hydraulic jump on adverse stilling basin is an unstable phenomenon which causes some complexities in controlling of the   jump. this paper considers the stability of free hydraulic jump on adverse stilling basins from a theoretical point of view. a minimum value of upstream froude number is needed to produce the free hydraulic jump on adverse stilling basins which was presented by a theoretical...

We obtain sufficient conditions, easily verifiable, for the existence and uniqueness of piecewise smooth solutions of a linear two-point boundaryvalue problem with general interface conditions. The coefficients of the differential equation may have jump discontinuities at the interface point. As an example, the conditions obtained are applied to a problem with typical interface such as perfect ...

Based on the uncertain optimal control with jump, in this paper, we study a special optimal control problem: linear quadratic uncertain optimal control problem with jump which has a quadratic objective functional for a linear uncertain control system with jump. We obtain the necessary and sufficient conditions for the existence of optimal control.

A jump system is a set of lattice points satisfying a certain " two-step " axiom. A Manhattan set is the convex hull of a two-dimensional jump system. Taking multiple Manhattan sets, in layers, forms a three-dimensional object. We determine under what conditions this object is, in turn, a jump system.