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 Dirichlet, Neumann, and eigenfunction problems for the elliptic operator div[p(x) grad u] minus q(x)u in domains where the coefficients have discontinuities across internal surfaces. Under Hölder-type assumptions on the coefficients and data, positivity conditions on p and q, Lyapu…
The paper generalizes harmonic Wilczynski nets and their Laplace sequences from three and four dimensional projective spaces to an arbitrary projective space. It defines \(L\)-nets and \(L\)-sequences separately for odd and even dimensional spaces through intersections of tangent, axial, and associa…
This note develops domain conditions under which Sobolev-type embedding theorems hold for spaces of functions on arbitrary Euclidean domains. Using level surfaces of functions, it defines several classes of domains characterized by measure inequalities, including conditions extending the cone condit…
This note studies how restrictions on the angular distribution of zeros, poles, and other value points of a meromorphic function influence its growth. Using Nevanlinna’s angular characteristics together with results of Nevanlinna, Hayman, and related growth estimates, it proves that bounded angular …
This note studies the extension of Vl. Markov’s least deviation problem from ordinary algebraic polynomials to polynomials formed from Chebyshev function systems. It introduces the notion of a regular T-system, defined by a bound on the number of maximum deviation points, and distinguishes regular T…
This note studies division of generalized functions and regularization in spaces of test functions of Gelfand and Shilov type. It relates solvability of the equation FU = T in K' to the existence of regularizations of powers of 1 divided by F times its conjugate, then uses a reduction via Weierstras…
This note studies the Cauchy problem in the large for a first order nonlinear Hamilton-Jacobi equation with strictly convex flux, allowing initially Lipschitz and then arbitrary bounded initial functions. It defines generalized solutions through Lipschitz regularity away from the initial line, almos…
The note determines defining relations for semigroups of partial transformations of a finite set with n at least 4 elements. It introduces irreducible generating sets for the semigroup of all one-to-one partial transformations and for the semigroup of all partial transformations, extending known gen…
This paper studies coefficient stability for three point finite difference schemes approximating a one dimensional second order boundary value problem with possibly discontinuous coefficients. The authors define stability with respect to small integral perturbations of the scheme coefficients, estab…
This note introduces a modified notion of strongly zero-dimensional mappings and the associated strong dimension of a continuous mapping between metric spaces. It proves that for a mapping from X to Y, the covering dimension satisfies dim X at most dim Y plus the strong dimension of the mapping, and…
The paper studies conditions under which summable or bounded functions possess prescribed smoothness, using integral operators generated by kernels with specified moment conditions and, separately, finite difference operators. It introduces function classes defined by the smallness of these kernel t…
The paper studies the occurrence of primes in short arithmetic progressions modulo k, refining earlier results of Linnik, Rodosskii, and the author. It outlines a proof that, for suitable absolute constants, every reduced residue class modulo k contains a prime in the interval (x, x k^ε) whenever ε …
This paper studies bounded operators that are Hermitian with respect to an indefinite inner product defined by a fundamental symmetry \(J=P-Q\) on a separable Hilbert space. It first records spectral symmetry properties of such \(J\)-Hermitian operators, then extends Pontryagin’s invariant subspace …
This paper studies Sobolev type classes with fractional smoothness on Euclidean spaces, bounded domains, and differentiable manifolds. It formulates trace and converse extension theorems for the classes \(W_p^r\), extending known results for Nikol’skii classes and for the Hilbert case \(p=2\), and p…
The paper studies mixed boundary value problems with an oblique derivative condition for second order parabolic equations in finite and infinite cylindrical domains. Using generalized heat potentials, it constructs a suitable fundamental solution modeled on the constant coefficient case and reduces …
The paper studies limiting self-similar solutions of a nonlinear parabolic equation, with attention to one-dimensional plane, cylindrical, and spherical forms, including generalized geometries described by a parameter. By introducing a converging-wave ansatz near a focusing point, the authors reduce…
This paper studies systems of linear inequalities in real vector spaces through lower-rank auxiliary systems called contractions or collapses, intended to preserve consistency information while reducing dimension. It develops criteria for consequences, consistency, and stability of such systems, inc…
The paper studies approximate solution methods for linear operator equations \(Ay=b\) in a real Hilbert space, where \(A\) is a bounded self-adjoint positive operator. Two iterative schemes, related to steepest descent and to Krasnosel’skii procedures for estimating spectral bounds, are introduced u…
The paper studies nonhomogeneous systems of linear difference equations whose coefficients depend linearly on the complex variable, extending earlier results for single equations and constant coefficient cases. Under nondegeneracy assumptions on the leading determinant matrices and a condition exclu…
This paper proves a version of Liouville’s theorem for conformal mappings in Euclidean space of dimension at least three without assuming differentiability in the definition of the mapping. Conformality is formulated topologically through the behavior of regular families of neighborhoods, and the pr…
This paper extends the Phragmén-Lindelöf type uniqueness principle from analytic functions to harmonic functions in three-dimensional domains, specifically an infinite circular cylinder and a circular cone. The authors prove that a harmonic function satisfying zero Dirichlet data and bounded normal …
This paper studies connection formulas for singular Tricomi boundary value problems for the Euler-Poisson equation in a wedge-type domain, with parameter-dependent boundary conditions on characteristic half-lines. It derives integral transformations relating solutions with different parameter values…
This note studies almost periodic oscillations in quasilinear systems with time lag and a small parameter in the degenerate case, where the characteristic equation of the unperturbed linear system has critical purely imaginary or zero roots while the remaining roots lie in the left half-plane. Using…
The paper studies approximation of periodic functions of several variables whose mixed derivatives of prescribed integer orders are uniformly bounded. Using the zeta function of an associated differential operator, its functional equation, and contour integral representations, it constructs trigonom…
The paper studies functional equations of Riemann type for pairs of functions represented by general Dirichlet series, extending earlier work of Hamburger, Bochner, Chandrasekharan, and Mandelbrojt by allowing polynomial factors in the gamma-normalized equation. It defines solutions associated with …
This note characterizes weakly countable-dimensional compacta, defined as compact spaces that are countable unions of closed finite-dimensional subsets, in terms of inverse limits of polyhedra. Extending Freudenthal’s representation theorem, it proves that such a compactum is precisely an inverse li…
This note studies the fundamental solution of the Cauchy problem for constant coefficient Petrovskii well posed partial differential equations in several spatial variables. It classifies relevant parabolic, properly parabolic, and properly Petrovskii well posed cases, then derives asymptotic expansi…
This paper introduces a general class of transformations of Markov processes based on multiplicative functionals, encompassing subprocess formation and changes of measure such as those related to drift transformations of Wiener processes. It defines multiplicative functionals, gives several examples…
This note studies homogeneous cones in finite-dimensional real linear spaces, with emphasis on convex cones and their relation to bounded homogeneous domains in several complex variables. It establishes invariant measure and metric properties for convex cones, proves a structural result on compact s…
This paper studies decompositions of continuous unitary representations of second countable locally compact groups into factor representations, using the center of the weakly closed operator algebra generated by the representation. It proves that in the canonical decomposition the factor components …
The paper studies torsion-free affine connections determined by a fundamental coframe of n vector fields on an n-dimensional differentiable manifold, defining the class of B-connections as associated symmetric parts of flat affine connections. It characterizes these spaces through their geodesic equ…
This paper estimates the epsilon entropy in the L2 metric for two classes of periodic complex-valued functions of several variables, defined through restrictions on their Fourier coefficients: the Sobolev-type classes W_s^alpha(B) and the coefficient-bounded classes E_s^{alpha,k}(B). Using Kolmogoro…
This note develops a scheme for applying harmonic analysis, specifically Bohr almost-periodic functions, to the spectral analysis of completely continuous linear operators in weakly complete Banach spaces under a boundedness condition on the group \(e^{iAt}\). For each vector and functional, the sca…
This paper studies real polynomials of degree n that deviate least from zero on the interval [-1, 1] when an arbitrary number of leading coefficients is prescribed, extending the classical Chebyshev, Zolotarev, and Akhiezer cases. Using conformal mappings of fundamental domains onto half-strips, it …
This paper extends V. A. Markov’s extremal problem for polynomials least deviating from zero under a linear normalization to generalized polynomials generated by regular Chebyshev and Chebyshev, Markov systems. It gives necessary and sufficient conditions for a nondegenerate solution in terms of dev…
This paper studies eigenfunction expansions for a class of non-self-adjoint boundary-value problems for functional integro-differential equations with retarded arguments, bounded-variation boundary terms, and Volterra-type kernels. It constructs a mutually adjoint pair of problems, proves that their…
This note studies extremal limit values of Stieltjes integrals with variable moment data under the conditions of A. A. Markov, extending the theory of principal and canonical representations in Chebyshev systems. It analyzes how canonical representations of index n plus 2 change when the moments var…
This paper develops a perturbation method for finding eigenvalues and eigenvectors of a non-Hermitian vibration operator of simple structure, motivated by applications to polyatomic molecular vibrations where standard Hermitian quantum-mechanical perturbation theory is not directly applicable. The a…
This paper studies growth estimates for solutions of a first order matrix system with nonhomogeneous boundary conditions on a strip, under spectral assumptions on the coefficient and boundary matrices. Using contour integral representations, estimates for a matrix kernel, and residues at poles assoc…
This note studies whether solvability and radicality of certain infinite groups are preserved under structural isomorphisms of subgroup lattices. Using criteria involving Dedekindian elements, periodic normal subgroups, and induced structural isomorphisms on factor groups, it proves that every struc…
This paper isolates a class of Kawaguchi spaces whose metric function is a homogeneous expression in derivatives of a curve up to order nu and whose leading skew-symmetric tensor admits a nonzero invariant. For these spaces, denoted L_n^nu, the author constructs a symmetric affine connection from th…
This note studies external bases for subspaces of bicompact spaces using separating systems and relative bases. It proves that if \(X\) is a Borel set of type \(G_{(\tau)}\) in a bicompactum \(\Phi\), and \(X\) has a network of cardinality \(\tau\), then \(X\) has an external base in \(\Phi\) of the…
The paper studies complex envelopes of compact homogeneous spaces associated with a connected compact Lie group and a connected closed subgroup. It constructs the complex envelope as a homogeneous space of the complex envelope of the group, proves extension results for representations and covariant …
The paper derives explicit representations for zeros of Dirichlet polynomials and quasipolynomials of exponential type, refining earlier results that gave only bounded remainder terms. It constructs the bounded correction for Dirichlet polynomial zeros by analytic continuation of implicit-function b…
This paper studies unique determinacy and flexibility of convex surfaces homeomorphic to an open disk, especially surfaces whose completion to the boundary of the convex hull is a planar convex domain. It formulates the problem in terms of gluing planar domains to the boundary curve and proves that …
The paper extends number-theoretic quadrature methods for multiple integrals from periodic function classes to nonperiodic functions with bounded mixed derivatives on the unit cube. It shows that, after a smooth change of variables with vanishing endpoint derivatives, suitable lattice rules achieve …
This paper studies regularity of generalized solutions to the stationary linearized and nonstationary nonlinear Navier-Stokes equations in a bounded smooth domain. For the stationary problem it derives a pressure representation and obtains estimates implying existence and smoothness properties for d…
This paper studies stationary groups of motions of spaces with affine connection, focusing on the local action near a fixed point through normal coordinates and geodesic development. It introduces a two-variable vector function measuring the development of geodesic broken lines and uses its equivari…
This note develops a method for solving the one-dimensional general Stefan problem with an arbitrary finite number of phases, variable coefficients in the parabolic equations, and variable coefficients in the phase interface conditions. A generalized solution is defined through an integral identity …
