Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica. La presenza del fulltext è lacunosa per i prodotti antecedenti maggio 2006.
Trovati 867 prodotti

QDD218  30/11/2015
Cirant, M.; Verzini, G.
Bifurcation and segregation in quadratic twopopulations Mean Field Games systems  Abstract   We consider a twopopulations ergodic Mean Field Games system, which describes Nash equilibria in differential games with identical players. In these models, each population consists of a very large number of indistinguishable rational agents, aiming at minimizing some longtime average criterion. Via the HopfCole transformation, such system reduces to a semilinear elliptic one, for normalized densities. Firstly, we discuss existence of nontrivial solutions; secondly, for selected families of nontrivial solutions, we address the appearing of segregation in the vanishing viscosity limit. 

QDD217  26/11/2015
Bertacchi, D.; Zucca, F.
A generating function approach to branching random walks  Abstract   It is well known that the behaviour of a branching process is completely described by the generating function of the offspring law and its fixed points. Branching random walks are a natural generalization of branching processes: a branching process can be seen as a onedimensional
branching random walk. We define a multidimensional generating function associated to a given branching random walk. The present paper investigates the similarities and the differences of the generating functions, their fixed points and the implications on the underlying stochastic process,
between the onedimensional (branching process) and the multidimensional case (branching random walk). In particular, we show that the generating function of a branching random walk can
have uncountably many fixed points and a fixed point may not be an extinction probability, even in the irreducible case (extinction probabilities are always fixed points). Moreover, the generating
function might not be a convex function. We also study how the behaviour of a branching random walk is affected by local modications of the process. As a corollary, we describe a general procedure by which we can modify a continuoustime branching random walk which has a weak
phase and turn it into a continuoustime branching random walk which has strong local survival for large or small values of the parameter and nonstrong local survival for intermediate values of the parameter. 

QDD216  11/11/2015
Bramanti, M.; Fanciullo, M. S.
The local sharp maximal function and BMO on locally homogeneous spaces  Abstract   We prove a local version of FeffermanStein inequality for the local sharp maximal function, and a local version of JohnNirenberg inequality for locally BMO functions, in the framework of locally homogeneous spaces, in the sense of BramantiZhu [Manuscripta Math. 138 (2012), no. 34, 477528]. 

QDD215  11/11/2015
Bramanti, M.; Toschi, M.
The sharp maximal function approach to L^p estimates for operators structured on Hörmander's vector fields  Abstract   We consider a nonvariational degenerate elliptic operator structured on a system of left invariant, 1homogeneous, Hörmander's vector fields on a Carnot group in R^n, where the matrix of coefficients is symmetric, uniformly positive on a bounded domain of R^n and the coefficients are bounded, measurable and locally VMO in the domain. We give a new proof of the interior L^p estimates on the second order derivatives with respect to the vector fields, first proved by BramantiBrandolini in [Rend. Sem. Mat. dell'Univ. e del Politec. di Torino, Vol. 58, 4 (2000), 389433], extending to this context Krylov' technique, introduced in [Comm. in P.D.E.s, 32 (2007), 453475], consisting in estimating the sharp maximal function of the second order derivatives. 

QDD214  14/10/2015
Dulio, P.; Finotelli, P.
A Graph Theoretical Approach to Neurobiological Databases Comparison  Abstract   Music is one of the best tools to evoke emotions and feelings in
people. Generally, people like classical music, hip hop, house,
disco, underground or other kinds of music. People choose songs
basing on their preferences. For example, a subject while performing
an action such as running, studying or relaxing tends to listen to songs that give her or him a pleasant feeling. Interesting issues emerge: First,
collecting the brain reactions when the brain is stimulated by songs
(classified as pleasant). Second, comparing them with the resting
state condition, and third representing the neural network changes in
terms of emergent subgraphs.
We propose a general methodology concerning phase transitions
analysis of an arbitrary number of conditions.
We also apply such a methodology to real acoustic data and, though
our findings generally seem to agree with others available in the
literature, they also point out the existence of functional connectivity
between pairs of cerebral areas, usually not immediately associated
to an acoustical task.
Our results may explain why people when listening to pleasant music
activated emotional cerebral areas in spite of the fact that the
music they classify as pleasant is different for each subject.
Possible applications to Neuropsychiatry are discussed.


QDD213  28/08/2015
Alpay, D.; Sabadini, I.
BeurlingLax type theorems in the complex and quaternionic setting: the halfspace case  Abstract   We give a generalization of the BeurlingLax theorem both in the complex and quaternionic settings. We consider in the first case
functions meromorphic in the right complex halfplane, and functions slice hypermeromorphic in the right quaternionic halfspace in the second case. In both settings we also discuss a unified framework, which includes both the disk and the halfplane for the complex case and the
open unit ball and the halfspace in the quaternionic setting.


QDD212  01/07/2015
Barchielli, A.
Quantum stochastic equations for an optomechanical oscillator with radiation pressure interaction and nonMarkovian effects  Abstract   The quantum stochastic Schroedinger equation or HudsonParthasareathy (HP) equation is a powerful tool to construct unitary dilations of quantum dynamical semigroups and to develop the theory of measurements in continuous time via the construction of output fields. An important feature of such an equation is that it allows to treat not only absorption and emission of quanta, but also scattering processes, which however had very few applications in physical modelling. Moreover, recent developments have shown that also some nonMarkovian dynamics can be generated by suitable choices of the state of the quantum noises involved in the HPequation. This paper is devoted to an application involving these two features, nonMarkovianity and scattering process. We consider a micromirror mounted on a vibrating structure and reflecting a laser beam, a process giving rise to a radiationpressure force on the mirror. We show that this process needs the scattering part of the HPequation to be described. On the other side, nonMarkovianity is introduced by the dissipation due to the interaction with some thermal environment which we represent by a phonon field, with a nearly arbitrary excitation spectrum, and by the introduction of phase noise in the laser beam. Finally, we study the full power spectrum of the reflected light and we show how the laser beam can be used as a temperature probe. 

QDD211  04/06/2015
Pagani,C.D.; Pierotti, D.; Pistoia, A.; Vaira, G.
Concentration along geodesics for a nonlinear Steklov problem arising in corrosion modelling  Abstract   We consider the problem of finding pairs (lambda; u), with lambda > 0 and u a harmonic function in a three dimensional toruslike domain D, satisfying the nonlinear boundary condition partial_n u = sinh u on partial D. This type of boundary condition arises in corrosion modelling (Butler Volmer condition). We prove existence of solutions
which concentrate along some geodesics of the boundary as the parameter lambda goes to zero. 
