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 differential games in which the payoff is the time required for a controlled trajectory to reach a target set, under restrictions on admissible phase states. The constrained motion is modeled by adding a normal reaction term to the differential inclusion, and the author extends no…
This paper studies regular differential operators on the basic affine space of a connected semisimple algebraic Lie group over an algebraically closed field of characteristic zero. It introduces a projection-like operation from regular functions on the group to regular functions on the quotient by t…
This paper studies polynomial approximation of continuous functions on bounded convex polyhedra in multidimensional Euclidean space, with attention to improved local estimates near vertices. It proves that for a function on a convex polyhedron there are polynomials whose error is controlled by the k…
This paper derives asymptotic formulas for the global error in numerical solutions of Cauchy problems for systems of ordinary differential equations. Under smoothness assumptions on the right-hand side and bounded local and round-off errors, it presents expansions for third- and fourth-order Runge-K…
The paper studies the first boundary-value problem for a class of quasilinear systems in divergent form, formulated through abstract additive homogeneous operators and variable Orlicz, Sobolev-type spaces. Building on a theorem of Browder and Dubinskii, it introduces structural, coercivity, monotoni…
This note studies the realization of homology and homotopy cycles in compact symmetric spaces by totally geodesic submanifolds, emphasizing metric restrictions absent from purely topological realization problems. It reduces the problem for compact Lie groups to Cartan embeddings of irreducible compa…
This note studies multiplier transformations that replace the symbol of a pseudodifferential operator by its product with a function depending on frequency and space variables, asking when such transformations preserve boundedness in spaces \(L_p(R^m)\). It introduces function space conditions on th…
This paper studies the existence of periodic solutions for systems of ordinary differential equations with periodic time dependence by reducing the problem to zeros of completely continuous vector fields in a Banach space. For systems whose leading term is positively homogeneous and whose perturbati…
This paper studies exponential dichotomy and Green’s functions for linear functional differential equations with almost periodic coefficients, formulated through operators acting on spaces of bounded continuous and almost periodic functions. Under stated bounded variation and almost periodicity assu…
The paper studies bifurcation and asymptotic bifurcation points for a nonlinear Hammerstein integral equation with a potential Carathéodory nonlinearity and a symmetric kernel whose associated self-adjoint operator has at most finitely many negative eigenvalues. Using ideal spaces of measurable func…
This paper studies interpolation of pseudoanalytic functions, a class of generalized analytic functions satisfying a homogeneous Vekua equation. Using Bers’ integration process and the Cauchy formula for pseudoanalytic functions, it derives analogues of the Lagrange-Hermite and Abel-Goncharov interp…
This paper proves uniqueness for a Tricomi boundary value problem for a class of nonlinear mixed type equations of the form \(y^m u_{xx}+u_{yy}=f(x,y,u)\), where the equation is elliptic in the upper half plane, hyperbolic in the lower half plane, and degenerates on the line \(y=0\). Under continuit…
The paper presents an iterative method for constructing cubic and polycubic spline functions by formulating spline interpolation as a boundary value problem for fourth order differential equations with coefficients vanishing at interpolation nodes. After finite difference discretization on a refined…
The paper presents a method for solving systems of linear algebraic equations with symmetric positive definite matrices by interpreting them as Ritz systems for a functional equation in an energy space. It derives an algorithm based on orthonormalizing a corresponding system of vectors, showing that…
This note studies when a sequence of approximate extremal minimization problems converges to a given original problem, both in the value of the functional and in the construction of minimizing elements. It formulates necessary and sufficient conditions using comparison mappings between the approxima…
The paper studies nonlinear operator equations in Banach spaces of the form F(u) plus B(u) equals a given functional, where F is monotone or strongly monotone and B is weakly continuous and orthogonal. It proves an existence theorem under reflexivity, coercivity, and hemicontinuity assumptions, and …
This paper studies nonlinear Hammerstein type equations of the form x + BFx = f in a complex Hilbert space, where F is a bounded hemicontinuous monotone nonlinear operator and B is a densely defined closed linear operator not assumed to be bounded or self-adjoint. Using monotonicity and coercivity h…
This note studies coefficient sequences in expansions with respect to seminormalized bases in uniformly convex and uniformly smooth Banach spaces, with special attention to Hilbert spaces. It proves upper and lower norm estimates in terms of sequence norms, derives a stability theorem for bases in u…
This paper studies linear equations for functionals involving higher order functional derivatives in normed spaces, with Cauchy data specified at a point. Using Frobenius-type complete integrability conditions, it formulates solvability criteria, including explicit conditions for a second-order equa…
This paper studies values of L(1, χD) for real Dirichlet characters when the modulus D is restricted to sparse arithmetic progressions and related sets. Using estimates for double sums with quadratic Dirichlet characters, it derives a main lemma reducing asymptotics for moments of modified L-values …
The paper studies conditions under which systems of ordinary differential equations with a principal positively homogeneous term admit proper guiding functions in the sense of Krasnosel’skii. It proves a necessary and sufficient criterion for constructing a homogeneous function with a prescribed pos…
The paper extends Lyapunov’s transfinite R-process for Delta-Sigma operations from chains of depth omega to full chains of depth omega_nu over systems of sets of strongly inaccessible cardinality tau. It defines omega_nu-conjunctive and disjunctive extensions, associated R and T operations, derivati…
This note proves that a homeomorphic correspondence between convex surfaces that preserves the variation of turn of every curve must be a similarity. The argument first shows that preservation of turn variation determines angles between arbitrary curve directions, hence the correspondence is conform…
The paper studies bicompactness and completeness of topological spaces through systems of canonical closed sets and their relation to the theory of absolutes. It introduces H-systems and H-ends, proves a criterion stating that a regular space is bicompact exactly when every H-system has nonempty int…
This paper studies a boundary value problem for a second order mixed type equation in a three dimensional domain divided by the plane where the coefficient changes sign. Weak solutions are defined by duality in Sobolev spaces, and the argument derives a priori estimates for the adjoint test function…
This paper develops variational theorems for several classes of analytic functions in circular annuli, aimed at reducing extremal problems for differentiable systems of complex-valued functionals to finite-parametric families of boundary functions. Using structural integral representations and earli…
This paper studies an infinite horizon two player linear differential game in which the state satisfies a controllable linear system and the payoff is a quadratic functional, with one player minimizing and the other maximizing. It formulates admissibility in terms of square integrability of the stat…
The paper studies embedding criteria for periodic function classes from \(L_r\) into \(L_p\), expressed through best trigonometric approximation and moduli of smoothness. Using Hardy, Littlewood, Paley type theorems, the Littlewood, Paley theorem, Nikolsky’s inequality, and Jackson type estimates, i…
This note extends earlier results on R and Rc operations from countable to uncountable systems of sets, using branching tables of strongly inaccessible cardinal rank and two branching hypotheses related to rank attainment and large disjunctive subsets. It formulates equivalent forms of these hypothe…
This paper examines bifurcations of one-dimensional point transformations, distinguishing internal and external bifurcations and classifying internal stability changes by characteristic roots passing through plus one or minus one. It develops a parametric diagram method in which curves of fixed poin…
This note studies when elements of homotopy groups of classical Lie groups and homogeneous spaces can be represented by totally geodesic spheres, relating minimal submanifold constructions to homotopic data. Using Bott periodicity for unitary and orthogonal groups, together with explicit sphere embe…
This paper studies estimation of a one-dimensional shift parameter from an independent sample with distribution function F(x minus theta), focusing on the admissibility of the sample mean under polynomial loss functions of the squared estimation error. It proves that, assuming F has two continuous d…
This note studies the construction of cubature formulas that are asymptotically close to optimal without depending on a particular choice of function space. After formulating optimality through the norm of the error functional, it defines universal asymptotic optimality for classes of weighted Sobol…
This paper develops several inequalities relating the Lévy distance between distribution functions to their characteristic functions and to weighted metrics. It proves a general smoothing inequality with an explicit truncation term, a broader bound using an auxiliary compactly supported distribution…
This paper gives a topological analogue of a theorem of Rokhlin on measure-preserving transformations, for homeomorphisms of separable metric spaces considered modulo sets of the first category. It proves that such a homeomorphism has a disjoint generator precisely when its set of periodic points is…
This paper studies criteria for the existence of nilpotent and supersolvable subgroups of prescribed order in finite groups, using invariant series, index series, and arithmetic conditions on sequences of indices. Extending earlier results on groups whose Sylow subgroups are invariant, it introduces…
This paper extends Leray and Schauder degree theory to a class of continuous mappings in real Hilbert space called almost-monotone mappings, including sums of strictly monotone and completely continuous mappings. It defines the class, establishes compactness and stability properties, and constructs …
The paper studies a class of nonlocal boundary value problems for properly elliptic differential equations, including formulations in which boundary conditions relate values and derivatives on the exterior boundary to those on a smooth interior manifold through a diffeomorphism. It defines elliptici…
The paper studies a linear system of ordinary differential equations with summable coefficients subject to general integral boundary conditions, including two-point and multipoint cases. It proposes a variant of the sweep method that avoids solving the homogeneous Cauchy problem directly, instead so…
The paper proves an eigenfunction expansion theorem for a non-self-adjoint Schrödinger operator in three-dimensional space with a complex exponentially decaying potential. The argument uses meromorphic continuation and estimates of the resolvent kernel, contour integration in the spectral parameter,…
This note develops a group algebra of analytic functionals on a complex Lie group, defining convolution on the strong dual of the space of holomorphic functions and proving that it forms a continuous associative algebra. It relates this algebra to hyperenveloping algebras, measure algebras, and alge…
The paper studies the oscillation problem for sequences of Fejér sums of periodic functions in the classes whose derivatives up to order p satisfy the stated smoothness and boundedness conditions, as well as for the corresponding conjugate sums. It determines extremal functions for the least upper b…
The paper studies completely regular Hausdorff spaces whose bicompact remainders have finite Iséki order, with emphasis on the classes defined by iterated sets of points of nonlocal bicompactness. It establishes structural and mapping properties for these classes, including behavior under open subse…
This note studies a singular boundary value problem for an nth order ordinary differential equation with initial conditions at one endpoint up to order n minus 2 and one additional derivative condition at the other endpoint. The coefficient function is allowed to have nonintegrable singularities at …
This paper studies the ill-posed problem of solving Stieltjes-type integral equations with a bounded continuous kernel when the unknown solution is known a priori to be bounded and nondecreasing. Using compactness arguments based on Helly’s theorem and uniqueness on the monotone class, the authors p…
This note studies asymptotic enumeration of several classes of labeled and unlabeled graphs, multigraphs, directed multigraphs, and initially connected directed multigraphs with prescribed numbers of vertices and edges or arcs. It defines families distinguished by connectivity, strong connectivity, …
The paper studies orthonormal systems in real Banach spaces, using differentiability of the norm to relate orthogonality of vectors to the corresponding supporting functionals. For smooth Banach spaces, whose norms and dual norms are Gâteaux differentiable, it proves that every orthonormal system is…
The paper studies classification problems for free filters and ultrafilters, comparing algebraic isomorphism of filters with equivalence induced by bijections of the underlying sets. It proves that these notions of equivalence coincide for free filters, gives criteria for equivalence of ultrafilters…
The paper studies finite Abelian n-groups and the extent to which converses to Lagrange’s theorem hold for prescribed divisors of the group order. After recalling definitions of n-groups, invariant and semi-invariant subgroups, and factor groups, it proves auxiliary results on subgroup recognition a…
