A note on the Almansi property

The first goal of this note is to study the Almansi property on an m-dimensional model in the sense of Greene and Wu and, more generally, in a Riemannian geometric setting. In particular, we shall prove that the only model on which the Almansi property is verified is the Euclidean space R^m. In the second part of the paper we shall study Almansi's property and biharmonicity for functions which depend on the distance from a given submanifold. Finally, in the last section we provide an extension to the semi-Euclidean case R^{p,q} which includes the proof of the classical Almansi property in R^m as a special instance.Comment: Dedicated to Prof. Renzo Caddeo, to appear in Mediterranean Journal of Mathematic

A general approach to equivariant biharmonic maps

In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute directly the analytical conditions which guarantee biharmonicity in the presence of suitable symmetries. In the second part of our work, we illustrate and discuss some examples. In particular, we obtain a 1-dimensional stability result, and also show that biharmonic maps do not satisfy the classical maximum principle proved by Sampson for harmonic maps.Comment: 13 pages, final version to appear in Mediterranean Journal of Mathematic

Reduction methods for the bienergy

This paper, in which we develop ideas introduced in \cite{MR}, focuses on \emph{reduction methods} (basically, group actions or, more generally, simmetries) for the bienergy. This type of techniques enable us to produce examples of critical points of the bienergy by reducing the study of the relevant fourth order PDE's system to ODE's. In particular, we shall study rotationally symmetric biharmonic conformal diffeomorphisms between \emph{models}. Next, we will adapt the reduction method to study an ample class of $G-$invariant immersions into the Euclidean space. At present, the known instances in these contexts are far from reaching the depth and variety of their companions which have provided fundamental solutions to classical problems in the theories of harmonic maps and minimal immersions. However, we think that these examples represent an important starting point which can inspire further research on biharmonicity. In this order of ideas, we end this paper with a discussion of some open problems and possible directions for further developments.Comment: to appear in REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES. arXiv admin note: text overlap with arXiv:1507.03964, arXiv:1109.620

Learning in a Landscape: Simulation-building as Reflexive Intervention

This article makes a dual contribution to scholarship in science and technology studies (STS) on simulation-building. It both documents a specific simulation-building project, and demonstrates a concrete contribution to interdisciplinary work of STS insights. The article analyses the struggles that arise in the course of determining what counts as theory, as model and even as a simulation. Such debates are especially decisive when working across disciplinary boundaries, and their resolution is an important part of the work involved in building simulations. In particular, we show how ontological arguments about the value of simulations tend to determine the direction of simulation-building. This dynamic makes it difficult to maintain an interest in the heterogeneity of simulations and a view of simulations as unfolding scientific objects. As an outcome of our analysis of the process and reflections about interdisciplinary work around simulations, we propose a chart, as a tool to facilitate discussions about simulations. This chart can be a means to create common ground among actors in a simulation-building project, and a support for discussions that address other features of simulations besides their ontological status. Rather than foregrounding the chart's classificatory potential, we stress its (past and potential) role in discussing and reflecting on simulation-building as interdisciplinary endeavor. This chart is a concrete instance of the kinds of contributions that STS can make to better, more reflexive practice of simulation-building.Comment: 37 page

On cohomogeneity one biharmonic hypersurfaces into the Euclidean space

The aim of this paper is to prove that there exists no cohomogeneity one $G-$invariant proper biharmonic hypersurface into the Euclidean space ${\mathbb R}^n$, where $G$ denotes a tranformation group which acts on ${\mathbb R}^n$ by isometries, with codimension two principal orbits. This result may be considered in the context of the Chen conjecture, since this family of hypersurfaces includes examples with up to seven distinct principal curvatures. The paper uses the methods of equivariant differential geometry. In particular, the technique of proof provides a unified treatment for all these $G-$actions.Comment: 13 page

A comparison of structural reform scenarios across the EU member states - Simulation-based analysis using the QUEST model with endogenous growth

This paper calibrates the Roeger-Varga-Veld (2008) micro-founded DSGE model with endogenous growth for all EU member states using country specific structural characteristics and employs the individual country models to analyse the macroeconomic impact of various structural reforms. We analyse the costs and benefits of reforms in terms of fiscal policy instruments such as taxes, benefits, subsidies and administrative costs faced by firms. We find that less R&D intensive countries would benefit the most from R&D promoting and skill-upgrading policies. We also find that shifting from labour to consumption taxes, reducing the benefit replacement rate and relieving administrative entry barriers are the most effective measures in those countries which have high labour taxes and entry barriers.Structural reforms, endogenous growth, DSGE modelling, EU member states, tax credits, tax shifts, entry barriers, human capital, D'Auria, Pagano, Ratto, Varga

Triharmonic curves in the 3-dimensional Sol space

The main aim of this paper is to study triharmonic curves in the 3-dimensional homogeneous space Sol. In the first part of the paper we shall obtain a complete classification of proper triharmonic curves with constant geodesic curvature and torsion. In the final section we shall show that these triharmonic curves form a constant angle with a suitable Killing field of constant length along the curve

Factor Mapping and Metamodelling

In this work we present some techniques, within the realm of Global Sensitivity Analysis, which permit to address fundamental questions in term of model's understanding. In particular we are interested in developing tools which allow to determine which factor (or group of factors) are most responsible for producing model outputs Y within or outside specified bounds ranking the importance of the various input factors in terms of their influence on the variation of Y. On the other hand, we look for representing in a direct way (graphically, analytically, etc.) the relationship between input factors X_1,..., X_k and output Y in order to get a better understanding of the model itself.JRC.G.9-Econometrics and statistical support to antifrau