Standard representations of irregular finite element meshes combine vertex data (sample coordinates and node values) and connectivity (tetrahedron–vertex incidence). Connectivity specifies how the samples should be interpolated. It may be encoded as four vertex-references for each tetrahedron, which requires 128m bits where m is the number of tetrahedra in the mesh. Our ‘Grow & Fold’ format red...

A new formula for the volume of a hyperbolic and spherical tetrahedron is obtained from the quantum 6j-symbol. This formula is of symmetric form with respect to the symmetry of the tetrahedron.

1 Abstract Standard representations of irregular nite element meshes combine vertex data sample coordinates and node values and connectivity tetrahedron-vertex incidence. Connectivity speciies how the samples should be interpolated. It may beencoded for each tetrahedron as four vertex-references,

The problem of equimomental systems a rigid body is considered. It shown that the system four equal masses located at vertices an isosceles tetrahedron to given body. A material points tetrahedron, which cometary nuclei 67P Churyumov-Gerasimenko, has been constructed.

Despite the rarity, large negative linear compressibility (NLC) was observed in metal-organic framework material Zn(HO3PC4H8PO3H)∙2H2O (ZAG-4) in experiment. We find a unique NLC mechanism in ZAG-4 based on first-principle calculations. The key component to realize its large NLC is the deformation of H3O(+) tetrahedron. With pressure increase, the oxygen apex approaches and then is inserted int...

A series of arylidine barbituric acid derivatives was synthesized by Knoevenagel condensation reaction of aromatic aldehydes with barbituric acid or thiobarbituric acid using dodecylbenzenesulfonic acid as a Brønsted acid-surfactant catalyst in aqueous media. Regardless of the nature of the substitution (electron-donating and -withdrawing), all the reactions were completed within 15-65 min in w...

We investigate charge-balanced hydrous magnesium and silicon defects [(2H)Mg, (4H)X Si] by first principles. Two new lowest-energy hydrogen configurations are proposed for (4H)Si. With these new configurations, the distribution of O-H stretching phonon frequencies in Group I (>3450 cm–1) are better reproduced. Substitution of silicon with four hydrogen atoms gives rise to significant elongation...