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
The paper studies error estimates for approximating integrals over the infinite-dimensional unit cube by finite averages at prescribed nodes. Using Haar series expansions, it refines finite-dimensional discrepancy estimates and extends them to function classes defined by bounds on Haar coefficients …
The paper introduces pluriparabolic differential operators as a multidimensional time analogue of Petrovskii parabolic operators, defined through weighted homogeneous polynomials whose nonvanishing properties are controlled by a hyperbolicity cone. It proves invariance of pluriparabolicity within th…
For the system \begin{equation} x(t)=\int_0^tK(t,s,x(s))\,ds+f(t)\tag{1}, \label{1} \end{equation}, where the vector function $K(t,s,x)$ has the form $$K(t,s,x)=K_1(t,s,x)-K_2(t,s,x),$$ and $K_j(t,s,x)$ ($j=1,2$) are continuous and non-decreasing with respect to $x$ in the domain $0\xi_2^j\quad (j=1…
This note studies whether finite-rank perturbations preserve closed range and homomorphism properties for linear maps between topological vector spaces, extending known results for closed operators in Banach and Hilbert spaces. Using quotient-space arguments, decompositions relative to kernels, and …
This note studies existence conditions for generalized smoothing and extrapolation problems for random functions and random vector functions when the quality criterion is more general than the usual variance of the error. It formulates the approximation problem in Hilbert spaces generated by covaria…
This paper studies irreducible representations of the projective group of unit quaternions over a nonconnected locally compact nondiscrete field of characteristic not equal to 2, under the stated exclusion of the 2-adic subfield. Using a filtration of the compact quaternion group by normal subgroups…
This paper derives estimates for the difference between the matricants, or fundamental matrix solutions, of two linear homogeneous systems of ordinary differential equations with continuous matrix coefficients. It introduces elementwise matrix majorants and a submultiplicative norm, then proves an e…
This paper studies zeta functions associated with positive definite ternary quadratic forms, focusing on whether the form corresponding to the densest sphere packing in three-dimensional Euclidean space is locally extremal. The author analyzes small determinant-preserving variations of the form, dec…
The paper studies continuous linear forms on a locally convex inductive limit formed from spaces of real-valued functions with the topology of pointwise convergence, associated with a projective system of sets. It constructs the canonical map from this inductive limit to the function space on the pr…
The paper develops a local theory of relaxation processes for solving nonlinear equations with potential operators in a real Hilbert space, under assumptions of local differentiability and positive bounded second variation of the associated functional. It introduces relaxation multipliers and angles…
This paper formulates a resource allocation problem for network planning with discrete time, multiple target events, directive completion dates, noninterchangeable and nonstorable resources, and noninterruptible activities. It shows that the direct schedule formulation leads to an integer nonconvex …
This paper studies covering and compactness properties of symmetrizable spaces using Arhangel’skii’s notion of weakly discrete systems. It proves that every open cover of a symmetrizable space contains a sigma-weakly discrete refinement, and uses this to show that finally compact symmetrizable space…
This paper develops a generalized stabilization method for numerical solution of boundary value problems for nonlinear second order ordinary differential equations with homogeneous endpoint conditions. The method introduces a continuous parameter and replaces the original nonlinear problem by an evo…
This note studies pairs of polynomial statistics of a repeated standard normal sample and the problem of when their independence, or the related decorrelation moment conditions, forces them to split after an orthogonal transformation into functions of disjoint coordinate sets. Using algebraic geomet…
This note studies a class of linear differential games in a Euclidean space with terminal manifold a subspace, where pursuit and evasion controls enter additively in a linear system. Under convexity and domination assumptions on the projected control images after the linear flow, the paper formulate…
The article is a continuation of the author's work [1] and is devoted to the derivation of two types of asymptotic expansions for Macdonald integrals $n$ of order $M_n(x,y)$. Two expansions of the first type are asymptotic as $|y|\sqrt{1+x^2}\to\infty$. The first expansion is an expansion in terms o…
This paper studies factor representations of the Clifford algebra with infinitely many generators, focusing on representations whose generated von Neumann algebra is a type II1 factor. It proves that all such type II1 factor representations are algebraically isomorphic, then gives a unitary classifi…
The paper studies representations of cubic orders over the integers and over p-adic integers, using the correspondence between cubic rings and classes of binary cubic forms. It proves that a cubic ring has only finitely many nonisomorphic indecomposable representations precisely when the smaller inv…
This paper studies the decidability of systems of equations in words with three unknowns, reducing the general problem to one-sided equations and then to the analysis of finite and nonfinite images under specified transformations. It introduces chains of nonfinite images and proves that, for three u…
This paper studies coercivity and well-posedness for the abstract Cauchy problem for parabolic equations in a Banach space, extending earlier results from Hölder-type settings to newly defined spaces of means. It introduces integral analogues of abstract Hölder and Sobolev-Slobodetskii spaces, toget…
This paper studies uniqueness and nonuniqueness classes for the Cauchy problem for linear evolution equations whose lower order coefficients may grow rapidly at spatial infinity. Under integrability and subordination assumptions on the coefficients, it gives growth conditions on solutions and their …
This paper studies anisotropic Sobolev type classes on smooth domains in which nonmixed derivatives of different orders are summable with powers of the distance to the boundary as weights. It generalizes a theorem on the summability of mixed derivatives from the whole space to weighted spaces on a c…
This note establishes several sum theorems for the large inductive dimension Ind in normal Hausdorff spaces, weakening earlier hereditary normality assumptions by imposing conditions on intersections or on normally situated closed subsets. It proves that a normal space that is the union of closed su…
The paper studies continuous mappings of closed n-dimensional manifolds onto closed n-dimensional manifolds when the mapping degree has absolute value greater than one, focusing on points whose full inverse image consists of a single point. It proves that the set of such points is homeomorphic to it…
The paper extends Engel’s theorem from Lie algebras to binary Lie algebras under Zorn’s formulation. It proves that if a binary Lie algebra satisfies the Engel condition, meaning every right multiplication operator is nilpotent, and also satisfies the maximality condition for subalgebras, then the a…
This paper studies continuous convex and linear programming problems arising in continuous time economic models. It formulates a continuous convex programming problem with time-dependent convex cone technologies and proves, under boundedness and feasibility assumptions, existence of an optimal contr…
The paper studies Lebesgue-Orlicz points for functions in Banach symmetric spaces on the unit interval and their role in convergence of singular integral representations. It introduces a pointwise definition based on the norm of localized oscillations and relates the size of the set of such points t…
This note addresses O. Yu. Schmidt’s problem on infinite groups whose proper subgroups are finite, focusing on infinite periodic groups that contain involutions. It proves that such a group either is equal to the centralizer of one of its involutions, or has a proper infinite subgroup with nontrivia…
This paper studies analytic systems of four differential equations near a saddle-focus equilibrium with two complex stable and unstable characteristic pairs, assuming the existence of a homoclinic trajectory whose stable and unstable two-dimensional manifolds have a first-degree nontransversal inter…
This note studies a complex second-order elliptic equation in a bounded plane domain, equivalent to a real linear elliptic system, with emphasis on representations of solutions and boundary-value problems. For parameter values outside the eigenvalues of an associated Fredholm integral equation, the …
This paper studies upcrossings of high levels by a stationary Gaussian process with twice differentiable correlation function satisfying local smoothness and weak long-range decay conditions. As the level and interval length increase in a coordinated way, it proves that multiple upcrossings occurrin…
This paper studies P. Hall’s conjectures relating verbal subgroups and marginal subgroups of groups, focusing on arbitrary words in linear groups over fields. Using arguments from algebraic group theory, Zariski closures, finite approximability by finite p-groups, and structural results on solvable …
The paper studies generalized extensions, in a rigged Hilbert space setting, of the differentiation operator on a finite interval with boundary condition f(0) = 0, a model for quasidissipative extensions without spectrum of a simple symmetric operator with deficiency indices (1,1). It constructs a o…
The paper develops a unified topological argument for several previously announced results concerning spaces that admit both a perfect mapping onto one space and a condensation onto another. It introduces the notion of a hereditary, product-stable property and proves a main theorem: if a space is pe…
This note studies essential variables of Boolean algebra functions, focusing on variables that remain essential after substitution of a constant and on separability relations between pairs of variables. Using Zhegalkin polynomial representations, it proves that the minimum possible number of strongl…
In this work, necessary and sufficient conditions are found for the existence of closed algebraic curves of the second order among the trajectories of the equation \begin{equation}yy'=Q_4(x,y)\tag{1}, \label{1} \end{equation} where $Q_4(x,y)$ is a polynomial of the fourth degree. At the same time, i…
The paper develops an analogue of Cartan-Weyl highest weight theory for infinite-dimensional representations of a semisimple complex connected Lie group in locally convex spaces. It introduces extremal irreducibility, generalized highest vectors in the dual space, and minimal representations associa…
For a certain class of autonomous differential equations of the $n$-th order, a three-parameter family of solutions is constructed, the derivative of which vanishes at infinity in the form of a Dirichlet series that converges uniformly and absolutely on the real semiaxis, starting from a certain neg…
The paper examines potential systems used in an approximate method for solving boundary value problems based on integral representations and auxiliary surfaces. It shows that such systems are unstable in the sense that their Gram determinants can become arbitrarily small, which may seriously affect …
The paper addresses a question of V. V. Proizvolov asking whether a bicompact space must be metrizable when it admits an open compact mapping onto a compact space. It constructs a modified topology on the square in the plane, proves that the resulting Hausdorff space is bicompact but nonmetrizable, …
This paper establishes sharp difference inequalities for harmonic functions in the unit disk whose boundary values are bounded, have zero mean, or belong to smoothness classes with bounded derivatives. It generalizes Schwarz type extremal estimates from values relative to the center to differences a…
This paper studies nonlinear operator equations in reflexive Banach spaces, focusing on the convergence and solvability of Ritz and Galerkin approximations for equations of the form F(x) = 0 when the operator need not have a compact component. It proves existence and convergence results for potentia…
This note studies involutive automorphisms, called invomorphisms, of compact Lie algebras and introduces principal, unitary, orthogonal, biunitary, central, and special types through the structure of their fixed-point subalgebras. Using the apparatus of involutive sums and superinvolutive decomposit…
