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
The paper studies limiting distributions for normalized values of additive arithmetic functions, focusing on functions whose values on primes possess an asymptotic distribution and for which the associated truncated second moment over primes diverges. It develops estimates for sums of complex multip…
The paper studies the joint distribution of transition counts in a finite homogeneous ergodic Markov chain with positive transition probabilities. It first derives, by an inductive enumeration of chains with prescribed initial and terminal states, an explicit combinatorial formula for the number of …
This paper studies the location of resonance poles and analytic continuation in the three-dimensional Schrödinger scattering problem with a potential. Using the integral equation for the scattering solution and analytic Fredholm theory, together with an estimate of an iterated kernel at large comple…
This item is a journal contents and errata page rather than a research article. It lists articles from an issue or volume of Differential Equations, with authors, titles, issue numbers, and page ranges, covering topics such as boundary-value problems, Green’s functions, averaging methods, integral e…
The paper studies linear continuous operators in countably normed spaces and their adjoints in spaces of test and generalized functions, with emphasis on normal solvability and Fredholm type properties. It proves criteria for an operator to be a Phi-plus or Phi-operator via composition with a suitab…
The paper studies global boundary value problems for the nonlinear degenerate elliptic equation \(y^m u_{xx}+u_{yy}=k(x,y)e^u\) in a simply connected domain in the upper half-plane whose boundary includes a segment of the degeneracy line. It proves existence and uniqueness for the Dirichlet problem …
This note formulates and outlines proofs of two metric results for bounded harmonic functions of two variables in a disk. The first theorem estimates the size of the set of levels whose level lines in the half disk have large total length, showing that for uniformly bounded harmonic functions the me…
This paper studies general mixed boundary value problems and the Cauchy problem for broad classes of linear parabolic systems with discontinuous coefficients in domains separated by an internal interface. It formulates algebraic complementing conditions for boundary, initial, and conjugation operato…
This paper studies measure-preserving dynamical systems that can be approximated by periodic, in particular cyclic, transformations with specified rates, and relates these approximation rates to entropy and spectral properties. It proves that sufficiently fast cyclic approximation implies zero entro…
This paper studies a coupled operator system of the form x equals mu A(x,y), y equals B(x,y) in products of Banach spaces, using Krasnosel’skii’s topological methods for completely continuous vector fields. It establishes formulas for rotations and fixed point indices in terms of a reduced linear op…
This note studies positive harmonic functions for convolution-type operators on nilpotent groups, extending known descriptions from the abelian case. Under a support-generation condition on the transition function, the argument uses compactness of normalized positive harmonic functions, Choquet repr…
This paper formulates necessary optimality conditions for controlled systems containing distributed-parameter elements, where the state is governed by parabolic partial differential equations with controlled boundary dynamics and additional ordinary differential equations at the endpoints. Extending…
The paper proves that every closed image of a metric space admits a condensation onto a metrizable space, with the essential interest lying in the nonseparable case. The proof uses a decomposition theorem of Lashnev to isolate a countable union of discrete sets over which fibers may fail to be compa…
This paper studies almost everywhere differentiability for functions in generalized Sobolev classes \(W_p^l(G)\), allowing the highest order derivatives to be measures when \(p=1\). It defines a complete differential of order \(l\) through convergence of rescaled remainders in a Banach function spac…
The paper studies linear operators on decomposed Banach spaces equipped with an indefinite J-metric, focusing on J-nonexpanding and related J-isometric operators defined on arbitrary linear manifolds rather than necessarily on the whole space. It establishes elementary structural properties of negat…
This paper develops necessary conditions for local extrema of differentiable functionals on subsets of Banach spaces using the cone of admissible directions, with particular attention to pseudoconvex sets that include convex sets and boundaries of convex bodies. It derives extremum conditions for Fr…
This paper studies a class of linear dynamic programming problems in which admissible controls may be unbounded and are treated as generalized functions, while phase coordinates may be discontinuous. It formulates the control system with linear dynamics, endpoint conditions on linear manifolds, and …
The paper constructs variational difference schemes with improved boundary approximation for the third boundary-value problem for a linear two-dimensional second-order elliptic equation, with corresponding applicability to the first boundary-value problem. The method uses a polygonal domain fitted t…
This paper studies point sets called \(\{k;n\}_q\)-arcs in finite projective Galois planes, focusing on upper bounds for \(k\), existence cases, and completeness. Using Diophantine systems associated with secants through absolute and external points, it gives another proof of Barlotti’s bounds and a…
This paper studies the mean-square closure of integral functionals of the form obtained by integrating a Borel function of a stationary zero-mean Gaussian process over a finite interval. Using expansions in normalized Hermite polynomials and estimates for powers of the correlation function, it gives…
The paper studies uniqueness in an inverse problem of potential theory: determining a density in a given open set from the exterior values of its metaharmonic potential, an integral equation of the first kind. It proves that although uniqueness need not hold in general, it does hold for certain clas…
This note gives intrinsic characterizations of those T1 spaces that arise as closed continuous images of metric spaces, and of complete metric spaces. It introduces hereditarily conservative systems of closed sets and almost refining sequences of closed covers, showing that a T1 space is a closed im…
The paper studies solvability and regularity for a class of quasilinear elliptic boundary value problems whose principal part is a linear uniformly elliptic operator of order 2m with first boundary conditions. Using homeomorphism theorems for elliptic operators in Sobolev scales, resolvent estimates…
The paper studies bivariate distributions with prescribed normal marginals represented by bilinear Hermite expansions and defines a generalized normal correlation through nonnegativity of the resulting density. It proves that such an expansion is a valid density if and only if its coefficients are t…
This paper formulates the detuning of a finite vibrational system from a resonance-dangerous frequency interval as a convex programming problem in the space of adjustable stiffnesses. Using variational properties of eigenvalues, it characterizes the antiresonance region as convex, gives a parametric…
The paper studies a class of singular integral equations with a shift on a finite union of Lyapunov contours, where the shift is an orientation preserving homeomorphism generating a finite cyclic group. By reducing the scalar shifted equation to an associated system of singular integral equations an…
The paper develops a method for estimating fractional powers and related operators for weakly positive operators in Banach and Lebesgue spaces. It proves interpolation type inequalities for seminorms on domains of fractional powers, derives bounds for operators of the form BA to a negative fractiona…
This paper studies order-preserving automorphisms of the partially ordered set of submultiplicative norms on the ring of real square matrices of fixed order. It extends the setting to generalized norms associated with subrings, then analyzes the induced action on minimal one-dimensional subrings, ra…
The paper formulates and solves an inverse mixed boundary value problem for an analytic function in a simply connected domain whose boundary consists of prescribed polygonal parts, up to unknown stretching factors, and unknown arcs of prescribed lengths. Boundary data on the arcs prescribe the real …
This paper develops the method of indexials for finite groups, addressing criteria for the existence of subgroups of prescribed orders, including cases where subgroup order and index need not be relatively prime. Building on earlier results on regular indexials, it introduces supplementary subgroups…
This paper studies when metrizability is preserved under quotient s-mappings from metrizable or locally separable metrizable spaces. It proves that a separable regular first-countable quotient s-image of a metric space is metrizable, extending Stone’s theorem, and shows that a regular weakly paracom…
The paper studies transcendence and algebraic independence of values of E-functions that satisfy second order linear nonhomogeneous differential equations. It introduces a lemma reducing certain algebraic differential relations for solutions of nonhomogeneous first order systems, and consequently hi…
The paper studies absolutely monotone segment functionals on polynomials of bounded degree, distinguishing nodal functionals with unique extremal structure from amorphous functionals lacking a definite nodal decomposition. It gives criteria, in terms of the number and placement of quota nodes, for w…
This note studies mixed best approximation of analytic functions in two opposite angular domains by entire functions of prescribed order and type in an \(L_p\) metric. Using a principle that reduces approximation questions in such unbounded domains to estimates on the boundary lines, the authors def…
This note derives Schauder-type estimates for the first boundary value problem for parabolic equations of order 2p, with p greater than 1, in bounded domains with suitably regular lateral boundary. The argument replaces techniques specific to second-order equations by an improved estimate for the de…
The paper studies locally finite groups containing a maximal complete abelian 2-subgroup whose normalizer is 2-infinitely isolated. It proves a structural alternative: under these hypotheses, either an almost regular involution is finitely approximable, the group is of type PGL(2,K) over a field of …
This paper studies the Cauchy problem for linear differential operators in a Banach space using weak approximation, without assuming in advance that the original problem is well posed. It introduces an auxiliary factorized problem corresponding to a decomposition of the operator into fractional step…
This paper studies the Dirichlet problem for the elliptic system of A. V. Bitsadze, focusing on how the Noether property fails in simply connected noncircular domains. Reducing the system to the complex equation with general solution expressed through holomorphic functions in the Smirnov class, the …
The paper establishes a priori estimates for one-dimensional parabolic equations whose coefficients may be merely measurable and may depend on the solution and its spatial derivative. Using an auxiliary spatial variable and a boundary smallness lemma for a related higher-dimensional quasilinear equa…
The paper studies invariant maximal positive and negative subspaces for bounded linear operators in Hilbert spaces with an indefinite metric. It proves property P for certain J-unitary operators with compact off-diagonal part, establishes existence and extension results for invariant maximal nonnega…
