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 develops a general tensor product construction for deriving multidimensional quadrature and interpolation formulas from one-dimensional approximations in normed spaces of linear functionals. A theorem estimates the error of a sparse tensor sum in terms of the one-dimensional approximation …
The paper introduces and studies spaces of countable type and point-countable type, defined through compact subsets of countable character, and shows that these classes include metric, locally compact, and Čech-complete spaces while forming subclasses of k-spaces with better stability properties. It…
The paper studies the Cauchy problem for linear Hamiltonian equations in a separable Hilbert space when the Hamiltonian operator coefficient is self-adjoint, positive, and generally unbounded, so that the resolving operator is also unbounded. Under a regularity condition on the square root of the co…
This paper outlines proofs of several results on finitely multiple open and closed continuous mappings of connected manifolds, formulated in terms of completely continuous decompositions into finite sets. It proves that every such finitely multiple mapping has bounded multiplicity, that in a bounded…
The paper studies first and second boundary value problems for elliptic equations whose coefficients degenerate at isolated interior points, at infinity, or at both points in the whole space. It introduces a beta-normality condition expressed through barrier inequalities and proves a generalized max…
Novikov studies manifolds of dimension 4k+2 through Thom space representatives, surgery, and invariants associated with kernels in middle homology, with particular attention to the 10-dimensional case. The paper defines and analyzes invariants generalizing Kervaire’s invariant by means of secondary …
This note extends classical estimates for bounded, positive-real-part, and related regular functions of two complex variables from bicircular domains to a broader class of circular domains defined by parametrized hypersurfaces and a conformal mapping of an associated planar Jordan domain. Using redu…
This note extends the theory of Pták’s B-completeness, originally developed for locally convex spaces and later related by Kelley to completeness properties of hyperspaces, to general uniform spaces. It defines multivalued uniformly continuous, almost continuous, open, regular, and biregular mapping…
This paper studies split linear groups over perfect fields, defined by closure under the semisimple and unipotent factors in the Jordan decomposition. It proves structural results for arbitrary locally nilpotent groups, including a direct product decomposition for split locally nilpotent groups and …
This paper formulates a general multidimensional linear programming problem of transportation type on an s-dimensional matrix, with constraints defined by summation over prescribed subsets of indices and a linear objective function. It derives necessary compatibility conditions for feasibility and g…
The paper studies the construction of the resolvent of the Sobolev type operator defined by the inverse Laplacian and the two-dimensional wave operator, reducing the problem to Green’s functions for an associated Dirichlet boundary value problem. Using a known fundamental solution and the method of …
The paper studies differential properties of solutions to a Dirichlet problem in the half-plane for higher-order equations with even derivatives in two variables. Using Fourier separation of variables, it derives integral representations of solutions for cases including s = 1, 2, and 3, with general…
The paper studies boundary value problems for linear uniformly elliptic second order equations in three-dimensional exterior domains, with coefficients and right-hand sides controlled by weighted Hölder norms defined through Dini functions. It establishes Schauder-type a priori estimates for the Dir…
This paper studies homotopy properties of groups of diffeomorphisms of spheres and disks, especially the quotients arising from the restriction fibration from diffeomorphisms of the disk to those of its boundary sphere. Using framed manifolds, Morse surgery, and relations between the Whitehead homom…
This paper studies when the transition function of a machine, in the sense of Ginzburg, can be represented by multiplication in an associated semigroup. It introduces right and left machines, p-machines with semigroup state sets, and m-semigroups that generate machines, then proves embedding results…
The paper introduces separating finite partitions for identifiable families of probability measures and relates them to the construction of simple consistent and asymptotically efficient parameter estimates. It defines the minimal size of such a partition and shows existence or bounds for several cl…
This paper studies error estimation for numerical solutions of nonlinear integral equations when only values at quadrature nodes are used. The equation is reduced by a quadrature formula to a finite system whose residual at the computed vector, together with the quadrature error, is used to bound th…
This note extends the Schiffer and Goluzin variational method to several classes of analytic functions in the unit disk, including bounded nonzero functions, functions with positive real part, typically real functions, spirally starlike and spirally convex functions, and functions of bounded rotatio…
The paper studies conditions under which a mapping from a subring of an ordered Boolean ring into a complete separated topological Abelian group can be extended to the closure of that subring. It formulates three compatibility and continuity conditions involving prescribed families of indexed mappin…
The paper studies the existence of regularly varying similar tests for a generalized Behrens-Fisher problem involving two independent normal samples with linear mean structures and unknown variances. It formulates invariance and sufficiency conditions extending Wald-type axioms, reduces admissible t…
This paper studies Radon integrals whose integrands and measures both depend on a parameter, focusing on conditions under which the integral converges uniformly with respect to that parameter, a property used in continuity questions. It proves a necessary and sufficient criterion analogous to the Va…
This paper studies two boundary value problems for the mixed type Lavrent’ev, Bitsadze equation in a domain whose upper part is elliptic and lower part is bounded by characteristics. For a generalized problem of type T1, the solution is represented in the hyperbolic part by characteristic data and i…
This paper studies a stability form of Liouville’s theorem for conformal mappings in n-dimensional Euclidean space within Sobolev classes. For topological mappings of the unit ball into itself whose normalized energy to Jacobian ratio is at most 1 plus a small epsilon, it proves the existence of a M…
The paper studies when a continuous direct integral of factor representations of a second countable locally compact group is itself a factor representation, motivated by the unclear structure of factor representations of types II and III. It introduces a measure-relative notion of weak equivalence, …
The paper studies Chebyshev subspaces of Banach spaces and introduces almost Chebyshev subspaces, for which uniqueness of best approximation may fail only on a first category set. It proves nonexistence results for Chebyshev and almost Chebyshev subspaces in certain nonseparable or nonreflexive sett…
This paper studies inequalities and sign properties for sums of trigonometric sine and cosine series whose coefficients satisfy weakened monotonicity or convexity conditions. Using decomposition lemmas for sequences of bounded variation and finite differences, it extends Fejér type positivity result…
This note estimates the growth of the epsilon entropy of compact classes of bounded continuous functions on a parallelepiped, defined by upper bounds on finite differences of arbitrary orders in each coordinate. Using a multidimensional polynomial approximation lemma extending Whitney’s result, the …
This paper studies general boundary value problems for elliptic systems in the sense of Douglis and Nirenberg, allowing operators of different orders in different components. It formulates a complementing condition for the principal boundary operators, analogous to the Agmon, Douglis, and Nirenberg …
The paper studies the problem of choosing m vertices of the unit n-dimensional cube so as to minimize the sum of reciprocal Hamming distances between all chosen pairs, a model motivated by arrangements of equal charges and by optimal error-correcting codes. It focuses on the case m equals half the n…
The paper studies scalar and general linear differential systems with bounded coefficients and a small retarded argument, focusing on the long term relation between arbitrary solutions and special delay free approximating solutions constructed by a small parameter method. For the equation x'(t) = p(…
This paper studies iterative averaging operators for functions on bounded plane domains, where the averaging radius varies with position and tends to zero at the boundary so that averaging sets remain inside the domain. It establishes basic order, linearity, boundedness, and equicontinuity propertie…
This paper examines the local structure of measurable functions at points where an asymptotic derivative does not exist, focusing on densities of sets determined by finite difference quotients. It constructs a measurable finite function on the unit interval, using an expansion into specially refined…
This paper studies first boundary value problems for classes of semibounded linear differential operators whose structure is described by convex polyhedra associated with the exponents of their symbols. It introduces principal and leading faces of these polyhedra and proves comparison estimates for …
This paper studies the equivalence classification of pencils of quadratic forms under linear changes of variables and linear transformations of generators, with emphasis on ternary forms over the complex numbers. It introduces general reductions using essential variables and generators, dual pencils…
This note develops a general construction of duality for admissible functors on a broad class of concrete categories, including abelian groups, topological spaces, sets, partially ordered sets, structures, and suitably restricted Banach spaces. It introduces the notion of a D-category with internal …
The paper constructs two sequent variants of the classical predicate calculus, denoted E1 and E'1, in which every derivable sequent has a unique derivation tree. Building on earlier calculi E0 and E'0, it introduces marked formulas and carefully constrained quantifier rules, including deterministic …
The paper studies a Dirichlet problem for a class of quasilinear elliptic equations in a bounded domain under monotonicity, growth, and summability assumptions that allow logarithmic nonlinear growth. It applies a Friedrichs involution transformation to replace the original formulation by an equival…
This note studies when a topological space that is the union of at most a cardinal τ many subspaces of weight at most τ must itself have weight at most τ. It extends earlier results on locally bicompact spaces by giving criteria involving networks, bicompactifications with small remainders, local ne…
This paper studies stationary traveling-wave solutions for a one-dimensional combustion model coupling temperature and active-substance concentration with diffusion and reaction terms. By reducing the partial differential system to an ordinary differential boundary-value problem and analyzing its ph…
This paper studies conformal mappings of finitely multiply connected plane domains onto multisheeted canonical surfaces, allowing prescribed logarithmic and principal singular parts at interior points. It proves existence and uniqueness results for mappings whose boundary components go to straight l…
The paper studies higher order asymptotics for the distribution of the maximum likelihood estimator of a scalar shift parameter in densities of the form c exp(−F(x−θ)). Under smoothness, integrability, growth, and regularity assumptions on F, the authors derive an expansion for the distribution of t…
This paper addresses whether the class of RI*-groups is radical, equivalently whether it coincides with Baer’s class of subsolvable groups in the minimal radical class generated by abelian groups. Using an Ado-McLain type group constructed from matrix-like generators indexed by rational numbers, the…
This note introduces classes of completely regular spaces defined by refining systems of covers, including spaces with tau-locally finite and tau-star finite bases, and relates them to generalized forms of metrizable, paracompact, and strongly paracompact spaces. It proves embedding and universality…
The paper addresses the computation of the mathematical expectation of a quasi-additive function defined on random paths in a finite multigraph with specified transition probabilities at each vertex. It defines quasi-additivity through an associated multiplicative path function and develops formulas…
This paper studies normal subgroups of the multiplicative group of a division ring, extending results related to the Cartan, Brauer, Hua theorem and Scott’s theorem on abelian normal subgroups modulo the center. Through a sequence of ring-theoretic and group-theoretic lemmas, it proves that locally …
The paper studies a generalized notion of periodic extension for functions in closed subspaces of L2 generated by exponential monomials associated with a complex sequence with finite multiplicities. It formulates the extension problem as a norm inequality on finite exponential sums and introduces re…
The paper studies the asymptotic distribution of integer matrices of order n with fixed determinant N after normalization to determinant one, restricted to a Jordan-measurable domain in the unimodular group. It proves an asymptotic formula for the number of such matrices, first for completely primit…
The paper studies a class of ultraparabolic partial differential equations with ellipticity in selected spatial variables and first order dependence on time and additional variables, motivated by problems in probability theory, Brownian motion, and boundary layer theory. Under specified regularity, …
This note studies simultaneous linear Diophantine approximation for triples of real numbers through inequalities involving two linear forms and an error of order \(1/\sqrt{x}\). Building on Minkowski’s lemma and a refinement attributed to Cassels’ method, it establishes infinite solvability with an …
This paper studies local to global questions for rational algebraic surfaces, focusing on analogues of the Minkowski-Hasse principles for curves of genus zero. Using forms of minimal rational surfaces and Galois cohomology of their automorphism groups, it proves that both principles hold for relativ…
