Leibniz's Principles and Topological Extensions

Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object", "everything can possibly exist, unless it yields contradiction", "the ideal elements correctly determine the real things". Here we give a precise formulation of these principles within the framework of the Topological Extensions of [8], structures that generalize at once compactifications, completions, and nonstandard extensions. In this topological context, the above Leibniz's principles appear as a property of separation, a property of compactness, and a property of analyticity, respectively. Abiding by this interpretation, we obtain the somehow surprising conclusion that these Leibnz's principles can be fulfilled in pairs, but not all three together.Comment: 16 page

A topological interpretation of three Leibnizian principles within the functional extensions

Three philosophical principles are often quoted in connection with Leibniz: "objects sharing the same properties are the same object" (Identity of indiscernibles), "everything can possibly exist, unless it yields contradiction" (Possibility as consistency), and "the ideal elements correctly determine the real things" (Transfer). Here we give a precise logico-mathematical formulation of these principles within the framework of the Functional Extensions, mathematical structures that generalize at once compactifications, completions, and elementary extensions of models. In this context, the above Leibnizian principles appear as topological or algebraic properties, namely: a property of separation, a property of compactness, and a property of directeness, respectively. Abiding by this interpretation, we obtain the somehow surprising conclusion that these Leibnizian principles may be fulfilled in pairs, but not all three together.Comment: arXiv admin note: substantial text overlap with arXiv:1012.434

Quasi-selective ultrafilters and asymptotic numerosities

We isolate a new class of ultrafilters on N, called "quasi-selective" because they are intermediate between selective ultrafilters and P-points. (Under the Continuum Hypothesis these three classes are distinct.) The existence of quasi-selective ultrafilters is equivalent to the existence of "asymptotic numerosities" for all sets of tuples of natural numbers. Such numerosities are hypernatural numbers that generalize finite cardinalities to countable point sets. Most notably, they maintain the structure of ordered semiring, and, in a precise sense, they allow for a natural extension of asymptotic density to all sequences of tuples of natural numbers.Comment: 27 page

L'effetto Gibbs

Nella tesi ho trattato l'effetto Gibbs,ovvero la presenza di forti oscillazioni nei polinomi di Fourier di funzioni con discontinuità di prima specie. Infine ho introdotto le somme di Fejér osservando come con questi polinomi trigonometrici si possa eliminare l'effetto Gibbs

Strumenti per lo Sviluppo Economico Locale: Meccanismi di Incentivazione in Italia e in Alcuni Paesi Europei

In questo paper vengono presentati i principali meccanismi di incentivazione in Italia ed in alcuni paesi europei, in termini sia di descrizione delle iniziative che di analisi del loro impatto economico. E’ importante tenere presente che il design italiano degli incentivi analizzati si orienta verso un modello con forti elementi di automatismo. Questo va messo a confronto con i meccanismi di incentivazione a livello di Unione Europea con i quali mostra forti similitudini, ma va a contrastare con le recenti esperienze di molti paesi europei, che hanno fatto dell’integrazione fra Agenzie di Sviluppo, meccanismi di incentivazione e marketing territoriale un pilastro portante delle politiche di sviluppo locale, con un forte orientamento a delegare alle Agenzie di Sviluppo la gestione degli incentivi.Incentive mechanism, local development, state aid

Dynamic factor models: improvements and applications

In the last two decades data collection, aided by an increased computational capability, has considerably increased both dimension and structure of the datasets; given this, statisticians and economists may today work with time series of remarkable dimension which may come from different sources. Dealing with such datasets may not be so easy and requires the development of ad hoc mathematical models. Dynamic Factor Models (DFM) represent one of the newest techniques in big data management. The adoption of those models allowed me to deepen the study of volatility while introducing Bayesian non-parametric techniques, and to do structural analysis improving the generated impulse response functions. The application of this all was made in the field of economics and finance

A Euclidean comparison theory for the size of sets

We discuss two main ways in comparing and evaluating the size of sets: the "Cantorian" way, grounded on the so called Hume principle (two sets have equal size if they are equipotent), and the "Euclidean" way, maintaining Euclid's principle "the whole is greater than the part". The former being deeply investigated since the very birth of set theory, we concentrate here on the "Euclidean" notion of size (numerosity), that maintains the Cantorain defiitions of order, addition and multiplication, while preserving the natural idea that a set is (strictly) larger than its proper subsets. These numerosities satisfy the five Euclid's common notions, and constitute a semiring of nonstandarda natural numbers, thus enjoying the best arithmetic. Most relevant is the natural set theoretic definition} of the set-preordering: X\prec Y\ \ \Iff\ \ \exists Z\ X\simeq Z\subset Y Extending this ``proper subset property" from countable to uncountable sets has been the main open question in this area from the beginning of the century.Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:2207.0750

Two characterization of BV functions on Carnot groups via the heat semigroup

In this paper we provide two different characterizations of sets with finite perimeter and functions of bounded variation in Carnot groups, analogous to those which hold in Euclidean spaces, in terms of the short-time behaviour of the heat semigroup. The second one holds under the hypothesis that the reduced boundary of a set of finite perimeter is rectifiable, a result that presently is known in Step 2 Carnot groups

Competitive balance and TV audience: An empirical analysis on the Italian Serie A

This paper investigates the behaviour of the “couch potato” audience in regards to the Italian Football League - Serie A - during the 2008/09 season. Using data from 380 matches, we considered a collection of variables suitable to influence the share of TV audience of satellite television. According to the standard prescriptions of sports economics literature and assessing peculiarities of Italian context, we estimated the “Football on TV’s” demand by an OLS regression model. Rating the dependent variable of TV audience by the share registered in each match, we introduced a set of independent variables in order to approximate match quality, the programme schedule placement, the follow-up of the involved teams and their rank. As other theoretical and empirical investigations have focused on Spanish and English championships, our attention concentrates particularly on the relationship between the closeness of the game and the television audience. In the regression model, uncertainty of outcome has been measured extracting information from the Italian fixed odds betting market. We found that all the theoretical expected relationships have been confirmed by the econometric analysis. In spite of the statistical significance of the outcome uncertainty on share, the estimation points out that more then 90% of variability concerning TV audience has been explained net of uncertainty factors and that the impact of a closest context on dependent variable is marginal. The overestimation of the role of match uncertainty on TV audience could support the opinion of top team’s management opposing the return to the collective bargaining of TV rights starting from next season, 2010/11, fixed by the law 9/2008 of Italian Parliament. In football context the competitive balance should then be considered a “meritorius good”, far from market assessment.