Synthesis of Heptagon-Containing Polyarenes by Catalytic C−H Activation

Nanocarbons incorporating non-hexagonal aromatic rings - such as five-, seven-, and eight-membered rings - have various intriguing physical properties such as curved structures, unique one-dimensional packing, and promising magnetic, optical, and conductivity properties. Herein, we report an efficient synthetic approach to polycyclic aromatics containing seven-membered rings via a palladium-catalyzed intramolecular Ar−H/Ar−Br coupling. In addition to all-hydrocarbon scaffolds, heteroatom-embedded heptagon-containing polyarenes can be efficiently constructed with this method. Rhodium- and palladium-catalyzed sequential six- and seven-membered ring formations also afford complex heptagon-containing molecular nanocarbons from readily available arylacetylenes and biphenyl boronic acids. Detailed mechanistic analysis by DFT calculations showed the feasibility of seven-membered ring formation by a concerted metalation-deprotonation mechanism. This reaction can serve as a template for the synthesis of a wide range of seven-membered ring-containing molecular nanocarbons.     

Formation and isomerisation of theO-sulphito complex of 1,4,7,10,13-penta-azacyclohexadecanecobalt(III)

Summary Dissolved SO₂ reacts rapidly with [Co([16]aneN₅)OH]²⁺ to give [Co([16]aneN₅OSO₂]⁺([16]aneN₅=1,4,7,10, 13-penta-azacyclohexadecane), which on immediate acidification loses SO₂ to give [Co([16]aneN₅)OH₂]³⁺. The O-bonded sulphito complex (_max 526 nm) undergoes a slow linkage isomerisation to give the S-bonded species [Co([16]aneN₅)SO₃]⁺ (_max 466 nm), rather than an internal redox reaction. The S-bonded complex has been isolated and characterised as the perchlorate salt [Co([16]aneN₅) (SO₃H)](ClO₄)₂.     

Extracting Charge and Mass Information from Highly Congested Mass Spectra Using Fourier-Domain Harmonics

Native mass spectra of large, polydisperse biomolecules with repeated subunits, such as lipoprotein Nanodiscs, can often be challenging to analyze by conventional methods. The presence of tens of closely spaced, overlapping peaks in these mass spectra can make charge state, total mass, or subunit mass determinations difficult to measure by traditional methods. Recently, we introduced a Fourier Transform-based algorithm that can be used to deconvolve highly congested mass spectra for polydisperse ion populations with repeated subunits and facilitate identification of the charge states, subunit mass, charge-state-specific, and total mass distributions present in the ion population. Here, we extend this method by investigating the advantages of using overtone peaks in the Fourier spectrum, particularly for mass spectra with low signal-to-noise and poor resolution. This method is illustrated for lipoprotein Nanodisc mass spectra acquired on three common platforms, including the first reported native mass spectrum of empty “large” Nanodiscs assembled with MSP1E3D1 and over 300 noncovalently associated lipids. It is shown that overtone peaks contain nearly identical stoichiometry and charge state information to fundamental peaks but can be significantly better resolved, resulting in more reliable reconstruction of charge-state-specific mass spectra and peak width characterization. We further demonstrate how these parameters can be used to improve results from Bayesian spectral fitting algorithms, such as UniDec.

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Representations of Hecke Algebras and Dilations of Semigroup Crossed Products

A family of Hecke C^*-algebras can be realised as crossed productsby semigroups of endomorphisms. It is shown by dilating representationsof the semigroup crossed product that the category of representationsof the Hecke algebra is equivalent to the category of continuousunitary representations of a totally disconnected locally compactgroup.     

Dynamics of Decision Making in Animal Group Motion

We analyze a continuous-time model of a multi-agent system motivated by simulation studies on dynamics of decision making in animal groups in motion. Each individual moves at constant speed in the plane and adjusts its heading in response to relative headings of others in the population. The population includes two subgroups that are “informed” such that individuals in each subgroup have a preferred direction of motion. The model exhibits fast and slow time scales allowing for a reduction in the dimension of the problem. The stable solutions for the reduced model correspond to compromise by individuals with conflicting preferences. We study the global phase space for the proposed reduced model by computing equilibria and exploring stability and bifurcations. B. Nabet’s and N.E. Leonard’s work is supported in part by AFOSR grant FA9550-07-1-0-0528 and ONR grants N00014-02-1-0826 and N00014-04-1-0534. I.D. Couzin’s work was supported by the Royal Society, Balliol College and EPSRC grants GR/S04765/01 and GR/T11234/01, a Searle Scholar Award and DARPA grant HR001-05-1-0057. S.A. Levin’s work was supported in part by DARPA grant HR0011-05-1-0057 and NSF grant EF-0434319.     

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 .

     

Deformation of bilayer lipid membranes in bio-inspired materials and systems

Planar bilayer lipid membranes (BLMs) are currently employed to construct many bio-inspired material systems and structures. In order to characterize the pressure effects on the equilibrium configurations of these biological membranes, a novel continuum model is proposed. The BLM is assumed to be a two-layer Smectic A liquid crystal. The mean orientation of the amphiphilic molecules comprising the membrane is postulated to be perpendicular to the layers and each layer is idealized as a two dimensional liquid. Moreover, the BLM is modeled as a simply supported plate undergoing small deformations. It is subjected to a pressure load that acts perpendicularly to the layers. The equilibrium equations and boundary conditions are derived from the bulk elastic energy for Smectic A liquid crystals as described by de Gennes and Prost (1993) by using variational methods. The resulting fourth-order linear partial differential equation is solved by employing cylindrical functions and the series solution is proved to be convergent. The solution is numerically computed for values of the model parameters that are reported in the literature. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Precision model independent determination of |Vub| from B --> pilnu

A precision method for determining |V(ub)| using the full range in q(2) of B --> pilnu data is presented. At large q(2) the form factor is taken from unquenched lattice QCD, at q(2) = 0 we impose a model independent constraint obtained from B --> pipi using the soft-collinear effective theory, and the shape is constrained using QCD dispersion relations. We find |V(ub)| = (3.54 +/- 0.170 +/- 0.44) x 10(-3). With 5% experimental error and 12% theory error, this is competitive with inclusive methods. Theory error is dominated by the input points, with negligible uncertainty from the dispersion relations.