The size function h°for a pure cubic field

A Relative Integral Basis over Q( √−3) for the Normal Closure of a Pure Cubic Field

Let K be a pure cubic field. Let L be the normal closure of K. A relative integral basis (RIB) for L over Q(√ −3) is given. This RIB simplifies and completes the one given by Haghighi (1986).

The shapes of pure cubic fields

We determine the shapes of pure cubic fields and show that they fall into two families based on whether the field is wildly or tamely ramified (of Type I or Type II in the sense of Dedekind). We show that the shapes of Type I fields are rectangular and that they are equidistributed, in a regularized sense, when ordered by discriminant, in the one-dimensional space of all rectangular lattices. W...

A new method for the preparation of pure topiramate with a micron particle size

Crude topiramate was prepared from the reaction between diacetonefructopyranose, sulfuric diamide, and 2-picoline. During a controlled processing the presence of Triton-X-100, crude topiramate in a methanol-water solvent, was converted to pure micron size topiramate particles. The factors affecting the purification and micronization of topiramate, such as solvent and anti-solvent type and conce...

Binomial squares in pure cubic number fields

Let K = Q(ω), with ω3 = m a positive integer, be a pure cubic number field. We show that the elements α ∈ K× whose squares have the form a − ω for rational numbers a form a group isomorphic to the group of rational points on the elliptic curve Em : y2 = x3 − m. This result will allow us to construct unramified quadratic extensions of pure cubic number fields K.

Computation of the Fundamental Units and the Regulator of a Cyclic Cubic Function Field