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 equation $\ddot{x}=f(x)-R(x,\dot{x})$ with a discontinuous right-hand side, which can be interpreted as a generalized pendulum equation, is considered. This work is devoted to the issues of the existence and relative positioning of global limit cycles. Estimates of the distance between two globa…
This note studies when a regular row-finite complex matrix transforms every sequence tending to infinity within a prescribed unbounded domain of the complex plane into a sequence tending to infinity within another such domain. It extends notions related to complete regularity from real divergent seq…
The paper studies periodic solutions of functional differential evolution equations with retarded arguments by analyzing the shift operator along trajectories in spaces of continuous vector functions. Using cone and wedge methods, it establishes semipositivity and complete continuity of the period s…
This paper formulates a class of convex stochastic programming problems in which the objective coefficients and constraint matrix elements are random variables with given second moments. By representing the decision variables in Hilbert spaces of square integrable random variables, the problem is re…
The paper studies Cauchy problems for second order nonlinear abstract hyperbolic equations in a Hilbert space with time dependent positive self-adjoint operators. Using semigroup methods, successive approximations, energy estimates, and a coefficient-freezing reduction for an operator depending on t…
The paper studies bases for the algebra of unary primitive recursive functions under addition, superposition, and iteration, extending earlier results based on second order arithmetic progressions. For any strictly increasing primitive recursive arithmetic progression of order k at least 2, it analy…
This paper studies uniqueness of weak solutions to the Cauchy problem for a first order conservation law with two independent variables, allowing nonconvex flux functions beyond the earlier convex setting. It introduces a broad class of bounded measurable functions possessing one sided traces on Lip…
The paper investigates a singular Cauchy problem for the generalized wave equation $$ z_{xx}=z_{ss}+\frac{a}{s}z_s+b^2z,\quad z(x,0)=\tau(x),\quad \tau_s(x,0)=0.\tag{1}$$ Using the integral representation of its solution, the author constructs basis series expansions of two types for $z(x,\lambda s;…
The paper studies upper bounds for the defect of a metrizable space, defined as the least dimension of a remainder in its compact extensions, in relation to the set of points at which the space is not peripherally compact. It proves auxiliary dimension theoretic lemmas on finite closed covers of tot…
In connection with the study of one-dimensional mixed problems for second-order parabolic systems containing time derivatives in the boundary conditions, this paper provides an asymptotic representation of the solution to the spectral problem (1)–(2) for a system of ordinary differential equations o…
The paper derives inversion formulas for the fundamental integral representation of p-analytic functions in the right half-plane with characteristic p = x^k. Using the adjoint p-analytic function, its relation to generalized analytic functions, and an auxiliary x^{2-k}-analytic function, the argumen…
This note studies abstract structures equipped only with a lattice order and scalar multiplication by nonnegative real numbers, motivated by the positive cone of a K-space. It defines and analyzes \((l,\lambda)\)-systems, their components and projections, and introduces additional axioms governing d…
This paper studies Cauchy and mixed boundary value problems for second order linear and quasilinear hyperbolic equations whose principal part may degenerate in the domain and on the boundary. It gives sufficient smoothness, integrability, and structural positivity conditions on the coefficients and …
The paper studies rings of cohomology operations and Adams type spectral sequences for extraordinary cohomology theories, with emphasis on complex cobordism and stable k-theory. It gives conditions under which an Adams spectral sequence based on a spectrum converges to stable homotopy groups, then c…
The paper develops a mod 2 degree theory for certain continuous mappings from bounded subsets of Banach spaces into the unit sphere, extending ideas related to the Leray Schauder degree. It defines a class of admissible mappings via finite-dimensional subspaces and linking coefficients, proves invar…
The paper proves a spatial global injectivity theorem for quasiconformal mappings: a locally homeomorphic quasiconformal mapping of three-dimensional Euclidean space into itself is in fact a homeomorphism, and its image is all of space. The argument develops modulus estimates for families of curves …
The paper studies algebraic unitary and orthogonal invariants of systems of square matrices, with emphasis on minimal integral rational bases and minimal complete systems. It establishes general reductions relating unitary and orthogonal invariants to affine invariants, showing that traces of produc…
This paper studies boundary value problems for properly elliptic equations in which the Shapiro-Lopatinskii condition fails at every boundary point but a uniform form of noncoercivity is present. Using generalized homogeneous expansions near the boundary and singular integro-differential or pseudodi…
The paper develops sharper inequalities for comparing distribution functions through their Fourier-Stieltjes transforms, improving on classical Berry and Esseen estimates in settings relevant to uniform central limit approximations. These inequalities are combined with a new bound for characteristic…
The paper studies boundary value problems for second order quasilinear elliptic equations in divergence form on a composite domain divided by an internal interface. It formulates Schauder type a priori estimates for a corresponding linear problem with conjugation conditions on the interface and an o…
This paper studies Hausdorff symmetrizable spaces through weak epsilon-maps and epsilon-maps onto auxiliary spaces. It proves that a sequence of continuous weak 1/n-maps induces an embedding into the product of the target spaces, and that closed 1/n-maps yield a homeomorphism onto the image, giving …
This paper studies the local behavior near the origin of a nonautonomous system of differential equations whose nonlinear term is small in a Lipschitz sense, comparing it with the corresponding linear system with constant matrix. Extending earlier one-sided asymptotic results to functions defined fo…
This paper studies admissibility of Monte Carlo cubature procedures for square integrable functions, using variance domination as the criterion within a specified class of unbiased randomized procedures. For procedures based on determinant ratios associated with a finite orthonormal bounded system, …
The note extends A. N. Kolmogorov’s uniform approximation theorem for sums of independent identically distributed variables to partial sums of random variables forming a homogeneous Markov chain under an exponential ergodicity condition. The proof uses Bernstein’s blocking method to separate the sum…
For a hyperbolic equation of the form $$U_{tx}=f(t,x,U(t,x),U(t-\tau,x),U_t(t,x),U_t(t-\tau,x),U_x(t,x)U_x(t-\tau,x))$$ with an initial function $\varphi(t,x)$ defined for $(t,x)\in[t_0-\tau_0,t_0]\times\Omega$ and with a delay $\tau=\tau(t,x,U,U_t,U_x)$ that depends not only on the independent vari…
This paper studies generators for perfect partitions in ergodic theory, focusing on ergodic automorphisms of Lebesgue spaces with finite entropy. Building on results of Rokhlin and Sinai, it proves by a direct construction that any perfect partition for such an automorphism has a countable generator…
This paper studies cyclic invariant subspaces of bounded dissipative operators in a separable Hilbert space whose spectrum is concentrated at zero and whose resolvent growth satisfies a logarithmic bound. Using a universal model built from a direct sum of simple Volterra dissipative operators and it…
This paper derives convergence rate estimates for projection type approximations to elliptic boundary value problems with positive definite self-adjoint differential operators of order 2k. Using a variational framework, it constructs approximating spaces based on regular cellular subdivisions, diffe…
The paper derives an explicit transformation for polynomial sums of iterated operators of the form \(t^\alpha D\), where \(D\) denotes differentiation and the powers \(t^\alpha\) are taken on fixed branches. It gives coefficients expressing such operator sums as ordinary differential operators with …
The paper studies multidimensional integral operators on domains in Euclidean space whose kernels are homogeneous of order minus the dimension, with attention to weighted Banach spaces of bounded, continuous, and integrable functions. Under rotational invariance and explicit summability conditions o…
This paper studies conditions under which infinite solvable, generalized solvable, and nilpotent groups contain proper infinite subgroups preserving the same derived length or nilpotency class. It introduces the notions of stably solvable and stably nilpotent groups, proves that infinite solvable or…
This paper studies singular Cauchy and Tricomi problems for second-order hyperbolic equations with coefficients singular on the coordinate axes, including equations with constant and variable perturbing terms. Using Riemann functions, Green-Hadamard resolvents, and special functions such as Humbert,…
A system of differential equations containing angular coordinates is considered. The phase space of such a system is cylindrical. Based on the behavior of trajectories on covering spaces, a classification of the trajectories of the system under consideration is introduced. Conditions for the absence…
The paper studies positive periodic solutions of a nonlinear second-order differential equation with periodic coefficients, nonnegative nonlinearity, and a nonoscillation assumption on the associated linear equation. Using cone-theoretic methods, it gives sufficient conditions for the existence of n…
This paper generalizes Chebyshev’s integral inequality from one variable to functions of several variables with a nonnegative weight. It proves that the weighted inequality over every subdomain holds if and only if the two functions are functionally dependent and one is a nondecreasing function of t…
This note derives a generating function for the eigenvalues of Casimir operators associated with irreducible representations of classical groups. Starting from previously obtained formulas for these eigenvalues, the authors express them through a product formula involving the shifted highest weights…
The paper develops Schauder-type estimates for solutions of higher-order elliptic equations and systems under general boundary conditions in spaces with refined Hölder exponents. It introduces function classes defined by moduli of the form r to the alpha of r, proves interior estimates for Douglis-N…
This note proposes an iterative method for linear and quadratic programming problems with nonnegativity inequalities and linear equality constraints, extending the method of steepest descent to constrained extremal problems. For linear programming, the method defines dual estimates through a weighte…
This paper develops a framework for spatial mappings with bounded distortion in Euclidean space using conformal norms, Sobolev class assumptions, Jacobians, and local degree. It defines distortion coefficients for linear and Sobolev mappings, proves continuity and almost everywhere differentiability…
This note studies best approximation of finite and infinite sets by elements of a convex subset of a Banach space, using convex monotone functionals to measure approximation error. It introduces support functionals at generalized points, that is, minimizing sequences, and proves criteria characteriz…
The paper addresses the numerical solution of Fredholm integral equations of the first kind, emphasizing the ill conditioning of direct discretization and its relation to smoothing problems in measurement. It proposes approximating the unknown and given functions by low degree expansions in Chebyshe…
This article conducts a qualitative study of a second-order differential equation with a discontinuous right-hand side: $$\ddot{x}+a\dot{x}+bx=-\varphi(x)\operatorname{sign}x(Ax+\dot{x})$$ where $a0$, and $b$ is of arbitrary sign. The function $\varphi(x)$ is assumed to be continuous for all $x$, pi…
The paper studies the asymptotic growth of Kolmogorov epsilon entropy and epsilon capacity for Arzelà compacta of real functions defined on bounded closed subsets of Euclidean space, with a prescribed modulus of continuity. It reviews known estimates for connected sets and then identifies the geomet…
The paper addresses the generalized Hardy-Littlewood problem for representations of a natural number in the form p plus a primitive positive binary quadratic form, with the additional restriction that the integer point lies in a prescribed sector. It outlines a proof of an asymptotic formula for the…
This paper studies uniform convergence of fundamental matrices for perturbed linear systems of ordinary differential equations on an interval, \(\dot X_n=(A+R_n)X_n\), toward the unperturbed system \(\dot X=AX\). It proves a reduction theorem showing that this convergence is independent of the backg…
The paper considers a class of systems of linear differential equations with almost-periodic coefficients. It is proved that the systems of the selected class are regular. Bibliography: 6 items.
