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On the boundary behavior of holomorphic and harmonic functions
No full textThis book collects some of the scientific contributions of the participants in the Conference in Harmonic Analysis held at the Istituto Nazionale di Alta Matematica from May 30th to June 4th, 2011
On the differentiation of integrals in measure spaces along filters: II
Get PDFLet be a complete measure space of finite measure. The Lebesgue transform of an integrable function on encodes the collection of all the mean-values of on all measurable subsets of of positive measure. In the problem of the differentiation of integrals, one seeks to recapture from its Lebesgue transform. In previous work we showed that, in all known results, may be recaputed from its Lebesgue transform by means of a limiting process associated to an appropriate family of filters defined on the collection of all measurable subsets of of positive measure. The first result of the present work is that the existence of such a limiting process is equivalent to the existence of a Von Neumann-Maharam lifting of .
In the second result of this work we provide an independent argument that shows that the recourse to filters is a \textit{necessary consequence} of the requirement that the process of recapturing from its mean-values is associated to a \textit{natural transformation}, in the sense of category theory. This result essentially follows from the Yoneda lemma. As far as we know, this is the first instance of a significant interaction between category theory and the problem of the differentiation of integrals.
In the Appendix we have proved, in a precise sense, that \textit{natural transformations fall within the general concept of homomorphism}. As far as we know, this is a novel conclusion: Although it is often said that natural transformations are homomorphisms of functors, this statement appears to be presented as a mere analogy, not in a precise technical sense. In order to achieve this result, we had to bring to the foreground a notion that is implicit in the subject but has remained hidden in the background, i.e., that of \textit{partial magma}
Prova iniziale di verifica: una terza via?
No full textRoars Review è una rassegna degli articoli che vengono pubblicati nel sito www.roars.it, in cui si svolge una discussione, aperta e documentata, sulla politica dell’università e della ricerca, sui temi della didattica e della valutazione, della scientometria e della bibliometria. Nel mio articolo di sei pagine mi sono occupato delle prove di verifica iniziale, previste dall'art. 6 del D.M. 270/2004
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Euler, Stirling, and Wallis: A Case Study in the Notion of Equivalence Between Theorems
No full textThe notion that two theorems may be equivalent to each other is sometimes met with hesitation. In this article we tell a story that shows that there is something interesting and useful in this notion. We look at the following three results: Stirling’s formula, Wallis’ product formula, and the evaluation of the probability integral. The task of giving simple proofs of these results is the object of unabated attention. In order to enhance our understanding of these results, we show in a precise way that these results are indeed equivalent to each other
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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