We completely describe the structure of the connected components of transversals to a collection of n line segments in R. Generically, the set of transversal to four segments consist of zero or two lines. We catalog the non-generic cases and show that n > 3 arbitrary line segments in R admit at most n connected components of line transversals, and that this bound can be achieved in certain conf...

In this paper, we propose a model of the web of data as a graph of interlinked graphs which goes beyond the standard single-graph RDF semantics, describe two different ways in which a query on this structure can be answered, and characterize semantically each of these ways in terms of restrictions on the relation between the domain of interpretation of each single component graph.

LetX be a smooth projective geometrically connected curve over a finite field with function field K. Let G be a connected semisimple group scheme over X . Under certain hypothesis we prove the equality of two numbers associated with G. The first is an arithmetic invariant, its Tamagawa number. The second, is a geometric invariant, the number of connected components of the moduli stack of G-tors...

We classify the unipotent character sheaves on a fixed connected component of a reductive algebraic group under a mild condition on the characteristic of the ground field.

We give a specific product decomposition of the base-point path connected component of the triple loop space of the suspension of the projective plane.

In general, not much is known about minimal submanifolds of Euclidean space of high codimension. In [1], Anderson studies complete minimal submanifolds of Euclidean space with finite total scalar curvature, trying to generalize classical results of minimal surfaces. More recently, Moore [10] continues the study of this kind of minimal submanifolds. Harvey and Lawson [6] also study a particular ...

We prove that there are only finitely many algebraically primitive Teichmüller curves in the minimal stratum in each prime genus at least 3. The proof is based on the study of certain special planes in the first cohomology of a translation surface which we call Hodge-Teichmüller planes. We also show that algebraically primitive Teichmüller curves are not dense in any connected component of any ...

The main result of the present paper is that the projective line over a ring R is connected with respect to the relation ``distant'' if, and only if, R is a GE2-ring. 2000 Mathematics Subject Classi®cation. 51C05, 20H25.

An n-tournament is an orientation of a complete n-partite graph. It was proved by J.A. Bondy in 1976 that every strongly connected n-partite tournament has an n-cycle. We characterize strongly connected n-partite tournaments in which a longest cycle is of length n and, thus, settle a problem in L. Volkmann, Discrete Math. 245 (2002) 19-53.

We investigate the structure of the bisector of point sites under arbitrary convex distance functions in three dimensions. Our results show that it is advantageous for analyzing bisectors to consider their central projection on the unit sphere, thereby reducing by one the dimension of the problem. From the concept of “silhouettes” and their intersections we obtain simple characterizations of im...