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This paper presents some exact solutions of problems in random function theory for the purpose of testing the validity of an approximate method known variously in the many different fields of its application as first order smoothing theory, first order cumulant discard, quasilinear theory, or the adiabatic approximation. The hydromagnetic dynamo equations are used here, as particularly appropriate for such an investigation. The calculations show that in one case the exact and approximate solutions agree. In the other case the approximate solution is wrong. Hence, in the absence of a general criterion for validity, a result based on first order smoothing theory is a conjecture rather than a fact. This impacts strongly on much of the recent work on hydromagnetic dynamos.

Dyadic formalism to prove Herglotz-Noether theorem for flat manifolds

Time-dependent Green function for moving isotropic nondispersive medium

Homogeneous solutions of Einstein-Lichnerowicz equations for electrically charged fluid with infinite conductivity universes

Adiabatic invariants and third integrals of motion in periodic potentials in periodically time- dependent Hamiltonian systems of n degrees of freedom