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
This note examines the gravitational collapse of a mass with small axial deviations from spherical symmetry, focusing on the behavior of nonspherical metric perturbations near the gravitational radius. Using a linear perturbation of the Schwarzschild metric, expansion in generalized spherical functi…
This note studies covering problems for plane analytic sets in Baire space whose vertical sections satisfy a hereditary property. Using Lyapunov’s general theorems on multiple separability, it gives a construction that covers an analytic set, or the relevant sections of such a set, by a Borel or coa…
The paper studies the analytic structure of Hilbert subspaces generated by homogeneous random fields on Euclidean space, reducing the problem through the spectral representation to weighted spaces generated by exponentials over bounded parameter sets. For rectangular sets, it gives sufficient logari…
This paper compares several restricted classes of predicates used in algorithm theory, including rudimentary, bounded-arithmetical, logarithmic Turing-computable, real-time, marked-machine, context-free, and s-rudimentary predicates. Its main tool is a sufficient condition showing that predicates co…
This paper develops a generalization of Mindlin’s method for elasticity problems in a half-space by using analytic continuation of elastic solutions through a plane boundary. It formulates reflection laws for body forces that allow boundary-value problems with either vanishing displacements or vanis…
This paper examines how shear stresses affect the acoustic parameters of longitudinal and transverse elastic waves in rock samples, a topic for which little experimental evidence was available compared with compression studies. Cylindrical samples of granite, sandstone, and marble were subjected to …
This note proposes a real analogue of Pyatetskii-Shapiro’s construction of Siegel domains, defined from a vector space with involution, a homogeneous convex cone, and a definite Hermitian bilinear mapping. It proves that homogeneous Siegel domains are affinely homogeneous, then specializes the const…
The paper applies a spin-dependent version of the factorizing quark model to high-energy production processes in which a pseudoscalar meson and proton produce a vector meson and a positive-parity baryon. It argues that, although quark spin-flip amplitudes are small relative to the main quark scatter…
The paper examines the limiting case of separating a crystallographic basic point system from its vector system when the selected vector peak has multiplicity two in the Fedorov group P1. It argues that when two pairs of points in the basic system define equal vectors, the corresponding vector syste…
This paper studies the stability of relaxation processes for minimizing a differentiable functional on a convex domain in a real Hilbert space under strong monotonicity and Lipschitz type bounds on its derivative. It analyzes perturbed iterations with additive noise, measuring perturbations first by…
This note studies sequential estimation for scalar parametric families, comparing non-Bayesian sequential plans with fixed-sample Pitman estimation under constraints on expected sample size. Under smoothness assumptions expressed as absence of discontinuities in information quantities, the authors s…
This paper reports a computational verification of Fermat’s Last Theorem for all odd prime exponents below 5500 using Vandiver’s criterion for irregular primes, together with Kummer’s result for regular primes. Computations on the BESM-6 computer rechecked earlier SWAC results below 4002, extended t…
This note studies a form of modeling finite pseudo-Boolean algebras by systems of arithmetical formulas under Kleene realizability, in connection with realizability of propositional formulas and intuitionistic arithmetic. It defines when such a system models an algebra, proves by induction that alge…
The paper studies error estimation for finite difference solutions of the Dirichlet problem for the Laplace and Poisson equations in a bounded plane domain. It derives weighted a priori estimates for the grid solution and for difference approximations to derivatives of arbitrary order, with dependen…
The paper constructs several compact Hausdorff spaces for which the covering dimension and the small and large inductive dimensions do not coincide. Using modified topologies obtained by replacing points of the square with circles or previously constructed compacta, it gives examples with dim equal …
The paper studies the decoding of finite Mealy automata treated as black boxes when no upper bound on the number of states is available, focusing on what can be achieved by simple experiments rather than multiple branching experiments. It formalizes decoding algorithms, introduces a uniform frequenc…
This note studies boundary behavior of the Poisson integral in a half-space and applies it to the Dirichlet problem for the Laplace equation with very general boundary data. It states several Fatou-type results showing when derivatives and mixed derivatives of the Poisson integral converge to corres…
This paper examines how crystal habit may be related analytically to the pressure and temperature conditions of growth, using diamond crystals as the principal example. It proposes a thermodynamic approach in which the numbers of faces and vertices of a convex crystal polyhedron are treated as addit…
The paper studies conditions under which topological and metrizable spaces can be compactified or condensed onto compacta, with special attention to points of noncompactness and non-pi-compactness. It shows by examples that compactifiability onto compacta is not determined simply by the correspondin…
This paper reports spectrophotometric observations of the Earth and its atmosphere made from the Soyuz-7 spacecraft during the October 1969 group flight, extending earlier measurements from Soyuz-5. Using a modified hand-held RSS-2 spectrograph, the authors measured the twilight halo and the spectra…
The paper studies uniqueness for the Cauchy problem for general linear partial differential equations with constant coefficients and zero initial data, under growth restrictions imposed only on one spatial half-axis rather than on the whole line. Using the Newton-Puiseux asymptotics of the roots of …
The paper studies Darboux problems for a second order hyperbolic equation whose coefficient of the second \(x\)-derivative may vanish on the boundary line, allowing parabolic degeneration. Using a weighted energy identity, an exponential change of unknown, and suitable choices of weights, it proves …
The paper reports radio astronomical measurements of right ascensions for Galactic sources of anomalously excited OH emission, motivated by the need to identify OH regions with infrared and other astronomical objects. Observations were made in 1969 with the Large Pulkovo Radio Telescope at 1612 MHz …
This study applies the solubility method to examine isomorphous substitution in yttrium aluminum and yttrium gallium garnets containing neodymium, using a PbF2, PbO, and B2O3 melt as solvent at 1100 °C. Solubility isotherms were obtained for systems involving Y3Al5O12, Y3Ga5O12, Nd3Al5O12, and Nd3Ga…
The paper proves that the Hilbert parallelepiped, or Hilbert cube, cannot be represented as a countable union of proper closed subsets whose pairwise intersections are weakly infinite-dimensional. The argument develops several auxiliary results on weakly infinite-dimensional spaces, normal adjoining…
This paper studies a differential game of approach in which two players choose constrained controls entering jointly, rather than separately, in the system dynamics. It formulates the problem in the class of mixed approximating strategies, introduces extremal strategies and a modified notion of posi…
This paper examines electron, phonon interaction in Nd3+ activated Y3Al5O12 crystals through temperature dependent induced emission spectroscopy. The authors analyze how generation energy, line width, wavelength shift, and saturation behavior vary with temperature, comparing experimental data with k…
The paper studies an algebraic representation problem arising in control theory for a controllable linear system with a Hermitian form in the state and input variables. It seeks conditions under which the form can be written as the derivative of a quadratic Lyapunov-type expression plus a quadratic …
This paper examines borderline conditions for convergence in the L metric of trigonometric Fourier series and their conjugate series. It constructs a summable periodic function whose integral modulus of continuity, and that of its conjugate function, are both of order 1 divided by log 1 over delta, …
This note studies the optimization of algorithms for numerical differentiation, numerical integration, and interpolation on classes of functions modeled by generalized Sobolev-type Hilbert spaces. Using the functional-analytic principle of minimizing the norm of the corresponding error functional, t…
This note revisits a theorem of M. V. Keldysh and M. A. Lavrentiev concerning boundary behavior of nonconstant harmonic functions attaining their lower limiting value at a boundary point, with implications for uniqueness in the Neumann problem. It extends the result from a three-dimensional parabolo…
This paper studies differential games in which the payoff is the time required for a controlled trajectory to reach a target set, under restrictions on admissible phase states. The constrained motion is modeled by adding a normal reaction term to the differential inclusion, and the author extends no…
This paper investigates the origin of hole conductivity in selenium and the role of oxygen impurities in determining carrier type. The authors measure electrical conductivity and thermoelectric emf in amorphous selenium with varying crystallinity and in single crystalline hexagonal selenium before a…
This paper studies regular differential operators on the basic affine space of a connected semisimple algebraic Lie group over an algebraically closed field of characteristic zero. It introduces a projection-like operation from regular functions on the group to regular functions on the quotient by t…
This paper studies polynomial approximation of continuous functions on bounded convex polyhedra in multidimensional Euclidean space, with attention to improved local estimates near vertices. It proves that for a function on a convex polyhedron there are polynomials whose error is controlled by the k…
This paper analyzes the dynamic buckling of cylindrical fiberglass shells treated as orthotropic under axial impact by a finite striking mass, including the effect of initial geometric imperfections. The authors formulate the problem using nonlinear shell equations, approximate rhomboidal dent shape…
This paper examines thermo-optical properties of neodymium-activated laser glasses, motivated by thermal gradients in optically pumped glass rods that can distort resonator wavefronts despite high initial optical homogeneity. It presents a direct interferometric method for measuring the thermo-optic…
This paper derives asymptotic formulas for the global error in numerical solutions of Cauchy problems for systems of ordinary differential equations. Under smoothness assumptions on the right-hand side and bounded local and round-off errors, it presents expansions for third- and fourth-order Runge-K…
This paper examines whether a decompression, or density decrease, zone may exist in the upper mantle corresponding to the seismic low-velocity layer, contrary to mantle density models that assume only positive density gradients. It reviews earlier rheological, thermodynamic, and seismological argume…
The paper presents a fitting method for solving the two-dimensional variometric inverse problem of potential theory, aimed at determining the contour of a subsurface body of constant excess density from measured horizontal gravity gradients. The variometric formulation is reduced to a gravimetric in…
This paper investigates how amorphous boundary layers can preserve and transmit structural information from crystal surfaces, focusing on a proposed photoelectret mechanism in selenium films deposited on NaCl cleavage surfaces. Amorphous selenium layers were formed under controlled illumination cond…
The paper studies the first boundary-value problem for a class of quasilinear systems in divergent form, formulated through abstract additive homogeneous operators and variable Orlicz, Sobolev-type spaces. Building on a theorem of Browder and Dubinskii, it introduces structural, coercivity, monotoni…
This paper estimates electron positron pair production when intense focused laser radiation irradiates a dense, initially nonrelativistic plasma. The authors argue that, at attainable laser intensities, pair creation involving electron scattering by nuclei is far more probable than production by int…
This note studies the realization of homology and homotopy cycles in compact symmetric spaces by totally geodesic submanifolds, emphasizing metric restrictions absent from purely topological realization problems. It reduces the problem for compact Lie groups to Cartan embeddings of irreducible compa…
This note studies multiplier transformations that replace the symbol of a pseudodifferential operator by its product with a function depending on frequency and space variables, asking when such transformations preserve boundedness in spaces \(L_p(R^m)\). It introduces function space conditions on th…
This paper studies the existence of periodic solutions for systems of ordinary differential equations with periodic time dependence by reducing the problem to zeros of completely continuous vector fields in a Banach space. For systems whose leading term is positively homogeneous and whose perturbati…
This paper studies exponential dichotomy and Green’s functions for linear functional differential equations with almost periodic coefficients, formulated through operators acting on spaces of bounded continuous and almost periodic functions. Under stated bounded variation and almost periodicity assu…
The paper studies bifurcation and asymptotic bifurcation points for a nonlinear Hammerstein integral equation with a potential Carathéodory nonlinearity and a symmetric kernel whose associated self-adjoint operator has at most finitely many negative eigenvalues. Using ideal spaces of measurable func…
This paper develops analytical expressions for the yield of characteristic X-ray photons emitted into one steradian per incident ionizing particle, as a parameter for comparing primary spectra excited by electrons and secondary spectra excited by X-ray photons. Using excitation-density models that i…
This paper proposes and analyzes a continuous-wave carbon dioxide laser in which the usual gas-discharge excitation is replaced by optical pumping from an alkali-metal resonance lamp. The authors describe an excitation chain in which resonant absorption by alkali-metal atoms transfers energy through…
