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 note addresses a gap in earlier results on rings of quotients, namely that the system of elements denoted S1(S2) in R(S2) need not be multiplicatively closed. It introduces maximality of a multiplicatively closed system relative to an almost S-prime ideal and proves a characterization: such max…
The paper develops a metric theory for linear systems of ordinary differential equations with bounded uniformly continuous coefficients, motivated by variational equations along families of trajectories in dynamical systems rather than along a single trajectory. It studies the shift dynamical system…
The paper studies the Cauchy problem and a mixed boundary value problem for a second order parabolic system modeling heat and substance transfer, with boundary conditions not involving time derivatives. Using the contour integral method, it constructs a fundamental matrix of solutions in closed form…
The paper studies the construction of proper guiding functions for planar systems of ordinary differential equations whose leading terms are homogeneous vector fields and whose remaining terms are asymptotically smaller. Using the rotation index of the homogeneous field and an angular quasi-monotoni…
The note studies resolvents of generalized self-adjoint extensions of symmetric operators within a rigged Hilbert space framework \(G_{+}\subseteq G_{0}\subseteq G_{-}\). It first characterizes eigenvalues of a generalized self-adjoint operator by non-density of the corresponding range and derives d…
This paper studies quadratic variational control problems in real Hilbert spaces in which the cost includes both control effort and deviation from prescribed terminal or trajectory data. A general existence and uniqueness theorem is formulated for bounded linear operators, reducing the minimization …
This paper studies bounded and structurally constrained solutions of the linear differential equation x dot plus Ax equals phi in a complex Banach space, where A is a bounded operator whose spectrum does not meet the imaginary axis. It introduces a general class of function spaces defined by a trans…
This note studies extremal quasiconformal homeomorphisms between closed Riemann surfaces of genus greater than one under additional constraints: prescribed homotopy class, conformality on specified subdomains, and prescribed values or jets at finitely many points. It generalizes Teichmüller’s extrem…
This note studies whether an analogue of the Brown-McCoy radical exists for Lie algebras through the notion of modular classes of simple Lie algebras. Using free Lie algebras, holomorphs, and derivations, it proves that in the class of all Lie algebras the only modular class is the empty one, giving…
The paper studies a general quadrature process for singular integrals with a Hilbert-type kernel, based on a special trigonometric interpolation polynomial determined by a minimum norm condition. It derives quadrature formulas, establishes their convergence in mean and uniformly under appropriate sm…
The paper studies dimension estimates for products of compact Hausdorff spaces in terms of large inductive dimension. It introduces a class of bicompacta characterized by a weakened sum theorem for boundary closed sets and an extension property for refinements, and proves that finite products of spa…
The paper studies factorization of mappings from normal spaces into metric spaces with simultaneous control of topological weight and dimension on specified systems of subsets. It introduces several forms of factorizability and proves reduction lemmas showing that factorization for spaces with count…
This paper establishes Schauder-type estimates for solutions of parabolic systems in the sense of Petrovskii in spaces with refined Hölder exponents. Under the minimal integral condition on the exponent, it proves interior estimates and well-posedness with estimates for the Cauchy problem, while est…
This paper studies the correctness, in the sense of Petrovskii well-posedness, of first differential approximations associated with finite difference schemes for first-order hyperbolic systems. It defines the first differential approximation by expanding the difference operator in the mesh parameter…
The paper studies the connected components of the space of real elliptic differential operators in two variables with constant matrix coefficients, formulated through the associated real elliptic matrix pencils. It addresses a problem posed by Gel'fand, Petrovskii, and Shilov, extending earlier resu…
This note studies conditions under which Hausdorff spaces can be strengthened to minimal Hausdorff spaces and examines related properties of non-Hausdorff T1-bicompact spaces. It proves that a Hausdorff space which is a countable union of nowhere dense bicompact subsets and is densely embedded in a …
The paper studies the existence of solutions on the half-line for nonlinear ordinary differential equations of order n that satisfy prescribed alternating monotonicity conditions and a limiting value at the singular endpoint t equals 0. It introduces a priori growth conditions for the right-hand sid…
This paper studies the minimaxity of Hotelling’s \(T^2\)-test for testing a zero mean vector in a multivariate normal population with unknown covariance matrix, against alternatives specified by a fixed or lower-bounded noncentrality parameter. The argument reduces the minimax problem, within an inv…
This note proves a fundamental theorem of homological dimension theory for bicompact spaces, and hence for normal spaces via the maximal bicompact extension. The argument gives a simplified formulation using only cycles and homology on finite simplicial complexes, avoiding inverse limits, and relies…
This note studies the spectral system associated with a three-component parabolic heat and mass transfer equation with constant coefficient matrix. It constructs the fundamental matrix of solutions for the system A Delta u minus lambda squared u equals 0 under the parabolicity assumption, expressing…
The paper introduces two-dimensional characteristic coefficients for bivariate distribution functions relative to two fixed continuous strictly monotone one-dimensional distribution functions. It derives Fourier-type representations of a bivariate distribution in terms of these coefficients, gives s…
The paper introduces spaces of test and generalized functions of exponential type, motivated by applications to infinite-dimensional representations of compact Lie groups and to operators of the form with exponential spectral weights. It defines these spaces through countable Hilbert norms on sequen…
The paper develops a posteriori error estimates for approximate solutions of nonlinear operator equations in Banach spaces, interpreting an error bound as an existence result for an exact solution in a ball around the approximation. It first recalls standard estimates based on invertibility of the l…
Dynkin studies how a diffusion process on a smooth manifold with an affine connection induces a diffusion process on the bundle of tensors of arbitrary valence. The paper defines stochastic parallel transport along sample paths using Itô stochastic differential equations, derives the associated tens…
This paper studies when a measure space, in particular the trajectory space of a stochastic process constructed from finite-dimensional distributions, contains a Lebesgue subspace. It introduces dense measurable partitions and proves that the existence of a Lebesgue subspace implies the existence of…
The paper studies the identity problem for finitely presented semigroups whose defining words satisfy a half-overlap restriction, formulated as the class K_{1/2}. It introduces normal decompositions of words and uses a sequence of lemmas to prove that, in this class, every word is equal in the semig…
This paper studies extensions of recursive hierarchies beyond the constructive second class of ordinal notations using Kolmogorov type R-operations. It defines iterated bases and associated classes of sets of natural numbers, proves closure and separation properties for these classes, and shows that…
This paper studies directional differentiability of maximin functions of the form defined by maximizing over one variable after minimizing over another, with dependence on a parameter. In finite-dimensional settings, it gives formulas for the one-sided directional derivative with respect to the para…
The paper develops a method for studying isochronicity of analytic planar differential systems with a center or focus type singularity at the origin. Using the complex variable formulation and a formal transformation to the linear harmonic oscillator, it derives recursive consistency conditions that…
This note studies global minimization of a generally multi-extremal, twice differentiable functional on a separable Hilbert space when only noisy function values are observed. It proposes a search process combining stochastic approximation, based on random directional finite differences, with random…
This note studies periodic solutions of scalar neutral differential equations with a small deviating argument, continuing earlier work on initial value problems for such equations. For an equation involving a delayed state and delayed derivative, it compares the solution with an omega-periodic solut…
The paper studies convergence of approximate solutions to a linear self-adjoint operator equation in a Hilbert space, with attention to ill-posed cases and perturbations of both the operator and the right-hand side. Under assumptions controlling approximation errors, components along null eigenvecto…
This note extends Sobolev’s results on asymptotically optimal cubature formulas from constant weights to weight functions square integrable on a bounded domain. It defines uniformly distributed interpolation operators on regular lattices and proves an error estimate in the dual Sobolev space, showin…
This paper studies the Lie group classification of quasilinear second-order differential equations with at least three independent variables, using equivalence transformations and the geometry of the associated Riemannian space. It derives determining equations for admitted infinitesimal transformat…
This note generalizes an earlier construction of universal bundles for principal bundles with Hausdorff bases from closed Lie subgroups of general linear groups to arbitrary topological groups. It introduces elementary G-objects and locally T-trivial principal bundles, proves their relation to class…
The note establishes an a priori upper estimate for the principal radii of curvature of a closed strictly convex hypersurface in Euclidean space of dimension n plus 1, when its Gaussian curvature is prescribed through the product of the principal radii as a positive function of the outward unit norm…
This note develops an axiomatic treatment of autonomous dynamical systems with delay, modeled by continuous evolution from initial functions on a compact subset of the nonnegative half-line. It shows how such systems induce a Birkhoff dynamical system on the space of initial functions, and uses this…
The paper develops general integral representations for functions holomorphic in complete circular domains of several complex variables, extending earlier constructions of Cauchy, Temlyakov, and Bierski. It introduces a family of differential operators depending on positive and nonnegative parameter…
The paper develops a nonparametric formulation of regression experiment design in which the unknown regression function is treated as an arbitrary element of an L2 space rather than as a fixed linear combination of prescribed basis functions. It introduces randomized experimental designs for estimat…
This paper studies a boundary value problem for a first order system of partial differential equations of composite type in a bounded simply connected plane domain, in the case where one equation has multiple real characteristics and the other remains elliptic. After reducing the original system by …
The paper studies uniqueness and nonuniqueness for a two-point boundary-value problem in an infinite spatial strip for second-order linear partial differential equations with constant coefficients. Using an adjoint problem, Fourier transformation, and Gelfand-Shilov type function spaces, it relates …
This paper classifies finite-dimensional central simple Malcev algebras over an arbitrary field of characteristic zero. It shows that every such algebra is either a simple Lie algebra or belongs to a seven-dimensional family A(alpha, beta, gamma) associated with Cayley-Dickson algebras, with simplic…
This paper studies planar autonomous differential systems near an isolated singular point and estimates the number of elliptic sectors adjoining that point. Building on Bendixson’s bound and later proposed refinements, it uses branching indices of curves defined by the vector field and its derivativ…
This note studies an analogue of the Hardy-Littlewood equation, counting representations of a large integer n in the form p1p2 plus a sum of two squares, with p1 and p2 prime. Building on Linnik’s dispersion method and estimates associated with Hooley, Bredikhin, and Bombieri, the paper removes earl…
The paper addresses the problem of effectively determining the entire set of optimal solutions of a linear programming problem after one optimal basic solution has been found by the simplex method. It shows that, rather than first constructing the full feasible polyhedron, one can exploit zero reduc…
The paper studies stability with respect to initial data for two-level difference schemes with operator coefficients in a real Hilbert space. It reduces schemes of general form to explicit schemes through transformations involving the operators defining the energy norms, and then derives estimates f…
This note studies the qualitative behavior of solutions of two-dimensional periodic differential systems through the Poincare transformation, with emphasis on rough dissipative systems and separatrices of saddle periodic points. It formulates properties of stable and unstable separatrices contained …
This paper studies Sobolev type boundary value problems for elliptic operators on a closed manifold when the submanifold on which boundary values are prescribed itself has a boundary. Using boundary and coboundary operators in Sobolev spaces, the argument reduces the local analysis near the edge of …
The paper studies extremal problems for classes of analytic functions in the unit disk defined by an integral bound involving a convex nondecreasing function of the logarithm of the modulus, thereby generalizing Hardy type classes. Using a Smirnov type representation and associated measures, it anal…
The paper proves that, in the weak topology on the space of invertible measure-preserving transformations of the unit interval, the automorphisms without simple spectrum form a set of first category. The argument constructs dense \(G_\delta\) classes of transformations approximable along subsequence…
