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 optimal prediction and filtering for functionals of random processes that solve nonlinear differential equations driven by Gaussian random functions, a setting that generally lies beyond the Markov diffusion case. It derives a conditional expectation formula by comparing the measur…
A method is developed for solving Dirichlet and Neumann boundary-value problems for open surfaces, motivated by applications in diffraction, electrostatics, and analytic function theory. For the inhomogeneous Helmholtz equation, the construction introduces auxiliary closed surfaces and uses Green’s …
This paper extends classical potential theory from Lyapunov surfaces to domains whose boundaries belong to the Lyapunov-Dini class, characterized by controlled variation of the surface normal. Using previously established uniqueness for the homogeneous Neumann problem and local geometric estimates f…
The paper formulates multidimensional analogues of the Darboux problem for a second-order hyperbolic equation in a three-dimensional domain bounded by characteristic conical surfaces and a plane, together with the corresponding formally adjoint problem. Using a weighted energy identity, suitable Hil…
This paper studies the large-time behavior of the energy of solutions to a mixed initial-boundary value problem for the wave equation in an unbounded exterior-type domain in Euclidean space. Using scattering eigenfunctions for the corresponding exterior domain, the solution and its energy are repres…
The paper studies a singular two-dimensional integral equation arising in the theory of generalized analytic functions when the coefficients of the associated generalized Cauchy, Riemann system have first-order singularities. Using a Fourier expansion in the polar angle, the equation is reduced to p…
This note addresses extension problems for continuous maps into spheres and their connection with P. S. Aleksandrov’s question on bicompact compactifications. It proves that if a bicompactum is a countable union of bicompacts whose distinct pairwise intersections have dimension at most n minus 1, th…
The paper studies the existence and uniqueness of almost-periodic solutions for linear and nonlinear evolution equations in separable Banach spaces, including equations with unbounded operators depending almost periodically on time. Using limiting equations, dynamical systems on product spaces, comp…
This paper studies growth rates of sums of independent random variables under conditions controlling the size of individual summands relative to normalizing sequences. It introduces classes of comparison functions and proves sufficient and sharpness results for strong laws of large numbers with vari…
This paper extends parts of James’ theory of bases from Banach spaces to sequentially complete locally convex spaces with Schauder bases. It proves characterizations of shrinking bases through strong completeness and strong basis properties of the conjugate system, and shows that a basis is both shr…
The paper applies the method of functionals to generalized Zolotarev-Psheborsky minimax problems for polynomials subject to two linear constraints. It first establishes criteria for decomposing a finite sequence of functional values with respect to prescribed nodes, and gives necessary and sufficien…
The paper studies an integral equation of convolution type that models a smooth transition between two limiting paired equations with different kernels. Under summability of the kernels and nonvanishing conditions on the corresponding Fourier transforms, the equation is transformed by Fourier method…
The paper studies groups in which every subgroup that is not completely splittable is invariant, extending earlier work on groups with invariant noncyclic or otherwise exceptional subgroups. Using known classifications of finite groups whose proper subgroups are completely splittable, the authors cl…
This paper studies uniform deviations between continuous functions and algebraic polynomials obtained either by best approximation or by discrete least squares with a positive weight on equally spaced nodes. It proves a general bound, depending only on the degree, number of nodes, and weight, for th…
This paper studies boundary limit sets of real harmonic functions in the unit ball of three-dimensional Euclidean space, motivated by earlier results on ambiguous boundary points and asymptotic values. It proves the existence of a harmonic function such that, for every boundary point and every real …
The paper develops a theory of symmetric Banach spaces of measurable operators in Segal spaces with a measure on projections. It introduces distribution functions and s-numbers for measurable operators, proves minimax and approximation formulas, establishes a Schmidt-type decomposition, and relates …
This paper studies reduced extremal polynomials on the interval [0,1] that share a prescribed subdistribution of alternation nodes. It describes the structure of all such polynomials through perturbations by the squared resolvent of the common subdistribution, establishes when the corresponding set …
This note gives structural representations for classes of harmonic and analytic functions in the unit disk associated with the operator defined by a system of weight functions. It defines harmonic functions whose transformed boundary integrals are uniformly bounded, analytic functions whose transfor…
The paper addresses the recursive analogue of decomposing fields of sets generated by sufficiently strong Kolmogorov type R-operations, extending the comparison with classical descriptive set theory and Kleene’s hyperarithmetic hierarchy. It defines stabilization and external indices for recursive s…
The paper studies a differential pursuit problem in which the pursuer and evader are governed by controlled dynamical systems with bounded closed control sets, and meeting is defined by membership of their relative position in a prescribed closed set. It formulates conditions under which an approxim…
This paper extends James’s theory of boundedly complete and shrinking bases in Banach spaces to minimal, biorthogonal sequences, and studies how these linear topological properties reflect structural features of the space. It proves duality results for boundedly complete and spanning minimal systems…
This note studies the emergence of limit cycles from an equilibrium of a smooth or analytic differential system with one pair of purely imaginary characteristic roots, remaining roots off the imaginary axis, and a nonzero Lyapunov quantity of order \(2m+1\). Using reductions to a special normal form…
This paper examines finite-time damping and controllability for a simple distributed oscillatory system consisting of two one-dimensional wave lines joined at a common controlled endpoint, with fixed opposite endpoints. Using the finite control method, the problem is reduced to interpolation conditi…
The paper studies whether infinite commutative rings can be endowed with a nondiscrete ring topology, beyond the trivial discrete topology. It proves this in full generality by reducing the problem through a series of structural lemmas concerning nil ideals, square-zero ideals, torsion and torsion-f…
The paper studies how equimorphisms of hyperbolic spaces act on curves approaching the absolute and on pairs of curves lying on the absolute. It refines earlier results showing preservation of tangency by distinguishing three qualitative types of contact, zero, finite, and infinite order, defined th…
This paper addresses spectral estimation for multidimensional homogeneous random fields when observations are available only on lower-dimensional sections, such as two intersecting lines, rather than over an area or volume. It proposes an estimator formed from the real part of the product of the Fou…
This paper studies the complexity of realizing propositional formulas in the framework of normal algorithms and logical arithmetic, extending earlier notions from formulas in one variable to arbitrary propositional formulas. It formulates a sufficient condition for a formula to have no recursive upp…
This note studies reduction problems in pure higher-level logic over type scales of sets, with attention to spectra of formulas and definability of cardinal classes. It introduces a translation on types relating truth over a set to truth over iterated power sets, then uses it to reduce questions abo…
This paper studies locally bicompact topological groups through the topology on classes of conjugate closed subgroups, identified with quotient spaces by normalizers. It proves that if conjugacy classes of bicompact subgroups topologically generated by one element are bicompact, then the bicompact e…
The paper studies a multidimensional multiphase Stefan-type free-boundary problem for a general second-order linear parabolic equation in noncylindrical domains with piecewise smooth boundaries, allowing both closed and nonclosed phase fronts. For the two-dimensional case, with extension to higher d…
The paper formulates and studies a general moment problem in interpolation theory for analytic functions, defined by contour integral conditions involving a univalent function, auxiliary analytic factors, and prescribed sequences of complex numbers. Under the assumption that the image domain is inva…
This paper studies uniqueness in mixed inverse problems of potential theory, especially the determination of both the shape of a body and its density from exterior volume potentials or simple-layer potentials. Using the method of generalized moments, it proves uniqueness theorems for classes of cont…
This paper formulates and solves an integral geometry problem for a pair of oriented real Grassmann manifolds, the spaces of l-dimensional and k-dimensional subspaces of Euclidean n-space, under the assumptions l < k, l + k ≤ n, and even k minus l. It defines a transform from homogeneous smooth func…
This paper proves that every enumerable predicate is Diophantine, thereby establishing the algorithmic unsolvability of Hilbert’s tenth problem for Diophantine equations. Building on results of Davis, Putnam, and Robinson, the argument reduces the problem to showing that a Diophantine predicate with…
The paper studies the partially ordered set of equivalence classes of H-closed extensions of a Hausdorff space, ordered by admissible continuous maps. It proves that every nonempty family of such extensions has a supremum, using products of representative extensions, the diagonal copy of the origina…
The paper studies boundary behavior of the derivative of a function analytic and univalent in the unit disk, focusing on radial and angular limiting values on the unit circle. Using Koebe distortion estimates, it first establishes that such derivatives are normal analytic functions, and then proves …
The paper studies an intrinsic characterization of relatively open convex subsets of real vector spaces through abstract axial structures, formalizing order-theoretic notions of lines, segments, convexity, dimension, and parallelism. It introduces a Euclidean condition for generalized vector spaces …
This note studies maximal two-sided ideals in the Banach algebra of regular complex Borel measures on a compact group, addressing whether every simple homomorphic image of this algebra must be finite-dimensional. The authors construct maximal ideals in products of finite-dimensional operator algebra…
This note studies universal polynomial iterative processes for solving linear operator equations with self-adjoint positive definite operators in a Hilbert space, assuming the spectrum lies in a fixed interval. Using the spectral representation of the error and orthogonal polynomials with appropriat…
This note studies shift families on the real line for which the optimal homogeneous estimator is essentially independent of the chosen symmetric loss or quality criterion. It defines strongly symmetric densities through a zero set condition and shows that, under regularity assumptions, such laws are…
The paper studies a Tricomi boundary value problem for a class of mixed type equations with parameter \(\lambda\), aiming to obtain estimates without assuming smallness of the coefficient or of the transition interval. By introducing an exponential substitution based on a Riccati equation and applyi…
The paper studies Fourier expansions of functions in Besov classes with respect to an arbitrary complete orthonormal system of eigenfunctions of a nonnegative self-adjoint extension of the Laplace operator in a star-shaped domain. It establishes estimates for dyadic blocks of Fourier coefficients of…
This note studies the asymptotic order, in the number of nodes, of the degree of exactness of Chebyshev’s equal-weight quadrature formula for a nonnegative summable weight on a finite interval. Using methods associated with Bernstein and Akhiezer, it derives local estimates from the behavior of the …
The paper studies mixed boundary value problems for partial differential equations in which part of the boundary carries nonstationary conditions, reducing them to Cauchy problems for evolution equations in orthogonal sums of Hilbert spaces. It constructs an operator generated by an elliptic boundar…
This paper addresses whether infinite rings, in particular countable rings, can be endowed with a Hausdorff nondiscrete topology compatible with ring operations. It proves a criterion for such a topologization with a prescribed open ideal, formulated in terms of avoiding roots of finitely many polyn…
The paper studies closed P-sets in bicompact topological spaces, focusing on their role in quasiextremal, or basically disconnected, bicompacts and in the theory of partially ordered vector lattices. It translates earlier results on extended K-sigma spaces into topological terms, showing that for a …
This note studies the Carleman boundary value problem with orientation reversing shift on the boundary of a finite multiply connected domain. It constructs a special conformal welding function that maps the problem to a Riemann boundary value problem on a contour consisting of open arcs, using integ…
This paper studies Green functions for a class of singular elliptic differential operators in a half-space, involving a Bessel-type operator in the normal variable and weighted Sobolev spaces adapted to the boundary singularity. It establishes coercive estimates for a shifted operator, constructs th…
The paper studies oscillation of vector-valued solutions of second-order differential equations in finite-dimensional Euclidean and real Hilbert spaces, proposing a coordinate-invariant definition based on zeros of all scalar projections. For equations of the form u''(t) + F(t,u(t))u(t)/||u(t)|| = 0…
The paper studies families of one-to-one mappings between metric spaces equipped with two metrics, motivated by distortion estimates in relative metrics for conformal, quasiconformal, and related mappings. It proves that a uniform two-sided distortion estimate in one metric is equivalent to equicont…
