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 formulates an existence theorem for time-optimal control processes under a compactness condition on trajectories and a convexity condition on sets determined by the maximizers of the Hamiltonian. The proof embeds the original controlled system into a convexified system, applies the known F…
This note studies ordinary differential equations with polynomial coefficients that are not of Fuchs type, focusing on solutions in spaces of generalized functions that permit regularization of exponential singularities. For equations of a specified form with an isolated singularity at zero, it anal…
This note studies how spatial quasiconformal mappings in three-dimensional domains are reflected on plane sections. It introduces a notion of two-dimensional quasiconformality for mappings of plane domains into Euclidean three-space and uses it to characterize spatial quasiconformal mappings by thei…
This paper studies embedding theorems for function spaces with mixed norms, focusing on removing earlier monotonicity restrictions on the norm parameters. It defines the relevant mixed norm and Sobolev-type spaces, proves ordering and interpolation lemmas, and establishes a general boundedness theor…
The paper develops a method for proving algebraic independence of values of E-functions satisfying linear differential equations, with particular attention to homogeneous equations of third order. It introduces a criterion of differential reducibility for algebraic differential equations, expressed …
This paper strengthens a key rank lemma used in Shidlovskii’s general theorem on transcendence and algebraic independence of values of E-functions satisfying linear differential equations with rational-function coefficients. By modifying Siegel-type auxiliary polynomial constructions and the estimat…
The paper studies uniqueness in inverse problems for metaharmonic and Newtonian potentials in Euclidean space: determining a density from a known exterior potential, and determining the shape of a body with prescribed density from exterior or interior potentials. It establishes a series of uniquenes…
This paper extends a theorem of Bass on decompositions of torsion-free modules into ideals from commutative domains to representation modules over noncommutative orders. For an order over a Dedekind ring in a finite-dimensional semisimple separable algebra, it proves that if every right ideal of the…
This note studies absolute and unconditional convergence of Fourier series with respect to the Haar system, emphasizing distinctions between pointwise absolute convergence, absolute convergence of coefficients, and almost-everywhere absolute convergence. It gives sufficient conditions in terms of in…
The paper studies a mixed problem for a class of multidimensional hyperbolic equations of arbitrary order whose coefficients, free term, and initial data may have jump discontinuities across prescribed analytic surfaces. It formulates general initial, boundary, and conjugation conditions, together w…
The note constructs infinite families of discrete groups acting on three-dimensional Lobachevsky space whose fundamental domains are noncompact but have finite volume. The construction begins with polyhedra associated to fine square decompositions of a horosphere, chooses dihedral angles of the form…
This note studies singular points of topological embeddings of manifolds in Euclidean space and the local flatness of unions of locally flat cells. It proves that, in dimensions \(n \ge 5\), singular interior points are removable except in codimension two, where local flatness is characterized by th…
This bibliographic survey records recent journal literature on differential equations, primarily from Soviet and Eastern European mathematical publications of 1965 and early 1966. The entries are organized under ordinary differential equations and cover qualitative theory, stability, asymptotic meth…
This paper studies when the subspace of null elements of a linear operator on a vector space admits an invariant complement. It proves several sufficient conditions, including bounded height of null elements, finite-dimensionality of the null subspace, stabilization conditions on kernels intersected…
This note studies the normal structure of finite groups through systems of cyclic chief factors, with particular attention to groups whose chief factors have cyclic Sylow p-subgroups. Using auxiliary results from modular representation theory, it gives criteria involving the Frattini subgroup, gener…
This note studies the growth of entire functions of several complex variables with respect to one variable when the remaining variables are fixed. Using notions of order, type, capacity, and exceptional sets defined by conditions of massiveness and rarity, it extends earlier results for two variable…
The paper studies integral functionals on algebraic polynomials generated by moment segments of nondecreasing functions on the unit interval, extending a problem concerning the functional with moments 1, xi/2, xi squared/3, and so on. Using determinant criteria for absolutely monotone segments and r…
This paper studies the stationary one-velocity kinetic transport equation with isotropic scattering in a bounded convex domain and proposes a splitting method for its solution. The authors formulate the boundary-value problem in an operator setting, define a class of generalized solutions in an \(L_…
The paper introduces left, right, and two-sided D-algebras as distributive algebras satisfying differential identities that generalize the Lie algebra identity while also encompassing structures equivalent to modules over Lie algebras. It proves that the quotient of a left D-algebra by its left cent…
This paper gives necessary and sufficient conditions for unitary equivalence of commutative symmetric algebras in a Pontryagin space with only real eigenfunctionals, using the structural realization developed in the author’s preceding work. The argument analyzes how an isometric equivalence transfor…
This note studies uniqueness for systems of Volterra integral equations with retarded argument, extending earlier results on differential equations with delay. It formulates conditions linking the modulus of continuity of the kernel in the unknown function to the rate at which the delayed argument a…
This paper constructs a functional equation whose prescribed particular solutions are functions of the form A(z, lambda_n), where A(z,h) is expanded in a parameter h and the sequence lambda_n satisfies a finite growth condition. The method introduces an auxiliary entire function L vanishing on the s…
This paper studies how pointwise cardinal bounds on systems of open sets in a topological space control their total cardinality, using the notion of a t-pseudobase. It proves that a t-pseudobase of a countably compact space is countable if it is point-countable on an everywhere dense subset, general…
This note gives an analogue of the Plancherel formula for the real unimodular group of third order. It describes two series of irreducible unitary representations of the group, including a principal series acting on analytic and measurable functions on a specified manifold and a second series acting…
The paper studies nonlinear parabolic type equations in a real Hilbert space with time dependent positive self-adjoint operators, monotone damping operators, and nonlinear potential or nonpotential terms. Using energy inequalities for the operator norm induced by the square root of the principal ope…
This paper studies finite groups through the conjugacy classes of their nilpotent maximal subgroups. It proves that a finite nonnilpotent group has at most two such classes, and characterizes the case of two classes as an extension of a nilpotent group by a group of type A, with specified action con…
This paper studies level lines arising from regular univalent conformal mappings in the unit disk, focusing on conditions under which an arc of such a level line is star-shaped. Using a method developed in earlier work, it determines the value domain of a functional involving the logarithm of the de…
The paper defines a sequent calculus J0 for constructive predicate logic that omits structural inference rules and modifies implication, negation, and quantifier rules to better support proof search. It compares J0 with the standard constructive calculus G1, showing that they are not equipollent in …
This paper studies relations between the best polynomial approximation of analytic functions of several variables and the coefficients of their orthogonal expansions. Using mean square approximation in a cube with weight, the author proves lemmas identifying generalized Fourier coefficients as optim…
The paper proposes a numerical method for Fredholm integral equations of the second kind that separates the choice of interpolation points for the unknown function from the quadrature points used to approximate the kernel integral. The method forms a linear system only at selected points for the sol…
The paper studies differential properties of traces of functions on hyperplanes of arbitrary dimension, extending earlier work mainly concerned with fixed dimensional hyperplanes and standard Nikol’skii or Sobolev type classes. It develops a framework with anisotropic decompositions of Euclidean spa…
This paper studies a boundary value problem for systems of second order elliptic equations in a finite multiply connected plane domain with smooth boundary and a first order linear boundary condition. Using a Green formula and a matrix fundamental type representation, the problem is reduced to an eq…
This paper studies extremal norm problems for linear polynomial operators on translation-invariant function spaces, especially operators agreeing with convolution-type polynomial transforms on trigonometric polynomials. It establishes exact values of the minimal operator norms in L2, including the c…
The paper studies traces and boundary values for weighted Sobolev-type classes of functions in a half-space, with weights satisfying monotonicity and doubling-type conditions. It defines corresponding fractional weighted spaces on the boundary and proves direct trace embeddings, inverse extension em…
This paper studies a non-self-adjoint boundary value problem on the half-axis for a second order differential equation with the singular term l(l+1)/x2 at the origin and a complex locally summable potential. It refines transformation-operator representations for the regular solution, proving differe…
This note studies multiple completeness and multiple expansions for systems of eigenvectors and associated vectors of polynomial operator pencils in Banach and Hilbert spaces. By reducing higher degree pencils to linear pencils on product spaces and applying known results on compact and Schatten typ…
This paper introduces and studies “D-series,” a class of series close to Dirichlet series whose basis functions have prescribed exponential asymptotics in a bounded domain and whose boundary of convergence contains a vertical segment. After reducing the general case by a linear change of variable, t…
