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 formulates a zero-sum dynamic pursuit game in Euclidean space for two particles with controllable force directions and prescribed force magnitudes, where the pursuer maximizes and the evader minimizes a terminal payoff. It derives a Hamilton-Jacobi type Cauchy equation as a necessary cond…
The paper studies the stable solution of linear functional equations in Hilbert spaces when both the right-hand side and the operator are known only approximately. It formulates a Tikhonov-type regularization functional on a weakly closed convex admissible set, proves existence and uniqueness of its…
The paper studies analytic functions of integer order and finite type in the upper half-plane, with emphasis on completely regular growth and the relation between growth indicators and zero distribution. It gives a canonical representation for such functions, introduces argument-boundary and boundar…
The paper establishes maximum principles for a class of second order hyperbolic equations in a characteristic triangle under explicit sign and integral conditions on the coefficients. These principles are applied to generalized Tricomi type mixed equations, using elliptic maximum arguments, Hopf typ…
The paper studies an assembly model in queueing theory with several independent Poisson input streams, where completed units require one element from each stream and the remaining elements form a queue vector. Using barycentric coordinates on a simplex lattice, it defines functions that express the …
The paper studies stability of the trivial solution of a general nonlinear system of differential equations under constantly acting perturbations in the neutral Lyapunov case, where the unperturbed system is stable but not assumed asymptotically stable. It proves a Lyapunov-type theorem showing that…
This paper studies a class of singular partial differential operators in a half-space-adjacent domain, involving the Bessel operator and acting in weighted spaces with weight y to the k. Under symmetry, smoothness, and a B-ellipticity positivity condition on the coefficients, the argument derives en…
This note studies constructive sets equipped with an equality relation, whose elements are words, and mappings between them defined by normal algorithms. It introduces a classification of infinite such sets according to enumerability properties of their bases and decidability or enumerability proper…
This note determines the maximum possible number of edges in a finite connected simple undirected graph with a prescribed number of vertices and radius. After recording bounds on vertex degrees, including a bound for pairs of vertices at distance at least three, it defines the extremal function for …
The non-stationary problem \begin{equation} u_{xx}=k^2(x)u_{tt}, \tag{1} \label{1} \end{equation} is investigated, where $k(x)=k_0$ for $xx_0$, under the initial condition $u_0(x,t) = \mu(t-k_0x)$ for $tz_0$$ is equal to $\lim_{t\to\infty}u(x,t)=\frac{2\mu_0k_0}{k_0+k_1}$. That is, the limit is the …
The paper studies decidability questions for elementary theories of lattice-ordered Abelian groups, structurally ordered Abelian groups, K-groups, and K-lineals. It proves broad undecidability results for classes of lattice-ordered Abelian groups containing certain Archimedean divisible examples wit…
This paper studies Chebyshev sets in normed and Banach spaces, with emphasis on approximative compactness, suns, and convexity. It proves a key extension lemma showing that certain distance-growth sets meet every sphere, then applies it to exclude approximatively compact Chebyshev complements of bou…
This paper proves an existence theorem for closed convex hypersurfaces in Euclidean space whose curvature functions satisfy a prescribed linear relation with positive continuous even coefficients on the unit sphere. After recalling the definition of curvature functions via the surface functions of e…
This note introduces new asymptotic characteristics of the unit sphere of a Banach space, denoted by delta and beta functions, defined through extremal behavior over finite-dimensional subspaces and subspaces of finite codimension. It establishes inequalities and continuity properties for these char…
This paper studies invariant subspaces of weighted shift operators on Hilbert sequence spaces, with emphasis on when such operators are unicellular, meaning that their invariant subspaces are totally ordered by inclusion. It gives sufficient regularity and summability conditions on the weights for u…
The paper studies flatness properties of generalized classical rings of fractions for associative rings with identity. Using the elementary relation-based definition of flat modules, it proves that a left generalized classical ring of fractions R(S), when it exists for a multiplicatively closed syst…
A solution is sought for an equation $$L_1L_2\dotsb L_n=f\quad(y>0),$$ which is strictly hyperbolic in a certain bounded domain $D$, where $$L_iU\equiv y^{a_i}U_{xx}-U_{yy}+a_i(x,y)U_x+b_i(x,y)U_y+c_i(x,y)U\quad(i=1,2,\dots,n),$$ satisfying the initial data $$\quad\lim_{y\to0}\frac{\partial^iU(x,y)}…
This article presents a commemorative scholarly biography of Iosif Zakharovich Shtokalo on the occasion of his seventieth birthday, tracing his education, teaching career, research, and public and organizational work. It surveys his mathematical contributions to linear differential equations with va…
In problems related to determining the number of limit cycles bifurcating from a singular point of the second group, it is sometimes (RZhMat, 1965, 7B199) essential to establish the fact that for a system close to a Hamiltonian one, depending on a parameter $\mu$, under certain additional conditions…
This paper studies regularized sums of zeros of entire functions represented as finite sums of exponential factors multiplied by functions with sectorial asymptotic expansions, a class arising in parameter-dependent boundary value problems for ordinary differential equations. The authors define an a…
This note reformulates Eckmann-Hilton type duality for functors in the category of weak homotopy types of pointed spaces, replacing an earlier point-set topological setting in order to make the construction homotopy invariant and avoid related topological difficulties. It defines continuous functors…
The equation \begin{equation} \ddot{\varphi}-f_1(\varphi)\dot{\varphi}-f_0(\varphi)=0\tag{1} \label{1} \end{equation} is considered in the case where $f_0(\varphi)$ and $f_1(\varphi)$ are trigonometric polynomials of degree no higher than $n$, where $n$ is a fixed natural number. Equation (1) is equ…
A system of differential equations \begin{equation}\frac{dx}{dz}=\sum_{j=0}^pa_j(z)y^{p-j},\quad\frac{dy}{dz}=\sum_{j=0}^kb_j(z)x^{k-j}\tag{1}, \end{equation} is considered, where $a_j$, $b_j$ are holomorphic functions and $k\ge p\ge2$. Necessary and sufficient conditions are provided for the movabl…
This paper studies completeness of the system of all translates of a function in weighted spaces whose norm involves an even subadditive weight, and relates this problem to regularity of the corresponding convolution normed ring. It proves that if the weight satisfies an integrability condition, the…
The paper studies uniform rational approximation on a plane compact set whose interior has several components, asking when approximation on each component can be glued to approximation on the whole set. Using Gleason parts for the algebra R(X), it proves a necessary and sufficient condition for ever…
The paper studies structural restrictions on extremally disconnected compact spaces and their homogeneous subspaces. It proves that every infinite compact subspace of an extremally disconnected space contains a copy of the Čech compactification of the natural numbers, yielding cardinality consequenc…
The paper presents the conditions for the existence and provides an algorithm for constructing periodic solutions of the equation $$\frac{d^2x}{dt^2}=f\biggl(t,x,\frac{dx}{dt}\biggr),$$ the right-hand side of which is periodic in $t$. Bibliography: 6 items.
This paper studies arithmetic sums of sets of integers within the theory of recursively projective sets, motivated by analogies with projective sets and earlier work on arithmetic summation. It introduces symmetrically dense enumerable sets and proves that every such set can be decomposed as a nonre…
The paper studies complete orthonormal systems of functions associated with the Laplace operator in arbitrary domains without imposing boundary conditions, defining their corresponding spectral parameters as fundamental numbers. It proves that for any such system the fundamental numbers are unbounde…
This note studies cohomology classes of connected closed Lie subgroups of general linear groups with coefficients in the sheaf of germs of continuous real-valued functions, using a category of locally trivial principal bundles over Hausdorff bases. It constructs universal-type principal bundles from…
This note develops constructive methods for generalized smoothing and extrapolation problems for random vector functions, using the Hilbert space framework and notation established in an earlier work. It relates optimization with respect to general forecast quality criteria to auxiliary minimum vari…
This paper studies the stability, for small values of a scalar parameter, of systems of linear differential equations with periodic coefficients in an operator polynomial form. It proposes a method based on associated integral equations and finite systems for selected Fourier harmonics, yielding alg…
The paper studies an extremal problem for finite systems of quadratic constraints associated with cosine coefficients and relates it to linear methods of summation of Fourier series. It proves that, when the cosine series with coefficients \(h_k\) converges uniformly to a function \(f\), the limitin…
This paper studies local features of smooth homogeneous random fields, including spikes, glints, and saddle points above a specified level, viewed as random point flows in Euclidean space. It develops a general framework for regular random flows, defines higher order measures and intensities, and re…
The paper extends results of A. F. Leont’ev on sequences of Dirichlet polynomials to functions of several complex variables, formulated mainly for two variables. It studies uniform convergence of double sequences of Dirichlet polynomials with prescribed exponent densities, proving extension of conve…
This paper studies the high energy asymptotics of the spectral function kernel for the Schrödinger operator on Euclidean space with a nonnegative potential. Under analyticity and growth conditions on the potential along the line segment joining two points, it derives a refined off diagonal asymptoti…
A set of systems of differential equations is constructed, possessing specified singular points (foci, centers, nodes, and saddles), limit cycles, and separatrices. Bibliography: 5 items.
This paper studies strong continuous summability methods for general trigonometric series and their application to Fourier series. It defines summability by a family of nonnegative weights, gives conditions for comparison between exponents, uniqueness of limits, and Toeplitz regularity, and shows th…
The paper studies finite-dimensional division algebras over the real numbers, especially those of dimensions 4 and 8 and those with associative powers. Using deformation and topological arguments, it shows that the set of real division algebras is open in the corresponding space of algebras and has …
This paper studies best unbiased estimation of parametric functions in incomplete exponential families whose natural parameters are restricted by polynomial equations. For samples summarized by sufficient statistics, it gives necessary and sufficient conditions under which a statistic with finite va…
The paper constructs extensions of a separated locally convex real topological vector space by replacing the scalar field with the Banach algebra of bounded real functions on an arbitrary nonempty set. It defines the associated modules built from continuous linear maps into this algebra, establishes…
This paper studies the global structure of connected complete analytic Riemannian spaces whose metric is locally semi-reducible, namely of the form \(ds^2=d\rho^2+f\,d\theta^2\) with the two factors depending on separate coordinate groups. Using maximal analytic continuations of the two orthogonal c…
The paper studies a nonlinear Riemann boundary value problem for functions analytic inside and outside a smooth closed contour, with a boundary condition containing an nth power and a singular integral nonlinear term. Under modulus of continuity assumptions on the given functions and growth and Lips…
