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 note studies the choice of step parameter in descent methods for minimizing twice continuously differentiable strongly convex functions in finite-dimensional space, where exact line search would require solving a nonlinear equation. It proposes a simple backtracking rule, including bisection as…
The paper studies bounded solvability, termed stability, for boundary value problems involving systems of linear partial difference equations with operator coefficients in a complex Banach space, without assuming commutativity of the coefficients. It derives necessary and sufficient spectral conditi…
This note studies bifurcation of almost periodic solutions from an equilibrium in nonlinear differential systems with a small parameter, a setting where standard compactness and normal solvability assumptions for classical bifurcation theory fail. Using averaging, simple-solution methods, cone techn…
This paper studies which topologies on a linearly ordered set make it a generalized continuum interval with the given order induced by connectedness. It establishes necessary and sufficient conditions for the existence of such Pi-topologies, notably excluding gaps and certain finite even partitions,…
This paper derives three-dimensional groups of similarity symmetry, building on Shubnikov’s concept of similarity symmetry and its extensions to antisymmetry and color symmetry. It establishes general structural properties of such groups, including the existence of a least similarity coefficient gre…
This paper studies best uniform approximation of continuous functions on an interval by generalized polynomials formed from a finite linearly independent system of continuous functions. It introduces systems of type k, defined through rank and sign-change conditions on determinants and complementary…
This note studies Paley-type singularities, lacunary Fourier coefficients, and interpolation for classes of analytic functions continuous on the closed unit disk but allowed prescribed boundary singularities. It formulates norm estimates for Fourier coefficients on arbitrary infinite index sets, sho…
The paper studies stability of solutions of linear differential equations with periodic operator coefficients in a Banach space through the associated monodromy operator. It shows that stability of the equation is equivalent to uniform boundedness of all integer powers of the monodromy operator, and…
This note studies the Riemann boundary value problem on a Lyapunov contour in cases where the coefficient is Hölder continuous or has first kind discontinuities, and where the free term belongs to suitable \(L_p\) or weighted \(L_p\) classes. The problem is reformulated in the dual of the Hölder spa…
This paper derives necessary optimality conditions for singular controls in a finite dimensional optimal control problem with terminal cost and bounded control set. Using needle variations and an expansion of the increment of the functional, it isolates second order terms for first order singular co…
This paper studies parametric resonance in canonical systems of linear differential equations with quasiperiodic coefficients and a small perturbation of a diagonal Hamiltonian form. It develops perturbative symplectic transformations that reduce the system to a form in which the nonresonant part is…
This paper studies boundary value problems of linear conjugation for functions holomorphic in bicylindrical domains, formulated on the product of two smooth closed contours with Hölder boundary data. Using Cauchy type integrals, singular operators, and reductions to elementary homogeneous and nonhom…
The paper studies boundary value problems in a half-space for constant-coefficient B-elliptic differential equations involving the Bessel operator, with homogeneous boundary operators satisfying the Lopatinskii condition. Using the Fourier-Bessel transform, the problem is reduced to ordinary differe…
This note studies simple positional operatives, including associative, alternative, and more general permutation-defined classes, and extends parts of the Rees, Sushkevich, Clifford theory of completely simple semigroups to these n-ary algebras. It develops structural results for i-simple, j-simple,…
This note introduces a class of pseudodifferential operators whose symbols are analytic in one complex half-plane variable and satisfy conditions analogous to Petrovskii correctness, strong correctness, and constancy of strength. The authors develop a symbolic calculus for these operators modulo ope…
This paper studies interpolation of functions analytic in the complex plane except for finitely many singularities by rational functions whose poles are prescribed at those singular points and whose interpolation nodes accumulate only at them. Using an integral representation of the interpolation re…
This paper studies instability of equilibria in systems of ordinary differential equations subject to small, constantly acting perturbations. Using an auxiliary Lyapunov-type function whose derivative along the unperturbed system is nonnegative, the argument derives sufficient instability conditions…
This paper studies boundary properties of generalized analytic functions satisfying a first order Vekua type equation with coefficients in an appropriate integrability class. Using estimates for the basic kernels, it extends classical results on Cauchy and Cauchy-Stieltjes integrals to this setting,…
The paper develops an algebraic approach to limits in which every indexed sequence has a limit, defined as a coset modulo a chosen normal divisor, subspace, ideal, or lattice ideal. It distinguishes fine and rough limits, relates them to reduced products and infinitesimal sequences, and shows that s…
The paper studies Vietoris hyperspaces of closed subsets of bicompact spaces and their behavior under inverse spectra. It proves that the hyperspace functor commutes with inverse limits of spectra of bicompacta, using exponential continuations of bonding maps, and develops auxiliary results on d-map…
This paper studies minimax properties of the usual squared multiple correlation test \(R^2\) for testing zero correlation in a multivariate normal sample, focusing on the case \(p=3\) with large sample size. Building on earlier work of Giri, Kiefer, Linnik, Prokhorov, and Shalaevskii, it proves that…
The note studies finite decompositions of compact bodies in a topological space under the action of a group whose transformations can place any body inside any other. It defines notions of G-composability, equivalence by rearrangement of finitely many transformed pieces, and G-complementability, equ…
The paper studies Cohn-Vossen’s problem of estimating changes in Euclidean distances on closed convex surfaces from changes in their intrinsic metrics. It proves that if two closed convex surfaces are related by a homeomorphism whose intrinsic distances differ by at most epsilon, then the correspond…
This paper studies primary ideals in the convolution Banach ring of functions on the positive half-line that are integrable with an increasing weight satisfying standard submultiplicativity and growth conditions. Using an approximation theorem for right translations, it describes the primary ideals …
This paper studies the high-energy growth of spectral functions for generalized second-order boundary-value problems with a boundary condition imposed at a regular endpoint. For a class of decreasing weight functions that includes powers with exponent between minus one and zero, it gives necessary a…
The paper studies Chebyshev minimax problems for general interpolation classes of continuous functions, with emphasis on the convergence of generalized methods of successive Chebyshev interpolations. After recalling the interpolation, continuity, and alternation properties defining such classes, the…
The paper studies eigenfunction expansions for a non-self-adjoint three-dimensional Schrödinger operator with a complex exponentially decreasing potential. Using solutions of the associated scattering problem, it analyzes solvability and analytic continuation of the Lippmann-Schwinger type integral …
The paper studies model-theoretic properties of infinitary languages \(L_{\alpha\beta}\), focusing on compactness for restricted classes of axioms, preservation theorems, and characterizations of axiomatizable classes. It proves universal compactness under a cardinality condition on the signature, d…
This paper studies a mixed initial boundary value problem on a finite interval for a third order quasilinear differential equation with a dissipative mixed derivative term and homogeneous Dirichlet boundary conditions. Using Fourier sine expansions, Banach spaces adapted to the boundary conditions, …
The paper studies the asymptotic distribution of eigenvalues for the three-dimensional Schrödinger operator with a continuous potential tending to infinity in unbounded domains whose boundaries may be infinite. It defines a class of admissible domains and proves discreteness and an approximation res…
The paper studies bifurcation and Lyapunov stability of small nonzero periodic solutions in parameter-dependent systems of ordinary differential equations whose linearized monodromy matrix has the eigenvalue one with multidimensional degeneracy. Using generalized eigenvectors, adjoint vectors, and a…
This paper studies periodic solutions of two-dimensional autonomous differential systems in which a small parameter multiplies the derivatives, focusing on trajectories inside a saddle separatrix cell that approach the separatrix cycle as the parameter tends to zero. Under smoothness and nondegenera…
This paper studies the law of the iterated logarithm for sums of independent random variables represented as measurable elements of a complete topological semifield equipped with a Boolean algebra and measure. After formulating integration, probability, independence, and Laplace transforms in this s…
The paper studies a variational problem for regular parametrized surfaces with prescribed spherical image and prescribed boundary support function, where the integrand is a positive, first-degree homogeneous, strictly convex function of the oriented area element. It reformulates the problem using th…
The paper studies error estimates for approximate differentiation obtained by differentiating Lagrange and Hermite interpolation polynomials on the interval [-1,1]. For node matrices related to Chebyshev polynomials of the first and second kind, including variants with and without endpoints, the aut…
The paper studies structural properties of segment-functionals that define extremal polynomials on the interval [0,1], extending earlier results for functionals with prescribed zero and normalized coefficients. Using the linear system relating functional moments to loads at extremal nodes, it analyz…
This paper studies commutative symmetric Banach algebras of bounded operators in the Pontryagin space with one negative square, using Naimark’s model classification into singular and nonsingular cases. It analyzes the parameter systems defining such algebras, the associated ideals and quotient norms…
This paper studies short exact sequences in a category whose objects are modules with varying operator rings and whose morphisms are compatible pairs of group and ring homomorphisms. It formulates the extension problem via coupling homomorphisms into quotient modules of multiplications and relates e…
The paper studies linear differential equations in a Banach space whose leading operator degenerates at an endpoint, reducing them to equations with a scalar degenerating coefficient and bounded operator terms. Using resolving operators and spectral separation assumptions on the limiting operator, i…
The paper establishes multiplicative inequalities that bound the uniform norm of functions in Hölder and weighted Guseinov type classes by products of Hölder type norms and Lebesgue norms, including versions on intervals, multidimensional cubes, and Lyapunov contours. These estimates are then applie…
The paper studies oscillations of solutions to the biharmonic boundary value problem in the unit disk with prescribed boundary values and zero normal derivative on the boundary. It derives estimates for radial oscillations in terms of the second modulus of smoothness of the boundary function, and ob…
The paper studies analytic continuation of Dirichlet series formed from eigenvalues of elliptic boundary value problems on bounded smooth domains. For the Laplace operator with Dirichlet or Neumann boundary conditions, it extends earlier low dimensional results by describing the meromorphic continua…
The paper studies the Cauchy problem in the complex domain for a second-order linear equation with two independent complex variables, analytic coefficients, and analytic initial data prescribed on a complex curve. Using differential forms and a holomorphic analogue of metric conjugation, it derives …
This paper addresses Minkowski’s problem for systems of inhomogeneous linear forms associated with unimodular matrices. It proves an upper bound for the minimum, over integral vectors, of the absolute product of the coordinates of A(X) plus an arbitrary shift, when the matrix A admits a decompositio…
This paper studies complete immersed two-dimensional surfaces in Euclidean three-space, with emphasis on nonpositive curvature and the global behavior of their level curves, spherical images, and ends. Using gradient lines, Morse-theoretic arguments, and properties of the limiting directions of norm…
The paper studies representations of an infinite-dimensional Clifford algebra by bounded self-adjoint operators on a separable Hilbert space, focusing on operators that commute with a given representation and on the type classification of the weakly closed ring it generates. Using the direct integra…
This note studies subsets of families of one-place recursive functions that are decidable relative to the ambient family, extending earlier observations beyond sets defined by finitely many function values and a recursive predicate. It constructs a broader class using recursively enumerable families…
This note extends a previously constructed Euler numerical algorithm for finding asymptotically stable singular points of ordinary differential equations to the setting of partial asymptotic stability. It establishes converse Lyapunov-type criteria for partial stability in the large, including versi…
The paper studies stability of the trivial solution of nonlinear perturbed motion equations on a finite time interval, using a variable ellipsoidal domain of admissible deviations. It introduces a transformation based on asymptotic diagonalization of the linear part, including recurrence formulas fo…
The paper addresses the existence of unconditional bases in quotient spaces associated with Hardy type subspaces, specifically \(L_1/H_0^1\) and \(L'/H'_0\). Using results of Pelczynski together with a Baire category argument and constructions involving bounded analytic functions and conformal mappi…
