We extend the construction of the authors’ paper of 2002 by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby obtain a universal algebra of generalized tensor fields canonically containing the space of distributional tensor fields. The canonical...

it has been proved that sphericity testing for digraphs is an np-complete problem. here, we investigate sphericity of 3-connected single source digraphs. we provide a new combinatorial characterization of sphericity and give a linear time algorithm for sphericity testing. our algorithm tests whether a 3-connected single source digraph with $n$ vertices is spherical in $o(n)$ time.

A weighted embedding for the generalized pontogram {Kn(t): 06t61} corresponding pointwise to a renewal process {N (s): 06s¡∞} via Kn(t)=n−1=2(N (nt)− tN (n)) is studied in this paper. After proper normalization, weak convergence results for the processes {Kn(t): 06t61} are derived both in sup-norm as well as in Lp-norm. These results are suggested to serve as asymptotic testing devices for dete...

The research in this paper was motivated by one of the most important open problems in the theory of generalized polygons, namely the existence problem for semi-finite thick generalized polygons. We show here that no semi-finite generalized hexagon of order (2, t) can have a subhexagon H of order 2. Such a subhexagon is necessarily isomorphic to the split Cayley generalized hexagon H(2) or its ...