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 uniqueness classes for the Cauchy problem for linear partial differential equations in one spatial variable with variable lower-order coefficients and constant leading coefficient, extending earlier results for constant-coefficient systems. It gives conditions, often necessary and …
This paper studies systems of singular integro-differential equations on compact smooth manifolds whose principal symbol is not elliptic but has constant rank deficiencies that can be resolved through successive compatibility relations. It defines a class of uniformly nonelliptic systems by iterativ…
This note studies dimension-theoretic properties of closed finite-to-one mappings between paracompact spaces, extending Hurewicz’s dimension-raising theorem. It introduces sheaf-theoretic tools, including partial inductive systems of sheaves and a spectral sequence associated with a closed finite-to…
This note studies unitary extensions, without exit from the given space, of an isometric shift operator with defect indices 1,1 in a finite-dimensional Pontryagin space, focusing on the case with one negative or positive square. Using the associated nondegenerate Toeplitz Gram form, it gives an expl…
The results published previously (Doklady Akademii Nauk SSSR, 167, No. 5, pp. 1004–1007) are presented in detail. Bibliography: 20 items.
This work is related to the papers $[1,2,3]$. The problem of finding periodic generalized solutions for nonlinear generalized systems of differential equations of the type $$\dot{\mu}=A(t)\mu+P(\mu,t)+\eta$$ is formulated and solved. Here $A(t)$ is a $n\times n$ matrix with infinitely differentiable…
The paper refines Kolmogorov’s superposition theorem for continuous functions of several variables by improving the regularity required of the fixed inner functions. It proves, with the two-variable case presented in detail, that every continuous function on the unit cube can be represented as a fin…
The paper proves that a perfect image of a paracompact feathered, or p, space is again a paracompact feathered space, resolving a problem posed by Arhangel’skii. The argument combines Michael’s preservation theorem for paracompactness under closed maps with a construction of suitable locally finite …
The paper develops generalized notions of well-posedness for equations defined by mappings between topological spaces, focusing on cases where the usual requirements of solvability, uniqueness, and continuous dependence fail. It introduces partial continuity for set-valued translations and defines g…
This note studies solvability of nonlinear operator equations of the form AF(x) = x in a real Hilbert space, relaxing earlier assumptions that the positive self-adjoint operator A be bounded. It establishes existence theorems for potential nonlinear operators under weak upper semicontinuity and coer…
This paper studies finite-dimensional subspaces of continuous functions on an interval, focusing on Chebyshev systems, bounded oscillation, and several notions of suitability defined by the realizability of prescribed alternating extrema. It formulates these properties topologically in terms of func…
The paper studies unitary extensions of isometric operators in the Pontryagin space with one negative square and applies these results to extension problems for nondegenerate finite Toeplitz sequences in the class with one positive square. It gives geometric criteria for bounded, continuously invert…
The paper develops a family of integral constructions for bounded functions on an interval, using modified upper and lower sums defined through outer Lebesgue measure and a parameter controlling exceptional subsets. It proves that for fixed positive parameter these sums converge to Lebesgue integral…
The paper addresses Aleksandrov’s problem on the existence of universal extremally disconnected bicompacta of a given weight and Antonovskii’s question on extremally disconnected bicompacta homogeneous with respect to character. Using the theory of absolutes, irreducible perfect mappings, and cardin…
This note derives a priori estimates for the principal radii of curvature of a closed convex surface satisfying an equation of the form f(R1, R2) = phi(n), where f is twice differentiable and strictly increasing in both curvature radii. Using the support function and local coordinates at points wher…
This paper studies sufficient conditions for an absolute minimum in an optimal control problem with endpoint constraints, state dependent control sets, and a Bolza type functional. It develops a generalized auxiliary functional method based on a lemma comparing minimization over the admissible class…
This paper develops a cover-based method for factoring continuous mappings while controlling weight and dimension, presented as an alternative to spectral techniques. It first reproves Mardešić’s factorization theorem for mappings of bicompacta, then formalizes refinement operations on families of c…
A solution $x(t,\lambda)$ is called a singular solution of the operator equation $x(t)=\lambda P(x(t))$ if $x(t,\lambda)\to\infty$ for $\lambda\to0$. Using the example of the equation $$\begin{aligned}\dot{x}(t)&=\lambda\int_0^1[A_1(t,s)x(s-\tau)+A_2(t,s)\dot{x}(s-\tau)+A_3(t,s)x^2(s)]\,ds+\\&\lambd…
This note studies the existence and multiplicity of square roots of measure-preserving automorphisms, with emphasis on transformations having continuous or simple spectrum. Using cyclic approximation by periodic transformations and skew products with fiber of order two, it constructs an automorphism…
This note studies a class of degenerate quasilinear elliptic equations and systems of arbitrary order with homogeneous first boundary conditions in a bounded smooth domain. Under differentiability, monotonicity-type degeneracy, and Lipschitz-like assumptions on the nonlinear coefficients, it formula…
The note formulates generalizations of Grobman and Hartman results on the topological equivalence of nonlinear systems of the form x dot equals Ax plus F(x) and their linear parts, under hyperbolicity of the matrix A. It introduces H-homeomorphisms and A-homeomorphisms with bounded displacement, the…
This paper proves a weighted \(L_2\) estimate for generalized derivatives near the boundary of a smooth domain, motivated by earlier boundary growth estimates for solutions of elliptic equations. Starting from a known inequality that bounds higher weighted derivative norms by a finite sum of lower o…
The paper studies conditions under which representations of semisimple Lie algebras over fields of characteristic zero remain completely reducible in infinite-dimensional spaces. It adapts the standard finite-dimensional proof by isolating the role of Whitehead’s lemma and proves complete reducibili…
This paper studies dense increasing sequences of integers for which the equation defining a greatest common divisor, gcd(ai, aj) = ar with r < i < j, has no solutions. Contrasting this problem with the corresponding least common multiple equation considered in earlier work, the authors prove that an…
This paper studies extension problems for continuous, theta-continuous, and delta-continuous mappings between Hausdorff topological spaces, especially in relation to H-closed extensions and paracombinatorial extensions. It proves that every perfect continuous onto mapping extends from a Hausdorff sp…
This note studies regularity of generalized solutions of linear partial differential equations with constant coefficients in domains containing unbounded Euclidean directions, under assumptions that selected derivatives are square integrable and decrease at infinity in an appropriate local sense. Us…
This note studies a nonlinear mixed problem for the string equation when the usual nondegeneracy condition at a boundary fails at a finite time during continuation of a smooth solution. It analyzes the limiting behavior at the critical time and proves that, depending on associated boundary quantitie…
This note studies ranks of elliptic curves over rational function fields over finite fields, with the aim of producing examples of arbitrarily large rank over a fixed field. Using Tate’s relation between rational points over a function field and homomorphisms from a Jacobian, the authors compute zet…
This note compares properties of constructive functions with operators acting on quasi-numbers, quasi-FL-numbers, and FR-numbers, focusing on equivalence, continuity, and uniform continuity. It shows that every constructive function has an equivalent operator of each considered type, but that the co…
The paper derives matrix elements for proper Lorentz transformations in unitary irreducible representations of the principal series, motivated by applications of noncompact symmetry groups in elementary particle classification. Using the canonical basis and representation formulas of Gelfand and Nai…
The note studies a disjunction property for propositional formulas under a constructive version of Rose’s notion of realizability, formulated through partial recursive functions and Kleene realizability after substitution of closed logical-arithmetical formulas. It proves that for any proposed reali…
The paper studies growth indicators for harmonic functions in unbounded three-dimensional domains, asking how rapidly a harmonic function may grow inside a domain while remaining bounded on the boundary and outside a prescribed set. It generalizes an earlier construction by defining a harmonic funct…
This note formulates and studies an operator-valued generalization of the classical power moment problem, motivated by structures related to Wightman field theory. For positive definite matrices of operators on tensor powers of a Hilbert space, a moment condition is expressed as the Hermiticity of a…
The paper studies finite general validity, in the sense of Medvedev, for a special class of propositional formulas built from initially negated variables using conjunction, disjunction, implication, and negation. It extends intuitionistic propositional calculus by adding a specific finitely valid ax…
A system of the form \begin{equation} x'(t)=z(x(t),t)-\int_0^tK(t,s)\psi(x(s),s)\,ds,\tag{*} \label{*} \end{equation} is considered, where $x(t)$, $z(x,t)$, $\psi(x,t)$ are $n$-dimensional vectors; $K(t,s)$ is a symmetric matrix of the $n$-th order, and $\psi_i(x,t)$ depends only on $x_i$ and $t$. C…
The work is devoted to the study of the Sturm–Liouville boundary value problem \begin{equation} \begin{gathered} y''+f(t,y,y')=0,\\ \alpha_{11}y(\alpha)+\alpha_{12}y'(\alpha)=0,\quad\alpha_{21}y(\beta)+\alpha_{22}y'(\beta)=0\end{gathered} \tag{1}, \end{equation}, which has been investigated by a num…
The paper gives a constructive justification, in a restricted formal setting, of A. A. Markov’s principle of constructive selection. It proves an algorithmic variant of P. S. Novikov’s theorem: if a normal algorithm decides a recursive property defined in the constructive arithmetical calculus and t…
This note studies a non-self-adjoint second order difference operator in l2 on the half-line, with a complex coefficient sequence and a boundary condition at the origin, as a discrete analogue of the Sturm-Liouville problem. It constructs special solutions of the associated difference equation, incl…
A system of equations \begin{equation} dx=\sum_{i=1}^np_i(x)\,dt^i, \tag{1} \label{1} \end{equation} is considered, where $x$ and $p_i(x)$ are $(n+1)$-dimensional vectors for which the conditions of complete integrability are satisfied. It is assumed that the system \eqref{1} possesses a closed traj…
The paper presents a recurrent method for recalculating the characteristic polynomial of a matrix when a single column is replaced, a situation arising in numerical linear programming methods. Using the Cayley-Hamilton relation and Cramer’s formula, it derives explicit recurrence formulas for updati…
