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 develops a two-sided collecting process for words in free groups with respect to bases of basic commutators, motivated by limitations of the Hall and Shirshov processes when computations are carried out only modulo a fixed term of the lower central series. It defines natural and layerwise …
This paper develops a method for studying Temlyakov-type integrals in their domain of nonanalyticity using first-order linear homogeneous differential operators. The approach combines a generalized Newton-Leibniz formula for such operators with formulas reducing multiple integrals to repeated integr…
This paper develops iterative methods for nonlinear systems of finite difference equations, with emphasis on difference analogues of strongly elliptic boundary value problems in a parallelepiped. It formulates abstract monotonicity and differentiability conditions in finite-dimensional Hilbert space…
This paper studies eigenfunction expansions for a second order differential equation in a Hilbert space with an unbounded operator coefficient of the form A minus q(t), where A is self-adjoint and semibounded below and q(t) is bounded self-adjoint. It develops weak and strong solution theory for the…
The paper formulates a two-player zero-sum variant of the discrete optimal stopping problem on an increasing sequence of sigma-algebras, where each player may stop only at times determined by the sign of an adapted process and the payoff is the stopped value of another adapted process. Under an inte…
The note studies stability of bases and defective bases in locally convex spaces under perturbations of the basis vectors. It gives criteria for equicontinuous, absolute, and Bessel bases in complete locally convex spaces, including conditions under which a perturbed sequence remains a basis equival…
This note proves an approximation theorem for analytic functions in the weighted Banach spaces defined by integrability of \((1-|z|^2)^q|\varphi(z)|\) over the unit disk. It shows that every such function can be approximated in the corresponding norm by rational functions with at most simple poles o…
The paper studies maximum principles for a class of second order mixed elliptic-hyperbolic equations with singular lower order coefficients in a domain divided by a transition line. It first proves a characteristic absolute extremum principle for an associated hyperbolic equation in a triangular cha…
The paper studies the large-time behavior of solutions to a two-component quasilinear hyperbolic conservation system under the Lax genuine nonlinearity condition. For smooth initial data that approach two constant states at spatial infinity and satisfy a nondegeneracy and monotonicity condition in R…
The paper studies the decay of a discontinuity for systems of two quasilinear conservation laws and gives an example showing that the usual Lax monotonicity condition does not by itself ensure existence of a self-similar Riemann solution. For the system with fluxes \(f=3\ln u+v\) and \(\varphi=2/u\)…
The paper studies hyperspaces of nonempty closed subsets with the Vietoris, or exponential, topology, focusing on the subspaces of compact sets and finite subsets. It establishes criteria relating topological properties of a space to those of its hyperspaces, including normality, paracompact p-space…
This paper studies uniform convergence of variational-difference schemes for elliptic Dirichlet problems, with emphasis on estimates that reflect the smoothness of the coefficients, data, boundary, and mesh geometry. It constructs schemes on simplicial complexes, introduces complexes with alpha-symm…
The paper develops a general framework for applying the Bogolyubov-Krylov averaging method to evolution equations, including equations with retarded arguments and generalized time transformations. It defines averaged right hand sides and averaged generalized times in suitable spaces of continuous an…
This note shows that the homology K-groups previously introduced by the author can be realized within the framework of generalized Steenrod homology groups. For a fixed locally finite complex K, it constructs a category of barycentric subdivisions of products K by L and defines corresponding chain c…
This paper studies Rosenblatt strong mixing for homogeneous Markov chains with a countable state space. It proves that an irreducible positive recurrent aperiodic chain satisfies the strong mixing condition, gives a null recurrent example where the condition fails, and relates the mixing coefficient…
The paper studies eigenfunctions of first boundary value problems for elliptic equations whose coefficients degenerate at an interior point, using weighted Hilbert spaces and a normality condition near the singularity. The method removes a small ball around the degeneracy, solves the corresponding r…
The paper addresses optimization of large-scale multiconnected systems formulated as linear programming problems with dense constraint matrices, where standard block programming or aggregation may be ineffective. It proposes reducing the constraint matrix to a special pseudodiagonal form, under cond…
This note studies expansions in eigenfunctions associated with only the negative eigenvalues of a second order non-self-adjoint boundary value problem, \(y''+2A\lambda y'+B\lambda^2y=0\), \(y(0)=y(1)=0\), under the condition \(A^2-B<0\). The proof reduces the question to an auxiliary elliptic proble…
The paper proves a conjecture of V. A. Efremovich that the horocyclic pocket, defined as the universal covering of the Beltrami pseudosphere or equivalently by gluing two horocyclic domains in the Lobachevsky plane along their boundary horocycle, is not equimorphic to any surface of revolution. The …
This note extends Dzhrbashyan’s generalized Riemann Liouville type operator from a single weight function to a finite system of functions satisfying the class conditions for \(\Omega\). It defines associated coefficient sequences and kernels, then proves generalized Cauchy and Schwarz formulas for h…
This paper studies factorizations of arbitrary finite groups in terms of composition blocks, defined from the arithmetically connected classes of indices in an invariant or composition series. It introduces properly embedded systems of subgroups, invariant-index systems, and total permutability, the…
This paper studies infinitesimal bendings of a surface with boundary and positive exterior curvature in a three-dimensional Riemannian space, subject to a generalized sliding boundary condition. Using isothermally conjugate coordinates, the geometric problem is reduced to boundary value problems for…
The paper studies boundary-value problems for elliptic-parabolic differential equations in bounded cylinders, with an elliptic spatial operator and a finite-order time differential operator. Using localization, eigenfunction expansions, Sobolev-type spaces, and parameter-dependent elliptic estimates…
The paper studies a class of two-dimensional integral equations of the first kind on an open Lyapunov surface, with kernels of the form \(Q(g,p)/R_{gp}\), arising in mathematical physics. It introduces an auxiliary singular kernel and uses potential-theoretic representations, limiting jump relations…
This paper studies necessary conditions for solvability and a priori estimates for pseudodifferential equations, extending earlier nonsolvability criteria of Lewy, Hörmander, Nirenberg, and Treves. It formulates conditions in terms of repeated commutators of an operator and its adjoint, and proves t…
The paper extends earlier results on a priori estimates to a broad class of second order degenerate elliptic operators in bounded domains with smooth characteristic boundary components. It formulates local normal-coordinate conditions defining alpha-ellipticity, classifies boundary components accord…
Bochvar analyzes comprehension axioms in the formal system K0 through the introduced notion of a measure of a kernel. For a kernel of a comprehension axiom, the paper defines maximal included and minimal covering predicates, called internal and external measures, and formulates extensions of K0 in w…
The paper studies Riemann and Hilbert type boundary value problems for a generalized Cauchy-Riemann system with a singular line, considering cases of positive and negative values of the parameter. Using integral representations of solutions in half-planes, the problems are reduced to classical conju…
This paper studies regularity conditions for properties of bases of Delta Sigma operations obtained by uniting chains of an original base, over an index space of strongly inaccessible cardinality. It defines regular and semiregular bases, proves lemmas giving sufficient closure conditions, and estab…
This paper describes a bifurcation mechanism in multidimensional dynamical systems that differs from previously studied cases involving the creation or disappearance of a single limiting element. For a smooth system with a saddle-saddle equilibrium having a zero characteristic root and finitely many…
This paper studies complete regularity for stationary random processes whose spectral density has the form f(lambda) = 1/g(lambda), with g a nonnegative entire function of finite degree. It proves a necessary and sufficient criterion: integrability of |ln f(lambda)|/(1 + lambda squared) over the rea…
The paper proposes a method of incomplete factorization for certain boundary value problems in the theory of analytic functions, where coefficients on one contour admit piecewise holomorphic continuation with jumps on another contour. The approach treats the original boundary condition as partially …
The paper studies closed convex hypersurfaces in Euclidean space whose elementary symmetric function of the principal radii of curvature is prescribed as a function of the exterior normal. It proves an a priori upper estimate for every radius of normal curvature in terms of the corresponding mean ra…
The paper studies a first-order Beltrami equation whose ellipticity degenerates on a simple analytic curve where the coefficient satisfies a finite-order vanishing condition for its modulus. It analyzes two geometric cases, according to whether the characteristic direction is transverse or tangent t…
The paper studies existence and uniqueness of bounded solutions on the whole real line for nonhomogeneous linear differential equations in a Banach space with generally unbounded time-dependent operators. It develops an approximation method based on bounded solutions of associated difference equatio…
This paper studies defect indices and self-adjointness of minimal symmetric differential operators with polynomial coefficients in spaces of square-integrable functions. By representing the operators in bases of Hermite functions, the analysis reduces them to infinite Jacobi matrices with matrix coe…
The paper formulates a notion of normal solvability for nonlinear operator equations in Banach spaces, modeled on Hausdorff normal solvability for linear equations. It proves that if a continuously differentiable operator maps a Banach space into a reflexive Banach space and has weakly closed range,…
The paper studies embeddings of compacta in Euclidean space through an invariant called embedding dimension, defined by pseudoisotopic approximation of a compactum by rectilinear polyhedra, and compares it with a dual embedding dimension defined via isotopic removal from polyhedra. It proves that th…
This paper studies multidimensional integral equations with difference kernels in a three-dimensional half-strip, under periodicity in two variables and summability of the kernel over the strip. By expanding the unknown function in Fourier series in the periodic variables, the equation is reduced to…
This note studies the remainder of partial sums of a generalized Fourier series for functions of two periodic variables, extending Kolmogorov-type asymptotic estimates from one-variable Fourier approximation. For the class of functions whose mixed derivative of orders p and q exists almost everywher…
This paper gives necessary and sufficient conditions for weighted a priori estimates for first-order constant-coefficient differential operators with exponential weights defined by a real homogeneous polynomial depending on spatial variables and nonnegative parameters. For real coefficient vectors, …
This paper studies choice-theoretic equivalents of Tychonoff’s theorem in topology, focusing on formulations that do not assume the weak axiom of choice. It proves that Tychonoff’s theorem for products of compact Hausdorff spaces is equivalent to Tychonoff’s theorem for finite spaces, Alexander’s cl…
The paper studies boundary value problems for elliptic overdetermined systems of two homogeneous second order constant coefficient equations in three variables. It first reduces such systems, by linear transformations of equations and coordinates, to two canonical forms, then analyzes edge boundary …
This note studies product inequalities and comparison results for large and small inductive dimensions in normal and completely regular spaces. It introduces auxiliary dimensional invariants defined through systems of closed sets, uses them to give conditions under which the usual inequalities for p…
This paper studies the local topological structure of the manifold of nontrivial jump states arising from discontinuities in finite-dimensional systems of quasilinear conservation laws. Motivated by entropy-type inequalities for potential or reducible systems, it shows that uniqueness questions can …
This paper studies the essential spectrum of operators on \(L_2(\Omega)\) obtained by restricting a singular integral operator in Euclidean space to a bounded domain with Lyapunov boundary. Using a known Noetherian criterion for singular integral operators, it characterizes the essential spectrum in…
The paper defines and studies spaces of functions with dominating mixed derivatives on an n-dimensional, not necessarily bounded, domain, including Besov-type spaces and Sobolev-type spaces with nonnegative smoothness vectors. It announces interpolation and embedding theorems for intersections of su…
The paper studies systems of singular integral equations in weighted spaces of vector functions on a smooth closed contour, with piecewise continuous matrix coefficients and power weights at finitely many discontinuities. It formulates necessary and sufficient conditions for the associated operators…
This paper studies purity properties for the locus where a locally finitely presented morphism of schemes fails to be smooth, distinguishing a local “from above” condition on irreducible components in the source from a “from below” condition on their images in the target for proper morphisms. Using …
