We establish some identities relating two sequences that are, as explained, related to the Tribonacci sequence. One of these sequences bears the same resemblance to the Tribonacci sequence as the Lucas sequence does to the Fibonacci sequence. Defining a matrix that we call Tribomatrix, which extends the Fibonacci matrix, we see that the other sequence is related to the sum of the determinants o...

Abstract In this work a procedure to compute the dispersion curves for one dimensional viscoelastic waveguides exploiting the finite element based global mass matrix and complex stiffness matrix is proposed. The global matrices of a finite length portion of the waveguide, the unit cell, are post-processed by enforcing Bloch-type boundary conditions along the wave propagation direction and next ...

Abstract. Suppose f(x) is a polynomial with all of its roots on the real line. We show that the roots of f (x) are more evenly spaced than the roots of f(x). The same holds for polynomials with all their zeros on a circle, as well as an entire function of order 1 with all its zeros on a line. Applications are given to the Riemann zeta-function and its connection to random matrix polynomials. We...

We introduce real Lösungen as an analogue of roots. For each mutation sequence arbitrary skew-symmetrizable matrix, we define a family reflections along with associated vectors which are and set curves on Riemann surface. The matrix consisting these is called L-matrix. explain how the L-matrix naturally arises in connection C-matrix. Then conjecture that depends (up to signs row vectors) only s...

This paper presents fast and reliable condition estimates for the roots of a real polynomial based on the method of statistical condition estimation (SCE) by Kenney and Laub. Using relative perturbations, we provide both a basic implementation of SCE and an advanced one via the condition of the eigenvalues of the corresponding companion matrix. New results for estimating the condition of eigenv...