Using a similarity transformation that maps the Calogero model into N decoupled quantum harmonic oscillators, we construct a set of mutually commuting conserved operators of the model and their simultaneous eigenfunctions. The simultaneous eigenfunction is a deformation of the symmetrized number state (bosonic state) and forms an orthogonal basis of the Hilbert (Fock) space of the model. This o...

Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials introduced by Cariñena et al., [3]. We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical...

This work attempts to give a uniied treatment of sensitivity issues in problems involving the application of-orthogonal transformations. Algorithms for such problems are sometimes implemented with minor variations in the way elementary hyperbolic transformations are used to construct a-orthogonal transformation. This results in a possible variation in the condition of the elementary transformat...

The tensor representation has proven a successful tool as a mean to describe local multi-dimensional orientation. In this respect, the tensor representation is a map from the local orientation to a second order tensor. This paper investigates how variations of the orientation are mapped to variation of the tensor, thereby giving an explicit equivariance relation. The results may be used in orde...

This book aims to introduce the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Möbius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model — the use of 2-by-2 matrices in this context is elaborated. For eac...

The tensor representation has proven a successful tool as a mean to describe local multi-dimensional orientation. In this respect, the tensor representation is a map from the local orientation to a second order tensor. This paper investigates how variations of the orientation are mapped to variation of the tensor, thereby giving an explicit equivariance relation. The results may be used in orde...

This article introduces meta-modeling hierarchies additional to the conventional metamodeling hierarchy in a model-driven architecture. Additional hierarchies are introduced orthogonal to the conventional meta-modeling hierarchy for an appropriate correlation of information on combined hierarchies. In particular, orthogonal meta-modeling enables the grouping of models on the same conventional m...

To automatically construct a three-dimensional (3-D) object model, it is necessary to merge a set of range images acquired from different views. The iterative closest point (ICP) algorithm has been widely used to find the transformation parameters between a pair of images. In this paper, a fast ICP algorithm is proposed by restricting the search space to one-dimensional (1-D) orthogonal lines t...