How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Spectrophotometric flow-injection determination of sucrose and total reducing sugar in sugar-cane juice and molasses

A flow-injection system with two sample carrier streams, one of them for on-line sucrose inversion, is proposed for the determination of sucrose and total reducing sugar. The method is based on the unselective oxidation of sugars by alkaline hexacyanoferrate(III) at ca. 95°C; the resulting hexacyanoferrate(II) is measured spectrophotometrically after addition of 1,10-phenanthroline and iron(III) sulphate. Two signals are recorded per cycle, reflecting the reducing sugar content of the sample before and after sucrose inversion. A debubber chamber removes the gases produced inside the heated reactors. Boiling water under reflux is used for heating. The effects of experimental variables and possible interferents are reported. The proposed system permits the analysis of about 40 samples per hour (80 measurements). Precise results (r.s.d.<1%) in agreement with those obtained with classical methods are achieved. Simplifications of the system are discussed.     

Evaluation of glucose biosensors based on Prussian Blue and lyophilised, crystalline and cross-linked glucose oxidases (CLEC(R))

Glucose biosensors based on lyophilised, crystalline and cross-linked glucose oxidase (GOx, CLEC(R)) and commercially available lyophilised GOx immobilised on top of glassy carbon electrodes modified with electrodeposited Prussian Blue are critically compared. Two procedures were carried out for preparing the biosensors: (1) deposition of one layer of adsorbed GOx dissolved in an aqueous solution followed by deposition of two layers of low molecular weight Nafion(R) dissolved in 90% ethanol, and (2) deposition of two layers of a mixture of GOx with Nafion dissolved in 90% ethanol. The performance of the biosensors was evaluated in terms of linear response range for hydrogen peroxide and glucose, detection limit, and susceptibility to some common interfering species (ascorbic acid, acetaminophen and uric acid). The operational stability of the biosensors was evaluated by applying a steady potential of -50 mV versus Ag/AgCl to the glucose biosensor and injecting standard solutions of hydrogen peroxide and glucose (50 muM and 1.0 mM, respectively, in phosphate buffer) for at least 5 h in a flow-injection system. Scanning electron microscopy was used for visualisation of the Prussian Blue redox catalyst and in the presence of the different GOx preparations on the electrode surface.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Protein extraction for proteome analysis from cacao leaves and meristems, organs infected by Moniliophthora perniciosa, the causal agent of the witches' broom disease

Preparation of high-quality proteins from cacao vegetative organs is difficult due to very high endogenous levels of polysaccharides and polyphenols. In order to establish a routine procedure for the application of proteomic and biochemical analysis to cacao tissues, three new protocols were developed; one for apoplastic washing fluid (AWF) extraction, and two for protein extraction--under denaturing and nondenaturing conditions. The first described method allows a quick and easy collection of AWF--using infiltration-centrifugation procedure--that is representative of its composition in intact leaves according to the smaller symplastic contamination detected by the use of the hexose phosphate isomerase marker. Protein extraction under denaturing conditions for 2-DE was remarkably improved by the combination of chemically and physically modified processes including phenol, SDS dense buffer and sonication steps. With this protocol, high-quality proteins from cacao leaves and meristems were isolated, and for the first time well-resolved 1-DE and 2-DE protein patterns of cacao vegetative organs are shown. It also appears that sonication associated with polysaccharide precipitation using tert-butanol was a crucial step for the nondenaturing protein extraction and subsequent enzymatic activity detection. It is expected that the protocols described here could help to develop high-level proteomic and biochemical studies in cacao also being applicable to other recalcitrant plant tissues.     

Cashew tree wood flour activated with cashew nut shell liquid for the production of functionalized composites

This work is aimed at the one-step chemical modification of the surface of cashew wood flour particles using the technical grade cashew nut shell liquid (CNSL). The goal is to develop an alternative way to introduce chemically active sites on the surface of the particles, which allows the addition of new functionalities to such particles. The influence of time and temperature and catalyst on the substitution of lignocellulosic hydroxyls with cardanol/cardol urethane derivatives was evaluated by thermogravimetric analysis, scanning electron microscopy, Fourier-transform infrared spectroscopy (FTIR), and contact angle measurements. The mechanical behavior of the modified particles in polypropylene composites was also evaluated by mechanical testing and dynamic mechanical thermal analysis. The FTIR, thermogravimetry, and contact angle results indicated changes on the particle surface, and the mechanical and thermomechanical behavior of the mercerized and modified particles in the composites was found to be similar. These results point that the CNSL approach is a viable way to chemically modify cashew wood flour particle surfaces, while maintaining their properties.