Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.41 (2009)

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CONTENTS

Marco Perone
On the Infinite Dual Goldie Dimension

Edoardo Ballico and Francesco Malaspina
Vector Bundles on Products of Projective Spaces and Hyperquadrics

Fernando Hernandez-Hernandez
Distributivity of Quotients of Countable Products of Boolean Algebras

Stefano Bianchini and Laura V. Spinolo
A Connection between Viscous Profiles and Singular ODEs

Marina Pireddu
Period Two implies Chaos for a Class of ODEs: a Dynamical System Approach

Lothar Göttsche
Invariants of Moduli Spaces and Modular Forms

Allal Ghanmi and Zouhaïr Mouayn
A Deformed Bargmann Transform by an SU(2) Matrix Parameter

Andrea Malchiodi
Variational Theory for Liouville Equations with Singularities

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Editorial policy The journal Rendiconti dell’Istituto di Matematica dell’università di Trieste publishes original articles in all areas of mathematics. Special regard is given to research papers, but attractive expository papers may also be considered for publication. The journal usually appears in one issue per year. Additional issues may however be published. In particular, the Managing Editors may consider the publication of supplementary volumes related to some special events, like conferences, workshops, and advanced schools. All submitted papers will be refereed. Manuscripts are accepted for review with the understanding that the work has not been published before and is not under consideration for publication elsewhere. Our journal can be obtained by exchange agreements with other similar journals.

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Now showing 1 - 5 of 8

Variational Theory for Liouville Equations with Singularities
(EUT Edizioni Università di Trieste, 2009)
Malchiodi, Andrea
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].
925 1063
A Deformed Bargmann Transform by an SU(2) Matrix Parameter
(EUT Edizioni Università di Trieste, 2009)
Ghanmi, Allal
;
Mouayn, Zouhaïr
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.
721 956
Invariants of Moduli Spaces and Modular Forms
(EUT Edizioni Università di Trieste, 2009)
Göttsche, Lothar
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.
1145 2149
Period Two implies Chaos for a Class of ODEs: a Dynamical System Approach
(EUT Edizioni Università di Trieste, 2009)
Pireddu, Marina
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.
929 772
A Connection between Viscous Profiles and Singular ODEs
(EUT Edizioni Università di Trieste, 2009)
Bianchini, Stefano
;
Spinolo, Laura V.
We deal with the viscous profiles for a class of mixed hyperbolic-parabolic systems in one space dimension. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form$\frac{dV}{dt} = \frac{1}{\zeta (V)} F(V).$ Here $V \in \mathbb{R}^d$ and the function $F$ takes values into $\mathbb{R}^d$ and is smooth. The real valued function $\zeta $ is as well regular: the equation is singular in the sense that $\zeta (V)$ can attain the value $0$.
1021 878

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