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 applies the contour integral method to multidimensional mixed problems for second order parabolic systems in a three-dimensional domain, with boundary conditions that include a time derivative. Under assumptions on the spectrum of the coefficient matrix, regularity and boundedness of the c…
The paper studies boundary value problems for quasilinear parabolic systems in the Douglis, Nirenberg, and Solonnikov sense, with linear boundary conditions and zero initial data in anisotropic Sobolev spaces. Using an abstract solvability theorem for nonlinear equations in Banach spaces together wi…
The paper extends Efimov-type results on complete surfaces of negative curvature from Euclidean three-space to three-dimensional Riemannian spaces with nonpositive sectional curvature. For a complete surface with negative extrinsic curvature, it derives generalized fundamental equations in asymptoti…
The paper addresses two classical descriptive set theory questions in their formal set theoretic formulation: the existence of an uncountable coanalytic set containing no perfect subset, and the existence of a non-Lebesgue-measurable set of projective type. It proves in Zermelo-Fraenkel set theory t…
This note establishes integral and local limit theorems for large deviations of normalized sums of independent, centered random variables with finite variances. Using three classes of growth functions introduced by Linnik and exponential moment conditions of the form involving h of the summands, it …
This note develops partial Fredholm-type solvability results for nonlinear operator equations in Banach spaces with completely continuous operators that possess an asymptotic derivative. Using a finite-dimensional algebraic lemma and the Schauder-Tikhonov fixed point principle, it proves necessary a…
This paper extends shortest path theorems for compact simply connected Riemannian manifolds to complete noncompact spaces with positive or nonnegative sectional curvature. It proves that in a complete noncompact Riemannian space with positive curvature bounded above by \(k_1>0\), every geodesic segm…
The paper studies topological Markov chains defined by shifts on the two-sided path space of a connected countable directed graph, focusing on when the supremum of metric entropies is attained by an invariant measure. It first analyzes a class of special graphs through a generating series for return…
This paper studies asymptotic behavior of densities and probability functions for normalized sums of independent identically distributed multidimensional random vectors with nondegenerate covariance matrix. It derives an explicit upper bound for the modulus of the characteristic function under a bou…
This note formulates general theorems on the space of isometric immersions and embeddings of pseudo-Riemannian manifolds, extending results of Nash, Kuiper, Janet, Cartan, Burstin, and Smale-Hirsch type immersion theory. Using bundle-theoretic conditions on isometric morphisms, monomorphisms, and se…
The paper studies absolute continuity of measures generated by solutions of differential equations with random Gaussian forcing in finite-dimensional Euclidean space. It compares a linear equation with a corresponding nonlinear equation containing an additional drift term, formulates conditions invo…
This paper studies stability of the residual method for ill-posed linear operator equations of the first kind in Banach spaces, where only a convex closed neighborhood filter of the exact right-hand side is given. The method selects the minimum-norm element among points whose image lies in the presc…
The paper extends a Hartogs type regularity result to generalized analytic functions of several complex variables satisfying first order systems with complex partial derivatives and analytic coefficient functions subject to compatibility conditions. It defines weak solutions through one variable wea…
This paper studies Lyapunov stability of the zero solution of a periodic analytic system of differential equations whose linear approximation has two purely imaginary characteristic exponents and all remaining exponents with negative real parts. Focusing on Lyapunov’s generally transcendental case, …
This note formulates a multidimensional Plateau problem for a new class of compact sets defined by homological boundary and relative cycle conditions in a compact Riemannian manifold. It proves an existence theorem for a measure-minimizing compact in this class and describes its regular part as a sm…
This note extends first main theorems in value distribution theory for holomorphic mappings to compact complex target manifolds without imposing Kähler, homogeneous, or projective structure. The main construction proves that on any compact complex manifold with a normalized volume form there is a co…
This note studies subdifferentials of composite convex functionals on Banach spaces, where a continuous convex mapping into a Banach lattice is composed with a monotone convex functional. It introduces a subdifferential for Banach lattice valued mappings and establishes conditions under which this s…
The paper studies the minimization over a convex compact constrained set of a nonsmooth function defined as the maximum of finitely many continuously differentiable functions. It formulates stationarity in terms of the intersection of the convex hull of active gradients with the conjugate cone of fe…
The paper studies approximation of continuous and differentiable functions on the unit cube by generalized polynomials, defined as finite linear superpositions of functions of fewer variables with respect to prescribed one variable systems. It establishes existence and characterization results for b…
The paper develops a refinement of uniform homology groups for metric spaces, motivated by the inability of earlier groups to distinguish manifolds whose bounding chains grow with different diameter orders. For each admissible order of growth, it defines subsets determined by cycles requiring chains…
This note studies isometric immersions of two-dimensional Riemannian metrics into Euclidean three-space by surfaces of class C1 under an added condition of regularity with respect to affine transformations. It introduces affine regularity and proves structural results for immersions of metrics of bo…
The paper proves a Fourier-type integral representation for entire functions of one complex variable with arbitrary prescribed growth. It defines a class of entire functions controlled by a convex growth function h and uses the Young conjugate H to construct a countably normed space of entire functi…
This paper studies how the geometry of weak discontinuities affects absolute and quasi-absolute convergence of multidimensional Fourier series and eigenfunction expansions of elliptic operators. For functions on the two-dimensional torus weakly discontinuous along a smooth curve, it introduces quasi…
The paper gives a proof of Hayman’s regularity theorem for coefficients of univalent functions by establishing a more general sufficient condition for regular coefficient growth. For functions normalized in the unit disk, it assumes a maximal growth condition along a radius and a square summability …
This note studies an averaging procedure for nonlinear integro-differential equations with a small parameter, in which the memory term is replaced by an integral over an infinite interval and the resulting vector field is time averaged. Under continuity, Lipschitz, boundedness, and growth assumption…
The paper studies a second order Schrödinger type differential operator in a Hilbert space of Bochner integrable functions, with an operator valued potential depending on the real variable. Under assumptions on sectorial boundedness, Hölder continuity, growth of the operator family, and compactness …
The paper proposes a general method for solving uniquely posed problems of mathematical physics by omitting different conditions, representing the resulting families of partial solutions as functional sets, and finding the original solution as their common element. It formulates both exact and far-z…
The paper studies the location of zeros of two simple classes of periodic Dirichlet functions defined by Dirichlet series with real coefficients and functional equations relating values at s and 1 minus s. Using shortened functional equations, it derives explicit classifications of possible zero con…
This paper studies estimates for the S-numbers of functions of positive linear operators in Banach spaces, including fractional powers, logarithms, iterated logarithms, and analytic semigroups. Using integral representations of fractional powers and logarithms together with standard inequalities for…
This paper studies an elliptic boundary value problem with two free boundaries, formulated as finding a Sobolev function constrained between two obstacles and satisfying complementary sign conditions for an elliptic operator. The analysis connects this problem with a two-sided optimal stopping game …
This paper studies periodic oscillations of systems that are close to essentially nonlinear differential systems with a small parameter, focusing on the special case in which the first solvability conditions for the principal amplitudes are identically satisfied for part of the arbitrary constants. …
The note classifies nontrivial trisymmetric homogeneous Riemannian spaces with simple compact Lie groups of motions. It reformulates trisymmetry in terms of invoproducts and corresponding involutive sums of Lie algebras, proves auxiliary restrictions on the mirrors and isotropy subgroups, and reduce…
This paper constructs a broad sequence of linear positive operators defined through analytic kernels and parameter sequences, encompassing classical Bernstein, Bernstein Chlodovsky, Mirakyan, and Baskakov operators as special cases. Using Korovkin type arguments, it establishes uniform convergence o…
The paper studies uniqueness for the Cauchy problem for linear evolution systems with variable coefficients, including systems of arbitrary type solved with respect to time and systems whose spatial part is elliptic or parabolic in the sense of Petrovsky. It develops a weighted L1 estimate in a thin…
This paper studies differential games of approach for linear controlled systems with convex control constraints, constraints on selected phase coordinates, and terminal payoffs measuring distance to a target set. It formulates a programmed approach problem and an adjoint optimization problem in dist…
The paper studies uniform approximation on a rectangle of continuous functions of two variables by sums of one-variable functions, \(\varphi(x)+\psi(y)\). It identifies a class of supermodular-type functions for which the best approximation error is given explicitly by one quarter of the alternating…
This paper studies steepest descent type methods for solving nonlinear operator equations in real Hilbert spaces under assumptions weaker than the usual uniform positivity condition on the derivative. It analyzes continuous trajectories defined by differential equations involving the residual and it…
This paper studies the Cauchy problem for nonstrictly hyperbolic linear partial differential equations with variable coefficients in Gevrey-type classes. It formulates conditions on the real characteristic roots and uses pseudodifferential factorization, Gårding estimates, and induction on the order…
The paper constructs and estimates the fundamental matrix for a second order elliptic system in a three-dimensional domain with a complex spectral parameter. Under smoothness assumptions on the matrix coefficients and a negativity condition on the real parts of the roots of the characteristic equati…
This paper studies regularization of solvable but unstable extremal problems over closed convex subsets of real Banach spaces, for quasiconvex lower semicontinuous functionals. The proposed method replaces the original minimization by the search for the least norm element in approximate level sets, …
This paper studies an inverse spectral problem for the Hill equation with a real periodic potential, focusing on what data beyond the discriminant are sufficient to determine the potential uniquely. It introduces a matrix built from the fundamental solutions over one period and proves that equality …
The paper justifies Bogolyubov’s averaging method for abstract parabolic equations in a Banach space, considering evolution equations with a rapidly varying nonlinear term and an unbounded linear operator generating an analytic semigroup. Under assumptions on fractional power spaces, compactness, di…
This note studies when realizability of propositional formulas coincides with derivability in Heyting’s intuitionistic propositional calculus, focusing on formulas with limited nesting of implication. It defines a hierarchy measuring the occurrence of implication and proves that every realizable for…
The paper studies two-dimensional integral equations on a disk whose kernels are homogeneous of order minus two and satisfy a weighted summability condition. Using complex notation, polar coordinates, and Fourier expansion in the angular variable, the equation is reduced to a diagonal system of one-…
The paper develops a method for constructing separatrix surfaces and stability regions in the phase spaces of nonlinear systems of the form consisting of a linear part plus a scalar nonlinearity. By transforming the system to diagonal coordinates and introducing two-dimensional revealing sections in…
The paper develops quotient and decomposition constructions for bicompact spaces designed to separate covering dimension, small inductive dimension, and large inductive dimension. After formulating a general scheme, it constructs families of bicompacta built from ordered compacta, Cantor sets, and m…
The paper studies continuous positive functionals that are linear with respect to Minkowski addition and nonnegative scalar multiplication on convex compact sets, equivalently on convex surfaces via support functions. It identifies these functionals with elements of the dual cone of sublinear functi…
This note studies estimation of unknown finite-dimensional regression functions in the mean of a random function with known correlation kernel. Using reproducing-kernel Hilbert spaces and extended kernels, it characterizes canonical isometries associated with the random function and derives uniforml…
