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 uniform distribution modulo one of vector-valued functions satisfying a first-order linear finite-difference system with integer coefficients and nonsingular coefficient matrix. It proves a criterion under which such a solution is uniformly distributed in multidimensional space, as…
This paper studies finite difference methods for the one-dimensional heat equation with homogeneous boundary conditions, focusing on higher accuracy, stability, and two-sided approximation of the exact solution. It analyzes a parameterized difference scheme and gives conditions under which its error…
This paper generalizes V. A. Markov’s inequalities for derivatives of algebraic polynomials on the interval [-1, 1] under a weighted majorization condition involving |alpha x + i sqrt(1 - x^2)|. It proves sharp upper bounds for all derivatives of a polynomial of degree at most n, expressed through d…
This paper studies the two-point boundary-value problem for the nonlinear second-order differential equation y'' = f(x,y,y') with homogeneous endpoint conditions. It introduces comparison conditions based on positively homogeneous auxiliary functions and on the Sturm-theoretic decomposition of regul…
The paper studies a second order equation for a dissipative system with one degree of freedom, in which the dissipative force depends on velocity and both the coefficients and a small external force vary on a slow time scale. Using the method of model equations, it constructs an approximate solution…
This note extends Levin’s transformation-operator approach for scalar non-self-adjoint second-order differential equations on the half-axis to matrix differential systems with complex coefficients. Under integrability conditions on the matrix potential, it establishes the existence of a principal so…
This note generalizes Mercer’s theorem for continuous symmetric positive kernels by constructing, from an arbitrary infinite sequence of bounded-variation constraints, a uniformly convergent bilinear expansion with a positive continuous residual kernel. It proves the positivity and convergence of th…
This paper studies generalized solutions of first-order evolution equations in a Hilbert space, with motivation from parabolic boundary-value problems. It establishes existence and uniqueness for a class of linear equations with time-dependent positive self-adjoint operators under weakened regularit…
The paper studies solutions of weakly perturbed differential systems in a neighborhood of periodic motions of an unperturbed system. Using a variation of constants and phase, it derives averaged equations for the slow evolution of the integrals defining the unperturbed periodic orbits, valid on time…
This note studies when Schauder’s theorem on complete continuity of adjoint operators extends from normed spaces to locally convex spaces. It introduces relative complete boundedness, strongly totally bounded sets, and two classes of locally convex spaces, types M0 and N, and proves polar set lemmas…
This note studies positivity of linear functionals on commutative real algebras with identity, where non-negativity is defined by evaluation on all real homomorphisms normalized at the identity. It proves, for algebras with countably many generators, the equivalence between positivity of a functiona…
This note extends finite difference methods for second order parabolic equations to parabolic equations of arbitrary even spatial order with homogeneous even derivative boundary conditions. It constructs a weighted time discretization and central spatial difference scheme, derives corresponding disc…
This note studies a generalized Riemann-Hilbert boundary value problem in the unit disk for a first order elliptic equation with negative index. By transforming the unknown, the problem is reduced to an index zero problem and then to an equivalent nonlinear integral equation, avoiding use of the gen…
This paper studies finite nonspecial groups through systems of nonspecial subgroups intended to parallel Sylow systems of special subgroups. It introduces and uses subgroup complexes based on groups of type S and the broader type S_p, proving existence results for such complexes under conditions inv…
This paper proposes a generalized differential-integral calculus in which differentiation or integration of arbitrary real or complex order is defined by a convergent series involving ordinary derivatives and gamma functions. It introduces an associated additional function, characterized as the gene…
This paper examines M. A. Lavrentiev’s approximate formulas for conformal mappings of narrow strips arising in wave and jet problems, and interprets them as initial terms of asymptotic expansions. The authors construct formal series solutions for harmonic boundary value problems in variable strips, …
The paper studies the method of lines for mixed initial boundary value problems for systems of one dimensional parabolic equations with homogeneous initial data and general nonhomogeneous linear boundary conditions. It reformulates the continuous problem through Green’s formula as a system of Volter…
The paper refines Perron-type asymptotic results for linear difference equations whose coefficients approach limiting values with additional regularity. It establishes representations of all solutions in terms of fundamental components with explicit product asymptotics determined by the varying root…
This note constructs homological invariants for equimorphic transformations, defined as bijections between metric spaces that are uniformly continuous in both directions, within the class of geodesic spaces. Using domains determined by cycles whose fillings must have large relative diameter, it defi…
The paper extends a previously proposed nine-point finite difference construction for axially symmetric Dirichlet problems from the Laplace equation to the Poisson equation in cylindrical coordinates. Using Taylor expansions, it derives grid equations for interior nodes and special formulas for node…
The paper proves global unique solvability for the two-dimensional boundary-value problem for the Navier-Stokes equations with homogeneous boundary data, arbitrary initial Reynolds number, and arbitrary external force, under stated finiteness assumptions on the initial data and force derivatives. Th…
This paper studies the first boundary value problem for one-dimensional parabolic equations with coefficients and data that are piecewise continuous across a finite set of moving curves. It formulates continuity and flux-type conjugation conditions, motivated in particular by heat conduction with di…
This paper examines whether a nomogram for a three-variable equation can be improved by applying a small projective transformation that compresses one of two boundary scales while preserving the rectangular drawing frame. The author derives the first-order effect of such a transformation on line ele…
This paper studies infinitesimal bendings and rigidity of surfaces, mainly surfaces of positive curvature with boundary collar constraints, including homogeneous and nonhomogeneous cases. Using the complex form of the infinitesimal bending equation in conjugate isometric coordinates and an index rel…
This note studies when subgroups of classical compact Lie groups are orthogonal with respect to the Cartan invariant metric, a question motivated by the geometry of homogeneous spaces and totally geodesic submanifolds. It defines subgroups of a real orthogonal group built as products of orthogonal, …
This paper studies the branching problem for continuous irreducible unitary representations of the principal series of the complex unimodular group, focusing on the restriction from the group of order 3 to a subgroup isomorphic to the complex unimodular group of order 2. The representation is realiz…
This paper studies large deviation asymptotics for the maximum of partial sums of independent identically distributed random variables, reformulated as the first passage time of a homogeneous random walk through an absorbing barrier. For bounded lattice jumps, it analyzes the singularities of the ge…
The paper strengthens earlier results on Pi-factorizations of finite groups by proving that such factorizations can always be chosen with pairwise permutable factors. For a finite group whose greatest Pi-divisor is written as a product of reduced Pi-integral divisors, it establishes the existence of…
This paper proves an isometric embedding theorem for polyhedra of dimensions 1 through 4 whose simplices lie in a space of constant curvature, allowing self-intersections and overlaps in the target space of the same dimension. The argument constructs Voronoi-type regions around a finite set of selec…
This paper develops an abstract geometric theory of conjugate Lyapunov norms in finite-dimensional Euclidean spaces, motivated by characteristic exponents of conjugate linear differential systems. It defines conjugate norms, defects of conjugate bases, and the irregularity coefficient, then proves t…
The paper studies best uniform approximation of periodic functions representable as convolutions with a fixed kernel and a function from an \(L^p\) unit ball, using polynomials in a prescribed Chebyshev system. It derives general formulas for the extremal approximation quantity \(M_n^{(p)}\), charac…
This paper studies representations of bicompact spaces as inverse spectra of polyhedra and relates the dimensions of the approximating polyhedra to covering, small inductive, and large inductive dimensions. It proves that every bicompactum is the space of a polyhedral spectrum, with a zero-dimension…
This note examines Petrovsky’s criterion for uniform well-posedness of the Cauchy problem for linear partial differential equations with two independent variables and constant coefficients. Using elementary lemmas and Newton polygon analysis of the characteristic equation, it studies the asymptotic …
This paper studies the structure of the sets of Markov numbers obtained from irrational numbers in the unit interval whose continued fraction partial quotients have a fixed limiting upper bound. Using continued fraction estimates for the quantities governing Diophantine approximation constants, it p…
This note studies limit logics, defined as countable closed subclasses of infinitely valued logic that contain homomorphic preimages of every finite valued logic. It introduces functions with a box structure and uses their behavior under superposition to associate invariants, encoded by real numbers…
The paper studies functionally closed completely regular spaces, also called Q-spaces, and their relation to complete topological spaces. It extends a theorem of A. A. Kubenskii by removing the normality assumption, proving that every complete topological space of attainable cardinality is functiona…
This note studies how planar area measure changes under a quasiconformal mapping whose dilatation is close to one. For a normalized mapping between rectangles, the argument estimates a boundary integral by the Jacobian and derives an inequality involving the square root of the Jacobian, then applies…
This paper studies the accumulation of perturbations in nonstationary linear oscillatory systems described by systems of differential equations with time dependent polynomial operator coefficients. The author reduces the general system to an equivalent first order linear matrix system, introduces ma…
This note studies the relation between Lagrange classes of irrational numbers with bounded continued fraction partial quotients and Markov extremal classes of indefinite binary quadratic forms, in the setting of rational approximation constants and extremal lattices for the region |uv| < 1. Using af…
This paper develops a theory of rings formed by closed, densely defined linear operators in a Hilbert space that commute with a possibly nonorthogonal resolution of the identity. It defines admissible classes and operator bases to make addition, multiplication, limits, inverses, and analytic functio…
This paper studies invariant constructions associated with an m-dimensional surface in an n-dimensional affine space using the invariant-group method. Starting from the sequence of fundamental objects obtained by prolonging the surface equations, it constructs relative tensors and invariants that ch…
The paper studies arithmetic schemes for evaluating a polynomial when its coefficients may be preprocessed once into auxiliary parameters, a setting motivated by repeated evaluation at many arguments. It constructs, over the complex numbers, a family of schemes for every degree n that uses floor((n+…
This note addresses the Galois embedding problem for a normal extension of algebraic number fields when the prescribed group is a split extension of the given Galois group. It announces that the problem is solvable for any algebraic number field when the kernel is nilpotent, thereby including earlie…
This paper studies homogeneous Riemannian spaces with positive definite metric whose isotropy group fixes a subspace of the tangent space and acts irreducibly on its orthogonal complement, in the case where commuting rotations may exist. Using invariant moving frames, Maurer-Cartan equations, and al…
This note studies differential equations of infinite order with polynomial coefficients, relaxing earlier restrictions that the polynomial degrees be uniformly bounded and that associated characteristic functions be analytic near the origin. Using the theory of infinite systems of linear algebraic e…
This paper studies existence questions for convex surfaces whose principal curvatures satisfy prescribed elliptic relations involving the product and sum of the principal curvatures. It extends the associated curvature operators from twice differentiable convex graphs to arbitrary convex functions b…
The paper studies the homogeneous Riemann-Hilbert problem in a multiply connected domain in the special range of the index, where the usual dimension formula for the space of solutions can fail. By reducing the problem to a canonical boundary condition on circular domains and analyzing associated me…
