Konstantinos Kontogiannis, András Sóbester University of Southampton, Southampton, UK Nigel Taylor MBDA, Filton, UK Nomenclature ICFA = Internal Conical Flow A α = osculating plane angle to the vertical axis β = effective shockwave angle γ = angle between shockwave profile and upper surface profile curve θ = inclination of the leading edge with respect to the horizontal plane λ = effective swee...

We study some sub-Riemannian objects (such as horizontal connectivity, horizontal connection, horizontal tangent plane, horizontal mean curvature) in hypersurfaces of sub-Riemannian manifolds. We prove that if a connected hypersurface in a contact manifold of dimension more than three is noncharacteristic or with isolated characteristic points, then given two points, there exists at least one p...

The Half-Plane Half-Comb walk is a random on the plane, when we have square lattice upper half-plane and comb structure lower half-plane, i.e., horizontal lines below x-axis are removed. We prove that probability this returns to origin in 2N steps asymptotically equal $$2/(\pi N).$$ 2 / ( ? N ) . As consequence, strong laws limit distribution for local time.

We exhibit a relation between folds and a tile of the plane. More precisely, given a -nite word coding vertical and horizontal folds we give a necessary and su/cient condition in order to tile the plane with a set of tiles constructed with copies of the unfold surface. c © 2004 Published by Elsevier B.V.

We investigate the motion of a liquid drop as it flows along the interface of a liquid film. Steady, two-dimensional solutions are found in the lubrication limit for a horizontal and inclined plane. The effects of the physical parameters on the interface shapes are studied. When the plane is inclined, solutions are found only for a special set of parameter values.