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 extends the critical point principle for even functionals on spheres to more general manifolds in Banach spaces defined by operator equations. Under reflexivity, boundedness, continuity, Lipschitz, and regularity assumptions on the functional and constraint operator, it proves first the ex…
The paper studies infinite matrix operators acting between Orlicz coordinate spaces under row and column summability assumptions expressed through monotone functions. It develops auxiliary criteria for products of sequences in Orlicz spaces and proves a general continuity result for a class of coord…
This note studies normalized quasiconformal mappings of the \(n\)-dimensional unit ball for \(n>2\), motivated by Liouville’s theorem and Lavrent’ev’s question on whether mappings locally close to conformal ones are globally close to conformal mappings. It proves that, for distortion \(q\) sufficien…
The paper establishes norm inequalities for complex polynomials and entire functions of finite degree. For polynomials of degree at most n with no zeros inside the unit circle, it gives an Lp bound for the norm on the circle of radius R greater than 1 in terms of the norm on the unit circle, with th…
The paper studies the topology of quotient spaces of locally bicompact groups by closed subgroups, using Yamabe’s reduction to projective Lie groups and inverse limit decompositions by compact normal divisors. It establishes a structural representation in which finite-dimensional quotients fiber loc…
This paper studies analytic solutions of essentially nonlinear operator equations of the form in which the derivative with respect to the unknown lacks an inverse, a setting that includes bifurcation, resonance, and related critical cases. In a framework of complex Banach spaces, it gives conditions…
The paper studies a class of one-dimensional nonlinear degenerate parabolic equations of the form \(u_{xx}-(A(u))_t=0\), where the coefficient of \(u_t\) vanishes at \(u=0\). Using uniformly parabolic regularizations, compactness arguments, integral identities, and maximum-principle comparisons, it …
This paper develops results on best approximation of functions of several variables by entire functions of finite spherical degree in weighted spaces. After defining weighted \(L_p\) norms, partial moduli of continuity for groups of variables, and directional Sobolev derivatives, it establishes a di…
The paper studies generalized solutions of quasilinear elliptic equations under boundedness and uniform ellipticity conditions on the coefficient derivatives. It reformulates the Dirichlet problem as a fixed point equation in a Sobolev space and shows that the associated operator is a contraction, s…
This paper formulates a spherically symmetric diffusion problem for the dissolution of a solid particle whose moving boundary recedes as reaction products diffuse into a surrounding liquid volume bounded by a sphere with zero flux at its outer surface. By transforming the concentration equation and …
This paper studies self-adjoint operators in the orthogonal sum of two Hilbert spaces that extend closed Hermitian operators with finite deficiency numbers acting in the component spaces. Using boundary spaces and boundary operators, it characterizes Hermitian and self-adjoint simple couplings of ad…
An iterative method is developed for arbitrary finite systems of linear inequalities, including inconsistent systems, using the maximal violation function and diminishing positive iteration coefficients with divergent sum. The method moves each iterate in the direction of the normal to a currently m…
This note develops cubature formulas for integrating functions over the unit ball in n-dimensional space, using surface integrals over concentric hyperspheres as generalized nodes. The construction reduces the determination of radii and coefficients to Gaussian and Markov-type one-dimensional quadra…
This paper generalizes the theory of differential equations with small multipliers at derivatives, previously developed by Tikhonov and Gradshtein, to systems in arbitrary linear topological spaces. It introduces notions of uniform asymptotic stability for parameterized equations and of the envelope…
This paper studies stationary Gaussian sequences with the strong mixing property, formulated through the decay of the dependence coefficient between past and future sigma-algebras. Using an analytic characterization in terms of the spectral density, it gives necessary structural conditions: the dens…
This paper studies when unions of spaces with strongly paracompact subspaces or closures inherit strong paracompactness, in analogy with known results for paracompact spaces. It proves a general preservation theorem for locally finite open coverings under suitable hereditary and additivity assumptio…
The paper studies when a continuous function of one linear form, interpreted as a plane wave in a prescribed direction, can be uniformly approximated on a domain in Euclidean space by finite sums of continuous functions of other linear forms whose directions belong to a fixed set. It introduces an a…
The paper studies first and second boundary value problems for a class of quasilinear elliptic equations whose coefficients may have strong nonlinear growth in the gradient. Under monotonicity and growth assumptions on the coefficient function, with convexity required for the Dirichlet problem, it p…
This paper revisits Sturm’s classical problem of determining when all nontrivial solutions of a second order linear differential equation with continuous coefficients are oscillatory. It reformulates a known necessary and sufficient oscillation criterion by removing the explicit nonnegativity requir…
This paper studies integral representations of linear operators on Orlicz spaces of vector fields over a locally compact space with a Radon measure. Starting from a given field of bounded operators into a Banach space, it constructs a linear mapping into the bidual by weak integration and proves an …
This paper studies the direct product decomposition of finite Pi-solvable groups using the notion of S-connectedness among prime divisors of the group order. It defines S-portions, consisting either of a single prime for which the group is p-decomposable or of an S-connected class of primes associat…
The paper studies spectral multiplicity for a self-adjoint multiplication operator generated by a matrix-valued distribution function constructed from two scalar R-functions, and applies the result to second-order differential operators. It proves that the spectrum is simple when the absolutely cont…
This note studies when special semigroups, defined by relations that set specified words equal to the empty word, can satisfy nontrivial identities without being groups. Using criteria based on left, right, and two-sided invertibility of generators and subwords, the paper proves that any such specia…
This note studies solutions of the Gauss and Codazzi equations for simply connected surfaces of strictly positive curvature with boundary, using an isometrically conjugate parametrization and a complex unknown formed from the coefficients of the second fundamental form. It proves an integral represe…
This paper studies associative rings with identity over which flat left modules are necessarily free. It first proves that a left module is flat if and only if it can be represented as the direct limit of a directed system of projective modules, and then strengthens this to a representation as the d…
The paper studies tangentially degenerate projective surfaces of rank r for which one focal image has no multiple components while the other may contain a single multiple component. Using moving frames and matrix relations governing the displacement of plane generators and tangent planes, it derives…
The paper introduces two sequent calculi, E0 and E0 prime, for the classical predicate calculus, designed to support a more practical search for derivations than Gentzen style systems G1 and G3. After defining formulas, sequents, purity, and almost congruence, it specifies axiom and inference schema…
This note studies invariant differential, or Laplace, operators on the symmetric space of real unimodular matrices modulo the special orthogonal subgroup, focusing on their restrictions to functions constant on horospheres defined by a unipotent triangular subgroup. Using diagonal coordinates and th…
This note studies a special class of Ribaucour transformations in three-dimensional conformal space, defined through the passage between the two sheets of the envelope of a sphere congruence while preserving Takasu conformally asymptotic lines. Using Gaidelman’s canonical moving frame, the paper der…
The paper studies uniqueness questions for semireducible decompositions of positive definite Riemannian metrics, expressed as a principal part plus conformally weighted supplementary metrics. It reformulates such decompositions through a system of equations for a symmetric tensor and a scalar functi…
The paper studies boundary problems for homogeneous random walks with independent identically distributed increments, focusing on generating functions for first passage, maxima of partial sums, terminal positions, and overshoots. Under general exponential moment and absolute continuity assumptions, …
This note studies extremal quasiconformal mappings between three-dimensional cylindrical domains, in the sense of minimizing the product of two distortion bounds associated with the axes of the infinitesimal image ellipsoid. Using the modulus method for families of curves in space, it proves two com…
This note studies the large-time behavior of solutions to the first boundary-value problem with zero lateral boundary data for a general uniformly parabolic equation in time-dependent domains. Using comparison functions and maximum-principle arguments, it derives exponential estimates whose decay ra…
This paper studies the limiting behavior of repeated compositions of symmetric probability measures on a symmetric space, formulated for the space of positive definite Hermitian unimodular matrices under the complex unimodular group. Using zonal spherical functions, the author defines a characterist…
This note studies the dual spaces of Sobolev spaces \(W_p^l(\Omega)\) and their zero-boundary subspaces for bounded domains with sufficiently smooth boundary and \(p>1\). It proves that, as sets of generalized elements, these conjugate spaces coincide with the corresponding \(W_q^l(\Omega)\) spaces,…
This note studies regularity restrictions for solutions of Dirichlet problems in rectangular and more general piecewise smooth domains with corner points. For the Laplace equation in a rectangle with polynomial boundary data, it proves that membership in a sufficiently high Hölder Sobolev class forc…
The paper addresses interpretability between algebraic models, motivated by Mostowski’s question on defining a group operation on the natural numbers that is mutually first-order interpretable with arithmetic. It introduces strict relatedness of models and recursively perfect algebras, proves that a…
The paper studies two classes of analytic functions of two complex variables in bounded complete bicircular domains and in bicylinders, defined by positivity conditions involving Temlyakov’s differential operator. Using reductions to one-variable starlike and convex univalent functions, it derives c…
The paper studies linearly enveloping cycloidal curves, defined as envelopes of straight lines fixed in the plane of a circle rolling without slipping on another circle or on a straight line. Using kinematic models of three-member satellite mechanisms, it derives equations for the family of line pos…
This note studies the algorithmic complexity of multiplying multi-digit binary numbers by binary automata, with attention to lower and upper estimates for the number of elements and computation time. It records elementary lower bounds and presents constructions due to Ofman that trade circuit size a…
This paper derives \(L_2\) estimates for polyharmonic functions and their partial derivatives of arbitrary order near the boundary of an \(N\)-dimensional domain with \(C^{(2)}\) boundary. The argument is developed primarily in three dimensions, using spherical representations, estimates for harmoni…
This note develops a generalized theory of expansions in rational functions with prescribed poles outside a continuum, extending Faber polynomial expansions through systems generated from Malmquist rational functions under conformal mapping. It defines modified rational systems depending on a parame…
This note develops an improved algorithm for asymptotic expansions of distributions of maximal deviations of normalized sums of independent identically distributed random variables, in both lattice and absolutely continuous cases. The method reduces the problem to a boundary value problem for an int…
This note studies how the number of conjunctions in an arbitrary irredundant disjunctive normal form of a Boolean function can exceed that in a minimal form, with attention to the function’s dimension, defined through maximal subcubes on which the function equals one. It proves that the general boun…
The paper studies a mixed initial boundary value problem for a fourth order equation with a small positive parameter multiplying the highest spatial derivative, which degenerates as the parameter tends to zero into a second order hyperbolic equation. Using the Vishik and Lyusternik asymptotic method…
The paper surveys applications of projection spectra and spectra of canonical closed coverings to the structure and dimension theory of topological spaces. It formulates characterizations of normal and paracompact spaces in terms of directed refining, strongly refining, or cofinally refining systems…
The paper addresses the problem of approximating an inconsistent system of linear equations by minimizing the sum of absolute residuals. It presents a finite monotone computational scheme based on Jordan eliminations, analogous to the simplex method, in which vertices of the polyhedral surface defin…
The paper generalizes S. N. Bernstein’s theorem on extremal nonnegative trigonometric polynomials from the case of two linear coefficient relations to an arbitrary finite number of such relations. It studies the minimization of an integral of a nonnegative trigonometric polynomial under prescribed l…
This paper examines whether Mergelyan’s uniform approximation theorem for functions analytic in a domain and continuous on its closure extends beyond finitely connected closed domains. It constructs a simply connected domain, equal to the interior of its closure, for which uniform approximation by r…
This paper studies the asymptotic behavior of approximation errors for multiply differentiable functions under arbitrary linear positive operators on finite intervals. It proves a necessary and sufficient condition, expressed through the vanishing ratio of higher even central moments of the operator…
