Corannulene and corazulene tiling of nanostructures

Tiling modification in nanostructure modeling can be achieved by map operations, as well as the well-known Stone-Wales bond rotation. In this respect, sequences of classical operations, or single generalized operations, were used to obtain corannulenic flowers and corannulene-like azulenic patterns. The first "corazulenic" tessellation is reported. The aromaticity of some cages tessellated by the above supra-faces is discussed in terms of several different criteria. The covering was given as a pi-electron partition within some Kekulé valence structures.The well-known geometric index of aromaticity HOMA (harmonic oscillator model of aromaticity) enabled the evaluation of local aromaticity of the discussed supra-faces and brought evidence for several dominant Kekulé valence structures. The most intriguing is the "Kekulé-Dewar" valence structure of the cage C(192) having a disjoint corazulenic tessellation.     

Synthesis of new polyaza heterocycles. Part 42: Diazines

Using Pd-catalyzed Stille cross-coupling reactions, we report here the synthesis of various mono- or bis(tri-n-butylstannyl)diazines which were reacted with various halogenated diazines to access to various polyaza heterocyclic derivatives.     

Parallel tensors and Ricci solitons in <Emphasis Type="Italic">N</Emphasis> (<Emphasis Type="Italic">k</Emphasis>)-quasi Einstein manifolds

The Eisenhart problem of finding parallel and symmetric tensors is considered in the framework ofN (k)-quasi Einstein manifolds and the result is connected with Ricci solitons. If the generator of the manifold provides a Ricci soliton then this is: i) shrinking on a class of conformally flat perfect fluid space-times and on quasi-umbilical hypersurfaces, in particular unit spheres; ii) expanding if the generator is of torse-forming type.     

The Size Distribution of Core Shell Polymeric Capsules as Revealed by Low-Field NMR Diffusometry

Time-dependent diffusion studies have been done on hexadecane molecules confined inside core shell polystyrene capsules in order to extract capsule-size distribution. The polymeric capsules were prepared by an emulsification–diffusion technique. The nuclear magnetic resonance (NMR) diffusometry technique implemented in our investigations is the so-called pulse gradient stimulated echo technique. With this technique, diffusion times between 20 and 500 ms could be probed. The distribution of the apparent diffusion coefficients was extracted using a numerical Laplace inversion. These data allowed us to obtain dimension distributions in good agreement with the direct observations from electron micrographs.     

Synthesis of nanosized zinc and magnesium chromites starting from PVA–metal nitrate solutions

In this article, we present a detailed study regarding the preparation of nanosized zinc and magnesium chromites starting from a 4% poly(vinyl)alcohol (PVA) aqueous solution and metal nitrates. The controlled thermal treatment of these solutions has permitted the isolation of an intermediary solid product, used as precursor of the preferred mixed oxides: zinc and magnesium chromites. The as-obtained precursors were characterized by FT-IR spectrometry and thermal analysis. FT-IR spectrometry has evidenced the disappearance of the NO₃ ^? anions at 140?°C, due to the redox interaction with PVA. The thermal decompositions of the synthesized precursors were different, as resulted from both thermal analysis and FT-IR spectrometry. Thus, while ZnCrPVA precursor decomposes up to 400?°C with formation of zinc chromite, the precursor MgCrPVA decomposes up to 500?°C, with formation of MgCrO₄ as intermediary amorphous phase. By thermal decomposition of MgCrO₄ at 500?°C, weakly crystallized MgCr₂O₄ powder is obtained. The obtained chromite powders consist of fine nanoparticles with diameters ranging from 10 to 30?nm at 500?°C; on raising the annealing temperature to 1000?°C, chromite particles become octahedral, with diameter up to 500?nm, but with no sign of sintering.     

Strain in Platonic fullerenes

Platonic fullerenes are those structures, either closed or open ones, covered by a single type of polygonal face. Excepting the graphite sheet, all the other nano-structures show non-zero strain energy. In this study, Platonic nanostructures, covered by polygonal faces f _k , k = 5–7, are designed and optimized at Hartree–Fock HF and DFT levels of theory. Next, their stability, in terms of total energy and HOMO–LUMO gap, strain energy (by POAV theory), HOMA index of aromaticity, and Kekulé structure count, is discussed. Vibrational spectra for the open fullerenes are also given.     

A convolution for complete and elementary symmetric functions

In this paper we give a convolution identity for complete and elementary symmetric functions. This result can be used to prove and discover some combinatorial identities involving r-Stirling numbers, r-Whitney numbers and q-binomial coefficients. As a corollary we derive a generalization of the quantum Vandermonde’s convolution identity.