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 the homogeneous Riemann boundary value problem for analytic functions on a closed Riemann surface of genus rho, with a nonvanishing Hölder coefficient on a finite system of smooth closed curves. Building on a prior reduction of solvability to an Abelian congruence and to conditions…
The paper studies the limiting amplitude principle for a class of half-line boundary-value problems for linear evolution equations with constant-coefficient spatial operator of even order and harmonic forcing. It analyzes the associated ordinary differential equation with complex spectral parameter,…
This paper studies generalized solutions of first order differential equations in a Banach space generated by strongly positive operators, extending earlier Hilbert space results. It establishes coercivity for equations with operators sharing a common domain, then treats nonautonomous equations with…
The paper develops a method for proving completeness of systems of eigen and associated elements for non-self-adjoint compact operator functions depending rationally, and in some cases meromorphically, on a spectral parameter. It first refines a Keldysh-type spectral result by showing that, near a p…
This paper studies the emergence of periodic motions in a parameter-dependent dynamical system when, at the critical parameter value, a trajectory leaves and returns to a simple saddle equilibrium, forming a homoclinic loop. The authors construct a Poincare-type return mapping by combining the local…
The paper studies the asymptotic behavior of orthonormal polynomials at interior zeros of weight functions, with emphasis on one-sided algebraic singularities where the order of vanishing differs across the point or where the polynomial itself vanishes there for infinitely many degrees. Using differ…
This paper formulates a general linear boundary value problem for an operator between separable linear topological spaces in terms of maximal subspaces complementary to the null space and the associated projection onto boundary data. It develops representation formulas for solutions, criteria for pr…
The paper studies mapping properties of fractional powers of positive linear operators in scales of Lebesgue, Lorentz, and Marcinkiewicz spaces, using the notion of an operator’s characteristic set in the unit square of integrability indices. It proves general theorems showing how the characteristic…
This note develops the constructive theory of the Riemann integral for constructive functions on the unit segment. It compares an epsilon-delta style definition of constructive Riemann integrability with a sequential definition based on regularly contracting sequences of integral sums, proving their…
This paper studies the boundary behavior of functions represented by Temlyakov integrals of the first kind over domains of type A in two complex variables, focusing on approach to the skeleton points from the domain where the integral is not analytic. Under specified Lipschitz and Fourier-series con…
This paper studies alternative quasigroups equipped with a finite invariant measure, including compact groups with Haar measure and finite quasigroups with normalized counting measure. It proves a covering or translation property: if a measurable subset has measure greater than \((k-1)/k\), then for…
The paper studies continual integration of analytic functionals on the space of continuous paths starting at zero with respect to a sign-alternating distribution associated with a higher-order heat-type equation. It defines the distribution through finite-dimensional quasi-intervals using the Green …
The paper studies inverse spectral problems for strings in the class associated with nondecreasing mass functions on intervals with a possible singular endpoint and a boundary condition at the singular left end. It defines spectral, orthogonal, and positive spectral functions and formulates uniquene…
The paper studies an autonomous system of nonlinear differential equations with a small parameter, including a two-dimensional oscillatory component coupled to slow variables, and develops an effective transformation suited to averaging near a particular solution. After shifting to amplitude and pha…
This paper develops modifications of the modulus of smoothness for periodic functions and Hilbert space elements, emphasizing moduli of primitives and an integrated \(\widetilde{L}\)-modulus. It derives criteria and estimates for absolute convergence of Fourier series in terms of best approximations…
The paper develops an abstract theory of quadratic relaxation processes for solving a linear equation with a positive definite bounded operator in a real Hilbert space, viewed equivalently as minimization of a quadratic potential. It introduces relaxation multipliers, relaxation angles, residual dis…
This paper derives a new coefficient estimate for normalized univalent functions in the unit disk. Using functions associated with the exterior univalent class and a logarithmic expansion introduced in earlier work, it relates the coefficients of a function in the class to partial sums generated by …
This paper solves a quasianalyticity problem for functions analytic in the unit disk and infinitely differentiable up to the boundary, together with the corresponding class of boundary functions. For derivative bounds governed by a nondecreasing positive sequence, it proves that quasianalyticity is …
This paper introduces the notion of an \((\omega,p)\)-mapping, a continuous onto map controlled by a given cover through fibers that admit subfamilies with specified finiteness or countability properties. A main lemma shows that such mappings onto paracompact or strongly paracompact spaces yield loc…
The paper studies whether energy-type a priori estimates for the one-dimensional wave equation with variable leading coefficient can be extended to the norms of \(C\), \(L_p\), and \(W_p^1\) for \(1 \le p < 2\), with constants depending only on uniform ellipticity bounds. Using periodic reductions, …
The paper studies rational approximation on compact subsets of the complex plane in relation to zero analytic capacity, focusing on whether Lp approximation by rational functions with poles off the set and with sums of coefficients tending to zero characterizes sets of zero analytic capacity. It sho…
The paper addresses B. V. Gnedenko’s problem of characterizing possible limiting distributions for normalized sums of independent random variables when only a fixed number r of distinct summand distributions occurs. It first gives an explicit example for r = 3 showing that the class of limits is bro…
The paper addresses Urysohn’s problem of whether there exists a continuum whose space under Mazurkiewicz’s relative metric is not zero-dimensional yet has no nondegenerate connected subsets. It constructs a one-dimensional continuum by an inductive self-similar process inside a tetrahedron, using pr…
This item is a compiled bibliography of journal articles published in 1965 on differential equations and related areas of analysis, numerical methods, control theory, and mathematical physics. The entries list authors, article titles, publication venues, issue information, page ranges when available…
This note studies error functionals for cubature formulas on a lattice whose deviations from the regular interior rule are confined to a boundary layer of fixed thickness. It defines regular boundary layers, proves structural lemmas showing that differences of such functionals reduce to zero point f…
This note studies how the zeros of even and odd trigonometric polynomials are determined by the zeros of associated algebraic polynomials. It proves interlacing and counting theorems for cosine and sine polynomials under hypotheses such as real interlacing algebraic roots or containment of algebraic…
This note extends Skornyakov’s theory of free T-extensions and free T-sums from linear algebras to Kurosh multioperator algebras over a field, including nonassociative cases. It defines T-homomorphisms and multioperator fields with divisions, constructs free T-extensions by adjoining solutions to un…
This note generalizes to dimensions greater than two a property of solutions of second order elliptic equations previously established for two independent variables. For elliptic equations with analytic coefficients, it proves that a function of class C1 which is a regular solution in a neighborhood…
The paper develops a capacity-based method for studying extremal properties of functions regular in multiply connected planar domains, extending symmetrization principles for annuli and related results of Hayman and Schiffer. It defines potential functions, admissibility, and condenser-type capacity…
The paper studies how solutions of mixed boundary value problems for the equations of small oscillations of a rotating fluid depend on perturbations of the boundary of the spatial domain. By reducing the pressure to an evolution equation and mapping perturbed planar and spatial domains onto a fixed …
This bibliographic notice surveys recently published books and collected volumes from 1963 to 1964 in differential equations, mathematical physics, integral equations, boundary value problems, stability theory, numerical methods, and related areas of analysis. The entries include textbooks for unive…
This note addresses finite axiomatizability of identities for finite algebras, following earlier results showing that all two element algebras have finite complete identity systems while certain larger finite algebras do not. It constructs a three element algebra with a single binary operation and p…
This paper analyzes two linearly coupled oscillators whose frequencies and coupling vary slowly in time, focusing on how adiabatic invariants behave when complex resonance points are encountered. Using an asymptotic expansion for the associated fourth-order system and a contour matching procedure an…
This note discusses coefficient estimates for bounded holomorphic functions of several complex variables in complete circular domains, comparing earlier results with those of I. A. Aleksandrov and emphasizing cases where the relevant extremal quantities can be effectively computed. It identifies an …
The paper studies Cauchy problems for a degenerate hyperbolic equation and for its iterated form, with initial data prescribed on the line of degeneration. Under specified smoothness and weighted continuity assumptions on the coefficients, right hand side, and initial functions, it proves existence …
This editorial introduces the new All-Union monthly journal Differential Equations, established in Minsk under the Academy of Sciences of the BSSR beginning in 1965. It argues for the importance of differential and related integral equations as central tools in physical, technical, and applied scien…
This paper studies when metrizability is preserved under quotient mappings from metric spaces, focusing on mappings satisfying a separation condition later described as a pi mapping. It proves that a paracompact p-space which is a quotient pi-image of a metric space is metrizable, first establishing…
The paper studies functionally invariant solutions of second-order elliptic equations in three independent variables with prescribed positive symmetric principal part. Working in Cartesian coordinates and avoiding the earlier geometric formulation through line congruences, it derives necessary and s…
