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Truncations and Compositions in Function Spaces Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-03-06 Hans Triebel
Abstract The paper deals with some recent assertions about truncations \(f\mapsto |f|\) and compositions \(f\mapsto g\circ f\) in the spaces \(A^s_{p,q}(\mathbb R^n)\), \(A\in\{B,F\}\).
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Interpolation of Operators in Hardy-Type Spaces Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-03-06 V. G. Krotov
Abstract A number of statements similar to the Marcinkiewicz interpolation theorem are presented. The difference from the classical forms of this theorem is that the spaces of integrable functions are replaced by certain classes of functions that are extensions of various Hardy spaces.
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Integral Representations and Embeddings of Spaces of Functions of Positive Smoothness on a Hölder Domain Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-03-06 O. V. Besov
Abstract We prove embedding theorems for spaces of functions of positive smoothness defined on a Hölder domain of \(n\)-dimensional Euclidean space.
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Bourgain–Morrey Spaces Mixed with Structure of Besov Spaces Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-03-06 Yirui Zhao, Yoshihiro Sawano, Jin Tao, Dachun Yang, Wen Yuan
Abstract Bourgain–Morrey spaces \(\mathcal{M}^p_{q,r}(\mathbb R^n)\), generalizing what was introduced by J. Bourgain, play an important role in the study related to the Strichartz estimate and the nonlinear Schrödinger equation. In this article, via adding an extra exponent \(\tau\), the authors creatively introduce a new class of function spaces, called Besov–Bourgain–Morrey spaces \(\mathcal{M}\dot{B}^{p
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On the Best Recovery of a Family of Operators on the Manifold $$\mathbb R^n\times\mathbb T^m$$ Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-03-06 G. G. Magaril-Il’yaev, E. O. Sivkova
Abstract Given a one-parameter family of operators on the manifold \(\mathbb R^n\times\mathbb T^m\), we solve the problem of the best recovery of an operator for a given value of the parameter from inaccurate data on the operators for other values of the parameter from a certain compact set. We construct a family of best recovery methods. As a consequence, we obtain families of best recovery methods
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On the Regularity of Characteristic Functions of Weakly Exterior Thick Domains Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-03-06 Winfried Sickel
Abstract Let \(E\) be a domain in \(\mathbb R^d\). We investigate the regularity of the characteristic function \(\mathcal X_E\) depending on the behavior of the \(\delta\)-neighborhoods of the boundary of \(E\). The regularity is measured in terms of the Nikol’skii–Besov and Lizorkin–Triebel spaces.
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A Generalized Translation Operator Generated by the Sinc Function on an Interval Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 V. V. Arestov, M. V. Deikalova
We discuss the properties of the generalized translation operator generated by the system of functions \(\mathfrak{S}=\{{(\sin k\pi x)}/{(k\pi x)}\}_{k=1}^{\infty}\) in the spaces \(L^{q}=L^{q}((0,1),{\upsilon})\), \(q\geq 1\), on the interval \((0,1)\) with the weight \(\upsilon(x)=x^{2}\). We find an integral representation of this operator and study its norm in the spaces \(L^{q}\), \(1\leq q\leq\infty\)
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Optimization of the Optimal Value Function in Problems of Convex Parametric Programming Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 O. V. Khamisov
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A Bicomposition of Conical Projections Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 E. A. Nurminski
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Polynomial-Time Approximability of the Asymmetric Problem of Covering a Graph by a Bounded Number of Cycles Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 M. Yu. Khachai, E. D. Neznakhina, K. V. Ryzhenko
Recently, O. Svensson and V. Traub have provided the first proof of the polynomial-time approximability of the asymmetric traveling salesman problem (ATSP) in the class of constant-factor approximation algorithms. Just as the famous Christofides–Serdyukov algorithm for the symmetric routing problems, these breakthrough results, applied as a “black box,” have opened an opportunity for developing the
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Comparison and Polyhedral Properties of Valid Inequalities for a Polytope of Schedules for Servicing Identical Requests Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 R. Yu. Simanchev, I. V. Urazova
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Asymptotics of a Solution to an Optimal Control Problem with a Terminal Convex Performance Index and a Perturbation of the Initial Data Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 A. R. Danilin, O. O. Kovrizhnykh
In this paper, we investigate a problem of optimal control over a finite time interval for a linear system with constant coefficients and a small parameter in the initial data in the class of piecewise continuous controls with smooth geometric constraints. We consider a terminal convex performance index. We substantiate the limit relations as the small parameter tends to zero for the optimal value
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Young Duality of Variational Inequalities. An Application for the Analysis of Interactions in Production Networks Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 N. K. Obrosova, A. A. Shananin
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Examples of Nonpronormal Relatively Maximal Subgroups of Finite Simple Groups Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 B. Li, D. O. Revin
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Reconstruction of a Function Analytic in a Disk from the Boundary Values of Its Real Part Using Interpolation Wavelets Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 N. I. Chernykh
For a function \(f(z)\) analytic in a disk, a method of approximate reconstruction from known (or arbitrarily specified) boundary values of its real part (under the condition of its continuity) using interpolation wavelets is proposed; the method is easy to implement numerically. Despite the fact that there are known exact analytical formulas for solving this problem, the explicit formulas for approximating
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On Intersections of Nilpotent Subgroups in Finite Groups with Simple Socle from the “Atlas of Finite Groups” Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 V. I. Zenkov
Earlier, the author described up to conjugacy all pairs \((A,B)\) of nilpotent subgroups of a finite group \(G\) with socle \(L_{2}(q)\) for which \(A\cap B^{g}\neq 1\) for any element of \(G\). A similar description was obtained by the author later for primary subgroups \(A\) and \(B\) of a finite group \(G\) with socle \(L_{n}(2^{m})\). In this paper, we describe up to conjugacy all pairs \((A,B)\)
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Minimizing Sequences in a Constrained DC Optimization Problem Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 A. S. Strekalovsky
A smooth nonconvex optimization problem is considered, where the equality and inequality constraints and the objective function are given by DC functions. First, the original problem is reduced to an unconstrained problem with the help of I. I. Eremin’s exact penalty theory, and the objective function of the penalized problem also turns out to be a DC function. Necessary and sufficient conditions for
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Sharp Carlson Type Inequalities with Many Weights Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 K. Yu. Osipenko
The paper is concerned with sharp Carlson type inequalities of the form \(\|w(\cdot)x(\cdot)\|_{L_{q}(T)}\leq K\|w_{0}(\cdot)x(\cdot)\|_{L_{p}(T)}^{ \gamma}\max_{1\leq j\leq n}\|w_{j}(\cdot)x(\cdot)\|_{L_{r}(T)}^{1-\gamma},\) where \(T\) is a cone in \(\mathbb{R}^{d}\) and the weight functions \(w_{j}(\cdot)\), \(j=1,\mathinner{\ldotp\ldotp\ldotp},n\), are homogeneous with some symmetry property.
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Periodic Groups with One Finite Nontrivial Sylow 2-Subgroup Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2024-02-12 D. V. Lytkina, V. D. Mazurov
The following results are proved. Let \(d\) be a natural number, and let \(G\) be a group of finite even exponent such that each of its finite subgroups is contained in a subgroup isomorphic to the direct product of \(m\) dihedral groups, where \(m\leq d\). Then \(G\) is finite (and isomorphic to the direct product of at most \(d\) dihedral groups). Next, suppose that \(G\) is a periodic group and
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Analytic Properties of Solutions to the Equation of Internal Gravity Waves with Flows for Critical Modes of Wave Generation Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 V. V. Bulatov
Abstract Issues related to the statement of problems of describing the dynamics of linear internal gravity waves in stratified media with horizontal shear flows in critical modes of wave generation are considered. Model physical statements of problems in which critical levels may arise are discussed in the two-dimensional case. Analytic properties of the solutions near critical levels are studied.
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Structures of Classical and Special Discontinuities for the Generalized Korteweg–de Vries–Burgers Equation in the Case of a Flux Function with Four Inflection Points Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 V. A. Shargatov, A. P. Chugainova, A. M. Tomasheva
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Mathematical Model of Replacing Methane in Hydrate with Carbon Dioxide When It Is Injected into a Reservoir Saturated with a Mixture of Hydrate, Methane, and Water Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 G. G. Tsypkin
Abstract A mathematical model is proposed for the replacement of methane with carbon dioxide in a hydrate contained in a reservoir in thermodynamic equilibrium with water and free methane. The substitution reaction region is assumed to be narrow enough to be approximated by the conversion front. A self-similar solution is found that reduces the problem to the numerical analysis of a system of transcendental
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Equilibrium Model of Density Flow Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 V. Yu. Liapidevskii
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On the Problem of Energy Concentration Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 A. N. Golubyatnikov, D. V. Ukrainskii
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Flows of Liquids with a Yield Strength in Pipes under a Pulsating Pressure Drop Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 M. E. Eglit, Yu. A. Drozdova, I. N. Usachev, A. V. Drozdov
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Nonuniqueness of a Self-similar Solution to the Riemann Problem for Elastic Waves in Media with a Negative Nonlinearity Parameter Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 A. P. Chugainova, R. R. Polekhina
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Exact Solutions of Second-Grade Fluid Equations Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 A. G. Petrova, V. V. Pukhnachev, O. A. Frolovskaya
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On Linear Equations of Dynamics Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 V. V. Kozlov
Abstract We consider linear autonomous systems of second-order differential equations that do not contain first derivatives of independent variables. Such systems are often encountered in classical mechanics. Of particular interest are cases where external forces are not potential. An important special case is given by the equations of nonholonomic mechanics linearized in the vicinity of equilibria
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On Isochronicity Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 D. V. Treschev
Abstract We obtain a complete set of explicit necessary and sufficient conditions for the isochronicity of a Hamiltonian system with one degree of freedom. The conditions are presented in terms of the Taylor coefficients of the Hamiltonian function and have the form of an infinite collection of polynomial equations.
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Internal Stresses in an Elastic Half-space under Discrete Contact Conditions Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 I. G. Goryacheva, A. A. Yakovenko
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A Topological–Analytical Method for Proving Averaging Theorems on an Infinite Time Interval in a Degenerate Case Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 Ivan Yu. Polekhin
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Separatrix Maps in Slow–Fast Hamiltonian Systems Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 Sergey V. Bolotin
Abstract We obtain explicit formulas for the separatrix map of a multidimensional slow–fast Hamiltonian system. This map is used to partly extend Neishtadt’s results on the jumps of adiabatic invariants at the separatrix to the multidimensional case.
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On Waves on the Surface of an Unstable Layer of a Viscous Fluid Flowing Down a Curved Surface Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 A. G. Kulikovskii, J. S. Zayko
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Nonlinear Effects and Run-up of Coastal Waves Generated by Billiards with Semi-rigid Walls in the Framework of Shallow Water Theory Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-20 S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. V. Tsvetkova
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Riemann–Liouville Space of Fractional Potentials on the Half-Line Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract We study the Riemann–Liouville space of fractional potentials on the half-line and establish its properties such as embeddings in Besov spaces, Liouville classes, and Lizorkin–Triebel spaces.
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Integral Inequalities for Entire Functions of Exponential Type in Morrey Spaces Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract We prove analogs of Bernstein’s inequalities and inequalities of different metrics and different dimensions for entire functions of exponential type. Such inequalities are well known for Lebesgue spaces. In this paper we prove them for Morrey spaces.
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Sobolev and Besov Classes on Infinite-Dimensional Spaces Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract We discuss various definitions of Sobolev and Besov classes on infinite-dimensional spaces, give a survey of the results on coincidence of some of these classes, and obtain a number of new results.
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Asset Tokenization and Related Problems Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract For a number of years, the authors have been working in the sphere of asset tokenization, especially in connection with precious metals. An approach (including algorithms, mathematical models, and software implementation) to the gold reserve management problem has been developed. This approach allows to effectively manage the gold reserve, taking into account the fact that the faster the money
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On Graphs in Which the Neighborhoods of Vertices Are Edge-Regular Graphs without 3-Claws Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract The triangle-free Krein graph Kre \((r)\) is strongly regular with parameters \(((r^{2}+3r)^{2},\) \(r^{3}+3r^{2}+r,0,r^{2}+r)\) . The existence of such graphs is known only for \(r=1\) (the complement of the Clebsch graph) and \(r=2\) (the Higman–Sims graph). A.L. Gavrilyuk and A.A. Makhnev proved that the graph Kre \((3)\) does not exist. Later Makhnev proved that the graph Kre \((4)\) does
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On Constants in the Bernstein–Szegő Inequality for the Weyl Derivative of Order Less Than Unity of Trigonometric Polynomials and Entire Functions of Exponential Type in the Uniform Norm Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract The Weyl derivative (fractional derivative) \(f_{n}^{(\alpha)}\) of real nonnegative order \(\alpha\) is considered on the set \(\mathscr{T}_{n}\) of trigonometric polynomials \(f_{n}\) of order \(n\) with complex coefficients. The constant in the Bernstein–Szegő inequality \({\|}f_{n}^{(\alpha)}\cos\theta+\tilde{f}_{n}^{(\alpha)}\sin\theta{\| }\leq B_{n}(\alpha,\theta)\|f_{n}\|\) in the
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On the Kegel–Wielandt $$\sigma$$ -Problem Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract For an arbitrary partition \(\sigma\) of the set \(\mathbb{P}\) of all primes, a sufficient condition for the \(\sigma\) -subnormality of a subgroup of a finite group is given. It is proved that the Kegel–Wielandt \(\sigma\) -problem has a positive solution in the class of all finite groups all of whose nonabelian composition factors are alternating groups, sporadic groups, or Lie groups
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Closed Mappings and Construction of Extension Models Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract The problem of reachability in a topological space is studied under constraints of asymptotic nature arising from weakening the requirement that the image of a solution belong to a given set. The attraction set that arises in this case in the topological space is a regularization of certain kind for the image of the preimage of the mentioned set (the image and the preimage are defined for
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Adaptive Subgradient Methods for Mathematical Programming Problems with Quasiconvex Functions Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract The paper is devoted to subgradient methods with switching between productive and nonproductive steps for problems of minimization of quasiconvex functions under functional inequality constraints. For the problem of minimizing a convex function with quasiconvex inequality constraints, a result is obtained on the convergence of the subgradient method with an adaptive stopping rule. Further
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The Structure of the Essential Spectrum and the Discrete Spectrum of the Energy Operator for Six-Electron Systems in the Hubbard Model. The Second Singlet State Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-12-01
Abstract We consider the energy operator of six-electron systems in the Hubbard model and study the structure of the essential spectrum and the discrete spectrum of the system for the second singlet state of the system. In the one- and two-dimensional cases, it is shown that the essential spectrum of the six-electron second singlet state operator is the union of seven closed intervals, and the discrete
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Free Vibration Analysis of a Cylindrical Shell of Variable Thickness Partially Filled with Fluid Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 S. A. Bochkarev, V. P. Matveenko
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Optimal Recovery on Classes of Functions Analytic in an Annulus Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 O. V. Akopyan, R. R. Akopyan
Let \(C_{r,R}\) be an annulus with boundary circles \(\gamma_{r}\) and \(\gamma_{R}\) centered at zero; its inner and outer radii are \(r\) and \(R\), respectively, \(00\)) to an intermediate circle \(\gamma_{\rho}\), \(r<\rho
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On the Group Classification of Ideal Gas-Dynamic Relaxing Media Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 S. V. Khabirov
The group analysis of differential equations of ideal gas dynamics is most developed. Earlier, the state equations for thermodynamic parameters were assumed to be time-independent. The time dependence may take place for relaxing media, for example, as a result of rheology or due to the energy averaging of processes in a multiphase medium. The problem of group analysis of relaxing media is posed. First
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Perturbation of a Simple Wave in a Domain Wall Model Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 L. A. Kalyakin
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Operator Estimates in Two-Dimensional Problems with a Frequent Alternation in the Case of Small Parts with the Dirichlet Condition Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 D. I. Borisov
A two-dimensional boundary value problem is studied for a general scalar elliptic second-order equation of the general form with frequent alternation of boundary conditions. The alternation is defined on small, closely spaced parts of the boundary on which the Dirichlet boundary condition and the nonlinear Robin boundary condition are set alternately. The distribution and size of these segments are
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On Some Classes of Free Convection Motions Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 O. N. Ul’yanov, L. I. Rubina
A system of equations of unsteady spatial free convection of an incompressible viscous fluid in the Boussinesq approximation is considered. The analysis is based on the methods of reduction of linear and nonlinear partial differential equations (PDEs) and systems of PDEs to ordinary differential equations (ODEs) and systems of ODEs. These methods were proposed by the authors earlier, and their general
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Richardson Method for a Diffusion Equation with Functional Delay Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 V. G. Pimenov, A. B. Lozhnikov
A diffusion equation with a functional delay effect is considered. The problem is discretized. Constructions of the Crank–Nicolson difference method with piecewise linear interpolation and extrapolation by continuation are given; the method here has the second order of smallness with respect to the sampling steps in time \(\Delta\) and space \(h\). The basic Crank–Nicolson method with piecewise cubic
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Assimilation of Boundary Data for Reconstructing the Absorption Coefficient in a Model of Stationary Reaction–Convection–Diffusion Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 A. I. Korotkii, I. A. Tsepelev
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On an Element-by-Element Description of the Monoid of all Endomorphisms of an Arbitrary Groupoid and One Classification of Endomorphisms of a Groupoid Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 A. V. Litavrin
The problem of element-by-element description of the monoid of all endomorphisms of an arbitrary groupoid is considered. It is established that this monoid is decomposed into a union of pairwise disjoint classes of endomorphisms; these classes are called basic sets of endomorphisms. Such sets of endomorphisms of a groupoid \(G\) are parameterized by mappings \(\gamma:G\to\{1,2\}\), which in this paper
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Some Properties of Ultrafilters Related to Their Use As Generalized Elements Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 A. G. Chentsov
Ultrafilters of broadly understood measurable spaces and their application as generalized elements in abstract reachability problems with constraints of asymptotic nature are considered. Constructions for the immersion of conventional solutions, which are points of a fixed set, into the space of ultrafilters and representations of “limit” ultrafilters realized with topologies of Wallman and Stone types
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Solution of a Parabolic Hamilton–Jacobi Type Equation Determined by a Simple Boundary Singularity Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 S. V. Zakharov
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On Essential Values of Oscillation Exponents for Solutions of a Linear Homogeneous Two-Dimensional Differential System Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 A. Kh. Stash
In this paper, we study various types of oscillation exponents for solutions of linear homogeneous differential systems with continuous bounded coefficients. The calculation of the oscillation exponents is carried out by averaging the number of zeros (signs, roots, or hyperroots) of the projection of a solution \(x\) of a differential system onto any straight line, and this line is chosen so that the
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Zeros of Solutions of Third-Order L–A Pairs and Linearizable Ordinary Differential Equations Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 B. I. Suleimanov
We study the form of the zero lines \(x=\varphi(t)\) of simultaneous solutions to an L–A pair of general form composed of an evolution equation \(\Psi^{\prime}_{t}=\Psi^{\prime\prime}_{xx}/2-G(t,x)\Psi\) and an ordinary differential equation \(\Psi^{\prime\prime\prime}_{xxx}=K(t,x)\Psi^{\prime\prime}_{xx}+L(t,x)\Psi^{ \prime}_{x}+M(t,x)\Psi\). It is shown that such lines are given by solutions of a
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Asymptotics of a Solution to an Optimal Control Problem with Integral Convex Performance Index, Cheap Control, and Initial Data Perturbations Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 A. R. Danilin, A. A. Shaburov
We consider an optimal control problem in the class of piecewise continuous controls with smooth geometric constraints for a linear system with constant coefficients and an integral convex performance index containing two small parameters (the first of them multiplying the integral term, and the second in the initial data). Such problems are called cheap control problems. It is shown that the limit
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The Problem of Diffusion Wave Initiation for a Nonlinear Second-Order Parabolic System Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 A. L. Kazakov, P. A. Kuznetsov, L. F. Spevak
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Quasilinear Equations with a Sectorial Set of Operators at Gerasimov–Caputo Derivatives Proc. Steklov Inst. Math. (IF 0.5) Pub Date : 2023-09-14 V. E. Fedorov, K. V. Boyko
The issues of unique solvability of the Cauchy problem are studied for a quasilinear equation solved with respect to the highest fractional Gerasimov–Caputo derivative in a Banach space with closed operators from the class \(A_{\alpha,G}^{n}\) in the linear part and with a nonlinear operator continuous in the graph norm. A theorem on the local existence and uniqueness of a solution to the Cauchy problem