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Vol 72, No 6 (2017)
- Year: 2017
- Articles: 7
- URL: https://journal-vniispk.ru/0027-1322/issue/view/10030
Article
221-225
226-232
Growth of codimensions of metabelian algebras
Abstract
Numerical invariants of identities of nonassociative algebras are considered. It is proved that the codimension sequence of any finitely generated metabelian algebra has an exponentially bounded codimension growth. It is shown that the upper PI-exponent increases at most by 1 after adjoining an external unit. It is proved that for two-step left-nilpotent algebras the lower PI-exponent increases at least by 1.
233-237
Fast algorithm for geometrical coding of digital images
Abstract
A fast algorithm for geometrical coding is presented in the paper. It allows one to perform the image analysis by methods of differential geometry rather than widespread methods based on gradient and Hessian calculations. Nowadays, one of the most important aspects in image analysis is the speed of computations. The algorithm for geometrical coding is comparable or faster than traditional algorithms of image analysis and in many cases it gives better results. Several examples of algorithm working results for contour detection are presented.
238-244
Comparison of the system “Chaplygin ball with a rotor” and the Zhukovskii system from the rough Liouville equivalence point of view
Abstract
A problem of symplectic geometry is considered, namely, topological analysis of a rolling dynamically balanced non-symmetric ball with a rotor on a rough horizontal plane is considered. The Liouville equivalence between this system and the Zhukovskii system is studied.
245-250
251-254
A cubature formula for periodic functions
Abstract
New many-dimensional cubature formulas are obtained for periodic functions with the use of the Chinese remainder theorem. This allows us to take into account the “equality” of all variables and the “uniformness” of distribution of nodes in numerical integration formulas.
255-257