http://www.openstarts.units.it:80/dspace/handle/10077/4003 2013-05-19T02:38:33Z http://www.openstarts.units.it:80/dspace/handle/10077/4011 Title: Variational Theory for Liouville Equations with Singularities Authors: Malchiodi, Andrea Abstract: In this note we consider a singular Liouville equation on compact surfaces, arising from the study of Chern-Simons vortices. Using improved versions of the Moser-Trudinger inequality and a min-max scheme, we prove existence of solutions in cases with lack of coercivity. Full details and further references can be found in the forthcoming paper [17]. Type: Articolo 2009-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/4010 Title: A Deformed Bargmann Transform by an SU(2) Matrix Parameter Authors: Ghanmi, Allal; Mouayn, Zouhaïr Abstract: The Laguerre 2D polynomials depending on an arbitrary matrix Q in SU(2) as a fixed parameter are used to construct a set of coherent states. The corresponding coherent state transforms constitute a deformation by matrix Q of a generalized Bargmann transform. Type: Articolo 2009-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/4009 Title: Invariants of Moduli Spaces and Modular Forms Authors: Göttsche, Lothar Abstract: Generating functions for invariants of moduli spaces in algebraic geometry of are often related to modular forms. In this paper we give an overview of many instances of this phenomenon and in some cases relate it to predictions from theoretical physics. In this paper we only consider moduli spaces of objects on surfaces. The examples include Euler numbers of moduli spaces of sheaves on surfaces, Donaldson invariants, and enumerative invariants of curves on surfaces. Type: Articolo 2009-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/4008 Title: Period Two implies Chaos for a Class of ODEs: a Dynamical System Approach Authors: Pireddu, Marina Abstract: The aim of this note is to set in the field of dynamical systems a recent theorem by Obersnel and Omari in [19] about the presence of subharmonic solutions of all orders for a class of scalar time-periodic first order differential equations without uniqueness, provided a subharmonic solution (for instance, of order two) does exist. Indeed, making use of the Bebutov flow, we try to clarify in what sense the term “chaos” has to be understood and which dynamical features can be inferred for the system under analysis. Type: Articolo 2009-01-01T00:00:00Z