Equiangular tight frames with centroidal symmetry

An equiangular tight frame (ETF) is a set of unit vectors whose coherence achieves the Welch bound, and so is as incoherent as possible. Though they arise in many applications, only a few methods for constructing them are known. Motivated by the connection between real ETFs and graph theory, we introduce the notion of ETFs that are symmetric about their centroid. We then discuss how well-known constructions, such as harmonic ETFs and Steiner ETFs, can have centroidal symmetry. Finally, we establish a new equivalence between centroid-symmetric real ETFs and certain types of strongly regular graphs (SRGs). Together, these results give the first proof of the existence of certain SRGs, as well as the disproofs of the existence of others.     

On the flexibility of the design of multiple try Metropolis schemes

The multiple try Metropolis (MTM) method is a generalization of the classical Metropolis–Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities, show different numerical simulations and discuss the implications of the results.     

An International Laboratory Comparison Study of Volumetric and Gravimetric Hydrogen Adsorption Measurements

In order to determine a material's hydrogen storage potential, capacity measurements must be robust, reproducible, and accurate. Commonly, research reports focus on the gravimetric capacity, and often times the volumetric capacity is not reported. Determining volumetric capacities is not as straight-forward, especially for amorphous materials. This is the first study to compare measurement reproducibility across laboratories for excess and total volumetric hydrogen sorption capacities based on the packing volume. The use of consistent measurement protocols, common analysis, and figure of merits for reporting data in this study, enable the comparison of the results for two different materials. Importantly, the results show good agreement for excess gravimetric capacities amongst the laboratories. Irreproducibility for excess and total volumetric capacities is attributed to real differences in the measured packing volume of the material.     

Controlling the shape of the molecular weight distribution for tailored tensile and rheological properties in thermoplastics and thermoplastic elastomers

Thermoplastics and thermoplastic elastomers compose roughly 80 percent of all polymeric materials manufactured today and play an important role in numerous sectors of modern society. While the effects of molecular weight and dispersity (Ð) on the tensile and rheological properties of these materials are well-known, only recent studies have evidenced the profound influence of the shape of the molecular weight distribution (MWD) on polymer properties. This development is largely due to the emergence of new synthetic strategies to control higher moments of the MWD. In this Perspective, we describe recent advancements by our group in understanding the effect of MWD shape on the mechanical and rheological properties of thermoplastics and thermoplastic elastomers. We highlight means to exploit MWD shape for improved processability and performance and discuss future directions in this field.     

Catalytic properties of transition metal salts immobilized on nanoporous silica polyamine composites II: hydrogenation

The transition metal compounds Pd(OAc)₂, RhCl₃·4H₂O and RuCl₃ · nH₂O were adsorbed onto the nanoporous silica polyamine composite (SPC) particles (150–250 µm), WP‐1 [poly(ethyleneimine) on amorphous silica], BP‐1 [poly(allylamine) on amorphous silica], WP‐2 (WP‐1 modified with chloroacetic acid) and BP‐2 (BP‐1 modified with chloroacetic acid). Inductively coupled plasma‐atomic emission spectrometry analysis of the dried samples after digestion indicated metal loadings of 0.4–1.2 mmol g^?1 except for RhCl₃·4H₂O on BP‐2 which showed a metal loading of only 0.1 mmol g^?1. The metal loaded composites were then screened as hydrogenation catalysts for the reduction of 1‐octene, 1‐decene, 1‐hexene and 1, 3‐cyclohexadiene at a hydrogen pressure of 5 atm in the temperature range of 50–90 °C. All 12 combinations of SPC and transition metal compound proved active for the reduction of the terminal olefins, but isomerization to internal alkenes was competitive in all cases. Under these conditions, selective hydrogenation of 1,3‐cyclohexadiene to cyclohexene was observed with some of the catalysts. Turnover frequencies were estimated for the hydrogenation reactions based on the metal loading and were in some cases comparable to more conventional heterogeneous hydrogenation catalysts. Examination of the catalysts before and after reaction with X‐ray photoelectron spectroscopy and transmission electron microscopy revealed that, in the cases of Pd(OAc)₂ on WP‐2, BP‐1 and BP‐2, conversion of the surface‐ligand bound metal ions to metal nano‐particles occurs. This was not the case for Pd(OAc)₂ on WP‐1 or for RuCl₃ · nH₂O and RhCl₃· 4H₂O on all four composites. The overall results are discussed in terms of differences in metal ion coordination modes for the composite transition‐metal combinations. Suggested ligand interactions are supported by solid state CPMAS ¹³C NMR analyses and by analogy with previous structural investigations of metal binding modes on these composite materials. Copyright © 2011 John Wiley & Sons, Ltd.     

Attrition-enhanced total resolution leads to homochiral families of amino acid derivatives

The total resolution of five structurally similar racemizable amino acid derivatives, three of which have racemic crystal structures, was performed simultaneously. By enantioselective incorporation in an amino acid derivative that forms a conglomerate the other four were deracemized on attrition-induced grinding. The outcome of the resolution was random (R) or (S), but all compounds had the same absolute configuration and high enantiomeric purities.