Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in the ‘quantum tetrahedron’. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R3, we use geometric quantization to obtain a Hilbert space of states. This Hilbert space has a basis of states labeled by the areas of the faces of the tetrahedron together wi...

Recent work on state sum models of quantum gravity in 3 and 4 dimensions has led to interest in thèquantum tetrahedron'. Starting with a classical phase space whose points correspond to geometries of the tetrahedron in R 3 , we use geometric quantization to obtain a Hilbert space of states. This Hilbert space has a basis of states labeled by the areas of the faces of the tetrahedron together wi...

India Human Development Survey was funded by grants R01HD041455 and R01HD061048 from the US National Institutes of Health and a supplementary grant from the Ford Foundation. Data analysis was funded by the UK government as part of its Knowledge Partnership Programme. We gratefully acknowledge inputs from Reeve Vanneman and Amaresh Dubey and participants in a roundtable on “Caring for the Elderl...

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...

The asymptotics of the quantum $6j$ symbols corresponding to a hyperbolic tetrahedron is investigated and first two leading terms are determined for case that has an ideal or ultra-ideal vertex. These given by volume determinant Gram matrix tetrahedron.