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 when the exact Künneth sequence for tensor products of complexes splits, especially in the case where only one factor is torsion free. It gives an explicit two term example, with one complex over the integers and one over the cyclic group of order 8, in which the degree one Künneth…
The paper studies linear operators on the space of continuous periodic functions that take values in trigonometric polynomials of bounded order, classifying such operators by an averaging procedure invariant under translations. It establishes a one-to-one correspondence, with natural algebraic inter…
The note studies representation numbers of positive definite integral quadratic forms in an odd number of variables through generating series connected with modular forms. For a squarefree parameter l, it defines weighted sums of the representation numbers r_f(lt²) and proves that their generating f…
This paper studies extremal properties of regular solutions to linear elliptic equations under general assumptions on the zeroth order coefficient and the right hand side, without requiring fixed signs for these functions. Using Chaplygin’s theorem on subcritical domains, it proves a criterion exclu…
This paper studies when topological spaces arise as images of metrizable spaces under continuous mappings with openness, closedness, compact fibers, or related conditions. It proves that a T1 space has a uniform base exactly when it is an open continuous compact image of a metrizable space, with a z…
This paper extends Sturm comparison and oscillation theory to strongly elliptic second order systems with symmetric matrix coefficients. It proves a comparison theorem showing that, under coefficient inequalities, the existence of a nontrivial solution of one system vanishing on the boundary forces …
This note studies when the root functions of an ordinary linear differential operator on a finite interval form a Riesz basis in the space of square integrable functions. For operators of arbitrary order with sufficiently smooth summable coefficients and strongly regular boundary conditions, the pap…
The paper studies inclinations between linear subspaces of a Banach space and their relation to the existence and stability of bases. It proves auxiliary results showing that finite-dimensional subspaces of an infinite-dimensional Banach space can be separated, in the sense of inclination, from suit…
The paper derives boundary growth estimates in the L2 metric for generalized solutions of elliptic-type Euler equations of arbitrary order associated with a positive definite Dirichlet integral, primarily in two dimensions with extension to higher dimensions indicated by analogy. Using normal coordi…
This note presents several theorems on embedding subgroups in finite groups under generalized Sylow-type hypotheses. It defines the strong \(N\)-Sylow condition for normalizers of \(\tau\)-subgroups and proves that, when a group contains a subgroup decomposed as a product of a \(\sigma\)-Hall subgro…
This paper studies computability questions for abelian groups equipped with constructive numberings, focusing on periodic parts, primary components, stability of numberings, and torsion-free groups of finite or countable rank. It proves that the periodic part of a constructive group is recursively e…
This paper studies a generalized form of Cayley’s problem on the congruence or collinearity of pencils and bundles determined by tetrahedra, plane point configurations, and conic sections. It proves two projective geometric theorems establishing finite or algebraic loci of corresponding points, incl…
The note studies how strict inequalities between the moduli of consecutive roots of a complex polynomial can be detected during transformations by the Lobachevsky-Graeffe method. It proves a necessary and sufficient criterion for the inequality |z_m| < |z_{m+1}| in terms of limiting ratios of select…
The paper studies lower bounds for the norms of linear operators that map continuous periodic functions to trigonometric polynomials of degree at most n, under approximate reproduction conditions on polynomials. Using averaging identities and the known logarithmic growth of Fourier projection norms,…
This note studies two-dimensional dually normalized surfaces of class D2 immersed in four-dimensional Euclidean space. Using the differential equations of such surfaces, it analyzes congruences of normals, determines their focal points, and introduces axes of curvature in the normal plane, with asso…
This paper studies extremal properties of regularly monotone polynomials on the interval [0,1] within subclasses determined by prescribed type numbers and endpoint monotonicity conditions. Using generalized Euler-Bernstein polynomials and associated sequences of generalized Euler-Bernstein numbers d…
The paper presents a complex-variable method for solving the boundary-value problem for the stationary linearized Navier-Stokes system in a plane disk with prescribed velocity on the boundary. By rewriting the system in terms of complex derivatives, the solution is represented through two holomorphi…
This paper studies uniform convergence of variational and approximation processes in domains with zero-angle conical boundary points, extending earlier results that assumed a cone condition. It derives pointwise estimates for functions in Sobolev-type spaces \(W_p^{(l)}\) in terms of integral norms,…
This paper introduces weak isomorphism for measure-preserving automorphisms, defined by mutual realization as homomorphic images, and studies its relation to entropy, spectral invariants, and the class of Kolmogorov automorphisms. It develops a method based on perfect partitions associated with an a…
This paper studies the nomographability of functions of several variables represented implicitly by determinants of admissible Massau matrices. It introduces Gronwall functions and associated functions for such matrices, derives differential identities they must satisfy, and relates them to a given …
This paper studies the asymptotic distribution of primitive integer points on quadratic cones, beginning with the cone defined by x squared plus y squared equals z squared in the region 0 less than z less than or equal to h. Using the standard parametrization of primitive Pythagorean triples, Möbius…
The paper studies approximation of two-variable periodic functions in classes defined by an \(L_p\) bound on a linear combination of Weyl fractional partial derivatives of orders \(r_1\) and \(r_2\). For the cases \(\theta=0\) and \(\theta=\pi\), it derives asymptotic formulas for the maximal deviat…
The paper studies constant coefficient hypoelliptic equations in the whole real space whose characteristic polynomial has real zeros forming smooth closed hypersurfaces with nonzero total curvature. A fundamental solution is constructed by an integral over a contour analogous to Hörmander’s ladder, …
This note studies topological analogues of FC-groups, especially groups whose conjugacy classes, or closures of conjugacy classes, are bicompact, with emphasis on locally bicompact groups. Using a lemma on bounded conjugation orbits of linear transformations, it proves that connected semisimple Lie …
This paper develops direct and inverse embedding theorems for a broad class of anisotropic fractional function spaces defined by norms involving directional differences, partial derivatives, mixed Lebesgue norms, and functionals of maximization type. It introduces the relevant class of functionals, …
This note examines whether written numerals and alphabetic characters exhibit statistical regularities when classified by topological genus, understood as the number of enclosed regions in a sign. Using decimal numerals and several scripts, including Russian, Latin, Gothic, Greek, Devanagari, Kannad…
This paper extends Martin boundary theory from the Laplace operator to a second order linear elliptic operator in an arbitrary domain, allowing possible degeneracy at the boundary, and relates the construction to the associated killed diffusion process. It establishes that a nonnegative fundamental …
This paper studies series of the form formed from an entire function evaluated at scaled arguments, with complex scaling sequences of finite density type. It gives convergence domains for such series, including a star-shaped domain described through the angular distribution of the scaling sequence a…
This note studies when Serre’s upper bound for the Poincaré series of a commutative Noetherian local ring is attained, using the homology of its Koszul complex on a minimal system of generators of the maximal ideal. It gives a necessary and sufficient condition: equality holds precisely when multipl…
This note studies the mean number of divisors of algebraic integers in imaginary quadratic fields, restricted by a norm bound and by the argument lying in a prescribed angular sector. It develops analytic continuations, functional equations, residue formulas, and critical strip estimates for Epstein…
This note studies finite difference methods for a model Cauchy problem for the Laplace equation, an elliptic problem that is ill-posed in the usual sense but well-posed under Tikhonov-type a priori restrictions. Using Fourier representations and mesh norms adapted to the imposed bounds, it derives e…
The paper develops a scale of spaces L_p^r intended as a direct extension of Sobolev spaces W_p^(l) to noninteger orders of differentiation for all p greater than 1. It defines generalized partial derivatives of arbitrary order through Fourier-transform multipliers and convolution operators on suita…
The paper addresses nonuniqueness for nonlinear parabolic systems with discontinuous initial data, following a correction to an earlier two-equation example. It constructs a three-equation system in one spatial variable by comparing self-similar solutions with diffusion coefficients depending on the…
This note formulates solvability conditions for generalized Neumann problems for the Laplace operator, treating both nonhomogeneous boundary fluxes and homogeneous boundary conditions with interior data. Using capacitary estimates and classes of domains or boundaries defined through conductors and 2…
This note extends Phragmen-Lindelof type results for harmonic functions in a half-cylinder from circular and rectangular cross-sections to an arbitrary domain whose lateral boundary is a Lyapunov surface. It proves that if a harmonic function and its normal derivative on the boundary decay like O(x …
This paper studies regularity and solvability for general second order quasilinear elliptic equations not necessarily representable in divergence form, extending gradient Hölder estimates previously known in two independent variables to arbitrary dimension. By refining De Giorgi type methods, it pro…
The paper proves Smale’s conjecture that the geodesic flow on the space of line elements of a compact Riemannian manifold with everywhere negative curvature is structurally stable. It formulates hyperbolicity conditions for a nonsingular flow, requiring a continuous invariant splitting into exponent…
This paper studies analytic iteration for transformations of two variables near a fixed point, seeking one-parameter families satisfying the group law and agreeing with a given analytic map at unit time. Under nonresonance and sign conditions on the characteristic roots, it establishes formal existe…
This note extends the method of separation of variables to stationary scattering by a body of arbitrary shape, without requiring the boundary to coincide with coordinate surfaces. The exterior Helmholtz solution is expanded in spherical harmonics, and Green’s formula is used to express incoming and …
The paper studies local finiteness conditions for single-layer p-groups, that is, p-groups whose elements all have order at most p. Using Kostrikin’s theorem on finite single-layer p-groups, it proves that such a group is an extension of a group with no nontrivial locally finite quotients by a local…
This paper studies transformation operators for Sturm-Liouville differential equations on the positive half-line in the non-self-adjoint case, allowing complex potentials and boundary parameters. Under the integrability condition that the first moment of the potential is finite, it uses the principa…
This note studies bounded classical solutions of parabolic boundary-value problems in infinite time cylinders, without prescribed initial conditions. Using a method adapted from elliptic theory and maximum principles, it proves existence and uniqueness results for linear Dirichlet and Neumann proble…
The paper develops a class of weighted Sobolev type spaces in Euclidean space defined by radial differential operators, including fractional radial derivatives, with weights determined by distance from a point or submanifold. It proves embedding and norm equivalence results showing that lower order …
The paper studies Green’s functions for arbitrary positive powers of elliptic operators associated with strongly continuous semigroups generated by parabolic Green kernels under boundary conditions. It defines negative fractional powers by semigroup integrals, derives integral kernel representations…
This note develops an algebraic approach to periodic and limit-periodic generalized Jacobi matrices, using commutation relations and operator-theoretic spectral arguments. It proves that commuting generalized Jacobi matrices satisfy an algebraic relation, and in the complex-symmetric periodic case d…
Tolstov proposes a highly general formal framework for differentiation and integration on an abstract space, defined through a linear correspondence between set functions and point functions satisfying positivity and normalization conditions. The paper derives basic properties of the resulting forma…
The paper studies how the growth of polynomials orthonormal on the unit circle with respect to a mass distribution depends on local and global properties of that distribution, especially the zeros of its density. It derives upper bounds in terms of the modulus of increase of the distribution and low…
This note develops spaces \(L_p^r(\Omega)\) with fractional order \(r\) for \(2 \le p n\), including estimates for first or second differences in the critical integer and noninteger cases.
