Direction problems in affine spaces

This paper is a survey paper on old and recent results on direction problems in finite dimensional affine spaces over a finite field.Comment: Academy Contact Forum "Galois geometries and applications", October 5, 2012, Brussels, Belgiu

Computational design of artificial organs

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Gapless interface states at the junction between two topological insulators

We consider a junction between two topological insulators, and calculate the properties of the interface states with an effective low energy Hamiltonian for topological insulators with a single cone on the surface. This system bears a close resemblance to bilayer graphene, as both result from the hybridization of Dirac cones. We find gapless interface states not only when the helicity direction of the topological surface states are oppositely oriented, but they can also exist if they are equally oriented. Furthermore, we find that the existence of the interface states can be understood from the closing of the bulk gap when the helicity changes orientation. Recently, superluminal tachyonic excitations were also claimed to exist at the interface between topological insulators. However, here we show that these interface states do not exist

The maximum size of a partial spread in H(5, q²) is q³+1

AbstractIn this paper, we show that the largest maximal partial spreads of the hermitian variety H(5,q2) consist of q3+1 generators. Previously, it was only known that q4 is an upper bound for the size of these partial spreads. We also show for q⩾7 that every maximal partial spread of H(5,q2) contains at least 2q+3 planes. Previously, only the lower bound q+1 was known