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 studies topological embeddings of compact polyhedra in Euclidean space under a codimension range expressed by dim Q less than two thirds of n minus 1. It outlines a proof that an embedding locally flat on the open simplices of a triangulation can be made piecewise linear, relative to the c…
The paper introduces almost metrizable topological groups, defined by the presence of a compact subset of countable character, and develops their basic structure. It proves that such groups can be represented via compact subgroups of countable character with metrizable quotient spaces and perfect op…
This note introduces the notion of a ring element linked with zero, a special case of a zero divisor defined through annihilators of the principal ideal it generates, and studies rings in which every element has this property. It establishes structural results relating linked rings to Baer radical r…
This paper extends results of Levin and Pfluger on completely regular growth from entire functions of noninteger order to functions analytic in a half-plane. It introduces a notion of order and indicator for functions in an angle, defines complete regularity in open and closed half-planes, and devel…
The paper studies direct and inverse embedding theorems for weighted anisotropic function spaces on products of positive Euclidean orthants. It defines weighted Lebesgue, Sobolev-type, and Besov-type spaces with mixed groups of variables and establishes conditions under which boundary traces of deri…
This paper studies derivability and decidability for restricted classes of sequents in classical, constructive, minimal, and positive predicate calculi without function symbols. It proves that absolute sequents derivable classically are derivable in the positive calculus, identifies a reduction clas…
The paper generalizes the notion of monotone nonlinear operators in Banach spaces by introducing B-monotonicity for operators whose values need not lie in the conjugate space of their domain. It establishes several equivalent criteria for B-monotonicity, including conditions in terms of Gâteaux deri…
This note proves the topological invariance of rational, equivalently real, Pontryagin classes for smooth or PL manifolds under a homeomorphism, with the proof outlined for the simply connected smooth case and reduction indicated for the general case. The argument centers on a basic lemma asserting …
The paper studies continuous representations of locally bicompact groups in the indefinite inner product space Pi_1 that are unitary with respect to that product. Using a maximal commutative algebra of bounded operators commuting with the representation and its canonical realization, the analysis re…
This note studies periodicity in partially ordered dynamical systems, where the acting parameter group is an arbitrary partially ordered group rather than the real line or a topological group. It defines periods of a point as group elements fixing that point, analyzes the resulting period subgroup u…
This note develops a constructive version of Lebesgue integration for everywhere defined constructive functions on the unit segment, using approximation by polygonal skeletons and associated primitives. It defines Lebesgue integrability through pointwise convergence together with an integral Cauchy …
The paper introduces evolutionary graphs, directed graphs with black and white vertices governed by linear transformation, summation, and branching rules, as a representation of systems of linear operator equations. It establishes a correspondence between such graphs and linear systems, gives condit…
This paper studies non-self-adjoint second order ordinary differential operators of the form l(y) = -y'' + q(x)y in L2(a,b), where the interval endpoints are arbitrary and the complex potential has prescribed limiting imaginary parts at the endpoints. Using Weyl limit point and limit circle methods,…
The paper develops a generalized multiplication for multidimensional matrices over real or complex fields, extending earlier contracted products by allowing both summed and connecting index sets in accordance with Cayley and Scott type rules. It defines the resulting contracted product, discusses as…
This paper studies an optimal control problem for a linear system in a normed finite-dimensional phase space when the terminal quantity to be minimized is the expected norm of the final state over finitely many random realizations. Using duality for the corresponding deterministic terminal minimizat…
The paper studies anisotropic classes of differentiable functions defined by integral norms of finite differences of generalized derivatives on domains stable under positive coordinate shifts. It constructs integral representations for functions in these quotient spaces, derives estimates using Hard…
The paper introduces alternative moduli of convexity and smoothness for Banach spaces, defined through the aperture of one-dimensional subspaces and hyperplanes. It proves that these moduli characterize the same uniformly convex and uniformly smooth spaces as the classical moduli, while satisfying s…
This note studies how the \(d\)-characteristic of a linear operator, consisting of the dimension of its kernel and the codimension of its range, changes under relations between two linear operators on vector spaces. Using direct-sum decompositions associated with the kernels and ranges of operators …
The paper studies extremal problems for real algebraic polynomials of bounded degree that are nonnegative on a prescribed real interval and whose coefficients satisfy an arbitrary finite system of linear relations. It represents such polynomials in factored form and derives structural restrictions o…
The paper studies a singular Cauchy problem for a generalized Euler, Poisson, Darboux type equation of order n, with a linear operator acting in the spatial variables and with singular coefficients depending on t. It derives integral and differential formulas relating solutions corresponding to diff…
This paper examines the classical localization principle for Fourier series expanded in eigenfunctions of the Laplace operator on multidimensional domains, with boundary conditions yielding a complete orthonormal eigenfunction system. It contrasts a positive localization theorem, requiring membershi…
This note studies the external stability number of a finite simple undirected graph, defined as the minimum size of a vertex set adjacent to every vertex outside it, in relation to the number of edges. It proves exact extremal formulas for the maximum number of edges in connected \(n\)-vertex graphs…
This paper studies the relation between Lebesgue measure and the level sets of the distance function to the complement of a bounded open set in Euclidean space. Using Lipschitz differentiability, Steklov averages, and Kronrod variation, it proves that for a bounded open set in the plane, almost all …
The paper introduces and studies classes of regular functions of several complex variables, primarily in two variables, that generalize p-valent, p-valently starlike, and p-valently convex functions of one complex variable through their restrictions to analytic sections of bounded complete bicircula…
The note studies when an analytic real periodic function can be represented as a finite sum of squares of real periodic functions, a question motivated by decompositions of positive definite differential and difference operators and their Fourier transforms. It introduces Maclaurin structures, trace…
This note examines how far the standard condition K(s)H(1-s)=1 on the critical Mellin line is necessary for the separate inversion and Parseval assertions in the theory of Watson transformations. The kernels are decomposed into two bounded Mellin components, and sufficient relations among the compon…
The paper develops criteria for uniform and absolute convergence of Fourier series of uniformly almost periodic functions whose Fourier exponents have restricted sets of finite limit points. Its method decomposes such functions into finite or countable sums of almost periodic functions with bounded …
This bibliographic notice surveys recent mathematical publications issued in 1964 and 1965, primarily in Russian translation or Soviet editions, with emphasis on differential equations, integral equations, mathematical physics, operational calculus, stability theory, oscillations, and boundary value…
The paper studies subgroups and normal divisors of the multiplicative group of a division ring, with attention to Sylow subgroups and centrality phenomena. It constructs a 16-dimensional division algebra over its center, a rational function field, whose multiplicative group has two nonconjugate type…
This paper studies first-kind integral equations on a finite interval whose kernel depends on the absolute difference of the arguments, with particular attention to the associated key equation. By comparing solutions on intervals of lengths h and h plus delta, the author derives transformation relat…
This note corrects an inaccuracy in the proof of a theorem from the author’s earlier paper on densely embedded ideals of semigroups, where certain equalities used in Lemma 3 require nonemptiness conditions that are not generally guaranteed. The correction modifies the original construction by adjoin…
This note studies nonlinear differential systems with almost periodic right hand sides and asks when the Fourier exponent module of an almost periodic solution is contained in the module of the system. It gives sufficient conditions based on invariant classes under translations, uniqueness within su…
The paper proposes a method for solving certain boundary value problems in complex function theory when the boundary conditions have analytic coefficients. The method analytically continues the boundary condition from an analytic contour into the complex plane, transforms the problem into a function…
This paper studies Engel elements, generalized central elements, and radical structures in groups embedded in PI-algebras, with applications to matrix groups and locally bicompact topological groups. It proves that for subgroups of PI-algebras over commutative rings, nil-elements coincide with the l…
The paper studies proper vertex colorings of connected loopless graphs of maximum degree three and proves that, except for the tetrahedral graph, such graphs have chromatic number at most three. The argument uses Kempe-chain style components, reductions by contracting two-edge cycles and low-degree …
This note continues the study of tensor products and functors in categories of Banach spaces associated with a KB-lineal E, where a Banach space X is sent to the completion of E tensor X under the crossnorm nE. It characterizes when this crossnorm coincides with the projective and injective tensor n…
This note studies complete regularity for multidimensional stationary processes with discrete time in terms of their spectral matrix density, with attention to rates of decay of the associated mixing coefficient. Using an analytic representation of the coefficient, it gives sufficient and necessary …
This note studies convergence and stability of a family of three level difference schemes for the one dimensional wave equation with variable coefficients and homogeneous boundary conditions. Using a direct algebraic approach, including noncommutative analysis for nonseparable coefficients, it formu…
This paper studies nonlinear spinor functions whose arguments and values transform under representations of the full orthogonal group in three-dimensional Euclidean space. It formulates a general invariance principle: the symmetry group of a spinor function is the intersection of the symmetry groups…
This paper studies the set of all Hausdorff compact extensions of a completely regular space, focusing on its possible cardinalities and its natural partial order. It proves that every infinite cardinal can occur as the cardinality of this system for a suitable space, using constructions involving S…
This paper establishes convergence results for a projection method for solving linear equations Ax equals y in Banach spaces when A is representable as a function of an isometric operator. Using conditions expressed through the nonvanishing and index of the associated function on the unit circle, th…
This paper formulates a categorical framework for mathematical statistics in which spaces of probability distributions are objects and Markov kernels are morphisms. It defines categories of families of distributions, interprets statistical equivalence through equality of attainable decision classes,…
This note studies a class of inverse problems for linear differential equations in which unknown coefficients are to be reconstructed in a bounded domain from a parameterized family of solutions known in a disjoint domain. By applying a Laplace transform in auxiliary variables and using a fundamenta…
The paper studies realizability for propositional formulas in the sense induced by Kleene realizability of arithmetical substitutions, asking whether a disjunction can be realizable when both disjuncts are unrealizable. It defines refutation of a propositional formula by arithmetical substitutions t…
This paper studies scattering operators for unitary couplings of two isometric semigroups in the Lax Phillips framework and relates them to characteristic operator functions of contractions. It defines wave and scattering operators for couplings possibly acting in different Hilbert spaces, proves cr…
