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 a one-dimensional mixed initial boundary value problem for a Kovalevskaya-type hyperbolic system of order p with matrix coefficients. It formulates smoothness assumptions, a strict hyperbolicity condition expressed through the real, distinct, nonzero roots of the characteristic ma…
The paper develops an application of the Schauder-Tikhonov fixed-point theorem to bounded operators on a Hilbert space equipped with an indefinite metric. It proves that, under positivity and compactness assumptions on the off-diagonal part of an operator, there exists an invariant maximal nonnegati…
The paper studies singular integral equations with shift on a finite union of closed Lyapunov contours, where the shift is a direction-preserving homeomorphism of finite order and the coefficients satisfy Hölder conditions. It defines a normality condition, an index, and an adjoint operator, then re…
This paper develops a variational method for the first boundary-value problem for self-adjoint elliptic equations in unbounded domains, focusing on the half-space and avoiding prior summability restrictions on the boundary data. The argument replaces ordinary lower boundedness of the quadratic funct…
This paper classifies finite nonsolvable groups in which every second maximal subgroup has an invariant 2-complement, using recent structural results on groups of odd order, groups with dihedral Sylow 2-subgroups, and minimal simple groups. The main theorem shows that such groups are precisely certa…
The paper develops orthonormal systems of analytic functions for finitely connected plane domains containing infinity, with analytic Jordan boundary components. It proves existence and uniqueness of a Taylor system and an associated Laurent system, establishes boundary orthogonality and asymptotic g…
This note develops a closed-form treatment of the Riemann-Hilbert boundary-value problem with discontinuous coefficients for the exterior of finitely many cuts lying on a straight line, with an analogous extension to arcs of a circle. The problem is reduced to a Riemann boundary-value problem for tw…
This paper studies boundary value problems for two variable differential operators whose principal part is nonhomogeneous, focusing on the binomial operator consisting of an mth derivative in time and an nth derivative in space with lower order perturbations. The roots of the characteristic equation…
This paper addresses a remaining unresolved case in Lyapunov’s analysis of stability for differential systems in the doubtful case of two zero roots with a nonsimple elementary divisor. The system is reduced by a small-parameter transformation to equations with periodic coefficients, and the argumen…
This paper proves a quantitative stability result for Liebmann’s rigidity theorem for the sphere. For a convex n-dimensional surface whose Gaussian curvature satisfies 1 minus epsilon less than or equal to K less than or equal to 1 plus epsilon, the author establishes linear estimates for the radius…
The paper studies projections of semilattices, understood as isomorphisms between the lattices of their subsemilattices, and formulates analogues of classification and rigidity problems known for groups, semigroups, and modules. It introduces weak isomorphisms, homogeneous completely isolated subsem…
The paper studies sharp growth estimates for entire functions of finite exponential type that are bounded by different constants on the negative and positive real semi-axes. Using a Phragmén, Lindelöf argument in the half-planes, it proves that if \(|f(x)| \leq A\) for \(x0\), then \(|f(re^{i\varphi…
This paper presents an algorithm for Chebyshev approximation of a continuous function by a linear polynomial in prescribed continuous functions when the coefficients may be subject to continuously specified convex constraints. The problem is reduced, by introducing an auxiliary variable, to a linear…
This note studies trigonometric sums associated with recurrent sequences modulo a prime ideal in a number field, where the recurrence has periodic nonconstant coefficients. Under hypotheses that the characteristic roots are distinct and have a common order exceeding a specified bound, it gives estim…
This paper studies simple Volterra dissipative operators in a separable Hilbert space whose imaginary component has finite dimension, using the characteristic matrix function as the main tool. It derives growth estimates for such matrix functions and gives necessary conditions for nondecomposability…
The paper develops spectral estimates for linear operators in Banach spaces semi-ordered by normal cones, extending earlier results for positive operators by relating spectral bounds to the action of operator powers on a single cone element. It proves resolvent existence and uniqueness results in or…
The paper studies groups in which subgroups, especially abelian subgroups, admit complements up to finite intersections satisfying a normality condition, termed completely F-factorizable and completely FN-factorizable groups. It proves that having all abelian subgroups FN-complemented is equivalent …
The note studies representations of ultraspherical polynomials through differential operators involving their generating function, extending a known construction for Hermite polynomials. Starting from the generating function for \(P_n^{(\lambda)}(x)\), it derives an identity expressing \(y^{n/2\lamb…
This note studies integral and local integral representations of finite groups, focusing first on cyclic groups of order mp squared with m prime to p. It determines the possible types of indecomposable representations over the ring of p-integral rational numbers by describing their rational irreduci…
The paper studies sufficient conditions for a strong extremum in variational and optimal-control problems when admissible curves have bounded derivatives or controls range over a compact set. It shows that, under the maximum principle, competitors uniformly close to an extremal and improving the fun…
This note studies how solutions, eigenvalues, and eigenfunctions of second order elliptic boundary value problems change when the boundary of the domain is analytically perturbed. For a disk whose boundary is displaced by a small analytic radial perturbation, the paper constructs formal power series…
This note studies boundary value problems for partial differential equations involving a differential Bessel operator in weighted Sobolev type spaces on half spaces and quadrant domains. It establishes trace theorems for derivatives defined through the operator x partial x and, equivalently in suita…
This paper studies paracompact spaces that admit perfect mappings onto metric spaces and their approximation by inverse spectra of metric spaces with perfect bonding maps. It proves a factorization theorem: given a perfect map from a paracompact space onto a metric space, every open cover admits a p…
This note studies an additive problem for algebraic number fields, extending sieve methods to representations of large algebraic integers as sums of prime and almost prime elements. For a number field K, it proves that every sufficiently large “even” integer, in the specified ideal-theoretic sense, …
The paper studies the asymptotic epsilon entropy of compact sets of differentiable functions in functional Banach spaces equipped with an arbitrary monotone translation invariant norm. It defines classes controlled by anisotropic and mixed smoothness norms, then derives lower entropy estimates for s…
The paper studies eigenfunction expansions for self-adjoint systems of second-order differential equations on the half-line with Hermitian matrix potentials whose norm is summable. Using Jost-type solutions, finite-interval approximation, and the unitarity of the associated scattering matrix, it der…
The paper studies density in weighted Sobolev-type spaces on Euclidean space, defined by integrability of generalized derivatives of order m with respect to a positive measurable weight. Under local boundedness conditions and radial assumptions on the weight at infinity, together with additional int…
The paper studies branching of almost-periodic solutions of nonlinear ordinary differential equations near a known almost-periodic solution when the associated variational system is degenerate. It reformulates the problem as a fixed point equation for a nonlinear integral operator in a Banach space …
The paper studies asymptotic methods for Fourier transforms and related integrals whose kernels decrease too slowly for standard moment or convergence assumptions. Extending a regularization method of Tikhonov and Samarskii, it derives the small-argument asymptotic expansion of the Fourier transform…
This note develops a class of singular integro-differential elliptic systems on a bounded smooth domain and extends the general theory of elliptic boundary-value problems with singular integro-differential boundary conditions. It defines ellipticity, proper ellipticity, admissible symbols, and the L…
The paper studies topological properties of solution sets for linear multidimensional differential equations of the form dy/dx = Ay in finite-dimensional real spaces, under the commutativity condition that ensures solvability of the Cauchy problem. It interprets the orbits of solutions as multidimen…
This note strengthens a previously established category result for spaces metrized over a semifield by studying the notion of phi-completeness for spaces metrized over R_Delta. After recalling the definitions of semifield-valued metric spaces, phi-fundamental sequences, phi-limits, and phi-completen…
The paper studies local saturation for families of linear positive operators through normalized remainder operators built from their algebraic moments. Under boundedness, asymptotic, and symmetry-type integral conditions, it proves that a uniformly vanishing normalized remainder forces the approxima…
This note studies stable automorphisms of arbitrary groups in relation to the quasinilpotent radical. Using normal series stable under automorphisms and properties of subinvariant subgroups, it proves that the quasinilpotent radical of a group coincides with the set of its stable elements, and exten…
This paper studies characteristic exponents of solutions to abstract differential equations in a Banach space generated by closed, generally unbounded, sectorial operators. It extends Krein’s results for bounded operators by relating exponents of the linear equation to the real parts of the spectrum…
Maslov presents an inverse method for establishing derivability in the narrow classical predicate calculus, building on Herbrand’s theorem and earlier metavariable approaches. For closed prenex formulas with conjunctive matrices, the paper defines resolvents, chains, bundles, and favorable sets, the…
This paper studies differentiation and integration for constructive real numbers and constructive functions, including functions of one and two variables, under a constructive interpretation of logical assertions. It formulates definitions of uniform differentiability, local uniform continuity, rect…
The paper classifies completely irreducible representations of the real unimodular group of second order, using induced representations realized on function spaces and their decomposition with respect to the orthogonal subgroup. It defines complete irreducibility through approximation of admissible …
Tolstov develops a classification of formal differentiation and the abstract integrals it generates by adding supplementary axioms to a previously defined general scheme. The paper distinguishes weak, medium, and strong differentiation, corresponding to integrals of Duhamel, Daniell, and Lebesgue ty…
This paper proves a lower bound for closed geodesics in a complete simply connected smooth Riemannian manifold whose sectional curvatures lie between a positive constant and 1. Extending earlier results for surfaces, even dimensions, and certain odd-dimensional cases, it establishes that every close…
The paper studies the cohomology algebra of the mod 2 Steenrod algebra as it appears in the Adams spectral sequence for stable homotopy groups of spheres. It constructs a spectral sequence converging to this cohomology algebra, with a polynomial first term, and develops the use of spectral cohomolog…
The paper develops a general method of multiplier enlargement for linear positive operators in Banach spaces and applies it to polynomial approximation of unbounded continuous functions. A convergence theorem is proved under normalization and singularity conditions, then used to construct and analyz…
The paper studies finite codimensional subspaces of the space of continuous functions on a bicompact space and gives criteria for proximinality, uniqueness of best approximation, and the Chebyshev property. Using the annihilator of the subspace, represented by finite systems of regular measures, it …
The paper studies a multidimensional linear second order differential equation for a scalar function on a real finite dimensional space, treating the Cauchy problem, the homogeneous equation, nonhomogeneous equations, and a special multipoint problem. It gives uniqueness for solutions with the same …
The note studies cardinality bounds for pseudobases in compactness-like topological spaces. It proves that if an H-closed space has a t-pseudobase such that, at each point, the family of pseudobase elements for which the point is a contact point has cardinality at most a, then the whole t-pseudobase…
The paper studies n-ary algebras, called n-operatives, whose single operation satisfies generalized associativity, alternativity, commutativity, or positional permutation identities. It develops notions of one-sided and two-sided invertibility, ideals, unitary elements, and identities, and proves st…
The paper studies multiplicative uniformly continuous families of random probability operators on spaces of bounded measurable functions, formulated with measurability and composition conditions indexed by time intervals. It proves a one-to-one correspondence between such multiplicative families and…
This paper studies extremal problems for bounded monotone entire functions of finite degree that are real on the real axis and satisfy one or two prescribed linear conditions. It proves that, for up to two admissible constraints, an extremal function of minimal uniform norm may be chosen so that its…
This paper studies spectral properties of quadratic operator pencils of the form L(lambda) = lambda squared I + lambda B + C in a Hilbert space, with B self-adjoint and C subject to compactness, positivity, or damping assumptions. The authors develop an approach based on the associated quadratic ope…
