La matematica come occasione e stimolo per la formulazione di un giudizio critico

The thesis develops an analysis of the scientific knowledge construction based on a psychological description of the mental procedures which in our mind help to construct the mathematical thought. The analysis was carried on in the Part I of the thesis and was supported by a deep insight in the scientific research experience concerning mathematics. This research was the opportunity for the personal encounter with the mathematical discipline and gave also the possibility and ispiration to question the meaning of the mathematical thinking and the reliability of its cognitive procedures. In Part II the results of psychological and cognitive experience of the scientific research, discussed in Part I, have been described in details. The results of the scientific research, both in basic and applied fields of mathematics, has been described in different papers appeared in national and international journals and are collected in the thesis' appendix

La nozione intuitiva di infinito e le sue possibili precisazioni. Il caso dell'aritmetica e della geometria.

Scopo del presente lavoro è analizzare a fondo i significati e i limiti del cosiddetto assioma di Archimede che gioca un ruolo fondamentale nel sistema assiomatico di D. Hilbert. In particolare ci si è interessati al ruolo svolto da tale assioma nella fondazione dell'aritmetica e nello studio delle proprietà piano assoluto, con particolare attenzione al caso delle geometrie non-euclidee. L'analisi così condotta ha portato in evidenza le relazioni che legano gli aspetti intuitivi a quelli razionali relativi alla nozione di infinito, la cui introduzione costituisce una delle più frequenti difficoltà gli studenti di ogni età si trovano ad affrontare lo studio della matematica

Complementarity models for restructured electricity markets under environmental regulations

Complementarity problems are recognized to be a general computational method for solving economic equilibrium models. There exist various problems describing the energy markets that rely on the complementarity models since they allow to analyze the interactions among different market players. Complementarity models generalize linear and non-linear problems because the Karush-Kuhn-Tucker optimality conditions are one particular instance of a complementarity problem. Moreover, the class of complementarity models is appropriate for modeling spatial price equilibrium, perfect and imperfect completion models, such as Cournot-Nash games, and other many models where both primal and dual variables can be constrained together. The first part of this paper provides a motivation and a description of complementarity models. In the second part, we investigate a capacity expansion problem applied to the restructured Italian electricity market that is currently subject to the European Union Emissions Trading System (EU-ETS). In accordance with the Kyoto Protocol, the EU-ETS aims to reduce greenhouse gas emissions from human activities provoking climate changes. This scheme is now subdivided into three phases and it is based on a cap and trade system that defines the maximum amount of CO2 that can be emitted in each compliance period. Our analysis shows that investments in renewables are mainly conditioned to incentive policies. The solution of the developed model is found by exploiting the mixed complementarity theoretical framework. The model is implemented in GAMS using the PATH solver

Absolute planes with elliptic congruence

We construct examples of non-archimedean absolute planes which are enbedded in elliptic planes, so that they admit an elliptic congruence

Evaluating the Impacts of the EU-ETS on Prices, Investments and Profits of the Italian Electricity Market

In this paper we investigate the economic impacts of the European Emission Trading Scheme (EU- ETS) on the Italian electricity market by a power generation expansion model. In particular, we assume that generators make their capacity expansion decisions in a Cournot or in a perfect competition manner. This model is used to measure the effects of the EU-ETS Directives on electricity prices and demand, investments and generators' profits both in an oligopolistic and in a perfectly competitive organization of the power market. We adopt a technological representation of the energy market which is discretized into six geographical zones (North, Center-North, Center- South, South, Sicily, Sardinia) and five virtual poles (Monfalcone, Foggia, Brindisi, Rossano, Priolo) with limited production for a total of eleven zones. We assume that generators operate in different zones connected by interconnections with limited capacity and produce energy by running existing or new plants in which they directly invest. We consider several investment scenarios under the CO2 regulation with and without incentives to renewables. The scenarios also include simulations on future effects of the third EU-ETS phase on the system. Our analysis shows that perfect competition induces generators to invest more than in an oligopolistic framework, but in both market configurations, investments are mainly concentrated in fossil-red plants (CCGT and coal), leaving a small proportion to new wind plants. This happens also in presence of incentives given to renewable technologies. We can thus conclude that investments in a secure and efficient technology like CCGT are preferable compared to those in renewables that cannot be used with continuity. This investment policy affects electricity prices that significantly increase in 2020 compared to their 2009 levels. The raise of electricity prices in 2020 is particularly favorable for generators operating as Cournot players which are able to increase their profits compared to 2009, despite the full auctioning system foreseen for the allocation of CO2 allowance to the power sector in the third EU- ETS phase. The solution of the overall system is found by exploiting the mixed complementarity theoretical framework and solution algorithms. The developed model is implemented as complementarity problems and solved in GAMS using the PATH solver

Evaluating the Impacts of the EU-ETS on Prices, Investments and Profits of the Italian Electricity Market

In this paper we investigate the economic impacts of the European Emission Trading Scheme (EU-ETS) on the Italian electricity market by a power generation expansion model. In particular, we assume that generators make their capacity expansion decisions in a Cournot or in a perfect competition manner. This model is used to measure the effects of the EU-ETS Directives on electricity prices and demand, investments and generators' profits both in an oligopolistic and in a perfectly competitive organization of the power market. We adopt a technological representation of the energy market which is discretized into six geographical zones (North, Center-North, Center-South, South, Sicily, Sardinia) and five virtual poles (Monfalcone, Foggia, Brindisi, Rossano, Priolo) with limited production for a total of eleven zones. We assume that generators operate in different zones connected by interconnections with limited capacity and produce energy by running existing or new plants in which they directly invest. We consider several investment scenarios under the CO2 regulation with and without incentives to renewables. The scenarios also include simulations on future effects of the third EU-ETS phase on the system. Our analysis shows that perfect competition induces generators to invest more than in an oligopolistic framework, but in both market configurations, investments are mainly concentrated in fossil-red plants (CCGT and coal), leaving a small proportion to new wind plants. This happens also in presence of incentives given to renewable technologies. We can thus conclude that investments in a secure and efficient technology like CCGT are preferable compared to those in renewables that cannot be used with continuity. This investment policy affects electricity prices that significantly increase in 2020 compared to their 2009 levels. The raise of electricity prices in 2020 is particularly favorable for generators operating as Cournot players which are able to increase their profits compared to 2009, despite the full auctioning system foreseen for the allocation of CO2 allowance to the power sector in the third EU-ETS phase. The solution of the overall system is found by exploiting the mixed complementarity theoretical framework and solution algorithms. The developed model is implemented as complementarity problems and solved in GAMS using the PATH solver

The steel industry: a mathematical model under environmental regulations

In this work, a spatial equilibrium problem is formulated for analyzing the impact of the application of the EU-ETS on the steel industry that has historically seen Europe as one of its major producers. The developed model allows us to simultaneously represent the interactions of several market players, to endogenously determine output and steel prices and to analyze the investment in the Carbon Capture and Storage (CCS) technology. In addition, the proposed model supports the evaluation of the CO2 emission costs on the basis of Directive 2009/29/EC, the “20-20-20” targets, and the Energy Roadmap 2050. In this light, two main processes for steelmaking have to be considered: integrated mills (BOF) and Electric Arc Furnace (EAF) in minimills

A General Nonconvex Multiduality Principle

We introduce a (possibly infinite) collection of mutually dual nonconvex optimization problems, which share a common optimal value, and give a characterization of their global optimal solutions. As immediate consequences of our general multiduality principle, we obtain Toland–Singer duality theorem as well as an analogous result involving generalized perspective functions. Based on our duality theory, we propose an extension of an existing algorithm for the minimization of d.c. functions, which exploits Toland–Singer duality, to a more general class of nonconvex optimization problems