Abstract:
We study the gradient flow of the $L^2-$norm of the second fundamental form of smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained for the Willmore flow in Riemannian manifolds, we prove lifespan estimates in terms of the $L^2-$concentration of the second fundamental form of the initial data and we show existence of blowup limits. Under special condition both on the initial data and on the target manifold, we prove a long time existence result for the flow and subconvergence to a critical immersion.

Abstract:
We consider isotropic non lower semicontinuous weighted perimeter functionals defined on partitions of domains in $\mathbb{R}^n$. Besides identifying a condition on the structure of the domain which ensures the existence of minimizing configurations, we describe the structure of such minima, as well as their regularity.

Abstract:
We consider the reduced Allen-Cahn action functional, which appears as the sharp interface limit of the Allen-Cahn action functional and can be understood as a formal action functional for a stochastically perturbed mean curvature flow. For suitable evolutions of generalized hypersurfaces this functional consists of the sum of the squares of the mean curvature and of the velocity vector, integrated over time and space. For given initial and final conditions we investigate the corresponding action minimization problem. We give a generalized formulation and prove compactness and lower semicontinuity properties of the action functional. Furthermore we characterize the Euler-Lagrange equation for smooth stationary points and investigate conserved quantities. Finally we present an explicit example and consider concentric spheres as initial and final data and characterize in dependence of the given time span the properties of the minimal rotationally symmetric connection.

Abstract:
We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth until the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists for all times and the network converges to the Steiner minimal connection between the three endpoints.

Abstract:
We show some computations related to the motion by mean curvature flow of a submanifold inside an ambient Riemannian manifold evolving by Ricci or backward Ricci flow. Special emphasis is given to the possible generalization of Huisken's monotonicity formula and its connection with the validity of some Li--Yau--Hamilton differential Harnack--type inequalities in a moving Riemannian manifold.

Abstract:
By means of a Kaluza-Klein type argument we show that the Perelman's F-functional is the Einstein-Hilbert action in a space with extra ``phantom'' dimensions. In this way, we try to interpret some remarks of Perelman in the introduction and at the end of the first section in his first famous paper. As a consequence the Ricci flow (modified by a diffeomorphism and a time-dependent factor) is the evolution of the ``real'' part of the metric under a constrained gradient flow of the Einstein-Hilbert gravitational action in higher dimension.

Several recent accounts have shown that anti-immigrant feeling among citizens seems to reduce the support for the welfare state. As a consequence, the rise of immigration could produce a deep change in industrialized countries’ social security systems. This paper provides evidence that support for redistribution is not decreased by generic xenophobia, but by a specific kind of xenophobic belief. It also shows that some other xenophobic beliefs tend rather to produce a demand for governmental protection programs. Based on a multivariate analysis on individual and contextual French data, findings show that the support for social protection programs is positively related to the fear of competition from immigrants and negatively with the fear that immigrants strain the welfare state. This result can be generalized to other countries where “redistributive xenophobia” is much more widespread.

Abstract:
In the writer’s opinion the frequently used expression “scientific theatre” is actually an ambiguous term, since it refers to a number of widely differing experiences. For this reason, the word “theatre” is preferred in this paper when referring to those events which take place in institutionalised settings, while the term “theatrical communic-action” is deemed more appropriate when referring to those taking place in settings devoted to scientific communication, such as museums. After a brief historical analysis of the various approaches of theatre to science and some examples of plays in Italy and abroad, the writer investigates how theatre can produce effective scientific communication in museums. Theatrical action can bring out the value of the exhibits of a museum, while creating a new way of experiencing the exhibitions. Theatrical actions link education and entertainment, consequently becoming a highly effective didactic instrument. The advantages of theatre are briefly outlined, considering it as an interpretative technique to communicate science from the point of view of the goals pursued by museums, of epistemology and of theatrical research. Hopefully, theatrical communic -action of science will become common practice in Italy, just like in Europe and the United States, where it has established itself for decades. In Italy this technique has been very seldom applied, thus hindering a thorough analysis of it. On the basis of various experiences abroad, however, the conclusion is drawn that there is probably no all-encompassing magical solution, and that the effectiveness of all different techniques of theatrical communic-action should be tested case by case.

Abstract:
Este trabalho entenderá a cr nica como um gênero híbrido, ligado tanto ao mundo objetivo das notícias quanto ao mundo subjetivo do cronista. Pelo estudo de algumas cr nicas de Luís Martins, cujo temário é a própria produ o dessa escrita, recolhemos algumas estruturas discursivas que est o na gênese dessa escrita. Luís Martins foi jornalista e escritor, trabalhou em diversos jornais cariocas e paulistas entre as décadas de 30 a 80 do século XX. Assim, numa aproxima o metalinguística, será dada voz ao cronista e jornalista Luís Martins, para que sejam exploradas as fronteiras entre a produ o jornalística e a literária. Podemos também entender que esses limites, de fato, deixam de existir quando estamos diante de um produtor que se prop e a rompê-los.

Abstract:
We present a modified two-dimensional random field Ising model, where a dipolar interaction term is added to the classic random field Hamiltonian. In a similar model it was already verified that the system state can exhibit domains in the form of stripe patterns, typical of thin materials with strong perpendicular anisotropy. In this work we show that the hysteresis loops obtained at zero temperature can display a strict similarity with the loops obtained in thin magnetic materials such as garnet films. In our model the processes of domain nucleation and domain wall motion are well separated in time as the system evolves. This remarkable fact allowed us to better understand the nucleation process in this family of spin systems.