The bi-periodic Horadam sequence and some perturbed tridiagonal 2-Toeplitz matrices: A unified approach.

In this note we consider the so-called bi-periodic Horadam sequences. Explicit formulas in terms of Chebyshev polynomials of the second kind and the determinant of some perturbed tridiagonal 2-Toeplitz matrices are established. Several illustrative examples are provided as well.

On the constant coefficients of a certain recurrence relation: A simple proof.

In this note, we provide a short proof for the explicit formulas of the coefficients of a particular 3-term recurrence relation derived from a k-periodic recurrence. Any of the recurrences can be naturally interpreted in terms of determinants of Hessenberg matrices families.

Comment on "Thermal transport in dimerized harmonic lattices: Exact solution, crossover behavior, and extended reservoirs".

In this Comment we recall the notion of a tridiagonal 2-Toeplitz matrix and its spectrum, confronting these results with others obtained recently on exact solutions of thermal transport in dimerized harmonic lattices.

Class of cooperative stochastic models: Exact and approximate solutions, simulations, and experiments using ionic self-assembly of nanoparticles.

We present exact and approximate results for a class of cooperative sequential adsorption models using matrix theory, mean-field theory, and computer simulations. We validate our models with two customized experiments using ionically self-assembled nanoparticles on glass slides. We also address the limitations of our models and their range of applicability. The exact results obtained using matrix theory can be applied to a variety of two-state systems with cooperative effects.