Una variazione del metodo di Halley

Sommario In questa nota si studia una classe di metodi iterativi, per la ricerca delle radici di una equazione, che include il metodo di Halley. Si prova che ogni metodo della classe è del terzo ordine e si calcola la costante di errore per ognuno di essi. Si individuano poi quei metodi della classe che sono globalmente convergenti per funzioni genus zero o uno. Infine is trova un metodo che ha una costante in valore assoluto più piccola di quella di Halley. Tale metodo è di tipo razionale e involge le stesse derivate di quello di Halley.

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We study a class of iterative methods devoted to the search of the roots of an equation. The class includes Halley's method. We prove each method belonging to the class to be of third order and for it evaluate the error constant. Among such methods we identify the ones which are globally convergent for zero or one genus functions. In particulary we find a method which has an error constant whose absolute value is less than the Halley's one. This is a rational one-point method which involves the same derivatives as Halley's method.

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Lavoro svolto nell'ambito del gruppo G.N.I.M.     

Structural study by 1H NMR of the first adducts of the telomerization of methylmethacrylate with thiophenol

The stereoselectivity of the different steps (addition step and transfer step) of the radical telomerization of methylmethacrylate with thiophenol has been determined by preparing and analyzing the first adducts by ¹H NMR analysis.     

Surjections and coverings

This paper determines the necessary and sufficient condition under which a collection of sequence covers on a finite set can be induced by a surjection. The relationship of sequence covers and surjections to generalized decomposition of an automaton allowing feedback, is the same as the relationship of partitions and bijections to series-parallel decompositions. The condition determined is a natural, but complex generalization of the known condition for the series-parallel case.     

An ergonomic study on plate shears, applying physical, physiological and psychophysical methods

An ergonomic evaluation model for hand tools was developed and applied in a project aiming at assessment of work with plate shears. Measurement variables were physical, physiological and psychophysical. They included tool force and opening angle, wrist movements, muscular strain and fatigue, subjective rating of symptoms, and localization of symptoms, in a group of male professional platers. Different hand grips were studied in a series of cutting tasks (4.2 m cutting length). Results showed that working with conventional plate shears is extremely physically demanding. The peak force required was in the range of 26 to 72 per cent of the subjects' maximal hand grip force. There was ample localized muscle fatigue in the forearm. Psychophysical and electrophysiological data agreed with respect to aspects of muscular strain and fatigue. Workers' preferences in the short run seemed to focus on productivity rather than on ergonomic quality. There is a need for development of improved tools, based on formulated requirements.     

Direct and indirect model reference adaptive control

The paper considers the control of an unknown linear time-invariant plant using Direct and Indirect Model Reference Adaptive Control. Employing a specific controller structure and the concept of positive realness, adaptive laws are derived using Indirect Control which are identical to those obtained in the case of Direct Control. The stability questions that arise are also shown to be the same. Simulation results using the new scheme are presented for the control of both stable and unstable plants.     

Decomposition of Ozone in Highly Concentrated Aqueous Solutions Under semi-Commercial Conditions

The use of ozone in the treatment of drinking water in the form of a highly concentrated aqueous solution yields technological advantages compared with the traditional use of ozone in its gaseous state. However, for a comparative calculation of profitability, it is essential to know the ozone decomposition rate in the water solution in question. The present paper reports for the first time investigations with respect to this question under semi-commercial conditions and compares the results with laboratory tests made at another place.     

Modification with Organometallic Compounds Improves Crossing of the Blood–Brain Barrier of [Leu5]‐Enkephalin Derivatives in an In Vitro Model System

Enkephalin peptides are thought to be suitable vectors for the passage of the blood–brain barrier (BBB). Modifications that do not alter the amino acid sequence are often used to improve the permeation through living membrane systems. As a new type of modification we introduce organometallic compounds, in particular ferrocene carboxylic acid. Derivatives of [Leu⁵]enkephalin were synthesised and labelled with organometallic compounds by using solid‐phase synthesis techniques. All new metal–peptide bioconjugates were comprehensively characterised by HPLC, NMR spectroscopy and mass spectrometry and found to be at least 95 % pure. For the first time, permeation coefficients in a BBB model for organometal–peptide derivatives were determined in this work. The uptake and localisation of fluorescein‐labelled enkephalins was monitored by fluorescence microscopy on three cancer cell lines. Octanol/H₂O partition coefficients of the compounds were measured by HPLC. The introduction of the organometallic moiety enhances the uptake into cells and the permeation coefficient of [Leu⁵]‐enkephalin. This could be due to an increase in lipophilicity caused by the organometallic label. The metal–peptide conjugates were found to be nontoxic up to mM concentrations. The low cytotoxicity encourages further experiments that could take advantage of the selectivity of enkephalin derivatives for opioid receptors.     

Oligomerization and Nitration of the Grass Pollen Allergen Phl p 5 by Ozone,Nitrogen Dioxide,and Peroxynitrite: Reaction Products,Kinetics, and Health Effects

The allergenic and inflammatory potential of proteins can be enhanced by chemical modification upon exposure to atmospheric or physiological oxidants. The molecular mechanisms and kinetics of such modifications, however, have not yet been fully resolved. We investigated the oligomerization and nitration of the grass pollen allergen Phl p 5 by ozone (O₃), nitrogen dioxide (NO₂), and peroxynitrite (ONOO^–). Within several hours of exposure to atmospherically relevant concentration levels of O₃ and NO₂, up to 50% of Phl p 5 were converted into protein oligomers, likely by formation of dityrosine cross-links. Assuming that tyrosine residues are the preferential site of nitration, up to 10% of the 12 tyrosine residues per protein monomer were nitrated. For the reaction with peroxynitrite, the largest oligomer mass fractions (up to 50%) were found for equimolar concentrations of peroxynitrite over tyrosine residues. With excess peroxynitrite, the nitration degrees increased up to 40% whereas the oligomer mass fractions decreased to 20%. Our results suggest that protein oligomerization and nitration are competing processes, which is consistent with a two-step mechanism involving a reactive oxygen intermediate (ROI), as observed for other proteins. The modified proteins can promote pro-inflammatory cellular signaling that may contribute to chronic inflammation and allergies in response to air pollution.