Learning objects along with their sequencing are being studied to support efficient e-learning systems. They could solve the problem of costly reproduction of learning materials for e-learning systems. The problem arising here is related to the size and complexity of methods used to achieve the appropriate composition of learning objects in order to generate courses with pedagogic efficiency an...

We give elementary and explicit arguments to show that the geodesic ow on the unit tangent bundle of a two dimensional Riemannian manifold with constant negative curvature provides an example of a \fast" dynamo for the magnetic kinematic dynamo equation.

412 NOTICES OF THE AMS VOLUME 51, NUMBER 4 Billiards are dynamical systems. In the simplest case, a “billiard table” is a compact domain Q ⊂ Rd with a piecewise smooth boundary. For a large part of the theory the class of smoothness plays no role. The reader is invited to think about components of the boundary ∂Q as subsets of C∞-submanifolds of codimension 1. The phase space M of the billiard ...

We study the geometric properties of the base manifold for the unit tangent bundle satisfying the η-Einstein condition with the standard contact metric structure. One of the main theorems is that the unit tangent bundle of 4-dimensional Einstein manifold, equipped with the canonical contact metric structure, is ηEinstein manifold if and only if base manifold is the space of constant sectional c...

For these distributions only the leading vehicle in a platoon has its speed measured. The rationale for measuring these is to get an estimate of the desired speed of traffic at the point of measurement. The distributions in Figure 1 are of this type. They are produced by combining the results of a number of surveys at different sites into a representative distribution weighted by the traffic fl...

In this article we give a geometric interpretation of the Hitchin component T (Σ) ⊂ Rep(π1(Σ),PSL4(R)) of a closed oriented surface of genus g ≥ 2. We show that representations in T (Σ) are precisely the holonomy representations of properly convex foliated projective structures on the unit tangent bundle of Σ. From this we also deduce a geometric description of the Hitchin component T (Σ, Sp4(R...

Modeling data on the sphere is fundamental to many problems in the geosciences. Classical approaches to these problems are based on expansions of spherical harmonics and/or approximations on latitude/longitude based grids. The former are quite algorithmically complex, while the latter suffer from the notorious pole problem. Additionally, neither of the methods can be easily generalized to other...

with respect to the Gaussian measure. Macdonald extended it from An−1 to other root systems and verified his conjecture for classical ones by means of the Selberg integrals [M1]. It was established by Opdam in [O1] in full generality using the shift operators. The integral is an important normalization constant for a k-deformation of the Hankel transform introduced by Dunkl [D]. The generalized...

A vertex in a mesh surface with planar faces may have the property that offsetting all the face planes incident with the vertex by a constant distance leads to planes which intersect again in a common point. This is equivalent to the property that the planes, consistently oriented via the connectivity of the mesh, are tangent to an oriented cone of revolution. We show that for vertices of valen...

Segmentation is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational approach and partial differential equation modelling. Wavelets have been used successfully in various problems in image processing, including segmentation, inpainting, noise removal, super-resolution image restora...