grade control structures are hydraulic structures used to stabilize a river bed. scour downstream of this structure is the main cause of its failure. studies have developed numerous empirical relations for scour depth prediction that designers must choose between to decide the most effective equation for a specific application. this study tested the condition of submerged jets over beds of sedi...

We introduce a new family of jump operators on Borel equivalence relations; specifically, for each countable group $\Gamma$ we the $\Gamma$-jump. study elementary properties $\Gamma$-jumps and compare them with other previously studied operators. One our main results is to establish that many groups $\Gamma$, $\Gamma$-jump \emph{proper} in sense any relation $E$ strictly higher than reducibilit...