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 extends classical dichotomy theorems for analytic, or A, sets in complete metric spaces beyond the separable case. After recalling equivalent forms of sigma-discreteness and introducing points of local sigma-discreteness, it proves that any A-set in a complete metric space is either sigma-…
The paper studies growth characteristics of functions of several positive variables that are convex with respect to the logarithms of the variables and monotone in each variable, a class including logarithmic maximum functions and related plurisubharmonic means arising in the theory of entire functi…
The paper extends the theory of triangular representations of bounded linear operators and multiplicative representations of characteristic functions beyond the case where the operator differs from a self-adjoint or unitary operator by a compact summand. It introduces conditions based on proper chai…
This paper studies invariant solutions of a system of partial differential equations modeling liquid and gas motion in long pipelines, including turbulent and laminar gas flow and drop-liquid flow as special cases. Using Lie group classification methods, it determines the principal symmetry group fo…
This paper studies uniqueness in recovering an even function of variables x and s from its integrals over confocal ellipsoids of revolution with one focus fixed at the origin and the other moving in the hyperplane s = 0, a problem related to a linearized inverse problem for the telegraph equation. T…
This note studies inverse boundary value problems in which coefficients of the differential equation are unknown together with the solution and are determined by additional boundary conditions. For a parabolic equation with two time dependent coefficients, and for a related ordinary differential equ…
The paper proposes a regularization method for studying asymptotic solutions of differential equations with small parameters, aiming to separate regular and singular parameter dependence by introducing an additional independent variable defined through a regularizing function. For first order system…
The paper studies averaging for systems of differential equations with a small parameter on a finite time interval, replacing the usual infinite-time mean by an average over the interval under consideration. It argues that this finite-interval averaging is applicable in cases where the infinite mean…
This note addresses the calculation of Clebsch-Gordan coefficients for symmetric irreducible representations of the groups SU_n, a problem relevant to representation theory in mathematical physics. Using recurrence relations derived from the action of infinitesimal operators, the authors first treat…
The paper studies limiting distributions of normalized sums of independent, not necessarily identically distributed, random variables whose individual distributions belong to one type, or to finitely many types, under bounded scale transformations. It gives a characterization of the resulting class …
The paper develops an algebraic theory of finite systems of linear inequalities over an arbitrary ordered field, avoiding topological arguments such as compactness or separation in real Euclidean space. Using finitary methods, it identifies two central results, the existence of nodal subsystems for …
This note classifies the irreducible unitary representations of the real general linear group GL(3,R). Using Kirillov’s theorem on the irreducibility of restrictions to a specified subgroup K, the argument reduces the classification to representations induced from K, whose inducing data involve irre…
The paper studies minimax testing for detecting a multivariate Gaussian signal with unknown nondegenerate covariance, using repeated observations and alternatives defined by a prescribed or lower bounded relative signal energy. It argues that Hotelling’s T squared test, previously known to be minima…
This paper studies singular convolution operators with anisotropic kernels arising, for example, from quasi-elliptic equations, extending the classical Calderón and Zygmund theory for isotropically homogeneous kernels. It introduces a generalized notion of homogeneity determined by a vector of dilat…
This paper studies invariant subalgebras for algebras acted on by Lie groups, focusing on finite generation, the number of algebraically independent invariants, and the relation between invariants of a group and of a maximal nilpotent subgroup. It constructs a universal algebra for every connected L…
This paper develops an analytic method for solving operator equations of the first kind \(Ax=f\) in a Hilbert space when \(A\) is positive self-adjoint and zero belongs to its spectrum but is not an eigenvalue. It derives series and regularized limiting formulas for solutions, relates them to succes…
The paper proves a reduction result for finite connected plane undirected multigraphs with distinguished poles under parallel-edge reduction, series reduction, and star-triangle transformations. It formulates a main lemma asserting that, after a finite sequence of pole-preserving star-triangle trans…
This note derives the Muskhelishvili and Vekua formula for the index of a system of one-dimensional singular integral equations by using elementary topological considerations. The system is represented through its symbol, equivalently an ordered pair of continuous nondegenerate matrix functions corr…
This note studies constructive mappings between sets equipped with equality relations, using normal algorithms as partial or complete mappings. It introduces nodal elements and proves that if a set contains such an element, then no nontrivial equality-preserving partial mapping complete on that elem…
This paper studies extremal problems for schlicht conformal mappings of a doubly connected domain bounded by the unit circle and a radial slit, normalized by sending the origin to the origin and prescribing the modulus of the derivative at the origin. It determines extremal mappings for maximizing a…
This note studies bases and subspaces in spaces of continuous functions on metric compacta and in a broader class of Banach spaces characterized by finite-dimensional approximations close to spaces of continuous functions on finite sets. It gives criteria and constructions for interpolating bases in…
The paper studies how analytic growth conditions on the radical of a commutative Banach algebra affect decomposability. It introduces the radical sequence, defined by the supremum of norms of powers of unit radical elements, and proves that if this sequence satisfies a rapid decay condition involvin…
This paper develops a method for computing Radon-Nikodym derivatives between Gaussian measures generated by Gaussian processes, using Aronszajn’s theory of reproducing kernel Hilbert spaces. It reformulates necessary and sufficient equivalence conditions in terms of the covariance kernels, showing t…
This paper studies when classes of infinitely differentiable functions, analytic in an angle on the complex plane or on the Riemann surface of the logarithm, are nontrivial under prescribed uniform bounds on all derivatives. It gives necessary and sufficient conditions on the bounding sequence for a…
The paper studies a constrained Chebyshev approximation problem in the complex domain for continuous complex-valued functions on a bicompact Hausdorff space, where admissible generalized polynomials have coefficients satisfying prescribed independent linear relations. Extending earlier results on Ma…
The paper studies Banach spaces decomposed into two complemented subspaces and equipped with an indefinite J-metric, focusing on maximal J-nonnegative subspaces and J-nonnegative operators. It establishes extension and maximality criteria for such subspaces, including conditions under which every J-…
The paper establishes limit theorems for distributions of functionals of stochastic processes that, after suitable normalization, are asymptotically close to Markov processes. It formulates recurrence, moment, and local conditional increment conditions for an underlying process, using cycles defined…
This note proves an upper semicontinuity property for the \(k\)-dimensional variation of closed subsets of Euclidean space, where variation is defined by integrating the number of connected components of intersections with complementary planes. The main theorem states that if closed sets converge in…
The paper studies linearly ordered spaces with the interval topology, focusing on ordered bicompact extensions, ordered proximity structures, ordered absolutes, and ordered products. It proves the existence and characterizes the maximal ordered bicompact extension, relates it to Čech and Aleksandrov…
This paper studies a parameter-dependent system of differential equations near a composite equilibrium of saddle-saddle type with one zero characteristic root, under the assumption that a trajectory leaves the equilibrium and returns to it. The author analyzes the local structure of separatrix surfa…
The paper studies the Dirichlet problem for strongly coupled elliptic systems of two second-order equations with constant coefficients, extending earlier work beyond special characteristic-root cases. It gives necessary and sufficient algebraic conditions for ellipticity and strong coupling, reduces…
The paper studies dissipative non-self-adjoint operators of class iOmega with absolutely continuous spectrum through Livshits characteristic matrix functions and triangular models. It establishes boundary value formulas for the associated multiplicative integral without a boundedness assumption on t…
The paper studies regularized trace formulas for differences of singular Sturm-Liouville operators on the half-line using Krein’s spectral shift function. For operators differing by an integrable potential, it proves integrability and asymptotic properties of the spectral shift function and derives …
This paper studies the summation of unbounded sequences by linear regular summability methods represented by regular matrices, with emphasis on fields of bounded summability and domains of effectiveness. It proves that when a regular matrix sums a bounded divergent sequence, its domain contains cont…
This note extends Hörmander’s hypoellipticity results for differential operators with variable coefficients to pseudodifferential operators, using techniques developed by Kohn and Nirenberg. It formulates a Hörmander type condition on the symbol, allowing the operator’s strength to vary from point t…
This paper applies Cartan’s method of exterior forms to the group classification of differential equations, focusing on one-dimensional gas flow in a tube of variable cross section with unspecified functions in the equation of state and geometry. It develops the canonization of the associated Pfaffi…
The paper studies uniqueness classes for normal solutions of the Cauchy problem for the second order equation u_t = a u_xx + q(x)u on the whole line, allowing complex nonzero a and unbounded real potentials q(x). It gives necessary and sufficient growth conditions for uniqueness in several weighted …
