It has been recognized that the arc statistics of gravitational lensing is a useful probe of the density profile of clusters of galaxies. We examine several systematic effects which are important in predicting the number of arcs, with particular attention to the difference between tangential and radial arcs. First we derive an analytic expression of the cross section for radial arcs taking acco...

In this paper, we revisit the conjecture of [1], stating that ε-free Petri nets with transfer arcs are strictly more expressive than ε-free Petri nets with reset arcs. In [1], an ε-free Petri net with transfer arcs is provided, whose language is conjectured not to be recognizable by any ε-free Petri net with reset arcs. We show that this latter conjecture is flawed, by exhibiting an ε-free Petr...

A complementation operation on a vertex of a digraph changes all outgoing arcs into non-arcs, and outgoing non-arcs into arcs. This defines an equivalence relation where two digraphs are equivalent if one can be obtained from the other by a sequence of such operations. We show that given an adjacency-list representation of a digraph G, many fundamental graph algorithms can be carried out on any...

Apart from hyperovals and their duals there are only three classes of maximal arcs known in Desarguesian projective planes. Two classes are due to J. A. Thas and one to R. H. F. Denniston. In this paper collineation stabiliser and isomorphism problems for those maximal arcs in Desarguesian projective planes are examined. The full collineation stabilisers of the known maximal arcs are calculated...

The reduced expressions for a given element w of a Coxeter group (W, S) can be regarded as the vertices of a directed graphR (w); its arcs correspond to the braid moves. Specifically, an arc goes from a reduced expression −→a to a reduced expression −→ b when −→ b is obtained from −→a by replacing a contiguous subword of the form stst · · · (for some distinct s, t ∈ S) by tsts · · · (where both...

We use numerical simulations of galaxy clusters in different cosmologies to study their ability to form large arcs. The cosmological models are: Standard CDM (SCDM;Ω0 = 1, ΩΛ = 0); τCDMwith reduced small-scale power (parameters as SCDM, but with a smaller shape parameter of the power spectrum); open CDM (OCDM; Ω0 = 0.3, ΩΛ = 0); and spatially flat, low-density CDM (ΛCDM;Ω0 = 0.3,ΩΛ = 0.7). All ...

We use arcs found by Storme and van Maldeghem in their classification of primitive arcs in PG(2, q) as seeds for constructing small complete arcs in these planes. Our complete arcs are obtained by taking the union of such a “seed arc” with some orbits of a subgroup of its stabilizer. Using this approach we construct five different complete 15arcs fixed by Z3 in PG(2, 37), a complete 20-arc fixe...

In [3] De Clerck, De Winter and Maes counted the number of non-isomorphic Mathon maximal arcs of degree 8 in PG(2, 2), h 6= 7 and prime. In this article we will show that in PG(2, 2) a special class of Mathon maximal arcs of degree 8 arises which admits a Singer group (i.e. a sharply transitive group) on the 7 conics of these arcs. We will give a detailed description of these arcs, and then cou...