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 examines whether the method of characteristic exponents, effective for estimating solutions of linear differential systems, extends to nonlinear systems satisfying a Lipschitz condition and having a trivial solution. It analyzes the possibility of choosing a uniform growth constant in the…
This note studies characteristic properties of curves that can realize absolute minima for positive definite regular and quasiregular single integrals in parametric form, without assuming differentiability of the integrand. It introduces a classification of quasiregular functionals by the linearity …
This paper develops projectively invariant moving frames for ruled surfaces contained in a fixed line congruence. Using Cartan exterior forms, it constructs two normalized frames, the K-frame and M-frame, related respectively to osculating complexes and median points, and derives their invariant dif…
This paper studies the Lie quadric associated with ruled surfaces belonging to a line congruence in projective space. Using Cartan’s method of exterior differential forms and first order adapted tetrahedra, it derives an invariant equation for the Lie quadric of an arbitrary ruled surface of the con…
This note studies linear extrapolation for discrete homogeneous random fields indexed by one spatial and one temporal integer variable. Using the spectral function of the field, it gives necessary and sufficient conditions for regularity and singularity, including logarithmic integrability criteria …
This paper studies one-sided and two-sided invertibility in abstract semigroups and applies these notions to semigroups of transformations. It establishes structural results relating products of invertible elements, cancellability, and the decomposition of a semigroup into classes of left, right, tw…
This note studies vector systems of singular convolution-type integral equations on the real line and on paired half-lines, extending earlier work on scalar equations. Using Fourier transforms, matrix function theory, and Riemann boundary-value problems for systems of analytic functions, the equatio…
This note generalizes the classical separation properties of consecutive Chebyshev polynomials to a broader class of pairs of functions satisfying boundedness, alternation, and a Chebyshev-type restriction on zeros of their linear combinations. The author proves, by counting zeros of the auxiliary f…
This note studies continuous mappings from an open subset of the product of an arbitrary topological space with a Euclidean space into a Euclidean space, focusing on the behavior of the fiber maps under variation of the topological parameter. Using topological degree and local degree, it proves stab…
This paper studies how rearrangements of the trigonometric system affect convergence, summability, and basis properties of Fourier series. It gives sufficient conditions, formulated through best approximation in the L2 metric and through an integral smoothness condition, under which a Fourier series…
This paper studies global stability of a class of nonlinear differential equations arising in indirect automatic control with one regulating element. It reformulates Lur’e’s Lyapunov method in invariant matrix form for systems with a stable open-loop matrix, using a quadratic Lyapunov function plus …
The paper introduces a comparison principle for linear operators in a Hilbert space based on the condition that their images form an acute angle, and derives consequences for defect indices, normal solvability, and approximation schemes. It proves convergence results for projection methods and for a…
This note studies a class of entire functions arising as kernels in integral representations connected with the Cauchy problem for second order ordinary linear differential operators. Starting from a generalized power series related to the function \(U_0^{(1)}\), the paper derives the third order di…
The paper studies when Fredholm theory extends from a nested family of Banach spaces to associated complete linear topological spaces formed as intersections, together with their conjugate spaces. It defines the relevant topologies, analyzes operators whose action is independent of the Banach parame…
The paper studies asymptotic stability of the zero solution for systems of ordinary differential equations whose right-hand sides are homogeneous functions. It derives necessary restrictions depending on the homogeneity order, establishes Lyapunov-type homogeneous functions satisfying associated dif…
The paper examines the use of chi-square goodness-of-fit statistics for testing independence in sequences of trials with finitely many states, especially against Markov chain alternatives. Using limiting normal distributions of transition-frequency vectors and their covariance matrices, it derives l…
This paper studies the one-dimensional two-phase Stefan problem with a moving interface, emphasizing the nonlinearity introduced by the boundary condition at the phase boundary. The author reduces the problem to an infinite system of ordinary differential equations by expanding the temperature field…
This note studies spaces of closed rectifiable curves on a closed Riemannian manifold, with and without marked points and orientations, and relates their homology to the theory of closed geodesics. It identifies circular connectivities with mod 2 Betti numbers of appropriate curve spaces, gives form…
This paper studies functionally closed completely regular spaces, also known as Hewitt Q-spaces, through the behavior of continuous real-valued functions under extensions. It gives criteria for an extension to be regular in terms of closures of countable intersections of zero-sets, constructs a cano…
The paper studies existence and uniqueness for Cauchy and first boundary value problems for one-dimensional quasilinear parabolic systems with coefficients depending on the unknown functions. Using Rothe’s method and a priori estimates for solutions and their derivatives, it proves solvability in re…
This note establishes several inequalities estimating derivatives of trigonometric and algebraic polynomials under pointwise or weighted norm constraints. It gives bounds for derivatives of trigonometric polynomials dominated by a nonnegative majorant with prescribed smoothness or modulus properties…
The paper studies positive definite Toeplitz forms and the associated orthonormal polynomials on the unit circle, focusing on the rate at which the ratios of consecutive Toeplitz determinants approach their limiting value. It introduces the quantity measuring this deviation and relates it to Verblun…
This note defines a class of continuous mappings of subsets of Hilbert space, denoted by Lambda and by basis-dependent classes Lambda with two orientations, using asymptotic control of projections, half-space behavior, and boundedness of inverse images of bounded sets. It proves that mappings in Lam…
This note proves uniqueness for Frankl’s boundary value problem for the Chaplygin equation in a mixed domain, under symmetry and monotonicity assumptions on the coefficient and a geometric monotonicity condition on the boundary arc. Introducing a conjugate function satisfying a first order system, t…
The paper proposes a method for reducing mixed boundary-value problems for certain partial differential equations to Riemann boundary-value problems, avoiding reliance on the Hopf and Wiener integral equation method. The argument is developed first for a modified Laplace equation in domains whose bo…
This note studies the Goursat problem for first order hyperbolic systems of differential equations with two independent variables, with data prescribed on straight lines and with solutions not assumed analytic. Using reduction to characteristic variables and Mellin transform methods, it derives crit…
This note proves convergence and derives error estimates for the method of lines applied to several boundary value problems for systems of partial differential equations. A general lemma relates the approximation error to the norm of the inverse differential difference operator and the consistency e…
The paper studies uniform equiconvergence on arcs of the unit circle between Fourier-Chebyshev expansions in orthonormal polynomials with respect to a weight and the ordinary Maclaurin expansion for analytic functions in the Hardy class H2. It proves that, under local positivity and a Dini-Lipschitz…
This note examines Dirichlet problems for model equations of mixed elliptic and hyperbolic type motivated by transonic gas flow, especially cases corresponding to supersonic zones adjacent to nozzle walls. Using explicit representations in characteristic variables, functional equations, singular int…
This paper studies boundary value problems for the wave equation on a half-space over the entire time axis, with a radiation-type condition requiring decay as the normal spatial coordinate tends to infinity. Using operational calculus and two-sided Laplace transforms, it derives explicit solution fo…
This note studies how essential cycles in compact carriers behave under continuous mappings into orientable manifolds or Euclidean spaces, motivated by a question of P. S. Aleksandrov concerning degree-zero maps of closed manifolds. Using the Phragmén-Brouwer separation theorem and linked cycles, it…
The paper studies boundary value problems for uniformly parabolic linear partial differential equations in a cylindrical domain, with mixed boundary conditions and nonpositive zeroth order coefficient. Using methods of Hopf and Oleinik, it proves a boundary point principle for solutions attaining an…
This paper addresses the classification of second-order scalar differential invariants of a quaternary differential quadratic form, emphasizing gaps in earlier treatments by Cartan and Rozenfeld. Using Thomas’s reduction of differential invariants to algebraic invariants of the fundamental tensor an…
This paper studies when a given affine connection on a three-dimensional manifold can arise from a Riemannian metric, equivalently when there exists a parallel positive-definite metric tensor satisfying the absolute differential equations for metric compatibility. It formulates algebraic integrabili…
This note studies singular integral operators in spaces \(L_p(E_m)\) and gives sufficient conditions for their boundedness in terms of the angular symbol and its derivatives. The argument represents the operator through angular spectral projections, proves their uniform \(L_p\) boundedness using a r…
This paper studies stability and uniqueness for the Cauchy problem for second-order linear elliptic equations, a problem known to be ill-posed in general but stable under boundedness-type restrictions. It states an a priori estimate for solutions in a cylinder with variable coefficients satisfying e…
The paper studies Lyapunov stability of a periodic solution of a system of differential equations whose right hand sides have first kind discontinuities across a periodic family of hypersurfaces. It defines an appropriate linear approximation consisting of ordinary variational equations between cros…
This paper determines the smallest radius of univalence for a subclass of analytic functions representable as the square of a function with square-summable Taylor coefficients and prescribed first coefficient modulus. The argument first treats polynomial approximants of even degree, analyzes their d…
This paper studies the role of left and right cancellation laws in presentations of semigroups by generators and defining relations. It compares ordinary finitely presented semigroups with semigroups obtained by adding cancellation rules, and also considers presentations using mixed relations contai…
This paper applies the theory of continuous transformation groups to qualitative questions for ordinary differential equations of the form dy/dx equals Y/X, where X and Y are real polynomials. It establishes, under stated analyticity and multiplicity assumptions, the existence of auxiliary functions…
This paper studies boundary value problems for a class of second order partial differential equations of mixed elliptic and hyperbolic type in a strip and in half planes, with a gluing condition imposed across the line where the type changes. For nonperiodic boundary data, the solution is constructe…
This paper studies the Cauchy problem for systems of linear partial differential equations whose weight is an integer greater than one, with coefficients depending on time. By reducing the system to first order in time and applying the Fourier transform, the analysis derives estimates for the fundam…
This paper studies the metric dimension of point sets and metric spaces, understood through arbitrarily fine open coverings of bounded multiplicity, in relation to classical covering dimension. It formulates several characterizations: by locally finite coverings in Euclidean space, by refinements of…
This note studies the decomposition of infinitely divisible probability laws, especially the class of such laws whose components are all infinitely divisible, using Lévy’s representation and the associated Poisson spectrum. For laws with a Gaussian component, it gives necessary conditions on the spe…
This paper presents an approximate method for solving the Dirichlet problem for the Laplace equation in a plane domain with rectifiable boundary, based on a finite difference scheme combined with a hierarchical decomposition into squares. The method expresses selected interior node values through Gr…
This paper studies boundary traces of functions on a smooth bounded planar domain whose generalized derivatives of order k have a finite weighted Dirichlet integral, with a weight comparable to the distance from the boundary raised by a parameter 0 ≤ alpha < 1. It establishes necessary and sufficien…
The paper develops a Hilbert space framework for describing degeneration when a sequence of self-adjoint operators with discrete spectra converges strongly to an operator with continuous spectrum. It constructs limiting spaces associated with spectral points, proves that the limiting action of the o…
The paper studies the Cauchy problem on the real line for equations of the form in which the time derivative of a differential polynomial operator applied to the unknown is equal to another differential polynomial operator applied to it. Using the theory of generalized functions and Fourier transfor…
This note studies the completeness of eigen and associated elements for a class of non-self-adjoint operator pencils that perturb a compact normal operator by bounded and completely continuous terms. Extending methods of Keldysh, it proves that under conditions on the finite order compact normal ope…
This paper studies the trace of the difference of two singular Sturm-Liouville operators on the half-line, a setting in which each operator has continuous spectrum and finitely many negative eigenvalues. Using spectral functions, scattering phase asymptotics, and a relation between the phase and the…
