Nonlinear stability analysis of natural convection in an inclined fluid layer

Abstract

Computation of discriminant as well as integral basis of an algebraic number field has been one of the most important problems in algebraic number theory. The research work carried out in the thesis has yielded some significant results regarding this problem. In the thesis, a formula for the discriminant together with an explicit construction of integral basis has been given for those quintic and sextic number fields which are generated over the field of rational numbers by a root of an irreducible trinomial of the type xn + ax + b having integer coefficients. The thesis also describes families of non-monogenic prime power degree algebraic number fields which are generated over the field of rational numbers by a root of an irreducible quadrinomial with integer coefficients. newline