We consider, in a superspace, new operator dependent noncommutative (NC) geometries of the nonlinear quantum Hall limit related to classes of f -deformed Landau operators in the spherical harmonic well. Different NC coordinate algebras are determined using unitary representation spaces of Fock-Heisenberg tensored algebras and of the Schwinger-Fock realisation of the su(1, 1) Lie algebra. A redu...

In a recent paper we proposed a possible generalization of L. Schwartz’s classical spectral synthesis result for continuous functions in several variables. The idea is based on Gelfand pairs and spherical functions while “translation invariance” is replaced by invariance with respect to the action of affine groups. In this paper we describe the function classes which play the role of the expone...

Combining the Mie scattering theory and a transfer matrix method, we investigate in detail the scattering of light by spherical Bragg "onion" resonators. We classify the resonator modes into two classes, the core modes that are confined by Bragg reflection, and the cladding modes that are confined by total internal reflection. We demonstrate that these two types of modes lead to significantly d...

In this research paper, the concept of hyperspherical/hyper-ellipsoidal separability is introduced. Method of arriving at the optimal hypersphere (maximizing margin) separating two classes is discussed. By projecting the quantized patterns into higher dimensional space (as in encoders of error correcting code), the patterns are made hyper-spherically separable. Single/multiple layers of spheric...

A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the shells are treated separately with constructive filtered polynomial approximation. The approximation error with respect to the supremum norm is shown to decay alg...

Hecke algebras were first studied because of their role in the representation theory of p-adic groups, or algebraic groups over 1-dimensional local fields. There are two important classes of Hecke algebras. One is spherical Hecke algebras attached to maximal compact open subgroups, and the other is Iwahori-Hecke algebras attached to Iwahori subgroups. A spherical Hecke algebra is isomorphic to ...

Global change research has placed new demands on methods of spatial analysis. In particular, spherical methods for spatial interpolation are required when spatial analyses are performed over large areas of the Earth's surface. In this article, spherical spatial interpolation procedures are reviewed, compared, and evaluated. Three classesof spherical interpolants are evaluated in detail: distanc...

In this note we discuss the structure of systems of coupled cells (which we view as systems of ordinary differential equations) where symmetries of the system are obtained through the group G of global permutations of the cells and the group L of local internal symmetries of the dynamics in each cell. We show that even when the cells are assumed to be identical with identical coupling, the way ...

The good sheik evidently holds the Copernican theory to be a "mere theory," not a "fact." In this he is technically correct. A theory can be verified by a mass of facts, but it becomes a proven theory, not a fact. The sheik was perhaps unaware that the Space Age had begun before he asked the king to suppress the Copernican heresy. The sphericity of the earth has been seen by astronauts, and eve...

We use techniques of Bannai and Sloane to give a new proof that there is a unique (22, 891, 1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in the uniqueness proof given by Bannai and Sloane for the (23, 4600, 1/3) spherical code.