Studies of resonance conditions on neutrino oscillations in matter
  We analytically discuss the resonance conditions among several neutrinos in matter. The discriminant for the characteristic equation of the Hamiltonian is expressed by the coefficients of the equation. The result of the computation for the discriminants tells us that the neutrino energy and the matter density are in inverse proportion to each other at the resonance states in not only 2- but also 3- and 4-neutrino models. 
Y. Kamo, S. Yajima, Y. Higasida, S.-I. Kubota, and S. Tokuo (Kumamoto   University)