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Three-Webs from Circles Russ. Math. Pub Date : 2024-02-28 A. M. Shelekhov
Abstract A new geometric condition necessary for regularity of a curved three-web is found. A class of three-webs from circles generalizing the regular three-web of Blaschke from three elliptic pencils of circles with pairwise coinciding vertices is considered, and it is shown that only webs equivalent to the Blaschke web are regular in this class.
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Generalized Integration over Nonrectifiable Flat Curves and Boundary Value Problems Russ. Math. Pub Date : 2024-02-28 D. B. Katz
Abstract Two closely related problems are discussed, viz., solving the Riemann boundary value problem for analytic functions and some of their generalizations in the domains of the complex plane with nonrectifiable boundaries and constructing a generalization of the curvilinear integral onto nonrectifiable curves that preserves the properties important for the complex analysis. This review reflects
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Main Properties of the Faddeev Equation for 2 × 2 Operator Matrices Russ. Math. Pub Date : 2024-02-28 T. H. Rasulov, E. B. Dilmurodov
Abstract In this paper we consider a \(2 \times 2\) operator matrix \(H\). We construct an analog of the well-known Faddeev equation for the eigenvectors of \(H\) and study some important properties of this equation, related with the number of eigenvalues. In particular, the Birman–Schwinger principle for \(H\) is proven.
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Equivalence of Computed Tomography Problem with the Problem of Recovery of Functions by Finite Convolutions in a Scheme of Computational (Numerical) Diameter Russ. Math. Pub Date : 2024-02-28 N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliyev, Ye. Ye. Nurmoldin, G. E. Taugynbayeva, A. Zh. Zhubanysheva
Abstract The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how computer science, previously established in the theory of computational (numerical) diameter, immediately leads to nontrivial results in computed tomography.
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A Problem in an Unbounded Domain with Combined Tricomi and Frankl Conditions on One Boundary Characteristic for One Class of Mixed-Type Equations Russ. Math. Pub Date : 2024-02-28 M. Mirsaburov, R. N. Turaev
Abstract In this work, in an unbounded domain, we prove the correctness of the problem with combined Tricomi and Frankl conditions on one boundary characteristic for one class of mixed-type equations.
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Convolution Kernel Determination Problem in the Third Order Moore–Gibson–Thompson Equation Russ. Math. Pub Date : 2024-02-28 D. K. Durdiev, A. A. Boltaev, A. A. Rahmonov
Abstract This article is concerned with the study of the inverse problem of determining the difference kernel in a Volterra type integral term function in the third-order Moore–Gibson–Thompson (MGT) equation. First, the initial-boundary value problem is reduced to an equivalent problem. Using the Fourier spectral method, the equivalent problem is reduced to a system of integral equations. The existence
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The Riemann Problem in a Half-Plane for Generalized Analytic Functions with a Supersingular Point on the Contour of the Boundary Condition Russ. Math. Pub Date : 2024-02-19 P. L. Shabalin
Abstract In this paper, we study an inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on the real axis for a generalized Cauchy–Riemann equation with supersingular coefficients. To solve the problem, it was necessary to derive a structural formula for the general solution to this equation and to investigate the solvability of the Riemann boundary value problem
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Method and Algorithm for Calculating Isobaric and Nonisobaric Three-Dimensional Turbulent Jets of Reacting Gases Russ. Math. Pub Date : 2024-02-19 S. Khodzhiev
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Compound Cubature Formulas on a Lattice Russ. Math. Pub Date : 2024-02-19 Kh. M. Shadimetov, N. Kh. Mamatova
Abstract In the present paper the lattice optimal cubature formulas are constructed by the variational method in the Sobolev space. In addition, the square of the norm of the error functional of the constructed lattice optimal cubature formulas in the conjugate Sobolev space is explicitly calculated.
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Approximation of the Lebesgue Constant of the Fourier Operator by a Logarithmic-Fractional-Rational Function Russ. Math. Pub Date : 2024-02-19 I. A. Shakirov
Abstract The Lebesgue constant of the classical Fourier operator is uniformly approximated by a logarithmic-fractional-rational function depending on three parameters; they are defined using the specific properties of logarithmic and rational approximations. A rigorous study of the corresponding residual term having an indefinite (nonmonotonic) behavior has been carried out. The obtained approximation
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Curves Whose Arcs with a Fixed Startpoint Are Similar Russ. Math. Pub Date : 2024-02-19 I. V. Polikanova
Abstract The author has previously put forward a hypothesis that in n-dimensional Euclidean space, curves, any two oriented arcs of which are similar, are rectilinear. The author also proved this statement for dimensions of n = 2 and n = 3. In a space of arbitrary dimension, this hypothesis was confirmed in the class of rectifiable curves. In this study, the author provides a complete solution to this
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Finite Element Modeling of Eigenvibrations of a Square Plate with an Attached Oscillator Russ. Math. Pub Date : 2024-02-19 D. M. Korosteleva, S. I. Solov’ev
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A Block Projection Operator in the Algebra of Measurable Operators Russ. Math. Pub Date : 2024-01-09 A. M. Bikchentaev
Abstract Let \(\tau \) be a faithful normal semifinite trace on a von Neumann algebra \(\mathcal{M}\). The block projection operator \({{\mathcal{P}}_{n}}\) \((n \geqslant 2)\) in the *-algebra \(S(\mathcal{M},\tau )\) of all \(\tau \)-measurable operators is investigated. It has been shown that \(A \leqslant n{{\mathcal{P}}_{n}}(A)\) for any operator \(A \in S{{(\mathcal{M},\tau )}^{ + }}\). If \(A
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Nonnegative Matrices and Their Structured Singular Values Russ. Math. Pub Date : 2024-01-09 M. Rehman, T. Rasulov, B. Aminov
Abstract In this article, we present new results for the computation of structured singular values of nonnegative matrices subject to pure complex perturbations. We prove the equivalence of structured singular values and spectral radius of perturbed matrix \((M\vartriangle )\). The presented new results on the equivalence of structured singular values, nonnegative spectral radius and nonnegative determinant
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Inverse Problem of Determining the Kernel of Integro-Differential Fractional Diffusion Equation in Bounded Domain Russ. Math. Pub Date : 2024-01-09 D. K. Durdiev, J. J. Jumaev
Abstract In this paper, an inverse problem of determining a kernel in a one-dimensional integro-differential time-fractional diffusion equation with initial-boundary and overdetermination conditions is investigated. An auxiliary problem equivalent to the problem is introduced first. By Fourier method this auxilary problem is reduced to equivalent integral equations. Then, using estimates of the Mittag–Leffler
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Polylinear Differential Realization of Deterministic Dynamic Chaos in the Class of Higher Order Equations with Delay Russ. Math. Pub Date : 2024-01-09 A. V. Banshchikov, A. V. Lakeev, V. A. Rusanov
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Inverse Coefficient Problems for a Time-Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative Russ. Math. Pub Date : 2024-01-09 H. H. Turdiev
Abstract This paper considers the inverse problem of determining the time-dependent coefficient in the fractional wave equation with Hilfer derivative. In this case, the direct problem is initial-boundary value problem for this equation with Cauchy type initial and nonlocal boundary conditions. As overdetermination condition nonlocal integral condition with respect to direct problem solution is given
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On Conformally Killing Vector Fields on a 2-Symmetric Indecomposable Lorentzian Manifold Russ. Math. Pub Date : 2024-01-09 M. E. Gnedko, D. N. Oskorbin, E. D. Rodionov
Abstract A natural generalization of Killing vector fields is conformally Killing vector fields, which play an important role in the study of the group of conformal transformations of manifolds, Ricci flows on manifolds, and the theory of Ricci solitons. In this paper, conformally Killing vector fields are studied on 2-symmetric indecomposable Lorentzian manifolds. It is established that the conformal
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On the Solvability of a Nonlocal Problem for a Boussinesq-Type Differential Equation Russ. Math. Pub Date : 2024-01-09 A. R. Khalmukhamedov, E. I. Kuchkorov
Abstract We study a nonlocal problem for a differential Boussinesq-type equations in a multidimensional domain. Conditions for the existence and uniqueness of the solution are established, and a spectral decomposition of the solution is obtained.
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Inverse Coefficient Problem for a Fractional-Diffusion Equation with a Bessel Operator Russ. Math. Pub Date : 2023-12-15 D. I. Akramova
Abstract The second initial-boundary value problem in a bounded domain for a fractional-diffusion equation with the Bessel operator and the Gerasimov–Caputo derivative is investigated. Theorems of existence and uniqueness of the solution to the inverse problem of determining the lowest coefficient in a one-dimensional fractional-diffusion equation under the condition of integral observation are obtained
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Exact Solution for Capillary Waves on the Surface of a Liquid of Finite Depth Russ. Math. Pub Date : 2023-12-15 M. M. Alimov
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Invariant Subspaces and Eigenvalues of the Three-Particle Discrete Schrödinger Operators Russ. Math. Pub Date : 2023-12-15 J. I. Abdullaev, A. M. Khalkhuzhaev, T. H. Rasulov
Abstract We consider three-particle Schrödinger operator \({{H}_{{\mu ,\gamma }}}({\mathbf{K}})\), \({\mathbf{K}} \in {{\mathbb{T}}^{3}}\), associated to a system of three particles (two of them are bosons with mass 1 and one is an arbitrary with mass \(m = {\text{1/}}\gamma < 1\)), interacting via zero-range pairwise potentials \(\mu > 0\) and λ > 0 on the three dimensional lattice \({{\mathbb{Z}}^{3}}\)
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Transformation Operator for the Schrödinger Equation with Additional Exponential Potential Russ. Math. Pub Date : 2023-12-15 A. Kh. Khanmamedov, M. F. Muradov
Abstract In this paper, we consider the one-dimensional Schrödinger equation on the semiaxis with an additional exponential potential. Using transformation operators with the asymptotics at infinity, a triangular representation of a special solution of this equation is found. An estimate is obtained with respect to the kernel of the representation.
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On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a 4nth-Order Nonlinear Ordinary Differential Equation Russ. Math. Pub Date : 2023-12-15 G. E. Abduragimov
Abstract The paper considers a two-point boundary value problem with homogeneous boundary conditions for a single 4nth-order nonlinear ordinary differential equation. Using the well-known Krasnoselskii theorem on the expansion (compression) of a cone, sufficient conditions for the existence of a positive solution to the problem under consideration are obtained. To prove the uniqueness of a positive
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Numerical Simulation of Compressible Gas Flow in Flat Channels in the Narrow Channel Approximation Russ. Math. Pub Date : 2023-12-15 S. Khodjiev
Abstract A compressible gas in plane channels of constant and variable cross sections is numerically simulated using two-dimensional parabolized Navier–Stokes equations. The system of equations is solved numerically using the narrow-channel approximation model. A number of transformations, such as nondimensionalization of the system of equations to reduce the given domain to a square and refinement
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Rings, Matrices over Which Are Representable As the Sum of Two Potent Matrices Russ. Math. Pub Date : 2023-12-01
Abstract This paper investigates conditions under which representability of each element \(a\) from the field \(P\) as the sum \(a = f + g\) , where \({{f}^{{{{q}_{1}}}}} = f\) , \({{g}^{{{{q}_{2}}}}} = g\) , and \({{q}_{1}},{{q}_{2}}\) are fixed natural numbers >1, implies a similar representability of each square matrix over the field \(P\) . We propose a general approach to solving this problem
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On the Optimal Interpolation of Functions Russ. Math. Pub Date : 2023-12-01
Abstract The construction of optimal interpolation formulas is discussed. First, an exact upper bound for the error of an interpolation formula in the Sobolev space is calculated. The existence and uniqueness are proved for the optimal interpolation formula with the smallest error. An algorithm for finding the coefficients of the optimal interpolation formula is presented. This algorithm makes it possible
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On a Functional Equation with Holomorphic Coefficients Associated with a Finite Group Russ. Math. Pub Date : 2023-11-20 F. N. Garif’yanov, E. V. Strezhneva
Abstract We consider a convex pentagon \(D\) that has a pair of parallel and equal sides without a common vertex. We study the linear difference equation associated with this polygon. The coefficients of the equation and the free term are holomorphic in \(D\). The solution is sought in the class of functions holomorphic outside the “half” of the \(\partial D\) boundary and vanishing at infinity. A
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Invertibility and Spectrum of the Riemann Boundary Value Problem Operator in a Countably Normed Space of Smooth Functions on a Circle Russ. Math. Pub Date : 2023-11-20 A. E. Pasenchuk
Abstract In a countably normed space of smooth functions on the unit circle, we consider the Riemann boundary value problem operator with smooth coefficients. The paper introduces the concept of smooth degenerate factorizations of types of plus and minus functions that are smooth on the unit circle. Criteria for the existence of such factorizations are given. An apparatus is proposed for calculating
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Study of Oscillatory Flows of a Viscoelastic Fluid in a Flat Channel Based on the Generalized Maxwell Model Russ. Math. Pub Date : 2023-11-20 K. Navruzov, A. Sh. Begjanov, Sh. B. Sharipova, J. Jumayev
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The Problem in the Unbounded Domain with the Frankl Condition on the Segment of the Degeneration Line and with a Missing Gellerstedt Condition for a Class of Mixed-Type Equations Russ. Math. Pub Date : 2023-11-20 M. Mirsaburov, S. B. Ergasheva
Abstract In an unbounded domain, for a class of equations of mixed type with a singular coefficient, the correctness of the problem is studied in which one of the internal characteristics is freed from the Gellerstedt condition and this missing local condition is replaced by an analogue of the Frankl condition on the degeneration line. The uniqueness of the solution to the stated problem is proved
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Inverse Source Problem for the Equation of Forced Vibrations of a Beam Russ. Math. Pub Date : 2023-11-20 U. D. Durdiev
Abstract Direct and inverse problems for the equation of forced vibrations of a finite length beam with a variable stiffness coefficient at the lowest term are investigated. The direct problem is the initial–boundary value problem for this equation with boundary conditions in the form of a beam fixed at one end and free at the other. The unknown variable in the inverse problem is a multiplier in the
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Large-Scale Equivalence of Norms of the Radon Transform and Initial Function Russ. Math. Pub Date : 2023-11-20 N. Temirgaliyev, G. E. Taugynbayeva, A. Zh. Zhubanysheva
Abstract This study aims to establish equivalences (in norm) of the problems of reconstructing computed tomography and computational (numerical) diameter (C(N)D), which was done in 2019 for functions of two variables. This was based on the equivalence of respective norms in the same two-dimensional Sobolev spaces proved by Frank Natterer. In this study, we prove the equivalence (in norm) of the Radon
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Diffraction of Harmonic Shear Waves on an Elliptical Cavity Located in a Viscoelastic Medium Russ. Math. Pub Date : 2023-11-20 M. Kh. Teshaev, I. M. Karimov, A. O. Umarov, Sh. I. Zhuraev
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Refined Transformational Model of Deformation of a Rod-Strip with a Fixed Section on One of the Front Surfaces Russ. Math. Pub Date : 2023-11-20 V. N. Paimushin, A. M. Kamalutdinov, M. A. Shishov, S. F. Chumakova
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Infinitely Many Solutions for Schrödinger–Kirchhoff-Type Equations Involving the Fractional p(x, ·)-Laplacian Russ. Math. Pub Date : 2023-11-20 Maryam Mirzapour
Abstract The aim of this paper is to study the existence of infinitely many solutions for Schrödinger–Kirchhoff-type equations involving nonlocal \(p(x, \cdot )\)-fractional Laplacian \(\left\{ {\begin{array}{*{20}{l}} {M({{\sigma }_{{p(x,y)}}}(u))\mathcal{L}_{K}^{{p(x, \cdot )}}(u) = \lambda {{{\left| u \right|}}^{{q(x) - 2}}}u + \mu {{{\left| u \right|}}^{{\gamma (x) - 2}}}u\;}&{{\text{in}}\;\Omega
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Solving Three Systems of Functional Equations Associated with Complex, Double, and Dual Numbers Russ. Math. Pub Date : 2023-11-13 V. A. Kyrov, G. G. Mikhailichenko
Abstract This paper considers three special systems of functional equations arising in the problem of embedding bimetric phenomenologically symmetric geometries of two sets of rank (3, 2) associated with complex, double, and dual numbers into a bimetric phenomenologically symmetric geometry of two sets of rank (4, 2), which is an affine group of transformations on the plane. Nondegenerate solutions
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Linear Uniformalization of the Countable Family of Topological Properties Russ. Math. Pub Date : 2023-11-13 Dz. N. Kazhamiakin
Abstract The well-known theorem on the uniformalization of topological properties [1] has been strengthened and generalized to the case of a countable family of properties given by relations of open coverings. Topological properties can be linearly uniformized (the dependence between constants \(\delta \) and \(\varepsilon \) is linear). In the framework of our result, the family can be treated to
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Fatou’s Theorem for A(z)-Analytic Functions Russ. Math. Pub Date : 2023-11-13 N. M. Zhabborov, B. E. Husenov
Abstract We consider \(A(z)\)-analytic functions in case when \(A(z)\) is anti-analytic function. This paper investigates the behavior near the boundary of the derivative of the function, \(A(z)\)-analytic inside the \(A(z)\)-lemniscate and with a bounded change of it at the boundary. Thus, this paper introduces the complex Lipschitz condition for \(A(z)\)-analytic functions and proves Fatou’s theorem
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On Estimates for Maximal Operators Russ. Math. Pub Date : 2023-11-13 I. A. Ikromov, A. M. Barakayev
Abstract The paper deals with boundedness problem for maximal operators associated to hypersurfaces in the space of integrable functions with degree p. A necessary condition for boundedness is given in the space of square-integrable functions in the case one nonvanishing principal curvature. A criterion for the boundedness of the maximal operators in the space of square-integrable functions is obtained
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Conditions for the Existence of Eigenvalues of a Three-Particle Lattice Model Hamiltonian Russ. Math. Pub Date : 2023-11-13 B. I. Bahronov, T. H. Rasulov, M. Rehman
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A Convex Combination of Two Quadratic Stochastic Operators Acting in the 2D Simplex Russ. Math. Pub Date : 2023-11-13 B. J. Mamurov
Abstract In this paper, we consider a quadratic operator on the two-dimensional simplex, which is a convex combination of two quadratic stochastic operators. It is proved that the center of the simplex is a unique fixed point of the operator and this fixed point is an attracting point.
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Grading of a Semigroup C*-Algebra by a Local Group Russ. Math. Pub Date : 2023-11-13 S. A. Grigoryan, A. Sh. Sharafutdinov
Abstract In this paper by a local group of the semigroup C*-algebra generated by the free product of Abelian semigroups is considered. The simplest of these algebras is the Cuntz–Toeplitz algebra \(T{{O}_{n}}\). For such algebras, an abstract version of the Fourier series by the local group is constructed. A number of properties of the “harmonics” of this series are given.
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Application of the Wu Model for Solving the Inverse Problem of Designing Supercavitating Hydrofoils Russ. Math. Pub Date : 2023-11-13 D. V. Maklakov, S. E. Gazizova
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Fundamental Solution of a Singular Bessel Differential Operator with a Negative Parameter Russ. Math. Pub Date : 2023-11-13 L. N. Lyakhov, E. L. Sanina, S. A. Roshchupkin, Yu. N. Bulatov
Abstract The singular differential Bessel operator \({{B}_{{ - \gamma }}}\) with negative parameter \( - \gamma < 0\) is considered. Solutions to the singular differential Bessel equation \({{B}_{{ - \gamma }}}u + {{\lambda }^{2}}u = 0\) are represented by linearly independent functions \({{\mathbb{J}}_{\mu }}\) and \({{\mathbb{J}}_{{ - \mu }}}\), \(\mu = \frac{{\gamma + 1}}{2}\). Some properties of
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Invariant Measure of a Circle Map with a Mixed Type of Singularities Russ. Math. Pub Date : 2023-11-13 U. A. Safarov
Abstract In this work, a critical circle homeomorphism with several break points is considered. The circle homeomorphism \(f\) with the irrational rotation number \(\rho \) is well known to be strictly ergodic; i.e., it has the unique \(f\)-invariant probability measure \(\mu \). The invariant measure of critical circle homeomorphisms with a finite number of break points is proved to be singular with
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A Modification of Visser’s Formal Logic and Its Connection with Solovay’s Modal Logic Russ. Math. Pub Date : 2023-11-01
Abstract We present a new logic called SPL, embedded into Solovay’s provability logic S, using a translation that embeds Visser’s formal logic FPL into Gödel–Löb’s provability logic GL. SPL is formulated as sequent and natural deduction calculi, and a the Kripke semantics is proposed for SPL.
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Invariant Subspaces in Nonquasianalytic Spaces of Ω-Ultradifferentiable Functions on an Interval Russ. Math. Pub Date : 2023-11-01
Abstract In this paper we consider a weakened version of the spectral synthesis for the differentiation operator in nonquasianalytic spaces of ultradifferentiable functions. We deal with the widest possible class of spaces of ultradifferentiable functions among all known ones. Namely, these are spaces of Ω‑ultradifferentiable functions which have been recently introduced and explored by Abanin. For
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Uniqueness of the Kernel Determination Problem in a Integro-Differential Parabolic Equation with Variable Coefficients Russ. Math. Pub Date : 2023-11-01
Abstract We investigate the inverse problem of determining the time and space dependent kernel of the integral term in the \(n\) -dimensional integro-differential equation of heat conduction from the known solution of the Cauchy problem for this equation. First, the original problem is replaced by the equivalent problem in which an additional condition contains the unknown kernel without integral.
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On the Stability of One Equation with a Discrete Retarded Argument and a Constant Concentrated Delay Russ. Math. Pub Date : 2023-10-01
Abstract A functional differential equation with a discrete retarded argument and a constant concentrated delay is considered. The problem of the asymptotic stability of this equation is reduced to the problem of location of the spectrum for the shift operator. Coefficient sufficient conditions for the asymptotic stability of this equation are obtained. The domain in the parameter space such that these
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Integral Estimates of Solutions to Boundary Values Problems for the Poisson Equation Russ. Math. Pub Date : 2023-10-01
Abstract We consider solutions to two boundary values problems for the Poisson equation on plane domains. We prove several estimates for integrals of solutions using geometric characteristics of domains.
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Solvability of an Infinite System of Linear Algebraic Equations with an Infinite Number of Unknowns Russ. Math. Pub Date : 2023-09-18 V. S. Mokeychev
Abstract A new theory of solvability of linear equations with an infinite number of unknowns has been developed.
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On Idempotents of Semigroup Varieties of m-Groups Russ. Math. Pub Date : 2023-09-18 N. V. Bayanova, A. V. Zenkov
Abstract An m-group is a pair \((G,\varphi )\), where \(G\) is an \(\ell \)-group and \(\varphi \) is a decreasing order two automorphisms of G. An \(m\)-group can be regarded as an algebraic system of signature \(m\) and it is obvious that the \(m\)-groups form a variety in this signature. The set \(M\) of varieties of all \(m\)-groups is a semigroup with respect to natural defined operation of multiplication
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On Game Problems of Controlling Pencil Trajectories under Integral Constraints on the Controls of Players Russ. Math. Pub Date : 2023-09-18 N. A. Mamadaliev, T. T. Ibaydullaev, G. M. Abdualimova
Abstract The game problems of control of pencil trajectories, described by a system of equations with a retarded argument under integral restrictions on the players’ controls, are studied. Modifications of the first (I) and third (III) pursuit methods are proposed for game problems of control pencil trajectories. For this game, sufficient conditions are obtained for the possibility of transferring
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The Structure of Differential Invariants for a Free Symmetry Group Action Russ. Math. Pub Date : 2023-09-18 A. A. Magazev, I. V. Shirokov
Abstract In the paper, we consider the problem of describing the general structure of differential invariants for transformation groups that act freely and regularly. We formulate two theorems describing the structures of differential invariants for intransitive and transitive free actions, respectively. In both cases it is shown that the differential invariants can be expressed in terms of the symbols
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Involutions in Algebras of Upper-Triangular Matrices Russ. Math. Pub Date : 2023-09-18 I. A. Kulguskin, D. T. Tapkin
Abstract In this paper we investigate the classification of involutions of the first kind in algebra of upper-triangular matrices over commutative rings. In case of a field \(F\) of characteristics 2, we obtain necessary and sufficient conditions for finiteness of the set of involutions equivalence classes of \({{T}_{n}}(F)\).
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Differential Calculuses on Group Algebras Russ. Math. Pub Date : 2023-09-18 A. A. Arutyunov
Abstract Families of operators obeying some inductive identities (such as the Leibniz rule—the case of derivations and Fox derivations) as characters on a suitable groupoid are described. First and foremost, this construction is implemented for derivations in group algebras and Fox derivations as characters on an action groupoid.
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To the Calculation of the Mapping Degree of Finite Dimensional Vector Field Russ. Math. Pub Date : 2023-09-18 E. Mukhamadiev, A. N. Naimov
Abstract In this paper we propose and justify a new method calculation of the mapping degree of n‑dimensional vector field on the unit sphere of the space \({{{\text{R}}}^{n}}\), \(n \geqslant 2\). The essence of the proposed method is that the calculation of the mapping degree of vector field is reduced to the calculation of the mapping degree of its tangent component on the components of the set
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On the Localization of Fractal Lines of Discontinuity from Noisy Data Russ. Math. Pub Date : 2023-09-01
Abstract An ill-posed problem of localization (determining the position) of discontinuity lines of a function of two variables is considered: outside the discontinuity lines, the function is smooth, and, at each point on the line, it has a discontinuity of the first kind. Under the Lipschitz conditions on the discontinuity line, averaging procedures are constructed and global discrete regularizing
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Determining the Jump of a Function of m-Harmonic Bounded Variation by Its Fourier Series Russ. Math. Pub Date : 2023-08-31 A. A. Kelzon
Abstract— In this article, the well-known formula for determining the jump of a periodic function using the derivative of the partial sums of its Fourier series is extended to a new class of functions.