Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.

     

Solid state NMR characterization of formation of poly(ϵ‐caprolactone)/maghnite nanocomposites by in situ polymerization

Results of multinuclear MAS NMR spectroscopy are reported for poly (ε‐caprolactone)/maghnite nanocomposite formation, with ε‐caprolactone in situ polymerized in the presence of maghnite, a proton exchanged montmorillonite clay. Exfoliated and intercalated materials with different maghnite loading in the range 3–15 wt % were investigated. ¹H NMR evidences Brønsted acid hydroxyl groups in the silicate layers and shows that their broad signal at 7.6 ppm present in the parent clay disappears in the nanocomposite material. ²⁷Al MAS NMR results show that beside the hexacoordinated aluminum signal, two additional peaks corresponding to two different tetrahedral Al sites are present in the clay framework. The NMR signal intensity of only one of them was found to be affected in the nanocomposites compared with the parent maghnite, suggesting that these specific aluminum sites are the reactive ones at the initial stages of the polymerization. However almost no changes occurred in the ²⁹Si NMR spectra, confirming that the polymer grafting, as indicated earlier by atomic force microscopy, took place on the aluminum tetracoordinated sites rather than on the silicon sites. A mechanism of maghnite surface catalyzed polymerization of ε‐caprolactone was proposed, involving Brønsted and Lewis acid sites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3060–3068, 2007     

Studies on the chemical constituents of the South China Sea sponge Phacellia fusca

Three pyrrololactam alkaloids have been isolated from the marine sponge Phacellia fusca Schmidt collected from the South China Sea, and their structures were determined as 1–3 , on the grounds of spectral data. This is the first report of these compounds from this sponge. The structure of 1 was confirmed by X-ray analysis.     

A study of electrostatic spring softening for dual-axis micromirror

Electrostatic spring softening is an important characteristic of electrostatically actuated dual-axis micromirror, since it lowers the resonant frequencies. This paper presents an approach based on approximating the electrostatic forces by the first-order Taylor's series expansion to investigate this characteristic. The dual-axis micromirror studied in this paper has three motion modes, two torsional (about x- and y-axis, respectively) and one translational (about z-axis). The stiffnesses of all these modes are softened by a DC bias voltage applied to the mirror plate. The resonant frequencies are lowered with the increment of the bias voltage. The relationship of the bias voltage and the resonant frequencies of all the motion modes is derived. The analytical results show that the resonant frequency curves are affected by the capacitor geometries, i.e. the gap between the mirror plate and the electrodes and the electrodes size. The lowering curves drop slowly when the bias voltage is small. While for large bias voltage, the lowering curves drop rapidly. The experiment results are consistent with those obtained by the analytical approach.     

Reactivity of polyesters in glycolysis reactions: Unexpected effect of the chemical structure of the polyester glycolic unit

Kinetic studies of PET glycolysis by diethylene glycol (DEG), dipropylene glycol (DPG), glycerol (Gly) and mixtures of these glycols have shown, in a previous study, that the order of reactivity of the glycols differs according to the conditions of temperature and catalysis. Indeed, their global reactivity depends both on their chemical reactivity and physico-chemical properties.Glycolysis of model polyesters which are liquid at the reaction temperature, which allows us to overcome the problem of the polyesters' solubility, were studied to compare the chemical reactivity of these glycols. Three oligoesters were synthesized from dimethyl terephthalate and three different glycols namely triethylene glycol, ethylene glycol and hexanediol to form, respectively, PE₃T, OET and PTHD.Results showed that the order of reactivity of the glycols is the same for PET, OET and PTHD but different for PE₃T. Indeed, DPG without catalyst has a particular and unexpected behaviour: its reactivity seems to be strongly influenced by the presence of oxygen atoms in the chain.     

Use of participant EQA results to assess sample homogeneity and stability for qualitative analytes

International requirements for PT and EQA state that providers must demonstrate that samples are homogeneous and stable. However, testing for homogeneity and stability can be expensive, use samples that could otherwise serve as quality-control materials, and can also fail to detect significant inhomogeneity and instability. In some situations it may be preferable to use the results from participants to identify problems with sample lots, if historic results follow predictable distributions and a statistical decision rule can be produced. An unusually high proportion of incorrect results may indicate that samples were inhomogeneous or unstable. Conditions under which this can be demonstrated are discussed, and the efficacy of the proposal is demonstrated with two examples. This procedure is especially effective when there are a large number of participants and/or a historic small proportion of incorrect results. Providers who adopt this proposal will need to retain samples for testing and assume the risk of distributing bad samples.Presented at the Eurachem PT Workshop September 2005, Portorož, Slovenia     

New Ba5M5−xPtxClO13 (M=Fe, Co) oxychlorides with layered perovskite-related structure

Crystals of Ba₅Fe_5−xPt_xClO₁₃ and Ba₅Co_5−yPt_yClO₁₃ were prepared for x=1.31, 1.51, 1.57, 1.59 and y=0, 0.97 and 1.08 in a BaCl₂ flux and investigated by X-ray diffraction methods. These compounds adopt a 10H perovskite structure built from the stacking of BaO₃ and BaOCl layers in the sequence (BaO₃)₄(BaOCl) with space group P6₃/mmc. The cation sites within the trimeric unit of face-sharing octahedra are occupied by Co or Fe and Pt ions, while the tetrahedral sites formed between BaO₃ and BaOCl layers are only occupied by Fe or Co. Moreover, oxygen stoichiometry indicates an average oxidation state for Co and Fe higher than +III, indicating the stabilization of Co⁴⁺ and Fe⁴⁺.     

Synthesis and antifolate activity of 8,10-dideazaminopterin

A synthesis of 8,10-dideazaminopterin, using 2,4-diamino-6-bromomethyl-8-deazapteridine ( 2 ) as a key intermediate, is described. Condensation of the triphenylphosphinylide derived from 2 with p-formylbenzoyl-L-glutamate afforded a 9,10-dehydro-8,10-dideazaminopterin ester intermediate 5 . Hydrogenation of the olefinic linkage and subsequent hydrolysis of the glutamate ester gave the title compound. 8,10-Dideazaminopterin was a potent growth inhibitor of folate dependent bacteria. It was 16 times more potent then methotrexate as an inhibitor of dihydrofolate reductase derived from L1210 leukemia cells, and showed strong activity against L1210 in mice.     

Chemiluminescence from the oxidation of urea and ammonia with hypobromite and N-bromosuccinimide

The spectral distribution for the chemiluminescent oxidation of ammonia with hypobromite is significantly different to that for the oxidation of ammonia with N-bromosuccinimide. Therefore, in contrast to the assumptions of several authors, the action of N-bromosuccinimide is not solely derived from the in situ formation of hypobromite. Neither the oxidation of urea with hypobromite nor the oxidation of urea with N-bromosuccinimide involves an initial hydrolysis of urea to ammonia in the alkaline solution. However, these two reactions lead to a common emitter. The addition of xanthene dyes, such as dichlorofluorescein, enhance the chemiluminescence intensity by energy transfer to the efficient fluorophore, but reaction between the sensitiser and hypobromite can result in a significant increase in the background signal. A list of potential interferences has been compiled; particular attention was paid to guanidino compounds, as the chemiluminescence accompanying the oxidation of this functional group has not been previously discussed.