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 note refines earlier results on semiregular topological spaces, finite spectra, and Urysohn, Ponomarev bicompact extensions. It identifies bicompact \(T_\lambda\)-spaces with bicompact \(T_\xi\)-spaces, proves that precisely \(T_\lambda\)-spaces admit bicompact \(T_\lambda\)-extensions, and int…
This note studies a nonlinear singular integral equation with a special Cauchy kernel on an interval in the weighted Hölder-type class \(H^k_{\alpha-\delta,\delta}(a,b)\), for \(0<\delta<\alpha<1\). It establishes mapping and continuity properties of the associated integral operator under Hölder and…
This paper studies the Cauchy problem for multidimensional second-order hyperbolic equations that degenerate on the initial hyperplane. For equations whose coefficients depend only on time, the problem is reduced by the Radon transform to a family of plane degenerate hyperbolic problems, allowing pr…
This paper studies selection problems for multivalued mappings into spaces of closed subsets, with emphasis on semicontinuity, canonical graph representations, and Borel measurability properties of selections. It establishes equivalences between upper or lower semicontinuity and openness or perfecti…
The paper studies Lyapunov stability of periodic solutions of nonautonomous quasilinear systems with a small parameter, without imposing special restrictions on the constant matrix in the linear part. After shifting a periodic solution to the origin, the stability problem is reduced to the analysis …
The paper studies bounded analytic solutions of a Riemann boundary-value problem on the complex plane cut along a ray, in the case of a plus-infinite index of power order. Under Hölder-type assumptions on the argument and modulus of the coefficient, it derives explicit representations for all bounde…
The paper derives consequences, in descriptive set theory and foundations, of hypotheses concerning the cardinality and measure-theoretic size of the set of constructive real numbers. Working within naive set theory but noting formalizability in systems such as ZF, it uses Gödel’s function on counta…
The paper extends Lyapunov’s first stability theorem to nonlinear differential equations in complex Banach spaces of the form given by a linear generator and an analytic perturbation. It treats both bounded operators with spectrum in the left half-plane and certain unbounded operators generating str…
This note studies two-dimensional Fréchet surfaces in Euclidean space whose external positive curvature, defined through multiplicities of supporting caps, is finite and whose boundary has finite length. The authors introduce the class of such surfaces and prove an isoperimetric-type area estimate i…
This note studies boundary-value problems for second-order differential equations in a Hilbert space with a variable unbounded self-adjoint uniformly positive operator. It establishes an a priori estimate implying uniqueness for several homogeneous boundary conditions, then constructs Green function…
The paper studies spectral properties of indecomposable positive linear operators in semi-ordered Banach spaces with normal reproducing cones. It gives variational characterizations of the spectral radius under several hypotheses, derives comparison results for ordered operators, and formulates inco…
The paper studies solvability and regularity for the abstract Cauchy problem \(v'(t)+Av(t)=f(t)\) in a Hilbert space, where \(A\) is a positive definite self-adjoint operator. It proves fractional integration by parts estimates in Slobodetskii spaces, including the limiting \(W_2^{1/2}\) case with b…
This paper formulates an inverse problem for a generalized wave equation with a point impulse source, asking whether the coefficient multiplying the unknown function can be reconstructed from boundary observations of the regular part of the solution at the travel time between two boundary points. Us…
The paper studies nonmeasurable partitions of a Lebesgue space into trajectories of measure-preserving automorphisms, asking which properties of an automorphism are determined by the trajectory partition alone. Using derived automorphisms, compatible maps along orbits, and Vershik’s theorem on decre…
The paper studies the Bubnov-Galerkin approximation for abstract parabolic equations in a Hilbert space with time-dependent positive self-adjoint operators and fixed domains. It develops uniform operator estimates, using logarithmic convexity and Heinz-type inequalities, for projected evolution oper…
The paper studies the field of fractions of the universal enveloping algebra of an arbitrary complex semisimple Lie algebra, extending earlier work on a structural hypothesis for such fields. It realizes the enveloping algebra as differential operators on the basic affine space and enlarges it by vi…
This note constructs test spaces for the cohomological dimension of paracompact spaces, extending earlier results for compact spaces. Using sheaf cohomology, product spectral sequences, and a large-base argument, it proves that for each prime p and integer N there is a compactum Y such that every pa…
This paper studies deficiency indices and self-adjointness for symmetric operators in direct sums of Hilbert spaces generated by finite infinite Hermitian matrices with operator coefficients. It proves a perturbation-type sufficient condition for self-adjointness, gives criteria for nonzero deficien…
This paper studies when empirical frequencies of all events in a class converge uniformly to their probabilities for independent samples, a question motivated in part by learning algorithms. It introduces the index and growth function of a class of measurable sets, proves that the growth function is…
This paper studies quantitative restrictions relating the area of a surface in Euclidean space to its diameter and curvature variation. For closed \(C^2\) surfaces contained in a ball, it proves an upper bound for area in terms of the integral of absolute Gaussian curvature and the square of the enc…
This paper addresses linear programming problems in which special algorithms are available when all constraint vectors belong to a set permitting simplified solution of associated linear systems, but only part of the vectors satisfy this condition. It proposes a general device for applying such spec…
The paper studies inductively semireflexive and inductively reflexive locally convex spaces, defined through the inductive topology on the dual generated by equicontinuous sets. It establishes criteria for these properties: inductive semireflexivity is equivalent to completeness in the strongest Sch…
This paper studies the rank of an abelian variety over a number field by relating it to Galois cohomology groups associated with a fixed prime and a maximal ramified p-extension. Under assumptions on the fields of definition of p-power torsion, it constructs global and local exact sequences involvin…
The paper studies quasi-equivalence of bases in finite centers of Hilbert scales, focusing on unconditional bases in centers associated with completely continuous, not necessarily nuclear, scales. It develops a proof using Hilbert norm equivalence for unconditional bases, estimates based on Kolmogor…
This paper studies the congruence class modulo 4 of the ideal class number of real quadratic fields K(sqrt p), where p is a prime congruent to 1 modulo 4 and p is represented as a sum of two squares. Using Hasse’s formulas for the circular unit, Gauss sums, and products over quadratic residues and n…
The paper studies a general boundary value problem for a two-function first order system of composite type in a simply connected plane domain, with one hyperbolic characteristic family and one elliptic Beltrami-type equation. Under smoothness assumptions on the coefficients and nondegeneracy conditi…
This note studies first-kind integrals of Temlyakov-Bavrin type associated with integral representations for holomorphic functions in bounded convex complete bicircular domains. For the special choice \(r_1(\tau)=\tau/a\) and \(r_2(\tau)=(1-\tau)/b\), it considers kernels defined on a product of par…
This paper studies how Banach space topology determines order-theoretic properties in normed partially ordered structures, especially KB-lineals and KN-spaces. It compares three notions of countable type, one order-theoretic and two topological, proving their equivalence for norm-complete KN-spaces …
The paper studies topological homogeneity of extremally disconnected bicompact spaces, especially absolutes of compact spaces of weight continuum, using cardinal invariants such as pi-weight, cellularity, and weakly inaccessible cardinals. It proves auxiliary results on the attainment of cellularity…
This note studies factorial s-mappings from spaces with a point-countable base onto Hausdorff spaces of point-countable type. It proves that such an image satisfies the first axiom of countability, by reducing to the bicompact case, establishing a sequence selection lemma, showing that the mapping i…
This paper studies the Cauchy problem for normally hyperbolic equations whose lower order coefficients may be unbounded in the usual Lebesgue scale. It introduces mixed norm Banach spaces and proves embedding results for Sobolev spaces into these spaces, including compactness under a strict paramete…
The paper studies homeomorphism theorems for elliptic boundary value operators in Sobolev type spaces, including spaces with boundary trace components and quotient or graph norm constructions. Starting from a known homeomorphism theorem for a properly elliptic operator with normal covering boundary …
This note studies the approximation of nonperiodic continuous functions on a finite interval by partial sums of their trigonometric Fourier series, focusing on the effect of a jump in the periodic continuation at an endpoint. Using estimates based on moduli of continuity and extremal constructions f…
This paper studies zero-sum games on the unit square whose continuous payoff kernels have a prescribed simple form on connected components outside a closed set. It introduces families of multivalued mappings associated with this closed set and proves a sufficient condition under which both players p…
This note studies numerical characteristics of the unit sphere of a Banach space, especially the functions beta and delta introduced in earlier work, and relates them to isomorphic norms, subspaces, bases, and reflexivity. It proves existence results for almost isometric copies of l1 and c0 under su…
The paper studies local solvability of quasilinear evolution equations in Banach spaces of the form v'(t)=A(t)v(t)+f(t,v(t)), where A(t) generates contraction semigroups with a common domain and the nonlinear term may be unbounded on the base space. It extends earlier existence and uniqueness result…
This paper extends earlier results on linear polynomial operations from periodic real functions to analytic functions in a finite complex domain with rectifiable boundary and simply connected complement. Using Faber polynomials and conformal mapping, it introduces shift and even shift operations and…
The paper studies dynamic instability in linear Hamiltonian systems with small almost periodic, specifically trigonometric polynomial, perturbations. It defines resonant frequency vectors through the leading Lyapunov exponent and uses averaging together with quadratic Lyapunov function estimates to …
The paper studies initial problems for general constant coefficient systems of partial differential equations that are not solved with respect to the highest time derivatives, motivated by cases where the usual Cauchy problem is ill posed. Using Fourier transformation in the spatial variables and es…
The paper studies the Dirichlet problem for nonlinear elliptic equations of arbitrary order under coercivity, growth, and monotonicity assumptions of Leray and Lions type. It constructs finite difference approximations on grid subspaces, proves solvability of the discrete problems using coercivity a…
This note studies extremal quasiconformal homeomorphisms between closed oriented Riemann surfaces of genus greater than one under a prescribed measurable restriction on the Beltrami characteristic, generalizing classical Teichmüller extremal mappings. Using Banach spaces of weighted Beltrami and qua…
This paper studies homeomorphic mappings of a ball in Euclidean space belonging to the Sobolev-type class \(BL^{n/2}\), with emphasis on obstructions to mapping onto domains in dimensions at least three. Using an inequality for such mappings and the theory of prime ends, it proves an analogue of Lin…
The paper studies absolute and uniform convergence of Fourier series with respect to eigenfunctions of a self-adjoint elliptic operator of arbitrary order 2m in an N-dimensional domain, under general boundary conditions. Extending earlier results for second order operators, it gives sufficient Sobol…
This paper studies internal inverse problems in potential theory, concerned with determining the domain and density of a body from equality of its potential on an interior intersection. For generalized potentials associated with uniformly elliptic second order operators, it gives a lemma reducing eq…
This note studies large deviation probabilities for sums of independent identically distributed centered random variables with unit variance when Cramér’s condition is violated, assuming a density with tails asymptotic to exp of minus a subexponential power. It gives asymptotic formulas for the tail…
This paper studies approximate finiteness for von Neumann algebras with finite trace, extending crossed product results from commutative algebras to approximately finite factors and algebras. It proves that crossed products of an approximately finite type II1 factor by finite cyclic, and more genera…
This paper studies third order dynamical systems in a bounded domain with a smooth contact free boundary, under the restriction that closed trajectories are absent. It formulates necessary and sufficient conditions for structural stability under small perturbations of the right hand sides and their …
This note extends local correction techniques for homeomorphisms to questions of stability and local flatness in higher-dimensional topology. It proves that for \(n \geq 5\), a homeomorphism of \(S^n\) fixed on \(S^{n-2}\) can be modified by a stable homeomorphism so that the composition is the iden…
This note studies convergence properties of polynomial Ritz approximations for positive definite elliptic boundary value problems, beyond the usual convergence in the energy norm. Using Kantorovich’s projection framework, it estimates the error through the norm of the Galerkin projector and the best…
The paper studies when boundary conditions prescribed on only part of the boundary of a bounded domain can be extended to boundary conditions that define a solvable extension of a constant coefficient differential operator in an L2 setting. It reduces the question to boundedness of the inverse of an…
