Many structured overlay networks rely on a ring invariant as a core network connectivity element. The responsibility ranges of the participating peers and navigability principles (greedy routing) heavily depend on the ring structure. For correctness guaran ...
Let K be a field with char(K) ≠ 2. The Witt-Grothendieck ring (K) and the Witt ring W (K) of K are both quotients of the group ring ℤ[𝓖(K)], where 𝓖(K) := K*/(K*)2 is the square class group of K. Since ℤ[𝓖(K)] is integra ...
We have fabricated three-quarter ring structures on silicon nitride membranes for magnetic domain imaging using Lorentz electron microscopy. The ring structures have linewidths of 100, 250, 350 and 700 nm, and outer diameters of 1.65 mu m. Using the Foucau ...
This thesis deals with the study of G-forms and particulary the trace form of a G-Galois algebra. Let k be a field of characteristic not two. Let G be a finite group and L a G-Galois algebra over k. We define the trace form qL by qL(x, y) = TrL/k(xy) for a ...