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 studies inclusion and boundedness properties of summability, boundedness, and absolute summability fields associated with matrix and integral summation methods. It gives necessary and sufficient lacunarity conditions under which subsequences of the Cesàro, Euler, Abel, and integral Borel …
This note studies families of intermediate extensions of a closed symmetric operator that are induced by self-adjoint extensions in a larger Hilbert space, with emphasis on their relation to generalized resolvents and projected eigenvectors. It characterizes such families for non-real spectral param…
The paper studies an integral-geometric equation in which weighted integrals over spheres through the origin are prescribed, and uses Radon transform methods to establish inversion and uniqueness results, including unitarity properties of associated operators in odd dimensions with analogous stateme…
The paper studies a boundary value problem for heat conduction in a semi-infinite plate composed of two homogeneous media separated along an interface, with different thermal diffusivities and conductivity constants. Under specified growth, continuity, and Hölder-type assumptions on the initial and …
This paper studies homogeneous Markov processes with discrete time on an abstract measurable space under recurrence and minorization conditions formulated on a measurable subset. It introduces return kernels to this subset and uses them to derive criteria for the existence of a limiting stationary d…
The paper studies connected subgroups of simply connected real simple Lie groups that correspond to simple subalgebras of real forms of classical Lie algebras. It develops methods for computing the kernel of the homomorphism from the simply connected group with a given subalgebra to its image, compa…
This note studies strong laws of large numbers for random variables forming nonhomogeneous Markov chains, using Dobrushin ergodicity coefficients to measure dependence. It gives sufficient variance summability conditions, including the uniformly ergodic case where the classical Kolmogorov condition …
This paper extends Sobolev’s embedding theory for classes of abstract additive set functions with values in a Banach space. It proves a limiting exponent embedding theorem for the classes under consideration, establishes a stability theorem for composite abstract functions satisfying a specified reg…
This note develops a geometric framework for a singular parametric variational problem defined by an invariant hypersurface hyperarea integral. It focuses on the case of singularity class one, interpreting the indicatrices as singular hypersurfaces in a centro-affine setting and deriving the associa…
This paper extends known results on the weight of compact Hausdorff spaces to broader classes of H-closed and noncompactifiable spaces. It proves that a continuous mapping from an H-closed space onto a canonical, equivalently noncompactifiable, space does not increase weight, and that the weight of …
This note studies pairs of line congruences characterized by the focality of their corresponding ruled surface submanifolds, with particular attention to the special class of congruences denoted H. Using the torsal frame formalism and differential relations for canonical frames, it identifies pairs …
This note outlines a proof of finiteness for the degree zero divisor class groups of the function fields defined by curves \(y^l=x^k(1-x)\) over the cyclotomic field generated by an \(l\)-th root of unity, for specified small primes and values of \(k\). The argument uses complex multiplication on th…
This note studies existence and uniqueness for multidimensional Itô stochastic integral equations with bounded coefficients that may be discontinuous on specified admissible sets, under nondegeneracy conditions on the diffusion near those sets. Using estimates on the occupation time of one-dimension…
This note studies when the norm in an Orlicz space on a bounded set satisfies a growth property requiring the modular integral divided by the norm to tend to infinity as the norm tends to infinity. A necessary condition is derived in terms of the complementary function and its inverse, showing in pa…
This note addresses the classification and analysis of unitary representations of connected nilpotent Lie groups. It constructs irreducible representations from linear functionals on the Lie algebra by inducing one-dimensional representations from maximal subordinate subalgebras, and identifies equi…
The paper studies the number of prime pairs \(p, p+2k\) lying below \(x\), with \(k\) varying up to \(x(\ln x)^{-C}\). Using I. M. Vinogradov’s method of trigonometric sums, in a form related to Chudakov’s work, it strengthens earlier almost-all results by obtaining the Hardy-Littlewood type asympto…
The paper studies the enumeration of subgroups of prescribed order in finite abelian p-groups, using invariant sequences describing the numbers of basis elements of each minimum order. Building on previously established formulas for the number of subgroups of a given type, it derives exact counts fo…
The paper studies constructive propositional calculi extended by a single-valued unary logical operation, with consistency defined by conservativity over the underlying pure propositional calculus. It introduces matrix models, exact models, submodels, and the natural model formed from equivalence cl…
This paper studies locally finite groups under the Pi-minimality condition and related classes of locally extremal and layerwise extremal groups. It gives necessary and sufficient conditions for such groups, when countable quasifull subgroups are solvable or locally nilpotent, to satisfy Pi-minimali…
The paper studies stability of solutions to a nonlinear integral equation in a Banach space generated by a strongly continuous evolution family. It develops auxiliary results on bounded solution subspaces, closed complements, and estimates for associated inhomogeneous linear equations, then applies …
The paper studies first-order formulas over locally free universal algebras of a fixed finite type, where local freeness is characterized by separation and injectivity conditions for the fundamental operations. It presents an algorithm that transforms any formula into an equivalent normal form on al…
This note gives a mathematical interpretation of the three-dimensional Schrödinger equation with a Dirac delta potential, whose formal Hamiltonian is not an operator in Hilbert space. The authors compare a cutoff regularization of the singular interaction, with a coupling constant depending on the c…
This note extends a method for representing solutions of differential equations by continual integrals to operator equations and systems associated with semigroups in Hilbert spaces. It defines matrix-valued set functions on path spaces, gives criteria for when they have bounded variation, and deriv…
This note studies boundary values of Sobolev functions in classes W_p^{(l)} on bounded plane domains whose piecewise smooth boundaries may have corner points. It first establishes matching criteria for fractional Sobolev classes across a point, then uses these results to characterize the traces of n…
This note studies conditions under which the Cauchy product of two numerical series is summable or absolutely summable when the factors are summable by complex normal triangular methods. It defines several classes of summation methods according to how they preserve ordinary summability, boundedness,…
The paper studies bounded solutions of a quasilinear system of differential equations with a rapidly varying forcing term, extending results on forced harmonic oscillations in weakly nonlinear systems. It introduces an exponential dichotomy type condition for the associated linear system, constructs…
This note studies structural properties of semigroups through the ordered set, and extended lattice, of their subsemigroups, focusing on structural characterizability and structural determinability. It gives lattice-theoretic criteria for several classes, including periodic semigroups, semigroups wi…
This note establishes two sharp estimates for a real function differentiable n times on an interval under prescribed zeros of the function and its successive derivatives at possibly different points. The first bound involves constants from the expansion of tan t plus sec t, while the second gives an…
This note studies well-posedness for a class of one-dimensional mixed initial-boundary value problems for systems of linear partial differential equations on several non-overlapping intervals with coupled boundary conditions. Using asymptotic fundamental solutions for the associated ordinary differe…
This note studies finite difference approximations to Dirichlet and Neumann boundary value problems for harmonic conjugate functions on paired triangular and hexagonal grids. It shows that although the local four point approximation of the Laplace operator on a hexagonal grid has only first order re…
This note gives necessary and sufficient conditions for a metric space of uniform dimension n to be uniformly embeddable in Euclidean space of dimension N at least 2n+1, and extends the formulation to uniform spaces with a countable base. The criterion combines a noncondensation condition, expressed…
This note studies the solvability of finite nonlinear systems arising from the Ritz method, equivalently from the Bubnov-Galerkin approximation, for minimizing a functional that is the potential of a nonlinear operator in a Hilbert space. Following Davidenko’s continuation idea, the Ritz equations a…
The paper introduces an alpha-base, a strengthening of a countable complete system of open coverings, and uses it to formulate criteria for paracompactness and metrizability in general separation settings. It proves that a space is paracompact exactly when every open cover majorizes some sequence of…
This paper studies the error functional of mechanical cubature formulas in n-dimensional domains, focusing on the first part of the minimax problem: determining the maximal error for fixed coefficients and nodes. The analysis is carried out for unit balls in Sobolev-type spaces with square-integrabl…
This paper develops two related classes of interpolation inequalities for sufficiently smooth functions of several variables, emphasizing inequalities that are sharp both with respect to dimension and differential order. It proves new inequalities for anisotropic smoothness norms defined through fin…
The paper studies approximation of functions by generalized linear Landau operators defined through kernels of the form \([1-(t-x)^{2k}]^n\), where \(k\) is a positive integer. It establishes pointwise and uniform convergence on subintervals of \((0,1)\), \(L^p\) convergence, estimates in terms of t…
This note studies the Cauchy problem for nonlinear parabolic systems whose highest spatial differentiation orders may differ in different variables, extending earlier results for linear and near-linear systems. It defines a class of 2b-parabolic systems and proves local existence, uniqueness, contin…
This note studies the alternating direction method for finite difference systems approximating a class of self-adjoint elliptic boundary value problems of order higher than two in a rectangle. A finite difference scheme is formulated for a fourth-order model problem with homogeneous first boundary c…
This paper studies classes of convex N-functions arising in the theory of Orlicz spaces, focusing on Delta-type growth conditions and their characterization through complementary N-functions. It proves necessary and sufficient dual conditions for several such classes, including the Delta prime, Delt…
This paper defines generalized Chebyshev line elements on a square using functions of bounded variation and an associated finitely additive curvature measure. It introduces the induced length of smooth curves and the resulting intrinsic metric space generated by such a line element. The main results…
The paper studies two existence problems for partial differential equations: mixed boundary-value problems for quasilinear parabolic systems with strongly elliptic spatial operators, and the Cauchy problem for linear hyperbolic equations of arbitrary order. For the parabolic case, a weak formulation…
This note studies nonnegative additive homogeneous functionals of standard Markov processes and their relation to representations of excessive functions as generalized potentials. It gives a necessary and sufficient condition for a finite excessive function to admit such a representation, extending …
This paper studies completeness of systems of the form \(z^{\tau_n}\log^j z\) on unbounded curves and in several types of domains in the complex plane, with weights and geometric conditions on the complement. The author derives sufficient conditions in weighted spaces of continuous functions and \(L…
This note generalizes an integral representation of one-variable divided differences to divided differences of order (m,n) for functions of two variables on a rectangular grid of nodes. Using repeated integration by parts over subrectangles, the author formulates a boundary-value problem for auxilia…
This note studies an autonomous system of n differential equations with a small parameter in a neighborhood containing an equilibrium at the origin and a limit cycle, under spectral assumptions and a nondegeneracy condition on the cubic terms. Using a Poincare-type transformation on an (n minus 1)-d…
This paper extends Sobolev-type embedding theorems for abstract additive set functions with values in a Banach space. It introduces a broader class of normal completely additive set functions, defines corresponding spaces with shift-continuous generalized derivatives, and proves that such functions …
This paper studies finite systems of pairwise disjoint \((n-1)\)-dimensional spheres embedded in an \(n\)-dimensional sphere and asks when such systems can be simplified by isotopy. Using consequences of Brown’s results on normally embedded spheres, it proves that if each sphere is normally embedded…
This paper studies a linear conjugation boundary value problem for analytic functions on domains separated by closed contours, with boundary data involving both a function and its complex conjugate. Using reductions to singular integral equations and comparison with the Riemann problem, it gives sol…
This paper develops and justifies an averaging method for singularly perturbed systems in which slow variables are coupled to fast variables whose unperturbed motion is explicitly solvable. It constructs formal near-identity transformations leading to averaged systems of arbitrary order, and proves …
