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 quasi-random behavior in a one-dimensional oscillator governed by a time-periodic force field in a confining potential well. Using a successor map defined by consecutive zero crossings and methods analogous to symbolic dynamics, it proves the existence of long-period periodic moti…
The paper studies the existence and estimation of symmetric periodic solutions for autonomous nonlinear differential systems with a single nonlinearity. Using refined bounds for norms of inverse operators, it reduces the problem to integral equations for the first harmonic amplitude, frequency, and …
The paper studies limit sets of multidimensional differential equations in which a two-dimensional independent variable maps into three-dimensional Euclidean space, focusing on complete integral manifolds of torus, cylinder, and plane type. It develops analogues of Poincare-Bendixson theory using tr…
The paper studies sufficient statistics for parametric families of transition densities when observations form a simple Markov chain with a continuous state space. Extending earlier results for independent samples and finite-state Markov chains, it defines regularity and smoothness conditions, intro…
The paper extends Dirac’s construction of extracting a square root from a vector in Clifford algebras to the symplectic case, where the underlying variables are anticommuting spinor coordinates over a Grassmann algebra. It associates symplectic vectors with elements generated by operators satisfying…
This paper studies prenuclear, equivalently absolutely summing, linear mappings within interpolation scales of Banach and Hilbert spaces. It relates such mappings to operators between sequence spaces, examines the behavior of the associated spaces under minimal, maximal, normal, and regular scales, …
This paper develops an analytic scheme for constructing dual problems for convex programming in Banach spaces and extends it to fractional-convex programming. It formulates the primal problem through a concave objective and cone constraints, defines the Lagrange functional, and obtains the dual by i…
This note studies the projective plane over the real algebra of degenerate octaves and its associated elliptic and hyperbolic unitary geometries. Using Jordan algebras of Hermitian 3 by 3 matrices, polarities, and fibrations to unitary non-Euclidean planes, it defines incidence, metrics, collineatio…
This note extends Khintchine-type metric results in Diophantine approximation to simultaneous inhomogeneous approximation by linear forms in at least two variables. For primitive integer vectors, it studies the frequency with which the fractional parts of associated linear forms fall in prescribed m…
The paper studies regularization of ill-posed equations involving singular integral kernels, where the usual construction of an equivalent Fredholm equation is unavailable because the range of the associated closed operator need not be closed. It extends Tikhonov-type regularization from bounded ope…
The paper studies gaps between neighboring prime ideals in an algebraic number field through analytic properties of the associated Dedekind zeta function. Using Vinogradov’s method for estimating trigonometric sums, together with derivative estimates and a reduction to exponential sums over lattice …
The paper extends Moser’s method for Harnack inequalities to generalized solutions of a class of second order quasilinear parabolic equations. After establishing an embedding estimate for functions in parabolic Sobolev spaces, it proves a local Harnack inequality for nonnegative generalized solution…
The paper proposes a general iterative method for extremal problems in Hilbert space with quasiconvex, possibly nonsmooth objectives and constraints. Instead of using gradients, the method moves along arbitrary supporting vectors to either the objective level set, when the current point is feasible,…
The paper studies irreducible and indecomposable Harish-Chandra modules over the Lie algebra of the proper Lorentz group, defined by their finite-multiplicity decomposition with respect to the maximal compact rotation subalgebra. It reduces the classification to algebraic categories determined by th…
This paper studies extremal sequences of regularly monotone polynomials on the interval [0,1] with periodically prescribed type numbers. It characterizes the derivatives of extremal polynomials, proves their least deviation property under endpoint vanishing conditions, and shows that the resulting s…
This review discusses A. V. Bitsadze’s monograph on boundary value problems for uniformly elliptic linear second-order partial differential equations and systems. It summarizes the book’s treatment of Dirichlet and oblique derivative problems, qualitative properties of solutions, fundamental solutio…
This paper generalizes Kolmogorov’s theorem on the density of points of local topologicity for countable-to-one open mappings by introducing the broader class of preopen mappings. It proves that a locally countable-to-one preopen mapping from a locally bicompact Hausdorff space has a dense set of po…
This paper studies partial sufficiency for repeated samples from a distribution with a shift parameter, with emphasis on polynomial estimators of functions of the parameter. It replaces ordinary partial sufficiency by a Hilbert space formulation for polynomials of bounded degree, defining sufficienc…
The paper studies individual asymptotic estimates for the number of integer solutions to Diophantine inequalities of the form measuring the distance of αq + β to the nearest integer against a decreasing function χ(q). It proves that when α satisfies a finite exceptional approximation condition, the …
The paper constructs a Green function for a two-sheeted Riemann space whose branch line is an ellipse, extending earlier potential-theoretic treatments of spaces with slits. Using coordinates adapted to an elliptic contour, it gives explicit integral formulas for the Dirichlet and Neumann problems i…
This paper studies Green matrices for homogeneous boundary value problems associated with linear Petrovsky parabolic systems satisfying the algebraic Lopatinskii condition. It proves that the solution operator is an integral operator and derives sharp pointwise and Hölder type estimates, up to the b…
This note develops a constructive-mathematical definition of generalized functions, modeled on the Mikusinski, Sikorski, and Korevaar approach. It first formalizes almost uniformly continuous functions, primitives, polynomial germs, and fundamental sequences of constructive function codes, then defi…
The article proves the following theorems: 1) If $A(t)$ is recurrent, then the system $\dot{x}=A(t)x$ can be reduced to the triangular form $\dot{u}=P(t)u$ with a recurrent matrix $P(t)$ by a Perron transformation $x=U(t)u$ with a recurrent matrix $U(t)$. 2) If $A(t)$ is almost periodic, then for th…
The paper studies multiplicative representations of the characteristic functions of contraction operators in a separable Hilbert space whose spectrum lies on the unit circle, with compact defect operator and a chain separating the spectrum. Building on work of Gohberg and Krein, it proves their conj…
This paper studies open continuous mappings in completely regular spaces, with emphasis on locally complete spaces and sigma-discrete or countably multiple fibers. It generalizes results of Aleksandrov and Kolmogorov by proving density of points of local topologicity for open locally sigma-discrete …
The paper studies restrictions on the induction schema in Kleene-style formal arithmetic, especially systems in which induction formulas contain at most a fixed number of quantifiers. Using Novikov’s method of regular classes, it shows that for every such bound there are formulas provable in full ar…
This paper studies the boundedness in Lp spaces of singular Cauchy-type integral operators taken over rectifiable Jordan curves whose tangent angle has bounded variation. It first establishes boundedness, and under continuity of the tangent angle compactness, for the real operator with kernel given …
The main results of the authors' previous note are generalized to a general linear second-order parabolic equation with a sign-definite lower-order coefficient $c(x,t)$ under very general boundary conditions. The presentation is primarily conducted for the case of a one-dimensional problem with cont…
This paper studies angular boundary values of quasiconformal mappings of a ball in Euclidean space. Using moduli of curve families, generalized curves, and capacity estimates, it proves that the exceptional set of boundary points at which angular boundary values fail has outer capacity zero: logarit…
Dragalin studies how parts of the theory of countable transfinite numbers can be transferred to constructive mathematics, with particular attention to defining algorithms by transfinite recursion. The paper introduces constructive transfinite systems equipped with a constructive order and transfinit…
This paper studies a differential game of pursuit for two linear controlled motions with bounded controls, where the pursuer seeks coincidence of specified coordinates in minimal worst case time. It relates the feedback synthesis problem to programmed minimax problems and formulates an extremal aimi…
The paper extends the averaging method to ordinary differential systems not solved explicitly with respect to the derivative, focusing first on equations of the form x dot equals epsilon times a function depending on time, the state, and the derivative. Under boundedness, Lipschitz, and uniform mean…
The paper studies best approximation by algebraic polynomials in the spaces \(L_q(-1,1)\), \(1 \le q \le \infty\), for functions with real singularities of the form \((x-a)^r |x-a|^\alpha \ln^m |x-a|\). Using a general limit theorem of S. N. Bernstein, it proves a generalized Bernstein-type inequali…
This note addresses lattice coverings of Euclidean space by equal balls, focusing on when the classical lattice associated with Voronoi’s principal form of the first type ceases to be optimal among lattice coverings. Using a modified lemma of Davenport and an analysis of orthogonal projections of Kr…
The paper studies systems of linear inequalities over an arbitrary ordered field and extends earlier results on polyhedrally closed systems beyond the real case. It defines polyhedral closedness via dual cones, develops the notion of hulls or convolutions with respect to subspaces, and gives consist…
This paper studies groups that are factorizable with respect to the system of all noninvariant subgroups, meaning that each such subgroup has a complement in the group. Building on earlier work on completely factorizable and primitively factorizable groups, it formulates an exhaustive classification…
This paper gives algebraic interpretations of Steiner triple and quadruple systems in terms of TS-quasigroups, TS-loops, and S-algebras with a ternary operation satisfying specified identities. It establishes one-to-one correspondences between Steiner triple systems, TS-quasigroups, and TS-loops, an…
This note studies contractible curves on nonsingular complex surfaces that preserve the canonical class, focusing on the curves whose contractions give rational double singularities. Using obstruction calculations for extending isomorphisms of infinitesimal neighborhoods, it proves that neighborhood…
This paper studies verbal subgroups of normal subgroups in nonabelian free groups and proves a general cancellation property for varieties of groups. It shows that if, for a group variety distinct from the variety of all groups, the inclusion of verbal subgroups V(R) contains V(S) holds for normal s…
This note solves the isomorphism problem for group algebras of countable abelian p-groups over fields, distinguishing the cases in which the field has characteristic p and characteristic different from p. It proves that in characteristic p the group algebra determines the countable abelian p-group, …
This note gives new examples of fields and classes of fields of finite characteristic whose elementary theories are decidable. It first characterizes elementary equivalence of separably closed fields of characteristic p by the invariant measuring the degree of imperfection, using model completeness …
