Some inequalities for nonhomogeneous quadratic forms

For 0≤μ<1, functions f(μ) are obtained such that for any real indefinite quadratic form Q(x, y, z) of type (1,2) and determinant D and real x0, y0, zo, the inequality μ(f(μ) D)⅓< Q(x + x0, y + y0, z + z0)<(f((μ) D)⅓ has a solution in integers x, y, z. This result is used to prove that for any real quaternary from Q(x,y. z, t) of type (1,3) and determinant D and real numbers x0, y0, z0, t0, the inequality 0<Q(x + x0, y + y0, z + z0, t + t0)< 128/25(2√7-I) IDI)¼ has a solution in integers x, y. z, and t