RussiaRxiv · Open Access in English
Translated research papers from Russian journals and repositories
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Generated abstract This paper studies choice-theoretic equivalents of Tychonoff’s theorem in topology, focusing on formulations that do not assume the weak axiom of choice. It proves that Tychonoff’s theorem for products of compact Hausdorff spaces is equivalent to Tychonoff’s theorem for finite spaces, Alexander’s cl…
Generated abstract This paper gives necessary and sufficient conditions for weighted a priori estimates for first-order constant-coefficient differential operators with exponential weights defined by a real homogeneous polynomial depending on spatial variables and nonnegative parameters. For real coefficient vectors, …
Generated abstract This note studies the remainder of partial sums of a generalized Fourier series for functions of two periodic variables, extending Kolmogorov-type asymptotic estimates from one-variable Fourier approximation. For the class of functions whose mixed derivative of orders p and q exists almost everywher…
Generated abstract The paper analyzes a mechanical model for the relative motion of a spacecraft and a cosmonaut connected by a cable that is reeled in at constant speed. Using Routh reduction for the cyclic angular coordinate, the dynamics are reduced to a second-order nonlinear equation for the cable orientation, to…
Generated abstract This paper develops asymptotic solutions for the diffraction of a plane electromagnetic wave by a perfectly conducting strip, formulated as a Neumann boundary-value problem for the Helmholtz equation. Using the method of edge waves together with the factorization method, the surface current and far-…
Generated abstract This paper studies multidimensional integral equations with difference kernels in a three-dimensional half-strip, under periodicity in two variables and summability of the kernel over the strip. By expanding the unknown function in Fourier series in the periodic variables, the equation is reduced to…
Generated abstract This paper examines the mechanism of charge compensation in oxygen-free solid solutions of calcium fluoride with trivalent rare-earth fluorides, using an X-ray diffraction study of a single crystal of composition Ca0.607Ce0.393F2.393. Analysis of reflection intensities, electron-density syntheses, a…
Generated abstract The paper formulates a notion of normal solvability for nonlinear operator equations in Banach spaces, modeled on Hausdorff normal solvability for linear equations. It proves that if a continuously differentiable operator maps a Banach space into a reflexive Banach space and has weakly closed range,…
Generated abstract The paper studies embeddings of compacta in Euclidean space through an invariant called embedding dimension, defined by pseudoisotopic approximation of a compactum by rectilinear polyhedra, and compares it with a dual embedding dimension defined via isotopic removal from polyhedra. It proves that th…
Generated abstract This paper analyzes recombination radiation from a nondegenerate electron-hole plasma in a semiconductor plate under current-induced pinch conditions. Using a one-dimensional plate model, the authors derive expressions for the spectral and integral radiation intensities in terms of carrier distribut…
Generated abstract The paper studies existence and uniqueness of bounded solutions on the whole real line for nonhomogeneous linear differential equations in a Banach space with generally unbounded time-dependent operators. It develops an approximation method based on bounded solutions of associated difference equatio…
Generated abstract The paper studies a first-order Beltrami equation whose ellipticity degenerates on a simple analytic curve where the coefficient satisfies a finite-order vanishing condition for its modulus. It analyzes two geometric cases, according to whether the characteristic direction is transverse or tangent t…
Generated abstract This paper analyzes the excitation of low-frequency nonpotential oscillations in the electron-hole plasma of a solid when an electric current flows across an external magnetic field. Using a hydrodynamic approximation with quasineutrality, Maxwell equations without displacement current, and conditio…
Generated abstract The paper proposes a method of incomplete factorization for certain boundary value problems in the theory of analytic functions, where coefficients on one contour admit piecewise holomorphic continuation with jumps on another contour. The approach treats the original boundary condition as partially …
Generated abstract This paper analyzes the absorption of laser radiation by vapor and condensate formed during rapid evaporation of an opaque solid surface. Using conservation laws, equilibrium equations of state, and estimates of radiation absorption by condensate particles and weakly ionized vapor, the authors deriv…
Generated abstract This paper studies complete regularity for stationary random processes whose spectral density has the form f(lambda) = 1/g(lambda), with g a nonnegative entire function of finite degree. It proves a necessary and sufficient criterion: integrability of |ln f(lambda)|/(1 + lambda squared) over the rea…
Generated abstract This paper examines periodic motions in a single-loop nonlinear impulse control system containing an ideal impulse element, an integrating element, a static nonlinearity, and a linear dynamic element. By deriving the point transformation over one and multiple impulse periods, the analysis formulates…
Generated abstract Potassium rare-earth double tungstates KLn(WO4)2 for the lanthanide series from lanthanum to lutetium were synthesized as single crystals by crystallization from a K2WO4 and WO3 melt and examined by powder X-ray diffraction, optical goniometry, and differential thermal analysis. The study distinguis…
Generated abstract This paper describes a bifurcation mechanism in multidimensional dynamical systems that differs from previously studied cases involving the creation or disappearance of a single limiting element. For a smooth system with a saddle-saddle equilibrium having a zero characteristic root and finitely many…
Generated abstract This paper estimates the probability of double beta decay in nuclei far from the beta stability band, where the available decay energy and number of accessible final states may be much larger than in stable nuclei. The authors derive and use expressions for two-neutrino and neutrinoless double beta …
Generated abstract The paper studies Riemann and Hilbert type boundary value problems for a generalized Cauchy-Riemann system with a singular line, considering cases of positive and negative values of the parameter. Using integral representations of solutions in half-planes, the problems are reduced to classical conju…
Generated abstract This paper analytically investigates the structure of weak shock waves in thermorelaxing two-component media, such as emulsions or gases containing suspended particles, where compression produces intercomponent temperature differences and heat-exchange relaxation. Using the Mandelstam-Leontovich tre…
Generated abstract This paper formulates alternative properties of physical systems, such as locality, causality, spectrality, and energy positivity, in terms of projection operators and associated constraint equations. It applies this framework to quantum field theory, deriving projector conditions for two-field and …
Generated abstract This paper studies necessary conditions for solvability and a priori estimates for pseudodifferential equations, extending earlier nonsolvability criteria of Lewy, Hörmander, Nirenberg, and Treves. It formulates conditions in terms of repeated commutators of an operator and its adjoint, and proves t…
Generated abstract This paper examines how the crystallographic orientation of single-crystal molybdenum and tungsten affects the angular and energy distributions of secondary ions scattered under low-energy ion bombardment. Using energy analysis of ions emitted from heated crystal faces while varying the azimuthal ro…
Generated abstract The paper extends earlier results on a priori estimates to a broad class of second order degenerate elliptic operators in bounded domains with smooth characteristic boundary components. It formulates local normal-coordinate conditions defining alpha-ellipticity, classifies boundary components accord…
Generated abstract The paper formulates the design of automatic machines as an optimization problem linking reliability, utilization, productivity, and production cost. It represents unit production cost as a separable nonlinear function of reliability related adjustment durations for machine mechanisms and input mate…
Generated abstract The paper studies boundary-value problems for elliptic-parabolic differential equations in bounded cylinders, with an elliptic spatial operator and a finite-order time differential operator. Using localization, eigenfunction expansions, Sobolev-type spaces, and parameter-dependent elliptic estimates…
Generated abstract This study examines whether the apparent differences between creep in homeopolar crystals and metals reflect bond type or the limited observation of early creep stages. Silicon single crystals were tested in uniaxial compression along the 111 direction in argon at 900 to 1300 degrees Celsius and 2 t…
Generated abstract The paper studies a class of two-dimensional integral equations of the first kind on an open Lyapunov surface, with kernels of the form \(Q(g,p)/R_{gp}\), arising in mathematical physics. It introduces an auxiliary singular kernel and uses potential-theoretic representations, limiting jump relations…
Generated abstract This paper proposes a method for identifying regional crustal structures of the Russian Platform by transforming anomalous geomagnetic field maps into maps of averaged horizontal gradients. The procedure calculates maximum rates of change of the magnetic field within equal map squares and uses the r…
Generated abstract This paper develops a weakly relativistic formulation of classical statistical mechanics for systems in which terms beyond order v squared over c squared may be neglected. It constructs the one-particle and Gibbs phase spaces using synchronized laboratory time, derives quasicanonical equations of mo…
Generated abstract A new lanthanum oxytungstate with composition 2La2O3·3WO3 was obtained as single crystals from the La2O3, WO3, NaCl system, although it had not been found in the binary La2O3, WO3 system. The crystals formed under isothermal conditions through evaporation of NaCl and partly WO3, with the largest col…
Generated abstract This paper reports an experimental study of luminescence in uranyl crystals and frozen solutions excited by high-power ruby laser radiation, with emphasis on whether the observed emission arises from two-photon absorption and whether stimulated emission can be obtained. Luminescence spectra were rec…
Generated abstract Electron paramagnetic resonance spectra of impurity Cu(II) were studied in binary oxide glasses based on phosphate, silicate, and borate formers with alkali or alkaline-earth modifiers, at room and liquid-nitrogen temperatures. The spectra are interpreted with an axial spin Hamiltonian and indicate …
Generated abstract This paper studies factorizations of arbitrary finite groups in terms of composition blocks, defined from the arithmetically connected classes of indices in an invariant or composition series. It introduces properly embedded systems of subgroups, invariant-index systems, and total permutability, the…
Generated abstract This note extends Dzhrbashyan’s generalized Riemann Liouville type operator from a single weight function to a finite system of functions satisfying the class conditions for \(\Omega\). It defines associated coefficient sequences and kernels, then proves generalized Cauchy and Schwarz formulas for h…
Generated abstract The paper proves a conjecture of V. A. Efremovich that the horocyclic pocket, defined as the universal covering of the Beltrami pseudosphere or equivalently by gluing two horocyclic domains in the Lobachevsky plane along their boundary horocycle, is not equimorphic to any surface of revolution. The …
Generated abstract This note studies expansions in eigenfunctions associated with only the negative eigenvalues of a second order non-self-adjoint boundary value problem, \(y''+2A\lambda y'+B\lambda^2y=0\), \(y(0)=y(1)=0\), under the condition \(A^2-B<0\). The proof reduces the question to an auxiliary elliptic proble…
Generated abstract This paper examines the use of electron-optical converters for recording soft X-ray radiation, focusing on the difficulty of reducing exposure while preserving image quality in X-ray diffraction imaging. The authors describe a four-stage converter with a thin mica input window, an internal photocath…
Generated abstract This paper examines the definition of entropy in nonequilibrium statistical mechanics, focusing on the relation between Planck, Boltzmann, and Gibbs coarse-grained entropies for an isolated classical system divided into weakly interacting subsystems. It defines coarse-graining by assigning a constan…
Generated abstract This paper applies the quasioptical potential method to simple exactly solvable quantum field theory models with a fixed heavy source, in order to clarify how energy dependent, time nonlocal interactions appear in scattering. Starting from a factorized nonlocal potential, the scattering amplitude is…
Generated abstract The paper addresses optimization of large-scale multiconnected systems formulated as linear programming problems with dense constraint matrices, where standard block programming or aggregation may be ineffective. It proposes reducing the constraint matrix to a special pseudodiagonal form, under cond…
Generated abstract This paper examines whether earthquake foci of widely different sizes can be treated as physically similar, given that focal dimensions range from tens of meters for weak events to hundreds or thousands of kilometers for the strongest events. Using similarity criteria derived from elastic equilibriu…
Generated abstract This paper investigates vibrational excitation and dissociation of diatomic oxygen in atom molecule collisions in a high temperature argon gas. Using a classical mechanical treatment with an anharmonic intramolecular potential, the authors compute level to level transition and dissociation probabili…
Generated abstract This note derives trace formulas for the connected part of the resolvent of the quantum mechanical Hamiltonian for three nonrelativistic particles with pairwise interactions, under regularity and spectral assumptions on the pair potentials. Using Faddeev’s framework, Hilbert’s identity, and direct i…
Generated abstract The paper studies eigenfunctions of first boundary value problems for elliptic equations whose coefficients degenerate at an interior point, using weighted Hilbert spaces and a normality condition near the singularity. The method removes a small ball around the degeneracy, solves the corresponding r…
Generated abstract This paper studies Rosenblatt strong mixing for homogeneous Markov chains with a countable state space. It proves that an irreducible positive recurrent aperiodic chain satisfies the strong mixing condition, gives a null recurrent example where the condition fails, and relates the mixing coefficient…
Generated abstract This note shows that the homology K-groups previously introduced by the author can be realized within the framework of generalized Steenrod homology groups. For a fixed locally finite complex K, it constructs a category of barycentric subdivisions of products K by L and defines corresponding chain c…
Generated abstract This paper studies the equivalent tensile stiffness of an infinite isotropic plate containing a doubly periodic array of identical circular holes reinforced by thin elastic rings of a different material. Assuming the rings carry only tensile stress, the authors derive boundary conditions on the hole…
