Polynomial extensions play a vital role in the analysis of the p and h-p FEM and the spectral element method. We construct explicitly polynomial extensions on standard elements: cubes, triangular prisms and pyramids, which together with the extension on tetrahedrons are used by the p and h-p FEM in three dimensions. These extensions are proved to be stable and compatible with FEM subspaces on t...

Platelet transfusions from donors matched for cross-reactive antigens have been shown to be effective in providing hemostasis in alloimmunized thrombocytopenic patients. A significant number of these transfusions, however, fail to provide posttransfusion platelet recoveries. We investigated incompatibility in the Bw4/bw6 system as a possible explanation for these failures. The Bw4/Bw6 system is...

In this paper, we study polynomials with only real zeros based on the method of compatible zeros. We obtain a necessary and sufficient condition for the compatible property of two polynomials whose leading coefficients have opposite sign. As applications, we partially answer a question proposed by M. Chudnovsky and P. Seymour in the recent publication [M. Chudnovsky, P. Seymour, The roots of th...