A fixed point theorem for Meir-Keeler contractions in ordered metric spaces

[EN] The purpose of this paper is to present some fixed point theorems for Meir-Keeler contractions in a complete metric space endowed with a partial order. MSC: 47H10.

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory

[EN] As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.

Enabling computationally intensive bioinformatics applications on the Grid platform

Bioinformatics is a recent and emerging discipline which aims at studying biological problems through computational approaches. Most branches of bioinformatics such as Genomics, Proteomics and Molecular Dynamics are particularly computationally intensive, requiring huge amount of computational resources for running algorithms of everincreasing complexity over data of everincreasing size. In the search for computational power, the EGEE Grid platform, world's largest community of interconnected clusters load balanced as a whole, seems particularly promising and is considered the new hope for satisfying the everincreasing computational requirements of bioinformatics, as well as physics and other computational sciences. The EGEE platform, however, is rather new and not yet free of problems. In addition, specific requirements of bioinformatics need to be addressed in order to use this new platform effectively for bioinformatics tasks. In my three years' Ph.D. work I addressed numerous aspects of this Grid platform, with particular attention to those needed by the bioinformatics domain. I hence created three major frameworks, Vnas, GridDBManager and SETest, plus an additional smaller standalone solution, to enhance the support for bioinformatics applications in the Grid environment and to reduce the effort needed to create new applications, additionally addressing numerous existing Grid issues and performing a series of optimizations. The Vnas framework is an advanced system for the submission and monitoring of Grid jobs that provides an abstraction with reliability over the Grid platform. In addition, Vnas greatly simplifies the development of new Grid applications by providing a callback system to simplify the creation of arbitrarily complex multistage computational pipelines and provides an abstracted virtual sandbox which bypasses Grid limitations. Vnas also reduces the usage of Grid bandwidth and storage resources by transparently detecting equality of virtual sandbox files based on content, across different submissions, even when performed by different users. BGBlast, evolution of the earlier project GridBlast, now provides a Grid Database Manager (GridDBManager) component for managing and automatically updating biological flatfile databases in the Grid environment. GridDBManager sports very novel features such as an adaptive replication algorithm that constantly optimizes the number of replicas of the managed databases in the Grid environment, balancing between response times (performances) and storage costs according to a programmed cost formula. GridDBManager also provides a very optimized automated management for older versions of the databases based on reverse delta files, which reduces the storage costs required to keep such older versions available in the Grid environment by two orders of magnitude. The SETest framework provides a way to the user to test and regressiontest Python applications completely scattered with side effects (this is a common case with Grid computational pipelines), which could not easily be tested using the more standard methods of unit testing or test cases. The technique is based on a new concept of datasets containing invocations and results of filtered calls. The framework hence significantly accelerates the development of new applications and computational pipelines for the Grid environment, and the efforts required for maintenance. An analysis of the impact of these solutions will be provided in this thesis. This Ph.D. work originated various publications in journals and conference proceedings as reported in the Appendix. Also, I orally presented my work at numerous international conferences related to Grid and bioinformatics.

Fixed point theorems in partially ordered spaces and aplications

[ES]Recientemente, en la Teoría del punto fijo, han aparecido muchos resultados que obtienen condiciones suficientes para la existencia de un punto fijo si trabajamos con aplicaciones en un conjunto dotado de un orden parcial. Generalmente, estos resultados combinan dos teoremas del punto fijo fundamentales: el Teorema de la contracción de Banach y el Teorema de Knaster-Tarski.

Catalytic liquid- and gas-phase oxidations for the synthesis of intermediates and specialty chemicals: some examples of industrial relevance

Nowadays, it is clear that the target of creating a sustainable future for the next generations requires to re-think the industrial application of chemistry. It is also evident that more sustainable chemical processes may be economically convenient, in comparison with the conventional ones, because fewer by-products means lower costs for raw materials, for separation and for disposal treatments; but also it implies an increase of productivity and, as a consequence, smaller reactors can be used. In addition, an indirect gain could derive from the better public image of the company, marketing sustainable products or processes. In this context, oxidation reactions play a major role, being the tool for the production of huge quantities of chemical intermediates and specialties. Potentially, the impact of these productions on the environment could have been much worse than it is, if a continuous efforts hadn’t been spent to improve the technologies employed. Substantial technological innovations have driven the development of new catalytic systems, the improvement of reactions and process technologies, contributing to move the chemical industry in the direction of a more sustainable and ecological approach. The roadmap for the application of these concepts includes new synthetic strategies, alternative reactants, catalysts heterogenisation and innovative reactor configurations and process design. Actually, in order to implement all these ideas into real projects, the development of more efficient reactions is one primary target. Yield, selectivity and space-time yield are the right metrics for evaluating the reaction efficiency. In the case of catalytic selective oxidation, the control of selectivity has always been the principal issue, because the formation of total oxidation products (carbon oxides) is thermodynamically more favoured than the formation of the desired, partially oxidized compound. As a matter of fact, only in few oxidation reactions a total, or close to total, conversion is achieved, and usually the selectivity is limited by the formation of by-products or co-products, that often implies unfavourable process economics; moreover, sometimes the cost of the oxidant further penalizes the process. During my PhD work, I have investigated four reactions that are emblematic of the new approaches used in the chemical industry. In the Part A of my thesis, a new process aimed at a more sustainable production of menadione (vitamin K3) is described. The “greener” approach includes the use of hydrogen peroxide in place of chromate (from a stoichiometric oxidation to a catalytic oxidation), also avoiding the production of dangerous waste. Moreover, I have studied the possibility of using an heterogeneous catalytic system, able to efficiently activate hydrogen peroxide. Indeed, the overall process would be carried out in two different steps: the first is the methylation of 1-naphthol with methanol to yield 2-methyl-1-naphthol, the second one is the oxidation of the latter compound to menadione. The catalyst for this latter step, the reaction object of my investigation, consists of Nb2O5-SiO2 prepared with the sol-gel technique. The catalytic tests were first carried out under conditions that simulate the in-situ generation of hydrogen peroxide, that means using a low concentration of the oxidant. Then, experiments were carried out using higher hydrogen peroxide concentration. The study of the reaction mechanism was fundamental to get indications about the best operative conditions, and improve the selectivity to menadione. In the Part B, I explored the direct oxidation of benzene to phenol with hydrogen peroxide. The industrial process for phenol is the oxidation of cumene with oxygen, that also co-produces acetone. This can be considered a case of how economics could drive the sustainability issue; in fact, the new process allowing to obtain directly phenol, besides avoiding the co-production of acetone (a burden for phenol, because the market requirements for the two products are quite different), might be economically convenient with respect to the conventional process, if a high selectivity to phenol were obtained. Titanium silicalite-1 (TS-1) is the catalyst chosen for this reaction. Comparing the reactivity results obtained with some TS-1 samples having different chemical-physical properties, and analyzing in detail the effect of the more important reaction parameters, we could formulate some hypothesis concerning the reaction network and mechanism. Part C of my thesis deals with the hydroxylation of phenol to hydroquinone and catechol. This reaction is already industrially applied but, for economical reason, an improvement of the selectivity to the para di-hydroxilated compound and a decrease of the selectivity to the ortho isomer would be desirable. Also in this case, the catalyst used was the TS-1. The aim of my research was to find out a method to control the selectivity ratio between the two isomers, and finally to make the industrial process more flexible, in order to adapt the process performance in function of fluctuations of the market requirements. The reaction was carried out in both a batch stirred reactor and in a re-circulating fixed-bed reactor. In the first system, the effect of various reaction parameters on catalytic behaviour was investigated: type of solvent or co-solvent, and particle size. With the second reactor type, I investigated the possibility to use a continuous system, and the catalyst shaped in extrudates (instead of powder), in order to avoid the catalyst filtration step. Finally, part D deals with the study of a new process for the valorisation of glycerol, by means of transformation into valuable chemicals. This molecule is nowadays produced in big amount, being a co-product in biodiesel synthesis; therefore, it is considered a raw material from renewable resources (a bio-platform molecule). Initially, we tested the oxidation of glycerol in the liquid-phase, with hydrogen peroxide and TS-1. However, results achieved were not satisfactory. Then we investigated the gas-phase transformation of glycerol into acrylic acid, with the intermediate formation of acrolein; the latter can be obtained by dehydration of glycerol, and then can be oxidized into acrylic acid. Actually, the oxidation step from acrolein to acrylic acid is already optimized at an industrial level; therefore, we decided to investigate in depth the first step of the process. I studied the reactivity of heterogeneous acid catalysts based on sulphated zirconia. Tests were carried out both in aerobic and anaerobic conditions, in order to investigate the effect of oxygen on the catalyst deactivation rate (one main problem usually met in glycerol dehydration). Finally, I studied the reactivity of bifunctional systems, made of Keggin-type polyoxometalates, either alone or supported over sulphated zirconia, in this way combining the acid functionality (necessary for the dehydrative step) with the redox one (necessary for the oxidative step). In conclusion, during my PhD work I investigated reactions that apply the “green chemistry” rules and strategies; in particular, I studied new greener approaches for the synthesis of chemicals (Part A and Part B), the optimisation of reaction parameters to make the oxidation process more flexible (Part C), and the use of a bioplatform molecule for the synthesis of a chemical intermediate (Part D).

Hybrid foundations for offshore wind turbines

Nowadays offshore wind turbines represents a valid answer for energy production but with an increasing in costs mainly due to foundation technology required. Hybrid foundations composed by suction caissons over which is welded a tower supporting the nacelle and the blades allows a strong costs reduction. Here a monopod configuration is studied in a sandy soil in a 10 m water depth. Bearing capacity, sliding resistance and pull-out resistance are evaluated. In a second part the installation process occurring in four steps is analysed. considering also the effect of stress enhancement due to frictional forces opposing to penetration growing at skirt sides both inside and outside. In a three dimensional finite element model using Straus7 the soil non-linearity is considered in an approximate way through an iterative procedure using the Yokota empirical decay curves.