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 closed convex hypersurfaces in Euclidean space whose principal radii of curvature satisfy a prescribed monotone symmetric inequality, and asks which pairs can occur as the radii of the smallest circumscribed sphere and largest inscribed sphere. It defines boundary functions through…
The paper develops a multiplicative method for constructing complete systems and bases in spaces of analytic functions, with emphasis on products of domains and complete Hartogs domains. It proves that a product system is complete, or is a basis, in the space of functions analytic on a product domai…
The paper extends the Lax convergence theorem for difference approximations of evolution equations in Banach spaces, addressing limitations concerning consistency requirements and the use of the same space for exact and approximate problems. It formulates finite-difference analogues in quotient norm…
The paper studies boundary value problems for elliptic equations in domains whose smooth boundary has conical singularities, using weighted Sobolev-type spaces adapted to the distance from the vertex. By reducing the model problem with frozen coefficients on a cone to an operator pencil after the ch…
The paper studies oscillation and nonoscillation intervals for linear ordinary differential operators of order n with continuous coefficients, relating these notions to generalized Vallée-Poussin boundary value problems and the sign of the corresponding Green’s function. It introduces conjugate poin…
This note establishes spectral criteria for boundedness of solutions on the half-axis for linear differential equations with periodic coefficients, a case not covered by earlier criteria for asymptotically constant coefficients. For first-order equations in a complex Banach space, it proves that bou…
This note studies similar tests for the Behrens-Fisher problem using analytic continuation in a complex parameter. Focusing on statistics depending on the normalized difference of sample means and the ratio of sample standard deviations, it derives an integral similarity condition and continues it t…
This note studies large deviation asymptotics for boundary crossing probabilities of polygonal trajectories formed by sums of independent identically distributed mean zero random variables, in the regime where the normalization is much larger than the classical square root scale, especially \(x\) ne…
The paper studies the minimization of a nonlinear sum of products of exponential terms with bases between zero and one, subject to row-sum and nonnegativity constraints on a matrix of variables. It introduces characteristic numbers associated with optimal points, proves their uniqueness, and uses th…
This paper studies a generalized Tricomi boundary value problem for the Lavrent’ev, Bitsadze mixed type equation with variable gluing conditions across the line of type change. The solution is represented in the hyperbolic region through boundary traces, while the elliptic region yields an integral …
This paper formulates spectral results for ergodic measure-preserving dynamical systems satisfying a density condition, Condition A, expressed through fourth-order spectral set functions and interpreted as a multiple-mixing requirement. It shows that, under this condition, the maximal spectral type …
This note studies remainder terms in limiting distribution problems for two arithmetic functions, Euler’s quotient \(\varphi(n)/n\) and the divisor sum \(t(n)=\sum_{d\mid n}2^{-d}\). Building on known existence of limiting distribution functions, it gives quantitative convergence estimates for the c…
This note studies extremal approximation problems associated with Urysohn’s metrization theorem, focusing on how changing the metric on a regular topological space with a countable base changes the corresponding class of Hölder functions. It gives a general formula for the uniform deviation of one s…
This paper studies boundary behavior and value distribution of meromorphic functions in the unit disk, extending Lange’s results on non-Euclidean filling disks for holomorphic functions. It introduces sequences of P-points for meromorphic functions, characterized by the property that in arbitrarily …
This paper studies semigroups of bounded linear operators on spaces of continuous or summable periodic functions through an averaging procedure over translations. It shows that the averaged operators form a measurable semigroup commuting with translations, have no larger norm than the original opera…
This paper studies solvable extensions of constant-coefficient pseudoparabolic and ultrahyperbolic operators in a parallelepiped, focusing on cases where classical local boundary conditions are inadequate. Using Fourier series in the spatial variables, it analyzes nonlocal boundary conditions linkin…
The paper develops a topological method for proving the existence of periodic solutions of differential equations whose right hand side may depend on delayed or functional arguments. Periodic solutions are represented as fixed points of a completely continuous operator on a space of continuous perio…
The paper develops a general framework for representing linear continuous operators on Banach function spaces by additive set functions with values in a Banach space. It defines spaces of such abstract functions, proves isometric isomorphisms with operator spaces and weakly continuous operator class…
This paper studies realizability for formulas of propositional logic in the sense of Kleene realizability under substitutions by closed logico-arithmetical formulas. It introduces several families of formulas, including variants extending Rose’s example, and proves relations among them: some are rea…
This paper formulates problems of best approximation in random normed spaces, motivated by approximation of stochastic processes observed up to a random time. It defines f-best approximation through the partial order on random norms, introduces a variance-based sigma squared best approximation, and …
This note studies real Siegel zeros of Dedekind zeta-functions and their implications for Brauer’s asymptotic formula for the class number and regulator of number fields. By combining Brauer’s method with a functional-equation argument, a generalization of Heilbronn’s theorem, and estimates for comp…
This paper reports results on cubature formulas for approximate integration over the sphere, emphasizing formulas whose nodes have the symmetry of regular polyhedra and whose construction uses group-character methods. It presents several invariant formulas exact for spherical polynomials up to speci…
This paper outlines a method for studying hypothesis tests and interval estimation problems with nuisance parameters when the underlying samples admit finite-rank sufficient statistics, leading under general conditions to exponential-family representations. The approach uses analytic continuation in…
This note studies the use of direct methods for proving existence of an optimal control in a class of Lebesgue measurable controls taking values in a closed domain. It formulates controlled processes as fixed points of uniformly contractive operators on a space of continuous vector functions and con…
This note studies nonrandomized similar tests for the Behrens-Fisher problem for two independent normal samples with unknown means and variances, under the first three of Wald’s axioms. Reducing such tests to measurable functions of two invariant statistics, the authors distinguish regularly and sin…
The paper studies quadrics in Cayley-Klein spaces whose absolute defines a quasi-Euclidean structure, with particular emphasis on quasi-elliptic spaces. Using characteristic matrices associated with the quadric and the absolute, it establishes invariant polynomials and coefficient data under the mot…
This note extends a uniqueness theorem for entire Dirichlet series with increasing exponents to the case in which the exponents satisfy asymptotics of the form λn comparable to c n1/q times a slowly increasing factor, with 1 < q < 2. Using Young conjugate functions to describe the corresponding grow…
The paper studies unitary representations, with respect to an indefinite scalar product, of locally compact groups in spaces of finite rank of indefiniteness, with emphasis on the complex unimodular group of second order, locally isomorphic to the Lorentz group. It develops auxiliary results on irre…
This paper addresses two questions posed by Dieudonné concerning locally convex spaces with a fundamental sequence of compact sets, namely whether a barrelled or bornological space with this property must coincide with the strong dual of a Fréchet-Montel space, and whether the result extends to infr…
The paper develops transference theorems in Diophantine approximation in which bounds are imposed on products of variables and fractional parts of linear forms, termed hyperbolic transference theorems, rather than on maxima as in the classical cubic case. Using a method based on estimates of trigono…
The paper addresses a problem of P. S. Urysohn asking whether there exists a continuum whose space of relative distances is zero-dimensional. It constructs such a continuum as an inverse limit of compacta in the Hilbert parallelepiped, using auxiliary plane continua and monotone nearly contractive p…
The paper studies the localization and computation of an eigenvalue of a complex block matrix whose off diagonal blocks are sufficiently small, so that an eigenvalue is expected near the scalar block entry. Using a determinant factorization via the Schur complement and bounds derived from a prescrib…
The paper studies Archimedean K-lineals in which every proper l-ideal is contained in a maximal l-ideal, a class introduced as MK-lineals and presented as a generalization of K-lineals with a strong unit. Using the representation of a K-lineal on its canonical bicompact space, the author characteriz…
This paper studies multidimensional nonisotropic surfaces in conformal space that carry a net of lines of curvature, defined by the simultaneous canonical reduction of the angular metric and an invariant pencil of quadratic forms. Using conformal frames, the Darboux transfer to projective geometry, …
This note studies testing hypotheses that an observed Gaussian process has zero trend or a known additive trend, focusing on when the induced probability measure with trend is absolutely continuous with respect to the zero-trend measure and on computing the corresponding likelihood ratio. Using a me…
This paper studies a one-dimensional mixed initial boundary value problem for a second order quasilinear hyperbolic equation with homogeneous boundary conditions. Using the Fourier method, it formulates sufficient conditions on the initial data, nonlinear term, parameter, and time interval for exist…
This paper studies singularities of fundamental solutions for homogeneous linear partial differential operators with constant real coefficients in three variables, focusing on cases where the associated algebraic characteristic geometry has real double singularities. Using local expansions of integr…
This paper develops an algebraic theory for first order elliptic systems on a closed Riemann surface, focusing on generalized constants, multiplicative generalized constants, and generalized analytic functions. It proves parity and existence results for generalized constants, establishes uniqueness …
This note gives sufficient conditions under which special automorphisms and special flows built over a Kolmogorov system are again K-systems. It proves that a special automorphism with an integer-valued roof function is a K-automorphism when the roof values are relatively prime and a specified decre…
This paper studies the spectrum of ordinary differential operators on the whole line with complex periodic coefficients, extending Floquet spectral analysis beyond the self-adjoint case. Using monodromy multipliers, conditional stability, Weyl-type approximate eigenfunctions, and resolvent kernel es…
The paper classifies Riemannian and pseudo-Riemannian spaces of the first three lacunarities with maximal mobility under homothetic motions. Using known lacunar results for isometry groups and the differential equations defining infinitesimal homotheties, it relates the order of homothetic motion gr…
This paper studies quotient mappings of Hausdorff spaces, focusing on the failure of quotient maps to be hereditary and introducing pseudo-open maps as the hereditary quotient maps. It proves that pseudo-open images of metric spaces are exactly Fréchet spaces, gives related characterizations for loc…
This note develops an analogue of Fisher information for parametric families whose densities need not be differentiable with respect to the parameter. It first introduces a nonsymmetric divergence between two probability measures and records its basic properties, including separation, monotonicity u…
This paper generalizes the notion of reductive homogeneous spaces to cases where an invariant affine connection cannot in general be introduced. It defines classes of homogeneous spaces indexed by a positive integer and corresponding families of differential groups, using decompositions of the stati…
The paper studies the spectral function of a self-adjoint elliptic differential operator, with emphasis on its smoothness near the boundary of the domain. It first formulates expansions in generalized eigenvectors for rigged Hilbert spaces and Carleman operators, showing that the spectral projection…
This paper applies Linnik’s dispersion method to several binary additive problems involving primes, products, and binary quadratic forms. It derives lower estimates for the number of representations of primes in the form p equals a shifted value of a quadratic form, yielding infinitude results for p…
This paper studies free polynilpotent groups defined by iterated terms of lower central series, a class that includes free solvable groups, and develops parallel notions for Lie rings. It proves that the Lie ring associated with a free polynilpotent group is the corresponding free polynilpotent Lie …
This paper studies boundary behavior of generalized solutions to uniformly elliptic Dirichlet problems with zero boundary data in bounded domains, using Wiener capacity conditions near a boundary point. It proves that an averaged positive capacity condition for the complement implies a Hölder estima…
