The Shapovalov determinant for the Poisson superalgebras

Among simple Z-graded Lie superalgebras of polynomial growth, there are several which have no Cartan matrix but, nevertheless, have a quadratic even Casimir element C_{2}: these are the Lie superalgebra k^L(1|6) of vector fields on the (1|6)-dimensional supercircle preserving the contact form, and the series: the finite dimensional Lie superalgebra sh(0|2k) of special Hamiltonian fields in 2k odd indeterminates, and the Kac--Moody version of sh(0|2k). Using C_{2} we compute N. Shapovalov determinant for k^L(1|6) and sh(0|2k), and for the Poisson superalgebras po(0|2k) associated with sh(0|2k). A. Shapovalov described irreducible finite dimensional representations of po(0|n) and sh(0|n); we generalize his result for Verma modules: give criteria for irreducibility of the Verma modules over po(0|2k) and sh(0|2k)

On certain approaches to the control methods development for the precipitation formation processes in convective clouds

The article aims at searching for the optimal way of emission of ice nucleating agent in convective cloud in order to prevent ‎formation of harmful hail by analyzing simulations of this process within a numerical model ‎of cloud‎. The state of the physics of clouds and active influences on them is discussed. It is noted that at the present time studies of the regularities of the formation and development of clouds as a whole begin taking into account their systemic properties. The main directions of research at the next stage of its development are discussed. The features of the existing methods of active action on convective clouds are noted, the main tasks encountered in the development of methods for controlling sedimentation in convective clouds by introducing reagents are formulated. It is noted that research on the development of methods for active influence on clouds should be conducted on the basis of new and more effective approaches, which should be based on the extensive use of mathematical modeling. Some approaches to solving this problem are discussed. According to the authors, the most promising of them are approaches based on the theory of optimal control and bifurcation theory. Some results of numerical modeling of the active effect on convective clouds are given

Submicron-sized MoRe-doped Si-MoRe Josephson junctions with a low specific capacitance

Abstract We start with a short look at the problem of low-capacitance Josephson junctions, its history, and actual state-of-the-art. It is argued that such devices are important for applications requiring nonhysteretic current-voltage characteristics since reduction of capacitance by several times makes it possible to increase the device resistance by the same amount while keeping the McCumber-Stewart damping parameter unaltered. Moreover, at very high frequencies the capacitance in the RCSJ circuit with a parallel connection starts to shunt the superconducting current component due to reduction of the corresponding reactance inversely proportional to C. Hence, to extend the operating frequency range of a Josephson junction its capacitance should be as small as possible. As a solution of a new type of the Josephson device, less resistive and with smaller capacitance, we propose and realize a submicron-sized trilayer with tens nm-thick Si interlayer doped by metallic ultra-small inclusions and superconducting Mo-Re alloy electrodes

Analysis of spatial humus distribution in virgin and arable Chernozems in the eroding landscapes

A statistical assessment of data on the content and spatial distribution of humus in virgin and arable Chernozems on slopes in the south of the forest-steppe zone of the Central Russian Upland was performed. The greatest number of statistically significant differences between arable and virgin Chernozems was found for the upper soil layer (0–20 cm

Representations of the Generalized Lie Algebra sl(2)_q

We construct finite-dimensional irreducible representations of two quantum algebras related to the generalized Lie algebra \ssll (2)_q introduced by Lyubashenko and the second named author. We consider separately the cases of $q$ generic and $q$ at roots of unity. Some of the representations have no classical analog even for generic $q$. Some of the representations have no analog to the finite-dimensional representations of the quantised enveloping algebra $U_q(sl(2))$, while in those that do there are different matrix elements.Comment: 14 pages, plain-TEX file using input files harvmac.tex, amssym.de

THE WORLD OF CHILDHOOD AND YOUTH IN RUSSIAN NOBLE FAMILIES OF THE FIRST HALF OF THE NINETEENTH CENTURY IN THE CONTEXT OF STRATIFICATION APPROACH

traditions. Hence, it is one of the criteria for evolutionary or revolutionary changes in a particular society, accentuating the culture of everyday life and the connection of generations. In a rigidly structured estate society, such as the population of the Russian Empire, the world of childhood and youth developed in the context of social traditionalism, adopted in one or another estate community. Methodology: The basis of the study is based on the principles of historicism, objectivity, and science. To prove these theses, comparative-historical, problem-chronological, logical-analytical methods were used, which made it possible to reliably reconstruct the world of childhood and youth in noble families of Russia of the first half of the nineteenth century. Result: The most detailed system of socialization of children and adolescents was developed in an environment of a noble family, distinguished by more strict and complex etiquette, where pride in belonging to a noble class was inculcated at an early age. But the feeling of belonging to the upper class among the young nobles was different and mediated by many factors, first of all, the ancient lineage, the level of the material wealth of the family, education, upbringing,  and culture. That is, the variability of the socialization of children and adolescents was extensive. Applications: This research can be used for universities, teachers, and students. Novelty/Originality: In this research, the model of The World of Childhood and Youth in Russian Noble Families of the First Half of the Nineteenth Century in the Context of Stratification Approach is presented in a comprehensive and complete manner