Characteristic polynomials of random unitary matrices have been intensively studied in recent years: by number theorists in connection with Riemann zetafunction, and by theoretical physicists in connection with Quantum Chaos. In particular, Haake and collaborators have computed the variance of the coefficients of these polynomials and raised the question of computing the higher moments. The ans...

The virial coefficients can be obtained from statistical mechanics in connection with the intermolecular potentials. The intermolecular potential of polyatomic molecules is usually assumed to consist of a spherically symmetric component plus a contribution due to asphericaity of the molecular charge distribution. In this study, the second virial coefficients have been calculated for N2...

For any sequence of polynomials {pk(t)} in one real or complex variable, where pk has degree k for k≥0, we find explicit expressions and recurrence relations infinite matrices whose entries are the numbers d(n,m,k), called linearization coefficients, that satisfypn(t)pm(t)=∑k=0n+md(n,m,k)pk(t),n,m≥0. pair polynomial sequences {uk(t)} e(n,m,k) satisfypn(t)pm(t)=∑k=0n+me(n,m,k)uk(t),n,m≥0. We als...

The Chebyshev-Boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closed-form expressions for these connection...

In sub-Riemannian geometry the coefficients of the Jacobi equation define curvature-like invariants. We show that these coefficients can be interpreted as the curvature of a canonical Ehresmann connection associated to the metric, first introduced in [15]. We show why this connection is naturally nonlinear, and we discuss some of its properties.

A theoretical proof of the computational function performed by a time-delayed neural network implementing a Hebbian associative learning-rule is shown to compute the equivalent of cross-correlation of time-series functions, showing the relationship between correlation coefficients and connection-weights. The values of the computed correlation coefficients can be retrieved from the connection-we...

This paper is devoted to the explicit computation of generating series for the connection coefficients of two commutative subalgebras of the group algebra of the symmetric group, the class algebra and the double coset algebra. As shown by Hanlon, Stanley and Stembridge (1992), these series gives the spectral distribution of some random matrices that are of interest to statisticians. Morales and...

We observe that polynomial measure modifications for families of univariate orthogonal polynomials imply sparse connection coefficient relations. We therefore propose connecting L2 expansion coefficients between a polynomial family and a modified family by a sparse transformation. Accuracy and conditioning of the connection and its inverse are explored. The connection and recurrence coefficient...