In the research of QSAR and QSPR correlations, topological indices such as Randi’c index, Zagreb ABC geometric-arithmetic index have been proposed to analyze bio-compatibility chemical compounds. Chemical graph theory is combination Chemistry Graph theory, this deals with topology mathematical study isomerism development which has applications in QSPR. article, we consider Octahedron networks f...

Fermi coordinates (FC) are supposed to be the natural extension of Cartesian coordinates for an arbitrary moving observer in curved space-time. Since their construction cannot be done on the whole space and even not in the whole past of the observer we examine which construction principles are responsible for this effect and how they may be modified. One proposal for a modification is made and ...

The weak binding of preformed metallic clusters to atomically smooth substrates has presented an impediment to the study of supported nanometer-size clusters using scanning probe techniques. The sweeping of supported clusters on flat substrates by a scanning probe tip has been identified as a problem. Unless special precautions are taken, only those clusters pinned at defect sites are routinely...

A diamond plate cut out of a transparent, colorless octahedral crystal gem quality, with small chromite inclusion in the core, sampled from XXIII CPSU Congress kimberlite (Yakutia, Mirny field, vicinities city), has been studied by several combined methods: absorption spectroscopy at different wavelengths (UV-visible, near- and mid-IR); photoluminescence, cathodoluminescence, Raman (local versi...

We study a recurrence defined on a three dimensional lattice and prove that its values are Laurent polynomials in the initial conditions with all coefficients equal to one. This recurrence was studied by Propp and by Fomin and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and conjectured that the coefficients were 1. Our proof establishes a bijection between the terms of the L...

Anyone familiar with the Sonobé module has probably assembled both the augmented octahedron and the augmented icosahedron Instructions for both appear in both Kasahara and Takahama and in Mukerji, and can also be found on most of the innumerable websites discoverable by googling the word “Sonobé”. Kasahara and Takahama give some sketchy instructions on how to build some other polyhedra with the...

A charge ordering phenomenon within the crystallographic sites as following Sr4(Fe0.143+Co0.363+)48h(Fe0.114+Co0.144+Co0.253+)48fO10.52 was previously reported thanks to neutron diffraction coupled with Mossbauer spectroscopy studies. Such distribution supports a natural magnetic layered structure combining both in-plane ferromagnetic super-exchange interactions mainly on octahedron “8 f” sub-l...