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.

     

The Rate Constant for Dissociative Electron Attachment to Ozone Revisited

The rate constant for dissociative electron attachment to ozone has been derived over the energy range from about 0 to 10 eV using recently measured and also corrected cross section data. The new rate constant data sets for two partial dissociative channels, as well as for the total dissociative electron attachment, are compared with previously reported values, and existing discrepancies are discussed.     

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.     

Detection of Anti-Ulcer Drugs and Their Metabolites in Horse Urine by Liquid Chromatography – Mass Spectrometry

This paper describes a convenient method for the extraction and detection of eight anti-ulcer drugs simultaneously in horse urine, a relatively complex and viscous matrix, using a single-step liquid-liquid extraction followed by high-performance liquid chromatography – mass spectrometry (LC-MS). Anti-ulcer drugs were isolated from horse urine by salting out and liquid-liquid extraction. Detection of these drugs at concentrations below 1 ng mL^?1 could be achieved using LC-MS-MS in the positive atmospheric pressure chemical ionisation (APCI) mode. The above analysis was also extended to elimination studies of horses administered with ranitidine and omeprazole. The urinary elimination data of these two drugs suggest that ranitidine was eliminated from horse urine at a much slower rate than omeprazole. In addition, three ranitidine metabolites and six omeprazole metabolites were identified for the first time in equine urine samples.