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 develops a method for solving differential equations whose variable coefficients include delta functions and their derivatives, motivated by models combining continuous structures with discrete concentrated elements. It first formulates a class of partially degenerate operator equations, t…
This note studies uniform convergence criteria for Fourier series of Bohr almost periodic functions whose Fourier exponents have a single limit point, considering separately the cases where the exponents tend to infinity or to zero. The criteria are formulated through rates of decrease of best appro…
The paper addresses closure in turbulence theory for chains of equations governing joint probability distributions of velocity and related random variables. It proposes a closure approach based on an exact cumulant expansion of joint characteristic and probability distributions, in which approximate…
This paper studies the asymptotic behavior of generalized Bayes posterior densities and posterior mean estimates for independent samples from parametric families, allowing the prior factor to be a measurable function rather than necessarily a probability density. It identifies normalizing factors an…
This paper studies elliptic boundary value problems for systems of linear differential equations in a smooth bounded domain when the boundary condition degenerates on a smooth codimension one submanifold of the boundary. The authors introduce weighted Sobolev-type spaces adapted to the degeneracy an…
This note studies the rate of uniform approximation of continuous periodic functions by partial sums of their Fourier series, using best trigonometric approximation and quantities measuring the tails of Fourier coefficients or remainders in related \(L_q\) metrics. It proves an estimate for \(\|f-S_…
The paper studies periodic convolution equations arising in mixed problems of elasticity, especially contact problems for finite bodies, in cases where the interval length is not assumed small relative to the period. For kernels with Fourier coefficients of order inverse linear decay, it establishes…
This paper addresses how to determine positions of a machine unit’s reduction link at which the characteristic criterion of a periodic limiting regime reaches extrema, indicating where inertia forces due to nonuniform initial motion are most significant relative to steady motion. Under standard assu…
The paper introduces condition R for varieties of universal algebras, a strengthening of the embedding theorem for partial algebras, and studies its consequences for free extensions, free closures, and free products. Under this condition, it proves analogues of the Nielsen-Schreier, Kurosh, and Grus…
The paper studies stability of abstract three-level operator difference schemes in a Hilbert space, extending earlier stability results expressed in compound norms to estimates in standard energy norms associated with the scheme operators. Under positivity, Lipschitz continuity in time, and the cond…
This note addresses a problem posed by Maskit concerning the existence of fundamental domains for finitely generated Kleinian groups. It reviews the relevant notions of regular and limit sets, forms the quotient of the regular set by the group, and analyzes its components as Riemann surfaces covered…
This paper develops a four-terminal network representation for an optocoupler with direct optical coupling, specifically an injection light-emitting diode coupled to a photoresistor. It derives the conductance, impedance, and hybrid parameter matrices in terms of differential device characteristics,…
The paper studies a generalized class of convolution type integral equations on the real line with bounded measurable coefficients having generalized limits at infinity, in a range of Banach function spaces including Lebesgue, bounded measurable, and continuous function spaces. By decomposing the op…
This paper analyzes the feasibility and optimal operating conditions of a single-pulse carbon dioxide laser intended to extract high pulse energy from a large gas volume. The authors argue that uniform electron production, preferably by photoionization of a small cesium additive, can overcome limita…
This paper studies the topological classification of normally solvable boundary value problems for Petrovskii elliptic systems in a simply connected planar domain. Using the invariant subspace associated with the upper half-plane spectrum of the principal symbol, the authors express normal solvabili…
This paper develops a duality framework for convex multidimensional variational problems involving partial derivatives. It first defines Banach spaces generated by normal convex integrands, closely related to Orlicz spaces, and describes their duals, including absolutely continuous and singular comp…
This paper addresses Efremovich’s problem of characterizing which boundary homeomorphisms of the absolute spheres of two \(n\)-dimensional Lobachevsky spaces are induced by equimorphisms of the spaces. It proves that, for \(n \geq 2\), such an equimorphism exists if and only if the given boundary ma…
This paper extends analytic function and contour integral methods for three-dimensional elasticity from bodies of revolution to certain non-axisymmetric bodies whose surfaces can be represented as envelopes of a moving cylindrical surface. The method superposes plane strain and antiplane deformation…
This paper studies function spaces generated by measurable modular functions, called genfunctions, on sigma-finite measure spaces, extending earlier Musielak and Orlicz constructions under weaker hypotheses. It gives necessary and sufficient conditions for the associated space to admit a normal F-no…
This paper studies one-dimensional nonstationary flows of a barotropic fluid with adiabatic index gamma equal to 2, a model relevant to several plasma, shallow-water, and nonlinear optical problems. Starting from the Euler equations, the authors show that this special case possesses an infinite sequ…
The paper studies completeness of systems of analytic functions of the form F(z, a_n), where F is generated by a power series with coefficients forming a complete analytic system and {a_n} is a sequence of complex numbers. Using a criterion that reduces completeness to uniform approximation of the g…
This paper examines satellite thermal sounding of the atmosphere, in which vertical temperature profiles are inferred from measurements of outgoing thermal radiation. Using Nimbus III interference spectrometer data for Brownsville, Texas, the authors compare two inversion approaches for the resultin…
The paper introduces theta-uniform spaces as a generalization of uniform spaces compatible with a topology, using theta-coverings of locally finite type by canonically open sets. It shows that every theta-uniformity induces a theta-proximity and that theta-uniformities on a space correspond to ordin…
This paper studies stability of two-level operator difference schemes on Hilbert spaces with respect to right-hand side perturbations, extending earlier stability results for initial data. Using energy norm estimates and the method of separating stationary inhomogeneities, it derives bounds for solu…
The paper calculates absorption of microradio waves by atmospheric water vapor dimers using a previously developed rotational-spectrum model, extending earlier results to larger assumed spectral-line half-widths of 0.4, 0.8, and 1.6 cm-1 under sea-level atmospheric conditions. It argues that dimer l…
The paper studies time-optimal control problems in Banach spaces with phase constraints, where admissible controls generate trajectories that must satisfy set-valued and functional restrictions. Using separation-type functionals defined on reachable and target sets, it establishes criteria for contr…
This paper introduces a weight function for finite incidence structures with block multiplicities and uses it to study structures whose block sizes belong to a prescribed finite set and whose weights on all subsets of fixed size are specified. By double counting incidences within each equiblock comp…
The paper extends triangular representation and characteristic function factorization results for bounded operators close to unitary operators, allowing invertible operators whose spectra need not lie on the unit circle. For operators T on a separable Hilbert space with I minus T*T in a symmetricall…
This paper studies weighted approximation of functions on the real line by algebraic polynomials with the Gaussian weight exp(-x²/2), using weighted Lp norms. It proves an inverse-type estimate for an antiderivative F of a function f, showing that the best weighted polynomial approximation error of …
This paper investigates crater formation produced by millimeter-scale balls impacting strong rocks, porous rocks, pumice, and sand at velocities of 3 to 11.5 km/sec. Experiments measuring crater volume, shape, penetration behavior, and fragment ejection show that a simple proportionality between eje…
This paper develops a theoretical treatment of combination scattering of sound by spin waves in cubic ferromagnets, including both magnetostrictive interactions and the intrinsic magnetoelastic effect. For a longitudinal incident sound wave propagating perpendicular to a constant internal magnetic f…
This paper examines possible secular changes in gravity across Ukraine using repeated gravity measurements made in 1962 and 1969 at 36 uniformly distributed points. Differences relative to a reference point in Kiev ranged from about +0.4 to −0.5 mGal, with estimated errors of approximately ±0.08 mGa…
This paper examines the anomalous shock compressibility of quartzite, specifically the observed constancy of shock wave velocity over a broad pressure range from about 120 to 330 kbar. The authors argue that the effect is associated with the shock induced quartz to stishovite transformation, but dif…
This note studies spectral synthesis for invariant subspaces of the shift operator in weighted sequence spaces and the corresponding classes of analytic functions in the unit disk. It relates synthesis to quasianalyticity and uniqueness theorems for functions smooth up to the boundary, formulating c…
The paper studies spectral expansions and Riesz means associated with arbitrary nonnegative self-adjoint extensions of the Laplace operator in arbitrary domains, including cases with point, continuous, or mixed spectrum. Combining earlier methods for spectral expansions with Gårding’s theorem, it es…
This paper examines how specular reflection of vapor molecules from capillary walls can alter gas transport in narrow capillaries, producing a flow regime distinct from ordinary Knudsen flow. The authors develop a model in which molecules reflected below a limiting angle have an increased transport …
This paper examines theoretical properties of solid-state lasers with very long resonators, motivated by the increased coupling of longitudinal modes, changes in spectral behavior, and possible approach to nonresonant feedback when resonator mode bands overlap. It proposes using an optical delay lin…
This paper develops an approximate selective modeling of the Sun’s gravitational field in Einstein’s theory by replacing selected Schwarzschild geodesics with non-geodesic curves in a flat four-dimensional model space. Imposing spherical symmetry, staticity, and Lorentz-type equations of motion, the…
This note reformulates the nonrelativistic hydrogen atom in terms of generators of the conformal group. Starting from the conformal commutation relations, the author constructs Heisenberg-representation generators, applies a canonical transformation to a light-cone constrained basis, and identifies …
This paper studies the local sample path structure of separable Gaussian fields on compact spaces with continuous covariance kernels. Using the Mercer, Hilbert-Schmidt expansion of the covariance operator, it establishes almost sure pointwise representation of the field by its spectral series, then …
This note extends generalized Cauchy, Schwarz, and Poisson integral formulas associated with systems of weight functions in the class considered by Dzhrbashyan and in the author’s earlier work. It introduces two systems of functions and the corresponding moment sequences, then defines transformed Ca…
The paper derives a fundamental equation for radiation acoustics by supplementing the linearized hydrodynamic equations for a quiescent homogeneous gas with radiative heat exchange under Kirchhoff’s law, neglecting scattering and mechanical radiation forces. It reduces the coupled system to fifth-or…
This paper presents a laser backscatter method for determining cloud microphysical parameters from lidar sounding data. The authors derive a layer by layer expression for the cloud scattering coefficient under the assumption of single scattering, then relate this coefficient to liquid water content …
This paper discusses theoretical and numerical issues in modeling ultralong atmospheric waves for possible medium range weather prediction over one to three weeks. It proposes using a two level Phillips type hydrodynamic model, augmented by effects of surface inhomogeneity, orography, boundary layer…
The paper studies the first boundary value problem for a second order elliptic equation in a planar domain where the equation degenerates parabolically on part of the boundary. Using Sobolev space formulations, adjoint integral identities, and a priori estimates under sign and boundary coefficient c…
This paper studies convergence of products of non-identical probability measures on compact groups, asking whether representatives can be chosen from each right-translate class so that every sequence of such representatives has a convergent product. It defines complete sets of measures, proves closu…
This paper develops a nonlinear analogue of the Newtonian, or Riesz, potential adapted to the study of \((p,l)\)-capacity in Euclidean space for \(p>1\), \(pl<n\). Using Fourier-defined Sobolev-type spaces and an associated energy for generalized functions and measures, it establishes potential-theo…
The paper studies generalized differentiation of continuous functions of two variables and related summability properties of double trigonometric Fourier series. It defines several mixed, symmetric, averaged, and circular difference quotients and proves existence theorems showing that a continuous f…
This note studies linear, integral, convolution, and superposition operators in generalized Hölder spaces defined by a concave modulus function. It proves continuity of positive linear operators between such spaces, establishes automatic continuity for integral operators under mapping assumptions, a…
