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 studies regular univalent functions without common values in finitely connected plane domains bounded by analytic Jordan curves. Using Dirichlet integrals and Bergman kernels of the first and second kind, it derives inequalities for systems of such functions, including versions for the sub…
The paper examines how conservation laws in Einstein’s theory of gravitation are connected with the transformation properties of the gravitational-field Lagrangian. Starting from the Lagrangian form of the Einstein equations, it computes the variation of the Lagrangian density under an infinitesimal…
This paper studies the integral transform that assigns to a rapidly decreasing smooth function on complex space its integrals over k-dimensional affine planes with compatible translation-invariant measures. It constructs a differential form valued operator on the complex Grassmannian, using derivati…
This paper derives exact self-similar solutions for one-dimensional unsteady soil motion with plane waves, using governing equations for velocity, density, pressure, and maximum historical pressure together with moving boundary conditions. The problem is reformulated in Lagrangian-type dimensionless…
The paper establishes sharp uniform estimates in a closed bounded domain for eigenfunctions of the biharmonic operator with homogeneous boundary conditions, a problem relevant to eigenfunction expansions for self-adjoint operators. For domains with sufficiently smooth boundary, the argument combines…
The note studies a generalized Hardy, Littlewood additive problem for representations of an even integer \(n\) in the form \(p+\varphi(\xi,\eta)=n\), where \(p\) is prime and \(\varphi\) is a positive primitive binary quadratic form with nonsquare discriminant. Using the theory of binary quadratic f…
This note studies harmonic analysis and almost periodicity of bounded solutions to linear operator differential equations in Hilbert and Banach spaces, with emphasis on parabolic equations whose coefficients are periodic in time. Using spectral properties of infinitesimal generators, compact resolve…
This paper develops finite difference methods for one-dimensional Stefan-type problems with multiple moving phase fronts governed by a parabolic equation. The authors introduce a front-straightening change of variables that maps each moving subdomain to a fixed interval, then formulate implicit iter…
The paper develops a functional statistical thermodynamic treatment of a solvent perturbed by a dissolved foreign particle, with emphasis on interactions that combine a strong impenetrable core and a weaker, longer range attractive tail. Using a generating functional for the configurational integral…
This paper investigates the photodielectric effect in vacuum-deposited phthalocyanine layers using capacitance and dielectric-loss measurements under illumination at room temperature. The authors model the sample as a capacitance shunted by the dark or light conductivity of the phthalocyanine and co…
This note studies when a continuous complex function can be uniformly approximated on a prescribed closed bounded set by rational functions. Using analytic capacity, Ahlfors functions, and auxiliary estimates for coverings by squares, it proves that approximation is possible if integrals of the func…
The paper studies eigenfunction expansions for a one-dimensional Dirac system on the half-line with real locally summable coefficients and a real boundary condition at the origin. Using the spectral function and spectral matrix associated with the boundary-value problem, it compares the generalized …
This paper studies the affine differential geometry of nonplanar m-dimensional surfaces in n-dimensional affine space without restrictions on m and n and without assuming maximal dimensions for all higher order tangent spaces, apart from ordinary points. It introduces surfaces of differential class,…
This bibliographic notice lists recently published mathematical books and article collections issued mainly in 1965 and 1966 by Soviet and translated publishers. The entries cover complex analysis, operational calculus, stability theory, linear operators in Hilbert space, mathematical physics, bound…
This note studies Fréchet differentiability of nonlinear Uryson integral operators acting from one Lebesgue space into another on finite measure sets. It introduces function spaces for kernels and uses continuity or complete continuity of associated superposition operators to give sufficient conditi…
The paper studies when a high-dimensional open smooth manifold with two ends and finite fundamental group is diffeomorphic to a product with the real line. It defines an obstruction in the reduced Grothendieck group of projective modules over the group ring, proves a duality relation for this invari…
The paper studies the structure of vector and axial current matrix elements for baryons within broken \(\widetilde U(12)\) symmetry, using a spurion formalism that restores formal invariance by treating particle momenta as components of higher-dimensional tensors before reducing to physical componen…
This paper analyzes cosmic-ray measurements obtained during the simultaneous interplanetary flights of the Zond-3 and Venera-2 stations in late 1965 and early 1966, when the spacecraft were moving respectively away from and toward the Sun. Using gas-discharge counter data, with comparison to neutron…
This paper studies the high-energy asymptotic behavior of the spectral matrix associated with a one-dimensional Dirac system on the half-line with a real boundary condition. After reducing the relativistic Dirac equation to a first-order two-component system, the author defines the corresponding spe…
This paper develops a kinetic description of relaxation and frequency shifts in a discrete spectrum under the approximation of instantaneous collisions, relaxing the earlier assumption that each collision completely restores equilibrium. Starting from a density matrix evolving freely between Poisson…
This note studies the topology of the set of strongly stable periodic complex self-adjoint first-order differential systems with nonsingular skew-Hermitian leading matrix and Hermitian coefficient matrix. Using Krein multiplier theory, the problem is reduced to the structure of curves in the group o…
This note generalizes inverse theorems of uniform approximation by rational functions with prescribed poles in complementary components of a bounded plane set. It establishes a lemma bounding such rational functions and their derivatives on and near the boundary using Green functions, level curves, …
The paper derives estimates for a Cauchy principal value singular integral on an interval in terms of interior suprema and moduli of continuity with explicit dependence on distances from the endpoints. Using these estimates, it defines a family of Banach spaces controlled by prescribed majorant func…
Turán proposes a function theoretic sieve method for additive prime problems that replaces parts of the Hardy, Littlewood, Vinogradov circle method by Dirichlet series and contour integration. The paper formulates the method for representations of an integer as a prime plus values of a positive defi…
This note studies the asymptotic behavior of solutions to differential equations with random right-hand sides containing a small parameter, especially in the case where the averaged first-order drift vanishes and the relevant time scale is of order 1 over epsilon squared. Under bounded smoothness, m…
This note extends Lavrent’ev’s notion of plane quasiconformality by introducing a three characteristic framework based on commutative rings associated with generalized complex numbers and parameter dependent curves. It defines t-convergence, t-continuity, t-differentiability, regularity, and t-quasi…
This paper investigates the optical anisotropy and dichroism of metallic textures composed of oriented anisometric gold microcrystals embedded in high-polymer films. The authors produced such textures experimentally and interpreted their visible and near-infrared absorption using scattering calculat…
The paper studies the complex J-functor for cell complexes, especially cases where the usual exact sequence for a pair fails, and introduces homology groups measuring this failure. Using Thom complexes, the author constructs a homomorphism from a kernel in complex K-theory to Q/Z and shows that it d…
This paper studies the high frequency behavior of the kernel appearing in the second Born approximation for a scattering equation, expressing it through an integral of the potential over ellipsoids with foci at two observation points. It develops basic properties of this ellipsoidal integral, includ…
The paper develops constructive analogues of basic notions from general topology by defining effectively metric and effectively topological spaces, effectively open and closed sets, computable and effectively continuous mappings, and effective versions of separation axioms. It examines how classical…
This article is a bibliographic survey of journal publications relevant to differential equations and adjacent areas of analysis, mathematical physics, numerical methods, stability theory, integral equations, and boundary value problems. It compiles alphabetically arranged entries, chiefly from 1965…
This paper reports measurements of soft corpuscular radiation made by gas-discharge counters on the Luna-10 lunar satellite during April and May 1966. The authors describe the response of SBT-9 and SF counters to electrons, protons, and soft X-radiation, and compare changes in counting rates with th…
This paper introduces a parameter-dependent class of finite-difference operators for the numerical integration of systems of ordinary differential equations, extending standard multistep operators by allowing shifted derivative terms. It establishes a representation of these operators as linear comb…
The paper studies semi-isomorphisms and structural isomorphisms of cancellative semigroups, extending a result of Scott by removing the assumption that the target semigroup is cancellative. It proves that every semi-isomorphism from a cancellative semigroup onto an arbitrary semigroup is necessarily…
This note studies coefficient-free equations in words over a finite alphabet, with emphasis on nontrivial solutions, defined as solutions not expressible as powers of a single word. It first shows that any finite system of such equations is equivalent, with respect to nontrivial solutions, to a sing…
This note studies the convergence rate of partial sums of Fourier-Jacobi expansions for functions on the interval [-1,1] with Jacobi weights. It derives an upper estimate for the associated Lebesgue function when the Jacobi parameters are at least -1/2, noting the sharpness of the endpoint order, an…
The paper studies bifurcation and stability of small nonzero periodic solutions of a parameter dependent system of ordinary differential equations with periodic right hand sides and a persistent zero solution. Assuming that the monodromy matrix of the linearized system has the multiplier 1 associate…
This paper studies generalized solutions of second order uniformly parabolic linear and quasilinear equations using mixed space time norms to describe coefficient and data integrability. It develops a level set lemma for functions satisfying Caccioppoli type inequalities, yielding power, exponential…
This paper examines the relation between molecular luminescence and absorption spectra, quantum yield, and luminescence duration, starting from Stepanov’s universal relation and its known conditions of validity. It derives a generalized expression that includes the number of excited molecules throug…
This bibliographic notice surveys recently published mathematical books and teaching materials available in 1965 and 1966, primarily from Soviet academic and educational presses. The entries cover monographs, textbooks, lecture notes, handbooks, and collected papers in differential equations, mathem…
This paper studies a locally convex algebra of entire functions whose growth is controlled by an arbitrary increasing majorant satisfying a logarithmic convexity condition. The author defines a natural topology on this algebra, establishes continuity of multiplication, and analyzes closed ideals thr…
