997 research outputs found
EAS spectrum in the primary energy region above 10 to the 15th power eV by the Akeno and Yakutsk array data
The extensive air showers spectrum on scintillation desity Rko in primary energy region E sub approx. 10 to the 15th power - 10 to the 20th power eV on the Yakutsk array data and recent results of the Akeno is given
ΠΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ Π³Π΅ΠΎΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΡ ΡΠΈΡΡΠ΅ΠΌ Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·Π½ΡΡ ΠΈΠ½ΠΆΠ΅Π½Π΅ΡΠ½ΠΎ-Π³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ Π·Π°Π΄Π°Ρ ΠΏΡΠΈ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ΅ ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΠΉ ΠΏΠΎΠ»Π΅Π·Π½ΡΡ ΠΈΡΠΊΠΎΠΏΠ°Π΅ΠΌΡΡ
One of the priorities of engineering geology in the development of underground mineral deposits is the dynamics of changes in geotechnical conditions as a result of anthropogenic factors and the degree of impact on existing buildings and structures. The most significant anthropogenic impact is associated with the extraction of minerals and host rocks. As a result of the development of the underground space, deformations of the earth's surface occur. It results in the subsidence features, changes in curvature, slope, compression and extension of rocks as a result of horizontal and vertical deformations. In turn, it leads to a change in the hydrological and hydrogeological regime, activation of exogenous processes, etc. This article presents the results of the creation of a GIS system to solve the forecast problems of changing engineering and geological conditions as a result of anthropogenic impact. The use of GIS technologies allows specialists to provide reliable and relevant information for assessing geotechnical risks in mining areas and making proper management decisions. The result of prognostic modeling should be a set of maps (cartographic layers) in the zone of influence of mining operations, containing the following information: forecast of the degree of anthropogenic impact, forecast of changes in geotechnical, hydrogeological, engineering and geological conditions, identification of objects on the earthβs surface that are in danger. Based on these predictive calculations, it is necessary to develop measures to reduce the negative impact. Such informational models of the territory should be supported at all stages of the life cycle of the field that will allow receiving high-quality information about the engineering and geological conditions of the developed territory at any time.ΠΠ΄Π½ΠΎΠΉ ΠΈΠ· ΠΏΡΠΈΠΎΡΠΈΡΠ΅ΡΠ½ΡΡ
Π·Π°Π΄Π°Ρ ΠΈΠ½ΠΆΠ΅Π½Π΅ΡΠ½ΠΎΠΉ Π³Π΅ΠΎΠ»ΠΎΠ³ΠΈΠΈ ΠΏΡΠΈ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ΅ ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΠΉ ΠΏΠΎΠ»Π΅Π·Π½ΡΡ
ΠΈΡΠΊΠΎΠΏΠ°Π΅ΠΌΡΡ
ΠΏΠΎΠ΄Π·Π΅ΠΌΠ½ΡΠΌ ΡΠΏΠΎΡΠΎΠ±ΠΎΠΌ ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΈΠ·ΡΡΠ΅Π½ΠΈΠ΅ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΈ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ ΠΈΠ½ΠΆΠ΅Π½Π΅ΡΠ½ΠΎ-Π³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ Π²Π»ΠΈΡΠ½ΠΈΡ ΡΠ΅Ρ
Π½ΠΎΠ³Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΠΊΡΠΎΡΠ° ΠΈ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ Π΅Π³ΠΎ Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ Π½Π° ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠΈΠ΅ Π·Π΄Π°Π½ΠΈΡ ΠΈ ΡΠΎΠΎΡΡΠΆΠ΅Π½ΠΈΡ. ΠΠ°ΠΈΠ±ΠΎΠ»Π΅Π΅ Π·Π½Π°ΡΠΈΠΌΠΎΠ΅ Π°Π½ΡΡΠΎΠΏΠΎΠ³Π΅Π½Π½ΠΎΠ΅ Π²Π»ΠΈΡΠ½ΠΈΠ΅ ΡΠ²ΡΠ·Π°Π½ΠΎ Ρ ΠΈΠ·Π²Π»Π΅ΡΠ΅Π½ΠΈΠ΅ΠΌ ΠΏΠΎΠ»Π΅Π·Π½ΠΎΠ³ΠΎ ΠΈΡΠΊΠΎΠΏΠ°Π΅ΠΌΠΎΠ³ΠΎ ΠΈ Π²ΠΌΠ΅ΡΠ°ΡΡΠ΅ΠΉ ΠΏΠΎΡΠΎΠ΄Ρ. Π ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ Π²ΡΡΠ°Π±ΠΎΡΠΊΠΈ ΠΏΠΎΠ΄Π·Π΅ΠΌΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π° ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΡΡ Π΄Π΅ΡΠΎΡΠΌΠ°ΡΠΈΠΈ Π·Π΅ΠΌΠ½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ²ΠΎΠ΄ΡΡΡΡ ΠΊ ΠΎΡΠ΅Π΄Π°Π½ΠΈΡ, ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ ΠΊΡΠΈΠ²ΠΈΠ·Π½Ρ, ΡΠΊΠ»ΠΎΠ½Π°, ΡΠΆΠ°ΡΠΈΡ ΠΈ ΡΠ°ΡΡΡΠΆΠ΅Π½ΠΈΡ Π³ΠΎΡΠ½ΡΡ
ΠΏΠΎΡΠΎΠ΄, ΡΡΠΎ Π² ΡΠ²ΠΎΡ ΠΎΡΠ΅ΡΠ΅Π΄Ρ ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ Π³ΠΈΠ΄ΡΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΈ Π³ΠΈΠ΄ΡΠΎΠ³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅ΠΆΠΈΠΌΠ°, Π°ΠΊΡΠΈΠ²ΠΈΠ·Π°ΡΠΈΠΈ ΡΠΊΠ·ΠΎΠ³Π΅Π½Π½ΡΡ
ΠΏΡΠΎΡΠ΅ΡΡΠΎΠ² ΠΈ Ρ.Π΄. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ ΠΠΠ‘-ΡΠΈΡΡΠ΅ΠΌΡ Π΄Π»Ρ ΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·Π½ΡΡ
Π·Π°Π΄Π°Ρ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ ΠΈΠ½ΠΆΠ΅Π½Π΅ΡΠ½ΠΎΠΉ Π³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΠ΅Ρ
Π½ΠΎΠ³Π΅Π½Π½ΠΎΠ³ΠΎ Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ. ΠΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΠΠ‘-ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΉ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΡΡ ΡΠΏΠ΅ΡΠΈΠ°Π»ΠΈΡΡΠΎΠ² Π΄ΠΎΡΡΠΎΠ²Π΅ΡΠ½ΠΎΠΉ ΠΈ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠ²Π½ΠΎΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠ΅ΠΉ Π΄Π»Ρ ΠΎΡΠ΅Π½ΠΊΠΈ ΠΈΠ½ΠΆΠ΅Π½Π΅ΡΠ½ΠΎ-Π³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠΈΡΠΊΠΎΠ² Π½Π° ΡΠ΅ΡΡΠΈΡΠΎΡΠΈΠΈ Π³ΠΎΡΠ½ΡΡ
ΠΎΡΠ²ΠΎΠ΄ΠΎΠ² ΠΈ ΠΏΡΠΈΠ½ΠΈΠΌΠ°ΡΡ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΡΠ΅ ΡΠΏΡΠ°Π²Π»Π΅Π½ΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅ΡΠ΅Π½ΠΈΡ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠΌ ΠΏΡΠΎΠ³Π½ΠΎΠ·Π½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π΄ΠΎΠ»ΠΆΠ΅Π½ ΡΡΠ°ΡΡ Π½Π°Π±ΠΎΡ ΠΊΠ°ΡΡ (ΠΊΠ°ΡΡΠΎΠ³ΡΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ»ΠΎΠ΅Π²) Π² ΠΏΡΠ΅Π΄Π΅Π»Π°Ρ
Π·ΠΎΠ½Ρ Π²Π»ΠΈΡΠ½ΠΈΡ Π³ΠΎΡΠ½ΡΡ
ΡΠ°Π±ΠΎΡ, ΡΠΎΠ΄Π΅ΡΠΆΠ°ΡΠΈΡ
ΡΠ»Π΅Π΄ΡΡΡΡΡ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡ: ΠΏΡΠΎΠ³Π½ΠΎΠ· ΡΡΠ΅ΠΏΠ΅Π½ΠΈ ΡΠ΅Ρ
Π½ΠΎΠ³Π΅Π½Π½ΠΎΠ³ΠΎ Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ, ΠΏΡΠΎΠ³Π½ΠΎΠ· ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ ΠΈΠ½ΠΆΠ΅Π½Π΅ΡΠ½ΠΎ-Π³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
, Π³ΠΈΠ΄ΡΠΎΠ³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
, Π³Π΅ΠΎΡΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ, Π²ΡΡΠ²Π»Π΅Π½ΠΈΠ΅ ΠΎΠ±ΡΠ΅ΠΊΡΠΎΠ² Π½Π° Π·Π΅ΠΌΠ½ΠΎΠΉ ΠΏΠΎΠ²Π΅ΡΡ
Π½ΠΎΡΡΠΈ, Π½Π°Ρ
ΠΎΠ΄ΡΡΠΈΡ
ΡΡ Π² Π·ΠΎΠ½Π΅ ΡΠΈΡΠΊΠ°. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΡΡΠΈΡ
ΠΏΡΠΎΠ³Π½ΠΎΠ·Π½ΡΡ
ΡΠ°ΡΡΠ΅ΡΠΎΠ² Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎ ΡΠ°Π·ΡΠ°Π±Π°ΡΡΠ²Π°ΡΡ ΠΌΠ΅ΡΠΎΠΏΡΠΈΡΡΠΈΡ Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ Π½Π΅Π³Π°ΡΠΈΠ²Π½ΠΎΠ³ΠΎ Π²ΠΎΠ·Π΄Π΅ΠΉΡΡΠ²ΠΈΡ. Π’Π°ΠΊΠΈΠ΅ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΡΠ΅ΡΡΠΈΡΠΎΡΠΈΠΈ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΡ Π½Π° Π²ΡΠ΅Ρ
ΡΡΠ°ΠΏΠ°Ρ
ΠΆΠΈΠ·Π½Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠΈΠΊΠ»Π° ΠΌΠ΅ΡΡΠΎΡΠΎΠΆΠ΄Π΅Π½ΠΈΡ, ΡΡΠΎ ΠΏΠΎΠ·Π²ΠΎΠ»ΠΈΡ Π² Π»ΡΠ±ΠΎΠΉ ΠΌΠΎΠΌΠ΅Π½Ρ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ ΠΏΠΎΠ»ΡΡΠΈΡΡ ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅Π½Π½ΡΡ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡ ΠΎΠ± ΠΈΠ½ΠΆΠ΅Π½Π΅ΡΠ½ΠΎ-Π³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΡΡ
ΠΎΡΠ²Π°ΠΈΠ²Π°Π΅ΠΌΠΎΠΉ ΡΠ΅ΡΡΠΈΡΠΎΡΠΈΠΈ
Status and challenges of black soils.
A global overview of black soils; Multiple benefits of black soils; Main threats to black soils; Challenges
Polymers pushing Polymers: Polymer Mixtures in Thermodynamic Equilibrium with a Pore
We investigate polymer partitioning from polymer mixtures into nanometer size
cavities by formulating an equation of state for a binary polymer mixture
assuming that only one (smaller) of the two polymer components can penetrate
the cavity. Deriving the partitioning equilibrium equations and solving them
numerically allows us to introduce the concept of "polymers-pushing-polymers"
for the action of non-penetrating polymers on the partitioning of the
penetrating polymers. Polymer partitioning into a pore even within a very
simple model of a binary polymer mixture is shown to depend in a complicated
way on the composition of the polymer mixture and/or the pore-penetration
penalty. This can lead to enhanced as well as diminished partitioning, due to
two separate energy scales that we analyse in detail.Comment: 10 pages, 6 figure
NASSAM: a server to search for and annotate tertiary interactions and motifs in three-dimensional structures of complex RNA molecules
Similarities in the 3D patterns of RNA base interactions or arrangements can provide insights into their functions and roles in stabilization of the RNA 3D structure. Nucleic Acids Search for Substructures and Motifs (NASSAM) is a graph theoretical program that can search for 3D patterns of base arrangements by representing the bases as pseudo-atoms. The geometric relationship of the pseudo-atoms to each other as a pattern can be represented as a labeled graph where the pseudo-atoms are the graph's nodes while the edges are the inter-pseudo-atomic distances. The input files for NASSAM are PDB formatted 3D coordinates. This web server can be used to identify matches of base arrangement patterns in a query structure to annotated patterns that have been reported in the literature or that have possible functional and structural stabilization implications. The NASSAM program is freely accessible without any login requirement at http://mfrlab.org/grafss/nassam/
37th All-Russian Scientific and Practical Conference "Geology and minerals of the Western Urals"
23-24 ΠΌΠ°Ρ 2017 Π³. Π½Π° Π±Π°Π·Π΅ ΠΠ΅ΡΠΌΡΠΊΠΎΠ³ΠΎ Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ Π½Π°ΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΡΠΊΠΎΠ³ΠΎ ΡΠ½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅ΡΠ° ΡΠΎΡΡΠΎΡΠ»Π°ΡΡ 37-Ρ ΠΡΠ΅ΡΠΎΡΡΠΈΠΉΡΠΊΠ°Ρ Π½Π°ΡΡΠ½ΠΎ-ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΊΠΎΠ½ΡΠ΅ΡΠ΅Π½ΡΠΈΡ Ρ ΠΌΠ΅ΠΆΠ΄ΡΠ½Π°ΡΠΎΠ΄Π½ΡΠΌ ΡΡΠ°ΡΡΠΈΠ΅ΠΌ Β«ΠΠ΅ΠΎΠ»ΠΎΠ³ΠΈΡ ΠΈ ΠΏΠΎΠ»Π΅Π·Π½ΡΠ΅ ΠΈΡΠΊΠΎΠΏΠ°Π΅ΠΌΡΠ΅ ΠΠ°ΠΏΠ°Π΄Π½ΠΎΠ³ΠΎ Π£ΡΠ°Π»Π°Β». Π ΡΡΠ°ΡΡΠ΅ ΠΎΠΏΠΈΡΠ°Π½Ρ ΠΎΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΌΠΎΠΌΠ΅Π½ΡΡ ΡΠ°Π±ΠΎΡΡ ΠΊΠΎΠ½ΡΠ΅ΡΠ΅Π½ΡΠΈΠΈ, ΠΎΡΠ²Π΅ΡΠ΅Π½Ρ Π·Π°ΡΡΠ°Π³ΠΈΠ²Π°Π΅ΠΌΡΠ΅ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΠΈ ΡΠ΅ΠΌΠ°ΡΠΈΠΊΠ° Π΄ΠΎΠΊΠ»Π°Π΄ΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ ΠΏΠΎΠ΄Π²Π΅Π΄Π΅Π½Ρ ΠΈΡΠΎΠ³ΠΈ.On May 23-24, 2017, the 37th All-Russian Scientific and Practical Conference with international participation "Geology of minerals of the Western Urals" was held on the basis of the Perm State University. The article describes the main aspects of the work of the conference, highlights the issues and topics covered in the reports, and summarizes the results
Fluctuations of development maximum depth and nuclear composition of primary cosmic radiation
The extensive air showers (EAS) cascade curves from the Cerenkov light lateral distribution measurements are recovered and the maximum depth fluctuations of the shower development theta x sub m both on the Cerenkov and charged EAS components are defined. At E sub 0 approximates 10 to the 18th power eV the mean content of protons is greater than 85%, and p-air cross section theta sub 0 p-air 750mb
ΠΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΏΠ°Π»ΠΈΠ½ΡΠΏΠ°ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ ΡΠ΅ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ ΠΏΡΠΈ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ Π΄ΠΎΠ½Π°Π΄Π²ΠΈΠ³ΠΎΠ²ΠΎΠ³ΠΎ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ ΡΠ»ΠΎΠΆΠ½ΠΎ Π΄ΠΈΡΠ»ΠΎΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ ΡΠ΅Π³ΠΈΠΎΠ½ΠΎΠ²
The paper briefly discusses some methods of palinspastic reconstructions and their application for studying of the Nizhneserginskaya thrust zone of the Urals using complex techniques that address both structural and kinematic principles of modeling. Based on the constructed model, the data reflecting the geological structure before the formation of thrust zones of the studied territory were obtained.Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ Π½Π΅ΠΊΠΎΡΠΎΡΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠΈ ΠΏΠ°Π»ΠΈΠ½ΡΠΏΠ°ΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ΅ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΉ. ΠΡΠΎΠ²Π΅Π΄Π΅Π½Π° ΠΏΠ°Π»ΠΈΠ½ΡΠΏΠ°ΡΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠ΅ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΡ ΠΠΈΠΆΠ½Π΅ΡΠ΅ΡΠ³ΠΈΠ½ΡΠΊΠΎΠΉ Π·ΠΎΠ½Ρ Π½Π°Π΄Π²ΠΈΠ³ΠΎΠ² Π£ΡΠ°Π»Π° Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊ, Π·Π°ΡΡΠ°Π³ΠΈΠ²Π°ΡΡΠΈΡ
ΠΊΠ°ΠΊ ΡΡΡΡΠΊΡΡΡΠ½ΡΠ΅, ΡΠ°ΠΊ ΠΈ ΠΊΠΈΠ½Π΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΡΠΈΠ½ΡΠΈΠΏΡ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΠΏΠΎΡΡΡΠΎΠ΅Π½Π½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Ρ Π΄Π°Π½Π½ΡΠ΅, ΠΎΡΡΠ°ΠΆΠ°ΡΡΠΈΠ΅ Π³Π΅ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΡΡΡΠΎΠ΅Π½ΠΈΠ΅ Π΄ΠΎ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π½Π°Π΄Π²ΠΈΠ³ΠΎΠ²ΡΡ
Π·ΠΎΠ½ ΠΈΠ·ΡΡΠ°Π΅ΠΌΠΎΠΉ ΡΠ΅ΡΡΠΈΡΠΎΡΠΈΠΈ
The central polynomials for the finite dimensional Grassmann algebras
In this note we describe the central polynomials for the finite dimensional unitary Grassmann algebras Gk over an infinite field F of characteristic β 2. We exhibit a set of generators of C(Gk), the T-space of the central polynomials of Gk in a free associative F-algebra
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