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 studies densely embedded ideals in abstract semigroups, extending earlier characterizations related to transformation semigroups. Using right and left shifts and their linked pairs, it constructs for a semigroup without equiacting elements a canonical semigroup in which the original semigr…
This note studies compactness, in the Fréchet metric, for families of surfaces of finite topological type lying in a bounded region and having uniformly bounded area. It shows that these Hilbert-type boundedness conditions are not sufficient by themselves, and formulates necessary and sufficient com…
This note studies the numerical stability of the Ritz method for solving equations with positive definite operators in Hilbert spaces, focusing on how the choice of coordinate system affects the behavior of the coefficients as the number of terms increases. It reviews reliable coordinate systems, re…
This note generalizes Hopf’s classification theorem for maps from n-dimensional polyhedra to the n-sphere to the setting of uniformly continuous mappings of uniform n-dimensional triangulations. It introduces uniform chains, uniform homology, and the uniform group, then uses simplicial approximation…
This paper studies the index of boundary value problems for systems of harmonic functions in a three dimensional convex domain with elliptic first order boundary operators. It associates the problem with elliptic first order systems on the boundary surface, defines a characteristic through a bundle …
The paper addresses the isomorphism problem for finitely defined structures by relating them to free extensions of finite structuroids. It defines irreducible tabular systems of relations, finitely free extensions, bases of finite structuroids, and removable elements, then proves that every finite s…
This paper extends the notion of the maximal correlation coefficient from two random variables to multiple correlation among random variables with a joint density. It defines maximal correlation between random vectors formed from nonintersecting subspaces through an extremal bilinear functional, rel…
This note studies the limiting term and filtration structure of the Adams spectral sequence modulo a fixed prime. It introduces p-spaces and p-systems, proves the existence and uniqueness, up to singular homotopy type, of a maximal p-system, and uses this construction to define a natural filtration …
The paper extends the Fourier transform in the weighted Hilbert space \(L_\varphi^2\), where the scalar product is defined with a positive weight \(\varphi\), under weaker assumptions than earlier work of Akhiezer. For weights extending to entire functions of zero order and class \(A\), it proves an…
This paper studies the asymptotic behavior, as the step parameter tends to zero, of a functional of a two-dimensional random walk defined by the expected value of a boundary function at first exit into a half-plane. Under assumptions on uniqueness, finite moments, and an expansion of the jump densit…
This note studies upper bounds for the number of zeros of the Riemann zeta function in rectangles near the line sigma equals 1, expressed through the exponent kappa of Delta in standard zero density estimates. It applies recent estimates of I. M. Vinogradov for trigonometric sums, together with auxi…
The paper introduces maximal and intrinsic correlation functions for stationary real processes and applies them to stationary Markov processes whose two-dimensional densities are symmetric and square-integrable in a specified sense. It shows that such a density defines a continuous Markov process pr…
This paper studies the stability of periodic motions in autonomous differential systems and in a special class of nonlinear canonical systems. It extends a theorem of Andronov and Witt to families of periodic solutions whose period depends on parameters, using variational equations, characteristic r…
This paper studies how coefficients of convergent orthogonal series behave when the underlying orthonormal system is complete, and asks whether complete systems can tend to zero almost everywhere. It develops a construction lemma for complete systems assembled from systems on disjoint subsets, then …
This note develops a variant of the theory of coalition games in which coalitions have nondivisible payoffs and mixed behavior is represented through consistent families of measures and systems of random transitions. It introduces internal consistent measures, Markovian extensions, realizable transi…
The paper studies ranges of logarithmic functionals involving values and derivatives of bounded univalent functions in the unit disk. Using Kufarev’s method, it derives parametric equations for the boundaries of these ranges in three settings: functions with prescribed modulus at a fixed point, the …
This note studies resolvent estimates for a class of singular elliptic matrix differential operators on Euclidean space, with strongly negative principal symbol and a confining matrix potential whose eigenvalues tend to negative infinity at a prescribed rate. Using estimates for the Green function o…
This note proves a growth theorem for entire functions satisfying a prescribed lower bound that deteriorates near the real axis through a power of the cosecant of the argument. The proof first derives a corresponding upper estimate using a transformed function in the half-plane, Carleman’s formula, …
This paper studies optimal approximation of periodic functions of several variables by trigonometric polynomials, emphasizing that in the multivariable case the ordering of Fourier modes should be chosen according to the function class rather than fixed in advance. For classes defined by quadratic b…
This paper establishes local large deviation theorems for sums of independent random variables beyond the classical Cramér exponential moment condition. Using methods associated with Linnik, it gives uniform asymptotic formulas for the densities, and for lattice probabilities, of normalized sums in …
This note studies the asymptotic behavior of solutions to linear difference equations with square-summable initial data and coefficients. Using the Fourier representation of sequences, it gives a stability criterion in terms of the multiplier and derives an asymptotic approximation when the multipli…
This paper studies the epsilon entropy of several classes of complex functions under smoothness and growth restrictions. For analytic functions in a bounded simply connected domain, entropy estimates are obtained in terms of the boundary regularity and Hölder smoothness of derivatives, using Kolmogo…
The paper studies a nonlinear Riemann type boundary value problem for analytic functions, in which the nth power of the interior boundary value is related linearly to the exterior boundary value and a given Hölder continuous term. By substituting the nth power of the interior function, the problem i…
This paper studies when the coordinate values of a multidimensional stationary random sequence form a basis in the Hilbert space generated by the process, with emphasis on representations relevant to linear prediction. Using the spectral density matrix, it gives necessary and sufficient conditions f…
This paper formulates a general interpolation theorem for operators acting between Banach spaces organized into analytic scales, defined through parameter-dependent analytic operator families and logarithmically convex norms. It develops examples including scales generated by fractional powers of po…
The paper studies uniform approximation of summable periodic functions whose generalized Weyl derivatives belong to bounded classes by linear polynomial means, with particular emphasis on de la Vallée-Poussin sums. It derives an integral representation for the approximation error associated with a g…
The paper studies a boundary value problem for a heat type equation in a plane layer with axial symmetry and a radial convective term, emphasizing the case in which the axis is a source of fluid and the temperature at the axis can be prescribed. Using Hankel transform methods and Bessel functions, i…
This paper applies Vinogradov’s method of trigonometric sums, in Chudakov’s form, to binary problems in prime number theory, especially the Hardy and Littlewood conjecture for prime pairs separated by a fixed even difference and the analogous problem of representing even integers as sums of two prim…
This note studies homogeneous and nonhomogeneous Riemann boundary value problems on closed Riemann surfaces, together with conjugate problems formulated for analytic differentials. Using the Riemann Roch theorem, it gives dimension counts for the solution space in terms of the index and genus, estab…
This paper develops a conformal differential geometry of two-parameter families of spheres in three-dimensional conformal space using Cartan moving frames and exterior forms. It identifies fundamental geometric objects of first, second, and third order, proves that the third-order object determines …
This note refines earlier results on multidimensional singular integral equations in the space Lp by replacing a restrictive Hölder-type condition on coefficients and characteristics with Sobolev-type smoothness assumptions on the angular symbol. It establishes boundedness and norm-convergent spheri…
The paper develops exact and high-order homogeneous three-point conservative difference schemes for one-dimensional boundary-value problems of the first, second, and third kinds for a second-order linear differential equation with variable coefficients. The construction uses local template functions…
This note studies when a subsemigroup of a free semigroup is itself free, allowing free semigroups that include both group-like generators with formal inverses and purely semigroup generators. After establishing basic properties concerning kernels, pure parts, bases, and cancellation, it introduces …
This paper studies approximation of uniformly almost-periodic functions whose Fourier exponents accumulate at zero, focusing on estimates obtained by deleting or approximating the low-frequency part of the spectrum. It introduces approximation quantities tied to a spectral cutoff and proves bounds i…
This paper develops implicit function theorems for analytic mappings between complex Banach spaces, using the representation of such mappings by homogeneous power series and a majorant series method. After establishing comparison lemmas for analytic functions and scalar majorants, it proves existenc…
This paper studies Bernstein type polynomials of two variables for continuous functions on the standard triangle and relates them to multinomial probabilities. It recalls uniform approximation and derivative convergence estimates, then develops recurrence relations for associated moment polynomials …
This note studies large deviation behavior for normalized sums of independent identically distributed random variables beyond the range covered by the classical central limit theorem. It defines zones of normal convergence and gives necessary and sufficient conditions, in terms of exponential moment…
This note establishes inequalities for differentiable functions of several variables in Sobolev spaces of integral and fractional order on domains satisfying a geometric sector condition. Using integral representations analogous to Sobolev’s identity, it derives pointwise, Hölder, and integral estim…
This paper studies spectral properties of operators associated with elliptic and hyperbolic fourth order equations in a four dimensional ball, formulated in Hilbert spaces defined by boundary compatible Sobolev type scalar products. It proves that the operator obtained from the inverse biharmonic op…
This paper proves a central limit theorem for a broad class of observables under geodesic flows on the space of line elements of compact manifolds of constant negative curvature. It formulates sufficient conditions involving local regularity, linear growth of variance, and a uniform integrability co…
The paper studies the identity problem for finitely presented associative systems whose defining relations have a special uniform form, in particular systems generated by relations of fixed word length. It proves that if the identity problem is decidable for all groups with a given number of nontriv…
The paper extends Temlyakov’s integral representation theory for analytic functions in bicircular domains of two complex variables to cases where parts of the boundary may be analytic hypersurfaces and the Levi determinant vanishes on boundary portions. By redefining the radius functions with condit…
This paper studies a singular integral equation on a closed Lyapunov contour whose Cauchy kernel contains a shift mapping the contour onto itself with reversed orientation. Under Carleman-type conditions on the shift and coefficients, the equation is transformed via the Sokhotski formulas into a bou…
This note studies when finitely presented semigroups with cancellation can be represented inside more general associative systems or groups. It gives an explicit embedding construction showing that every finitely presented semigroup with two-sided cancellation embeds in a finitely presented associat…
The paper extends topological methods in complex function theory to analytic functions whose real parts may be multivalued because of finite power-logarithmic singularities in finite or infinite multiply connected domains. It defines admissible cuts that make the relevant branches single-valued and …
This note studies regular solutions of the differential system describing stationary axisymmetric incompressible, irrotational flow in cylindrical coordinates, whose complex form has coefficients singular on the axis. Using Vekua’s continuation method, the problem is reduced to a complex equation re…
This note studies multidimensional moment problems through positive-definite functionals on nuclear algebras of sequences and formal power series. Using an integral representation scheme for nuclear spaces, it proves representation theorems by positive measures on the real line, Euclidean spaces, an…
The paper studies the asymptotic behavior near a higher order singular point for analytic multidimensional systems of ordinary differential equations whose right hand sides have no constant or linear terms. Using a supporting hyperplane construction for the exponent sets, it extracts a quasihomogene…
This note studies dimension theory for locally bicompact topological groups, extending known results for bicompact groups. It proves first that every locally bicompact group is strongly paracompact, by exhibiting an open and closed subgroup as a countable union of bicompact sets and applying Smirnov…
This paper studies the persistence of invariant toroidal surfaces for a two-dimensional nonautonomous system of differential equations with periodic time dependence under a small analytic perturbation. It treats the case in which the unperturbed invariant torus has rational rotation number but does …
