We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx2)(l x2)~1/2, k>0.

A series expansion method in three dimensional tomography is presented. While the function to be reconstructed is expanded in terms of spherical harmonics and orthogonal polynomials, the projection of the function is expanded in terms of Euler angles in the angular part and orthogonal polynomials in the radial part. The computer simulation of the reconstruction demonstrates the applicability of...

We present a new scale-invariant cost function for non-orthogonal joint-diagonalization of a set of symmetric matrices with application to Independent Component Analysis (ICA). We derive two gradient minimization schemes to minimize this cost function. We also consider their performance in the context of an ICA algorithm based on non-orthogonal joint diagonalization.

Polynomials orthogonal with respect to a perturbation of the Freud weight function by the addition of a mass point at zero are considered. These polynomials, called Freud-type orthogonal polynomials, satisfy a second order linear differential equation with varying polynomial coefficients. It plays an important role in the electrostatic interpretation for the distribution of zeros of the corresp...

An orthogonal double cover (ODC) of the complete graph Kn by some graph G is a collection of n spanning subgraphs of Kn, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kn is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n− 1 edges. We show that for any given positive integer d, al...

This paper describes the application of a combined orthogonal array design and overlapping resolution mapping to the optimization of miceller electrokinetic chromatography for the separation of 10 substituted benzenes. The most important factors were first determined according to an OA16(2(15)) through 16 pre-designed experiments; a second set of experiments was carried out according to a trian...