Constructing a Tetrahedron with Prescribed Heights and Widths

iH CO r A TRACES , TERM RANKS , WIDTHS AND HEIGHTS

Elliptic solution for modified tetrahedron equations

As is known, tetrahedron equations lead to the commuting family of transfer-matrices and provide the integrability of corresponding three-dimensional lattice models. We present the modified version of these equations which give the commuting family of more complicated two-layer transfer-matrices. In the static limit we have succeeded in constructing the solution of these equations in terms of e...

Rapid synthesis of an electron-deficient t-BuPHOX ligand: cross-coupling of aryl bromides with secondary phosphine oxides.

Herein an efficient and direct copper-catalyzed coupling of oxazoline-containing aryl bromides with electron-deficient secondary phosphine oxides is reported. The resulting tertiary phosphine oxides can be reduced to prepare a range of PHOX ligands. The presented strategy is a useful alternative to known methods for constructing PHOX derivatives.

Construction of Three-Dimensional Improved-Quality Triangulations Using Local Transformations

Three-dimensional Delaunay triangulations are the most common form of three-dimensional triangulations known, but they are not very suitable for tetrahedral nite element meshes because they tend to contain poorly-shaped sliver tetrahedra. In this paper, we present an algorithm for constructing improved-quality triangulations with respect to a tetrahedron shape measure. This algorithm uses combi...

Polynomial Extension Operators. Part I

In this series of papers, we construct operators that extend certain given functions on the boundary of a tetrahedron into the interior of the tetrahedron, with continuity properties in appropriate Sobolev norms. These extensions are novel in that they have certain polynomial preservation properties important in the analysis of high order finite elements. This part of the series is devoted to i...