Wavelet Filter Functions,the Matrix Completion Problem,and Projective Modules Over <Emphasis Type="Italic">C</Emphasis>(<Emphasis Type="Bold">T</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>)

We discuss how one can use certain filters from signal processing to describe isomorphisms between certain projective C(T ⁿ )-modules. Conversely, we show how cancellation properties for finitely generated projective modules over C(T ⁿ ) can often be used to prove the existence of continuous high pass filters, of the kind needed for multivariate wavelets, corresponding to a given continuous low-pass filter. However, we also give an example of a continuous low-pass filter for which it is impossible to find corresponding continuous high-pass filters. In this way we give another approach to the solution of the matrix completion problem for filters of the kind arising in wavelet theory.     

Investigation of two phase flow and phase trapping by secondary imbibition within Fontainebleau sandstone

Pulsed magnetic field gradient stimulated echo NMR is used to investigate the simultaneous flow of two phases (an aqueous phase and an hydrocarbon phase) within a strongly water-wet sample of Fontainebleau sandstone. The Fontainebleau sandstone is prepared in increasing steady-state water saturations by a secondary imbibition process. The increase in the water saturation causes an increasing fraction of the oil phase (non-wetting phase) to become trapped within the sample. The stimulated echo dependence on the gradient pulse area, q, is used to derive the displacement probability, PX, for a fixed observation time. These displacement probabilities clearly show the progressive trapping of the hydrocarbon phase with increasing steady-state water saturations. Quantitative measurements of the fraction of the oil phase trapped were made from the echo attenuation function Edelta(q), both as a function of water saturation and observation time.     

Magnetic resonance in porous media: forty years on

A personal view of the field of magnetic resonance in porous media is presented in which an attempt is made to survey the current status and achievements, to highlight some of the contributions made by my group over the years and, at the end, to try and identify where further effort and growth points may be perceived. All this is done with the knowledge that the first and last sections are certain to be partial, incomplete and wrong, at least in part, and that the middle section describes work carried out by some of the many excellent students, post-doctoral researchers and other colleagues with whom it has been a pleasure to collaborate over a forty year research career.     

Validation of an inductively coupled plasma mass spectrometry (ICP-MS) method for the determination of cerium, strontium, and titanium in ceramic materials used in radiological dispersal devices (RDDs)

This work describes the optimization of a cloud point extraction (CPE) method for casein proteins from cow milk samples. To promote phase separation, polyoxyethylene(8) isooctylphenyl ether (Triton^® X-114) and sodium chloride (NaCl) were used as nonionic surfactant and electrolyte, respectively. Using multivariate studies, four major CPE variables were evaluated: Triton^® X-114 concentration, sample volume, NaCl concentration, and pH. The results show that surfactant concentration and sample volume were the main variable affecting the CPE process, with the following optimized parameters: 1% (w/v) Triton^® X-114 concentration, 50 μL of sample volume, 6% (w/v) NaCl concentration and extractions carried out at pH 7.0. At these conditions, 923 ± 66 and 67 ± 2 μg mL⁻¹ of total protein were found in the surfactant-rich and surfactant-poor phases, respectively. Finally, matrix-assisted laser desorption ionization-time of flight mass spectrometry (MALDI-TOF MS) was then used to evaluate those target proteins (_s1-casein, _s2-casein and β-casein) separation as well as to check the efficiency of the extraction procedure, making a fingerprint of those target proteins possible.     

Structural Feature Ions for Distinguishing N- and O-Linked Glycan Isomers by LC-ESI-IT MS/MS

Glycomics is the comprehensive study of glycan expression in an organism, cell, or tissue that relies on effective analytical technologies to understand glycan structure–function relationships. Owing to the macro- and micro-heterogeneity of oligosaccharides, detailed structure characterization has required an orthogonal approach, such as a combination of specific exoglycosidase digestions, LC-MS/MS, and the development of bioinformatic resources to comprehensively profile a complex biological sample. Liquid chromatography-electrospray ionization-mass spectrometry (LC-ESI-MS/MS) has emerged as a key tool in the structural analysis of oligosaccharides because of its high sensitivity, resolution, and robustness. Here, we present a strategy that uses LC-ESI-MS/MS to characterize over 200 N- and O-glycans from human saliva glycoproteins, complemented by sequential exoglycosidase treatment, to further verify the annotated glycan structures. Fragment-specific substructure diagnostic ions were collated from an extensive screen of the literature available on the detailed structural characterization of oligosaccharides and, together with other specific glycan structure feature ions derived from cross-ring and glycosidic-linkage fragmentation, were used to characterize the glycans and differentiate isomers. The availability of such annotated mass spectrometric fragmentation spectral libraries of glycan structures, together with such substructure diagnostic ions, will be key inputs for the future development of the automated elucidation of oligosaccharide structures from MS/MS data.

Determining a 'safe' high-mass limit in matrix-assisted laser desorption/ionisation time-of-flight mass spectra of coal derived materials with reference to instrument noise

Three methods for determining a 'safe' estimate for high-mass limits of MALDI spectra of coal derived liquids were explored, using a sample of coal-tar pitch and its pyridine-insoluble fraction. Co-addition of increasing numbers of single-shot spectra (10, 30, 50 and 100 pulses) showed visually observable reductions in noise levels, consistent with robust and statistically meaningful signals. Three separate types of post-acquisition calculation were used to identify high-mass limits of the spectra. (i) A literature method indicated high-mass limits similar to those observed visually-as a shift from baseline at the highest masses, nearly 350 000 u for the coal tar pitch and about 390 000 u for its pyridine insoluble fraction. (ii) Comparing instrument signal with pre-selected multiples of the standard deviation, upper mass estimates of between 40-60 000 u for the coal-tar pitch and about 95 000 u for its pyridine-insoluble fraction were found. (iii) Calculation of the slope was used to identify 'lift-off' of the spectrum from baseline. The angle between the smoothed spectrum and the baseline was matched to a pre-selected value (e.g. 0.5 degrees and 1 degrees ). However, the arbitrary specification of the key parameter did not establish this last method on a firm basis. The choice of a criterion for estimating high-mass limits of MALDI spectra remains a semi-quantitative procedure; a reasonably conservative high-mass limit may be estimated by comparison of signal with five times the standard deviation. However, evaluation of size exclusion chromatograms of the present samples using polystyrene standards suggests that molecular mass distributions of pitch samples arrived at by MALDI mass spectrometry are, at least partly, determined by the limitations of available instruments. Copyright 1999 John Wiley & Sons, Ltd.