We present an algorithm for local subdivision of Powell-Sabin spline surfaces. The construction of such a spline is based on a particular PS-refinement of a given triangulation. We build the new triangulation on top of this PS-refinement by applying a √ 3-subdivision scheme on a local part of the domain. To avoid degeneration we introduce a simple heuristic for refinement propagation, driven by...

Widespread use of the Sabin live attenuated poliovirus vaccine has had tremendous impact on the disease worldwide, virtually eliminating it from a number of countries, including the United States. Early proof of its safety and effectiveness was presented in 1959 by Russian investigators, who had staged massive trials in the USSR, involving millions of children. Their positive results were at fi...

Penny, P. T. Correspondence. Influenza in schools. British Medical Journal i: 298 (1978). Sabin, A. B. Amantadine hydrochloride: analysis of data relating to its proposed use for the prevention of A2 influenza virus disease in human beings. Journal of the American Medical Association 200: 943-50 (1967). Sabin, A. B. Personal correspondence: amantadine and influenza (1978). Smorodintsev, A. A. e...

Two hundred forty pyridazinamine derivatives were tested for the ability to stabilize the antigenicity and infectivity of oral poliovirus vaccine subjected to 45 degrees C for 2 h. Seven compounds stabilized the antigenicity of all three vaccine strains and neutralized the viral particles in a way that is reversible by dilution. Of these, R 77975 (pirodavir) was selected for vaccine potency tes...

Hierarchical Powell-Sabin splines are C-continuous piecewise quadratic polynomials defined on a hierarchical triangulation. The mesh is obtained by partitioning an initial conforming triangulation locally with a triadic split, so that it is no longer conforming. We propose a normalized quasi-hierarchical basis for this spline space. The B-spline basis functions have a local support, they form a...

We present a multigrid algorithm for the solution of the linear systems that arise from a finite element discretization of second order elliptic partial differential equations with Powell-Sabin splines. We show that the method yields a uniform convergence independent of the mesh size.

We derive low-order, inf-sup stable and divergence-free finite element approximations for the Stokes problem using Worsey-Farin splits in three dimensions Powell-Sabin two dimensions. The velocity space simply consists of continuous, piecewise linear polynomials, where as pressure is a subspace constants with weak continuity properties at singular edges (3D) vertices (2D). discuss implementatio...