Another proof of Pell identities by using the determinant of tridiagonal matrix

In this paper, another proof of Pell identities is presented by using the determinant of tridiagonal matrices. It is calculated via the Laplace expansion

On Hessenberg and pentadiagonal determinants related with Fibonacci and Fibonacci-like numbers

In this paper, we establish several new connections between the generalizations of Fibonacci and Lucas sequences and Hessenberg determinants. We also give an interesting conjecture related to the determinant of an infinite pentadiagonal matrix with the classical Fibonacci and Gaussian Fibonacci numbers

Horadam sequences: A survey update and extension.

We give an update on work relating to Horadam sequences that are generated by a general linear recurrence formula of order two. This article extends a first ever survey published in early 2013 in this Bulletin, and includes coverage of a new research area opened up in recent times.N/

Dynamics of disordered harmonic lattices

Extensive numerical and analytic studies of vibrational spectra, normal modes, thermodynamic properties, and dynamical properties of harmonic systems with varying degrees of substitutional disorder have been made. The effects on observable properties of random mixtures of two or more species of atoms with differing masses and differing couplings to nearest-and next-nearest-neighbors have been investigated. Using the IBM-7030 digital computer, spectra for linear chains of 100,000 atoms have been obtained. Calculations in two and three dimensions have been limited to arrays of approximately 1000 atoms. Varying composition, mass ratio, and order affect the spectra in two and three dimensions in ways analogous to those effected in the linear chain. A physical interpretation of the complex nature of the disordered spectrum is given. The effects of disorder on the dynamics of binary disordered harmonic chains have been studied and have been found to be quite pronounced --Abstract, page ii