On ultra-high energy cosmic rays: origin in AGN jets and transport in   expanding Universe
  The cosmic ray source spectrum produced by AGN (Active Galactic Nucleus) jets is calculated. A distinctive feature of these calculations is the account for the jet distribution on kinetic energy. The expected cosmic ray spectrum at the Earth is determined with the use of a simple numerical code which takes into account interactions of ultra-high energy protons and nuclei with the background radiation in an expanding universe. 
V.S.Ptuskin, S.I.Rogovaya, V.N.Zirakashvili
astro-ph.CO hep-ph