2014 Issue №10

In the present paper the generalization of Legendre polynomials with the help of generating function is studied. The explicit form of considered functions is found. Some special cases are considered. Particular attention is paid to the case when the parameters defining the studied functions are different, symmetric about zero real numbers. Some properties of constructed functions are obtained. Based on the results of numerical experiment a hypothesis about zeroes of these functions is stated.

Described and analyzed in terms of computational efficiency different types of pairings on hyperelliptic curves, especially on curves of genus 2 and p-rank one for the cryptographic applications.

We present a preconditioner for large systems of linear equations based on the incomplete block decomposition for block-tridiagonal matrices. This method generalizes frequency-filtering method of G. Wittum [1] and methods developed in [2–4] etc.

The question of the application of remote sensing data to choose areas of the great oceans with increased biological productivity is considered. Submitted algorithm allows sharing this areas in accordance with the data of fisheries statistics. The method of minimum curvature in tension for the solution of problems of gridding data to required grid is considered.