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 the stability and convergence of line and finite-difference approximations for first boundary-value problems for one-dimensional quasilinear parabolic equations with variable coefficients. Using energy inequalities, difference analogues of Gronwall-type estimates, the Schauder prin…
This paper studies pairs of cones in a real Banach space, with a narrower cone ordered by a wider cone, and analyzes the notions of K-regularity, complete K-regularity, and K-normality introduced in connection with monotone convergence problems. It establishes relations among these properties, inclu…
The paper studies the solution of fixed point functional equations with nonlinear monotone operators in semi-ordered Banach spaces by a modified successive approximation scheme using a scalar relaxation parameter. It formulates conditions under which uniqueness and bounding of the solution follow fr…
The paper studies when a symmetric two-dimensional density of spectral form defines a stationary Markov process, focusing on the role of finite versus infinite expansions in eigenfunctions. It proves that if the a priori density and eigenfunctions are continuous and the density is positive on the in…
The paper examines exceptional cases in integral equations of convolution type with two kernels, including equations of the first kind, where the associated Riemann boundary-value problem has zeros or poles in its coefficient, especially at infinity and at common zeros of transformed kernels. Using …
This paper solves a Riemann boundary value problem for piecewise holomorphic automorphic functions with prescribed poles and a discontinuity line in a fundamental domain of a fractional linear group. It treats the case in which the group is characterized not by one invariant but by two simple automo…
This note proves that, for each dimension n, the number of topologically distinct regular normal partitions of n-dimensional Euclidean space by convex stereohedra is bounded by a function depending only on n. The argument reduces the problem to bounding the number of faces of a stereohedron and the …
This note gives necessary and sufficient conditions for stability, in the l2 norm, of linear systems of difference equations with bounded shifts. Using the Fourier transform, the system is reduced to powers of a parameter dependent matrix, and an analytic similarity transformation is used to put the…
This letter comments on G. E. James-Levy’s paper on general anamorphosis, arguing that several of its assertions and constructions are incorrect or insufficiently justified. The authors identify problems with assumed functional representations, criteria for excluding rectilinear scales, and the deri…
This note studies semiboundedness and discreteness of the spectrum for one-dimensional differential operators of the form a constant-sign even derivative plus a real potential. Using localization identities and estimates on variational eigenvalues over finite intervals, it proves a sufficient condit…
This paper studies singular Tricomi boundary value problems for a mixed type equation near both a finite singular line and an infinitely remote singular line. Using a Duhamel principle, the solutions are represented through discontinuous kernels expressible by modified incomplete Euler beta function…
The paper proposes an iterative approach to a linear programming problem by replacing the original minimization over a closed convex polyhedral set with a perturbed auxiliary problem involving a positive definite matrix and a small parameter. Existence, boundedness, uniqueness, continuity in the par…
This note studies elliptic differential operators on two-dimensional plane domains and smooth orientable closed surfaces through the algebraic and topological structure of their characteristic polynomials. It shows that on closed orientable surfaces not homeomorphic to a torus, every elliptic polyno…
This note studies infinite-dimensional metric spaces and transfinite dimension, using Sklyarenko representations to relate noncompact cases to compact weakly infinite-dimensional components. It proves that every infinite-dimensional metric space is either strongly infinite-dimensional or becomes str…
The paper studies the Dirichlet problem for the nonlinear elliptic equation ΔU = U² in a bounded planar domain with continuous boundary data. Using a variational argument, eigenfunction expansions of the Green kernel, and the Ritz method, it first proves the existence of a nontrivial solution for ze…
The paper studies the index of boundary value problems for invariant elliptic first order systems that generalize the inhomogeneous Cauchy-Riemann equations to higher dimensions. Using a Hodge-Friedrichs theorem for harmonic differential forms on the doubled manifold of a bounded Euclidean domain, i…
The paper studies singular Goursat problems for a class of hyperbolic equations with a singular characteristic at zero and, by transformation, at infinity. It develops Duhamel-type representations with discontinuous Riemann kernels, proves uniqueness under sign conditions, and derives transformation…
The paper establishes criteria for reflexivity of a Banach space in terms of the behavior of its unit ball under weaker compatible topologies. Using the characteristic of weakly dense subspaces of the dual and a formula involving annihilators in the bidual, it proves that a Banach space is reflexive…
The paper develops a general reduction scheme for closed bounded plane sets relative to any regular class defined by monotonicity and finite additivity. It introduces transfinite derived sets and kernels for such classes, proves a decomposition lemma characterizing reducible sets as countable unions…
This paper develops several invariants related to the genus of a fibred space or, equivalently, of a space with a topological group action. It introduces the S-genus, dual genus, dual homological genus, and dual S-genus, establishes comparison results with homological genus, and relates dual genus t…
This paper studies the stability of an elliptic equilibrium of an analytic, time-periodic Hamiltonian system with one degree of freedom, in the nondegenerate general elliptic case. It proves stability for irrational linear frequencies belonging to a full-measure Diophantine class by establishing the…
This paper studies the closure and completion in L2 on the positive half-line of systems of exponential monomials with complex exponents of positive real part, in the case where the Müntz completeness condition fails. Using Blaschke products, Fourier boundary values, orthogonalization, and the analy…
This note classifies homogeneous nonsymmetric Riemannian spaces of the form G/H whose connected compact stationary subgroup acts irreducibly on the tangent space, for compact simple motion groups of orthogonal and symplectic types, with comments on exceptional cases. The problem is reduced to determ…
This paper gives a construction and classification of all finite-dimensional irreducible representations of an arbitrary connected Lie group, developed in detail for connected semisimple complex Lie groups and then reduced to the general case. Using a global Gauss decomposition with Cartan and nilpo…
This paper studies the representation of functions on an interval by quasi-power series defined through a prescribed nondecreasing sequence of exponents and associated generalized derivatives. It introduces classes characterized by finite order of uniform convergence and by integral bounds on succes…
The paper formulates an infinite-dimensional analogue of the linear programming problem in spaces of continuous functions and functions of bounded variation, with inequality and equality constraints expressed by Radon-Stieltjes integrals. It establishes an optimality criterion in terms of nonnegativ…
This note studies centers and cocenters, defined as projective and inductive limits of nuclear Riesz scales of Banach spaces, and relates them to Hilbert scales and Köthe sequence spaces. It proves that centers of nuclear Riesz scales admit Hilbert scale representations, have bases, and are isomorph…
This paper studies asymptotic properties of polynomials orthogonal on a finite interval with weight functions that may vanish or become infinite at specified points, a setting not covered by standard analytic methods. It establishes a differential recurrence equation for such orthogonal polynomials …
This note studies ultimate boundedness for several classes of nonlinear third order differential equations with bounded nonautonomous perturbations. It extends a previous boundedness result by formulating three theorems under growth and sign conditions on the nonlinear terms, using changes of variab…
This paper studies the geodesic flow on the space of line elements of a compact two-dimensional Riemannian surface of negative curvature, extending Hopf’s ergodicity result to questions of spectrum and mixing. Using horocycles on variable negative curvature surfaces, estimates for their contraction …
This paper studies solvability and index properties for general elliptic boundary value problems with one unknown function in a smooth bounded domain of Euclidean space. It formulates ellipticity through the Lopatinskii condition for the differential operator and boundary operators, proves equivalen…
This paper studies a degenerate variational problem whose Euler equation is the elliptic Monge-Ampère equation, with convexity replacing the missing second boundary condition. The functional is extended from smooth functions to nonnegative continuous functions with prescribed boundary values by usin…
This paper studies propagation of smoothness for generalized solutions of linear partial differential equations with constant coefficients. It gives conditions under which a solution that is infinitely differentiable near part of the boundary of a domain, or outside a closed convex set, is in fact i…
This paper studies convergence in nonlinear systems of ordinary differential equations with periodic right hand sides, understood as existence, uniqueness, Lyapunov stability, and global attraction of a periodic solution. It gives necessary and sufficient conditions in terms of the time period map: …
This note studies polynomials with fixed leading coefficient that minimize the weighted uniform deviation from zero on the two intervals [-1, -lambda] and [lambda, 1], with weight sqrt(1 - x^2). It defines and constructs Akhiezer polynomials of the second kind, treating even degrees by reduction to …
The paper studies the large time behavior of solutions to a boundary value problem posed by S. L. Sobolev for a mixed spatial operator in a bounded plane domain with a smooth convex boundary. Using geometric constructions of closed broken lines inscribed in the boundary, it establishes differentiabi…
This paper studies finite-dimensional metabelian Lie algebras over an algebraically closed field through the weights of their derivation algebras. It establishes that linear dependencies among weights follow from the basic commutator relations, derives nonvanishing and separation properties of first…
This paper studies definite lineals in complex linear spaces equipped with a possibly indefinite Hermitian bilinear metric, without assuming an underlying topology or Hilbert space structure. It introduces regular and singular definite lineals through boundedness of induced linear functionals, gives…
This note proves A. I. Mal'cev's hypothesis that the class of multiplicative semigroups of rings is not axiomatizable. It first establishes a general criterion relating axiomatizability to pseudoaxiomatizability and arithmetic closedness, then applies results on arithmetic equivalence of abelian gro…
This paper generalizes the notion of decomposing a topological space by a closed subset to decompositions of order k, defines an equivalence relation via decompositions of X times the unit interval, and studies the resulting classes for completely normal spaces. Using separation and extension proper…
The paper studies a separable nonlinear extremal problem in which a sum of continuous piecewise smooth concave functions is maximized subject to linear equality constraints and bounds on the variables. It gives a necessary and sufficient optimality criterion in terms of multipliers analogous to Kant…
This paper studies the Cauchy problem for a nonlinear second order differential equation with a small parameter multiplying the highest derivative and a large initial derivative. It analyzes the formation of an initial jump in the geometric limit of integral curves as the parameter tends to zero, un…
This paper studies representations of positive integers by integral positive quadratic forms in at least four variables, with prescribed congruence classes and, more generally, with lattice points restricted to regions on the corresponding ellipsoid. It defines an elliptic solid angle and a generali…
The paper defines cohomology groups for uniform spaces and proximity spaces using finite-valued cochains on nerves of uniform coverings and direct limits over refinements. It establishes standard functorial properties, exact sequences, homotopy invariance, excision-type results, agreement with cohom…
The paper proposes a method for approximating all fixed points of a nonlinear operator equation y = F(y), where F is a completely continuous operator on a Banach space and maps a convex compact set into itself. Using uniform continuity, the method constructs successive finite nets of decreasing mesh…
This paper studies holonomic conjugate systems of the third order in projective differential geometry, focusing on three-dimensional surfaces whose geometry is governed by conjugacy of triples of tangent directions. Using moving projective frames, canonical forms of quadratic and cubic asymptotic fo…
This paper studies a mixed initial boundary value problem for Petrovskii parabolic systems of order 2p with sufficiently smooth coefficients and boundary data satisfying compatibility conditions. Using the method of potentials and Levi’s reduction, it constructs the Green matrix by representing the …
The note studies Engel properties of Burnside groups of prime power exponent and of their nilpotent quotients. Using Novikov’s result on irreducible words in free groups, it proves that the groups \(B_{k,p^\alpha}\) with \(p^\alpha>72\) are not Engel, by showing that iterated commutator words \([a,b…
This note studies approximation of functions on a multidimensional domain that satisfy homogeneous boundary conditions up to order s minus 1. It considers approximants of the form a fixed boundary-vanishing factor multiplied by polynomials of bounded degree in each variable, for domains whose bounda…
