  In this paper, we are concerned with the local exact relationship for
third-order structure functions in the temperature equation, the inviscid MHD
equations and the Euler equations in the sense of Duchon-Robert type and Eyink
type. It is shown that the local version of Yaglom's $4/3$ law is valid for the
dissipation rates of conserved quantities such as the energy, cross-helicity
and helicity in these systems. In the spirit of Duchon-Robert's classical work,
we derive the dissipation term resulted from the lack of smoothness of the
solutions in corresponding conservation relation. It seems that these results
suggest that the Yaglom's law of the hydrodynamic equations holds if an
analogue of dissipation term as Duchon-Robert's is obtained. Base on this, the
first Yaglom's relation for the Oldroyd-B model and, inspired by the very
recent work due to Boutros-Titi, six new 4/3 laws for subgrid scale
$\alpha$-models of turbulence are also presented.
