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 sums of nonnegative multiplicative functions evaluated at shifted primes, motivated by problems where the function may take values less than one on primes. It proves an upper estimate for sums of the form \(\sum_{p\le N} f(N-p)\) under mild growth conditions on prime powers, using …
The paper studies topological spaces through the behavior of chi-points under continuous mappings, introducing two invariant classes: spaces whose continuous images are discrete or contain a chi-point, and spaces whose continuous images have every nonisolated point as a chi-point. It proves structur…
The paper develops conditions for applying a continuous analogue of Newton’s method to nonlinear functional equations in Banach spaces and to a nonlinear second order boundary value problem. It proves local convergence to a known unique solution under assumptions on differentiability, bounded invert…
This note develops a Hölder space regularity theory for special heat potentials associated with noncylindrical lateral surfaces and oblique derivative boundary problems for second order parabolic equations. It studies the direct boundary values of the oblique derivative potential Q and the simple la…
The paper constructs a sequence of strongly independent superintuitionistic propositional calculi using finite Gödelian Brouwer algebras. It defines a class of finite algebras, called Lambda algebras, and proves that any two such algebras are either incomparable in the relevant derivability ordering…
The paper studies normalized extremal trigonometric polynomials of mixed cosine and sine type and relates their construction to extremal algebraic polynomials. It establishes a one-to-one correspondence between such trigonometric polynomials and pairs of analytic functions on the interval of the for…
The paper develops a spectral analysis of a class of unbounded non-self-adjoint operators in Hilbert spaces equipped with an indefinite metric, using characteristic matrix functions. It defines quasi-Hermitian operators of finite rank, introduces their characteristic matrix function through defect s…
The paper establishes sufficient criteria for absolute convergence of Fourier series of numerical almost-periodic functions in Besicovitch and Bohr classes. Using Parseval-type identities, Riesz-Fischer arguments, and best approximation quantities defined by spectral truncation, it relates convergen…
This note studies when a convex cone or convex set admits a supporting linear functional whose components lie between prescribed lower and upper bounds. It proves a general theorem, using positive bases and schemes of sections of a convex set, that characterizes the existence of a vector satisfying …
This note studies definability and reducibility questions in higher order logic, introducing generally definable ordinals and formulas whose variable types are governed by such ordinals. It proves that every generally definable formula can be effectively reduced to a second-order formula preserving …
The paper studies realizations of Maslov’s canonical operator for hyperbolic equations in the setting where the auxiliary space is \(L^2(E^1)\) and the operator is \(-i\,d/d\tau\). Using a generalized stationary phase method, it derives convergent series representations for oscillatory integrals nea…
The paper studies structural properties of hierarchies of sets in topological spaces of weight τ, including the spaces Dτ, Jτ, Dων, and Jων, under the assumption that τ is strongly inaccessible. It establishes the existence of universal sets and universal families for several basic classes, derives …
This paper studies abstract Cauchy problems for operator differential equations in a Hilbert space, especially cases of order greater than two that are generally ill posed in the Hadamard, Petrovskii sense. It proves well posedness in Tikhonov’s sense under strict parabolic conditions, constructs a …
The paper presents an iterative averaging method for solving stationary linear boundary value problems by embedding them in an auxiliary nonstationary problem. A two-step process is analyzed in both continuous and finite-difference forms, using a special double-averaging operator applied to the solu…
The paper studies similar tests for a general linear hypothesis in normal linear models when observation variances, or weights, are unknown and may differ. Extending results of Linnik on Scheffé-type tests and Neyman structures beyond the Behrens-Fisher setting, it considers tests defined through in…
The paper strengthens earlier results on topological equivalents of a set-theoretic branching hypothesis for a strongly inaccessible cardinal. It introduces notions such as open cardinal subbases, directed spectra, and generalized Vietoris exponential spaces, then formulates several compactness-type…
The paper constructs an analogue of the topology of a space of measurable functions in a foundation of an Archimedean K-lineal with unit, complete in the sense of bounded elements. Using a representation by continuous functions, possibly infinite valued, on a bicompact space, it defines neighborhood…
The paper proves a trace formula for the self-adjoint operator associated with the Jacobi equation along a fixed geodesic on a complete Riemannian manifold. By reducing the covariant Jacobi operator to a vector-valued Sturm-Liouville problem via parallel transport, the argument analyzes resolvent ke…
This note extends earlier one-dimensional criteria for complete regularity to multidimensional stationary processes in both discrete and continuous time. For a vector stationary process, it derives necessary factorization forms for the spectral matrix density, with a diagonal polynomial factor and a…
This paper studies regularity of boundary points for the Dirichlet problem for second order linear elliptic equations with discontinuous coefficients under uniform ellipticity and boundedness assumptions. It introduces an s-capacity adapted to such operators and proves sufficient Wiener-type capacit…
This paper studies boundary value problems on the half-line for second-order differential equations arising after transformations of third-order equations in boundary-layer theory and gas-jet mixing. It proves an existence theorem for solutions of y'' = F(x,y,y') constrained between prescribed upper…
The paper derives identities connecting complete finite differences of functions of several variables with mixed finite differences of the same total order. These identities are used to obtain relations between mixed partial derivatives and directional derivatives, including representations of mixed…
This note studies sequences of finite linear aggregates formed from dilations of an entire function of several complex variables, under growth conditions on the generating function and on the dilation parameters. It constructs integral linear operators with a characteristic function and uses them to…
The paper studies stationary random processes generated by interval endomorphisms of the form defined by Rényi’s number-theoretic transformations and their invariant measures. Under bounded distortion and variation assumptions on the inverse branches, it strengthens known exactness results by provin…
This paper studies inverse problems for uniform approximation of functions of several real variables by algebraic polynomials on a closed domain. Extending known one-dimensional results, it defines function classes in which smoothness in the direction normal to the boundary may deteriorate at twice …
This paper studies how uniformities on a topological space induce Hausdorff-type uniformities and topologies on spaces of nonempty subsets and closed subsets. Motivated by counterexamples to Isbell’s claim that the hyperspace of closed subsets distinguishes uniformities, it proves that distinct comp…
The paper studies self-adjoint extensions of field operators in Hilbert spaces generated by positive functionals, motivated by cases in quantum field theory where vacuum moments grow too rapidly to ensure essential self-adjointness. Using analogies with the classical moment problem and difference op…
The paper studies linear parabolic systems on a half space in which ordinary spatial derivatives are combined with powers of a Bessel operator, under a Petrovskii type parabolicity condition. Using the Fourier-Bessel transform and the associated generalized shift operator, it defines the Green matri…
This paper studies the local structure near a homoclinic tube formed by transverse intersections of the stable and unstable manifolds of a saddle-type invariant torus for a smooth mapping. Using contraction arguments and graph-transform estimates, it constructs stable and unstable sequences of surfa…
The paper generalizes the notion of lacunarity from systems of functions to Riesz basic sequences of elements in Banach spaces densely embedded in Hilbert spaces. It gives intrinsic criteria for an E-lacunary system, including a uniform l2 to E norm estimate and an equivalent square summability cond…
The paper examines the approximation of periodic functions in \(L_p\), \(1 \le p \le \infty\), by Zygmund normal means of order \(k\), with emphasis on the distinction between even and odd orders. After recalling known equivalences between the approximation error and the \(k\)-th modulus of smoothne…
Chernavskii strengthens a theorem of Bryant and Seebeck of engulfing type for embeddings of compact manifolds in Euclidean space, extending the discussion to all codimensions under conditions described as local homotopic unknottedness. The paper defines relevant local abelianness and local connectiv…
This paper examines contours of constant characteristic exponent for the Mathieu equation in its instability regions, a topic needed in applications involving parametric resonance and insufficiently covered for larger modulation depths. Using numerical computation based on a previously described met…
This paper studies stochastic behavioristic models of learning in which behavior evolves through contracting transformations determined by stimulus, response, and reinforcement events. It formulates finite order approximations of such models, including approximations to the Bush-Mosteller linear mod…
The paper studies Haar series that converge not everywhere in the ordinary sense but along point-dependent subsequences of partial sums. It introduces derivatives and Perron-type majorants and minorants relative to subsequences of dyadic nets, defines the corresponding generalized integral, and prov…
The paper develops constructive analogues of spaces of infinitely differentiable functions with compact support, defining countably normed spaces of complete records of such functions that vanish outside a fixed interval. It establishes completeness and separability for these spaces, studies convex …
This note introduces generalized motions of an n-dimensional Riemannian space by treating the metric equations as a partially invariant manifold under the induced action of a Lie group on the space of coordinates and metric components. It derives generalized Killing equations characterizing the inva…
The paper studies conditional minimization of a real functional on a subset of a Banach space defined by an inequality constraint and a closed set, with emphasis on characterizing when a given sequence is minimizing. It introduces a directional derivative based quantity measuring stationarity and pr…
This paper examines how different choices of neighborhoods in pseudo-Euclidean space lead to distinct topologies in relativistic mechanics, unlike the equivalent constructions available in positive definite Riemannian spaces. It argues that the intrinsic topology of particle trajectories is more fun…
This paper studies boundary value problems for the stationary and nonstationary linearized Navier-Stokes equations in a three-dimensional layer-like domain with a no-slip condition on the lower boundary and vanishing stress conditions on a free upper surface. Generalized solutions are formulated in …
This paper proposes a local method for solving a class of antagonistic differential pursuit games with geometric constraints on the players’ admissible motion. It defines action sets for the pursuer and pursued, introduces a mapping to a “center of pursuit,” and proves that when this center is uniqu…
This note studies how the growth of functions depending on several complex variables varies with fixed values of some variables, with particular attention to zero counting functions for entire functions in one distinguished variable. Ronkin introduces a class of functions whose radial extensions are…
This paper studies global solvability for nonlinear ordinary differential equations on the half-axis when the forcing term is square integrable. It proves that, under monotonicity or coercivity-type integral conditions on the nonlinear term, the Cauchy problem is solvable after adding a finite-dimen…
This paper studies singularly perturbed nonlinear systems of ordinary differential equations in which a small parameter multiplies the highest derivative and the initial value of one variable grows unboundedly as the parameter tends to zero. Under specified growth and sign assumptions on the nonline…
This paper studies bounded linear operators on a separable Hilbert space whose imaginary parts belong to the symmetrically normed ideal defined by a weighted summability condition on singular values. Using maximal chains of orthoprojectors and Shatunovskii type operator integrals, it proves an abstr…
The paper studies hyperspaces of nonempty closed subsets of a topological space endowed with the finite Vietoris-type topology, focusing on how cardinal invariants and dimension are reflected between a space and its hyperspace. It proves, under stated compactness or general hypotheses, results on eq…
This paper studies conditions for the existence of factorial moments of the number of upward crossings of a fixed level by a Gaussian stationary process. Starting from the standard integral representation for these moments, it gives sufficient conditions in terms of integrability of conditional mean…
