This work was supported by grants from the Interuniversity Attraction Poles Program-Belgian State-Belgian Science Policy, the National Cancer Plan of the Federal Ministry of Health, the Stichting tegen Kanker, the Vlaamse Kanker Liga, an Integrated Project and an EU FP6funded Network of Excellence, an IWT-TBM program, the FWO-Vlaanderen and the Scientific Fund Willy Gepts of the University hosp...

We discuss in detail the relation between the gauge fixed and gauge invariant BRST cohomology. We showed previously that in certain gauges some cohomology classes of the gauge-fixed BRST differential do not correspond to gauge invariant observables. We now show that in addition “accidental” conserved currents may appear. These correspond one-toone to observables that become trivial in this gaug...

Seiberg-Witten maps and a recently proposed construction of noncommutative Yang-Mills theories (with matter fields) for arbitrary gauge groups are reformulated so that their existence to all orders is manifest. The ambiguities of the construction which originate from the freedom in the Seiberg-Witten map are discussed with regard to the question whether they can lead to inequivalent models, i.e...

In this paper, we study stability and linearization of multivalued nonlinear feedback shift registers which are considered as logic networks. First, the linearization of multi-valued nonlinear feedback shift registers (NFSRs) is discussed, which is to find their state transition matrices by considering it as a logical network via a semi-tensor product approach. For a multi-valued NFSR, the new ...

We present a short and conceptual proof of Gauss’ quadratic reciprocity law. It is an optimized version of V.A. Lebesgue’s 1838 proof computing the number of solutions to x1 + x 2 2 + · · · + xp ≡ 1 mod q. Let p, q be distinct odd prime numbers. The law of quadratic reciprocity states that ( p q )( q p ) = (−1) p−1 2 q−1 2 , where ( · · ) is the Legendre symbol. In 1838, V.A. Lebesgue gave a pr...

The chords of a twisted cubic in PG(3, q) are mapped via their Plucker coordinates to the points of a Veronese surface lying on the Klein quadric in PG(5, q). This correspondence over a finite field gives a cap in PG(5, q), that is, a set of points no three of which are collinear. The dual structure, namely the axes of the osculating developable, is also mapped to a Veronese surface. The two su...

Looking to the history of mathematics one could find out two outer approaches to Geometry. First one (algebraic) is due to Descartes and second one (group-theoretic)—to Klein. We will see that they are not rivalling but are tied (by Galois). We also examine their modern life as philosophies of non-commutative geometry. Connections between different objects (see keywords) are discussed. ∗Support...

The Bulletin of the Belgian Mathematical Society Simon Stevin is published by The Belgian Mathematical Society, with financial support from the Universitaire Stichting van Belgie – Fondation Universitaire de Belgique and the Fonds National de la Recherche Scientifique (FNRS). It appears quarterly and is indexed and/or abstracted in Current

In the context of massless higher spin gauge fields in constant curvature spaces, we compute the surface charges which generalize the electric charge for spin one, the color charges in Yang-Mills theories and the energy-momentum and angular momentum for asymptotically flat gravitational fields. We show that there is a one-to-one map from surface charges onto divergence free Killing tensors. The...

Two different constructions are given of a rank 8 arc-transitive graph with 165 vertices and valency 8, whose automorphism group is M11. One involves 3-subsets of an 11-set while the other involves 4-subsets of a 12-set, and the constructions are linked with the Witt designs on 11, 12 and 24 points. Four different constructions are given of a rank 9 arc-transitive graph with 55 vertices and val...