Non-radial sign-changing solutions for the Schroedinger-Poisson problem in the semiclassical limit

We study the existence of nonradial sign-changing solutions to the Schroedinger-Poisson system in dimension N>=3. We construct nonradial sign-changing multi-peak solutions whose peaks are displaced in suitable symmetric configurations and collapse to the same point. The proof is based on the Lyapunov-Schmidt reduction

Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary

Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary conditions or for the singularly perturbed Klein Gordon Maxwell system with mixed Dirichlet Neumann homogeneous boundary conditions. We prove that stable critical points of the mean curvature of the boundary generates solutions when the perturbation parameter is sufficiently small.Comment: arXiv admin note: text overlap with arXiv:1410.884

Low Energy Solutions for the Semiclassical Limit of Schrodinger–Maxwell Systems

We show that the number of positive solutions of Schrodinger– Maxwell system on a smooth bounded domain depends on the topological properties of the domain. In particular we consider the Lusternik– Schnirelmann category and the Poincaré polynomial of the domain

Preliminary data validation and reconstruction of temperature and precipitation in Central Italy

This study assesses the method of data validation of temperature and precipitation in Middle Italy. The procedure proposes a method of validation that may be applied worldwide, provided that calibration relative to the respective climate zones is worked out. The method performs data validation by considering that historical time series show different types of errors such as typing, sensor and reading/recording errors. It takes also into account the procedures for data validation as prescribed by the World Meteorological Organization, implementing them with five types of controls: gross error checking, internal consistency check, tolerance test, temporal consistency and spatial consistency. This work contributes to the development of different standardized methodologies for each type of control to validate climate data; it also provides an innovative procedure to reconstruct missing data in absence of reliable reference time series. The outcomes of this method have led to the removal of 375 records (0.02%) of temperature data from 40 weather stations and 1286 records (1.67%) of precipitation data from 118 weather stations

Le renouvellement des élites et le marché de la presse à l’époque napoléonienne

Les bouleversements politiques qui caractérisent la Révolution et l’ère napoléonienne vont de pair avec les transformations du marché de la presse, l’importance croissante de la sphère publique, ainsi qu’un intérêt grandissant pour l’historiographie contemporaine à la croisée entre analyse politique et historicisation du présent. C’est dans ce contexte que naît un auteur d’un nouveau genre dans tous les grands Etats européens que l’on peut qualifier d’« historien journaliste ». Dans cet article, ces évolutions sont présentées à travers l’exemple des Etats allemands. Les opportunités de carrière toujours plus nombreuses pour les intellectuels sont préalablement discutées : celles-ci se situent dans des sphères sociales encore non établies qui gravitent entre une politique énergique de l’Etat en matière de presse et le développement d’un marché de périodiques historiques. Les relations franco-allemandes dans le champ du journalisme historique sont ensuite présentées à partir des exemples de deux journalistes allemands très influents en leur temps (Joseph Widemann et Friedrich Buchholz). Enfin, la continuité de ces réseaux de presse européens au-delà de l’ère napoléonienne, lors de la période de réformes dans l’espace germanique, est démontrée.The political changes in the revolutionary and Napoleonic age went hand in hand with changes in the press market, a rising significance of the public sphere and a growing interest in immediate historiography at the interface of political analysis and the historicization of ongoing events. In the process of these developments a new type of author emerged in all the larger European states who can be called a “journalist historiographer” („historien journaliste“). In this article, these developments are presented through the example of the German states. In a first step the growing career opportunities for intellectuals are discussed which are located in not-yet-established social spheres situated between the state’s active press politics and a growing public market for historical periodicals. In a second step, the Franco-German relations in the field of historical journalism are sketched by referring to the examples of two of the most influential German journalists of that time (Joseph Widemann and Friedrich Buchholz). And finally, the continuities of these European press networks beyond the Napoleonic era in the German reform period are outlined

Nature-Culture, Link Educational Design, Integrated Learning Process, Landscapes

Framed within the ideal horizon of an integrated research system, the research project FIR “Nature-Culture. Educational Design, Integrated Learning Process, Landscapes” aims at giving value to the many, variously articulated, educational, didactic, re-educational, socially inclusive experiences brought about on the Sicilian territory through land cultivation and farming practices, promoting a network of various organizations involved in teaching, education, rehabilitative therapy, urban regeneration. Looking mainly (but not exclusively) at the school context (and other “intentionally” educational contexts, such as penitentiary institutions or rehabilitation centers), the land becomes the place of educational care, the ground for a contact between nature and nurture, the space of a possible dialogue between different cultures, a privileged experience of intercultural education. The vegetable garden, and more extensively the “garden”, represents the ideal place for a series of exchanges between the subject and nature, the environment and the community, offering a great metaphor for the respectful and balanced cooperation which characterizes the relationship between mankind and other existances

Spazi formativi all’aperto e territori oltreconfine dell’innovazione educativo-didattica

Il saggio restituisce le principali direttrici di ricerca di ambito pedagogico intorno ai modelli e alle prassi di educazione e didattica all’aperto che si avvalgono della coltura/cultura della terra in chiave formativa. Ponendo in dialogo modelli ed esperienze degli inizi del Novecento e sperimentazioni educative odierne, il testo presenta, inoltre, una rassegna delle principali iniziative di carattere scientifico, anche di livello internazionale, promosse dal gruppo di ricerca di Pedagogia presso il Dipartimento di Scienze della Formazione dell’Università di Catania. This essay presents the main directions of a piece of education research concerning the models and practices of outdoor teaching that are used in land cultivation for training purposes. This work compares models and experiences at the beginning of the 20th century with today’s educational experiments; moreover, it presents a collection of the main initiatives of a scientific nature, also at an international level, promoted by the pedagogical research group at the Education Department of the University of Catania

Multiple solutions for a nonhomogeneous Schr\"odinger-Maxwell system in R3R^3

The paper considers the following nonhomogeneous Schr\"odinger-Maxwell system -\Delta u + u+\lambda\phi (x) u =|u|^{p-1}u+g(x),\ x\in \mathbb{R}^3, -\Delta\phi = u^2, \ x\in \mathbb{R}^3, . \leqno{(SM)} where $\lambda>0$, $p\in(1,5)$ and $g(x)=g(|x|)\in L^2(\mathbb{R}^3)\setminus{0}$. There seems no any results on the existence of multiple solutions to problem (SM) for $p \in (1,3]$. In this paper, we find that there is a constant$C_p>0$ such that problem (SM) has at least two solutions for all $p\in (1,5)$ provided $\|g\|_{L^2} \leq C_p$, but only for $p\in(1,2]$ we need $\lambda>0$ is small. Moreover, $C_p=\frac{(p-1)}{2p}[\frac{(p+1)S^{p+1}}{2p}]^{1/(p-1)}$, where $S$ is the Sobolev constant.Comment: 12 page

Stable standing waves for a class of nonlinear Schroedinger-Poisson equations

We prove the existence of orbitally stable standing waves with prescribed $L^2$-norm for the following Schr\"odinger-Poisson type equation \label{intro} %{%{ll} i\psi_{t}+ \Delta \psi - (|x|^{-1}*|\psi|^{2}) \psi+|\psi|^{p-2}\psi=0 \text{in} \R^{3}, %-\Delta\phi= |\psi|^{2}& \text{in} \R^{3},%. when $p\in \{8/3\}\cup (3,10/3)$. In the case $3<p<10/3$ we prove the existence and stability only for sufficiently large $L^2$-norm. In case $p=8/3$ our approach recovers the result of Sanchez and Soler \cite{SS} %concerning the existence and stability for sufficiently small charges. The main point is the analysis of the compactness of minimizing sequences for the related constrained minimization problem. In a final section a further application to the Schr\"odinger equation involving the biharmonic operator is given

Relativistic point dynamics and Einstein formula as a property of localized solutions of a nonlinear Klein-Gordon equation

Einstein's relation E=Mc^2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton's law with the mass satisfying Einstein's relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the "concentration" assumptions hold for a wide class of rectilinear accelerating motions