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 a class of finitely presented groups whose defining relators are closed under inverses and cyclic permutations and satisfy cancellation restrictions of small cancellation type. It proves structural lemmas on products of conjugates of defining relators and on cyclic words represent…
The paper derives explicit formulas for eigenvalues of Casimir operators of arbitrary order for the classical groups. Using highest weight vectors and recursive relations for the generators, it reduces the computation for unitary, special unitary, orthogonal, and symplectic groups to powers of an ex…
This commemorative article surveys the life and work of Soviet mathematician Nikolai Pavlovich Erugin on the occasion of his sixtieth birthday. It outlines his academic career in Leningrad and Minsk, his wartime service and subsequent return to research, and his major contributions to the theory of …
This note studies local and global transformation groups associated with a nondegenerate homogeneous form on a real or complex vector space, using as invariants a generalized double ratio of four points and a measure of k-angles defined by polarization of the form. It derives necessary and sufficien…
The paper addresses a problem of Mal'tsev on whether a ring without zero divisors whose nonzero multiplicative semigroup embeds in a group must itself be embeddable in a field. Using the theory of SN-rings and their completions, it describes generators and defining relations for the multiplicative s…
This note studies linear differential games governed by a controlled linear vector differential equation, with two players choosing controls on a unit sphere and with termination defined as reaching a prescribed subspace. It formulates sufficient geometric conditions, involving convexity and local c…
This paper studies homotopy properties of complements of locally flat codimension two spheres in Euclidean space for dimensions at least five, with particular attention to finite and infinite connected sums of knots. It proves finite generation of the fundamental group of any such complement and, un…
The paper studies penalty methods for convex programming problems with inequality and equality constraints, comparing the original constrained maximization problem with auxiliary problems in which part of the constraint violation is incorporated into the objective. It develops estimates relating opt…
The paper studies best approximation in \(L_p(D)\), \(1<p<\infty\), of functions on a bounded domain by sums of finitely many plane waves with prescribed directions. Using a functional analytic extremal lemma and a characterization of generalized plane waves as solutions of constant coefficient diff…
The paper studies provability in Ackermann’s calculus of strict implication and in the related Anderson and Belnap system, treated jointly as systems of strict implication. Using Ackermann matrices, it establishes several necessary conditions for derivability, including polarity constraints on share…
The paper studies coefficient estimates for univalent functions in the unit disk, including functions with p-fold rotational symmetry, using logarithmic coefficients and associated functions generated by exterior univalent mappings. Building on an inequality for these associated functions, it proves…
The paper specifies the integrability criteria for three nonlinear second-order differential equations. Bibliography: 8 items.
This paper extends Maslov’s inverse method for establishing derivability in classical predicate calculus with function symbols from prenex formulas to formulas of arbitrary, including non-prenex, form. It introduces generalized notions of atoms, links, favorable sets, and modified construction rules…
This note establishes general integral representation formulas for holomorphic functions in several complex variables, especially in convex complete circular domains and convex domains of complex space. The argument first derives an auxiliary formula for functions holomorphic in star-shaped domains,…
The paper presents the application of the contour integral method to solving mixed problems for a system of differential equations of heat and mass transfer under molecular and molar transport of energy and matter in an arbitrary three-dimensional domain. Furthermore, the contour integral method is …
In the article "Stability of Generalized Processes. I" ("Differential Equations", 1966, No. 7, pp. 872–881), the concept of stability with respect to generalized actions was introduced. The purpose of this article is to present those perspectives on classical stability that served as the starting po…
This paper extends the abstract Noether theory of general singular equations from closed contours to open contours, including equations with Cauchy kernels and discontinuous coefficients. Using a reduction of the Riemann boundary value problem on an open contour to a closed contour and a system of r…
This note derives an upper bound for the distance between two probability distributions on Euclidean space, defined as the supremum of the absolute difference of their probabilities over all convex sets. Using Fourier inversion, smoothing by an independent random vector with integrable characteristi…
This paper studies Zolotarev stability for segment functionals associated with polynomials of passport [n,n,0] in the critical parameter interval. Using expansions with respect to the nodes of the Zolotarev polynomials, it derives sign conditions on the corresponding loads and proves that, for any f…
A number of problems in mathematical physics lead to the consideration of divergent integrals. Cauchy and Hadamard developed an algorithm that allows assigning a well-defined finite part to certain divergent integrals. This article proposes a method for introducing the finite part of singular functi…
This paper studies Mal’tsev algebras over fields of characteristic not equal to 2 that satisfy the nth Engel condition, extending results known for Lie algebras. Using identities for Mal’tsev algebras and a series of lemmas on solvable ideals, finite generation, and powers of the algebra, it proves …
This note studies an inverse problem in integral geometry for a two-parameter family of curves in the upper half-plane: to recover a continuous function from its integrals over the curves. Under assumptions of uniqueness of curves through point pairs, nesting of bounded regions, and smooth dependenc…
The paper develops a summation formula for analytic functions with isolated singularities, analogous to the Euler-Maclaurin formula, and uses it to derive convergent series representations for several special functions. The resulting expansions include formulas for the gamma and psi functions with a…
This note studies double Fourier series of periodic functions in two variables, their conjugate functions and series, and related maximal functions defined through Cesàro means and singular integral truncations. It examines a question of almost everywhere existence for the double conjugate function,…
The paper extends the variational method of Goluzin and Kufarev from simply and doubly connected settings to finitely connected circular domains. It first develops a Schwarz-type integral representation for analytic functions in such domains, then uses it to prove differentiability formulas for conf…
The paper studies whether Banach spaces of analytic functions on polydiscs of different dimensions can be distinguished by a finer invariant than linear dimension. It introduces the growth invariant of a linear topological space, based on complemented extension of dual functionals, and applies estim…
A system of nonlinear integro-differential equations of the form \begin{equation} \frac{dx}{dt}=\varepsilon f(t,x,\int_0^t\varphi(t,s,x(s))\,ds),\tag{1} \label{1} \end{equation} is considered, where $\varepsilon>0$ is a small parameter. The system \eqref{1} is associated with a system of averaged eq…
This note studies topological groups in which every closed subgroup has a closed complement, extending the theory of completely factorizable abstract groups to locally compact settings. It proves that every locally compact completely factorizable group is totally disconnected and metabelian, and der…
The paper develops a method for deriving fixed point principles by reducing equations of the form F(x,x)=0 in Banach spaces to locally defined fixed point equations x=R(x) and assigning an index via the rotation of the associated vector field. A homotopy invariance theorem is proved for a parameter-…
The paper studies left D-algebras, a generalization of Lie algebras, and formulates a Cartan-Eilenberg type homology theory for them through a suitable notion of representation. It shows that polynomial representations satisfying a nonnilpotence condition reduce to Lie representations, allowing the …
This paper presents a general method for deriving maximum principle theorems for bounded lower semicontinuous functions in multidimensional domains with absolutely continuous support mappings. The argument reduces differential inequalities of the form involving second derivatives, first derivatives,…
This note proves a general existence and uniqueness theorem for closed convex polyhedra whose face directions are prescribed and whose faces are assigned prescribed positive values of functions defined on parallel convex polygons. The functions are assumed positive, continuous, translation invariant…
This paper proves uniqueness for second-kind integral equations used to formulate wave diffraction by open, infinitely thin screens. For scalar Helmholtz diffraction with Dirichlet and Neumann boundary conditions, including a formulation involving Green’s functions for complementary domains, the arg…
The study of characteristic vectors, initiated in the author's previous article, is continued. The concept of a superior vector is introduced, which is used to investigate the distribution of characteristic vectors of linear differential systems under small perturbations. This leads to stability cri…
This note studies the bifurcation and Lyapunov stability of small almost-periodic solutions of analytic ordinary differential systems with an almost-periodic right-hand side depending on a scalar parameter. Under a spectral assumption in which the mean linear part has a single zero eigenvalue on the…
The paper derives boundary estimates for upper normal derivatives of solutions to second order elliptic equations and inequalities with zero Dirichlet data, allowing degenerate nonnegative principal coefficients and weak differentiability assumptions based on absolutely continuous support mappings. …
The paper develops integral inequalities for positive elements acted on by Volterra type operators in a partially ordered linear setting. Using resolvent operators and commutation order assumptions, it derives bounds for solutions of inequalities of the form \(u \leq \psi + Lu\) through products of …
This note studies a first-order axiomatic system for arithmetic that is equivalent to classical arithmetic with a constructive rule of infinite induction, but omits the usual explicit logical rules such as modus ponens. Formulas are put into a normal form built by additive and multiplicative operati…
This paper applies a general local method for operators to multidimensional convolution type operators, with particular attention to Wiener-Hopf equations in cones. It introduces a compactification of Euclidean space adapted to conic geometry, defines generalized and composite convolutions, and asso…
The paper studies decidability questions for formal logical calculi obtained from the predicate calculus by deleting selected axioms and inference rules. Using a sequence of formula translations that preserve provability, it reduces Church’s undecidability result for predicate calculus to calculi co…
We consider the equation \begin{equation} \frac{\partial u}{\partial t} = \int_0^1 k\biggl(x,y,u(y,t),\frac{\partial u(y,t)}{\partial t}t\biggr)\,dy \tag{1} \label{1} \end{equation} where $$k(x,y,u_1,u_2t)=\sum_{l+k+j\ge1}^\infty k_{l,k,j}(x,y)u_1^l u_2^k t^j,$$ subject to the initial condition \beg…
This note studies holomorphic functions of several complex variables in bounded convex complete circular domains and in star-shaped domains. It introduces a family of integro-differential operators defined by coordinate dilations and proves an integral identity showing that the corresponding integra…
This note extends Menshov’s theorem on the correction of measurable functions to functions of several variables on the torus, with attention to convergence of multiple expansions. Focusing on two variables, it considers double trigonometric Fourier series, double Fourier-Walsh series, and mixed seri…
This note studies order reflexivity for combinations of partially ordered K-spaces, especially sums and connections formed from families of reflexive component spaces. It introduces several obstruction properties, denoted R0, R1, R2, and R3, and proves necessary and sufficient criteria for reflexivi…
