Cohomologies of the Poisson superalgebra

Cohomology spaces of the Poisson superalgebra realized on smooth Grassmann-valued functions with compact support on $R^{2n}$ ($C^{2n}) are investigated under suitable continuity restrictions on cochains. The first and second cohomology spaces in the trivial representation and the zeroth and first cohomology spaces in the adjoint representation of the Poisson superalgebra are found for the case of a constant nondegenerate Poisson superbracket for arbitrary n>0. The third cohomology space in the trivial representation and the second cohomology space in the adjoint representation of this superalgebra are found for arbitrary n>1.Comment: Comments: 40 pages, the text to appear in Theor. Math. Phys. supplemented by computation of the 3-rd trivial cohomolog

ACCURACY EVALUATION OF THE OBJECT LOCATION VISUALIZATION FOR GEO-INFORMATION AND DISPLAY SYSTEMS OF MANNED AIRCRAFTS NAVIGATION COMPLEXES

The paper deals with the issue of accuracy estimating for the object location display in the geographic information systems and display systems of manned aircrafts navigation complexes. Application features of liquid crystal screens with a different number of vertical and horizontal pixels are considered at displaying of geographic information data on different scales. Estimation display of navigation parameters values on board the aircraft is done in two ways: a numeric value is directly displayed on the screen of multi-color indicator, and a silhouette of the object is formed on the screen on a substrate background, which is a graphical representation of area map in the flight zone. Various scales of area digital map display currently used in the aviation industry have been considered. Calculation results of one pixel scale interval, depending on the specifications of liquid crystal screen and zoom of the map display area on the multifunction digital display, are given. The paper contains experimental results of the accuracy evaluation for area position display of the aircraft based on the data from the satellite navigation system and inertial navigation system, obtained during the flight program run of the real object. On the basis of these calculations a family of graphs was created for precision error display of the object reference point position using the onboard indicators with liquid crystal screen with different screen resolutions (6 "×8", 7.2 "×9.6", 9"×12") for two map display scales (1:0 , 25 km, 1-2 km). These dependency graphs can be used both to assess the error value of object area position display in existing navigation systems and to calculate the error value in upgrading facilities

INDUSTRY 4.0 DIGITAL PRODUCTION ORGANIZATION BASED ON CYBER AND PHYSICAL SYSTEMS AND ONTOLOGIES

Subject of Research. The paper proposes the work organization schemes in the Industry 4.0 instrument making production companies of “smart factory” type equipped with cyber and physical systems. Studies on the production cyber-physiphication are being carried out aimed at the development and implementation of ideas and decisions in the domestic industry, which will help to establish “smart companies” in our country capable of functioning in the conditions of digital economy and possessing new production technologies. Method.We used the work organization methods for item design manufacturing with the cyber and physical systems and ontologies implementation in the conditions of the companies of the future on the basis of the design automation general theory. Main Results. It is shown that the effect of the production companies proposed organization principles implementation in the factories of the future format can boost the Russian Federation industry transfer to the most advanced digital, intellectual production technologies, robotized systems, new materials and designing methods that corresponds to the Russian Federation State Scientific and Technical Policy in the field of instrument making and machine manufacturing. Practical Relevance. The results of this research can be applied in the development of automation design algorithms for instrument making (machine manufacturing) digital production operating in the conditions of the Russian Federation digital economy

Modeling a Two-Stage High-Power Anode Layer Thruster and its Plume

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76625/1/AIAA-22185-240.pd

Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions

Analytical solution of second Stokes problem of behaviour of rarefied gas with Cercignani boundary accomodation conditions The second Stokes problem about behaviour of rarefied gas filling half-space is analytically solved. A plane, limiting half-space, makes harmonious fluctuations in the plane. The kinetic BGK-equation (Bhatnagar, Gross, Krook) is used. The boundary accomodation conditions of Cercignani of reflexion gaseous molecules from a wall are considered. Distribution function of the gaseous molecules is constructed. The velocity of gas in half-space is found, also its value direct at a wall is found. The force resistance operating from gas on border is found. Besides, the capacity of dissipation of the energy falling to unit of area of the fluctuating plate limiting gas is obtained.Comment: 26 pages, 5 figure

Twisted convolution and Moyal star product of generalized functions

We consider nuclear function spaces on which the Weyl-Heisenberg group acts continuously and study the basic properties of the twisted convolution product of the functions with the dual space elements. The final theorem characterizes the corresponding algebra of convolution multipliers and shows that it contains all sufficiently rapidly decreasing functionals in the dual space. Consequently, we obtain a general description of the Moyal multiplier algebra of the Fourier-transformed space. The results extend the Weyl symbol calculus beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure

Study of the process e+e−→ppˉe^+e^-\to p\bar{p} in the c.m. energy range from threshold to 2 GeV with the CMD-3 detector

Using a data sample of 6.8 pb$^{-1}$ collected with the CMD-3 detector at the VEPP-2000 $e^+e^-$ collider we select about 2700 events of the $e^+e^- \to p\bar{p}$ process and measure its cross section at 12 energy ponts with about 6\% systematic uncertainty. From the angular distribution of produced nucleons we obtain the ratio $|G_{E}/G_{M}| = 1.49 \pm 0.23 \pm 0.30$

Local conservation laws of second-order evolution equations

Generalizing results by Bryant and Griffiths [Duke Math. J., 1995, V.78, 531-676], we completely describe local conservation laws of second-order (1+1)-dimensional evolution equations up to contact equivalence. The possible dimensions of spaces of conservation laws prove to be 0, 1, 2 and infinity. The canonical forms of equations with respect to contact equivalence are found for all nonzero dimensions of spaces of conservation laws.Comment: 11 pages, minor correction

Morita base change in Hopf-cyclic (co)homology

In this paper, we establish the invariance of cyclic (co)homology of left Hopf algebroids under the change of Morita equivalent base algebras. The classical result on Morita invariance for cyclic homology of associative algebras appears as a special example of this theory. In our main application we consider the Morita equivalence between the algebra of complex-valued smooth functions on the classical 2-torus and the coordinate algebra of the noncommutative 2-torus with rational parameter. We then construct a Morita base change left Hopf algebroid over this noncommutative 2-torus and show that its cyclic (co)homology can be computed by means of the homology of the Lie algebroid of vector fields on the classical 2-torus.Comment: Final version to appear in Lett. Math. Phy