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 regularization of elliptic boundary-value problems by potentials is equivalent to the original problem, a question not settled by the construction of regular integral equations alone. For a normally solvable boundary-value problem for a single elliptic equation in an n-dim…
This paper develops a homotopy method for computing the index of locally trivial families of Fredholm pseudodifferential structures on compact manifolds with boundary, including elliptic differential boundary-value problems. After formulating augmented and framed pseudodifferential homomorphisms in …
The paper studies self-adjoint extensions of ordinary differential operators of arbitrary order on a finite interval in a Hilbert space of vector-valued functions, with continuous operator coefficients. It introduces Hermitian relations in a Hilbert space and describes their Cayley transform represe…
This note introduces d-centered systems and d-ends of a topological space as tools for studying ultrafilters, relaxations, and decomposability. It gives several proofs, without the continuum hypothesis, of the existence of ultrafilters with bases of crowded self-dense sets in every nonempty crowded …
The paper develops expansions of arbitrary functions on two-dimensional and three-dimensional Lobachevsky spaces as superpositions of wave eigenfunctions of the Laplace operator. Using spherical and cylindrical means, it derives inversion formulas for expansions in pseudospherical waves in three dim…
This paper establishes an analogue of P. Fatou’s boundary theorem for regular quaternion functions in four-dimensional Euclidean space. For a right-regular quaternion function in a star-shaped domain bounded by a Lyapunov hypersurface, satisfying a uniform integral bound on homothetic interior hyper…
This note studies closed form solvability of singular integral equations on a closed contour with kernels satisfying Hölder type regularity and analytic continuation assumptions. It proves that a singular integral operator with a kernel analytic in both variables and normalized on the diagonal is in…
This note studies endomorphisms of the lattice of closed subgroups of a locally compact topological group, especially maps of the form X to X joined with S for a proper closed subgroup S. Using criteria for distributive and dually distributive pairs of closed subgroups, it derives structural restric…
The paper develops a generalization of Cauchy’s fundamental theorem for finite-dimensional associative algebras over the real numbers. It defines line integrals of continuous algebra-valued functions along rectifiable arcs and proves that, for every closed rectifiable contour, the integral of a powe…
The paper studies bounded solutions of an inhomogeneous diffusion equation on a semi-infinite interval with a zero boundary condition and a source term that switches between constant input and removal according to the value of the solution at a fixed point. Using heat-kernel representations, the pro…
This paper studies local existence of solutions for a neutral differential equation with deviating argument in which the derivative depends on delayed values of both the unknown function and its derivative. Instead of imposing Lipschitz conditions in all phase variables, the authors assume continuit…
This paper studies the stable approximation of solutions to ill-posed operator equations when additional a priori information specifies that the unknown function is bounded and monotone. Using Helly’s selection theorem, the authors show that the class of bounded monotone functions is compact in an \…
The paper examines graphs whose associated invariant matrix algebra is a cell, a class characterized by a regular zero-one basis and uniform counts of vertex sequences with prescribed adjacency patterns. It addresses a previously stated hypothesis that any graph with such a cell algebra must have a …
This note generalizes Sobolev-type projection representations for function spaces on rectangular domains to a finite collection of partial differential operators that factor into ordinary differential operators in separate variables. Under a stated algebraic compatibility condition on the solution s…
The paper develops a unified approach to results on dyadic bicompact spaces by introducing cardinal invariants based on monolithic subspaces and a suppression property, combined with the Hewitt, Marczewski, Pondiczery theorem. It defines dense, adherent, and dant spaces, proves their stability under…
The paper studies bounded dissipative operators in a separable Hilbert space whose spectrum is concentrated at zero and whose resolvent is an entire function of exponential type. Using exponential nodes and their characteristic operator functions, it constructs invariant subspaces with prescribed ty…
This paper studies magnitudes of deviation for meromorphic functions of finite lower order less than one, quantities analogous in some respects to Nevanlinna deficiencies. It establishes conditions under which a sufficiently large positive deviation from one value, for lower order below one half, fo…
The paper studies weak invariance of discrete dynamical systems with respect to external perturbations under a terminal quality criterion. Using a reference perturbation and the associated reference function, it derives necessary and sufficient conditions for invariance, including an equivalent form…
The paper addresses the ill-posed problem of computing values of an unbounded linear closed operator from approximate input data in Hilbert spaces, where small perturbations may leave the domain or produce unbounded changes in the output. It proposes a stabilizing variational construction that, for …
This paper studies the two-dimensional zeta function of a lattice with a real parameter, seeking lattices of fixed determinant that give local minima for a fixed value of the parameter. Positive binary quadratic forms of determinant one are parametrized in a reduction domain, and the behavior of the…
This paper develops a framework for random and stationary processes taking values in a topological semifield, using probability distributions defined through measures on the Boolean algebra of idempotents. It introduces notions of stationarity in the broad and narrow senses, establishes their relati…
The paper studies structural properties of R and Rc operations using Kurepa’s apparatus of ramified tables, with particular attention to countable tables, rigid bases, and chains of finite tuples. It establishes dichotomy results for countable subsets of such tables, proves that rigid Rc chains cons…
The paper studies completely irreducible class I representations of connected real semisimple Lie groups with finite center, relative to a maximal compact subgroup. Using the group algebra, the commutative algebra of bi-invariant test functions, and spherical functions, it constructs a family of rep…
This paper studies spectra of self-adjoint extensions of a closed symmetric semibounded operator with infinite deficiency index, under the assumption that the Friedrichs extension has compact inverse and eigenvalues with a prescribed power asymptotic. It proves that for any slower power growth expon…
This note extends Reifenberg and Morrey type results for the multidimensional Plateau problem to compact subsets of a compact Riemannian manifold that satisfy prescribed Čech homological conditions. It defines classes of compact sets with a given algebraic boundary relative to a compact set and with…
This paper studies eigenfunctions and spectral properties of the polyharmonic operator on an arbitrary domain, beginning with solutions of a polyharmonic eigenvalue equation. It proves a spherical mean-value formula for such solutions and their iterated Laplacians, involving Bessel functions and exp…
The paper studies selection problems for multivalued mappings whose values lie in complete systems of closed subsets of completely regular spaces, with emphasis on spaces having countable or sigma-discrete networks. It develops transfer results for selection properties under measurable homeomorphism…
The paper studies discrete Wiener-Hopf equations in a quarter-plane with absolutely summable data and kernel, seeking solutions in l1. It establishes Fredholm, or Noether, criteria for the associated operator in terms of nonvanishing of the symbol on the two-torus and zero winding indices in each co…
The paper studies general criteria for convergence of arbitrary, possibly non-Markovian stochastic processes to Markov diffusion processes. It compares three forms of assumptions on increments over intermediate time intervals: cyclic conditions involving recurrent state sets, high-probability sets o…
The paper studies topological entropy for two-sided topological Markov chains defined by finite or countable directed graphs, where the countable case is complicated by the noncompactness of the path space. It defines entropy as the supremum of the logarithms of the maximal eigenvalues over finite s…
This note studies quantitative stability estimates for epsilon-quasiconformal mappings of the three-dimensional unit ball onto itself, under a normalization fixing three boundary points. Extending earlier planar results, it derives nonsharp bounds for the deviation of such mappings from the identity…
The paper studies regularization of minimization problems for a continuous convex functional on a bounded closed convex subset of a Hilbert space, where ordinary minimizing sequences need not converge strongly because the minimizer may be nonunique. It proposes an algorithm based on intersecting the…
This paper develops an operational calculus for closed densely defined linear operators in countably normed locally convex spaces whose resolvents may be unbounded and whose spectrum may fill the complex plane. Under sectorial hypotheses expressed through a finite asymptotic resolvent expansion and …
The paper studies boundary-value problems for a class of high-order differential-operator equations in a Hilbert space, termed partially hyperbolic, extending known results for first and second order cases to arbitrary order. It formulates weighted function spaces and analyzes equations on the whole…
The paper studies removable singularity sets for mappings with bounded distortion and for quasiconformal mappings in Euclidean space. It introduces zero alpha-capacity sets, establishes auxiliary results relating such sets to Hausdorff measure and projections of measure zero, and proves an estimate …
This note studies least common residues and least mixed residue or nonresidue values of polynomial systems modulo a prime. Using estimates for rational points and exponential sums on algebraic curves over finite fields, it proves that under absolute irreducibility hypotheses the least common natural…
The paper studies the Cauchy problem for linear nonhomogeneous differential equations with retarded argument in a Banach space, with initial data taken either from an \(L_p\) space or from the space of continuous functions. Its main method is to replace the delay equation by an equivalent ordinary d…
The paper studies infinite nonabelian groups satisfying the minimality condition for noninvariant abelian subgroups, with emphasis on locally soluble and periodic cases. It proves that any such group containing elements of infinite order is a JH-group, having an infinite abelian normal divisor of fi…
This note studies the enumeration of precomplete classes in finite k-valued logics, a central component of completeness criteria for such logics. Using Rosenberg’s classification of precomplete classes into six families, the authors reduce the asymptotic count to the enumeration of central predicate…
This note studies whether Lagrange interpolation at an arbitrary infinite triangular matrix of nodes on a finite interval can be made convergent for every function in the class \(ACG_*\). Building on known positive results for absolutely continuous functions under Chebyshev and related node systems,…
This paper addresses the arithmeticity problem for lattices in semisimple real Lie groups, focusing on noncompact finite-volume quotients and irreducible pairs in real rank at least two. It outlines a proof that such a discrete subgroup is commensurable, along a parabolic subgroup, with the rational…
This note studies structural closure operations on classes of groups, with emphasis on Baer groups and their relation to nilpotent and radical constructions. It first constructs, for each integer n at least 1, a Baer p-group that is not generated by its n-generated nilpotent subgroups, using iterate…
The paper studies periodic solutions of the one-dimensional diffusion equation on a finite interval, motivated by self-oscillatory phenomena previously treated mainly for semi-infinite domains. It formulates the bounded-domain problem with a fixed concentration at one endpoint and a nonlinear, possi…
This paper studies peripherally bicompact tree-like spaces, using earlier results that such spaces have bases of connected open sets with finite boundaries and are linearly connected. It proves that the density of such a space equals its weight, establishing in particular that separability implies c…
The paper proposes a family of successive approximation methods for solving nonlinear functional equations in Banach spaces under differentiability and local invertibility assumptions. The iteration is constructed by choosing operator coefficients recursively so that the first k derivatives of the i…
The paper studies commutative nilpotent associative algebras over the complex numbers through the complete lattice of their ideals, asking which algebraic properties and isomorphism classes can be recovered from this lattice. It develops lattice-theoretic characterizations of dimension, annihilators…
The paper develops a method for deriving interpolation theorems in symmetric Banach spaces of measurable functions on the unit interval. The approach represents norms in such spaces as suprema of Lorentz-type norms and uses boundedness results for operators between these auxiliary spaces, together w…
