Geometry of W-algebras from the affine Lie algebra point of view

To classify the classical field theories with W-symmetry one has to classify the symplectic leaves of the corresponding W-algebra, which are the intersection of the defining constraint and the coadjoint orbit of the affine Lie algebra if the W-algebra in question is obtained by reducing a WZNW model. The fields that survive the reduction will obey non-linear Poisson bracket (or commutator) relations in general. For example the Toda models are well-known theories which possess such a non-linear W-symmetry and many features of these models can only be understood if one investigates the reduction procedure. In this paper we analyze the SL(n,R) case from which the so-called W_n-algebras can be obtained. One advantage of the reduction viewpoint is that it gives a constructive way to classify the symplectic leaves of the W-algebra which we had done in the n=2 case which will correspond to the coadjoint orbits of the Virasoro algebra and for n=3 which case gives rise to the Zamolodchikov algebra. Our method in principle is capable of constructing explicit representatives on each leaf. Another attractive feature of this approach is the fact that the global nature of the W-transformations can be explicitly described. The reduction method also enables one to determine the ``classical highest weight (h. w.) states'' which are the stable minima of the energy on a W-leaf. These are important as only to those leaves can a highest weight representation space of the W-algebra be associated which contains a ``classical h. w. state''.Comment: 17 pages, LaTeX, revised 1. and 7. chapter

Возможности диагностики и лечения больных ХОБЛ в рамках реальной клинической практики. Подходы к терапии пациентов с различными фенотипами по GOLD (2019): материалы Совета экспертов Сибирского федерального округа, Читы и Бурятии от 15.03.19

Chronic obstructive pulmonary disease (COPD) is a global problem in modern medicine. In recent years, the medical community’s understanding of COPD has changed significantly, which is primarily due to the emergence of a new classification and the identification of various phenotypes of the disease. These changes could not affect the tactics of COPD treatment. The article discusses not only the debatable issues of treating COPD; it provides an overview of changes in international (Global Initiative for Chronic Obstructive Lung Disease, 2018) and national (2019) recommendations, but also the significance and benefits of triple therapy in terms of evidence-based medicine as well as the benefits of extra-fine drugs in the treatment of bronchial obstructive syndrome.Хроническая обструктивная болезнь легких (ХОБЛ) представляет собой глобальную проблему современной медицины. За последние годы представление медицинского сообщества о ХОБЛ существенно изменилось, что связано в первую очередь с появлением новой классификации и выделением различных фенотипов заболевания. Эти изменения не могли не повлиять на тактику лечения ХОБЛ. В статье рассматриваются не только дискуссионные вопросы лечения ХОБЛ, представлен обзор изменений в международных (Гло - бальная инициатива по диагностике, лечению и профилактике ХОБЛ (Global Initiative for Chronic Obstructive Lung Disease, 2018)) и национальных (2019) рекомендациях, но и значение и преимущества тройной терапии с точки зрения доказательной медицины, а также преимущества экстрамелкодисперсных препаратов при лечении бронхообструктивного синдрома