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Ali Fröhlich was one of the truly great mathematicians of his generation. In addition to making fundamental contributions, he is one of the very few of whom it can be said, “he founded a new subject”: namely that area now known as Galois module theory. In addition to establishing a theoretical basis for the subject, he also formulatedsome very deep and wonderful conjectures that would thrust him onto the world's stage. He also built up a school of researchers that played a central part in establishing British algebraic number theory as a world force. The outstanding nature of his contributions to mathematics was recognised in 1992 when the London Mathematical Society awarded him the De Morgan Medal: their highest and most distinguished prize, which is awarded triennially. [ABSTRACT FROM AUTHOR]

Although there are technical standards and guides relating to specific aspects of computer network development and implementation, there appear to be no overall frameworks or approaches aimed specifically at computer network development and implementation, particularly those that are smaller in scale. In this paper the application of an action research approach to the technically oriented process of computer network development and implementation is examined. In particular, this paper examines the soft issues relating to small-scale computer network development and implementation encountered in a 2-year project in a small engineering company. [ABSTRACT FROM AUTHOR]

We establish comparison results between the Hasse–Witt invariants wt (E) of a symmetric bundle E over a scheme and the invariants of one of its twists Ea. For general twists we describe the difference between wt (E) and wt (Ea) up to terms of degree 3. Next we consider a special kind of twist, which has been studied by A. Fröhlich. This arises from twisting by a cocycle obtained from an orthogonal representation. A simple important example of this twisting procedure is the bilinear trace form of an étale algebra, which is obtained by twisting the standard/sum-of-squares form by the orthogonal representation attached to the algebra. We show how to explicitly describe the twist for representations arising from very general tame actions. This involves the ‘square root of the inverse different’ which Serre, Esnault, Kahn, Viehweg and ourselves had studied before. For torsors we show that, in our geometric set-up, Jardines generalisation of Fröhlichs formula holds. Namely let (X, G) be a torsor with quotient Y, let E be a symmetric bundle over Y, let ?: G ? O(E) be an orthogonal representation and let E?, X be the corresponding twist of E. Then we verify up to degree 3 that the formula wt (E?, X) Spt (?) = wt (E) wt (?) holds. Here Spt (?) and wt (?) are respectively the spinor invariant and the Stiefel–Whitney class of ?. The case of genuinely tamely ramified actions is geometrically more involved and leads us to introduce an invariant of ramification, which in a sense gives a decomposition in terms of representations of the inertia groups of the invariant introduced by Serre for curves.The comparison result in the tamely ramified case proceeds by reduction to the case of a torsor. The reduction is carried out by means of a partial normalisation procedure, which we had introduced in a previous paper. An important lemma of Esnault, Kahn and Viehweg allows us to express the difference between the invariants of bundles before and after the normalisation procedure in terms of Chern classes of certain sub-bundles. As noted elsewhere, this result can be best understood in the context of symmetric complexes and their invariants. Our results are new even for bundles over curves and they allow us to weaken the regularity assumptions that we had to impose in previous work of ours. [ABSTRACT FROM AUTHOR]