549 research outputs found
Conformal Metrics with Constant Q-Curvature
We consider the problem of varying conformally the metric of a four dimensional manifold in order to obtain constant Q-curvature. The problem is variational, and solutions are in general found as critical points of saddle type. We show how the problem leads naturally to consider the set of formal barycenters of the manifold
Existence of solutions to a higher dimensional mean-field equation on manifolds
For we prove an existence result for the equation on a closed Riemannian
manifold of dimension for certain values of .Comment: 15 Page
An improved geometric inequality via vanishing moments, with applications to singular Liouville equations
We consider a class of singular Liouville equations on compact surfaces
motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the
Gaussian curvature prescription with conical singularities and Onsager's
description of turbulence. We analyse the problem of existence variationally,
and show how the angular distribution of the conformal volume near the
singularities may lead to improvements in the Moser-Trudinger inequality, and
in turn to lower bounds on the Euler-Lagrange functional. We then discuss
existence and non-existence results.Comment: some references adde
New improved Moser-Trudinger inequalities and singular Liouville equations on compact surfaces
We consider a singular Liouville equation on a compact surface, arising from
the study of Chern-Simons vortices in a self dual regime. Using new improved
versions of the Moser-Trudinger inequalities (whose main feature is to be
scaling invariant) and a variational scheme, we prove new existence results.Comment: to appear in GAF
Fostering Computational Thinking in Primary School through a LEGO®-based Music Notation
This paper presents a teaching methodology mixing elements from the domains of music and informatics as a key enabling to expose primary school pupils to basic aspects of computational thinking. This methodology is organized in two phases exploiting LEGO\uae bricks respectively as a physical tool and as a metaphor in order to let participants discover a simple notation encoding several basic concepts of the classical musical notation. The related activities, grounded on active learning theory, challenge groups of students to solve musical encoding problems of increasing difficulty
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