On the numerical integration of nonlinear initial value problems by linear multistep methods

We study the numerical solution of the nonlinear initial value problem $$\left\{ {\begin{array}{*{20}c} {{{du(t)} \mathord{\left/ {\vphantom {{du(t)} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} + Au(t) = f(t),t > 0} \\ {u(0) = c,} \\ \end{array} } \right.$$ whereA is a nonlinear operator in a real Hilbert space. The problem is discretized using linear multistep methods, and we assume that their stability regions have nonempty interiors. We give sharp bounds for the global error by relating the stability region of the method to the monotonicity properties ofA. In particular we study the case whereAu is the gradient of a convex functional φ(u).     

Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces

LetA be anm-accretive operator in a Banach spaceE. Suppose thatA ⁻¹0 is not empty and that bothE andE ^* are uniformly convex. We study a general condition onA that guarantees the strong convergence of the semigroup generated by—A and of related implicit and explicit iterative schemes to a zero ofA. Rates of convergence are also obtained. In Hilbert space this condition has been recently introduced by A. Pazy. We also establish strong convergence under the assumption that the interior ofA ⁻¹0 is not empty. In Hilbert space this result is due to H. Brezis. Sponsored by the United States Army under Contract No. DAAG29-75-C-0024.     

Sulphur KLL auger spectra of gaseous sulphur compounds

Measurements of the diagram-line energies and intensities of sulphur KLL Auger spectra for the gaseous compounds H₂S, SO₂ and SF₆ are p     

The influence of ionic strength, nutrients and pH on bacterial adhesion to metals

Bacteria-metal interactions in aqueous solutions are important in biofilm formation, biofouling and biocorrosion problems in the natural environment and engineered systems. In this study, the adhesion forces of two anaerobes (Desulfovibrio desulfuricans and Desulfovibrio singaporenus) and an aerobe (Pseudomonas sp.) to stainless steel 316 in various aqueous systems were quantified using atomic force microscopy (AFM) with a cell probe. Results show that the nutrient and ionic strength of the solutions influence the bacteria-metal interactions. The bacteria-metal adhesion force was reduced in the presence of the nutrients in the solution, because a trace organic film was formed and thus decreased the metal surface wettability. Stronger ionic strength in the solution results in a larger bacteria-metal adhesion force, which is due to the stronger electrostatic attraction force between the positively charged metal surface and negatively charged bacterial surface. Solution pH also influences the interaction between the bacterial cells and the metal surface; the bacteria-metal adhesion force reached its highest value when the pH of the solution was near the isoelectric point of the bacteria, i.e. at the zero point charge. The adhesion forces at pH 9 were higher than at pH 7 due to the increase in the attraction between Fe ions and negative carboxylate groups.     

Force measurements of bacterial adhesion on metals using a cell probe atomic force microscope

The adhesion of microbial cells to metal surfaces in aqueous media is an important phenomenon in both the natural environment and engineering systems. The adhesion of two anaerobic sulfate-reducing bacteria (Desulfovibrio desulfuricans and a local marine isolate) and an aerobe (Pseudomonas sp.) to four polished metal surfaces (i.e., stainless steel 316, mild steel, aluminum, and copper) was examined using a force spectroscopy technique with an atomic force microscope (AFM). Using a modified bacterial tip, the attraction and repulsion forces (in the nano-Newton range) between the bacterial cell and the metal surface in aqueous media were quantified. Results show that the bacterial adhesion force to aluminum is the highest among the metals investigated, whereas the one to copper is the lowest. The bacterial adhesion forces to metals are influenced by both the electrostatic force and metal surface hydrophobicity. It is also found that the physiological properties of the bacterium, namely the bacterial surface charges and hydrophobicity, also have influence on the bacteria-metal interaction. The adhesion to the metals by Pseudomonas sp. and D. desulfuricans was greater than by the marine SRB isolate. The cell-cell interactions show that there are strong electrostatic repulsion forces between bacterial cells. Cell probe atomic force microscopy has provided some useful insight into the interactions of bacterial cells with the metal surfaces.     

Comprehensive Two-Dimensional Gas Chromatography–Mass Spectrometry Analysis of Exhaled Breath Compounds after Whole Grain Diets

Exhaled breath is a potential noninvasive matrix to give new information about metabolic effects of diets. In this pilot study, non-targeted analysis of exhaled breath volatile organic compounds (VOCs) was made by comprehensive two-dimensional gas chromatography–mass spectrometry (GCxGC-MS) to explore compounds relating to whole grain (WG) diets. Nine healthy subjects participated in the dietary intervention with parallel crossover design, consisting of two high-fiber diets containing whole grain rye bread (WGR) or whole grain wheat bread (WGW) and 1-week control diets with refined wheat bread (WW) before both diet periods. Large interindividual differences were detected in the VOC composition. About 260 VOCs were detected from exhaled breath samples, in which 40 of the compounds were present in more than half of the samples. Various derivatives of benzoic acid and phenolic compounds, as well as some furanones existed in exhaled breath samples only after the WG diets, making them interesting compounds to study further.     

A note on ℝ‐linear GMRES for solving a class of ℝ‐linear systems

We prove that ?‐linear GMRES for solving a class of ?‐linear systems is faster than GMRES applied to the related ?‐linear systems in terms of matrix–vector products. Numerical examples are given to demonstrate the theoretical result. Copyright © 2011 John Wiley & Sons, Ltd.