In this article, we give a new version of n-tuple diamond-alpha H¨older inequality on time scales, result generalizes some results known in the literature. Second, present with two parameters scales. It is tool to generalize integral inequalities its goal create an restarted from left side parameter right parameters. Moreover, Minkowski given, and interesting are found.

The extent of mixed regions around convective zones is one the biggest uncertainties in stellar evolution. 1D overshooting descriptions introduce a free parameter ($f_{ov}$) that general not well constrained from observations. Especially small central value highly uncertain due to its tight connection pressure scale height. Long-term multi-dimensional hydrodynamic simulations can be used study ...