PROPERTIES OF THE SCALAR UNIVERSAL EQUATIONS

The variational properties of the scalar so-called 'universal' equatio ns are reviewed and generalized. In particular, we note that each memb er of the Euler hierarchy may have an explicit field dependence. The E uler hierarchy itself is given a new interpretation in terms of the fo rmal complex of variational calculus, and is shown to be related to th e algebra of variational symmetries of the first source form.