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 feasibility conditions for multi-index linear programming problems, including transportation-type problems with equality and inequality constraint blocks. It develops reduction and “cutting” arguments showing how feasible solutions of lower-dimensional subproblems can be embedded i…
The paper establishes a closed graph theorem for multivalued mappings between uniform spaces, extending earlier results for locally convex and related uniform spaces. After defining ultracompleteness via completeness of the hyperspace of closed subsets with the Hausdorff uniformity, it studies unifo…
This paper develops an asymptotic treatment for a fourth-order differential equation with two small parameters arising in hydrodynamic stability and related wave problems in weakly inhomogeneous media. It examines the failure of standard WKB approximations near zeros of both coefficient functions an…
This note addresses the minimization of a concave function over a convex polyhedron, a problem in which local minima need not be global. It proposes a finite procedure based on two observations: a minimum, when it exists, is attained at a vertex, and a suitable concave extension can be used to exclu…
The paper studies sums over Dirichlet characters of powers of Dirichlet L-functions in the critical strip and their application to the distribution of products of integers in arithmetic progressions. Extending methods of Yu. V. Linnik, it obtains uniform estimates for sums of |L(1 minus 1/k plus it,…
This paper studies infinite-order differential equations with polynomial coefficients whose degrees may grow linearly but with ratio less than one. Under summability conditions on the coefficients, it establishes solvability results in classes of entire functions of prescribed order and type, includ…
This note studies homotopy classifications of mappings between Banach spaces that differ from Fredholm operators by completely continuous operators, and relates these classifications to stable homotopy groups of spheres. It defines admissible mappings on balls and more general metric pairs, proving …
This paper studies locally bicompact topological groups under three types of conditions: minimality for closed abelian subgroups, purity in the sense of absence of bicompact elements, and completeness. Using structural results related to the Cartan, Mal'cev, and Iwasawa theorem, together with projec…
This note generalizes Volterra type integral equations from intervals or rectangles to arbitrary open subsets of n-dimensional space by defining classes of supports for square integrable Fredholm kernels that have no eigenvalues. It introduces sets of type V and proves a necessary and sufficient con…
This note studies normal isogonal decompositions of three-dimensional Euclidean space associated with a group of parallel translations, a setting previously treated mainly for isohedral translational decompositions. It proves that such a decomposition is centrally symmetric with respect to every poi…
This note studies a mixed boundary value problem in a half-space for constant-coefficient systems that are parabolic in the sense of Petrovskii and may contain time derivatives of order higher than one. Under a stated regular solvability rank condition, the problem is transformed by Fourier and Lapl…
This paper characterizes regular distributive structures in terms of the exponential topology on the underlying lattice. For a Urysohn structure, it proves that regularity is necessary and sufficient for the inclusion relation set of pairs satisfying x contained in y to be closed in the product expo…
This paper classifies commutative symmetric algebras of bounded linear operators in the Pontryagin space \(\Pi_1\) with an indefinite inner product, up to equivalence. Using invariant nonnegative one-dimensional subspaces, the analysis separates the problem into three cases according to whether such…
This paper develops an area method for the theory of univalent functions, centered on a system of functions defined through logarithmic expansions associated with mappings in the class of functions univalent outside the unit disk. Using a generalized external area theorem, it establishes orthogonali…
This note develops several finite difference schemes for the Cauchy problem for linear symmetric hyperbolic systems with square-integrable initial data in multiple space variables. The schemes use decompositions of the coefficient matrices into positive and negative characteristic parts, product or …
This note proves a uniqueness theorem for an inverse problem for the two-dimensional wave equation with spatially varying coefficient \(n(x,y)\), assumed positive, continuous, and equal to one outside a bounded domain. The data consist of a family of solutions generated by point-source initial veloc…
The paper studies uniform stabilization as time tends to infinity for solutions of the Cauchy problem for Petrovskii parabolic systems with coefficients independent of spatial variables. Using Green matrix estimates and the Poisson integral representation, it proves that such a solution stabilizes u…
The paper studies the space of unoriented loops based at a point on a Riemannian manifold homeomorphic to an n-dimensional sphere, motivated by improving variational estimates for geodesic loops beyond those obtained from oriented loop spaces. Using spectral sequence methods and explicit cycle const…
The paper examines how the method of rotating the vector field can be used in the theory of structurally stable, or rough, dynamical systems on the torus, in analogy with its use for planar systems. After discussing natural function classes for structural stability, including smooth, analytic, and p…
The paper studies initial boundary value problems for a broad class of linear parabolic systems in a bounded cylinder, defined by algebraic homogeneity and root conditions on the principal matrix determinant. It formulates admissible initial and boundary operators through rank and complementing cond…
This paper studies the dependence on a parameter of nonlinear integral operators arising in Krasnoselskii’s method for proving existence of periodic solutions of ordinary differential equations with deviating argument. It establishes conditions under which such operators are continuous with respect …
The paper studies higher dimensional analogues of Ahlfors’ mappings quasiconformal on the average, defined as Sobolev topological mappings whose mean distortion satisfies an integral bound. Using oscillation estimates of Courant type and approximation arguments, it proves interior uniform continuity…
This note studies iterative methods for solving nonlinear equations of the form F(x) = 0 in a real Hilbert space, where F is the gradient of a twice continuously differentiable functional. Under strong monotonicity and boundedness assumptions on the derivative, it establishes existence and uniquenes…
The paper extends the Fourier transform associated with a non-self-adjoint differential operator on the half-line from square-integrable functions to functions whose square is locally integrable. Under hypotheses ensuring only finitely many eigenvalues and spectral singularities, the construction av…
The paper studies the spectrum and generalized eigenfunctions of Hermitian difference equations with periodic coefficients and a shift incommensurable or commensurable with the coefficient period. It argues that the spectral structure is governed by the continued fraction expansion of the shift para…
The paper studies second order nonlinear hyperbolic equations in a real Hilbert space with time dependent positive self-adjoint operators, possible damping terms, and nonlinear forces that may be potential or nonpotential. It derives energy estimates under structural inequalities on the operator der…
This note studies a priori estimates for generalized solutions of the Dirichlet problem for elliptic differential equations whose coefficients may degenerate. Using the Markov process associated with the operator, the solution is represented probabilistically, and conditions are formulated in terms …
The paper introduces and studies anisotropic function spaces defined by finite differences with fractional smoothness indices, including variants of Besov type and simultaneous spaces formed by intersecting over coordinate subsets. It proves direct embedding theorems for derivatives of functions in …
The paper studies criteria for unconditional bases in complex Banach spaces, using biorthogonal functionals and properties of subseries and coefficient transforms. It proves that a basis is unconditional exactly when every subsequence spans a complemented subspace, and gives equivalent formulations …
The paper addresses the slow convergence of successive approximation methods for solving linear systems of the form x = Bx + b when the norm of B is close to one or high accuracy is required. It derives a transformation of the finite matrix geometric sum appearing after n iterations, factoring it in…
This note studies infinite groups through conditions imposed on their infinite subgroups, focusing on three equivalences concerning minimality, normalizers, and complemented subgroups. It proves that, for several classes including locally soluble nonabelian groups and locally finite groups with norm…
This paper studies strong equivalence of Gaussian measures on function spaces generated by real separable processes with stationary Gaussian increments and zero mean. Using likelihood ratios for finite-dimensional increment vectors, covariance matrices, and trace criteria, it formulates necessary an…
This paper studies integral operators of potential type with kernels of the form a negative power of the metric on bounded subsets of a complete metric space equipped with abstract absolutely continuous measures. It introduces a measure-dependent notion of dimension, defined through estimates for th…
The paper studies smooth compactly supported functions from Euclidean space to the real line whose highest derivatives satisfy a Hölder condition, focusing on the topology of level sets outside components associated with critical points. It introduces “rings,” connected regions on which the function…
This note proves a Phragmen-Lindelof type uniqueness and boundedness theorem for nonnegative harmonic functions in spatial domains contained in an infinite rectangular cylinder. Using only properties of subharmonic and logarithmically subharmonic functions, rather than Dirichlet series or Fourier tr…
This paper studies G. Fichera’s boundary value problem for second order degenerate elliptic-parabolic equations with nonnegative characteristic form in a bounded domain. It formulates generalized solutions using an adjoint integral identity and analyzes the boundary decomposition determined by the d…
The paper studies boundary value problems with shift for analytic and piecewise analytic functions on closed abstract Riemann surfaces and on domains bounded by smooth Jordan contours. It proposes reductions of several Haseman, Hilbert, and Carleman type problems to the classical Riemann problem on …
This paper formulates the optimal staging problem for multistage rockets as a Bolza-Mayer variational problem in which the control functions have known forms between discontinuities, while the discontinuity times are to be determined. Using Lagrange multipliers, it derives necessary extremum conditi…
The paper establishes Weyl-type asymptotic formulas for the eigenvalue counting function of self-adjoint elliptic operators of arbitrary even order in Euclidean space with a confining potential. Under regularity, ellipticity, growth, and Tauberian conditions on the leading coefficients and on the po…
This note addresses the existence of abelian subgroups of infinite rank in locally solvable groups, focusing on periodic groups and related locally nilpotent cases. It proves that every periodic locally solvable group of infinite rank contains an abelian subgroup of infinite rank, using bounds on th…
The paper studies a Riemann-Hilbert boundary-value problem for a holomorphic vector in a three-dimensional half-space, with Hölder-continuous boundary coefficients and boundary data in appropriate Lebesgue classes. Using an integral representation of holomorphic vectors, the problem is reduced to a …
The paper studies spectral functions for generalized second order differential systems associated with string operators when a boundary condition is imposed at a singular left end. It relates the behavior of the mass distribution function near negative infinity to the high energy growth of spectral …
This paper develops splitting methods for solving multidimensional one-speed neutron transport equations with isotropic scattering, including both nonstationary mixed Cauchy problems and corresponding stationary boundary value problems. The authors formulate incomplete and complete operator splittin…
The paper examines a theorem of D. Stancu concerning an asymptotic expansion for bivariate Bernstein-type polynomials on the standard simplex under bounded partial derivatives of order N. It shows that the stated result is false already for N = 2 by constructing a function with bounded second partia…
The paper develops a general boundary integral representation for functions holomorphic in a bounded domain with smooth boundary in several complex variables. It introduces a differential form built from auxiliary functions satisfying nonvanishing, decomposition, and holomorphy conditions, and prove…
This note introduces notions of tau-continuity and tau-differentiability for complex-valued functionals on the space of real piecewise-continuous functions on an interval, using localized perturbations of the independent variable. It establishes basic closure and continuity properties, compares tau-…
This paper studies a non-self-adjoint second order differential operator on the half-axis with complex potential and boundary condition, focusing on analytic continuation of the Jost-type solution and consequences for spectral theory. Assuming the potential is summable on the half-axis and holomorph…
The paper studies when arcs of level lines of normalized univalent holomorphic functions in the unit disk are starlike with respect to the origin. Using Loewner’s differential equation and sharp estimates for functionals involving the modulus of the image point and the argument of zf′(z)/f(z), it de…
