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 paper studies singular integral operators with homogeneous degree zero symbols in weighted Sobolev type spaces on Euclidean space and in cones. It establishes necessary and sufficient conditions on the weight exponent for boundedness in one dimension and in higher dimensions, including cases ou…
This paper studies when a linear positive functional defined on a subspace of a real Banach space with a cone can be extended to the whole space while preserving linearity and positivity. It gives several necessary and sufficient criteria in terms of closures of algebraic sums involving the cone and…
This paper studies weak solutions of a mixed initial boundary value problem for a hyperbolic equation with a nonlinear term, where the linear part is generated by a self-adjoint positive operator. The solution is defined through an integral identity with test functions adapted to the operator domain…
This paper studies the minimality condition for subgroups in locally finite and periodic groups, continuing earlier work on quasi-extremal and extremal groups. It reduces the minimality problem for locally finite groups to the case of infinite simple quasi-extremal groups with involutions, and descr…
The paper studies the first boundary value problem for linear parabolic equations in a bounded cylinder, allowing discontinuous leading coefficients and unbounded lower order coefficients and free terms. For the case in which relevant spatial integrability exponents may be below the dimension, it fo…
This paper proves three results on nonlinear equations involving monotone operators in Banach spaces. It first establishes convergence of the least squares method for equations with strongly monotone operators under either finite-dimensional continuity with completeness of the approximating system o…
The paper addresses Aleksandrov’s problem on the possible noncoincidence of covering dimension and small inductive dimension for bicompact spaces, with attention to examples satisfying separability and the first axiom of countability. It constructs a separable bicompactum whose topology is defined o…
This paper develops a variational framework for solving higher order elliptic equations with possibly irregular or degenerate coefficients on arbitrary open sets. It introduces weighted Sobolev type spaces and uses generalized Hardy inequalities to obtain embedding results, local summability and dif…
The paper introduces generalized self-adjoint extensions of densely defined symmetric operators using a scale of Hilbert spaces generated by the graph norm on the domain of the adjoint. It shows that every closed symmetric operator can be extended from the domain of its adjoint into the correspondin…
This paper studies groups possessing rational series, whose factors embed in the additive group of rational numbers, and examines the relation between rational rank and special rank. Using properties of solvable torsion-free groups of finite rank and groups satisfying the weak minimal condition for …
The paper studies coordinate transformations in an arbitrary Riemannian space that map every harmonic coordinate system to another harmonic coordinate system, treating the question locally and using Lie group methods for differential equations. It proves that, when such transformations form a contin…
The paper studies the lattice point discrepancy for plane convex domains whose boundary is a small smooth perturbation of a circle. Assuming a polar representation with the perturbation and its first four angular derivatives uniformly of order o(R), the argument applies Fourier coefficients of chara…
This paper extends Liouville-type results for generalized analytic functions to first-order elliptic systems with constant coefficients in the plane. It studies entire regular solutions of the system ∂w/∂z̄ + aw + b w̄ = 0 subject to polynomial growth of order at most N, using Fourier transforms of …
The note studies oriented quasiconformal mappings in Euclidean space, defined in the Sobolev class by a distortion inequality with nonnegative Jacobian almost everywhere. Using an integral estimate for the Jacobian, it derives local \(L^n\) bounds for the differential in terms of one coordinate func…
This note studies analytic irreducible representations of the finite general linear group GL(n, Kq), defined by the absence of degenerate one-dimensional constituents upon restriction to the upper unitriangular subgroup. Using the structure of a parabolic-type subgroup Hn as a semidirect product and…
Maslov introduces semisyntopogenic spaces, a generalization of Császár’s syntopogenic spaces based on families of semitopogenic orders, and develops basic notions such as open and closed sets, connectedness, separation, and continuity. The paper constructs induced semisyntopogenic structures on spac…
This paper studies compact classes of algebraic systems in model theory, especially their behavior under enrichments, ultraproduct constructions, and product-like operations. It gives criteria for compactness in terms of elementary equivalence and ultraproduct closure, derives conditions for strict …
This paper studies a boundary value problem for a nonlinear system of second order equations of mixed type in a domain whose boundary includes an elliptic part and characteristic arcs. It develops maximum principle type lemmas and solvability results for an associated linear system with a positive d…
The paper studies complete homeomorphisms associated with quaternionic differential equations in four-dimensional Euclidean space, focusing on equations of the form DU = aU. It proposes a method based on Hadamard’s global homeomorphism theorem: construct a solution by an integral equation, prove loc…
The paper addresses decision problems for finitely generated commutative semigroups with defining relations, focusing on the truth of closed first-order formulas in a signature that records multiples of generators. It replaces an earlier completeness-based universal procedure with a more constructiv…
This paper studies bounded solutions on the real line and half-line for systems of second-order ordinary differential equations of the form y'' = F(x, y, y'). Using maximum-principle arguments and iterative approximation schemes, it establishes uniqueness, existence, and a priori bounds for linear a…
The paper addresses the conjugacy problem for braid groups, a question arising in knot theory and the theory of closed braids, previously solved only for low-order cases. It defines braid groups algebraically by generators and relations and outlines an algorithmic proof based on a sequence of lemmas…
The paper studies dyadicity for a class of topologies on Cartesian and restricted products of topological spaces, motivated by Aleksandrov’s question on whether every countable topological group has a dyadic underlying space. It defines product topologies associated with free filters on the index se…
This paper studies when topological spaces arise as factor images of metric or generalized metric spaces, motivated by questions on the topologies induced on quotient sets by varying the metric on the preimage. It gives characterizations of generally metrizable and symmetrizable T1 spaces in terms o…
The paper studies bicompact extensions of topological spaces through inverse limits of finite projection spectra associated with canonical coverings. It defines refinements, correct refinements, lambda-strengthenings, and H-strengthenings of the spectrum of a space, then proves that bicompact semire…
This paper studies a nonlinear fourth order boundary value problem arising from the depth averaged two dimensional theory of steady ocean currents, with mixed no slip and slip type boundary conditions on solid and liquid parts of the boundary. It formulates the problem in a Sobolev space setting, es…
The paper studies the asymptotic average of composite functions F(phi(n)/n), where phi is Euler’s totient function, and addresses a refinement of an error estimate previously obtained by M. M. Tan. Assuming that F has a derivative on [0,1] satisfying a first order Lipschitz condition, the argument u…
The paper studies the Dirichlet problem for quasilinear elliptic equations arising from the construction of a hypersurface in Euclidean space with prescribed mean curvature. It introduces a class of nonuniformly elliptic equations broad enough to include the mean curvature equation, and derives nece…
This note extends Denjoy, Carleman quasianalyticity by introducing alpha-quasianalytic classes on the half-line and on finite intervals, defined through Weyl and Riemann, Liouville fractional differentiation operators. It asks which growth conditions on a sequence of bounds determine a function uniq…
The paper studies nilpotent operators that are self-adjoint with respect to an indefinite metric in Hilbert and Pontryagin spaces. It gives examples showing that nonzero nilpotent operators can be \(J\)-self-adjoint, analyzes their invariant maximal positive and negative subspaces, and proves that s…
This note studies continuous mappings of zero-dimensional bicompact spaces onto generalized Cantor discontinuums, using a local cardinal invariant called the delta-character, defined through systems of canonically closed sets. Under the generalized continuum hypothesis, it proves that if every point…
This note studies the characteristic classes of Lagrangian bundles associated with the Maslov and Arnold construction, viewing the Lagrangian Grassmannian as the homogeneous space U(n)/O(n). It defines geometric cycles in this space via incidence conditions on Lagrangian planes, analyzes their orien…
The paper studies the distribution of the numbers of runs of individual states and of the total number of runs in finite homogeneous Markov chains. It derives explicit formulas for selected cases where the general combinatorial expressions and asymptotic normal parameters are otherwise cumbersome, i…
This paper studies the approximation of differentiable functions on the real line by partial sums of their Fourier Hermite expansions, for classes whose r-th derivative has a prescribed modulus of continuity. Extending a previous result for the nondifferentiable case, it derives an asymptotic formul…
The paper studies convergence of approximate methods for boundary value problems of the transport equation, especially schemes that combine simple iteration with variational acceleration. For symmetrizable one-velocity and energy problems satisfying detailed balance, the transport problem is reduced…
The paper studies a mixed boundary value problem for the wave equation in a half-space where Dirichlet data are prescribed on one part of the boundary and Neumann data on the complementary part, producing discontinuous boundary conditions along a timelike manifold. Using Fourier transform methods, p…
This paper extends several classical limit and decomposition theorems to complex distribution functions of bounded variation and their characteristic functions. It defines normal complex distributions through characteristic functions of exponential polynomial form, relates their admissibility to Shi…
The paper studies a two-point boundary value problem in an infinite spatial layer for second-order linear partial differential equations with constant coefficients, with data prescribed at two times. It introduces criteria for well-posed solvability in classes of bounded functions and functions with…
This paper studies self-adjoint operators in spaces of vector functions generated by first-order symmetric differential systems with Hermitian matrix coefficients. It establishes criteria for the defect indices and self-adjointness of the minimal operator in terms of endpoint behavior of the coeffic…
This note studies when partial sums of trigonometric Fourier series approximate periodic functions as well, in order, as the best trigonometric polynomial approximation, without the logarithmic loss known for the full class of functions with prescribed modulus of continuity. Using estimates for Four…
This note develops a topological method for studying condensing nonlinear operators in Banach spaces, extending fixed point ideas previously known for completely continuous and weakly continuous vector fields. The authors prove that a condensing operator, and also suitable homotopic families and pos…
This paper studies approximation in the mean on measurable subsets of the complex plane by functions analytic in a neighborhood of the set. For \(L^2\) approximation on arbitrary Borel sets, it gives necessary and sufficient conditions in terms of Cartan’s fine topology and thinness of the complemen…
The paper studies representations of partial and general recursive functions using primitive recursive functions of large range, in connection with a conjecture of Skolem. It proves that any partial recursive function can be represented, up to a correction at zero or undefinedness at zero, through t…
The paper studies eigenvectors of Hammerstein integral operators with potential Carathéodory nonlinearities in ideal Banach spaces of measurable vector functions, allowing kernels whose associated self-adjoint linear operator is positive or has finitely many negative eigenvalues. Using a variational…
The paper proposes a combinatorial-topological framework for constructing finite difference approximations to linear equations of mathematical physics expressed through the exterior derivative and its adjoint on a Riemannian manifold. Using cellular decompositions, cochains, the coboundary operator,…
This paper studies closed symmetric operators in a Hilbert space whose domains need not be dense, focusing on extensions, characteristic functions, and generalized resolvents. It introduces and uses an isometric operator associated with the defect subspaces to parametrize dissipative, accumulative, …
This note studies subsemigroups of torsion-free groups through the lattice-like structure of all subsemigroups of a group. Using the notions of S-products, S-elements, and singly covering elements, it establishes necessary and sufficient structural conditions on the ideal generated by a subsemigroup…
This note studies mathematical programming problems in partially ordered Banach spaces with regular minihedral cones, where the feasible set is defined by inequalities involving an operator and the objective is any monotone functional. It shows that, for continuous monotone operators, nonemptiness o…
This note refines Lavrent’ev’s theorem on locally homeomorphic quasiconformal mappings of Euclidean space in dimensions at least three by allowing the quasiconformality characteristic to grow with radius. Using modulus estimates for curve families and Grötzsch principles, it proves that if the local…
