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 note studies a neutral differential equation with a constant small delay, in which the right hand side depends on the delayed derivative, and examines the behavior of its solution as the delay tends to zero. Under smoothness assumptions and a stability condition bounding the derivative of the r…
The paper studies singular Cauchy problems for the Chaplygin equation in a half-plane near the degeneracy line, focusing on the construction of singular kernels and Riemann type functions. It introduces Duhamel and Doetsch resolvents with discontinuous boundary data, reduces their computation to mix…
The paper studies weak solutions of the first boundary-value problem for uniformly strongly elliptic systems of order 2m in a bounded domain, using Sobolev space formulations and Gårding-type coercive inequalities. It reduces the weak problem to an operator equation in a Hilbert space involving a bo…
This note formulates a general best approximation problem in Banach spaces with additional linear equality constraints and cone-defined inequality constraints. Under a regularity condition, it proves an analogue of Chebyshev’s theorem, giving necessary and sufficient optimality conditions in terms o…
This paper studies conjugate nets in three-dimensional projective space whose successive Laplace transforms have fibering congruences of first and second axes. Using a moving projective frame and Cartan’s exterior differential forms, the author derives the differential systems expressing the require…
The paper studies elliptic and parabolic second order differential equations with a small parameter multiplying the highest derivatives, motivated by oscillatory systems subject to small random perturbations and fast motion along closed trajectories. It proves averaging results for solutions in an a…
The paper studies the planar set swept out by segments joining the line y = 0 to the line y = 1 when the segment through each base point has a prescribed inclination, asking what can occur when the inclination function is discontinuous. It develops a construction using finite systems of parallelogra…
This paper gives a constructive characterization of continuous periodic functions whose trigonometric conjugates, together with the original functions, satisfy the Lipschitz condition of order one. The criterion is formulated in terms of approximation by Jackson interpolation polynomials at equally …
This note studies when a complete Boolean algebra is normable, meaning that it admits a strictly positive countably additive probability measure, by examining groups of automorphisms of the algebra. It introduces complete homogeneity, defined by a transitivity condition and a uniform continuity cond…
This note studies whether spaces of analytic functions associated with two nested nonseparating continua in the extended plane can possess a common basis when the inclusion is not strict in the sense used in earlier positive results. It introduces the notion of a continuum being a metrically separab…
This note proves sufficient conditions for essential self-adjointness of the minimal operator in L2 on the real line generated by the even-order differential expression ly = (-1)n y(2n) + q(x)y, where q is real and continuous. The argument uses interval conditions controlling the negative part of q …
The paper extends the Goluzin-Schiffer variational method to a class of normalized univalent, nonvanishing functions in finitely connected circular domains. Using a decomposition of a conformal map into successive one-to-one conformal components associated with boundary continua, it derives variatio…
This note studies whether Riemann’s localization principle extends from trigonometric Fourier series to systems of the form \(\{\varphi(nx)\}\) whose generating function satisfies specified absolute convergence and Dirichlet series nonvanishing conditions. Although such \(T\)-systems share several g…
This note studies continuation of solutions of partial differential equations across a boundary segment under boundary conditions, using transformation operators. After recalling one-dimensional transformation operators and their kernels, it constructs reflection-type continuations for elliptic equa…
This note extends an earlier asymptotic averaging method for singularly perturbed systems of differential equations to intervals that may be unbounded in time. It formulates additional hypotheses involving Lyapunov stability of a solution of the degenerate fast system, uniform existence of time aver…
This paper studies the asymptotic distribution of eigenvalues for linear Fredholm integral equations with bounded kernels having a finite jump discontinuity on the diagonal. Under smoothness, nondegeneracy, and boundary-type conditions expressed through auxiliary resolvent kernels, the equation is r…
This note develops embedding and conjugacy theorems for subgroups of finite groups in settings extending the usual theory of Hall subgroups. It introduces quasi-Hall and quasi-Sylow divisors and formulates conditions under which properties such as existence, conjugacy, embedding into larger subgroup…
This paper studies a general linear boundary value problem for the equation \(\Delta u+\lambda c(x,y)u=0\) in a bounded plane domain, with a boundary operator of arbitrary order and a real parameter \(\lambda\). The problem is reduced to a Riemann-Hilbert boundary value problem for a first order ell…
The paper extends the notion of weak ellipticity for even order linear partial differential operators in two real variables by using a directional first order operator with arbitrary nonzero constants. It formulates the basic homogeneous boundary value problem for a broad class of weakly elliptic eq…
The paper derives formulas for indices of reduced residue classes using formal logarithmic and exponential series interpreted modulo a natural number. It first treats odd prime powers and powers of two, giving congruences for discrete logarithm type indices and describing suitable choices of primiti…
The paper studies characteristic functionals of probability measures on spaces in duality, focusing on extensions of Bochner-type characterization theorems beyond the setting considered by Kolmogorov. It shows that the relevant theorem remains valid when the dual space is a separable countably pre-H…
This paper studies linear difference equations with coefficients affine in the independent variable and fixed shifts, focusing on entire and meromorphic solutions beyond the previously treated case of at most exponential growth. Using a matrix method and the associated transposed differential equati…
The paper studies the planar Poincare boundary value problem for a second order elliptic equation whose first order coefficients have first order polar singularities and whose zeroth order coefficient has a second order polar singularity. After showing conformal invariance, the problem is reduced in…
The paper characterizes when a commutative semisimple regular normed ring with identity, represented by the Gelfand transform as functions on its maximal ideal space, is the full ring of continuous functions on that compact space. It removes the symmetry assumption from Katznelson’s theorem, proving…
The paper formulates a first boundary-value problem for a broad class of linear partial differential equations determined by a convex set of multiindices and an associated quadratic energy functional. Using boundary data described through a skeleton of admissible derivative traces, it defines an aff…
This note studies laws of large numbers for sequences of random variables associated with generally nonhomogeneous Markov chains, using Dobrushin-type coefficients of ergodicity for the transition functions. It gives sufficient variance conditions, expressed through the minimal ergodicity coefficien…
This note introduces the class of alpha spaces, locally convex spaces whose weak duals have the property that every sequentially closed subspace is closed, and studies related alpha prime spaces defined through sequential completeness of the weak dual in the Mackey topology. It proves permanence pro…
This paper establishes congruences for the number of representations of a natural number as a sum of an odd number of integer squares. Using known formulas for the principal term involving the singular series, together with generalized Bernoulli numbers and Voronoi type congruences, it derives relat…
This note studies commutative semigroups with zero that have only finitely many nonregular elements, equivalently those admitting a finite Rees ideal composition series, with particular attention to the case \(A^2=A\). It introduces reduced ideal series whose factors are elementary semigroups, prove…
This paper addresses Fuchs’s problem of characterizing which complete direct sums of torsion-free abelian groups of rank 1 are separable. It states necessary and sufficient conditions formulated entirely in terms of the types of the rank 1 components: termination of decreasing sequences of component…
This paper studies the first boundary value problem for general second order quasilinear parabolic equations, extending earlier work on equations with divergent principal part. Under natural growth, parabolicity, smoothness, and compatibility assumptions, with a smallness condition on certain deriva…
This note derives an estimate for sums over primes of products of a nonprincipal character modulo a prime q evaluated at a rational function and an additive exponential of another rational function. Extending a problem indicated by I. M. Vinogradov, it applies Vinogradov’s method together with stren…
The paper studies compactifiability properties of completely regular spaces and spaces obtained by deleting countable sets from products of compacta. It constructs a completely regular, peripherally bicompact space using a product of an interval with an ordinal space, and proves via an auxiliary lem…
This paper studies existence, uniqueness, and regularity for a boundary value problem in a cylinder for a class of higher order linear differential equations with elliptic spatial part and time derivative of arbitrary order. It establishes a priori estimates in anisotropic Sobolev spaces for both st…
The paper studies second-order differential equations in a Banach space with time-dependent unbounded operators, including linear, nonlinear, and singularly perturbed problems. Using evolution operators associated with first-order equations and integral representations, it proves existence and uniqu…
This note studies spectral properties of non-self-adjoint differential operators with complex potentials, chiefly a half-line Sturm-Liouville operator with complex boundary condition and an analogous three-dimensional Schrödinger operator. Using properties of the Weyl function, zeros of the Jost-fun…
This note studies differentiability properties of Fourier series in generalized spherical functions for functions on the three parameter domain associated with the sphere. It introduces Sobolev type Hilbert spaces defined through the differential operators B1, B2, and B3, proves density of generaliz…
The paper solves an extremal problem for algebraic polynomials with real coefficients normalized by maximum modulus one on the interval [0,1], determining which polynomial maximizes the modulus of the real or imaginary part at a prescribed complex point. Using interval functionals associated with th…
The paper studies associative algebras with polynomial identities over a field of characteristic zero and special Lie algebras admitting faithful embeddings into associative PI-algebras. It describes a basis for the T-ideal generated by the third-degree commutator, using Specht bases and related mod…
The paper addresses linear ill-posed equations with a continuous operator whose inverse is unbounded, emphasizing the instability caused when approximate data fall outside the range corresponding to an a priori compact set of admissible solutions. It proposes replacing exact solvability by the notio…
This note develops a module-theoretic formulation of special radicals of associative rings, extending the familiar descriptions of the Jacobson and Baer radicals via irreducible and primary modules. It defines special classes of modules, the associated radical as an intersection of annihilators, and…
This paper extends Mal’tsev’s results on discrete groups with the maximality condition for abelian subgroups to bicompact topological groups. It proves that a bicompact solvable group satisfying the maximality condition for abelian subgroups also satisfies the maximality condition for all subgroups,…
The paper characterizes standard Markov processes in Euclidean space whose exit distributions from domains are dominated by those of Brownian motion and which satisfy a local nondegeneracy condition. It proves a converse to the evident property of subprocesses of the Wiener process under random time…
The paper studies small time periodic perturbations of a planar autonomous Hamiltonian system with a center, focusing on trajectories near resonant closed orbits whose unperturbed period is rationally related to the forcing period. By introducing action angle type variables, rescaling near a resonan…
The paper studies a measure-preserving dynamical system on the unit square associated with the distribution of fractional parts of a quadratic polynomial, extending Khinchin’s earlier system for linear functions. Using Fourier expansions in L2 and the irrationality of a fixed parameter, it proves th…
This paper studies quasianalytic classes of infinitely differentiable functions of several variables defined by bounds on mixed derivatives. It extends a previously proved criterion for quasianalyticity of type I from the whole plane to arbitrary domains, showing that the class is quasianalytic exac…
This paper extends results on the double-layer potential from Radon’s plane domains to a broader class of plane and spatial domains with irregular boundaries. The authors impose a uniform boundedness condition on the absolute variation of the spherical projection of the boundary, a condition includi…
This note studies criteria for when a line bundle, described as a fibred space of lines, gives projective embeddings of complete algebraic varieties. It extends a previously stated positivity criterion from nonsingular complete varieties to arbitrary complete varieties by defining an inductive degre…
This note studies finite pi d-groups through the number of conjugacy classes of noninvariant pi d-subgroups, using the associated notions of pi-rank and pi-type. Building on earlier work and applying results of Schmidt, Burnside, Chunikhin, the Trofimov-Toropov lemma, and Trofimov’s method of inters…
