Dynamic Analysis and FPGA Implementation of a Kolmogorov-Like Hyperchaotic System

Chaotic systems have high potential for engineering applications due to their extremely complex dynamics. In the paper, a five-dimensional (5D) Kolmogorov-like hyperchaotic system is proposed. First, the hyperchaotic property is uncovered, and numerical analysis shows that the system displays the coexistence of different kinds of attractors. This system presents a generalized form of fluid and forced-dissipative dynamic systems. The vector field of the hyperchaotic system is decomposed to inertial, internal, dissipative and external torques, respectively, and the energies are analyzed in detail. Then, the bound of the 5D dissipative hyperchaos is estimated with a constructed spherical function. Finally, the system passes the NIST tests and an FPGA platform is used to realize the hyperchaotic system.

STUDY OF THE ACCURACY OF MODEL CONSTRUCTION BY SIFT ALGORYITHM FOR LARGE SPAN STRUCTURES

The article considers the accuracy of floor models creation in large span structures with the use of unmanned aerial vehicles for the purpose of determining their deformations. There were performed 4 aero shootings of Water Sports Palace in Dushambe, which were processed by SIFT algorithm. Syn-chronically with the UAV shooting there was performed the measurements on deformation marks within the frames of geodetic monitoring. There was performed the statistical analysis of models accu-racy by method of interpolation of spherical function, which showed that 80% of points has devia-tions less than 30 mm, and the rest 20% has deviations up to 80 mm. The use of collocation method for smoothing optimal filtering allowed to decrease the differences between settlement surfaces ob-tained by geodetic measurement and UAV shooting up to 26mm., which is 10 % of acceptable devia-tions of this object. It was found out that there is a necessity of further investigations of SIFT algo-rithm and filtering its results for the purpose of increasing the accuracy of object’s models.

A Characteristic Map for the Symmetric Space of Symplectic Forms Over a Finite Field

The characteristic map for the symmetric group is an isomorphism relating the representation theory of the symmetric group to symmetric functions. An analogous isomorphism is constructed for the symmetric space of symplectic forms over a finite field, with the spherical functions being sent to Macdonald polynomials with parameters $(q,q^2)$. An analogue of parabolic induction is interpreted as a certain multiplication of symmetric functions. Applications are given to Schur positivity of skew Macdonald polynomials with parameters $(q,q^2)$ as well as combinatorial formulas for spherical function values.

APPROXIMATION BY SPHERICAL NEURAL NETWORKS WITH ZONAL FUNCTIONS

We address the construction and approximation for feed-forward neural networks (FNNs) with zonal functions on the unit sphere. The filtered de la Vallée-Poussin operator and the spherical quadrature formula are used to construct the spherical FNNs. In particular, the upper and lower bounds of approximation errors by the FNNs are estimated, where the best polynomial approximation of a spherical function is used as a measure of approximation error.