837 research outputs found
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)
Star Formation History in the Galactic Thin Disk
The behavior of the relative magnesium abundances in the thin-disk stars
versus their orbital radii suggests that the star formation rate in the thin
disk decreases with increasing Galactocentric distance, and there was no star
formation for some time outside the solar circle while this process was
continuous within the solar circle. The decrease in the star formation rate
with increasing Galactocentric distance is responsible for the existence of a
negative radial metallicity gradient in the thin disk. At the same time the
relative magnesium abundance exhibits no radial gradient. It is in detail
considered the influence of selective effects on the form of both age -
metallicity and age - relative magnesium abundance diagrams. It is shown that
the first several billion years of the formation of the thin disk interstellar
medium in it was on the average sufficiently rich in heavy elements ( =
-0.22), badly mixed (\sigma_[Fe/H] = 0.21), and the average relative magnesium
abundance was comparatively high ( = 0.10). Approximately 5 billion
years ago average metallicity began to systematically increase, and its
dispersion and the average relative magnesium abundance - to decrease. These
properties may be explained by an increase in star formation rate with the
simultaneous intensification of the processes of mixing the interstellar medium
in the thin disk, provoke possible by interaction the Galaxy with the
completely massive by satellite galaxy
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
Noncommutative reduction of nonlinear Schrödinger equation on Lie groups
We propose a new approach that allows one to reduce nonlinear equations on Lie groups to equations with a fewer number of independent variables for finding particular solutions of the nonlinear equations. The main idea is to apply the method of noncommutative integration to the linear part of a nonlinear equation, which allows one to find bases in the space of solutions of linear partial differential equations with a set of noncommuting symmetry operators. The approach is implemented for the generalized nonlinear Schrödinger equation on a Lie group in curved space with local cubic nonlinearity. General formalism is illustrated by the example of the noncommutative reduction of the nonstationary nonlinear Schrödinger equation on the motion group E(2) of the two-dimensional plane R2. In this particular case, we come to the usual (1+1)-dimensional nonlinear Schrödinger equation with the soliton solution. Another example provides the noncommutative reduction of the stationary multidimensional nonlinear Schrödinger equation on the four-dimensional exponential solvable group
Thermal interaction of biological tissue with nanoparticles heated by laser radiation
We explore the problem of thermal interaction of nanoparticles heated by laser radiation with a biological tissue after particle flow entering the cell. The solution of the model equations is obtained numerically under the following assumptions: a single particle is located in a neighborhood exceeding the particle size; the environment surrounding the particle is water with the conventional thermal characteristics. The model equations are deduced from the particle and the environment energy conditions taking into account the heat transfer in the particle and in its environment by conduction. We also assume that at the boundary between the particle and the surrounding water the perfect thermal contact takes place
Quantum R-matrix and Intertwiners for the Kashiwara Algebra
We study the algebra presented by Kashiwara and introduce
intertwiners similar to -vertex operators. We show that a matrix determined
by 2-point functions of the intertwiners coincides with a quantum R-matrix (up
to a diagonal matrix) and give the commutation relations of the intertwiners.
We also introduce an analogue of the universal R-matrix for the Kashiwara
algebra.Comment: 21 page
Li+ intercalation in isostructural Li2VO3 and Li2VO2 with O2- and mixed O2-/F- anions
Mixed-anion materials for Li-ion batteries have been attracting attention in view of their tunable electrochemical properties. Herein, we compare two isostructural (Fm3m) model intercalation materials Li2VO3 and Li2VO2F with O2- and mixed O2-/F- anions, respectively. Synchrotron X-ray diffraction and pair distribution function data confirm large structural similarity over long-range and at the atomic scale for these materials. However, they show distinct electrochemical properties and kinetic behaviour arising from the different anion environments and the consequent difference in cationic electrostatic repulsion. In comparison with Li2VO3 with an active V4+/5+ redox reaction, the material Li2VO2F with oxofluoro anions and the partial activity of V3+/5+ redox reaction favor higher theoretical capacity (460 mA h g-1vs. 230 mA h g-1), higher voltage (2.5 V vs. 2.2 V), lower polarization (0.1 V vs. 0.3 V) and faster Li+ chemical diffusion (~10-9 cm2 s-1vs. ~10-11 cm2 s-1). This work not only provides insights into the understanding of anion chemistry, but also suggests the rational design of new mixed-anion battery materials
COMPARATIVE ANALYSIS OF EDUCATIONAL PROGRAMS ON SOCIAL ENTREPRENEURSHIP
Рассмотрены особенности образовательных программ по социальному предпринимательству в отечественной и зарубежной практике. Представлен опыт Северо-Кавказского федерального университета по реализации основных и дополнительных образовательных программ по социальному предпринимательствуThe features of educational programs on social entrepreneurship in domestic and foreign practice are considered. The experience of the North Caucasus Federal University on the implementation of basic and additional educational programs on social entrepreneurship is presente
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