Mixed methods on quadrilaterals and hexahedra

We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.     

Concise and enantioselective synthesis of the aminocyclitol core of hygromycin A

[reaction: see text] Stereoselective aminohydroxylation and dihydroxylation using osmium(VIII) oxidants enabled the short and efficient synthesis of the aminocyclitol core of hygromycin A. In addition to allowing the selective introduction of the heteroatoms N and O, the use of osmium (via an osmate ester) as a protecting group for a 1,2-glycol is also reported. This tactic allowed efficient differentiation of otherwise equivalent hydroxyl groups and allowed us to complete the synthesis in short order (14 steps) and excellent overall yield (12%).     

Efficient acyclic stereocontrol using the tethered aminohydroxylation reaction

[reaction: see text] The tethered aminohydroxylation (TA) of acyclic allylic carbamates has been achieved in a stereospecific and stereoselective manner. Unusually high levels of stereocontrol were observed in the oxidation of 1,1-disubstituted substrates.     

Observation of a multiply ionized plasma with index of refraction greater than one

We present clear experimental evidence showing that the contribution of bound electrons can dominate the index of refraction of laser-created plasmas at soft x-ray wavelengths. We report anomalous fringe shifts in soft x-ray laser interferograms of Al laser-created plasmas. The comparison of measured and simulated interferograms shows that this results from the dominant contribution of low charge ions to the index of refraction. This usually neglected bound electron contribution can affect the propagation of soft x-ray radiation in plasmas and the interferometric diagnostics of plasmas for many elements.     

The utility of ultra-performance liquid chromatography/electrospray ionisation time-of-flight mass spectrometry for multi-residue determination of pesticides in strawberry

The utility of ultra-performance liquid chromatography/orthogonal-acceleration time-of flight mass spectrometry (UPLC/TOFMS) for the rapid qualitative and quantitative analysis of 100 pesticides targeted in strawberry was assessed by comparing results with those obtained using a validated in-house UPLC tandem mass spectrometry (MS/MS) multi-residue method. Crude extracts from retail strawberry samples received as part of the 2007 annual UK pesticide residues in food surveillance programme were screened for the presence of pesticide residues using UPLC/TOFMS. Accurate mass measurement of positive and negative ions allowed their extraction following 'full mass range data acquisition' with negligible interference from background or co-eluting species observed during UPLC gradient separation (in a cycle time of just 6.5 min per run). Extracted ion data was used to construct calibration curves and to detect and identify any incurred residues (i.e. pesticides incorporated in or on the test material following application during cultivation, harvest and storage). Calibration using matrix-matched standards was performed over a narrow concentration range of 0.005-0.04 mg kg(-1) with determination coefficients (r2) > or =0.99 for all analytes with the exception of malathion/fenarimol/fludioxanil (r2 = 0.98), quassia/pymetrazine (r2 = 0.97) and fenthion sulfone (r2 = 0.95). Residues found in selected samples ranged from 0.025-0.28 mg kg(-1) and were in excellent agreement with results obtained using UPLC/MS/MS. Mass measurement accuracies of < or =5 ppm were achieved consistently throughout the separation, mass range and concentration range of interest thus providing the opportunity to obtain discrete elemental compositions of target ions.     

Rheological complexity in simple chain models

Dynamical properties of short freely jointed and freely rotating chains are studied using molecular dynamics simulations. These results are combined with those of previous studies, and the degree of rheological complexity of the two models is assessed. New results are based on an improved analysis procedure of the rotational relaxation of the second Legendre polynomials of the end-to-end vector in terms of the Kohlrausch-Williams-Watts (KWW) function. Increased accuracy permits the variation of the KWW stretching exponent beta to be tracked over a wide range of state points. The smoothness of beta as a function of packing fraction eta is a testimony both to the accuracy of the analytical methods and the appropriateness of (eta(0)-eta) as a measure of the distance to the ideal glass transition at eta(0). Relatively direct comparison is made with experiment by viewing beta as a function of the KWW relaxation time tau(KWW). The simulation results are found to be typical of small molecular glass formers. Several manifestations of rheological complexity are considered. First, the proportionality of alpha-relaxation times is explored by the comparison of translational to rotational motion (i.e., the Debye-Stokes-Einstein relation), of motion on different length scales (i.e., the Stokes-Einstein relation), and of rotational motion at intermediate times to that at long time. Second, the range of time-temperature superposition master curve behavior is assessed. Third, the variation of beta across state points is tracked. Although no particulate model of a liquid is rigorously rheologically simple, we find freely jointed chains closely approximated this idealization, while freely rotating chains display distinctly complex dynamical features.