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A note on the critical Laplace Equation and Ricci curvature

We study strictly positive solutions to the critical Laplace equation −∆u = n(n − 2)u n+2 n−2 , decaying at most like d(o, x) −(n−2)/2 , on complete noncompact manifolds (M, g) with nonnegative Ricci curvature, of dimension n ≥ 3. We prove that, under an additional mild assumption on the volume growth, such a solution does not exist, unless (M, g) is isometric to R n and u is a Talenti function. The method employs an elementary analysis of a suitable function defined along the leve...

Local Rule-Based Explanations of Black Box Decision Systems

The recent years have witnessed the rise of accurate but obscure decision systems which hide the logic of their internal decision processes to the users. The lack of explanations for the decisions of black box systems is a key ethical issue, and a limitation to the adoption of machine learning components in socially sensitive and safety-critical contexts. %Therefore, we need explanations that reveals the reasons why a predictor takes a certain decision. In this paper we focus on the problem o...

Database degli esercizi (EDB)

This web site contains a mathematics project, called “EDB”. This presents mathematical exercises for first year students, that I collected in a decade of teaching. It is published at the address https://coldoc.sns.it/CD/EDB EDB contains elements of theory, roughly 1000 exercises and 600 solutions. EDB implements a simple game to engage students. Theory and exercises are public, whereas solutions are reserved. But solutions may be bought: each student has a...

ColDoc Project

There are two main frameworks currently used to present information (in particular, related to scientific fields). A document redacted with the standard LaTeX / PDF toolbox. Pros: these documents are state-of-the-art quality. Cons: the final user has no way of interacting with a PDF document (other than sending an e-mail to the original authors) The Web 2.0 way (think of: Wikipedia or Stack Exchange ). Pros: in those frameworks, content is continuously...

E-Stampages. La collection de Ca' Foscari. Grèce (provenances diverses) et Sicile

The ‘Venice Squeeze Project’, coordinated by Claudia Antonetti, is the first initiative in Italy to enhance the historical and documentary value of the epigraphic squeezes. Its aims include publishing the Ca’ Foscari collection of epigraphic squeezes within the ’E-stampages’ website. The collection is the richest and most coherent in Italy and it counts 605 items. Most squeezes were produced from inscriptions from Central Greece. A smaller group of squeezes reproduces inscriptions from Sicily...

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5 Altro: [264] Home page macrotipologia

Prodotti recenti

A note on the critical Laplace Equation and Ricci curvature

Local Rule-Based Explanations of Black Box Decision Systems

Database degli esercizi (EDB)

ColDoc Project

E-Stampages. La collection de Ca' Foscari. Grèce (provenances diverses) et Sicile

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