This article presents the technology for the preparation of a nitrogen-containing nanoporous bio-carbon and investigates its properties. It has been shown that the synthesised bio-carbon is characterised by a high degree of homogeneity, which has been confirmed by energy dispersive spectroscopy. The obtained bio-carbon has a micromesoporous structure, which has been confirmed by the results of studies using the method of low-temperature nitrogen adsorption and desorption. It was found that the specific surface area of biochar is 1247 m²/g. The data on nitrogen adsorption and desorption were compared with the data on small-angle X-ray scattering, and it was found that the micropores in the synthesised bio-carbon are open pores, while mesopores remain closed. The energy dispersion analysis showed that the structure of the bio-carbon does not contain ferromagnetic atoms, but due to the addition of nitrogen, the synthesised bio-carbon in a magnetic field has the properties of a ferromagnet with a characteristic hysteresis of the specific magnetisation. It was found that this material has a saturation magnetisation σ_s of 1.4 A∙m²∙kg⁻¹ and a coercive force H_c of 10 kA/m. Symmetric supercapacitors were fabricated from the synthesised bio-carbon material with 30% aqueous KOH and 1 M Na₂SO₄ as electrolytes. It was found that for bio-carbon synthesised at 800 °C, the specific capacitance in a 30% aqueous solution of KOH is 180 F/g, and in a 1 M aqueous solution of Na₂SO₄, it is 124 F/g. The cyclic voltammetry of the fabricated supercapacitors at different rates of potential expansion was investigated and analysed. Impedance studies on these supercapacitors were carried out. The equivalent electrical circuits describing the electrochemical processes in the studied supercapacitors were constructed and characterised.

In this paper the investigation of the process of thermoelastic energy dissipation in the electroconductive cylindrical sensor under the radioimpulse action is presented. We obtaine that the influence of the process of thermoelastic energy dissipation on the maximum values of temperature and stresses is insignificant under the radioimpulse action of microsecond and milisecond duration and it does not affect the accuracy of the sensor measurement.

We construct a system of functions biorthogonal with Chebyshev polynomials of the second kind on closed contours in the complex plane. Properties of these functions and sufficient conditions of expansion of analytic functions into series in Chebyshev polynomials of the second kind in complex domains are investigated. The examples of such expansions are given. In addition, combinatorial identities of self-interest are obtained.