We consider a substitutive version of the Arnoux-Yoccoz Interval Exchange Transformation (IET) related to the Tribonacci substitution. We construct the so-called stepped lines associated to the fixed points of the substitution in the Abelianisation (symbolic) space. We analyse various projections of the stepped line recovering the Rauzy Fractal, a Peano Curve related to the work of Arnoux [1], ...

A proposal is made for what could well be the most natural symmetrical Riemannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant Riemannian curvature, that is, beyond the spaces which are homogeneous and isotropic, or, still, the spaces which satisfy the axiom of free mobility.

The article is dealing with novel and relatively complex computer system for automatic creation of human tissues geometrical models. Applications of the created models can be found in orthopedy, aesthetic surgery, dental surgery, etc. On the input are discrete volume CT/MR data in DICOM 3.0 data format. The models creation process consist of several steps: tissue segmentation, volume data vecto...

The thesis studies the following problem: Given a set of geometrical figures (such as planar polygons), each one labelled according to whether or not it resembles some "ideal" figure, find a good approximation to that ideal figure which can be used to classify other figures in the same way. We work within the PAC learning model introduced by Valiant in 1984. Informally, the concepts under consi...

We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.

This paper summarises a report (Brown, Jones & Taylor, 2003) to the UK Qualifications and Curriculum Authority of the work of one geometry group. The group was charged with developing and reporting on teaching ideas that focus on the development of geometrical reasoning at the secondary school level. The group was encouraged to explore what is possible both within and beyond the current require...

X iv :q ua nt -p h/ 06 05 07 9 v1 8 M ay 2 00 6 Geometrical aspects of entanglement Jon Magne Leinaas, Jan Myrheim and Eirik Ovrum (a) Department of Physics, University of Oslo, P.O. Box 1048 Blindern, 0316 Oslo, Norway (b) Centre of Mathematics for Applications, P.O. Box 1053 Blindern, 0316 Oslo, Norway and (c) Department of Physics, The Norwegian University of Science and Technology, 7491 Tro...

In this paper, we propose a novel classification algorithm, called geometrical probability covering (GPC) algorithm, to improve classification ability. On the basis of geometrical properties of data, the proposed algorithm first forms extended prototypes through computing means of any two prototypes in the same class. Then Gaussian kernel is employed for covering the geometrical structure of da...

We consider the wave and ray dynamics of an electromagnetic field in a parabolic dome microcavity. The structure of the fundamental s wave involves a main lobe in which the electromagnetic field is confined around the focal point in an effective volume of the order of a cubic wavelength, while modes with finite angular momentum have a structure that avoids the focal area and have correspondingl...

Generation of Bessel-like beam array from polymeric microstructures, which were created using four-beam interference lithography is demonstrated. Quality of the produced Bessel-like beams depends on the geometrical parameters of the manufactured axicon-like structures, and their shape can be efficiently controlled through the laser treatment parameters. The output beam characteristics indicate ...