SovietRxiv · Open Access in English
Rediscovering the Soviet scientific archive, in English
25357 full-text translations 14926 English PDFs 22539 abstracts
Showing 50 of 25357 papers
This paper studies a priori estimates and hypoellipticity for second order differential operators with nonnegative characteristic form, extending Hörmander type results to operators with multiple characteristics. It introduces a rank condition defined through iterated commutators of associated diffe…
The paper studies regularizing algorithms for ill-posed linear operator equations in Hilbert spaces when both the right-hand side and the operator may be subject to random perturbations. It considers pointwise regularization operators acting on random variables in Bochner spaces and shows that a bro…
The paper studies the Dirichlet problem for parameter-dependent pseudodifferential equations in a smooth bounded domain, under homogeneity, ellipticity with parameter, smoothness, and boundary factorization assumptions on the symbol. It extends the Agranovich and Vishik solvability theory from ellip…
This paper studies continuous and homeomorphic mappings whose associated Sobolev-type integral functionals are uniformly bounded below by weighted powers of the derivative norm. It introduces a metric determined by the weight function and proves a fundamental integral inequality relating the metric …
This paper examines nonlinear instability of homogeneous magnetization precession in ferromagnetic resonance when both shape anisotropy and cubic crystallographic anisotropy are included, without restricting the precession angle to be small. Starting from the Landau-Lifshitz equation with damping an…
This note extends several notions from linear spectral theory to nonlinear operators in Hilbert and Banach spaces, focusing on regular values, spectra, and eigenfunctions. It proves localization results for the spectrum of continuous operators in Hilbert space, establishes openness of the set of reg…
The paper develops a form of optimality conditions intended for large multidimensional optimal process problems, especially those with phase coordinate constraints and suitability for machine implementation. Using a generalized Lagrange method in Banach-type spaces, it derives necessary conditions f…
The paper extends magnetic-translation symmetry from the nonrelativistic charged particle to the Dirac equation for a relativistic charged particle in a uniform magnetic field. It shows that the corresponding unitary magnetic-translation operators commute with the Dirac Hamiltonian and, using the sq…
This paper develops an infinitesimal and operational formulation of partial invariance for manifolds under local Lie groups of point transformations. For a regularly defined manifold, it proves that the defect of invariance equals the generic rank, on the manifold, of the matrix obtained by applying…
The paper studies resonant transfer of optical excitation in collisions of identical heavy one-electron atoms, with particular attention to the case where fine splitting of the excited P state is large. Using a semiclassical straight-line collision model and dipole-dipole interaction, it derives cou…
This paper studies when embeddings of simple arcs and closed contours in three-dimensional Euclidean space can be obtained from polyhedral models by pseudoisotopies of the ambient space. It proves that every locally unknotted simple arc admits a pseudoisotopy carrying a line segment onto it, with no…
The paper studies the index of singular integro-functional operators on Hölder vector functions defined on a finite system of Lyapunov contours, where the functional shifts are generated by an orientation-preserving homeomorphism of finite cyclic order. It relates these operators to a broader class …
This paper studies upper semicontinuity and Hausdorff upper semicontinuity of the metric projection onto convex subsets of Banach spaces, relating these continuity properties to geometric conditions on the unit sphere and supporting hyperplanes. It introduces several conditions, including EPS, compa…
The paper analyzes induced one-quantum transitions of a relativistic electron in a homogeneous constant magnetic field under interaction with a plane monochromatic electromagnetic wave. Using exact electron wave functions with spin projection fixed along the magnetic-field direction, it derives matr…
This paper evaluates whether large lunar craters and round maria can be explained by meteoritic explosions using experimental scaling relations for large ejection explosions rather than simple extrapolations from terrestrial craters and smaller explosions. It calculates meteorite penetration depths …
This paper studies linear automatic-control systems with monotonically varying parameters whose time dependence can be represented by convergent infinite exponential series. Applying the Laplace transform and the shift theorem, the authors reduce the governing differential equation to a one-sided in…
This paper examines how hydrostatic compression affects the luminescence decay time of europium benzoylacetonate, focusing on the rare-earth ion transition from the excited state to the split ground multiplet. The authors argue that pressure can increase the probability of normally parity-forbidden …
This paper studies tensor invariants of subgroups of the Lorentz group that can be defined by invariance of a finite set of tensors. It states that any invariant tensor of arbitrary rank for such a subgroup can be expressed as a linear combination of tensors obtained from basic invariant tensors by …
This paper reports the development and testing of the EMV-100L electron microscope, designed to approach the theoretical resolving power set by objective spherical aberration and diffraction. The authors discuss the optical formulas for the theoretical limit, identify practical factors that degrade …
This paper studies proximally open, or equi-open, mappings of proximity spaces, with emphasis on metrizability and completeness of their images. Using quasiuniform covers and Leader’s metrization criterion, it proves that the equi-open image of a metrizable proximity space is metrizable, and derives…
This paper addresses a problem of Aleksandrov and Urysohn on the possible cardinalities of bicompact topological spaces satisfying the first axiom of countability. Using transfinite constructions, branching systems, and the notion of a free sequence, it proves a general cardinal estimate for Hausdor…
The paper addresses the ill-posed synthesis problem for a linear radiator with a prescribed radiation pattern, formulated as a regularized integral equation for the amplitude-phase current distribution. It proposes solving this equation by expanding the current in eigenfunctions of the kernel, ident…
This note derives asymptotic formulas for the plane and spherical albedo of a planet with an atmosphere of infinite optical thickness, allowing an arbitrary scattering indicatrix and assuming the single-scattering parameter is close to unity. Using relations between the atmospheric reflection coeffi…
This paper studies a one-dimensional nonlinear model of firehose instability in an anisotropic plasma with finite ion Larmor radius effects included in magnetohydrodynamic equations. For a circularly polarized monochromatic perturbation, the authors derive an analytic nonlinear solution in which the…
This paper extends Lyapunov’s principle of comparison of indices for stabilizing set-theoretic transformations to broader classes of operations on topological spaces of weight τ, including Z, T, Q, R, and ΔΣ operations with transfinite chain depth under suitable cardinal and base conditions. It prov…
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 how to assign mathematical meaning to the infinite Feynman diagram series for the coefficient functions in the normal-product expansion of the scattering matrix for a real scalar field with quartic interaction. It derives two systems of relations for these functions in the Euclidea…
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 paper applies the principle of maximum stability of averaged turbulent flows to determine the turbulent friction law in the core region of channel flow. Using a generalized Prandtl-Taylor representation with a constant near-axis mixing length, the authors reduce the mean velocity profile to a p…
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 develops a perturbation theory for two-time retarded spin Green’s functions arising in the calculation of kernels for integro-differential equations describing the macroscopic magnetic moment of a paramagnet in an external magnetic field. Under high magnetic-temperature assumptions, fixed…
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 partial stability of probabilistic automata under arbitrary small perturbations of initial and transition probabilities, asking which portions of behavior may remain invariant when full stability fails. It defines isolated cut points and stability relative to an event, relates stab…
This paper studies steady finite-amplitude surface waves in an ideal incompressible heavy fluid of finite depth, generated by a prescribed periodic pressure distribution on the free surface. Using conformal mapping of one wavelength of the flow region to an annulus, Bernoulli’s condition is reduced …
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…
This paper derives generalized kinetic equations for quantum systems with separated relaxation time scales using the nonequilibrium statistical operator formalism associated with Zubarev and McLennan. For a Hamiltonian split into an unperturbed part and a small interaction, the argument expresses th…
This paper examines how nonanalytic temperature dependence associated with phase transitions can arise from exact thermodynamic Green functions in a nonrelativistic system of interacting Bose or Fermi particles. Using Schwinger equations, functional integrals over external fields, and path integral …
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…
The paper examines direct methods for determining the chemical composition of the lunar surface as a basis for comparing lunar material with terrestrial rock types and stony meteorites. Using published lunar measurements and average elemental abundances in major terrestrial rocks and chondrites, it …
This paper examines similarity in natural river channels formed in noncohesive deposits, arguing that dynamically similar flows should have geometrically similar channels. Using width to depth ratio, curvature, sediment scale, Froude number, and suspended sediment content as similarity criteria, it …
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 investigates the crystallization kinetics of amorphous antimony films, a process for which earlier methods provided limited kinetic information. Thin amorphous films were annealed isothermally at 135, 150, 180, and 200 °C and examined by kinematic electron diffraction, with crystalline ph…
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 reports the development of a special photographic emulsion whose light sensitivity can be controlled during exposure by a pulsed electric field, with intended application to recording tracks of charged particles. The emulsion was synthesized using methods typical for nuclear photographic …
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 develops a kinetic theory treatment of transport phenomena in reacting gas mixtures when inelastic, reaction-producing molecular collisions occur with frequencies comparable to elastic collisions. Starting from the Boltzmann equation with separate elastic and reactive collision terms, it …
This paper analyzes emission regimes in a gas laser with a rotating ring resonator, focusing on how counterpropagating waves interact through resonator scattering, spatial modulation of the active medium, unequal losses, and multimode effects. Using coupled amplitude and phase equations for the trav…
