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

The generalized non-conservative model of a 1-planet system - revisited

We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular momentum and the spin vectors of the bodies. Thus, we analyze full, spatial model of the planetary system. Both objects are assumed to be deformed due to their own rotations, as well as due to the mutual tidal interactions. The general relativity corrections are considered in terms of the post-Newtonian approximation. Besides the conservative contributions to the perturbing forces, there are also taken into account non-conservative effects, i.e., the dissipation of the mechanical energy. This dissipation is a result of the tidal perturbation on the velocity field in the internal zones with non-zero turbulent viscosity (convective zones). Our main goal is to derive the equations of the orbital motion as well as the equations governing time-evolution of the spin vectors (angular velocities). We derive the Lagrangian equations of the second kind for systems which do not conserve the mechanical energy. Next, the equations of motion are averaged out over all fast angles with respect to time-scales characteristic for conservative perturbations. The final equations of motion are then used to study the dynamics of the non-conservative model over time scales of the order of the age of the star. We analyze the final state of the system as a function of the initial conditions. Equilibria states of the averaged system are finally discussed.Comment: 37 pages, 13 figures, accepted to Celestial Mechanics and Dynamical Astronom

Adrenal incidentaloma: management of patients with functionally autonomous cortisol synthesis

Over recent decades due to improved visualization (ultrasound, computer tomography and magnetic resonance imaging) prevalence of adrenal incidentaloma has increased. The term «adrenal incidentaloma» is generic and includes a group of tumors of various morphology and over 1 cm in diameter accidentally discovered during radiologic investigation. The found tumor can be hormonally inactive or actively releasing different hormones, malignant or benign, and originating from different adrenal zones or having non-specific organ origin. Based on the frequency of revealing and clinical significance the most noteworthy is functionally autonomous cortisol synthesis. It means changes of hypothalamic pituitary adrenal axis without classic clinically prominent signs of cortisol excess such as proximal myopathy, stretch marks, body fat redistribution and other metabolic changes related to cortisol. Currently a large number of recommendations on the management and tactics of treatment of adrenal incidentaloma can be found in the literature. Based on the analysis of these guidelines the conclusions were made about the diagnostic errors and incorrect approaches to the choice of treatment of such patients. Recently a lot of studies have been directed to the early detection of carbohydrate and lipid metabolism disorders, relation with obesity and type 2 diabetes mellitus, arterial hypertension and osteoporosis for preserved quality of life of such patients. Influence of hypercorticism is considered to worsen the course of these conditions but at the moment no effect of adrenalectomy on mortality and life duration was confirmed

Сверхпроводимость: достижения в применении

A superconductor is a material that undergoes a transition into the superconducting state when cooled below a certain critical temperature. Firstly, the superconductor offers no resistance to the passage of electrical current. Secondly, external magnetic fields do not penetrate the superconductor, but remain at its surface. This phenomenon enables a range of innovative technological applications in different spheres of industry. New superconducting materials are constantly being discovered and even more new prototype devices are being developed. The recently developed prototypes based on the phenomenon of superconductivity include a three-state memory nanodevice and a terahertz emitter. The performance of these devices proves the possibility of practical applications of superconductors and stimulates future development of superconducting materials. Moreover, application of bulk superconductors is also quite promising as bulk superconductors offer a number of advantages over conventional permanent magnets. However, many problems must be solved before superconducting technology can be successfully and widely commercialized.Сверхпроводник – это материал, который переходит в сверхпроводящее состояние при охлаждении ниже определенной критической температуры. Во-первых, сверхпроводник не оказывает сопротивления прохождению электрического тока, который может протекать без потерь энергии. Во-вторых, внешние магнитные поля не проникают в сверхпроводник, а остаются только вокруг его поверхности. Эти свойства позволяют применить сверхпроводники в различных сферах промышленности. Освоение явления сверхпроводимости может по-настоящему совершить прорыв в науке. Учёные открывают всё новые сверхпроводящие материалы и разрабатывают новые устройства. Одни из недавно разработанных прототипов устройств, основанных на явлении сверхпроводимости, включают запоминающее наноустройство с тремя устойчивыми состояниями и терагерцевый излучатель. Работоспособность этих устройств доказывает возможность практического применения сверхпроводников и стимулирует дальнейшее исследование сверхпроводящих материалов. Сверхпроводники обладают рядом преимуществ по сравнению с обычными постоянными магнитами, поэтому их практическое применение становится всё более перспективным. Однако поддержание условий для работы сверхпроводников – очень трудный и дорогостоящий процесс. Поэтому, прежде чем сверхпроводящие технологии смогут быть успешно введены в сферу промышленности, необходимо решить множество проблем и вопросов

Evolution in Binary and Triple Stars, with an application to SS Lac

We present equations governing the way in which both the orbit and the intrinsic spins of stars in a close binary should evolve subject to a number of perturbing forces, including the effect of a third body in a possibly inclined wider orbit. We illustrate the solutions in some binary-star and triple-star situations: tidal friction in a wide but eccentric orbit of a radio pulsar about a B star, the Darwin and eccentricity instabilities in a more massive but shorter-period massive X-ray binary, and the interaction of tidal friction with Kozai cycles in a triple such as Algol (beta-Per), at an early stage in that star's life when all 3 components were ZAMS stars. We also attempt to model in some detail the interesting triple system SS Lac, which stopped eclipsing in about 1950. We find that our model of SS Lac is quite constrained by the relatively good observational data of this system, and leads to a specific inclination (29 deg) of the outer orbit relative to the inner orbit at epoch zero (1912). Although the intrinsic spins of the stars have little effect on the orbit, the converse is not true: the spin axes can vary their orientation relative to the close binary by up to 120 deg on a timescale of about a century.Comment: 30 pages, 6 figure

The Multiple Origin of Blue Straggler Stars: Theory vs. Observations

In this chapter we review the various suggested channels for the formation and evolution of blue straggler stars (BSSs) in different environments and their observational predictions. These include mass transfer during binary stellar evolution - case A/B/C and D (wind Roche-lobe overflow) mass transfer, stellar collisions during single and binary encounters in dense stellar cluster, and coupled dynamical and stellar evolution of triple systems. We also explore the importance of the BSS and binary dynamics in stellar clusters. We review the various observed properties of BSSs in different environments (halo and bulge BSSs, BSSs in globular clusters and BSSs in old open clusters), and compare the current observations with the theoretical predictions for BSS formation. We try to constrain the likely progenitors and processes that play a role in the formation of BSSs and their evolution. We find that multiple channels of BSS formation are likely to take part in producing the observed BSSs, and we point out the strengths and weaknesses of each the formation channel in respect to the observational constraints. Finally we point out directions to further explore the origin of BSS, and highlight eclipsing binary BSSs as important observational tool.Comment: Chapter 11, in Ecology of Blue Straggler Stars, H.M.J. Boffin, G. Carraro & G. Beccari (Eds), Astrophysics and Space Science Library, Springe

Some aspects of the distribution of Fusarium on cereals of Russia

Since 1995 the pathogens of genus Fusarium causing Root Rot, Snow Mold, Fusarium Head Blight of grain crops have been monitored in the Volga-Vyatka, Central, Central Chernozem and North Caucasian regions of the Russian Federation and in there were identified 15 Fusarium spp.: F. culmorum, F. heterosporum, F. sporotrichioides, F. oxysporum, F. nivale, F. graminearum, F. avenacеum, F. gibbosum, F. sambucinum, F. moniliforme, F. semitectum, F. poae, F. lateritium, F. solani, F. redolens. The high uniformity of Fusarium spp. has been revealed for the regions due to the susceptibility of crops to the soil-inhabiting micromycetes. Consistent long-term monitoring of the dynamics and frequency of occurrence of Fusarium spp. in a wide range of climatic areas has made it possible to characterize the state of the species of fungi in the regions and also to study their intraspecific and interspecific variability in toxicity and pathogenicity depended on biotic and abiotic factors. The prevalence of Fusarium spp. in the mycobiota has been determined by their plasticity and viability in the soil, on the weed roots and in the stubble of many crops and high competitive ability expressed pathogenicity and toxicity

Hot Jupiters from Secular Planet--Planet Interactions

About 25 per cent of `hot Jupiters' (extrasolar Jovian-mass planets with close-in orbits) are actually orbiting counter to the spin direction of the star. Perturbations from a distant binary star companion can produce high inclinations, but cannot explain orbits that are retrograde with respect to the total angular momentum of the system. Such orbits in a stellar context can be produced through secular (that is, long term) perturbations in hierarchical triple-star systems. Here we report a similar analysis of planetary bodies, including both octupole-order effects and tidal friction, and find that we can produce hot Jupiters in orbits that are retrograde with respect to the total angular momentum. With distant stellar mass perturbers, such an outcome is not possible. With planetary perturbers, the inner orbit's angular momentum component parallel to the total angular momentum need not be constant. In fact, as we show here, it can even change sign, leading to a retrograde orbit. A brief excursion to very high eccentricity during the chaotic evolution of the inner orbit allows planet-star tidal interactions to rapidly circularize that orbit, decoupling the planets and forming a retrograde hot Jupiter.Comment: accepted for publication by Nature, 3 figures (version after proof - some typos corrected

Antiproliferative activity of a new derivative from the class of N-glycoside of indolo [2,3-a] pyrrolo [3,4-c] carbazoles

The aim of the study was to evaluate an antiproliferative activity of a new, Russian derivative of N-glycoside substituted indolocarbazole 6-amino-12-(α-L-arabinopyranosyl)indolo [2,3-a] pyrrolo [3,4-c] carbazole-5,7-dione (LCS-1208) on models of transplantable tumors of mice and on human tumors in Balb/c nude mic

Some Issues of Terminating a Criminal Case

This publication continues the experience of covering the work of the Scientific and Meth­odological Council under the Prosecutor of the Omsk Region, among the main tasks of which remains the development and discussion, together with representatives of legal science, of sound recommenda­tions on problematic issues of prosecutorial supervision, legislation and law enforcement practice, legal advisory opinions on issues arising in prosecutorial practice. In this regard, the article proposes to dis­cuss certain topical problems of law enforcement practice raised at one of the last meetings of the Scien­tific and Methodological Council under the Prosecutor of the Omsk Region. Thus, based on a systematic analysis of errors in the implementation of the institution of a judicial fine, it is proposed to provide prosecutors with systematic supervision over compliance with the requirements of the law when it is ap­plied, which requires a more thorough study of criminal cases, as well as a proper initiative to establish the circumstances associated with the application of a judicial fine, and timely challenging unfounded court decisions. In addition, the practice of law enforcement highlights the fundamental problem of a unified interpretation of the grounds for terminating a criminal case (criminal prosecution) against a person who has committed an act prohibited by criminal law in a state of insanity. Based on the analy­sis of legal situations and various approaches to their resolution, the article argues for the need to make a decision on the studied criminal cases on the grounds of paragraph 4 of part 1 of Art. 24 of the Criminal Procedure Code of the Russian Federation in connection with the death of a person involved in criminal proceedings. In other similar situations, but related to the criminal prosecution of these persons, the deci­sion must be made taking into account the specific circumstances of the criminal case