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Dielectric relaxation spectroscopy (1 Hz - 20 GHz) has been performed on supercooled glass-formers from the temperature of glass transition (T_g) up to that of melting. Precise measurements particularly in the frequencies of MHz-order have revealed that the temperature dependences of secondary beta-relaxation times deviate from the Arrhenius relation in well above T_g. Consequently, our results indicate that the beta-process merges into the primary alpha-mode around the melting temperature, and not at the dynamical transition point T which is approximately equal to 1.2 T_g.

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