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 addresses the ill-posedness of optimal control problems in which minimizing sequences for a cost functional may fail to converge uniformly to an optimal control, even when the corresponding trajectories and functional values are close to optimal. It proposes a regularization approach based…
The paper studies error estimates for cubature formulas on regular lattices applied to periodic infinitely differentiable functions, extending earlier results for Sobolev spaces. It introduces classes of functions defined by bounds on derivatives with specified growth order and type, relates these c…
The paper formulates an abstract Banach space analogue of the Rudin-Carleson theorem on extending continuous functions from measure zero subsets of the unit circle by functions analytic in the disk. It proves that, under a decomposition of the dual space into two subspaces satisfying weak closedness…
The paper studies invariant equipping of special type submanifolds in projective space whose higher order osculating spaces fail to have maximal dimension, a case not covered by existing equipping schemes. For the case where the third order osculating space has dimension lowered by one, the author c…
This note studies homotopy and topological invariance properties of rational Pontryagin classes of closed orientable manifolds, expressed through Hirzebruch L-classes. It proves that the class Lk in dimension 4k+1 is a homotopy invariant, establishes a conditional homotopy invariance result for cert…
The paper studies branching of small solutions of analytic nonlinear operator equations in Banach spaces when the kernel of the linearized operator has finite dimension greater than one. Using the Lyapunov-Schmidt reduction, Weierstrass preparation, greatest common divisors in rings of convergent po…
The paper studies the divisor problem in segments of arithmetic progressions, seeking asymptotic formulas for sums of the k-fold divisor function over residue classes with moduli as large as possible. It proves a uniform asymptotic formula for primitive progressions, with an explicit main term invol…
This paper studies infinitesimal bendings of convex surfaces with plane boundary subject to sleeve constraints, distinguishing elastic sleeves that move as rigid bodies from nonelastic sleeves that may themselves bend. For simply connected caps and doubly connected belts of positive curvature satisf…
The paper introduces characteristic coefficients for probability distributions as expectations of exponentials under the transformation z equals 2 arctan x, providing bounded quantities that exist for all distributions and can be statistically estimated when ordinary moments may fail to exist. It de…
The paper investigates whether constructive propositional logic has analogues of Sheffer’s stroke, understood as single formulas from which all formulas are expressible under substitution and equivalence in a given logic. It defines functional completeness and Shefferian formulas for superconstructi…
This note develops a theory of linear polynomial operations for functions on a compact commutative topological group with invariant normalized measure, generalizing trigonometric polynomial operators on the circle. Generalized trigonometric polynomials are defined as finite linear combinations of ch…
This note extends general ergodic theory for semigroups of linear operators from Banach spaces to spaces weakly normed over semifields, including complete locally convex settings. Using norms with values in the cone of a semifield, it defines basic systems of averaging operators and proves a Cesàro …
The paper studies free algebraic groups and free abelian groups generated by a space equipped with a system of pseudometrics, with emphasis on how left-invariant and invariant group topologies affect dimension. It constructs maximal compatible left-invariant and invariant pseudometrics extending a g…
This paper studies metric distortion for plane topological univalent mappings of bounded domains whose coordinate functions, together with those of the inverse mapping, belong to a Sobolev-type class with bounded Dirichlet integral. Using the Carathéodory compactification by prime ends and the relat…
This note reformulates the general Kurosh and Amitsur theory of radicals of associative rings in terms of modules and representations. It introduces general classes of modules, defines the corresponding module-theoretic radical as the intersection of annihilators, and proves standard radical propert…
This note develops a stationary formulation of abstract scattering theory for self-adjoint operators, initially under a nuclear perturbation assumption. Using boundary values of resolvents and differentiability properties of spectral measures, it derives integral representations for wave operators a…
This paper studies elliptic and more general boundary value problems in which different boundary conditions are imposed on different parts of a smooth boundary, meeting along lower dimensional transition surfaces. Using factorization conditions for the associated boundary symbols and systems of pair…
The paper investigates whether uniqueness properties of analytic functions, known for limits of uniformly convergent analytic sequences in domains, can be extended to closures of analytic functions on nowhere dense closed sets. It constructs Cantor-type bounded closed sets by iteratively removing ce…
This paper extends regularization methods for linear ill-posed integral equations of the first kind to a class of nonlinear equations, with motivation including inverse problems such as gravimetry. It introduces a smoothing functional combining the squared residual in the data space with a weighted …
The paper studies transitive-differential transformation groups through their associated graded Lie algebras of polynomial vector fields and formulates irreducibility in terms of invariant subspaces of the underlying vector space. It proves that irreducible algebras can have order at most two, relat…
The note generalizes a theorem of E. M. Landis on the possible rate of decrease of solutions of elliptic equations in a half-strip. It shows that for a self-adjoint second-order elliptic equation in divergence form, the same lower bound on decay holds under minimal assumptions: the leading coefficie…
The paper studies the global Cauchy problem in a half-space for a first-order nonlinear equation with several spatial variables, under convexity assumptions on the dependence of the flux on the spatial gradient and Lipschitz bounded initial data. It defines a generalized solution satisfying Lipschit…
This paper studies the large eigenvalue asymptotics of the discrete spectrum for the boundary value problem \(w''(x)-\lambda^2 p(x)w(x)=0\), \(w(\pm\infty)=0\), where \(p\) is first a polynomial and then an entire function. The method continues the asymptotics of a solution decaying at \(+\infty\) i…
This paper generalizes the Riemann-Schwarz symmetry principle for holomorphic functions by replacing the usual condition on the real part with a Riemann-Hilbert boundary condition involving a nonvanishing Hölder coefficient. It shows that, after multiplication by an explicitly constructible holomorp…
This note extends a variational method for quasiconformal mappings to closed Riemann surfaces represented by Fuchsian groups. It derives local and integral variational formulas for the mapping function and for changes in the moduli of a surface, and relates these formulas to Abelian differentials an…
This paper studies effective error estimates for finite difference solutions of the Dirichlet problem for the Laplace equation on polygonal domains, where corner singularities can make higher derivatives unbounded and invalidate standard smooth-domain estimates. It derives explicit bounds for deriva…
The paper studies a fourth-order Sturm-Liouville type boundary-value problem with continuous potential and finite endpoint limits, analyzing its eigenfunctions as entire functions of the spectral parameter. Using identities for third-order minors of the Wronskian, the author constructs a resolvent-t…
This paper develops a power expansion method for approximate solutions of one-dimensional boundary-value problems on a finite interval. The proposed representation expresses a polynomial approximation through derivative values at both endpoints, allowing boundary conditions and the differential equa…
The paper addresses gradient relaxation for nonquadratic twice continuously differentiable functionals on finite-dimensional Euclidean space, under assumptions ensuring a unique stationary point and suitable behavior of level sets. It shows why standard steepest descent and stationary relaxation met…
This paper studies boundary value problems for quasilinear elliptic systems generated by a strongly positive self-adjoint elliptic operator in a Sobolev space with homogeneous boundary conditions. Using growth and sign conditions on the nonlinear term, together with compactness properties of the inv…
The paper studies inequalities relating norms of mixed, including fractional, derivatives of functions of several variables to norms of finite differences. It introduces functionals of maximization type and special functionals, defines maximal bodies of smoothness via weighted mixed differences, and…
This note develops a method for estimating resolvents of non-self-adjoint operators in abstract spaces, especially compact operators in Hilbert spaces, using determinant-type functions, singular numbers, and function-theoretic estimates. An auxiliary finite-dimensional lemma bounds modified determin…
The paper formulates a linear programming model for distributing multiple product types from enterprises to consumers through intermediate points with limited processing capacities, covering operations such as transshipment, storage, sorting, packaging, assembly, or further production. It gives nece…
The paper studies products of varieties of groups through a generalized wreath product construction based on verbal products. It defines the verbal wreath product associated with a system of identities, records its basic functorial and structural properties, and proves an embedding theorem for quoti…
The paper develops a general local method for studying the Noether property of bounded linear operators of local type on vector-valued spaces over finite-dimensional compact Hausdorff measure spaces. It introduces local left and right regularizers, equivalence and quasi-equivalence at a point, and e…
This paper studies when infinite products of nonatomic Lebesgue measure spaces are isomorphic, as measure spaces, to the corresponding direct product. Using notions of metric weight, homogeneity, Lebesgue sub-sigma-algebras, independent sigma-algebras, and measurable partitions, it proves that any p…
This paper addresses Mahler’s hypothesis on the metric approximation of transcendental complex numbers by values of integral polynomials of bounded degree, formulated in terms of the exponents eta_n. It outlines a proof of the upper bound eta_n <= 1/2, complementing the known lower bound, by estimat…
The paper studies interference phenomena for entire functions of finite degree in the class defined by bounded values on a uniform real lattice and a mild sublinear condition at infinity, a class broader than functions bounded on the real axis. It determines when finite sums of shifted values, espec…
This note gives an example of instability in a nearly integrable Hamiltonian system with a five-dimensional extended phase space, showing that the existence of many conditionally periodic motions does not imply global stability in this dimension. It introduces whiskered tori, screening sets, and tra…
This note studies the spectrum of a singular second order non-self-adjoint boundary-value problem on the half-line with complex coefficients and a complex weight, formulated as a pair of operators \((L_\theta,Q)\) in \(L^2(0,\infty)\). Under growth and regularity assumptions on \(p\) and \(q\), asym…
This note studies completeness for a selected part of the eigenfunctions of a non-self-adjoint second order differential operator whose coefficients depend on a spectral parameter, with constant boundary conditions and the assumption that the relevant characteristic roots are complex. For the bounda…
This note studies the oblique derivative problem for harmonic functions in a multidimensional domain when the boundary vector field has polynomial coefficients. The problem is reduced to a polyharmonic Dirichlet problem and then to a first-order linear partial differential equation associated with t…
This note studies when a complete Boolean algebra equipped with a group of automorphisms admits a countably additive probability measure invariant under the whole group. Vladimirov formulates several conditions on the richness, continuity, and non-paradoxical behavior of the automorphism group, incl…
This note studies arbitrary, possibly uncountable, inverse and direct spectra of locally convex spaces whose bonding maps are weakly completely continuous. It defines spaces of types W and W′ as projective and inductive limits of such spectra, proves completeness, semireflexivity, Banach spectrum re…
The paper develops an algorithm for perturbation theory of self-adjoint operators with simple continuous spectrum. It introduces a diagonally singular matrix representation of an operator relative to a spectral resolution, separating off-diagonal and diagonal parts through Radon-Nikodym derivatives …
This paper studies flat infinitesimal connections in principal bundles over smooth manifolds and relates their holonomy homomorphisms to one-dimensional nonabelian cohomology, extending de Rham’s theorem on closed forms and prescribed periods. It defines an action of bundle automorphisms on the set …
