Formal methods in the theories of rings and domains

In recent years, Hilbert's Programme has been resumed within the framework of constructive mathematics. This undertaking has already shown its feasability for a considerable part of commutative algebra. In particular, point-free methods have been playing a primary role, emerging as the appropriate language for expressing the interplay between real and ideal in mathematics. This dissertation is written within this tradition and has Sambin's notion of formal topology at its core. We start by developing general tools, in order to make this notion more immediate for algebraic application. We revise the Zariski spectrum as an inductively generated basic topology, and we analyse the constructive status of the corresponding principles of spatiality and reducibility. Through a series of examples, we show how the principle of spatiality is recurrent in the mathematical practice. The tools developed before are applied to specific problems in constructive algebra. In particular, we find an elementary characterization of the notion of codimension for ideals of a commutative ring, by means of which a constructive version of Krull's principal ideal theorem can be stated and proved. We prove a formal version of the projective Eisenbud-Evans-Storch theorem. Finally, guided by the algebraic intuition, we present an application in constructive domain theory, by proving a finite version of Kleene-Kreisel density theorem for non-flat information systems.In den vergangenen Jahren wurde das Hilbertsche Programm im Rahmen der konstruktiven Mathematik wiederaufgenommen. Diese Unternehmung hat sich vor allem in der kommutativen Algebra als praktikabel erwiesen. Insbesondere spielen punktfreie Methoden eine wesentliche Rolle: sie haben sich als die angemessene Sprache herausgestellt, um das Zwischenspiel von "real'" und "ideal" in der Mathematik auszudrücken. Die vorliegende Dissertation steht in dieser Tradition; zentral ist Sambins Begriff der formalen Topologie. Zunächst entwickeln wir ein allgemeines Instrumentarium, das geeignet ist, diesen Begriff seinen algebraischen Anwendungen näherzubringen. Sodann arbeiten wir das Zariski-Spektrum in eine induktiv erzeugte "basic topology" um und analysieren den konstruktiven Status der einschlägigen Varianten von Spatialität und Reduzibilität. Durch Angabe einer Reihe von Instanzen zeigen wir, wie häufig das Prinzip der Spatialität in der mathematischen Praxis vorkommt. Die eigens entwickelten Werkzeuge werden schließlich auf spezifische Probleme aus der konstruktiven Algebra angewandt. Insbesondere geben wir eine elementare Charakterisierung der Kodimension eines Ideals in einem kommutativen Ring an, mit der eine konstruktive Fassung des Krullschen Hauptidealsatzes formuliert und bewiesen werden kann. Ferner beweisen wir eine formale Fassung des Satzes von Eisenbud-Evans-Storch im projektiven Fall. Geleitet von der algebraischen Intuition stellen wir zuletzt eine Anwendung in der konstruktiven Bereichstheorie vor, indem wir eine finite Variante des Dichtheitssatzes von Kleene und Kreisel für nicht-flache Informationssysteme beweisen

Formal methods in the theories of rings and domains

In recent years, Hilbert's Programme has been resumed within the framework of constructive mathematics. This undertaking has already shown its feasability for a considerable part of commutative algebra. In particular, point-free methods have been playing a primary role, emerging as the appropriate language for expressing the interplay between real and ideal in mathematics. This dissertation is written within this tradition and has Sambin's notion of formal topology at its core. We start by developing general tools, in order to make this notion more immediate for algebraic application. We revise the Zariski spectrum as an inductively generated basic topology, and we analyse the constructive status of the corresponding principles of spatiality and reducibility. Through a series of examples, we show how the principle of spatiality is recurrent in the mathematical practice. The tools developed before are applied to specific problems in constructive algebra. In particular, we find an elementary characterization of the notion of codimension for ideals of a commutative ring, by means of which a constructive version of Krull's principal ideal theorem can be stated and proved. We prove a formal version of the projective Eisenbud-Evans-Storch theorem. Finally, guided by the algebraic intuition, we present an application in constructive domain theory, by proving a finite version of Kleene-Kreisel density theorem for non-flat information systems.In den vergangenen Jahren wurde das Hilbertsche Programm im Rahmen der konstruktiven Mathematik wiederaufgenommen. Diese Unternehmung hat sich vor allem in der kommutativen Algebra als praktikabel erwiesen. Insbesondere spielen punktfreie Methoden eine wesentliche Rolle: sie haben sich als die angemessene Sprache herausgestellt, um das Zwischenspiel von "real'" und "ideal" in der Mathematik auszudrücken. Die vorliegende Dissertation steht in dieser Tradition; zentral ist Sambins Begriff der formalen Topologie. Zunächst entwickeln wir ein allgemeines Instrumentarium, das geeignet ist, diesen Begriff seinen algebraischen Anwendungen näherzubringen. Sodann arbeiten wir das Zariski-Spektrum in eine induktiv erzeugte "basic topology" um und analysieren den konstruktiven Status der einschlägigen Varianten von Spatialität und Reduzibilität. Durch Angabe einer Reihe von Instanzen zeigen wir, wie häufig das Prinzip der Spatialität in der mathematischen Praxis vorkommt. Die eigens entwickelten Werkzeuge werden schließlich auf spezifische Probleme aus der konstruktiven Algebra angewandt. Insbesondere geben wir eine elementare Charakterisierung der Kodimension eines Ideals in einem kommutativen Ring an, mit der eine konstruktive Fassung des Krullschen Hauptidealsatzes formuliert und bewiesen werden kann. Ferner beweisen wir eine formale Fassung des Satzes von Eisenbud-Evans-Storch im projektiven Fall. Geleitet von der algebraischen Intuition stellen wir zuletzt eine Anwendung in der konstruktiven Bereichstheorie vor, indem wir eine finite Variante des Dichtheitssatzes von Kleene und Kreisel für nicht-flache Informationssysteme beweisen

Mini-FLOTAC, an Innovative Direct Diagnostic Technique for Intestinal Parasitic Infections: Experience from the Field.

Soil-transmitted helminths and intestinal protozoa infection are widespread in developing countries, yet an accurate diagnosis is rarely performed. The aim of this study was to evaluate the recently developed mini-FLOTAC method and to compare with currently more widely used techniques for the diagnosis of intestinal parasitic infections in different settings. The study was carried out in Dharamsala, Himachal Pradesh, India, and in Bukumbi, Tanzania. A total of 180 pupils from two primary schools had their stool analyzed (n = 80 in Dharamsala and n = 100 in Bukumbi) for intestinal parasitic infections with three diagnostic methods: direct fecal smear, formol-ether concentration method (FECM) and mini-FLOTAC. Overall, 72% of the pupils were positive for any intestinal parasitic infection, 24% carried dual infections and 11% three infections or more. The most frequently encountered intestinal parasites were Entamoeba coli, Entamoeba histolytica/dispar, Giardia intestinalis, hookworm, (and Schistosoma mansoni, in Tanzania). Statistically significant differences were found in the detection of parasitic infections among the three methods: mini-FLOTAC was the most sensitive method for helminth infections (90% mini-FLOTAC, 60% FECM, and 30% direct fecal smear), whereas FECM was most sensitive for intestinal protozoa infections (88% FECM, 70% direct fecal smear, and 68% mini-FLOTAC). We present the first experiences with the mini-FLOTAC for the diagnosis of intestinal helminths and protozoa. Our results suggest that it is a valid, sensitive and potentially low-cost alternative technique that could be used in resource-limited settings--particularly for helminth diagnosis

Computational fluid dynamics (CFD) modelling and experimental validation of thermal processing of canned fruit salad in glass jar

In this paper the heat transfer of a fruit salad during the pasteurization treatment was investigated. The objective of the paper was to develop and validate a computational fluid dynamics (CFD) model for predicting the temperature profiles during the thermal processing of this sample. Samples of a commercial fruit salad, composed of five different fruits with different shapes, sizes and thermal properties, submerged in water/sugar syrup, were submitted to thermal treatments in a pilot plant and temperature profiles at different locations were experimentally recorded. Results showed that the slowest heating point (SHP) was positioned at 19–20% of the can height: fruit closest to the SHP such as pear presented the lowest F value. Moreover, F values resulted to be influenced by the distance from the jar bottom as function of natural convection motion of the syrup. CFD model simulations data were then successfully validated against the experimental ones: results, expressed as RMSE, showed a good fitting between calculated and experimental data, both for syrup (mean RMSE 1.47 C) and fruit pieces (mean RMSE 1.63 C). In addition, F values calculated from both experimental and simulated temperatures resulted very similar with only little differences. In conclusion, the proposed approach and mathematical model can thus be usefully applied for the simulation and prediction of thermal processes of canned fruit salad for process design and optimization

Effects of alternative steeping methods on composition, antioxidant property and colour of green, black and oolong tea infusions

Cold water steeping is reported to maximise tea health benefits, but requires long infusion time. In this work, the employment of a brief hot infusion step followed by ice addition was evaluated. The comparison of this innovative method with hot and cold steeping was investigated on green, black and oolong teas. Catechins, xanthines and gallic acid content, antioxidant power, total phenolics and colour analysis were evaluated. Hot infusion shown rapid extractive power, but relevant compound degradation. On the contrary, cold infusion extracted higher level of healthy molecules with slow kinetic. The innovative method achieved in short time similar properties of cold infusion in terms of antioxidant power. As for bioactive compounds, such as gallic acid and epigallocatechin gallate, highest values, about double than in hot infusion, were recorded for green and black teas. This steeping method may represent an alternative approach for industrial beverage preparation

First-order phase transitions in Yang-Mills theories and the density of state method

When studied at finite temperature, Yang-Mills theories in $3+1$ dimensions display the presence of confinement/deconfinement phase transitions, which are known to be of first order -- the $SU(2)$ gauge theory being the exception. Theoretical as well as phenomenological considerations indicate that it is essential to establish a precise characterisation of these physical systems in proximity of such phase transitions. We present and test a new method to study the critical region of parameter space in non-Abelian quantum field theories on the lattice, based upon the Logarithmic Linear Relaxation (LLR) algorithm. We apply this method to the $SU(3)$ Yang Mills lattice gauge theory, and perform extensive calculations with one fixed choice of lattice size. We identify the critical temperature, and measure interesting physical quantities near the transition. Among them, we determine the free energy of the model in the critical region, exposing for the first time its multi-valued nature with a numerical calculation from first principles, providing this novel evidence in support of a first order phase transition. This study sets the stage for future high precision measurements, by demonstrating the potential of the method.Comment: 25 pages, 21 figures. Version accepted for publicatio

Implementation of the Control System for the LHCb Muon Detector

The Muon Detector of LHCb will be equipped with 1368 Multi- Wire Proportional Chambers and 24 Triple-GEM Detectors. Within the Framework of the CERN Control System Project, using PVSS as the main tool, we are developing an instrument to manage the Muon System of LHCb. Adjustment and monitoring of High and Low Voltage power supplies, on-line diagnostics and ne tuning of the Front-End read-out devices, data acquisition from the gas system and the monitoring of pressure and temperature of the experimental hall are being implemented. The system will also look after long term data archiving and alert handling. The Control System performance is currently under evaluation in a cosmic ray station. Built as a nal quality control of the LHCb Multi-Wire Proportional Chambers, allowing acquisition of data from as many as 600 Front-End readout channels, the cosmic ray station is fully managed by means of a Control System prototype