IKBFU's Vestnik

2014 Issue №10

Generating function and its application for generalization of Legendre polynomials

Abstract

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.

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About pairing on abelian varieties p-rank one and their cryptographic applications

Abstract

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.

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Algorithms for detecting high-gradient areas of the great oceans has increased biological productivity

Abstract

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.

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