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 type problem for Riemann surfaces associated with gluing two half-disks, reformulated in terms of gluing two half-strips by a prescribed boundary homeomorphism. It constructs a class of simply connected Riemann surfaces with first-order algebraic branch points, decomposed into …
This paper studies higher order averaging for singularly perturbed systems with slow variables and fast degenerate motion whose trajectories admit uniform mean values. It formulates a second approximation averaged system, constructed through characteristic equations and auxiliary correction function…
This paper studies regularization of closed and bounded linear operators between Banach spaces, focusing on Phi and Phi-plus operators with finite-dimensional kernels and closed ranges. It proves that the difference of two regularizers of a Phi-operator is completely continuous, derives descriptions…
This paper develops a theory of modules over a \(K\)-space with unit, treating the \(K\)-space as a generalized scalar ring and using suitable notions of quotient, convergence, norm, and scalar product. It defines generalized \(M_Z\)-modules, normed \(B_Z\)-modules, and inner product \(H_Z\)-modules…
The paper develops a representation of tensor functions by extending the Pfaffian form representation of vector fields. Using canonical forms of Pfaffian forms, it derives general formulas for vector components in n-dimensional space and applies them to tensor functions viewed as vectors in the spac…
This note studies the regularity of convex surfaces in Lobachevsky space determined by the regularity of their intrinsic metric, without imposing the previously used assumption of positive Gaussian curvature. It states that if a convex surface has a regular metric and Gaussian curvature greater than…
This note studies integrals of the modulus of convolutions of even trigonometric polynomials with functions of bounded variation, relating them to diagonal Fourier-Stieltjes coefficients of the integrating functions. For polynomial coefficients forming a convex or concave sequence, and for variation…
This note examines how far Hilbert’s nonexistence theorem for complete regular surfaces of constant negative curvature in Euclidean three-space depends on the constancy of curvature. After recalling a strengthened strip form of Hilbert’s theorem, it shows that negative curvature bounded away from ze…
The paper studies the structure of Galois groups associated with local fields, focusing first on regular finite extensions of the p-adic numbers and on maximal normal p-extensions over a finite regular extension without higher ramification. It gives an explicit presentation of the resulting Galois g…
The paper studies a boundary-value problem for a higher-order mixed-type equation whose type degenerates on the x-axis, in a domain bounded by a curve in the elliptic region and characteristics in the hyperbolic region. The argument reduces the equation to a system of second-order problems of Bitsad…
The paper studies uniform and integral approximation of real functions by algebraic polynomials with integer coefficients on intervals of length less than 4, emphasizing the arithmetic restrictions that distinguish this problem from ordinary polynomial approximation. It establishes direct approximat…
The paper studies how correction vectors arising in iterative methods for approximating spectral bounds of a bounded positive self-adjoint operator can provide additional spectral information. It defines extremal, strongly minimizing, strongly maximizing, and biextremal sequences in terms of the Ray…
The paper studies asymptotic expansions, with respect to a small parameter, for solutions of degenerating quasilinear second order equations, chiefly hyperbolic equations whose limiting problems have lower order, and related elliptic and hyperbolic problems degenerating to parabolic ones. Using iter…
This note applies the method of frames of submanifolds to the projective differential geometry of pairs of complexes in three-dimensional projective space. It constructs a semicanonical frame using k-flecnodal points, derives invariant frame formulas for pairs of nonholonomic congruences associated …
This paper studies geometric properties of level lines under univalent conformal mappings of the unit disk and of the corresponding exterior class. Building on earlier examples showing nonmonotonic changes in inflection and loss of starlikeness, it proves that sufficiently rapid growth of the mappin…
The paper establishes a criterion for when a simple Volterra operator in a separable Hilbert space is unicellular, meaning that its invariant subspaces are totally ordered by inclusion. It develops the criterion through the characteristic operator function associated with the imaginary part of the o…
The paper studies small analytic solutions of a class of nonlinear integral equations in the space of continuous complex-valued functions, in the case where the linear kernel has the eigenvalue one with finite multiplicity. It investigates the Nekrasov-Nazarov construction using series in fractional…
The paper studies limiting forms of a priori estimates for elliptic boundary value problems and related integral operators when standard \(L_p\) and Hölder estimates approach critical parameter values. By analyzing the growth of constants as \(p\) tends to infinity and as the Hölder exponent tends t…
This paper develops a general theory of semieuclidean and semineuclidean spaces, extending earlier work that treated only special cases. It defines these spaces by systems of scalar products with prescribed signatures, introduces distances, angles, hyperspheres, absolute cones and planes, and descri…
The paper studies level sets of bounded solutions to a uniformly elliptic second order linear equation in an infinite strip, under regularity and boundedness assumptions on the coefficients. It proves that two proper components of the zero level set, both extending to infinity without meeting the ho…
This note studies the large time behavior of solutions to a one dimensional Stefan problem with Cauchy data for parabolic equations with variable coefficients. Using maximum principle comparison arguments and similarity solutions of the constant coefficient heat equation, it derives asymptotic resul…
This note proposes the axiomatic notion of a radical as a means of organizing numerous group classes related to abelian, finite, soluble, and generalized soluble groups. It formulates radical and semisimple classes of groups through closure and series conditions, describes minimal radical and semisi…
This paper addresses the direct solution of large block systems of linear algebraic difference equations arising from grid methods for partial differential equations, with boundary conditions represented at the first and last grid layers. It proposes a combined sweep and pivoting elimination procedu…
This note develops a nonholonomic analogue of W congruences within the equiaffine theory of linear complexes. Using semicanonical and canonical moving frames, it derives invariant conditions under which a nonholonomic congruence has corresponding asymptotic lines on its nonholonomic focal surfaces, …
The paper proves the existence of a trigonometric series that is universal with respect to subseries: for every almost everywhere finite measurable function on the interval, some subseries converges to that function almost everywhere. This strengthens Menshov’s theorem on representation of measurabl…
The paper studies approximation of multivariable functions that vanish on the boundary of a domain together with derivatives up to a prescribed order, using expressions of the form a boundary defining function raised to a power times a polynomial. Building on earlier results for smoother or more reg…
The paper studies when limits of rational functions with prescribed poles near a continuum determine a unique quasianalytic continuation across domains separated from that continuum. It proves geometric convergence criteria, expressed through level curves of the conformal map of the exterior of the …
This note generalizes Spanier and Whitehead homotopic duality to spaces equipped with a fixed point free action of a topological group. It defines stable classes of equivariant mappings by iterated joins with a chosen equivariant sphere-like space, introduces an equivariant duality operator on finit…
This paper studies when a smooth closed simply connected manifold can be embedded in Euclidean space of dimension \(2n-1\), extending Whitney’s methods for embeddings in \(E^{2n}\) using ideas related to Pontryagin’s work on homotopy groups of spheres. The argument analyzes regular and completely re…
The note studies how homogeneity assumptions influence the dimension theory of locally bicompact infinite-dimensional spaces. It first observes that a metrizable locally bicompact doubly homogeneous infinite-dimensional space cannot have transfinite dimension omega, under the stated definition. The …
The paper studies geometric properties of pairs of cones in a real Banach space, extending classical notions of normal, generating, nonflattening, and regular cones to the setting of a subcone ordered by a larger cone. It proves the equivalence of two definitions of relative normality, gives a chara…
This note studies boundary behavior of normal meromorphic functions in the unit disk, focusing on whether limits along sufficiently dense sequences of interior points can replace limits along curves. Using results of Lehto and Virtanen, Privalov, Noshiro, and properties of normal families, it proves…
This paper extends results on bases in spaces of analytic functions from the open disk setting to the space of functions analytic in the closed disk, endowed with its inductive limit topology. Using duality between this space and the corresponding analytic function space on the reciprocal disk, toge…
This paper studies locally convex real linear spaces ordered by a convex cone under compactness, positivity, and independence assumptions on quasi-indecomposable vectors. It defines a ring of order-bounded linear operators and identifies it with the ring of continuous real functions on the compact s…
The paper studies monic polynomials orthogonal on a finite system of intervals with respect to weights involving a positive function, extending earlier work on the associated hyperelliptic Riemann surface. Using Abelian integrals, the authors give a parametric representation for auxiliary functions …
The paper presents a simplified numerical scheme for a previously developed finite monotone algorithm for Chebyshev approximation of inconsistent systems of linear equations. Keeping the geometric structure of the earlier method, it reformulates the computations through Jordan eliminations analogous…
This paper studies eigenvalue boundary problems for the hyperbolic equation of string vibrations, replacing the usual homogeneous boundary condition by conditions involving a constant coefficient differential operator, possibly of arbitrary finite order. For the unit disk, the authors relate these p…
This paper generalizes Hilbert’s nonexistence theorem for complete regular surfaces of constant negative curvature in Euclidean three-space. It considers a simply connected complete two-dimensional Riemannian manifold with negative Gaussian curvature satisfying explicit bounds on the curvature, its …
This note studies systems of quasilinear elliptic equations in divergence form on an n-dimensional torus under periodic boundary conditions. Using a Galerkin approximation with trigonometric basis functions and a topological lemma for finite nonlinear systems, it establishes existence of weak soluti…
This paper extends the study of invariant first-order differential systems expressed through exterior differentiation and its metric adjoint beyond previously treated elliptic and hyperbolic cases. It constructs parabolic, semi-degenerate parabolic, and intermediate systems on covariants, relates th…
The paper gives sufficient conditions for the existence of a periodic solution in a nonlinear nonautonomous system of differential equations with a constant linear part and a continuous time-periodic perturbation satisfying uniqueness. It considers the Poincare transformation over one period and com…
This note studies systems of linear differential equations with constant coefficients and the problem of when one operator system is subordinate to another in an \(L_2\) setting on a bounded domain. It proves a necessary and sufficient criterion for subordination, expressed through determinants obta…
This paper studies quasilinear second order parabolic equations in divergence form with many spatial variables, under uniform parabolicity, smoothness, and monotonicity assumptions. It proves a priori bounds and Hölder estimates for solutions and their first time and first and second spatial derivat…
This note studies directional growth indicators for subharmonic functions of finite order and normal type in multidimensional Euclidean space, extending an analogy with indicators of entire functions. After defining the indicator by radial limiting growth on the unit sphere, the paper records its po…
This note studies weakly infinite-dimensional spaces and transfinite dimension in dimension theory. It extends Hurewicz-type theorems on dimension-lowering mappings to weakly infinite-dimensional bicompact and strongly paracompact spaces, proving criteria under which a space or the domain of a close…
The paper studies two-person minimax games associated with diffusion processes whose drift is modified by competing vector fields subject to local convex constraints. For payoffs given by the expected boundary value plus an additive running functional, the argument connects the value of the game to …
The paper studies approximate solution of linear Volterra integral equations of the second kind with smooth kernels and free terms. It adapts Ryaben’kii interpolation formulas based on number theoretic grids, first proving an interpolation error estimate for functions with bounded derivatives of ord…
The paper studies Medvedev’s density relation on subsets of the natural numbers, with emphasis on hyperimmune sets, whose densities are below that of the full set of natural numbers. It characterizes the induced partially ordered structure of density degrees, introduces rarefied and weakly rarefied …
This note studies a complex analogue of the Chebyshev problem for best uniform approximation of continuous functions on a compact set by generalized polynomials whose complex coefficients satisfy linear equality constraints and convex-domain inequality constraints. Under a regularity condition ensur…
