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 introduces classes of plane mappings defined by an integral condition involving a convex function of the generalized derivative, extending the previously studied class with bounded Dirichlet-type integral. Using Suvorov’s method, it establishes sharp two-sided estimates for the distortion …
This note studies positive classical solutions of second order linear elliptic equations whose coefficients satisfy a Cordes type condition expressed through a comparison inequality for the fundamental radial power function. Using maximum principle arguments and auxiliary integral barriers, it prove…
The paper develops a method for solving nonlinear integral equations in a Lipschitz function space by introducing a continuous parameter, yielding a continuous analogue of Newton’s method for the associated operator equation. Under assumptions of local uniqueness, differentiability of the kernel, Li…
This paper develops systems of symmetric functions associated with barycentric coordinates in Euclidean space and the permutation group of the vertices of a regular simplex. It defines symmetrized functions on the lattice of integral barycentric coordinates, gives generating and integral representat…
The paper develops an algebraic framework for difference operators in convolutions on uniform grids, intended as discrete analogues of pseudodifferential operators and as tools for analyzing difference schemes. It defines grid Sobolev-type spaces, homogeneous and general difference operators through…
The paper studies conditionally periodic solutions of analytic Hamiltonian systems with periodic angle variables, starting from a known invariant solution and reducing the Hamiltonian by canonical transformations to a normal form near that solution. Under simplicity, nonresonance, and nondegeneracy …
This paper studies numerical solution of ill-posed linear integral equations of convolution type in the Hilbert space setting, motivated by problems in exploration geophysics. Building on Tikhonov regularization and Ivanov’s notion of uniform regularization, it introduces two-parameter regularizing …
This note studies regular Dirichlet decompositions of three-dimensional Euclidean space for the second triclinic group, using the representation of a generic orbit as a bilattice. It proposes a method based on decomposing a Dirichlet parallelohedron into pieces and analyzing the possible positions o…
This paper establishes embedding theorems for weighted anisotropic function spaces on the half space into spaces with mixed norms on boundary sections. It defines weighted spaces through fractional differences with weight in the normal variable and formulates conditions on the smoothness indices, in…
This note addresses the failure, in general normal spaces and some compact spaces, of the classical covering dimension to coincide with the small and large inductive dimensions. It proposes modified inductive invariants, denoted ind* and Ind*, in which dimensional restrictions are imposed not direct…
This paper studies PS-isomorphisms, that is, isomorphisms between the lattices of all subsemigroups of groups, in the setting of structurally ordered groups. Using properties of cyclic subsemigroups, C-products, and the positive cone of a partially ordered torsion-free group, it shows that a PS-isom…
The paper studies cardinal bounds for families of open subsets in dyadic bicompact spaces, extending Shpilrain’s result on point-countable systems. It proves that if every point of a dyadic bicompactum belongs to at most an infinite cardinal number of members of an open family, then the whole family…
The paper studies mean-square approximation of a square-integrable function of several variables on a parallelepiped by a sum of functions depending only on prescribed smaller subsets of variables, with respect to a product Lebesgue-Stieltjes measure. Using elementary properties of averaging over se…
This paper proposes a Fourier transform approach to infinite-dimensional parabolic equations in functional derivatives, treating the unknown not as a pointwise functional but as a sigma-additive charge on the dual of a rigged Hilbert space. For the Cauchy problem with a Laplace operator defined thro…
The paper studies which tuples of real characteristic numbers can occur for stochastic matrices of simple structure, motivated by applications to finite probabilistic automata. It introduces the notion of a matrix spectrum, a system of idempotent, mutually annihilating matrices summing to the identi…
The paper studies convergence conditions for projection methods for solving linear operator equations in Banach and Hilbert spaces, extending a result of N. I. Polskii to subspaces that need not be finite-dimensional. It gives necessary and sufficient conditions in terms of limiting density, one-to-…
This paper extends Reiter’s section theorem for quotient spaces of locally bicompact groups. It proves that for a locally bicompact group with a closed subgroup, every paracompact zero-dimensional subset of the quotient admits a homeomorphic section under the natural projection, using inverse spectr…
The paper studies when a Hölder continuous function prescribed on a Lyapunov boundary is the boundary value of a function analytic in several complex variables. It constructs Cauchy and Cauchy-type integrals for an elliptic first-order system built from a Clifford algebra representation, derives pri…
This note studies smooth projective curves of genus greater than one over function fields and addresses Shafarevich’s finiteness conjecture in this setting. Using height bounds on Hilbert scheme points associated with canonical embeddings, estimates for minimal fibrations, and a rigidity argument ba…
The paper studies the reconstruction of a function from Fourier coefficients known with small square summable random errors, using regularized summation factors. It formulates optimality problems for choosing either a regularization parameter for a fixed stabilizing functional or the full sequence o…
The paper studies finite form solutions of a Hill equation with real period containing first and second harmonics. By applying an exponential substitution and seeking the remaining factor as a finite trigonometric sum with integral or half integral frequencies, the problem is reduced to algebraic ei…
The paper studies spaces of smooth mappings from a compact Riemannian manifold into a compact Riemannian manifold of negative, or in parts nonpositive, curvature through the Dirichlet functional and its harmonic critical points. It derives second variation type identities, analyzes the associated pa…
This note studies inverse boundary-value problems with two unknown coefficients for a quasilinear parabolic equation and for a related ordinary differential equation with piecewise constant spatial coefficients. It formulates overdetermined boundary and matching conditions, defines the appropriate s…
The paper develops an averaging approach for constructing asymptotic approximations of arbitrary order for differential systems with deviating arguments and small parameters. It treats retarded systems with constant, variable, state-dependent, and parameter-dependent delays, including cases where th…
The paper studies differential properties of solutions to constant coefficient quasielliptic equations in the whole space, focusing on estimates in unbounded domains rather than local regularity. It introduces Sobolev type, interpolation, weighted trace, and Hölder type function classes adapted to t…
This paper studies limit theorems for continuous functionals of measurable random processes, extending earlier results for functionals of integral type. For processes on the unit interval whose finite-dimensional distributions converge and which satisfy a uniform moment bound together with a stochas…
This paper studies the local analytic behavior of eigenvalues and eigenvectors of a positively directed symplectic curve arising from a linear differential system with analytic periodic coefficients and positive definite Hamiltonian matrix, near a point where a multiple eigenvalue lies on the unit c…
The paper studies regularization algorithms for approximately solving linear equations with closed, densely defined unbounded operators between real Hilbert spaces, in the case where the inverse is not bounded. Using the spectral resolution of the self-adjoint operator A*A, it constructs a family of…
The paper studies the Riemann boundary value problem for analytic functions in domains bounded by rectifiable Jordan curves whose tangent angle is the sum of a bounded variation term and a Hölder continuous term, including curves of bounded rotation. It proves boundedness of the Cauchy singular inte…
The paper studies large intervals, or cube faces contained in the support, of a random Boolean function on n variables with independent equiprobable values at the vertices. It introduces the number of k-dimensional intervals and the maximum interval dimension, then proves that when k grows with n an…
The paper studies which Whitehead torsions can occur for homotopy equivalences of closed odd-dimensional manifolds, especially under the restriction that tangent bundles are identified and the relative normal invariant is trivial. Using a cobordism whose relative homology is concentrated in the midd…
The paper studies a special concave programming problem in which a separable concave objective is minimized over a polyhedron defined by nonnegativity and nested cumulative linear inequalities. It shows that an optimum is attained at a vertex and derives structural properties of these vertices, limi…
This note surveys and extends an operator approach to integral representations of holomorphic functions, chiefly for bounded convex complete multicircular domains in several complex variables. It argues that Temlyakov’s integral formula should be understood as operatorial both in the function and in…
The paper studies generalized equiparametric manifolds associated with an m-dimensional surface in an n-dimensional projective space, focusing on manifolds whose elements are an invariant basic plane with a marked point and, more generally, a point, tangent m-plane, and associated (m+1)-planes. Usin…
This paper studies closed extensions of differential operators in a bounded domain and the stability of normal solvability and Fredholm index under weak perturbations of boundary conditions. Using Hilbert space decompositions associated with maximal and adjoint operators, compactness criteria, and r…
This note proposes an axiomatic treatment of measure theory in real linear spaces that avoids assuming a locally convex topology and instead formulates compatibility between the linear and measure structures through measurable partitions and generalized convolutions. The argument centers on linear m…
This paper introduces the weak minimal condition for subgroups, excluding infinite descending chains in which each successive subgroup has infinite index, as a relaxation of the usual minimal condition. It proves basic closure properties, including stability under extensions, and shows that for loca…
This note establishes an effective lower bound for a nonhomogeneous linear form in logarithms of algebraic numbers under a rational linear independence assumption on the logarithms. It defines height-like parameters through the lengths of the algebraic numbers and states an explicit inequality depen…
The paper studies solvability of nonlinear operator equations in locally convex and reflexive Banach spaces, extending ideas related to A. N. Tikhonov’s fixed point principle. It proves an existence theorem for equations \(F(x)=0\) under a boundary positivity condition on a set surrounding the origi…
This paper studies the first Dirichlet problem in \(W_2^1\) for uniformly elliptic second-order equations in divergence form whose lower-order coefficients have integrability at or below the usual \(L_p\), \(p>n/2\), threshold. It introduces mixed-norm spaces \(L_{(r_1,r_2)}\), proves embedding and …
This paper studies the uniform accuracy of the normal approximation for normalized sums of independent identically distributed random variables, especially when higher moments needed for classical asymptotic expansions are infinite. It introduces functionals of truncated moments and tail integrals t…
This paper studies the asymptotic behavior of positive solutions to systems of integral equations on the half-axis with nonnegative matrix kernels of finite forward range. By comparing two solutions and deriving a recursive integral equation for their componentwise ratio, it establishes conditions u…
This paper studies criteria under which nonunitary operators are linearly similar to unitary or self-adjoint operators with absolutely continuous spectrum. Using characteristic matrix and operator functions, it proves boundedness conditions that imply similarity for the simple parts of bounded opera…
This paper studies projective hierarchies of classes of sets in topological spaces of weight τ, including the spaces Dτ, Jτ, Dων, and Jων, under the assumption that τ is strongly inaccessible. Using set-theoretic operations with variable bases and ΔΣ-operations, it characterizes how projections of F…
This paper studies factorizations of finite groups through additions to normal subgroups and through decompositions associated with invariant and chief series. It proves several criteria concerning when additions yield complements, including generalizations of results of Hall, Huppert, Roquette, Sch…
This note develops a finite-dimensional projection construction for proving fixed point existence for mappings on weakly compact convex subsets of Banach spaces, extending the Schauder and Tikhonov principle beyond compact or weakly continuous operators. The authors associate to a mapping a family o…
This paper studies integral-geometric transforms that assign to a rapidly decreasing smooth function on complex affine space its integrals over planes belonging to an algebraic complex of k-dimensional planes. It defines admissible complexes, for which an inversion formula follows from earlier gener…
The paper studies dimension properties of products of one-dimensional bicompacta, proving that for a finite product of n bicompact spaces with large inductive dimension one, the covering, small inductive, and large inductive dimensions all equal n. The argument develops partition lemmas for normal s…
This paper extends the concept of theta-proximity to arbitrary Hausdorff spaces and relates it to irreducible theta-perfect mappings of completely regular spaces and their bicompact extensions. Using centered systems of open sets, it proves representation and uniqueness theorems showing that every t…
This paper studies spectral expansion for Schrödinger operators in Euclidean space with strongly singular potentials that become infinite on a set, motivated by approximating an impenetrable barrier by finite barriers. Using semigroup convergence for truncated potentials and scattering solutions sat…
