SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 5847 papers in Mathematics
This paper extends the Cauchy integral operator to suitable classes of generalized functions by introducing spaces of test functions, analytic test functions in a strip, and their continuous duals. It gives sufficient decay conditions under which a generalized function belongs to the relevant dual s…
This paper studies uniqueness of an integral curve adjoining the origin for a first order differential equation in a normal Frommer domain of the second type. Under assumptions controlling the sign and growth of the principal term, the smallness of a perturbation, and a one sided Lipschitz type boun…
This paper derives error estimates for finite difference solutions of the Dirichlet problem for the Poisson equation, addressing the lack of estimates analogous to those known for the Laplace equation. The argument decomposes the solution into a zero-boundary Poisson component and a harmonic compone…
This paper studies boundary value problems for quasilinear elliptic systems in divergence form with nonlinear growth and subordinate lower order terms. Using Sobolev space formulations, Galerkin approximations, monotonicity type estimates, bicontinuity of the associated operator, and degree argument…
The paper proves a multidimensional analogue of the mean value theorem motivated by questions in partial differential equations. For a twice continuously differentiable function of oscillation less than one on a bounded domain of measure less than one crossing a strip, it establishes the existence o…
This note develops analogues of enumerable and decidable sets, and of decidable predicates, using finite automata with outputs over a word semigroup rather than partial recursive functions. It distinguishes finite enumerability from strong enumerability, gives examples showing that these notions div…
This note studies the Dirichlet problem for a class of second order linear elliptic systems with constant real matrix coefficients, in the case where the characteristic equation has one conjugate pair of roots of multiplicity equal to the number of equations. Using the known representation of regula…
This note studies when the norm of a Fourier transform over a measurable subset is equivalent to the natural \(L_2\) norm for transforms of functions supported in a bounded set. It formulates the problem in terms of a positive self-adjoint operator associated with the excluded frequency set, introdu…
The paper gives intrinsic semigroup-theoretic characterizations of semigroups associated with a simple arc, chiefly the topological semigroup of all continuous self-transformations and the semigroup of homeomorphisms into the arc. It introduces inner topologies on minimal two-sided ideals, shows tha…
The paper extends earlier constructions of modules over a real K-space with unit to a complex partially ordered setting. It defines a complex partially ordered space V equals Z squared, develops its algebraic operations, modulus, conjugation, disjointness, traces, inverses, quotients, and convergenc…
The paper introduces the i^n erfc, or complex Gauss-Poisson, distribution for counts governed by a Poisson law whose parameter is a random variable with a normal distribution truncated at zero. It derives an integral and special-function representation for the probabilities and obtains formulas for …
This paper extends Sobolev and Nikol’skii type embedding theorems to function classes with weighted integral norms and anisotropic smoothness in several variables. Using results on best approximation by entire functions of finite degree in weighted norms, it formulates embeddings for classes with ge…
This paper studies boundary-value problems for quasilinear elliptic equations with divergent principal part under boundary conditions generalizing the second and third problems, and extends analogous questions to quasilinear elliptic systems. It establishes a priori boundary estimates, including Höl…
The paper studies existence and uniqueness for an elliptic constant coefficient equation in the whole plane, focusing on the operator whose characteristic polynomial is \(s_1^{2n}+s_2^{2n}-k^{2n}\). It constructs two special fundamental solutions by contour integrals over suitable manifolds and rela…
This paper develops a method for deriving asymptotics of solutions of nonlinear differential systems near points with zero or infinite coordinates, especially for solutions approaching with a definite tangent direction. It introduces orders of functions and vector-functions, defines truncations by r…
The paper presents a method for constructing models of Bernays-Gödel axiomatic set theory using functions on an infinite set modulo a maximal ideal. It defines equivalence classes of suitably bounded functions, introduces membership and class notions for the resulting structure, and states that the …
This note studies the asymptotic distribution of special absolutely abelian fields, specifically composites of two cyclic fields of prime degree in which at least one component has a prescribed number of critical prime divisors. Using Dirichlet series with a parameter, Euler products over primes in …
This note studies binary additive problems involving primes of the form p minus a binary quadratic expression equal to a fixed nonzero integer. Using Linnik’s dispersion method, strengthened by covariance and coherent numbers, together with Hooley’s results on almost-primes in arithmetic progression…
This paper studies transformations that preserve the value of flows in finite transport networks and applies them to graph theoretic problems. It proves that a flow has a distinct equivalent flow precisely when an admissible cycle exists, and shows that any two equivalent flows can be connected thro…
The paper studies the limiting behavior, as a small parameter tends to zero, of solutions to a mixed boundary value problem for second order elliptic differential equations with Dirichlet conditions on one part of the boundary and oblique derivative conditions on another. The method represents the s…
This note gives a proof that every unitary irreducible representation of the full real or complex matrix group remains irreducible when restricted to the subgroup whose last row is fixed as \((0,\ldots,0,1)\). The argument avoids explicit classification formulas for representations and instead uses …
This paper studies stability criteria for the second order linear equation with periodic coefficient, focusing on the zero stability zone in the sense of Lyapunov. It proves a lower estimate for the separation of zeros of nontrivial solutions under integral bounds on the positive part of the coeffic…
This paper studies a singularly perturbed autonomous system near a two-frequency torus generated by periodic solutions of the corresponding reduced system. Under smoothness assumptions, negativity of the real parts of the fast eigenvalues, and stability conditions for the nonzero characteristic expo…
This note studies spectral and metric isomorphism questions for normal dynamical systems through the spectral invariants of unitary multiplication operators. It relates the spectral invariants of an operator defined by multiplication by an exponential to Rokhlin’s metric invariants of the underlying…
This paper studies measurable functions integrable in the sense of the A-integral, defined through limits of truncated integrals together with a tail condition, and addresses the failure of ordinary almost everywhere A-integrability to behave well under multiplication. It shows that multiplication b…
This paper formulates an analogue of the first boundary-value problem for a class of stable hypoelliptic differential operators in a bounded domain. It defines a Hilbert space associated with the principal quadratic form, introduces a generalized solution through an integral identity, and uses coerc…
This paper studies conditional stability of the zero solution for analytic systems of differential equations in a critical case, where the linear part has one block with eigenvalues of positive real part and another with eigenvalues of nonpositive real part. Building on the known invariant manifold …
This paper studies nilpotent algebraic linear groups over perfect fields, extending structural results previously established mainly over algebraically closed fields. It proves several auxiliary results, including finiteness of periodic algebraic matrix groups in characteristic zero, nilpotency of t…
This paper studies strongly continuous semigroups of operators on Fréchet spaces in cases where the usual bounded-orbit condition required in the Hille-Yosida-Phillips theorem holds only on an everywhere dense subset. It develops conditions under which such dense subsets form suitable Fréchet spaces…
This paper characterizes Fourier transforms of certain generalized functions defined through square mean estimates of finite differences. It proves that every generalized function in the class of derivatives of locally summable functions satisfying a Wiener type \(L^2\) central difference condition …
This note studies statistically similar zones for families of measures in repeated sampling, focusing on linear zonal statistics whose distributions do not depend on a scalar parameter. Using characteristic functions and methods from the theory of identically distributed linear statistics, it proves…
The paper gives a functional analytic formulation of A. I. Markushevich’s duality principle for linear topological spaces forming a dual system. It proves that, for a continuous linear operator between such spaces, relative completeness of the image system in the operator range is equivalent to a co…
This note studies determining sets in a Hilbert space of Fourier transforms of square integrable functions supported in a bounded domain, where the problem is to characterize when a norm defined by integration over a measurable subset is equivalent to the usual norm. It introduces a refined set char…
This note studies the Dirichlet problem for a singularly perturbed elliptic equation whose coefficients may have first-kind discontinuities across a smooth hypersurface inside the domain. Using a stopped Markov diffusion associated with the operator, the solution is represented as the expected bound…
This note extends asymptotic formulas for solutions of singularly perturbed ordinary differential systems with a small parameter multiplying the highest derivative from finite intervals to the semi-infinite interval. For a scalar fast and slow variable system, the argument imposes stability of the a…
The paper studies boundary value problems for a second order differential equation in a Hilbert space, motivated by questions from periodic waveguide theory. It reduces the equation to first order systems and then to integral equations, analyzing self-adjoint boundary conditions and the compactness …
This note extends work related to Kloosterman’s formula and Linnik’s generalized additive problem for norms of ideals by addressing the dependence on an unproved form of Siegel’s theorem and the possible vanishing of the singular series. It outlines a proof of a Siegel-type bound for exceptional rea…
This note extends S. N. Bernstein’s inequality for applying a polynomial differential operator to a trigonometric polynomial of degree n. It shows that the theorem, originally proved for real polynomials with only real zeros and illustrated by a special family with nonreal zeros, remains valid when …
The paper examines whether parabolic equations with merely continuous bounded coefficients admit fundamental solutions having the usual boundedness properties away from the initial time. It constructs a one-dimensional uniformly parabolic equation with continuous coefficient \(a(t,x)\), bounded betw…
The paper studies the first boundary value problem for a coupled system consisting of a quasilinear parabolic diffusion equation and an ordinary time evolution equation, motivated in part by neutron diffusion with delayed neutrons. Under monotonicity and Lipschitz assumptions on the coupling terms, …
This paper studies cubature formulas on the sphere that are invariant under finite rotation groups associated with regular polyhedra, with the aim of determining exactness for spherical harmonics. It proves that an invariant formula is exact for all harmonics of a given order if and only if it is ex…
This paper studies integral operators with kernels satisfying two Orlicz type integral bounds on bounded sets, seeking criteria for their continuity and complete continuity between Orlicz spaces. It develops comparison conditions on the defining functions, including complementary functions and Delta…
This paper examines conditions for the existence of a linear integral in the equations governing the motion of a heavy rigid body about a fixed point, reconsidering Chaplygin’s formulation in light of later particular solutions. By reducing the assumed integral to a constant component of angular mom…
The paper studies completeness of systems of analytic functions formed from solutions of second order differential equations with a spectral parameter, under initial conditions given by entire functions of exponential type. By transforming the general equation to a normal form and applying a transfo…
This note studies conjugacy of Sylow subgroups associated with an arbitrary set of primes in infinite groups, introducing the property of finite Pi-conjugacy: if one finite conjugacy class of Pi-Sylow subgroups exists, then all Pi-Sylow subgroups are conjugate. The main tool is a lemma reducing this…
This paper proves sharp covering theorems for classes of univalent functions in the unit disk that omit two prescribed points of equal modulus. Using properties of extremal univalent mappings, Lavrent'ev’s inverse-function representation, and elliptic functions, it derives an optimal lower bound for…
The paper studies the singular limiting behavior of solutions to a second order linear homogeneous ordinary differential equation in a Banach space, where a small parameter multiplies both the first and second derivatives. Under boundedness and smoothness assumptions on the operator coefficient, the…
This paper develops continuous analogues and Hilbert space generalizations of triangular matrix factorization and Fredholm integral operator factorization. For bounded operators relative to a maximal continuous chain of orthogonal projections, it defines special factorizations of the form \(A=(I+X_+…
The paper studies conjugate nets in projective three-space through the two congruences formed by their first and second axes, asking when these congruences constitute a one-sided pair of type T1. Using a projective moving frame adapted to the net and its Laplace transforms, the author derives focal …
