bluuebunny/crossref_metadata_2025 huggingface dataset:
Quasi-Solution Method and Global Minimization of the Residual Functional in Conditionally Well-Posed Inverse Problems
Authors: Kokurin M. Yu.
Published: April 2024

A class of conditionally well-posed problems characterized by a Hölder conditional stability estimate on a convex compact set in a Hilbert space is considered. The operator of the direct problem and the right-hand side of the equation are given with errors, and the derivatives of the exact and perturbed operators are not assumed to be close to each other. The convexity and single-extremality of the residual functional of the quasi-solution method are examined. For this functional, each of its stationary points on the set of conditional well-posedness that lies not too far from the sought solution of the original inverse problem is shown to belong to a small neighborhood of the solution. The diameter of this neighborhood is estimated in terms of the errors in the input data. It is shown that this neighborhood is an attractor of the iterations of the gradient projection method, and the convergence rate of the iterations to the attractor is estimated. The necessity of the used conditional stability estimate for the existence of iterative processes with the indicated properties is established.
On the Reconstruction of an Input Disturbance in a Reaction–Diffusion System
Authors: Maksimov V. I.
Published: April 2024

The problem of dynamic reconstruction of an unknown boundary input disturbance for a nonlinear system of reaction–diffusion differential equations with distributed parameters is considered. A solution algorithm based on constructions of feedback control theory is presented.
A Posteriori Identities for Measures of Deviation from Exact Solutions of Nonlinear Boundary Value Problems
Authors: Repin S. I.
Published: April 2024

Functional identities that hold for deviations from the exact solutions of boundary value and initial boundary value problems with monotone operators are obtained. These identities hold for any function from the corresponding functional class that contains the exact solution of the problem. The left-hand side of an identity is the sum of terms that measure deviation of the approximate solution from the exact one. It is shown that these measures are natural characteristics of the accuracy of approximate solutions. In some cases, the right-hand side of the identity contains only known data of the problem and functions that characterize the approximate solution. Such an identity can be directly used for error control. In other cases, the right-hand side includes unknown functions. However, they can be eliminated to obtain fully computable two-sided bounds. In this case, it is necessary to use special functional inequalities relating the deviation measures to the properties of the monotone operator under consideration. As an example, such bounds and the exact values of the corresponding constants are obtained for a class of problems with the-Laplacian operator. It is shown that the identities and the resulting bounds make it possible to estimate the error of any approximation regardless of the method used to obtain it. In addition, they open a way for comparing exact solutions of problems with different data, which makes it possible to evaluate the errors of mathematical models, e.g., those that arise when the coefficients of a differential equation are simplified. In the first part of the paper, the theory and applications concern stationary models, and then the main results are extended to evolutionary models with monotone spatial operators.
On Solutions of a Boundary Value Problem for a Second-Order Differential Equation with a Parameter and Discontinuous Right-Hand Side
Authors: Baskov O. V. , Potapov D. K.
Published: April 2024

A boundary value problem for a second-order ordinary differential equation with a parameter and discontinuous right-hand side is considered. Theorems on the number of solutions to the problem are established. The resulting solutions are illustrated by plots. The process of numerically solving the problem is described.
Numerical Simulation of Phase Transfer during Cryosurgery for an Irregular Tumor using Hybrid Approach
Authors: Nishad Surabhi , Bhargava Rama
Published: April 2024

In the current paper, numerical simulation has been performed for the two dimensional time dependent Pennes’ heat transfer model which is solved for irregular diseased tumor cells. An elliptic cryoprobe of varying sizes is taken at the center of the computational domain in such a manner that the location of the probe is fixed throughout the computation. The phase transition occurs due to the effect of probe with infusion of different nanoparticles Au, Al2O3, Fe3O4. The cooling performance of these nanoparticles injected at very low temperature, has been studied by implementing hybrid FEM/EFGM method in which the whole domain is decomposed into two subdomains. The results are shown in terms of temperature profile inside the computational domain. Rate of cooling is obtained for various nanoparticles and it is observed that infusion of Au nanoparticles is very much efficient on increasing the heating rate than other nanoparticles. Such numerical scheme has direct applications where the domain is irregular.
The Effect of Nonlocal Scale Value and Phase Lags on Thermoelastic Waves in a Multilayered LEMV/CFRP Composite Cylinder
Authors: Mahesh S. , Selvamani R. , Ebrahimi Farzad
Published: April 2024

In this study, the effect of nonlocal scale value and two phase lags on the free vibration of generalized thermoelastic multilayered LEMV (Linear Elastic Material with Voids)/CFRP (Carbon Fiber Reinforced Polymer) composite cylinder is studied using nonlocal form of linear theory of elasticity. The governing equation of motion is established in longitudinal axis and variable separation model is used to transform the governing equations into a system of differential equations. To investigate vibration analysis from frequency equations, the stress free boundary conditions are adopted at the inner, outer and interface boundaries. The graphical representation of the numerically calculated results for frequency shift, natural frequency, and thermoelastic damping is presented. A special care has been taken to inspect the effect of nonlocal parameter on the aforementioned quantities. The results suggest that the nonlocal scale and the phase lag parameters alter the vibration characteristics of composite cylinders significantly.
A Novel Uniform Numerical Approach to Solve a Singularly Perturbed Volterra Integro-Differential Equation
Authors: Cakira M. , Cimena E.
Published: April 2024

In this paper, the initial value problem for the second order singularly perturbed Volterra integro-differential equation is considered. To solve this problem, a finite difference scheme is constructed, which based on the method of integral identities using interpolating quadrature rules with remainder terms in integral form. As a result of the error analysis, it is proved that the method is first-order convergent uniformly with respect to the perturbation parameter in the discrete maximum norm. Numerical experiments supporting the theoretical results are also presented.
Modeling Epidemics: Neural Network Based on Data and SIR-Model
Authors: Krivorotko O. I. , Zyatkov N. Yu. , Kabanikhin S. I.
Published: April 2024

Earlier, a method for constructing an initial approximation for solving the inverse problem of acoustics by a gradient method based on a convolutional neural network trained to predict the distribution of velocities in a medium from wave response was proposed [9]. It was shown that the neural network trained on responses from simple layered media can be successfully used for solving the inverse problem for a significantly more complex model. In this paper, we present algorithms for processing data about epidemics and an example of applying a neural network for modeling the propagation of COVID-19 in Novosibirsk region (Russia) based only on data. A neural network NN-COVID-19 that uses data about the epidemics is constructed. It is shown that this neural network predicts the propagation of COVID-19 for five days by an order of magnitude better than SEIR-HCD. When a new variant (Omicron) appeared, this neural network was able to predict (after retraining) the propagation of the epidemics more accurately. Note that the proposed neural network uses not only epidemiological data but also social ones (such as holidays, restrictive measures, etc.). The proposed approach makes it possible to refine mathematical models. A comparison of the curves constructed by SEIR-HCD model and by the neural network shows that the plots of solutions of the direct problem almost coincide with the plots constructed by the neural network. This helps refine coefficients of the differential model.
Coordinated Control of Multiple Surface Unmanned Vehicle Clusters under the Influence of Wind Field and Tides
Authors: Liu Yanshan , Dang Zhiqing , Dai Zhaopeng , Hao Xinran , Cui Yan , Gao Hongwei
Published: April 2024

This paper investigates the problem of coordinated control for multiple surface unmanned vehicles in a cluster under the influence of time-varying disturbances such as wind field and tides, based on state feedback controllers. With the rapid development of offshore cluster formation control technology, studying the cluster formation control problem of surface unmanned vehicles in multiple clusters under the influence of wind field and tides in complex and changing sea environments has important practical significance. This paper proposes a complete solution based on the Hamiltonian method. Firstly, each cluster is set to be located within a ellipsoidal virtual container throughout the entire motion process, and the trajectory of the virtual ellipsoid is used as an external state constraint for the cluster. Based on this, the dynamic equation of the system and the corresponding value function under the influence of wind field and tides on the sea surface are established, and the Hamilton–Jacobi–Bellman equation is used to solve the energy constraint and mutual avoidance between clusters and their members to obtain the optimal control and trajectory of each cluster. Finally, numerical simulation results demonstrate the effectiveness of the proposed method.
Formulas for Computing Euler-Type Integrals and Their Application to the Problem of Constructing a Conformal Mapping of Polygons
Authors: Bezrodnykh S. I.
Published: April 2024

This paper deals with Euler-type integrals and the closely related Lauricella function , which is a hypergeometric function of many complex variables. For new analytic continuation formulas are found that represent it in the form of Horn hypergeometric series exponentially converging in corresponding subdomains of, including near hyperplanes of the form, . The continuation formulas and identities for found in this paper make up an effective apparatus for computing this function and Euler-type integrals expressed in terms of it in the entire complex space , including complicated cases when the variables form one or several groups of closely spaced neighbors. The results are used to compute parameters of the Schwarz–Christoffel integral in the case of crowding and to construct conformal mappings of polygons.
Optimal Control of Quasi-Stationary Equations of Complex Heat Transfer with Reflection and Refraction Conditions
Authors: Chebotarev A. Yu.
Published: April 2024

The paper considers a class of optimal control problems for a nonlinear parabolic-elliptic system simulating radiative heat transfer with Fresnel matching conditions on surfaces of discontinuity of the refractive index. New estimates for the solution of the initial-boundary value problem are obtained, on the basis of which the solvability of optimal control problems is proved. Non-degenerate first-order optimality conditions are derived. The results are examplified by control problems with final, boundary, and distributed observations.
A FAST SINGLE-PASS METHOD FOR SOLVING THE GENERALIZED EIKONAL EQUATION IN A MOVING MEDIUM
Authors: Ho M. , Pak J.
Published: April 2024

We develop a fast method for approximating the solution to the generalized eikonal equation in a moving medium. Our approach consists of the following two steps. First, we convert the generalized eikonal equation in a moving medium into a Hamilton–Jacobi–Bellman equation of anisotropic eikonal type for an anisotropic minimum-time control problem. Second, we modify the Neighbor–Gradient Single-pass method (NGSPM developed by Ho et al.), so that it not only suits the converted Hamilton–Jacobi–Bellman equation but also can be faster than original NGSPM. In the case of that Mach number is not comparable than 1, we compare our method and Characteristic Fast Marching Method (CFMM developed by Dahiya) via several numerical examples to show that our method is faster and more accurate than CFMM. We also compare the numerical solutions obtained from our method with the solutions obtained using the ray theory to show that our method captures the viscosity solution accurately even when the Mach number is comparable to 1. We also apply our method to 3D example to show that our method captures the viscosity solution accurately in 3D cases.
TRIPLE SERIES EVALUATED IN π AND LN 2 AS WELL AS CATALAN’S CONSTANT G
Authors: Li Chunli , Chu Wenchang
Published: April 2024

By computing definite integrals, several infinite triple series are explicitly evaluated in terms of @ and ln2 as well as Catalan’s constant G.
Study of Nonclassical Transport by Applying Numerical Methods for Solving the Boltzmann Equation
Authors: Aristov V. V. , Voronich I. V. , Zabelok S. A.
Published: April 2024

This paper overviews the state of the art in the study of nonequilibrium gas flows with nonclassical transport, in which the Stokes and Fourier laws are violated (and, accordingly, the Chapman–Enskog method is inapplicable). For a reliable validation of anomalous transport effects, we use computational methods of different nature: the direct solution of the Boltzmann equation and direct simulation Monte Carlo. Nonclassical anomalous transport is manifested on scales of 5–10 mean free paths, which confirms the fact that a highly nonequilibrium flow is a prerequisite for the detection of the effects. Two-dimensional flow problems are considered, namely, the supersonic flow over a flat plate in the transient regime and the supersonic flow through membranes (lattices), where the flow behind the lattice corresponds to the spatially nonuniform relaxation problem. In this region, nonequilibrium distributions demonstrating anomalous transport are formed. The relationship of the effect with the second law of thermodynamics is discussed, the possibilities of experimental verification are considered, and the prospects of creating new microdevices on this basis are outlined.
Study of the Gardner Equation with Homogeneous Boundary Conditions via Fourth Order Modified Cubic B-Spline Collocation Method
Authors: Dahiya S. , Singh A. , Singh S. P.
Published: April 2024

In this work, the well-known Gardner equation is converted into a coupled system of nonlinear partial differential equations and a modified cubic B-spline collocation method has been applied to find its numerical solution. Time discretization and linearization of Gardner equation has been carried out using Crank–Nicolson method and quasi-linearization respectively. A linear system of algebraic equations is obtained which is found to be unconditionally stable by Von Neumann analysis. Numerical investigations are performed on the Gardner equation subjected to homogeous boundary conditions in different situations such as propagation of initial positive pulse and kink like wave, propagation and interaction of two solitons, wave production from a single soliton, evolution of non-propagating solitons. The results obtained are compared with those available in the literature and are found to be better. The conserved quantities are also computed to show that the conservation laws are preserved as expected from the theoretical aspect. Numerical results demonstrate the accuracy and validity of the present method which can be further applied to solve other nonlinear problems
Projection-Grid Schemes on Irregular Grids for a Parabolic Equation
Authors: Olkhovskaya O. G.
Published: April 2024

A family of projection-grid schemes has been constructed for approximating parabolic equations with a variable diffusion coefficient in tensor form. The schemes are conservative and retain the self-adjointness of the original differential operator and are destined for calculations on 3D irregular difference grids, including tetrahedral, mixed (grids of arbitrary polyhedra), and locally adaptive (octal-tree type).
STUDYING THE ABILITY FOR RESEARCH ACTIVITY IN MONKEYS
Authors: Anikaev A. E. , Chalyan V. G. , Meishvili N. V. , Anikaeva E. N.
Published: April 2024

The level of research ability in four species of lower monkeys was studied: green monkeys (Chlorocebus aethiops), Javanese macaques (Macaca fascicularis), rhesus monkeys (Macaca mulatta) and hamadryas baboons (Papio hamadryas). The assessment was made according to such indicators as the level of research activity, the dynamics of research activity, the diversity of research activities. The results found indicate a higher level of the studied parameters in Javan macaques and hamadryas baboons in comparison with rhesus macaques and green monkeys.
NEUROBIOLOGICAL FACTORS OF EXECUTIVE DYSFUNCTION IN AUTISM SPECTRUM DISORDERS
Authors: Kozunova G. L. , Zakirov F. Kh. , Rytikova A. M. , Stroganova T. A. , Chernyshev B. V.
Published: April 2024

Autism is a pervasive neurodevelopmental disorder that is defined by difficulties in social interaction and abnormal preoccupation in repetitive and stereotypic activities. Deficit of basic executive functions, such as cognitive flexibility, inhibitory control, working memory may strongly contribute to these symptoms. Prefrontal and cingulate cortices play a crucial role in the executive functions. These brain structures are regulated by neuromodulatory systems of the brain: cholinergic, noradrenergic, serotonergic, and dopaminergic. During the early brain development these neuromodulators act as neurotrophic factors, and they regulate excitation-inhibition balance in the brain. Pathogenesis of autism is hypothesized to be linked to impairment in metabolism of one or more of these neuromodulators. The aim of this review is to consider the functional role of these neuromodulators and the significance of their imbalance in mature and developing brain, as an important factor in the development of autistic symptoms in children and adults.
AUDITORY AFTER-EFFECT: STATIONARY ADAPTER CHANGES THE PERCEIVED TRAJECTORIES OF MOVING SOUNDS
Authors: Shestopalova L. B. , Salikova D. A. , Petropavlovskaia E. A.
Published: April 2024

Perceived trajectories of dichotically presented sound stimuli with different spatial patterns were investigated in silence and after listening to stationary adapters. The spatial position of all stimuli was determined by the interaural level differences. The subjects indicated the perceived position of the beginning and end of the stimulus trajectory. Lateralized stationary adapters had no effect on the perceived position of the neighboring (ipsilateral) stimuli, but “pushed away” the stimuli located on the opposite side of the acoustic space. After exposure to the central adapter, the lateral points of the perceived trajectories were pushed away from the adapter, regardless of the motion direction. The motion starting points located near the central adapter shifted in the direction of the stimulus motion, but the perceived position of the central endpoints was not affected by the central adapter. The effect of stationary adapters on the perceived trajectories of moving sounds can be best explained by a three-channel model of the neural coding of auditory space.
DETECTING PHENOMENON OF “COVERT COGNITION” IN PATIENTS WITH CHRONIC DISORDERS OF CONSCIOUSNESS: A REVIEW OF fMRI DATA WITH PARADIGMS
Authors: Cherkasova A. N. , Yatsko K. A. , Kovyazina M. S. , Varako N. A. , Kremneva E. I. , Ryabinkina Y. V. , Suponeva N. A. , Piradov M. A.
Published: April 2024

In recent decades, the use of instrumental methods has significantly expanded the diagnosis of signs of consciousness in patients with chronic disorders of consciousness (DOC). The phenomenon of “covert cognition” was described with their help. This review highlights studies on the detection of “covert cognition” in patients with DOC using functional magnetic resonance imaging. Most types of passive and active paradigms used for this purpose are analyzed and systematized. Special attention is paid to an integrated approach with a combination of different paradigms and research methods. The importance of detecting the phenomenon of “covert cognition” for the neurorehabilitation of patients with DOC is emphasized.
REACTIVITY OF THE EEG SENSORIMOTOR RHYTHMS IN CHILDREN 4–7 YEARS OLD IN SITUATIONS OF HELPING BEHAVIOR
Authors: Kaida A. I. , Mikhailova A. A. , Portugalskaya A. A. , Pavlenko V. B.
Published: April 2024

We studied the reactivity features of the EEG mu rhythm amplitude in the individually determined frequency range, as well as the beta rhythm in the central, frontal and parietal EEG leads in children while performing tasks for instrumental, emotional and altruistic helping behavior. The study engaged 24 children aged 4 to 7 years. ANOVA showed a significant decrease of the mu rhythm amplitude in the central and parietal regions, which is supposed to be associated with the activation of the mirror system of the brain. When performing tasks for instrumental and altruistic helping behavior, there was an increase in the amplitude of the beta rhythm in the frontal, central, and parietal regions, which may be associated with children observing actions that are emotionally charged and cause empathy with a person in need of help. The more the beta rhythm increased, the sooner the children provided help, which can be explained by a greater degree of emotional involvement and activation of cognitive processes in children with high performance of prosocial behavior.
REVERSE INHIBITORY CONNECTIONS THROUGH GABA B-RECEPTORS SYNCHRONIZE INTERICTAL DISCHARGES IN THE CORTEX
Authors: Marchenko V. G. , Zaichenko M. I.
Published: April 2024

Modern experimental data show that interictal discharges consist of a short spike and a slow wave, which is regarded as a prolonged hyperpolarization. On the model of interictal discharges synchronization, a study of reciprocal inhibitory connections was carried out. In rats in light narcotic sleep, after application of GABA A-receptor blockers to the cortex, interictal discharges occurred in neighboring cortical areas independently of each other, and then synchronization occurred. In the experiments in which the interictal discharges occurred simultaneously, the durations of the slow wave (inhibitory phase) were the same. During the registration in these and other experiments, there was an increase in the time delay between the moments of interictal discharges generation. Under conditions of increased synchronization, the duration of the slow wave (inhibitory phase) of interictal discharges increased. Interictal discharges, which occurred first, had a longer duration of inhibition compared to the duration in the neighboring point, because the inhibition from the neighboring networks via feedback inhibitory connections is added to its own inhibition in the neuronal network. When excitation occurred, it was followed by inhibition via feedback, which limited the period of excitation, and thus created a temporary integration window, and this also happened in the neighboring neural networks of the cortex.
SPATIO-TEMPORAL PATTERNS OF CORTICAL-MUSCULAR INTERACTION DURING LOCOMOTION
Authors: Moiseev S. A. , Gorodnichev R. M.
Published: April 2024

The paper considers the synergetic effects manifested at the cortical and muscular levels during locomotor activity showed in conditions of horizontal hanging of the lower extremities. The analysis of the synergies’ spatio-temporal structure was carried out using the data matrix factorization methods. It was found out the control of the movements’ structure is mainly realized through the three muscle synergies. The activity synchronization of the motor, associative, visual and sensorimotor regions of the cortex bilateral part is due to the specifics of performing locomotion in conditions of gravitational unloading and the associated features of receptor signaling. The identified components indicating synchronization of different areas of the right and left cortex may reflect the control processes associated with the control of alternate activation of the flexor and extensor muscles of the contralateral limb during locomotion. The data on the cortical activity spatial-temporal structuring indicate the separate management of muscle synergies through synchronization of cortical commands and the temporary organization of muscle synergies in the frequency ranges 0.30 to 8.00 Hz. Such patterns may reflect the activity of the rhythm-generating mechanism involved in the management of cyclic locomotor activity.
CORRELATION BETWEEN SUBTHALAMIC ALPHA RHYTHMIC ACTIVITY AND MOTOR CONTROL IMPAIRMENT IN PARKINSONIAN PATIENTS
Authors: Nezvinskiy A. A. , Belova E. M. , Sayfulina K. E. , Gamaleya A. A. , Tomskiy A. A. , Sedov A. S.
Published: April 2024

Increased oscillatory beta activity in basal ganglia is one of the main electrophysiological biomarkers of impaired motor control in Parkinson’s disease. However, the functional role of dynamical rhythmic processes during movements is still not investigated in detail. We used microelectrode recordings to investigate the subthalamic nucleus neuronal activity in 9 patients with Parkinson’s disease during deep brain stimulation surgery. We have shown that the amplitude of the subthalamic nucleus alpha (7–12 Hz) and low-beta (12–20 Hz) activity correlated with motor impairment indices in patients with Parkinson’s disease. Also, we have shown that, in contrast to beta rhythmic activity, the magnitude of alpha activity decreased significantly during motor tests execution. Moreover, the degree of rhythmic activity suppression in the alpha band correlated with the severity of bradykinesia. These results allow us to suppose that, along with beta activities, subthalamic nucleus neuronal alpha activity also participate in motor control of Parkinson’s disease patients.
THE EFFECTS OF VARIOUS MODES OF INTERVAL HYPOXIC TRAINING IN EXPERIMENTAL MODELS OF ANXIETY AND DEPRESSION IN RATS
Authors: Zenko M. Y. , Baranova K. A. , Kukina M. V. , Rybnikova E. A.
Published: April 2024

The development of non-drug methods for correcting stress-induced disorders and improving adaptation to stressful factors remains an urgent task of physiology, which has a great translational potential. Previously, we proposed effective methods of hypoxic hypobaric preconditioning and distant ischemic conditioning in this regard. The purpose of this work was to transfer the principles of preconditioning to the approaches of normobaric intermittent hypoxic training (IHT). The effects of five new IHT regimens (3 five-minute sessions of hypoxia of 16% O2 per day, 3 sessions of 12% O2, 7 sessions of 12% O2, 15 sessions of 12% O2, 3 sessions of 9% O2) were studied in experimental models of depression and post-traumatic stress disorder in rats. The preconditioning regime of high intensity 3x9%O2 had the most pronounced antidepressant and anxiolytic effect in models of both pathologies. With a decrease in the level of hypoxia to 12% O2, IHT regimens partially retained their effectiveness with an increase in the number of sessions. The training regime of the longest duration – 15 × 12%O2, was effective in correcting the formation of experimental depression. The intermediate regime – 7 × 12%O2, had an anxiolytic effect, while the preconditioning regime of medium intensity – 3 × 12%O2, demonstrated both an antidepressant and anxiolytic effect. The results indicate that the intensity of hypoxic exposure had the greatest impact on the effectiveness. At the same time, a decrease in the intensity to 16% O2 led to a weakening or loss of stress-protective properties. With regard to the 3 × 9%O2 regime as the most promising, it is advisable to conduct further studies to identify the molecular mechanisms that implement its stress-protective and anxiolytic effects.
On a Nonlinear Second-Order Ordinary Differential Equation
Authors: Kosov A. A , Semenov E. I
Published: April 2024

We consider a nonlinear second-order ordinary differential equation of a special form whose particular case arises when constructing exact solutions of the nonlinear heat equation with a power-law coefficient. Conditions are obtained for the parameters under which the equation admits a single integration. A number of examples of constructing exact solutions expressed in terms of elementary functions or in terms of the Lambert function are given.
Boundary Value Problem for an Inhomogeneous Fourth-Order Equation with Lower-Order Terms
Authors: Apakov Yu. P , Mamazhonov S. M
Published: April 2024

We consider the first boundary value problem in a rectangular domain for an inhomogeneous fourth-order differential equation with lower-order terms. The uniqueness of a solution of the stated problem is proved. The solution is obtained explicitly using the Green’s function constructed.
Finding the Two-Dimensional Relaxation Kernel of an Integro-Differential Wave Equation
Authors: Durdiev D. K , Safarov Zh. Sh
Published: April 2024

We consider the multidimensional inverse problem of determining the kernel of the integral term in an integro-differential wave equation. In the direct problem, it is required to find the displacement function from an initial–boundary value problem, and in the inverse one, to determine the kernel of the integral term depending on both time and one of the spatial variables. The local unique solvability of the problem in the class of functions continuous in one of the variables and analytic in the other one is proved on the basis of the method of scales of Banach spaces of real analytic functions.
On the Stability of Solutions to Control Problems for a Nonlinear Reaction–Diffusion–Convection Model
Authors: Brizitskiy R. V , Maksimov P. A
Published: April 2024

The problems of multiplicative control for the reaction–diffusion–convection model with coefficients that are nonlinearly dependent on the solution and also dependent on spatial variables are studied. In the case of a power-law dependence of the model coefficients on the solution, optimality systems are derived for extremum problems. With their help, estimates of the local stability of solutions of specific control problems with respect to small perturbations of both the cost functionals and one of the given functions of the boundary value problem are obtained.
Uniqueness of the Solution of the Dirichlet Problem for the Poisson Equation with a Singular
-Kipriyanov Operator
Authors: Lyakhov L. N , Bulatov Yu. N , Roshchupkin S. A , Sanina E. L
Published: April 2024

Functions satisfying the Laplace equation for the Kipriyanov-operator are said to be-harmonic. The following properties of-harmonic functions are presented and proved: the Green-type integral representation of-functions, the spherical mean theorem, and the maximum principle. As a corollary, the uniqueness of the solution of the interior and exterior Dirichlet problems is proved.
On Some Properties of Solutions of Systems of Linear Difference Equations with Periodic Right-Hand Sides
Authors: Ignat'ev A. O
Published: April 2024

We consider homogeneous and inhomogeneous systems of linear difference equations with coefficients that are-periodic functions of discrete time. For homogeneous systems, sufficient conditions for the existence of periodic and almost periodic solutions are obtained. For inhomogeneous systems, it is shown that a necessary and sufficient condition for the existence of an N-periodic solution is the existence of a bounded solution. Necessary and sufficient conditions for theN orthogonality of the fundamental matrix of the homogeneous system are established. Illustrative examples are given.
On the Pinsky Phenomenon for B-Elliptic Operators
Authors: Alimov Sh. A , Pirmatov Sh. T
Published: April 2024

Necessary conditions for the summability of spectral expansions in eigenfunctions of an elliptic operator with a Bessel operator in one of the variables in an arbitrary-dimensional domain adjacent to the singularity hypersurface are obtained. It is proved that if the spectral expansion of an arbitrary function at some point of this hypersurface is summable by Riesz means, then its average value over the half-ball centered at the specified point has generalized smoothness.
Kolebatel'nye resheniya obyknovennogo differentsial'nogo uravneniya vtorogo poryadka s trekhpozitsionnym gisterezisnym rele bez vykhoda v zony nasyshcheniya
Authors: Evstaf'eva V. V
Published: April 2024

A second-order ordinary differential equation with an essential nonlinearity and an external perturbation in the form of a continuous periodic function is studied. Nonlinearity is given by a symmetrical relay characteristic with hysteresis, dead zone, and saturation zones. The traversal of the characteristic without entering the saturation zones is considered for some finite time and time commensurate with the period of the perturbation function. Conditions for the existence of an oscillating solution with a closed phase trajectory and four switching points during one traversal of the characteristic are obtained. Existence theorems for periodic solutions, including solutions with a symmetric trajectory, are proved. A numerical example is given.
Neanaliticheskie pervye integraly analiticheskikh sistem differentsial'nykh uravneniy v okrestnosti ustoychivykh polozheniy ravnovesiya
Authors: Kozlov V. V
Published: April 2024

In even-dimensional phase spaces, we give examples of analytic systems of differential equations that have isolated equilibria and admit nonanalytic first integrals. These integrals are positive definite in a neighborhood of the equilibria, which proves the stability of the equilibria (on the entire time axis). However, such systems of differential equations do not admit nontrivial first integrals in the form of formal power series at all. In particular, the Lyapunov stability of equilibria of analytic systems does not imply their formal stability. In the case of an odd-dimensional phase space, all isolated equilibria are apparently unstable.
O nekotorykh svoystvakh otobrazheniya sdviga na beskonechnomernom tore
Authors: Glyzin S. D , Kolesov A. Yu
Published: April 2024

We study the question, classical in the theory of dynamical systems, about the minimality of the shift on an infinite-dimensional torus; more precisely, the problem of finding sufficient conditions guaranteeing the absence of the minimality property is solved
Global'no ustoychivye raznostnye skhemy dlya uravneniya fishera
Authors: Matus P. P , Pylak D.
Published: April 2024

Unconditionally monotone and globally stable difference schemes for the Fisher equation are constructed and investigated. It is shown that for a certain choice of input data, these schemes inherit the main property of a stable solution of the differential problem. The unconditional monotonicity of the difference schemes under consideration is proved, and an a priori estimate for the difference solution in the uniform norm is obtained. The stable behavior of the difference solution in the nonlinear case is proved under strict constraints on the input data. The results obtained are generalized to multidimensional equations, for the approximation of which economical difference schemes are used.
Sushchestvovanie edinstvennoy nepodvizhnoy tochki otobrazheniy, porozhdennykh mnogomernoy sistemoy s releynym gisterezisom
Authors: Kamachkin A. M , Evstaf'eva V. V , Potapov D. K
Published: April 2024

A multidimensional system of ordinary differential equations with relay hysteresis is considered. The system parameters are assumed to be such that there exists a family of continuous operators each of which maps some connected compact set into itself. In this case, the operator corresponds to a periodic orbit with an even number of switching points in the phase space of the system. For the operator family, a necessary and sufficient condition for the existence of a single fixed point is obtained.
Ob ogranichennykh traektoriyakh avtonomnoy sistemy s vydelennoy polozhitel'no odnorodnoy nelineynost'yu
Authors: Mukhamadiev E. , Naimov A. N , Bystretskiy M. V
Published: April 2024

Bounded trajectories of an autonomous system with an isolated positively homogeneous nonlinearity that is the gradient of a smooth function are studied. We prove the existence of nonstationary bounded trajectories lying in connected components of the set of points where the positively homogeneous function is negative and nonzero stationary points in those connected components whose closure has nonzero Euler characteristic. The existence of nonstationary bounded trajectories is substantiated using the Waűewski method; and the existence of stationary points, using methods for calculating the winding number of finite-dimensional vector fields.
Classical Solution of the First Mixed Problem for the Telegraph Equation with a Nonlinear Potential in a Curvilinear Quadrant
Authors: Korzyuk V. I , Rud'ko Ya. V
Published: April 2024

For the telegraph equation with a nonlinear potential in a curvilinear quadrant, we consider a mixed problem with the Cauchy conditions on a spatial half-line and the Dirichlet condition on a noncharacteristic curve. The solution of the problem is constructed by the method of characteristics in an implicit analytical form as a solution of integral equations. We study the solvability of these equations depending on the initial data and their smoothness. For the problem under consideration, the uniqueness of the solution is proved and conditions under which there exists a classical solution are established. A mild solution is constructed in the case of insufficiently smooth data of the problem.
Regularity of the Pressure Function for Weak Solutions of the Nonstationary Navier–Stokes Equations
Authors: Amosova E. V.
Published: April 2024

We study the nonstationary system of Navier–Stokes equations for an incompressible fluid. Based on a regularized problem that takes into account the relaxation of the velocity field into a solenoidal field, the existence of a pressure function almost everywhere in the domain under consideration for solutions in the Hopf class is substantiated. Using the proposed regularization, we prove the existence of more regular weak solutions of the original problem without smallness restrictions on the original data. A uniqueness theorem is proven in the two-dimensional case
Construction of Integral Representations of Fields in Problems of Diffraction by Penetrable Bodies of Revolution
Authors: Eremin Yu. A. , Lopushenko V. V.
Published: April 2024

Based on integral representations with densities distributed along a segment of the symmetry axis, a representation of the solution of the boundary value problem of plane wave diffraction by a local penetrable body of revolution with smooth surface is constructed and justified. The resulting integral representation allows one to avoid resonances of the interior domain when analyzing the scattering frequency characteristics.
On the Properties of the Root Vector Function Systems of a th-Order Dirac Type Operator with an Integrable Potential
Authors: Ibadov E. Dzh.
Published: April 2024

We consider a Dirac type operator with matrix coefficients. Estimates for the root vector functions are established, and criteria for the Bessel property and the unconditional basis property of the root vector function systems of this operator in the space L2m2(G) , where G=(a,b)⊂R is a finite interval, are obtained.
Partial Stability of Systems of Itô Linear Delay Differential Equations
Authors: Kadiev R. I
Published: April 2024

We study the moment stability of solutions in part of the variables with respect to the initial data for systems of Itô linear delay differential equations using a modified regularization method based on the choice of an auxiliary equation and an application of the theory of nonnegatively invertible matrices. For these systems, sufficient stability conditions are obtained in terms of nonnegative invertibility of matrices constructed from the parameters of these systems. The satisfiability of these conditions is verified for specific classes of systems of Itô linear equations with delay.
Analytical Solution of Mixed Problems for the One-Dimensional Ionization Equations in the Case of Constant Velocities of Atoms and Ions
Authors: Gavrikov M. B , Tayurskiy A. A
Published: April 2024

We consider the main initial–boundary value (mixed) problems for the nonlinear system of one-dimensional gas ionization equations in the case of constant velocities of gas atoms and ions resulting from ionization. The atom and ion concentrations are the unknowns in this system. We find a general formula for a sufficiently smooth solution of the system. It is shown that mixed problems for the system of one-dimensional ionization equations admit integration in closed-form analytical expressions. In the case of a mixed problem for a finite interval, the analytical solution is constructed using recurrence formulas each of which is defined in a triangle belonging to some triangulation, specified in the paper, of the domain where the unknown functions are defined.
One-Dimensional Inverse Problem for Nonlinear Equations of Electrodynamics
Authors: Romanov V. G
Published: April 2024

For the system of nonlinear electrodynamics equations, we consider the problem of determining the medium conductivity coefficient multiplying the nonlinearity. It is assumed that the permittivity and permeability are constant and the conductivity depends only on one spatial variable, with this conductivity being zero on the half-line x . For a mode in which only two electromagnetic field components participate, the wave propagation process caused by the incidence of a plane wave with a constant amplitude from the domain x0 onto an inhomogeneity localized on the half-line x0 is considered. With a given conductivity coefficient, the conditions for the solvability of the direct problem and the properties of its solution are studied. To solve the inverse problem, the trace of the electrical component of the solution of the direct problem is specified on a finite segment of the axis x=0. A theorem on the local existence and uniqueness of the solution of the inverse problem is established, and a global estimate of the conditional stability of its solutions is found.
Some Theoretical Aspects of the Neural Network Approach to Stabilization of Switched Interval Systems
Authors: Fursov A. S , Mosolova Yu. M
Published: April 2024

We consider the problem of stabilization of a switched interval linear system with slow switchings that are inaccessible to observation. It is proposed to look for a solution in the class of variable structure controllers. To ensure the functionality of such a controller, it is necessary to construct an observer of the switching signal. This paper is devoted to some theoretical issues related to the period of quantization of the neural observer’s operating time.
Existence of an Anti-Perron Effect of Change of Positive Exponents of the Linear Approximation System to Negative Ones under Perturbations of a Higher Order of Smallness
Authors: Izobov N. A. , Il'in A. V.
Published: April 2024

We prove the existence of a two-dimensional linear system x˙ = A(t)x, t ≥ t0, withbounded infinitely differentiable coefficients and all positive characteristic exponents, as wellas an infinitely differentiable m-perturbation f(t, y) having an order m 1 of smallness ina neighborhood of the origin y = 0 and an order of growth not exceeding m outside it, such thatthe perturbed system y˙ = A(t)y + f(t, y), y ∈ R2, t ≥ t0, has a solution y(t) with a negativeLyapunov exponent.
On Exact Solutions of a Multidimensional System of Elliptic Equations with Power-Law Nonlinearities
Authors: Kosov A. A. , Semenov E. I.
Published: April 2024

Equations and systems of elliptic type with power-law nonlinearities are considered.Such equations are found in modeling distributed robotic formations, as well as in chemical kinetics,biology, astrophysics, and many other fields. The problem of constructing multidimensionalexact solutions is studied. It is proposed to use a special type of ansatz that reduces the problemto solving systems of algebraic equations. A number of multiparameter families of new exactmultidimensional solutions (both radially symmetric and anisotropic) represented by explicitformulas are obtained. Examples are given to illustrate the exact solutions found.
Initial–Boundary Value Problems for Homogeneous Parabolic Systems in a Semibounded Plane Domain and Complementarity Condition
Authors: Sakharov S. I.
Published: April 2024

We consider initial–boundary value problems for homogeneous parabolic systems with coefficients satisfying the double Dini condition with zero initial conditions in a semiboundedplane domain with nonsmooth lateral boundary. The method of boundary integral equations is used to prove a theorem on the unique classical solvability of such problems in the space of functions that are continuous together with their first spatial derivative in the closure of the domain. An integral representation of the obtained solutions is given. It is shown that the condition for the solvability of the posed problems considered in the paper is equivalent to the well-known complementarity condition.
On the Solvability of Linear Differential Operators on Vector Bundles over a Manifold
Authors: Smirnov M. S.
Published: April 2024

Necessary and sufficient condition is established for the closedness of the rangeor surjectivity of a differential operator acting on smooth sections of vector bundles. For connectednoncompact manifolds it is shown that these conditions are derived from the regularityconditions and the unique continuation property of solutions. An application of these results toelliptic operators (more precisely, to operators with a surjective principal symbol) with analyticcoefficients, to second-order elliptic operators on line bundles with a real leading part, and to theHodge–Laplace–de Rham operator is given. It is shown that the top de Rham (respectively, Dolbeault)cohomology group on a connected noncompact smooth (respectively, complex-analytic)manifold vanishes. For elliptic operators, we prove that solvability in smooth sections impliessolvability in generalized sections.
Three-component synthesis and crystalline structure of 2-amino-3-cyano-4H-pyran and thiopyran derivatives
Authors: Dyachenko I. V , Dyachenko V. D , Dorovatovskii P. V , Khrustalev V. N , Rivera D. G , Nenajdenko V. G
Published: April 2024

Derivatives of 2-amino-3-cyano-4 H -pyran and thiopyran were synthesized by three-component condensation of aldehydes, dimedone and CH-acids. Their molecular and crystal structure was studied by X-ray diffraction analysis.
Recyclization reaction of S-, N-containing cyclic peroxides with aromatic amines
Authors: Makhmudiyarova N. N , Ishmukhametova I. R
Published: April 2024

The recyclization reaction of tetraoxathiaspiroalkanes and tetraoxathiocanes with primary amines ( o , p -fluoroanilines, m , p -chloroanilines, o -toluidine, o , p -anisidines, ammonium chloride) to obtain cycloazadiperoxides under the action of samarium nitrate crystal hydrate as a catalyst was studied. The possibility of recycling N -( tert -butyl)hexaoxaazadispirocycloalkanes with arylamines to the corresponding azatriperoxides was shown. It was found that the rate of the recyclization reaction depends on the nature of the central heteroatom in the heterocycle (S > N > O).