We show how to construct a stable hierarchical basis for piecewise quadratic C continuous splines defined on Powell–Sabin triangulations. We prove that this hierarchical basis is well suited for compressing surfaces. Our compression method does not require the construction of wavelets which are usually expensive to compute, but instead we construct a stable quasi-interpolation scheme for our sp...

This paper aims to study the flow of an incompressible, isothermal Eyring-Powell fluid in a helical screw rheometer. The complicated geometry of the helical screw rheometer is simplified by "unwrapping or flattening" the channel, lands, and the outside rotating barrel, assuming the width of the channel is larger as compared to the depth. The developed second order nonlinear differential equatio...

We give two different possibilities for subdivision of Powell–Sabin spline surfaces on uniform triangulations. In the first case, dyadic subdivision, a new vertex is introduced on each edge between two old vertices. In the second case, p 3–subdivision, a new vertex is introduced in the center of each triangle of the triangulation. We give subdivision rules to find the new control points of the ...

In this paper, we consider the recognition problem on two classes of perfectly orderable graphs, namely, the HHD-free and the Welsh-Powell opposition graphs (or WPOgraphs). In particular, we prove properties of the chordal completion of a graph and show that a modified version of the classic linear-time algorithm for testing for a perfect elimination ordering can be efficiently used to determin...

In this paper we construct Powell–Sabin spline multiwavelets on the hexagonal lattice in a shift-invariant setting. This allows us to use Fourier techniques to study the range of the smoothness parameter s for which the wavelet basis is a Riesz basis in the Sobolev space H(R), and we find that 0.431898 < s < 5/2. For those s, discretizations of H -elliptic problems with respect to the wavelet b...

Dynamic eet management problems are normally formulated as networks over dynamic networks. Additional realism usually implies the inclusion of complicating constraints, typically producing exceptionally large integer programs. In this paper, we present for the rst time the formulation of dynamic eet management problems in an optimal control setting, using a novel formulation called a Logistics ...