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...

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...

High-resolution optical observations by the University of Calgary Portable Auroral Imager show a frequent occurrence of asymmetric multiple small-scale auroral arc structures during auroral substorms. Whereas the classical multiple arc array tends to exhibit a fairly symmetrical configuration, with parallel motions within individual discrete arcs being opposite in direction across the center of...

For some applications of computer-aided geometric design it is important to maintain strictly monotone curvature along a curve segment. Here we analyze the curvature distributions of segments of conic sections represented as rational quadratic Bézier curves in standard form. We show that if the end points and the weight are fixed, then the curvature of the conic segment will be strictly monoton...

Let tt : (V, E, W ) be a finite, connected, weighted graph without loops and multiple edges. In a weighted graph each arc is assigned a weight by the weight function W : E +. A u v path P in tt is called a weighted u v geodesic if the weighted distance between u and v is calculated along P . The strength of a path is the minimum weight of its arcs, and length of a path is the number of edges in...

Given a graph G = (V, E) and a weight function on the edges w : E 7→ R, we consider the polyhedron P (G, w) of negative-weight flows on G, and get a complete characterization of the vertices and extreme directions of P (G, w). As a corollary, we show that, unless P = NP , there no output polynomial-time algorithm to generate all the vertices of a 0/1-polyhedron. This strengthens the NP-hardness...

It is shown that the parameters of a linear code over Fq of length n, dimension k, minimum weight d and maximum weight m satisfy a certain congruence relation. In the case that q = p is a prime, this leads to the bound m ≤ (n− d)p− e(p− 1), where e ∈ {0, 1, . . . , k− 2} is maximal with the property that ( n− d e ) 6≡ 0 (mod pk−1−e). Thus, if C contains a codeword of weight n then n ≥ d/(p− 1) ...

Let G : (V, E, ω) be a finite, connected, weighted graph without loops and multiple edges. In a weighted graph each arc is assigned a weight by the weight function ω: E    . A u−v path P in G is called a weighted u−v geodesic if the weighted distance between u and v is calculated along P. The strength of a path is the minimum weight of its arcs, and length of a path is the number of edges in...