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 paper studies generalized solutions of second order uniformly parabolic linear and quasilinear equations using mixed space time norms to describe coefficient and data integrability. It develops a level set lemma for functions satisfying Caccioppoli type inequalities, yielding power, exponential…
This bibliographic notice surveys recently published mathematical books and teaching materials available in 1965 and 1966, primarily from Soviet academic and educational presses. The entries cover monographs, textbooks, lecture notes, handbooks, and collected papers in differential equations, mathem…
This paper studies a locally convex algebra of entire functions whose growth is controlled by an arbitrary increasing majorant satisfying a logarithmic convexity condition. The author defines a natural topology on this algebra, establishes continuity of multiplication, and analyzes closed ideals thr…
This paper studies Dirichlet Sobolev problems for elliptic operators on closed manifolds with trace data imposed on submanifolds, and asks how the resulting change in analytic index can be computed. Using Atiyah Singer characteristic classes, Todd classes, Euler classes, symmetric and exterior power…
This item is a bibliographic and editorial notice from a 1966 issue of Differential Equations. It lists recent 1965 publications in differential equations, mathematical physics, numerical analysis, stability theory, boundary value problems, and related areas, giving authors, titles, journal details,…
The paper addresses V. A. Efremovich’s problem of characterizing when a general uniform space, defined by symmetric binary relations interpreted as orders of nearness, induces a proximity satisfying the standard nearness axioms. It proves a necessary and sufficient criterion consisting of three cond…
The paper examines the onset of statistical, or stochastic, behavior in longitudinal oscillations of a nonlinear string with fixed ends, modeled as a finite chain of nonlinear oscillators related to the Fermi, Pasta, and Ulam problem. By transforming to normal coordinates and treating the nonlinear …
This paper studies Schottky-Ahlfors forms on compact oriented Riemannian manifolds with boundary, using the double of the manifold and Hilbert space decompositions of differential forms. It characterizes forms that extend harmonically to the double as a sum of boundary-vanishing harmonic forms and t…
This paper studies a class of singular integral equations on the unit sphere in three-dimensional Euclidean space, with Hölder-continuous coefficients and data. By introducing spherical coordinates, expanding the unknown and right-hand side in trigonometric series, and reducing the problem to one-di…
The paper studies decision problems for the class K1 of finitely presented semigroups whose defining words do not occur inside distinct defining words. It constructs a 15-generator semigroup in this class containing a Tseitin semigroup as a subsemigroup, thereby showing that K1 includes a semigroup …
This note studies when the algebra of functions continuous on a closed bounded plane set and analytic at its interior points coincides with the uniform closure on that set of rational functions with poles off the set. Using a new approximation scheme based on partitions of unity and estimates involv…
This note studies how solutions of certain constant coefficient hyperbolic equations depend on initial data on the base of the characteristic cone, with emphasis on the existence of lacunae and weak lacunae. For strictly hyperbolic equations in two independent variables, it proves a necessary and su…
This paper establishes lower estimates for the exponential type of entire functions of order one whose values on the real axis satisfy prescribed decay bounds. Using convex regularization of the bounding sequence, it proves an estimate sharp up to an absolute constant and gives a converse constructi…
The paper studies a discontinuous Riemann boundary value problem on simple closed rectifiable curves of class K, with coefficients and free terms belonging to integral Hölder classes. It establishes auxiliary results on products of such functions, proves a Poincaré-Bertrand formula for Cauchy type s…
This paper gives a constructive representation of zero order Besov and Nikolsky type classes of generalized functions of several variables, using approximation by entire functions of exponential type. Working in the Schwartz distribution framework, it defines regularity in the sense of Lp, introduce…
This paper introduces Hausdorff spaces of minimal weight, defined by the requirement that every open cover separating points has cardinality at least the weight of the space. It gives equivalent and sufficient conditions for this property, proves that Tychonoff products of spaces of minimal weight a…
This note studies self-maps of the n-dimensional sphere whose point preimages are cellular, motivated by the relation between such maps and maps approximable by homeomorphisms. It proves that, for n not equal to 4, every pointlike mapping of the sphere onto itself is cellular, meaning that the preim…
This note studies criteria for equivalence, orthogonality, and strong equivalence of Gaussian measures on spaces of real functions, focusing on cases where one measure is generated by a Wiener process or by a Gaussian Markov process. Using reproducing kernel Hilbert spaces and the operator criterion…
The paper proves embedding theorems for the spaces W and B with mixed norms and anisotropic smoothness parameters, allowing the orders of smoothness to be arbitrary positive numbers. It first establishes weighted integral inequalities for kernels defined by anisotropic metrics in products of Euclide…
This paper develops an abstract Banach space method for studying boundary value problems for parabolic equations whose associated elliptic operators have domains depending on time, as occurs with variable boundary conditions. The main result establishes the existence and properties of an evolution o…
This note proves that in every uncountable perfectly normal bicompact space, each countable Hausdorff Borel class below the first uncountable ordinal is nonempty. The argument reduces to spaces without isolated points, uses a continuous surjection onto an interval, and establishes a key factorizatio…
This note studies the homology of spaces of smooth embeddings of a compact smooth manifold into another smooth manifold in the high codimension range, especially for based embeddings. It develops exact sequences and spectral sequences by filtering spaces of immersions according to singularity type, …
The paper studies the confluent hypergeometric functions of Humbert and Horn, especially the series H3 and Xi2, in connection with the generalized wave equation with singular coefficient. It derives integral relations, inverse formulas, limiting transitions, addition and expansion theorems, and redu…
This paper studies expansion in eigenfunctions for a non-self-adjoint Sturm-Liouville boundary-value problem on a finite interval, with a complex potential whose behavior near the right endpoint determines the spectral asymptotics. Using contour integration, Green’s functions, and asymptotic formula…
This paper studies strong convergence of generalized minimizing sequences for constrained extremum problems in Banach spaces, allowing approximating points that need not satisfy the constraints exactly but approach the feasible set. It proves convergence theorems under conditions involving closed co…
This paper studies pointwise stabilization as time tends to infinity for solutions of the Cauchy problem for parabolic equations, beginning with higher order constant coefficient equations generated by powers of the Laplacian. Using Wiener’s Tauberian theorem and analysis of the Fourier transforms o…
This paper studies covering dimension of remainders of bicompact extensions of proximity and topological spaces, distinguishing it from proximity and inductive dimensions. It introduces prolongable framings, borderings, and structures of rims, and gives necessary and sufficient conditions for a rema…
This note generalizes two results in finite group theory associated with Carter and Wielandt. It introduces auxiliary lemmas on Carter subgroups, the Carter property, Hall subgroups, and abnormal subgroups, and proves that a pi-solvable group has the Carter property when all its pi-prime subgroups h…
This note addresses Minkowski’s conjecture on the critical determinant of the planar domain defined by |x|^p + |y|^p ≤ 1, reducing the question to the minimization of a two-variable function subject to an implicit constraint. It describes a computer-assisted method for testing the conjecture for par…
This note studies the location of zeros of entire functions represented as finite Fourier transforms of continuous functions on an interval, with particular attention to whether zeros can have arbitrarily large imaginary parts when the left endpoint value is nonzero. It first shows that bounded vari…
This note studies finite order compact extensions and remainders of completely regular Hausdorff spaces, with particular attention to Čech extensions and the classes of spaces whose nth order remainder is compact. It introduces a partial ordering on equivalence classes of finite order extensions, id…
This paper studies factor representations of the canonical anticommutation relations in separable Hilbert spaces, using a measure-theoretic realization based on diagonalizing the commuting number projections. It proves that factor representations require an ergodic quasi-invariant measure, analyzes …
The paper studies recurrent algorithms that solve infinite, possibly cyclic, systems of inequalities under the assumption that a strictly feasible solution exists, a setting motivated by learning procedures in pattern recognition. It gives a general finite convergence criterion based on a decreasing…
The paper studies regularization of the supremum and upper limit of families of plurisubharmonic functions that are uniformly bounded above in domains of complex Euclidean space. Extending a theorem of H. Cartan, it proves that the exceptional sets where these functions differ from their upper semic…
This paper studies vector Riemann-Hilbert problems on the real line with piecewise continuously differentiable, nonsingular matrix coefficients and data in \(L^p\), \(1<p<\infty\). It develops a factorization method that removes coefficient jumps by holomorphic correcting factors, reduces the proble…
The paper studies approximation of functions in Sobolev, Slobodetskii spaces by piecewise polynomial functions on cube partitions, under the continuity condition alpha p greater than the dimension. It proves sharp order estimates for uniform approximation and for approximation in Lq with respect to …
The paper develops a generalization of projection methods for solving operator equations in which trial functions need not satisfy either the differential expression or boundary conditions in advance. It formulates the problem in a Hilbert space direct sum, treating the interior operator and boundar…
This paper formulates and proves analogues of Herbrand’s theorem for the classical predicate calculus with equality and functional symbols, using sequent calculi with and without equality. It defines reductions of formulas through functional forms, finite term sets generated from the lexicon of a fo…
