An X-ray absorption spectroscopy study of the local environment of iron in degradable iron–phosphate glasses

Degradable iron–phosphate glasses with the composition of (CaO)_0.30–(Na₂O)_0.20?x–(Fe₂O₃)_x–(P₂O₅)_0.50, x = 0.01–0.05, were studied by Fe K-edge X-ray absorption spectroscopy (both near-edge, XANES, and extended, EXAFS). The addition of up to 5 mol% iron oxide is known to enhance the durability of the phosphate glass while maintaining biocompatibility. The results from the two techniques used here both show that iron is in the Fe(III) oxidation state and has octahedral coordination. This suggests that Fe is cross-linking the phosphate chains and therefore strengthening the network structure, resulting improved chemical durability of the glasses.     

Arc Spaces and Equivariant Cohomology

We present a new geometric interpretation of equivariant cohomology in which one replaces a smooth, complex G-variety X by its associated arc space J _∞ X, with its induced G-action. This not only allows us to obtain geometric classes in equivariant cohomology of arbitrarily high degree, but also provides more flexibility for equivariantly deforming classes and geometrically interpreting multiplication in the equivariant cohomology ring. Under appropriate hypotheses, we obtain explicit bijections between $ \mathbb{Z} $ -bases for the equivariant cohomology rings of smooth varieties related by an equivariant, proper birational map. We also show that self-intersection classes can be represented as classes of contact loci, under certain restrictions on singularities of subvarieties. We give several applications. Motivated by the relation between self-intersection and contact loci, we define higher-order equivariant multiplicities, generalizing the equivariant multiplicities of Brion and Rossmann; these are shown to be local singularity invariants, and computed in some cases. We also present geometric $ \mathbb{Z} $ -bases for the equivariant cohomology rings of a smooth toric variety (with respect to the dense torus) and a partial flag variety (with respect to the general linear group).     

Okounkov bodies and toric degenerations

Let $\varDelta $ be the Okounkov body of a divisor $D$ on a projective variety $X$ . We describe a geometric criterion for $\varDelta $ to be a lattice polytope, and show that in this situation $X$ admits a flat degeneration to the corresponding toric variety. This degeneration is functorial in an appropriate sense.     

On non‐Hamiltonian circulant digraphs of outdegree three

We construct infinitely many connected, circulant digraphs of outdegree three that have no Hamiltonian circuit. All of our examples have an even number of vertices, and our examples are of two types: either every vertex in the digraph is adjacent to two diametrically opposite vertices, or every vertex is adjacent to the vertex diametrically opposite to itself. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 319–331, 1999     

Actions of Semisimple Lie Groups on Circle Bundles

Suppose G is a connected, simple, real Lie group with -rank(G) 2, M is an ergodic G-space with invariant probability measure , and : G × M Homeo( ) is a Borel cocycle. We use an argument of É. Ghys to show that there is a G-invariant probability measure on the skew product M × , such that the projection of to M is . Furthermore, if (G × M) Diff¹( ), then can be taken to be equivalent to × , where is Lebesgue measure on ; therefore, is cohomologous to a cocycle with values in the isometry group of .     

Detection and assessment of co‐association in inhalable drug particles using aerosol time‐of‐flight mass spectrometry

Aerosol Time‐of‐Flight Mass Spectrometry (AToFMS) was used to examine co‐association between two inhaled drugs, fluticasone propionate (FP) and salmeterol xinofoate (SX), in fine aerosolised particles emitted from Seretide®/Advair® inhaled combination products. Principal Component Analysis (PCA) was used to identify fragmentation patterns indicative of either pure or co‐associated particles (particles containing both drugs). A third component of the particles emitted from dry powder inhalers (DPIs), lactose, gave only a very weak mass spectral signal and no interpretable data was acquired for this compound; however, it was not found to interfere with the detection of the two drug substances. High levels of co‐association were found in the emitted doses from both pressurised metered dose inhaler (pMDI) and dry powder inhaler (DPI) products. Copyright © 2008 John Wiley & Sons, Ltd.     

Group homomorphisms inducing isomorphisms in cohomology

In this article, we call a ring R right generalized semiregular if for any a ∈ R there exist two left ideals P, L of R such that lr(a) = P⊕ L, where P ? Ra and Ra ∩ L is small in R. The class of generalized semiregular rings contains all semiregular rings and all AP-injective rings. Some properties of these rings are studied and some results about semiregular rings and AP-injective rings are extended. In addition, we call a ring R semi-π-regular if for any a ∈ R there exist a positive integer n and e ² = e ∈ a ⁿ R such that (1 ? e)a ⁿ  ∈ J(R), the Jacobson radical of R. It is shown that a ring R is semi-π-regular if and only if R/J(R) is π-regular and idempotents can be lifted modulo J(R).     

Heteroatoms and substituent effects: The importance of heteroatom hyperconjugation

We have found that the specific rate of α‐sulfonyl carbanion formation in a β‐substituted sulfone shows a sizable dependence on the H C_α C_β X torsion angle. Defining k_N = (k_exch)_X/(k_exch)_model (where the model has X = H or an alkyl group) we observed for a collection of β‐alkoxy sulfones (X = OR) acceptable agreement with the expression log k_N = a + b cos² θ (where a = 1.70 and b = 2.62). Extension to other β‐substituents (X = RS, R₂N, and R₃N⁺) yields the same pattern, with the last showing very large dependence of k_N on the torsion angle (b = 6.3). These observations are ascribed to the presence (in addition to the inductive and field effects) of negative hyperconjugation responsible for accelerations of 1000‐fold and more, deriving from donation of the incipient negative charge on carbon into the σ*_{C X} orbital in the transition state. These observations reflect, and at the same time underline, the importance of the low‐lying antibonding orbitals present in heteroatomic molecules. © 2002 Wiley Periodicals, Inc. Heteroatom Chem 13:397–405, 2002; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/hc.10067