The problem of finding new estimates of uniform approximations by the Fourier – Chebyshev rational integral operator on classes of Markov functions, functions with a power singularity, conjugate functions with a density having a power singularity, and singular integrals with a Cauchy kernel, Chebyshev weight of the second kind and density having a power singularity. In some cases, the estimates found have a greater descending order, in comparison with the previously known corresponding results. 

In this paper, we obtain an approximate analytical expression for the topological percolation constant, which characterizes the most general topological properties of fractals, primarily such as connectivity near the percolation threshold. 

The peculiarities of propagation of vector Bessel – Gaussian (BG) beams, the distinguishing feature of which is the quadrature of phases of electric and magnetic fields, are considered. The expression for vector BG beams is obtained on the basis of common approach in a form of linear superposition of known accurate solutions of the Maxwell equations. By selection of weight function of superposition there are found the equations for all components of electric and magnetic field of the BG beam, and also expressions for square field functions, such as linear density of energy, pulse and pulse moments along the direction of beam propagation. The particular case is considered when weight functions of the superposition do not depend on azimuthal mode index m of the vortex beam. For this case the expression is found for the ratio of linear density of the pulse moment to linear density of BG beam energy with a quadrature of electric and magnetic fields. From the equation obtained it follows that linear density of the pulse moment per one photon for non-paraxial beams essentially differs from the value ћ(m + 1) for large cone angles (of about several tens of degrees). Particularly, this result is important for the correct estimation of angular momentum of the field on the basis of measurement by the photoreceivers with direct detection of azimuthal index m, which are being developed in the recent time. It is also shown that when increasing the cone angle of BG beam its polarization differs from angular one, and the longitudinal component increases. Here the functional dependence of transverse and longitudinal components on radial coordinate is different. The obtained results are important when developing compact elements for the optical communication systems, microscopy, laser tweezers and others.

Al/SiO₂/n-Si/Al MOS structures fabricated on (100) wafers of single-crystal n-type silicon grown with the Czochralski method were studied. The electrical resistivity of silicon was 4.5 Ohm · cm at room temperature. The thickness of the SiO₂ layer thermally formed in dry oxygen was 420 nm. The thickness of the aluminum layer deposited on top of SiO₂ was 0.7 µm. The area of aluminum metallization was 1.85 × 1.85 mm². At a room temperature, the structures were irradiated with helium ions (kinetic energy of an ion was 5 MeV). The radiation fluence ranged from 10¹⁰ to 10¹³ cm⁻². According to calculations performed in the SRIM program, the average projective range of the helium ion in the structure was ≈ 24 µm. The impedance modulus Z and the phase shift angle φ between the current and voltage were measured in the frequency range from 20 Hz to 2 MHz using an E4980A LCR meter. The signal amplitude was 40 mV. The constant bias voltage U varied from −40 to 40 V. The MOS structures were kept in the dark at a room temperature. The DLTS spectra were recorded using CE-7C capacitance spectrometer in the temperature range of 80–300 K. The voltage pulses for filling traps U_p with c-band electrons and the voltage of emission U_e of electrons from traps to c-band of n-Si varied in the range from −0.5 to −9 V. The pulse duration for filling traps with electrons was t_p = 0.75 ms, and the pulse duration for emission of electrons from traps was t_e = 20 ms. It was found that for the Al/SiO₂/n-Si/Al structures irradiated with helium ions with fluences of ≤10¹² cm⁻², the dependence of the capacitance on the frequency in the depletion mode is determined by the recharging of the surface electron states at the SiO₂/n-Si interface. It was shown that in the initial structures for fast (recharging time <1 µs) surface states, the dependence of the energy density of states N_ss on the potential energy eψ of an electron in n-Si near the SiO₂/n-Si interface has its maximum at eψ ≈ E_F – 0.1 eV (here e is the elementary charge, ψ is the electric potential, E_F is the Fermi energy level). After irradiation with helium ions with a fluence of 10¹² cm⁻², this maximum shifts towards lower energies down to eψ ≈ E_F – 0.2 eV. In the irradiated structures, a second maximum appears on the N_ss(eψ) dependence in the region of eψ > 0. For an irradiation fluence of 10¹² cm⁻², the maximum is located at eψ ≈ E_F + 0.1 eV. The possibility of studying surface states with the DLTS spectroscopy method in the selected energy range by varying the emission voltage U_e at a constant value of the filling voltage U_p and/or varying the filling voltage U_p at a constant value of the emission voltage U_e is shown. 

The processes of scattering, dispersion and absorption accompanying the propagation of an electromagnetic wave lead to the fact that the radio signal slows down and weakens when passing through electron clusters in the ionosphere. The article solves the problem of restoration of the electron concentration field based on ionospheric radiography. The derivation of analytical relationships for determining the total electron content (TEC) in the ionosphere based on radio signals of the global navigation satellite system (GNSS) at two frequencies is considered. The methods for calculating TEC both from direct satellite signals and cross-relaying based on a small-sized CubeSat retransmission satellite are considered. Analytical relationships are given and algorithms for estimating TEC calculated based on phase and pseudo-distance measurements are described. They are then used to construct computing tomography algorithms in order to estimate the structures of the restored electron density images. As a result, the proposed radio tomography algorithms use TEC data to synthesize two-dimensional images of the electron concentration field in the ionosphere which allows the estimation both of the structure and dynamics of the ionosphere.

This paper considers the problem of developing a rigorous analytical model for estimating pedestrian delays at a signalized intersection when the pedestrian traffic at this intersection is controlled by a “smart” algorithm that operates according to the following principle: if “the pedestrian call button has not been pressed”, skip the pedestrian service interval reserved by the control scheme and pass the unused time to conflicting road users (thereby preserving the length of the control cycle), otherwise activate the reserved interval and serve the pedestrians. Under the assumption of a Poisson process of arrivals, a rigorous development of the corresponding model and its comparison with the existing best-known and used analogue is performed based on the apparatus of probability theory. By means of a computational experiment it is shown that the proposed model is much more accurate and correct than this analogue. Finally, a primary analysis of the model is performed, with results allowing to assess the appropriateness of implementing such a control algorithm in terms of the significant increase in individual pedestrian delays.

The problem of optimizing the equipment of urban transport network nodes with charging stations of various types and the daily charging schedule for them for a fleet of battery electric buses is considered. Charging stations of depots should provide slow charging of electric bus batteries at night to the maximum level, charging stations of route terminals are intended for fast partial recharging of batteries, sufficient for electric buses to perform next trips of their daytime tasks within a representative period of the day. The criterion of optimality is the minimization of the total daily cost of charging stations, wear of electric bus batteries and consumed electricity. A mathematical model of the problem in the form of mixed integer linear programming has been developed. The means of increasing the efficiency of the model through additional constraints have been studied, and the most efficient subset of such constraints has been identified. A computer experiment with randomly generated problem instances has confirmed a good performance of the model for medium and large-scale problems.