“... nihil omnino in mundo contingint, in quo non maximi minimive ratio quapiam eluceat”, translated into “... nothing in all the world will occur in which no maximum or minimum rule is somehow shining forth”, used to say L.Euler in 1744. This is confirmed by numerous applications of mathematics in physics, mechanics, economy, etc. In this note, we show that it is also the case for the classica...

We introduce and study tetrahedron instantons, which can be realized in string theory by D$1$-branes probing a configuration of intersecting D$7$-branes flat spacetime with proper constant $B$-field. Physically they capture instantons on $\mathbb{C}^{3}$ the presence most general real codimension-two supersymmetric defects. Moreover, we construct as particular solutions instanton equations nonc...

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 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 reduces t...

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...

High yielding synthetic routes to 3’,5’-diamino-2’,3’,5’-trideoxycytidine and 3’,5’-diamino-2’,3’,5’-trideoxyadenosine are described. In addition, the protonation behavior of 3’,5’-diamino-2’,3’,5’-trideoxycytidine, 3’,5’-diamino-2’,3’,5’-trideoxyadenosine, 3’,5’diamino-3’,5’-dideoxythymidine, and 3’,5’-diamino-2’,3’,5’-trideoxyuridine has been studied by means of pH-metric measurements and NMR...