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 trace properties of functions in weighted first order Sobolev classes on a half-space, where each first derivative is integrable with a possibly different power weight degenerating at the boundary. It establishes a direct trace theorem identifying the boundary values as elements of…
The paper studies polynomial ideals in complete spaces of infinitely differentiable functions with prescribed polynomial growth, motivated by solvability and homogeneous solution problems for constant coefficient partial differential equations in spaces of slowly increasing functions or functionals.…
This paper develops a theory of radicals for group pairs, where one group acts by automorphisms on another. It defines abstract properties of group pairs, associated theta-radicals in the acting group and in the domain of action, and studies locally stable and locally theta elements under closure co…
For each prime number q, the paper constructs a class of three-dimensional compacta P3(q) as inverse limits of polyhedra obtained by controlled tube identifications generalizing Pontryagin’s compactum P2(q). It analyzes their homological and cohomological dimensions with several coefficient groups, …
The paper studies the absolute minimum of an integral functional over piecewise smooth curves whose derivative is constrained through a parameter with bounded range. By transforming the independent variable along extremal boundary families, the problem is reformulated in terms of generalized lines w…
This note studies rearrangements of Fourier series with respect to the Haar system, general bases in L2, and orthonormal complete systems, focusing on almost everywhere divergence and nonsummability under arbitrary summability methods. It introduces property D for series whose terms can be rearrange…
The paper establishes existence and uniqueness results for the first boundary value problem for a one dimensional quasilinear parabolic equation with coefficients depending on time, space, the solution, and its spatial derivative. It weakens earlier growth assumptions on the ratio of the lower order…
This paper generalizes the Cantor-Hausdorff completion process beyond metric and uniform spaces by introducing Cauchy directions, defined through primary ideals of an open base in a regular Hausdorff space. It develops basic convergence properties of these directions and proves that suitable equival…
This note studies semigroups through order-theoretic properties of their lattices or posets of subsemigroups, distinguishing between the ordinary subsemigroup structure and the version enlarged by the empty set. It gives structural characterizations for semigroups whose subsemigroups are linearly or…
This note studies infinitesimal rigidity of closed surfaces with positive extrinsic curvature in Riemannian spaces, focusing on surfaces not homeomorphic to the sphere. For a surface homeomorphic to a torus, the argument uses conformal coordinates associated with the second quadratic form, passes to…
This paper studies linear differential expressions with polynomial coefficients whose order is reduced by the generalized differentiation operator with Euler Cauchy kernel. Under regularity conditions making infinity a regular singular point, the authors derive algebraic conditions on the transforme…
This paper gives an invariant construction of spaces with centro-projective connection from a third-order differential neighborhood using Cartan’s exterior differential equations for the prolonged pseudogroup of analytic transformations. It represents such a space as an n-dimensional submanifold in …
This note introduces isotropic flows, a class of tangent dynamical systems on spaces of frames over a Riemannian manifold in which the speed is constant and the curvatures of trajectories depend only on the base point. It proves that such flows preserve the natural measure on the frame space, relate…
The paper extends a classical existence criterion for meromorphic functions on a closed Riemann surface with prescribed principal parts to quasianalytic functions satisfying a first order elliptic equation. Using periods of complex normalized quasianalytic differentials and residue computations over…
This paper develops a local differential-geometric theory for a pair of second-order ordinary differential equations on the plane under arbitrary analytic point transformations. Using Cartan-type frame canonization for the representation space of the infinite transformation group, it constructs inva…
This paper studies local geodesic surfaces in a 2n-dimensional manifold equipped with a complex structure and a torsion-free almost complex affine connection. Using adapted frames and complex differential forms, it relates analytic real submanifolds of the manifold to complex analytic submanifolds o…
This paper identifies a class of quasilinear systems written in divergence form through derivatives of generating functions and shows that it includes several equations of mathematical physics, including variational Lagrange equations, crystal optics, and gas dynamics. The author gives explicit redu…
This note develops a formulation of asymptotic methods for nonlinear oscillations based on separating motion into fast unperturbed dynamics and slow evolutionary dynamics. For perturbed systems with a small parameter, it derives a necessary and sufficient commutation condition for exact separation a…
This note studies Paley-Wiener type questions for the Hilbert space of Fourier transforms of square integrable functions on a bounded domain, focusing on when integration over a measurable subset of frequency space defines a norm equivalent to the usual \(L^2\) norm. It introduces a quantity measuri…
The paper develops an asymptotic treatment of scalar diffraction by an elliptic cylinder, with extensions to an ellipsoid of revolution, in the high-frequency regime when the eccentricity may approach unity. For the Dirichlet problem on an elliptic cylinder, the Green function is represented through…
This paper studies inverse spectra and their relations to dimension theory, especially polyhedral, simplicial, and combinatorial spectra and the dimensions of their limit spaces. It gives criteria for an inverse spectrum of compact spaces or finite complexes to have a limit of covering dimension at …
The paper develops a construction representing compact topological spaces as limits of direct spectra of finite discrete sets, in contrast to the standard inverse spectrum representation. It defines spectra equipped with a proximity relation, constructs threads and pencils, and shows that these dete…
This letter examines a claimed generalization of Voronoi’s normal basis for cubic fields to algebraic fields of arbitrary degree. The authors identify an error in B. Epelbaum’s proof, arguing that the relevant systems of equations do not yield the asserted additional relations because their independ…
The paper constructs continual analogues of orthogonal polynomials for spectral measures whose support is the positive half-axis with finitely many removed intervals. For two explicit absolutely continuous weights, it studies the associated entire functions analogous to cosine and sine transforms an…
This note derives integral limit theorems for large deviations corresponding to earlier local results for sums of independent random variables. For identically distributed centered variables with finite positive variance, it gives uniform asymptotic formulas for the tails of normalized sums in range…
This paper gives a criterion for when two normally embedded Banach spaces are related in the sense of belonging to a continuous normal scale with logarithmic convexity of norms. The main result states that, for a Banach space E1 densely and norm-decreasingly embedded in E0, relatedness is equivalent…
This paper studies how spectral functions for a Sturm-Liouville equation are related when the differential expression and terminal boundary condition are fixed but the initial conditions are changed. Using functions of the second kind and their Stieltjes transforms, it derives formulas connecting th…
This paper estimates a class of trigonometric sums whose phases have coefficients with descending powers of a prime modulus. Using Vinogradov’s mean value theorem, a lemma of Korobov, and the special structure of the polynomial phase, it proves a power saving bound for these sums when the prime is s…
This note defines and studies crossed products of an arbitrary semigroup with identity and an associative ring with identity, using a semigroup action by automorphisms and an invertible factor system. It extends several questions and results from group rings to this broader setting, proving that cro…
The paper generalizes Nash’s continuity result for uniformly parabolic equations by deriving an a priori Hölder modulus of continuity for bounded solutions of linear divergence-form parabolic equations with bounded lower-order terms and inhomogeneity. The estimate is proved first for equations witho…
This note studies translation surfaces of constant curvature and related structures in differential geometry. Using a conjugate Chebyshev net of translation curves, the author derives the Gauss and Peterson-Codazzi equations, transforms them by taking the coordinate-line curvatures as variables, and…
The paper studies a boundary value problem for the two-dimensional heat equation in a half-plane with zero initial data and a general constant-coefficient differential boundary condition on the boundary. Using heat-potential representations, the boundary trace is reduced first to an integro-differen…
This paper addresses the global isometric immersion of a closed two-dimensional Riemannian manifold homeomorphic to a sphere into a complete three-dimensional Riemannian space. It proves that if the manifold has Gaussian curvature everywhere greater than a constant c and the ambient sectional curvat…
This paper studies normal and subinvariant subgroup structure in the multiplicative groups of noncommutative division rings. It first shows that any division ring can be embedded in a formal Laurent series division ring whose multiplicative group has an infinite descending invariant series with cent…
This note studies linear methods for approximating continuous doubly periodic functions whose increments are controlled by two prescribed moduli of continuity. For matrices of Fourier multipliers satisfying monotonicity and sign conditions on second and mixed finite differences, the paper derives an…
This paper studies measurable partitions associated with measure-preserving automorphisms of Lebesgue spaces, focusing on the relation between entropy, Pinsker’s maximal zero-entropy factor, and Kolmogorov automorphisms. Using conditional entropy identities and limiting arguments for increasing sequ…
The paper studies multidimensional surfaces in affine space whose asymptotic quadratic forms can be simultaneously reduced to canonical form, equivalently surfaces carrying a net of conjugate lines. Using moving affine frames and the matrix of eigenvalues of the asymptotic quadratic forms, it relate…
This paper constructs integral equation kernels for periodic solutions of Whittaker’s differential equation, with periods pi and 2 pi, by reducing the kernel condition to auxiliary differential equations. Two families of kernels are derived: one based on separated products involving confluent hyperg…
This paper addresses the difficulty of decomposing an unbounded operator into real and imaginary parts when the operator and its adjoint have different domains. Using generalized elements of a Hilbert space, it defines a basic-element manifold and studies operators whose inverse has a finite-dimensi…
This note studies how solutions of mixed boundary value problems for linear parabolic equations in one space variable depend on variations of the moving lateral boundary curves. Using Gevrey’s heat potential method, it establishes estimates for simple and double layer heat potentials under Hölder an…
This paper studies multipoint finite difference methods for the Cauchy problem for first order ordinary differential equations, allowing implicit and explicit schemes with arbitrary numbers of points. It gives necessary and sufficient conditions for unconditional convergence under continuity and Lip…
This note studies when the inverse limit of an inverse spectrum of exact sequences of discrete Abelian groups remains exact, rather than only semi-exact. For spectra indexed by a directed set with a countable cofinal subset, it proves sufficient epimorphism conditions on the bonding homomorphisms, f…
The paper studies a boundary value problem for piecewise analytic functions on a Lyapunov contour, involving values at a point and at its image under an orientation reversing involution, as a generalization of the Carleman problem. Under Hölder and compatibility assumptions on the coefficients, the …
The paper studies the mathematical problem of inelastic scattering represented by an infinite system of coupled Helmholtz equations in three-dimensional space, with outgoing radiation conditions for elastic and inelastic scattered waves. It reformulates the system as an operator equation in the Hilb…
This note studies distortion estimates for quasiconformal mappings of the unit disk and for Ahlfors classes of quasiconformal mappings in the mean. Using a recent improved bound for the Teichmüller function, it refines Lavrent’ev’s modulus distortion theorem to a sharp two-sided estimate for distanc…
This note studies the emergence of conditionally periodic motion on a torus from a degenerate family of periodic motions, for analytic differential equations of the form dy/dx equals a small perturbation. Arnold treats the case in which the unperturbed rotation number is zero and proves that, under …
This note proves an identity expressing the L2 norm squared of a function on the unit interval as an infinite sum of squares of L1 means generated by a simple iterative procedure. Starting with a function y, the authors define successive functions by subtracting from the absolute value of the preced…
This paper formulates an algebraic-geometric analogue of Kodaira’s projective embedding theorem for nonsingular complete abstract algebraic varieties over an algebraically closed field of characteristic zero. It proves that if a divisor has positive top self-intersection and positive intersection wi…
This note studies when continuous functions on a domain in Euclidean space can be uniformly approximated by finite sums of one variable continuous functions evaluated along prescribed linear directions, interpreted as superpositions of plane waves. The authors formulate directions as points in proje…
The paper studies approximation in Sobolev and Slobodetskii type spaces on domains of Euclidean space, focusing on when functions in the spaces defined by highest order generalized derivatives can be approximated in the corresponding norms by functions smooth in the whole space. It introduces geomet…
