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 proves several undecidability results for fields connected with rational functions and formal power series. It introduces relative elementary definability as a transfer principle for hereditary undecidability, then applies Hasse’s theorem on quadratic forms and properties of Hilbert symbol…
This paper studies two-dimensional singular integral equations whose homogeneous symbols may vanish on finitely many rays, in contrast to the nondegenerate case. Working in spaces of generalized functions formulated via polar coordinates and Fourier transforms, the authors describe solvability for c…
This paper studies characteristic functions of bounded operators that are close to unitary operators in the sense of symmetrically normed ideals. Using earlier factorization results, it gives necessary and sufficient conditions for such an operator with unitary spectrum to be represented as a produc…
The paper addresses two problems posed by Mardešić concerning continua connected by ordered continua and their relation to ordered continua and dimension theory. It constructs a locally connected continuum \(X^*\), obtained as a continuous decomposition of the product of the Aleksandrov transfinite …
The paper studies a general class of singular integral functional equations on a Lyapunov contour involving a finite-order Carleman shift, complex conjugation, Cauchy kernels, and Fredholm perturbation terms. It reduces the equation and its adjoint to systems of singular integral equations with Cauc…
The paper studies Taylor, Dirichlet type series with separated exponents, nondecreasing powers, and coefficients of subexponential growth after reduction. It introduces principal indices and proves a gap theorem: if sufficiently long blocks of coefficients following principal indices vanish, the sum…
This review examines M. L. Rasulov’s book on the residue method and the contour integral method for differential equations, focusing on mixed problems whose associated spectral problems may be non-self-adjoint, have multiple spectra, discontinuous coefficients, nonseparated variables, or time deriva…
This paper studies factorization of finite groups using indexials associated with invariant and normal series, extending earlier criteria based on the orders of principal-series factor groups. It defines indexial systems for factorizations of the factor groups in an invariant series and introduces s…
This paper studies when a densely defined linear operator in \(L_2(\Omega)\) can be represented as an integral operator with a Carleman kernel, addressing the representability formulation of von Neumann’s problem for the full class of such kernels. It first proves that an operator is of Carleman typ…
This paper studies conditions under which two Gaussian distributions generated by a stationary process on a finite interval are mutually absolutely continuous, and how to express the Radon, Nikodym density between them. After recalling the known criterion for equal covariance functions and differing…
The paper studies expansion in only one half of the eigenfunctions and associated functions of a non-self-adjoint ordinary differential operator of order 2m with boundary conditions at two endpoints and coefficients polynomial in the spectral parameter. The argument reduces the completeness question…
The paper studies the number of limit cycles that can bifurcate from a singular point of focus or center type in a planar differential system with cubic homogeneous nonlinear terms. By reducing the system to a normal form, analyzing the succession function in polar coordinates, and using center cond…
This paper studies univalence criteria for a finite class of meromorphic functions expressed as sums of principal parts with poles away from the origin. Under the assumption that the arguments of the ratios of coefficients to the corresponding pole powers are constant, the author proves that such fu…
This paper studies omega-limit sets generated by iterates of a continuous self-map of a compact space, focusing on the structure of attracting sets and the sets of points attracted to them. It establishes intrinsic characterizations of the map restricted to an omega-limit set, including criteria imp…
This note studies conjugate functions, defined through the Wiener space framework and Fourier transforms, for entire functions of finite exponential type. Using the Wiener, Paley representation, it shows that the conjugate of an entire function of type at most sigma satisfying the Wiener integrabili…
The paper studies asymptotic best approximation by algebraic polynomials in the space \(L_q(-1,1)\), \(q \geq 1\), for functions with algebraic singularities of the form \((x-c)^{r-1}|x-c|^{1+\alpha}\). Extending Bernstein’s method beyond the uniform and \(L_1\) cases, it proves that the best approx…
The paper studies saddle surfaces in Euclidean space bounded by a rectifiable curve, focusing on isoperimetric estimates for simply connected domains. It proves that a simply connected saddle surface in the plane satisfies the inequality \(4\pi S - l^2 \le 0\), where \(S\) is area and \(l\) is bound…
This bibliographic section compiles recent Soviet publications from early 1965 concerning differential equations and related areas of mathematical analysis, numerical methods, stability theory, control, integral equations, spectral theory, and mathematical physics. The entries list journal articles,…
This note studies how local best approximation of functions by algebraic polynomials reflects smoothness properties in spaces such as Lp, C, and bounded functions on intervals. It introduces generalized r-oscillations and proves their equivalence, up to constants, with best approximation by polynomi…
This note studies division and factorization of Laurent series convergent in an annulus, with attention to subannuli determined by the zeros of the divisor and to the associated principal index. It derives a canonical representation of a zero-free Laurent series in an annulus as a monomial times a c…
This note refines a general extension theorem for continuous functions by treating bounded real Hölder-continuous functions defined on closed subsets of an arbitrary metric space. It proves that such a function can be extended to the whole space without increasing the maximum of its modulus, while p…
This paper gives an abstract characterization of simple projective groups of type PGL(2,K) over fields of nonzero characteristic not equal to 2, within the class of locally finite groups. It introduces 2-infinitely isolated subgroups, approximable elements, and almost regular elements, and proves th…
The paper develops an analytic framework for similar randomized tests and unbiased estimation by treating precotests as functions whose expectations vanish on the null hypothesis. For dominated statistical families with holomorphic expectation images, it associates the null hypothesis with a cotest …
This paper studies generalizations of primary ideals in associative noncommutative rings satisfying the maximal condition for two-sided ideals. It introduces an abstract notion of s-primarity defined through annihilators modulo an ideal, compares it with existing notions such as primary, simple, irr…
This review examines G. N. Polozhii’s textbook on equations of mathematical physics, emphasizing its nontraditional organization and its systematic use of Green’s functions, delta-type source functions, potentials, and integral transformations across elliptic, parabolic, and hyperbolic equations. It…
This paper studies weighted Sobolev type classes of differentiable functions of several variables in exterior domains, with weights of the form involving a radial factor satisfying an integral growth condition. It proves embedding theorems for these classes, extending earlier results for particular …
The paper establishes estimates for Hartogs coefficients of functions of several complex variables that are regular in bounded complete multiple Hartogs domains with coordinate symmetry planes. Using known coefficient estimates for functions in polydiscs, the argument fixes the base variables, appli…
This note studies extremal problems for real entire functions of finite exponential type that are nonnegative on the real axis and integrable, under one or two admissible linear constraints. It proves that, for at most two such constraints, an extremal function minimizing the integral norm exists an…
This paper studies limiting Cauchy problems at infinity for first and second order evolution equations in a Hilbert space with time dependent unbounded positive self-adjoint operators and nonlinear potential terms. Using Lyapunov-type energy functionals built from the operator square root and the no…
The paper develops a framework for generalized extensions of unbounded operators using a Hilbert scale \(H_+ \subseteq H_0 \subseteq H_-\), where \(H_-\) is defined as the space of generalized elements dual to \(H_+\). For bounded operators from \(H_+\) to \(H_-\), it introduces a generalized adjoin…
This note studies decision problems for elementary first-order theories of finite-dimensional Lie algebras in the language with addition and multiplication. Using structural facts about complex simple Lie algebras, root decompositions, and an effective interpretation of finite structures with two eq…
This paper extends the Bogolyubov averaging method from ordinary differential equations to systems of integro-differential equations with a small parameter and memory integral. Under boundedness, Lipschitz, and uniform averaging assumptions on the functions defining the system, it constructs an aver…
This paper studies regularity of generalized solutions to second order degenerate elliptic boundary value problems of Fichera type and to degenerate parabolic Cauchy problems. Using elliptic regularization, Bernstein type gradient estimates, Schauder estimates, and an auxiliary inequality for nonneg…
The paper studies optimal mechanical cubature formulas whose nodes lie on regular lattices, focusing on the norm of the error functional in the dual Sobolev space \(L_2^{(m)*}\). Using Babushka’s characterization of optimal coefficients, discrete polyharmonic potentials, Green’s formula, and density…
This note presents an elementary method for separating variables in equations of many variables by transforming an equation into an equivalent form with functions of disjoint groups of variables. Under assumptions of solvability with respect to individual variables and monotonicity allowing an inver…
The paper studies regular nonuniform finite difference schemes for parabolic equations, focusing on checkerboard arrangements that interlace explicit and implicit formulas on different subsets of grid nodes. It introduces the notion of quasi-stability as a generalization of von Neumann stability for…
The paper develops a framework for isoinvolutive decompositions of compact real semisimple Lie algebras, defined through triples of subalgebras fixed by commuting involutive automorphisms and related by inner conjugation. It establishes existence results for such decompositions, introduces types I, …
This note studies the error of cubature formulas on a domain in n variables as a linear functional in the Sobolev factor space of functions with square integrable derivatives of order m, under the condition m greater than n/2 and exactness on polynomials of degree below m. It proves a lower bound fo…
This note studies how solutions of a one-dimensional Dirac system on the half-axis can be continued to the negative half-axis when the coefficients are extended there. Using transformation operators, the authors express the values of the continued solution at negative points as integral linear opera…
This paper studies measure spaces of continuum weight, defining their weight, subspaces, maximality, compact and bicompact approximating classes, and weak compactness. It proves that within any fixed metric structure there exists a unique maximal measure space of continuum weight, described in the h…
