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 general linear systems of partial differential equations with constant coefficients, including underdetermined and overdetermined cases not covered by square nonsingular matrices. Using syzygy chains over the polynomial ring of differential operators and associated Ext modules, it …
This paper proves undecidability results for the elementary theories of the classes of finite symmetric groups, finite alternating groups, and finite simple groups. The argument reduces from the theory of two equivalence relations, using an effective translation of formulas into the group signature …
The paper studies uniqueness for systems of nonlinear integral equations and points out limitations of standard majorant estimates based on a single Banach norm, especially their inability to reflect componentwise behavior and the role of the free term. It develops refined comparison criteria using …
The paper studies duality for covariant functors on the category of sets with a distinguished point, using the associated internal Hom and smash product constructions. It develops formulas for duals of functors built from products, bouquets, and specified unions, and analyzes a class of subfunctors …
This paper studies convergence of approximate eigenvectors produced by a projection method for holomorphic operator pencils between Hilbert spaces. Given projection-complete finite-dimensional subspaces, it first proves that the component of a normalized approximate eigenvector orthogonal to the eig…
This note studies a special oblique derivative problem for harmonic functions in a three-dimensional domain, focusing on the unit ball with boundary vector field proportional to the shifted radius vector. The boundary condition is reduced to a first-order linear equation for a harmonic function, all…
The paper studies existence and uniqueness for systems of Hammerstein integral equations beyond the commonly treated cases of positive, quasi-positive, or quasi-negative kernels. It establishes sufficient monotonicity and convexity-type conditions for nonlinear potential operators in Orlicz and Hilb…
This paper proves solvability of the first boundary-value problem for a class of degenerate quasilinear elliptic systems of order 2m. The argument develops integral inequalities and compact embedding results adapted to functions whose highest derivatives need not be square-summable, but for which de…
This paper studies multidimensional linear differential equations with constant coefficients in finite-dimensional real or complex spaces, treating the Cauchy problem, conjugate equations, and associated operator equations. It gives a necessary and sufficient commutativity condition for solvability …
The paper develops an operator-ring approach to one-sided invertibility for functions of several commuting isometric operators, extending earlier results for a single operator. It introduces decomposing normed rings of functions on the multidimensional torus and proves factorization criteria that de…
This paper studies an inhomogeneous Riemann boundary value problem on a ray for coefficients whose argument has infinite index, under Hölder-type assumptions and vanishing conditions on the inhomogeneous term. For the case of positive infinite index, the problem is solved in classes of functions of …
The paper studies when a finite group has only finitely many indecomposable matrix representations over rings of integers in quadratic number fields and quadratic extensions of p-adic fields. Using reductions to Sylow p-subgroups and modules over cyclotomic extensions, it gives explicit classificati…
This paper studies the dependence on a small parameter of the fundamental matrix solution for a Petrovskii parabolic system of order 2p with matrix coefficients. Under boundedness, Hölder continuity in the spatial variables, and suitable continuity assumptions in time, it proves estimates showing th…
The paper studies the asymptotic behavior, as a small positive parameter tends to zero, of solutions to a Cauchy problem for a second order linear ordinary differential equation whose limiting first order equation is singular at the initial point. It constructs the expansion by dividing the domain i…
This note studies analytic matrix functions in the unit disk whose entries belong to standard scalar growth classes, including A, D, Hardy type classes, bounded functions, and contractive bounded functions. Using Potapov’s multiplicative integral methods and Blaschke type products, it gives parametr…
This paper studies density of the initial manifold for the abstract Cauchy problem generated by a linear operator in a Banach space, that is, the set of initial vectors for which a strong smooth solution exists. It first gives a Hilbert space obstruction showing that, for certain symmetric operators…
This paper extends finite difference methods to boundary value problems for second order elliptic equations on finite Riemann surfaces represented as bounded multi-sheeted domains. It constructs mesh equations for ordinary points, boundary nodes, and branch points, using local parameters near ramifi…
The paper studies linear superpositions of smooth functions and their limitations in representing continuous functions of several real variables. It introduces a notion of dimensionality for function spaces based on distinguishability at small scales, showing that dense classes such as analytic func…
This paper studies uniform approximation of an arbitrary continuous function on the unit interval by Bernstein polynomials, with the error expressed in terms of the function’s modulus of continuity. Starting from earlier constants due to Popoviciu and Li Wen-ching, it estimates the asymptotic behavi…
The paper studies finite homomorphisms of the natural numbers, that is, completely multiplicative functions with finitely many complex values, whose summatory functions have the form S(x) = alpha x + O(1). It addresses the principal case of the character problem by proving that every principal gener…
This note studies uniform approximation of superpositions generated by one continuous functional by superpositions generated by another, within classes of bounded real functions satisfying a Lipschitz, or Hölder with constant one, condition. It gives exact best approximation bounds for linear functi…
This paper addresses multidimensional problems in the calculus of variations in the large, focusing on the construction of shortening deformations without relying on local uniqueness. It proposes deformations along parabolic steepest descent trajectories for the variational functional and uses stabi…
The paper studies a Carleman-type boundary value problem for single-valued analytic functions in a finite multiply connected domain with Lyapunov boundary, where the boundary correspondence is an involutive orientation-preserving homeomorphism on each component. It develops integral representations …
The paper studies an inverse problem for the metaharmonic potential: determining a body of unit density from a prescribed exterior metaharmonic function close to the potential of a given star-shaped body. Under smoothness and smallness assumptions, the boundary of the unknown body is represented as …
The paper develops a method of basis expansions for linear differential equations with singular coefficients in which the unknown solution is represented as a series of basis functions satisfying a related equation and a recurrence relation in the parameter. A recurrence formula is derived for the c…
This paper studies conditions under which a one-dimensional stationary Feller Markov process on an interval is reversible, assuming the existence of a transition density and governing backward and forward diffusion equations. Using Yaglom’s reversibility theorem together with Feller’s boundary class…
This paper presents a simplified method for proving Hölder continuity and obtaining Hölder norm estimates for solutions and derivatives of linear and quasilinear elliptic and parabolic equations. Building on earlier class-based estimates and incorporating Moser’s logarithmic subsolution idea, the au…
The paper studies singular integral equations with continuous and piecewise continuous matrix symbols, extending a previously developed local method for operators on Lebesgue spaces. It defines generalized singular integrals through local equivalence to shift-invariant homogeneous operators and char…
This paper studies hypoellipticity for systems of linear differential equations with infinitely differentiable variable coefficients, extending known criteria beyond scalar formally hypoelliptic operators and previously treated special systems such as elliptic, parabolic, and quasi-elliptic cases. A…
This note studies Lie algebras of arbitrary dimension over fields of characteristic zero through elements whose one-dimensional subalgebras are subinvariant or attainable in normal series. It introduces the corresponding B-radical and SB-radical, using results on nilderivations, nil elements, locall…
The paper derives boundary growth estimates in weighted L2 norms for generalized solutions of elliptic-type equations of arbitrary order with variable coefficients in a bounded smooth domain. It treats the equation as the Euler equation of a Dirichlet integral whose coefficients may degenerate at th…
This note studies completeness of eigenvectors and associated vectors for non-self-adjoint second order differential equations on the real line with complex weight functions. The equations are transformed by means of the positive self-adjoint operator associated with \(-d^2/dx^2+q(x)\), reducing the…
The paper studies uniform approximation of continuous functions on compact subsets of Euclidean space by functions harmonic in neighborhoods of the compact set. Building on the Keldysh, Brelot, and Deny capacity criterion, it reformulates the approximation condition through local Newtonian capacity …
The paper addresses the possible lower orders of entire functions of finite order that possess a finite deficient value, a question arising in Nevanlinna theory and related to the Edrei and Fuchs conjecture. It constructs, for arbitrary parameters satisfying one half less than the lower order and th…
This note proves a topological classification result for systems of ordinary differential equations in neighborhoods of closed trajectories, analogous to Grobman’s theorem for singular points. Using local coordinates near a periodic orbit, the system is reduced to a periodic nonautonomous equation t…
The paper develops a one-parameter class of iterative methods for solving nonlinear operator equations in normed linear spaces, using first and second order divided differences rather than derivatives. Starting from a Newton interpolation formula and replacing nonlinear terms by a chord-method appro…
The paper studies optimal distribution of a time-dependent flow among several directions when the accumulated quantities and distribution fractions may be subject to bounds. It introduces the notion of a distributor that is optimal not only for a fixed terminal time but throughout an interval, and d…
This paper studies finitely presented groups whose defining relators satisfy specified small cancellation conditions, including restrictions on overlap and triangular cancellation. It gives a Dehn type reduction algorithm for the word problem and proves that a nonempty irreducible word representing …
This paper studies completeness of the linear span of finite-dimensional invariant subspaces associated with the nonselfadjoint singular second-order differential equation with a real weight acting in \(L^2\) on the whole real line. The argument reduces the problem for the operator pair \((L,Q)\) to…
This paper studies free decompositions in the intersection of two primitive classes of universal algebras whose operation sets are disjoint or meet only in a nullary zero operation subject to compatible zero identities. Under stated hypotheses ensuring good behavior of free products, subalgebras, an…
This paper establishes a formal normal form for systems of ordinary differential equations near a singular point, extending classical results of Poincaré, Picard, Dulac, and Sternberg. For a formal system with zero constant term, it proves that an invertible formal change of variables can put the li…
This paper studies linear continuous operators between spaces of measurable functions, focusing on compactness in measure and related notions of improving, co-improving, Ando property, and regularity. It defines these properties and proves several structural results, including that operators from Lp…
The paper studies generalized solvable groups through normal systems associated with varieties of groups and applies these constructions to free groups and group rings. It introduces normal varieties and proves that, for a free group modulo a nontrivial normal divisor, certain normal systems with fa…
This paper studies Dirichlet and Neumann boundary-value problems for a class of quasilinear elliptic equations arising in the stationary theory of thermal explosion. Using lower and upper solutions and convergence of associated parabolic problems, it establishes a solvability criterion for the Neuma…
This paper studies a generalized boundary value problem for the Tricomi equation in a mixed elliptic hyperbolic domain, allowing first kind discontinuities of the unknown function and its normal derivative across the parabolic degeneration line. The problem is formulated with gluing conditions invol…
This paper studies the relation between finitely projective and finitely reduction classes of models, addressing whether every finitely reduction class is finitely projective. Building on Mal’tsev’s result and a refinement showing that the infinite part of any finitely reduction class lies inside a …
