The contribution in this paper is two-folded. First, a complete characterization is given of the square roots of a real nonsingular skew-Hamiltonian matrix W . Using the known fact that every real skew-Hamiltonian matrix has infinitely many real Hamiltonian square roots, such square roots are described. Second, a structure-exploiting method is proposed for computing square roots of W , skew-Ham...

We discuss the relationship between the multiple Hamiltonian structures of the generalized Toda lattices and that of the generalized Volterra lattices.

In this paper, we introduce the notions of C-numerical range and C-spectrum of matrix polynomials. Some algebraic and geometrical properties are investigated. We also study the relationship between the C-numerical range of a matrix polynomial and the joint C-numerical range of its coefficients.

in this paper, we introduce the concept of the   generalized aip-rings as a generalization of the generalized quasi-   baer rings   and generalized p.p.-rings. we show that the class of the generalized aip-rings is closed under direct products and morita invariance. we also characterize the 2-by-2 formal upper triangular matrix rings of this new class of rings. finally, we provide sever...

The quantum dynamics of a driven single-band tight-binding model is considered. The relation between this Hamiltonian and Hamiltonian of the discrete-charge mesoscopic quantum circuits is investigated. It is shown that the former Hamiltonian, with closed boundary conditions, can be considered as a realization of the generalized para-fermionic polynomial algebras.

We show that the notion of generalized Lenard chains allows to formulate in a natural way the theory of multi–separable systems in the context of bi–Hamiltonian geometry. We prove that the existence of generalized Lenard chains generated by a Hamiltonian function and by a Nijenhuis tensor defined on a symplectic manifold guarantees the separation of variables. As an application, we construct su...