Keywords :
Spectral curvature0003-4916/$ - see front matter 2006 Elsevier Inc. All rights reserved.doi:10.1016/j.aop.2006.11.005* Fax: +81 824 240717.E-mail address: tom@geminga.orgAnn , Spectral averaging , Tachyonic c-rays , Superluminal radiation , cosmic rays