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 paper studies optimal regularization for ill-posed convolution integral equations of the first kind when the right-hand side contains random noise and the solution and noise are modeled as stationary uncorrelated processes. It compares Wiener-type optimal filtering with Tikhonov regularization,…
The paper studies approximation of continuous periodic functions by linear operators formed from Fourier coefficients and by weighted sums of Fourier partial sums. It derives general pointwise estimates for the deviation of such operators from the function in terms of the sequence of best uniform tr…
The paper addresses the moduli problem for marked Riemann surfaces of type \((g,n)\) through Teichmüller space, using quasiconformal mappings associated with a Fuchsian group and their restrictions to the unit disk. It introduces global moduli given by the first \(m=3g-3+n\) nontrivial Taylor coeffi…
This paper develops a method for estimating nonprincipal character sums over boxes in finite fields and applies it to the distribution of primitive roots. For a finite field of order p^n defined by an irreducible polynomial, it proves that sums over n dimensional intervals of side length H are bound…
This paper extends the Smale and Hirsch weak homotopy classification of immersions to mappings transverse to general distributions, especially foliations. It defines transversality for a map between distributions via injectivity of the induced bundle homomorphism, proves that for a foliation whose d…
The paper extends K. Itô’s theorem on the independence of jump counts for processes with independent increments from real-valued processes to processes taking values in topological groups with a countable base. Using a generalized P. Lévy inequality, it proves that stochastically continuous separabl…
This note studies completeness of systems of eigenvectors and associated vectors for several classes of polynomial and rational operator pencils in a separable Hilbert space. Using resolvent estimates in the style of V. I. Macaev, together with Poisson integral estimates, Levinson’s lemma, and confo…
The paper studies the approximate solution of singular integral equations on the unit circle with Cauchy-type kernels by the method of mechanical quadratures, a method for which general justification had previously been limited. It formulates algebraic computational schemes for equations of zero and…
This paper studies when the functors in complex K-theory defined by skeletal completion and by homotopy classes of maps to BU coincide for locally finite CW-complexes. It gives a necessary and sufficient criterion in terms of rational cohomology and the Atiyah-Hirzebruch spectral sequence, with coro…
The paper studies the Cauchy problem for a class of second order nonlinear differential equations in a Hilbert space with a time dependent, generally unbounded self-adjoint linear operator and a nonlinear term depending on time, the solution, and its derivative. Under coercivity, differentiability, …
This note develops criteria, using modular forms and estimates for the least quadratic nonresidue, for determining when representation numbers of positive integral quadratic forms admit Liouville-type formulas. It defines Liouvillean quadratic forms through the decomposition of their theta series in…
This paper studies infinitesimal rigidity of Darboux surfaces with boundary in a three-dimensional Riemannian space, under a generalized sliding boundary condition determined by a prescribed vector field along the boundary. Using isothermally conjugate coordinates, the bending equations are reduced …
This paper studies a periodic solution of the one-dimensional diffusion equation on a half-line with a nonlinear multivalued S-shaped boundary condition and an a priori unknown period. In the symmetric case, the boundary-value problem is reduced to a nonlinear integral equation for the boundary trac…
This note studies direct product representations of the canonical commutation relations arising from countable tensor products of one degree of freedom Schrödinger representations. It proves an equivalence criterion for irreducible components generated by product vectors, characterizes these represe…
This note formulates several results on Orlicz spaces in the sense of Zaanen over a complete continuous sigma-finite measure space, with attention to the Young class, associated norms, and distinguished closed subspaces. It gives criteria, mainly in terms of Delta conditions for the Young function a…
This note studies spectral properties of a non-self-adjoint matrix differential operator on the half-line associated with the equation involving matrix coefficients C(x) and Q(x), under boundary conditions defined by constant matrices. Extending earlier scalar results, it establishes existence and a…
This paper studies uniqueness in contact inverse problems for generalized magnetic potentials associated with a second order uniformly elliptic operator with variable coefficients. The potentials are represented as combinations of volume mass potentials and simple layer potentials, and the problem i…
The paper studies abstract Cauchy problems in a Banach space for differential equations with unbounded operators whose resolving semigroups need not be analytic and may have power singularities at the origin. For the autonomous problem, it gives conditions under which the variation of constants form…
The paper studies a rank-one non-self-adjoint perturbation of the operator of multiplication by the independent variable in L2 on the real line, assuming analytic continuation and strip-type square-integrability conditions on the perturbing vectors. It characterizes nonreal eigenvalues as zeros of a…
The paper develops several parameterized analogs of Stirling’s formula for the gamma function, motivated by applications requiring expansions in variables other than the argument itself. It derives asymptotic expansions for the gamma function and its reciprocal using a shift parameter, with coeffici…
This note studies how restrictions on subgroups of finite groups determine the structure of the whole group, with particular attention to solvability, maximal subgroups, and classes of finite p-groups. It introduces several auxiliary classes, including generalized Schmidt and Frobenius groups, E-gro…
The paper develops duality formulas for variational problems in which an integral functional is minimized subject to an integral constraint. Using Young transforms and convexity, it proves that the value function of a basic calculus of variations problem can be represented as a maximum over a scalar…
The paper extends a quadrature identity for trigonometric polynomials, previously shown to include M. Riesz’s formula as a special case, to analytic functions associated with a finite plane domain and to half-integer trigonometric polynomials. Using Faber polynomials and a shift operator defined thr…
The paper considers the problem of maximizing a linear function over a closed bounded convex body in finite-dimensional Euclidean space. It proposes a cutting-plane procedure that starts from an enclosing polyhedron and an interior point, repeatedly solves a linear programming relaxation, and, when …
This paper studies invariant subspaces of simple dissipative Volterra operators whose imaginary components are nuclear, with emphasis on the nonunicellular case. Using characteristic operator functions, their divisors, and relations between type and weight, it develops lattice operations for invaria…
This note studies the maximal minimum norm among ideal classes in imaginary quadratic fields, focusing on effective lower bounds for the quantity defined by the least norm in each class. Building on analytic identities for Epstein zeta type sums attached to reduced binary quadratic forms, the author…
The paper studies relations between the coefficients of extremal polynomials on the interval [0,1] and the number of their Chebyshev alternants. Using Voronovskaya’s functional method together with convex geometric arguments, it characterizes projections of the unit ball of polynomials with bounded …
This note studies extremal problems for univalent analytic functions and related classes of quasiconformal mappings. Using variational methods, it characterizes extremal slit mappings in the unit disk, relates them to quasiconformal extension problems with prescribed interpolation data, and proves c…
This note studies approximation of continuous periodic functions by linear methods, focusing on relations between semiadditive bounded functionals, best trigonometric approximation, and moduli of smoothness. It proves general theorems in which assumptions verified only on trigonometric polynomials y…
This note addresses the abstract characterization of relativized semigroups equipped with multiplication and the three relations corresponding to semicompatibility and first and second projection inclusion for partial transformations. It develops an elementary, though infinite, system of axioms for …
This note studies a convolution type integral equation on the real line with different kernels acting on a finite partition of the integration domain, in function spaces including Lebesgue, bounded, continuous, uniformly continuous, and vanishing continuous functions. The equation is reformulated as…
This paper studies linear homomorphisms between linear topological spaces, with emphasis on closedness, products, powers, and restrictions of such operators. It proves that a homomorphism with closed kernel and closed range is a closed operator, establishes conditions under which products of homomor…
This note refines and extends results on estimation from grouped samples to multidimensional distributions depending on a vector parameter. It formulates maximum likelihood estimation after partitioning the observation space into finitely many cells, gives conditions for existence and uniqueness of …
This paper studies Lyapunov stability in the autonomous determination of the coordinates of a moving object by an inertial navigation system with a horizon-stabilized platform. The nonlinear equations for latitude, longitude, and platform orientation are transformed using Rodrigues-Hamilton paramete…
This paper studies nonlinear equations of the form x = BF(x) in separable locally convex spaces embedded in a Hilbert space, where F maps into the strong dual and B is a bounded linear operator whose Hilbert-space restriction has positivity or quasi-positivity properties. By reducing the equation to…
This note studies the asymptotic behavior of a generalized \(L\)-norm integral associated with sequences of trigonometric polynomials and functions of bounded variation whose variation is concentrated near two symmetric points. It proves a uniform asymptotic formula for these integrals, with a remai…
This paper studies a class of pseudodifferential operators of principal type characterized by a priori Sobolev estimates with loss parameter δ. It gives necessary and sufficient algebraic conditions on the principal symbol at characteristic points for the estimate with δ = 2/3, using auxiliary nonex…
This paper studies linear polynomial operators on spaces of analytic functions and their relation to Faber polynomial expansions in a finite domain with simply connected complement and rectifiable boundary. A shift operation is defined through the conformal mapping of the exterior of the domain, ext…
This paper studies finite symmetry groups of general linear homogeneous second order partial differential equations with nondegenerate principal tensor. By interpreting the principal coefficients as a Riemannian metric and using equivalence transformations involving conformal changes of the metric a…
This note generalizes inverse approximation theorems for rational approximation on bounded closed subsets of the complex plane whose complement has finitely many components. Using Green functions, Dirichlet problem solutions, and moduli of continuity tied to level curves of the complementary domains…
The paper extends the notion of mappings of type s, previously studied for normed spaces, to separated locally convex spaces by defining them through images of neighborhoods as strongly nuclear sets. It establishes several equivalent characterizations, including representation by rapidly decreasing …
The paper studies large deviation limit theorems for normalized sums of independent, not necessarily identically distributed random variables, in settings where the classical Cramér exponential moment condition may fail. It derives integral and local asymptotic formulas comparing tail probabilities …
The paper studies a dimension invariant, denoted Dind, proposed by A. V. Arkhangel’skii, which combines covering and inductive approaches to topological dimension. It proves that for normal spaces the large inductive dimension satisfies Ind X ≤ Dind X, and that for perfectly normal spaces the two di…
The paper studies continuation of solutions to nonlinear mixed boundary value problems for second order hyperbolic equations in a plane strip when a boundary nondegeneracy condition fails at a finite time. It analyzes the resulting loss of classical continuation, proves blowup behavior of first deri…
The paper studies periodic boundary value problems for second order ordinary differential equations with summable periodic coefficients, focusing on existence of the Green function, its sign, and related differential inequality methods. Using the distribution of zeros of solutions of the associated …
This paper derives an upper estimate for the modulus of a classical solution of the first boundary-value problem with zero lateral boundary data for a second-order linear parabolic equation in an expanding space-time domain. Under uniform ellipticity and a sign condition on the divergence of the low…
This paper studies embedding theorems for classes of one-variable functions whose first moduli of continuity in Lp are controlled by a given modulus. It establishes sufficient conditions, expressed as weighted series involving the modulus of continuity, for membership in Orlicz-type spaces such as L…
This note studies associative rings without nonzero nilpotent elements through completely prime and completely semiprime ideals. Using m-systems and a Zorn lemma argument, it proves the existence of completely prime ideals over a completely semiprime ideal and shows that every completely semiprime i…
The paper derives a priori boundary estimates for solutions of the Dirichlet problem for uniformly elliptic second order equations with analytic coefficients in domains with analytic boundary. It introduces norms based on iterated tangential analytic differential operators, proves their basic produc…
