In particular, I will discuss the higher differentiability of such minimizers under some restrictions on the exponents of anisotropy.

In the two dimensional case I will also show that minimizers are Lipschitz continuous without any limitation on the exponents of anisotropy.]]>

In recent years, the Smoluchowski equation has been considered in biomedical research to model the aggregation and diffusion of beta-amyloid peptide in the cerebral tissue, a process thought to be associated with the development of Alzheimer's disease. In this work, we study the homogenization of a Smoluchowski system of discrete diffusion-coagulation equations with non-homogeneous Neumann boundary conditions, defined in a periodically perforated domain through a two scale convergence technique.

]]>In the context of international nuclear safeguards, the International Atomic Energy Agency (IAEA) has recently approved passive gamma emission tomography (PGET) as a method for inspecting spent nuclear fuel assemblies (SFAs). The PGET instrument is essentially a single photon emission computed tomography (SPECT) system that allows the reconstruction of axial cross-sections of the emission map of SFA. The fuel material heavily self-attenuates its gamma-ray emissions, so that correctly accounting for the attenuation is a critical factor in producing accurate images. Due to the nature of the inspections, it is desirable to use as little a priori information as possible about the fuel, including the attenuation map, in the reconstruction process. Current reconstruction methods either do not correct for attenuation, assume a uniform attenuation throughout the fuel assembly, or assume an attenuation map based on an initial filtered back-projection reconstruction. We propose a method to simultaneously reconstruct the emission and attenuation maps by formulating the reconstruction as a constrained minimization problem with a least squares data fidelity term and regularization terms. Using simulated data, we show that our approach produces clear reconstructions which allow for a highly reliable classification of spent, missing, and fresh fuel rods.

]]>In the context of international nuclear safeguards, the International Atomic Energy Agency (IAEA) has recently approved passive gamma emission tomography (PGET) as a method for inspecting spent nuclear fuel assemblies (SFAs). The PGET instrument is essentially a single photon emission computed tomography (SPECT) system that allows the reconstruction of axial cross-sections of the emission map of SFA. The fuel material heavily self-attenuates its gamma-ray emissions, so that correctly accounting for the attenuation is a critical factor in producing accurate images. Due to the nature of the inspections, it is desirable to use as little a priori information as possible about the fuel, including the attenuation map, in the reconstruction process. Current reconstruction methods either do not correct for attenuation, assume a uniform attenuation throughout the fuel assembly, or assume an attenuation map based on an initial filtered back-projection reconstruction. We propose a method to simultaneously reconstruct the emission and attenuation maps by formulating the reconstruction as a constrained minimization problem with a least squares data fidelity term and regularization terms. Using simulated data, we show that our approach produces clear reconstructions which allow for a highly reliable classification of spent, missing, and fresh fuel rods.

]]>of rank n is the group of birational transformations of the projective

space of dimension n. In sharp contrast with the case of surfaces, I

will describe how one can construct many group homomorphisms from the

Cremona group to Z/2 as soon as the rank is at least 3. I will give an

idea of the ingredients of the proof, which relies on the Minimal Model

Program, via some previous work of A-S. Kaloghiros (relations in the

Sarkisov program), and also via the recent famous breakthrough of C.

Birkar (solution of the BAB conjecture about finiteness of log Fano

varieties).

]]>

Abstract: Le equazioni di Schrödinger nonlineari appaiono in numerosissimi contesti in fisica: ad esempio sono spesso utilizzate come modelli per la propagazione di onde in mezzi dispersivi debolmente nonlineari, oppure per descrivere la dinamica di condensati di Bose-Einstein (equazione di Gross-Pitaevskii). In questo seminario presenteremo gli strumenti principali per l'analisi delle soluzioni ad energia finita di una classe di equazioni di Schrödinger nonlineari, localmente e globalmente in tempo. Inoltre discuteremo l'estensione di alcuni modelli, tramite l'aggiunta di ulteriori termini nell'equazione, studiandone le proprietà delle soluzioni.

]]>Prof. Guido Sciavicco, Università di Murcia - Spagna

In this talk I will survey the most important aspects in automated reasoning over temporal logics, and in particular interval-based ones - ITLs. In ITLs properties are defined over extended intervals of time, instead of points, giving rise to a huge variety of syntactical as well as semantical possibilities. While reasoning in ITLs is generally very difficult, as their satisfiability problems are often undecidable, I will focus on those interesting exceptions that have been found in the last 15 years of research, and try to point out the different ideas and stratiegies that have been proven useful in searching for computationally well-behaved ITLs. I will also try to give a sufficiently clear idea on how ITLs can be applied, and how the research in this sense is still very much active.

]]>Title: On the root uncertainty principle.

Abstract:

This talk will focus on a recent result of Bourgain, Clozel and Kahane. One of its versions states that a real-valued function which equals its Fourier transform and vanishes at the origin necessarily has a root which is larger than c>0, where the best constant c satisfies 0.41<c<0.64. A similar result holds in higher dimensions. I will show how to improve the one-dimensional result to 0.45<c<0.60, and the lower bound in higher dimensions. I will also argue that extremizers for this problem exist, and necessarily possess infinitely many double roots. Time permitting, I will make the connection to several related problems. This is joint work with Felipe Gonçalves and Stefan Steinerberger.

preprint: https://arxiv.org/abs/1602.03366

]]>Il Prof. Panaite è disponibile per collaborazione scientifica con tutti gli interessati.

Il Prof. Panaite terrà una serie di seminari.

]]>