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 studies unsteady long waves generated by initial disturbances in a rotating channel of constant depth, including disturbances relevant to tsunami-type wave formation. Using Laplace and Fourier transforms, the governing linear hydrodynamic equations are reduced to an inhomogeneous Helmholt…
The Galerkin method is used to solve the mixed problem $$\begin{aligned} \frac{\partial^2u}{\partial t^2}&=\frac{\partial}{\partial x}\biggl(p(x)\frac{\partial u}{\partial x}\biggr)+f(t,x,u,u_t,u_x), \\ u(0,x)&=\varphi_0(x),\quad u_t(0,x)=\varphi_1(x), \\ u(t,0)&=u(t,\pi)=0, \end{aligned} \tag{1}$$ …
This paper investigates multiphoton excitation and laser induced decomposition of organic molecules using high intensity ruby laser radiation and, for selected compounds, dysprosium laser irradiation. Luminescence measurements on polycrystalline samples at 77 K and 300 K show fluorescence consistent…
The paper considers a spectral problem for a system of first-order ordinary linear differential equations of the form \begin{gather} \frac{dY}{dx}=AY+f\tag{1}, \label{1} \\ \alpha Y(a,\lambda)+\beta Y(b,\lambda)=0\tag{2}, \label{2} \end{gather} where \begin{equation} A=A(x,\lambda)=\lambda A(x)+\sum…
This note studies the normal solvability of a generalized Abel integral equation and its adjoint, including a compact perturbation term, by reducing them to conjugate singular integral equations with a Cauchy kernel. It establishes identities connecting fractional Abel-type operators with Cauchy sin…
This paper examines how thermal vibrations of a crystal lattice affect the anisotropy of sputtering coefficients and ion-electron emission in copper single crystals under 30 keV argon ion bombardment. Experiments on copper (110) and near (111) faces, together with polycrystalline copper, measured an…
The paper presents an approximate algorithm for a resource allocation problem in network planning, where an integer schedule must satisfy precedence, deadline, and resource capacity constraints while minimizing the maximum lateness relative to prescribed event times. The method refines a general sch…
This paper analyzes the geological structure of the lunar crater Alphonsus using Ranger 9 imagery at multiple scales, supplemented by ground-based photographs for regional context. The author interprets regional and intracrater fault patterns, ring fractures, axial ridges, graben-like depressions, a…
This paper generalizes a previously proposed group-theoretical method for classifying the allowed states of bound impurity-ion pairs in crystals to symmetric complexes of N paramagnetic impurity ions. Starting from impurity-ion states in their local crystal fields, it defines the symmetry of the com…
The paper studies fundamental solutions for linear singular partial differential operators of B-elliptic type involving the Bessel operator in a half-space. Using weighted plane-wave expansions and F. John’s method, it derives integral representations for fundamental solutions in the constant-coeffi…
This note proposes a derivation of mass formulas in SU(3) unitary symmetry without assuming a specific perturbative form, such as an octet mass operator. The argument introduces a rotated quark triplet and, assuming the mass operator is diagonal in isotopic spin and hypercharge, compares mean masses…
Sufficient conditions are established for the dissipativity of systems \begin{gather}\dot{x}=y,\quad\dot{y}=-yf(x,y,t)-g(x)+e(t),\tag{1}\\\dot{x}=y-f(x,y,t),\quad\dot{y}=-g(x)\tag{2}\end{gather} in the case where the function $f$ satisfies substantially different constraints for $x>x_0>0$ and for $x…
The paper addresses the localization problem for Fourier series with respect to arbitrary fundamental systems of functions of the Laplace operator in an arbitrary multidimensional domain, including eigenfunction expansions for standard boundary value problems and multiple trigonometric Fourier serie…
The paper studies a singular mixed type boundary value problem for an equation that is elliptic in one subdomain and hyperbolic in another, with Frankl and Tricomi type boundary data, a gluing condition across the line of type change, and a curvilinear jump condition. It develops representations for…
This paper studies aggregation methods for solving large systems of linear equations of the form x = Ax + B, motivated by intersectoral balance models in economics. It shows how a system can be reduced to lower dimensional aggregated systems using proportional vectors, and describes both a finite me…
This paper estimates Cauchy integrals of bounded analytic functions in terms of the analytic capacity of the set of singularities, addressing a problem arising in approximation theory. It proves that for a function analytic in the unit disk outside a closed exceptional set and continuous on the boun…
This paper develops operator schemes for proving existence of solutions to classes of nonlinear equations in Banach spaces that model quasilinear problems in mechanics. Using Galerkin approximations, it establishes solvability theorems for stationary equations under ellipticity, orthogonality, and w…
The paper considers the problem of minimizing a convex functional $$J=\int_{t_0}^{t_0+T}F(x,t)\,dt$$ along the trajectories of a linear control system $$\frac{dx}{dt}=A(t)x+B(t)u,$$ with both endpoints being free. It is proved that the Pontryagin maximum principle provides a sufficient optimality co…
This paper examines the contribution of higher order light scattering to zenith brightness in the twilight sky, a factor that cannot be separated directly from observations and is often underestimated in optical sounding of the upper atmosphere. A theoretical calculation is developed by treating the…
The paper studies nonlocal solvability of initial boundary value problems for quasilinear hyperbolic partial differential equations in a bounded domain, with formally self-adjoint strongly elliptic operators of order 2m and boundary conditions satisfying the Shapiro-Lopatinskii condition. The proble…
This paper investigates the mechanism by which a jet in a fluidic amplifier attaches to a diffuser wall, the Coanda effect, with emphasis on the role of pressure pockets and vortex motion. Experiments were conducted in water using a symmetric jet amplifier model with a splitter, high Reynolds number…
The paper generalizes the Schaeffer-Duffin extremal problem for algebraic polynomials subject to prescribed bounds at n plus 1 points on an interval, replacing pointwise derivatives by an arbitrary finite linear functional. Using the Lagrange interpolation representation, it gives an explicit charac…
The paper examines whether continuous phase transitions and critical phenomena may occur in the Earth’s mantle under high pressure and temperature, despite the mantle’s seismic behavior as a solid. Using thermodynamic arguments, it distinguishes true phase equilibrium, spinodal instability, and a qu…
The paper studies locally perfect mappings between T1 spaces as a local analogue of perfect mappings and constructs, for any such map, a canonical perfect extension obtained by adjoining one point over each point where the original map fails to be perfect. It proves uniqueness and minimality propert…
The paper studies the limiting behavior of solutions to Cauchy problems for linear parabolic systems whose highest derivatives are multiplied by a small parameter, with emphasis on convergence to the corresponding hyperbolic limiting system as the parameter tends to zero. It establishes sufficient c…
This paper derives exact solutions for axially symmetric motions of a gravitating gas undergoing homogeneous radial deformation with a transverse velocity component. Starting from the gas-dynamical equations in spherical coordinates, it assumes a radial velocity proportional to radius and obtains ad…
In the peer-reviewed work, the following one-dimensional mixed problem is investigated: \begin{gather}\frac{\partial^2u}{\partial t^2}-\frac{\partial^2u}{\partial x^2}-\alpha\frac{\partial^3u}{\partial t\partial x^2}=\lambda F[t,x,U,U_x,U_t,U_{xx},U_{tx}],\tag{1}\label{1}\\U(t,0)=U(t,\pi)=0,\quad U(…
The paper examines the role of the dissipative function in the mathematical theory of plastic media and its relation to the conventional formulation based on a loading function and associated flow law. Starting from the Mises maximum principle for hardening plastic bodies, it shows that a first degr…
This paper investigates polarization effects associated with Coulomb scattering of 4 MeV neutrons by copper, lead, and uranium nuclei at small angles. Using polarized neutrons from the D-D reaction, the authors measured differential elastic scattering cross sections at angles near 2, 4, and 6 degree…
This paper investigates whether electrons can acquire high energies during the initial stage of a pulsed spark discharge in air at atmospheric pressure. Using nanosecond voltage pulses across a short electrode gap, the authors detect bremsstrahlung produced by fast electrons decelerating in electrod…
This paper corrects and refines a result of Bass on one-dimensional local commutative Noetherian reduced rings whose integral closure is finite, concerning when every indecomposable finitely generated torsion-free module is isomorphic to an ideal. The authors focus on the case where the integral clo…
The paper examines the construction of invariant information and measuring devices based on a two-channel operating principle, focusing on conditions under which the output remains insensitive to bounded symmetric disturbances while retaining sensitivity to the measured quantity. It formulates invar…
This paper examines the role of the Earth’s deep heat flow as a major energy source for geological development, using an analysis of roughly 2000 heat-flow measurements and their spatial and statistical distribution across tectonic regions. It argues that characteristic heat-flow patterns correspond…
This paper studies rectilinear stationary motions of an incompressible viscoplastic medium using a variational formulation rather than local differential equations with unknown plastic flow boundaries. For pipe flow under a pressure gradient, the minimization functional is used to establish existenc…
Pontryagin extends earlier work on linear differential games for systems of the form dz/dt = Cz + u - v in a vector space of arbitrary dimension, with pursuing and evading controls drawn from closed bounded convex sets and termination on a closed convex set. The paper introduces operations on convex…
The paper considers an application of the theory of Panya’s special heat potential of a simple layer to a boundary value problem for a system of parabolic equations with discontinuous coefficients, arising in the study of the distribution of concentrations of substances involved in the vital process…
The paper formulates a linearized problem for the dynamics of a baroclinic ocean, motivated by forecasting sea currents and atmosphere ocean interaction. Starting from equations for velocity, pressure, density, temperature, and salinity, it introduces deviations from a standard vertical state and re…
This note studies strictly cosingular bounded linear operators between Banach spaces and their relation to Fredholm type perturbation theory. Using duality, weakly closed subspaces of dual spaces, and compactness arguments, it proves equivalent characterizations of strict cosingularity in terms of t…
