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On Solutions of the Navier Problem for a Polyharmonic Equation in Unbounded Domains Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 H.A. Matevossian
Abstract The polyharmonic Navier problem is considered, the uniqueness (non-uniqueness) of its solution is studied in unbounded domains under the assumption that the generalized solution of this problem has a finite Dirichlet integral with weight \(|x|^a\). Depending on the values of the parameter \(a\), uniqueness theorems are proved and exact formulas are found for calculating the dimension of the
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Transport Equation for the Harmonic Crystal Coupled to a Klein–Gordon Field Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 T.V. Dudnikova
Abstract We consider the Hamiltonian system consisting of the Klein–Gordon field coupled to an infinite harmonic crystal. The dynamics of the coupled system is translation-invariant with respect to the space translations in \(\mathbb{Z}^d\), \(d\ge1\). We study the Cauchy problem and assume that the initial date is a random function. We introduce the family of initial probability measures \(\{\mu_0^\varepsilon
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Analytic Solution of the System of Integro-Differential Equations for the Plasma Model in an External Field Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 S.I. Bezrodnykh, N.M. Gordeeva
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Probabilistic Degenerate Bell Polynomials Associated with Random Variables Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 T. Kim, D. S. Kim
Abstract The aim of this paper is to study probabilistic versions of the degenerate Stirling numbers of the second kind and the degenerate Bell polynomials, namely the probabilisitc degenerate Stirling numbers of the second kind associated with \(Y\) and the probabilistic degenerate Bell polynomials associated with \(Y\), which are also degenerate versions of the probabilisitc Stirling numbers of the
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Classification of Singularities of the Liouville Foliation of an Integrable Elliptical Billiard with a Potential of Fourth Degree Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 S.E. Pustovoitov
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The Mean Square of the Pauli–Jordan–Dirac Anticommutator With Respect to Spatial Variables Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 E.A. Karatsuba
Abstract The Pauli–Jordan–Dirac anticommutator mean-square formula is presented. DOI 10.1134/S1061920823040088
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Method of Potential Operators for Interaction Problems on Unbounded Hypersurfaces in $$\mathbb{R}^{n}$$ for Dirac Operators Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 V. S. Rabinovich
Abstract We consider the \(L_{p}\)-theory of interaction problems associated with Dirac operators with singular potentials of the form \(D=\mathfrak{D}_{m,\Phi }+\Gamma\delta_{\Sigma}\) where $$\mathfrak{D}_{m,\Phi}=\sum_{j=1}^{n}\alpha_{j}(-i\partial_{x_{j}} )+m\alpha_{n+1}+\Phi\mathbb{I}_{N}$$ is a Dirac operator on \(\mathbb{R}^{n}\), \(\alpha_{1},\alpha_{2},\dots,\alpha _{n},\alpha_{n+1}\) are
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Estimation of the Approximation of Continuous Periodic Functions by Fourier Sums Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 T.Yu. Semenova
Abstract An asymptotically exact estimate for the norm of the difference between a function and the partial sum of its Fourier series is obtained in terms of the modulus of continuity of the function. The values of the modulus of continuity of the argument that are less than the optimal one are considered. DOI 10.1134/S1061920823040179
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Elementary Differential Singularities of Three-Dimensional Nijenhuis Operators Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 D. Akpan, A. Oshemkov
Abstract In the paper, three-dimensional Nijenhuis operators are studied that have differential singularities, i.e., such points at which the coefficients of the characteristic polynomials are dependent. The case is studied in which the differentials of all invariants of the Nijenhuis operator are proportional, as well as the case when two invariants are functionally independent and the third defines
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Asymptotics of the Whispering Gallery-Type in the Eigenproblem for the Laplacian in a Domain of Revolution Diffeomorphic To a Solid Torus Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 D.S. Minenkov, S.A. Sergeev
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High-Energy Homogenization of a Multidimensional Nonstationary Schrödinger Equation Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 M. Dorodnyi
Abstract In \(L_2(\mathbb{R}^d)\), we consider an elliptic differential operator \(\mathcal{A}_\varepsilon \! = \! - \operatorname{div} g(\mathbf{x}/\varepsilon) \nabla + \varepsilon^{-2} V(\mathbf{x}/\varepsilon)\), \( \varepsilon > 0\), with periodic coefficients. For the nonstationary Schrödinger equation with the Hamiltonian \(\mathcal{A}_\varepsilon\), analogs of homogenization problems related
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On Degenerate Orbits of Real Lie Algebras in Multidimensional Complex Spaces Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 A.V. Atanov, A.V. Loboda
Abstract The article studies (locally) holomorphically homogeneous real hypersurfaces of complex spaces. Currently, the problem of classifying such hypersurfaces is completely solved only in the spaces \(\mathbb{C}^{2}\) and \(\mathbb{C}^{3}\). As the dimension of the ambient space grows, so does the relative part of Levi-degenerate manifolds in the family of all homogeneous hypersurfaces. In particular
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Asymptotics of Long Nonlinear Propagating Waves in a One-Dimensional Basin with Gentle Shores Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 D.S. Minenkov, M.M. Votiakova
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Nonlinear Long Standing Waves with Support Bounded by Caustics or Localized in the Vicinity of a Two-Link Trajectory Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 A.I. Klevin, A.V. Tsvetkova
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Variations on the theme of the Trotter-Kato theorem for homogenization of periodic hyperbolic systems Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-25 Yu.M. Meshkova
Abstract In \(L_2(\mathbb{R}^d;\mathbb{C}^n)\), we consider a matrix elliptic second order differential operator \(B_\varepsilon >0\). Coefficients of the operator \(B_\varepsilon\) are periodic with respect to some lattice in \(\mathbb{R}^d\) and depend on \(\mathbf{x}/\varepsilon\). We study the quantitative homogenization for the solutions of the hyperbolic system \(\partial _t^2\mathbf{u}_\varepsilon
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Lie’s Theorem for Solvable Connected Lie Groups Without the Continuity Assumption Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-01
Abstract It is proved that if \(G\) is a connected solvable group and \(\pi\) is a (not necessarily continuous) representation of \(G\) in a finite-dimensional vector space \(E\) , then there is a basis in \(E\) in which the matrices of the representation operators of \(\pi\) have upper triangular form. The assertion is extended to connected solvable locally compact groups \(G\) having a connected
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Trace of the Resolvent of the Laplace Operator on a Metric Graph Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-01
Abstract In the paper, using Krein’s resolvent formula, we find an asymptotics of the resolvent of the trace of the Laplace operator on a metric graph. DOI 10.1134/S1061920823040192
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Averaging Method for Quasi-Linear Hyperbolic Systems Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-01
Abstract The paper considers the Cauchy problem for a multidimensional quasilinear hyperbolic system of differential equations with the data rapidly oscillating in time. This data do not explicitly depend on spatial variables. The method by N. M. Krylov–N. N. Bogolyubov is developed and justified for these systems. Also an algorithm is developed and justified, based on this method and the method of
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Flow Around a Curved Plate with Small Periodic Irregularities: a Double-Deck Boundary Layer Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-01
Abstract In this paper, equations describing a double-dimensional flow along a curved smooth plate with small periodic irregularities are derived. The parameters of the irregularities are chosen so that the flow has a double-deck structure. The equations describing the terms of the asymptotic solution are written in the original coordinate system, which required changes in the form of the usual ansatz
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Asymptotics of the Cauchy Problem for the One-Dimensional Schrödinger Equation with Rapidly Oscillating Initial Data and Small Addition to the Smooth Potential Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-12-01
Abstract We study the asymptotic solution of the Cauchy problem with rapidly changing initial data for the one-dimensional nonstationary Schrödinger equation with a smooth potential perturbed by a small rapidly oscillating addition. Solutions to such a Cauchy problem are described by moving, rapidly oscillating wave packets. According to long-standing results of V.S. Buslaev and S.Yu. Dobrokhotov,
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Normal Ordering Associated with $$\lambda$$ -Whitney Numbers of the First Kind in $$\lambda$$ -Shift Algebra Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 D. S. Kim, T. K. Kim
Abstract It is known that the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra. The aim of this paper is to consider the \(\lambda\)-shift algebra, which is a \(\lambda\)-analogue of the shift algebra, and to study \(\lambda\)-analogues of Whitney numbers of the first kind (called \(\lambda\)-Whitney numbers of the first kind) and those of \(r\)-Whitney
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Inverse Resonance Problem for Jacobi Operators on a Half-Lattice Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 E. Korotyaev, E. Leonova
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Monodromization and a $$ \mathcal{P} \mathcal{T} $$ -Symmetric Nonself-Adjoint Quasi-Periodic Operator Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 D. I. Borisov, A. A. Fedotov
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Real Submanifolds of $$\mathbf{C}^2$$ With Singularities Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 V. K. Beloshapka
Abstract We consider real submanifolds of \(\mathbf{C}^2\) with singularities of three types: \(RC\)-singular 2 - dimensional surfaces, real quadratic cones, and hypersurfaces with degeneration of the Levi form. The holomorphic automorphisms of singular germs are evaluated. We also discuss resolution of singularities in the context of \(\mathit{CR}\) geometry.
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Rectilinear Vortex Thread in a Radially Nonhomogeneous Bingham Solid Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 V. A. Banko, D. V. Georgievskii
Abstract We study an initial boundary value problem of axially symmetric one-dimensional unsteady shear in the viscoplastic space (a Bingham solid) initiated by a rectilinear vortex thread located along the symmetry axis. The force intensity of the thread is represented by a given monotone piecewise continuous function of time. The density and the dynamical viscosity of the medium are constant, and
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Reflexivity for Spaces With Extended Norm Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 I. G. Tsar’kov
Abstract An analogue of reflexivity in asymmetric cone spaces is introduced and studied. Some classical results known for ordinary normalized spaces are carried over to the case of essentially asymmetric spaces.
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Boundary-Value Problem for Singularly Perturbed Integro-Differential Equation with Singularly Perturbed Neumann Boundary Condition Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 N. N. Nefedov, A. G. Nikitin, E. I. Nikulin
Abstract We consider a boundary-value problem for singularly perturbed integro-differential equation describing stationary reaction–diffusion processes with due account of nonlocal interactions. The principal feature of the problem is the presence of a singularly perturbed Neumann condition describing intense flows on the boundary. We prove that there exists a boundary-layer solution, construct its
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Darwin’s Algorithms Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 Yu. N. Zhuravlev, M. A. Guzev
Abstract An algorithmic concept of the physical world is proposed in which the main ideas of the Darwinian evolution act as algorithms of becoming.
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Miura Type Transform Between Non-Abelian Volterra and Toda Lattices and Inverse Spectral Problem for Band Operators Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 A. Osipov
Abstract We study a discrete Miura-type transformation between the hierarcies of non-Abelian semi-infinite Volterra (Kac–van Moerbeke) and Toda lattices with operator coefficients in terms of the inverse spectral problem for three-diagonal band operators, which appear in the Lax representation for such systems. This inverse problem method, which amounts to reconstruction of the operator from the moments
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Whitney–Sullivan Constructions for Transitive Lie Algebroids–Smooth Case Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 A. S. Mishchenko, J. R. Oliveira
Abstract Let \(M\) be a smooth manifold, smoothly triangulated by a simplicial complex \(K\), and \( {\cal A} \) a transitive Lie algebroid on \(M\). A piecewise smooth form on \( {\cal A} \) is a family \(\omega=(\omega_{\Delta})_{\Delta\in K}\) such that \(\omega_{\Delta}\) is a smooth form on the Lie algebroid restriction of \( {\cal A} \) to \(\Delta\), satisfying the compatibility condition concerning
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Localized Waves Propagating Along an Angular Junction of Two Thin Semi-Infinite Elastic Membranes Terminating an Acoustic Medium Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-09-05 M. A. Lyalinov
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Trajectory Symbols and the Fredholm Property of Boundary Value Problems for Differential Operators with Shifts Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 A. V. Boltachev, A. Yu. Savin
Abstract Boundary value problems are considered in which the main operator and the operators of boundary conditions include differential and shift operators corresponding to the action of a discrete group. The manifold on which the boundary value problem is considered is not assumed to be group invariant. A definition of trajectory symbols for this class of boundary value problems is given. It is shown
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Thick Elements and States in $$C^*$$ -Algebras in View of Frame Theory Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 D. V. Fufaev
Abstract We study some classes of noncommutative \(C^*\)-algebras and generalize some results which were originally obtained for commutative algebras in topological terms. In particular, we are interested in results obtained for topological spaces with properties close to separability and \( \sigma \)-compactness. To obtain the algebraic, noncommutative versions of corresponding properties, we define
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Identification of the Potential Coefficient in the Schrödinger Equation with Incomplete Initial Conditions from a Boundary Observation Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 B. Elhamza, A. Hafdallah
Abstract This paper deals with an inverse problem of the Schrödinger equation, a fundamental equation in quantum mechanics. Specifically, we focus on incomplete data, where there are missing terms in the potential term and the initial condition. The potential term is a critical part of the equation, representing the potential energy of the system under investigation. Our objective is to obtain valuable
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Ice-Water Phase Transition on a Substrate Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 V. G. Danilov, R. K. Gaydukov
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Lattice Equations and Semiclassical Asymptotics Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 V. L. Chernyshev, V. E. Nazaikinskii, A. V. Tsvetkova
Abstract We consider linear equations with shifts of the arguments on the rectangular lattice with small step \(h\) in \(\mathbb{R}^n\) and construct a version of the canonical operator providing semiclassical asymptotics for such equations. Examples include the Feynman checkers model arising in quantum theory and a problem on the wave packet propagation on a homogeneous tree.
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A Version of the Weyl Complete Reducibility Theorem for Not Necessarily Continuous Representations of Connected Lie Groups Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 A. I. Shtern
Abstract A version of the Weyl complete reducibility theorem for finite-dimensional quasirepresentations of general connected Lie groups is proved.
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On Homogenization for Piecewise Locally Periodic Operators Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 N. N. Senik
Abstract We discuss homogenization of a strongly elliptic operator \(\mathcal A^\varepsilon=-\operatorname{div}A(x,x/\varepsilon_\#)\nabla\) on a bounded \(C^{1,1}\) domain in \(\mathbb R^d\) with either Dirichlet or Neumann boundary condition. The function \(A\) is piecewise Lipschitz in the first variable and periodic in the second one, and the function \(\varepsilon_\#\) is identically equal to
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Semiclassical Asymptotic Expansions for Functions of the Bochner–Schrödinger Operator Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 Y. A. Kordyukov
Abstract The Bochner–Schrödinger operator \(H_{p}=\frac 1p\Delta^{L^p\otimes E}+V\) on tensor powers \(L^p\) of a Hermitian line bundle \(L\) twisted by a Hermitian vector bundle \(E\) on a Riemannian manifold of bounded geometry is studied. For any function \(\varphi\in \mathcal S(\mathbb R)\), we consider the bounded linear operator \(\varphi(H_p)\) in \(L^2(X,L^p\otimes E)\) defined by the spectral
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Solitary Wave Solutions to a Generalization of the mKdV Equation Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 G. Omel’yanov, J. Noyola Rodriguez
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Quantization of Nonsmooth Curves and the Semiclassical Spectrum of the One-Dimensional Schrödinger Operator with a Localized Perturbation of the Potential Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 I. A. Lavrinenko, A. I. Shafarevich
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Conclusive Discrimination by $$N$$ Sequential Receivers between $$r\geq2$$ Arbitrary Quantum States Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 E. R. Loubenets, M. Namkung
Abstract In the present paper, we develop a general mathematical framework for discrimination between \(r\geq2\) quantum states by \(N\geq1\) sequential receivers for the case in which every receiver obtains a conclusive result. This type of discrimination constitutes an \(N\)-sequential extension of the minimum-error discrimination by one receiver. The developed general framework, which is valid for
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Smoothness of Solutions of the Eikonal Equation and Regular Points of Their Level Surfaces Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 I. G. Tsar’kov
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Inverse Semigroups of Metrics on Doubles Related to Certain Subsets Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-06-18 V. Manuilov
Abstract Recently we have shown that the equivalence classes of metrics on the double of a metric space \(X\) form an inverse semigroup. Here we define an inverse subsemigroup related to a family of isometric subspaces of \(X\), which is more computable. As a special case, we study this subsemigroup related to the family of geodesic rays starting from the basepoint, for Euclidean spaces and for trees
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Model $$CR$$ Surfaces: Weighted Approach Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 V. K. Beloshapka
Abstract In the paper, a systematic construction of the theory of “weighted” model surfaces using the Bloom–Graham–Stepanova concept of the type of a CR-manifold is given. The construction is based on the Poincaré construction. It is shown how the use of weighted model surfaces expands the abilities of the method. New questions are being posed.
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Continuity Criterion for Locally Bounded Endomorphisms of Connected Reductive Lie Groups Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 A. I. Shtern
Abstract We prove that every locally bounded endomorphism \(\pi\) of a connected reductive Lie group taking the center of the group to the center is continuous if and only if the restriction \(\pi|_Z\) of \(\pi\) to the center \(Z\) of \(G\) is continuous with respect to the same topology.
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On the Domain of Constancy of the Sign of a Harmonic Function in the Unit Disk with Additional Conditions on the Boundary Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 T. Yu. Semenova
Abstract An estimate for the domain of constant sign for a function harmonic in the unit disk is obtained under the condition that the function is represented on the boundary of the circle as a sine series with monotonic coefficients.
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Some Identities Involving Degenerate Stirling Numbers Associated with Several Degenerate Polynomials and Numbers Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 T. K. Kim, D. S. Kim
Abstract The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate Stirling numbers of both kinds associated with degenerate hyperharmonic numbers and also with degenerate Bernoulli, degenerate Euler, degenerate Bell, and degenerate Fubini polynomials.
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Classification of Singularities of Smooth Functions with a Finite Cyclic Symmetry Group Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 E. A. Kudryavtseva, M. V. Onufrienko
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On Relationships between the Spectral Potential of Transfer Operators, $$\boldsymbol t$$ -Entropy, Entropy and Topological Pressure Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 V. I. Bakhtin, A. V. Lebedev
Abstract The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic characteristics of information theory and thermodynamic formalism (entropy and topological pressure). We present explicit formulas linking these objects with the \(t\)-entropy and spectral potential. Herewith we uncover
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Global Asymptotics for Functions of Parabolic Cylinder and Solutions of the Schrödinger Equation with a Potential in the Form of a Nonsmooth Double Well Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 S. Yu. Dobrokhotov, A. V. Tsvetkova
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An Inverse Spectral Problem for a Special Class of Band Matrices and Bogoyavlensky Lattice Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 A. S. Osipov
Abstract We study the inverse spectral problem method for one class of band matrices which can be applied to the integration (via Lax formalism) of Bogoyavlensky lattice $$\overset{\cdot}{a}_i=a_i^2(a_{i+1}-a_{i-1}),$$ in the finite case. Such matrices have a special structure which differs from the three-diagonal one of the matrices which appear in the Lax representation for Toda and Volterra lattices
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Estimates of the Chebyshev Radius in Terms of the MAX-Metric Function and the MAX-Projection Operator Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 I. G. Tsar’kov
Abstract Singleton approximations of sets in asymmetric spaces are studied. Estimate of the Chebyshev radius of a set depending on the behavior of the MAX-distance function and if the MAX - projection operator has not too many points of discontinuity.
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Extension of the Generalized Lebesgue–Feynman–Smolyanov Measure on a Hilbert Space Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-03-17 M. G. Shelakov
Abstract As is well known, on an infinite-dimensional Hilbert space, there is no countably additive sigma-finite locally finite nonzero translation-invariant nonnegative Borel measure (Andre Weil’s theorem, [1]). For this reason, to formalize the Feynman path integrals [2], one has to introduce a generalized translation-invariant measure (Lebesgue–Feynman in the sense of the definition in [2]) as a
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Almost Differentially Nondegenerate Nijenhuis Operators Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-01-24 D. Zh. Akpan
Abstract The paper is devoted to the study of Nijenhuis operators of arbitrary dimension \(n\) in a neighborhood of a point at which the first \(n-1\) coefficients of the characteristic polynomial are functionally independent and the last coefficient (the determinant of the operator) is an arbitrary function. We prove a theorem on the general form of such Nijenhuis operators and also obtain their complete
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A Metric Graph for Which the Number of Possible End Positions of a Random Walk Grows Minimally Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-01-24 V. L. Chernyshev, A. A. Tolchennikov
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A Corollary to a Triviality Theorem for Quasirepresentations of an Amenable Group in Reflexive Banach Spaces Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-01-24 A. I. Shtern
Abstract As is known, for a sufficiently small defect of a (not necessarily bounded) quasirepresentation of an amenable group in a reflexive Banach space \(E\) with dense set of bounded orbits, there is an extension of this quasirepresentation for which there is a close ordinary representation of the group in the space of this extension. In the present note it is proved that, if the original quasirepresentation
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On the Propagation of Local Perturbations in Yang–Mills Fields with $$SU(2)$$ Symmetry Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-01-24 A. S. Rabinowitch
Abstract In the present paper, the classical Yang–Mills equations with \(SU\)(2) symmetry are considered. The application of a generalized Wu–Yang form for field potentials results in a nonlinear differential equation of the second order. This equation is studied for a Yang–Mills field generated by a point-like source acting at the instant \(t=0\). In the examined case, the considered partial differential
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Finite Perturbations by Yield Stress of the Constitutive Relations of Nonlinear Viscous Media Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-01-24 D. V. Georgievskii
Abstract Flows of incompressible continuous media with tensor-linear constitutive relations and an arbitrary scalar nonlinearity are investigated in the cases of absence of the yield stress (nonlinear-viscous liquids) and its presence (viscoplastic media with nonlinear viscosity). The occurrence of a finite yield stress of a medium is interpreted as a finite perturbation of the scalar dependence linking
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Trace Formulas for Schrödinger Operators on a Lattice Russ. J. Math. Phys. (IF 1.4) Pub Date : 2023-01-24 E. L. Korotyaev
Abstract We consider Schrödinger operators with complex decaying potentials (in general, not of trace class) on a lattice. We determine trace formulas in terms of the eigenvalues and the singular measure and some integrals of a Fredholm determinant. The proof is based on estimates of the free resolvent and analysis of functions in Hardy spaces. Moreover, we obtain an estimate for eigenvalues and singular