Algoritmy hledání shluků řešení diofantické rovnice popisující resonanci Rossbyho vln

Abstract

Tato prace se zabyva zkoumanim meteorologickeho fenomenu atmosferickych vln z hle- diska teorie cisel a algebry. Z fyzikalniho popisu dynamiky systemu techto vln vyplyva diofanticka rovnice, jejiz reseni tvori ve dvourozmerne souradnicove soustave neoriento- vany graf slozeny ze sestiuhelniku. Za ucelem hledani techto reseni byl implementovan funkcni program v prostredi Wolfram Mathematica.This thesis concerns about investigating a meteorological phenomenon of atmospheric waves from a number-theoretical and algebraic view. From the physical description of the dynamics of the system we get a Diophantine equation, solutions of which create an undirected graph consisting of hexagons in the 2D plane. For the purpose of finding these solutions a program in Wolfram Mathematica was implemented.