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 derives an error estimate for numerical approximations to a Fredholm integral equation of the second kind at a prescribed set of nodes. Using an arbitrary quadrature formula on those nodes, the argument expresses the discrepancy between the exact nodal values and a computed vector in terms…
The note proves a completeness criterion for the eigen and associated vectors of a polynomial operator pencil in a Hilbert space. It extends Keldysh’s result for linear pencils by reducing the polynomial pencil to a linear pencil on the orthogonal sum of n copies of the space, then applying estimate…
This paper studies Riemannian spaces fibered by totally geodesic parallel submanifolds whose associated holonomy group is one-parameter. Using Cartan’s exterior forms, it derives the structural consequences of such a holonomy: a transverse foliation, induced tensors on the base and on the space of t…
The paper refines an existing algorithm for a generalized linear programming problem: maximizing, over a closed convex polyhedron, the minimum deviation from a given family of hyperplanes. It reformulates the numerical procedure using Jordan eliminations analogous to those employed in the simplex me…
This paper studies modular representations of the group Z2 x Z2 over an algebraically closed field of characteristic 2, a basic case in which infinitely many indecomposable representations occur. By translating the problem into the module theory of a quotient of the group algebra, the classification…
This paper studies multiplicative representations of analytic operator functions in a separable Hilbert space that are holomorphic off a bounded real set, have a compact-operator expansion at infinity, and satisfy a J-nonexpansive positivity condition in the upper half-plane. Extending earlier finit…
This paper addresses the non-uniqueness of Levi-Civita representations of Riemannian metrics arising in the theory of geodesic mappings, focusing on exceptional metrics whose associated spaces have constant negative curvature. It reduces the description of all such representations to two tasks: clas…
This note formulates direct and inverse scattering problems for one-dimensional difference equations, first with scalar coefficients and then with operator coefficients in a Hilbert space. Using radiation conditions, weighted Banach spaces, compactness of associated resolvent-type operators, and Fre…
This note studies constant coefficient differential operators through a notion of partial hypoellipticity for their defining polynomials, measured by growth of imaginary parts of zeros in selected variables. Using the Seidenberg Tarski theorem and a Hörmander type criterion, it gives necessary and s…
This paper addresses a mixed boundary value problem for the Laplace equation describing the stationary temperature field in an unbounded hollow cylinder. The inner surface is insulated, while the outer surface is prescribed a temperature distribution on one half and exchanges heat with the surroundi…
This paper develops a refinement of Kantorovich’s majorant method for operator fixed point equations in complete metric spaces. It introduces the notion of a strict majorant for an operator satisfying only Lipschitz-type assumptions and proves that the scalar equation defined by such a majorant prov…
The paper studies Bergman and Cauchy-Szegő integral kernels for Siegel domains of the second kind, with emphasis on affinely homogeneous domains associated with self-adjoint cones. Using the action of linear automorphism groups, the kernels are reduced to functions on the cone, and their normalizati…
This paper studies approximation in the mean by algebraic polynomials for analytic functions in bounded simply connected domains, relating the best \(L_p\) approximation over a domain to integral moduli of continuity and Lipschitz type conditions. It proves direct and inverse theorems for domains wi…
This note proves a real analogue of the Morozov and Borel conjugacy theorem for linear Lie groups. After developing criteria for triangular real linear groups and a fixed point argument on the flag variety, it introduces decomposable groups admitting a polar decomposition into compact and triangular…
The paper studies convergence of a finite difference scheme for the multidimensional heat conduction equation with variable coefficients under mixed initial and boundary conditions. Using the equivalence theorem for stability and consistency, the authors analyze the step operator through a sequence …
This note studies transition solutions of nonlinear ordinary differential equations of arbitrary order, motivated by shock wave structure and uniqueness questions for hyperbolic quasilinear systems. For a quasilinear equation with a linear differential operator whose characteristic roots satisfy spe…
This note studies a model of a point pulse moving around a circle with velocity depending on the time elapsed since the pulse last passed each point. By unrolling the circle to a line, the authors reduce the one pulse case to an integral equation for this elapsed time function and prove, under diffe…
This note constructs counterexamples concerning nilpotent and periodic sets of automorphisms of groups, especially automorphism groups of abelian groups. Using wreath products, locally finite p-groups, and explicitly defined automorphisms of direct products of cyclic groups, it shows that groups of …
This paper studies conjugate functions, singular Cauchy integrals, and Cauchy type representations using a general linear Phi integral that includes the previously used A and B integrals as examples. It proves that several results formerly derived from special properties of the A integral follow ins…
This note gives characterizations of paracompact and finally compact, Lindelöf, spaces in terms of mappings subordinate to arbitrary open covers. It proves that a Hausdorff space is paracompact exactly when every open cover admits an associated continuous omega-mapping onto a metric space, and that …
The paper extends de Rham and Dolbeault type methods to cohomology with coefficients in certain non-Abelian sheaves, interpreting the classification of principal fibered spaces through differential forms with values in Lie algebra bundles. It develops integrability criteria for equations defined by …
The paper studies invariant torsion-free affine connections on a homogeneous space defined by a Lie group and a framed chain of subgroups. Using decompositions of the Lie algebra and the associated structure equations, it defines a multiparameter family of so-called C' connections and characterizes …
This note studies the first boundary-value problem for the nonstationary Navier-Stokes equations in three spatial variables, aiming to weaken previously known conditions for classical solvability. Using the theory of nonstationary hydrodynamic potentials, the authors give simplified formulas and est…
This paper studies convex polyhedral sets in arbitrary real linear spaces, defined as solution sets of finite systems of linear inequalities. It establishes strict separation of disjoint convex polyhedral sets by a plane, relates this separation to corner cones embracing the sets, and extends the di…
The paper studies the representation of Klein spaces by Kawaguchi metrics, using invariant curve functionals and their associated indicatrices. It argues that for any Klein space with automorphism group G, one can construct a Kawaguchi metric whose automorphism group is exactly G and which admits no…
This note characterizes classes of models that are finitely axiomatizable in the narrow predicate calculus without restricting the form of the axioms. It reduces finite axiom systems to single prenex axioms with alternating quantifiers, introduces generalized covering relations between models and su…
This note proves that for every complete orthonormal system in \(L^2[0,1]\) there is a continuous function whose Fourier series, after a suitable rearrangement of its terms, diverges almost everywhere. The proof first establishes the result for the Haar system by constructing a bounded function with…
This paper studies multidimensional principal value singular integral operators on bounded smooth manifolds in Euclidean space, with kernels determined by positive definite variable quadratic forms and homogeneous singularities. It proves boundedness of these operators in Lp spaces for p greater tha…
This paper studies solvability conditions for a boundary-value problem for a two-component parabolic system with constant real coefficients in an infinite strip, with zero initial data and mixed linear boundary conditions. The authors represent solutions by heat-kernel double-layer potentials associ…
This paper studies inverse problems for sums of finite sets of integers and residues modulo a prime, focusing on structural consequences when the sumset or double sumset is small. Using exponential sums and a concentration lemma for points on the unit circle, it proves that if the number of residues…
This paper derives asymptotic formulas for the Green function of one dimensional Sobolev Galpern equations with constant coefficients, for fixed positive time as the spatial variable tends to infinity. Using the saddle point method, it first treats equations of first order in time and separates the …
This note studies maximum-type estimates for positive solutions of second-order elliptic equations in divergence form with lower-order terms, extending earlier results that required either a nonpositive zeroth-order coefficient or vanishing first-order coefficients. Under ellipticity, boundedness, a…
The paper studies nonnegative solutions of the eigenvalue equation for the Laplace Beltrami operator on a negatively curved symmetric space whose motion group is isomorphic to the complex unimodular group. Using Martin’s method, it constructs an explicit Green’s function in terms of spectral coordin…
This note studies automorphisms of nilpotent groups, focusing on when a finite set or group of automorphisms is nilpotent relative to the underlying group. It proves that for a nilpotent group, a finite set of automorphisms is nilpotent relative to the group exactly when it is nilpotent relative to …
This note studies the realization of functions over a fixed alphabet by restricted classes of algorithms, extending earlier questions about minimal alphabets for normal algorithms. For algorithms of type sigma, it gives several nonrealizability criteria for covering and stretching functions, derives…
The paper studies a nonlinear perturbation of a normally solvable linear operator equation in complex Banach spaces, with a small parameter and polynomial nonlinear terms. By rescaling the unknown and applying branching theory, including Newton diagram arguments and a generalized Jordan chain relati…
This note studies dynamical systems whose right-hand sides are multivalued or discontinuous, motivated by systems with incomplete information such as relay or hysteresis characteristics. It represents multivalued values as images of a unit ball under essentially bounded measurable mappings, thereby …
The paper studies the Cauchy problem for a linear parabolic system with a bounded continuous matrix coefficient multiplying the unknown vector and bounded continuous initial data. It derives an integral equation formulation, expands its solution by successive substitutions, proves absolute and unifo…
This paper develops a framework for continual integrals associated with groups of operators in a Hilbert space using generalized elements and kernels defined through a complete system of generalized eigen-elements. It derives product-limit representations for generalized kernels of evolution operato…
This note studies generalized boundary-value problems for second-order quasilinear elliptic equations whose coefficients have power growth. The method introduces a parameter into the equation to reduce it, for fixed parameter values, to an elliptic problem with bounded nonlinearities, then passes to…
The paper develops a method for reducing periodic boundary value problems of mathematical physics to integro-differential equations containing singular Cauchy integrals. Using finite Fourier transforms, the author treats the biharmonic equation in planes, half-planes, strips, and configurations with…
This paper determines the exact upper bound for the best uniform approximation by trigonometric polynomials of degree at most n on the class of periodic differentiable functions whose first derivative has a prescribed convex modulus of continuity. The proof uses a lemma approximating functions with …
The paper studies uniform Chebyshev approximation of a continuous real function on a compact set by generalized polynomials whose coefficients are restricted to a prescribed closed set, allowing nonlinear relations among the coefficients. Using a geometric interpretation in coefficient space, it pro…
This note studies prescribed convergence and unbounded divergence sets for trigonometric Fourier series, with attention to pairs of conjugate series. Building on constructions of Kolmogorov and the Herzog, Piranian, and Zeller method, it proves two auxiliary lemmas for producing trigonometric polyno…
This paper studies boundary value problems for a class of higher order parabolic and backward parabolic equations with principal part of order 2p in domains whose boundary may have characteristic contact with horizontal time planes. It proves unique solvability in appropriate Slobodetskii type Sobol…
This note proposes a generalization of locally compact unimodular groups, called ring groups, intended to accommodate both groups and the noncommutative objects arising as their duals. The construction replaces the commutative algebra of bounded functions on a group by a standard operator ring equip…
The note constructs a homeomorphic embedding of separable Hilbert space into itself whose image consists only of points with coordinates between zero and one in a fixed orthonormal basis. The construction first replaces signs by separate coordinate directions to obtain nonnegative coordinates, then …
