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 the existence of periodic solutions for systems of differential operator equations in Banach spaces, with a small parameter multiplying one derivative and with a known smooth periodic solution of the degenerate system. The method reduces the periodic boundary problem to nonlinear i…
This paper generalizes a known property of quadratic forms in normal variables, whose characteristic functions satisfy linear homogeneous differential equations with polynomial coefficients, to broader polynomial statistics. It defines a class of suitable polynomial forms and statistics, based on th…
This paper proposes a unified scheme for formulating dual extremal problems arising in linear programming, game theory, moment problems, and approximation theory. It defines primal problems through two ordered families of subsets and constructs a dual problem using real-valued functions that separat…
The paper studies boundary behavior of homeomorphisms from a Euclidean ball onto a domain that belong to a class defined through preservation of zero Mazurkiewicz-type distance between connected sets, a class including quasiconformal and conformal mappings. It introduces attainable boundary points, …
This paper studies the full lattice of polyverbal subgroups of a countable free product of free groups and the corresponding polyverbal operations on groups, extending earlier work focused mainly on neutral cases. It decomposes each polyverbal subgroup into verbal and neutral components, establishes…
This paper studies best approximation in the first degree mean metric on the unit circle for analytic functions with singularities outside or inside the circle, including rational functions, logarithms, and powers. Using a criterion for best approximation in \(L_p\) on rectifiable curves, specialize…
This note studies the cohomological equation for a measurable flow on a Lebesgue space with an indecomposable invariant measure, seeking an \(L^2\) function whose derivative along trajectories equals a given observable minus its mean. Using the spectral representation of the unitary group associated…
The paper studies the Dirichlet problem for a general elliptic system of two second-order differential equations in a bounded simply connected plane domain, with emphasis on when the problem is normally solvable rather than merely elliptic. It identifies boundary conditions on the characteristic roo…
This note extends Jackson type approximation results of Timan, Dzyadyk, Freud, Brudnyi, and Trigub to bounded functions defined outside an interval or on separated unions of intervals. It proves the existence, for every positive degree parameter, of entire functions of finite exponential degree that…
This note studies one-dimensional diffusion processes depending on a numerical parameter and associated with parabolic equations whose diffusion coefficient may vanish. Under Hölder and boundedness assumptions on the coefficients and on the initial random variable, it establishes mean-square and alm…
The paper studies when the Banach space of continuous functions on an n-dimensional cube can be isomorphically embedded into the space of continuous functions on an m-dimensional cube, with n greater than m, so that functions with a prescribed smoothness are sent to functions with higher prescribed …
This note addresses how to choose defining parameters that characterize the geometric anisotropy of a continuous medium, with emphasis on media classified by point symmetry groups such as crystals and textures. It formulates a tensorial framework in which tensors invariant under a given finite or co…
This paper studies oscillation of solutions of nonlinear nonautonomous second order equations in the presence of multiple equilibrium positions. It proposes a classification of motions by zeros relative to equilibria, defines corresponding domains of initial data, and formulates problems concerning …
This note studies differentiability at zero, and at general points, of the Nemytskii operator between Orlicz spaces under Carathéodory assumptions. It establishes necessary conditions showing that a differentiable nonlinear operator requires the domain Orlicz function to grow essentially faster than…
This paper studies the convolution ring of finite, locally constant functions on the group of unimodular two by two matrices over a totally disconnected locally compact nondiscrete field of characteristic not equal to two. Using the continuous and discrete series of representations of the group, the…
This note addresses Phragmen-Lindelof type growth questions for harmonic functions in a three-dimensional half-cylinder, especially when both the function and its normal derivative may grow on the lateral boundary. Using a modification of an integral representation method, it establishes a represent…
This note studies projections, or structural isomorphisms, of arbitrary torsion-free metabelian groups, with particular attention to non-locally cyclic groups. Using preliminary lemmas on induced correspondences over abelian subgroups, two-generator torsion-free metabelian subgroups, and the behavio…
The paper improves the remainder term in Mertens’ formula for the partial Euler product at one. It introduces an averaged Euler product and analyzes its logarithmic derivative by means of a contour integral involving the logarithmic derivative of the Riemann zeta function, followed by standard conto…
This paper studies Fourier-type transforms associated with a second-order boundary-value problem on the half-line for the operator defined by a complex potential satisfying an exponential decay condition and a general complex boundary parameter. Using spaces of test functions and generalized functio…
This paper formulates regularization for ill-posed problems, with emphasis on Fredholm integral equations of the first kind and related inverse problems where exact solutions may fail to exist or depend discontinuously on data. It defines regularizing algorithms and constructs them through minimizat…
The paper develops a general method for constructing integral rational bases of polynomial tensor invariants for crystallographic groups, extending earlier procedures for invariant tensors. It formulates the problem through group averaging operators acting on spaces of monomials in tensor components…
The paper studies the Dirichlet problem for equations involving the Monge-Ampère operator, focusing on cases where the right-hand side may have high growth in the gradient variables and where the boundary curve may have curvature that vanishes. It develops estimates for generalized convex solutions …
This paper studies first boundary-value problems for two classes of differential operators: anisotropic hypoelliptic operators with semi-bounded principal part, and operators of odd order in one distinguished variable and even order in the remaining variables, including parabolic-type cases. Using g…
This note studies convergence of the collocation method for boundary value problems involving ordinary and partial integro-differential equations. Using Kantorovich’s general theory of approximate methods, it formulates solvability and convergence theorems for polynomial collocation approximations w…
The paper proves two general theorems for estimating the error of approximate solutions of linear equations when the error is measured in a normed subspace rather than in the whole underlying linear space. These results are applied to Wiener-Hopf integral equations, first-kind equations with general…
This note gives a new proof of Vinogradov’s mean value theorem for the number of solutions of systems equating sums of like powers, with the aim of improving the dependence on the degree parameter in the resulting estimates. The argument introduces a congruence lemma for variables distinct modulo a …
This paper studies tensor fields on the n-dimensional sphere in Euclidean space and seeks invariant irreducible spaces under the full orthogonal group whose finite sums uniformly approximate arbitrary continuous tensor fields. It introduces tensor fields induced from tensors in the ambient Euclidean…
This paper develops interpolation and extrapolation results for linear operators in Orlicz spaces, using quasipower growth conditions on defining functions and endpoint boundedness between Lebesgue spaces. It proves that an operator bounded between two pairs of Lebesgue spaces is bounded between cor…
This paper studies the tensor product of two irreducible discrete series representations of the real unimodular group of second order, realized through its isomorphic action on analytic functions in the unit disk. Using explicit Hilbert space models and strongly convergent operator kernels, it const…
This paper studies algorithmic questions for partially ordered groups, both for finitely presented groups equipped with positive invariant subsemigroups and for groups specified by finitely many generators and defining inequalities. It relates effective partial orderability to decidability of member…
This paper addresses the recovery of particle size distributions in dilute turbid media from spectral transparency measurements, a problem formulated as the inversion of a first-kind Fredholm integral equation and known to be highly unstable under direct numerical treatment. Using Mellin transforms …
The paper develops a least squares approach for approximating eigenvalues of operator equations depending on a complex parameter in Hilbert spaces. It defines a nonnegative functional measuring the minimal residual norm and shows that, for an appropriate complete trial system, the local minima of fi…
This paper studies asymptotic questions for the Dirichlet Laplacian on the unit square, whose eigenvalues reduce to counting lattice points satisfying a quadratic inequality. Using a known estimate for lattice points in a circle, it gives an asymptotic formula for the eigenvalue counting function wi…
This note studies standard Markov processes whose trajectories are killed at a random time and distinguishes two modes of termination. It defines sigma trajectories, for which termination can in suitable settings be associated with a limiting point of the path, and delta trajectories, characterized …
This note develops an analogue for semiheaps of the Sushkevich, Rees, and Clifford structure theory for completely simple semigroups. It defines left, right, lateral, and two-sided ideals in semiheaps, constructs semiheaps from groups with zero, inverse automorphisms, and sandwich matrices, and prov…
The paper studies simple systems of paths on the surface of the complete pretzel of genus 2 and asks when equivalence of the induced systems in the fundamental group is sufficient to realize equivalence by a homeomorphism of the surface. It analyzes nonintersecting chord systems on a punctured torus…
The paper addresses Kolmogorov’s question whether the Hausdorff length of every planar set of finite positive length is bounded by an absolute constant times its minimal linear measure. It constructs, by an iterative splitting and displacement of horizontal intervals with carefully chosen parameters…
The paper studies the maximum possible length of a cycle in the graph of the n-dimensional Boolean cube, a problem motivated by algorithms for simplifying disjunctive normal forms and related coding questions. It formulates lower bounds for this maximum length, including an explicit construction for…
This paper studies restrictions on the behavior of the boundary of a simply connected surface of positive Gaussian curvature under isometric bending. Using Vekua’s theory of generalized analytic functions, it formulates a nonlinear boundary value problem for the complex function of the bending and p…
This paper strengthens Olevskii’s result on the divergence of Fourier series after rearrangement for complete orthonormal systems, focusing on the trigonometric system. It proves, using auxiliary lemmas on unbounded divergence of continuous functional series and on modified trigonometric polynomials…
This paper develops a theory of generalized functions on a basic space of infinitely differentiable functions defined on a sufficiently smooth Jordan contour, using Faber polynomials associated with the contour. It proves expansion theorems for ordinary and generalized functions in systems built fro…
This note examines Shilov’s analysis and synthesis of homogeneous regular normed rings of continuous functions of type C on compact groups, focusing on whether synthesis from a local ring recovers the same local ring under subsequent analysis. For strict type C rings on a torus, the authors reformul…
The paper studies a first order elliptic system in the plane, reduced to the generalized analytic equation with a nonzero constant complex coefficient. Using its connection with the modified Helmholtz type equation, the author constructs two fundamental kernels in terms of Hankel functions and verif…
The paper introduces almost geodesic curves in torsion-free affinely connected spaces as curves admitting a parallel two-plane field containing the tangent direction, and derives their differential equation. It studies mappings between affine and Riemannian spaces that send geodesics or almost geode…
This note studies exact similar tests for comparing the means of two normal samples when the variances are unequal, allowing randomized tests whose rejection probability is a measurable function of the observations. It observes that any similar test can be projected onto the sufficient statistics, y…
This note develops a generalized formulation of Ehresmann jet theory that does not require the underlying sets to be topological spaces. It introduces localizable families of subsets through order-theoretic notions of connectedness and partial left filtering, proves equivalent characterizations usin…
This paper studies the bifurcation and stability of small periodic solutions of parameter-dependent ordinary differential equations with a periodic right-hand side and a persistent zero equilibrium. Using the Poincaré-Andronov map, multiplier theory, topological index arguments, and concavity or con…
This note studies uniqueness of classical solutions for a boundary value problem associated with a broad class of higher order differential equations, including elliptic and hypoelliptic types, in bounded convex domains. Building on earlier definitions of regular domains, stable boundary values, and…
