The convergence of spline collocation for strongly elliptic equations on curves

Summary Most boundary element methods for two-dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions. Here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order. The equations are collocated at the breakpoints for odd degree and the internodal midpoints for even degree splines. The crucial assumption for the generalized boundary integral and integro-differential operators is strong ellipticity. Our analysis is based on simple Fourier expansions. In particular, we extend results by J. Saranen and W.L. Wendland from constant to variable coefficient equations. Our results include the first convergence proof of midpoint collocation with piecewise constant functions, i.e., the panel method for solving systems of Cauchy singular integral equations.Dedicated to Prof. Dr. Dr. h.c. mult. Lothar Collatz on the occasion of his 75th birthdayThis work was begun at the Technische Hochschule Darmstadt where Professor Arnold was supported by a North Atlantic Treaty Organization Postdoctoral Fellowship. The work of Professor Arnold is supported by NSF grant BMS-8313247. The work of Professor Wendland was supported by the Stiftung Volkswagenwerk     

Oxygen quenching of tris(2,2′-bipyridine) ruthenium(II) complexes in thin organic films

A study is presented of the quenching, by oxygen, of the luminescence of tris(2,2′-bipyridine) ruthenium(II) complexes immobilized in thin, transparent, polymer-based films. The film media consist of a water-insoluble linear polymer plasticized with a trialkylphosphate ester, in which the complex ruthenium cations are solubilized by ion pairing with organophilic anions such as tetraphenylborate.

Luminescence lifetimes were studied in relation oxygen concentration in a gas stream contiguous with the film medium, film thickness and concentration of the metal complex within the film medium. It is shown that the microheterogeneous environment of the luminescent complex, which has recently been implicated in the non-linear quenching responses of polymer-immobilized, transition metal complex oxygen sensors, may arise simply as a consequence of the limited solubility of the complex in the film medium. When solubility is limited, the partial precipitation of the complex results in a colloidal of luminescent particles which exhibit non- uniform susceptibilities to quenching by oxygen. Good solubility, and therefore linear quenching characteristics, are promoted by methyl substitution of the bipyridyl ligand and by use of a plasticizer (tributylphosphate) with marked cation solvating powers.     

Synthesis of fluorinated 1,8-naphthyridinone derivatives

Processes for the synthesis of fluorinated 1,8-naphthyridinone derivatives including 6,7-difluoro-1,8-naphthyridin-2-one are described.     

Novel mass spectral fragmentation of heptafluorobutyryl derivatives of acyl analogues of platelet-activating factor

Direct derivatization of the acyl analogue of platelet-activating factor (acyl-PAF) with heptafluorobutyric anhydride results in replacement of the phosphocholine moiety with a heptafluorobutyryl (HFB) group. Electron capture (EC) mass spectrometric analysis of this compound that makes use of negative ion detection along with subsequent accurate mass measurement and tandem mass spectrometry studies revealed that in addition to expected fragmentation due to losses of elements of HF, ketene, and/or acetic acid, there is a rearrangement reaction between the HFB group and the substituent on carbon-2 of the glycerol backbone. For 2-acetyl isomers, this fragmentation yields a characteristic ion at m/z 237; for 1-acetyl isomers, the analogous ion is observed at [M-135]⁻, along with a corresponding carboxylate anion. The use of the HFB derivative is invaluable for analysis of PAF homologues and analogues because it provides detailed structural information in combination with the high sensitivity of a gas chromatography combined with EC-mass spectrometry assay.     

Chemical modification of a viral cage for multivalent presentation

Here we present generalized methods for chemically modifying the surface of a viral protein cage; this exploits the chemistry of native and engineered surface exposed functional groups for multivalent presentation of ligands.     

Charge-transfer hybrids containing covalently bonded polyoxometalates and ferrocenyl units

Two new charge-transfer hybrids with one or two ferrocenyl units covalently attached to a hexamolybdate cluster through an extended pi-conjugated bridge have been prepared using Pd-catalyzed coupling reactions on monoiodo- or diiodo-functionalized cluster substrates in over 60% yields. These hybrids have been characterized by (1)H NMR, FTIR, electrospray ionization mass spectrometry, and X-ray diffraction. The electronic spectra of these hybrids show a broad absorption tail extending beyond 550 nm, indicating the existence of charge-transfer transition from the ferrocenyl donor to the cluster acceptor. The observation of the clear charge-transfer transition indicates the contribution of charge-transfer resonance to the ground state in both 2a and 2b even though the donor-acceptor separation distance of 11.29 A is rather long, signaling a through-bond charge-transfer nature made possible by the organic pi-conjugated bridge. Cyclic voltammetry studies reveal a one-electron oxidation wave and a one-electron reduction wave for the hybrid with one ferrocenyl unit. For the one with two ferrocenyl units, a lower reduction potential and a two-electron oxidation wave are observed, indicating negligible electronic interactions between the two ferrocenyl units.     

Evaluation of cellulase preparations for hydrolysis of hardwood substrates

Seven cellulase preparations from Penicillium and Trichoderma spp. were evaluated for their ability to hydrolyze the cellulose fraction of hardwoods (yellow poplar and red maple) pretreated by organosolv extraction, as well as model cellulosic substrates such as filter paper. There was no significant correlation among hydrolytic performance on pretreated hardwood, based on glucose release, and filter paper activity. However, performance on pretreated hardwood showed significant correlations to the levels of endogenous β-glucosidase and xylanase activities in the cellulase preparation. Accordingly, differences in performance were reduced or eliminated following supplementation with a crude β-glucosidase preparation containing both activities. These results complement a previous investigation using softwoods pretreated by either organosolv extraction or steam explosion. Cellulase preparations that performed best on hardwood also showed superior performance on the softwood substrates.     

Fluorescence spectroscopy for monitoring deterioration of extra virgin olive oil during heating

The potential of fluorescence spectroscopy for characterizing the deterioration of extra virgin olive oil (EVOO) during heating was investigated. Two commercial EVOO were analysed by HPLC to determine changes in EVOO vitamin E and polyphenols as a result of heating at 170°C for 3 h. This thermal oxidation of EVOO caused an exponential decrease in hydroxytyrosol and vitamin E (R²=0.90 and 0.93, respectively) whereas the tyrosol content was relatively stable. At the same time, amounts of preformed hydroperoxides (ROOH), analysed by an indirect colorimetric method, decreased exponentially during the heating process (R²=0.94), as a result of their degradation into secondary peroxidation products. Fluorescence excitation spectra with emission at 330 and 450 nm were recorded to monitor polyphenols and vitamin E evolution and ROOH degradation, respectively. Partial least-squares calibration models were built to predict these indicators of EVOO quality from oil fluorescence spectra. A global approach was then proposed to monitor the heat charge from the overall fluorescence fingerprint. Different data pretreatment methods were tested. This study indicates that fluorescence spectroscopy is a promising, rapid, and cost-effective approach for evaluating the quality of heat-treated EVOO, and is an alternative to time-consuming conventional analyses. In future work, calibration models will be developed using a wide range of EVOO samples.