In natural ionic solids, cationic and anionic species are alternately arranged to minimize electrostatic energy. Aggregation of identical ionic species is commonly prohibited due to the repulsive, long-range nature of Coulombic interactions. Recently, we synthesized unique ionic solids, [AuI4CoIII2(dppe)2(D-pen)4]X2·nH2O (dppe = 1,2-bis(diphenylphosphino)ethane, D-pen = D-penicillaminate), in w...

The packing of the title compound, [Na(C(9)H(5)ClNOS(2))(H(2)O)](n), in the crystal structure occurs by pairwise attachment of +sc- and -sc-arranged 4-(4-chloro-phen-yl)-2-thioxo-2,3-dihydro-thia-zol-3-olate subunits via S to sodium. Water mol-ecules that are bound in the axial position of the distorted octa-hedral coordination octahedron give rise to a stereogenic center at sodium.

Simple equations are derived that give the shapes of various convex polyhedra. The five regular polyhedra, called Platonic solids (the tetrahedron, hexahedron or cube, octahedron, dodecahedron and icosahedron), and polyhedra composed of crystallographically low-index planes are treated. The equations also give shapes that are nearly polyhedral with round edges, or intermediate shapes between a ...

In power generation and other production settings, technological constraints force restrictions on the number of time-periods that a machine must stay up once activated, and stay down once deactivated. We characterize the polyhedral structure of a model representing these restrictions. We also describe a cutting-plane method for solving integer programs involving such min-up and min-down times ...

We present the necessary and sufficient conditions for stability and instability of the stationary rotation of a system of n identical point vortices located at the same latitude on a sphere at vertices of a regular n-gon. We also examine stability of the equilibrium configuration of identical point vortices, situated at the vertices of a regular polyhedra. It is proved that vortex tetrahedron,...

Is every edge unfolding of every Platonic solid overlapfree? The answer is yes. In other words, if we develop a Platonic solid by cutting along its edges, we always obtain a flat nonoverlapping simple polygon. We also give self-overlapping general unfoldings of Platonic solids other than the tetrahedron (i.e., a cube, an octahedron, a dodecahedron, and an icosahedron), and edge unfoldings of so...

We will present that the forbidden minors for 3-realizable graph are K5 and the octahedron. You can directly go to Theorem 13 and if necessary refer to the definitions, lemmas and theorems before it. Definition 1 A graph G is d-realizable if, given any realization p1, · · · , pn of the graph in some finite dimensional Euclidean space, there exists a realization q1, · · · , qn in E with the same...

Density functional theory (DFT) including van der Waals weak interaction in conjunction with the so called rotational invariant DFT+U, where U is Hubbard of iron site, used to show that fluorinated spin crossover Fe(phen)2(NCS)2 molecule whether gas phase or adsorbed on Cu(001) surface switches from original low state high state. The calculated minimal energy path by means both nudged elastic b...