RussiaRxiv · Open Access in English
Translated research papers from Russian journals and repositories
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Generated abstract This paper addresses the formulation of integral conservation laws for continuous media in general relativity, where conventional treatments are complicated by nonunique energy momentum complexes and ambiguous integration in curved spacetime. Using Sedov’s variational principle, tetrad variables, an…
Generated abstract This paper examines the kinetics of unipolar charging of highly radioactive beta-emitting aerosol particles in an external electric field, a problem relevant to electrostatic precipitation and atmospheric or industrial electric fields. The authors model a particle as an absorbing sphere emitting ele…
Generated abstract This paper addresses the motion of a rigid body with a fixed point under Kovalevskaya-type inertia and center-of-mass conditions, in the presence of a nonzero gyrostatic moment. Starting from the standard differential equations for angular velocity and the gravity direction cosines, the authors impo…
Generated abstract The paper studies weighted Sobolev-type spaces for functions on unbounded domains and addresses the failure of compact embeddings in such settings. For a broad class of unbounded domains, it establishes sharp weighted embedding estimates and compactness theorems for embeddings between spaces of diff…
Generated abstract The paper studies the number of solutions to congruences modulo a prime power of the form F(x,y) congruent to 0 modulo p^m, where F is an absolutely irreducible polynomial and the variables range over incomplete residue intervals. Using a Hensel-type lifting argument, algebraic number theory, estima…
Generated abstract This paper studies axisymmetric vibrations and stresses in a homogeneous isotropic elastic circular disk whose rotation is reduced by partial braking through a rigid rim. Because residual angular velocity couples radial and tangential displacements through rotational inertia, the authors formulate c…
Generated abstract This paper studies Hamiltonian systems in action angle variables that are small perturbations of an integrable system, under a nondegeneracy condition on the Hessian of the unperturbed Hamiltonian near a fixed action value. A variational method is proposed, based on minimizing a functional that meas…
Generated abstract This note studies the location of points of maximal deviation in best uniform trigonometric approximation of continuous periodic functions. Extending related results for algebraic polynomial approximation, it analyzes differences of successive best approximating trigonometric polynomials, introduces…
Generated abstract The paper studies existence and uniqueness for nonlinear Hammerstein type integral equations and systems in Lebesgue spaces, allowing measurable sets of finite or infinite measure and avoiding assumptions such as complete continuity, self-adjointness, or restrictions like \(p \geq 2\). It formulates…
Generated abstract The paper studies when compact Hausdorff spaces contain Stone-Cech compactifications of discrete spaces, reducing the problem to the existence of continuous maps onto Tikhonov cubes and to dyadic systems of zero-sets. It introduces the cardinal invariants massiveness and tightness, proves mapping th…
Generated abstract This paper examines whether focused coherent laser radiation can produce electron, positron pairs from the vacuum, a quantum electrodynamic effect requiring fields near the critical Schwinger value. Using the nonlinear effective Lagrangian for slowly varying electromagnetic fields, the authors deriv…
Generated abstract This paper studies the direct and inverse spectral theory for a half-line Sturm-Liouville equation whose potential has a singularity at the origin stronger than the Bessel type. Under specified growth, smoothness, and integrability assumptions on the singular part and perturbation, the authors estab…
Generated abstract The paper studies weak and generalized solutions of linear evolutionary systems whose spatial part is elliptic in the sense of Petrovsky, including cases beyond hypoelliptic equations and systems with complex-valued solutions constrained by cones. It develops several lateral smoothing estimates in l…
Generated abstract This paper analyzes kinematic magnetohydrodynamic field amplification by a convective vortex cell intended as a simplified model for processes relevant to the solar dynamo. The induction equation is solved for an incompressible toroidal vortex with both meridional circulation and an azimuthal veloci…
Generated abstract The note develops new general integral representations for holomorphic functions in one and several complex variables, extending earlier operator methods introduced by the author. It defines composite inverse operator families and applies them to functions on star-shaped domains in one complex varia…
Generated abstract The paper studies when the natural map from the inductive limit of the intersections of a subspace with the terms of a countable inductive system into the subspace has a bijective adjoint on duals. It relates this question to weak homomorphisms and surjectivity of adjoint operators, then uses invers…
Generated abstract This paper examines the additional condition required at the end of a crack, which is not determined by the equations of motion and deformation alone. Using general local and energetic considerations for continuous media with displacement discontinuities, the authors argue that crack growth laws can…
Generated abstract The paper studies two-layer, one-step iterative schemes for solving linear equations with positive non-self-adjoint operators in Hilbert spaces. It reduces implicit stationary iterations to explicit schemes and analyzes the norm of the transition operator in order to choose optimal or near-optimal i…
Generated abstract This paper studies localization and convergence of Fourier series associated with fundamental systems of functions of the polyharmonic operator, a class that includes eigenfunction systems of nonnegative self-adjoint extensions of the minimal polyharmonic operator. Using earlier methods together wit…
Generated abstract A variational formulation is developed for the Helmholtz boundary value problem describing monochromatic wave propagation in a three dimensional waveguide with general smooth boundary and either impedance type or Dirichlet boundary conditions. The solution is expanded in prescribed transverse functi…
Generated abstract This paper studies relationships among dyadicity, dimension, metrizability, and cardinal invariants for bicompact spaces, with particular attention to open images of products of metric compacta. It introduces openly dyadic bicompacta, establishes structural properties of this class, and proves metri…
Generated abstract This note studies necessary first order conditions for a class of nonsmooth minimization problems with equality constraints, convex inequality constraints, and an additional constraint requiring one variable to be selected by an operator depending on the other. Using a feasible directions framework,…
Generated abstract This paper introduces and studies multistage matrix games with inertia, in which each player’s admissible mixed strategies at a given step are constrained by the pure strategies realized in several preceding steps. The authors formalize inertia of finite depth, define limiting expected average payof…
Generated abstract This paper studies local analytic quasigroups defined by analytic mappings between equal-dimensional manifolds and develops canonical power-series decompositions for their defining equations. Using isotopic coordinate transformations and an induction on homogeneous degree, it proves the existence an…
Generated abstract This paper applies Feynman path integrals to the numerical calculation of the helium atom energy spectrum, with emphasis on the ground state as a test case for a many-particle quantum system. The electronic action is discretized along broken-line trajectories in reduced units, the finite-dimensional…
Generated abstract This note develops estimates for surface potential type singular integrals whose kernels depend on a generalized difference of arguments defined through a Bessel generalized shift operator. The authors introduce weighted fractional norms in a half space, relate them in the Hilbert case to norms defi…
Generated abstract Observations with the DKR-1000 radio telescope at Pushchino in the meter-wavelength range led to the discovery and initial characterization of the pulsar PP 0943. The paper reports intermittent pulse detections at 70 to 90 MHz, estimates its position, and gives a principal period of about 1.093 s, w…
Generated abstract This paper studies non-uniqueness phenomena in the coefficient problem for normalized univalent functions in the unit disk, focusing on solutions of the differential-functional equations that give necessary extremality conditions for the coefficient functional. Using subclasses with p-fold rotationa…
Generated abstract This paper proves the consistency of the fragment NF3 of Quine’s New Foundations, consisting of those axioms whose stratification uses at most three type levels. Using Specker’s criterion, the argument reduces consistency to the construction of a model of three-type theory admitting an epsilon-isomo…
Generated abstract This paper reports optical experiments on negative dispersion of light in a neodymium-activated calcium tungstate crystal near the 1.06 micrometer transition of Nd3+, a region where ordinary absorption from the lower level is not observed because that level is nearly unpopulated. The authors use opt…
Generated abstract This note studies a singular Nicoletti boundary value problem for a system of first order ordinary differential equations with conditions imposed at prescribed points, allowing the right hand sides to have nonintegrable singularities at those points. Using Carathéodory type assumptions, comparison f…
Generated abstract This paper addresses the determination of the Prandtl Karman constant in wall-bounded turbulent flow using a phenomenological stability principle for averaged velocity profiles. The authors argue that the logarithmic region governed by the Prandtl Taylor friction law is central to the formation of t…
Generated abstract This paper numerically investigates ionization instability in a low-temperature magnetized plasma carrying an electric current, using a simplified two-dimensional model with constant electron temperature, constant conductivity, and no diffusion processes. The formulation couples an elliptic equation…
Generated abstract This note studies two-level iterative schemes for solving linear operator equations with a self-adjoint positive operator in a Hilbert space. Implicit schemes are reduced to equivalent explicit schemes, allowing convergence estimates to be expressed through norms of resolving or transition operators…
Generated abstract This paper examines the electric field at the cathode surface in the cathode spot of a vacuum arc and assesses the applicability of Mackeown’s collisionless space-charge equation. Using estimates of the cathode-fall thickness, particle mean free paths, and collision cross sections for electron scatt…
Generated abstract This note formulates existence results for elliptic boundary value problems in bounded plane domains with corners and with internal curves of coefficient or boundary condition discontinuity reaching the boundary. Using weighted Sobolev spaces, the argument reduces local model problems near corners a…
Generated abstract This paper studies boundedness of Calderón-Zygmund type singular integral transformations in weighted \(L_p\) spaces, extending results of Riesz, Babenko, and Stein. Using a method related to Hardy and Littlewood, it gives necessary and sufficient sharp ranges for several multidimensional weights, i…
Generated abstract This note studies how holomorphic quadratic differentials on closed Riemann surfaces of genus greater than one depend on the moduli of the surface. Using the Bers-Teichmüller realization of moduli by normalized quasiconformal mappings and a variational formula for solutions of the Beltrami equation,…
Generated abstract This note gives necessary and sufficient conditions for subelliptic estimates for pseudodifferential operators in a domain, expressed through the principal symbol and the leading symbols of iterated commutators of the operator with its formal adjoint. The argument introduces an integer invariant mea…
Generated abstract This paper proposes a speculative framework for a unified theory of elementary particles based on special-relativistic space-time, pointlike world lines, and a universal ensemble of equally probable trajectories subject to topological restrictions. Drawing analogies with Edwards’s treatment of polym…
Generated abstract The paper examines radiative transfer in a plane semi-infinite atmosphere whose quantum survival probability and scattering indicatrix may vary arbitrarily with optical depth. Using an expansion of the scattering indicatrix in Legendre polynomials, it presents integral expressions for the components…
Generated abstract This paper studies cones in affine space whose associated family of parallel translated cones is invariant under a group acting transitively on nonvertex points, with attention to when such symmetry forces the cone to be elliptic. It proves several classification theorems: under closedness, sharpnes…
Generated abstract This study examines whether ultrasound can enhance or replace mechanical expansion in a liquid-hydrogen bubble chamber for recording high-energy particle tracks. Experiments were performed in a 25 cm chamber exposed to 340 MeV negative pions, using a cylindrical focusing barium-titanate ultrasonic t…
Generated abstract This paper examines short-period transformations of Northern Hemisphere tropospheric circulation in relation to the macrostructure of the solar wind, especially transitions between fast quasi-stationary streams and quiet solar wind. Using solar synoptic charts, coronal observations, plasma and field…
Generated abstract This paper studies extremal cases in compact simply connected Riemannian spaces with sectional curvature bounded above by a positive constant and with closed geodesics bounded below in length by the corresponding spherical value. It proves that equality in the length of a closed geodesic, in the per…
Generated abstract The paper studies a class of nonlinear differential systems formed by a finite-dimensional linear part in feedback with a possibly history-dependent nonlinearity, under controllability, spectral, and quadratic inequality assumptions. Using a frequency-domain negativity condition for an associated He…
Generated abstract This paper studies a quasilinear equation used as an approximate model for unsteady transonic potential flow, for which the usual Cauchy problem is inappropriate because planes of constant time are characteristic. A mixed boundary-value problem is formulated in a half-space with data prescribed on t…
Generated abstract This paper studies conformally flat solutions of the Einstein equations for dust-like matter, reducing the problem for metrics conformal to flat spacetime to conditions on a single scalar conformal factor. It derives compatibility equations for this factor, together with expressions for the matter d…
Generated abstract This paper studies spectra associated with uniformly bounded families of finite-dimensional operators acting in normed spaces, introducing several notions of spectral kernels defined through asymptotic approximate eigenvalues. It establishes basic topological and inclusion properties of these kernel…
Generated abstract This note studies relations among absolutely summing, semi-integral, quasi-nuclear, and generalized p- and q-quasi-nuclear mappings between locally convex and Banach spaces. Using tensor product formulations and nuclearity criteria, it characterizes absolutely summing operators via continuity of ind…
