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 pairs of elements in a lattice satisfying additive or multiplicative distributive identities, emphasizing when one property implies the other and when strict examples can occur. It gives criteria for an additively distributive pair to be multiplicatively distributive within a princ…
This paper studies the asymptotic behavior of solutions to a boundary value problem for a second order uniformly elliptic equation in a cylindrical domain whose height is small compared with its other dimensions. After rescaling the thin coordinate, the solution is constructed as a sum of an interio…
This paper discusses normal solvability, Noetherianity, Fredholmness, and index for elliptic boundary value problems, emphasizing the need for criteria that determine when orthogonality conditions to adjoint homogeneous solutions are also sufficient for solvability. It analyzes the Dirichlet problem…
This paper studies when metrizability is preserved under quotient mappings from metrizable spaces, using the notion of a regular mapping defined by positive metric separation of inverse images of nested neighborhoods. It proves that every continuous mapping from a metrizable space onto a metrizable …
The paper studies upper bounds for the number of integer solutions to equations of the form \(x_1^n+\cdots+x_k^n=y_1^n+\cdots+y_k^n\) with variables bounded by \(P\), a problem connected with estimates used in Waring’s problem. Using a main theorem on the number of solutions of related systems of co…
The paper addresses the instability of determining normal solutions of linear algebraic systems, especially singular or nearly singular systems, where small perturbations in the matrix or right hand side can produce widely scattered solutions. It defines the normal solution as the minimum norm solut…
The paper applies the parameter variation method to construct higher accuracy iterative formulas for numerical solutions of nonlinear integral equations. After replacing the integral equation by a finite system using an arbitrary quadrature formula, the residual is treated as a vector parameter, and…
This note studies generalized eigenfunctions of the homogeneous Dirichlet problem for the string vibration equation in a domain with piecewise smooth boundary, viewed through the self-adjoint operator associated with the problem. Using boundary automorphisms generated by characteristic directions an…
This paper studies boundary value problems for two-component second order elliptic systems with constant real matrix coefficients in a bounded simply connected plane domain, under a first order linear boundary condition that may fail the Lopatinskii condition. Using representations of solutions by a…
This paper studies reflexivity in Banach spaces constructed from partially ordered KB-spaces by means of N-functions, extending classical results on reflexive Orlicz spaces. It first establishes characterizations of N-functions whose complementary functions also satisfy the Delta 2 condition, showin…
This paper studies nonautonomous differential equations in a separable locally convex space and addresses a hypothesis of V. V. Nemytskii concerning recurrent and almost periodic behavior after enlarging the set of solutions by limit trajectories. The author defines this enlargement using closures o…
This paper studies Uryson integral operators with Carathéodory kernels acting between Lebesgue spaces, focusing on criteria for continuity and complete continuity. It introduces and uses a notion of regularity for nonlinear integral operators, showing that regular Uryson operators from Lp to Lq with…
The paper studies necessary and sufficient conditions for an absolute minimum of an integral functional with boundary terms, subject to a system of first-order partial differential constraints and admissible state-control pairs. Using auxiliary functions, Ostrogradsky’s formula, and needle variation…
This paper studies dynamical systems of the first degree of non-structural stability on the torus, extending earlier results for the plane and cylinder and highlighting features specific to surfaces of positive genus. Using a rotation of the vector field by a parameter and an analysis of lifted traj…
This paper studies periodic linear groups over arbitrary fields and their connections with algebraic and Lie groups. It proves conjugacy of Sylow subgroups and a Schur Zassenhaus type theorem for periodic linear groups, gives examples of infinite simple locally finite linear groups, and completes th…
This paper studies commutative symmetric algebras of bounded operators in a Pontryagin space of finite negative index and seeks their classification up to equivalence. It analyzes eigenfunctionals and root lineals, separates the contribution of nonreal eigenfunctionals, and constructs invariant prin…
The paper studies boundary value problems for elliptic equations of arbitrary even order in a cylindrical domain whose height is a small parameter. Extending earlier results for second order equations, it constructs an asymptotic expansion of the solution by combining an interior iterative expansion…
The paper proves undecidability results for restricted classes of formulas in constructive and minimal predicate calculi, focusing on formulas of the form double negation followed by universal and existential quantifier blocks with a quantifier-free matrix. It reduces the compatibility problem for s…
The paper reformulates the problem of M-convexity for systems of linear partial differential equations with constant coefficients in terms of finite modules over the polynomial ring in differential operators. It relates the cohomology of sheaves of local homogeneous solutions to Ext groups via a Dol…
The paper studies growth characteristics of entire functions of several complex variables, presented for two variables, when the space is exhausted by products of circles rather than by one-parameter surfaces. It introduces systems of conjugate refined orders and corresponding conjugate types, prove…
The note surveys several problems in approximation theory in Banach spaces: best approximation of individual elements by finite-dimensional subspaces, approximation of convex sets, Kolmogorov widths, and related codimensional widths. It gives general criteria for best approximation in spaces of cont…
This note studies the asymptotic behavior of generalized solutions to a nonlinear parabolic boundary value problem in a bounded smooth domain, where the linear elliptic part satisfies standard ellipticity and complementing boundary conditions and the nonlinearity is Lipschitz with time-dependent con…
This note studies weak generalized solutions of the third boundary value problem for a general second order linear parabolic equation with measurable bounded coefficients and data in square integrable classes. It defines the solution by an integral identity including boundary values, then states an …
This paper applies earlier results on the local structure of Darboux surfaces to infinitesimal bendings of surfaces, considering both local and global questions. For surfaces of positive curvature, it proves several uniqueness criteria showing when prescribed behavior of associated bending fields on…
This paper studies analogues in \(L_p\) metrics of Favard-type inequalities relating the approximation of a periodic function by Fourier partial sums or trigonometric polynomials to the corresponding approximation of its derivative. It proves an \(L_p\) estimate for the deviation of a function from …
This paper studies boundary value problems for operators of the form du/dt minus A in a Hilbert space, where A is an unbounded normal operator, with emphasis on constant coefficient differential operators on the torus. It analyzes scalar boundary conditions relating the values at t = 0 and t = a, es…
This paper studies almost everywhere summability of Fourier series in eigenfunctions of the Laplace operator on an arbitrary multidimensional domain under boundary conditions yielding a complete orthonormal eigenfunction system. It proves that for every function in \(L_2(g)\), the eigenfunction expa…
The paper studies the countably normed algebra of entire functions of order at most one and minimal type, with norms defined by exponential bounds, and asks for a description of its nontrivial closed ideals. It proves that every such ideal consists exactly of the functions vanishing, with prescribed…
This paper studies the behavior of solutions to the incompressible Navier-Stokes equations in a bounded domain as viscosity, equivalently the Reynolds number, passes through a critical value. The problem is reduced by expansion in eigenfunctions of the Stokes operator to an infinite system of ordina…
The paper studies the local behavior of holomorphic and meromorphic functions near an essential singularity through sequences of points on which the function assumes almost all values in shrinking neighborhoods. It introduces and extends notions of M and mu point sequences with a scale parameter p, …
This note studies how equi-morphisms of hyperbolic spaces act on the sphere at infinity, especially with respect to tangency in the spherical Poincaré model. It proves that tangency of a curve in hyperbolic space to the sphere at infinity is invariant under equi-morphisms, using a characterization b…
This note studies the local extrinsic geometry of the Darboux surfaces associated with an infinitesimal bending of a positively curved surface of class \(C^{n,\alpha}\). Using local coordinates, properties of the bending and rotation fields, and Stoilow’s theory of interior mappings, it analyzes the…
This paper studies the branching of an irreducible finite-dimensional representation of a complex reductive Lie algebra when restricted to a regular reductive subalgebra of the same rank. Using character identities, Kostant’s weight multiplicity formula, and finite difference operators applied to pa…
This note studies when applying the inverse limit and its right derived functors to an exact sequence of inverse spectra of abelian groups preserves exactness. Using homological algebra, it constructs a spectral sequence with second term given by the homology of the complexes formed from the derived…
This paper studies the behavior at infinity of polynomials in real variables with parameter-dependent coefficients, using the Newton polyhedron associated with the set of nonzero monomials. It introduces principal faces, completeness, and nondegeneracy, and proves that for complete nondegenerate pol…
This paper studies convergence criteria for sequences of positive linear functionals and operators in Banach spaces ordered by a cone, extending Korovkin-type results beyond spaces of continuous functions. It introduces smoothness points of a cone and saturated, uniformly saturated, and completely s…
The paper proposes analogues of the classical classes of analytic functions A, D, and Hδ on open hyperbolic Riemann surfaces whose ideal boundary is described by Martin compactification and is largely attainable by Green lines. It defines surfaces with univalently attainable boundary, constructs ass…
This paper constructs a complete holomorphic family of deformations of a holomorphic principal fiber bundle with compact base and complex structure group. Using differential forms with values in the adjoint bundle, the deformation problem is expressed through the integrability equation for a form of…
This paper derives elementwise upper estimates for the spherical matrix norm, or spectral norm, and for the corresponding logarithmic norm, without using the block decompositions employed in earlier work. It presents a general comparison principle based on bounds for the spectral radius of positive …
The paper develops an asymptotic averaging method for calculating oscillatory regimes in nonlinear, generally non-Hamiltonian systems subject to small perturbations and slowly varying parameters. Assuming that an integral of the unperturbed periodic system is known, the authors introduce amplitude c…
This paper studies sharp covering and extremal problems for functions regular and univalent in the unit disk that omit two prescribed values, with separate treatment of general and starlike subclasses. It derives exact upper bounds for the initial coefficient in these classes, identifies the corresp…
This paper improves known sieve-theoretic approximations to the Goldbach and twin prime problems by reducing the required number of prime factors in the almost-prime term from four to three. Using Brun’s sieve together with distribution estimates for primes in arithmetic progressions due to Barban, …
