A note on certain biorthogonal polynomials

Note on Certain Orthogonal Polynomials

A NOTE ON CERTAIN MATRICES WITH h(x)-FIBONACCI POLYNOMIALS

In this paper, it is considered a g-circulant, right circulant, left circulant and a special kind of tridiagonal matrices whose entries are h(x)-Fibonacci polynomials. The determinant of these matrices is established and with the tridiagonal matrices we show that the determinant is equal to the nth term of the h(x)-Fibonacci polynomials.

A note on biorthogonal ensembles

Abstract. We consider ensembles of random matrices, known as biorthogonal ensembles, whose eigenvalue probability density function can be written as a product of two determinants. These systems are closely related to multiple orthogonal functions. It is known that the eigenvalue correlation functions of such ensembles can be written as a determinant of a kernel function. We show that the kernel...

Interlacing properties of roots of certain biorthogonal polynomials

In this paper we consider the biorthogonal polynomials with respect to the maesure e −x 4 −y 2 +2τ xy dxdy, and show that their roots interlace. The proof involves showing total nonnegativity of matrices related to Jacobi type matrices.

A Note on Artinianess of Certain Generalized

Let ?: R0?R be a ring homomorphism and suppose that a and a0, respectively, are ideals of R and R0 such that is an Artinian ring. Let M and N be two finitely generated R-modules and suppose that (R0,m0) is a local ring. In this note we prove that the R-modules and are Artinian for all integers i and j, whenever and . Also we will show that if a is principal, then the R-modules and ...