Exact Diagonalisation of The XY-Hamiltonian of Open Linear Chains with   Periodic Coupling Constants and Its Application to Dynamics of   One-Dimensional Spin Systems
  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 in the approximation of the next nearest interactions.   {\it Key words:} linear spin chain, nearest--neighbour approximation, three--diagonal matrices, diagonalisation, fermions, multiple--quantum NMR, multiple--quantum coherence, intensities of multiple--quantum coherences.   {\it PACS numbers:} 05.30.-d; 76.20.+q 
K.E.Feldman