Let P∈Q[t,x] be a polynomial in two variables with rational coefficients, and let G the Galois group of P over field Q(t). It follows from Hilbert's Irreducibility Theorem that for most numbers c specialized P(c,x) has isomorphic to factors same way as P. In this paper we discuss methods computing obtaining an explicit description exceptional c, i.e., those which different or differently To ill...

A Hilbert manifold structure is described for the phase space F of asymptotically flat initial data for the Einstein equations. The space of solutions of the constraint equations forms a Hilbert submanifold C ⊂ F . The ADM energy-momentum defines a function which is smooth on this submanifold, but which is not defined in general on all of F . The ADM Hamiltonian defines a smooth function on F w...