Multiple points of singular maps, Part II

Plane Maps with denominator. Part II: Noninvertible Maps with Simple Focal Points

This paper is the second part of an earlier work devoted to the properties specific to maps of the plane characterized by the presence of a vanishing denominator, which gives rise to the generation of new types of singularities, called set of nondefinition, focal points and prefocal curves. A prefocal curve is a set of points which are mapped (or “focalized”) into a single point, called focal p...

Distance-preserving Maps in Generalized Polygons Part II: Maps on Points and/or Lines

In this paper, we characterize isomorphisms of generalized polygons (in particular automorphisms) by maps on points and/or lines which preserve a certain fixed distance. In Part I, we considered maps on flags. Exceptions give rise to interesting properties, which on their turn have some nice applications. MSC 2000: 51E12

Asymptotics of Multivariate Sequences , Part I : Smooth Points Ofthe Singular

Asymptotics of Multivariate Sequences II: Multiple Points of the Singular Variety

Let F (z) = P r arz r be a multivariate generating function which is meromorphic in some neighborhood of the origin of C, and let V be its set of singularities. Effective asymptotic expansions for the coefficients can be obtained by complex contour integration near points of V. In the first article in this series, we treated the case of smooth points of V. In this article we deal with multiple ...

Generalized Helices and Singular Points

In this paper, we define X-slant helix in Euclidean 3-space and we obtain helix, slant helix, clad and g-clad helix as special case of the X-slant helix. Then we study Darboux, tangential darboux developable surfaces and their singular points. Especially we show that the striction lines of these surfaces are singular locus of the surfaces.