‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

In 1935, G. I. Taylor invoked rotational symmetry to derive a remarkable formula for the turbulent dissipation rate. That derivation, though ingenious, leaves it unclear if truly conforms with symmetry. We use machinery of Lie groups furnish rigorous derivation Taylor's under and also not considered by Taylor, reflectional