Colouring triangle-free graphs with local list sizes

We prove two distinct and natural refinements of a recent breakthrough result of Molloy (and a follow-up work of Bernshteyn) on the (list) chromatic number of triangle-free graphs. In both our results, we permit the amount of colour made available to vertices of lower degree to be accordingly lower. One result concerns list colouring and correspondence colouring, while the other concerns fractional colouring. Our proof of the second illustrates the use of the hard-core model to prove a Johansson-type result, which may be of independent interest.Comment: 16 pages; v2 includes minor corrections after review; to appear in Random Structures & Algorithm

Антибактериальная терапия при недонашивании и дородовом излитии околоплодных вод

Preterm labor and prelabor rupture of fetal membranes is one of the most challenging and contradictory problems of obstetrics. From one hand, prolongation of preterm pregnancy increases the gestational age of the fetus. From the other hand, the risk of infectious complications increases – both in the fetus, because of apparent hypamnion, and in the mother, followed by chorioamnionitis and sepsis.Преждевременные роды и ДИОВ – это одна из актуальных и противоречивых проблем акушерства. С одной стороны, пролонгирование недоношенной беременности увеличивает гестационный возраст плода, с другой стороны, увеличивается риск инфекционных осложнений у плода из-за выраженного маловодия, а также у матери с последующим развитием хориоамнионита (ХА) и септических состояний

Simultaneous Embeddability of Two Partitions

We study the simultaneous embeddability of a pair of partitions of the same underlying set into disjoint blocks. Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region that contains exactly those points that belong to the elements in the block and that is bounded by a simple closed curve. We establish three main classes of simultaneous embeddability (weak, strong, and full embeddability) that differ by increasingly strict well-formedness conditions on how different block regions are allowed to intersect. We show that these simultaneous embeddability classes are closely related to different planarity concepts of hypergraphs. For each embeddability class we give a full characterization. We show that (i) every pair of partitions has a weak simultaneous embedding, (ii) it is NP-complete to decide the existence of a strong simultaneous embedding, and (iii) the existence of a full simultaneous embedding can be tested in linear time.Comment: 17 pages, 7 figures, extended version of a paper to appear at GD 201

Multicomponent Biofuels for Agricultural Diesel Machines

Biofuels derived from vegetable oils are increasingly used in diesel engines. The article analyzes the physicochemical properties of petroleum diesel fuel and biofuels of various compositions. A technique has been developed to optimize the composition of multicomponent composite biofuels for diesel engines of agricultural machinery. The optimal composition of a mixture of petroleum diesel fuel, rapeseed oil and rapeseed oil methyl ester has been determined, providing the best combination of fuel efficiency and exhaust emissions. The optimization calculations made it possible to select the composition of a multicomponent mixed biofuel for the D-245.12S engine installed on domestic agricultural machines. © Published under licence by IOP Publishing Ltd

Estimation of the parameters of traveling ionospheric disturbances using a chirp-ionosondes network

In this article, the results of our observations of traveling ionospheric disturbances are discussed using the data from a network of chirp stations for oblique ionospheric sounding in December 2019. All observations were made with the same type of chirp stations located in the village of Vasilsursk, as well as in the cities of Yoshkar-Ola, Kazan, and Nizhny Novgorod. The stations formed six synchronous sounding paths with a length from 120 to 320 km. The amplitude-frequency and distance-frequency characteristics were registered per minute by the stations of oblique chirp sounding. Based on the data obtained, a method for determining the parameters of traveling ionospheric disturbances using the network of three chirp ionosondes was proposed. Since the ionosonde had both a receiver and a transmitter, it was possible to get data on six radio paths while using three ionosondes and, thus, to estimate the disturbance parameters only from the experimental data, without resorting to any model concepts. From a practical perspective, our research is highly relevant: the international reference ionosphere (IRI) prognostic model is widely used to calculate the ionospheric propagation of radio waves, but variations in the ionosphere can nullify the effectiveness of such forecasting under real conditions

Nonreciprocity Effect in Quasi-Vertical Sounding of the Ionosphere

The paper considers an automated system for ionosphere sounding by chirp signals. The experimental scheme for quasi-vertical sounding of the ionosphere is described. It has been experimentally shown that there is no reciprocity in the characteristics of the signal propagation when changing the direction of propagation. This effect is explained by the difference in the phase incursion due to the rotation of the polarization plane. The results of numerical simulation are presented