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 gives a rigorous formulation and solution for diffraction of an obliquely incident plane electromagnetic wave by two coaxial perfectly conducting circular disks in a homogeneous medium. Using electric Hertz vectors and separation of variables in oblate spheroidal coordinates, the scattere…
This note addresses O. Yu. Schmidt’s problem on infinite groups whose proper subgroups are finite, focusing on infinite periodic groups that contain involutions. It proves that such a group either is equal to the centralizer of one of its involutions, or has a proper infinite subgroup with nontrivia…
This paper examines the influence of nonlinear inertial terms on wind-driven equatorial ocean currents in a homogeneous fluid, using a closed zonal channel model for the region adjacent to the equator. The authors formulate an iterative numerical method that determines the stream function and sea-le…
This paper studies analytic systems of four differential equations near a saddle-focus equilibrium with two complex stable and unstable characteristic pairs, assuming the existence of a homoclinic trajectory whose stable and unstable two-dimensional manifolds have a first-degree nontransversal inter…
The paper studies finite difference schemes with operator splitting for initial boundary value problems involving systems of the form L0 partial u over partial t plus L1u equals f, where L0 and L1 are strongly elliptic spatial operators. It formulates a multi-dimensional factorized difference scheme…
This note studies a complex second-order elliptic equation in a bounded plane domain, equivalent to a real linear elliptic system, with emphasis on representations of solutions and boundary-value problems. For parameter values outside the eigenvalues of an associated Fredholm integral equation, the …
This paper examines constitutive relations between stress and strain in nonlinear viscoelasticity using an operator formulation in Hilbert spaces over a fixed Lagrangian coordinate system. Assuming a sufficiently smooth stress operator expandable in Fréchet series with an invertible linear part, it …
This paper studies upcrossings of high levels by a stationary Gaussian process with twice differentiable correlation function satisfying local smoothness and weak long-range decay conditions. As the level and interval length increase in a coordinated way, it proves that multiple upcrossings occurrin…
This paper studies P. Hall’s conjectures relating verbal subgroups and marginal subgroups of groups, focusing on arbitrary words in linear groups over fields. Using arguments from algebraic group theory, Zariski closures, finite approximability by finite p-groups, and structural results on solvable …
The paper studies generalized extensions, in a rigged Hilbert space setting, of the differentiation operator on a finite interval with boundary condition f(0) = 0, a model for quasidissipative extensions without spectrum of a simple symmetric operator with deficiency indices (1,1). It constructs a o…
The paper develops a unified topological argument for several previously announced results concerning spaces that admit both a perfect mapping onto one space and a condensation onto another. It introduces the notion of a hereditary, product-stable property and proves a main theorem: if a space is pe…
This note studies essential variables of Boolean algebra functions, focusing on variables that remain essential after substitution of a constant and on separability relations between pairs of variables. Using Zhegalkin polynomial representations, it proves that the minimum possible number of strongl…
In this work, necessary and sufficient conditions are found for the existence of closed algebraic curves of the second order among the trajectories of the equation \begin{equation}yy'=Q_4(x,y)\tag{1}, \label{1} \end{equation} where $Q_4(x,y)$ is a polynomial of the fourth degree. At the same time, i…
The paper develops an analogue of Cartan-Weyl highest weight theory for infinite-dimensional representations of a semisimple complex connected Lie group in locally convex spaces. It introduces extremal irreducibility, generalized highest vectors in the dual space, and minimal representations associa…
For a certain class of autonomous differential equations of the $n$-th order, a three-parameter family of solutions is constructed, the derivative of which vanishes at infinity in the form of a Dirichlet series that converges uniformly and absolutely on the real semiaxis, starting from a certain neg…
The paper examines potential systems used in an approximate method for solving boundary value problems based on integral representations and auxiliary surfaces. It shows that such systems are unstable in the sense that their Gram determinants can become arbitrarily small, which may seriously affect …
The paper addresses a question of V. V. Proizvolov asking whether a bicompact space must be metrizable when it admits an open compact mapping onto a compact space. It constructs a modified topology on the square in the plane, proves that the resulting Hausdorff space is bicompact but nonmetrizable, …
This paper establishes sharp difference inequalities for harmonic functions in the unit disk whose boundary values are bounded, have zero mean, or belong to smoothness classes with bounded derivatives. It generalizes Schwarz type extremal estimates from values relative to the center to differences a…
This study investigates hyperfine interactions and electronic spin relaxation of Fe57 impurity nuclei in the ferromagnetic compounds MnSb and CrTe below and near their Curie temperatures using Mössbauer spectroscopy. Samples containing 5 at.% iron were prepared by diffusion, and spectra were measure…
This paper studies nonlinear operator equations in reflexive Banach spaces, focusing on the convergence and solvability of Ritz and Galerkin approximations for equations of the form F(x) = 0 when the operator need not have a compact component. It proves existence and convergence results for potentia…
This note studies involutive automorphisms, called invomorphisms, of compact Lie algebras and introduces principal, unitary, orthogonal, biunitary, central, and special types through the structure of their fixed-point subalgebras. Using the apparatus of involutive sums and superinvolutive decomposit…
This study investigates nuclear resonance fluorescence from highly excited states of nickel-62, cadmium-114, and lead-208 using gamma rays produced by thermal neutron capture in iron and a self-absorption method for determining radiative widths. Measurements of scattered gamma spectra, temperature e…
This paper examines the fragmentation of meteoric bodies using instantaneous photographic observations obtained in Dushanbe and Odessa, with detailed analysis of two meteors that separated into multiple fragments. From measured velocities, decelerations, masses, ablation coefficients, fragment displ…
This paper examines the polarization of Pc-1 hydromagnetic oscillations, or “pearls,” recorded simultaneously at the magnetically conjugate stations Sogra and Kerguelen in February and March 1965. Using two horizontal magnetic-field components and sonogram-based separation of simple and complex wave…
This note studies the growth of Lebesgue functions associated with uniformly bounded orthonormal systems on the interval and its consequences for Fourier series. It proves that such systems necessarily have Lebesgue functions with at least logarithmic growth on a set of positive measure, in the sens…
This paper revisits the gas kinetic calculation of thermal slip, or thermal creep, of a gas along a solid wall in the presence of a tangential temperature gradient. Using analytically corrected values for several linearized Boltzmann collision integral moments, it revises a previously derived molecu…
The paper examines thermal slip of a gas along a solid wall in the presence of a tangential temperature gradient, revisiting Maxwell’s classical result in light of the non-equilibrium velocity distribution within the Knudsen layer. It applies the Bhatnagar, Gross, and Krook relaxation approximation …
This paper studies the spatial Newtonian three-body problem in the case of nonzero angular momentum and negative total energy, where total escape and triple collision are excluded. Using an inequality relating moment of inertia, kinetic energy, and angular momentum, it derives restrictions on possib…
We consider the Dirichlet and Neumann boundary value problems for the equations \begin{align}L_u&\equiv\Delta u=v(x,y)\tag{1}\label{1},\\L_u&\equiv\Delta u-\lambda u=v(x,y)\tag{2}\label{2}\end{align} in the square $R[0 \le x, y \le \pi]$. Approximate solutions are sought in the form \begin{equation}…
The paper studies how dynamic production models with differing production-cycle durations, reproduction coefficients, and delayed capacity growth can be connected into parallel, sequential, and more complex production schemes. It formulates a differential-inequality model for individual production u…
The paper extends Bernstein’s averaged interpolation processes from real intervals to the complex domain for functions regular in a bounded domain with analytic Jordan boundary and continuous on its closure. Using interpolation nodes obtained from a conformal mapping of the exterior of the domain an…
This note studies a general mathematical model of production represented by set-valued mappings between ordered finite-dimensional spaces, where each mapping assigns feasible output sets to input vectors over successive time periods. Under assumptions such as monotonicity, upper semicontinuity, conc…
This paper studies oscillatory and capture phenomena in a class of second order differential equations with periodic time dependence, including the Sitnikov-type restricted three-body problem with two equal masses and a massless third body. Under stated regularity, monotonicity, and integrability as…
This paper examines the massless two-dimensional Thirring model, focusing on the relation between the Glaser and Berezin construction in an auxiliary field space and ordinary perturbation theory in the physical Fock space. It compares the different contraction rules and current commutators in the tw…
The paper studies the spectrum of quantum mechanical energy operators for molecular systems under prescribed permutation, rotational, and reflection symmetries, with pair potentials satisfying stated regularity and decay conditions. Using decompositions of the particle system into subsystems and the…
This note studies sufficient conditions for the Szegő limit formula for Toeplitz determinants associated with a nonnegative integrable function on the unit circle. Using parameters defined from the moments, the associated outer function, and orthonormal polynomials on the circle, it proves that for …
The paper studies general analytic properties and solution methods for equations of the Chu-Low type arising in pion scattering by a fixed source under unitarity and crossing symmetry. By transforming the spectral variable to linearize the unitarity condition, the scattering functions are treated as…
This paper studies steady plane motion of an ideal incompressible fluid in a reservoir under Coriolis forces, with particular attention to when a through-flow region cannot occupy the whole basin. The authors formulate a free-boundary problem for the stream function in which flowing zones satisfy a …
An approximate method is developed for integrating the Rayleigh equation with cubic velocity nonlinearity for arbitrary values of the parameter governing nonlinearity, a range in which both amplitude and period may vary strongly. The method uses a harmonic change of variables, quarter-cycle averagin…
This paper revisits the theory of diffusiophoretic motion of large volatile droplets in a binary gas mixture, addressing a discrepancy between an earlier thermodynamic result and a previous direct force calculation. The authors solve the coupled convective diffusion and viscous hydrodynamic equation…
This paper studies problem E for a class of nonlinear elliptic equations that degenerate parabolically on part of the boundary, of the form \(y^m u_{yy}+u_{xx}-f(x,y,u,u_x,u_y)=0\) in a simply connected domain in the upper half-plane. Under differentiability, monotonicity, and boundedness assumption…
This paper addresses the existence of closed convex surfaces whose principal radii of curvature satisfy a prescribed relation \(f(R_1,R_2)=\varphi(n)\), extending classical cases associated with Christoffel and Minkowski. Using the support function formulation, elliptic equations on the sphere, uniq…
Thermal conductivity in sodium chloride single crystals was measured at helium temperatures to examine phonon scattering by dislocations, point defects, and crystal boundaries. Using a steady-state heat-flow method, specimens with dislocation densities from 5 x 10^4 to 5 x 10^7 cm^-2 were studied be…
This paper studies convergence rates for coordinate relaxation methods applied to a positive definite quadratic functional in finite dimensional Euclidean space, allowing general control sequences in which each coordinate recurs arbitrarily far along the iteration. Using an error measure defined by …
