Solving the frustrated spherical model withq-polynomials

Solving the Frustrated Spherical Model with q-Polynomials

We analyse the Spherical Model with frustration induced by an external gauge field. In infinite dimensions, this has been recently mapped onto a problem of qdeformed oscillators, whose real parameter q measures the frustration. We find the analytic solution of this model by suitably representing the q-oscillator algebra with q-Hermite polynomials. We also present a related Matrix Model which po...

Quaternion Zernike spherical polynomials

Abstract. Over the past few years considerable attention has been given to the role played by the Zernike polynomials (ZPs) in many di↵erent fields of geometrical optics, optical engineering, and astronomy. The ZPs and their applications to corneal surface modeling played a key role in this development. These polynomials are a complete set of orthogonal functions over the unit circle and are co...

Eulerian polynomials of spherical type

The Eulerian polynomial of a finite Coxeter system (W, S) of rank n records, for each k ∈ {1, . . . , n}, the number of elements w ∈ W with an ascent set {s ∈ S | l(ws) > l(w)} of size k, where l(w) denotes the length of w with respect to S. The classical Eulerian polynomial occurs when the Coxeter group has type An, so W is the symmetric group on n + 1 letters. Victor Reiner gave a formula for...

Harmonic polynomials and the spherical Laplacian

Evolutionary Strategies for Solving Frustrated Problems

The main elementary processes and strategies of evolution are investigated and described by simple mathematical models (stochastic networks). Special attention is devoted to Fisher-Eigen type models as well as to Boltzmann-, Darwin-and Haeckel-strategies modelling basic elements of frustrated problems in biological evolution respectively. Several applications of evolutionary strategies to frust...