Search

An issue related to using cable products for building structures is to ensure their stability and durability when operating within wide limits. Therefore, the object of research was a change in the properties of the polymer sheath of the cable during the formation of a swollen coating layer under the influence of high temperature. It is proved that in the process of thermal action on the flame retardant coating, the process of thermal insulation of the cable involves the formation of particulate products on the surface of the sample. Under the action of the burner flame, a temperature was reached on the surface of the sample, which led to a swelling of the coating of more than 16mm. The measured temperature on the inverse surface of the sample was no more than 160°C, which indicates the formation of a barrier for temperature. In this regard, a calculation and experimental method for determining thermal conductivity when using a flame retardant as a coating has been developed, which makes it possible to estimate the coefficients of temperature conductivity and thermal conductivity under high-temperature action. According to the experimental data and established dependences, the coefficients of temperature conductivity and thermal conductivity of wood were calculated, which are 214.4·10–6m2/s and 0.62W/(m∙K), respectively, due to the formation of a heat-insulating swollen layer. The maximum possible temperature penetration through the thickness of the coating was assessed. A temperature was created on the surface of the sample, which significantly exceeds the ignition temperature of the polymer sheath of the cable, and, on a non-heated surface, does not exceed 160°C. Thus, there is reason to argue about the possibility of directed adjustment of the fire protection processes of an electrical cable by using coatings capable of forming a protective layer on the surface of the material, which inhibits the rate of heat transfer.

The test methods for flame propagation of long elements of the electrical wiring system, in particular, cables, cable conduits and ducts, are analyzed, and differences in them are found in the test conditions and criteria for evaluating the resistance to flame propagation. Using a substrate of a wooden board covered with a layer of tissue paper with an areal density of (21±9)g/m2, adopted for testing other elements of the electrical wiring system, a cable was identified that is not resistant to flame propagation. It is proposed to use this substrate for testing the flame propagation of cables instead of a substrate made of a double layer of filter paper with a surface density of (80±15)g/m2. In one of three experiments, a cable that was not resistant to flame propagation was found based on the criterion of the presence of ignition of the substrate located under it. To reduce the risk of making an incorrect decision on compliance, it is proposed that the assessment of long elements of the wiring system be carried out according to the rules established for cable ducts, trays and ladders in EN 50085-1 and IEC 61537. For the AVVG cable with an outer diameter of 10mm to 60mm, when it touches the blue flame cone of 1kW, the correlation coefficient of the dependence of the length of the charred part on the diameter was 0.969. For a distance of 100mm between the sample and the burner along its axis, a correlation coefficient of 0.985 was obtained. It is proposed to test cables under the second condition recommended in IEC 60695-11-2. For two conduits, flame propagation was revealed when exposed to a 1kW flame for 120 s and 240 s. However, for these pipelines, flame propagation did not occur under standard conditions of exposure to such a flame for 20 s and 25 s. To identify long elements of the wiring system that are not resistant to flame propagation, it is proposed to test them at a duration of exposure to a flame of 1kW, established for cables in IEC 60332-1-2

We show that if $G$ is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then $G$ has $2^{\aleph_0}$ many continuous ergodic invariant random subgroups. If $G$ is a nonabelian free group then $G$ has $2^{\aleph_0}$ many continuous $G$-ergodic characteristic random subgroups. We also provide a complete classification of characteristic random subgroups of free abelian groups of countably infinite rank and elementary $p$-groups of countably infinite rank.

Let R be the ring of algebraic integers in a number field K and let Λ be a maximal order in a finite dimensional semisimple K-algebra B. Building on our previous work [3], we compute the smallest number of algebra generators of Λ considered as an R-algebra. This reproves and vastly extends the results of P.A.B. Pleasants, who considered the case when B is a number field. In order to achieve our goal, we obtain several results about counting generators of algebras which have finitely many elements. These results should be of independent interest.