In this paper, we give a ‘direct’ construction of the endomorphism ring of supersingular elliptic curves over a prime field Fp from ‘ideal classes’ of Q( √−p). We use the result to prove that the result of Kaneko on ‘minimal’ CM liftings of such supersingular elliptic curves is a best possible result. We also prove that the result of Elkies on ‘minimal’ CM liftings of all supersingular elliptic...

Multichannel microphone array designs often use the localisation curves that have been derived for 2-0 stereophony. Previous studies showed that side and rear perception of phantom image locations require somewhat different curves. This paper describes an experiment conducted to evaluate localisation curves using an octagonal loudspeaker setup. Interchannel level differences were produced betwe...

abstract in this research, a radial basis function artificial neural network (rbf-ann) model was developed to predict the hot deformation flow curves of api x65 pipeline steel. the results of the developed model was compared with the results of a new phenomenological model that has recently been developed based on a power function of zener-hollomon parameter and a third order polynomial functio...