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
The paper studies small-amplitude periodic solutions near the stationary singular point of autonomous second-order dynamical systems satisfying symmetry assumptions. It reformulates the search for periodic motions of a given period as a nonlinear operator equation and applies topological and bifurca…
This paper gives necessary and sufficient conditions for the complete approximative solvability of broad classes of equations when both operators and right hand sides are approximated. It shows that, for sequences of linear mappings converging uniformly, all solutions of a limiting equation can be a…
This paper studies measures of Hausdorff type on metric spaces with a countable base, defined from countable Vitali covering systems with prescribed elementary measures. It proves that such measures have the F-property for analytic sets: finite-measure analytic sets contain closed subsets with measu…
This note studies linear functionals on the spaces of multivariable functions \(C_{s_1\ldots s_n}\) and \(L^p_{s_1\ldots s_n}\) that vanish on systems of generalized polynomials defined by prescribed one-variable function systems with nonzero Wronskians. It extends earlier representation results for…
This paper proves inverse theorems for polynomial approximation of functions on a finite interval, addressing the fact that classical Jackson type direct theorems do not have complete converses in this setting. Building on a strengthened Jackson estimate that improves approximation near the endpoint…
This paper extends several sharp results from univalent conformal mapping to non-univalent meromorphic or regular functions whose ranges have no common values. It develops derivative and value estimates in finitely connected domains, gives extremal systems, describes the attainable boundary for pair…
This note studies the Cauchy problem for a quasilinear hyperbolic equation in two independent variables by replacing the classical wave operator with Böğel’s generalized hyperbolic operator. Using normal families and an analogue of Peano’s method, in the style of Montel’s treatment of the Goursat pr…
The paper studies periodic solutions of a nonlinear self oscillation equation with a small parameter, under assumptions ensuring that the corresponding unperturbed equation has only periodic solutions. Using a previously developed method, it derives finite equations determining the leading positive …
This note studies the relation between points where a real function has an infinite derivative and points where its derivative is finite. It proves that, for any measure zero set of type F sigma delta contained in a G delta set, there exists a continuous increasing function whose derivative is posit…
This paper studies bounded non-self-adjoint operators of the class iOmega with continuous spectrum, focusing on when such operators can be transformed to a diagonal multiplication operator. Using triangular models, the author gives sufficient regularity and rank conditions on the non-Hermitian part …
This paper develops a local theory of nomography by expressing conditions for local nomographability in invariant form under admissible transformations of the variables. It defines and studies nomographic invariants built from the quantities associated with a function z = f(x,y), including determina…
This paper studies a one-dimensional filtration problem in an elastic-plastic regime, where the governing parabolic equation changes according to the sign of the time derivative of the pressure. The problem is reformulated as a single nonlinear equation containing an absolute value term, with the ha…
This note develops sufficient criteria for nonoscillation of the fourth-order differential equation \(y^{(4)}+(a(x)y')'+b(x)y=0\), where nonoscillation is understood in terms of the eventual absence of more than one double zero for any nontrivial solution. Using an analogue of Sturm comparison based…
This paper studies the extremal problem of maximizing the conformal radius at the origin among simply connected domains that are fundamental, up to cuts, for a doubly periodic translation group and that avoid a prescribed finite system of points and their translates. Using variational formulas for u…
This paper develops an analogue of the extension theory of Hermitian operators for operators that are symmetric with respect to a conjugation operator in a Hilbert space. It introduces the notions of J-symmetric and J-self-adjoint dissipative operators, characterizes J-self-adjointness by vanishing …
This paper extends the notion of an n-dimensional Cantor manifold to infinite-dimensional compact metric spaces, defining such a compactum as one that cannot be separated by any finite-dimensional closed subset. It addresses the relation between this concept and the open problem of whether every inf…
This note studies linear operators on the topological ring of analytic functions in several complex variables on a polyannulus, with convergence defined by uniform convergence on compact subannuli. It first states Fredholm-type invertibility results for operators that act diagonally on Laurent monom…
This paper develops improved finite difference schemes for the axially symmetric Dirichlet problem for the Laplace equation in cylindrical coordinates. Using a lemma that combines harmonic functions with logarithmic terms, it constructs alternative harmonic basis functions and derives five point and…
This paper studies infinitesimal rigidity criteria for surfaces of revolution subject to contour constraints, extending earlier results on ovaloids with planar openings to nonorthogonal constraints. The bending equations are reduced to a Fourier decomposition and ordinary differential equations for …
This note studies the homology groups of finite rank nilpotent associative algebras over an arbitrary field, with trivial coefficients, and the associated Poincaré functions formed from their Betti numbers. Using a special complete resolution, the authors derive structural relations and estimates fo…
This paper studies an inverse problem for first order systems of linear differential equations with a complex parameter, asking when the coefficient matrix can be recovered uniquely from the terminal fundamental matrix. It develops the problem through characteristic matrix functions of nonselfadjoin…
This paper studies local solutions near a singular point for systems of two Briot and Bouquet differential equations with holomorphic nonlinear terms vanishing to first order in the dependent variables. Extending earlier results of Picard and subsequent work on exceptional cases, it classifies the s…
This note studies the possible values of the exponent of an elliptic curve over the rational numbers, defined as the least positive degree of a divisor on the curve. Using Weil’s group of principal homogeneous spaces with a fixed Jacobian and its cohomological description, the paper analyzes relevan…
This paper studies operations and predicates on algebras that are definable by formulas of the restricted predicate calculus, extending the usual notion of derived operations as terms. For universally axiomatized classes of algebras, it proves that any formula defining a total single-valued operatio…
This paper studies upper bounds for the curvature of level lines, the images of circles under univalent conformal mappings in exterior domains. Using known estimates of Goluzin, Löwner, Privalov, and Bazilevich, it derives sharp curvature inequalities for the class of normalized functions with a sim…
This paper studies algorithmic recognition problems for invariant properties of finitely presented groups. Extending earlier results and using Novikov’s finitely presented group with unsolvable word problem, it proves that if an invariant property is possessed by some finitely presented group but ex…
The paper gives a method for converting certain monotone irreducible mappings of continua into monotone-open mappings by composing them with suitable continuous decompositions or small shifts of the target space. Under hypotheses on the connectedness of the set of points of uniqueness in domains, it…
This note studies the possible limit functions obtained from subsequences of partial sums of a trigonometric series on sets of positive measure. It introduces limit elements in a broad sense and a corresponding notion of closure in the narrow sense for sets of measurable functions. The main result g…
This note studies embedding and trace properties for a function space defined by completing smooth functions under a quadratic metric involving second derivatives, where the metric coefficients may degenerate on a rectilinear part of the boundary. Using Sobolev embedding results away from the degene…
This paper studies spectral functions of self-adjoint ordinary differential expressions of even order on intervals with regular or singular endpoints, using the generalized resolvent formula previously obtained by the author. It defines a characteristic matrix for each generalized resolvent, establi…
This note generalizes and refines the Siegel, Maass, and Selberg integral formula for positive definite symmetric matrices in the setting of homogeneous cones. It gives a representation-theoretic proof based on harmonic differential operators, irreducibility considerations, and Bochner’s theorem, wh…
The paper studies whether analytic functions given by Lebesgue Cauchy type integrals over closed rectifiable contours can be reconstructed from their nontangential boundary values, even when those boundary values need not be Lebesgue or Denjoy integrable. It introduces an A-integral along smooth con…
This note refines Kolmogorov’s notions of epsilon entropy for compact metric spaces by distinguishing relative entropy, defined with respect to a metric extension, from absolute entropy, defined through economical coverings by sets of bounded diameter. It proves that absolute epsilon entropy is the …
The paper studies a two-phase moving-boundary parabolic problem introduced by N. N. Verigin, related to the Stefan problem but involving two coupled diffusion regions and interface conditions. By transforming the moving boundary to a fixed coordinate system, the author derives integral representatio…
The paper introduces Lebesgue-Orlicz points by extending the usual Lebesgue point condition from \(L_p\) metrics to Orlicz norms associated with complementary \(N\)-functions. It establishes their position between ordinary Lebesgue points and points of continuity on sets of full measure, gives crite…
This note proves that the defective cohomology groups assigned to infinite-dimensional subsets of Hilbert space are invariant under different cell decompositions. The argument introduces cellular mappings between cells of fixed defect, defines an admissibility condition and a degree for such mapping…
The paper introduces the notion of a determining statistic, a statistic whose exact distribution uniquely reconstructs the parent distribution within a specified class, and presents this as a generalization of the classical moment problem. It studies homogeneous definite statistics with star-shaped …
This note decomposes the space of continuous tangent vector fields on the n-dimensional sphere into irreducible invariant subspaces under the rotation group. Using zonal fields determined by their values at a fixed pole, the argument derives the possible polynomial components, separates gradient and…
This note studies the behavior at infinity of eigenfunctions of self-adjoint operators in square-integrable function spaces, motivated by earlier results on Sturm-Liouville and Schrödinger operators. It proves that if a resolvent, or a suitable power of it, is an integral operator whose kernel satis…
This paper studies operators in generalized Orlicz spaces in connection with the weak-topological treatment of nonlinear Hammerstein integral equations. It first establishes necessary and sufficient conditions for a multiplication operator \(Hu=b(x)u(x)\) to map one generalized Orlicz space into ano…
This note studies well-posedness for selected boundary-value and Cauchy-type problems associated with partial differential equations, including equations of backward heat type and certain elliptic equations. The problems are reformulated as ordinary differential equations in a Hilbert space with unb…
This note formulates results on uniform approximation of continuous functions on a finite interval by linear combinations of eigenfunctions of a regular Sturm, Liouville problem with separated boundary conditions. It establishes direct estimates for best approximation in terms of moduli of continuit…
This note studies the reduction of quasiunitary operators in Hilbert space to triangular form, under finite-dimensional nonunitarity and a regularity condition inside the unit disk. It defines a normalized characteristic matrix function for such operators and uses Potapov’s factorization theorem to …
This note studies structural properties of groups with finite conjugacy classes and related locally normal and periodic groups. It gives a characterization of layer-finite groups as locally normal groups whose Sylow subgroups satisfy the minimal condition for abelian subgroups, deriving finiteness a…
This paper extends a variational problem of Hilbert from the complex plane to real \(n\)-dimensional space, considering functions with finite Dirichlet integral on the complement of a smooth hypersurface and prescribed linear jump-type boundary data. It formulates a class of admissible Sobolev funct…
This paper studies the Cartan differential graded algebra associated with a homogeneous polynomial ideal and its homology, viewed as a graded vector space. It introduces complete independence of generators in terms of the absence of nontrivial relations, relates Cartan homology to Koszul modules, an…
This paper studies lower bounds for tabulating and reconstructing functions from finite stored data under restrictions on the number of arithmetic operations. It formalizes an epsilon-representation by piecewise rational functions with parameters and barriers, then relates the number of stored param…
This paper studies local and global representation of solutions of the Euler, Poisson, Darboux equation with parameter 0 < c < 1 near an interval of the singular line y = 0. It proves that if either the boundary trace or the weighted normal derivative has analytic values on the interval, then the so…
