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 nonnegative solutions of a nonlinear boundary value problem arising from the Thomas-Fermi and Thomas-Fermi-Dirac equations, with boundary data depending on parameters y0, q, and R. Under monotonicity, continuity, integrability, and Lipschitz-type assumptions on the nonlinear term,…
This paper develops a general theory for products of independent random variables, treating multiplication as an operation on distribution functions analogous to convolution in the additive scheme. It introduces a characteristic transform based on powers of the absolute value and signs of a random v…
This note studies overconvergence for series of rational functions that converge uniformly on a continuum or, more generally, a set of positive harmonic capacity, without restrictions on the locations of their poles. It establishes quantitative relations between the rate of convergence on the set an…
This paper studies traces of functions in Sobolev spaces on hyperplanes, including the case where the hyperplane dimension is too small for the classical Sobolev trace embedding to yield an ordinary integrability statement. Treating the trace as an abstract function of the transverse variables, the …
This paper studies time optimal control for linear discrete systems subject to cyclic constraints on the control, where admissible controls are bounded over repeated intervals of a fixed length. Four variants of such constraints are formulated, including blockwise sums, maxima, and p norm conditions…
This note studies cubature formulas on the sphere, with emphasis on how many nodes are needed to obtain exactness for prescribed systems of spherical functions or analytic functions. It proves a duality criterion relating exact cubature with fixed nodes to interpolation conditions, and gives a suffi…
The paper characterizes semigroups whose lattice of subsemigroups has relative complements in every interval, termed RK semigroups. It develops structural lemmas showing, among other things, that such semigroups are periodic, that their idempotents form a subsemigroup, and that semigroups with more …
This note extends von Neumann’s ergodic theorem for stationary processes to homogeneous random fields in broader settings. It introduces ergodic generalized sequences of averaging functions on Euclidean space and locally bicompact groups, then proves mean-square convergence of the corresponding aver…
This paper solves a problem of A. A. Zykov concerning a recursively defined vertex function on finite directed graphs without loops, whose definition depends initially on an ordering of the vertices. It derives necessary and sufficient algebraic conditions on the ring parameters under which the func…
The paper presents two finite algorithms for systems of linear inequalities: successive puncturing, which constructs a vertex solution from a given feasible point, and successive folding, which moves from a vertex solution to one optimizing a specified coordinate when the rank equals the number of u…
This note studies Chebyshev sets in Banach spaces through the concept of approximative compactness, introduced to replace bounded compactness in settings where the latter is too restrictive. It proves criteria and structural results for approximatively compact sets in uniformly convex spaces, includ…
This note studies the structure of angular boundary values for meromorphic functions that are normal in the unit disk in the sense of Lehto and Virtanen. Using results of Collingwood and Cartwright, it establishes a correspondence between certain angular limit value sets and boundary point sets, and…
The paper studies the word problem for the nth nilpotent product of two groups given by finitely many generators and defining relations, assuming that each factor has a word identity algorithm. It reduces the problem to the mutual commutant of the two factors and constructs, using basic commutators …
This paper studies diffusion processes defined by stochastic differential equations whose coefficients and initial conditions depend on a finite-dimensional parameter. Under Lipschitz and smoothness assumptions, it proves almost sure continuity of the solution in time and parameter, establishes exis…
This note constructs an example showing that a nonlinear parabolic system can fail to have a unique solution for discontinuous step initial data, even when the competing solutions are bounded. The argument compares two self-similar solutions of auxiliary diffusion systems, one with constant diffusio…
This paper constructs a geometry for the ordinary second order differential equation y'' = f(x,y,y') under the conformal group of transformations of two variables, using the invariant method of Laptev and Vasil’ev. It derives relative and absolute invariants of the equation, associates to it spaces …
This note develops a theory of the second variation for nonparametric discontinuous variational problems in several dimensions with movable endpoints and one discontinuity surface. Extending Morse’s method, it derives the second variation for a polygonal extremal, formulates the associated secondary…
This paper studies superconvergence and quasianalytic continuation for sequences of rational functions with prescribed poles outside a continuum in the complex plane. It proves that sufficiently rapid convergence on the continuum, especially of order whose nth root tends to zero, forces uniform conv…
This paper studies bounded homogeneous domains in complex Euclidean space that are homeomorphic to Euclidean space and analytically equivalent to affinely homogeneous domains, termed regular domains. It reduces their classification to the classification of normal j-algebras, proving a correspondence…
This paper studies a nonlinear boundary-value problem for analytic functions in the interior and exterior of a smooth closed contour, with boundary relation involving an nth power term, a Hölder continuous coefficient, and a nonlinear perturbation. Under growth and Hölder-type assumptions on the per…
This note continues a study of divided differences of order (m,n) for functions of two variables, using a previously established representation as a double integral over the rectangle determined by the interpolation nodes. It analyzes the piecewise polynomial kernel in that integral, proving through…
This paper extends a theorem of A. G. Postnikov by proving two Abel-type limit theorems for weighted power series. The first shows that if a series converges and the function x f(x) is continuous and of bounded variation on [0,1], then the transformed series with terms a_i x^i f(x^i) tends to the or…
This note strengthens earlier undecidability results for elementary theories by proving effective inseparability between formulas true in all models and formulas refutable in some finite model for several algebraic classes. The argument constructs, for formulas over rings of prime characteristic, un…
The paper develops a general framework for completeness of systems in locally convex linear spaces when approximation error is considered together with a convex functional controlling the coefficients. It proves a dual criterion, in terms of continuous linear functionals, for an element to be approx…
The paper studies zeros of real entire functions of exponential type relative to specially defined regular sequences of real points. It introduces a characteristic for such zero sets, analogous to the degree of a polynomial, and uses canonical products and functions in class B to derive bounds on ad…
This paper formulates interpolation of functions of several variables from values at finite nodes in matrix terms, emphasizing polynomial interpolation by monomials of bounded degree and the role of right and left inverse interpolation matrices. It describes a classical multivariate Newton-type cons…
This note describes continuous solutions of bounded variation for linear differential equations in a Banach space and in a normed ring with identity, under prescribed initial conditions. Using multiplicative Stieltjes integrals associated with normalized primitives of the coefficient function, it sh…
This paper studies solvability of the first boundary-value problem for strongly elliptic equations of order 2m in domains without relying only on small measure assumptions. It introduces a capacity associated with the differential order, establishes basic properties of this capacity, and uses it to …
The paper develops a scale of function spaces defined by norms expressed through distribution functions of measurable functions, interpolating between the spaces L1 and L infinity. It establishes basic properties of these spaces, including logarithmic convexity, a lemma reducing norm estimates to es…
The paper studies a special singular integral equation and the associated Riemann boundary value problem on contours belonging to a newly defined class R of rectifiable curves. It introduces this class through one-sided tangents and limiting tangent directions, proves structural properties such as f…
This paper proposes a method for constructing global generalized solutions of the Cauchy problem for quasilinear hyperbolic systems after classical solutions develop singularities. It introduces a stability concept based on potentials of solutions and a corresponding metric, then constructs disconti…
This note develops a stability criterion for ordinary differential equations whose linear approximation has only neutral, purely imaginary eigenvalues, after any stable component has been removed by reduction. Using separation of motions and averaging over the unperturbed almost periodic motion, it …
The paper presents an example showing non-uniqueness of generalized solutions for a Cauchy problem for a quasilinear hyperbolic system of two equations. Using a vanishing viscosity formulation with identical viscous terms, it analyzes stationary profiles associated with trajectories of the gradient …
The paper presents a numerical method for constructing characteristic equations for one-dimensional eigenvalue boundary-value problems by repeated integration and replacement of the resulting multiple integrals with finite sums based on Lagrange interpolation coefficients. It compares several quadra…
The paper studies boundary value problems for second order elliptic equations whose coefficients degenerate strongly on a boundary segment, focusing on formulations that allow singular behavior at the degenerate boundary. Using weighted variational methods and trace characterizations, it proves exis…
This paper studies perfect bicompact extensions of completely regular spaces, defined by a boundary preservation condition for open subsets, and gives several equivalent characterizations in terms of proximity, splitting by remainders, behavior of disjoint open sets, and monotone maps from the Čech …
This paper studies locally topologically complete spaces, defined as completely regular spaces in which each point lies in an open Čech complete subspace. It shows that paracompact locally complete spaces are complete, that every locally complete space contains a dense open complete subspace, and th…
This paper studies probability distributions on the space of generalized Borel measures on a compact Hausdorff space, endowed with the weak topology, with particular attention to distributions concentrated on the cone of nonnegative measures. It gives necessary and sufficient conditions for a functi…
This note studies a class of unbounded linear operators in a Banach space whose range, finite-dimensional null space, and bounded inverse on a chosen complement satisfy specified analytic estimates. It constructs an operator-adapted basis and associated series, proves convergence and uniqueness resu…
The paper studies homogeneous boundary value problems arising from separation of variables for equations involving two second order constant coefficient differential operators on an ellipsoidal domain. It considers a variant of a known polynomial eigenfunction problem in which the boundary operator …
This note studies zeros and extremal properties of real entire functions of exponential type, especially functions bounded on the real axis and related comparison families. It establishes estimates for canonical products obtained by perturbing the zeros of sine, proves stability results for function…
The paper studies the two-point boundary value problem for the nonlinear second-order equation y'' = F(x,y,y') under continuity, uniqueness, and continuous dependence assumptions. It proves extension theorems showing that solvability on intervals of length at most d can, under suitable matching and …
This note proposes a precise formulation of homotopic duality, addressing limitations of the Eckmann and Hilton approach in which dual objects and theorems were often identified only intuitively. The paper defines duality at the level of covariant functors on pointed Hausdorff spaces, using spaces o…
This paper formulates a general operator model for transporting mass through directed road networks in which transfers along edges incur losses, and studies optimal sequences of transfers that bring vertex loads from an initial state to prescribed terminal lower bounds. For special networks with lin…
The paper studies existence for mixed initial boundary value problems for nonlinear second order parabolic equations in a bounded domain, with either Dirichlet or oblique boundary conditions. The problem is reformulated as an ordinary differential equation in an \(L_p\) space with an elliptic operat…
The paper studies the first boundary-value problem for a quasilinear parabolic equation in noncylindrical domains over an arbitrary time interval. Under parabolicity, Hölder regularity, boundary smoothness, and structural assumptions on the lower-order terms and nonlinear right-hand side, the author…
The paper studies estimates for generalized mixed derivatives of functions whose first derivatives and unmixed second derivatives belong to \(L_p\). It reviews known cases in which an interior estimate can be extended to the whole domain, then proves that for \(1<p<\infty\) the full-domain estimate …
This note constructs a generating function for Clebsch-Gordan coefficients of the three-dimensional rotation group, using a realization of irreducible representations in polynomial spaces and the action of the associated infinitesimal operators. The canonical basis polynomials in the Kronecker produ…
This paper studies metric properties of group endomorphisms of the n-dimensional torus by representing them through integral linear transformations of Euclidean space. It proves a decomposition theorem that splits an arbitrary torus endomorphism into invariant toral factors corresponding to irreduci…
