A class of Nevanlinna functions related to singular Sturm-Liouville problems

The class of Nevanlinna functions consists of functions which are holomorphic off the real axis, which are symmetric with respect to the real axis, and whose imaginary part is nonnegative in the upper halfplane. The Kac subclass of Nevanlinna functions is defined by an integrability condition on the imaginary part. In this note a further subclass of these Kac functions is introduced. It involves an integrability condition on the modulus of the Nevanlinna functions (instead of the imaginary part). The characteristic properties of this class are investigated. The definition of the new class is motivated by the fact that the Titchmarsh-Weyl coefficients of various classes of Sturm-Liouville problems (under mild conditions on the coefficients) actually belong to this class.

     

Observation of baker’s yeast strains used in biotransformation by atomic force microscopy

Different strains of baker’s yeast(Saccharomyces cerevisiae) were imaged with an atomic force microscope (AFM). The images of uncoated and nonfixed samples were reproducible with high-constrast and nanometer-resolution. Molecules from the polysaccharide surface of the cell wall were pictured and the distance of atoms was measured. The preparation of samples was easy, suggesting that AFM is a useful tool in this type of analyses.     

Robust stabilization of internally delayed uncertain systems via sliding mode control

Summary The problem of robust stabilization of internally delayed uncertain systems via sliding mode controllers (SMC's) is studied in this paper. The robustness property and assymptotic stability of the system are discussed. Some sufficient conditions for the design of SMC and the switching hyperplane are given. Further generalization results, which lead to a simple design and implementation, are made for the system being described in companion form. A method is suggested for the elimination of limit cycles in systems being regulated by a relay SMC while allowing the generation of sliding motion and thus ensuring the closed-loop asymptotic stability.     

Electroanalytical and chromatographic determination of pentachlorophenol and related molecules in a contaminated soil: a real case example

Electroanalytical and chromatographic methodologies have been applied for the determination of pentachlorophenol (PCP) and some of its derivatives in real soil samples contaminated by industrial discharge. The analytes were extracted with hexane from soil samples collected at different points of the site and mixed to produce a representative sample. Square wave voltammetry (SWV) experiments were carried out on either a boron-doped diamond (BDD) electrode or a gold ultramicroelectrode (Au-UME) in an analyte composed by the Britton-Robinson (B-R) buffer at pH 5.5 with the direct addition of proper amounts of the extract. The voltammetric responses revealed an irreversible anodic peak at approximately 0.80 V vs. Ag/AgCl with a peak current showing a linear dependence on PCP concentration. This linear relationship yielded a detection limit (DL) of 2×10⁻⁸ mol l⁻¹ (or 5.5 μg l⁻¹) for the BDD electrode and 6.9×10⁻⁸ mol l⁻¹ (18.4 μg l⁻¹) for the Au-UME, while the independently measured HPLC detection limit was 1.1×10⁻⁸ mol l⁻¹ (3.0 μg l⁻¹). The application of electroanalytical and chromatographic methodologies in the analysis of soil extracts revealed, besides the PCP responses, signals for some related molecules such as o-tetrachlorobenzoquinone (o-chloranil), hexachlorobenzene and tetrachlorophenol. Recovering experiments for PCP showed a concentration of 27.5 mg kg⁻¹ for the electroanalytical determinations and 26.8 mg kg⁻¹ for the HPLC analysis, values exceedingly high if considering that the maximum residue limit established for natural waters by the Brazilian Environmental Agency is 10 μg l⁻¹.