Two procedures for partitioning large collections of highly intermixed datasets of different classes into a number of hyper-spherical or hyper-ellipsoidal clusters are presented. The incremental procedures are to generate a minimum numbers of hyper-spherical or hyper-ellipsoidal clusters with each cluster containing a maximum number of data points of the same class. The procedures extend the mo...

In this paper, we derive explicit product formulas and positive convolution structures for three continuous classes of Heckman-Opdam hypergeometric functions of type BC. For specific discrete series of multiplicities these hypergeometric functions occur as the spherical functions of non-compact Grassmann manifolds G/K over one of the (skew) fields F = R,C,H. We write the product formula of thes...

In this short note we propose a new method for construction new nice arrangement on the sphere Sd using the spaces of spherical harmonic.

We study integrable and superintegrable systems with magnetic field possessing quadratic integrals of motion on the three-dimensional Euclidean space. In contrast case without vector potential, corresponding may no longer be connected to separation variables in Hamilton-Jacobi equation can have more general leading order terms. focus two cases extending physically relevant cylindrical- spherica...

Consider a sequence of point sets on S, where each set X is a spherical ndesign with m points, where m = O(n), and where the spherical distance between points of X is at least λ/ √ m, for some λ common to all sets of the sequence. For each X of such a sequence, the Coulomb energy E(X) is bounded by E(X) 6 1 2 m2 + O(m). The first term and the order of the second term are the same as for the bou...

Self-dual plane graphs have been studied extensively. C. A. B Smith and W. T. Tutte published A class of self-dual maps in 1950 [9]; in 1992, Archdeacon and Richter [1] described a method for constructing all self-dual plane graphs and a second construction was produced by Servatius and Christopher [5] in 1992. Both constructions are inductive. In this paper, we produce four templates from whic...

If a fullerene is defined as a finite trivalent graph made up solely of pentagons and hexagons, embedding in only four surfaces is possible: the sphere, torus, Klein bottle, and projective (elliptic) plane. The usual spherical fullerenes have 12 pentagons; elliptic fullerenes, 6; and toroidal and Klein-bottle fullerenes, none. Klein-bottle and elliptic fullerenes are the antipodal quotients of ...

This paper considers the problem of shape-based recognition and pose estimation of 3-D free-form objects in scenes that contain occlusion and clutter. Our approach is based on a novel set of discriminating descriptors called spherical spin images, which encode the shape information conveyed by classes of distributions of surface points constructed with respect to reference points on the surface...

A new formula for predicting the mobility of spatial mechanisms is introduced. Instead of counting rigid links and the constraints between them, as is done in the usual Grübler-Kutzbach formulae, we count vertices and edges in a polyhedral model of the mechanism. It is well known that the conventional formula underpredicts the mobility of certain exceptional classes of mechanisms, and in partic...

Self-dual plane graphs have been studied extensively. C. A. B Smith and W. T. Tutte published A class of self-dual maps in 1950 [9]; in 1992, Archdeacon and Richter [1] described a method for constructing all self-dual plane graphs and a second construction was produced by Servatius and Christopher [5] in 1992. Both constructions are inductive. In this paper, we produce four templates from whic...