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 the existence of homeomorphic plane mappings between simply connected domains that solve first order elliptic systems whose ellipticity may degenerate. It develops an approximation approach, replacing the degenerate system or the domain by nondegenerate ones and passing to a limit …
The paper studies when a commutative associative ring without nonzero nilpotents and with torsion-free additive group can be equipped with partial orders compatible with multiplication, especially orders stronger than those of partially ordered rings of functions. It introduces u-cones and phi-cones…
The paper studies the computation of saddle points for twice continuously differentiable functions that are strictly convex in one variable and strictly concave in the other, when both variables are constrained to bounded polyhedra. It characterizes saddle points by the vanishing of distances from t…
The paper studies entire functions of several complex variables that are real on real vectors and transform a vector of independent standard normal variables into a standard normal variable. It strengthens a result of Linnik and Eidlin by proving that any such function is either a normalized real li…
The paper studies a continuous function of three variables, vanishing outside a ball, through three notions of variation defined by the structure, planar sections, and area of its level sets. It proves comparison estimates for partial variations over disjoint balls and a geometric lemma relating loc…
The paper studies growth scales for entire functions of several complex variables through the majorant of the function and the geometry of associated convex or quasiconvex functions. It analyzes Goldberg-type orders and shows how they correspond to scales built from homogeneous logarithmically conve…
The paper studies a singularly perturbed initial value problem for a system of quasilinear first order equations with a common principal part, where the initial condition for one component is scaled by a parameter dependent on the small parameter. Under sign and growth assumptions on the nonlinear t…
This paper studies repeated two-person zero-sum matrix games in which each pair of pure strategies has both a payoff and a mean duration, and the total encounter time is large but finite or random. It argues that ordinary optimal strategies for the payoff matrix, and generally also those for payoff …
The paper studies convergence of the Bubnov-Galerkin method for equations \(Af=g\) with self-adjoint operators in a separable Hilbert space, focusing on cases where the negative or positive part of the spectrum is finite in the sense of eigenvalues of finite multiplicity. It reformulates the method …
This note studies differential operators with smooth coefficients depending on a complex parameter on a ray, focusing on cases where the usual nonvanishing condition for the principal symbol fails. It derives necessary conditions for weighted a priori estimates in terms of the imaginary part of a Po…
This paper studies additive functionals of time-homogeneous semi-Markov processes with a countable state space, under recurrence and stationarity assumptions on the embedded Markov chain. Using regeneration at returns to a fixed state, it derives limit theorems that reduce the asymptotic behavior of…
This paper gives a parametric characterization of the class of normalized univalent holomorphic functions in the unit disk. It introduces a compact class of nondecreasing two variable functions and uses Stieltjes integrals to formulate a Löwner type differential equation whose solutions yield exactl…
This note studies when the steepest descent process in Euclidean space can converge to a nondegenerate saddle point of a twice continuously differentiable function. It derives necessary equations for points in the saddle’s domain of attraction, using the descent operator and the negative eigenspace …
The paper studies when linear operators from normed spaces into spaces of measurable functions can be represented by scalar products with strongly measurable dual-valued kernels, extending earlier integral-operator representation results beyond separable settings. It introduces C-operators and chara…
This paper develops a multiplicative notion of dispersion for probability measures on compact groups, formulated as a continuous nonnegative homomorphism on a semigroup of measures that vanishes on invariant measures of nontrivial subgroups. It derives basic properties of such dispersions, applies t…
The paper studies step-sum processes formed from random rewards attached to the states of a finite semi-Markov process, with holding times and increments depending on the current state. Under ergodicity of the embedded Markov chain and finite second-moment assumptions, it establishes convergence of …
This note studies a class of Bessel-kernel integral equations arising in mixed boundary-value problems of elasticity and mathematical physics for a layer with a circular change of boundary conditions, with emphasis on the large-radius limit. Under analyticity, factorization, and asymptotic assumptio…
The paper introduces two characteristics of probability distributions, called the r-center and r-spread, defined through integrals of the imaginary and real parts of the logarithm of the characteristic function. It develops their basic properties, including behavior under scaling and reflection, add…
This paper extends the theory of abelian groups in which all L-closed subgroups are complemented to a nonabelian setting. It defines a nonabelian CL-group as a group satisfying a complement condition for L-closed subgroups of maximal abelian subgroups and possessing an invariant maximal abelian subg…
This paper studies the iteration behavior of the fully integer Gomory cutting-plane algorithm, formulated more generally as a class of algorithms differing only in the rule for selecting the row used to construct the cut. It constructs pathological integer linear programming tableaux with bounded co…
This paper studies the metric classification of decreasing sequences of measurable partitions of Lebesgue spaces, with emphasis on homogeneous dyadic sequences whose finite initial segments are all isomorphic. It introduces the accompanying partition and universal projectors as tools for identifying…
This paper studies finite groups that are not decomposable into a uniform product of their Sylow subgroups while all proper subgroups are so decomposable, termed groups of type CS. Using skew products of cyclic groups with finite fields and presentations by generators and relations, it develops stru…
This paper studies minimax time-to-encounter differential games for systems with additive controls of two players, using approximation strategies defined through set-valued contingent dynamics. It introduces stability and absorption notions for families of closed sets and constructs extremal strateg…
This note studies stabilization as time tends to infinity for solutions of the Cauchy problem for the heat equation in Euclidean space with continuous initial data of controlled exponential growth. It formulates necessary and sufficient conditions for uniform stabilization in all space in terms of c…
The paper studies an abstract first order anticanonical differential equation in a complex Hilbert space with periodic operator coefficients, motivated by second order equations arising in periodic acoustic and electromagnetic waveguides. Under positivity, domain, and smoothness assumptions on the p…
The paper studies a necessary topological condition for Tikhonov regularizability of approximate solutions to injective equations between metric spaces. It proves that if such a problem is regularizable, then the images under the regularizing operators of any dense subset of the data space form a de…
The paper studies the number of integral solutions to the Thue equation defined by a binary form of degree at least three representing unity. Building on earlier finiteness results of Thue and uniform bounds known mainly for cubic forms, it addresses whether a bound depending only on the degree can …
The paper studies asymptotic formulas for the number of solutions of Waring-type congruences modulo prime powers, especially in cases where such formulas may fail when the number of variables equals the exponent. It replaces the fixed right-hand side by a variable ranging over a short interval and i…
This paper studies maximal functions formed from the partial sums of cosine and sine trigonometric series whose coefficients tend to zero and form a quasiconvex sequence. It proves asymptotic estimates for the integrals, away from the origin, of the majorants of these partial sums in terms of tail m…
This note studies inverse polyhedral representations of metric spaces, with emphasis on irreducibility, standardness, and behavior on systems of closed subsets. It extends results of Freudenthal, Isbell, and Pasynkov by proving that every sigma-locally finite system of closed subsets of a complete m…
The paper investigates mean values and partial sums of complex multiplicative functions under restrictions on their values at prime powers and on weighted prime sums. Building on Halász’s analytic method, the authors analyze the associated Dirichlet series near the line Re s = 1, establishing an alt…
This paper studies continuous mappings of p-spaces and related preservation and representation problems in general topology. It establishes conditions under which images of paracompact p-spaces under open, bicompact, regularly complete, or uniformly complete mappings are weakly paracompact or p-spac…
This paper studies systems of nonlinear integral equations with deviating arguments under measurability, continuity, and boundedness assumptions on the kernels, deviations, and prescribed outside values. It proves compactness of the associated integral operator in a space of continuous vector functi…
The paper studies lower bounds on the complexity of finite decision procedures for recursively enumerable sets, introducing the notion of effective nonrecursiveness in terms of unbounded recursive lower estimates. It analyzes enumerations of recursively enumerable sets, giving criteria involving reg…
The paper addresses the difficulty of extending maximum likelihood estimation from discrete Gaussian measurement vectors to continuously observed Gaussian processes, where the inverse of a correlation function cannot be used directly as a matrix inverse. It approximates the correlation function by a…
This paper formulates differential games in mixed strategies for systems governed by ordinary differential equations when a value may fail to exist in pure strategies. Mixed controls are represented by time-dependent distribution functions and Lebesgue, Stieltjes measures on the players’ admissible …
The paper studies singular integral operators in weighted Hölder spaces on smooth contours, with weights having prescribed power singularities at finitely many boundary points. It establishes compactness of commutators with Hölder coefficients and gives necessary and sufficient Fredholm type conditi…
This note studies the continuous cohomology of the topological Lie algebra of smooth vector fields on a connected compact orientable smooth manifold. Building on earlier descriptions of the cohomology of formal vector fields, it introduces and analyzes filtrations of the standard cochain complex, as…
The paper introduces the notion of a variational structure, a partially ordered Hilbert space in which every finite set has a unique upper bound minimizing a natural quadratic functional over all its upper bounds. It develops basic properties of these variational upper and lower bounds, showing that…
This paper studies the distribution in arithmetic progressions of integers of the form p(p′ + a), where p and p′ are primes, for prime moduli D that may grow with the main parameter. Using Vinogradov’s method for estimating trigonometric sums over primes, together with character sums and combinatori…
The paper establishes three-cylinder type estimates for weak solutions of linear evolution quasi-elliptic equations of arbitrary order, including parabolic equations and models for transverse vibrations of elastic plates and rods. Using algebraic ellipticity and sectoriality conditions on the princi…
The paper studies when the Wallman compactification of a space coincides with the Ponomarev, Zaitsev compact extension defined via finite intersections of canonically closed sets. It introduces the notion of a seminormal space, a T1 space in which any two disjoint closed sets can be contained in dis…
This paper studies Noether properties and index formulas for integral operators on the real line whose kernels combine convolution terms with essentially bounded measurable coefficients having prescribed limiting values at infinity. A class of admissible coefficient functions is defined, and the mai…
This paper establishes conditions for localization and uniform convergence of Fourier series associated with arbitrary fundamental systems of functions of the Beltrami operator on multidimensional domains or suitable Riemannian submanifolds. Using previously developed properties of such fundamental …
The paper studies restrictions on the cardinalities of infinite extremally disconnected bicompact spaces and complete Boolean algebras, using Stone duality and cardinal invariants such as type, weight, Suslin number, and algebraic weight. It develops embedding and generation arguments for complete B…
This paper studies extremal problems for univalent functions in the class S through the structure of first variations and their associated Hilbert spaces. It introduces a positive bilinear form on variations of an extremal function, relates the second variation of linear coefficient functionals to a…
The paper studies error distributions in linear discriminant analysis for two multivariate normal populations with common covariance when the dimension is comparable to the training sample sizes. It represents the Anderson classification statistic and the associated conditional error probabilities t…
The paper constructs compact Hausdorff spaces, bicompacta, whose covering dimension and small and large inductive dimensions do not coincide. Using lexicographically ordered zero-dimensional compacta, decompositions and gluings over marked subsets of the square and the Sierpiński carpet, it gives ex…
The paper studies the topology of classes of elliptic constant coefficient matrix differential operators in the plane, focusing on the connected components of operators satisfying a positivity condition for the associated matrix pencil. It gives a necessary and sufficient criterion, expressed throug…
This paper studies time-optimal transitions for linear controlled systems with closed bounded convex control domains and closed convex endpoint sets, extending earlier optimality criteria beyond the case of a strongly stable terminal set and without assuming nondegeneracy. It reviews extremal proces…
