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 infinitesimal bendings of convex surfaces subject to nonsingular sleeve, or collar, boundary constraints, with emphasis on how nonrigid constraints are distributed among all such constraints. Using reductions to elliptic boundary value problems and compact operator arguments, it pr…
The paper introduces elementary refinements of structural characterizability for semigroups in terms of first-order axiomatizability and elementary definability of their subsemigroup lattices. It proves general non-closure results for classes of such structures, including cases involving infinite cy…
This note constructs fundamental solutions for certain constant coefficient partial differential operators involving the singular Bessel operator in one variable. It introduces a basic test function space, generalized functions, convolution, translation, and the mixed Fourier-Bessel transform, then …
This note addresses decision problems for finitely presented semigroups, with emphasis on constructing presentations with very few defining relations whose identity problem is undecidable. It proves that a semigroup on four generators with six defining relations has an unsolvable identity problem fo…
The paper addresses Nevanlinna’s conjecture that an entire function of finite order has only finitely many deficient values. It proves that for every sequence of complex numbers and every order greater than one half, there exists an entire function of that order, of normal type, for which all member…
This paper studies Cauchy problems for second-order differential equations in Banach spaces, covering abstract parabolic and hyperbolic equations with nonlinear terms. For parabolic equations, it uses resolvent estimates, fractional powers, and reduction to first-order systems to prove local existen…
This paper studies higher order approximations in the Bogolyubov, Krylov averaging method for ordinary differential equations with a small parameter, with the aim of weakening unnecessary smoothness and regularity assumptions used in earlier justifications. It introduces Hölder-type conditions for t…
This note studies well-posed solvability of the Cauchy problem for a linear evolution equation with variable coefficients on the real line, assuming that the highest coefficient is constant and the remaining coefficients converge at infinity to those of a constant-coefficient equation well-posed in …
This note studies nonlinear transformations of probability measures on functional spaces, motivated by determining the law of a transformed random process from the law of the input process. Working in a separable Hilbert space, it gives conditions under which the image measure induced by a measurabl…
This paper addresses the instability of Lyapunov characteristic exponents for nonautonomous linear systems under small perturbations and proposes a modified framework based on generalized, or limit, solutions. It defines the spectrum as the set of characteristic exponents of all generalized solution…
This paper develops a probabilistic model for crystallization of a semi-infinite multicomponent chain whose particles attach to and detach from the chain end with transition frequencies depending only on the terminal pair. It derives equations for the survival probabilities of chain configurations, …
The paper studies stationary subsets of metrizable spaces, understood via a compatible metric as sets that must meet the image of every sufficiently small continuous self-map. It proves that every finite-dimensional metrizable space contains a closed zero-dimensional stationary subset, using standar…
The paper introduces effective Phi-inseparability for two disjoint subsets of a metric space, extending earlier notions of effective non-enumerability and effective distinguishability. It defines inseparability through a continuous selection function on a compact metric base and studies how the prop…
This note gives a simplified proof, for the case \(lp>n\), of a theorem concerning the density of finitely supported functions in discrete Sobolev type spaces \(l_p^{(l)}\). Sobolev proves that if a function belongs to \(L_p^{(l)}(E_n)\), then its values on any regular lattice form an element of \(l…
The paper studies conditional extremal problems for real entire functions of finite exponential degree that are nonnegative on the real axis and belong to an Lp class, subject to admissible linear constraints. Using a Nikolskii type inequality and comparison with extremal problems in L1 and uniform …
This paper studies asymptotic formulas for the eigenvalue counting function of singular strongly elliptic differential operators with matrix-valued coefficients on unbounded domains. The approach relates the counting function to the trace of the Green matrix for an associated parabolic Cauchy proble…
This paper studies representations of topological semigroups as semigroups of continuous transformations, using the compact-open topology and related bicompact extensions. It proves that every topological semigroup is topologically isomorphic to a semigroup of continuous transformations of a topolog…
The paper proves an undecidability result for a restricted fragment of the pure narrow predicate calculus with prenex formulas of the form involving a universal, existential, and universal quantifier prefix followed by an existential block. The argument reduces recursively inseparable halting and cy…
The paper studies quasi-numbers and algorithms acting on them, introducing quasi-functions, their domains of definedness, and operators from quasi-numbers to quasi-numbers in a constructive setting. It proves that quasi-functions cannot have constructive discontinuities, using a lemma on the impossi…
This note studies normalized positive definite class functions on discrete nilpotent linear algebraic groups over a field of characteristic zero, with emphasis on describing the extreme points of this convex set. Using reductions to special nilpotent groups associated with Lie algebras of type gener…
This paper gives a criterion for the existence of time-periodic solutions of a quasilinear parabolic boundary value problem on a bounded domain, with coefficients and nonlinear terms periodic in time and satisfying ellipticity, Hölder, Lipschitz, and growth assumptions. The problem is formulated as …
This paper studies the description of dual functors in categories of topological spaces with a distinguished point and in more general D-categories. For continuous functors on suitable categories of completely regular spaces, it proves that the dual functor is determined by its restriction to a smal…
This paper studies Lyapunov asymptotic stability of the zero solution for nonlinear differential equations in a Banach space with generally unbounded time-dependent linear operators. Using the Gateaux differentiability of the norm, it introduces one-sided estimates through the duality mapping and de…
This paper studies uniform approximation of continuous functions on simple Jordan arcs in complex Euclidean space by functions holomorphic on the arc. It proves that for a simple Jordan arc in complex two-space whose projection onto one coordinate is nowhere dense, every continuous function on the a…
This note studies asymptotic formulas for fixed moments of the number of classes of purely radical quadratic forms of negative determinant. Using Gauss’s formula, the problem is reduced to estimating moments of Dirichlet L-series at 1, and then to bounds in the critical strip via the A. I. Vinogrado…
The paper develops a dual formulation of measure theory on linear spaces by associating a linear space with measure to the ring of measurable functions together with the closed generating subspace of measurable linear functionals. It shows that every such space is linearly isomorphic, modulo null se…
This paper studies mutually adjoint boundary value problems for a first order system of three partial differential equations of composite type, reducible to a canonical form combining a real characteristic component with a Beltrami type equation. For a simply connected domain with prescribed boundar…
This paper studies boundary value problems for second order abstract elliptic equations in a Banach space, with time dependent closed operators and general linear boundary conditions involving endpoint values and derivatives. Using analytic semigroups generated by square roots of the operators, the …
The paper studies the decomposition of tensor products of representations in the positive discrete unitary series of the Lorentz group L3, with parameters allowed to be arbitrary positive real numbers. Using a basis method, it first derives the irreducible decomposition of the product of two such re…
This paper studies curvature restrictions for Kähler metrics that arise as Bergman metrics of bounded domains in complex Euclidean space. Building on known estimates for sectional curvature in analytic directions, it derives an upper bound for the Ricci curvature, showing that for a bounded domain i…
The paper studies systems of ordinary differential equations with a small parameter whose unperturbed part has an isolated rotational and oscillatory solution, while the perturbing terms are almost periodic in time and in angular variables. Under smoothness, Lipschitz, and nonresonance-type isolatio…
This note studies differentiable functions on Euclidean space whose derivatives have finite mixed norm and whose higher derivatives satisfy a multiple Hölder condition in the same norm. It gives a necessary and sufficient characterization of the class by representation as finite sums of series of en…
This note studies convergence and divergence of Fourier series of uniformly almost periodic functions whose Fourier exponents have a single limit point, considering separately the cases where the exponents tend to infinity or to zero. It recalls known convergence criteria of Bochner and Levitan, the…
The paper studies the local analytic problem of determining all Riemannian spaces that admit a nontrivial geodesic mapping onto a given space, without restrictions on metric signature. It reformulates the existence of such mappings as a first order differential system for an auxiliary symmetric tens…
This note studies analogues in characteristic p of Cartan’s simple transitive pseudogroup Lie algebras, realized as derivation algebras of truncated polynomial rings. It describes the resulting Cartan type Lie p-algebras, general, special, Hamiltonian, and contact, and formulates the conjecture that…
The paper derives explicit coefficient formulas for asymptotic expansions that refine classical limit approximations among common probability distributions. It treats convergence of binomial and multinomial laws to Poisson and normal laws, Poisson probabilities to the normal density, binomial distri…
The paper studies stable solution of functional equations Au = f in settings where the inverse problem may be ill posed, relating stability to regularizability. In a Hilbert space framework with a positive self-adjoint operator defining a stronger norm, it analyzes a quadratic regularization functio…
This paper studies sector-restricted versions of the Hardy-Littlewood problem for representations of a large integer as a prime plus two squares, and of its indefinite analogue for primes of the form a fixed integer plus two squares. Combining Linnik’s dispersion method with unimodular transformatio…
This paper studies linear differential systems whose coefficient matrices are uniformly almost periodic and belong to the class of R-systems, aiming to extend Floquet-type structural results beyond the periodic and quasiperiodic cases. It develops auxiliary lemmas on limiting increments of functions…
The paper studies preservation of metrizability under finite-to-one mappings in general topology, focusing on spaces that map openly and closedly onto metric spaces. It proves that the inverse image of a metric space under an open-closed finite-to-one continuous mapping is metrizable, by constructin…
The paper studies upper bounds for the number of integer points in multidimensional boxes at which several parameter-dependent integral polynomials simultaneously take prime absolute values. Under irreducibility, non-association, coefficient growth, and local solubility assumptions, it combines alge…
