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 note studies line congruences whose harmonic ruled surfaces are quadrics, using Cartan’s method of exterior forms and differential invariants of a moving tetrahedron. It derives conditions for harmonic ruled surfaces of focal surfaces to be quadrics and shows that such congruences generate a sp…
The paper studies when a homogeneous proper Riemannian space whose stationary subgroup splits as a direct product acting on two orthogonal tangent subspaces admits a corresponding orthogonal decomposition into submanifolds. Using invariant moving frames, structure equations, and a lemma on matrices …
The paper studies whether generalized random processes, specified as consistent cylindrical probability measures on the dual of a topological vector space, can be extended to completely additive measures on a full Borel sigma algebra. Using Gel'fand's formulation and an extension criterion of Erokhi…
This paper studies universal classes of algebras of a fixed finite type, understood as abstract classes definable by universal first order axioms without quantifiers in the matrix. It introduces a closure operation and associated notions of relative universality, closed classes defined through conve…
This paper studies the Aizerman problem for a three-dimensional system of differential equations reducible to a canonical form with one scalar nonlinearity satisfying generalized Hurwitz conditions. It classifies parameter regimes for which the zero solution is globally stable for every admissible n…
This note studies local nomographic representation of sufficiently smooth functions of two variables near a point where the first partial derivatives are nonzero. Building on earlier results using the Massau determinant and Saint-Robert invariant, it derives conditions under which such functions can…
This note examines convergence difficulties in the method of lines when applied to boundary value problems for nonrectangular planar domains, focusing on the Dirichlet problem for the Laplace equation. It shows that the customary scheme can require artificial continuation of boundary data and may le…
This note develops special integro-differential operators related to Riemann-Liouville and Weyl fractional integration and applies them to Dirichlet series and generalized quasianalytic classes. It defines operator classes for functions on half-lines, proves a Taylor-type expansion whose coefficient…
This note gives a brief proof of Pontryagin’s maximum principle for a general optimal control problem in which a trajectory of a controlled differential system joins two prescribed points while minimizing an integral functional. The argument treats admissible controls as bounded measurable mappings …
The paper studies the construction and asymptotic analysis of Orlicz complementary \(N'\)-functions without imposing prior growth restrictions on a given \(N'\)-function. It associates to \(M(u)\) the entire function \(F(z)=\sum_{n\ge 0} e^{-M(n)}z^n\) and proves that \(\ln F(e^v)\) is equivalent to…
This note studies the Cauchy problem for first order differential equations in a Hilbert space with a time dependent positive definite self-adjoint operator whose full domain may vary, but whose fractional power has a fixed domain. Under a Lipschitz condition on the fractional-power conjugates \(A^\…
This paper studies extremal functions for linear methods of approximation of periodic functions whose r-th derivative satisfies a Lipschitz condition of order alpha. Building on Timan’s asymptotic estimate for deviations of Fourier multiplier polynomials, it asks whether an extremal function can be …
The paper establishes topological criteria for the existence of bounded, periodic, and almost-periodic solutions of systems of ordinary differential equations with continuous right-hand sides, without assuming uniqueness or global continuability of all solutions. The authors introduce a condition in…
This paper studies interpolation by entire functions at prescribed complex nodes, focusing on growth restrictions expressed through refined order and indicators. It introduces associated functions for node sequences of refined order growth and gives necessary and sufficient conditions, involving the…
This note announces new estimates for finite trigonometric sums with polynomial phase of degree n plus 1, under a condition relating the summation length to the leading coefficient. The main theorem improves the dependence on n in the exponent compared with earlier bounds, replacing a growth conditi…
The paper studies a self-adjoint fourth-order boundary-value problem on an interval in which a small parameter multiplies the highest derivative, with the highest-derivative signs matching those of the limiting second-order operator. It identifies exceptional parameter values for which zero becomes …
This note relates the representation of large integers by primitive positive ternary quadratic forms to zero-free regions for Dirichlet L-series. Assuming a hypothesis excluding zeros near s = 1 for a family of characters depending on the represented integer, the paper removes an auxiliary prime-res…
This note studies bicompact extensions of completely regular topological spaces through an axiomatic theory of subordination between closed and open sets. It formulates axioms for such subordinations and shows, in a form equivalent to Smirnov’s theorem, that every subordination yields a bicompact ex…
The paper studies the approximate construction of quasiconformal mappings from the unit disk onto a prescribed domain whose boundary is given implicitly, for mappings satisfying a linear elliptic first order system with normalization conditions. The boundary correspondence is reduced to a nonlinear …
The paper studies boundary value problems for linear differential equations in which small parameters multiply the highest derivatives, with emphasis on convergence as the parameters tend to zero. Using integral a priori estimates and generalized solution spaces, it proves that subsequences of solut…
This paper describes the use of transparent nomograms for approximate representation of functions of one variable by families containing three or four adjustable parameters. It formulates general relations representable by a movable transparent overlay and shows how such nomograms can be applied to …
This paper studies entire functions of finite exponential degree in several complex variables and the behavior of their growth indicators when some variables are fixed. It proves measure and exceptional set results showing that points where the degree or directional indicator falls below its maximal…
This note studies a nonlinear operator arising from the minimization of integral functionals of higher derivatives in Orlicz spaces, with homogeneous boundary conditions and a linear term determined by a right-hand side in the complementary Orlicz space. Under growth, convexity, and semicontinuity a…
This note addresses the local nilpotence of Lie rings satisfying the nth Engel condition, a problem previously settled only for small values of n. Kostrikin proves that such a Lie ring is locally nilpotent when it has characteristic zero or finite characteristic p greater than n plus the integer par…
This paper studies three-dimensional Finsler spaces whose metric is defined by a cubic differential form with nonzero discriminant, using algebraic concomitants of the fundamental tensor to construct affine connections. It derives the transformation law of Tonooka’s connection under conformal change…
The paper studies the approximate construction of conformal mappings from the unit disk onto domains bounded by sufficiently smooth closed contours that need not be star-shaped. It reduces the mapping problem to a nonlinear singular integral equation and argues that Theodorsen’s iteration is inadequ…
This paper studies the uniqueness of net nomographic representations, or anamorphoses, for analytic equations in three pairs of variables under a prescribed partition of variables. Using conditions on multipliers, rationality results for algebraic anamorphoses, and a lemma identifying when two nomog…
This note studies inductive and projective limits of normed spaces, with particular attention to limits formed from reflexive normed spaces. It formulates conditions under which bounded sets in an inductive limit are already contained, and in the normed case bounded, in one of the constituent spaces…
This note gives an internal characterization of cubic complexes that arise as limiting complexes of cubic resolvents, proving that this occurs exactly for complexes satisfying the stated EN conditions. The proof constructs the associated resolvent inductively from the groups of cubes belonging to a …
The paper examines whether, for a continuous function on the two-dimensional torus, continuity of the pure second derivatives in a Banach function space implies continuity or membership of the mixed second derivative. It shows that although Bernstein had obtained affirmative results for certain spac…
This note proves partial converse results to earlier Lie-type direct theorems for operators of generalized translation on analytic manifolds. For two classes of infinitesimal differential operators, it gives commutation conditions under which the associated overdetermined Cauchy problems are compati…
The paper studies homogeneous singular integral equations in L2 on a finite system of smooth closed contours with continuous coefficients satisfying a nonvanishing condition. Extending a result previously known for Hölder coefficients, it proves that the number of linearly independent solutions is d…
The paper studies extremal inequalities for trigonometric polynomials of several variables, motivated by problems in approximation theory and by earlier results of Bernstein, Bari, and Nikol’skii. It establishes a general bound for linear functionals defined by integration against an arbitrary integ…
The paper addresses Freudenthal’s proposed necessity of semibicompactness for spaces admitting compactifications with zero-dimensional remainders, identifying a flaw in the assertion that adjoining one point preserves zero-dimensionality in general. Using Dowker’s normal zero-dimensional space with …
The paper gives criteria for the existence of bounded, periodic, quasiperiodic, and almost-periodic solutions of nonlinear differential equations with constant-coefficient linear part. It first proves a lemma on the unique bounded solution of a linear inhomogeneous equation on the whole real axis, i…
This note extends earlier results on the negative spectrum of self-adjoint differential operators acting on vector-valued functions, especially higher-order one-dimensional operators with Hermitian matrix potentials. Using quadratic form estimates expressed through the smallest and largest eigenvalu…
This paper studies homological restrictions on dimension-raising continuous mappings from closed orientable manifolds, using the Vietoris theorem in Begle’s form. It proves that an n-dimensional closed orientable manifold cannot be mapped onto a higher-dimensional polyhedron with all point preimages…
This note studies implicit operators between Banach spaces, focusing on the convergence domain of the power series defining an analytic implicit solution and on estimates for its remainder. Under standard hypotheses of analyticity, a zero condition, and invertibility of the partial derivative with r…
This note extends the theory of Foss surfaces from three-dimensional Euclidean space to two-dimensional surfaces in four-dimensional Euclidean space, defined by a conjugate net whose two families are geodesics. Using moving frames and exterior differential systems, it derives the structural equation…
The paper studies criteria for analytic continuation of a power series initially convergent near infinity into a simply connected exterior domain whose complement is a compact set. Using Faber polynomials associated with the conformal map of the domain and Köthe’s description of continuous linear fu…
This paper studies perturbed planar systems whose unperturbed motions form a family of periodic trajectories depending on slowly varying parameters. Using a change to variables given by an integral of the unperturbed system, the parameters, and the oscillation phase, the author applies averaging ove…
This paper develops a reduction method for studying stability of the zero solution of a system of ordinary differential equations split into two groups of variables. It formulates notions of strong stability for the reduced subsystem and gives Lyapunov-type sufficient conditions under which stabilit…
The paper studies representation of large integers by integral primitive positive ternary quadratic forms with odd relatively prime invariants. It proves lower and upper bounds, in terms of class numbers of positive binary quadratic forms, for the number of primitive representations satisfying local…
The paper studies solvability of boundary value problems for general second order partial differential operators, including nonelliptic cases, in a class of generalized solutions. Using negative Sobolev norms and a Hilbert space constructed from the differential expression, it formulates solvability…
The paper studies best uniform Chebyshev approximation on the interval [0,1] of analytic functions by algebraic polynomials of bounded degree, focusing on the distribution of extremal deviations and its relation to known extremal polynomials of finite functionals. It proves representation criteria e…
This paper studies linear differential systems with meromorphic coefficients that are invariant under a fractional linear transformation, with attention to cases not covered by classical Floquet and Picard theory. It analyzes the transformation of a fundamental matrix of solutions, reduces the assoc…
