An equivariant Brauer semigroup and the symmetric imprimitivity theorem

Suppose that is a second countable locally compact transformation group. We let denote the set of Morita equivalence classes of separable dynamical systems where is a -algebra and is compatible with the given -action on . We prove that is a commutative semigroup with identity with respect to the binary operation for an appropriately defined balanced tensor product on -algebras. If and act freely and properly on the left and right of a space , then we prove that and are isomorphic as semigroups. If the isomorphism maps the class of to the class of , then is Morita equivalent to .

     

Synthesis of two dihydropyrroloindoledione‐based copolymers for organic electronics

Two novel dihydropyrroloindoledione (DPID)‐based copolymers have been synthesized in a two directional approach and characterized (gel permeation chromatography (GPC), ultraviolet‐visible (UV–vis), cyclic voltammetry, and computational models). These planar, broad absorption copolymers show promise for use in organic electronics, with deep energy levels and low bandgaps. The two‐directional Knoevenagel condensation used demonstrates the versatility of DPID as a useful yet underexploited conjugated unit. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

The phase behavior of a polymer‐fullerene bulk heterojunction system that contains bimolecular crystals

Polymer:fullerene blends have been widely studied as an inexpensive alternative to traditional silicon solar cells. Some polymer:fullerene blends, such as blends of poly(2,5‐bis(3‐tetradecylthiophen‐2‐yl)thieno[3,2‐b]thiophene (pBTTT) with phenyl‐c71‐butyric acid methyl ester (PC₇₁BM), form bimolecular crystals due to fullerene intercalation between the polymer side chains. Here we present the determination of the eutectic pBTTT:PC₇₁BM phase diagram using differential scanning calorimetry (DSC) and two‐dimensional grazing incidence X‐ray scattering (2D GIXS) with in‐situ thermal annealing. The phase diagram explains why the most efficient pBTTT:PC₇₁BM solar cells have 75–80 wt % PC₇₁BM since these blends lie in the center of the only room‐temperature phase region containing both electron‐conducting (PC₇₁BM) and hole‐conducting (bimolecular crystal) phases. We show that intercalation can be suppressed in 50:50 pBTTT:PC₇₁BM blends by using rapid thermal annealing to heat the blends above the eutectic temperature, which forces PC₇₁BM out of the bimolecular crystal, followed by quick cooling to kinetically trap the pure PC₇₁BM phase. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

The chromatic polynomial of fatgraphs and its categorification

Motivated by Khovanov homology and relations between the Jones polynomial and graph polynomials, we construct a homology theory for embedded graphs from which the chromatic polynomial can be recovered as the Euler characteristic. For plane graphs, we show that our chromatic homology can be recovered from the Khovanov homology of an associated link. We apply this connection with Khovanov homology to show that the torsion-free part of our chromatic homology is independent of the choice of planar embedding of a graph. We extend our construction and categorify the Bollobás-Riordan polynomial (a generalization of the Tutte polynomial to embedded graphs). We prove that both our chromatic homology and the Khovanov homology of an associated link can be recovered from this categorification.     

Use of ion mobility mass spectrometry and a collision cross‐section algorithm to study an organometallic ruthenium anticancer complex and its adducts with a DNA oligonucleotide

We report the development of an enhanced algorithm for the calculation of collision cross‐sections in combination with Travelling‐Wave ion mobility mass spectrometry technology and its optimisation and evaluation through the analysis of an organoruthenium anticancer complex [(η⁶‐biphenyl)Ru^II(en)Cl]⁺. Excellent agreement was obtained between the experimentally determined and theoretically determined collision cross‐sections of the complex and its major product ion formed via collision‐induced dissociation. Collision cross‐sections were also experimentally determined for adducts of this ruthenium complex with the single‐stranded oligonucleotide hexamer d(CACGTG). Ion mobility tandem mass spectrometry measurements have allowed the binding sites for ruthenium on the oligonucleotide to be determined. Copyright © 2009 John Wiley & Sons, Ltd.     

A versatile route to 3-(pyrimidin-4-yl)-imidazo[1,2-a]pyridines and 3-(pyrimidin-4-yl)-pyrazolo[1,5-a]pyridines

A two-step synthesis of 3-(2-chloropyrimidin-4-yl)imidazo[1,2-a]pyridines is presented. The late stage elaboration of the imidazopyridine through a cyclocondensation allows a rapid access to a variety of substitution patterns. The intermediate enol ethers were obtained from inexpensive reagents in a ligand-free Heck coupling. This methodology has been extended to the formation of pyrazolo[1,5-a]pyridines via a formal 1,3-dipolar cycloaddition.     

Shape changes induced by N-terminal platination of ubiquitin by cisplatin

The three-dimensional conformation of a protein is an important property and plays a key role in its biological activity. We show here that ion mobility-mass spectrometry (IM-MS) can be used to detect conformational changes in the protein ubiquitin in the gas phase induced by reaction with the anticancer drug cisplatin. The primary adduct was ubiquitin-{Pt(NH₃)₂} under denaturing conditions. Up to three different conformations appear to be generated upon platination depending on the charge state. The collision cross-sections (Ω) for each conformation indicate that the conformations of the platinated protein are contracted in size compared with unmodified ubiquitin with generally smaller Ω values. Ion mobility-tandem MS allowed determination of the platinum binding site without a requirement for prior Chromatographic separation. A rapid 30-min digestion of cisplatin-modified ubiquitin with trypsin allowed the platination site to be identified as the N-terminal methionine following low-energy collision-induced dissociation (CID) studies of the modified peptide. The data were generated using a Traveling-Wave based ion mobility-MS approach. Such cisplatin-induced shape changes may have a significant effect on its function in vivo. This work highlights the usefulness of the ion-mobility mass spectrometry technique for shedding new light on such protein interactions.     

The Wacker Process: Inner‐ or Outer‐Sphere Nucleophilic Addition? New Insights from Ab Initio Molecular Dynamics

The Wacker process consists of the oxidation of ethylene catalyzed by a Pd^II complex. The reaction mechanism has been largely debated in the literature; two modes for the nucleophilic addition of water to a Pd‐coordinated alkene have been proposed: syn‐inner‐ and anti‐outer‐sphere mechanisms. These reaction steps have been theoretically evaluated by means of ab initio molecular dynamics combined with metadynamics by placing the [Pd(C₂H₄)Cl₂(H₂O)] complex in a box of water molecules, thereby resembling experimental conditions at low [Cl^?]. The nucleophilic addition has also been evaluated for the [Pd(C₂H₄)Cl₃]^? complex, thus revealing that the water by chloride ligand substitution trans to ethene is kinetically favored over the generally assumed cis species in water. Hence, the resulting trans species can only directly undertake the outer‐sphere nucleophilic addition, whereas the inner‐sphere mechanism is hindered since the attacking water is located trans to ethene. In addition, all the simulations from the [Pd(C₂H₄)Cl₂(H₂O)] species (either cis or trans) support an outer‐sphere mechanism with a free‐energy barrier compatible with that obtained experimentally, whereas that for the inner‐sphere mechanism is significantly higher. Moreover, additional processes for a global understanding of the Wacker process in solution have also been identified, such as ligand substitutions, proton transfers that involve the aquo ligand, and the importance of the trans effect of the ethylene in the nucleophilic addition attack.     

On the inversion of diffusion NMR data: Tikhonov regularization and optimal choice of the regularization parameter

The analysis of diffusion NMR data in terms of distributions of diffusion coefficients is hampered by the ill-posed nature of the required inverse Laplace transformation. Na?ve approaches such as multiexponential fitting or standard least-squares algorithms are numerically unstable and often fail. This paper updates the CONTIN approach of the application of Tikhonov regularization to stabilise this numerical inversion problem and demonstrates two methods for automatically choosing the optimal value of the regularization parameter. These approaches are computationally efficient and easy to implement using standard matrix algebra techniques. Example analyses are presenting using both synthetic data and experimental results of diffusion NMR studies on the azo-dye sunset yellow and some polymer molecular weight reference standards.     

Beam thrust cross section for Drell-Yan production at next-to-next-to-leading-logarithmic order

At the LHC and Tevatron strong initial-state radiation (ISR) plays an important role. It can significantly affect the partonic luminosity available to the hard interaction or contaminate a signal with additional jets and soft radiation. An ideal process to study ISR is isolated Drell-Yan production, pp → X?+ ?- without central jets, where the jet veto is provided by the hadronic event shape beam thrust τB. Most hadron collider event shapes are designed to study central jets. In contrast, requiring τ B < 1 provides an inclusive veto of central jets and measures the spectrum of ISR. For τ B < 1 we carry out a resummation of α s(n)ln(m)τ B corrections at next-to-next-to-leading-logarithmic order. This is the first resummation at this order for a hadron-hadron collider event shape. Measurements of τ B at the Tevatron and LHC can provide crucial tests of our understanding of ISR and of τ B's utility as a central jet veto.