On bilinear invariant differential operators acting on tensor fields on the symplectic manifold

Let $M$ be an $n$-dimensional manifold, $V$ the space of a representation $\rho: GL(n)\longrightarrow GL(V)$. Locally, let $T(V)$ be the space of sections of the tensor bundle with fiber $V$ over a sufficiently small open set $U\subset M$, in other words, $T(V)$ is the space of tensor fields of type $V$ on $M$ on which the group \Diff (M) of diffeomorphisms of $M$ naturally acts. Elsewhere, the author classified the \Diff (M)-invariant differential operators $D: T(V_{1})\otimes T(V_{2})\longrightarrow T(V_{3})$ for irreducible fibers with lowest weight. Here the result is generalized to bilinear operators invariant with respect to the group \Diff_{\omega}(M) of symplectomorphisms of the symplectic manifold $(M, \omega)$. We classify all first order invariant operators; the list of other operators is conjectural. Among the new operators we mention a 2nd order one which determins an ``algebra'' structure on the space of metrics (symmetric forms) on $M$

Once More About the Possibility of Determining the Local Electron Concentration by the Dispersion Method with the Help of AES and on New Ionization Maxima in the Ionosphere

Reliability of ionospheric density measurements by satellites using dispersion metho

Programs written in C# in the mathematical logic course

Mathematical logic is included in the curriculum of students of high schools and colleges in all fields related to microprocessors and programming. In this paper we describe a program in C#, developed for a mathematical logic course. Targets are set for improving the program.Математическая логика входит в программу обучения студентов вузов и колледжей по всем направлениям, связанным с микропроцессорами и программированием. В настоящей работе описывается программа на языке С#, разработанная для курса математической логики. Поставлены задачи для совершенствования программ

Controlling the beginning of viewing the datagridview objects inc + + and c # languages

The IT-students' teaching program includes the "Object-oriented programming" training course. This course studying involves the development of window applications using the Windows Forms Application template and the DataGridView control element. Some approaches of working with DataGridView are describedВ программу обучения студентов по направлениям, связанным с информатикой, входит курс «Объектно-ориентированное программирование». Изучение этого курса предполагает разработку оконных приложений с использованием шаблона Windows Forms Application и элемента управления DataGridView. Описаны некоторые приемы работы с DataGridVie

Mirror instability in a plasma with cold gyrating dust particles

In this work linear stability analysis of a magnetized dusty plasma with an anisotropic dust component having transversal motions much stronger than motions parallel to the external magnetic field, and isotropic light plasma components is described. Such a situation presumably establishes in a shock compressed space dusty plasma downstream the shock front. Oblique low-frequency magneto-hydrodynamic waves ($\omega\ll \omega_{cd}$, $\omega_{cd}$ being the dust cyclotron frequency) are shown to be undergone to the mirror instability. Consequences for nonthermal dust destruction behind shock fronts in the interstellar medium are discussed.Comment: 13 pages, 5 figs, accepted to Phys. Pasma

Websites development and maintenance technology

The student training program in courses related to the computer sciences, includes laboratory classes, using a server running Unix-like operating systems. However, methods and tools for the labs for the "Operating Systems" courses and WEB-technologies courses are differentВ программу обучения студентов по направлениям, связанным с информатикой, входят лабораторные занятия, использующие сервер под управлением Unix-подобных операционных систем. Однако методы и инструменты для лабораторных занятий по курсам «Операционные системы» и WEB-технологии различн