Stability theorems for wedges

Centerpoint Theorems for Wedges

The Centerpoint Theorem states that, for any set S of n points in R, there exists a point p in R such that every closed halfspace containing p contains at least dn/(d+ 1)e points of S. We consider generalizations of the Centerpoint Theorem in which halfspaces are replaced with wedges (cones) of angle α. In R, we give bounds that are tight for all values of α and give an O(n) time algorithm to f...

Stability theorems for cancellative hypergraphs

A cancellative hypergraph has no three edges A;B;C with ADBCC: We give a new short proof of an old result of Bollobás, which states that the maximum size of a cancellative triple system is achieved by the balanced complete tripartite 3-graph. One of the two forbidden subhypergraphs in a cancellative 3-graph is F5 1⁄4 fabc; abd; cdeg: For nX33 we show that the maximum number of triples on n vert...

Stability theorems for semi{groups via Multiplier theorems

Stability of Supersonic Boundary Layers Over Blunt Wedges

Receptivity and stability of supersonic boundary layers over blunt flat plates and wedges are numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 10/inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization a...

Existence and Stability of Supersonic Euler Flows past Lipschitz Wedges

It is well known that, when the vertex angle of a straight wedge is less than the critical angle, there exists a shock-front emanating from the wedge vertex so that the constant states on both sides of the shock-front are supersonic. Since the shock-front at the vertex is usually strong, especially when the vertex angle of the wedge is large, then such a global flow is physically required to be...