The real vector space of non-oriented graphs is known to carry a differential graded Lie algebra structure. Cocycles in the Kontsevich graph complex, expressed using formal sums on $n$ vertices and $2n-2$ edges, induce -- under orientation mapping infinitesimal symmetries classical Poisson structures arbitrary finite-dimensional affine manifolds. Willwacher has stated existence nontrivial cocyc...

The neighbor distribution in hard-sphere and hard-disk fluids is analyzed using Voronoi tessellation. The statistical measures analyzed are the nth neighbor coordination number (Cn), the nth neighbor distance distribution [fn(r)], and the distribution of the number of Voronoi faces (Pn). These statistics are sensitive indicators of microstructure, and they distinguish thermodynamic and annealed...

Sequences with zero autocorrelation are of interest because of their use in constructing orthogonal matrices and because of applications in signal processing, range finding devices, and spectroscopy. Golay sequences, which are pairs of binary sequences (i.e., all entries are \1) with zero autocorrelation, have been studied extensively, yet are known only in lengths 21026. Ternary complementary ...

This study aimed to answer two research questions. First, is pair programming more cost effective than solo programming in all situations? Second, in what situations is pair programming more cost effective than solo programming? We adopted and extended economic models specified by prior researchers. We examined two different scenarios and conducted simulations where we varied across a wide rang...

Relative concentrations of six isomeric Eu@C 72 -one based on the IPR C 72 cage (i.e., obeying the isolated-pentagon rule, IPR), two cages with a pentagon-pentagon junction (symmetries C 2 and C 2 v ), a cage with one heptagon, a cage with two heptagons, and a cage with two pentagon-pentagon fusions-are DFT computed using the Gibbs energy in a broad temperature interval. It is shown that the tw...

We show that every heptagon is a section of a 3-polytope with 6 vertices. This implies that every n-gon with n > 7 can be obtained as a section of a (2 + ⌊ n 7 ⌋ )dimensional polytope with at most ⌈ 6n 7 ⌉ vertices; and provides a geometric proof of the fact that every nonnegative n ×m matrix of rank 3 has nonnegative rank not larger than ⌈ 6min(n,m) 7 ⌉ . This result has been independently pro...