Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

A Blue Straggler Binary System with at least Three Progenitors in the Core of a Globular Cluster?

We show that the X-ray source W31 in the core of the globular cluster 47 Tucanae is physically associated with the bright blue straggler BSS-7. The two sources are astrometrically matched to 0.061\arcsec, with a chance coincidence probability of less than 1%. We then analyse optical time-series photometry obtained with the {\em Hubble Space Telescope} (HST) and find that BSS-7 displays a 1.56 day periodic signal in the I band. We also construct a broad-band (far-ultraviolet through far-red) spectral energy distribution for BSS-7 and fit this with single and binary models. The binary model is a better fit to the data, and we derive the corresponding stellar parameters. All of our findings are consistent with BSS-7 being a detached binary consisting of a blue straggler primary with an X-ray-active, upper-main-sequence companion. The formation of such a system would necessarily involve at least three stars, which is consistent with recent N-body models in which blue stragglers often form via multiple encounters that can involve both single and binary stars. However, we cannot yet entirely rule out the possibility that BSS-7 descended directly from a binary system via mass transfer. The system parameters needed to distinguish definitively between these scenarios may be obtainable from time-resolved spectroscopy.Comment: 19 pages, 3 figures, accepted for publication in ApJ; revised version includes a discussion of an alternative 2-progenitor binary evolution scenario, and an appendix discussing other probable/possible BSS/X-ray matches in globular clusters and related source

Planets in habitable zones: A study of the binary Gamma Cephei

The recently discovered planetary system in the binary GamCep was studied concerning its dynamical evolution. We confirm that the orbital parameters found by the observers are in a stable configuration. The primary aim of this study was to find stable planetary orbits in a habitable region in this system, which consists of a double star (a=21.36 AU) and a relatively close (a=2.15 AU) massive (1.7 Mjup sin i) planet. We did straightforward numerical integrations of the equations of motion in different dynamical models and determined the stability regions for a fictitious massless planet in the interval of the semimajor axis 0.5 AU < a < 1.85 AU around the more massive primary. To confirm the results we used the Fast Lyapunov Indicators (FLI) in separate computations, which are a common tool for determining the chaoticity of an orbit. Both results are in good agreement and unveiled a small island of stable motions close to 1 AU up to an inclination of about 15 deg (which corresponds to the 3:1 mean motion resonance between the two planets). Additionally we computed the orbits of earthlike planets (up to 90 earthmasses) in the small stable island and found out, that there exists a small window of stable orbits on the inner edge of the habitable zone in GamCep even for massive planets.Comment: 4 pages, 5 figures, changed 2 references made minor changes due to referees advic

The role of olfactory transport in the penetration of manganese oxide nanoparticles from blood into the brain

There is no doubt that various nanoparticles (NPs) can enter the brain from the nasal cavity. It is assumed that NPs can penetrate from blood into the central nervous system (CNS) only by breaking the blood–brain barrier (BBB). The accumulation of NPs in CNS can provoke many neurological diseases; therefore, the understanding of its mechanisms is of both academic and practical interest. Although hitting from the surface of the lungs into the bloodstream, NPs can accumulate in various mucous membranes, including the nasal mucosa. Thus, we cannot rule out the ability of NPs to be transported from the bloodstream to the brain through the olfactory uptake. To test this hypothesis, we used paramagnetic NPs of manganese oxide (Mn3O4-NPs), whose accumulation patterns in the mouse brain were recorded using T1-weighted magnetic resonance imaging. The effect of intranasal application of endocytosis and axonal transport inhibitors on the brain accumulation patterns of intranasally or intravenously injected Mn3O4-NPs was evaluated. A comparative analysis of the results showed that the transport of Mn3O4-NPs from the nasal cavity to the brain is more efficient than their local permeation through BBB into CNS from the bloodstream, for example with the accumulation of Mn3O4NPs in the dentate gyrus of the hippocampus, and through the capture and transport of NPs from the blood by olfactory epithelium cells. Also, experiments with the administration of chlorpromazine, a specific inhibitor of clathrin-dependent endocytosis, and methyl-β-cyclodextrin, inhibitor of the lipid rafts involved in the capture of substances by endothelium cells, showed differences in the mechanisms of NP uptake from the nasal cavity and from the bloodstream. In this study, we show a significant contribution of axonal transport to NP accumulation patterns in the brain, both from the nasal cavity and from the vascular bed. This explains the accumulation of different sorts of submicron particles (neurotropic viruses, insoluble xenobiotics, etc.), unable to pass BBB, in the brain. The results will add to the understanding of the pathogenesis of various neurodegenerative diseases and help studying the side effects of therapeutics administered intravenously

The Evolution of Cool Algols

We apply a model of dynamo-driven mass loss, magnetic braking and tidal friction to the evolution of stars with cool convective envelopes; in particular we apply it to binary stars where the combination of magnetic braking and tidal friction can cause angular-momentum loss from the {\it orbit}. For the present we consider the simplification that only one component of a binary is subject to these non-conservative effects, but we emphasise the need in some circumstances to permit such effects in {\it both} components. The model is applied to examples of (i) the Sun, (ii) BY Dra binaries, (iii) Am binaries, (iv) RS CVn binaries, (v) Algols, (vi) post-Algols. A number of problems regarding some of these systems appear to find a natural explanation in our model. There are indications from other systems that some coefficients in our model may vary by a factor of 2 or so from system to system; this may be a result of the chaotic nature of dynamo activity

Костные останки из могильников Перми Вычегодской (XI–XIV вв.): результаты мультидисциплинарных научных исследований и эколого-исторические реконструкции

Using a wide range of modern mineralogical and physicochemical methods, a representative collection of human bones from seven burial grounds of the Vychegda Permians of the 11th–14th centuries was studied. The microstructureof bones, their chemical and normative-mineral composition, the content of microelements, the nanoporosity of the organo-mineral composite, the composition and properties of bioanatite and bone collagen were analyzed. Fundamental differences in the properties of raw and so-called calcified bones are determined. Based on isotope data on bioapatite and collagen of raw bones, the climatic conditions for the existence of the Vychegda Permians and their diets were reconstructed.С применением широкого комплекса современных минералогических, физико-химических и изотопных методов исследована представительная коллекция человеческих костей из семи могильников вычегодских пермян XI–XIV вв. Проанализированы микростроение костей, их химический и нормативно-минеральный состав, содержание микроэлементов, нанопористость органо-минерального композита, состав и свойства биоапатита и костного коллагена. Определены принципиальные различия в свойствах сырых и так называемых кальцинированных костей. На основании изотопных данных по биоапатиту и коллагену сырых костей реконструированы климатические условия существования вычегодских пермян и рационы их питани

Olfactory transport efficiency of the amorphous and crystalline manganese oxide nanoparticles

The ability to deliver particulated xenobiotics and therapeutic drugs directly from the nasal cavity to the central nervous system, bypassing the hemato-encephalic barrier, determines a high importance of investigation of factors influencing this process. It was shown that the bioavailability of solid particles is influenced by their size and surface charge. At the same time, the impact of a crystal structure (crystalline/amorphous) has been poorly investigated. In this study, using sexually mature male C57BL/6J mice, we analyzed the efficiency of the nose-to-brain transport of crystalline and amorphous manganese oxide nanoparticles. T1-weighted magnetic resonance imaging (MRI) was used to evaluate the accumulation of manganese nanoparticles in olfactory bulb (OB) and olfactory epithelium (OE). So, it has been established that amorphous particles have higher accumulation rate in OE and OB in comparison with crystalline particles after their intranasal administration. The unequal ability of amorphous and crystalline particles to overcome the mucosal layer covering the OE may be one of the possible reasons for the different nose-to-brain transport efficiency of particulated matter. Indeed, the introduction of mucolytic (dithiothreitol) 20 minutes prior to intranasal particle application did not influence the accumulation of amorphous particles in OE and OB, but enhanced the efficiency of crystalline nanoparticle entry. Data on the different intake of amorphous and crystalline nanoparticles from the nasal cavity to the brain, as well as the evidence for the key role of the mucosal layer in differentiating the penetrating power of these particles will be useful in developing approaches to assessing air pollution and optimizing the methods of inhalation therapy

Influence of magnesium deficiency on the outcome of pregnancy and labors

The article presents the results of study the effect of magnesium deficiency, detected using a standardized questionnaire, on during pregnancy and childbirth according to primary medical documentation (form №003/y and №096/y). As a result of the study, conclusions were drawn about the need to prevent hypomagnesemia in women at all stages of pregnancy.В статье представлены результаты исследования влияния дефицита магния, выявленного с использованием стандартизированного опросника, на исход беременности и родов по данным первичной медицинской документации (форма №003/у и №096/у). В результате исследования были сделаны выводы о необходимости профилактики гипомагнезиемии у беременных женщин

Current epidemiological situation on leptospirosis in the territories adjacent to Lake Baikal

Background. In presence the epizootiological situation on leptospirosis in the territories adjacent to Lake Baikal is not studied well. The showing up of natural focus, discovering of host animal’s species composition and etiological structure of leptospirosis causative agents are essential to plan any epidemiological response and to organize the specific prophylaxis.Aim: to analyze contemporary characteristics of leptospirosis natural foci at the territories adjacent to Lake Baikal.Materials and methods. From 2011 till 2020 the territory of nine Irkutsk Region's administrative districts was investigated. Trapping has been done at four kind of sites (wetland, meadow, forest-shrub, steppificated meadow) and boroughs. 1152 small mammals which belonged to 35 species were collected. Collected samples were studied by complex of methods. Serogroup belonging was detected by micro agglutination and decomposition test, and genomic species – by Microflex LT mass analyzer.Results. A leptospirosis natural foci in the Irkutsk city boundary was newly founded and there were isolated (from small mammals) four pathogenic cultures of leptospiras belonging to Javanica serogroup. Main hosts of causative agents at the territories adjacent to Lake Baikal were defined (insect-eating mammals: tundra shrew, largetoothed Siberian shrew, even-toothed shrew, shrew-mouse, and rodents: root vole, ground vole, narrow-skulled vole, sewer rat). By micro agglutination were defined pathogenic leptospirosis serogroups (Icterohaemorrhagiae, Grippotyphosa, Javanica, Pomona, Sejroe, Autumnalis, Australis), all over 2.4 ± 0.45 % seropositive. Antibody dilution at survey animals ranged from 1 : 20 to 1 : 640. On the grounds of PCR results the mean value of infected animals in studied sample was 16.4 ± 1.14 %. Positive PCR findings were at 19 from 35 animal species.Conclusion. At the territories adjacent to Lake Baikal In the Baikal region, the proportion of animals that have had contact with pathogenic leptospira is quite high. Natural focus of this infection are highly pervasive in this region, they are evolved mainly in dewy sites

Stability of Terrestrial Planets in the Habitable Zone of Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208

We have undertaken a thorough dynamical investigation of five extrasolar planetary systems using extensive numerical experiments. The systems Gl 777 A, HD 72659, Gl 614, 47 Uma and HD 4208 were examined concerning the question of whether they could host terrestrial like planets in their habitable zones (=HZ). First we investigated the mean motion resonances between fictitious terrestrial planets and the existing gas giants in these five extrasolar systems. Then a fine grid of initial conditions for a potential terrestrial planet within the HZ was chosen for each system, from which the stability of orbits was then assessed by direct integrations over a time interval of 1 million years. The computations were carried out using a Lie-series integration method with an adaptive step size control. This integration method achieves machine precision accuracy in a highly efficient and robust way, requiring no special adjustments when the orbits have large eccentricities. The stability of orbits was examined with a determination of the Renyi entropy, estimated from recurrence plots, and with a more straight forward method based on the maximum eccentricity achieved by the planet over the 1 million year integration. Additionally, the eccentricity is an indication of the habitability of a terrestrial planet in the HZ; any value of e>0.2 produces a significant temperature difference on a planet's surface between apoapse and periapse. The results for possible stable orbits for terrestrial planets in habitable zones for the five systems are summarized as follows: for Gl 777 A nearly the entire HZ is stable, for 47 Uma, HD 72659 and HD 4208 terrestrial planets can survive for a sufficiently long time, while for Gl 614 our results exclude terrestrial planets moving in stable orbits within the HZ.Comment: 14 pages, 18 figures submitted to A&