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 characterizes additional conditions needed to make the heat equation in a plane domain with an oblique derivative boundary condition well posed when the oblique field has exceptional boundary points where its normal component changes sign. Using the language of positive contraction semigro…
This paper investigates short range intermolecular forces in oxygen and nitrogen systems using elastic scattering of fast neutral molecular beams in oxygen, nitrogen, and argon. From the energy dependence of total effective scattering cross sections at 0.6 to 4 keV, the authors derive parameters for…
This study uses nuclear quadrupole resonance to examine whether statistically disordered crystals of p-nitrochlorobenzene can be converted into ordered modifications by growth on crystalline matrices of p-bromo- and p-iodonitrobenzene. Mixtures were prepared by zone melting to create impurity gradie…
This paper studies mutual convergence of two principal functions within finite systems of auxiliary functions subject to uniform increment bounds and sublinear error terms. It defines comparison sets and extremal auxiliary quantities that measure how closely auxiliary functions approximate the princ…
The paper develops an asymptotic splitting method for linear automatic control systems with slowly varying coefficients and an arbitrary continuous forcing term regular in a small parameter. Under a spectral separation condition for groups of eigenvalues of the leading matrix, it constructs formal t…
This paper formulates asymptotically optimal control as a model for learning in statistical control systems with unknown object equations and unknown disturbance characteristics. It considers a discrete controlled process and a quality criterion defined by an expected function of output, input, and …
This paper introduces sampled Boolean functions over finite Galois fields and defines their discrete Laplace, or Laplace-Galois, transform as a tool for analyzing sequential machines. It gives direct and inverse transform formulas, including a residue-based inversion method, and states basic operati…
This note studies solutions, in the space of generalized functions \((S_0^\beta)'\) with \(\beta>1\), of a class of ordinary differential equations with polynomial coefficients of the form \(\sum_{p=0}^{n}\sum_{k=0}^{m_p} a_{kp}x^{k+p}y^{(k)}=0\). It first characterizes solutions concentrated at the…
This paper studies finite-dimensional approximation of an infinite-horizon optimal control problem for linear systems with aftereffect, where the control must stabilize the system while minimizing a quadratic integral cost. Krasovskii formulates approximating systems and cost functionals, specifies …
The study investigates damage produced by ordinary and giant laser pulses in transparent dielectrics, including alkali halide single crystals, polymethyl methacrylate, and glasses. Experiments varied pulse energy, focal position, temperature, and lens focal length, showing that damage morphology dep…
The paper studies a mathematical problem arising in biophysics, namely diffusion and transformation of substances inside and outside a living cell with membrane permeability conditions. It formulates a more general system of parabolic equations in two adjoining domains with special discontinuities i…
The paper derives nonlinear equilibrium equations for elastic shells of arbitrary shape, addressing the need to include not only rotations and elongations of middle-surface line elements but also shear effects. Using curvilinear coordinates along the lines of curvature and moving trihedra attached t…
The paper studies resonances in multifrequency oscillatory systems with slow variables and fast phase variables, defining resonance surfaces, resonance phases, and a complexity index for states satisfying independent integer resonance relations. It shows that, by an integer change of phase variables…
This paper examines the dynamics of Earth’s crust in Atlantic-type transition zones between continents and oceans, focusing on submerged shelves, submarine canyons, truncation of continental structures, and the form of continental slopes and rises. It argues that these features are not adequately ex…
The paper addresses cycling in the simplex method for linear programming, noting that existing anti-cycling procedures increase the number of divisions relative to the nondegenerate case. It introduces a lexicographic polynomial framework for simplex tableaux and proves a main theorem showing how, u…
This paper examines the distinction between exact natural vibrational coordinates, defined by changes in molecular geometrical parameters, and approximate natural coordinates, defined as linear functions of atomic displacements from equilibrium. It shows that approximate coordinates simplify the kin…
This paper derives Einstein’s gravitational equations from a flat space field-theoretic treatment of an interacting symmetric tensor field. Starting with a massive tensor field subject to a Hilbert-Lorentz type supplementary condition and then taking the massless limit, the authors require minimal i…
The paper studies the main homogeneous boundary-value problem for a parabolic equation whose principal part degenerates on part of the boundary, in a cylindrical domain with a planar cross-section satisfying geometric and elliptic solvability conditions. Weighted Sobolev spaces adapted to the degene…
The paper studies existence of solutions for a two-point boundary-value problem for a nonlinear ordinary differential equation of order n, with initial conditions imposed at one endpoint up to order n minus 2 and one derivative condition at the other endpoint. It proves an existence theorem under a …
High-temperature X-ray diffraction was used to examine phase transitions in ceramic bismuth ferrite, BiFeO3, over 20 to 850 degrees, with particular attention to the previously unstudied interval near the expected Curie temperature. Measurements of rhombohedral cell parameters at 38 temperatures rev…
The paper studies when molecular measures, finite linear combinations of point masses, approximate broader classes of measures under locally convex topologies defined by families of test functions. It formulates a general duality between a free linear space on a set and a function space, then gives …
This note responds to a critical remark in K. S. Sibirskii’s article on the number of limit cycles near a singular point, specifically concerning Bautin’s earlier work on focus and center type equilibria. Bautin argues that the remark is incorrect because the relevant divisibility condition for the …
This paper studies completeness of systems of analytic functions of the form z^n F^(n)(lambda_n z), where F is an entire function and the moduli of the complex parameters lambda_n increase to infinity. Using the Abel-Goncharov interpolation formula, the authors derive conditions under which the inte…
The paper studies almost everywhere divergence of Fourier series in eigenfunctions of the Laplace operator for functions on multidimensional domains, focusing on the ball in dimensions at least two with homogeneous Dirichlet or Neumann boundary conditions. Using spherically symmetric eigenfunctions …
The paper studies the reconstruction of a smooth compactly supported function in odd-dimensional Euclidean space from its integrals over ellipsoids determined by a positive definite quadratic form. Using generalized functions, convolution identities, and Fourier transforms involving Bessel functions…
This paper examines how melting in a shock wave affects the shock adiabat of lead, a substance that expands on heating, and argues that the two-phase and liquid portions of the adiabat should deviate toward larger specific volume. The authors combine thermodynamic considerations with plane-impact ex…
This paper reports measurements of penetrating radiation made by the Luna-9 station during its flight to the Moon and after its soft landing in Oceanus Procellarum. Using an SBM-10 gas-discharge counter shielded by approximately 1 g/cm2 of aluminum, the authors compare counting rates in interplaneta…
The paper studies anisotropic Sobolev spaces with fractional Bessel derivatives in different coordinate directions and introduces corresponding anisotropic Bessel potentials defined through Fourier multipliers. It proves that these potentials of functions in \(L_p\) coincide with the spaces \(L_p^{(…
The paper develops a model for the surface brightness distribution in a cometary head, treating particles emitted from the nucleus under solar repulsive acceleration and then extending the calculation to a Maxwellian dispersion of initial velocities. It derives expressions for the visible particle d…
This note studies representations of cusp forms for the group of prime level by quaternary theta series, refining Eichler’s results on Hecke’s conjecture. For cusp forms of type with trivial character that are simultaneous eigenfunctions of the Hecke operators, the argument compares the Hecke repres…
This paper studies the local behavior near a singular point of a completely solvable multidimensional first order differential equation with analytic nonlinear terms. It extends classical one-dimensional linearization results of Poincaré, Picard, and Dulac by deriving conditions under which a formal…
This note extends Jacobi’s rule for determining the numbers of positive and negative squares of a Hermitian form to arbitrary finite Hermitian Toeplitz forms, including cases where leading principal minors vanish. It analyzes the structure of zero blocks in the sequence of Toeplitz determinants, pro…
This paper addresses the problem of determining the preatmospheric size of iron meteorites and the original depth of recovered specimens within their parent meteoroids. It develops a method based on modeled depth distributions of cosmogenic isotope production rates, using differences in excitation f…
The paper examines whether solar neutrino measurements can be used to determine the temperature of the solar interior more directly than is possible from evolutionary solar models. It argues that high threshold detectors are chiefly sensitive to boron 8 neutrinos, while gallium detectors are sensiti…
This paper studies approximation by piecewise linear extensions of grid functions on simplicial complexes and applies the results to grid methods for elliptic boundary value problems in n-dimensional domains. It constructs families of complexes adapted to smooth boundaries and proves estimates for a…
This note analyzes pseudoscalar meson photoproduction on nucleons in a p state under absorption of magnetic dipole gamma quanta within SU(6) symmetry. Using SU(6) tensor methods for baryons, mesons, the photon operator, and an angular spurion, the authors count the invariant structures in the releva…
This note studies pseudodifferential operators on smooth manifolds for which Sobolev estimates of subelliptic type hold with loss parameter between 0 and 1. It characterizes such operators, termed operators of principal type, by conditions depending only on the principal symbol, reducing the verific…
The paper studies the interpretation of logical formulas by finitary problems and gives algebraic criteria for finite universal validity. It represents reduced systems of finitary problems by closed families in a Boolean algebra with closure, obtains corresponding Brouwer algebras, and proves that a…
This paper examines the dynamic buckling of a hinged elastic rod with initial curvature subjected to longitudinal impact by a rigid mass, accounting for the propagation and reflection of compression waves along the rod. Nonlinear equations for axial and transverse motion are formulated and solved nu…
This note studies periodic nilpotent subgroups of the full linear group over the field of rational numbers. It first classifies irreducible such subgroups, showing that they can occur only in degrees equal to Euler’s function of an integer and describing maximal irreducible cases by Kronecker produc…
The paper addresses the inverse scattering problem for a canonical half-line Dirac system with real decaying coefficients and boundary condition at the origin. It introduces scattering data consisting of the scattering phase, discrete eigenvalues in the spectral gap, and corresponding norming consta…
This note studies centrally symmetric self-similar motion of a relativistic gas in comoving coordinates, motivated by late-stage stellar collapse. Using Podurets’s reformulation of the Einstein equations in terms of the enclosed gas mass, the author reduces the field equations to ordinary differenti…
This paper examines the reconstruction of images of transparent and refracting objects using phase holograms, with attention to the improved brightness and contrast obtainable relative to amplitude phase holograms. The authors describe a transmission holography arrangement using a helium neon laser,…
This paper proposes a structural interpretation of electrooptic and thermooptic effects in triglycine sulfate type ferroelectric crystals, emphasizing the role of distorted sulfate or selenate tetrahedral ions in addition to nitrogen displacement in glycine groups. The authors argue that changes in …
