An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...

Piezoelectric (strain) coefficients dij of quartz are calculated in terms of molecular dynamics as a function of pressure and temperature. We review the necessary formulas for the computation of electromechanical materials coefficients obtained at constant stress and temperature, and discuss how to overcome complications of the definition of polarization variations due to fluctuating box geomet...

A Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. The aim of this paper is to compute the automorphism group of the Euclide...

There are 339 combinatorial types of generic metrics on six points. They correspond to the 339 regular triangulations of the second hypersimplex ∆(6, 2), which also has 14 non-regular triangulations. 1. The Metric Fan We consider the cone of all metrics on the finite set {1, 2, . . . , n}: Cn = { d ∈ R( n 2 ) : dij ≥ 0 and dij + djk ≥ dik for all 1 ≤ i, j, k ≤ n } . This is a closed convex poin...

It is necessary to generate the automorphism group of a chemical graph in computer-aided structure elucidation. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce...

We show that if we expand the language of CAω by finitely many substitutions corresponding to bijective maps, then no quantifier free set of formulas containing only finitely many variables axiomatize RCAω. Let U be a set. Then B(U) is the boolean set algebra with unit U . Let τ : ω → ω, i, j < ω and X ⊆ U. Then sτ X = {s ∈ U : s ◦ τ ∈ X}, ci X = {t ∈ U : (∃s ∈ X)[t(j) = s(j) for all j 6= i]}, ...

We investigate, for the first time, navigation on networks with a Lévy walk strategy such that the step probability scales as pij ~ dij(-α), where dij is the Manhattan distance between nodes i and j, and α is the transport exponent. We find that the optimal transport exponent α(opt) of such a diffusion process is determined by the fractal dimension df of the underlying network. Specially, we th...

it is necessary to generate the automorphism group of a chemical graph in computer-aidedstructure elucidation. an euclidean graph associated with a molecule is defined by a weightedgraph with adjacency matrix m = [dij], where for i≠j, dij is the euclidean distance between thenuclei i and j. in this matrix dii can be taken as zero if all the nuclei are equivalent. otherwise,one may introduce dif...

A method is described for folding polymers to specific target conformations. The approach uses a fast but approximate dynamics algorithm, coupled with a genetic algorithm that is used to evolve the large number of free parameters needed. The dynamics algorithm uses a state transition matrix approach. At each time step, the distances between pairs of atoms are adjusted by shifting them from Dij ...

Magnetoelectric thin-film sensors based on the delta-E effect have widely been reported for detection of low frequency and small amplitude magnetic fields. Such are usually fabricated with microelectromechanical system technology, where aluminum nitride (AlN) is established piezoelectric material. Here, we present scandium (AlScN) instead compare it AlN using two identical design. The experimen...