Electrochemical meso-functionalization of magnesium(II) porphine

Regioselective meso-functionalization of the totally unsubstituted magnesium(II) porphine was performed by controlled potential electrolysis with pyridine and triphenylphosphine as nucleophiles leading to the original pyridinium and phosphonium substituted derivatives, respectively. The crystallographic structure of the latter is described as the only meso-phosphonium porphyrin reported to date.     

Hétérocycles contenant du phosphore. XXII—Etude par RMP de dérivés de l'oxazaphospholane-1,3,2: II—Analyse des spectres de composés monosubstitués en 5 ou disubstitués en 4 et 5.

The influence of various factors (temperature, nature and concentration of solvent) or the utilisation of various physical methods (tickling or INDOR experiments, for example) are employed to analyse the PMR spectra of some 5-monosubstituted or 4,5-disubstituted 1,3,2-oxazaphospholane derivatives.     

The Fermi surface of In2Bi

De Haas van Alphen experiments in high magnetic fields up to 35 T are presented. Earlier results from lower magnetic field investigations are re-interpreted. A model for the Fermi surface of In₂Bi is proposed, consistent with the available experimental information, using the fact that the energy bands along AL are double-degenerate and that In₂Bi is a compensated metal. The proposed model is essentially a two band model.     

Phosphoranes par fermeture trans-annulaire: III—Conformation—configuration—labilité

The analysis of the n.m.r. spectra of the two isomers of 1,6,6-trimethyl-3-phenyl-2,8-dioxa-5-aza-1-phospha ^vbicyclo[3.3.0]octane allows us to propose a conformation for each 5-membered ring and for the configuration of the phosphorus atom. The lability of the H? P proton, revealed by high temperature experiments and by P? H ? P? D exchange, is significantly different in the two isomers.     

Heterocycles contenant du phosphore-XXI. Etude par RMP de déeriveés de l'oxazaphospholane-l,3,2: I-Analyse des spectres des composksés non substitués en 4 et 5.

The PMR spectra of the title 1,3,2-oxazaphospholane derivatives present an ABKLX pattern. The subspectral analysis of such a system shows that there are eight solutions. INDOR experiments permit the establishment of the energy diagram and the selection of the correct solution.     

Efficiently navigating a random Delaunay triangulation

Planar graph navigation is an important problem with significant implications to both point location in geometric data structures and routing in networks. However, whilst a number of algorithms and existence proofs have been proposed, very little analysis is available for the properties of the paths generated and the computational resources required to generate them under a random distribution hypothesis for the input. In this paper we analyse a new deterministic planar navigation algorithm with constant spanning ratio (w.r.t the Euclidean distance) which follows vertex adjacencies in the Delaunay triangulation. We call this strategy cone walk. We prove that given n uniform points in a smooth convex domain of unit area, and for any start point z and query point q; cone walk applied to z and q will access at most sites with complexity with probability tending to 1 as n goes to infinity. We additionally show that in this model, cone walk is ‐memoryless with high probability for any pair of start and query point in the domain, for any positive ξ. We take special care throughout to ensure our bounds are valid even when the query points are arbitrarily close to the border. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 95–136, 2016     

Molecular precursor route to bulk and silica-supported Nb2Mo3O14 using water-soluble oxo-oxalato complexes

The catalytically relevant Nb2Mo3O14 phase has been prepared in bulk and silica-supported forms via the so-called "multiple molecular precursors method" from water-soluble oxo-oxalato complexes of Nb and Mo, (NH4)3[NbO(ox)3].H2O, and (NH4)2[MoO3(ox)].H2O. Thermal treatment of the mixed Nb-Mo precursor has been optimized for the formation of the pure Nb2Mo3O14 phase, either as bulk oxide or a silica-supported phase with high specific surface area. A characterization of the bulk phase obtained via the conventional ceramic route has also been carried out and a comparison has been made with the precursors route. According to this route, the Nb2Mo3O14 phase is shown to be formed in a pure form at 700 degrees C (i.e., 100 degrees C below the lowest temperature reported so far for the formation of the phase by the ceramic method). The supported samples have appreciable specific surface areas of 60-70 m(2) g(-1), much larger than those reached in the previous attempts under vacuum in sealed vials. The SEM and EDX analyses reveal a high dispersion of the desired phase on the silica support.     

Weighted intriguing sets of finite generalised quadrangles

We construct and analyse interesting integer valued functions on the points of a generalised quadrangle which lie in the orthogonal complement of a principal eigenspace of the collinearity relation. These functions generalise the intriguing sets introduced by Bamberg et al. (Combinatorica 29(1):1?C17, 2009), and they provide the extra machinery to give new proofs of old results and to establish new insight into the existence of certain configurations of generalised quadrangles. In particular, we give a geometric characterisation of Payne??s tight sets, we give a new proof of Thas?? result that an m-ovoid of a generalised quadrangle of order (s,s ²) is a hemisystem, and we give a bound on the values of m for which it is possible for an m-ovoid of the four dimensional Hermitian variety to exist.