bluuebunny/crossref_metadata_2025 huggingface dataset:
Synthesis, antibacterial and antimonooxidase activity of 4-(2-methyl-1,3-oxazol-5-yl)benzenesulfonamide
Authors: Gasilina O. A. , Romanycheva A. A. , Shetnev A. A. , Korsakov M. K.
Published: April 2024

A new method for obtaining 4-(2-methyl-1,3-oxazol-5-yl)benzenesulfonamide an antiglaucomatous drug candidate oxazopt was developed using a diazotization reaction. A combined potentiated effect of the antimicrobial action of carbapenems (meropenem) and aminoglycosides (gentamicin) against antibiotic-resistant gram-positive bacteria Enterococcus faecium, Enterococcus faecalis and gram-negative bacteria Escherichia coli and antimonooxidase effect in vitro was revealed for this compound.
Pseudo-three-component spiro[dihydrofuran-2,3′-oxindoles] synthesis: in situ generation of diazooxindole
Authors: Topanov P. A. , Dmitriev M. V. , Balandina S. Yu. , Shklyaev Y. V. , Mashevskaya I. V. , Maslivets A. N.
Published: April 2024

Upon reaction with N -substituted pyrroloquinoxalinetriones, isatin hydrazone is oxidized to diazooxindole and enters into a formal [4+1] cycloaddition reaction with N -substituted pyrroloquinoxalinetriones to form compounds containing a spiro[dihydrofuran-2,3′-oxindole] fragment, which is interesting for medicinal chemistry. The reaction of diazooxindoles with N -unsubstituted pyrroloquinoxalinetriones afforded analogous substituted spiro[dihydrofuran-2,3′-oxindoles]. The resulting compounds have moderate antimicrobial activity.
Aqueous submicron dispersions of surfactants as wetting agents and permeability enhancers of potato leaves
Authors: Zadymova N. M. , Aleksandrov Yu. D. , Kalinina N. O. , Taliansky M. E. , Skvortsova Z. N.
Published: April 2024

For aqueous solutions and submicron dispersions of non-micelle-forming surfactants (Tween 85, Brij L4, and Silwet L-77) kinetic tensiometric dependences and isotherms of wetting of leaves of the Prime potato variety were obtained. A technique has been developed for determining the rate of penetration of the studied liquids into potato leaves. The rate of penetration rises with increasing surfactant concentration. An increase in permeability and wetting efficiency is observed as following: Tween 85 < Brij L4 < Silwet L-77. The data obtained make it possible to evaluate the prospects for using the studied aqueous surfactant dispersions as platforms for the delivery of biologically active components into the leaves of potato plants to inhibit the proliferation of pathogens.
Synthesis of azole derivatives of 1,2,3-dithiazole-5-imines and study of their fungicidal
Authors: Tsaplin G. V. , Bashkalova E. I. , Alekseenko A. L. , Popkov S. V.
Published: April 2024

A three-stage method was proposed for the synthesis of new 4-[4-(2-azolylethyl)piperazine-1-yl]- N -aryl-5 H 1,2,3-dithiazole-5-imines. This approach includes the reaction of Appel salt with anilines to produce 1,2,3-dithiazole-5-imines, which were converted into 4-[(4-chloroethyl)piperazine-1-yl]-5 H -1,2,3-dithiazole-5-imines, alkylating azoles at the final stage. The high fungicidal activity of target compounds and intermediate 4-chloro N -aryl-1,2,3-dithiazole-5-imines was shown in vitro tests versus six species of phytopathogenic fungi.
Synthesis and phosphonylation of 6-amino-4-aryl-2-thioxo-1,2,3,4-tetrahydropyrimidine-5-carbonitriles
Authors: Nosova N. A. , Fatuev E. D. , Krylov A. S. , Egorov D. M.
Published: April 2024

A series of 6-amino-4-aryl-2-thioxo-1,2,3,4-tetrahydropyrimidine-5-carbonitriles was synthesized, further reaction of which with dimethyl chloroethynylphosphonate yielded a series of new dimethyl (8-cyano-7-aryl-5-thioxo-5,6-dihydroimidazo[1,2- c ]pyrimidin-2-yl)phosphonates.
Functionalization of the position 5 of thiopyran fragment of 4-(diethoxyphosphoryl)-4,7-dihydro-5 Н-thiopyrano[3,4-b]furan
Authors: Pevzner L. M. , Aleksandrova E. K. , Petrov M. L.
Published: April 2024

Alkaline hydrolysis of ethyl 4-(diethoxyphosphoryl)-4,7-dihydro-5 Н -thiopyrano[3,4- b ]furan-5-carboxylate proceeded selectively at the ester group. The acid obtained formed the corresponding acid chloride when treated with thionyl chloride. The acid chloride was used for acylation of glycine, α- and β-alanine esters. Under the conditions of phase transfer catalysis this acid chloride formed acyl azide which under mild conditions undergoes rearrangement to isocyanate. The latter reacted with primary amines to give ureas, and with the amino acid esters in forms ureidoesters. Reducing of acid chloride with sodium borohydride led to the corresponding alcohol. It was converted to chloride which in the reactions with sodium azide and iodide gives usual substitution products. When treated with potassium thiocyanate it formed thiocyanate. Iodide in the reaction with triethyl phosphite gave the corresponding phosphonate. Oxidation of alcohols with Collins reagent and acetic acid-DMSO system was studied.
The first representatives of phosphonium salts based on the ammonium acylhydrazone scaffold: synthesis and biological activity
Authors: Bogdanov A. V. , Bukharov S. V. , Rozhkova M. A. , Voloshina A. D.
Published: April 2024

The acid-catalyzed reaction of substituted benzaldehydes with Girard’s reagent T leads to the formation of new water-soluble mixed ammonium-phosphonium salts. The obtained compounds exhibit high antimicrobial and moderate antitumor activities with low hemotoxicity.
Reaction of diphenylphosphinal formic acid hydrazide with isothiocyanates
Authors: Isaeva A. O. , Krutov I. A. , Burangulova R. N. , Komunarova D. K. , Samigullina A. I. , Gavrilova E. L.
Published: April 2024

A new method was proposed for the preparation of diphenylphosphinylformic acid hydrazide based on the reaction of phosphine oxide and trimethylchlorosilane in the presence of a tertiary amine, followed by interaction with chloroformic acid ester and then hydrazine hydrate. The hydrazide moiety was modified into a thiosemicarbazide moiety by reacting diphenylphosphinylformic acid hydrazide with organic isothiocyanates. It was found that in an aqueous alkaline medium, thiosemicarbazides do not heterocyclize to 1,2,4-triazole-3-thiones, as expected. As a result of the rupture of the P-C bond, diphenylphosphinic acid and a 5-thioxo-1,2,4-triazolidin-3-one were formed.
Effect of synthesis conditions on molecular characteristics of coumarin and N-vinylpyrrolidone copolymers
Authors: Nesterova N. A. , Zakharova N. V. , Sazhina Yu. A. , Gavrilova I. I. , Panarin E. F.
Published: April 2024

Radical copolymerization was used to synthesize copolymers of coumarin and N -vinylpyrrolidone with molecular masses and compositions varying over wide limits. Molecular and hydrodynamic characteristics of the prepared copolymers and their dependence on the synthesis conditions were studied by dynamic and static light scattering.
Hydrolysis of polyacrylamide in the presence of nano-sized copper particles
Authors: Donetskova L. Yu. , Ozerin A. S. , Mikhailyuk A. E. , Radchenko F. S. , Andreev D. S. , Titova E. S. , Babkin V. A. , Novakov I. A.
Published: April 2024

The process of hydrolysis of amide groups of polyacrylamide in the presence of a dispersion of nanosized copper particles obtained by the reduction of copper cations with sodium tetraborate was studied. Quantum chemical calculations showed an increase in the effective positive charge on the carbon atom in the amide group upon formation of a complex with copper. Calculation of the energy of interaction of polyacrylamide and polyacrylic acid macromolecule units with copper particles showed the possibility of replacing amide groups of the polymer that underwent hydrolysis from the surface of copper particles with amide groups that did not participate in the reaction. The degree of hydrolysis of polyacrylamide in the presence of copper particles was 89%, and in the absence of particles 22%.
Vaporization processes and thermodynamic properties of the SrO-ZrO2  system at high temperatures
Authors: Lopatin S. I. , Stolyarov V. L. , Fedorova A. V. , Selyutin A. A.
Published: April 2024

Vaporization processes and thermodynamic properties of the SrO-ZrO2 system in the concentration range from 10 to 90 mol% SrO were studied by high-temperature differential mass spectrometry. Evaporation of the studied samples were carried out from tungsten Knudsen effusion cell. Partial pressures of vapor species in the temperature range of 1975-2800 K were determined. The values of SrO and ZrO2 activities, as well as Gibbs energies and excess Gibbs energies in the composition range from 90 to 45 mol% SrO were obtained at the temperature of 1940 K and from 45 to 10 mol% SrO at the temperature of 2123 K. It is established that in the SrO-ZrO2 system minor negative deviations from ideal behavior are observed.
FAD Technique and Differentiation of a Composite Function
Authors: Albu A. F. , Gorchakov A. Yu. , Zubov V. I.
Published: April 2024

Different approaches to the calculation of the gradient of a composite function of several variables are compared, namely, exact analytically derived formulas, formulas based on the fast automatic differentiation (FAD) technique, and standard software packages implementing the ideas of the FAD technique. The approaches are compared as applied to a composite function representing the energy of a system of atoms with the Tersoff interatomic potential. The comparison criterion is the computer time required for computing the gradient of the function. The results show that the FAD technique is superior to the analytical formulas. The standard packages take nearly the same time to compute the function gradient as the FAD technique formulas.
Learning port-Hamiltonian Systems—Algorithms
Authors: Lozienko D. , Salnikov V. , Falaize A.
Published: April 2024

In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from “unlabelled” ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in two phases. It starts by constructing the connectivity structure of the system using machine learning methods – producing thus a graph of interconnected subsystems. Then this graph is enhanced by recovering the Hamiltonian structure of each subsystem as well as the corresponding ports. This second phase relies heavily on results from symplectic and Poisson geometry that we briefly sketch. And the precise solutions can be constructed using methods of computer algebra and symbolic computations. The algorithm permits to extend the port-Hamiltonian formalism to generic ordinary differential equations, hence introducing eventually a new concept of normal forms of ODEs.
Generalization of the Subset Sum Problem and Cubic Forms
Authors: Seliverstov A. V.
Published: April 2024

A new algorithm is proposed for deciding whether a system of linear equations has a binary solution over a field of zero characteristic. The algorithm is efficient under a certain constraint on the system of equations. This is a special case of an integer programming problem. In the extended version of the subset sum problem, the weight can be positive or negative. The problem under consideration is equivalent to the analysis of solution existence for several instances of this problem simultaneously. New sufficient conditions are found under which the computational complexity of almost all instances of this problem is polynomial. In fact, the algorithm checks the existence of a cubic hypersurface that passes through each vertex of the unit cube, but does not intersect a given affine subspace. Several heuristic algorithms for solving this problem have been known previously. However, the new methods expand the solution possibilities. Although only the solution existence problem is considered in detail, binary search allows one to find a solution, if any.
On the Structure of Solutions to the Key Gosper Equation in Problems of Symbolic Summation
Authors: Zima E. V.
Published: April 2024

The structure of polynomial solutions to the Gosper’s key equation is analyzed. A method for rapid “extraction” of simple high-degree factors of the solution is given. It is shown that in cases when equation corresponds to a summable non-rational hypergeometric term the Gosper’s algorithm can be accelerated by removing non-essential dependency of its running time on the value of dispersion of its rational certificate.
MEMORY RESPONSE ON THERMOELASTIC BEHAVIOUR WITH TEMPERATURE DEPENDENT MATERIAL MODULI UNDER MECHANICAL STRIP LOAD
Authors: Seikh Aktar , Shaw Soumen , Pal (Sarkar) Smita
Published: April 2024

Temperature of the medium has a significant impact on the deformation and stress distribution into the medium. Material moduli is another key component that determines the deformation of the structural element. The present paper deals with the thermal memory response on stress and temperature fields in an isotropic medium. The material moduli of the medium are considered to be varying with temperature. Consequently, the classical heat conduction law is replaced by the memory dependent generalized theory of heat conduction. Analytical solutions of the field functions are obtained in the integral transform domain. The variations of the field functions in the space-time coordinate system are displayed graphically for different empirical constants and kernel functions.
A Unified Analysis of Variational Inequality Methods: Variance Reduction, Sampling, Quantization, and Coordinate Descent
Authors: Beznosikov A. N. , Gasnikov A. V. , Zainullina K. E. , Maslovskii A. Yu. , Pasechnyuk D. A.
Published: April 2024

We present a unified analysis of methods for such a wide class of problems as variational inequalities, which include minimization and saddle point problems as special cases. The analysis is developed relying on the extragradient method, which is a classic technique for solving variational inequalities. We consider the monotone and strongly monotone cases, which correspond to convex-concave and strongly-convex-strongly-concave saddle point problems. The theoretical analysis is based on parametric assumptions about extragradient iterations. Therefore, it can serve as a strong basis for combining existing methods of various types and for creating new algorithms. Specifically, to show this, we develop new robust methods, including methods with quantization, coordinate methods, and distributed randomized local methods. Most of these approaches have never been considered in the generality of variational inequalities and have previously been used only for minimization problems. The robustness of the new methods is confirmed by numerical experiments with GANs.
On a Flow Around a Cylinder Over Uneven Bottom
Authors: Baikov N. D. , Petrov A. G.
Published: April 2024

A plane problem of a potential fluid flow around a cylinder of arbitrary section over an uneven bottom with a flow velocity at infinity directed parallel to the bottom is considered. The circulation of the velocity field is determined from Goldshtik’s postulate: the maximum velocity on the contour of the cylinder must be minimal. Two numerical schemes of the boundary element method are developed for solving this problem. The first scheme determines the flow on a bounded but arbitrarily defined bottom surface. The second scheme determines the flow around a contour in a half plane. The comparison of calculations using these numerical schemes with the exact solutions shows the convergence of the method as the grid elements increase. The pressure on the cylinder surface and on the bottom obtained using numerical calculations by the–model is compared with experimental data. Streamlines are also compared taking into account the separation region.
On Stable Flows and Preflows
Authors: Karzanov A. V.
Published: April 2024

We propose a new algorithm of finding a stable flow in a network with several sources and sinks. It is based on the idea of preflows (applied in the 1970s for a faster solution of the classical maximal flow problem) and has time complexity for a network with O(nm) vertices and m edges. The obtained results are further generalized to a larger class of objects, the so-called stable quasi-flows with bounded deviations from the balanced relations in nonterminal vertices.
On One Inverse Problem for the Kolmogorov–Fokker–Planck Equation
Authors: Trusov N. V.
Published: April 2024

A mathematical description of the household economic behavior with the help of the Kolmogorov–Fokker–Planck equation is studied. This equation describes the dynamics of the household distribution density with respect to two characteristics: financial state and income. The agreement between statistical data and the solution of the Kolmogorov–Fokker–Planck equation is examined using statistical Rosstat data on the economic state of households in Russia. The problem is formalized as minimizing the deviation of the solution to the Kolmogorov–Fokker–Planck equation from the statistical data by managing household consumption. The extremal problem is solved numerically, and numerical results are presented.
Shapley Value of Homogeneous Cooperative Games
Authors: Vasil’ev V. A.
Published: April 2024

The paper gives a description of the integral representation of the Shapley value for polynomial cooperative games. This representation obtained using the so-called Shapley functional. The relationship between the proposed version of the Shapley value and the polar forms of homogeneous polynomial games is analyzed for both a finite and an infinite number of participants. Special attention is paid to certain classes of homogeneous cooperative games generated by products of non-atomic measures. A distinctive feature of the approach proposed is the systematic use of extensions of polynomial set functions to the corresponding measures on symmetric powers of the original measurable spaces.
Numerical Study of Instability of Medium Interface During Thermonuclear Combustion of a Cylindrical Shelled Microtarget
Authors: Khishchenko K. V. , Charakhch’yan A. A.
Published: April 2024

The study is limited to two-dimensional disturbances of the interface between media. A computational technology based on the explicit interface separation in the form of one of the lines of a regular grid is used. A method for visualizing spontaneous disturbances at an early stage when they cannot yet be seen on the interface profile is proposed. It is shown that the computer rounding error plays an insignificant role in their formation. For the late stage of the disturbance development, a method for obtaining the profile of the local oscillation amplitude along the interface is proposed. The features of spontaneous disturbance at different stages of its development are studied. It is shown that the spontaneous disturbance tends to grid convergence, at least until the beginning of the process of formation of a quasi-stationary shockless combustion wave. It is shown that during the formation of a quasi-stationary wave and its subsequent motion, an additional spontaneous disturbance arises. The interaction of a specified sinusoidal disturbance having an initial amplitude of up to 0.1 of the wavelength with a quasi-stationary combustion wave is studied. It is shown that the Kelvin–Helmholtz instability is the main mechanism for the development of instability at the nonlinear stage. The combustion wave is not destroyed. The profiles of the oscillation amplitude of the given disturbance are obtained, from which it is possible to extract the universal time-independent part.
Improved Accuracy Estimation of the Tikhonov Method for Ill-Posed Optimization Problems in Hilbert Space
Authors: Kokurin M. M.
Published: April 2024

The Tikhonov method is studied as applied to ill-posed problems of minimizing a smooth nonconvex functional. Assuming that the sought solution satisfies the source condition, an accuracy estimate for the Tikhonov method is obtained in terms of the regularization parameter. Previously, such an estimate was obtained only under the assumption that the functional is convex or under a structural condition imposed on its nonlinearity. Additionally, a new accuracy estimate for the Tikhonov method is obtained in the case of an approximately specified functional.
Estimating the Domain of Absolute Stability of a Numerical Scheme Based on the Method of Solution Continuation with Respect to a Parameter for Solving Stiff Initial Value Problems
Authors: Kuznetsov E. B. , Leonov S. S. , Tsapko E. D.
Published: April 2024

The modeling of physical and technological processes often involves solving stiff initial value problems. In most cases, their exact solution is difficult to find, while numerical schemes sometimes fail to produce a sufficiently accurate solution in acceptable computation time. Moreover, for some classes of problems, numerical solution schemes are unsuitable because of their insufficient stability. This paper deals with numerical methods based on solution continuation with respect to arguments of various types that make it possible to enhance the stability of explicit numerical schemes. Most frequently, the used best argument is hardly applicable to problems in which the integral curves grow at a superpower or nearly exponential rate. Previously, the authors proposed a modification of the best argument that alleviates these disadvantages. In the present paper, we estimate the domain of absolute stability of the explicit Euler scheme as applied to problems transformed to a modified best argument of special form and refine the proof of a similar estimate for initial value problems transformed to the best argument. A test initial value problem is used to verify the resulting theoretical estimates and to analyze the application of the modified best argument of solution continuation.
ALTERNATIVE DIRECTION IMPLICIT METHOD FOR SOLVING FIRST ORDER 2D HYPERBOLIC DELAY DIFFERENTIAL EQUATIONS
Authors: Karthick S. , Subburayan V.
Published: April 2024

This article considers delayed two-dimensional first order hyperbolic differential equations. The propagation of the discontinuity of the solution is also established. An alternating implicit finite difference method and backward Euler finite difference methods are presented. We proved that this method is first-order convergent. Illustrating numerical examples are given for validation. We also present an application of the proposed approach to the variable delay problem.
A GENERALIZED SIMPLIFIED HERMITIAN AND SKEW-HERMITIAN SPLITTING PRECONDITIONER FOR DOUBLE SADDLE POINT PROBLEMS
Authors: Meng L. , He Y. W. , Li J.
Published: April 2024

In this work, we mainly propose a generalized simplified Hermitian and skew-Hermitian splitting (GSHSS) preconditioner for solving double saddle point problems and the eigenvalue distribution of the GSHSS preconditioner is analyzed in detail. In addition, we also study the eigenvector distribution and the degree of the minimal polynomial of the preconditioned matrix. Finally, numerical experiments show the effectiveness of the proposed preconditioner.
On a Method for Solving a Mixed Boundary Value Problem for a Parabolic Equation Using Modified Sinc-Approximation Operators
Authors: Trynin A. Yu.
Published: April 2024

A new method is proposed for obtaining a generalized solution of a mixed boundary value problem for a parabolic equation with boundary conditions of the third kind and a continuous initial condition. Generalized functions are understood in the sense of the sequential approach. As an intermediate approximation, a modified sinc-approximation operator is used. The solution is obtained in the form of a series uniformly converging inside the solution domain.
ON THE RADIAL BASIS FUNCTION INTERPOLATION I: SPECTRAL ANALYSIS OF THE INTERPOLATION MATRIX AND THE RELATED OPERATORS
Authors: Xiao Jianping
Published: April 2024

In this paper, we study the spectral properties of the periodized Radial Basis Function interpolation matrix as well as the related harmonic operators discretized using Radial Basis Functions. For Gaussian RBF, this procedure could be easily extended to an arbitrarily high dimensional space on a tensor-product grid as presented in the later parts of the paper. The experimental result of Boyd’s condition number [1] is analytically well predicted in the context of periodized RBF.
A Waveguide Model of the Developed Turbulent Boundary Layer
Authors: Zharov V. A. , Lipatov I. I. , Selim R. S.
Published: April 2024

A study of the developed turbulent boundary layer that emerges when incompressible viscous fluid flows around a plate at a zero angle of attack and with zero longitudinal pressure gradient is presented. The waveguide approach is used for describing the turbulent boundary layer; in this approach, turbulent fluctuations are related with Tollmien–Schlichting waves that are in three-wave resonance. To study the original nonlinear system of equations, an estimate of hydrodynamic quantities is proposed that does not violate the generally accepted approach in the boundary layer but leads to the appearance of a new small parameter—the ratio of the thickness of the boundary layer momentum loss to the damping length of the least damped mode of the Tollmien–Schlichting waves. Equations for the coherent and stochastic parts of fluctuations are obtained on the basis of the method of multiple scales. The dispersion characteristics of waves of the least damped mode on the profile of the average longitudinal velocity of the developed turbulent boundary layer are determined, and the conditions for the multiple three-wave resonance of this mode of the Tollmien–Schlichting waves are analyzed. For the coherent part of the fluctuations, the fluctuation characteristics are compared with the known numerical results.
Comparison of Upwind and Symmetric WENO Schemes in Large Eddy Simulation of Basic Turbulent Flows
Authors: Bakhne S. , Troshin A. I.
Published: April 2024

The properties of modern WENO schemes are examined as applied to large eddy simulation (LES). The WENO-ZM5 scheme with modified smoothness indicators (“upwind”) and the WEN-O‑SYMBOO6 scheme on a symmetric stencil (“symmetric WENO scheme”) are chosen. The schemes are compared on one-dimensional test problems (advection, Hopf, and Burgers equations) with both smooth and discontinuous solutions. The decay of isotropic turbulence is modeled within LES and the results are discussed. The solutions produced by the new schemes are compared with those based on the central difference scheme, the classical WENO5 scheme, and a hybrid scheme. The level of dissipation of the schemes is compared by analyzing their energy spectra. A similar comparison is made between the LES computations of the temporal evolution of a mixing layer, where the profiles of mean velocity and Reynolds stresses are considered in addition to the energy spectrum.
p-Regularity Theory and the Existence of a Solution to a Boundary Value Problem Continuously Dependent on Boundary Conditions
Authors: Evtushenko Yu. G. , Medak B. , Tret’yakov A. A.
Published: April 2024

For a given boundary value problem, the existence of a solution depending continuously on the boundary conditions is analyzed. Previously, such a fact has been known only for the Cauchy problem, which is a classical result in the theory of differential equations. We prove a similar result for boundary value problems in the case when they are p-regular. In the general case, this result does not hold. Several implicit function theorems are proved in the degenerate case, which is a development of p-regularity theory concerning the existence of a solution to nonlinear differential equations. The results are illustrated by an example of a classical boundary value problem, namely, a degenerate Van der Pol equation is considered, for which the existence of a solution depending continuously on the boundary conditions of the perturbed problem is proved.
On a Class of Exact Solutions to the Incompressible Navier–Stokes System in a Ball and a Spherical Layer
Authors: Galkin V. A.
Published: April 2024

A class of exact solutions to the Navier–Stokes equations for rotational incompressible flows is obtained. A three-parameter family of solutions in a ball, spherical layers, and the entire spaceis constructed.
ON NORMALITY IN OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS
Authors: Karamzin D. Yu. , Pereira F.
Published: April 2024

A general optimal control problem with endpoint, mixed and state constraints is considered. The question of normality of the known necessary optimality conditions is investigated. Normality stands for the positiveness of the Lagrange multiplier λ0 corresponding to the cost functional. In order to prove the normality condition, an appropriate derivative operator for the state constraints is constructed, which acts in a specific Hilbert space and has the properties of surjection and continuity.
OPTICAL SOLITARY WAVES AND SOLITON SOLUTIONS OF THE (3 + 1)-DIMENSIONAL GENERALIZED KADOMTSEV–PETVIASHVILI–BENJAMIN–BONA–MAHONY EQUATION
Authors: Mahmud A. A. , Baskonus H. M. , Tanriverdi T. , Muhamad K. A.
Published: April 2024

In this investigation, an appropriate traveling wave transformation has been employed to analyze the fourth-order nonlinear (3+1)-dimensional generalized Kadomtsev–Petviashvili–Benjamin–Bona–Mahony (KP-BBM) equation for an offshore structure. In addition to being integrable and having constant coefficients, the examined model represents fluid flow in the context of an offshore structure. The aforesaid nonlinear system is subjected to the initial application of two trustworthy and dependable approaches, namely the improved Bernoulli sub-equation function method and the modified extended-function method. Investigating and obtaining certain explicitly exact traveling waves, periodic waves, and soliton solutions is the major objective. The generated solutions take the form of trigonometric hyperbolic functions, exponential functions, rational functions, and multiple forms of trigonometric functions. The proposed solutions are both novel and important in that they provide light on the relevant aspects of the physical phenomena. The characteristics of the solutions have been displayed in a variety of figures, including two- and three-dimensional ones, for the best visual optical discernment.
WELL-POSEDNESS AND ASYMPTOTIC BEHAVIOR FOR THE DISSIPATIVE P-BIHARMONIC WAVE EQUATION WITH LOGARITHMIC NONLINEARITY AND DAMPING TERMS
Authors: Zhang Mengyuan , Liu Zhiqing , Zhang Xinli
Published: April 2024

This paper concerns with the initial and boundary value problem for a p-biharmonic wave equation with logarithmic nonlinearity and damping terms. We establish the well-posedness of the global solution by combining Faedo–Galerkin approximation and the potential well method, and derive both the polynomial and exponential energy decay by introducing an appropriate Lyapunov functional. Moreover, we use the technique of differential inequality to obtain the blow-up conditions and deduce the life-span of the blow-up solution.
On the Existence of Optimal Control in the Problem of Optimizing the Lowest Coefficient of a Semilinear Evolutionary Equation
Authors: Chernov A. V.
Published: April 2024

The paper studies the problem of optimizing the lowest coefficient understood as a function with values in a Banach space, which enters linearly into an abstract semilinear pseudoparabolic evolutionary differential equation in a Banach space. For this problem, an existence theorem for an optimal control is proved. Due to the nonlinearity of the equation under study, the author uses his previous results on the total preservation of the unique global solvability (on the totally global solvability) and on the estimation of solutions for similar equations. This estimate turns out to be significant in the course of the study. As an example, the Oskolkov’s hydrodynamic system of equations is considered.
Local Solvability, Blow-Up, and Hölder Regularity of Solutions to Some Cauchy Problems for Nonlinear Plasma Wave Equations: III. Cauchy Problems
Authors: Korpusov M. O. , Ovsyannikov E. A.
Published: April 2024

Three Cauchy problems for Sobolev-type equations with a common linear part from the theory of ion acoustic and drift waves in a plasma are considered. The problems are reduced to equivalent integral equations. We prove the existence of unextendable solutions for two problems and the existence of a local-in-time solution for the third problem. For one of the problems, by applying a modified method of Kh.A. Levin, sufficient conditions for finite time blow-up of solutions are obtained and an upper bound for the solution blow-up time is found. For another problem, S.I. Pohozaev’s nonlinear capacity method is used to obtain a finite time blow-up result and two results concerning the nonexistence of even local solutions, and an upper bound for the solution blow-up time is obtained as well.
Duality Method for Solving 3D Contact Problems with Friction
Authors: Namm R. V. , Tsoy G. I.
Published: April 2024

The article studies a 3D contact problem with Coulomb friction for an elastic body resting on a rigid support. The solution of the quasi-variational formulation of the problem is defined as a fixed point of some mapping that associates the given force of the normal reaction of the support with the value of the normal stress in the contact zone. The fixed point is sought by the method of successive approximations, the convergence of which is proved using modified Lagrange functionals. The results of the numerical solution using finite element modeling and the proximal gradient method are presented.
Laser-Induced Thermoelastic Response in an Isotropic Medium Having Variable Material Moduli
Authors: Seikh Aktar , Shaw Soumen , Pal (Sarkar) Smita
Published: April 2024

Thermal displacement and stress distribution are analysed in the domain of plane-strain geometry of an isotropic thermoelastic medium having variable material moduli. In this context of the analysis, laser induced heat sources are planted on the reference plane. To analyse the thermal responses due to the injected heat sources into the medium, hyperbolic type heat conduction model with three phase-lags incorporated. Analytical solutions are expressed in-terms of Laplace–Fourier integral transform domain and the physical behaviour of displacement and stresses are depicted through a discretised form of inverse-integral transformation technique. Finally, parameterized characteristic analysis are presented graphically and the salient features of thermal displacements are highlighted.
A Modified Runge–Kutta Scheme for the Generalized Benjamin–Bona–Mahony–Burgers Equation
Authors: Xu Qiubin , Liu Yan
Published: April 2024

This paper presents a modified Runge–Kutta (MRK) scheme for the generalized Benjamin–Bona–Mahony–Burgers equation. The MRK method separate this equation into two parts which apply different finite difference scheme in space, and finally use fourth-order Runge–Kutta method in time.The scheme is conditionally stable and convergent with order of O (тау4+h2), the Comparisons of the existing numerical methods demonstrate that this scheme is capable of high accuracy and stability.
Generalization of the Fast Fourier Transform with a Constant Structure
Authors: Bespalov M. S.
Published: April 2024

The widely popular famous fast Cooley–Tukey algorithms for the discrete Fourier transform of mixed radix are presented in two forms: classical and with a constant structure. A matrix representation of these algorithms is proposed in terms of two types of tensor product of matrices: the Kronecker product and the b-product. This matrix representation shows that the structure of these algorithms is identical to two fast Good algorithms for a Kronecker power of a matrix. A technique for constructing matrix-form fast algorithms for the discrete Fourier and Chrestenson transforms with mixed radix and for the discrete Vilenkin transform is demonstrated. It is shown that the constant-structured algorithm is preferable in the case of more sophisticated constructions
Internal Gravity Waves from a Localized Source in Stratified Medium Flow with a Model Buoyancy Frequency Distribution
Authors: Bulatov V. V. , Vladimirov I. Yu.
Published: April 2024

The problem of calculating internal gravity wave fields generated by a localized source in a stratified flow of finite thickness with a model buoyancy frequency distribution is considered. By using analytical representations of the buoyancy frequency, an implicit form of the dispersion relation is obtained, which depends on the Bessel functions of real index. Numerical results for dispersion curves, lines of equal phase, and wave amplitudes for various wave modes and stratified flow velocities are presented. The thickness of the stratified layer, the vertical gradient of the buoyancy frequency, and the magnitude of the flow velocity are the main factors affecting the amplitude-phase spatial transformation of the wave fields excited downstream.
Simulation of Emission Processes in Strong Electromagnetic Fields
Authors: Kudryashova T. A. , Polyakov S. V. , Tarasov N. I.
Published: April 2024

The problem of calculating the processes of electron emission from metal surfaces in strong electromagnetic fields is considered with allowance for relativistic effects. One of the methods of simulation in these processes is the particle method combined with grid calculation of fields on the basis of Maxwell’s equations. Similar techniques have been developed since the 1960s to the present. However, existing approaches have certain limitations. In this work, for an axisymmetric geometry of the generating system, a new numerical technique simulating the processes of electron emission from metal cathode surfaces is presented. The technique uses the representation of large smoothed Gaussian particles and implements the calculation of electromagnetic fields on Cartesian spatial grids. The software implementation is oriented to parallel computing. The aim of numerical experiments was to determine the parameters of electron emission. Diode and triode cylindrical systems were chosen as test problems. In numerical calculations, the spatiotemporal characteristics of relativistic electron beams generated by emission processes are obtained, including the reproduction of the Child–Langmuir current. The numerical technique developed has confirmed its correctness and efficiency.
An Improved Difference Scheme for the Cauchy Problem in the Case of a Transport Equation
Authors: Shishkin G. I. , Shishkina L. P.
Published: April 2024

The Cauchy problem for the regular transport equation is considered. The Richardson technique is used to construct an improved difference scheme that converges in the maximum norm with the second order of convergence.
Analogue of Kellogg’s Theorem for Piecewise Lyapunov Domains
Authors: Soldatov A. P.
Published: April 2024

In weighted Hölder spaces, classes of smooth arcs and piecewise smooth contours are introduced that are invariant under power mappings. The boundary properties of conformal mappings are described in terms of these classes by analogy with Kellogg’s classical theorem.
Approximation of Differential Operators with Boundary Conditions
Authors: Varin V. P.
Published: April 2024

The use of spectral methods for solution of boundary value problems is very effective but involves great technical difficulties associated with the implementation of the boundary conditions. There exist several methods of such an implementation, but they are either very cumbersome or require a preliminary analysis of the problem and its reduction to an integral form. We propose a universal means of implementation of the boundary conditions for linear differential operators on a finite interval, which is very simple in its realization. The use of the rational arithmetic allows to assess the effectiveness of this method without interference of the round-off errors. We apply this approach for computation of rational approximations for some fundamental constants. We obtained approximations that in a number of cases are better than those that are given by convergents of regular continued fractions of these constants.
On Some Elliptic Boundary Value Problems in Conic Domains
Authors: Vasilyev V. B.
Published: April 2024

A model elliptic pseudodifferential equation in a polyhedral cone is considered, and the situation when some of the parameters of the cone tend to their limiting values is investigated. In Sobolev–Slobodetskii spaces, a solution of the equation in the cone is constructed in the case of a special wave factorization of the elliptic symbol. It is shown that a limit solution of the boundary value problem with an additional integral condition can exist only under additional constraints on the boundary function.
Interaction of Boundary Singular Points in an Elliptic Boundary Value Problem
Authors: Bogovskii A. M.
Published: April 2024

The paper continues the construction of the Lp-theory of elliptic Dirichlet and Neumann boundary value problems with discontinuous piecewise constant coefficients in divergent form for an unbounded domain R2 with a piecewisesmooth noncompact Lipschitz boundary and C1 smooth discontinuity lines of the coefficients. An earlier constructed Lp-theory is generalized to the case of different smallest eigenvalues corresponding to a finite and an infinite singular point, and the effect of their interaction is further studied in the class of functions with first derivatives from Lp( ) in the entire range of the exponent p (1, )..
Inverse Problems for the Diffusion–Drift Model of Charging of an Inhomogeneous Polar Dielectric
Authors: Brizitskii R. V. , Maksimova N. N. , Maslovskaya A. G.
Published: April 2024

The problems of reconstructing the unknown parameters of the model of electron-induced charging of an inhomogeneous polar dielectric from additional information about the volume charge density distribution and the electric field strength are studied. Within the optimization approach, these inverse problems are reduced to control problems and their solvability is proved. For extremum problems, optimality systems are derived and, based on their analysis, local uniqueness of the solution of one of the considered problems is proved. Taking into account the introduced characteristic of the inhomogeneity of the dielectric, auxiliary results on the solvability and properties of solutions of the boundary value problem, obtained earlier for the model of charging of a homogeneous dielectric, are corrected.
Universal Approach to Analysis of Dissipation Properties of a Numerical Method for Solving Gas Dynamic Equations
Authors: Chuvakhov P. V. , Pogorelov I. O. , Shubin K. V.
Published: April 2024

A universal approach to the verification of a numerical method for solving the Navier–Stokes equations is proposed, through which the dissipation properties of the method can be reliably assessed. The approach is based on viscous damping of weak elementary perturbations propagating in uniform flow. The corresponding theoretical solution allows one to determine the order of convergence of the numerical method.
Calculation of nth Derivative with Minimum Error Based on Function’s Measurement
Authors: Kochurov A. S. , Demidov A. S.
Published: April 2024

A solution of the problem that arises in all cases where it is required to approximately calculate the derivatives of an a priori smooth function by its experimental discrete values is proposed. The problem is reduced to finding an “optimal” step of difference approximation. This problem has been studied by many mathematicians. It turned out that to find an optimal approximation step for the kth-order derivative, it is required to know a highly accurate estimate of the modulus of the derivative of order k+1. The proposed algorithm, which gives such an estimate, is applied to the problem of thrombin concentration, which determines the dynamics of blood coagulation. This dynamics is represented by plots and provides a solution of the thrombin concentration problem, which is of interest to biophysicists.
Influence of Damping of a Compliant Surface on Inviscid Instability of Overlying Incompressible Boundary Layer
Authors: Savenkov I. V.
Published: April 2024

The instability of an incompressible boundary layer on a compliant plate with respect to inviscid perturbations in the limit of high Reynolds numbers is analyzed using triple-deck theory. It is shown that unstable inviscid perturbations can exist only if the inertia and/or damping of the plate are taken into account. A twofold role of damping is revealed: it suppresses instability under certain conditions, while leading to its generation under other conditions.
Three-Dimensional Numerical Transfer Model Using a Monotonized Z-Scheme
Authors: Kashchenko N. M. , Ishanov S. A. , Zubkov E. V. , Zinin L. V.
Published: April 2024

The aim of this work is to investigate a three-dimensional second-order monotone finite-difference scheme for the transport equation. The investigation is conducted for model three-dimensional transport equations of an incompressible medium. The properties of the three-dimensional extension of the Z-scheme with nonlinear correction are studied in this work. This study is an extension of the author’s previous works, where a nonlinear correction of one-dimensional transport equations was constructed. The proposed scheme uses “skew differences” containing values from different time layers instead of fluxes for the correction. The monotonicity of the obtained nonlinear scheme is numerically studied for a family of limiter functions for both smooth and non-smooth continuous solutions. The constructed scheme is absolutely stable but loses the monotonicity property when the Courant step is exceeded. The distinctive feature of the proposed finite-difference scheme is the minimalism of its template. The constructed numerical scheme is designed for models of plasma instabilities of various scales in the low-latitude ionospheric plasma of the Earth. One of the real problems that arise in solving such equations is the numerical modeling of strongly non-stationary medium- and small-scale processes in the low-latitude ionosphere of the Earth under conditions of the occurrence of the Rayleigh–Taylor instability and other types of instabilities, leading to the phenomenon of F‑scattering. Due to the fact that transport processes in the ionospheric plasma are controlled by the magnetic field, it is assumed that the plasma is incompressible in the direction perpendicular to the magnetic field.
Construction of Solutions and Study of Their Closeness in L2 for Two Boundary Value Problems for a Model of Multicomponent Suspension Transport in Coastal Systems
Authors: Sidoryakina V. V. , Sukhinov A. I.
Published: April 2024

Three-dimensional models of suspension transport in coastal marine systems are considered. The associated processes have a number of characteristic features, such as high concentrations of suspensions (e.g., when soil is dumped on the bottom), much larger areas of suspension spread than the reservoir depth, complex granulometric (multifractional) content of suspensions, and mutual transitions between fractions. Suspension transport can be described using initial-boundary value diffusion–convection–reaction problems. According to the authors' idea, on a time grid constructed for the original continuous initial-boundary value problem, the right-hand sides are transformed with a “delay” so that the right-hand side concentrations of the components other than the underlying one (for which the initial-boundary value problem of diffusion–convection is formulated) are determined at the preceding time level. This approach simplifies the subsequent numerical implementation of each of the diffusion–convection equations. Additionally, if the number of fractions is three or more, the computation of each of the concentrations at every time step can be organized independently (in parallel). Previously, sufficient conditions for the existence and uniqueness of a solution to the initial-boundary value problem of suspension transport were determined, and a conservative stable difference scheme was constructed, studied, and numerically implemented for test and real-world problems. In this paper, the convergence of the solution of the delay-transformed problem to the solution of the original suspension transport problem is analyzed. It is proved that the differences between these solutions tends to zero at an O(τ) rate in the norm of the Hilbert space L2 as the time step t approaches zero.