SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 5847 papers in Mathematics
This paper addresses inverse spectral problems for Sturm-Liouville equations on a finite interval with a singular endpoint term of the form l(l+1)/(pi minus x) squared. It gives necessary and sufficient conditions for prescribed eigenvalues and norming constants to arise from such a boundary value p…
This note studies necessary and sufficient spectral conditions for the limiting amplitude principle for second order evolution equations governed by a semibounded Hilbert space operator. Under hypotheses on the analytic and boundary behavior of the resolvent kernel, it formulates results connecting …
This paper studies when the asymptotic behavior of solutions of a linear nonautonomous system is preserved under nonlinear perturbations whose Lipschitz constant is controlled by a given function. It establishes necessary and sufficient integral conditions, expressed through a fundamental family of …
This note formulates a constructive version of locally convex linear topological spaces, giving axioms for the underlying linear structure, neighborhoods of zero, continuity of addition and scalar multiplication, and comparison of topologies. It examines constructive analogues of closedness and sepa…
This note studies limits in measure and limiting functions for sequences of measurable functions, comparing their behavior with that of trigonometric series and series in normalized bases of spaces Lp, p greater than 1. It introduces narrow upper and lower limits in measure and associated sets of su…
This paper generalizes a theorem of Sklyarenko on extending perfect mappings from completely regular spaces with bicompact extensions to the setting of T1 spaces and omega alpha extensions. It proves several lemmas on Wallman extensions, maximal centered systems of closed sets, and the behavior of r…
The paper develops iterative formulas for refining approximate inverse matrices by applying the method of variation of a parameter to a matrix equation involving an auxiliary parameter matrix. Starting from an approximate inverse, the approach interprets refinement as numerical integration of differ…
This note studies approximation of bounded periodic functions in a Hausdorff-type metric defined through supplementary graphs, allowing treatment of functions with jumps under a modulus of nonmonotonicity. It establishes a general estimate for convolution approximants with nonnegative even kernels, …
The paper studies ill-posedness in optimal planning problems formulated as linear programming with possibly dependent constraint equations and data known only approximately. It shows by example that arbitrarily small perturbations of coefficients and right-hand sides can produce arbitrarily large ch…
This note develops a theory of the first variation for broad variational problems, including optimal control problems, formulated through quasiconvex families of measurable vector fields. It defines quasiconvexity, gives common examples involving essentially bounded and \(L^p\) controls, and uses an…
This note studies rates of convergence in the central limit theorem for sums of independent identically distributed random variables whose distribution lies in the domain of attraction of the normal law. It gives necessary and sufficient conditions for the uniform error in approximation by the norma…
This note studies sequences that are almost periodic with respect to generalized shift operators generated by ultraspherical orthogonal polynomials. Building on earlier work of Levitan, it defines the relevant scalar product and Fourier coefficients, then proves that Parseval’s equality holds for th…
The paper extends decomposition criteria known for groups to a broader class of algebras, including loops, equipped with a distinguished element and operations satisfying specified compatibility conditions. It develops a notion of normal divisor as a homomorphism kernel, proves characterizations via…
This note studies locally flat embeddings of the sphere of codimension two in Euclidean space and defines an equivalence relation for such multidimensional knots using stable homeomorphisms. It introduces connected sum for the resulting classes and states that, for dimensions at least four, these cl…
This note studies when commutative real algebras and torsion-free rings can be endowed with a structural order making them \(f\)-algebras or \(f\)-rings, and when that order is unique. Using annihilators as components, projections, fragments, and \(p\)-closed cones generated by sums of squares, it c…
This paper studies representation of small categories as full subcategories of categories built from binary relations, directed graphs, ordered relations, and certain topological spaces. It introduces admissible and strongly admissible mappings for relations, develops several constructions that pres…
This paper studies forced discrete impulse systems with one nonlinear block, formulated as vector difference equations with a scalar feedback nonlinearity. It derives frequency-domain conditions, expressed through the amplitude-phase characteristic of the linear part, that ensure dissipativity, exis…
The paper studies an inverse problem of potential theory: whether the shape and position of a bounded connected body can be uniquely determined from equality of its external Newtonian or metaharmonic potential with that of another body. It formulates uniqueness theorems for domains in Euclidean spac…
This paper studies an iterative method for finding a point in the nonempty intersection of closed convex sets in a real Hilbert space by successive projection onto selected sets. It proves weak convergence of the generated sequence under several index selection rules, including cyclic selection for …
This review presents Yu. A. Mitropolsky’s monograph on asymptotic methods for non-stationary nonlinear oscillations governed by differential equations with slowly varying coefficients. It outlines the book’s development of Krylov-Bogolyubov type techniques for systems with one and many degrees of fr…
The paper studies uniform approximation of solutions to polyanalytic and related elliptic equations of the form involving iterated complex derivatives, including the polyharmonic equation as a special case. Using a representation of sufficiently smooth solutions by analytic functions and a key lemma…
The paper studies a trigonometric analogue of Zolotarev’s extremal problem: among trigonometric polynomials of degree n with prescribed leading coefficients, it seeks those with minimal uniform deviation from zero on the full period. Using Chebyshev alternance and a criterion of Videnskii, it charac…
The paper studies mixed initial-boundary value problems on a semi-infinite interval in which the solution satisfies a hyperbolic equation on a finite subinterval and a parabolic equation on the remaining half-line, with possible finite jumps of the function and derivative at the interface. Using the…
The paper addresses the realizability of unimodular integral quadratic forms as intersection forms of simply connected closed smooth four-dimensional manifolds. Building on the classification of homotopy types by intersection forms, it constructs explicit four-manifolds using membranes, surgeries on…
This paper studies conformal metric properties of doubly connected domains and their role in generalized Blaschke products. It establishes uniform bounds for boundary distortion under classes of univalent conformal maps of annuli into the unit disk, with constants depending only on the modulus of th…
The paper studies a stochastic linear programming problem in which the right-hand sides of linear constraints are independent random variables with known means and variances. It compares the random feasible region with regions defined by shifted lower and upper constraints, uses Chebyshev bounds to …
This paper studies boundary properties and embedding type results for anisotropic Sobolev classes with weighted summability in smooth domains, where different coordinate directions may have different differentiability and integrability parameters. It identifies a class of regular domains, defined re…
This paper introduces a multidimensional analogue of the one-dimensional Green functions used in scattering and inverse scattering theory for the Schrödinger equation with a decreasing potential. It defines Green kernels associated with a non-self-adjoint Laplacian in exponentially weighted spaces a…
This paper studies how aggregating states in a finite reversible stationary Markov chain changes the spectrum of the associated stochastic matrix and when such aggregation preserves the Markov property. Using the spectral decomposition of a symmetric correlation table, it characterizes “stationary” …
This note studies boundary elements associated with quasiconformal mappings of domains in n-dimensional Euclidean space, continuing an earlier definition in terms of equivalence classes of regular sequences of subdomains. It proves that, for domains quasiconformally equivalent to a ball, every bound…
The paper studies the oblique derivative boundary value problem for a second order uniformly parabolic equation in a possibly noncylindrical domain with Hölder continuous data and coefficients. Its method derives boundary Schauder estimates by first treating the heat equation in a half strip with a …
The paper studies the representation of the modular group on spaces of cusp forms of even weight for a normal subgroup of finite index, a question connected with the structure of modular forms and Hecke operators. It proves a formula for the combined multiplicity of a nonprincipal irreducible charac…
This note studies the periodic problem in the calculus of variations for positive regular reversible functionals on closed differentiable manifolds, with particular attention to nondegenerate closed extremals and their iterates. Using Morse theory, Bott’s index formula, homological arguments for spa…
This review summarizes V. A. Pliss’s monograph on nonlocal problems in the qualitative theory of ordinary differential equations and nonlinear oscillations, with emphasis on systems with periodic time dependence and related autonomous systems. It outlines the book’s treatment of dissipative and conv…
The paper introduces incomplete Macdonald functions defined by splitting the standard integral representation at a finite limit, and notes their occurrence in parabolic partial differential equations for turbulent diffusion and in calculations of scintillation detector response to gamma radiation. I…
This paper studies smoothness properties of heat single-layer, double-layer, and volume potentials in domains bounded by time lines and moving curves. It formulates anisotropic Hölder-type classes adapted to the heat equation and gives regularity tables and norm estimates relating the smoothness of …
This note studies orders in a finite separable field extension over a Dedekind ring and the module-theoretic condition under which finitely generated torsion-free modules split as direct sums of ideals. Building on a previously proved sufficiency result and on a theorem of Bass, it proves that such …
This paper studies affine types of Voronoi decompositions associated with higher dimensional lattices and their relation to lattice coverings of Euclidean space by equal spheres. Using Selling frames and Voronoi reduction, it gives explicit parameter inequalities and simplex-chain descriptions for l…
