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 addresses the numerical solution of Fredholm integral equations of the first kind, emphasizing the ill conditioning of direct discretization and its relation to smoothing problems in measurement. It proposes approximating the unknown and given functions by low degree expansions in Chebyshe…
This article conducts a qualitative study of a second-order differential equation with a discontinuous right-hand side: $$\ddot{x}+a\dot{x}+bx=-\varphi(x)\operatorname{sign}x(Ax+\dot{x})$$ where $a0$, and $b$ is of arbitrary sign. The function $\varphi(x)$ is assumed to be continuous for all $x$, pi…
The paper studies the asymptotic growth of Kolmogorov epsilon entropy and epsilon capacity for Arzelà compacta of real functions defined on bounded closed subsets of Euclidean space, with a prescribed modulus of continuity. It reviews known estimates for connected sets and then identifies the geomet…
The paper addresses the generalized Hardy-Littlewood problem for representations of a natural number in the form p plus a primitive positive binary quadratic form, with the additional restriction that the integer point lies in a prescribed sector. It outlines a proof of an asymptotic formula for the…
The paper examines the Green’s function formulation of the Ising ferromagnet and its relation to Bogolyubov’s statistical variational principle. Using temperature perturbation theory for Pauli operators, it shows that the variational approximation corresponds to summing a restricted class of diagram…
This paper studies uniform convergence of fundamental matrices for perturbed linear systems of ordinary differential equations on an interval, \(\dot X_n=(A+R_n)X_n\), toward the unperturbed system \(\dot X=AX\). It proves a reduction theorem showing that this convergence is independent of the backg…
The paper considers a class of systems of linear differential equations with almost-periodic coefficients. It is proved that the systems of the selected class are regular. Bibliography: 6 items.
This paper studies finite nonnilpotent groups in which every proper subgroup lacking a specified special property is contained in a proper normal subgroup, generalizing earlier work on invariantly coverable groups. For special properties inherited by subgroups and homomorphic images, the paper prove…
This paper analyzes the stochastic destruction of magnetic surfaces in a stellarator, focusing on resonant perturbations of magnetic field lines and the limits of stabilization by nonlinear rotational transform. Using Hamiltonian field-line equations reduced to a discrete mapping, it derives estimat…
This paper develops duality principles for nonlinear boundary-value problems for systems of ordinary differential equations with general continuous, possibly nonlinear, boundary functionals. The authors associate the problem both with a finite-dimensional vector field on the space of initial data, d…
The paper studies the structure, up to similarity, of the module of principal units of a normal p-extension of a finite p-adic field over the completed group ring of its Galois p-group. It relates this module to a Z-splitting extension of a known module by the augmentation ideal, identifies the rele…
This paper formulates a numerical approach for calculating unsteady ocean currents and tides in a closed basin, extending earlier work on steady currents to include wind stress, atmospheric pressure variations, climatological effects, tide-generating forces, horizontal momentum exchange, and variabl…
This paper analyzes the nonlinear evolution of drift waves in an inhomogeneous plasma with a density gradient transverse to the magnetic field. Using hydrodynamic ion equations, quasineutrality, and a Boltzmann electron response, it derives a simple Riemann-wave solution showing that the wave phase …
This paper studies autonomous systems of differential equations possessing a saddle type periodic motion and a trajectory homoclinic to it. Under a rough, transverse dimensional condition on the intersection of the stable and unstable integral manifolds along the homoclinic curve, the author constru…
This note extends stability and analytic perturbation results for linear operators to analytic operator functions with values in bounded operators on a Banach space. It defines characteristic numbers, eigenvectors, associated chains, geometric and algebraic multiplicities, and the root number inside…
A solution to the equation \begin{equation} \frac{\partial^2u(t,x)}{\partial t^2}=a^2\frac{\partial^2u(t,x)}{\partial x^2}-b^2\frac{\partial^2u(t-\tau,x)}{\partial t^2}\tag{1} \label{1} \end{equation} for $t\ge\tau$ is sought, satisfying zero boundary conditions \begin{equation} u(t,0)\equiv0,\quad …
The paper studies conformal mappings of the upper half-plane onto slit domains whose boundaries are composed of finitely many circular arcs and line segments, with particular attention to the Schwarz derivative and its accessory parameters. It derives evolution equations for the logarithmic derivati…
The paper develops elements of a theory of representations of continuous Lie groups by unbounded operators, motivated by infinite-dimensional and generally nonunitary representations arising in problems of complex angular momentum and spin. It defines representations, topology, irreducibility, and e…
This paper investigates transient relaxation processes associated with anomalously large photovoltages in cadmium telluride films, a phenomenon previously studied mainly under steady state conditions. The authors model the films as multi-element structures containing many micro p-n junctions, derive…
This paper examines the coupling between volumetric and shear plastic deformations in soft soils, challenging models that treat hydrostatic compaction and shear flow as independent. Drawing on triaxial test evidence for sands, clayey soils, and lead shot, it formulates an idealized rigid dilatant mo…
This paper derives equations for the radiation dynamics of solid-state optical quantum generators in which multiple standing-wave resonator modes interact nonlinearly with a two-level active medium. Starting from a quantum-mechanical Hamiltonian, the authors introduce relaxation, pumping, and linewi…
This note studies distal dynamical systems on tori and related classes of distal functions. It proves that every finite or infinite dimensional torus admits a distal flow for which the torus is a minimal set, and gives a construction on the three dimensional torus that is distal and minimal but not …
This paper reports an experimental study of supersonic rarefied gas flow past a 5 mm radius sphere in the transition regime between continuum and free molecular behavior. Using multiple beam interferometry and photometric interpretation with axial symmetry, the authors measured density fields, shock…
The article investigates the exponential growth rates of solutions to the equations \begin{gather}\frac{dx}{dt}=Ax,\tag{1}\\\frac{dx}{dt}=Ax+h(x,t),\tag{2}\end{gather} where $A$ is a linear unbounded operator in a complex Banach space $X$, and $h(x,t)$ is a nonlinearity. It is assumed that the opera…
This paper develops comparison and perturbation estimates for fractional powers of weakly positive operators in Banach spaces. Using bounds on bilinear forms representing the difference between two operators and their adjoints, it derives inequalities for expressions involving \(A_1^\alpha - A_2^\al…
This paper examines whether the 1908 Tunguska event can be explained by a thermal air explosion of a cosmic body powered solely by its kinetic energy, and considers implications for the body’s structure, density, size, and velocity. Using observed forest-fall patterns, the author argues that the mai…
The paper investigates anomalous dependences of the critical current of superconducting niobium based alloy wires on magnetic field and temperature, comparing short wire coil specimens with solenoids made from the same material. Measurements on binary niobium titanium and ternary niobium zirconium t…
The differential equation \begin{equation} u^{(n)}+a(x)u=f(x,u,u',\dots,u^{(n)}) \tag{1} \label{1} \end{equation} is considered. A series of sufficient conditions is established under which equation \eqref{1} has solutions with the same asymptotic form as the solutions of the equation $u^{(n)}+a(x)u…
This paper studies optimal control problems for two-parameter discrete systems defined on a rectangular grid, with dynamics involving mixed and one-direction finite differences and a terminal linear cost. Using a discrete adjoint system and summation-by-parts identities, it derives variation formula…
This paper addresses quasi-continuous pulse systems in which time quantization is an intermediate transformation and system quality depends on the continuous useful component and its quantization distortions. It argues that the output of a pulse element can be represented by step Fourier series, who…
The paper derives solvability and sign preservation conditions for Green’s functions of second order linear ordinary differential boundary value problems with summable real coefficients. Using the fork principle, it formulates integral inequalities involving the coefficients that ensure existence of…
This article considers a third-order differential equation: $$x'''+P_1(t)x''+P_2(t)x'+P_3(t)x=0,$$ where $P_1(t)$ and $P_3(t)$ are $\omega$-periodic odd coefficients that are non-negative on the interval $[0,\omega/2]$, and $P_2(t)$ is an $\omega$-periodic even positive coefficient satisfying the co…
This note studies when a Blaschke product with zeros in the unit disk belongs to the class of analytic functions defined by bounded Riemann, Liouville fractional mean integrals for a parameter between minus one and zero. It proves that membership in this class is equivalent to the finiteness of the …
The article constructs a solution to the equation \begin{equation} u'=U_0(\nu)u+\sum_{n=1}^\infty(\nu)u^{1+\alpha_n}\equiv U(u,\nu)\tag{1} \label{1} \end{equation} where $u$ and $\nu$ are polar coordinates. At the same time, there is one case where the solution to equation \eqref{1} cannot be obtain…
The paper studies branching of periodic solutions for analytic autonomous systems with a small parameter and for nonautonomous differential equations in Banach spaces. By applying Poincaré’s reduction to initial data and period corrections, the existence problem is transformed into finite-dimensiona…
This paper studies iterative methods for solving the transcendental equation f(x)=0 under minimal regularity assumptions. It introduces auxiliary functions based on a strictly increasing comparison function g and derives bounds and monotonicity conditions used to locate zeros on intervals to the rig…
This paper examines the behavior of ultralong quasi-stationary atmospheric waves, especially their observed phase oscillations and amplitude variations. It develops a simplified linear model for an incompressible fluid with an interface, a basic westerly flow, and a stationary forcing term represent…
The paper generalizes an approximate method for electromagnetic wave propagation in irregular waveguides from perfectly conducting walls to the case of impedance boundary conditions. It formulates the Maxwell boundary value problem for a transition section with anisotropic filling and finite wall co…
The paper studies interpolation problems for analytic functions in which derivatives of orders divisible by a fixed integer are prescribed at rotating systems of points. It reduces the problem for entire functions of exponential type to lacunary auxiliary functions satisfying infinite order linear d…
The paper studies the Riemann-Hilbert boundary value problem for uniformly elliptic first order quasilinear systems in complex form, focusing on the case of discontinuous boundary coefficients and initially with vanishing lower order term. By reducing the boundary data to piecewise constant form, th…
Problems $$N[y]=y''f(t,y,y')=0,\\\alpha_0 y(a)+\alpha_1 y'(a)=A,\quad\beta_0 y(b)+\beta_1 y'(b)=0$$ are considered under the assumption that $f(t,y,y')$ satisfies the Carathéodory condition, the Lipschitz condition with respect to $y$, and there exists a continuous $\partial f(t,y,y')/\partial y'$. …
The question of the equivalence of systems of two differential equations \cite{4} \begin{gather}\frac{dx}{dt}=X[R(t)+Q(t)],\label{1}\\\frac{dx}{dt}=YR(t)\label{2}\end{gather} in the sense of $x=YA(t)$, where $A(t)\to A=\operatorname{const}$ as $t\to\infty$, is considered. Here $R+Q=P_0+P_1t^{-1}+P_2…
This note proves that, for any integers p greater than or equal to 0, s greater than or equal to 1, and n greater than or equal to 2, the Banach space of s times continuously differentiable functions on an n-dimensional cube is not isomorphic to the corresponding space of p times differentiable func…
We consider the difference equation \begin{equation} x(m+1)=A(m)x(m)+u(m),\tag{1} \label{1} \end{equation} where $x(m)$, $u(m)$ are functions of the argument $m$ ($m=0,1,2,\dots$), the values of which belong to some Banach space $E$; $A(m)$ is a linear operator-function mapping (for each $m$) the sp…
Under certain conditions imposed on the right-hand sides of the system of equations, the existence of upper and lower solutions to the boundary value problem for finite and countable systems of ordinary differential equations on an interval of a specific length is proven. Bibliography 2.
