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 studies a nonlinear free boundary problem for a harmonic function in a doubly connected domain inside the unit disk, with prescribed constant boundary values and prescribed gradient magnitude on the unknown inner boundary. Using conformal mapping to an annulus, the problem is reformulated …
This note outlines a mathematically rigorous proof of phase transition for the two-dimensional and three-dimensional Ising models at low temperature and intermediate density, expressed through an explicit sufficient condition involving a function Q(T). The argument replaces analytic methods with a q…
This note studies coefficient-free equations in free groups, defined as equations in which each unknown or its inverse occurs and no coefficients from the ambient group are used. It proves that every solution of a normal coefficient-free equation in n unknowns over a free group of rank at least n is…
The paper studies functors on categories of Banach spaces generated by KB-lineals. It defines a natural crossnorm on the tensor product of a KB-lineal E with a Banach space X, forming a functor Phi_E, and shows that this construction includes previously studied functors associated with minimal norme…
This paper studies lower estimates for entire functions of refined finite order whose zeros lie in an angle and approach the positive real axis. It gives a necessary and sufficient condition, expressed through an averaged local counting function for zeros, for the normalized lower limit of the logar…
The paper studies finite and infinite Markov systems and their relation to Chebyshev systems, focusing on extension problems for such function systems and on continuation beyond an interval. It proves that, after suitable normalization and triangular linear transformation, every right-continuous Mar…
The paper studies general mixed initial boundary value problems in a straight cylinder for multidimensional hyperbolic integro-differential equations of arbitrary order with analytic coefficients. It formulates a decomposition of the lateral boundary according to the signs of the characteristic root…
This note studies Phragmen Lindelof type growth estimates and uniqueness classes for solutions of uniformly elliptic second order linear equations in unbounded domains, with zero boundary values. Replacing earlier volume based conditions by conditions expressed through capacity, it derives lower bou…
This note proves that any bundle of locally finite semigroups is locally finite. The argument develops structural lemmas for commutative and matrix bundles, formulates closure conditions for abstract semigroup properties, and then verifies the needed conditions for local finiteness using results on …
The paper presents a geometric construction of infinitely many Fedorov groups in three-dimensional Lobachevsky space, avoiding the arithmetic methods commonly used for such examples. Starting from regular partitions of a Lobachevsky plane into regular n-gons with 3, 4, or 5 polygons at each vertex, …
This note establishes Lyapunov type regularity theorems for heat potentials associated with time dependent surfaces in parabolic potential theory. It formulates anisotropic Hölder smoothness conditions on the boundary surface and on the density under which the heat potential of a simple layer, the h…
This note studies infinite order differential operators built from Gel’fond and Leont’ev generalized derivatives associated with an entire function of finite order and nonzero finite type, extending Sikkema’s operator with ordinary derivatives. It gives necessary and sufficient conditions for such a…
The paper studies extremal problems for conformal mappings of finitely connected planar domains onto multi-sheeted Riemann surfaces with rectilinear slits, allowing prescribed pole and logarithmic singularities. It constructs uniquely determined auxiliary functions satisfying mixed boundary conditio…
This paper studies Poincare polynomials of compact homogeneous spaces using invariant polynomial algebras of compact Lie groups and their Weyl groups. It first identifies generators for the invariant polynomial algebras of exceptional simple Lie algebras in terms of sums of powers of weights of the …
This paper introduces and studies a class of differentiable functions on n-dimensional Euclidean space whose generalized derivatives up to prescribed orders have finite mixed Lebesgue norms and whose higher derivatives satisfy mixed norm multiple Hölder conditions. It defines the space with a norm f…
This note studies the removability of level sets for solutions of second order uniformly elliptic equations in the plane with Hölder continuous coefficients. It proves first that a continuously differentiable function that is harmonic near every point where it is nonzero must be harmonic throughout …
This paper studies sufficient conditions for absolute convergence of Fourier series of periodic functions in terms of symmetric finite differences and related integral moduli of smoothness. It proves coefficient tail estimates for \(0<m\leq 2\), bounding sums of powers of Fourier coefficients by qua…
This paper examines the arbitrariness in applying the WKB method to Sturm-Liouville problems and argues that the transformation variable should be chosen so that asymptotic solutions have the correct behavior at singular points. By selecting a transformation that maps such points to infinity, the au…
This note studies how far classical results of Zygmund on lacunary trigonometric series can be extended when intervals or sets of positive measure are replaced by exceptional sets, especially first category perfect sets of measure zero. It introduces and uses \(M\)-\(\omega(n)\)-sets, defined throug…
This note revisits singular integral equations with a finite cyclic shift on Lyapunov contours, correcting an inaccuracy in an earlier proof concerning the adjoint problem and the index formula. The author proves the solvability criterion by relating the shifted equation and its adjoint to an associ…
The paper studies fluctuations in the distribution of fractional parts on the unit interval through bounds relating local concentration in short half-intervals to trigonometric sums. It generalizes a theorem of G. A. Freiman by proving that, if no interval of length 1/2m and no pair of intervals of …
The paper studies linear isometries of nondegenerate vector spaces with symmetric or skew-symmetric bilinear metrics over an arbitrary field of characteristic not equal to 2. Using elementary divisors of the characteristic polynomial, it classifies invariant components into types according to recipr…
The paper studies complete rational trigonometric sums modulo a prime for sparse polynomials such as \(Ax^n+Bx\) and \(ax^n+bx^k\), in ranges where Weil’s general bound may become trivial. Using invariance under multiplication by roots of unity modulo \(p\), together with Cauchy’s inequality and kno…
This paper studies decision problems for the nth nilpotent product of groups, extending known results for direct and free products. It proves that the embedding problem is undecidable in the nth nilpotent product of two free groups of rank two, while a weak embedding problem is decidable under hypot…
This paper studies sets in metric spaces that are effectively different from all sets generated by a given delta-s operation, using Novikov’s notion of effective difference. For operations satisfying a chain condition, it proves that such a set contains, inside a perfect compact subset, an absolute …
The paper introduces an averaged symmetric-difference quantity, called the L-modulus of smoothness, and applies it to estimates of Fourier coefficients of periodic functions. Using Parseval’s equality and related arguments, it derives bounds for weighted sums and individual Fourier coefficients in t…
This note introduces a function-level notion of quasianalyticity in the space of integrable functions on the real line, defined through the behavior of continuous linear functionals on translates of a single function. It proves that any function satisfying this definition is infinitely differentiabl…
The paper develops a relaxation method for finding a solution, or a nonnegative solution, of a consistent finite system of inequalities whose left hand sides are smooth convex functions on Euclidean space. The argument is based on Fejér monotonicity with respect to convex sets and on supporting half…
The paper introduces spaces and subspaces of universal, almost universal, and a-universal disposition for classes of Banach spaces, especially finite-dimensional and separable spaces. Using an extension construction for isomorphisms between embedded pairs of Banach spaces, together with compactness …
The paper develops a theory of singular integral operators on nondiscrete commutative locally compact groups, defining them through Fourier multipliers with homogeneous degree zero symbols and establishing analogues of classical Mikhlin and Gohberg results. It proves compactness of commutators with …
This note introduces commutative systems, or k-systems, consisting of two mutually centralizing systems of transformations on a set, as a generalization of semigroups with left and right translations. It characterizes when such systems arise from semigroups or groups, develops analogues of Green-typ…
The paper studies the spectral matrix of a self-adjoint fourth-order differential operator on the half-axis with an integrable nonnegative potential and two boundary conditions at the origin. The argument first treats the corresponding problem on a finite interval, constructs asymptotic fundamental …
The paper proves a general estimate for the uniform deviation between the distribution of a normalized sum of independent, not necessarily identically distributed, mean zero random variables and the standard normal distribution. Using a truncation argument and Esseen’s Berry, Esseen bound for variab…
This paper studies the sequential order topology on the Boolean ring of all subsets of a set and records its basic topological and algebraic properties. It shows that translations are homeomorphisms, the space is Hausdorff and totally disconnected, is noncompact for uncountable underlying sets, has …
This paper studies the existence of almost-periodic solutions for differential equations in Hilbert space. It formulates multiplier problems for equations with commuting self-adjoint operators, proves a solvability criterion for the bounded strong case, and notes a special hyperbolic case in which a…
This note studies a Riemann, Hilbert type boundary value problem for a holomorphic vector in a three dimensional domain, with two real linear boundary conditions on the vector components. It first derives an integral representation of such vectors using a Cauchy type integral and the Green function …
This paper studies a three-dimensional analytic differential system with a saddle-focus equilibrium whose one-dimensional separatrix returns to the equilibrium, forming a homoclinic trajectory. Using local coordinates near the saddle-focus and a Poincare point transformation decomposed into a local …
The paper studies metric properties of homeomorphic mappings in three-dimensional domains belonging to the class BL^{3/2}, with bounded Dirichlet integral for the mapping and, in the principal class considered, for its inverse. An example shows that an earlier notion of relative distance does not al…
The paper studies dynamic stability problems for systems with distributed parameters that reduce to a linear Hamiltonian equation in a separable Hilbert space with periodic perturbation. It proves a structural representation of the solution operator as a unitary operator plus a completely continuous…
This paper studies exceptional convolution-type integral equations with two kernels and paired equations in spaces of generalized functions, allowing Fourier transforms of the kernels to have real zeros of integral multiplicity, including behavior at infinity. The equations are reduced by Fourier tr…
This note develops a general scheme for boundary value problems in spaces of generalized functions on a smooth closed contour. It treats the Riemann problem, linear conjugation with shift, Carleman type problems, and the Hilbert problem by reducing solvability and representation to corresponding adj…
This paper develops duality principles for the existence problem of periodic solutions of nonlinear systems of higher-order ordinary differential equations with periodic coefficients. It compares the fixed-point formulation given by the shift operator on initial data with fixed-point formulations fo…
This note studies the probability that a random system of n linear equations over Boolean functions has a unique solution, equivalently that its determinant over the two element field equals one. For independent but not necessarily identically distributed Boolean matrix entries with probabilities un…
This paper studies numberings of mathematical objects whose induced equality relation is recursively enumerable, called positive, or whose inequality relation is recursively enumerable, called negative. It develops basic closure and uniqueness properties for computable subnumberings, showing in part…
