A new method of diagonalisation of the XY-Hamiltonian of inhomogeneous open linear chains with periodic (in space) changing Larmor frequencies and coupling constants is developed. As an example of application, multiple quantum dynamics of an inhomogeneous chain consisting of 1001 spins is investigated. Intensities of multiple quantum coherences are calculated for arbitrary inhomogeneous chains ...

The diagonalisation of the transfer matrices of solvable vertex models with alternating spins is given. The crystal structure of (semi-)infinite tensor products of finite dimensional Uq(ŝl2) crystals with alternating dimensions is determined. Upon this basis the vertex models are formulated and then solved by means of Uq(ŝl2) intertwiners.

An algorithm for blind source separation based on several time-delayed second-order correlation matrices is proposed. The technique to construct the unmixing matrix employs rst a whitening step and then an approximate simultaneous diagonalisation of several time-delayed second-order correlation matrices. Its eeciency and stability are demonstrated for linear artiicial mixtures with 17 sources.

We generalise theorems of Cochran-Lickorish and Owens-Strle to the case of links with more than one component. This enables the use of linking forms on double branched covers, Heegaard Floer correction terms, and Donaldson’s diagonalisation theorem to complete the table of unlinking numbers for nonsplit prime links with crossing number nine or less.

We discuss the phase diagram of the Shastry–Sutherland model for arbitrary spin S and derive rigorous lower and upper bounds on the phase boundaries of the dimer phase by using various versions of a variational ansatz in combination with the exact diagonalisation method.

Joint diagonalisation (JD) is a technique used to estimate an average eigenspace of a set of matrices. Whilst it has been used successfully in many areas to track the evolution of systems via their eigenvectors; its application in network analysis is novel. The key focus in this paper is the use of JD on matrices of spanning trees of a network. This is especially useful in the case of real-worl...

In this note we develop tools and techniques for the treatment of anisotropic thermo-elasticity in two space dimensions. We use a diagonalisation technique to obtain properties of the characteristic roots of the full symbol of the system in order to prove L–L decay rates for its solutions.

We construct the Darboux transformation with Dihedral reduction group for the 2–dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix we ...