOR AND MONOCHROME IMAGES
Authors: Podvigina D. N. , Ivanova L. E. , Harauzov A. K.
Published: April 2024

In behavioral experiments, we studied the ability of rhesus monkeys (Macaca mulatta) to keep in working memory visual objects that differ either in shape, or in color, or in a combination of these features. Six male rhesus monkeys performed a delayed matching-to-sample task, with three geometric shapes from a set of stimuli as samples. In the first series of experiments, these were colored figures of various shapes, in the second – circles of different colors, in the third – monochrome images of various figures from the set of stimuli. When using both features to memorize objects, the monkeys showed the maximum result, and the task of matching by color performed better than the task of matching by shape. The latter result disagrees with the data (Fehring et al., 2022), where in similar experiments, though with one sample, the opposite bias was observed. The reason for this may be the shift from local features (contours of shapes) to global ones (color) when recognizing and memorizing visual objects under conditions of a greater memory load in our study.
INCREASE OF INTRACRANIAL EEG ALPHA PEAK FREQUENCY AS A RESPONSE TO THE OWN-NAME STIMULUS DURING GENERAL ANESTHESIA IN ELEVEN PATIENTS WITH BRAIN TUMORS
Authors: Portnova G. V. , Kantserova A. O. , Oknina L. B. , Pitskhelauri D. I. , Podlepich V. V. , Vologdina Ya. O. , Masherov E. L.
Published: April 2024

The few existing studies demonstrated that hearing one’s name could have an arousal or alertness impact during unconsciousness. At the same time, the brain areas involved in this reactivity remained unknown. In this study, we attempted to register a response from two brain areas, the mesencephalon and cerebral cortex, in eleven patients who underwent posterior third ventricle or posterior fossa tumor removals under general anesthesia. We used 2 deep electrodes and 16 scalp electrodes and a registered electroencephalogram (EEG) for 2 states: the resting state, and stimulation state (which included sounds of one’s name, another name, and noise, presented in random order). Our results indicated that patients under general anesthesia could respond to their names (demonstrated by accelerated alpha-peak frequency), compared to other sounds and the resting state EEG, which was registered both on the cerebral and mesencephalon levels, indicating activated brain systems.
THE LABELING BENEFIT IN FAST MAPPING AND EXPLICIT ENCODING
Authors: Perikova E. I. , Filippova M. G. , Makarova D. N. , Gnedykh D. S.
Published: April 2024

The aim of this study was exploring the role of labels in acquisition of information about new objects depending on the learning strategy. In order to reach this aim we investigated efficiency of identification of new objects presented through fast mapping or explicit encoding taking into consideration eye movement patterns. 32 subjects were presented with 8 new fruits 8 times each. The images were accompanied with unique audial labels in 50% of the cases. Visual search of the target image among distractors was used as an assessment task. The results showed that fast mapping speeded learning of information about new objects compared to explicit encoding. We found positive impact of unique labels of new fruits on the results of visual search task. This impact was stronger for fast mapping compared to explicit encoding.
WEEGIT – software for visualization and annotation of the electrophysiological activity registration data
Authors: Suchkov D. S. , Shumkova V. V. , Sitdikova V. R. , Silaeva V. M. , Logashkin A. E. , Mamleev A. R. , Minlebaev M. G.
Published: April 2024

Wizard for EEG Information Tabling – “WEEGIT” is a software designed for visualization and annotation of the long-lasting records of activity. Long-lasting records of raw data are used in various areas of life sciences and well represented in neuroscience. In spite of development of other techniques and approaches the electrophysiological activity registration remains the “golden standard” in neurobiological research. Therefore, we developed and verified “WEEGIT” as a powerful and convenient tool for electrophysiological recordings’ description. We combined the most important features presented in other commercial and noncommercial software in the “WEEGIT”. Presented software can operate with widely used formats of records. ”WEEGIT” allows adaptive visualizing of up to 512 channels of record in different timescale without loss of efficiency and consumption of large machine resources. Visualizing also includes optional built-in temporal-spatial analysis (density of current sources or the density of action potentials) displayed as a background image. Integration of a set of optional filtering and signal transforming procedures allows improving record visualization. “WEEGIT” has a convenient graphical user interface with opportunity of simultaneous time browsing and annotating of the records in one workspace. Annotation can be done by simple text information typing as well as an interactive placing of specialized labels and objects. Software also allows saving data in the resampled format, both for the whole record and for user-defined events. In conclusion, “WEEGIT” provides a great set of benefits for the convenient workflow for beginners and specialists in the electrophysiological area of research, including preparation of the data for further specialized analysis.
RECOGNITION OF ORAL SPEECH ACCORDING TO MEG DATA BY COVARIANCE FILTERS
Authors: Verkhlyutov V. M. , Burlakov E. O. , Gurtovoy K. G. , Vvedensky V. L.
Published: April 2024

Speech recognition based on EEG and MEG data is the first step in the development of BCI and AI systems for their further use in inner speech decoding. Great advances in this direction have been made using ECoG and stereo-EEG. At the same time, there are few works on this topic on the analysis of data obtained by non-invasive methods of recording brain activity. Our approach is based on the evaluation of connections in the space of sensors with the identification of a pattern of MEG connectivity specific for a given segment of speech. We tested our method on 7 subjects. In all cases, our processing pipeline was quite reliable and worked either without recognition errors or with a small number of errors. After “training”, the algorithm is able to recognise a fragment of oral speech with a single presentation. For recognition, we used segments of the MEG recording 50–1200 ms from the beginning of the sound of the word. For high-quality recognition, a segment of at least 600 ms was required. Intervals longer than 1200 ms worsened the recognition quality. Bandpass filtering of the MEG showed that the quality of recognition is equally effective in the entire frequency range. Some decrease in the level of recognition is observed only in the range of 9–14 Hz.
Projector Approach to Constructing the Asymptotics of Solution of Initial Value Problems for Weakly Nonlinear Discrete Systems with Small Step in the Critical Case
Authors: Kurina G. A , Khoay Nguen Tkhi
Published: April 2024

An algorithm for constructing an asymptotic solution containing boundary functions for an initial value problem for a weakly nonlinear system of discrete equations with small step in the critical case under certain conditions is given in the article by V.F. Butuzov and A.B. Vasil’eva in Differ. Uravn., 1970, vol. 6, no. 4, pp. 650–664. In the present paper, orthogonal projectors are used to construct the asymptotics of the solution of this problem. This projector approach greatly simplifies the understanding of the algorithm for constructing the asymptotics and permits explicitly writing the problems from which one can find the terms of any order in the asymptotics of the solution.
Asymptotics of Solutions of Linear Singularly Perturbed Optimal Control Problems with a Convex Integral Performance Index and a Cheap Control
Authors: Danilin A. R , Shaburov A. A
Published: April 2024

We consider an optimal control problem for a linear system with constant coefficients with an integral convex performance index containing a small parameter multiplying the integral term in the class of piecewise continuous controls with smooth geometric constraints. Such problems are called cheap control problems. It is shown that the limit problem will be a problem with a terminal performance index. It is established that if the terminal term of the performance index is a convex (strictly convex) and continuously differentiable function, then the performance functional in the limit problem has similar properties. It is proved that, in the general case, convergence with respect to the performance functional is valid, and under the condition of strict convexity of the terminal term of the performance index in the original problem, convergence to the minimum point of the terminal summand of the performance index in the limit problem is valid. The limit of the defining vector in the original problem is found as the small parameter tends to zero. In particular, it is shown that the first component of the defining vector in the original problem converges to the defining vector in the limit problem. The problems of controlling a point of low mass in a medium with and without resistance with a terminal part depending on both slow and fast variables are considered in detail, and complete asymptotic expansions of the defining vectors in these problems are constructed.
On Linearization of Single-Input Nonlinear Control Systems Based on Time Scaling and a One-Fold Prolongation
Authors: Fetisov D. A
Published: April 2024

We prove a necessary and sufficient condition for the linearizability of single-input nonlinear control systems in the class of transformations containing time scaling and preserving the state manifold. A description is given for systems that are obtained by a 1-fold prolongation of a single-input nonlinear control system and are-orbitally linearizable. It is proved that the-orbital linearizability of the system obtained by a 1-fold prolongation of a single-input affine control system implies the-orbital linearizability of the original system as well. It is shown that if the system obtained by a fold prolongation of a single-input nonlinear control system, where, is orbitally linearizable, then the system obtained from the original system by its 1-fold prolongation is-orbitally linearizable as well.
Solvability of the Pursuit Problem for One Differential Game in a Banach Space
Authors: Mukhsinov E. M
Published: April 2024

In a Banach space, we study the solvability of the pursuit problem in the sense of L.S. Pontryagin for a differential game whose dynamics is described by a functional-differential equation of neutral type
On the Gröbner Basis of the Ideal of Lyapunov Quantities of the Kukles System
Authors: Rudenok A. E , Vasilevich M. N
Published: April 2024

The center problem and the cyclicity of singular points of the Kukles system are studied. The necessary conditions for the center at the origin are obtained as the variety of the ideal of Lyapunov quantities calculated by direct solution of the polynomial system whose left-hand sides form the Gröbner basis of the ideal. This ideal is also used to calculate the cyclicity of the centers and foci of the system. A theorem is proved that allows one to find the cyclicity of the centers of polynomial systems by using its Gröbner basis instead of the ideal of Lyapunov quantities.
On the Bifurcation of Thresholds of the Essential Spectrum with a Spectral Singularity
Authors: Borisov D. I , Zezyulin D. A
Published: April 2024

We consider the Schrödinger operator on the plane with bounded potential, where is a real potential, and are compactly supported complex potentials, andis a small parameter, assuming that the lower part of the spectrum of the one-dimensional Schrödinger operator consists of a pair of isolated eigenvalues and the essential spectrum of the operator has a virtual level at its lower edge and a spectral singularity inside.
Additionally, we assume that there is a certain superposition of eigenvalues of the operator with the virtual level and spectral singularity of the operator; this leads to the emergence of a special threshold in the essential spectrum of the perturbed operator, with the perturbation leading to a bifurcation of this threshold into eigenvalues and resonances with multiplicity doubling. The bifurcation scenario described in this paper is qualitatively different from the previously known ones.
On the Solvability of a Periodic Problem for a System of Ordinary Differential Equations with the Main Positive Homogeneous Nonlinearity
Authors: Mukhamadiev E. , Naimov A. N
Published: April 2024

We study the solvability of a periodic problem for a system of ordinary differential equations in which we separate the main nonlinear part that is positive homogeneous mapping (of order greater than unity), with the rest called a perturbation. It is proved that if the unperturbed system of equations has no nonzero bounded solutions, then the periodic problem is solvable under any perturbation if and only if the degree of the positive homogeneous mapping on the unit sphere is nonzero. The result obtained is of interest from the point of view of the application and development of methods of nonlinear analysis in the theory of differential and integral equations.
On the Spectral Properties of High-Order Differential Operators with Periodic Boundary Conditions
Authors: Kerimov N. B
Published: April 2024

We study the spectral properties of the differential operator $L_0,$generated by the differential expression $l_0(y)=(-1)^{m}y^{2m}+q(x)y,$ $0 x 1,$,, and the boundary conditions$y^{(s)}(1)-y^{(s)}(0)=0$ $(s=\overline{0,2m-1}),$, where $m\in\mathbb{N},$ $q(x) $andis an arbitrary complex-valued function in the class $L_1^{+}(0,1)=\{q(x)\in L_1(0,1):\int_0^1q(t)e^{-2\pi ikt} dt=0,$ $k\le0\}.$,.
Asymptotics of the Solution of a Singularly Perturbed System of Equations with a Single-Scale Internal Layer
Authors: Simakov R. E
Published: April 2024

We consider a boundary value problem for a singularly perturbed system of two second-order ordinary differential equations with different powers of the small parameter multiplying the second derivatives. A specific feature of the problem is that one of the two equations of the degenerate system has a double root and the other has three nonintersecting simple roots. It is proved that for sufficiently small values of the small parameter the problem has a solution that has a fast transition in a neighborhood of some interior point of the interval. A complete asymptotic expansion of this solution is constructed and justified. It qualitatively differs from the well-known expansion in the case where all the roots of the degenerate equations are simple but also does not coincide with the expansions in the previously studied problems with double roots; in particular, the inner transition layer turns out to be single-scale.
Multistep Methods for Second-Order Differential-Algebraic Equations
Authors: Bulatov M. V , Solovarova L. S
Published: April 2024

We consider the initial value problem for linear systems of second-order ordinary differential equations with an identically singular matrix multiplying the principal part. Sufficient conditions for the existence of a unique solution are given in terms of matrix polynomials. For such problems, multistep difference schemes are proposed. An analysis of their stability and calculations of a model example are carried out.
A Numerical Method for the Optimization of the Diffraction Efficiency of Thin-Layer Coatings with Diffraction Gratings
Authors: Martynova V. Yu , Smirnov Yu. G , Tikhonravov A. V
Published: April 2024

A method is proposed for optimizing the diffraction efficiency of multilayer dielectric gratings in the problem of spectral addition of signals in a wide range of wavelengths. From a physical point of view, we pose a direct problem of electromagnetic wave diffraction on multilayer dielectric gratings for the solution of which a modified method of separation of variables is applied. To optimize the diffraction efficiency, a gradient method with a constant step is used, while the gradient is calculated analytically. Numerical results are presented
On the Asymptotic Stability and Ultimate Boundedness of Solutions of a Class of Nonlinear Systems with Delay
Authors: Aleksandrov A. Yu
Published: April 2024

For a certain class of nonlinear systems of differential equations with constant delay, we study the conditions for the asymptotic stability of the zero solution and the ultimate boundedness of the solutions. To obtain such conditions, we propose special constructions of Lyapunov–Krasovskii full-type functionals. Estimates of the transient time are found, and an analysis of the influence of perturbations on the dynamics of systems is carried out. In addition, we study the case in which the systems have switching operation modes and determine conditions under which the asymptotic stability or ultimate boundedness is preserved for any admissible switching laws.
Spectral Properties of the Operator in the Problem of Oscillations in a Mixture of Viscous Compressible Fluids
Authors: Zakora D. A
Published: April 2024

We study the problem of normal oscillations of a homogeneous mixture of several viscous compressible fluids that fills a bounded domain in three-dimensional space with infinitely smooth boundary. We prove that the essential spectrum of the problem is a finite set of segments located on the real axis. The remaining spectrum consists of isolated eigenvalues of finite algebraic multiplicity and is located on the real axis, with the possible exception of finitely many complex conjugate eigenvalues. The spectrum of the problem contains a subsequence of eigenvalues with a limit point at infinity and a power-law asymptotic distribution.
On the Stability of a Switched Affine System for a Class of Switching Signals
Authors: Fursov A. S , Krylov P. A
Published: April 2024

We study the problem of stability of the zero equilibrium of a switched affine system closed by a linear static state feedback. The concept of feasible control for a given set of switching signals is introduced, and a constructive condition for checking this property for an arbitrary linear feedback is obtained. A sufficient condition for the stability of the zero equilibrium of a switched affine system closed by a feasible control is formulated.
Asymptotics of Relaxation Cycles in the Generalized Logistic Delay Equation
Authors: Kashchenko S. A
Published: April 2024

Asymptotic methods are used to study solutions of a modified logistic delay equation containing a large parameter. A result on the existence and stability of a relaxation cycle is given.
Singularly Perturbed Integro-Differential Systems with Kernels Depending on Solutions of Differential Equations
Authors: Bobodzhanov A. A , Kalimbetov B. T , Safonov V. F
Published: April 2024

We consider integro-differential equations (IDEs) with a rapidly oscillating inhomogeneity and with a Volterra-type integral operator whose kernels can contain both a classical rapidly decreasing exponential (the simplest case) and fundamental solutions of differential systems (the general case). Difficulty in constructing a regularized (according to S.A. Lomov) asymptotics in the general case is due to the complex asymptotic structure of the fundamental solution matrix (Cauchy matrix) of the homogeneous differential system. In the present paper, we first construct a regularized asymptotics of the Cauchy matrix, which is then used to construct a regularized asymptotics of the solution of the IDE.
Issledovanie pokazateley koleblemosti, vrashchaemosti i bluzhdaemosti po pervomu priblizheniyu
Authors: Sergeev I. N
Published: April 2024

Oscillation, rotation, and wandering indicators similar to Lyapunov exponents and adapted to nonlinear systems of differential equations are studied. A variety of both guaranteed and various realizable relationships between linear, spherical, radial, and ball versions of these indicators are listed, and their relationships with similar indicators of the first approximation system are considered
Printsip minimuma funktsionala Tikhonova v zadache ustoychivogo prodolzheniya polya potentsiala s poverkhnosti
Authors: Laneev E. B , Chernikova N. Yu
Published: April 2024

We consider the ill-posed problem of continuation of a potential field into a cylindrical domain from a surface in three-dimensional space. An approximate solution of the problem is constructed that is stable with respect to the given field. The continuation of the potential field is carried out by solving an ill-posed mixed problem for the Laplace equation in a cylindrical domain of rectangular cross-section. Tikhonov’s regularization method is used to construct a stable solution of the problem.
O kvaziakusticheskoy skheme A.P. Favorskogo
Authors: Abakumov M. V , Isakov V. A
Published: April 2024

We consider an explicit conservative quasi-monotone difference scheme of the second order of accuracy proposed by A.P. Favorskii for the numerical solution of the equations of gas dynamics. Substantiation of the main methods and approaches underlying its construction is given
Zadacha o neideal'nom teplovom kontakte
Authors: Galanin M. P , Rodin A. S
Published: April 2024

We consider the problem of determining the thermomechanical state of a fuel element in a nuclear reactor. A finite element algorithm for solving the thermal problem together with the problem of mechanical contact is described, and a model one-dimensional problem is studied to clarify the main features and a numerical algorithm for solving it. The leading term of the asymptotic expansion of the solution of this problem and a difference scheme for its solution, including iterative methods, are constructed. A cycle of test calculations is carried out to confirm the theoretical estimates. The comparison of calculations for real problems with theoretical predictions shows that the algorithm for solving a multidimensional nonlinear problem qualitatively corresponds to the behavior of one-dimensional calculations.
Algoritm podvizhnogo okna dlya parametricheskoy identifikatsii dinamicheskikh sistem s pryamougol'nymi i ellipsoidnymi oblastyami neopredelennosti parametrov
Authors: Morozov A. Yu , Reviznikov D. L
Published: April 2024

The parametric identification problem for dynamical systems with rectangular and ellipsoid parameter uncertainty domains is solved for the case in which the experimental data are given in the form of intervals. The state of the considered dynamical systems at each moment of time is a parametric set. An objective function that characterizes the degree of deviation of the parametric sets of states from experimental interval estimates is constructed in the space of parameter uncertainty domains. To minimize the objective function, a sliding window algorithm has been developed, which is related to gradient methods. It is based on an adaptive interpolation algorithm that allows one to explicitly obtain parametric sets of states of a dynamical system within a given parameter uncertainty domain (window). The efficiency and performance of the proposed algorithm are demonstrated.
On the Monotonicity of Solutions of Nonlinear Systems with Respect to the Initial Conditions
Authors: Rodina L. I , Voldeab M. S
Published: April 2024

We consider the autonomous system of differential equations x˙=f(x) and the solution φ(t,x) of this system with the initial condition φ(0,x)=x. Sufficient conditions for the following monotonicity property of solutions with respect to the initial conditions are obtained: if x(0)∈Rn и y(0)∈Rn and x(0)≤\linebreak≤y(0),, then φ(t,x(0))≤φ(t,y(0)) for all t≥0. This property is used to study the problem of almost surely estimating the average time gain for systems with random parameters.