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 introduces preclosed mappings, a class of topological mappings containing both open and closed mappings, and compares them with Whyburn’s quasicompact mappings. It proves that under a countability-type condition the two notions coincide, gives an example showing that they differ in genera…
This note addresses A. Wald’s proposed approach to the Behrens-Fisher problem for two normal samples of equal size, in which invariant and monotonicity conditions lead to a critical region determined by a boundary function of the ratio of sample variances. Wald had constructed an approximate similar…
The paper studies the relation between four-dimensional symmetric conformally Euclidean spaces of zero signature and line geometries associated with subgroups of projective transformations of three-dimensional projective space. It introduces generalized biplanar spaces defined by absolute collineati…
The paper studies the asymptotic distribution of eigenvalues of the Laplace operator in an arbitrary polygonal domain, including nonconvex polygons, under either Dirichlet or Neumann boundary conditions. It derives trace formulas for an auxiliary wave equation by localizing the Green function in the…
This paper studies derivability in intuitionistic propositional calculus through finite algebraic matrices called finite implicative structures. It defines refutation, validity, Gödelian implicative structures, and characteristic formulas associated with such structures, then establishes criteria co…
The paper studies analytic small solutions of operator equations obtained by perturbing linear equations with multivalued solvability in complex Banach spaces, with a finite-dimensional kernel component. It gives necessary and sufficient conditions for existence and uniqueness under linear perturbat…
The paper introduces categories with divisibility by defining morphisms in an auxiliary category as nonempty subsets of morphism sets, and studies the resulting quasi-order on objects, with special attention to module categories. It proves finiteness-type criteria for associated objects to yield non…
This paper studies geometric characterizations of nonreflexive Banach spaces using convex cones, nested families of closed convex bounded sets, and special bounded sequences. It proves that a Banach space is nonreflexive exactly when it contains a cone locally isomorphic to the positive cone generat…
This note studies how the family of bicompact subsets determines and constrains the topology of Hausdorff spaces, with applications to metrization and mapping theory. It introduces strongly uniform bases and strongly refining sequences of open covers, proving that each gives an exact characterizatio…
The paper studies spectral changes under compression of a self-adjoint operator with simple spectrum to the orthogonal complement of a generating vector, using Herglotz representations and associated measures. It proves that the absolutely continuous parts of the original and compressed operators ar…
This note studies the high energy asymptotics of the spectral function for a class of constant coefficient hypoelliptic differential operators in two variables on a bounded plane domain. Using Carleman’s method, Laplace transforms of the spectral function, and Tauberian theorems of Karamata and Gane…
The paper studies the Cauchy problem for higher order parabolic equations containing a small parameter, with initial data having a jump discontinuity across a hyperplane. It analyzes the behavior of the solution as the parameter tends to zero, showing convergence to the corresponding first order lim…
This paper develops a qualitative method for analyzing strong resonance near the origin in a nonlinear, periodically time-dependent planar system with analytic nonlinear terms. By transforming the system to complex variables and reducing it to canonical form, it identifies resonant terms associated …
This note studies boundary behavior of univalent mappings of simply connected plane domains through the theory of prime ends, focusing on metric conditions under which sets of prime ends correspond to boundary sets of measure zero. It defines sets of prime ends of generalized measure zero using cove…
The paper studies bifurcation points of an analytic nonlinear equation in a complex Banach space, where the linear part is given by a completely continuous operator and the nonlinear term is of higher order near the origin. It proves a linearization principle: a parameter value is a bifurcation poin…
The paper derives an integral representation with a holomorphic kernel for functions holomorphic in bounded convex domains of complex n-dimensional space and continuous on the closure. Under smoothness and nondegeneracy assumptions on a defining function of the domain, the author proves the formula …
This note studies cardinal properties of dyadic spaces, that is, completely regular spaces admitting a dyadic compact extension. Using representations of fibers under continuous maps from generalized Cantor discontinua and a lemma on closures of unions of layers with bounded base cardinality, the pa…
This paper studies classes of functions in \(L_p\) on the real line, and briefly in the periodic case, through estimates for symmetric finite differences and their Fourier analytic characterization. Using Fourier transform methods associated with Butzer, it proves uniqueness under smallness conditio…
This note studies an infinite system of linear algebraic equations whose coefficients define convolution and Hankel type operators, with solutions sought in the Banach space of sequences growing no faster than a fixed polynomial. The system is reformulated as a Carleman type boundary value problem f…
This note extends a previously established characterization of inversion complexity from individual Boolean functions to systems of Boolean functions. It defines breaks and the fall of a system along increasing sequences of Boolean vectors, then proves that the inversion complexity of any finite sys…
This paper studies embedding theorems for functions on unbounded domains whose highest order derivatives need not be p-summable in the usual sense, but are p-summable with weights that decay at infinity. It introduces weighted Sobolev-type spaces on Euclidean space, the half-space, and boundary hype…
This paper establishes Schauder-type boundary a priori estimates of order 2 plus alpha for the third boundary-value problem for second-order parabolic equations with conormal derivative boundary conditions. Under Hölder regularity, parabolicity, smoothness of the lateral boundary, and compatibility …
The paper studies expansions in eigenfunctions and associated functions for ordinary differential operators on a finite interval with irregular split boundary conditions. It establishes asymptotic formulas for the eigenvalues, including eventual simplicity, and derives necessary conditions for unifo…
This paper studies optimal one-dimensional quadrature formulas on an equidistant partition for Sobolev spaces of functions with square-integrable derivatives, allowing values of derivatives up to a prescribed order at the mesh points. It formulates the quadrature error as a variational problem, iden…
This note develops an algebra of positive matrices in which ordinary addition and multiplication are replaced by elementwise maximization or minimization and by corresponding max-product or min-product matrix multiplication. It records the basic algebraic laws of these operations, including distribu…
The paper studies upper bounds for the number of points in finite subsets of powers of the ring of integers of an algebraic number field at which a polynomial value generates an ideal with at most a prescribed number of prime ideal factors. It introduces regular systems of sets and strongly primitiv…
This note studies when Frobenius’ theorem on complements to isolated subgroups extends from finite groups to infinite groups. It gives sufficient conditions: if an infinite group has a suitably complete locally nilpotent normal subgroup with locally finite quotient, then every isolated subgroup has …
The paper establishes quantitative bounds for the diameter and width of a convex hypersurface in Euclidean space whose Gaussian curvature is close to one. It first proves comparison lemmas for surfaces of revolution, then uses Minkowski and Steiner symmetrization, volume inequalities, and curvature …
This note studies when crossed products of groups with a division ring can be embedded in division rings, extending the Mal’cev-Neumann embedding theorem and a result of Ikeda on crossed products of certain groups. It proves auxiliary results on automorphisms of quotient division rings for invariant…
This note proves that if every left cyclic module over an associative ring with identity is injective, then the ring is semisimple in the classical sense. The argument uses homological algebra and the theory of regular and left continuous rings, developing a sequence of lemmas on cyclic submodules, …
This paper studies a one-phase Stefan problem for a quasilinear heat equation describing heating and melting of a rod with removal of molten material under prescribed boundary heat fluxes. It formulates an implicit finite-difference scheme in which the moving boundary advances by one spatial mesh in…
This note studies the existence of homeomorphic solutions for a class of first order elliptic systems in four dimensional space whose coefficient matrices have quaternionic form. The system is reduced to a special equation involving quaternionic Cauchy Riemann type operators, and solutions are sough…
This paper studies bases in Banach spaces of continuous functions using Grinblum’s index, which measures the inclination between initial and subsequent spans of a sequence. It proves that certain differentiable, in particular analytic, systems in the real space of continuous functions on an interval…
The paper studies the first boundary-value problem for elliptic quasilinear equations and systems of order 2m whose principal coefficients may grow faster than any power in the highest derivatives. It formulates structural, monotonicity, and subordination conditions under which solutions are sought …
This note extends the rotation, or topological degree, of vector fields to completely continuous and weakly continuous operators acting on invariant subsets of locally convex and Banach spaces. Using Schauder finite-dimensional approximations, it establishes homotopy invariance, additivity, and fixe…
This paper studies Psi-stability in cooperative games in reduced characteristic-function form, using linear programming criteria for systems of coalition inequalities. It formulates a covering condition, in terms of reduced weighted coverings of the player set, that is necessary and sufficient for t…
The paper studies general boundary value problems for a linear parabolic equation of order 2p in one spatial variable on a plane domain bounded by sufficiently smooth moving curves. It formulates compatibility and nondegeneracy conditions for boundary operators, including conditions involving deriva…
The paper solves a problem posed by S. N. Bernstein on the least uniform deviation from zero of trigonometric polynomials of degree at most n with prescribed sine and cosine coefficients at a fixed harmonic h. Reducing the question to maximization of the first cosine coefficient over normalized trig…
This paper studies conjugate functions of two variables and the summability of double Fourier series, extending questions known for one-dimensional conjugate functions. It establishes sharp logarithmic integrability conditions for the summability of double conjugate functions, including examples sho…
This note generalizes Hadamard’s three circles theorem from analytic functions of one complex variable to solutions of second order linear elliptic equations in several variables. Under uniform ellipticity, boundedness and smoothness assumptions on the coefficients, and a simplifying sign condition …
This paper extends the theory of polynomials orthogonal on the unit circle to weights supported on a finite system of arcs, allowing the weight to vanish on complementary arcs. It constructs orthogonal polynomials for special quasipolynomial weights by using rational functions on a two sheeted Riema…
This note proves a generalization of Hilbert’s theorem on complete surfaces of constant negative curvature in three-dimensional Euclidean space. Efimov shows that no complete twice continuously differentiable regular surface in Euclidean 3-space can have Gaussian curvature bounded above by a negativ…
This note studies extension of functions in \(L_p\) from an interval to a larger interval while preserving differential difference estimates expressed through moduli of smoothness. Using Steklov means and a Whitney Hestenes type reflection construction, it proves that a function with a Sobolev gener…
This paper studies the fibration of a pair of corresponding two-parameter families of straight lines in an n-dimensional projective space, with n greater than 3, under the assumption that one family has two distinct focal surfaces. Using a moving projective frame and exterior differential forms, the…
This paper studies optimal stopping for Markov processes, where one chooses a Markov time to maximize the expected reward from stopping, possibly after subtracting an additive observation cost. For countable discrete Markov chains, the problem is reduced to the zero-cost case and characterized throu…
This note generalizes Sherman’s method for plane doubly connected domains to spatial boundary value problems in domains bounded by two Lyapunov surfaces. For the Dirichlet and Neumann problems of potential theory, auxiliary boundary data are introduced on one surface and combined with simple or doub…
This note studies functions in local L2 on the real line whose translates generate a proper closed subspace, focusing on the case where the associated exponential spectrum is regular. It gives necessary and sufficient conditions for a function to be regular in terms of periodicity in the mean with r…
This note studies the use of the Fourier method for a mixed initial boundary value problem for a class of quasilinear hyperbolic equations with a self-adjoint elliptic spatial operator and homogeneous boundary condition. The authors reduce the problem to a countable system of nonlinear integro-diffe…
This paper studies expansions in eigenfunctions for a family of non-selfadjoint singular second-order differential operators on the half-axis, generated by a complex potential and a boundary condition whose coefficient is a rational function of the spectral parameter. Using Naimark’s method, it desc…
