Luigi Pepe

Giuseppe Vitali e l'analisi reale

SuntoIn questo lavoro si presenta la produzione di Giuseppe Vitali (1875–1932) in analisi reale, con particolare riferimento al suo teorema di ricoprimento. In appendice sono pubblicate due lettere inedite riguardanti il Vitali di F. Enriques e N. Lusin.SummaryIn this paper we present the works of Giuseppe Vitali (1875–1932) in real analysis. In particular we consider Vitalis covering theorem. Two letters concerning Vitali of F. Enriques and N. Lusin are also published in the appendix.

UNIVERSITIES, ACADEMIES, AND SCIENCES IN ITALY IN THE MODERN AGE

In order to explain the centrality of the university system in Italy it may be useful to examine the relations between the universities and the many academies, which were in a somewhat precarious position since they had been unable to obtain continuous public financing. From this point of view the crucial period in Italy was to be in the two decades of Napoleonic government (1796–1814), when the whole education system was financed by the State; not only the universities, but also the academies, particularly the Istituto Nazionale and the Atenei civici. Because of these public funds an increasing number of scientists were able to live on their research and their professions as engineers, doctors, university professors, or public functionaries. In this way the contemporary Italian scientific community was created. During the Restoration of the old governments, however, many scholars were obliged to leave Italy; some, like Ottaviano Fabrizio Mossotti in Argentina and Agostino Codazzi in Venezuela, took part in furthering science in South America. 1

IL COLLGE DE FRANCE DURANTE LA RIVOLUZIONE FRANCESE DUE MEMORIE APOLOGETICHE

title SUMMARY /title The College de France (College Royal) founded by Franois I in 1530 was unable to be completely independent from the University. However Louis XV in 1772 added this to the Colleges of the University and erected his building in Place Cambrai. Only during the French Revolution the College de France became completely independent through the suppression, in 1793, of the other educational Institutions. The same College was seriously threatened by suppression as documented in the memoirs of Garnier and Lalande. These memoirs are now fully published also for their epistemological interest.

Approssimabilità degli aperti diR n di perimetro finito

RiassuntoSi provano, utilizzando certe misure di ricoprimento, risultati di approssimazione in perimetro e in misura per gli aperti limitati di perimetro finito, il cui perimetro coincide con la misura di Hausdorff (n−1)-dimensionale della frontiera.SummaryWe prove some results of approximation of a limited open Caccioppoli set, whose perimeter equals the (n−1)-dimensional Hausdorff measure of its boundary. A special geometric covering measure is employed.

Sulla disuguaglianza di Sobolev-Poincaré

RiassuntoSi dimostra la disuguaglianza di Sobolev-Poincaré per una classe generale di domini che intervengono in problemi non uniformemente ellittici.SummarySobolev-Poincaré inequality for general domains connected with some non uniformly-elliptic problems is proved.

Su di una impostazione parametrica del problem dei capillari

RiassuntoIn questo lavoro si studia il problema dell’esistenza di superfici parametriche che risolvono il problema dei capillari in forma generale; si studiano le relazioni con i problemi soliti della capillarità e si esamina un caso non regolare.SummaryIn this paper we studied the problem of existence of parametric surfaces satisfying capillary boundary conditions. Some relations are proved with «standard» capillary problems. We consider also a nonregular case.