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 the rigidity and unique determination of ovaloids with cuts under boundary conditions weaker than the usual gluing conditions on curvature and torsion increments along the cut. Using Vekua’s theory of generalized analytic functions, it formulates the equations for the complex bendi…
The paper studies long-time stabilization for bounded solutions of the Cauchy problem for a uniformly parabolic divergence-form equation with variable coefficients in the whole space. Using Nash estimates for the fundamental solution and its modulus of continuity, it proves that if the bounded initi…
This note studies fundamental solutions for uniformly elliptic second order operators in the whole Euclidean space with coefficients that become constant outside a bounded domain, and with a complex spectral parameter. Using Levi’s parametrix method, an integral equation for the correction kernel, L…
This note studies when the norm of a mixed partial derivative of a smooth function of several variables can be estimated by a finite sum of norms of other partial derivatives. It formulates sufficient structural conditions on the multiindices of the derivatives, first for inequalities in the same Lp…
The paper develops a constructive theory of mappings between locally finite simplicial complexes, using standard geometric realizations as constructive metric spaces. It defines constructive complexes, their points and bodies, and proves that any constructive operator between complexes, where define…
This paper studies divisor sums for integers in real quadratic fields, ordered by absolute norm and restricted by the logarithmic argument determined by the fundamental unit. Using analytic continuation and functional equations for associated Dirichlet series, together with contour integration and F…
This paper studies a class of projective R-nets in three-dimensional space whose congruences of first and second axes are foliated by the corresponding axis congruences of their Laplace transforms. Using moving frames and exterior differential systems, it gives intrinsic characterizations of the net…
The paper studies superconstructive propositional calculi obtained by adding finitely many axioms to Heyting’s intuitionistic calculus, with modus ponens and substitution as rules. Using finite implicative structures, including Jaśkowski structures and related families constructed by cardinal produc…
This note studies a mixed initial boundary value problem for a second order hyperbolic equation in a cylinder, where a small parameter multiplies the highest derivatives and the limiting equation is first order. It constructs an asymptotic expansion of the solution by combining an outer iterative so…
The paper studies economical finite difference schemes with splitting operators for multidimensional hyperbolic equations with variable coefficients under initial and boundary conditions. It constructs a discrete analogue of the problem, establishes second order approximation under smoothness assump…
This note studies approximation of unbounded twice continuously differentiable functions on the whole Euclidean plane by modified Landau polynomials and two forms of modified Bernstein polynomials. Under conditions on the scaling sequence and on the exponential growth of the function, it derives asy…
This paper extends the Poincaré, Andronov point transformation method to periodic solutions of functional differential equations with delay, allowing arbitrary relations between the delay length and the period. It formulates the shift operator on a space of initial functions, proves that periodic so…
The paper studies differentiability with respect to a fixed set of increments Q tending to zero, asking when Q-differentiability or bounded Q-derivative numbers on a set of positive measure imply asymptotic differentiability almost everywhere. It introduces a structural class D for such sets Q, char…
The paper studies harmonic functions on the complex group GL(2), where harmonicity is defined by the real and imaginary parts of a bi-invariant second-order Laplace operator. It constructs such functions from functions on pairs of linear elements of the complex plane, identified with the homogeneous…
The paper extends Glivenko’s theorem, and Kreisel’s related result for prenex predicate formulas, to a broader class of formulas in predicate calculus. It proves that if a formula contains no negative occurrences of the universal quantifier, then the negation of that formula is derivable in classica…
The paper studies semigroups defined by sets of identities and asks which identity systems force the corresponding variety to lie in specified classes of semigroups. It develops a consequence relation for identities, relates it to free semigroups in the class determined by a set of identities, and i…
This paper studies linear extremal problems for analytic functions with positive real part in finitely connected domains, subject to additional interpolation and inequality constraints on their real and imaginary parts. To treat these problems, it develops auxiliary results on compatibility and extr…
This note studies second order nonautonomous systems with small periodic perturbations of a rough autonomous planar system, using the period map associated with the perturbation. It proves persistence, for sufficiently small nonzero perturbation, of special structures corresponding to hyperbolic equ…
This paper presents a Fourier transform method for determining coefficients in mechanical cubature formulas that are exact on polynomials up to a prescribed degree at given nodes. It proves that exactness of the error functional on polynomials of degree less than m is equivalent to the Fourier trans…
This paper studies stability of generalized solutions to periodic Hamiltonian equations in a separable Hilbert space when the operator coefficient is unbounded. The coefficient is decomposed into a positive self-adjoint part and a subordinated perturbation, under conditions ensuring existence and un…
A numerical method is proposed for solving linear Fredholm integral equations of the first kind with convolution kernels, under the assumption that the solution exists and the relevant functions are integrable. The approximate solution is represented as a finite linear combination of shifted values …
The paper studies quasiprojective classes of models, defined as abstract classes closed under ultraproducts, and develops general closure and compactness properties for such classes. It proves that membership on an ultrafilter-large set is preserved in ultraproducts, derives a finite-intersection co…
The paper introduces the Hilbert space K^m_Lambda(Omega), a subspace of weighted Sobolev spaces adapted to boundary constraints expressed through boundary functionals. It proves a key inequality controlling lower order norms by weighted highest derivatives and boundary integrals, establishes complet…
This paper studies recurrence, periodicity, Poisson stability, and transitivity for semigroups of multivalued mappings on uniform separated spaces, a setting intended to include dynamical systems without uniqueness. It introduces several recurrence conditions and periodicity conditions for points, a…
The paper studies primitive integral solutions of a cubic Diophantine equation defined by a determinant in four variables. It gives an explicit parametrization of all such solutions by three coprime integer parameters through four cubic forms, with a common divisor factor, and relates the constructi…
Assuming the continuum hypothesis, the paper studies the Čech remainder of the natural numbers, identified with the Boolean algebra of subsets of the integers modulo finite sets, as a universal bicompact space of weight \(\aleph\). It gives a topological characterization of this remainder as the uni…
This note studies deformations of compact complex structures, with particular attention to when members of a complex analytic family are algebraic. Using Kodaira’s criterion via Hodge metrics, it shows locally that algebraic fibers occur along analytic subvarieties of codimension bounded by the dime…
This note studies norm estimates for linear operators acting on classes of entire functions of finite degree in several variables, with particular attention to relations between uniform and Lebesgue norms. Using integral representations of entire functions of exponential type and shift invariance as…
This note generalizes the Friedrichs space used in variational treatments of operator equations in Hilbert space. It considers pairs of distributive operators A and B, introduces the notions of B-symmetry and B-positivity, and defines corresponding extensions in the senses of Friedrichs and Sobolev.…
The paper develops a class of differential equations with compact convex multivalued right-hand sides that may be discontinuous in time, motivated by optimal control problems where optimal controls can be discontinuous on sets of positive measure. It formulates measurability and semicontinuity condi…
This paper studies representations of the elementary abelian group of order p squared over a field of characteristic p, with p not equal to 2. It argues that, unlike the cyclic case and the known case of the group of order 4 in characteristic 2, classifying these representations by normal forms is a…
This note studies inequalities bounding the \(L_q\) norm of a mixed partial derivative of a smooth function of several variables by a finite sum of \(L_p\) norms of other mixed derivatives on a rectangular parallelepiped. Using a geometric formulation in terms of integer multi-indices as points in E…
This paper studies the completeness of classical orthogonal systems in Sobolev-type spaces whose norms include square integrals of functions and their derivatives, a property needed in direct methods for differential equations. It proves completeness of Laguerre functions on the half-line and Jacobi…
This note addresses the effective reconstruction of a Sturm-Liouville equation on a finite interval from two spectra corresponding to the same left boundary condition and two different right boundary conditions. Building on the Gel'fand-Levitan reconstruction from eigenvalues and norming constants, …
This paper studies a finite-interval Wiener-Hopf type equation arising in statistical problems for multidimensional stationary random processes whose spectral density matrix is rational and nondegenerate almost everywhere. It extends earlier one-dimensional results by reducing general rational spect…
The paper studies uniqueness of continuous self-similar solutions of the Riemann problem for strictly hyperbolic systems of three quasilinear conservation laws. It reformulates the characteristic structure using Riemann invariants of the second family and constructs an explicit local example in whic…
The paper studies theta series associated with positive definite integral quaternary quadratic forms and the decomposition of their Fourier coefficients into Eisenstein and cusp form parts. Using Petersson inner products for modular cusp forms of level q, it proves explicit bounds for the norm of th…
The paper studies the field embedding problem for an exact sequence of groups with abelian kernel of finite period, relative to a finite normal extension containing the required roots of unity. The problem is translated into the construction of a suitable module extension and analyzed through homolo…
This note studies whether properties of Fourier series of summable functions are invariant under metric equivalence, defined by invertible measure-preserving transformations of the interval. Using weak and uniform topologies on the transformation group, it formulates density results for rearrangemen…
This paper studies boundary value problems for the mixed composite type equation \(y^m u_{xxx}+u_{xyy}=0\), where \(m\) is an odd positive integer, in domains divided by the line of type change and characteristic arcs. Using the representation of regular solutions as a sum of a solution of the relat…
The paper studies universal sequences of measurable functions on an interval, meaning sequences whose subsequences can converge almost everywhere to arbitrary measurable target functions, and introduces refined types governed by prescribed lower and upper bounds. It defines classes A, B, and C in te…
The paper studies uniqueness for the zero-initial Cauchy problem for operator-differential equations in Banach spaces, allowing closed linear operators whose domains need not be dense and interpreting solutions in a weak sense. It gives sufficient uniqueness conditions in terms of lower bounds for o…
This note proves an inequality for trigonometric polynomials of degree n evaluated at conjugate complex arguments, bounding a weighted symmetric combination by the maximum modulus on the real period and a factor involving hyperbolic functions. The proof reduces the problem to an algebraic polynomial…
The paper studies when uniform properties of metric spaces can be characterized by topological properties of the remainder of their canonical bicompact extension associated with the natural proximity. It proves that, for a metric space, completeness is equivalent to several topological conditions on…
This note studies metrization and perfect mappings through countable systems of coverings, decompositions, and projection spectra associated with a topological space. It proves several equivalence theorems characterizing completely metrizable spaces, Baire spaces of given weight, spaces of fixed cov…
This paper presents a collection of results on second order linear differential equations, focusing on comparison principles, oscillation and nonoscillation criteria, eigenvalue estimates, and boundedness or asymptotic behavior of solutions. It proves a comparison theorem for proper fundamental syst…
The paper studies expansions in eigenfunctions and associated functions for a non-self-adjoint Schrödinger type differential operator on the half-line when spectral singularities occur in the continuous spectrum. Under an exponential summability condition on the complex potential, it defines an appr…
This paper proves embedding theorems for Sobolev spaces and Orlicz classes in the critical case where the order and integrability satisfy pl = n. It establishes that functions in the corresponding Sobolev spaces, including spaces with zero boundary values and general domains satisfying a cone condit…
The paper studies spectral functions of closed symmetric operators in a Hilbert space and interprets the corresponding spectral expansions as expansions in generalized eigenvectors of the adjoint operator. Using Naimark’s dilation theorem and associated self-adjoint extensions, it introduces paramet…
This note studies isolated weakly irregular points on surfaces in three-dimensional Euclidean space with negative Gaussian curvature and a regular metric, where the surface remains smooth enough but the second fundamental form may be discontinuous. Using estimates for the asymptotic net, index argum…
