MAR/APR 2007 • VOLUME 17 • NUMBER 2 How do new regulators in the UK develop and implement their consumer policies? Do they follow the examples of more established regulators, or do they do something new? And if so, are they as effective as older regulators? Taking the examples of the financial services and communications markets, both of which have had regulators established by and Act of Parli...

We use the theory of flag algebras to find new upper bounds for several small graph and hypergraph Ramsey numbers. In particular, we prove the exact values R(K− 4 ,K − 4 ,K − 4 ) = 28, R(K8, C5) = 29, R(K9, C6) = 41, R(Q3, Q3) = 13, R(K3,5,K1,6) = 17, R(C3, C5, C5) = 17, and R(K− 4 ,K − 5 ; 3) = 12, and in addition improve many additional upper bounds.

In this note we compute the (uni)versal deformation of two types of mod 3 Galois representations ρ̄ : Gal(Q3/Q3)→ GL2(F3). In the cases considered the (uni)versal ring is not formally smooth over a ring of Witt vectors. The main result is that this ring is an integral domain. This has applications to the local Langlands conjecture. The computations are based on [Bö] but made more explicit.

In this paper, we show that one can associate a pseudoregulus with every scattered linear set of rank 3n in PG(2n − 1, q3). We construct a scattered linear set having a given pseudoregulus as associated pseudoregulus and prove that there are q − 1 different scattered linear sets that have the same associated pseudoregulus. Finally, we give a characterisation of reguli and pseudoreguli in PG(3, ...

Protein structure prediction has always been an important research area in biochemistry. In particular, the prediction of protein secondary structure has been a well-studied research topic. The experimental methods currently used to determine protein structure are accurate, yet costly both in terms of equipment and time. Despite the recent breakthrough of combining multiple sequence alignment i...