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 differential equation $$\ddot{x}+a\dot{x}+f(x)=-u_0\operatorname{sign}(\dot{x}-\varphi(x)),$$ is considered, where $a>0$; $u_0>0$; $f(x)$ and $\varphi(x)$ are periodic and everywhere continuously differentiable functions that vanish at $x=0$ and $x=+\pi$. This equation describes, in particular, …
This paper examines how non-exponential terms in quantum decay, required by the lower boundedness of the energy spectrum, may be detected despite their negligible effect on ordinary decay probabilities at experimentally accessible times. Using the asymptotic form of the survival amplitude for a pole…
The paper considers the conditions for the existence and uniqueness of the solution to the specified problem, while simultaneously providing estimates for both the solution and its derivatives. The main results are Theorems $1$, $2$, $3$, and $4$. The periodic boundary value problem for third- and f…
This note studies almost periodicity and stability of bounded solutions of nonlinear ordinary differential systems using a generalized Lyapunov function depending on pairs of phase points. It introduces \(V\)-monotonicity and an associated \(A\)-property, proves their equivalence under bounded-domai…
This paper reports experimental studies of waves, moving striations, and noise in the positive column of low-pressure dc discharges in helium, neon, argon, and neon-helium mixtures. Using optical detection, oscillography, spectrum analysis, and externally driven excitation, the authors measured stri…
This paper examines how the adiabatic hypothesis should be formulated within axiomatic quantum field theory, where the S-matrix is introduced in terms of physical asymptotic fields but products of generalized functions still require prescriptions beyond the energy surface. Using a one-dimensional mo…
This paper studies the Cauchy problem on a finite time strip for a first order in time linear equation with variable spatial coefficients of order n, under assumptions that the coefficients approach constants at spatial infinity and that the limiting constant coefficient equation is well posed in Pe…
This paper studies preservation and characterization properties of Hewitt \(Q\)-spaces, also called functionally closed spaces, in general topology. It proves that a perfect image of a normal countably paracompact \(Q\)-space is again normal, countably paracompact, and a \(Q\)-space, giving a partia…
This paper studies best approximation of elements in real and complex Banach spaces by elements of convex sets. It extends known duality relations and Rubinshtein’s criterion for best approximation from the real to the complex case, relates this criterion to Garkavi’s formulation using extreme point…
The paper studies generalized mean values of the support function of a convex body in n-dimensional Euclidean space, motivated in part by their role as sharp majorants for solutions of second-order elliptic equations with zero boundary values. It establishes basic monotonicity and convexity or conca…
The paper presents a computer algorithm for a class of planning and economic problems representable on acyclic directed graphs with arbitrarily numbered vertices and unordered arc data. It formulates a general recurrence over graph vertices that covers specification compilation, determination of pro…
This paper studies density estimates for zeros of Dirichlet L-functions, motivated by Bombieri’s refinement of Linnik’s large sieve method and its applications to primes in arithmetic progressions and additive number theory. It proves two strengthened average zero-density inequalities for primitive …
The paper studies boundary value problems for an ordinary differential equation of order n under Carathéodory assumptions on the right hand side. It establishes existence results for problems with initial conditions on derivatives up to order n minus 2 and an additional boundary condition at a termi…
The paper studies inductive and projective limits in categories of commutative topological groups, locally quasi-convex groups, and locally quasi-convex groups equipped with quasi-convex boundedness. It establishes existence and universal properties of strongest and weakest compatible topologies and…
The paper introduces theta spaces, defined by a weakened proximity relation on regular topological spaces, as a generalization of proximity spaces compatible with completely regular spaces. It establishes that each theta space determines a completely regular perfect irreducible preimage together wit…
This paper investigates the anisotropy of optical transitions in metallochlorins and chlorophyll using low-temperature fluorescence polarization spectra, with comparison to absorption spectra. Measurements on zinc tetraphenylchlorin and chlorophyll a indicate that bands near the long-wavelength abso…
Infrared absorption spectra of tetraethoxysilane and methylethoxysilanes, with compositions varying from trimethylethoxysilane to tetraethoxysilane, are analyzed through integral intensities, peak absorption coefficients, and band half-widths in the 400 to 3000 cm⁻¹ region. The study assigns princip…
This commemorative article surveys the life and scientific work of Evgenii Alekseevich Barbashin on the occasion of his fiftieth birthday. It traces his education, academic appointments, and role in building research groups in Sverdlovsk and Minsk, while emphasizing his contributions to qualitative …
The paper develops a framework for studying set-valued translations between topological spaces using generalized neighborhoods and a hierarchy of eight types of convergence for sequences of sets. It defines completeness, regularity, restrictions, inverse translations, and continuity of a given type,…
This note studies classes of functions that are quasi-analytic with respect to an ordinary linear differential operator with continuous coefficients, extending classical Denjoy-Carleman type classes through bounds on iterates of the operator. It gives sufficient conditions, expressed by convex regul…
The article considers a system of fourth-order differential equations describing, in particular, the motion of coupled Froude pendulums of equal masses suspended on a shaft rotating at a speed $\Omega$. The paper provides upper and lower bounds for the values of the speed $\Omega$ in the case of the…
This note studies optimal control problems for distributed-parameter systems governed by parabolic equations with third-kind boundary conditions, extending earlier results from terminal-cost functionals to integral functionals over time and space. It treats measurable controls with values in a bound…
This note studies duality operators for additive covariant functors in categories of abelian groups, especially finite, finitely generated, and arbitrary abelian groups. It introduces the functor \(T_{A,B}X=\operatorname{Hom}(\operatorname{Hom}(X,A),B)\), uses it to analyze reflexivity, and establis…
This note formulates the complexity of electrical modeling of lossless distributed-parameter lines as approximation of their input impedances by rational functions realizable as passive lumped-parameter two-terminal networks. It relates circuit complexity to the number of terms in a canonical class …
This paper studies when formal transformations that reduce analytic systems of ordinary differential equations near a singular point to normal form are convergent or necessarily divergent. It formulates two arithmetic and structural conditions on the eigenvalues and on the normal form, including a s…
This paper investigates the structural origin of optical inhomogeneities in natural and synthetic quartz, including schlieren, banding, sectoriality, and zonal structures. Using X-ray diffraction topography with a Lang camera and comparing the resulting images with optical observations and etching p…
This paper studies stability in the uniform metric for systems of linear difference equations with constant matrix coefficients and bounded initial data. Using the characteristic matrix obtained by Fourier transformation, it gives a necessary and sufficient condition in terms of boundedness, uniform…
This paper develops a statistical theory of irreversible processes in liquids or gases whose molecules have internal rotational degrees of freedom. Starting from a second-quantized Hamiltonian, it derives conservation laws for energy, momentum, particle number, and internal angular momentum, showing…
An approximate method for analyzing systems of equations describing controllers with digital computers is presented. The method consists of the artificial introduction of a “small” parameter for a subset of derivatives or differences, which allows for reducing the order of the equations under consid…
A method is developed for obtaining uniform asymptotics of linear differential systems with a small parameter multiplying the derivative. The fundamental matrix is represented as a product of a diagonal exponential factor and a matrix having a finite limit as the parameter tends to zero, with the la…
The paper studies open finite-to-one continuous mappings in general topology, especially their effect on metrizability and covering properties. It proves that a regular p-space mapped openly and finite-to-one onto a metrizable space is metrizable, and that hereditary weak paracompactness, hereditary…
This commemorative article surveys the development of Soviet mathematics, especially the theory of differential equations and its applications, over the fifty years following the October Revolution. It argues that Soviet science transformed a formerly backward country into a major center of mathemat…
This note studies the spectral radius of positive operators on ordered Banach spaces with a reproducing normal cone, focusing on indecomposable or semi-non-supporting operators. It proves a limit formula expressing the spectral radius through scalar quantities of the form involving iterates of the o…
A quasilinear autonomous system with many degrees of freedom and delays is considered. Under the assumption that the generating system possesses a multi-frequency periodic regime, the solution of the system is constructed using the asymptotic method of N. M. Krylov and N. N. Bogolyubov. The possibil…
This paper examines whether dispersion sum rule methods admit a static limit for pion-nucleon scattering and virtual pion photoproduction on nucleons. Under assumed high-energy behavior permitting unsubtracted dispersion relations, the analysis formulates static-model amplitudes with baryon recoil n…
The paper studies the spatial Cauchy-Poisson problem for small long waves on the free surface of a viscous liquid of finite depth, with prescribed initial surface displacement and surface pressure. After linearizing the Navier-Stokes equations, the authors apply Fourier transforms in the horizontal …
This paper challenges the interpretation of earlier micrometeor impact measurements as evidence for a near-Earth dust cloud. It reports measurements from the Kosmos 135 satellite at altitudes of 260 to 650 km using piezoelectric impact sensors modified to reduce thermal, acoustic, and electrical int…
The paper studies the local structure of trajectories of a multidimensional smooth dynamical system near a homoclinic motion doubly asymptotic to a saddle periodic orbit. Using a Poincare map on a transverse section, stable and unstable manifolds, and a transversality assumption for their return int…
The paper examines an unusual complex splitting of the proton nuclear magnetic resonance spectrum in polycrystalline zeolites containing water molecules associated with sodium nuclei. It interprets the observed doublet, each component split into four partly resolved lines, by modeling a two-proton w…
The paper studies the computation of saddle points for continuously differentiable concave-convex functions on Euclidean spaces and on convex bounded domains. It gives necessary, and under concave-convexity sufficient, stationarity conditions, then develops continuous dynamical systems whose traject…
This paper investigates the hyperfine structure of electron paramagnetic resonance spectra of vanadium-containing borate, silicate, and phosphate glasses in order to relate spectral parameters to chemical bonding. Using room-temperature and liquid-nitrogen-temperature EPR measurements and an axial s…
This paper studies finite groups satisfying the QP condition, namely that any two distinct nonprimary maximal nilpotent subgroups of even order intersect trivially. It develops a centralizer criterion for such groups, proves heredity for subgroups and factor groups, and classifies solvable QP-groups…
This note studies analogues of the Weierstrass canonical product for entire functions of several complex variables when only a specially chosen codimension-one part of the zero set is specified. It defines averaged zero-counting functions on radial and cylindrical sections of the analytic zero set a…
This paper studies inverse boundary value problems in which coefficients of a parabolic equation and of an ordinary differential equation are unknown, with the spatial dependence of one coefficient assumed piecewise constant. Using additional data prescribed at finitely many points and boundary flux…
This paper examines whether hard X-ray emission from solar flares can acquire linear polarization through bremsstrahlung from anisotropic accelerated electrons. Using bremsstrahlung cross sections in the nonrelativistic Born approximation, the author derives polarization for a parallel monoenergetic…
