bluuebunny/crossref_metadata_2025 huggingface dataset:
Synthesis and extraction ability of amide derivatives of calix[4]resorcinarene and 1,1′-dinaphthylmethane toward metal cations
Authors: Glushko V. V , Serkova O. S , Kamkina A. V , Isaeva S. A , Toropygin I. Yu. , Maslennikova V. I
Published: April 2024

Aminolysis of ester derivatives of 1,1′-dinaphthylmethane and rctt -calix[4]resorcinarene afforded a series of ligands, which differ in molecular platform structure, the number of electron-donating sites, the nature of terminal amide component, the nature and size of the spacers connecting the polycyclic core with amide group. Using liquid extraction method, the effect of ligand structural features on its ability to recognize and bind s -, p -, d -, f -metal cations was investigated, and the stoichiometry of formed complexes was calculated.
Preparation, thermal properties and electrical conductivity of solutions of pyridinium ionic liquids with tetrachloroferrate anion
Authors: Zhuravlev O. E , Kaftanov A. D , Yulmasov G. S
Published: April 2024

Thermal stability of N -alkylpyridinium tetrachloroferrates(III) [C5H5NR]FeCl4 [R = C4H9, (CH2)3CN, CH2C6H5, C8H17, C10H21] in air in the range of 25-600°C was studied, as well as the thermal stability of N -alkylpyridinium chlorides. The equivalent electrical conductivity of N -alkylpyridinium tetrachloroferrates(III) in acetonitrile solution at 25°C was investigated. The ionic association constants K a , the limiting molar electrical conductivity (λ0) and the standard Gibbs energy of the association (Δ G °) in acetonitrile solutions were calculated based on conductometric data by the Lee-Wheaton method.
Synthesis, structure, and biological activity of new metal carboxylate complexes containing a glycoluril fragment
Authors: Baranov V. V , Vikrishchuk N. I , Zubenko A. A , Estrin I. A , Lipatov E. S , Svyatogorova A. E
Published: April 2024

Cu(II), Ni(II), Zn(II), Co(II), Fe(II), Mn(II) carboxylates containing a pharmacophoric glycoluril fragment were obtained for the first time. The proposed structure of the complexes was established using elemental analysis, spectral methods, and magnetochemistry. Structure of one of the copper(II) complexes was proved by X-ray diffraction analysis. Antibacterial and fungicidal activity of all the compounds was studied. It was shown that the starting acids are inactive, while some complexes exhibit antibacterial activity.
α-Thiosubstituted boron difluoride dibenzoylmethanates
Authors: Svistunova I. V , Tretyakova G. O , Tikhonov C. A
Published: April 2024

Treatment of tetraketone, in which two dibenzoylmethane groups are connected by a disulfide bridge through central (α) carbon atoms, gave a dinuclear complex containing boronodibenzoylmethanate fragments. Like an aromatic disulfide, this compound is cleaved by the action of sulfuryl chloride and bromine to form sulfenyl chloride or sulfenyl bromide derivatives. It was shown that these compounds enter into substitution and addition reactions common for sulfenyl halides, making it possible to obtain boronodibenzoylmethanate complexes containing various functional groups linked to the chelate cycle through the central carbon atom. Based on the results of studying the UV spectra of the obtained compounds, an assumption was made about the nature of the interaction of α and β substituents with the chelate ring.
Synthesis and some properties of 4-{4-[tris(4- octyloxyphenyl)methyl]phenoxy}phthalonitrile and copper, nickel, and cobalt phthalocyaninates on its basis
Authors: Ivakin V. A , Rumyantseva T. A , Galanin N. E
Published: April 2024

In four stages, by o -alkylation of phenol with 1-bromooctane, alkylation of octyloxybenzene with carbon tetrachloride, alkylation of phenol with tris(4-octyloxyphenyl)methanol, and nucleophilic substitution of the nitro group in 4-nitrophthalonitrile with tris(4-octyloxyphenyl)- 4-hydroxyphenylmethane, 4-{4-[tris(4-octyloxyphenyl)methyl]phenoxy}phthalonitrile was synthesized. Its reactions with copper(II), nickel(II), and cobalt(II) acetates in the presence of urea gave the corresponding metal phthalocyanines. The spectral properties of the obtained compounds were studied. All the phthalocyanines are not associated in chloroform at concentrations up to ~4×10-5 mol/L. They do not exhibit mesomorphic properties, but upon cooling after heating, the copper and nickel complexes pass into a glass state.
Pyridine-containing benzocyclopentaquinolines and benzacridines and their quaternary salts
Authors: Dikusar E. A , Akishina E. A , Kovalskaya S. S , Grigoriev M. S , Fedoseeva M. A , Alekseeva K. A , Potkin V. I
Published: April 2024

Three-component cascade condensation of 2-naphthylamine, pyridinecarbaldehydes, and 1,3-cycloalkanediones in butanol under reflux conditions was used to synthesize 11-pyridinyl-7,8,9,11-tetrahydro-10 H -benzo[ f ]cyclopenta[ b ]quinolin-10-ones and 12-pyridinyl-8,9,11,12-tetrahydrobenzo[ a ]acridin-11(7 H )-ones. Quaternary ammonium salts of a number of benzocyclopentaquinolines and benzoacridines derivatives were obtained.
1,3-dipolar cycloaddition of stable azomethine ylide based on ninhydrin and l-proline to phosphorylated acetylenes
Authors: Sokolov A. A , Egorov D. M , Pronina Yu. A. , Ramsh S. M , Stepakov A. V
Published: April 2024

The reaction of 1,3-dipolar cycloaddition of a stable azomethine ylide formed from ninhydrin and L-proline to activated acetylenic phosphonates was studied. It was found that the reactions proceed under mild conditions with high regioselectivity with the formation of cycloadducts with a spiro[inden-2,3’-pyrrolysine]-1,3-dione backbone.
Metal exchange kinetics of asymmetrically substituted cd(II)- tetraarylporphyrins with cobalt and zinc chlorides in dmf
Authors: Zvezdina S. V , Chizhova N. V , Mamardashvili N. Z
Published: April 2024

The metal exchange reactions of Cd(II)-5-(4-nitrophenyl)-10,15,20-triphenylporphyrin and Cd(II)-5,10,15-tri-(4-nitrophenyl)-20-phenylporphyrin with cobalt and zinc chlorides in dimethylformamide were studied by the spectrophotometric method. The kinetic parameters of metal exchange were calculated and a possible stoichiometric mechanism of the process is established. The influence of the nature of the solvate salt and the chemical modification of the tetrapyrrole macrocycle on the kinetic parameters of the metal exchange reaction was revealed.
5-(2-pyridyl)tetrabenzoporphyrin and its complexes with zinc, cobalt, copper and iron. synthesis, spectral, electrochemical and electrocatalytic properties
Authors: Mayorova E. I , Rumyantseva T. A , Bazanov M. I , Galanin N. E
Published: April 2024

The interaction of phthalimide with 2-picoline in the presence of zinc oxide synthesized 3-(pyridin-2-ylmethylene)isoindolin-1-one. Heating its mixture with an excess of phthalimide and zinc acetate leads to the formation of zinc 5-(2-pyridyl)tetrabenzoporphyrinate, which, upon treatment with acid, is converted to 5-(2-pyridyl) tetrabenzoporphyrin. The latter, when interacting with cobalt(II), copper(II), and iron(III) chlorides in DMF, forms the corresponding metal complexes. The composition and structure of the obtained compounds were confirmed by mass spectrometry, vibrational, 1H NMR, and electron spectroscopy. The results of quantum-chemical calculations of complexes by the DFT method are presented. A correlation is established between the energy gap between the frontier orbitals and the positions of the first bands in the electronic absorption spectra. All the synthesized tetrabenzoporphyrins exhibit catalytic activity in the electroreduction of oxygen, the highest activity being exhibited by cobalt and copper complexes.
Iron-containing polyoxotungstophosphates and their thermolysis products
Authors: Moroz Ya. A. , Lozinskii M. S , Zaritovskii A. N , Lopanov A. N , Burkhovetskii V. V , Glazunova V. A
Published: April 2024

Thermolysis of ferrocenium tungstophosphate [(C5H5)2Fe]3[PW12O40]∙H2O and tungstophosphatoferrates with the general formula of Cat4[PW11O39Fe(H2O)]∙ m H2O, where Cat = (NH4)+, Rb+, Cs+, (CH3)4N+, with the Keggin anion structure were studied using differential scanning calorimetry, infrared spectroscopy, X-ray phase analysis, and electron microscopy. The crystalline products of their thermal decomposition - phases with the structure of pyrochlore and tungsten bronzes - were identified. The synthesized compounds are catalysts for the oxidation reactions of organic compounds and the production of carbon nanomaterials.
Colloidal and nanosized catalysts in organic synthesis. XXVI. Аmines alkylation with alcohols catalyzed by γ-al2o3-supported nickel and copper nanoparticles
Authors: Nebykov D. N , Razvalyaeva A. V , Panov A. O , Latyshova S. E , Mokhov V. M
Published: April 2024

Amines alkylation with alcohols catalyzed by γ-Al2O3-supported nickel and copper nanoparticles under continuous process conditions at atmospheric hydrogen pressure and 180-220°С leads to the formation of alkylated products with selectivity up to 100%.
Synthesis and some properties of magnesium, zinc, and erbium tetra-3(4)-methylphenyldiazenylphtalocyanines
Authors: Bychkova A. N. , Tikhomirova T. V. , Kazaryan K. Yu. , Mykina E. A. , Vashurin A. S.
Published: April 2024

The peripherally and non-peripherally substituted Zn(II), Mg(II), and Er(III) phthalocyanine complexes were obtained from 3(4)-(4-methylphenyldiazenylphenoxy)phthalonitrile. The effect of the complexing metal and the location of the substituent on the spectral properties of the obtained compounds was shown. The acid-base properties of non-peripherally substituted metal phthalocyanines were studied. The quantum yield and fluorescence lifetime for the synthesized metal complexes were determined.
Reaction features of nitrosulfodienes of thiolene-1,1-dioxide series with semicarbazide
Authors: Efremova I. E , Savel′ev I. I , Baichurin R. I , Ozerova O. Yu. , Serebryannikova A. V
Published: April 2024

The influence of the electronic and spatial structure of the diene system 2-benzylidene-3-methyl-4-nitro-2,5-dihydrothiophene-1,1-dioxides on the result of the reaction with semicarbazide in different media (in ethanol and DMSO) was studied. The structure of the obtained compounds was established by IR, 1Н, 13С{1Н}, 1Н-13С HMQC, 1Н-13С HMBC, 1Н-1Н NOESY spectroscopy methods.
Reaction of N,N′-diphenyldithiomalondiamide with aromatic aldehydes and cyanoacetamide
Authors: Dotsenko V. V , Sinotsko A. E , Varzieva E. A , Buryi D. S , Vasilin V. K , Aksenov N. A , Aksenova I. V
Published: April 2024

The reaction of dithiomalondianilide ( N,N′-diphenyldithiomalondiamide) with aromatic aldehydes and cyanoacetamide in the presence of morpholine c yielded previously undescribed 6-amino-4-aryl-7-phenyl-3(phenylimino)-4,7-dihydro-3 H -[1,2]dithiolo[3,4- b ]pyridine-5-carboxamides.
Effect of 1-alkyl-3-methylimidazolium di-2-ethylhexylsulfosuccinate on the extraction of lanthanides(III) with 1,3-bis[(diphenylphosphorylacetamido)methyl]benzene from nitric acid solutions
Authors: Turanov A. N. , Karandashev V. K. , Artyushin O. I. , Sharova E. V.
Published: April 2024

It was found that the efficiency of extraction of lanthanide(III) ions from nitric acid solutions with 1,3-bis[(diphenylphosphorylacetamido)methyl]benzene significantly increases in the presence of ionic liquids, 1-alkyl-3-methylimidazolium di-2-ethylhexylsulfosuccinates, in the organic phase. The partition of ionic liquids between the organic and aqueous phases was studied depending on the concentration of the ionic liquid and nitric acid. The stoichiometry of the extractable lanthanide(III) complexes was determined by the equilibrium shift method. The influence of the length of alkyl radicals in the cationic part of the ionic liquid and the concentration of HNO3 in the aqueous phase on the efficiency of the extraction of metal ions into the organic phase containing the ionic liquid was considered.
Synthesis of 3,5-dichlorosalicylic acid anilides bearing a carboxymethoxyl group in aniline fragment
Authors: Dudarev V. G. , Vasendin M. I. , Moskvin A. V. , Lisovsky D. S. , Kolotilova N. V. , Lalaev B. Y.
Published: April 2024

Reaction of (aminodichlorophenoxy)acetic acids with 3,5-dichlorosalicylic acid chloride in acetonitrile produced salicylanilides containing carboxymethoxyl group in aniline fragment. The yield of the target compounds depends on the structure of the acylated amine and the order of addition of amine, acid chloride and proton acceptor. Also, the synthesis procedure of some intermediates necessary for the synthesis, in particular 2,6-dichloro-4-nitrophenoxyacetic acid methyl ester, was improved.
Real Normal Form of a Binary Polynomial at a Second-Order Critical Point
Authors: Batkhin A. B. , Bruno A. D.
Published: April 2024

A real polynomial in two variables is considered. Its expansion near the zero critical point begins with a third-degree form. The simplest forms to which this polynomial is reduced with the help of invertible real local analytic changes of coordinates are found. First, for the cubic form, normal forms are obtained using linear changes of coordinates. Altogether, there are three of them. Then three nonlinear normal forms are obtained for the complete polynomial. Simplification of the calculation of a normal form is proposed. A meaningful example is given.
Symbolic-Numerical Modeling of the Propagation of Adiabatic Waveguide Mode in a Smooth Waveguide Transition
Authors: Divakov D. V. , Tyutyunnik A. A.
Published: April 2024

In this work, the model of adiabatic waveguide modes is studied by means of computer algebra. Within the model, the solution of the system of Maxwell’s equations is reduced to a form expressed via the solution of a system of four ordinary differential equations and two algebraic equations for six components of the electromagnetic field. In the case of multilayer waveguides, by means of a computer algebra system, the equations are reduced to a homogeneous system of linear algebraic equations, which is studied symbolically. The condition for non-trivial solvability of the system defines a dispersion relation, which is solved by the symbolic-numerical method, while the system is solved symbolically. The paper presents solutions that describe adiabatic waveguide modes in the zeroth approximation, taking into account the small slope of the interface of the waveguide layer, which are qualitatively different from solutions that do not take into account this slope.
On the Simultaneous Reduction of a Pair of Unitoid Matrices to Diagonal Form
Authors: Ikramov Kh. D.
Published: April 2024

Let A and B be Hermitian n*n matrices with A being nonsingular. According to a well-known theorem of matrix analysis, these matrices can be brought to diagonal form by one and the same Hermitian congruence transformation if and only if the matrix C = A-1B has a real spectrum and can be diagonalized by a similarity. An extension of this assertion to the case where two unitoid matrices are simultaneously reduced to diagonal form is stated and proved.
Singular Nonlinear Problems for Phase Trajectories of Some Self-Similar Solutions of Boundary Layer Equations: Correct Formulation, Analysis, and Calculations
Authors: Konyukhova N. B. , Kurochkin S. V.
Published: April 2024

We study a singular initial value problem for a nonlinear non-autonomous ordinary differential equation of the second order, defined on a semi-infinite interval and degenerating in the initial data for the phase variable. The problem arises in the dynamics of a viscous incompressible fluid as an auxiliary problem in the study of self-similar solutions of the boundary layer equations for a stream function with a zero pressure gradient (plane-parallel laminar flow in a mixing layer). It is also of independent mathematical interest. Using the previously obtained results on singular nonlinear Cauchy problems and parametric exponential Lyapunov series, a correct formulation and a complete mathematical analysis of this singular initial value problem are given. Restrictions on the “self-similarity parameter” for the global existence of solutions are formulated, two-sided estimates of solutions, and results of calculations of the phase trajectories of solutions for different values of this parameter are given.
A Simple Criterion for Estimating the Grid Level of Detail for RANS Methods
Authors: Gavrilov A. A. , Dekterev A. A. , Shebelev A. V.
Published: April 2024

A simple criterion for evaluating the grid resolution needed to obtain a grid-independent solution of turbulent flow problems in the framework of statistical approach to turbulence simulation is proposed. The criterion is derived on the basis of an a posteriori estimate of the local interpolation error of the field of turbulent kinetic energy. A good resolution should ensure a small local interpolation error of the discrete turbulent kinetic energy. The equation for the transport of turbulent kinetic energy and realizability conditions for the turbulent stress tensor made it possible to reduce the estimation of relative interpolation error to an explicit formula for the estimate of the maximal grid step required for obtaining a grid-independent solution. The proposed criterion is applied to a steady problem for a flow past a backward facing step and to the problem of unsteady flow around a half-circular profile arranged at a zero angle of attack for the Reynolds number Re = 45 000. A numerical study showed that the proposed criterion gives a good estimate of the grid resolution required for obtaining a grid-independent solution away from a wall. This criterion can be used both for estimating the grid independence of the solution and for adapting the computation grid.
Synthesis of an Optimal System with Stable Sliding Modes
Authors: Ashchepkov L. T.
Published: April 2024

A method for synthesizing an optimal control that ensures the existence and stability of sliding modes for a system of nonlinear ordinary differential equations is proposed. This method uses an auxiliary optimal control problem. The solution gives a control in analytical form. It is proved that the trivial solution of the closed-loop system is Lyapunov stable. Application of the proposed method to linear and quasi-linear systems of equations is demonstrated, and an illustrative example is discussed.
Calculation of a Strong Resonance Condition in a Hamiltonian System
Authors: Batkhin A. B. , Khaidarov Z. Kh.
Published: April 2024

A method for symbolic computation of a condition of existence of a third- and fourth-order resonance for investigations of formal stability of an equilibrium state of a multiparameter Hamiltonian system with three degrees of freedom in the case of general position is proposed. This condition is formulated in the form of zeros of a quasi-homogeneous polynomial of the coefficients of the characteristic polynomial of the linear part of the Hamiltonian system. Computer algebra (Gröbner bases of elimination ideals) and power geometry (power transformations) are used to represent this condition for various resonance vectors in the form of rational algebraic curves. Given a linear approximation of the characteristic polynomial in the space of its coefficients, these curves are used to obtain a description of a partition of the stability domain into parts in which there are no strong resonances. An example of a description of resonance sets for a two-parameter pendulum-type system is given. All computations are carried out in the computer algebra system Maple.
Approximate Solution of an Inverse Problem for a Singularly Perturbed Integro-Differential Heat Equation
Authors: Denisov A. M.
Published: April 2024

The paper considers an inverse problem for a singularly perturbed integro-differential heat equation, which consists in determining the boundary condition from additional information on the solution of the initial-boundary value problem. It is proved that an approximate solution of the inverse problem can be obtained by using a finite number of terms in the expansion of the solution of the initial-boundary value problem in a small parameter.
Characteristic-Based Volume Penalization-Imposed Wall Function Method for Turbulent Boundary Layer Modeling
Authors: Vasilyev O. V. , Zhdanova N. S.
Published: April 2024

A method to approximate near-wall boundary conditions for the compressible Reynolds-Averaged Navier–Stokes equations is proposed. The differential formulation to match the external and the wall function solutions is reformulated in a form of the generalized characteristic-based volume penalization method to model the transfer of the shear stress from the outer region of the boundary layer to the wall. The exchange location is specified implicitly in terms of a localized source term in the boundary layer equation written as a function of the distance from the wall normalized by the viscous length scale. The shear stress on the wall is determined by solving an auxiliary equation for the wall-stress imposing the analytical wall function solution through the characteristic-based volume penalization method. The proposed method noticeably reduces the near-wall mesh resolution requirements without a significant modification of the numerical algorithm and completely eliminates the ill-defined explicit solution matching procedure. The developed approach is numerically implemented using the vertex-centered control volume method on structured meshes. Its effectiveness is demonstrated by solving two test problems: the two-dimensional channel flow and turbulent flow over an infinitely thin plate.
On the Absence of Weak Solutions of Nonlinear Nonnegative Higher Order Parabolic Inequalities with a Nonlocal Source
Authors: Admasu V. E.
Published: April 2024

The paper proves the absence of solutions of semilinear parabolic inequalities and higher order systems with a singular potential and nonlocal sources. The proofs are based on the test function method developed by E. Mitidieri and S.I. Pokhozhaev.
The Method of Optical Paths for the Numerical Solution of Integrated Photonics Problems
Authors: Belov A. A. , Dombrovskaya Zh. O.
Published: April 2024

A number of topical problems of integrated photonics are reduced to oblique incidence of radiation on a plane-parallel scatterer. For such problems, a method for integrating Maxwell’s equations along the direction of beam propagation is proposed. As a result, the original two-dimensional problem is reduced to a one-dimensional problem, and it is solved using recently proposed one-dimensional bicompact schemes. This significantly reduces the computational cost compared with the conventional two-dimensional finite difference and finite element methods. The proposed method is verified by solving test problems for which exact solutions are known.
On Singular Points of Linear Differential-Algebraic Equations with Perturbations in the Form of Integral Operators
Authors: Chistyakov V. F.
Published: April 2024

The paper consideres linear systems of ordinary differential equations of arbitrary order with a matrix identically degenerate in the domain of definition at the highest derivative of the desired vector function and with loads in the form of Volterra and Fredholm integral operators. The initial value problems are formulated using projections onto admissible sets of initial vectors. Special attention is paid to systems having singular points on the interval of integration. The concept of a singular point is formalized. Their classification in the case of differential equations is given. A number of examples illustrating the theoretical results are presented.
Stability Indicators of Nonnegative Matrices: Parametric and Sparse Cases
Authors: Razzhevaikin V. N.
Published: April 2024

Methods for the algorithmic construction of stability indicators of nonnegative matrices is described, and the application of these indicators to problems of modern mathematical biology and epidemiology is discussed. Specific features of such indicators when they are applied to problems about the parametric loss of stability of trivial equilibrium states of discrete dynamical systems are pointed out. Estimates of the efficiency of algorithms based on the proposed methods for the case of systems determined by sparse matrices are given. Examples of using the constructed algorithms for such systems are discussed.
Gradient-free Federated Learning Methods with l1 and l2-randomization for Non-smooth Convex Stochastic Optimization Problems
Authors: Alashqar B. A. , Gasnikov A. V. , Dvinskikh D. M. , Lobanov A. V.
Published: April 2024

This paper studies non-smooth problems of convex stochastic optimization. Using the smoothing technique based on the replacement of the function value at the considered point by the averaged function value over a ball (in l1-norm or l2-norm) of a small radius centered at this point, and then the original problem is reduced to a smooth problem (whose Lipschitz constant of the gradient is inversely proportional to the radius of the ball). An essential property of the smoothing used is the possibility of calculating an unbiased estimation of the gradient of a smoothed function based only on realizations of the original function. The obtained smooth stochastic optimization problem is proposed to be solved in a distributed federated learning architecture (the problem is solved in parallel: nodes make local steps, e.g. stochastic gradient descent, then communicate—all with all, then all this is repeated). The goal of the article is to build on the basis of modern achievements in the field of gradient–free non-smooth optimization and in the field of federated learning gradient-free methods for solving problems of non-smooth stochastic optimization in the architecture of federated learning.
Dynamics of Chains of Many Oscillators with Unidirectional and Bidirectional Delay Coupling
Authors: Kashchenko S. A.
Published: April 2024

Chains of Van der Pol equations with a large delay in coupling are considered. It is assumed that the number of chain elements is also sufficiently large. In a natural manner, a chain is replaced by a Van der Pol equation with an integral term in the space variable and with periodic boundary conditions. Primary attention is given to the local dynamics of chains with unidirectional and bidirectional coupling. For sufficiently large values of the delay parameter, parameters are explicitly determined for which critical cases occur in the stability problem for the zero equilibrium state. It is shown that the problems under consideration have an infinite-dimensional critical case. The well-known methods of invariant integral manifolds and the methods of normal forms are inapplicable in these problems. Proposed by this paper’s author, the method of infinite normalization—the method of quasi-normal forms—is used to show that the leading terms of the asymptotics of the original system are determined by solutions of (nonlocal) quasi-normal forms, i.e., special nonlinear boundary value problems of the parabolic type. As the main results, corresponding quasi-normal forms are constructed for the considered chains.
On the Uniqueness of Solution to Systems of Linear Algebraic Equations to Which the Inverse Problems of Gravimetry and Magnetometry Are Reduced: A Regional Variant
Authors: Kolotov I. I. , Lukyanenko D. V. , Stepanova I. E. , Shchepetilov A. V. , Yagola A. G.
Published: April 2024

Conditions for the unique solvability of systems of linear algebraic equations to which many inverse problems of gravitational and magnetic exploration are reduced are considered. The mathematical statements of inverse problems take into account the sphericity of the Earth.
Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization
Authors: Zvonareva T. A. , Kabanikhin S. I. , Krivorotko O. I.
Published: April 2024

An algorithm has been developed for numerically solving the source determination problem in the model of information dissemination in synthetic online social networks, described by reaction–diffusion-type equations, using additional information about the process at fixed time points. The degree of ill-posedness of the source determination problem for a parabolic equation is studied based on the analysis of singular values of the linearized operator of the inverse problem. The algorithm developed is based on a combination of the tensor optimization method and gradient descent supplemented with the A.N. Tikhonov regularization. Numerical calculations demonstrate the smallest relative error in the reconstructed source obtained by the developed algorithm in comparison with classical approaches.
Stability Analysis of Several Time Discrete Schemes for Allen–Cahn and Cahn–Hilliard Equations
Authors: He Qiaoling , Yan Junping , Abuduwaili Abudurexiti
Published: April 2024

In this paper, the stability of several time discrete schemes for Allen–Cahn and Cahn–Hilliard equations and an error estimate for Cahn–Hilliard equation are analyzed. In order to discuss the Allen–Cahn and Cahn–Hilliard equations, a skew symmetric positive operatoris defined, wherein Allen–Cahn equation andin Cahn–Hilliard equation. We analyze stabilities of some schemes for the Allen–Cahn and the Cahn–Hilliard equation. The error estimates of Cahn–Hilliard equation are based on fully discrete scheme, its main idea is to use the finite element method to discretize in space, and then use two approximate results of the elliptic projection operator to analyze. Finally, we numerically verify convergence rates of this scheme.
Simulation of Propagation of Dynamic Perturbations in Porous Media by the Grid-Characteristic Method with Explicit Description of Heterogeneities
Authors: Mitskovets I. A. , Khokhlov N. I.
Published: April 2024

Wave perturbations propagating through heterogeneous media with porous inclusions are numerically simulated, and an explicit description of porous heterogeneities is considered. The method of overlapping meshes is proposed for an explicit description of heterogeneities. The arising systems of partial differential equations are solved numerically by applying the grid-characteristic method. The features of the method are discussed, the proposed algorithms are verified, and a series of test computations is conducted.
Boundary and Contact Conditions of Higher Order of Accuracy for Grid-Characteristic Schemes in Acoustic Problems
Authors: Shevchenko A. V. , Golubev V. I.
Published: April 2024

Seismic wave propagation through geological media is described by linear hyperbolic systems of equations. They correspond to acoustic, isotropic, and anisotropic linear elastic porous fluid-saturated models. They can be solved numerically by applying grid-characteristic schemes, which take into account propagation of solution discontinuities along characteristics. An important property of schemes used in practice is their high order of accuracy, due to which signal wavefronts can be clearly resolved. Previously, much attention was given to this property at interior points of the computational domain. In this paper, we study the order of a scheme up to the boundary of the domain inclusive. An approach is proposed whereby arbitrary linear boundary and contact conditions can be set up to high accuracy. The presentation is given for the system of one-dimensional acoustic equations with constant coefficients.
Grid-Characteristic Numerical Method on an Irregular Grid with Extending the Interpolation Stencil
Authors: Vasyukov A. V. , Smirnov I. E.
Published: April 2024

A grid-characteristic numerical method for solving a multidimensional transport equation on an unstructured grid with an order higher than one is proposed; this method does not use auxiliary points on edges and faces. The avoidance of auxiliary points on edges and faces simplifies the topology of the computational grid during its motion, which is important for solving dynamic problems of mechanics of deformable solids. To increase the approximation order, an analog of the grid stencil extension implemented for an unstructured grid is used. Results of testing the proposed numerical scheme for continuously differentiable, continuous, discontinuous solutions are presented.
Modeling the Motion of an Elongated Contour under Free Surface of a Heavy Fluid under Large Froude Numbers
Authors: Filippov S. I.
Published: April 2024

The flow around an elongated smooth contour under the free surface of a fluid is considered. The fluid is perfect, incompressible, and heavy. The critical flow branching and flow shedding points are located on the contour. The depth of the contour immersion and its length are given. It is assumed that the velocity magnitude on the free surface is close to its value in the undisturbed flow. A nonlinear approximation of the Bernoulli integral on the free surface associated with logarithm is used. Two auxiliary planes in which the flow domain is a half-plane with an excluded circle and an annular region are used. The complex potential is determined in the first parametric plane using a conformal mapping onto the annular region. A system of equations is derived for finding the defining parameters. This system is solved using the minimization of a functional and an iteration method over two sets of parameters. An algorithm and computer program for solving this system are developed. The hydrodynamic characteristics of a specific hydrofoil are computed. Results for the coefficients of wave drag, lift force, moment, and position of the contour center are analyzed depending on the Froude number and circulation of different signs. Examples of computations of nonlinear waves formed on the free surface at significant Froude numbers are given.
Analyticity and Pseudo-Analyticity in the Small Parameter Method
Authors: Kachalov V. I. , Maslov D. A.
Published: April 2024

The small parameter method allows one to construct solutions of differential equations in the form of power series and has become widespread in mathematical physics. In most cases, these series are asymptotically convergent. The aim of this work is to find conditions for the ordinary convergence of series in powers of a small parameter representing solutions of perturbation theory problems.
ON NUMERICAL BEAMFORMING FOR CORRELATED DIPOLE TYPE SOURCES
Authors: Kozubskaya T. K. , Plaksin G. M. , Sofronov I. L.
Published: April 2024

A numerical beamforming method for correlated dipole-type sources in the frequency domain is developed. The typical configuration of the location of acoustic field sources and microphones is considered to analyze the noise generated under an aircraft flying in turbulent flow regimes. Three problems of numerical beamforming are studied, allowing one to take into account a priori information about connections between the components of the dipole function at a point. They differ in the number of real functions to be found: six (no connection), four (components are in phase) and two (the direction of the dipole moment is known). The discretization parameters of source function grids and microphones are estimated to ensure stable matrix inversion in numerical beamforming algorithms. The issues of nonuniqueness of solutions for the tangent components of the dipole function in the first and second problems are identified and discussed; for the third problem such an issue does not arise.
Differential-Difference Equations with Optimal Parameters
Authors: Mastryukov A. F.
Published: April 2024

The paper considers difference schemes with optimal parameters for solving Maxwell’s equations. Using Laguerre transforms, the numerical values of the optimal parameters are determined and differential-difference equations are constructed. Differential-difference equations are solved by the finite-difference method with iterations over small optimal parameters. Optimal second-order difference schemes for one-dimensional and two-dimensional Maxwell’s equations are considered. Optimal parameters of difference schemes are given. It is shown that the use of optimal difference schemes leads to an increase in the accuracy of solution.
LOWER BOUNDS FOR COLUMN MATRIX APPROXIMATIONS
Authors: Osinsky A. I.
Published: April 2024

We show a connection between lower and upper bounds on the column matrix approximation accuracy and the bounds on the norms of the pseudoinverses of the submatrices of orthogonal matrices. This connection is exploited to derive lower bounds for column approximations accuracy in spectral and Frobenius norms.
CONTROLLING CHAOS IN 3D POROUS MEDIA IN THE PRESENCE OF ORIENTATION EFFECT
Authors: Rouaha H. , Joundy Y. , Taika A.
Published: April 2024

The influence of orientation on the control of chaotic behaviors of the system in a porous medium is studied in this article based on the theory of dynamical systems. A three-dimensional system model is obtained using the spectral method. The results showed that chaos can be suppressed in the case of a low or moderate Prandtl number by choosing appropriate tilt angles.
On Weak Solvability of a Flow Problem for Viscoelastic Fluid with Memory
Authors: Zvyagin V. G. , Orlov V. P.
Published: April 2024

The existence of weak solutions of the initial-boundary value problem for the equations of motion of a viscoelastic fluid with memory along trajectories of a nonsmooth velocity field and with an inhomogeneous boundary condition is proved. The study relies on Galerkin-type approximations of the original problem followed by passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to examine the behavior of trajectories of a nonsmooth velocity field.
Multipole Representation of the Gravitational Field for Asteroid (16) Psyche
Authors: Nikonov V. I.
Published: April 2024

An approach to calculating multipole approximations of the gravitational potential of small celestial bodies with an irregular mass distribution is demonstrated for the asteroid (16) Psyche as an example.
Conformal Mapping of a Z-Shaped Domain
Authors: Skorokhodov S. L.
Published: April 2024

For the problem of conformal mapping of a half-plane onto a Z-shaped domain with arbitrary geometry, an efficient method is developed for finding parameters of the Schwarz–Christoffel integral, i.e., the preimages of the vertices (prevertices) and the pre-integral multiplier. Special attention is given to the situation of crowding prevertices, in which case conventional integration methods face significant difficulties. For this purpose, the concept of a cluster is introduced, its center is determined, and all integrand binomials with prevertices from this cluster are expanded into a fast-convergent series by applying a unified scheme. Next, the arising integrals are reduced to single or double series in terms of Gauss hypergeometric functions F(a, b, c, q). The fast convergence of the resulting expansions is ensured by applying formulas for analytic continuation of F(a, b, c, q) to a neighborhood of the point q = 1 and using numerically stable recurrence relations. The constructed expansions are also fairly efficient for choosing initial approximations for prevertices in Newton’s iteration method. By using the leading terms of these expansions, the approximations for the prevertices are expressed in explicit form in terms of elementary functions, and the subsequent iterations ensure the fast convergence of the algorithm. After finding the parameters in the integral, the desired mapping is constructed as a combination of power series expansions at prevertices, regular expansions at the preimage of the center of symmetry, a Laurent series in a semi-annulus, and special series near the preimages of the vertical segments. Numerical results demonstrate the high efficiency of the developed method, especially in the case of strong crowding of prevertices.
Three-Dimensional Simulation of a High-Velocity Body Motion in a Tube with Rarefied Gas
Authors: Yakunchikov A. N. , Iuldasheva A. R.
Published: April 2024

Flow around a body moving at a high subsonic velocity in a tube filled with rarefied gas is studied. This aerodynamic problem is considered as applied to the task of designing a high-speed vacuum transport at finite Knudsen numbers. Parameters that are close to target characteristics of such systems are chosen, more precisely, speed of about 1000 km/h, significant transverse size of the body, and nitrogen–oxygen mixture (air) as the filling gas are chosen. The problem was solved in a three-dimensional statement.
EVALUATION OF EFFICIENCY OF USING OF BRAIN-COMPUTER INTERFACE IN LEARNING IMAGINATION OF MOVEMENTS OF UPPER AND LOWER LIMBS
Authors: Gerasimenko Yu. P. , Bobrova E. V. , Reshetnikova V. V. , Vershinina E. A. , Grishin A. A. , Isaev M. R. , Bobrov P. D.
Published: April 2024

The effectiveness of brain-computer interface (BCI) control and the success of imagination of movement of the upper and lower extremities were evaluated by the accuracy of recognition of EEG signals (classification accuracy) when imagining movements of the hands, feet and locomotion during 10-day training of 10 volunteers. Averaged data of all the volunteers revealed, that, on the first day of training, the classification accuracy is higher when imagining locomotion than foot movements, on the second day – hands than locomotion, on the fifth day – feet than hands. The average values of classification accuracy when imagining movements of the hands and feet increase by the 3rd day of training, further changes are specific depending on which movement is imagined. When learning the imagination of locomotion, the accuracy of classification does not significantly change. An assessment of the dynamics of individual changes in the accuracy of classification according to linear trends showed that in three participants, training led to an increase in the accuracy of classification (of the hand movements and locomotion – in one subject, of feet – in two subjects); in other three participants – to decrease (of the movements of the hands and locomotion – in one subject, of the locomotion – in the second subject, of feet – in the third). The four participants, as well as the sample average, had no significant changes. The results are discussed in terms of changes in the activity of brain structures during learning and depending on the type of imaginary movements.
EVOLUTIONARY PATH OF CONSCIOUSNESS AND REASON: COGNITOME FROM A PHILOSOPHICAL PERSPECTIVE
Authors: Kanaev I. A. , Dryaeva E. D.
Published: April 2024

The ability of an organism to experience subjective states is an object of research for many disciplines of science. This article seeks to consider consciousness on the foundation of advances in neuroscience, cognitive science, anthropology, and philosophy. Particular attention is given to the concept of “cognitome” suggested by K.V. Anokhin. We agree with understanding conscious activity as a particular ability of an organism, which cannot be reduced to a mass of simpler systems. However, we believe that subjective ability for the cognition or “anticipatory reflection” of the environment must be considered under the history of natural evolution. We suggest that a particular interference pattern that emerges from the activity of neural domain systems can be a foundation for a critical enhancement of a system’s efficiency and cause further evolution of cognitive systems. This theory is coherent with the most elaborated neuroscientific explanations of consciousness and can explain the direct match between the neural system’s dynamics and states of subjective reality.
MULTI-VOXEL PATTERN ANALYSIS OF fMRI DATA DURING SELF- AND OTHER-REFERENTIAL PROCESSING
Authors: Knyazev G. G. , Savostyanov A. N. , Rudych P. D. , Bocharov A. V.
Published: April 2024

The study of brain activity in the processing of self-referential information, as compared to the processing of information related to other people, is based on the application of mass-univariate analysis, based on the assumption that activity in one region is independent of activity in other regions. Recently, there has been a growing interest in neuroimaging to investigate spatially distributed information using multivariate approaches such as multivoxel pattern analysis (MVPA). In this paper, we used MVPA to analyze fMRI data recorded during self-evaluation and evaluation of other people of varying proximity. In all pairwise classifications tested, the number of correct identifications was significantly higher than the level of random matches. Predictively significant structures were widely distributed over different brain regions and included areas of the visual, lateral prefrontal, and many other cortical areas in addition to the cortical midline structures that contributed the most. In the self-other classification, ventral areas of the medial prefrontal and cingulate cortex were the most informative for the self condition, whereas parietal and occipital medial areas were the most informative for the other condition. The combination of brain structures, which included the anterior cingulate cortex and both amygdalae, revealed by principal component analysis, correlated positively with the psychometric scale of sensitivity to reward, and negatively with neuroticism scales. Overall, the results show the fruitfulness of using machine learning methods to analyze data from such kinds of experiments.
BALANCE OF RESTING STATE NETWORKS AFTER MIGRATION TO THE NORTH REGION
Authors: Bocharov A. V. , Savostyanov A. N. , Tamozhnikov S. S. , Karpova A. G. , Saprigyn A. E. , Milakhina N. S. , Zavarzin E. A. , Rudich P. D. , Merkulova E. A. , Knyazev G. G.
Published: April 2024

The study involved 45 students (all men) of different nationalities (mostly Tajiks and Kyrgyzs) aged from 17 to 28 years who had moved to the conditions of the North (Yakutsk, Republic of Sakha (Yakutia)). The aim of the study was to investigate the balance of connectivity of resting state networks in the first condition, when the participants got into a new unfamiliar environment and in the second condition after one year of staying in these conditions. A 128-channel EEGs were recorded at rest. Connectivity measures were calculated between nodes of resting state networks and the rest of the brain. Connectivity contrasts Attention Networks vs Default Mode Network in the first and in the second conditions were performed. In the first condition, a predominance of Attention networks over Default mode network was revealed, which could be related to an increased attention to new stimuli and tasks in a new unfamiliar environment. In the second condition, after one year of staying in these environmental conditions, the balance of resting state networks shifted toward a predominance of the Default mode network over Attention networks.
ОСОБЕННОСТИ ГЛАЗОДВИГАТЕЛЬНЫХ РЕАКЦИЙ У ВЫСОКОТРЕВОЖНЫХ ДОБРОВОЛЬЦЕВ С РАЗНЫМ УРОВНЕМ ИМПУЛЬСИВНОСТИ ПРИ РЕШЕНИИ РАЗНЫХ ВАРИАНТОВ АНТИСАККАДНОЙ ЗАДАЧИ
Authors: Khayrullina G. M. , Panfilova E. A. , Martynova O. V.
Published: April 2024

Введение. В зависимости от уровня импульсивности лица с повышенной тревожностью по-разному реагируют на задачи, требующие тормозного контроля. Антисаккадная задача является одним из психофизиологических подходов к оценке зрительного внимания и тормозного контроля. Это исследование было направлено на проверку гипотезы о том, что люди с высоким уровнем импульсивности и тревожности будут иметь разные модели движения глаз в задаче на антисаккады по сравнению с людьми с высокой тревожностью и низким уровнем импульсивности. Метод. В исследовании двадцать добровольцев с высоким уровнем тревожности и низким уровнем импульсивности и четырнадцать человек с высоким уровнем тревожности и импульсивности выполняли антисаккадные задачи в трех блоках, которые отличались способами разделения по времени появления целевого стимула (step, overlap, gap) с фиксационными и целевыми стимулами негативной, позитивной и нейтральной модальностей. Глазодвигательные паттерны записывались методом айтрекинга. Результаты. Значительные различия наблюдались между группами в латентности регулярных ошибок в overlap-последовательности и в амплитуде регулярных ошибок в gap-последовательности. Лица с высокой тревожностью и высокой импульсивностью совершали регулярные ошибки с большей латентностью в overlap-блоке и с меньшей амплитудой в gap-блоке только на нейтральные стимулы. Заключение. Наши результаты показывают, что различные схемы антисаккадной задачи способны выявлять специфические паттерны движений глаз, связанные с переключением внимания и тормозным контролем при импульсивном поведении.