Relativistic Sunyaev-Zeldovich Effect for Clusters of Galaxies

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The Present research project "Relativistic Sunyaev-Zeldovich. Effect for Clusters of Galaxies" has successfully produced fruitful research results. First of all, we held International Workshop "Cosmology with SZ and X-Ray Observatories" at Sophia University for the period 2005 March 5-6. We invited 5 overseas researchers: K. Grainge (Cambridge), L Lamagna (Rome), L Knox (University of California, Davis), C. Li (Taipei), and J. Mohr (Illinois). The workshop turned out to be extremely successful. During the course of this research project we published 12 research papers in the refereed journals. The most recent published paper "An Improved Formula for the Relativistic Corrections to the Kinematical Sunyaev-Zeldovich Effect" (Nuovo Cimento, 121B, 487-500) summarizes most of our theoretical results. In this paper we have shown that the analytic results obtained by the Fokker-Planck expansion method agrees with the results obtained by the numerical integration of the Boltzmann equation with the accuracy better than 10-5 in the Rayleigh-Jeans regime. Our theoretical results are being used by the observers for their analysis of the Sunyaev-Zeldovich effect observations. In conclusion, the present research project "Relativistic Sunyaev-Zeldovich Effect fur Clusters of Galaxies" has achieved its initial prospective goal This evaluation is evidenced by the fact that the present head investigator was invited to give a lecture at the prestigious International School of Physics " Enrico Fermi" Course 159 held in Varenna, Italy, for the period 2004July 6-16.