SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 25357 papers
The paper presents the conditions for the existence and provides an algorithm for constructing periodic solutions of the equation $$\frac{d^2x}{dt^2}=f\biggl(t,x,\frac{dx}{dt}\biggr),$$ the right-hand side of which is periodic in $t$. Bibliography: 6 items.
The paper develops a method for obtaining lower bounds on vibration frequencies for a class of connected elastic systems. The approach replaces a given system by a sequence of less rigid auxiliary systems constructed from the original one, expresses their influence kernels through determinant formul…
This paper studies arithmetic sums of sets of integers within the theory of recursively projective sets, motivated by analogies with projective sets and earlier work on arithmetic summation. It introduces symmetrically dense enumerable sets and proves that every such set can be decomposed as a nonre…
The paper studies complete orthonormal systems of functions associated with the Laplace operator in arbitrary domains without imposing boundary conditions, defining their corresponding spectral parameters as fundamental numbers. It proves that for any such system the fundamental numbers are unbounde…
This paper addresses the measurement of magnetostriction in very thin ferromagnetic films, a quantity important for understanding internal stresses, anisotropy, and magnetization processes in film materials. The authors develop an interferometric method using nickel films deposited on both sides of …
This note studies cohomology classes of connected closed Lie subgroups of general linear groups with coefficients in the sheaf of germs of continuous real-valued functions, using a category of locally trivial principal bundles over Hausdorff bases. It constructs universal-type principal bundles from…
This note develops constructive methods for generalized smoothing and extrapolation problems for random vector functions, using the Hilbert space framework and notation established in an earlier work. It relates optimization with respect to general forecast quality criteria to auxiliary minimum vari…
This paper studies the stability, for small values of a scalar parameter, of systems of linear differential equations with periodic coefficients in an operator polynomial form. It proposes a method based on associated integral equations and finite systems for selected Fourier harmonics, yielding alg…
The paper investigates anisotropy in angular scattering and the structure of energy spectra for alkali ions scattered from single crystal tungsten surfaces, with emphasis on the [100] face. Using an electrostatic analyzer with improved resolution, the authors measure energy distributions of secondar…
The paper studies an extremal problem for finite systems of quadratic constraints associated with cosine coefficients and relates it to linear methods of summation of Fourier series. It proves that, when the cosine series with coefficients \(h_k\) converges uniformly to a function \(f\), the limitin…
This paper studies local features of smooth homogeneous random fields, including spikes, glints, and saddle points above a specified level, viewed as random point flows in Euclidean space. It develops a general framework for regular random flows, defines higher order measures and intensities, and re…
The paper extends results of A. F. Leont’ev on sequences of Dirichlet polynomials to functions of several complex variables, formulated mainly for two variables. It studies uniform convergence of double sequences of Dirichlet polynomials with prescribed exponent densities, proving extension of conve…
This paper studies the high energy asymptotics of the spectral function kernel for the Schrödinger operator on Euclidean space with a nonnegative potential. Under analyticity and growth conditions on the potential along the line segment joining two points, it derives a refined off diagonal asymptoti…
The paper develops a dynamic macroeconomic model with two products and two departments, in which the first department produces accumulation funds and the second produces consumption goods. Using homogeneous production functions, given labor resources and consumption, and assumptions on nontransferab…
This paper proposes that the Einstein gravitational action may arise from changes in the action of quantum vacuum fluctuations when spacetime is curved, rather than being a fundamental postulate. By expanding the vacuum Lagrangian density in powers of curvature, the argument identifies the term line…
A set of systems of differential equations is constructed, possessing specified singular points (foci, centers, nodes, and saddles), limit cycles, and separatrices. Bibliography: 5 items.
This paper studies strong continuous summability methods for general trigonometric series and their application to Fourier series. It defines summability by a family of nonnegative weights, gives conditions for comparison between exponents, uniqueness of limits, and Toeplitz regularity, and shows th…
The paper addresses the variational formulation of dynamic problems in elastic shell theory when the motion is specified by initial conditions rather than by prescribed terminal positions as in Hamilton’s principle. For a linear Timoshenko-type shell model, it introduces kinematic variables, stress …
The paper studies finite-dimensional division algebras over the real numbers, especially those of dimensions 4 and 8 and those with associative powers. Using deformation and topological arguments, it shows that the set of real division algebras is open in the corresponding space of algebras and has …
This paper addresses radiative diffusion in media whose scattering indicatrix is strongly elongated in the forward direction, a case relevant to dusty nebulae, planetary atmospheres, and water. It proposes an approximate reduction of the integro-differential radiative transfer equation to a second-o…
The study examines the size dependence of the mechanical strength of tungsten microcrystals with diameters far below one micron, a range previously difficult to test for whisker crystals. Tungsten needle specimens were prepared by electrochemical polishing and studied at 77 K using field-ion microsc…
The paper examines the stability of transverse motion of a charged particle in a spatially homogeneous, cylindrically symmetric magnetic field whose strength is sinusoidally modulated in time, including the associated induction electric field near the cylinder axis. The equations of motion are trans…
This paper formulates variational principles for equations of gas kinetic theory by treating the gas as a continuous medium in phase space and varying phase trajectories under conservation of phase density. Starting from Hamilton’s principle for an N-particle system, the author derives a variational…
This paper experimentally investigates the probability distribution of the square of the temperature difference between two closely spaced points in a turbulent atmospheric flow, motivated by theories of intermittency and lognormal dissipation in high Reynolds number turbulence. Temperature differen…
This paper studies best unbiased estimation of parametric functions in incomplete exponential families whose natural parameters are restricted by polynomial equations. For samples summarized by sufficient statistics, it gives necessary and sufficient conditions under which a statistic with finite va…
The paper constructs extensions of a separated locally convex real topological vector space by replacing the scalar field with the Banach algebra of bounded real functions on an arbitrary nonempty set. It defines the associated modules built from continuous linear maps into this algebra, establishes…
This paper develops a lattice-based treatment of dislocations in a two-row crystal, addressing limitations of continuum descriptions and of the Frenkel-Kontorova model, particularly the assumption of an undeformable row. The authors formulate equilibrium difference equations for rectangular and hexa…
This paper studies the global structure of connected complete analytic Riemannian spaces whose metric is locally semi-reducible, namely of the form \(ds^2=d\rho^2+f\,d\theta^2\) with the two factors depending on separate coordinate groups. Using maximal analytic continuations of the two orthogonal c…
The paper studies a nonlinear Riemann boundary value problem for functions analytic inside and outside a smooth closed contour, with a boundary condition containing an nth power and a singular integral nonlinear term. Under modulus of continuity assumptions on the given functions and growth and Lips…
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 addresses the definition of gravitational energy in general relativity under Zelmanov’s chronometric invariance, arguing that observable energy should be invariant under admissible time transformations and transform appropriately under spatial coordinate changes. Using Noether’s theorem fo…
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 examines the applicability and simplification of hydrodynamic equations for modeling the structure and general circulation of the upper atmosphere above roughly 30 to 50 km. Using Knudsen number estimates based on reference atmospheric parameters, it argues that Navier-Stokes equations are…
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 paper examines how the radio emission flux of local solar sources is related to the optical structure of active regions, using statistical processing of daily observations from 1961 and 1963. A least squares model separates contributions from main sunspots, other spots in the same groups, plage…
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…
This study examines the low-temperature polarization spectra of asymmetric aza-tetrabenzoporphins and their magnesium complexes in order to clarify how aza substitution affects the electronic transitions of the porphyrin chromophore. Using polarization of fluorescence as a function of excitation wav…
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 considers a third-order dynamical system with a variable structure. The switching surface is defined by a pair of intersecting planes. Necessary and sufficient conditions for the existence of a sliding mode, stability conditions for motion along the switching surface, and necessary and suf…
This paper examines multiple collisions in the scattering of keV noble gas ions by crystalline and polycrystalline metal surfaces, focusing on how double-scattering peaks can shape measured energy spectra. Experiments with neon, argon, and krypton ions scattered from nickel and copper crystals, with…
The paper develops an asymptotic calculation of retarded Green’s functions for a superfluid Bose system in the viscous hydrodynamic approximation at small wave number and frequency. External scalar, vector, and particle-source fields are introduced into the Hamiltonian, allowing hydrodynamic variabl…
