We prove that for a finitely generated infinite nilpotent group G with a first order structure (G, ·, . . .), the connected component G of a sufficiently saturated extension G of G exists and equals ⋂ n∈N {g : g ∈ G}. We construct a first order expansion of Z by a predicate (Z,+, P ) such that the type-connected component Z ∅ is strictly smaller than Z. We generalize this to finitely generated ...

The union of two disjoint (n, 4n−1, 2) MDS codes in {0, 1, 2, 3}n is a double-MDS-code. If the adjacency graph of the double-MDS-code is not connected, then the double-code can be decomposed into double-MDS-codes of smaller lengths. If the graph has more than two connected components, then the MDS codes are also decomposable. The result has an interpretation in terms of n-quasigroups of order 4...

We define the character sheaves on a connected component of a reductive group and we show that the restriction functor takes a character sheaf to a direct sum of character sheaves.

Abstract. We consider a finite number of particles initially close to spherical but of varying size exhibiting the property of preserving the measure of each connected component. We show that under the assumptions i) particle size/interparticle distance 1 and ii) initial deviation from sphericity/particle size 1 the particles retain their almost spherical shape and the dynamics of the system is...