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 positive weak solutions, in the Sobolev sense, of elliptic equations of arbitrary order in bounded domains with smooth boundary, including uniformly elliptic equations with bounded coefficients and equations degenerating at the boundary. It introduces weighted integrability spaces …
This note studies the approximate construction of fixed points of continuous mappings under hypotheses related to the Brouwer, Kakutani, and Lefschetz-Hopf theorems, using numberings induced by simplicial subdivisions. It defines representative and normal simplices through vector functions associate…
This paper studies nonlinear mixed boundary value problems for almost linear first order hyperbolic systems in a plane rectangle, focusing on the case where a classical solution loses regular continuability because the boundary relation becomes degenerate while the solution remains bounded. Under in…
This paper studies first boundary-value problems with weighted boundary conditions for higher-order degenerate elliptic equations in bounded domains whose boundary includes a flat degeneracy portion. It introduces weighted Sobolev-type spaces defined by iterated differential operators with measurabl…
This paper generalizes Esseen’s inequalities for estimating the uniform distance between a nondecreasing bounded function and a function of bounded variation from the closeness of their Fourier-Stieltjes transforms on a finite interval. It proves an inequality bounding the supremum of |F(x) minus G(…
This paper studies the asymptotic distribution of eigenvalues for the Friedrichs extension of a symmetric constant coefficient differential operator on a bounded domain. Assuming the symbol tends to infinity and that the area of the level surface is negligible relative to the volume of the sublevel …
This note studies Whitney’s problem on the possible normal Euler numbers of smooth embeddings of nonorientable closed surfaces in four-dimensional Euclidean space, focusing on the projective plane and the Klein bottle. The argument reduces embeddings to special forms and translates the question into…
The paper studies vector bundles equipped with fiberwise module structures over finite-dimensional associative algebras and applies these structures to cobordism theory. It establishes criteria for local triviality via linear homogeneity, constructs universal fibered modules for fixed typical fibers…
The paper studies scattering for a self-adjoint system of ordinary differential equations on a half-line with a compactly supported Hermitian matrix potential, comparing the perturbed wave group with the free Dirichlet wave group. Using the Lax-Phillips and Adamyan-Arov framework, it derives an expl…
This note extends Michael’s theorems on continuous selectors of lower semicontinuous multivalued mappings to mappings whose values lie in separated uniform spaces. It introduces uniform metrizability and uniform almost metrizability relative to a weaker countably based uniformity, and proves selecto…
The paper studies differential and geometric properties of the boundary of the coefficient region for normalized univalent functions of class S. It describes extremal functions associated with singular boundary points through algebraic relations and quadratic differential equations, relates their bo…
The paper studies quasiconformal mappings of Euclidean space that arise as gradients of harmonic functions, motivated by Liouville-type rigidity results for holomorphic quasiconformal mappings. For dimension three, it proves that any nonconstant harmonic quasiconformal mapping from three-dimensional…
The paper studies solvability of quasielliptic nonstationary differential equations and Sobolev type problems in cylinders infinite in the time direction, including settings motivated by equations such as Laplace and heat conduction without initial conditions. It introduces weighted Sobolev spaces w…
The paper studies how lower bounds on the complexity of finite decision procedures for enumerable sets characterize forms of universality in recursive function theory. It defines several notions of effective, strict, weak, and strong nonrecursiveness and complexity, using decision algorithms, charac…
This paper studies two-dimensional systems of differential equations whose right-hand sides are formed from linear combinations of minima and maxima of linear functions, a class motivated by bottleneck processes and dual systems in optimal control. It shows that a pencil of lines through the origin …
The paper studies discrete and integral Wiener-Hopf operators in exceptional cases where the symbol vanishes on the unit circle or real axis. It introduces a notion of normalization for bounded linear operators with nonclosed range by changing the range space so as to obtain a Noether operator, and …
The paper studies how covering dimension behaves when a topology is represented as the intersection of several zero-dimensional topologies on the same set. For metrizable spaces, it proves that dim X is at most n exactly when the topology can be expressed as the intersection of n plus 1 metrizable z…
This note studies extended Hermite-Fejér interpolation processes formed from Chebyshev nodes with the endpoints added and one endpoint derivative condition imposed. Motivated by earlier examples of pointwise divergence, it asks whether such a weakened process can diverge at every point of the open i…
This note studies moduli of families of curves and higher dimensional surfaces in Euclidean space, with emphasis on surfaces passing through a point and on Hausdorff measurability. It derives an explicit modulus formula for a rotational family of two dimensional surfaces in three space, then uses it…
This paper develops sufficient conditions for hypoellipticity of linear differential operators with smooth coefficients in terms of Sobolev norm estimates and commutator bounds. It formulates conditions A, B, and C, proves that they imply local gain of regularity from \(Pu\) to \(u\), and derives hy…
The paper studies stability criteria for the Dirichlet and Neumann problems in three-dimensional potential theory, using a notion of stable capacity for open sets. It relates the stability of boundary value problems in a domain to the stable capacity of domains obtained by inversion from the complem…
This note studies one-dimensional singular integral operators with piecewise continuous matrix coefficients on contours consisting of finitely many closed and open Lyapunov arcs, acting in vector-valued L2 spaces. It defines a matrix-valued symbol on an associated cylinder that accounts for jumps an…
This paper studies the asymptotic distribution of Pearson’s chi-square statistic in multinomial schemes when the usual condition that all expected cell counts tend to infinity is not satisfied. It introduces an integral representation for characteristic functions of additively separable frequency st…
The paper presents a double reduction method for solving infinite systems of linear equations that arise when expanding unknown functions with edge or corner singularities in boundary value problems of mathematical physics. Instead of truncating all higher expansion coefficients to zero, the method …
This paper studies absolute stability of stationary nonlinear control systems whose linear part has a critical pair of purely imaginary eigenvalues and all other eigenvalues in the left half-plane. For a scalar sector-bounded nonlinearity, it formulates conditions under which Yakubovich’s frequency …
This paper studies periodic and locally finite groups satisfying finiteness conditions on Sylow subgroups, especially SF-groups and S2F-groups. It gives a criterion ensuring that a maximal complete abelian 2-subgroup is invariant in an S2F-group with infinite Sylow 2-subgroups, and uses this to show…
This paper studies Deheuvels homology for metric compact spaces with coefficients in precosheaves of Abelian groups or modules, motivated by the failure of exactness in Alexander-Cech homology. Using injective resolutions of inverse systems of chain complexes of open covers and the associated spectr…
This note establishes necessary and sufficient conditions for pointwise convergence of sequences of continuous linear mappings between analytic spaces, formulated through equicontinuity, convergence on total sets, and uniform bounds in projective and inductive systems of Banach spaces. The general c…
This note studies representations of large integers by nondegenerate diagonal ternary quadratic forms and the distribution of integer points on the corresponding quadratic surfaces. Under a stated zero-free region assumption for real Dirichlet L-functions, it proves uniform distribution estimates fo…
This paper studies the motion of a mass attached to a one-dimensional elastic-plastic element, modeled by a second order differential equation containing a Prager-Ishlinskii hysteresis operator. Under finiteness of the total elastic modulus and summability of the initial plastic state, the authors p…
This paper studies Hadamard well-posedness of the Cauchy problem for an abstract evolution equation with a closed linear operator in a Banach space, under the assumption that the positive half-axis is excluded from the point spectrum. It defines a maximal domain of well-posedness in terms of bounded…
This paper develops an analogue of the Kuratowski and Dugundji extension theorem for metrizable uniform spaces and uniformly continuous maps. It introduces and uses the relative large dimension of a subset, defined through Isbell’s large uniform dimension and the nearness relation, to formulate exte…
This note establishes criteria for normal solvability, meaning closed range, of systems of singular integral operators on vector-valued \(L_2\) spaces of the form \(T=aP+bQ\), where \(P\) and \(Q\) are complementary Cauchy projection operators and \(a,b\) are continuous matrix functions on the unit …
This paper studies uniform best rational approximation of convex functions and functions of bounded variation on finite intervals, comparing the decay of rational approximation errors with polynomial approximation. It proves upper bounds for continuous convex functions, including an order n inverse …
This paper establishes a homeomorphism theorem for general elliptic boundary value problems in Sobolev type spaces without assuming that the boundary conditions are normal. For a properly elliptic operator with boundary expressions that may be pseudodifferential tangentially and differential normall…
This paper formulates a fiducial approach for statistical models dominated by a common measure, defining the fiducial distribution as a limiting posterior obtained from maximum entropy priors on increasing finite-measure subsets of the parameter space. For models with sample and parameter spaces act…
The paper studies homotopy invariance of rational Pontryagin numbers for closed oriented smooth and PL manifolds, focusing on pairings of Hirzebruch L-polynomials with intersections of codimension one homology classes. It proves that numbers of the form obtained by evaluating L_k on such intersectio…
This paper presents an exact algorithm for the maximum flow problem in a directed network with arbitrary nonnegative capacities, avoiding the rounding required by earlier methods for noncommensurable data. The method iteratively augments flow along shortest augmenting paths in the residual network, …
This paper determines the number of topological types of several classes of dyadic spaces for an infinite cardinal parameter. It proves that dyadic compact spaces of weight τ have exactly 2^τ types, dyadic compact spaces of density τ have exactly 2^(2^τ) types, and dyadic spaces of density τ have ex…
This paper studies ergodicity for generally noncommutative, partially semigroup families of stochastic linear operators acting on spaces of summable elements in complete topological semifields. It defines distributions, stochastic operators, ergodic and strongly ergodic families, and introduces a co…
The paper studies superintuitionistic propositional logics through their associated pseudoboolean algebras, focusing on whether finitely axiomatizable intermediate logics are finitely approximable. It develops algebraic criteria using finite separation, pretrue formulas, Gödelian and narrow structur…
This paper studies boundary value problems for elliptic equations, elliptic equations with a complex parameter, and related parabolic mixed problems in unbounded exterior domains. Under uniform ellipticity, Shapiro-Lopatinskii conditions, and additional assumptions describing behavior at infinity, i…
This paper studies a conjugation problem for three analytic functions connected by boundary conditions on a smooth closed contour through two branches of the square root. The authors reduce an associated jump problem to two classical Riemann boundary value problems, construct canonical factorizing f…
This note establishes embedding theorems for Besov spaces with mixed norm on Euclidean space and for weighted Besov spaces on the half-space. The author defines the relevant spaces through mixed Lebesgue norms and difference norms of derivatives, then states conditions under which functions or their…
The paper studies pseudodifferential operators with a finite group of shifts on a connected manifold with an effective finite group action. By associating such an operator to a group invariant pseudodifferential operator on the product of the manifold with the group, it gives a necessary and suffici…
The paper studies integral operators in \(L_2\) spaces whose kernels satisfy Carleman, semi-Carleman, Akhiezer majorization, and symmetric variants of these conditions. It formulates and solves classification problems giving necessary and sufficient conditions for an operator to belong to each class…
The paper proposes an axiomatic construction of locally Euclidean, locally symplectic, and locally non-Euclidean geometries of constant curvature as instances of the theory of physical structures. It formulates a principle of phenomenological symmetry for a set of points equipped with symmetric or a…
This paper studies one-to-one mappings between affine spaces that carry the family of all translates of a bounded set onto the family of translates of its image. Using an iterative construction of associated centrally symmetric sets, it proves that tangent supporting hyperplanes at suitable extreme …
The paper studies conditions under which a normal subgroup of a finite group admits a complement or, more generally, a complement relative to a specified set of primes. It proves that a normal subgroup has a prime set complement when, for each prime in the set, the intersection with a Sylow subgroup…
