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 paper classifies Harish-Chandra modules for the group SL(2,C), understood as representations whose dense subspace decomposes algebraically with finite multiplicities under a maximal compact subgroup. It constructs elementary modules from associated homogeneous functions, describes their composi…
This paper studies a Cauchy problem for second order hyperbolic equations containing a small positive parameter, with initial data that produce an initial jump in the singular limit. It constructs a matched asymptotic expansion in powers of the parameter, combining regular terms satisfying reduced f…
This note applies Strassen’s fast matrix multiplication to the computation of the transitive closure of a directed graph. It observes that Boolean matrix multiplication can be carried out by ordinary multiplication of zero one matrices followed by thresholding, giving a bound of order n to the log b…
The paper studies traces of functions in anisotropic Sobolev spaces on smooth hypersurfaces under a condition relating the minimum and maximum smoothness indices. Building on a general characterization of trace spaces by an integral equation with kernel determined by the surface and the Sobolev norm…
The paper studies the decomposition of the tensor product of two irreducible maximally degenerate unitary representations of the group of complex matrices of order n with determinant 1, for n at least 3. Using a modification of the horosphere transform method of Gelfand and Graev, the tensor product…
This paper investigates antiferromagnetic resonance absorption in copper chloride dihydrate in an inclined magnetic field at low microwave frequencies between 0.65 and 5.2 GHz. Measurements of the resonance field as a function of the angle between the easy axis and the external field show frequency-…
This paper studies harmonic vector functions in the upper half-space satisfying generalized Cauchy-Riemann conditions, with emphasis on multidimensional analogues of classical results on conjugate harmonic functions. It defines Hardy-type classes H^p and S^p, gives a Fourier-transform characterizati…
The paper studies the low-energy and long-wavelength asymptotics of one-particle Green’s functions in a weakly nonideal Bose gas at low temperature. Using a projection method for decoupling equations of motion, the analysis extends the operator basis to include collective variables associated with q…
The paper studies nonlinear periodic waves governed by the Korteweg de Vries equation in a weakly inhomogeneous medium, focusing on exponentially small changes of wave quantities analogous to adiabatic invariants. By decomposing the Hamiltonian into a homogeneous part and a small inhomogeneous pertu…
This paper analyzes the radial stability of an infinite cylindrical incompressible conductor placed eccentrically inside a cylindrical surface carrying an azimuthal traveling-wave current. Using the quasi-stationary approximation, the Leontovich boundary condition, and Bessel-function expansions, it…
This paper reports an experimental observation of low-frequency ultrasonic modulation in the radiation intensity of solid-state traveling-medium lasers, in addition to previously noted high-frequency kinematic modulation. Oscillograms from ruby and neodymium-glass traveling-medium lasers show intens…
The paper studies local questions in Banach analytic spaces where closed subspaces need not be complemented, a difficulty that obstructs direct extension of finite-dimensional analytic arguments. It introduces a completeness condition and proves existence and factorization results for finite-dimensi…
The paper introduces the polyhedron defined by positive quadratic forms with fixed arithmetic minimum and develops its basic properties in the coefficient space of quadratic forms. It shows that this polyhedron is locally finite, invariant under integral unimodular transformations, has vertices corr…
This paper presents a colorimetric analysis of twilight sky aureole spectra observed near the horizon from the Soyuz-5 spacecraft under conditions of continuous cloud cover and a solar depression angle near zero. Using measured monochromatic brightness and standard colorimetric functions, the author…
This paper studies absolute stochastic stability for automatic control systems represented by nonlinear Volterra integral equations with random external inputs. It defines stochastic stability in terms of functionals measuring the input process and the corresponding solution, and derives frequency-d…
This paper proposes a small-angle X-ray scattering method for estimating distances between heavy atoms introduced into macromolecules in solution. The authors derive the scattering contributions from the macromolecule, the heavy atoms, and their interference, arguing that the heavy-atom term can pro…
The study determines the crystal structure of the anhydrous plate form of copper DL-alpha-alaninate, a compound unsuitable for conventional X-ray analysis because it forms very thin, brittle plates. Electron diffraction patterns from textured polycrystalline specimens and spot patterns were indexed …
This paper studies infinitely divisible probability laws whose alpha-components are all infinitely divisible, a subclass arising in the theory of decompositions of probability laws. It gives a sufficient condition, distinct from earlier criteria of Linnik, for a law with a compound Poisson type Lévy…
This paper studies lower bounds on the complexity, defined as representation length, of normal algorithms that decide or enumerate predicates on finite sets of words. It introduces a reducibility notion for normal algorithms and proves that universality with respect to this reducibility is equivalen…
The paper proves a decomposition theorem in dimension theory: an n-dimensional cube cannot be represented as a countable union of proper closed subsets whose pairwise intersections have dimension at most n minus 2. The argument extends Urysohn’s two-set result by using continua joining opposite face…
This paper examines the distribution of mercury in meteorites and its possible significance for interpreting elemental abundances in planetary materials. Using a chemical analytical method with sensitivity sufficient for iron and stony iron meteorites, the authors report about 100 determinations fro…
This paper studies illumination from within of the boundary of unbounded convex bodies in Euclidean space, where a boundary point is illuminated by another if the open segment between them lies in the interior. It proves that the entire boundary of an unbounded convex body is internally illuminable …
This note studies the existence of Poisson-stable solutions for differential equations in Banach spaces, allowing nonunique solutions and without assuming global solvability for all initial data. It develops a method of limiting transformations based on convergence of shifted functions, compactness …
This study examines how ion species and irradiation dose affect the crystallization of amorphous silicon dioxide films during subsequent annealing. Films deposited from tetraethoxysilane in an argon oxygen plasma were irradiated with 50 keV argon, phosphorus, or boron ions over a range of doses, ann…
This paper studies the unsteady magnetohydrodynamic flow of a supersonic electrically conducting ideal gas in a plane dielectric channel as it enters or exits a nonuniform transverse magnetic field. The authors formulate the coupled gas-dynamic and electrodynamic problem for finite magnetohydrodynam…
This note studies the boundary behavior of regular solutions to uniformly elliptic second order equations in bounded domains whose boundary points admit inner or outer contact by generalized paraboloids. Using barrier constructions and assuming the maximum principle, it establishes lower estimates n…
This note formulates the approximate solution of nonlinear operator equations in Banach spaces as a controlled process in which different iterative methods are switched according to an admissible control. It introduces optimization problems that seek either the best accuracy under a cost bound or th…
This paper examines relations among topological entropy, Kolmogorov epsilon entropy, and metric entropy for homeomorphisms of compact metric spaces. It proves that topological entropy can be obtained as the limiting growth rate of the epsilon entropy of orbit metrics, and establishes, for compact me…
The paper studies equivalence relations among absolute bases in Köthe spaces, focusing on when bases are equivalent up to isomorphism, scalar multiplication, and permutation. It introduces the multiplicity of a basis as the minimal number of regular subsequences needed after permutation, defines Ris…
The paper develops a generalized form of Lyapunov’s second method for systems with small perturbations, including stability with respect to only part of the variables in the neutral case. It replaces standard definiteness requirements on a Lyapunov function and its derivative by conditions involving…
The paper studies complete orthonormal systems of Laplace eigenfunctions in bounded domains and the corresponding spectra of nonnegative self-adjoint extensions of the minimal Laplacian. It first shows that in one dimension, for an interval or a finite union of intervals, the fundamental numbers hav…
This note studies exact upper bounds for best approximation of differentiable periodic function classes by trigonometric polynomials in the uniform and integral metrics. For classes whose r-th derivative has a prescribed convex modulus of continuity, the author proves that the extremal error is atta…
The note studies space complexity analogues of known undecidability results for algorithmic problems in finitely presented groups and semigroups, especially word, conjugacy, and individual conjugacy problems. By refining constructions of Bokut, Collins, and Shepherdson and estimating the associated …
The paper studies topological spaces defined by generalized distance functions, especially continuous, weakly continuous, and semicontinuous o-metrics, symmetric o-metrics, and Delta-metrics. It formulates analytic conditions on these functions and proves several metrization and structural results, …
This paper studies fundamental systems of functions for the Beltrami operator on a Riemannian domain, a framework that includes trigonometric systems and eigenfunctions of elliptic boundary value problems without imposing boundary conditions. It proves a mean value formula for regular solutions of t…
This paper studies probabilistic properties of pairwise Hamming distances among a random subset of vertices of the n-dimensional unit cube, where vertices are chosen with independent Bernoulli coordinates. For prescribed distance intervals, it analyzes the counts of pairs whose distances fall in eac…
This paper studies the existence of values in differential pursuit games in Euclidean space, where two players choose measurable controls under standard continuity, Lipschitz, compactness, and growth assumptions. It defines piecewise-programmed strategies and examines three payoff types: terminal di…
This paper examines nonstationary finite-amplitude wave propagation in nondispersive dissipative media, focusing on plane and cylindrically symmetric acoustic, and by analogy magnetoacoustic, disturbances. By applying self-similar substitutions, the governing nonlinear partial differential equations…
This paper examines features of Patterson syntheses that are directly connected with symmetry elements in crystal structures, extending earlier use of triples of Patterson peaks beyond centrosymmetric cases. The authors represent the basic atomic system and its Patterson vector system as systems of …
The crystal structures of ammonium bis(dimethylglyoximato)bis(selenocyanato)cobaltate(III) trihydrate and the corresponding thiocyanato compound are determined and compared. X-ray diffraction data, Patterson and electron-density maps, and least-squares refinement establish monoclinic P21/n cells wit…
This paper studies the large-time asymptotic behavior of solutions to the exterior Neumann boundary-value problem for the two-dimensional wave equation outside a convex contour with positive bounded curvature. The solution is decomposed into a free Cauchy-wave part and a correction term, whose Lapla…
The paper studies two singular integral operators on rectifiable Jordan curves and associated nonlinear integral equations in subspaces of Lp characterized by modulus of continuity conditions. It derives norm and continuity estimates, including analogues of Zygmund type inequalities, under generaliz…
This paper constructs a compactification of a noncompact symmetric Riemannian space using admissible projective representations of its motion group. Starting from the root system and lattice of the space, it defines a family of boundary, or epsilon, spaces associated with admissible tuples in Cartan…
The paper develops a regularizer for pseudodifferential Cauchy problems with complex symbols and for multilayer difference schemes, using bicharacteristics and a canonical operator on a Lagrangian manifold with a complex germ. It proves existence, uniqueness, and propagation of smoothness for a clas…
This paper studies homogeneous generalized functions on the space of rectangular matrices over a non-discrete locally compact disconnected field, focusing on the analytic family defined by powers of the maximal norm of the maximal minors. It determines the poles and residues of these generalized fun…
This paper studies separable topological groups containing a Weil-complete almost metrizable normal subgroup, in the sense that the subgroup contains a compact set of countable character. It proves that for such a group G with normal subgroup H, one can choose a subset A of G meeting every coset mod…
The paper studies a boundary value problem posed by A. V. Bitsadze for the three-dimensional Lavrentiev-Bitsadze equation, which is elliptic in one half-space, hyperbolic in the other, and degenerates on the separating plane. For a bounded domain bounded partly by characteristic cones, it introduces…
This note states and outlines a proof of a rigidity theorem for compact manifolds of constant negative curvature: if two such manifolds of dimension at least three have isomorphic fundamental groups as abstract groups, then they are isometric. The argument equips the common finitely generated group …
This paper studies the spectral problem arising from the membrane approximation to axisymmetric vibrations of a shell of revolution with clamped edges, obtained by setting the small thickness parameter to zero in the shell equations. The authors formulate the associated self-adjoint operator, analyz…
This paper formulates Petrov’s algebraic classification of gravitational fields in chronometrically invariant terms for a fixed reference system in general relativity. Using an orthonormal frame, it expresses the Weyl tensor through three-dimensional chronometrically invariant tensors and represents…
