Feigin-Frenkel center in types B, C and D

For each simple Lie algebra g consider the corresponding affine vertex algebra V_{crit}(g) at the critical level. The center of this vertex algebra is a commutative associative algebra whose structure was described by a remarkable theorem of Feigin and Frenkel about two decades ago. However, only recently simple formulas for the generators of the center were found for the Lie algebras of type A following Talalaev's discovery of explicit higher Gaudin Hamiltonians. We give explicit formulas for generators of the centers of the affine vertex algebras V_{crit}(g) associated with the simple Lie algebras g of types B, C and D. The construction relies on the Schur-Weyl duality involving the Brauer algebra, and the generators are expressed as weighted traces over tensor spaces and, equivalently, as traces over the spaces of singular vectors for the action of the Lie algebra sl_2 in the context of Howe duality. This leads to explicit constructions of commutative subalgebras of the universal enveloping algebras U(g[t]) and U(g), and to higher order Hamiltonians in the Gaudin model associated with each Lie algebra g. We also introduce analogues of the Bethe subalgebras of the Yangians Y(g) and show that their graded images coincide with the respective commutative subalgebras of U(g[t]).Comment: 29 pages, constructions of Pfaffian-type Sugawara operators and commutative subalgebras in universal enveloping algebras are adde

Cyclotomic Gaudin models: construction and Bethe ansatz

This is a pre-copyedited author produced PDF of an article accepted for publication in Communications in Mathematical Physics, Benoit, V and Young, C, 'Cyclotomic Gaudin models: construction and Bethe ansatz', Commun. Math. Phys. (2016) 343:971, first published on line March 24, 2016. The final publication is available at Springer via http://dx.doi.org/10.1007/s00220-016-2601-3 © Springer-Verlag Berlin Heidelberg 2016To any simple Lie algebra $\mathfrak g$ and automorphism $\sigma:\mathfrak g\to \mathfrak g$ we associate a cyclotomic Gaudin algebra. This is a large commutative subalgebra of $U(\mathfrak g)^{\otimes N}$ generated by a hierarchy of cyclotomic Gaudin Hamiltonians. It reduces to the Gaudin algebra in the special case $\sigma = \text{id}$. We go on to construct joint eigenvectors and their eigenvalues for this hierarchy of cyclotomic Gaudin Hamiltonians, in the case of a spin chain consisting of a tensor product of Verma modules. To do so we generalize an approach to the Bethe ansatz due to Feigin, Frenkel and Reshetikhin involving vertex algebras and the Wakimoto construction. As part of this construction, we make use of a theorem concerning cyclotomic coinvariants, which we prove in a companion paper. As a byproduct, we obtain a cyclotomic generalization of the Schechtman-Varchenko formula for the weight function.Peer reviewe

Miniband-related 1.4–1.8 μm luminescence of Ge/Si quantum dot superlattices

The luminescence properties of highly strained, Sb-doped Ge/Si multi-layer heterostructures with incorporated Ge quantum dots (QDs) are studied. Calculations of the electronic band structure and luminescence measurements prove the existence of an electron miniband within the columns of the QDs. Miniband formation results in a conversion of the indirect to a quasi-direct excitons takes place. The optical transitions between electron states within the miniband and hole states within QDs are responsible for an intense luminescence in the 1.4–1.8 µm range, which is maintained up to room temperature. At 300 K, a light emitting diode based on such Ge/Si QD superlattices demonstrates an external quantum efficiency of 0.04% at a wavelength of 1.55 µm

СИСТЕМА КОМАНД И УПРАВЛЕНИЕ ДВИЖЕНИЕМ МАЛОГО БЕСПИЛОТНОГО ЛЕТАТЕЛЬНОГО АППАРАТА

A review of domestic and foreign work in the field of building automatic control systems for various small serial unmanned aerial vehicles such as Parrot AR.Drone, Crazyfl ie 2.0, Blade mQX, AscTec Hummingbird performed. Particular attention is paid to solving the problems of working out various rectilinear movements and typical curves, including using spline interpolation and neural networks. The command system of the quadcopter DJI Phantom 3 Standard is examined in detail. Developed software modules in Python 3, necessary for generating trajectories, flight control and visualization of movements. A series of experiments in the simulation environment and full-scale tests of the apparatus under calm and disturbed air conditions were carried out with piecewise linear testing of typical meander and saw trajectories. Based on tests of the command system, the characteristics of an unmanned vehicle are obtained. The studies conducted are aimed at the subsequent construction of an integrated intelligent system for autonomous control of unmanned aerial vehicles.Выполнен обзор отечественных и зарубежных работ в области построения систем ав томатического управления различными малыми серийными беспилотными летатель ными аппаратами типа Parrot AR.Drone, Crazyflie 2.0, Blade mQX, AscTec Hummingbird. Особое внимание уделено решению задач отработки различных прямолинейных дви жений и типовых кривых, в том числе с помощью сплайновой интерполяции и нейрон ных сетей. Подробно рассмотрена и исследована система команд квадрокоптера DJI Phantom 3 Standard. Разработаны программные модули на языке Python 3, необходимые для генерации траекторий, управления полетами и визуализации перемещений. Прове дена серия экспериментов в среде моделирования и натурные испытания аппарата в условиях штиля и возмущенной воздушной среды при кусочно-линейной отработке ти повых траекторий «меандр» и «пила». На основе данной системы команд получены ха рактеристики беспилотного аппарата. Проведенные исследования направлены на по следующее построение встроенной интеллектуальной системы автономного управле ния беспилотными летательными аппаратами

ОПЕРАТИВНОЕ ЛЕЧЕНИЕ РЕБЕНКА С УДВОЕНИЕМ ВОСХОДЯЩЕЙ ОБОДОЧНОЙ КИШКИ

This clinical case of a child of 3 years from cystic duplication of the colon, as manifested clinic acute intestinal obstruction and the presence of space-occupying lesion in the abdomen. Surgical treatment was the only effective method of treatment. Indications for surgical treatment clinic served as intestinal obstruction, refractory to conservative treatment.Проведено клиническое наблюдение за ребенком в возрасте 3-х лет с кистозной формой удвоения толстой кишки, что проявилось клиникой острой кишечной непроходимости и наличием объемного образования в брюшной полости. Оперативное лечение стало единственным эффективным методом лечения больного. Показанием для проведения оперативного лечения послужила клиника кишечной непроходимости, не поддающейся консервативному лечению

Методы оценки личностных факторов по визуальной информации, публикуемой в социальных сетях (обзор)

The article raised the question of the relevance of the analysis of visual information published by the users of social networks. This information is used to predict the “Big Five” psychological factors. Openness to experience, conscientiousness, extraversion, agreeableness, and neuroticism are the main defined factors. It is noted that while identifying personal characteristics, domestic researchers are limited, as a rule, to text polls. On the other hand, a new information technology, based on an analysis of the color-brightness features and content of photographic and video information published on the social networks “Twitted’, “Instagram”, “Facebook”, etc., is actively developing abroad. It is vital to note that visual information is invariant to a multilingual audience, which allows to overcome language barriers and related discrepancies in translations. The article provides an overview of the works in this area, it is shown how visual information correlates with the psychological factors of the users of social networks. In turn, the factors themselves correlate well among themselves and with other important characteristics of a person related to the ability to perform intellectual work, with the state of depression, aggressiveness, etc. On the basis of the performed analysis of modern works, the article specifies the connection between visual information and factors. The study was carried out separately for each type of social networks, which is determined by the preferences of psychologists to work, as a rule, within the framework of only one network, but at the same time the closeness of the patterns found by them is traced. Based on the results of the review, a conclusion was drawn on the necessity for a combined analysis of psychological factors based on visual and textual information. The study is planned to expand in the areas of connection to the analysis of images published on the social network “VKontakte”; clarification of the correlation coefficients linking the entire set of selected factors; generalization of the results