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Generalized Super-\v{C}erenkov Radiations (S\v{C}R), as well as their S\v{C}R-signatures are investigated. Two general S\v{C}R-coherence conditions are found as two natural extremes of the same spontaneous particles decays in (dielectric, nuclear or hadronic) media. The main results on the experimental test of the super-coherence conditions, obtained by using the experimental data from BNL, are presented. The interpretation of the observed anomalous \v{C}erenkov rings as experimental evidence for the HE-component of the S\v{C}R is discussed.

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