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 studies plane homeomorphisms whose quasiconformal characteristic is unbounded but satisfies an exponential integral bound. It defines a class of mappings with Tonelli absolute continuity properties for the map and its inverse, proves an area integral estimate leading to equicontinuity, an…
The paper studies optimal control problems for systems with parameters governed by integro-differential equations not solved with respect to the derivative, including neutral type delay equations. It formulates adjoint equations and derives necessary optimality conditions for controls and finite-dim…
The paper studies the expansion of functions in approximately orthonormal systems, a situation arising in numerical orthonormalization when rounding and integration errors perturb the Gram matrix. It compares the usual Fourier coefficient method with a recursive coefficient construction in which eac…
The paper studies preservation problems for strong paracompactness and strong metrizability under continuous mappings, focusing on the role of open closed sets rather than on openness or quasi monotonicity alone. It introduces Lambda mappings, defined by preservation of open closed sets and a finite…
The paper studies structural and completeness properties of topological groups and their quotient spaces under weakened compactness assumptions. It proves that a topological group is a Lie group precisely when it is locally pseudocompact, locally connected, and finite-dimensional, extending the usua…
The paper studies parametric algorithmic problems, in which one seeks a general recursive function selecting a solution for each parameter, and introduces the stronger notion of effective refutability. It proves a criterion characterizing effective refutability in terms of effectively assigning to e…
The paper presents a procedure for applying Newton’s method to compute an isolated eigenvalue of a parameter-dependent square matrix without explicitly expanding its determinant. Using orthogonal transformations, the matrix at a fixed parameter value is reduced to a triangular form whose final diago…
This note studies a class of singular integral operators in a half-space whose kernels have singularities on a hypersurface and are related to the generalized shift operator. The authors formulate the operators in several equivalent forms, identify a necessary and sufficient cancellation condition f…
The paper studies whether all unconditional Schauder bases in certain countably Hilbert spaces are quasi-equivalent, extending earlier results from nuclear spaces and finite centers of Hilbert scales. It considers the infinite center of a completely continuous Hilbert scale, represented by weighted …
This paper proves an extension theorem for consistent sequences of sublinear functionals defined on a second category vector subspace of a Fréchet space. Using Baire category arguments, the author first derives continuity estimates for the functionals, then constructs continuous sublinear extensions…
This note studies the distribution, not only the mean, of the number of intersections between a plane curve and a random straight line meeting a containing convex domain, extending the setting of Crofton’s theorem. The author applies invariant imbedding by first treating polygonal curves through a l…
This note studies a boundary value problem for a multidimensional equation of mixed type in a bounded domain divided by a degeneracy plane, with an elliptic-parabolic operator on one side and a hyperbolic operator with parabolic degeneration on the other. Using adjoint formulations, weighted integra…
The paper develops a topological invariant, called the rotation of a multivalued vector field, for completely continuous multivalued mappings with convex values. In finite-dimensional spaces, the rotation is defined through sufficiently fine single-valued simplicial approximations, equivalently thro…
This paper studies the computation of normalized equilibrium points in concave n-person games on a bounded convex feasible set defined by concave constraints, under a strict monotonicity condition on the vector of partial payoff gradients. It presents two algorithms: one reformulates the problem as …
This paper studies minimization of quadratic functionals of the form \(\|Af-g\|^2\), where a linear operator maps a Banach space into a Hilbert space, with motivation from optimal control problems. It reduces sums of squared residuals involving several operators to this general form and uses project…
The paper studies perfect irreducible continuous mappings of locally bicompact and completely regular spaces, using proximity structures to construct a bicompact extension denoted d_XY and to analyze its functorial properties. It proves that irreducible mappings between bicompact spaces can be repre…
This paper studies a generalized Abel integral equation on the real line in Lebesgue spaces, with variable Hölder coefficients and a potential-type kernel. Using Fourier transform characterizations of fractional integration and properties of the singular Cauchy operator, it describes the range of th…
This paper studies a special class of integer linear programming problems defined by binary equality constraints and bounds between zero and one. It proves that the set of integer vertices of the corresponding polyhedron is complete, using lemmas relating complementary integer solutions to total uni…
This note gives new asymptotic mean value results for multiplicative functions under hypotheses on their values at primes and prime powers. A modification of earlier methods yields a general formula for sums of multiplicative functions, together with sufficient conditions involving angular restricti…
This paper develops a broader generalized polyharmonic operator for Lebesgue integrable functions in domains of n-dimensional space. Starting from iterated differences between spherical surface means and ball means, it defines upper, lower, and limiting generalized polyharmonic operators of the seco…
This paper studies when the resolvent of a densely defined unbounded linear operator in an \(L_2\) space is an integral operator of Carleman type. It proves necessary and sufficient criteria in terms of local essential boundedness properties of functions in the operator domain, including formulation…
This paper develops a method for proving a central limit theorem for Y-flows on three-dimensional compact manifolds, avoiding the homogeneous-space techniques previously used for geodesic flows of constant negative curvature. The argument represents such flows as special flows over Y-diffeomorphisms…
The paper studies continuous partitions of completely regular collectively normal spaces in relation to the uniform weight of the ambient space. After defining tau-discrete systems and uniform weight, it proves that if a collectively normal space has uniform weight tau, then for any continuous parti…
The paper constructs an explicit Behnke-Stein kernel, an analogue of the Cauchy kernel, on the torus represented as the Riemann surface of the algebraic function w squared equals (1 minus z squared)(1 minus k squared z squared). Using this kernel and a discontinuous normalized variant, it derives So…
The paper studies generalized Schauder systems in the space of continuous functions, obtained by replacing the linear tent function with a continuous function \(\varphi\) on the unit interval. It gives sufficient conditions, including monotonicity, interpolation at dyadic points, and a bound on seco…
The paper develops a theory of strongly continuous semigroups of bounded linear operators on a Banach space that may have a summable singularity at zero. It defines the class L, studies the infinitesimal operator and generator, and proves criteria for when the Laplace transform of the semigroup is t…
This paper establishes direct and inverse theorems for best uniform approximation of continuous functions on a finite interval by algebraic polynomials, using a modulus defined through averaging associated with the Legendre operator. Unlike earlier inverse results that yielded smoothness information…
This paper studies an inverse problem for the telegraph equation \(u_{xy}=a(x,y)u\) in a rectangle, where the unknown continuous coefficient is to be recovered from characteristic data and an additional boundary trace depending on a parameter. The solution is represented through a Volterra integral …
This paper studies maximal irreducible primitive solvable subgroups of general linear groups over an arbitrary field through an invariant series involving the maximal abelian normal subgroup and its centralizer. It proves that the subgroup A in this series is uniquely determined by the group, and de…
This note derives a representation for the Laplace transform of exp(−t2) erf(at) over the positive half-line, under stated conditions on the complex parameters a and p. The proof identifies the transform as the solution of a first-order differential equation with a vanishing condition at infinity, y…
This paper studies a class of convolution integral equations on a finite interval that arise in elasticity theory and mathematical physics, focusing on kernels whose Fourier transforms are even, nonvanishing analytic functions in a strip-like domain and have prescribed algebraic behavior at infinity…
The paper studies when weak Gaussian distributions, or realizations of Gaussian processes indexed by a compact subset of a Hilbert space, extend to measures on a Banach space or define bounded and continuous linear forms. It formulates conditions in terms of the epsilon entropy type of the compact u…
The paper studies integral equations of potential type on closed Jordan curves of bounded rotation without return points, considered in the spaces \(L_p\) for \(1<p<\infty\). Following earlier work on weighted \(L_1\) spaces, it reduces the local behavior near corner points to convolution-type opera…
This note generalizes the Weierstrass, Dedekind theorem on finite-dimensional algebras without nilpotent elements over an algebraically closed field. It proves that associativity and commutativity may be replaced by the weaker zero-associativity condition \(x(yz)=0\) if and only if \((xy)z=0\), toge…
The paper studies the possible arrangements of ovals of nonsingular real plane curves of degree six, especially those with nine to eleven ovals, in relation to earlier constructions of Harnack and Hilbert and restrictions from Petrovskii’s theorem. It states a corrected classification claim: types b…
This paper proves a transfer theorem for sums of a random number of independent, identically distributed random variables in a triangular array. Under convergence of a fixed-index sum, convergence of the normalized counting variable, and proportional growth of the normalizing constants, the limiting…
This paper studies a priori estimates and hypoellipticity for second order differential operators with nonnegative characteristic form, extending Hörmander type results to operators with multiple characteristics. It introduces a rank condition defined through iterated commutators of associated diffe…
The paper studies regularizing algorithms for ill-posed linear operator equations in Hilbert spaces when both the right-hand side and the operator may be subject to random perturbations. It considers pointwise regularization operators acting on random variables in Bochner spaces and shows that a bro…
The paper studies the Dirichlet problem for parameter-dependent pseudodifferential equations in a smooth bounded domain, under homogeneity, ellipticity with parameter, smoothness, and boundary factorization assumptions on the symbol. It extends the Agranovich and Vishik solvability theory from ellip…
This paper studies continuous and homeomorphic mappings whose associated Sobolev-type integral functionals are uniformly bounded below by weighted powers of the derivative norm. It introduces a metric determined by the weight function and proves a fundamental integral inequality relating the metric …
This note extends several notions from linear spectral theory to nonlinear operators in Hilbert and Banach spaces, focusing on regular values, spectra, and eigenfunctions. It proves localization results for the spectrum of continuous operators in Hilbert space, establishes openness of the set of reg…
The paper develops a form of optimality conditions intended for large multidimensional optimal process problems, especially those with phase coordinate constraints and suitability for machine implementation. Using a generalized Lagrange method in Banach-type spaces, it derives necessary conditions f…
This paper develops an infinitesimal and operational formulation of partial invariance for manifolds under local Lie groups of point transformations. For a regularly defined manifold, it proves that the defect of invariance equals the generic rank, on the manifold, of the matrix obtained by applying…
This paper studies when embeddings of simple arcs and closed contours in three-dimensional Euclidean space can be obtained from polyhedral models by pseudoisotopies of the ambient space. It proves that every locally unknotted simple arc admits a pseudoisotopy carrying a line segment onto it, with no…
The paper studies the index of singular integro-functional operators on Hölder vector functions defined on a finite system of Lyapunov contours, where the functional shifts are generated by an orientation-preserving homeomorphism of finite cyclic order. It relates these operators to a broader class …
This paper studies upper semicontinuity and Hausdorff upper semicontinuity of the metric projection onto convex subsets of Banach spaces, relating these continuity properties to geometric conditions on the unit sphere and supporting hyperplanes. It introduces several conditions, including EPS, compa…
This paper studies tensor invariants of subgroups of the Lorentz group that can be defined by invariance of a finite set of tensors. It states that any invariant tensor of arbitrary rank for such a subgroup can be expressed as a linear combination of tensors obtained from basic invariant tensors by …
This paper studies proximally open, or equi-open, mappings of proximity spaces, with emphasis on metrizability and completeness of their images. Using quasiuniform covers and Leader’s metrization criterion, it proves that the equi-open image of a metrizable proximity space is metrizable, and derives…
This paper addresses a problem of Aleksandrov and Urysohn on the possible cardinalities of bicompact topological spaces satisfying the first axiom of countability. Using transfinite constructions, branching systems, and the notion of a free sequence, it proves a general cardinal estimate for Hausdor…
This paper extends Lyapunov’s principle of comparison of indices for stabilizing set-theoretic transformations to broader classes of operations on topological spaces of weight τ, including Z, T, Q, R, and ΔΣ operations with transfinite chain depth under suitable cardinal and base conditions. It prov…
