SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 47 of 5847 papers in Mathematics
This paper studies linear and nonlinear evolution equations in Hilbert space of the form dx/dt plus A(t)x equals f(t), where A(t) is an unbounded self-adjoint operator depending on time. Under differentiability and boundedness assumptions on fractional powers of A(t), it refines the construction of …
This paper develops a priori estimates for analytic and generalized solutions of the Monge-Ampère equation rt minus s squared equals a positive function of the independent variables, the solution, and its first derivatives. Extending estimates of Bernstein and Pogorelov, it derives bounds for the so…
This note establishes an integral form of the maximum principle for solutions of strongly elliptic second-order systems, since such systems need not satisfy the usual pointwise maximum principle. For a vector solution in a cylinder with zero lateral boundary values, the argument studies the time dep…
This paper studies a mixed boundary and Cauchy problem for the hyperbolic equation \(\psi_{\sigma\sigma}-K(\sigma)\psi_{\theta\theta}=0\), with zero boundary values on two parallel lines after reduction and Cauchy data prescribed on a noncharacteristic curve. The problem is transformed to a strip an…
This note studies a class of operator equations in a Hilbert space whose coefficients depend nonlinearly on a complex parameter and have simple real poles. Under compactness, self-adjointness, bounded trace and norm, and sign assumptions on the finite-dimensional pole terms, the paper develops a spe…
This note studies the perturbation of unbounded self-adjoint linear operators \(H_\varepsilon=H_0+\varepsilon V\) in a Hilbert space, where the perturbing operator may have a narrower domain than \(H_0\). Under positivity, compactness, and an approximation condition, it proves convergence of the dis…
This paper develops a family of arbitrary order iterative approximations for finding a simple root of an algebraic or transcendental equation with an analytic complex function. The method rewrites the equation as a fixed point problem using a polynomial multiplier chosen so that successive derivativ…
This paper proposes a finite difference method for the approximate solution of the Dirichlet problem for Laplace’s equation, with attention to how computational work depends on the amount of boundary data needed to prescribe the solution to a given accuracy. For two-dimensional domains with prescrib…
This paper addresses the construction and recognition of quadrature-free nomograms for equations of the form \(z = F(x,y)\), using Massau determinants for aligned-point nomograms. It derives algebraic procedures for determining the scale functions by comparing derivatives of the original equation wi…
This paper studies regularity for the Dirichlet problem for a uniformly elliptic second order differential equation in a bounded domain with sufficiently smooth boundary. Extending earlier results for Holder continuous data and for square integrable data, it considers right hand sides in \(L_p\) wit…
This paper studies a boundary value problem in a rectangle for a first order hyperbolic system equivalent to the vibrating string equation, with a linear boundary condition prescribed on the entire boundary. For rational side ratio, Sobolev’s method is extended by using closed reflected characterist…
This note introduces strongly minimal surfaces, a class of even-dimensional minimal submanifolds of a Riemannian space defined by special relations between the second fundamental object and the metric tensor. It derives necessary tensorial conditions involving odd mean curvatures, observes that ordi…
This note extends a Chaplygin-type differential inequality theorem to the characteristic Cauchy problem for the hyperbolic equation \(u_{xy}=f(x,y,u,p,q)\), where data for \(u\) are prescribed on the intersecting characteristics \(x=x_0\) and \(y=y_0\). Under continuity, differentiability, and monot…
This paper studies binary error-correcting codes as subsets of the vector space over the field with two elements, with Hamming distance used to characterize correction of a fixed number of errors. It improves a known sufficient condition for constructing \(2^m\) codewords of length \(n=m+k\) and min…
This paper proves the combinatorial invariance of the reduced Pontryagin classes of smooth closed manifolds under homeomorphisms induced by isomorphisms of their \(C^1\)-triangulations, and derives equality of Pontryagin numbers for orientable manifolds with such triangulations. The proof reduces th…
This note generalizes a theorem of M. G. Krein on the growth of meromorphic functions representable as sums of simple fractions with prescribed summability conditions on poles and residues. Removing Krein’s assumption that the function has no zeros, it proves an asymptotic estimate for the Nevanlinn…
This paper studies analytic continuation of principal solutions for a hyperbolic equation with a regular singular line and coefficients expandable in odd powers of the distance to that line. Using majorant principal solutions from a previously solved special case, it establishes existence, uniquenes…
This paper justifies two approximation procedures, the method of moments and a mixed collocation type method, for singular integral equations on the unit circle. It first treats the characteristic equation in Hilbert and related function spaces, using polynomial approximations and associated algebra…
This note studies the first boundary-value problem for quasilinear elliptic equations arising as Euler-Lagrange equations of variational functionals on bounded domains whose boundary may include lower-dimensional manifolds and points. Using Sobolev embedding for \(p>n\), lower semicontinuity, and un…
This paper gives a differential geometric characterization of complex-analytic real surfaces of dimension \(2n\) in Euclidean space \(R_{2N}\). Using the moving-frame formalism and an isometric correspondence with analytic \(n\)-dimensional surfaces in unitary space, it proves that such a surface is…
This note studies the possible rate of approximation of continuous functions by sequences of linear positive operators whose values are algebraic or trigonometric polynomials. It proves that, for algebraic polynomial operators on an interval, the basic test functions 1, t, and t squared cannot all b…
This paper studies singular perturbations of elliptic boundary value problems in which small parameters multiply the highest derivatives and the limiting equation has odd order, including the case of a second-order elliptic equation degenerating into a first-order Cauchy problem. The authors constru…
This paper studies covering area questions for functions regular in an annulus whose logarithmic derivative has winding number at least one around nontrivial contours. It revises an earlier notion of the “star” of the Riemann surface associated with such mappings, giving a construction by nested cut…
The paper studies convergence of a modified Galerkin method for linear boundary-value problems and abstract operator equations under weaker assumptions than earlier treatments requiring a positive definite self-adjoint principal operator. It constructs trial functions satisfying the boundary conditi…
This paper studies the convergence class for expansions of entire functions in polynomial systems biorthogonal to a prescribed sequence of linear functionals. Under asymptotic conditions on the functions defining the functionals and smooth growth assumptions on a scaling sequence, it constructs an a…
This note develops an analogue of Mikusiński’s operational calculus for the operator obtained by applying differentiation to t times differentiation, which is closely related to the Bessel operator after a change of variables in Bessel’s equation. It defines a convolution-type multiplication on a cl…
This note studies spectral expansion for self-adjoint operators on the half-line generated by a system of second-order differential expressions with a summable real symmetric matrix potential and a Hermitian boundary condition at the origin. Using a method of M. A. Naimark, the author constructs asy…
This note generalizes the variational method for solving linear equations in a Hilbert space from positive definite self-adjoint operators to operators representable as a product of a self-adjoint operator and a closed operator. It defines generalized positivity and generalized positive definiteness…
This paper studies a one-parameter class of iterative methods for approximately solving nonlinear operator equations in Banach spaces, encompassing the Chebyshev process, the tangent hyperbolas process, and a related previously proposed method. It formulates convergence theorems for twice differenti…
This paper formulates generalized solutions of Monge-Ampère equations through the geometry of convex surfaces and the prescribed weighted area of their normal images. It defines an R-area measure associated with supporting planes, relates classical twice differentiable solutions to this measure, and…
This paper studies the birational classification of elliptic curves over a field of characteristic not equal to 2 or 3, especially when the field is not algebraically closed. Using Galois descent, automorphisms of a Weierstrass model, crossed homomorphisms, and cohomology, it describes curves with a…
This paper studies a boundary value problem for the hyperbolic equation with coefficient depending on one variable, with data prescribed on a characteristic segment and on two straight lines. The problem is reduced by changes of variables to a normalized equation with a potential term, and its solut…
This paper studies nonlinear oscillations with one degree of freedom governed by a second order equation whose principal restoring force depends slowly on time and whose perturbation is small. Building on earlier formulas for slowly varying amplitudes and periods, it derives an asymptotic representa…
This note extends a theorem of S. M. Lozinskii on summability methods for trigonometric interpolation to expansions in ultraspherical orthogonal polynomials. For ultraspherical polynomials orthonormal on \([-1,1]\) with weight \((1-x^2)^\alpha\), \(-1/2 \leq \alpha \leq 1/2\), it proves that any mul…
This note extends the theory of strictly Markov processes from the time-homogeneous case to nonhomogeneous processes. It formulates two definitions of the strict, or strong, Markov property using stopping times independent of the future and corresponding measurability conditions on transition probab…
This paper presents an approximate method for computing eigenvalues of the Sturm-Liouville problem with Dirichlet boundary conditions by using regularized trace identities for positive powers of the differential operator. The potential is replaced by a finite cosine expansion, and asymptotic coeffic…
This paper studies a singular integral equation with a contour integral whose kernel depends on the squared distance along a sufficiently smooth closed curve and on time. The solution is expanded in Fourier series along the contour, reducing the problem to associated equations for Fourier coefficien…
The paper studies the nomographability of equations of the form z = phi(x,y) through differential invariants associated with the operators m and its adjoint counterpart. It reformulates the Gronwall differential equations using the principal part of the Gronwall function, its complement, and two adj…
This paper studies representations of analytic function classes that form Hilbert spaces with reproducing kernels. It first describes kernels associated with isometric mappings between such spaces and derives a generalization of Aronszajn’s embedding theorem, yielding integral representations and mi…
This note gives sufficient conditions for uniqueness in the inverse problem for the logarithmic potential of plane domains with positive mass density. It proves that two distinct convex domains whose boundaries lie in a specified circular annulus cannot have identical exterior logarithmic potentials…
This note studies nonlinear superposition and integral operators in Orlicz spaces, together with differentiability properties of Orlicz norms. It gives sufficient conditions, expressed through complementary Young functions and growth conditions such as Delta-type assumptions, for Fréchet differentia…
The paper studies analytic solutions near the origin for a third-order partial differential equation in three independent variables with homogeneous boundary conditions on the coordinate planes. Extending Günter’s finite-difference method, it derives recurrence relations for the Taylor coefficients …
This note studies closed ideals in the convolution normed ring of functions on the real line with exponential weight, focusing on ideals whose Fourier-transform hull is finite in the strip determined by the weight. It introduces asymptotic invariants of Fourier transforms and uses them to describe p…
